0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.11/0.38 % Computer : n007.cluster.edu 0.11/0.38 % Model : x86_64 x86_64 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.38 % Memory : 8046.5625MB 0.11/0.38 % OS : Linux 6.8.0-71-generic 0.11/0.38 % CPULimit : 1440 0.11/0.38 % WCLimit : 180 0.11/0.38 % DateTime : Mon Jul 27 13:20:49 UTC 2026 0.11/0.38 % CPUTime : 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.11/0.41 Running higher-order theorem proving 0.11/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.65/0.59 % (1095827)Detected a higher-order problem, will run a greedy HOL sequence. 0.65/0.59 % (1095834)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=793714459:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.65/0.59 % (1095834)Instruction limit reached! 0.65/0.59 % (1095834)------------------------------ 0.65/0.59 % (1095834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.65/0.59 % (1095834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.65/0.59 % (1095834)CaDiCaL version: 2.1.3 0.65/0.59 % (1095834)Termination reason: Instruction limit 0.65/0.59 % (1095834)Termination phase: shuffling 0.65/0.59 % (1095834)Time elapsed: 0.001 s 0.65/0.59 % (1095834)Peak memory usage: 9 MB 0.65/0.59 % (1095834)Instructions burned: 5 (million) 0.65/0.59 % (1095838)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.65/0.59 % (1095838)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.65/0.59 % (1095833)lrs+10_16_si=on:nwc=1.5:random_seed=65041683:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.65/0.59 % (1095832)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2081030666:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.65/0.59 % (1095835)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2643215611:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi) 0.65/0.59 % (1095836)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2523372884:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.65/0.59 % (1095838)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2598006858:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.65/0.59 % (1095837)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2746106519:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.65/0.59 % (1095833)Instruction limit reached! 0.65/0.59 % (1095833)------------------------------ 0.65/0.59 % (1095833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.65/0.59 % (1095833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.65/0.59 % (1095833)CaDiCaL version: 2.1.3 0.65/0.59 % (1095833)Termination reason: Instruction limit 0.65/0.59 % (1095833)Termination phase: shuffling 0.65/0.59 % (1095833)Time elapsed: 0.008 s 0.65/0.59 % (1095833)Peak memory usage: 10 MB 0.65/0.59 % (1095833)Instructions burned: 19 (million) 0.65/0.59 % (1095836)Instruction limit reached! 0.65/0.59 % (1095836)------------------------------ 0.65/0.59 % (1095836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.65/0.59 % (1095836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.65/0.59 % (1095836)CaDiCaL version: 2.1.3 0.65/0.59 % (1095836)Termination reason: Instruction limit 0.65/0.59 % (1095836)Termination phase: Property scanning 0.65/0.59 % (1095836)Time elapsed: 0.011 s 0.65/0.59 % (1095836)Peak memory usage: 10 MB 0.65/0.59 % (1095836)Instructions burned: 25 (million) 0.65/0.59 % (1095840)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=869974924:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.65/0.59 % (1095840)Instruction limit reached! 0.65/0.59 % (1095840)------------------------------ 0.65/0.59 % (1095840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.65/0.59 % (1095840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.65/0.59 % (1095840)CaDiCaL version: 2.1.3 0.65/0.59 % (1095840)Termination reason: Instruction limit 0.65/0.59 % (1095840)Termination phase: shuffling 0.65/0.59 % (1095840)Time elapsed: 0.002 s 0.65/0.59 % (1095840)Peak memory usage: 10 MB 0.65/0.59 % (1095840)Instructions burned: 4 (million) 0.65/0.59 % (1095837)Instruction limit reached! 0.65/0.59 % (1095837)------------------------------ 0.65/0.59 % (1095837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.64 % (1095837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.64 % (1095837)CaDiCaL version: 2.1.3 0.97/0.64 % (1095837)Termination reason: Instruction limit 0.97/0.64 % (1095837)Termination phase: Preprocessing 3 0.97/0.64 % (1095837)Time elapsed: 0.018 s 0.97/0.64 % (1095837)Peak memory usage: 12 MB 0.97/0.64 % (1095837)Instructions burned: 76 (million) 0.97/0.64 % (1095848)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.97/0.64 % (1095851)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.97/0.64 % (1095851)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.97/0.64 % (1095848)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2110440760:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.97/0.64 % (1095851)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1456344494:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 0.97/0.64 % (1095847)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2814122489:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.97/0.64 % (1095848)Instruction limit reached! 0.97/0.64 % (1095848)------------------------------ 0.97/0.64 % (1095848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.64 % (1095848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.64 % (1095848)CaDiCaL version: 2.1.3 0.97/0.64 % (1095848)Termination reason: Instruction limit 0.97/0.64 % (1095848)Termination phase: shuffling 0.97/0.64 % (1095848)Time elapsed: 0.004 s 0.97/0.64 % (1095848)Peak memory usage: 10 MB 0.97/0.64 % (1095848)Instructions burned: 7 (million) 0.97/0.64 % (1095850)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=370792693:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.97/0.64 % (1095851)Instruction limit reached! 0.97/0.64 % (1095851)------------------------------ 0.97/0.64 % (1095851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.64 % (1095851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.64 % (1095851)CaDiCaL version: 2.1.3 0.97/0.64 % (1095851)Termination reason: Instruction limit 0.97/0.64 % (1095851)Termination phase: shuffling 0.97/0.64 % (1095851)Time elapsed: 0.006 s 0.97/0.64 % (1095851)Peak memory usage: 10 MB 0.97/0.64 % (1095851)Instructions burned: 28 (million) 0.97/0.64 % (1095847)Instruction limit reached! 0.97/0.64 % (1095847)------------------------------ 0.97/0.64 % (1095847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.64 % (1095847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.64 % (1095847)CaDiCaL version: 2.1.3 0.97/0.64 % (1095847)Termination reason: Instruction limit 0.97/0.64 % (1095847)Termination phase: shuffling 0.97/0.64 % (1095832)Instruction limit reached! 0.97/0.64 % (1095832)------------------------------ 0.97/0.64 % (1095832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.64 % (1095847)Time elapsed: 0.005 s 0.97/0.64 % (1095847)Peak memory usage: 9 MB 0.97/0.64 % (1095847)Instructions burned: 5 (million) 0.97/0.64 % (1095832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.64 % (1095832)CaDiCaL version: 2.1.3 0.97/0.64 % (1095832)Termination reason: Instruction limit 0.97/0.64 % (1095832)Termination phase: Preprocessing 3 0.97/0.64 % (1095832)Time elapsed: 0.040 s 0.97/0.64 % (1095832)Peak memory usage: 12 MB 0.97/0.64 % (1095832)Instructions burned: 87 (million) 0.97/0.64 % (1095850)Instruction limit reached! 0.97/0.64 % (1095850)------------------------------ 0.97/0.64 % (1095850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.64 % (1095850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.64 % (1095850)CaDiCaL version: 2.1.3 0.97/0.64 % (1095850)Termination reason: Instruction limit 0.97/0.68 % (1095850)Termination phase: shuffling 0.97/0.68 % (1095850)Time elapsed: 0.006 s 0.97/0.68 % (1095850)Peak memory usage: 10 MB 0.97/0.68 % (1095850)Instructions burned: 13 (million) 0.97/0.68 % (1095857)lrs+10_1_si=on:cs=on:random_seed=4287119299:i=8:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/8Mi) 0.97/0.68 % (1095857)Instruction limit reached! 0.97/0.68 % (1095857)------------------------------ 0.97/0.68 % (1095857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.68 % (1095857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.68 % (1095857)CaDiCaL version: 2.1.3 0.97/0.68 % (1095857)Termination reason: Instruction limit 0.97/0.68 % (1095857)Termination phase: shuffling 0.97/0.68 % (1095857)Time elapsed: 0.003 s 0.97/0.68 % (1095857)Peak memory usage: 10 MB 0.97/0.68 % (1095857)Instructions burned: 13 (million) 0.97/0.68 % (1095859)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1318497794:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/38Mi) 0.97/0.68 % (1095860)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1063314300:st=2:i=249:sd=1:rtra=on:ss=axioms_1799 on theBenchmark for (1799ds/249Mi) 0.97/0.68 % (1095862)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3200934168:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/25Mi) 0.97/0.68 % (1095858)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 0.97/0.68 % (1095855)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3246730417:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 0.97/0.68 % (1095858)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3262582142:i=2:add=on:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.97/0.68 % (1095838)Instruction limit reached! 0.97/0.68 % (1095838)------------------------------ 0.97/0.68 % (1095838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.68 % (1095838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.68 % (1095838)CaDiCaL version: 2.1.3 0.97/0.68 % (1095838)Termination reason: Instruction limit 0.97/0.68 % (1095838)Termination phase: Property scanning 0.97/0.68 % (1095838)Time elapsed: 0.070 s 0.97/0.68 % (1095838)Peak memory usage: 13 MB 0.97/0.68 % (1095838)Instructions burned: 159 (million) 0.97/0.68 % (1095862)Instruction limit reached! 0.97/0.68 % (1095862)------------------------------ 0.97/0.68 % (1095862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.68 % (1095862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.68 % (1095862)CaDiCaL version: 2.1.3 0.97/0.68 % (1095862)Termination reason: Instruction limit 0.97/0.68 % (1095862)Termination phase: Property scanning 0.97/0.68 % (1095862)Time elapsed: 0.007 s 0.97/0.68 % (1095862)Peak memory usage: 10 MB 0.97/0.68 % (1095862)Instructions burned: 30 (million) 0.97/0.68 % (1095858)Instruction limit reached! 0.97/0.68 % (1095858)------------------------------ 0.97/0.68 % (1095858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.68 % (1095858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.68 % (1095858)CaDiCaL version: 2.1.3 0.97/0.68 % (1095858)Termination reason: Instruction limit 0.97/0.68 % (1095858)Termination phase: shuffling 0.97/0.68 % (1095858)Time elapsed: 0.003 s 0.97/0.68 % (1095858)Peak memory usage: 10 MB 0.97/0.68 % (1095858)Instructions burned: 7 (million) 0.97/0.68 % (1095859)Instruction limit reached! 0.97/0.68 % (1095859)------------------------------ 0.97/0.68 % (1095859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.97/0.68 % (1095859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.97/0.68 % (1095859)CaDiCaL version: 2.1.3 0.97/0.68 % (1095859)Termination reason: Instruction limit 0.97/0.68 % (1095859)Termination phase: Saturation 0.97/0.68 % (1095859)Time elapsed: 0.017 s 0.97/0.68 % (1095859)Peak memory usage: 12 MB 0.97/0.68 % (1095859)Instructions burned: 39 (million) 0.97/0.68 % (1095869)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3096421553:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 1.53/0.72 % (1095870)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3949332872:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 1.53/0.72 % (1095871)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2567330436:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1798 on theBenchmark for (1798ds/2Mi) 1.53/0.72 % (1095871)Instruction limit reached! 1.53/0.72 % (1095871)------------------------------ 1.53/0.72 % (1095871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.72 % (1095871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.72 % (1095871)CaDiCaL version: 2.1.3 1.53/0.72 % (1095871)Termination reason: Instruction limit 1.53/0.72 % (1095871)Termination phase: shuffling 1.53/0.72 % (1095871)Time elapsed: 0.002 s 1.53/0.72 % (1095871)Peak memory usage: 9 MB 1.53/0.72 % (1095871)Instructions burned: 4 (million) 1.53/0.72 % (1095870)Instruction limit reached! 1.53/0.72 % (1095870)------------------------------ 1.53/0.72 % (1095870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.72 % (1095870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.72 % (1095870)CaDiCaL version: 2.1.3 1.53/0.72 % (1095870)Termination reason: Instruction limit 1.53/0.72 % (1095870)Termination phase: shuffling 1.53/0.72 % (1095870)Time elapsed: 0.007 s 1.53/0.72 % (1095870)Peak memory usage: 10 MB 1.53/0.72 % (1095870)Instructions burned: 16 (million) 1.53/0.72 % (1095868)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2712233088:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 1.53/0.72 % (1095855)Instruction limit reached! 1.53/0.72 % (1095855)------------------------------ 1.53/0.72 % (1095855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.72 % (1095855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.72 % (1095855)CaDiCaL version: 2.1.3 1.53/0.72 % (1095855)Termination reason: Instruction limit 1.53/0.72 % (1095855)Termination phase: Saturation 1.53/0.72 % (1095855)Time elapsed: 0.037 s 1.53/0.72 % (1095855)Peak memory usage: 12 MB 1.53/0.72 % (1095855)Instructions burned: 87 (million) 1.53/0.72 % (1095868)Instruction limit reached! 1.53/0.72 % (1095868)------------------------------ 1.53/0.72 % (1095868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.72 % (1095868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.72 % (1095868)CaDiCaL version: 2.1.3 1.53/0.72 % (1095868)Termination reason: Instruction limit 1.53/0.72 % (1095868)Termination phase: shuffling 1.53/0.72 % (1095868)Time elapsed: 0.013 s 1.53/0.72 % (1095868)Peak memory usage: 10 MB 1.53/0.72 % (1095868)Instructions burned: 15 (million) 1.53/0.72 % (1095875)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3706030381:i=26:ep=R:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/26Mi) 1.53/0.72 % (1095876)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1420288620:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.53/0.72 % (1095878)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=421096707:cond=on:i=60:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/60Mi) 1.53/0.72 % (1095875)Instruction limit reached! 1.53/0.72 % (1095875)------------------------------ 1.53/0.72 % (1095875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.72 % (1095875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.72 % (1095875)CaDiCaL version: 2.1.3 1.53/0.72 % (1095875)Termination reason: Instruction limit 1.53/0.72 % (1095875)Termination phase: shuffling 1.53/0.72 % (1095875)Time elapsed: 0.011 s 1.53/0.72 % (1095875)Peak memory usage: 10 MB 1.53/0.72 % (1095875)Instructions burned: 26 (million) 1.53/0.72 % (1095879)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 1.53/0.72 % (1095879)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 1.53/0.79 % (1095876)Instruction limit reached! 1.53/0.79 % (1095876)------------------------------ 1.53/0.79 % (1095876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.79 % (1095876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.79 % (1095876)CaDiCaL version: 2.1.3 1.53/0.79 % (1095876)Termination reason: Instruction limit 1.53/0.79 % (1095876)Termination phase: shuffling 1.53/0.79 % (1095876)Time elapsed: 0.013 s 1.53/0.79 % (1095876)Peak memory usage: 10 MB 1.53/0.79 % (1095876)Instructions burned: 24 (million) 1.53/0.79 % (1095879)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3100999595:i=14:add=off:nm=40:rtra=on:rawr=on_1798 on theBenchmark for (1798ds/14Mi) 1.53/0.79 % (1095879)Instruction limit reached! 1.53/0.79 % (1095879)------------------------------ 1.53/0.79 % (1095879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.79 % (1095879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.79 % (1095879)CaDiCaL version: 2.1.3 1.53/0.79 % (1095879)Termination reason: Instruction limit 1.53/0.79 % (1095879)Termination phase: shuffling 1.53/0.79 % (1095879)Time elapsed: 0.006 s 1.53/0.79 % (1095879)Peak memory usage: 10 MB 1.53/0.79 % (1095879)Instructions burned: 14 (million) 1.53/0.79 % (1095883)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 1.53/0.79 % (1095878)Instruction limit reached! 1.53/0.79 % (1095878)------------------------------ 1.53/0.79 % (1095878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.79 % (1095878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.79 % (1095878)CaDiCaL version: 2.1.3 1.53/0.79 % (1095878)Termination reason: Instruction limit 1.53/0.79 % (1095878)Termination phase: Preprocessing 3 1.53/0.79 % (1095878)Time elapsed: 0.026 s 1.53/0.79 % (1095878)Peak memory usage: 11 MB 1.53/0.79 % (1095878)Instructions burned: 60 (million) 1.53/0.79 % (1095883)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3300293519:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1798 on theBenchmark for (1798ds/8Mi) 1.53/0.79 % (1095883)Instruction limit reached! 1.53/0.79 % (1095883)------------------------------ 1.53/0.79 % (1095883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.79 % (1095883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.79 % (1095883)CaDiCaL version: 2.1.3 1.53/0.79 % (1095883)Termination reason: Instruction limit 1.53/0.79 % (1095883)Termination phase: shuffling 1.53/0.79 % (1095883)Time elapsed: 0.004 s 1.53/0.79 % (1095883)Peak memory usage: 9 MB 1.53/0.79 % (1095883)Instructions burned: 9 (million) 1.53/0.79 % (1095869)Instruction limit reached! 1.53/0.79 % (1095869)------------------------------ 1.53/0.79 % (1095869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.79 % (1095869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.79 % (1095869)CaDiCaL version: 2.1.3 1.53/0.79 % (1095869)Termination reason: Instruction limit 1.53/0.79 % (1095869)Termination phase: Saturation 1.53/0.79 % (1095869)Time elapsed: 0.079 s 1.53/0.79 % (1095869)Peak memory usage: 16 MB 1.53/0.79 % (1095869)Instructions burned: 331 (million) 1.53/0.79 % (1095886)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1723718695:i=7:hud=5:bd=preordered:rtra=on:bet=on_1798 on theBenchmark for (1798ds/7Mi) 1.53/0.79 % (1095884)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1734934567:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1798 on theBenchmark for (1798ds/31Mi) 1.53/0.79 % (1095887)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1244500553:i=23:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.53/0.79 % (1095886)Instruction limit reached! 1.53/0.79 % (1095886)------------------------------ 1.53/0.79 % (1095886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.53/0.79 % (1095886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.53/0.79 % (1095886)CaDiCaL version: 2.1.3 2.01/0.85 % (1095886)Termination reason: Instruction limit 2.01/0.85 % (1095886)Termination phase: shuffling 2.01/0.85 % (1095886)Time elapsed: 0.004 s 2.01/0.85 % (1095886)Peak memory usage: 10 MB 2.01/0.85 % (1095886)Instructions burned: 8 (million) 2.01/0.85 % (1095890)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3092173232:i=1240:rtra=on:ixr=off_1797 on theBenchmark for (1797ds/1240Mi) 2.01/0.85 % (1095860)Instruction limit reached! 2.01/0.85 % (1095860)------------------------------ 2.01/0.85 % (1095860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.01/0.85 % (1095860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.01/0.85 % (1095860)CaDiCaL version: 2.1.3 2.01/0.85 % (1095860)Termination reason: Instruction limit 2.01/0.85 % (1095860)Termination phase: Saturation 2.01/0.85 % (1095860)Time elapsed: 0.111 s 2.01/0.85 % (1095860)Peak memory usage: 15 MB 2.01/0.85 % (1095860)Instructions burned: 249 (million) 2.01/0.85 % (1095889)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1917941302:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1798 on theBenchmark for (1798ds/20Mi) 2.01/0.85 % (1095887)Instruction limit reached! 2.01/0.85 % (1095887)------------------------------ 2.01/0.85 % (1095887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.01/0.85 % (1095887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.01/0.85 % (1095887)CaDiCaL version: 2.1.3 2.01/0.85 % (1095887)Termination reason: Instruction limit 2.01/0.85 % (1095887)Termination phase: shuffling 2.01/0.85 % (1095887)Time elapsed: 0.011 s 2.01/0.85 % (1095887)Peak memory usage: 10 MB 2.01/0.85 % (1095887)Instructions burned: 24 (million) 2.01/0.85 % (1095889)Instruction limit reached! 2.01/0.85 % (1095889)------------------------------ 2.01/0.85 % (1095889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.01/0.85 % (1095889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.01/0.85 % (1095889)CaDiCaL version: 2.1.3 2.01/0.85 % (1095889)Termination reason: Instruction limit 2.01/0.85 % (1095889)Termination phase: shuffling 2.01/0.85 % (1095889)Time elapsed: 0.009 s 2.01/0.85 % (1095889)Peak memory usage: 10 MB 2.01/0.85 % (1095889)Instructions burned: 22 (million) 2.01/0.85 % (1095894)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3115734697:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1797 on theBenchmark for (1797ds/143Mi) 2.01/0.85 % (1095884)Instruction limit reached! 2.01/0.85 % (1095884)------------------------------ 2.01/0.85 % (1095884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.01/0.85 % (1095884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.01/0.85 % (1095884)CaDiCaL version: 2.1.3 2.01/0.85 % (1095884)Termination reason: Instruction limit 2.01/0.85 % (1095884)Termination phase: Property scanning 2.01/0.85 % (1095884)Time elapsed: 0.025 s 2.01/0.85 % (1095884)Peak memory usage: 10 MB 2.01/0.85 % (1095884)Instructions burned: 32 (million) 2.01/0.85 % (1095896)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=598589951:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/193Mi) 2.01/0.85 % (1095898)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4139955229:i=42:hud=10:rtra=on_1797 on theBenchmark for (1797ds/42Mi) 2.01/0.85 % (1095899)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 2.01/0.85 % (1095899)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3222479398:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1797 on theBenchmark for (1797ds/7Mi) 2.01/0.85 % (1095899)Instruction limit reached! 2.01/0.85 % (1095899)------------------------------ 2.01/0.85 % (1095899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.01/0.85 % (1095899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.01/0.85 % (1095899)CaDiCaL version: 2.1.3 2.01/0.85 % (1095899)Termination reason: Instruction limit 2.01/0.85 % (1095899)Termination phase: shuffling 2.01/0.85 % (1095899)Time elapsed: 0.004 s 2.01/0.85 % (1095899)Peak memory usage: 10 MB 2.01/0.85 % (1095899)Instructions burned: 8 (million) 2.01/0.85 % (1095902)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3680036658:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/181Mi) 2.41/0.95 % (1095898)Instruction limit reached! 2.41/0.95 % (1095898)------------------------------ 2.41/0.95 % (1095898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/0.95 % (1095898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/0.95 % (1095898)CaDiCaL version: 2.1.3 2.41/0.95 % (1095898)Termination reason: Instruction limit 2.41/0.95 % (1095898)Termination phase: Unused predicate definition removal 2.41/0.95 % (1095898)Time elapsed: 0.018 s 2.41/0.95 % (1095898)Peak memory usage: 11 MB 2.41/0.95 % (1095898)Instructions burned: 42 (million) 2.41/0.95 % (1095905)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1828150932:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1797 on theBenchmark for (1797ds/169Mi) 2.41/0.95 % (1095907)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 2.41/0.95 % (1095907)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3496603212:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1797 on theBenchmark for (1797ds/6Mi) 2.41/0.95 % (1095907)Instruction limit reached! 2.41/0.95 % (1095907)------------------------------ 2.41/0.95 % (1095907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/0.95 % (1095907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/0.95 % (1095907)CaDiCaL version: 2.1.3 2.41/0.95 % (1095907)Termination reason: Instruction limit 2.41/0.95 % (1095907)Termination phase: shuffling 2.41/0.95 % (1095907)Time elapsed: 0.003 s 2.41/0.95 % (1095907)Peak memory usage: 10 MB 2.41/0.95 % (1095907)Instructions burned: 6 (million) 2.41/0.95 % (1095894)Instruction limit reached! 2.41/0.95 % (1095894)------------------------------ 2.41/0.95 % (1095894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/0.95 % (1095894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/0.95 % (1095894)CaDiCaL version: 2.1.3 2.41/0.95 % (1095894)Termination reason: Instruction limit 2.41/0.95 % (1095894)Termination phase: Function definition elimination 2.41/0.95 % (1095894)Time elapsed: 0.062 s 2.41/0.95 % (1095894)Peak memory usage: 13 MB 2.41/0.95 % (1095894)Instructions burned: 144 (million) 2.41/0.95 % (1095910)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1228681799:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1797 on theBenchmark for (1797ds/22Mi) 2.41/0.95 % (1095910)Instruction limit reached! 2.41/0.95 % (1095910)------------------------------ 2.41/0.95 % (1095910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/0.95 % (1095910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/0.95 % (1095910)CaDiCaL version: 2.1.3 2.41/0.95 % (1095910)Termination reason: Instruction limit 2.41/0.95 % (1095910)Termination phase: shuffling 2.41/0.95 % (1095910)Time elapsed: 0.010 s 2.41/0.95 % (1095910)Peak memory usage: 10 MB 2.41/0.95 % (1095910)Instructions burned: 22 (million) 2.41/0.95 % (1095911)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3837795677:i=19:add=on:rtra=on_1797 on theBenchmark for (1797ds/19Mi) 2.41/0.95 % (1095896)Instruction limit reached! 2.41/0.95 % (1095896)------------------------------ 2.41/0.95 % (1095896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/0.95 % (1095896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/0.95 % (1095896)CaDiCaL version: 2.1.3 2.41/0.95 % (1095896)Termination reason: Instruction limit 2.41/0.95 % (1095896)Termination phase: Property scanning 2.41/0.95 % (1095896)Time elapsed: 0.082 s 2.41/0.95 % (1095896)Peak memory usage: 13 MB 2.41/0.95 % (1095896)Instructions burned: 194 (million) 2.41/0.95 % (1095911)Instruction limit reached! 2.41/0.95 % (1095911)------------------------------ 2.41/0.95 % (1095911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/0.95 % (1095911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/0.95 % (1095911)CaDiCaL version: 2.1.3 2.41/0.95 % (1095911)Termination reason: Instruction limit 2.41/0.95 % (1095911)Termination phase: shuffling 2.41/1.00 % (1095911)Time elapsed: 0.008 s 2.41/1.00 % (1095911)Peak memory usage: 10 MB 2.41/1.00 % (1095911)Instructions burned: 19 (million) 2.41/1.00 % (1095913)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4160133022:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/316Mi) 2.41/1.00 % (1095915)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=27654377:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1796 on theBenchmark for (1796ds/853Mi) 2.41/1.00 % (1095902)Instruction limit reached! 2.41/1.00 % (1095902)------------------------------ 2.41/1.00 % (1095902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/1.00 % (1095902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/1.00 % (1095902)CaDiCaL version: 2.1.3 2.41/1.00 % (1095902)Termination reason: Instruction limit 2.41/1.00 % (1095902)Termination phase: Saturation 2.41/1.00 % (1095902)Time elapsed: 0.086 s 2.41/1.00 % (1095902)Peak memory usage: 14 MB 2.41/1.00 % (1095902)Instructions burned: 182 (million) 2.41/1.00 % (1095916)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=290038768:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1796 on theBenchmark for (1796ds/45Mi) 2.41/1.00 % (1095905)Instruction limit reached! 2.41/1.00 % (1095905)------------------------------ 2.41/1.00 % (1095905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/1.00 % (1095905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/1.00 % (1095905)CaDiCaL version: 2.1.3 2.41/1.00 % (1095905)Termination reason: Instruction limit 2.41/1.00 % (1095905)Termination phase: Property scanning 2.41/1.00 % (1095905)Time elapsed: 0.073 s 2.41/1.00 % (1095905)Peak memory usage: 13 MB 2.41/1.00 % (1095905)Instructions burned: 169 (million) 2.41/1.00 % (1095919)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1293552927:i=480:rtra=on_1796 on theBenchmark for (1796ds/480Mi) 2.41/1.00 % (1095916)Instruction limit reached! 2.41/1.00 % (1095916)------------------------------ 2.41/1.00 % (1095916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/1.00 % (1095916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/1.00 % (1095916)CaDiCaL version: 2.1.3 2.41/1.00 % (1095916)Termination reason: Instruction limit 2.41/1.00 % (1095916)Termination phase: SInE selection 2.41/1.00 % (1095916)Time elapsed: 0.019 s 2.41/1.00 % (1095916)Peak memory usage: 11 MB 2.41/1.00 % (1095916)Instructions burned: 45 (million) 2.41/1.00 % (1095921)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=599539624:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1796 on theBenchmark for (1796ds/21Mi) 2.41/1.00 % (1095921)Instruction limit reached! 2.41/1.00 % (1095921)------------------------------ 2.41/1.00 % (1095921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/1.00 % (1095921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/1.00 % (1095921)CaDiCaL version: 2.1.3 2.41/1.00 % (1095921)Termination reason: Instruction limit 2.41/1.00 % (1095921)Termination phase: shuffling 2.41/1.00 % (1095921)Time elapsed: 0.010 s 2.41/1.00 % (1095921)Peak memory usage: 10 MB 2.41/1.00 % (1095921)Instructions burned: 22 (million) 2.41/1.00 % (1095835)Instruction limit reached! 2.41/1.00 % (1095835)------------------------------ 2.41/1.00 % (1095835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 2.41/1.00 % (1095835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 2.41/1.00 % (1095835)CaDiCaL version: 2.1.3 2.41/1.00 % (1095835)Termination reason: Instruction limit 2.41/1.00 % (1095835)Termination phase: Saturation 2.41/1.00 % (1095835)Time elapsed: 0.332 s 2.41/1.00 % (1095835)Peak memory usage: 18 MB 2.41/1.00 % (1095835)Instructions burned: 635 (million) 2.41/1.00 % (1095923)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 2.41/1.00 % (1095923)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3200608104:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/200Mi) 4.05/1.14 % (1095925)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2685850775:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1796 on theBenchmark for (1796ds/13Mi) 4.05/1.14 % (1095926)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1734357258:i=66:s2at=3:nm=2:rtra=on:rawr=on_1796 on theBenchmark for (1796ds/66Mi) 4.05/1.14 % (1095925)Instruction limit reached! 4.05/1.14 % (1095925)------------------------------ 4.05/1.14 % (1095925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.05/1.14 % (1095925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.05/1.14 % (1095925)CaDiCaL version: 2.1.3 4.05/1.14 % (1095925)Termination reason: Instruction limit 4.05/1.14 % (1095925)Termination phase: shuffling 4.05/1.14 % (1095925)Time elapsed: 0.007 s 4.05/1.14 % (1095925)Peak memory usage: 10 MB 4.05/1.14 % (1095925)Instructions burned: 15 (million) 4.05/1.14 % (1095930)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2405886054:i=51:fsr=off:rtra=on_1796 on theBenchmark for (1796ds/51Mi) 4.05/1.14 % (1095926)Instruction limit reached! 4.05/1.14 % (1095926)------------------------------ 4.05/1.14 % (1095926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.05/1.14 % (1095926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.05/1.14 % (1095926)CaDiCaL version: 2.1.3 4.05/1.14 % (1095926)Termination reason: Instruction limit 4.05/1.14 % (1095926)Termination phase: SInE selection 4.05/1.14 % (1095926)Time elapsed: 0.028 s 4.05/1.14 % (1095926)Peak memory usage: 11 MB 4.05/1.14 % (1095926)Instructions burned: 67 (million) 4.05/1.14 % (1095932)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=271240189:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1795 on theBenchmark for (1795ds/31Mi) 4.05/1.14 % (1095930)Instruction limit reached! 4.05/1.14 % (1095930)------------------------------ 4.05/1.14 % (1095930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.05/1.14 % (1095930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.05/1.14 % (1095930)CaDiCaL version: 2.1.3 4.05/1.14 % (1095930)Termination reason: Instruction limit 4.05/1.14 % (1095930)Termination phase: Preprocessing 3 4.05/1.14 % (1095930)Time elapsed: 0.024 s 4.05/1.14 % (1095930)Peak memory usage: 11 MB 4.05/1.14 % (1095930)Instructions burned: 53 (million) 4.05/1.14 % (1095932)Instruction limit reached! 4.05/1.14 % (1095932)------------------------------ 4.05/1.14 % (1095932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.05/1.14 % (1095932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.05/1.14 % (1095932)CaDiCaL version: 2.1.3 4.05/1.14 % (1095932)Termination reason: Instruction limit 4.05/1.14 % (1095932)Termination phase: Property scanning 4.05/1.14 % (1095932)Time elapsed: 0.014 s 4.05/1.14 % (1095932)Peak memory usage: 10 MB 4.05/1.14 % (1095932)Instructions burned: 32 (million) 4.05/1.14 % (1095934)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2144762840:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1795 on theBenchmark for (1795ds/137Mi) 4.05/1.14 % (1095923)Instruction limit reached! 4.05/1.14 % (1095923)------------------------------ 4.05/1.14 % (1095923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.05/1.14 % (1095923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.05/1.14 % (1095923)CaDiCaL version: 2.1.3 4.05/1.14 % (1095923)Termination reason: Instruction limit 4.05/1.14 % (1095923)Termination phase: Saturation 4.05/1.14 % (1095923)Time elapsed: 0.086 s 4.05/1.14 % (1095923)Peak memory usage: 14 MB 4.05/1.14 % (1095923)Instructions burned: 202 (million) 4.05/1.14 % (1095935)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2140506465:cond=on:i=34:hud=10:nm=10:rtra=on_1795 on theBenchmark for (1795ds/34Mi) 4.05/1.14 % (1095919)Refutation not found, incomplete strategy 4.05/1.14 % (1095919)------------------------------ 4.05/1.14 % (1095919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.00/1.26 % (1095919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.00/1.26 % (1095919)CaDiCaL version: 2.1.3 5.00/1.26 % (1095919)Termination reason: Refutation not found, incomplete strategy 5.00/1.26 % (1095919)Time elapsed: 0.122 s 5.00/1.26 % (1095919)Peak memory usage: 16 MB 5.00/1.26 % (1095919)Instructions burned: 269 (million) 5.00/1.26 % (1095890)Instruction limit reached! 5.00/1.26 % (1095890)------------------------------ 5.00/1.26 % (1095890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.00/1.26 % (1095890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.00/1.26 % (1095890)CaDiCaL version: 2.1.3 5.00/1.26 % (1095890)Termination reason: Instruction limit 5.00/1.26 % (1095890)Termination phase: Saturation 5.00/1.26 % (1095890)Time elapsed: 0.266 s 5.00/1.26 % (1095890)Peak memory usage: 14 MB 5.00/1.26 % (1095890)Instructions burned: 1243 (million) 5.00/1.26 % (1095919)------------------------------ 5.00/1.26 % (1095919)------------------------------ 5.00/1.26 % (1095937)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=2307822150:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1795 on theBenchmark for (1795ds/67Mi) 5.00/1.26 % (1095939)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 5.00/1.26 % (1095935)Instruction limit reached! 5.00/1.26 % (1095935)------------------------------ 5.00/1.26 % (1095935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.00/1.26 % (1095935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.00/1.26 % (1095935)CaDiCaL version: 2.1.3 5.00/1.26 % (1095935)Termination reason: Instruction limit 5.00/1.26 % (1095935)Termination phase: Property scanning 5.00/1.26 % (1095935)Time elapsed: 0.015 s 5.00/1.26 % (1095935)Peak memory usage: 10 MB 5.00/1.26 % (1095935)Instructions burned: 35 (million) 5.00/1.26 % (1095939)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=910201900:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1795 on theBenchmark for (1795ds/180Mi) 5.00/1.26 % (1095940)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1399511824:st=2:i=246:sd=3:rtra=on:ss=axioms_1795 on theBenchmark for (1795ds/246Mi) 5.00/1.26 % (1095913)Instruction limit reached! 5.00/1.26 % (1095913)------------------------------ 5.00/1.26 % (1095913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.00/1.26 % (1095913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.00/1.26 % (1095913)CaDiCaL version: 2.1.3 5.00/1.26 % (1095913)Termination reason: Instruction limit 5.00/1.26 % (1095913)Termination phase: Saturation 5.00/1.26 % (1095913)Time elapsed: 0.170 s 5.00/1.26 % (1095913)Peak memory usage: 15 MB 5.00/1.26 % (1095913)Instructions burned: 317 (million) 5.00/1.26 % (1095942)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3285255117:cond=on:i=96:bd=all:rtra=on_1795 on theBenchmark for (1795ds/96Mi) 5.00/1.26 % (1095937)Instruction limit reached! 5.00/1.26 % (1095937)------------------------------ 5.00/1.26 % (1095937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.00/1.26 % (1095937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.00/1.26 % (1095937)CaDiCaL version: 2.1.3 5.00/1.26 % (1095937)Termination reason: Instruction limit 5.00/1.26 % (1095937)Termination phase: Preprocessing 3 5.00/1.26 % (1095937)Time elapsed: 0.030 s 5.00/1.26 % (1095937)Peak memory usage: 12 MB 5.00/1.26 % (1095937)Instructions burned: 69 (million) 5.00/1.26 % (1095934)Instruction limit reached! 5.00/1.26 % (1095934)------------------------------ 5.00/1.26 % (1095934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.00/1.26 % (1095934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.00/1.26 % (1095934)CaDiCaL version: 2.1.3 5.00/1.26 % (1095934)Termination reason: Instruction limit 5.00/1.26 % (1095934)Termination phase: Function definition elimination 5.00/1.26 % (1095934)Time elapsed: 0.059 s 5.00/1.26 % (1095934)Peak memory usage: 13 MB 5.00/1.26 % (1095934)Instructions burned: 137 (million) 5.00/1.26 % (1095945)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=949969471:i=427:sd=1:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/427Mi) 5.00/1.26 % (1095939)Instruction limit reached! 5.00/1.26 % (1095939)------------------------------ 5.00/1.26 % (1095939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.33 % (1095939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.33 % (1095939)CaDiCaL version: 2.1.3 5.66/1.33 % (1095939)Termination reason: Instruction limit 5.66/1.33 % (1095939)Termination phase: Saturation 5.66/1.33 % (1095939)Time elapsed: 0.038 s 5.66/1.33 % (1095939)Peak memory usage: 12 MB 5.66/1.33 % (1095939)Instructions burned: 181 (million) 5.66/1.33 % (1095947)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3517917449:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/874Mi) 5.66/1.33 % (1095950)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=4196806111:st=1.5:i=130:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/130Mi) 5.66/1.33 % (1095948)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1511146393:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1794 on theBenchmark for (1794ds/515Mi) 5.66/1.33 % (1095942)Instruction limit reached! 5.66/1.33 % (1095942)------------------------------ 5.66/1.33 % (1095942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.33 % (1095942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.33 % (1095942)CaDiCaL version: 2.1.3 5.66/1.33 % (1095942)Termination reason: Instruction limit 5.66/1.33 % (1095942)Termination phase: Property scanning 5.66/1.33 % (1095942)Time elapsed: 0.044 s 5.66/1.33 % (1095942)Peak memory usage: 13 MB 5.66/1.33 % (1095942)Instructions burned: 98 (million) 5.66/1.33 % (1095950)Refutation not found, incomplete strategy 5.66/1.33 % (1095950)------------------------------ 5.66/1.33 % (1095950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.33 % (1095950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.33 % (1095950)CaDiCaL version: 2.1.3 5.66/1.33 % (1095950)Termination reason: Refutation not found, incomplete strategy 5.66/1.33 % (1095950)Time elapsed: 0.023 s 5.66/1.33 % (1095950)Peak memory usage: 13 MB 5.66/1.33 % (1095950)Instructions burned: 98 (million) 5.66/1.33 % (1095950)------------------------------ 5.66/1.33 % (1095950)------------------------------ 5.66/1.33 % (1095954)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1195513978:i=44:ep=R:rtra=on:ntd=on_1794 on theBenchmark for (1794ds/44Mi) 5.66/1.33 % (1095955)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1039069531:s2a=on:i=571:nm=16:rtra=on_1794 on theBenchmark for (1794ds/571Mi) 5.66/1.33 % (1095954)Instruction limit reached! 5.66/1.33 % (1095954)------------------------------ 5.66/1.33 % (1095954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.33 % (1095954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.33 % (1095954)CaDiCaL version: 2.1.3 5.66/1.33 % (1095954)Termination reason: Instruction limit 5.66/1.33 % (1095954)Termination phase: Property scanning 5.66/1.33 % (1095954)Time elapsed: 0.020 s 5.66/1.33 % (1095954)Peak memory usage: 10 MB 5.66/1.33 % (1095954)Instructions burned: 46 (million) 5.66/1.33 % (1095940)Instruction limit reached! 5.66/1.33 % (1095940)------------------------------ 5.66/1.33 % (1095940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.33 % (1095940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.33 % (1095940)CaDiCaL version: 2.1.3 5.66/1.33 % (1095940)Termination reason: Instruction limit 5.66/1.33 % (1095940)Termination phase: Saturation 5.66/1.33 % (1095940)Time elapsed: 0.107 s 5.66/1.33 % (1095940)Peak memory usage: 15 MB 5.66/1.33 % (1095940)Instructions burned: 246 (million) 5.66/1.33 % (1095958)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1518977688:i=450:rtra=on:ixr=off:ntd=on_1794 on theBenchmark for (1794ds/450Mi) 5.66/1.33 % (1095959)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2047698662:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1793 on theBenchmark for (1793ds/95Mi) 5.66/1.33 % (1095959)Instruction limit reached! 5.66/1.33 % (1095959)------------------------------ 5.66/1.33 % (1095959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.66/1.33 % (1095959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.66/1.33 % (1095959)CaDiCaL version: 2.1.3 5.93/1.44 % (1095959)Termination reason: Instruction limit 5.93/1.44 % (1095959)Termination phase: Property scanning 5.93/1.44 % (1095959)Time elapsed: 0.044 s 5.93/1.44 % (1095959)Peak memory usage: 13 MB 5.93/1.44 % (1095959)Instructions burned: 99 (million) 5.93/1.44 % (1095962)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3182546732:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1793 on theBenchmark for (1793ds/65Mi) 5.93/1.44 % (1095945)Instruction limit reached! 5.93/1.44 % (1095945)------------------------------ 5.93/1.44 % (1095945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.93/1.44 % (1095945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.93/1.44 % (1095945)CaDiCaL version: 2.1.3 5.93/1.44 % (1095945)Termination reason: Instruction limit 5.93/1.44 % (1095945)Termination phase: Saturation 5.93/1.44 % (1095945)Time elapsed: 0.186 s 5.93/1.44 % (1095945)Peak memory usage: 17 MB 5.93/1.44 % (1095945)Instructions burned: 427 (million) 5.93/1.44 % (1095962)Instruction limit reached! 5.93/1.44 % (1095962)------------------------------ 5.93/1.44 % (1095962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.93/1.44 % (1095962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.93/1.44 % (1095962)CaDiCaL version: 2.1.3 5.93/1.44 % (1095962)Termination reason: Instruction limit 5.93/1.44 % (1095962)Termination phase: Property scanning 5.93/1.44 % (1095962)Time elapsed: 0.027 s 5.93/1.44 % (1095962)Peak memory usage: 11 MB 5.93/1.44 % (1095962)Instructions burned: 66 (million) 5.93/1.44 % (1095955)Instruction limit reached! 5.93/1.44 % (1095955)------------------------------ 5.93/1.44 % (1095955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.93/1.44 % (1095955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.93/1.44 % (1095955)CaDiCaL version: 2.1.3 5.93/1.44 % (1095955)Termination reason: Instruction limit 5.93/1.44 % (1095955)Termination phase: Saturation 5.93/1.44 % (1095955)Time elapsed: 0.145 s 5.93/1.44 % (1095955)Peak memory usage: 17 MB 5.93/1.44 % (1095955)Instructions burned: 574 (million) 5.93/1.44 % (1095964)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=4016317654:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1792 on theBenchmark for (1792ds/105Mi) 5.93/1.44 % (1095966)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3389351098:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/375Mi) 5.93/1.44 % (1095965)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=1973227327:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1792 on theBenchmark for (1792ds/5755Mi) 5.93/1.44 % (1095915)Instruction limit reached! 5.93/1.44 % (1095915)------------------------------ 5.93/1.44 % (1095915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.93/1.44 % (1095915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.93/1.44 % (1095915)CaDiCaL version: 2.1.3 5.93/1.44 % (1095915)Termination reason: Instruction limit 5.93/1.44 % (1095915)Termination phase: Saturation 5.93/1.44 % (1095915)Time elapsed: 0.414 s 5.93/1.44 % (1095915)Peak memory usage: 19 MB 5.93/1.44 % (1095915)Instructions burned: 853 (million) 5.93/1.44 % (1095970)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1217683892:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1792 on theBenchmark for (1792ds/495Mi) 5.93/1.44 % (1095964)Instruction limit reached! 5.93/1.44 % (1095964)------------------------------ 5.93/1.44 % (1095964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.93/1.44 % (1095964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.93/1.44 % (1095964)CaDiCaL version: 2.1.3 5.93/1.44 % (1095964)Termination reason: Instruction limit 5.93/1.44 % (1095964)Termination phase: Saturation 5.93/1.44 % (1095964)Time elapsed: 0.044 s 5.93/1.44 % (1095964)Peak memory usage: 12 MB 5.93/1.44 % (1095964)Instructions burned: 107 (million) 5.93/1.44 % (1095972)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2099885703:cond=on:i=34:hud=10:nm=10:rtra=on_1792 on theBenchmark for (1792ds/34Mi) 6.73/1.53 % (1095972)Instruction limit reached! 6.73/1.53 % (1095972)------------------------------ 6.73/1.53 % (1095972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.73/1.53 % (1095972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.73/1.53 % (1095972)CaDiCaL version: 2.1.3 6.73/1.53 % (1095972)Termination reason: Instruction limit 6.73/1.53 % (1095972)Termination phase: Property scanning 6.73/1.53 % (1095972)Time elapsed: 0.015 s 6.73/1.53 % (1095972)Peak memory usage: 10 MB 6.73/1.53 % (1095972)Instructions burned: 36 (million) 6.73/1.53 % (1095966)Instruction limit reached! 6.73/1.53 % (1095966)------------------------------ 6.73/1.53 % (1095966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.73/1.53 % (1095966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.73/1.53 % (1095966)CaDiCaL version: 2.1.3 6.73/1.53 % (1095966)Termination reason: Instruction limit 6.73/1.53 % (1095966)Termination phase: Saturation 6.73/1.53 % (1095966)Time elapsed: 0.089 s 6.73/1.53 % (1095966)Peak memory usage: 16 MB 6.73/1.53 % (1095966)Instructions burned: 379 (million) 6.73/1.53 % (1095958)Instruction limit reached! 6.73/1.53 % (1095958)------------------------------ 6.73/1.53 % (1095958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.73/1.53 % (1095958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.73/1.53 % (1095958)CaDiCaL version: 2.1.3 6.73/1.53 % (1095958)Termination reason: Instruction limit 6.73/1.53 % (1095958)Termination phase: Saturation 6.73/1.53 % (1095958)Time elapsed: 0.210 s 6.73/1.53 % (1095958)Peak memory usage: 17 MB 6.73/1.53 % (1095958)Instructions burned: 451 (million) 6.73/1.53 % (1095974)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3960495927:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1791 on theBenchmark for (1791ds/91Mi) 6.73/1.53 % (1095975)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2827200216:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1791 on theBenchmark for (1791ds/66Mi) 6.73/1.53 % (1095948)Instruction limit reached! 6.73/1.53 % (1095948)------------------------------ 6.73/1.53 % (1095948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.73/1.53 % (1095948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.73/1.53 % (1095948)CaDiCaL version: 2.1.3 6.73/1.53 % (1095948)Termination reason: Instruction limit 6.73/1.53 % (1095948)Termination phase: Saturation 6.73/1.53 % (1095948)Time elapsed: 0.293 s 6.73/1.53 % (1095948)Peak memory usage: 18 MB 6.73/1.53 % (1095948)Instructions burned: 517 (million) 6.73/1.53 % (1095976)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3957536947:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1791 on theBenchmark for (1791ds/22Mi) 6.73/1.53 % (1095975)Instruction limit reached! 6.73/1.53 % (1095975)------------------------------ 6.73/1.53 % (1095975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.73/1.53 % (1095975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.73/1.53 % (1095975)CaDiCaL version: 2.1.3 6.73/1.53 % (1095975)Termination reason: Instruction limit 6.73/1.53 % (1095975)Termination phase: Saturation 6.73/1.53 % (1095975)Time elapsed: 0.017 s 6.73/1.53 % (1095975)Peak memory usage: 13 MB 6.73/1.53 % (1095975)Instructions burned: 68 (million) 6.73/1.53 % (1095976)Instruction limit reached! 6.73/1.53 % (1095976)------------------------------ 6.73/1.53 % (1095976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.73/1.53 % (1095976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.73/1.53 % (1095976)CaDiCaL version: 2.1.3 6.73/1.53 % (1095976)Termination reason: Instruction limit 6.73/1.53 % (1095976)Termination phase: shuffling 6.73/1.53 % (1095976)Time elapsed: 0.010 s 6.73/1.53 % (1095976)Peak memory usage: 10 MB 6.73/1.53 % (1095976)Instructions burned: 24 (million) 6.73/1.53 % (1095979)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=945441048:i=338:bd=all:ins=4:rtra=on_1791 on theBenchmark for (1791ds/338Mi) 6.73/1.53 % (1095981)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2295792177:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1791 on theBenchmark for (1791ds/28Mi) 7.28/1.63 % (1095981)Instruction limit reached! 7.28/1.63 % (1095981)------------------------------ 7.28/1.63 % (1095981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.28/1.63 % (1095981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.28/1.63 % (1095981)CaDiCaL version: 2.1.3 7.28/1.63 % (1095981)Termination reason: Instruction limit 7.28/1.63 % (1095981)Termination phase: Property scanning 7.28/1.63 % (1095981)Time elapsed: 0.007 s 7.28/1.63 % (1095981)Peak memory usage: 10 MB 7.28/1.63 % (1095981)Instructions burned: 32 (million) 7.28/1.63 % (1095974)Instruction limit reached! 7.28/1.63 % (1095974)------------------------------ 7.28/1.63 % (1095974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.28/1.63 % (1095974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.28/1.63 % (1095974)CaDiCaL version: 2.1.3 7.28/1.63 % (1095974)Termination reason: Instruction limit 7.28/1.63 % (1095974)Termination phase: Preprocessing 3 7.28/1.63 % (1095974)Time elapsed: 0.041 s 7.28/1.63 % (1095974)Peak memory usage: 13 MB 7.28/1.63 % (1095974)Instructions burned: 92 (million) 7.28/1.63 % (1095982)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 7.28/1.63 % (1095982)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=490154105:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1791 on theBenchmark for (1791ds/137Mi) 7.28/1.63 % (1095985)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=3021849098:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1791 on theBenchmark for (1791ds/340Mi) 7.28/1.63 % (1095986)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=995577870:i=227:sd=1:bd=all:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/227Mi) 7.28/1.63 % (1095982)Instruction limit reached! 7.28/1.63 % (1095982)------------------------------ 7.28/1.63 % (1095982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.28/1.63 % (1095982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.28/1.63 % (1095982)CaDiCaL version: 2.1.3 7.28/1.63 % (1095982)Termination reason: Instruction limit 7.28/1.63 % (1095982)Termination phase: Saturation 7.28/1.63 % (1095982)Time elapsed: 0.056 s 7.28/1.63 % (1095982)Peak memory usage: 12 MB 7.28/1.63 % (1095982)Instructions burned: 137 (million) 7.28/1.63 % (1095947)Instruction limit reached! 7.28/1.63 % (1095947)------------------------------ 7.28/1.63 % (1095947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.28/1.63 % (1095947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.28/1.63 % (1095947)CaDiCaL version: 2.1.3 7.28/1.63 % (1095947)Termination reason: Instruction limit 7.28/1.63 % (1095947)Termination phase: Saturation 7.28/1.63 % (1095947)Time elapsed: 0.407 s 7.28/1.63 % (1095947)Peak memory usage: 18 MB 7.28/1.63 % (1095947)Instructions burned: 874 (million) 7.28/1.63 % (1095990)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 7.28/1.63 % (1095990)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=1336244304:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1790 on theBenchmark for (1790ds/373Mi) 7.28/1.63 % (1095985)Instruction limit reached! 7.28/1.63 % (1095985)------------------------------ 7.28/1.63 % (1095985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.28/1.63 % (1095985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.28/1.63 % (1095985)CaDiCaL version: 2.1.3 7.28/1.63 % (1095985)Termination reason: Instruction limit 7.28/1.63 % (1095985)Termination phase: Saturation 7.28/1.63 % (1095985)Time elapsed: 0.080 s 7.28/1.63 % (1095985)Peak memory usage: 17 MB 7.28/1.63 % (1095985)Instructions burned: 343 (million) 7.28/1.63 % (1095991)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3903107079:i=116:ep=RSTC:rtra=on:ntd=on_1790 on theBenchmark for (1790ds/116Mi) 7.28/1.63 % (1095993)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2889354892:i=575:rtra=on_1790 on theBenchmark for (1790ds/575Mi) 7.52/1.77 % (1095986)Instruction limit reached! 7.52/1.77 % (1095986)------------------------------ 7.52/1.77 % (1095986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.77 % (1095986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.77 % (1095986)CaDiCaL version: 2.1.3 7.52/1.77 % (1095986)Termination reason: Instruction limit 7.52/1.77 % (1095986)Termination phase: Saturation 7.52/1.77 % (1095986)Time elapsed: 0.104 s 7.52/1.77 % (1095986)Peak memory usage: 13 MB 7.52/1.77 % (1095986)Instructions burned: 229 (million) 7.52/1.77 % (1095970)Instruction limit reached! 7.52/1.77 % (1095970)------------------------------ 7.52/1.77 % (1095970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.77 % (1095970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.77 % (1095970)CaDiCaL version: 2.1.3 7.52/1.77 % (1095970)Termination reason: Instruction limit 7.52/1.77 % (1095970)Termination phase: Saturation 7.52/1.77 % (1095970)Time elapsed: 0.229 s 7.52/1.77 % (1095970)Peak memory usage: 16 MB 7.52/1.77 % (1095970)Instructions burned: 497 (million) 7.52/1.77 % (1095979)Instruction limit reached! 7.52/1.77 % (1095979)------------------------------ 7.52/1.77 % (1095979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.77 % (1095979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.77 % (1095979)CaDiCaL version: 2.1.3 7.52/1.77 % (1095979)Termination reason: Instruction limit 7.52/1.77 % (1095979)Termination phase: Saturation 7.52/1.77 % (1095979)Time elapsed: 0.141 s 7.52/1.77 % (1095979)Peak memory usage: 18 MB 7.52/1.77 % (1095979)Instructions burned: 340 (million) 7.52/1.77 % (1095996)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=898286979:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1790 on theBenchmark for (1790ds/270Mi) 7.52/1.77 % (1095991)Instruction limit reached! 7.52/1.77 % (1095991)------------------------------ 7.52/1.77 % (1095991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.77 % (1095991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.77 % (1095991)CaDiCaL version: 2.1.3 7.52/1.77 % (1095991)Termination reason: Instruction limit 7.52/1.77 % (1095991)Termination phase: Property scanning 7.52/1.77 % (1095991)Time elapsed: 0.051 s 7.52/1.77 % (1095991)Peak memory usage: 13 MB 7.52/1.77 % (1095991)Instructions burned: 118 (million) 7.52/1.77 % (1095997)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3579129528:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1790 on theBenchmark for (1790ds/9840Mi) 7.52/1.77 % (1095998)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2412343393:i=421:rtra=on:ss=axioms_1789 on theBenchmark for (1789ds/421Mi) 7.52/1.77 % (1096000)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 7.52/1.77 % (1096000)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=3399310812:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/270Mi) 7.52/1.77 % (1095998)Refutation not found, incomplete strategy 7.52/1.77 % (1095998)------------------------------ 7.52/1.77 % (1095998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.77 % (1095998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.77 % (1095998)CaDiCaL version: 2.1.3 7.52/1.77 % (1095998)Termination reason: Refutation not found, incomplete strategy 7.52/1.77 % (1095998)Time elapsed: 0.022 s 7.52/1.77 % (1095998)Peak memory usage: 13 MB 7.52/1.77 % (1095998)Instructions burned: 49 (million) 7.52/1.77 % (1095998)------------------------------ 7.52/1.77 % (1095998)------------------------------ 7.52/1.77 % (1096004)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2118410129:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/31Mi) 8.26/1.95 % (1096004)Instruction limit reached! 8.26/1.95 % (1096004)------------------------------ 8.26/1.95 % (1096004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.26/1.95 % (1096004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.26/1.95 % (1096004)CaDiCaL version: 2.1.3 8.26/1.95 % (1096004)Termination reason: Instruction limit 8.26/1.95 % (1096004)Termination phase: Property scanning 8.26/1.95 % (1096004)Time elapsed: 0.014 s 8.26/1.95 % (1096004)Peak memory usage: 10 MB 8.26/1.95 % (1096004)Instructions burned: 32 (million) 8.26/1.95 % (1096006)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 8.26/1.95 % (1096006)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 8.26/1.95 % (1096006)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3424515802:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1789 on theBenchmark for (1789ds/1440Mi) 8.26/1.95 % (1095990)Instruction limit reached! 8.26/1.95 % (1095990)------------------------------ 8.26/1.95 % (1095990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.26/1.95 % (1095990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.26/1.95 % (1095990)CaDiCaL version: 2.1.3 8.26/1.95 % (1095990)Termination reason: Instruction limit 8.26/1.95 % (1095990)Termination phase: Saturation 8.26/1.95 % (1095990)Time elapsed: 0.149 s 8.26/1.95 % (1095990)Peak memory usage: 15 MB 8.26/1.95 % (1095990)Instructions burned: 375 (million) 8.26/1.95 % (1095996)Instruction limit reached! 8.26/1.95 % (1095996)------------------------------ 8.26/1.95 % (1095996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.26/1.95 % (1095996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.26/1.95 % (1095996)CaDiCaL version: 2.1.3 8.26/1.95 % (1095996)Termination reason: Instruction limit 8.26/1.95 % (1095996)Termination phase: Saturation 8.26/1.95 % (1095996)Time elapsed: 0.110 s 8.26/1.95 % (1095996)Peak memory usage: 12 MB 8.26/1.95 % (1095996)Instructions burned: 270 (million) 8.26/1.95 % (1096008)dis+10_2_sil=128000:si=on:random_seed=732402806:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1788 on theBenchmark for (1788ds/339Mi) 8.26/1.95 % (1095993)Instruction limit reached! 8.26/1.95 % (1095993)------------------------------ 8.26/1.95 % (1095993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.26/1.95 % (1095993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.26/1.95 % (1095993)CaDiCaL version: 2.1.3 8.26/1.95 % (1095993)Termination reason: Instruction limit 8.26/1.95 % (1095993)Termination phase: Saturation 8.26/1.95 % (1095993)Time elapsed: 0.152 s 8.26/1.95 % (1095993)Peak memory usage: 18 MB 8.26/1.95 % (1095993)Instructions burned: 578 (million) 8.26/1.95 % (1096011)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=4202994211:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1788 on theBenchmark for (1788ds/122Mi) 8.26/1.95 % (1096010)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1867820921:i=111:add=on:fgj=on:rtra=on:fdi=1024_1788 on theBenchmark for (1788ds/111Mi) 8.26/1.95 % (1096000)Instruction limit reached! 8.26/1.95 % (1096000)------------------------------ 8.26/1.95 % (1096000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.26/1.95 % (1096000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.26/1.95 % (1096000)CaDiCaL version: 2.1.3 8.26/1.95 % (1096000)Termination reason: Instruction limit 8.26/1.95 % (1096000)Termination phase: Saturation 8.26/1.95 % (1096000)Time elapsed: 0.117 s 8.26/1.95 % (1096000)Peak memory usage: 15 MB 8.26/1.95 % (1096000)Instructions burned: 270 (million) 8.26/1.95 % (1096011)Instruction limit reached! 8.26/1.95 % (1096011)------------------------------ 8.26/1.95 % (1096011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.26/1.95 % (1096011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.26/1.95 % (1096011)CaDiCaL version: 2.1.3 11.25/2.15 % (1096011)Termination reason: Instruction limit 11.25/2.15 % (1096011)Termination phase: Property scanning 11.25/2.15 % (1096011)Time elapsed: 0.028 s 11.25/2.15 % (1096011)Peak memory usage: 13 MB 11.25/2.15 % (1096011)Instructions burned: 124 (million) 11.25/2.15 % (1096014)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=3102604367:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1788 on theBenchmark for (1788ds/136Mi) 11.25/2.15 % (1096015)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2682619489:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1788 on theBenchmark for (1788ds/232Mi) 11.25/2.15 % (1096010)Instruction limit reached! 11.25/2.15 % (1096010)------------------------------ 11.25/2.15 % (1096010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.25/2.15 % (1096010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.25/2.15 % (1096010)CaDiCaL version: 2.1.3 11.25/2.15 % (1096010)Termination reason: Instruction limit 11.25/2.15 % (1096010)Termination phase: Property scanning 11.25/2.15 % (1096010)Time elapsed: 0.049 s 11.25/2.15 % (1096010)Peak memory usage: 13 MB 11.25/2.15 % (1096010)Instructions burned: 112 (million) 11.25/2.15 % (1096018)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2742563157:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1788 on theBenchmark for (1788ds/1254Mi) 11.25/2.15 % (1096014)Instruction limit reached! 11.25/2.15 % (1096014)------------------------------ 11.25/2.15 % (1096014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.25/2.15 % (1096014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.25/2.15 % (1096014)CaDiCaL version: 2.1.3 11.25/2.15 % (1096014)Termination reason: Instruction limit 11.25/2.15 % (1096014)Termination phase: Property scanning 11.25/2.15 % (1096014)Time elapsed: 0.062 s 11.25/2.15 % (1096014)Peak memory usage: 16 MB 11.25/2.15 % (1096014)Instructions burned: 138 (million) 11.25/2.15 % (1096020)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 11.25/2.15 % (1096020)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=276959708:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1787 on theBenchmark for (1787ds/281Mi) 11.25/2.15 % (1096015)Instruction limit reached! 11.25/2.15 % (1096015)------------------------------ 11.25/2.15 % (1096015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.25/2.15 % (1096015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.25/2.15 % (1096015)CaDiCaL version: 2.1.3 11.25/2.15 % (1096015)Termination reason: Instruction limit 11.25/2.15 % (1096015)Termination phase: Saturation 11.25/2.15 % (1096015)Time elapsed: 0.091 s 11.25/2.15 % (1096015)Peak memory usage: 15 MB 11.25/2.15 % (1096015)Instructions burned: 236 (million) 11.25/2.15 % (1096022)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2457960500:i=619:add=on:rtra=on_1787 on theBenchmark for (1787ds/619Mi) 11.25/2.15 % (1096008)Instruction limit reached! 11.25/2.15 % (1096008)------------------------------ 11.25/2.15 % (1096008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.25/2.15 % (1096008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.25/2.15 % (1096008)CaDiCaL version: 2.1.3 11.25/2.15 % (1096008)Termination reason: Instruction limit 11.25/2.15 % (1096008)Termination phase: Saturation 11.25/2.15 % (1096008)Time elapsed: 0.160 s 11.25/2.15 % (1096008)Peak memory usage: 14 MB 11.25/2.15 % (1096008)Instructions burned: 341 (million) 11.25/2.15 % (1096024)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4291773003:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1787 on theBenchmark for (1787ds/865Mi) 11.25/2.15 % (1096018)Refutation not found, incomplete strategy 11.25/2.15 % (1096018)------------------------------ 11.25/2.15 % (1096018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.25/2.15 % (1096018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.25/2.15 % (1096018)CaDiCaL version: 2.1.3 11.25/2.15 % (1096018)Termination reason: Refutation not found, incomplete strategy 12.62/2.31 % (1096018)Time elapsed: 0.097 s 12.62/2.31 % (1096018)Peak memory usage: 15 MB 12.62/2.31 % (1096018)Instructions burned: 221 (million) 12.62/2.31 % (1096018)------------------------------ 12.62/2.31 % (1096018)------------------------------ 12.62/2.31 % (1096026)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2327610326:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1786 on theBenchmark for (1786ds/212Mi) 12.62/2.31 % (1096020)Instruction limit reached! 12.62/2.31 % (1096020)------------------------------ 12.62/2.31 % (1096020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.62/2.31 % (1096020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.62/2.31 % (1096020)CaDiCaL version: 2.1.3 12.62/2.31 % (1096020)Termination reason: Instruction limit 12.62/2.31 % (1096020)Termination phase: Saturation 12.62/2.31 % (1096020)Time elapsed: 0.115 s 12.62/2.31 % (1096020)Peak memory usage: 12 MB 12.62/2.31 % (1096020)Instructions burned: 282 (million) 12.62/2.31 % (1096028)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=699018815:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1786 on theBenchmark for (1786ds/130Mi) 12.62/2.31 % (1096026)Instruction limit reached! 12.62/2.31 % (1096026)------------------------------ 12.62/2.31 % (1096026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.62/2.31 % (1096026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.62/2.31 % (1096026)CaDiCaL version: 2.1.3 12.62/2.31 % (1096026)Termination reason: Instruction limit 12.62/2.31 % (1096026)Termination phase: Saturation 12.62/2.31 % (1096026)Time elapsed: 0.090 s 12.62/2.31 % (1096026)Peak memory usage: 14 MB 12.62/2.31 % (1096026)Instructions burned: 214 (million) 12.62/2.31 % (1096030)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3438008337:st=1.5:i=346:rtra=on:ss=axioms_1785 on theBenchmark for (1785ds/346Mi) 12.62/2.31 % (1096022)Instruction limit reached! 12.62/2.31 % (1096022)------------------------------ 12.62/2.31 % (1096022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.62/2.31 % (1096022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.62/2.31 % (1096022)CaDiCaL version: 2.1.3 12.62/2.31 % (1096022)Termination reason: Instruction limit 12.62/2.31 % (1096022)Termination phase: Saturation 12.62/2.31 % (1096022)Time elapsed: 0.162 s 12.62/2.31 % (1096022)Peak memory usage: 18 MB 12.62/2.31 % (1096022)Instructions burned: 622 (million) 12.62/2.31 % (1096028)Instruction limit reached! 12.62/2.31 % (1096028)------------------------------ 12.62/2.31 % (1096028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.62/2.31 % (1096028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.62/2.31 % (1096028)CaDiCaL version: 2.1.3 12.62/2.31 % (1096028)Termination reason: Instruction limit 12.62/2.31 % (1096028)Termination phase: Property scanning 12.62/2.31 % (1096028)Time elapsed: 0.057 s 12.62/2.31 % (1096028)Peak memory usage: 13 MB 12.62/2.31 % (1096028)Instructions burned: 131 (million) 12.62/2.31 % (1096032)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2884273989:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_1785 on theBenchmark for (1785ds/152Mi) 12.62/2.31 % (1096033)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2862949728:i=75:ep=R:rtra=on:ntd=on_1785 on theBenchmark for (1785ds/75Mi) 12.62/2.31 % (1096030)Refutation not found, incomplete strategy 12.62/2.31 % (1096030)------------------------------ 12.62/2.31 % (1096030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.62/2.31 % (1096030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.62/2.31 % (1096030)CaDiCaL version: 2.1.3 12.62/2.31 % (1096030)Termination reason: Refutation not found, incomplete strategy 12.62/2.31 % (1096030)Time elapsed: 0.045 s 12.62/2.31 % (1096030)Peak memory usage: 13 MB 12.62/2.31 % (1096030)Instructions burned: 99 (million) 12.62/2.31 % (1096030)------------------------------ 12.62/2.31 % (1096030)------------------------------ 12.62/2.31 % (1096032)Instruction limit reached! 12.62/2.31 % (1096032)------------------------------ 12.62/2.31 % (1096032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.62/2.31 % (1096032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.62/2.31 % (1096032)CaDiCaL version: 2.1.3 12.62/2.31 % (1096032)Termination reason: Instruction limit 13.94/2.51 % (1096032)Termination phase: Inequality splitting 13.94/2.51 % (1096032)Time elapsed: 0.034 s 13.94/2.51 % (1096032)Peak memory usage: 13 MB 13.94/2.51 % (1096032)Instructions burned: 152 (million) 13.94/2.51 % (1096033)Instruction limit reached! 13.94/2.51 % (1096033)------------------------------ 13.94/2.51 % (1096033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.94/2.51 % (1096033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.94/2.51 % (1096033)CaDiCaL version: 2.1.3 13.94/2.51 % (1096033)Termination reason: Instruction limit 13.94/2.51 % (1096033)Termination phase: Property scanning 13.94/2.51 % (1096033)Time elapsed: 0.032 s 13.94/2.51 % (1096033)Peak memory usage: 11 MB 13.94/2.51 % (1096033)Instructions burned: 77 (million) 13.94/2.51 % (1096037)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3130299309:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_1785 on theBenchmark for (1785ds/148Mi) 13.94/2.51 % (1096036)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2949242804:st=2.5:i=387:sd=2:rtra=on:ss=axioms_1785 on theBenchmark for (1785ds/387Mi) 13.94/2.51 % (1096039)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1936803873:i=161:piset=and:rtra=on:ntd=on_1785 on theBenchmark for (1785ds/161Mi) 13.94/2.51 % (1096037)Instruction limit reached! 13.94/2.51 % (1096037)------------------------------ 13.94/2.51 % (1096037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.94/2.51 % (1096037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.94/2.51 % (1096037)CaDiCaL version: 2.1.3 13.94/2.51 % (1096037)Termination reason: Instruction limit 13.94/2.51 % (1096037)Termination phase: Saturation 13.94/2.51 % (1096037)Time elapsed: 0.032 s 13.94/2.51 % (1096037)Peak memory usage: 12 MB 13.94/2.51 % (1096037)Instructions burned: 149 (million) 13.94/2.51 % (1096042)lrs+10_1_sil=128000:si=on:random_seed=812850970:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_1784 on theBenchmark for (1784ds/888Mi) 13.94/2.51 % (1096039)Instruction limit reached! 13.94/2.51 % (1096039)------------------------------ 13.94/2.51 % (1096039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.94/2.51 % (1096039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.94/2.51 % (1096039)CaDiCaL version: 2.1.3 13.94/2.51 % (1096039)Termination reason: Instruction limit 13.94/2.51 % (1096039)Termination phase: Property scanning 13.94/2.51 % (1096039)Time elapsed: 0.070 s 13.94/2.51 % (1096039)Peak memory usage: 13 MB 13.94/2.51 % (1096039)Instructions burned: 163 (million) 13.94/2.51 % (1096044)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=3920645401:i=136:add=on:ins=4:rtra=on:sup=off_1784 on theBenchmark for (1784ds/136Mi) 13.94/2.51 % (1096036)Instruction limit reached! 13.94/2.51 % (1096036)------------------------------ 13.94/2.51 % (1096036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.94/2.51 % (1096036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.94/2.51 % (1096036)CaDiCaL version: 2.1.3 13.94/2.51 % (1096036)Termination reason: Instruction limit 13.94/2.51 % (1096036)Termination phase: Saturation 13.94/2.51 % (1096036)Time elapsed: 0.156 s 13.94/2.51 % (1096036)Peak memory usage: 12 MB 13.94/2.51 % (1096036)Instructions burned: 388 (million) 13.94/2.51 % (1096044)Instruction limit reached! 13.94/2.51 % (1096044)------------------------------ 13.94/2.51 % (1096044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.94/2.51 % (1096044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.94/2.51 % (1096044)CaDiCaL version: 2.1.3 13.94/2.51 % (1096044)Termination reason: Instruction limit 13.94/2.51 % (1096044)Termination phase: Property scanning 13.94/2.51 % (1096044)Time elapsed: 0.058 s 13.94/2.51 % (1096044)Peak memory usage: 13 MB 13.94/2.51 % (1096044)Instructions burned: 137 (million) 13.94/2.51 % (1096046)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=4082354861:i=88:s2at=3:nm=2:rtra=on:rawr=on_1783 on theBenchmark for (1783ds/88Mi) 13.94/2.51 % (1096047)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=617764041:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_1783 on theBenchmark for (1783ds/93Mi) 14.22/2.68 % (1096046)Instruction limit reached! 14.22/2.68 % (1096046)------------------------------ 14.22/2.68 % (1096046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.22/2.68 % (1096046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.22/2.68 % (1096046)CaDiCaL version: 2.1.3 14.22/2.68 % (1096046)Termination reason: Instruction limit 14.22/2.68 % (1096046)Termination phase: Property scanning 14.22/2.68 % (1096046)Time elapsed: 0.036 s 14.22/2.68 % (1096046)Peak memory usage: 11 MB 14.22/2.68 % (1096046)Instructions burned: 88 (million) 14.22/2.68 % (1096047)Instruction limit reached! 14.22/2.68 % (1096047)------------------------------ 14.22/2.68 % (1096047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.22/2.68 % (1096047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.22/2.68 % (1096047)CaDiCaL version: 2.1.3 14.22/2.68 % (1096047)Termination reason: Instruction limit 14.22/2.68 % (1096047)Termination phase: Saturation 14.22/2.68 % (1096047)Time elapsed: 0.038 s 14.22/2.68 % (1096047)Peak memory usage: 12 MB 14.22/2.68 % (1096047)Instructions burned: 93 (million) 14.22/2.68 % (1096050)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=751678958:i=2186:rtra=on:ixr=off_1782 on theBenchmark for (1782ds/2186Mi) 14.22/2.68 % (1096051)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=527571105:s2a=on:i=240:rtra=on:ntd=on_1782 on theBenchmark for (1782ds/240Mi) 14.22/2.68 % (1096042)Instruction limit reached! 14.22/2.68 % (1096042)------------------------------ 14.22/2.68 % (1096042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.22/2.68 % (1096042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.22/2.68 % (1096042)CaDiCaL version: 2.1.3 14.22/2.68 % (1096042)Termination reason: Instruction limit 14.22/2.68 % (1096042)Termination phase: Saturation 14.22/2.68 % (1096042)Time elapsed: 0.222 s 14.22/2.68 % (1096042)Peak memory usage: 19 MB 14.22/2.68 % (1096042)Instructions burned: 889 (million) 14.22/2.68 % (1096006)Instruction limit reached! 14.22/2.68 % (1096006)------------------------------ 14.22/2.68 % (1096006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.22/2.68 % (1096006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.22/2.68 % (1096006)CaDiCaL version: 2.1.3 14.22/2.68 % (1096006)Termination reason: Instruction limit 14.22/2.68 % (1096006)Termination phase: Saturation 14.22/2.68 % (1096006)Time elapsed: 0.670 s 14.22/2.68 % (1096006)Peak memory usage: 21 MB 14.22/2.68 % (1096006)Instructions burned: 1440 (million) 14.22/2.68 % (1096054)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2914144659:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_1782 on theBenchmark for (1782ds/805Mi) 14.22/2.68 % (1096055)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on 14.22/2.68 % (1096055)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2735211147:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_1782 on theBenchmark for (1782ds/391Mi) 14.22/2.68 % (1096024)Instruction limit reached! 14.22/2.68 % (1096024)------------------------------ 14.22/2.68 % (1096024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.22/2.68 % (1096024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.22/2.68 % (1096024)CaDiCaL version: 2.1.3 14.22/2.68 % (1096024)Termination reason: Instruction limit 14.22/2.68 % (1096024)Termination phase: Saturation 14.22/2.68 % (1096024)Time elapsed: 0.504 s 14.22/2.68 % (1096024)Peak memory usage: 19 MB 14.22/2.68 % (1096024)Instructions burned: 866 (million) 14.22/2.68 % (1096058)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=498545048:i=355:av=off:fsr=off:rtra=on:ixr=off_1781 on theBenchmark for (1781ds/355Mi) 14.22/2.68 % (1096051)Instruction limit reached! 14.22/2.68 % (1096051)------------------------------ 14.22/2.68 % (1096051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.22/2.68 % (1096051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.22/2.68 % (1096051)CaDiCaL version: 2.1.3 15.76/2.93 % (1096051)Termination reason: Instruction limit 15.76/2.93 % (1096051)Termination phase: Saturation 15.76/2.93 % (1096051)Time elapsed: 0.105 s 15.76/2.93 % (1096051)Peak memory usage: 14 MB 15.76/2.93 % (1096051)Instructions burned: 244 (million) 15.76/2.93 % (1096060)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=3851082883:lrd=on:i=314:sd=1:rtra=on:ss=axioms_1781 on theBenchmark for (1781ds/314Mi) 15.76/2.93 % (1096060)Refutation not found, incomplete strategy 15.76/2.93 % (1096060)------------------------------ 15.76/2.93 % (1096060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.76/2.93 % (1096060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.76/2.93 % (1096060)CaDiCaL version: 2.1.3 15.76/2.93 % (1096060)Termination reason: Refutation not found, incomplete strategy 15.76/2.93 % (1096060)Time elapsed: 0.033 s 15.76/2.93 % (1096060)Peak memory usage: 13 MB 15.76/2.93 % (1096060)Instructions burned: 70 (million) 15.76/2.93 % (1096060)------------------------------ 15.76/2.93 % (1096060)------------------------------ 15.76/2.93 % (1096062)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=355953306:s2a=on:i=251:fsr=off:rtra=on_1780 on theBenchmark for (1780ds/251Mi) 15.76/2.93 % (1096055)Instruction limit reached! 15.76/2.93 % (1096055)------------------------------ 15.76/2.93 % (1096055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.76/2.93 % (1096055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.76/2.93 % (1096055)CaDiCaL version: 2.1.3 15.76/2.93 % (1096055)Termination reason: Instruction limit 15.76/2.93 % (1096055)Termination phase: Saturation 15.76/2.93 % (1096055)Time elapsed: 0.159 s 15.76/2.93 % (1096055)Peak memory usage: 12 MB 15.76/2.93 % (1096055)Instructions burned: 393 (million) 15.76/2.93 % (1096064)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=646893879:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1780 on theBenchmark for (1780ds/2470Mi) 15.76/2.93 % (1096058)Instruction limit reached! 15.76/2.93 % (1096058)------------------------------ 15.76/2.93 % (1096058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.76/2.93 % (1096058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.76/2.93 % (1096058)CaDiCaL version: 2.1.3 15.76/2.93 % (1096058)Termination reason: Instruction limit 15.76/2.93 % (1096058)Termination phase: Saturation 15.76/2.93 % (1096058)Time elapsed: 0.169 s 15.76/2.93 % (1096058)Peak memory usage: 15 MB 15.76/2.93 % (1096058)Instructions burned: 355 (million) 15.76/2.93 % (1096054)Instruction limit reached! 15.76/2.93 % (1096054)------------------------------ 15.76/2.93 % (1096054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.76/2.93 % (1096054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.76/2.93 % (1096054)CaDiCaL version: 2.1.3 15.76/2.93 % (1096054)Termination reason: Instruction limit 15.76/2.93 % (1096054)Termination phase: Saturation 15.76/2.93 % (1096054)Time elapsed: 0.230 s 15.76/2.93 % (1096054)Peak memory usage: 18 MB 15.76/2.93 % (1096054)Instructions burned: 808 (million) 15.76/2.93 % (1096067)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3305522263:i=116:ep=RSTC:rtra=on:ntd=on_1779 on theBenchmark for (1779ds/116Mi) 15.76/2.93 % (1096066)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=2501736706:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_1780 on theBenchmark for (1780ds/673Mi) 15.76/2.93 % (1096062)Instruction limit reached! 15.76/2.93 % (1096062)------------------------------ 15.76/2.93 % (1096062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.76/2.93 % (1096062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.76/2.93 % (1096062)CaDiCaL version: 2.1.3 15.76/2.93 % (1096062)Termination reason: Instruction limit 15.76/2.93 % (1096062)Termination phase: Saturation 15.76/2.93 % (1096062)Time elapsed: 0.107 s 15.76/2.93 % (1096062)Peak memory usage: 15 MB 15.76/2.93 % (1096062)Instructions burned: 252 (million) 15.76/2.93 % (1096067)Instruction limit reached! 15.76/2.93 % (1096067)------------------------------ 15.76/2.93 % (1096067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.99/3.29 % (1096067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.99/3.29 % (1096067)CaDiCaL version: 2.1.3 18.99/3.29 % (1096067)Termination reason: Instruction limit 18.99/3.29 % (1096067)Termination phase: Property scanning 18.99/3.29 % (1096067)Time elapsed: 0.027 s 18.99/3.29 % (1096067)Peak memory usage: 13 MB 18.99/3.29 % (1096067)Instructions burned: 119 (million) 18.99/3.29 % (1096070)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3760962170:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1779 on theBenchmark for (1779ds/270Mi) 18.99/3.29 % (1096071)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4294198262:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1779 on theBenchmark for (1779ds/30Mi) 18.99/3.29 % (1096071)Instruction limit reached! 18.99/3.29 % (1096071)------------------------------ 18.99/3.29 % (1096071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.99/3.29 % (1096071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.99/3.29 % (1096071)CaDiCaL version: 2.1.3 18.99/3.29 % (1096071)Termination reason: Instruction limit 18.99/3.29 % (1096071)Termination phase: shuffling 18.99/3.29 % (1096071)Time elapsed: 0.007 s 18.99/3.29 % (1096071)Peak memory usage: 10 MB 18.99/3.29 % (1096071)Instructions burned: 32 (million) 18.99/3.29 % (1096074)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off 18.99/3.29 % (1096074)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2749308656:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_1779 on theBenchmark for (1779ds/39Mi) 18.99/3.29 % (1096074)Instruction limit reached! 18.99/3.29 % (1096074)------------------------------ 18.99/3.29 % (1096074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.99/3.29 % (1096074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.99/3.29 % (1096074)CaDiCaL version: 2.1.3 18.99/3.29 % (1096074)Termination reason: Instruction limit 18.99/3.29 % (1096074)Termination phase: Property scanning 18.99/3.29 % (1096074)Time elapsed: 0.009 s 18.99/3.29 % (1096074)Peak memory usage: 10 MB 18.99/3.29 % (1096074)Instructions burned: 39 (million) 18.99/3.29 % (1096076)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3268129226:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1779 on theBenchmark for (1779ds/365Mi) 18.99/3.29 % (1096070)Instruction limit reached! 18.99/3.29 % (1096070)------------------------------ 18.99/3.29 % (1096070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.99/3.29 % (1096070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.99/3.29 % (1096070)CaDiCaL version: 2.1.3 18.99/3.29 % (1096070)Termination reason: Instruction limit 18.99/3.29 % (1096070)Termination phase: Saturation 18.99/3.29 % (1096070)Time elapsed: 0.110 s 18.99/3.29 % (1096070)Peak memory usage: 12 MB 18.99/3.29 % (1096070)Instructions burned: 272 (million) 18.99/3.29 % (1096078)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=316946705:i=158:av=off:rtra=on_1778 on theBenchmark for (1778ds/158Mi) 18.99/3.29 % (1096076)Instruction limit reached! 18.99/3.29 % (1096076)------------------------------ 18.99/3.29 % (1096076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.99/3.29 % (1096076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.99/3.29 % (1096076)CaDiCaL version: 2.1.3 18.99/3.29 % (1096076)Termination reason: Instruction limit 18.99/3.29 % (1096076)Termination phase: Saturation 18.99/3.29 % (1096076)Time elapsed: 0.088 s 18.99/3.29 % (1096076)Peak memory usage: 17 MB 18.99/3.29 % (1096076)Instructions burned: 365 (million) 18.99/3.29 % (1096080)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 18.99/3.29 % (1096080)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2312409340:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_1778 on theBenchmark for (1778ds/252Mi) 20.59/3.40 % (1096078)Instruction limit reached! 20.59/3.40 % (1096078)------------------------------ 20.59/3.40 % (1096078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.40 % (1096078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.40 % (1096078)CaDiCaL version: 2.1.3 20.59/3.40 % (1096078)Termination reason: Instruction limit 20.59/3.40 % (1096078)Termination phase: Saturation 20.59/3.40 % (1096078)Time elapsed: 0.084 s 20.59/3.40 % (1096078)Peak memory usage: 14 MB 20.59/3.40 % (1096078)Instructions burned: 160 (million) 20.59/3.40 % (1096082)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2432225262:i=213:rtra=on:ss=axioms_1777 on theBenchmark for (1777ds/213Mi) 20.59/3.40 % (1096082)Refutation not found, incomplete strategy 20.59/3.40 % (1096082)------------------------------ 20.59/3.40 % (1096082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.40 % (1096082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.40 % (1096082)CaDiCaL version: 2.1.3 20.59/3.40 % (1096082)Termination reason: Refutation not found, incomplete strategy 20.59/3.40 % (1096082)Time elapsed: 0.017 s 20.59/3.40 % (1096082)Peak memory usage: 13 MB 20.59/3.40 % (1096082)Instructions burned: 38 (million) 20.59/3.40 % (1096082)------------------------------ 20.59/3.40 % (1096082)------------------------------ 20.59/3.40 % (1096084)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=4288723775:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_1776 on theBenchmark for (1776ds/160Mi) 20.59/3.40 % (1096080)Instruction limit reached! 20.59/3.40 % (1096080)------------------------------ 20.59/3.40 % (1096080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.40 % (1096080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.40 % (1096080)CaDiCaL version: 2.1.3 20.59/3.40 % (1096080)Termination reason: Instruction limit 20.59/3.40 % (1096080)Termination phase: Saturation 20.59/3.40 % (1096080)Time elapsed: 0.112 s 20.59/3.40 % (1096080)Peak memory usage: 15 MB 20.59/3.40 % (1096080)Instructions burned: 252 (million) 20.59/3.40 % (1096066)Instruction limit reached! 20.59/3.40 % (1096066)------------------------------ 20.59/3.40 % (1096066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.40 % (1096066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.40 % (1096066)CaDiCaL version: 2.1.3 20.59/3.40 % (1096066)Termination reason: Instruction limit 20.59/3.40 % (1096066)Termination phase: Saturation 20.59/3.40 % (1096066)Time elapsed: 0.317 s 20.59/3.40 % (1096066)Peak memory usage: 17 MB 20.59/3.40 % (1096066)Instructions burned: 675 (million) 20.59/3.40 % (1096086)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3626068207:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_1776 on theBenchmark for (1776ds/763Mi) 20.59/3.40 % (1096087)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on 20.59/3.40 % (1096087)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2843316608:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_1776 on theBenchmark for (1776ds/237Mi) 20.59/3.40 % (1096084)Instruction limit reached! 20.59/3.40 % (1096084)------------------------------ 20.59/3.40 % (1096084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.40 % (1096084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.40 % (1096084)CaDiCaL version: 2.1.3 20.59/3.40 % (1096084)Termination reason: Instruction limit 20.59/3.40 % (1096084)Termination phase: Function definition elimination 20.59/3.40 % (1096084)Time elapsed: 0.069 s 20.59/3.40 % (1096084)Peak memory usage: 13 MB 20.59/3.40 % (1096084)Instructions burned: 162 (million) 20.59/3.40 % (1096090)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=3054853737:s2a=on:i=386:rtra=on:ntd=on_1776 on theBenchmark for (1776ds/386Mi) 20.59/3.40 % (1096087)Instruction limit reached! 20.59/3.40 % (1096087)------------------------------ 20.59/3.40 % (1096087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.50 % (1096087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.50 % (1096087)CaDiCaL version: 2.1.3 20.59/3.50 % (1096087)Termination reason: Instruction limit 20.59/3.50 % (1096087)Termination phase: Saturation 20.59/3.50 % (1096087)Time elapsed: 0.104 s 20.59/3.50 % (1096087)Peak memory usage: 15 MB 20.59/3.50 % (1096087)Instructions burned: 237 (million) 20.59/3.50 % (1096092)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=2754981279:i=300:piset=and:nm=32:rtra=on_1775 on theBenchmark for (1775ds/300Mi) 20.59/3.50 % (1096090)Instruction limit reached! 20.59/3.50 % (1096090)------------------------------ 20.59/3.50 % (1096090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.50 % (1096090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.50 % (1096090)CaDiCaL version: 2.1.3 20.59/3.50 % (1096090)Termination reason: Instruction limit 20.59/3.50 % (1096090)Termination phase: Saturation 20.59/3.50 % (1096090)Time elapsed: 0.155 s 20.59/3.50 % (1096090)Peak memory usage: 12 MB 20.59/3.50 % (1096090)Instructions burned: 387 (million) 20.59/3.50 % (1096094)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=401518973:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_1774 on theBenchmark for (1774ds/567Mi) 20.59/3.50 % (1096092)Instruction limit reached! 20.59/3.50 % (1096092)------------------------------ 20.59/3.50 % (1096092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.50 % (1096092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.50 % (1096092)CaDiCaL version: 2.1.3 20.59/3.50 % (1096092)Termination reason: Instruction limit 20.59/3.50 % (1096092)Termination phase: Saturation 20.59/3.50 % (1096092)Time elapsed: 0.123 s 20.59/3.50 % (1096092)Peak memory usage: 14 MB 20.59/3.50 % (1096092)Instructions burned: 300 (million) 20.59/3.50 % (1096096)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=2155108325:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_1773 on theBenchmark for (1773ds/379Mi) 20.59/3.50 % (1096050)Instruction limit reached! 20.59/3.50 % (1096050)------------------------------ 20.59/3.50 % (1096050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.50 % (1096050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.50 % (1096050)CaDiCaL version: 2.1.3 20.59/3.50 % (1096050)Termination reason: Instruction limit 20.59/3.50 % (1096050)Termination phase: Saturation 20.59/3.50 % (1096050)Time elapsed: 0.966 s 20.59/3.50 % (1096050)Peak memory usage: 17 MB 20.59/3.50 % (1096050)Instructions burned: 2186 (million) 20.59/3.50 % (1096086)Instruction limit reached! 20.59/3.50 % (1096086)------------------------------ 20.59/3.50 % (1096086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.50 % (1096086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.50 % (1096086)CaDiCaL version: 2.1.3 20.59/3.50 % (1096086)Termination reason: Instruction limit 20.59/3.50 % (1096086)Termination phase: Saturation 20.59/3.50 % (1096086)Time elapsed: 0.357 s 20.59/3.50 % (1096086)Peak memory usage: 17 MB 20.59/3.50 % (1096086)Instructions burned: 765 (million) 20.59/3.50 % (1096099)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=2516855:i=478:bd=all:rtra=on_1772 on theBenchmark for (1772ds/478Mi) 20.59/3.50 % (1096098)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=319904783:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_1772 on theBenchmark for (1772ds/429Mi) 20.59/3.50 % (1096096)Instruction limit reached! 20.59/3.50 % (1096096)------------------------------ 20.59/3.50 % (1096096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.59/3.50 % (1096096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.59/3.50 % (1096096)CaDiCaL version: 2.1.3 20.59/3.50 % (1096096)Termination reason: Instruction limit 20.59/3.50 % (1096096)Termination phase: Saturation 20.59/3.50 % (1096096)Time elapsed: 0.173 s 20.59/3.50 % (1096096)Peak memory usage: 17 MB 20.59/3.50 % (1096096)Instructions burned: 380 (million) 20.59/3.50 % (1096102)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=902939280:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1772 on theBenchmark for (1772ds/445Mi) 20.59/3.50 % (1096094)Instruction limit reached! 20.59/3.50 % (1096094)------------------------------ 20.59/3.50 % (1096094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.57/3.82 % (1096094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.57/3.82 % (1096094)CaDiCaL version: 2.1.3 22.57/3.82 % (1096094)Termination reason: Instruction limit 22.57/3.82 % (1096094)Termination phase: Saturation 22.57/3.82 % (1096094)Time elapsed: 0.238 s 22.57/3.82 % (1096094)Peak memory usage: 12 MB 22.57/3.82 % (1096094)Instructions burned: 570 (million) 22.57/3.82 % (1096099)Instruction limit reached! 22.57/3.82 % (1096099)------------------------------ 22.57/3.82 % (1096099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.57/3.82 % (1096099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.57/3.82 % (1096099)CaDiCaL version: 2.1.3 22.57/3.82 % (1096099)Termination reason: Instruction limit 22.57/3.82 % (1096099)Termination phase: Saturation 22.57/3.82 % (1096099)Time elapsed: 0.124 s 22.57/3.82 % (1096099)Peak memory usage: 18 MB 22.57/3.82 % (1096099)Instructions burned: 481 (million) 22.57/3.82 % (1096104)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3221681164:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_1771 on theBenchmark for (1771ds/71Mi) 22.57/3.82 % (1096105)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=509311535:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_1771 on theBenchmark for (1771ds/302Mi) 22.57/3.82 % (1096104)Instruction limit reached! 22.57/3.82 % (1096104)------------------------------ 22.57/3.82 % (1096104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.57/3.82 % (1096104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.57/3.82 % (1096104)CaDiCaL version: 2.1.3 22.57/3.82 % (1096104)Termination reason: Instruction limit 22.57/3.82 % (1096104)Termination phase: Property scanning 22.57/3.82 % (1096104)Time elapsed: 0.030 s 22.57/3.82 % (1096104)Peak memory usage: 11 MB 22.57/3.82 % (1096104)Instructions burned: 73 (million) 22.57/3.82 % (1096108)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=392065627:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_1771 on theBenchmark for (1771ds/4980Mi) 22.57/3.82 % (1096108)Refutation not found, incomplete strategy 22.57/3.82 % (1096108)------------------------------ 22.57/3.82 % (1096108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.57/3.82 % (1096108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.57/3.82 % (1096108)CaDiCaL version: 2.1.3 22.57/3.82 % (1096108)Termination reason: Refutation not found, incomplete strategy 22.57/3.82 % (1096108)Time elapsed: 0.018 s 22.57/3.82 % (1096108)Peak memory usage: 12 MB 22.57/3.82 % (1096108)Instructions burned: 40 (million) 22.57/3.82 % (1096108)------------------------------ 22.57/3.82 % (1096108)------------------------------ 22.57/3.82 % (1096098)Instruction limit reached! 22.57/3.82 % (1096098)------------------------------ 22.57/3.82 % (1096098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.57/3.82 % (1096098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.57/3.82 % (1096098)CaDiCaL version: 2.1.3 22.57/3.82 % (1096098)Termination reason: Instruction limit 22.57/3.82 % (1096098)Termination phase: Saturation 22.57/3.82 % (1096098)Time elapsed: 0.205 s 22.57/3.82 % (1096098)Peak memory usage: 17 MB 22.57/3.82 % (1096098)Instructions burned: 430 (million) 22.57/3.82 % (1096105)Instruction limit reached! 22.57/3.82 % (1096105)------------------------------ 22.57/3.82 % (1096105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.57/3.82 % (1096105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.57/3.82 % (1096105)CaDiCaL version: 2.1.3 22.57/3.82 % (1096105)Termination reason: Instruction limit 22.57/3.82 % (1096105)Termination phase: Saturation 22.57/3.82 % (1096105)Time elapsed: 0.076 s 22.57/3.82 % (1096105)Peak memory usage: 14 MB 22.57/3.82 % (1096105)Instructions burned: 305 (million) 22.57/3.82 % (1096110)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 22.57/3.82 % (1096110)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 22.57/3.82 % (1096110)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4003478646:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1770 on theBenchmark for (1770ds/100Mi) 25.25/4.06 % (1096112)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=288696314:i=289:rtra=on_1770 on theBenchmark for (1770ds/289Mi) 25.25/4.06 % (1096111)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1866450689:i=76:piset=equals:rtra=on:ntd=on_1770 on theBenchmark for (1770ds/76Mi) 25.25/4.06 % (1096110)Instruction limit reached! 25.25/4.06 % (1096110)------------------------------ 25.25/4.06 % (1096110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.25/4.06 % (1096110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.25/4.06 % (1096110)CaDiCaL version: 2.1.3 25.25/4.06 % (1096110)Termination reason: Instruction limit 25.25/4.06 % (1096110)Termination phase: Twee Goal Transformation 25.25/4.06 % (1096110)Time elapsed: 0.041 s 25.25/4.06 % (1096110)Peak memory usage: 11 MB 25.25/4.06 % (1096110)Instructions burned: 102 (million) 25.25/4.06 % (1096111)Instruction limit reached! 25.25/4.06 % (1096111)------------------------------ 25.25/4.06 % (1096111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.25/4.06 % (1096111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.25/4.06 % (1096111)CaDiCaL version: 2.1.3 25.25/4.06 % (1096111)Termination reason: Instruction limit 25.25/4.06 % (1096111)Termination phase: Property scanning 25.25/4.06 % (1096111)Time elapsed: 0.032 s 25.25/4.06 % (1096111)Peak memory usage: 11 MB 25.25/4.06 % (1096111)Instructions burned: 78 (million) 25.25/4.06 % (1096116)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=2380756606:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_1770 on theBenchmark for (1770ds/493Mi) 25.25/4.06 % (1096117)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1953358014:cond=on:i=34:hud=10:nm=10:rtra=on_1770 on theBenchmark for (1770ds/34Mi) 25.25/4.06 % (1096112)Instruction limit reached! 25.25/4.06 % (1096112)------------------------------ 25.25/4.06 % (1096112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.25/4.06 % (1096112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.25/4.06 % (1096112)CaDiCaL version: 2.1.3 25.25/4.06 % (1096112)Termination reason: Instruction limit 25.25/4.06 % (1096112)Termination phase: Saturation 25.25/4.06 % (1096112)Time elapsed: 0.070 s 25.25/4.06 % (1096112)Peak memory usage: 15 MB 25.25/4.06 % (1096112)Instructions burned: 289 (million) 25.25/4.06 % (1096117)Instruction limit reached! 25.25/4.06 % (1096117)------------------------------ 25.25/4.06 % (1096117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.25/4.06 % (1096117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.25/4.06 % (1096117)CaDiCaL version: 2.1.3 25.25/4.06 % (1096117)Termination reason: Instruction limit 25.25/4.06 % (1096117)Termination phase: Property scanning 25.25/4.06 % (1096117)Time elapsed: 0.015 s 25.25/4.06 % (1096117)Peak memory usage: 10 MB 25.25/4.06 % (1096117)Instructions burned: 35 (million) 25.25/4.06 % (1096120)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 25.25/4.06 % (1096120)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=4241281517:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_1769 on theBenchmark for (1769ds/372Mi) 25.25/4.06 % (1096102)Instruction limit reached! 25.25/4.06 % (1096102)------------------------------ 25.25/4.06 % (1096102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.25/4.06 % (1096102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.25/4.06 % (1096102)CaDiCaL version: 2.1.3 25.25/4.06 % (1096102)Termination reason: Instruction limit 25.25/4.06 % (1096102)Termination phase: Saturation 25.25/4.06 % (1096102)Time elapsed: 0.211 s 25.25/4.06 % (1096102)Peak memory usage: 16 MB 25.25/4.06 % (1096102)Instructions burned: 446 (million) 25.25/4.06 % (1096064)Instruction limit reached! 25.25/4.06 % (1096064)------------------------------ 25.25/4.06 % (1096064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.84/4.17 % (1096064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.84/4.17 % (1096064)CaDiCaL version: 2.1.3 25.84/4.17 % (1096064)Termination reason: Instruction limit 25.84/4.17 % (1096064)Termination phase: Saturation 25.84/4.17 % (1096064)Time elapsed: 1.064 s 25.84/4.17 % (1096064)Peak memory usage: 18 MB 25.84/4.17 % (1096064)Instructions burned: 2470 (million) 25.84/4.17 % (1096121)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=2094342522:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_1769 on theBenchmark for (1769ds/670Mi) 25.84/4.17 % (1096123)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4031697669:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1769 on theBenchmark for (1769ds/647Mi) 25.84/4.17 % (1096125)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=1491966903:i=857:add=off:kws=frequency:rtra=on:ntd=on_1769 on theBenchmark for (1769ds/857Mi) 25.84/4.17 % (1096120)Instruction limit reached! 25.84/4.17 % (1096120)------------------------------ 25.84/4.17 % (1096120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.84/4.17 % (1096120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.84/4.17 % (1096120)CaDiCaL version: 2.1.3 25.84/4.17 % (1096120)Termination reason: Instruction limit 25.84/4.17 % (1096120)Termination phase: Saturation 25.84/4.17 % (1096120)Time elapsed: 0.088 s 25.84/4.17 % (1096120)Peak memory usage: 16 MB 25.84/4.17 % (1096120)Instructions burned: 377 (million) 25.84/4.17 % (1096128)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=1558058459:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_1768 on theBenchmark for (1768ds/693Mi) 25.84/4.17 % (1096116)Instruction limit reached! 25.84/4.17 % (1096116)------------------------------ 25.84/4.17 % (1096116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.84/4.17 % (1096116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.84/4.17 % (1096116)CaDiCaL version: 2.1.3 25.84/4.17 % (1096116)Termination reason: Instruction limit 25.84/4.17 % (1096116)Termination phase: Saturation 25.84/4.17 % (1096116)Time elapsed: 0.269 s 25.84/4.17 % (1096116)Peak memory usage: 15 MB 25.84/4.17 % (1096116)Instructions burned: 493 (million) 25.84/4.17 % (1096128)Instruction limit reached! 25.84/4.17 % (1096128)------------------------------ 25.84/4.17 % (1096128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.84/4.17 % (1096128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.84/4.17 % (1096128)CaDiCaL version: 2.1.3 25.84/4.17 % (1096128)Termination reason: Instruction limit 25.84/4.17 % (1096128)Termination phase: Saturation 25.84/4.17 % (1096128)Time elapsed: 0.149 s 25.84/4.17 % (1096128)Peak memory usage: 13 MB 25.84/4.17 % (1096128)Instructions burned: 695 (million) 25.84/4.17 % (1096131)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on 25.84/4.17 % (1096131)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=3652094698:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_1767 on theBenchmark for (1767ds/52Mi) 25.84/4.17 % (1096130)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=3948885516:i=285:hud=10:bd=all:rtra=on:ss=axioms_1767 on theBenchmark for (1767ds/285Mi) 25.84/4.17 % (1096131)Instruction limit reached! 25.84/4.17 % (1096131)------------------------------ 25.84/4.17 % (1096131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.84/4.17 % (1096131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.84/4.17 % (1096131)CaDiCaL version: 2.1.3 25.84/4.17 % (1096131)Termination reason: Instruction limit 25.84/4.17 % (1096131)Termination phase: Preprocessing 3 25.84/4.17 % (1096131)Time elapsed: 0.012 s 25.84/4.17 % (1096131)Peak memory usage: 11 MB 25.84/4.17 % (1096131)Instructions burned: 55 (million) 25.84/4.17 % (1096134)dis+10_1_si=on:random_seed=1010642665:i=407:sd=4:rtra=on:ss=axioms:sgt=20_1767 on theBenchmark for (1767ds/407Mi) 25.84/4.17 % (1096121)Instruction limit reached! 26.09/4.23 % (1096121)------------------------------ 26.09/4.23 % (1096121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096121)CaDiCaL version: 2.1.3 26.09/4.23 % (1096121)Termination reason: Instruction limit 26.09/4.23 % (1096121)Termination phase: Saturation 26.09/4.23 % (1096121)Time elapsed: 0.318 s 26.09/4.23 % (1096121)Peak memory usage: 18 MB 26.09/4.23 % (1096121)Instructions burned: 672 (million) 26.09/4.23 % (1096136)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=106748389:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_1766 on theBenchmark for (1766ds/2240Mi) 26.09/4.23 % (1096123)Instruction limit reached! 26.09/4.23 % (1096123)------------------------------ 26.09/4.23 % (1096123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096123)CaDiCaL version: 2.1.3 26.09/4.23 % (1096123)Termination reason: Instruction limit 26.09/4.23 % (1096123)Termination phase: Saturation 26.09/4.23 % (1096123)Time elapsed: 0.344 s 26.09/4.23 % (1096123)Peak memory usage: 18 MB 26.09/4.23 % (1096123)Instructions burned: 648 (million) 26.09/4.23 % (1096134)Instruction limit reached! 26.09/4.23 % (1096134)------------------------------ 26.09/4.23 % (1096134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096134)CaDiCaL version: 2.1.3 26.09/4.23 % (1096134)Termination reason: Instruction limit 26.09/4.23 % (1096134)Termination phase: Saturation 26.09/4.23 % (1096134)Time elapsed: 0.098 s 26.09/4.23 % (1096134)Peak memory usage: 17 MB 26.09/4.23 % (1096134)Instructions burned: 408 (million) 26.09/4.23 % (1096130)Instruction limit reached! 26.09/4.23 % (1096130)------------------------------ 26.09/4.23 % (1096130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096130)CaDiCaL version: 2.1.3 26.09/4.23 % (1096130)Termination reason: Instruction limit 26.09/4.23 % (1096130)Termination phase: Saturation 26.09/4.23 % (1096130)Time elapsed: 0.124 s 26.09/4.23 % (1096130)Peak memory usage: 16 MB 26.09/4.23 % (1096130)Instructions burned: 287 (million) 26.09/4.23 % (1096139)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=1016705784:s2a=on:i=1142:s2at=3:bd=all:rtra=on_1765 on theBenchmark for (1765ds/1142Mi) 26.09/4.23 % (1096138)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=3934461958:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_1766 on theBenchmark for (1766ds/336Mi) 26.09/4.23 % (1096125)Instruction limit reached! 26.09/4.23 % (1096125)------------------------------ 26.09/4.23 % (1096125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096125)CaDiCaL version: 2.1.3 26.09/4.23 % (1096125)Termination reason: Instruction limit 26.09/4.23 % (1096125)Termination phase: Saturation 26.09/4.23 % (1096125)Time elapsed: 0.371 s 26.09/4.23 % (1096125)Peak memory usage: 17 MB 26.09/4.23 % (1096125)Instructions burned: 859 (million) 26.09/4.23 % (1096140)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=885281033:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_1765 on theBenchmark for (1765ds/376Mi) 26.09/4.23 % (1096143)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=967740633:i=766:bd=all:rtra=on_1765 on theBenchmark for (1765ds/766Mi) 26.09/4.23 % (1096140)Instruction limit reached! 26.09/4.23 % (1096140)------------------------------ 26.09/4.23 % (1096140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096140)CaDiCaL version: 2.1.3 26.09/4.23 % (1096140)Termination reason: Instruction limit 26.09/4.23 % (1096140)Termination phase: Saturation 26.09/4.23 % (1096140)Time elapsed: 0.170 s 26.09/4.23 % (1096140)Peak memory usage: 16 MB 26.09/4.23 % (1096140)Instructions burned: 376 (million) 26.09/4.23 % (1096138)Instruction limit reached! 26.09/4.23 % (1096138)------------------------------ 26.09/4.23 % (1096138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096138)CaDiCaL version: 2.1.3 26.09/4.23 % (1096138)Termination reason: Instruction limit 26.09/4.23 % (1096138)Termination phase: Saturation 26.09/4.23 % (1096138)Time elapsed: 0.182 s 26.09/4.23 % (1096138)Peak memory usage: 16 MB 26.09/4.23 % (1096138)Instructions burned: 336 (million) 26.09/4.23 % (1095965)Instruction limit reached! 26.09/4.23 % (1095965)------------------------------ 26.09/4.23 % (1095965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1095965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1095965)CaDiCaL version: 2.1.3 26.09/4.23 % (1095965)Termination reason: Instruction limit 26.09/4.23 % (1095965)Termination phase: Saturation 26.09/4.23 % (1095965)Time elapsed: 2.865 s 26.09/4.23 % (1095965)Peak memory usage: 23 MB 26.09/4.23 % (1095965)Instructions burned: 5755 (million) 26.09/4.23 % (1096146)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on 26.09/4.23 % (1096146)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=4032954003:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_1764 on theBenchmark for (1764ds/959Mi) 26.09/4.23 % (1096147)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=3727085674:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_1764 on theBenchmark for (1764ds/6359Mi) 26.09/4.23 % (1096148)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1422449713:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1763 on theBenchmark for (1763ds/35Mi) 26.09/4.23 % (1096148)Instruction limit reached! 26.09/4.23 % (1096148)------------------------------ 26.09/4.23 % (1096148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096148)CaDiCaL version: 2.1.3 26.09/4.23 % (1096148)Termination reason: Instruction limit 26.09/4.23 % (1096148)Termination phase: SInE selection 26.09/4.23 % (1096148)Time elapsed: 0.015 s 26.09/4.23 % (1096148)Peak memory usage: 10 MB 26.09/4.23 % (1096148)Instructions burned: 36 (million) 26.09/4.23 % (1096152)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=1223087033:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_1763 on theBenchmark for (1763ds/53Mi) 26.09/4.23 % (1096152)Instruction limit reached! 26.09/4.23 % (1096152)------------------------------ 26.09/4.23 % (1096152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096152)CaDiCaL version: 2.1.3 26.09/4.23 % (1096152)Termination reason: Instruction limit 26.09/4.23 % (1096152)Termination phase: Property scanning 26.09/4.23 % (1096152)Time elapsed: 0.023 s 26.09/4.23 % (1096152)Peak memory usage: 10 MB 26.09/4.23 % (1096152)Instructions burned: 54 (million) 26.09/4.23 % (1096139)Instruction limit reached! 26.09/4.23 % (1096139)------------------------------ 26.09/4.23 % (1096139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096139)CaDiCaL version: 2.1.3 26.09/4.23 % (1096139)Termination reason: Instruction limit 26.09/4.23 % (1096139)Termination phase: Saturation 26.09/4.23 % (1096139)Time elapsed: 0.280 s 26.09/4.23 % (1096139)Peak memory usage: 19 MB 26.09/4.23 % (1096139)Instructions burned: 1146 (million) 26.09/4.23 % (1095997) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1095827-1095997"... 26.09/4.23 % (1096154)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=1039622980:s2a=on:i=876:s2at=6:nm=2:rtra=on_1763 on theBenchmark for (1763ds/876Mi) 26.09/4.23 % (1096155)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2956503436:i=57:ep=R:rtra=on:ntd=on_1763 on theBenchmark for (1763ds/57Mi) 26.09/4.23 % (1096155)Instruction limit reached! 26.09/4.23 % (1096155)------------------------------ 26.09/4.23 % (1096155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.23 % (1096155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.23 % (1096155)CaDiCaL version: 2.1.3 26.09/4.23 % (1096155)Termination reason: Instruction limit 26.09/4.23 % (1096155)Termination phase: Property scanning 26.09/4.23 % (1096155)Time elapsed: 0.013 s 26.09/4.23 % (1096155)Peak memory usage: 11 MB 26.09/4.23 % (1096155)Instructions burned: 58 (million) 26.09/4.23 % (1096158)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 26.09/4.23 % (1096158)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3185938779:i=306:bd=all:rtra=on_1762 on theBenchmark for (1762ds/306Mi) 26.09/4.23 % (1095997)...printing done. 26.09/4.23 % (1095997)Refutation found. Thanks to Tanya! 26.09/4.23 % SZS status Theorem for theBenchmark 26.09/4.23 % SZS output start Proof for theBenchmark 26.09/4.23 thf(type_def_5, type, term: $tType). 26.09/4.23 thf(type_def_6, type, subst: $tType). 26.09/4.23 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType). 26.09/4.23 thf(type_def_8, type, d_term: $tType). 26.09/4.23 thf(type_def_9, type, d_subst: $tType). 26.09/4.23 thf(func_def_0, type, one: term). 26.09/4.23 thf(func_def_1, type, ap: (term > term > term)). 26.09/4.23 thf(func_def_2, type, lam: (term > term)). 26.09/4.23 thf(func_def_3, type, sub: (term > subst > term)). 26.09/4.23 thf(func_def_4, type, id: subst). 26.09/4.23 thf(func_def_5, type, sh: subst). 26.09/4.23 thf(func_def_6, type, push: (term > subst > subst)). 26.09/4.23 thf(func_def_7, type, comp: (subst > subst > subst)). 26.09/4.23 thf(func_def_8, type, var: (term > $o)). 26.09/4.23 thf(func_def_9, type, pushprop_lem1v2: $o). 26.09/4.23 thf(func_def_10, type, pushprop_lem1_gthm: $o). 26.09/4.23 thf(func_def_11, type, axmap: $o). 26.09/4.23 thf(func_def_12, type, pushprop_lem0_gthm: $o). 26.09/4.23 thf(func_def_13, type, shinj: $o). 26.09/4.23 thf(func_def_14, type, hoasinduction_lem1v2: $o). 26.09/4.23 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o). 26.09/4.23 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)). 26.09/4.23 thf(func_def_17, type, induction2lem: $o). 26.09/4.23 thf(func_def_18, type, hoasinduction_lem3v2_f: $o). 26.09/4.23 thf(func_def_19, type, axvarshift: $o). 26.09/4.23 thf(func_def_20, type, hoasapinj2: $o). 26.09/4.23 thf(func_def_21, type, hoasapnotvar_gthm: $o). 26.09/4.23 thf(func_def_22, type, hoasapinj1: $o). 26.09/4.23 thf(func_def_23, type, ulamvar1: $o). 26.09/4.23 thf(func_def_24, type, induction2lem_lthm: $o). 26.09/4.23 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o). 26.09/4.23 thf(func_def_26, type, apnotvar: $o). 26.09/4.23 thf(func_def_27, type, pushprop_lthm_orig: $o). 26.09/4.23 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o). 26.09/4.23 thf(func_def_29, type, hoasinduction_lthm: $o). 26.09/4.23 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o). 26.09/4.23 thf(func_def_31, type, hoaslaminj: $o). 26.09/4.23 thf(func_def_32, type, hoasinduction_lem3aaa: $o). 26.09/4.23 thf(func_def_33, type, induction2lem_gthm: $o). 26.09/4.23 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o). 26.09/4.23 thf(func_def_35, type, hoasinduction_lem3: $o). 26.09/4.23 thf(func_def_36, type, hoasinduction_lem2: $o). 26.09/4.23 thf(func_def_37, type, termmset_lthm: $o). 26.09/4.23 thf(func_def_38, type, hoasinduction_lem1: $o). 26.09/4.23 thf(func_def_39, type, hoaslamnotap_lthm: $o). 26.09/4.23 thf(func_def_40, type, pushprop_lem1v2_lthm: $o). 26.09/4.23 thf(func_def_41, type, hoasapnotvar: $o). 26.09/4.23 thf(func_def_42, type, hoasinduction_lem0: $o). 26.09/4.23 thf(func_def_43, type, hoasinduction: $o). 26.09/4.23 thf(func_def_44, type, hoasinduction_gthm: $o). 26.09/4.23 thf(func_def_45, type, axapp: $o). 26.09/4.23 thf(func_def_46, type, hoaslamnotvar_lthm: $o). 26.09/4.23 thf(func_def_47, type, pushprop_lem3v2_lthm: $o). 26.09/4.23 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o). 26.09/4.23 thf(func_def_49, type, ulamvarind: $o). 26.09/4.23 thf(func_def_50, type, induction: $o). 26.09/4.23 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o). 26.09/4.23 thf(func_def_52, type, termmset_gthm: $o). 26.09/4.23 thf(func_def_53, type, hoasinduction_lem3aa: $o). 26.09/4.23 thf(func_def_54, type, pushprop_lem1v2_gthm: $o). 26.09/4.23 thf(func_def_55, type, hoaslamnotap_gthm: $o). 26.09/4.23 thf(func_def_56, type, hoaslamnotvar_gthm: $o). 26.09/4.23 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o). 26.09/4.23 thf(func_def_58, type, pushprop_lem2v2: $o). 26.09/4.23 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o). 26.09/4.23 thf(func_def_60, type, axclos: $o). 26.09/4.23 thf(func_def_61, type, axassoc: $o). 26.09/4.23 thf(func_def_62, type, hoasinduction_lem2v2: $o). 26.09/4.23 thf(func_def_63, type, pushprop_lthm: $o). 26.09/4.23 thf(func_def_64, type, apinj2: $o). 26.09/4.23 thf(func_def_65, type, apinj1: $o). 26.09/4.23 thf(func_def_66, type, hoasapinj2_lthm: $o). 26.09/4.23 thf(func_def_67, type, hoasinduction_lem3v2a: $o). 26.09/4.23 thf(func_def_68, type, hoasapinj1_lthm: $o). 26.09/4.23 thf(func_def_69, type, hoaslaminj_lthm: $o). 26.09/4.23 thf(func_def_70, type, axvarcons: $o). 26.09/4.23 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)). 26.09/4.23 thf(func_def_72, type, axscons: $o). 26.09/4.23 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o). 26.09/4.23 thf(func_def_74, type, axidr: $o). 26.09/4.23 thf(func_def_75, type, pushprop_lem1: $o). 26.09/4.23 thf(func_def_76, type, laminj: $o). 26.09/4.23 thf(func_def_77, type, hoasinduction_lem3_lthm: $o). 26.09/4.23 thf(func_def_78, type, pushprop_lem0: $o). 26.09/4.23 thf(func_def_79, type, pushprop_gthm: $o). 26.09/4.23 thf(func_def_80, type, axabs: $o). 26.09/4.23 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o). 26.09/4.23 thf(func_def_82, type, hoasinduction_lem2_lthm: $o). 26.09/4.23 thf(func_def_83, type, hoasapinj2_gthm: $o). 26.09/4.23 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)). 26.09/4.23 thf(func_def_85, type, hoasinduction_lem1_lthm: $o). 26.09/4.23 thf(func_def_86, type, lamnotap: $o). 26.09/4.23 thf(func_def_87, type, hoasapinj1_gthm: $o). 26.09/4.23 thf(func_def_88, type, hoaslamnotvar: $o). 26.09/4.23 thf(func_def_89, type, axidl: $o). 26.09/4.23 thf(func_def_90, type, hoaslaminj_gthm: $o). 26.09/4.23 thf(func_def_91, type, induction2_lthm: $o). 26.09/4.23 thf(func_def_92, type, hoasinduction_lem0_lthm: $o). 26.09/4.23 thf(func_def_93, type, substmonoid_lthm: $o). 26.09/4.23 thf(func_def_94, type, pushprop: $o). 26.09/4.23 thf(func_def_95, type, hoasinduction_lem3_gthm: $o). 26.09/4.23 thf(func_def_96, type, hoasinduction_lem2_gthm: $o). 26.09/4.23 thf(func_def_97, type, hoasinduction_lem3b: $o). 26.09/4.23 thf(func_def_98, type, substmonoid: $o). 26.09/4.23 thf(func_def_99, type, lamnotvar: $o). 26.09/4.23 thf(func_def_100, type, hoasinduction_lem3a: $o). 26.09/4.23 thf(func_def_101, type, hoasinduction_lem1_gthm: $o). 26.09/4.23 thf(func_def_102, type, hoasinduction_no_psi_cond: $o). 26.09/4.23 thf(func_def_103, type, induction2_gthm: $o). 26.09/4.23 thf(func_def_104, type, pushprop_lem2v2_lthm: $o). 26.09/4.23 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)). 26.09/4.23 thf(func_def_106, type, hoaslamnotap: $o). 26.09/4.23 thf(func_def_107, type, substmonoid_gthm: $o). 26.09/4.23 thf(func_def_108, type, ulamvarsh: $o). 26.09/4.23 thf(func_def_109, type, induction2: $o). 26.09/4.23 thf(func_def_110, type, pushprop_lem3v2: $o). 26.09/4.23 thf(func_def_111, type, pushprop_lem2v2_gthm: $o). 26.09/4.23 thf(func_def_112, type, pushprop_lem1_lthm: $o). 26.09/4.23 thf(func_def_113, type, hoasinduction_lem3v2: $o). 26.09/4.23 thf(func_def_114, type, axshiftcons: $o). 26.09/4.23 thf(func_def_115, type, termmset: $o). 26.09/4.23 thf(func_def_116, type, pushprop_lem0_lthm: $o). 26.09/4.23 thf(func_def_117, type, hoasapnotvar_lthm: $o). 26.09/4.23 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o). 26.09/4.23 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)). 26.09/4.23 thf(func_def_120, type, axvarid: $o). 26.09/4.23 thf(func_def_121, type, hoasinduction_lthm_3: $o). 26.09/4.23 thf(func_def_122, type, d2term: (d_term > term)). 26.09/4.23 thf(func_def_123, type, d2subst: (d_subst > subst)). 26.09/4.23 thf(func_def_124, type, d_one: d_term). 26.09/4.23 thf(func_def_125, type, d_id: d_subst). 26.09/4.23 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)). 26.09/4.23 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)). 26.09/4.23 thf(func_def_131, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 26.09/4.23 thf(func_def_132, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 26.09/4.23 thf(func_def_133, type, db2: !>[X0: $tType]:(X0)). 26.09/4.23 thf(func_def_134, type, db4: !>[X0: $tType]:(X0)). 26.09/4.23 thf(func_def_135, type, db3: !>[X0: $tType]:(X0)). 26.09/4.23 thf(func_def_136, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 26.09/4.23 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_138, type, sP1: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_139, type, sP2: $o). 26.09/4.23 thf(func_def_140, type, sP3: $o). 26.09/4.23 thf(func_def_141, type, sP4: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_142, type, sP5: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_143, type, sP6: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_144, type, sP7: $o). 26.09/4.23 thf(func_def_145, type, sP8: $o). 26.09/4.23 thf(func_def_146, type, sP9: $o). 26.09/4.23 thf(func_def_147, type, sP10: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_148, type, sP11: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_149, type, sP12: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_150, type, sP13: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_151, type, sP14: $o). 26.09/4.23 thf(func_def_152, type, sP15: $o). 26.09/4.23 thf(func_def_153, type, sP16: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_154, type, sP17: $o). 26.09/4.23 thf(func_def_155, type, sP18: $o). 26.09/4.23 thf(func_def_156, type, sP19: ((subst > term > subst > $o) > $o)). 26.09/4.23 thf(func_def_157, type, sP20: $o). 26.09/4.23 thf(func_def_158, type, sP21: $o). 26.09/4.23 thf(func_def_159, type, sP22: $o). 26.09/4.23 thf(func_def_160, type, sP23: $o). 26.09/4.23 thf(func_def_161, type, sP24: $o). 26.09/4.23 thf(func_def_162, type, sP25: $o). 26.09/4.23 thf(func_def_163, type, sP26: $o). 26.09/4.23 thf(func_def_164, type, sP27: $o). 26.09/4.23 thf(func_def_165, type, sK28: (subst > term > subst > $o)). 26.09/4.23 thf(func_def_166, type, sK29: ((subst > term > term) > term)). 26.09/4.23 thf(func_def_167, type, sK30: ((subst > term > term) > term)). 26.09/4.23 thf(func_def_168, type, sK31: ((subst > term > term) > subst)). 26.09/4.23 thf(func_def_169, type, sK32: ((subst > term > term) > subst)). 26.09/4.23 thf(func_def_170, type, sK33: term). 26.09/4.23 thf(func_def_171, type, sK34: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.23 thf(func_def_172, type, sK35: (term > (subst > term > subst > $o) > term)). 26.09/4.23 thf(func_def_173, type, sK36: (subst > term > subst > $o)). 26.09/4.23 thf(func_def_174, type, sK37: term). 26.09/4.23 thf(func_def_175, type, sK38: term). 26.09/4.23 thf(func_def_176, type, sK39: (term > $o)). 26.09/4.23 thf(func_def_177, type, sK40: ((term > $o) > (subst > term > subst > $o) > term)). 26.09/4.23 thf(func_def_178, type, sK41: ((subst > term > subst > $o) > term)). 26.09/4.23 thf(func_def_179, type, sK42: ((subst > term > subst > $o) > term)). 26.09/4.23 thf(func_def_180, type, sK43: ((subst > term > subst > $o) > term)). 26.09/4.23 thf(func_def_181, type, sK44: ((subst > term > subst > $o) > subst)). 26.09/4.23 thf(func_def_182, type, sK45: ((subst > term > subst > $o) > subst)). 26.09/4.23 thf(func_def_183, type, sK46: ((subst > term > subst > $o) > subst)). 26.09/4.23 thf(func_def_184, type, sK47: ((subst > term > subst > $o) > subst)). 26.09/4.23 thf(func_def_185, type, sK48: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_186, type, sK49: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_187, type, sK50: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_188, type, sK51: (term > $o)). 26.09/4.24 thf(func_def_189, type, sK52: subst). 26.09/4.24 thf(func_def_190, type, sK53: term). 26.09/4.24 thf(func_def_191, type, sK54: (term > term)). 26.09/4.24 thf(func_def_192, type, sK55: ((term > $o) > term)). 26.09/4.24 thf(func_def_193, type, sK56: ((term > $o) > term)). 26.09/4.24 thf(func_def_194, type, sK57: (subst > (term > $o) > term)). 26.09/4.24 thf(func_def_195, type, sK58: ((term > $o) > term)). 26.09/4.24 thf(func_def_196, type, sK59: term). 26.09/4.24 thf(func_def_197, type, sK60: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_198, type, sK61: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_199, type, sK62: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_200, type, sK63: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_201, type, sK64: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_202, type, sK65: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_203, type, sK66: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_204, type, sK67: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_205, type, sK68: ((term > $o) > term)). 26.09/4.24 thf(func_def_206, type, sK69: ((term > $o) > term)). 26.09/4.24 thf(func_def_207, type, sK70: ((term > $o) > term)). 26.09/4.24 thf(func_def_208, type, sK71: ((term > $o) > term)). 26.09/4.24 thf(func_def_209, type, sK72: term). 26.09/4.24 thf(func_def_210, type, sK73: (term > $o)). 26.09/4.24 thf(func_def_211, type, sK74: (term > term)). 26.09/4.24 thf(func_def_212, type, sK75: term). 26.09/4.24 thf(func_def_213, type, sK76: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_214, type, sK77: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_215, type, sK78: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_216, type, sK79: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_217, type, sK80: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_218, type, sK81: ((subst > term > subst > $o) > term > term)). 26.09/4.24 thf(func_def_219, type, sK82: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_220, type, sK83: term). 26.09/4.24 thf(func_def_221, type, sK84: term). 26.09/4.24 thf(func_def_222, type, sK85: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_223, type, sK86: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_224, type, sK87: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_225, type, sK88: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_226, type, sK89: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_227, type, sK90: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_228, type, sK91: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_229, type, sK92: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_230, type, sK93: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_231, type, sK94: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_232, type, sK95: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_233, type, sK96: term). 26.09/4.24 thf(func_def_234, type, sK97: (term > $o)). 26.09/4.24 thf(func_def_235, type, sK98: (term > term)). 26.09/4.24 thf(func_def_236, type, sK99: ((term > $o) > term)). 26.09/4.24 thf(func_def_237, type, sK100: ((term > $o) > term)). 26.09/4.24 thf(func_def_238, type, sK101: ((term > $o) > term)). 26.09/4.24 thf(func_def_239, type, sK102: ((term > $o) > term)). 26.09/4.24 thf(func_def_240, type, sK103: term). 26.09/4.24 thf(func_def_241, type, sK104: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_242, type, sK105: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_243, type, sK106: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_244, type, sK107: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_245, type, sK108: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_246, type, sK109: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_247, type, sK110: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_248, type, sK111: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_249, type, sK112: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_250, type, sK113: ((subst > term > subst > $o) > term > term)). 26.09/4.24 thf(func_def_251, type, sK114: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_252, type, sK115: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_253, type, sK116: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_254, type, sK117: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_255, type, sK118: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_256, type, sK119: (term > $o)). 26.09/4.24 thf(func_def_257, type, sK120: term). 26.09/4.24 thf(func_def_258, type, sK121: (term > term)). 26.09/4.24 thf(func_def_259, type, sK122: ((term > $o) > term)). 26.09/4.24 thf(func_def_260, type, sK123: ((term > $o) > term)). 26.09/4.24 thf(func_def_261, type, sK124: ((term > $o) > term)). 26.09/4.24 thf(func_def_262, type, sK125: ((term > $o) > term)). 26.09/4.24 thf(func_def_263, type, sK126: term). 26.09/4.24 thf(func_def_264, type, sK127: ((term > $o) > term)). 26.09/4.24 thf(func_def_265, type, sK128: (subst > (term > $o) > term)). 26.09/4.24 thf(func_def_266, type, sK129: ((term > $o) > term)). 26.09/4.24 thf(func_def_267, type, sK130: ((term > $o) > term)). 26.09/4.24 thf(func_def_268, type, sK131: (term > $o)). 26.09/4.24 thf(func_def_269, type, sK132: term). 26.09/4.24 thf(func_def_270, type, sK133: subst). 26.09/4.24 thf(func_def_271, type, sK134: (term > term)). 26.09/4.24 thf(func_def_272, type, sK135: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_273, type, sK136: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_274, type, sK137: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_275, type, sK138: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_276, type, sK139: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_277, type, sK140: subst). 26.09/4.24 thf(func_def_278, type, sK141: term). 26.09/4.24 thf(func_def_279, type, sK142: (term > $o)). 26.09/4.24 thf(func_def_280, type, sK143: (term > term)). 26.09/4.24 thf(func_def_281, type, sK144: subst). 26.09/4.24 thf(func_def_282, type, sK145: term). 26.09/4.24 thf(func_def_283, type, sK146: subst). 26.09/4.24 thf(func_def_284, type, sK147: term). 26.09/4.24 thf(func_def_285, type, sK148: ((term > $o) > subst > term)). 26.09/4.24 thf(func_def_286, type, sK149: ((term > $o) > term)). 26.09/4.24 thf(func_def_287, type, sK150: ((term > $o) > term)). 26.09/4.24 thf(func_def_288, type, sK151: ((term > $o) > term)). 26.09/4.24 thf(func_def_289, type, sK152: subst). 26.09/4.24 thf(func_def_290, type, sK153: ((term > $o) > term)). 26.09/4.24 thf(func_def_291, type, sK154: ((term > $o) > term)). 26.09/4.24 thf(func_def_292, type, sK155: ((term > $o) > term)). 26.09/4.24 thf(func_def_293, type, sK156: ((term > $o) > term)). 26.09/4.24 thf(func_def_294, type, sK157: (term > $o)). 26.09/4.24 thf(func_def_295, type, sK158: term). 26.09/4.24 thf(func_def_296, type, sK159: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_297, type, sK160: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_298, type, sK161: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_299, type, sK162: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_300, type, sK163: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_301, type, sK164: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_302, type, sK165: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_303, type, sK166: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_304, type, sK167: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_305, type, sK168: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_306, type, sK169: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_307, type, sK170: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_308, type, sK171: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_309, type, sK172: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_310, type, sK173: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_311, type, sK174: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_312, type, sK175: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_313, type, sK176: term). 26.09/4.24 thf(func_def_314, type, sK177: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_315, type, sK178: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_317, type, sK180: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_318, type, sK181: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_319, type, sK182: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_320, type, sK183: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_321, type, sK184: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_322, type, sK185: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_323, type, sK186: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_324, type, sK187: ((term > $o) > term)). 26.09/4.24 thf(func_def_325, type, sK188: ((term > $o) > term)). 26.09/4.24 thf(func_def_326, type, sK189: ((term > $o) > term)). 26.09/4.24 thf(func_def_327, type, sK190: ((term > $o) > term)). 26.09/4.24 thf(func_def_328, type, sK191: (term > $o)). 26.09/4.24 thf(func_def_329, type, sK192: term). 26.09/4.24 thf(func_def_330, type, sK193: (term > term)). 26.09/4.24 thf(func_def_331, type, sK194: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_332, type, sK195: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_333, type, sK196: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_334, type, sK197: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_335, type, sK198: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_336, type, sK199: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_337, type, sK200: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_338, type, sK201: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_339, type, sK202: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_340, type, sK203: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_341, type, sK204: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_342, type, sK205: term). 26.09/4.24 thf(func_def_343, type, sK206: term). 26.09/4.24 thf(func_def_344, type, sK207: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_345, type, sK208: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_346, type, sK209: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_347, type, sK210: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_348, type, sK211: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_349, type, sK212: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_350, type, sK213: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_351, type, sK214: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_352, type, sK215: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_353, type, sK216: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_354, type, sK217: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_355, type, sK218: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_356, type, sK219: term). 26.09/4.24 thf(func_def_357, type, sK220: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_358, type, sK221: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_359, type, sK222: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_360, type, sK223: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_361, type, sK224: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_362, type, sK225: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_363, type, sK226: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_364, type, sK227: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_365, type, sK228: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_366, type, sK229: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_367, type, sK230: ((term > $o) > term)). 26.09/4.24 thf(func_def_368, type, sK231: ((term > $o) > term)). 26.09/4.24 thf(func_def_369, type, sK232: ((term > $o) > term)). 26.09/4.24 thf(func_def_370, type, sK233: ((term > $o) > term)). 26.09/4.24 thf(func_def_371, type, sK234: term). 26.09/4.24 thf(func_def_372, type, sK235: (term > $o)). 26.09/4.24 thf(func_def_373, type, sK236: (term > term)). 26.09/4.24 thf(func_def_374, type, sK237: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_375, type, sK238: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_376, type, sK239: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_377, type, sK240: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_378, type, sK241: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_379, type, sK242: ((subst > term > term) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_380, type, sK243: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_381, type, sK244: term). 26.09/4.24 thf(func_def_382, type, sK245: subst). 26.09/4.24 thf(func_def_383, type, sK246: term). 26.09/4.24 thf(func_def_384, type, sK247: subst). 26.09/4.24 thf(func_def_385, type, sK248: (subst > term > term)). 26.09/4.24 thf(func_def_386, type, sK249: (subst > term > term)). 26.09/4.24 thf(func_def_387, type, sK250: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_388, type, sK251: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_389, type, sK252: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_390, type, sK253: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_391, type, sK254: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_392, type, sK255: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_393, type, sK256: subst). 26.09/4.24 thf(func_def_394, type, sK257: (subst > d_subst)). 26.09/4.24 thf(func_def_395, type, sK258: term). 26.09/4.24 thf(func_def_396, type, sK259: term). 26.09/4.24 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > term > $o)). 26.09/4.24 thf(func_def_398, type, sK261: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_399, type, sK262: ((term > $o) > term)). 26.09/4.24 thf(func_def_400, type, sK263: term). 26.09/4.24 thf(func_def_401, type, sK264: subst). 26.09/4.24 thf(func_def_402, type, sK265: term). 26.09/4.24 thf(func_def_403, type, sK266: (subst > term > term)). 26.09/4.24 thf(func_def_404, type, sK267: term). 26.09/4.24 thf(func_def_405, type, sK268: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_406, type, sK269: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_407, type, sK270: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_408, type, sK271: (term > subst > term > term)). 26.09/4.24 thf(func_def_409, type, sK272: term). 26.09/4.24 thf(func_def_410, type, sK273: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_411, type, sK274: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > term > $o)). 26.09/4.24 thf(func_def_413, type, sK276: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_414, type, sK277: ((term > $o) > term > term)). 26.09/4.24 thf(func_def_415, type, sK278: ((term > $o) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_416, type, sK279: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_417, type, sK280: ((term > $o) > term)). 26.09/4.24 thf(func_def_418, type, sK281: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_419, type, sK282: term). 26.09/4.24 thf(func_def_420, type, sK283: (term > $o)). 26.09/4.24 thf(func_def_421, type, sK284: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_422, type, sK285: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_423, type, sK286: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_424, type, sK287: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_425, type, sK288: term). 26.09/4.24 thf(func_def_426, type, sK289: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_427, type, sK290: term). 26.09/4.24 thf(func_def_428, type, sK291: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_429, type, sK292: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_430, type, sK293: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_431, type, sK294: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_432, type, sK295: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_433, type, sK296: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_434, type, sK297: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_435, type, sK298: term). 26.09/4.24 thf(func_def_436, type, sK299: subst). 26.09/4.24 thf(func_def_437, type, sK300: (term > $o)). 26.09/4.24 thf(func_def_438, type, sK301: (term > $o)). 26.09/4.24 thf(func_def_439, type, sK302: ((term > $o) > (term > $o) > subst > term > term)). 26.09/4.24 thf(func_def_440, type, sK303: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_441, type, sK304: (term > $o)). 26.09/4.24 thf(func_def_442, type, sK305: term). 26.09/4.24 thf(func_def_443, type, sK306: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_444, type, sK307: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_445, type, sK308: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_446, type, sK309: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_447, type, sK310: (term > subst > term > term)). 26.09/4.24 thf(func_def_448, type, sK311: (term > (term > $o) > term)). 26.09/4.24 thf(func_def_449, type, sK312: ((term > $o) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_450, type, sK313: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_451, type, sK314: term). 26.09/4.24 thf(func_def_452, type, sK315: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_453, type, sK316: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_454, type, sK317: term). 26.09/4.24 thf(func_def_455, type, sK318: term). 26.09/4.24 thf(func_def_456, type, sK319: term). 26.09/4.24 thf(func_def_457, type, sK320: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_458, type, sK321: (term > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_459, type, sK322: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_460, type, sK323: term). 26.09/4.24 thf(func_def_461, type, sK324: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_462, type, sK325: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_463, type, sK326: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_464, type, sK327: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_465, type, sK328: term). 26.09/4.24 thf(func_def_466, type, sK329: term). 26.09/4.24 thf(func_def_467, type, sK330: term). 26.09/4.24 thf(func_def_468, type, sK331: (term > $o)). 26.09/4.24 thf(func_def_469, type, sK332: subst). 26.09/4.24 thf(func_def_470, type, sK333: (term > $o)). 26.09/4.24 thf(func_def_471, type, sK334: subst). 26.09/4.24 thf(func_def_472, type, sK335: term). 26.09/4.24 thf(func_def_473, type, sK336: ((term > $o) > subst > (term > $o) > term > term)). 26.09/4.24 thf(func_def_474, type, sK337: term). 26.09/4.24 thf(func_def_475, type, sK338: (term > subst > term > term)). 26.09/4.24 thf(func_def_476, type, sK339: subst). 26.09/4.24 thf(func_def_477, type, sK340: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_478, type, sK341: ((term > $o) > term)). 26.09/4.24 thf(func_def_479, type, sK342: ((subst > term > subst > $o) > term > $o)). 26.09/4.24 thf(func_def_480, type, sK343: term). 26.09/4.24 thf(func_def_481, type, sK344: term). 26.09/4.24 thf(func_def_482, type, sK345: (term > $o)). 26.09/4.24 thf(func_def_483, type, sK346: (term > $o)). 26.09/4.24 thf(func_def_484, type, sK347: subst). 26.09/4.24 thf(func_def_485, type, sK348: term). 26.09/4.24 thf(func_def_486, type, sK349: term). 26.09/4.24 thf(func_def_487, type, sK350: term). 26.09/4.24 thf(func_def_488, type, sK351: term). 26.09/4.24 thf(func_def_489, type, sK352: term). 26.09/4.24 thf(func_def_490, type, sK353: term). 26.09/4.24 thf(func_def_491, type, sK354: term). 26.09/4.24 thf(func_def_492, type, sK355: term). 26.09/4.24 thf(func_def_493, type, sK356: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_494, type, sK357: (term > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_495, type, sK358: term). 26.09/4.24 thf(func_def_496, type, sK359: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_497, type, sK360: term). 26.09/4.24 thf(func_def_498, type, sK361: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_499, type, sK362: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_500, type, sK363: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_501, type, sK364: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_502, type, sK365: (term > subst > term > term)). 26.09/4.24 thf(func_def_503, type, sK366: term). 26.09/4.24 thf(func_def_504, type, sK367: term). 26.09/4.24 thf(func_def_505, type, sK368: term). 26.09/4.24 thf(func_def_506, type, sK369: term). 26.09/4.24 thf(func_def_507, type, sK370: term). 26.09/4.24 thf(func_def_508, type, sK371: term). 26.09/4.24 thf(func_def_509, type, sK372: term). 26.09/4.24 thf(func_def_510, type, sK373: term). 26.09/4.24 thf(func_def_511, type, sK374: term). 26.09/4.24 thf(func_def_512, type, sK375: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_513, type, sK376: term). 26.09/4.24 thf(func_def_514, type, sK377: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_515, type, sK378: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_516, type, sK379: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_517, type, sK380: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_518, type, sK381: (term > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_519, type, sK382: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_520, type, sK383: subst). 26.09/4.24 thf(func_def_521, type, sK384: subst). 26.09/4.24 thf(func_def_522, type, sK385: subst). 26.09/4.24 thf(func_def_523, type, sK386: subst). 26.09/4.24 thf(func_def_524, type, sK387: term). 26.09/4.24 thf(func_def_525, type, sK388: term). 26.09/4.24 thf(func_def_526, type, sK389: term). 26.09/4.24 thf(func_def_527, type, sK390: term). 26.09/4.24 thf(func_def_528, type, sK391: (term > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_529, type, sK392: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_530, type, sK393: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_531, type, sK394: term). 26.09/4.24 thf(func_def_532, type, sK395: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_533, type, sK396: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_534, type, sK397: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_535, type, sK398: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_536, type, sK399: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_537, type, sK400: term). 26.09/4.24 thf(func_def_538, type, sK401: ((subst > term > term) > term > subst)). 26.09/4.24 thf(func_def_539, type, sK402: ((subst > term > term) > term > subst)). 26.09/4.24 thf(func_def_540, type, sK403: ((subst > term > term) > term > term)). 26.09/4.24 thf(func_def_541, type, sK404: ((subst > term > term) > term > term)). 26.09/4.24 thf(func_def_542, type, sK405: ((subst > term > term) > term > subst)). 26.09/4.24 thf(func_def_543, type, sK406: ((subst > term > term) > term > subst)). 26.09/4.24 thf(func_def_544, type, sK407: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_545, type, sK408: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_546, type, sK409: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_547, type, sK410: (term > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_548, type, sK411: term). 26.09/4.24 thf(func_def_549, type, sK412: subst). 26.09/4.24 thf(func_def_550, type, sK413: (subst > term > term)). 26.09/4.24 thf(func_def_551, type, sK414: (subst > term > term)). 26.09/4.24 thf(func_def_552, type, sK415: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_553, type, sK416: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_554, type, sK417: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_555, type, sK418: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_556, type, sK419: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_557, type, sK420: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_558, type, sK421: term). 26.09/4.24 thf(func_def_559, type, sK422: term). 26.09/4.24 thf(func_def_560, type, sK423: subst). 26.09/4.24 thf(func_def_561, type, sK424: term). 26.09/4.24 thf(func_def_562, type, sK425: subst). 26.09/4.24 thf(func_def_563, type, sK426: term). 26.09/4.24 thf(func_def_564, type, sK427: ((subst > term > subst > $o) > term > term)). 26.09/4.24 thf(func_def_565, type, sK428: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_566, type, sK429: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_567, type, sK430: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_568, type, sK431: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_569, type, sK432: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_570, type, sK433: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_571, type, sK434: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_572, type, sK435: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_573, type, sK436: term). 26.09/4.24 thf(func_def_574, type, sK437: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_575, type, sK438: term). 26.09/4.24 thf(func_def_576, type, sK439: (term > (term > $o) > subst > term > $o)). 26.09/4.24 thf(func_def_577, type, sK440: subst). 26.09/4.24 thf(func_def_578, type, sK441: (term > $o)). 26.09/4.24 thf(func_def_579, type, sK442: term). 26.09/4.24 thf(func_def_580, type, sK443: ((term > $o) > term)). 26.09/4.24 thf(func_def_581, type, sK444: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_582, type, sK445: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_583, type, sK446: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_584, type, sK447: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_585, type, sK448: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_586, type, sK449: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_587, type, sK450: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_588, type, sK451: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_589, type, sK452: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_590, type, sK453: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_591, type, sK454: term). 26.09/4.24 thf(func_def_592, type, sK455: subst). 26.09/4.24 thf(func_def_593, type, sK456: term). 26.09/4.24 thf(func_def_594, type, sK457: term). 26.09/4.24 thf(func_def_595, type, sK458: term). 26.09/4.24 thf(func_def_596, type, sK459: (term > $o)). 26.09/4.24 thf(func_def_597, type, sK460: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_598, type, sK461: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_599, type, sK462: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_600, type, sK463: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_601, type, sK464: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_602, type, sK465: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_603, type, sK466: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_604, type, sK467: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_605, type, sK468: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_606, type, sK469: ((term > $o) > term > term)). 26.09/4.24 thf(func_def_607, type, sK470: ((subst > term > subst > $o) > (term > $o) > term)). 26.09/4.24 thf(func_def_608, type, sK471: term). 26.09/4.24 thf(func_def_609, type, sK472: term). 26.09/4.24 thf(func_def_610, type, sK473: term). 26.09/4.24 thf(func_def_611, type, sK474: term). 26.09/4.24 thf(func_def_612, type, sK475: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_613, type, sK476: term). 26.09/4.24 thf(func_def_614, type, sK477: (term > $o)). 26.09/4.24 thf(func_def_615, type, sK478: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_616, type, sK479: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_617, type, sK480: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_618, type, sK481: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_619, type, sK482: ((term > $o) > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_620, type, sK483: ((term > $o) > term > term)). 26.09/4.24 thf(func_def_621, type, sK484: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_622, type, sK485: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_623, type, sK486: term). 26.09/4.24 thf(func_def_624, type, sK487: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_625, type, sK488: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_626, type, sK489: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_627, type, sK490: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_628, type, sK491: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_629, type, sK492: (term > (subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_630, type, sK493: subst). 26.09/4.24 thf(func_def_631, type, sK494: term). 26.09/4.24 thf(func_def_632, type, sK495: (term > $o)). 26.09/4.24 thf(func_def_633, type, sK496: ((term > $o) > term)). 26.09/4.24 thf(func_def_634, type, sK497: ((term > $o) > term > subst > term > $o)). 26.09/4.24 thf(func_def_635, type, sK498: term). 26.09/4.24 thf(func_def_636, type, sK499: ((subst > term > subst > $o) > (term > $o) > term)). 26.09/4.24 thf(func_def_637, type, sK500: (term > (term > $o) > term)). 26.09/4.24 thf(func_def_638, type, sK501: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_639, type, sK502: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_640, type, sK503: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_641, type, sK504: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_642, type, sK505: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_643, type, sK506: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_644, type, sK507: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_645, type, sK508: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_646, type, sK509: (term > $o)). 26.09/4.24 thf(func_def_647, type, sK510: term). 26.09/4.24 thf(func_def_648, type, sK511: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_649, type, sK512: ((subst > term > subst > $o) > term > term)). 26.09/4.24 thf(func_def_650, type, sK513: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_651, type, sK514: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_652, type, sK515: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_653, type, sK516: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_654, type, sK517: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_655, type, sK518: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_656, type, sK519: ((subst > term > subst > $o) > term)). 26.09/4.24 thf(func_def_657, type, sK520: ((subst > term > subst > $o) > subst)). 26.09/4.24 thf(func_def_658, type, sK521: term). 26.09/4.24 thf(func_def_659, type, sK522: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_660, type, sK523: ((subst > term > subst > $o) > subst > term > term)). 26.09/4.24 thf(func_def_661, type, sK524: (term > (term > $o) > term)). 26.09/4.24 thf(func_def_662, type, sK525: ((subst > term > subst > $o) > (term > $o) > term)). 26.09/4.24 thf(func_def_663, type, sK526: ((subst > term > subst > $o) > term > $o)). 26.09/4.24 thf(func_def_664, type, sK527: term). 26.09/4.24 thf(func_def_665, type, sK528: (term > $o)). 26.09/4.24 thf(func_def_666, type, sK529: term). 26.09/4.24 thf(func_def_667, type, sK530: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_668, type, sK531: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_669, type, sK532: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_670, type, sK533: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_671, type, sK534: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_672, type, sK535: (subst > term > subst > $o)). 26.09/4.24 thf(func_def_673, type, sK536: ((term > $o) > term)). 26.09/4.24 thf(func_def_674, type, sK537: (term > d_term)). 26.09/4.24 thf(func_def_675, type, sK538: term). 26.09/4.24 thf(func_def_676, type, sK539: ((subst > term > term) > term)). 26.09/4.24 thf(func_def_677, type, sK540: ((subst > term > term) > subst)). 26.09/4.24 thf(func_def_678, type, sK541: (term > subst > term > term)). 26.09/4.24 thf(func_def_679, type, sK542: subst). 26.09/4.24 thf(func_def_680, type, sK543: subst). 26.09/4.24 thf(func_def_681, type, sK544: ((term > $o) > term)). 26.09/4.24 thf(func_def_682, type, sK545: ((term > $o) > term)). 26.09/4.24 thf(func_def_683, type, sK546: ((term > $o) > term)). 26.09/4.24 thf(func_def_684, type, sK547: ((term > $o) > term)). 26.09/4.24 thf(func_def_685, type, sK548: (term > $o)). 26.09/4.24 thf(func_def_686, type, sK549: term). 26.09/4.24 thf(func_def_687, type, sK550: (term > $o)). 26.09/4.24 thf(func_def_688, type, sK551: (term > $o)). 26.09/4.24 thf(func_def_689, type, sK552: subst). 26.09/4.24 thf(func_def_690, type, sK553: term). 26.09/4.24 thf(func_def_691, type, sK554: term). 26.09/4.24 thf(func_def_692, type, sK555: term). 26.09/4.24 thf(func_def_693, type, sK556: subst). 26.09/4.24 thf(func_def_694, type, sK557: subst). 26.09/4.24 thf(func_def_695, type, sK558: term). 26.09/4.24 thf(func_def_696, type, sK559: term). 26.09/4.24 thf(func_def_697, type, sK560: term). 26.09/4.24 thf(func_def_698, type, sK561: term). 26.09/4.24 thf(func_def_699, type, sK562: term). 26.09/4.24 thf(func_def_700, type, sK563: term). 26.09/4.24 thf(func_def_701, type, sK564: term). 26.09/4.24 thf(func_def_702, type, sK565: term). 26.09/4.24 thf(func_def_703, type, sK566: term). 26.09/4.24 thf(func_def_704, type, sK567: term). 26.09/4.24 thf(func_def_705, type, vNOT: ($o > $o)). 26.09/4.24 thf(func_def_707, type, inv_lam_569: (term > term)). 26.09/4.24 thf(func_def_708, type, inv_lam_570: (term > term)). 26.09/4.24 thf(f1,axiom,( 26.09/4.24 pushprop_lem1_gthm & (! [X11 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X7 : subst,X6 : term] : (((sub @ X11 @ (push @ X6 @ X7))) = ((X15 @ X7 @ X6))) <=> hoasinduction_lem3v2_f) & (induction2 <=> ! [X8 : (term > $o),X16 : term] : ((X8 @ X16) | ~ ! [X6 : term,X11 : term] : (~(X8 @ X6) | (X8 @ (ap @ X6 @ X11)) | ~(X8 @ X11)) | ~ ! [X6 : term] : ((X8 @ X6) | ~(var @ X6)) | ~ ! [X6 : term] : (~ ! [X11 : term] : (~(X8 @ X11) | (X8 @ (sub @ X6 @ (push @ X11 @ id)))) | (X8 @ (lam @ X6))))) & hoasinduction_lem2v2_gthm & ((! [X6 : term] : (X6 = ((sub @ X6 @ id))) => (! [X8 : (subst > term > subst > $o),X28 : term] : (~ ! [X11 : term] : (~(X8 @ id @ X11 @ id) | (X8 @ id @ (sub @ X28 @ (push @ X11 @ id)) @ id)) | (X8 @ id @ (lam @ (sub @ X28 @ (push @ one @ sh))) @ id) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)))) => ! [X21 : term,X8 : (subst > term > subst > $o)] : (~ ! [X11 : term] : ((X8 @ id @ (sub @ X21 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id)) | (X8 @ id @ (lam @ X21) @ id) | ~ ! [X6 : term,X20 : subst,X19 : subst,X7 : subst] : (~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | (X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X7 : subst,X6 : term,X20 : subst,X19 : subst] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X7 : subst,X6 : term,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id))))) <=> hoasinduction_lem3_lthm) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (axshiftcons <=> ! [X6 : term,X7 : subst] : (X7 = ((comp @ sh @ (push @ X6 @ X7))))) & induction2_gthm & hoaslaminj_gthm & ! [X5 : d_subst] : (X5 = d_id) & (pushprop_lem1v2_lthm <=> (! [X7 : subst,X6 : term] : (X6 = ((sub @ one @ (push @ X6 @ X7)))) => ! [X9 : (term > $o),X6 : term,X8 : (term > $o),X7 : subst] : (~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ (sub @ X10 @ (push @ X6 @ X7))))) | (X9 @ one) | ~(X8 @ X6)))) & (pushprop_lem1_lthm <=> (! [X6 : term,X7 : subst] : (X6 = ((sub @ one @ (push @ X6 @ X7)))) => (! [X6 : term,X7 : subst] : (X7 = ((comp @ sh @ (push @ X6 @ X7)))) => ! [X7 : subst,X6 : term,X8 : (term > $o),X11 : term,X20 : (term > $o)] : ((X20 @ (sub @ X6 @ (push @ X11 @ X7))) | ~(X8 @ X6))))) & (! [X6 : term] : (X6 = ((sub @ X6 @ id))) <=> termmset) & hoasapinj2_gthm & hoasapnotvar_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (pushprop_lem1 <=> ! [X11 : term,X20 : (term > $o),X6 : term,X8 : (term > $o),X7 : subst] : (~(X8 @ X6) | (X20 @ (sub @ X6 @ (push @ X11 @ X7))))) & (hoasinduction_lem0 <=> ! [X8 : (subst > term > subst > $o)] : ~ ! [X9 : (term > $o)] : ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id)))) & pushprop_lem3v2 & ((! [X7 : subst] : (X7 = ((comp @ id @ X7))) => (! [X7 : subst] : (X7 = ((comp @ X7 @ id))) => (! [X7 : subst] : (X7 = ((comp @ id @ X7))) & ! [X7 : subst] : (X7 = ((comp @ X7 @ id)))))) <=> substmonoid_lthm) & ((! [X11 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X6 : term,X7 : subst] : (((sub @ X11 @ (push @ X6 @ X7))) = ((X15 @ X7 @ X6))) => (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => ! [X9 : (term > $o),X8 : (subst > term > subst > $o),X23 : term] : (~ ! [X15 : (subst > term > term)] : (~ ! [X7 : subst,X19 : subst,X6 : term] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id))) | ~ ! [X11 : term] : (~(X9 @ X11) | (X9 @ (sub @ X23 @ (push @ X11 @ id)))) | (X9 @ (lam @ X23)) | ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id)))))) <=> hoasinduction_lem3v2a_lthm) & (one = ((d2term @ d_one))) & (hoasinduction_lem3aa_lthm <=> ! [X28 : term,X8 : (subst > term > subst > $o)] : (~ ! [X11 : term] : ((X8 @ id @ (sub @ X28 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id)) | (X8 @ id @ (lam @ (sub @ X28 @ (push @ one @ sh))) @ id) | ~ ! [X15 : (subst > term > term)] : (~ ! [X19 : subst,X6 : term,X7 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id)))) & (substmonoid <=> (! [X7 : subst] : (X7 = ((comp @ id @ X7))) & ! [X7 : subst] : (X7 = ((comp @ X7 @ id))))) & ulamvarsh & (hoasinduction_lthm <=> (! [X8 : (term > $o),X16 : term] : (~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~ ! [X11 : term] : ((X8 @ (sub @ X6 @ (push @ X11 @ id))) | ~(X8 @ X11))) | (X8 @ X16) | ~ ! [X6 : term] : ((X8 @ X6) | ~(var @ X6)) | ~ ! [X6 : term,X11 : term] : (~(X8 @ X6) | (X8 @ (ap @ X6 @ X11)) | ~(X8 @ X11))) => (! [X18 : term,X8 : (subst > term > subst > $o),X17 : term] : (~(X8 @ id @ X17 @ id) | ~(X8 @ id @ X18 @ id) | ~ ! [X7 : subst,X19 : subst,X20 : subst,X6 : term] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | (X8 @ id @ (ap @ X17 @ X18) @ id) | ~ ! [X7 : subst,X19 : subst,X20 : subst,X6 : term] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X6 : term,X11 : term] : (~(X8 @ id @ X11 @ id) | ~(X8 @ id @ X6 @ id) | (X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id))) => (! [X8 : (subst > term > subst > $o),X21 : term] : (~ ! [X11 : term] : ((X8 @ id @ (sub @ X21 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id)) | ~ ! [X19 : subst,X20 : subst,X7 : subst,X6 : term] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | (X8 @ id @ (lam @ X21) @ id) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term,X19 : subst,X7 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id))) | ~ ! [X19 : subst,X6 : term,X7 : subst,X20 : subst] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19)))) => ! [X8 : (subst > term > subst > $o),X22 : term] : ((X8 @ id @ X22 @ id) | ~ ! [X6 : term,X11 : term] : ((X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id) | ~(X8 @ id @ X11 @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X15 : (subst > term > term)] : ((X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))) | ~ ! [X6 : term,X19 : subst,X20 : subst,X7 : subst] : (~(X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | (X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X6 : term] : ((X8 @ id @ X6 @ id) | ~(var @ (sub @ X6 @ id))) | ~ ! [X20 : subst,X6 : term,X7 : subst,X19 : subst] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19))))))) & lamnotvar & hoasinduction_lem3_gthm & hoasinduction_lem1_gthm & (! [X28 : term,X8 : (subst > term > subst > $o)] : ((X8 @ id @ (lam @ (sub @ X28 @ (push @ one @ sh))) @ id) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term,X19 : subst,X7 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))) | ~ ! [X11 : term] : ((X8 @ id @ (sub @ X28 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id))) <=> hoasinduction_lem3aa) & hoasinduction_lem3v2_gthm & (induction2lem <=> ! [X12 : term,X13 : subst,X8 : (term > $o)] : (~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~ ! [X11 : term] : (~(X8 @ X11) | (X8 @ (sub @ X6 @ (push @ X11 @ id))))) | ~ ! [X6 : term,X11 : term] : ((X8 @ (ap @ X6 @ X11)) | ~(X8 @ X6) | ~(X8 @ X11)) | ~ ! [X11 : term] : (~(var @ X11) | (X8 @ (sub @ X11 @ X13))) | (X8 @ (sub @ X12 @ X13)))) & (! [X15 : (subst > term > term),X33 : term,X32 : term] : ((((lam @ (X15 @ sh @ one))) != ((ap @ (sub @ X32 @ id) @ X33))) | ~ ! [X7 : subst,X19 : subst,X6 : term] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))) <=> hoaslamnotap) & hoasinduction_lem2_lthm & axassoc & (! [X11 : term,X6 : term] : ((((lam @ X6)) != ((lam @ X11))) | (X6 = X11)) <=> laminj) & substmonoid_gthm & (hoasinduction_lem3a_lthm <=> (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => (! [X8 : (subst > term > subst > $o),X28 : term] : (~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | (X8 @ id @ (lam @ (sub @ X28 @ (push @ one @ sh))) @ id) | ~ ! [X11 : term] : ((X8 @ id @ (sub @ X28 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id))) => ! [X29 : term,X8 : (subst > term > subst > $o)] : (~ ! [X15 : (subst > term > term)] : ((X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id))) | ~ ! [X11 : term] : ((X8 @ id @ (sub @ X29 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id)) | (X8 @ id @ (lam @ X29) @ id))))) & pushprop_lem0_gthm & axvarshift & (! [X7 : subst] : (X7 = ((comp @ X7 @ id))) <=> axidr) & ((! [X8 : (subst > term > subst > $o)] : ~ ! [X9 : (term > $o)] : ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) => (! [X16 : term,X8 : (term > $o)] : ((X8 @ X16) | ~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~ ! [X11 : term] : ((X8 @ (sub @ X6 @ (push @ X11 @ id))) | ~(X8 @ X11))) | ~ ! [X6 : term] : ((X8 @ X6) | ~(var @ X6)) | ~ ! [X11 : term,X6 : term] : ((X8 @ (ap @ X6 @ X11)) | ~(X8 @ X11) | ~(X8 @ X6))) => (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => (! [X8 : (subst > term > subst > $o),X9 : (term > $o),X23 : term] : (~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) | ~ ! [X15 : (subst > term > term)] : ((X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | ~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id))) | (X9 @ (lam @ X23)) | ~ ! [X11 : term] : (~(X9 @ X11) | (X9 @ (sub @ X23 @ (push @ X11 @ id))))) => ! [X8 : (subst > term > subst > $o),X24 : term] : ((X8 @ id @ X24 @ id) | ~ ! [X6 : term,X11 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id) | ~(X8 @ id @ X11 @ id)) | ~ ! [X15 : (subst > term > term)] : ((X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X19 : subst,X7 : subst,X6 : term] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))))))))) <=> hoasinduction_no_psi_cond_lthm) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_p_and_p_prime = (^[X8 : (subst > term > subst > $o), X9 : (term > $o)] : (! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id)))))) & induction2lem_gthm & pushprop_lem1v2_gthm & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (axidl <=> ! [X7 : subst] : (X7 = ((comp @ id @ X7)))) & pushprop_lthm_orig & (! [X6 : term,X8 : (term > $o),X7 : subst] : ~ ! [X9 : (term > $o)] : ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ (sub @ X10 @ (push @ X6 @ X7))))) <=> pushprop_lem0) & ! [X47 : d_subst,X48 : d_subst] : ((((d2subst @ X47)) = ((d2subst @ X48))) => (X47 = X48)) & pushprop_lem2v2_gthm & axabs & hoasinduction_lem2_gthm & (id = ((d2subst @ d_id))) & apnotvar & ((! [X6 : term] : (X6 = ((sub @ X6 @ id))) => ! [X8 : (subst > term > subst > $o),X9 : (term > $o),X34 : term] : (~ ! [X7 : subst,X20 : subst,X19 : subst,X6 : term] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) | ~ ! [X11 : term] : ((X9 @ (sub @ X34 @ (push @ X11 @ id))) | ~(X9 @ X11)) | (X9 @ (lam @ X34)) | ~ ! [X7 : subst,X6 : term,X20 : subst,X19 : subst] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term,X19 : subst,X7 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))))) <=> hoasinduction_lem3v2_lthm) & (! [X9 : (term > $o),X35 : term,X8 : (subst > term > subst > $o),X36 : term] : (~(X9 @ X35) | ~ ! [X19 : subst,X7 : subst,X20 : subst,X6 : term] : (~(X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | (X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X11 : term,X6 : term] : (~(X8 @ id @ X6 @ id) | ~(X8 @ id @ X11 @ id) | (X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id)) | ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) | (X9 @ (ap @ X35 @ X36)) | ~ ! [X7 : subst,X6 : term,X20 : subst,X19 : subst] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~(X9 @ X36)) <=> hoasinduction_lem2v2) & (! [X11 : term] : ~ ! [X15 : (subst > term > term)] : (((X15 @ sh @ one)) != ((sub @ X11 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoasinduction_lem1v2 & (hoasapinj1_lthm <=> (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => (! [X31 : term,X6 : term,X11 : term,X30 : term] : ((((ap @ X6 @ X30)) != ((ap @ X11 @ X31))) | (X6 = X11)) => ! [X31 : term,X30 : term,X11 : term,X6 : term] : ((((ap @ (sub @ X6 @ id) @ X30)) != ((ap @ (sub @ X11 @ id) @ X31))) | (X6 = X11))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoaslaminj_lthm <=> (! [X7 : subst,X6 : term] : (X6 = ((sub @ one @ (push @ X6 @ X7)))) => (! [X6 : term,X7 : subst] : (X7 = ((comp @ sh @ (push @ X6 @ X7)))) => (! [X6 : term,X11 : term] : ((((lam @ X6)) != ((lam @ X11))) | (X6 = X11)) => ! [X26 : subst,X25 : (subst > term > term),X27 : term,X15 : (subst > term > term)] : ((((X15 @ X26 @ X27)) = ((X25 @ X26 @ X27))) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (((lam @ (X15 @ sh @ one))) != ((lam @ (X25 @ sh @ one)))) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X25 @ X7 @ X6) @ X19)) = ((X25 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))))))) & pushprop_gthm & (shinj <=> ! [X11 : term,X6 : term] : ((((sub @ X6 @ sh)) != ((sub @ X11 @ sh))) | (X6 = X11))) & (! [X7 : subst] : (X7 = ((push @ (sub @ one @ X7) @ (comp @ sh @ X7)))) <=> axscons) & hoasinduction_lem3a_gthm & (! [X37 : term,X8 : (subst > term > subst > $o)] : ((X8 @ id @ (lam @ (sub @ X37 @ (push @ one @ sh))) @ id) | ~ ! [X11 : term] : (~(X8 @ id @ X11 @ id) | (X8 @ id @ (sub @ X37 @ (push @ X11 @ id)) @ id)) | ~ ! [X38 : term,X15 : (subst > term > term)] : (~ ! [X40 : term,X39 : subst,X41 : subst] : (((X15 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X38 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X44 : subst,X42 : subst,X43 : term] : (((sub @ (X15 @ X42 @ X43) @ X44)) = ((sub @ (sub @ X38 @ (push @ X43 @ X42)) @ X44))))) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3v2 <=> ! [X9 : (term > $o),X8 : (subst > term > subst > $o),X34 : term] : ((X9 @ (lam @ X34)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X7 : subst,X6 : term,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id))) | ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) | ~ ! [X6 : term,X20 : subst,X19 : subst,X7 : subst] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X11 : term] : (~(X9 @ X11) | (X9 @ (sub @ X34 @ (push @ X11 @ id)))) | ~ ! [X6 : term,X19 : subst,X7 : subst,X20 : subst] : (~(X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | (X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)))) & ((! [X8 : (subst > term > subst > $o)] : ~ ! [X9 : (term > $o)] : ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) => (! [X8 : (term > $o),X16 : term] : (~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~ ! [X11 : term] : (~(X8 @ X11) | (X8 @ (sub @ X6 @ (push @ X11 @ id))))) | ~ ! [X6 : term] : ((X8 @ X6) | ~(var @ X6)) | ~ ! [X11 : term,X6 : term] : (~(X8 @ X6) | ~(X8 @ X11) | (X8 @ (ap @ X6 @ X11))) | (X8 @ X16)) => (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => (! [X9 : (term > $o),X23 : term,X8 : (subst > term > subst > $o)] : ((X9 @ (lam @ X23)) | ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) | ~ ! [X11 : term] : ((X9 @ (sub @ X23 @ (push @ X11 @ id))) | ~(X9 @ X11)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X7 : subst,X6 : term,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)))) => ! [X8 : (subst > term > subst > $o),X22 : term] : (~ ! [X6 : term,X11 : term] : ((X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id) | ~(X8 @ id @ X11 @ id) | ~(X8 @ id @ X6 @ id)) | (X8 @ id @ X22 @ id) | ~ ! [X20 : subst,X6 : term,X19 : subst,X7 : subst] : (~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | (X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X19 : subst,X6 : term,X7 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | ~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | ~ ! [X20 : subst,X6 : term,X19 : subst,X7 : subst] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X6 : term] : (~(var @ (sub @ X6 @ id)) | (X8 @ id @ X6 @ id))))))) <=> hoasinduction_lthm_3) & hoasinduction_lem1v2_gthm & (pushprop_p_and_p_prime = (^[X6 : term, X7 : subst, X8 : (term > $o), X9 : (term > $o)] : (! [X10 : term] : (((X9 @ X10)) = ((X8 @ (sub @ X10 @ (push @ X6 @ X7)))))))) & pushprop_lthm & (sh = ((d2subst @ d_id))) & axmap & (! [X9 : (term > $o),X8 : (subst > term > subst > $o),X23 : term] : (~ ! [X11 : term] : ((X9 @ (sub @ X23 @ (push @ X11 @ id))) | ~(X9 @ X11)) | ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) | (X9 @ (lam @ X23)) | ~ ! [X15 : (subst > term > term)] : ((X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))))) <=> hoasinduction_lem3v2a) & hoaslamnotap_gthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X18 : term,X8 : (subst > term > subst > $o),X17 : term] : (~(X8 @ id @ X17 @ id) | ~ ! [X6 : term,X19 : subst,X7 : subst,X20 : subst] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X6 : term,X11 : term] : (~(X8 @ id @ X6 @ id) | ~(X8 @ id @ X11 @ id) | (X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id)) | (X8 @ id @ (ap @ X17 @ X18) @ id) | ~ ! [X6 : term,X19 : subst,X20 : subst,X7 : subst] : (~(X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | (X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~(X8 @ id @ X18 @ id)) <=> hoasinduction_lem2) & hoasinduction_gthm & hoasapnotvar_lthm & ~lamnotap & (axvarcons <=> ! [X7 : subst,X6 : term] : (X6 = ((sub @ one @ (push @ X6 @ X7))))) & hoaslamnotap_lthm & hoaslamnotvar & (induction2_lthm <=> (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => (! [X12 : term,X13 : subst,X8 : (term > $o)] : (~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~ ! [X11 : term] : ((X8 @ (sub @ X6 @ (push @ X11 @ id))) | ~(X8 @ X11))) | ~ ! [X11 : term] : (~(var @ X11) | (X8 @ (sub @ X11 @ X13))) | (X8 @ (sub @ X12 @ X13)) | ~ ! [X6 : term,X11 : term] : ((X8 @ (ap @ X6 @ X11)) | ~(X8 @ X6) | ~(X8 @ X11))) => ! [X16 : term,X8 : (term > $o)] : (~ ! [X6 : term] : (~ ! [X11 : term] : (~(X8 @ X11) | (X8 @ (sub @ X6 @ (push @ X11 @ id)))) | (X8 @ (lam @ X6))) | ~ ! [X6 : term] : ((X8 @ X6) | ~(var @ X6)) | ~ ! [X11 : term,X6 : term] : (~(X8 @ X11) | ~(X8 @ X6) | (X8 @ (ap @ X6 @ X11))) | (X8 @ X16))))) & (! [X27 : term,X25 : (subst > term > term),X26 : subst,X15 : (subst > term > term)] : (~ ! [X7 : subst,X19 : subst,X6 : term] : (((sub @ (X25 @ X7 @ X6) @ X19)) = ((X25 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (((lam @ (X15 @ sh @ one))) != ((lam @ (X25 @ sh @ one)))) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (((X15 @ X26 @ X27)) = ((X25 @ X26 @ X27)))) <=> hoaslaminj) & (pushprop_lem1v2 <=> ! [X6 : term,X8 : (term > $o),X7 : subst,X9 : (term > $o)] : (~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ (sub @ X10 @ (push @ X6 @ X7))))) | ~(X8 @ X6) | (X9 @ one))) & axclos & (hoasinduction <=> ! [X22 : term,X8 : (subst > term > subst > $o)] : (~ ! [X6 : term,X19 : subst,X20 : subst,X7 : subst] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19))) | ~ ! [X6 : term] : (~(var @ (sub @ X6 @ id)) | (X8 @ id @ X6 @ id)) | (X8 @ id @ X22 @ id) | ~ ! [X6 : term,X11 : term] : ((X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id) | ~(X8 @ id @ X11 @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X7 : subst,X19 : subst,X6 : term,X20 : subst] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X15 : (subst > term > term)] : ((X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)) | ~ ! [X6 : term,X7 : subst,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))))) & hoasinduction_lem1_lthm & hoaslamnotvar_gthm & pushprop_lem2v2_lthm & (! [X7 : subst,X8 : (term > $o),X6 : term] : ~ ! [X9 : (term > $o)] : ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ (sub @ X10 @ (push @ X6 @ X7))))) <=> pushprop_lem0_lthm) & (hoasinduction_lem3b_lthm <=> ! [X11 : term] : ~ ! [X15 : (subst > term > term)] : (((X15 @ sh @ one)) != ((sub @ X11 @ (push @ one @ sh))))) & ! [X1 : d_term] : (X1 = d_one) & hoasapnotvar & (! [X8 : (subst > term > subst > $o)] : ~ ! [X9 : (term > $o)] : ~ ! [X10 : term] : (((X9 @ X10)) = ((X8 @ id @ X10 @ id))) <=> hoasinduction_lem0_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X11 : term] : ~ ! [X15 : (subst > term > term)] : ~ ! [X6 : term,X7 : subst] : (((sub @ X11 @ (push @ X6 @ X7))) = ((X15 @ X7 @ X6)))) & pushprop_lem2v2 & (hoasinduction_lem3 <=> ! [X21 : term,X8 : (subst > term > subst > $o)] : (~ ! [X7 : subst,X19 : subst,X6 : term,X20 : subst] : ((X8 @ X7 @ X6 @ (comp @ X20 @ X19)) | ~(X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19)) | ~ ! [X11 : term] : ((X8 @ id @ (sub @ X21 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | ~ ! [X7 : subst,X6 : term,X19 : subst] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | (X8 @ id @ (lam @ X21) @ id) | ~ ! [X7 : subst,X20 : subst,X19 : subst,X6 : term] : ((X8 @ (comp @ X7 @ X20) @ (sub @ X6 @ X20) @ X19) | ~(X8 @ X7 @ X6 @ (comp @ X20 @ X19))))) & (axvarid <=> ! [X6 : term] : (X6 = ((sub @ X6 @ id)))) & ((^[X45 : subst, X46 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (induction2lem_lthm <=> (! [X6 : term,X7 : subst] : (X6 = ((sub @ one @ (push @ X6 @ X7)))) => (! [X7 : subst,X6 : term] : (X7 = ((comp @ sh @ (push @ X6 @ X7)))) => (! [X7 : subst] : (X7 = ((comp @ X7 @ id))) => (! [X14 : term,X8 : (term > $o)] : (~ ! [X11 : term,X6 : term] : (~(X8 @ X11) | ~(X8 @ X6) | (X8 @ (ap @ X6 @ X11))) | (X8 @ X14) | ~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~(X8 @ X6)) | ~ ! [X6 : term] : (~(var @ X6) | (X8 @ X6))) => ! [X12 : term,X13 : subst,X8 : (term > $o)] : (~ ! [X11 : term] : ((X8 @ (sub @ X11 @ X13)) | ~(var @ X11)) | (X8 @ (sub @ X12 @ X13)) | ~ ! [X6 : term] : ((X8 @ (lam @ X6)) | ~ ! [X11 : term] : ((X8 @ (sub @ X6 @ (push @ X11 @ id))) | ~(X8 @ X11))) | ~ ! [X11 : term,X6 : term] : (~(X8 @ X6) | ~(X8 @ X11) | (X8 @ (ap @ X6 @ X11))))))))) & ((! [X31 : term,X11 : term,X6 : term,X30 : term] : ((X30 = X31) | (((ap @ X6 @ X30)) != ((ap @ X11 @ X31)))) => ! [X31 : term,X11 : term,X30 : term,X6 : term] : ((X30 = X31) | (((ap @ (sub @ X6 @ id) @ X30)) != ((ap @ (sub @ X11 @ id) @ X31))))) <=> hoasapinj2_lthm) & hoasapinj1_gthm & hoasinduction_lem3b_gthm & ~ulamvar1 & hoaslamnotvar_lthm & ~(var @ (d2term @ d_one)) & axapp & (! [X24 : term,X8 : (subst > term > subst > $o)] : ((X8 @ id @ X24 @ id) | ~ ! [X11 : term,X6 : term] : (~(X8 @ id @ X6 @ id) | ~(X8 @ id @ X11 @ id) | (X8 @ id @ (ap @ (sub @ X6 @ id) @ X11) @ id)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X7 : subst,X19 : subst,X6 : term] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19)))) | ~ ! [X6 : term] : ((X8 @ id @ (X15 @ id @ X6) @ id) | ~(X8 @ id @ X6 @ id)) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id))) <=> hoasinduction_no_psi_cond) & (apinj1 <=> ! [X31 : term,X6 : term,X30 : term,X11 : term] : ((((ap @ X6 @ X30)) != ((ap @ X11 @ X31))) | (X6 = X11))) & (hoasapinj2 <=> ! [X31 : term,X30 : term,X11 : term,X6 : term] : ((((ap @ (sub @ X6 @ id) @ X30)) != ((ap @ (sub @ X11 @ id) @ X31))) | (X30 = X31))) & pushprop & (! [X8 : (term > $o),X14 : term] : (~ ! [X6 : term] : (~(X8 @ X6) | (X8 @ (lam @ X6))) | ~ ! [X6 : term] : (~(var @ X6) | (X8 @ X6)) | (X8 @ X14) | ~ ! [X6 : term,X11 : term] : (~(X8 @ X11) | (X8 @ (ap @ X6 @ X11)) | ~(X8 @ X6))) <=> induction) & (hoasinduction_lem3a <=> ! [X8 : (subst > term > subst > $o),X29 : term] : ((X8 @ id @ (lam @ X29) @ id) | ~ ! [X15 : (subst > term > term)] : (~ ! [X6 : term] : (~(X8 @ id @ X6 @ id) | (X8 @ id @ (X15 @ id @ X6) @ id)) | (X8 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X7 : subst,X19 : subst,X6 : term] : (((sub @ (X15 @ X7 @ X6) @ X19)) = ((X15 @ (comp @ X7 @ X19) @ (sub @ X6 @ X19))))) | ~ ! [X11 : term] : ((X8 @ id @ (sub @ X29 @ (push @ X11 @ id)) @ id) | ~(X8 @ id @ X11 @ id)))) & (termmset_lthm <=> (! [X6 : term] : (X6 = ((sub @ X6 @ id))) => ! [X6 : term] : (X6 = ((sub @ X6 @ id))))) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & ulamvarind & (hoasapinj1 <=> ! [X6 : term,X11 : term,X30 : term,X31 : term] : ((((ap @ (sub @ X6 @ id) @ X30)) != ((ap @ (sub @ X11 @ id) @ X31))) | (X6 = X11))) & (apinj2 <=> ! [X30 : term,X6 : term,X11 : term,X31 : term] : ((((ap @ X6 @ X30)) != ((ap @ X11 @ X31))) | (X30 = X31))) & termmset_gthm & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & pushprop_lem3v2_lthm), 26.09/4.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)). 26.09/4.24 thf(f2,conjecture,( 26.09/4.24 (hoasinduction_lem3a = ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : subst,X2 : subst,X3 : term] : (((sub @ (X1 @ X2 @ X3) @ X4)) = ((X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)))) => (! [X3 : term] : ((X0 @ id @ X3 @ id) => (X0 @ id @ (X1 @ id @ X3) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X2 : subst, X3 : term] : ((X1 @ X2 @ X3)))) @ id))) => ! [X3 : term] : (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (sub @ X3 @ (push @ X5 @ id)) @ id)) => (X0 @ id @ (lam @ X3) @ id))))), 26.09/4.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a)). 26.09/4.24 thf(f3,negated_conjecture,( 26.09/4.24 ~ (hoasinduction_lem3a = ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : subst,X2 : subst,X3 : term] : (((sub @ (X1 @ X2 @ X3) @ X4)) = ((X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)))) => (! [X3 : term] : ((X0 @ id @ X3 @ id) => (X0 @ id @ (X1 @ id @ X3) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X2 : subst, X3 : term] : ((X1 @ X2 @ X3)))) @ id))) => ! [X3 : term] : (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (sub @ X3 @ (push @ X5 @ id)) @ id)) => (X0 @ id @ (lam @ X3) @ id))))), 26.09/4.24 inference(negated_conjecture,[status(cth)],[f2])). 26.09/4.24 thf(f4,plain,( 26.09/4.24 ~ (hoasinduction_lem3a = ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X2 : subst,X3 : subst,X4 : term] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2)))) => (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (X1 @ id @ X5) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X6 : subst, X7 : term] : ((X1 @ X6 @ X7)))) @ id))) => ! [X8 : term] : (! [X9 : term] : ((X0 @ id @ X9 @ id) => (X0 @ id @ (sub @ X8 @ (push @ X9 @ id)) @ id)) => (X0 @ id @ (lam @ X8) @ id))))), 26.09/4.24 inference(rectify,[],[f3])). 26.09/4.24 thf(f5,plain,( 26.09/4.24 ~((hoasinduction_lem3a = $true) <=> ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : term,X2 : subst,X3 : subst] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2)))) => (! [X5 : term] : ((((X0 @ id @ X5 @ id)) = $true) => ($true = ((X0 @ id @ (X1 @ id @ X5) @ id)))) => ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))))) => ! [X8 : term] : (! [X9 : term] : (($true = ((X0 @ id @ X9 @ id))) => ($true = ((X0 @ id @ (sub @ X8 @ (push @ X9 @ id)) @ id)))) => ($true = ((X0 @ id @ (lam @ X8) @ id))))))), 26.09/4.24 inference(fool_elimination,[],[f4])). 26.09/4.24 thf(f6,plain,( 26.09/4.24 pushprop_lem1_gthm & (! [X0 : term] : ~ ! [X1 : (subst > term > term)] : ~ ! [X2 : subst,X3 : term] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2)))) <=> hoasinduction_lem3v2_f) & (induction2 <=> ! [X4 : (term > $o),X5 : term] : ((X4 @ X5) | ~ ! [X6 : term,X7 : term] : (~(X4 @ X6) | (X4 @ (ap @ X6 @ X7)) | ~(X4 @ X7)) | ~ ! [X8 : term] : ((X4 @ X8) | ~(var @ X8)) | ~ ! [X9 : term] : (~ ! [X10 : term] : (~(X4 @ X10) | (X4 @ (sub @ X9 @ (push @ X10 @ id)))) | (X4 @ (lam @ X9))))) & hoasinduction_lem2v2_gthm & ((! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X14 : term] : (~(X12 @ id @ X14 @ id) | (X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)) | (X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term,X17 : subst,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) = ((sub @ (X15 @ X17 @ X16) @ X18))) | (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X19 : term] : (~(X12 @ id @ X19 @ id) | (X12 @ id @ (X15 @ id @ X19) @ id)))) => ! [X20 : term,X21 : (subst > term > subst > $o)] : (~ ! [X22 : term] : ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id) | ~(X21 @ id @ X22 @ id)) | (X21 @ id @ (lam @ X20) @ id) | ~ ! [X23 : term,X24 : subst,X25 : subst,X26 : subst] : (~(X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25) | (X21 @ X26 @ X23 @ (comp @ X24 @ X25))) | ~ ! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : ((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30) | ~(X21 @ X27 @ X28 @ (comp @ X29 @ X30))) | ~ ! [X31 : (subst > term > term)] : (~ ! [X32 : term] : ((X21 @ id @ (X31 @ id @ X32) @ id) | ~(X21 @ id @ X32 @ id)) | ~ ! [X33 : subst,X34 : term,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35)))) | (X21 @ id @ (lam @ (X31 @ sh @ one)) @ id))))) <=> hoasinduction_lem3_lthm) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (axshiftcons <=> ! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37)) & induction2_gthm & hoaslaminj_gthm & ! [X38 : d_subst] : (d_id = X38) & (pushprop_lem1v2_lthm <=> (! [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) = X40) => ! [X41 : (term > $o),X42 : term,X43 : (term > $o),X44 : subst] : (~ ! [X45 : term] : (((X41 @ X45)) = ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (X41 @ one) | ~(X43 @ X42)))) & (pushprop_lem1_lthm <=> (! [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) = X46) => (! [X48 : term,X49 : subst] : (((comp @ sh @ (push @ X48 @ X49))) = X49) => ! [X50 : subst,X51 : term,X52 : (term > $o),X53 : term,X54 : (term > $o)] : ((X54 @ (sub @ X51 @ (push @ X53 @ X50))) | ~(X52 @ X51))))) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> termmset) & hoasapinj2_gthm & hoasapnotvar_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (pushprop_lem1 <=> ! [X56 : term,X57 : (term > $o),X58 : term,X59 : (term > $o),X60 : subst] : (~(X59 @ X58) | (X57 @ (sub @ X58 @ (push @ X56 @ X60))))) & (hoasinduction_lem0 <=> ! [X61 : (subst > term > subst > $o)] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id)))) & pushprop_lem3v2 & ((! [X64 : subst] : (((comp @ id @ X64)) = X64) => (! [X65 : subst] : (((comp @ X65 @ id)) = X65) => (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)))) <=> substmonoid_lthm) & ((! [X68 : term] : ~ ! [X69 : (subst > term > term)] : ~ ! [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) = ((sub @ X68 @ (push @ X70 @ X71)))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => ! [X73 : (term > $o),X74 : (subst > term > subst > $o),X75 : term] : (~ ! [X76 : (subst > term > term)] : (~ ! [X77 : subst,X78 : subst,X79 : term] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) | (X74 @ id @ (lam @ (X76 @ sh @ one)) @ id) | ~ ! [X80 : term] : (~(X74 @ id @ X80 @ id) | (X74 @ id @ (X76 @ id @ X80) @ id))) | ~ ! [X81 : term] : (~(X73 @ X81) | (X73 @ (sub @ X75 @ (push @ X81 @ id)))) | (X73 @ (lam @ X75)) | ~ ! [X82 : term] : (((X74 @ id @ X82 @ id)) = ((X73 @ X82)))))) <=> hoasinduction_lem3v2a_lthm) & (one = ((d2term @ d_one))) & (hoasinduction_lem3aa_lthm <=> ! [X83 : term,X84 : (subst > term > subst > $o)] : (~ ! [X85 : term] : ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id) | ~(X84 @ id @ X85 @ id)) | (X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id) | ~ ! [X86 : (subst > term > term)] : (~ ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))) | ~ ! [X90 : term] : ((X84 @ id @ (X86 @ id @ X90) @ id) | ~(X84 @ id @ X90 @ id)) | (X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)))) & (substmonoid <=> (! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92))) & ulamvarsh & (hoasinduction_lthm <=> (! [X93 : (term > $o),X94 : term] : (~ ! [X95 : term] : ((X93 @ (lam @ X95)) | ~ ! [X96 : term] : ((X93 @ (sub @ X95 @ (push @ X96 @ id))) | ~(X93 @ X96))) | (X93 @ X94) | ~ ! [X97 : term] : ((X93 @ X97) | ~(var @ X97)) | ~ ! [X98 : term,X99 : term] : (~(X93 @ X98) | (X93 @ (ap @ X98 @ X99)) | ~(X93 @ X99))) => (! [X100 : term,X101 : (subst > term > subst > $o),X102 : term] : (~(X101 @ id @ X102 @ id) | ~(X101 @ id @ X100 @ id) | ~ ! [X103 : subst,X104 : subst,X105 : subst,X106 : term] : ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)) | ~(X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)) | (X101 @ id @ (ap @ X102 @ X100) @ id) | ~ ! [X107 : subst,X108 : subst,X109 : subst,X110 : term] : ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108) | ~(X101 @ X107 @ X110 @ (comp @ X109 @ X108))) | ~ ! [X111 : term,X112 : term] : (~(X101 @ id @ X112 @ id) | ~(X101 @ id @ X111 @ id) | (X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id))) => (! [X113 : (subst > term > subst > $o),X114 : term] : (~ ! [X115 : term] : ((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id) | ~(X113 @ id @ X115 @ id)) | ~ ! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : ((X113 @ X118 @ X119 @ (comp @ X117 @ X116)) | ~(X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)) | (X113 @ id @ (lam @ X114) @ id) | ~ ! [X120 : (subst > term > term)] : (~ ! [X121 : term,X122 : subst,X123 : subst] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X120 @ X123 @ X121) @ X122))) | (X113 @ id @ (lam @ (X120 @ sh @ one)) @ id) | ~ ! [X124 : term] : (~(X113 @ id @ X124 @ id) | (X113 @ id @ (X120 @ id @ X124) @ id))) | ~ ! [X125 : subst,X126 : term,X127 : subst,X128 : subst] : ((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125) | ~(X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) => ! [X129 : (subst > term > subst > $o),X130 : term] : ((X129 @ id @ X130 @ id) | ~ ! [X131 : term,X132 : term] : ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id) | ~(X129 @ id @ X132 @ id) | ~(X129 @ id @ X131 @ id)) | ~ ! [X133 : (subst > term > term)] : ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id) | ~ ! [X134 : term] : ((X129 @ id @ (X133 @ id @ X134) @ id) | ~(X129 @ id @ X134 @ id)) | ~ ! [X135 : term,X136 : subst,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137)))) | ~ ! [X138 : term,X139 : subst,X140 : subst,X141 : subst] : (~(X129 @ X141 @ X138 @ (comp @ X140 @ X139)) | (X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) | ~ ! [X142 : term] : ((X129 @ id @ X142 @ id) | ~(var @ (sub @ X142 @ id))) | ~ ! [X143 : subst,X144 : term,X145 : subst,X146 : subst] : ((X129 @ X145 @ X144 @ (comp @ X143 @ X146)) | ~(X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146))))))) & lamnotvar & hoasinduction_lem3_gthm & hoasinduction_lem1_gthm & (! [X147 : term,X148 : (subst > term > subst > $o)] : ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id) | ~ ! [X149 : (subst > term > term)] : (~ ! [X150 : term] : (~(X148 @ id @ X150 @ id) | (X148 @ id @ (X149 @ id @ X150) @ id)) | (X148 @ id @ (lam @ (X149 @ sh @ one)) @ id) | ~ ! [X151 : term,X152 : subst,X153 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152)))) | ~ ! [X154 : term] : ((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id) | ~(X148 @ id @ X154 @ id))) <=> hoasinduction_lem3aa) & hoasinduction_lem3v2_gthm & (induction2lem <=> ! [X155 : term,X156 : subst,X157 : (term > $o)] : (~ ! [X158 : term] : ((X157 @ (lam @ X158)) | ~ ! [X159 : term] : (~(X157 @ X159) | (X157 @ (sub @ X158 @ (push @ X159 @ id))))) | ~ ! [X160 : term,X161 : term] : ((X157 @ (ap @ X160 @ X161)) | ~(X157 @ X160) | ~(X157 @ X161)) | ~ ! [X162 : term] : (~(var @ X162) | (X157 @ (sub @ X162 @ X156))) | (X157 @ (sub @ X155 @ X156)))) & (! [X163 : (subst > term > term),X164 : term,X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ~ ! [X166 : subst,X167 : subst,X168 : term] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X163 @ X166 @ X168) @ X167)))) <=> hoaslamnotap) & hoasinduction_lem2_lthm & axassoc & (! [X169 : term,X170 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170)) <=> laminj) & substmonoid_gthm & (hoasinduction_lem3a_lthm <=> (! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : (subst > term > subst > $o),X173 : term] : (~ ! [X174 : (subst > term > term)] : (~ ! [X175 : term] : (~(X172 @ id @ X175 @ id) | (X172 @ id @ (X174 @ id @ X175) @ id)) | ~ ! [X176 : term,X177 : subst,X178 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) = ((sub @ (X174 @ X177 @ X176) @ X178))) | (X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) | (X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id) | ~ ! [X179 : term] : ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id) | ~(X172 @ id @ X179 @ id))) => ! [X180 : term,X181 : (subst > term > subst > $o)] : (~ ! [X182 : (subst > term > term)] : ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id) | ~ ! [X183 : term,X184 : subst,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) | ~ ! [X186 : term] : ((X181 @ id @ (X182 @ id @ X186) @ id) | ~(X181 @ id @ X186 @ id))) | ~ ! [X187 : term] : ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id) | ~(X181 @ id @ X187 @ id)) | (X181 @ id @ (lam @ X180) @ id))))) & pushprop_lem0_gthm & axvarshift & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> axidr) & ((! [X189 : (subst > term > subst > $o)] : ~ ! [X190 : (term > $o)] : ~ ! [X191 : term] : (((X190 @ X191)) = ((X189 @ id @ X191 @ id))) => (! [X192 : term,X193 : (term > $o)] : ((X193 @ X192) | ~ ! [X194 : term] : ((X193 @ (lam @ X194)) | ~ ! [X195 : term] : ((X193 @ (sub @ X194 @ (push @ X195 @ id))) | ~(X193 @ X195))) | ~ ! [X196 : term] : ((X193 @ X196) | ~(var @ X196)) | ~ ! [X197 : term,X198 : term] : ((X193 @ (ap @ X198 @ X197)) | ~(X193 @ X197) | ~(X193 @ X198))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => (! [X200 : (subst > term > subst > $o),X201 : (term > $o),X202 : term] : (~ ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203))) | ~ ! [X204 : (subst > term > term)] : ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id) | ~ ! [X205 : term,X206 : subst,X207 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X204 @ X206 @ X205) @ X207))) | ~ ! [X208 : term] : (~(X200 @ id @ X208 @ id) | (X200 @ id @ (X204 @ id @ X208) @ id))) | (X201 @ (lam @ X202)) | ~ ! [X209 : term] : (~(X201 @ X209) | (X201 @ (sub @ X202 @ (push @ X209 @ id))))) => ! [X210 : (subst > term > subst > $o),X211 : term] : ((X210 @ id @ X211 @ id) | ~ ! [X212 : term,X213 : term] : (~(X210 @ id @ X212 @ id) | (X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id) | ~(X210 @ id @ X213 @ id)) | ~ ! [X214 : (subst > term > term)] : ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id) | ~ ! [X215 : term] : ((X210 @ id @ (X214 @ id @ X215) @ id) | ~(X210 @ id @ X215 @ id)) | ~ ! [X216 : subst,X217 : subst,X218 : term] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))))))))) <=> hoasinduction_no_psi_cond_lthm) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_p_and_p_prime = (^[X219 : (subst > term > subst > $o), X220 : (term > $o)] : (! [X221 : term] : (((X219 @ id @ X221 @ id)) = ((X220 @ X221)))))) & induction2lem_gthm & pushprop_lem1v2_gthm & ! [X222 : term] : ? [X223 : d_term] : (((d2term @ X223)) = X222) & (axidl <=> ! [X224 : subst] : (((comp @ id @ X224)) = X224)) & pushprop_lthm_orig & (! [X225 : term,X226 : (term > $o),X227 : subst] : ~ ! [X228 : (term > $o)] : ~ ! [X229 : term] : (((X228 @ X229)) = ((X226 @ (sub @ X229 @ (push @ X225 @ X227))))) <=> pushprop_lem0) & ! [X230 : d_subst,X231 : d_subst] : ((((d2subst @ X230)) = ((d2subst @ X231))) => (X230 = X231)) & pushprop_lem2v2_gthm & axabs & hoasinduction_lem2_gthm & (id = ((d2subst @ d_id))) & apnotvar & ((! [X232 : term] : (((sub @ X232 @ id)) = X232) => ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : (~ ! [X236 : subst,X237 : subst,X238 : subst,X239 : term] : ((X233 @ X236 @ X239 @ (comp @ X237 @ X238)) | ~(X233 @ (comp @ X236 @ X237) @ (sub @ X239 @ X237) @ X238)) | ~ ! [X240 : term] : (((X234 @ X240)) = ((X233 @ id @ X240 @ id))) | ~ ! [X241 : term] : ((X234 @ (sub @ X235 @ (push @ X241 @ id))) | ~(X234 @ X241)) | (X234 @ (lam @ X235)) | ~ ! [X242 : subst,X243 : term,X244 : subst,X245 : subst] : ((X233 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244) @ X245) | ~(X233 @ X242 @ X243 @ (comp @ X244 @ X245))) | ~ ! [X246 : (subst > term > term)] : (~ ! [X247 : term] : (~(X233 @ id @ X247 @ id) | (X233 @ id @ (X246 @ id @ X247) @ id)) | (X233 @ id @ (lam @ (X246 @ sh @ one)) @ id) | ~ ! [X248 : term,X249 : subst,X250 : subst] : (((sub @ (X246 @ X250 @ X248) @ X249)) = ((X246 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249))))))) <=> hoasinduction_lem3v2_lthm) & (! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o),X254 : term] : (~(X251 @ X252) | ~ ! [X255 : subst,X256 : subst,X257 : subst,X258 : term] : (~(X253 @ X256 @ X258 @ (comp @ X257 @ X255)) | (X253 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257) @ X255)) | ~ ! [X259 : term,X260 : term] : (~(X253 @ id @ X260 @ id) | ~(X253 @ id @ X259 @ id) | (X253 @ id @ (ap @ (sub @ X260 @ id) @ X259) @ id)) | ~ ! [X261 : term] : (((X253 @ id @ X261 @ id)) = ((X251 @ X261))) | (X251 @ (ap @ X252 @ X254)) | ~ ! [X262 : subst,X263 : term,X264 : subst,X265 : subst] : ((X253 @ X262 @ X263 @ (comp @ X264 @ X265)) | ~(X253 @ (comp @ X262 @ X264) @ (sub @ X263 @ X264) @ X265)) | ~(X251 @ X254)) <=> hoasinduction_lem2v2) & (! [X266 : term] : ~ ! [X267 : (subst > term > term)] : (((sub @ X266 @ (push @ one @ sh))) != ((X267 @ sh @ one))) <=> hoasinduction_lem3b) & hoasinduction_lem1v2 & (hoasapinj1_lthm <=> (! [X268 : term] : (((sub @ X268 @ id)) = X268) => (! [X269 : term,X270 : term,X271 : term,X272 : term] : ((((ap @ X271 @ X269)) != ((ap @ X270 @ X272))) | (X270 = X271)) => ! [X273 : term,X274 : term,X275 : term,X276 : term] : ((((ap @ (sub @ X276 @ id) @ X274)) != ((ap @ (sub @ X275 @ id) @ X273))) | (X275 = X276))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoaslaminj_lthm <=> (! [X277 : subst,X278 : term] : (((sub @ one @ (push @ X278 @ X277))) = X278) => (! [X279 : term,X280 : subst] : (((comp @ sh @ (push @ X279 @ X280))) = X280) => (! [X281 : term,X282 : term] : ((((lam @ X282)) != ((lam @ X281))) | (X281 = X282)) => ! [X283 : subst,X284 : (subst > term > term),X285 : term,X286 : (subst > term > term)] : ((((X286 @ X283 @ X285)) = ((X284 @ X283 @ X285))) | ~ ! [X287 : term,X288 : subst,X289 : subst] : (((sub @ (X286 @ X288 @ X287) @ X289)) = ((X286 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289)))) | (((lam @ (X284 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))) | ~ ! [X290 : term,X291 : subst,X292 : subst] : (((sub @ (X284 @ X291 @ X290) @ X292)) = ((X284 @ (comp @ X291 @ X292) @ (sub @ X290 @ X292))))))))) & pushprop_gthm & (shinj <=> ! [X293 : term,X294 : term] : ((((sub @ X293 @ sh)) != ((sub @ X294 @ sh))) | (X293 = X294))) & (! [X295 : subst] : (((push @ (sub @ one @ X295) @ (comp @ sh @ X295))) = X295) <=> axscons) & hoasinduction_lem3a_gthm & (! [X296 : term,X297 : (subst > term > subst > $o)] : ((X297 @ id @ (lam @ (sub @ X296 @ (push @ one @ sh))) @ id) | ~ ! [X298 : term] : (~(X297 @ id @ X298 @ id) | (X297 @ id @ (sub @ X296 @ (push @ X298 @ id)) @ id)) | ~ ! [X299 : term,X300 : (subst > term > term)] : (~ ! [X301 : term,X302 : subst,X303 : subst] : (((sub @ X299 @ (push @ (sub @ X301 @ X303) @ (comp @ X302 @ X303)))) = ((X300 @ (comp @ X302 @ X303) @ (sub @ X301 @ X303)))) | (X297 @ id @ (lam @ (X300 @ sh @ one)) @ id) | ~ ! [X304 : term] : ((X297 @ id @ (X300 @ id @ X304) @ id) | ~(X297 @ id @ X304 @ id)) | ~ ! [X305 : subst,X306 : subst,X307 : term] : (((sub @ (X300 @ X306 @ X307) @ X305)) = ((sub @ (sub @ X299 @ (push @ X307 @ X306)) @ X305))))) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3v2 <=> ! [X308 : (term > $o),X309 : (subst > term > subst > $o),X310 : term] : ((X308 @ (lam @ X310)) | ~ ! [X311 : (subst > term > term)] : (~ ! [X312 : subst,X313 : term,X314 : subst] : (((sub @ (X311 @ X312 @ X313) @ X314)) = ((X311 @ (comp @ X312 @ X314) @ (sub @ X313 @ X314)))) | (X309 @ id @ (lam @ (X311 @ sh @ one)) @ id) | ~ ! [X315 : term] : ((X309 @ id @ (X311 @ id @ X315) @ id) | ~(X309 @ id @ X315 @ id))) | ~ ! [X316 : term] : (((X309 @ id @ X316 @ id)) = ((X308 @ X316))) | ~ ! [X317 : term,X318 : subst,X319 : subst,X320 : subst] : ((X309 @ X320 @ X317 @ (comp @ X318 @ X319)) | ~(X309 @ (comp @ X320 @ X318) @ (sub @ X317 @ X318) @ X319)) | ~ ! [X321 : term] : (~(X308 @ X321) | (X308 @ (sub @ X310 @ (push @ X321 @ id)))) | ~ ! [X322 : term,X323 : subst,X324 : subst,X325 : subst] : (~(X309 @ X324 @ X322 @ (comp @ X325 @ X323)) | (X309 @ (comp @ X324 @ X325) @ (sub @ X322 @ X325) @ X323)))) & ((! [X326 : (subst > term > subst > $o)] : ~ ! [X327 : (term > $o)] : ~ ! [X328 : term] : (((X327 @ X328)) = ((X326 @ id @ X328 @ id))) => (! [X329 : (term > $o),X330 : term] : (~ ! [X331 : term] : ((X329 @ (lam @ X331)) | ~ ! [X332 : term] : (~(X329 @ X332) | (X329 @ (sub @ X331 @ (push @ X332 @ id))))) | ~ ! [X333 : term] : ((X329 @ X333) | ~(var @ X333)) | ~ ! [X334 : term,X335 : term] : (~(X329 @ X335) | ~(X329 @ X334) | (X329 @ (ap @ X335 @ X334))) | (X329 @ X330)) => (! [X336 : term] : (((sub @ X336 @ id)) = X336) => (! [X337 : (term > $o),X338 : term,X339 : (subst > term > subst > $o)] : ((X337 @ (lam @ X338)) | ~ ! [X340 : term] : (((X337 @ X340)) = ((X339 @ id @ X340 @ id))) | ~ ! [X341 : term] : ((X337 @ (sub @ X338 @ (push @ X341 @ id))) | ~(X337 @ X341)) | ~ ! [X342 : (subst > term > term)] : (~ ! [X343 : subst,X344 : term,X345 : subst] : (((sub @ (X342 @ X343 @ X344) @ X345)) = ((X342 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345)))) | (X339 @ id @ (lam @ (X342 @ sh @ one)) @ id) | ~ ! [X346 : term] : ((X339 @ id @ (X342 @ id @ X346) @ id) | ~(X339 @ id @ X346 @ id)))) => ! [X347 : (subst > term > subst > $o),X348 : term] : (~ ! [X349 : term,X350 : term] : ((X347 @ id @ (ap @ (sub @ X349 @ id) @ X350) @ id) | ~(X347 @ id @ X350 @ id) | ~(X347 @ id @ X349 @ id)) | (X347 @ id @ X348 @ id) | ~ ! [X351 : subst,X352 : term,X353 : subst,X354 : subst] : (~(X347 @ (comp @ X354 @ X351) @ (sub @ X352 @ X351) @ X353) | (X347 @ X354 @ X352 @ (comp @ X351 @ X353))) | ~ ! [X355 : (subst > term > term)] : (~ ! [X356 : subst,X357 : term,X358 : subst] : (((sub @ (X355 @ X358 @ X357) @ X356)) = ((X355 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356)))) | ~ ! [X359 : term] : (~(X347 @ id @ X359 @ id) | (X347 @ id @ (X355 @ id @ X359) @ id)) | (X347 @ id @ (lam @ (X355 @ sh @ one)) @ id)) | ~ ! [X360 : subst,X361 : term,X362 : subst,X363 : subst] : ((X347 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362) | ~(X347 @ X363 @ X361 @ (comp @ X360 @ X362))) | ~ ! [X364 : term] : (~(var @ (sub @ X364 @ id)) | (X347 @ id @ X364 @ id))))))) <=> hoasinduction_lthm_3) & hoasinduction_lem1v2_gthm & (pushprop_p_and_p_prime = (^[X365 : term, X366 : subst, X367 : (term > $o), X368 : (term > $o)] : (! [X369 : term] : (((X368 @ X369)) = ((X367 @ (sub @ X369 @ (push @ X365 @ X366)))))))) & pushprop_lthm & (sh = ((d2subst @ d_id))) & axmap & (! [X370 : (term > $o),X371 : (subst > term > subst > $o),X372 : term] : (~ ! [X373 : term] : ((X370 @ (sub @ X372 @ (push @ X373 @ id))) | ~(X370 @ X373)) | ~ ! [X374 : term] : (((X371 @ id @ X374 @ id)) = ((X370 @ X374))) | (X370 @ (lam @ X372)) | ~ ! [X375 : (subst > term > term)] : ((X371 @ id @ (lam @ (X375 @ sh @ one)) @ id) | ~ ! [X376 : term] : ((X371 @ id @ (X375 @ id @ X376) @ id) | ~(X371 @ id @ X376 @ id)) | ~ ! [X377 : term,X378 : subst,X379 : subst] : (((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))) = ((sub @ (X375 @ X378 @ X377) @ X379))))) <=> hoasinduction_lem3v2a) & hoaslamnotap_gthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X380 : term,X381 : (subst > term > subst > $o),X382 : term] : (~(X381 @ id @ X382 @ id) | ~ ! [X383 : term,X384 : subst,X385 : subst,X386 : subst] : ((X381 @ X385 @ X383 @ (comp @ X386 @ X384)) | ~(X381 @ (comp @ X385 @ X386) @ (sub @ X383 @ X386) @ X384)) | ~ ! [X387 : term,X388 : term] : (~(X381 @ id @ X387 @ id) | ~(X381 @ id @ X388 @ id) | (X381 @ id @ (ap @ (sub @ X387 @ id) @ X388) @ id)) | (X381 @ id @ (ap @ X382 @ X380) @ id) | ~ ! [X389 : term,X390 : subst,X391 : subst,X392 : subst] : (~(X381 @ X392 @ X389 @ (comp @ X391 @ X390)) | (X381 @ (comp @ X392 @ X391) @ (sub @ X389 @ X391) @ X390)) | ~(X381 @ id @ X380 @ id)) <=> hoasinduction_lem2) & hoasinduction_gthm & hoasapnotvar_lthm & ~lamnotap & (axvarcons <=> ! [X393 : subst,X394 : term] : (((sub @ one @ (push @ X394 @ X393))) = X394)) & hoaslamnotap_lthm & hoaslamnotvar & (induction2_lthm <=> (! [X395 : term] : (((sub @ X395 @ id)) = X395) => (! [X396 : term,X397 : subst,X398 : (term > $o)] : (~ ! [X399 : term] : ((X398 @ (lam @ X399)) | ~ ! [X400 : term] : ((X398 @ (sub @ X399 @ (push @ X400 @ id))) | ~(X398 @ X400))) | ~ ! [X401 : term] : (~(var @ X401) | (X398 @ (sub @ X401 @ X397))) | (X398 @ (sub @ X396 @ X397)) | ~ ! [X402 : term,X403 : term] : ((X398 @ (ap @ X402 @ X403)) | ~(X398 @ X402) | ~(X398 @ X403))) => ! [X404 : term,X405 : (term > $o)] : (~ ! [X406 : term] : (~ ! [X407 : term] : (~(X405 @ X407) | (X405 @ (sub @ X406 @ (push @ X407 @ id)))) | (X405 @ (lam @ X406))) | ~ ! [X408 : term] : ((X405 @ X408) | ~(var @ X408)) | ~ ! [X409 : term,X410 : term] : (~(X405 @ X409) | ~(X405 @ X410) | (X405 @ (ap @ X410 @ X409))) | (X405 @ X404))))) & (! [X411 : term,X412 : (subst > term > term),X413 : subst,X414 : (subst > term > term)] : (~ ! [X415 : subst,X416 : subst,X417 : term] : (((X412 @ (comp @ X415 @ X416) @ (sub @ X417 @ X416))) = ((sub @ (X412 @ X415 @ X417) @ X416))) | (((lam @ (X412 @ sh @ one))) != ((lam @ (X414 @ sh @ one)))) | ~ ! [X418 : term,X419 : subst,X420 : subst] : (((sub @ (X414 @ X419 @ X418) @ X420)) = ((X414 @ (comp @ X419 @ X420) @ (sub @ X418 @ X420)))) | (((X414 @ X413 @ X411)) = ((X412 @ X413 @ X411)))) <=> hoaslaminj) & (pushprop_lem1v2 <=> ! [X421 : term,X422 : (term > $o),X423 : subst,X424 : (term > $o)] : (~ ! [X425 : term] : (((X424 @ X425)) = ((X422 @ (sub @ X425 @ (push @ X421 @ X423))))) | ~(X422 @ X421) | (X424 @ one))) & axclos & (hoasinduction <=> ! [X426 : term,X427 : (subst > term > subst > $o)] : (~ ! [X428 : term,X429 : subst,X430 : subst,X431 : subst] : ((X427 @ (comp @ X431 @ X430) @ (sub @ X428 @ X430) @ X429) | ~(X427 @ X431 @ X428 @ (comp @ X430 @ X429))) | ~ ! [X432 : term] : (~(var @ (sub @ X432 @ id)) | (X427 @ id @ X432 @ id)) | (X427 @ id @ X426 @ id) | ~ ! [X433 : term,X434 : term] : ((X427 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) | ~(X427 @ id @ X434 @ id) | ~(X427 @ id @ X433 @ id)) | ~ ! [X435 : subst,X436 : subst,X437 : term,X438 : subst] : ((X427 @ X435 @ X437 @ (comp @ X438 @ X436)) | ~(X427 @ (comp @ X435 @ X438) @ (sub @ X437 @ X438) @ X436)) | ~ ! [X439 : (subst > term > term)] : ((X427 @ id @ (lam @ (X439 @ sh @ one)) @ id) | ~ ! [X440 : term] : (~(X427 @ id @ X440 @ id) | (X427 @ id @ (X439 @ id @ X440) @ id)) | ~ ! [X441 : term,X442 : subst,X443 : subst] : (((X439 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443))) = ((sub @ (X439 @ X442 @ X441) @ X443)))))) & hoasinduction_lem1_lthm & hoaslamnotvar_gthm & pushprop_lem2v2_lthm & (! [X444 : subst,X445 : (term > $o),X446 : term] : ~ ! [X447 : (term > $o)] : ~ ! [X448 : term] : (((X447 @ X448)) = ((X445 @ (sub @ X448 @ (push @ X446 @ X444))))) <=> pushprop_lem0_lthm) & (hoasinduction_lem3b_lthm <=> ! [X449 : term] : ~ ! [X450 : (subst > term > term)] : (((X450 @ sh @ one)) != ((sub @ X449 @ (push @ one @ sh))))) & ! [X451 : d_term] : (d_one = X451) & hoasapnotvar & (! [X452 : (subst > term > subst > $o)] : ~ ! [X453 : (term > $o)] : ~ ! [X454 : term] : (((X453 @ X454)) = ((X452 @ id @ X454 @ id))) <=> hoasinduction_lem0_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X455 : term] : ~ ! [X456 : (subst > term > term)] : ~ ! [X457 : term,X458 : subst] : (((X456 @ X458 @ X457)) = ((sub @ X455 @ (push @ X457 @ X458))))) & pushprop_lem2v2 & (hoasinduction_lem3 <=> ! [X459 : term,X460 : (subst > term > subst > $o)] : (~ ! [X461 : subst,X462 : subst,X463 : term,X464 : subst] : ((X460 @ X461 @ X463 @ (comp @ X464 @ X462)) | ~(X460 @ (comp @ X461 @ X464) @ (sub @ X463 @ X464) @ X462)) | ~ ! [X465 : term] : ((X460 @ id @ (sub @ X459 @ (push @ X465 @ id)) @ id) | ~(X460 @ id @ X465 @ id)) | ~ ! [X466 : (subst > term > term)] : (~ ! [X467 : term] : ((X460 @ id @ (X466 @ id @ X467) @ id) | ~(X460 @ id @ X467 @ id)) | ~ ! [X468 : subst,X469 : term,X470 : subst] : (((sub @ (X466 @ X468 @ X469) @ X470)) = ((X466 @ (comp @ X468 @ X470) @ (sub @ X469 @ X470)))) | (X460 @ id @ (lam @ (X466 @ sh @ one)) @ id)) | (X460 @ id @ (lam @ X459) @ id) | ~ ! [X471 : subst,X472 : subst,X473 : subst,X474 : term] : ((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473) | ~(X460 @ X471 @ X474 @ (comp @ X472 @ X473))))) & (axvarid <=> ! [X475 : term] : (((sub @ X475 @ id)) = X475)) & ((^[X476 : subst, X477 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (induction2lem_lthm <=> (! [X478 : term,X479 : subst] : (((sub @ one @ (push @ X478 @ X479))) = X478) => (! [X480 : subst,X481 : term] : (((comp @ sh @ (push @ X481 @ X480))) = X480) => (! [X482 : subst] : (((comp @ X482 @ id)) = X482) => (! [X483 : term,X484 : (term > $o)] : (~ ! [X485 : term,X486 : term] : (~(X484 @ X485) | ~(X484 @ X486) | (X484 @ (ap @ X486 @ X485))) | (X484 @ X483) | ~ ! [X487 : term] : ((X484 @ (lam @ X487)) | ~(X484 @ X487)) | ~ ! [X488 : term] : (~(var @ X488) | (X484 @ X488))) => ! [X489 : term,X490 : subst,X491 : (term > $o)] : (~ ! [X492 : term] : ((X491 @ (sub @ X492 @ X490)) | ~(var @ X492)) | (X491 @ (sub @ X489 @ X490)) | ~ ! [X493 : term] : ((X491 @ (lam @ X493)) | ~ ! [X494 : term] : ((X491 @ (sub @ X493 @ (push @ X494 @ id))) | ~(X491 @ X494))) | ~ ! [X495 : term,X496 : term] : (~(X491 @ X496) | ~(X491 @ X495) | (X491 @ (ap @ X496 @ X495))))))))) & ((! [X497 : term,X498 : term,X499 : term,X500 : term] : ((X497 = X500) | (((ap @ X499 @ X500)) != ((ap @ X498 @ X497)))) => ! [X501 : term,X502 : term,X503 : term,X504 : term] : ((X501 = X503) | (((ap @ (sub @ X504 @ id) @ X503)) != ((ap @ (sub @ X502 @ id) @ X501))))) <=> hoasapinj2_lthm) & hoasapinj1_gthm & hoasinduction_lem3b_gthm & ~ulamvar1 & hoaslamnotvar_lthm & ~(var @ (d2term @ d_one)) & axapp & (! [X505 : term,X506 : (subst > term > subst > $o)] : ((X506 @ id @ X505 @ id) | ~ ! [X507 : term,X508 : term] : (~(X506 @ id @ X508 @ id) | ~(X506 @ id @ X507 @ id) | (X506 @ id @ (ap @ (sub @ X508 @ id) @ X507) @ id)) | ~ ! [X509 : (subst > term > term)] : (~ ! [X510 : subst,X511 : subst,X512 : term] : (((X509 @ (comp @ X510 @ X511) @ (sub @ X512 @ X511))) = ((sub @ (X509 @ X510 @ X512) @ X511))) | ~ ! [X513 : term] : ((X506 @ id @ (X509 @ id @ X513) @ id) | ~(X506 @ id @ X513 @ id)) | (X506 @ id @ (lam @ (X509 @ sh @ one)) @ id))) <=> hoasinduction_no_psi_cond) & (apinj1 <=> ! [X514 : term,X515 : term,X516 : term,X517 : term] : ((((ap @ X515 @ X516)) != ((ap @ X517 @ X514))) | (X515 = X517))) & (hoasapinj2 <=> ! [X518 : term,X519 : term,X520 : term,X521 : term] : ((((ap @ (sub @ X521 @ id) @ X519)) != ((ap @ (sub @ X520 @ id) @ X518))) | (X518 = X519))) & pushprop & (! [X522 : (term > $o),X523 : term] : (~ ! [X524 : term] : (~(X522 @ X524) | (X522 @ (lam @ X524))) | ~ ! [X525 : term] : (~(var @ X525) | (X522 @ X525)) | (X522 @ X523) | ~ ! [X526 : term,X527 : term] : (~(X522 @ X527) | (X522 @ (ap @ X526 @ X527)) | ~(X522 @ X526))) <=> induction) & (hoasinduction_lem3a <=> ! [X528 : (subst > term > subst > $o),X529 : term] : ((X528 @ id @ (lam @ X529) @ id) | ~ ! [X530 : (subst > term > term)] : (~ ! [X531 : term] : (~(X528 @ id @ X531 @ id) | (X528 @ id @ (X530 @ id @ X531) @ id)) | (X528 @ id @ (lam @ (X530 @ sh @ one)) @ id) | ~ ! [X532 : subst,X533 : subst,X534 : term] : (((X530 @ (comp @ X532 @ X533) @ (sub @ X534 @ X533))) = ((sub @ (X530 @ X532 @ X534) @ X533)))) | ~ ! [X535 : term] : ((X528 @ id @ (sub @ X529 @ (push @ X535 @ id)) @ id) | ~(X528 @ id @ X535 @ id)))) & (termmset_lthm <=> (! [X536 : term] : (((sub @ X536 @ id)) = X536) => ! [X537 : term] : (((sub @ X537 @ id)) = X537))) & ! [X538 : subst] : ? [X539 : d_subst] : (((d2subst @ X539)) = X538) & ulamvarind & (hoasapinj1 <=> ! [X540 : term,X541 : term,X542 : term,X543 : term] : ((((ap @ (sub @ X541 @ id) @ X543)) != ((ap @ (sub @ X540 @ id) @ X542))) | (X540 = X541))) & (apinj2 <=> ! [X544 : term,X545 : term,X546 : term,X547 : term] : ((((ap @ X546 @ X547)) != ((ap @ X545 @ X544))) | (X544 = X547))) & termmset_gthm & ! [X548 : d_term,X549 : d_term] : ((((d2term @ X548)) = ((d2term @ X549))) => (X548 = X549)) & pushprop_lem3v2_lthm), 26.09/4.24 inference(rectify,[],[f1])). 26.09/4.24 thf(f7,plain,( 26.09/4.24 (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X0 : term] : ~ ! [X1 : (subst > term > term)] : ~ ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2))))) & ((induction2 = $true) <=> ! [X4 : (term > $o),X5 : term] : (($true = ((X4 @ X5))) | ~ ! [X6 : term,X7 : term] : (~ ($true = ((X4 @ X6))) | (((X4 @ (ap @ X6 @ X7))) = $true) | ~ ($true = ((X4 @ X7)))) | ~ ! [X8 : term] : ((((X4 @ X8)) = $true) | ~ (((var @ X8)) = $true)) | ~ ! [X9 : term] : (~ ! [X10 : term] : (~ (((X4 @ X10)) = $true) | ($true = ((X4 @ (sub @ X9 @ (push @ X10 @ id)))))) | ($true = ((X4 @ (lam @ X9))))))) & (hoasinduction_lem2v2_gthm = $true) & ((! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X14 : term] : (~ ($true = ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X15 : (subst > term > term)] : (~ ! [X18 : subst,X16 : term,X17 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) = ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ~ ! [X19 : term] : (~ ($true = ((X12 @ id @ X19 @ id))) | ($true = ((X12 @ id @ (X15 @ id @ X19) @ id)))))) => ! [X20 : term,X21 : (subst > term > subst > $o)] : (~ ! [X22 : term] : (($true = ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id))) | ~ ($true = ((X21 @ id @ X22 @ id)))) | ($true = ((X21 @ id @ (lam @ X20) @ id))) | ~ ! [X23 : term,X24 : subst,X25 : subst,X26 : subst] : (~ (((X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25)) = $true) | ($true = ((X21 @ X26 @ X23 @ (comp @ X24 @ X25))))) | ~ ! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : ((((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30)) = $true) | ~ (((X21 @ X27 @ X28 @ (comp @ X29 @ X30))) = $true)) | ~ ! [X31 : (subst > term > term)] : (~ ! [X32 : term] : (($true = ((X21 @ id @ (X31 @ id @ X32) @ id))) | ~ (((X21 @ id @ X32 @ id)) = $true)) | ~ ! [X34 : term,X33 : subst,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35)))) | (((X21 @ id @ (lam @ (X31 @ sh @ one)) @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) <=> (axshiftcons = $true)) & (induction2_gthm = $true) & (hoaslaminj_gthm = $true) & ! [X38 : d_subst] : (d_id = X38) & ((pushprop_lem1v2_lthm = $true) <=> (! [X40 : term,X39 : subst] : (((sub @ one @ (push @ X40 @ X39))) = X40) => ! [X41 : (term > $o),X42 : term,X43 : (term > $o),X44 : subst] : (~ ! [X45 : term] : (((X41 @ X45)) = ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true) | ~ (((X43 @ X42)) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X47 : subst,X46 : term] : (((sub @ one @ (push @ X46 @ X47))) = X46) => (! [X48 : term,X49 : subst] : (((comp @ sh @ (push @ X48 @ X49))) = X49) => ! [X50 : subst,X51 : term,X52 : (term > $o),X53 : term,X54 : (term > $o)] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ~ ($true = ((X52 @ X51))))))) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> (termmset = $true)) & (hoasapinj2_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1 = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ((pushprop_lem1 = $true) <=> ! [X56 : term,X57 : (term > $o),X58 : term,X59 : (term > $o),X60 : subst] : (~ ($true = ((X59 @ X58))) | ($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))))) & (! [X61 : (subst > term > subst > $o)] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2 = $true) & ((! [X64 : subst] : (((comp @ id @ X64)) = X64) => (! [X65 : subst] : (((comp @ X65 @ id)) = X65) => (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)))) <=> (substmonoid_lthm = $true)) & ((! [X68 : term] : ~ ! [X69 : (subst > term > term)] : ~ ! [X71 : subst,X70 : term] : (((X69 @ X71 @ X70)) = ((sub @ X68 @ (push @ X70 @ X71)))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => ! [X73 : (term > $o),X74 : (subst > term > subst > $o),X75 : term] : (~ ! [X76 : (subst > term > term)] : (~ ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) | ($true = ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) | ~ ! [X80 : term] : (~ ($true = ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id))))) | ~ ! [X81 : term] : (~ ($true = ((X73 @ X81))) | ($true = ((X73 @ (sub @ X75 @ (push @ X81 @ id)))))) | ($true = ((X73 @ (lam @ X75)))) | ~ ! [X82 : term] : (((X74 @ id @ X82 @ id)) = ((X73 @ X82)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X83 : term,X84 : (subst > term > subst > $o)] : (~ ! [X85 : term] : (($true = ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) | ~ (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ~ ! [X86 : (subst > term > term)] : (~ ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))) | ~ ! [X90 : term] : ((((X84 @ id @ (X86 @ id @ X90) @ id)) = $true) | ~ (((X84 @ id @ X90 @ id)) = $true)) | (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true)))) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) <=> (substmonoid = $true)) & (ulamvarsh = $true) & ((hoasinduction_lthm = $true) <=> (! [X93 : (term > $o),X94 : term] : (~ ! [X95 : term] : (($true = ((X93 @ (lam @ X95)))) | ~ ! [X96 : term] : ((((X93 @ (sub @ X95 @ (push @ X96 @ id)))) = $true) | ~ ($true = ((X93 @ X96))))) | ($true = ((X93 @ X94))) | ~ ! [X97 : term] : (($true = ((X93 @ X97))) | ~ (((var @ X97)) = $true)) | ~ ! [X98 : term,X99 : term] : (~ (((X93 @ X98)) = $true) | ($true = ((X93 @ (ap @ X98 @ X99)))) | ~ ($true = ((X93 @ X99))))) => (! [X100 : term,X101 : (subst > term > subst > $o),X102 : term] : (~ (((X101 @ id @ X102 @ id)) = $true) | ~ (((X101 @ id @ X100 @ id)) = $true) | ~ ! [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (($true = ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)))) | ~ ($true = ((X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)))) | ($true = ((X101 @ id @ (ap @ X102 @ X100) @ id))) | ~ ! [X107 : subst,X108 : subst,X109 : subst,X110 : term] : (($true = ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108))) | ~ (((X101 @ X107 @ X110 @ (comp @ X109 @ X108))) = $true)) | ~ ! [X111 : term,X112 : term] : (~ (((X101 @ id @ X112 @ id)) = $true) | ~ ($true = ((X101 @ id @ X111 @ id))) | ($true = ((X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id))))) => (! [X113 : (subst > term > subst > $o),X114 : term] : (~ ! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ~ ($true = ((X113 @ id @ X115 @ id)))) | ~ ! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ~ ($true = ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ($true = ((X113 @ id @ (lam @ X114) @ id))) | ~ ! [X120 : (subst > term > term)] : (~ ! [X122 : subst,X123 : subst,X121 : term] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X120 @ X123 @ X121) @ X122))) | ($true = ((X113 @ id @ (lam @ (X120 @ sh @ one)) @ id))) | ~ ! [X124 : term] : (~ (((X113 @ id @ X124 @ id)) = $true) | ($true = ((X113 @ id @ (X120 @ id @ X124) @ id))))) | ~ ! [X125 : subst,X126 : term,X127 : subst,X128 : subst] : ((((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true) | ~ ($true = ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))))) => ! [X129 : (subst > term > subst > $o),X130 : term] : ((((X129 @ id @ X130 @ id)) = $true) | ~ ! [X131 : term,X132 : term] : (($true = ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id))) | ~ ($true = ((X129 @ id @ X132 @ id))) | ~ ($true = ((X129 @ id @ X131 @ id)))) | ~ ! [X133 : (subst > term > term)] : (($true = ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id))) | ~ ! [X134 : term] : (($true = ((X129 @ id @ (X133 @ id @ X134) @ id))) | ~ (((X129 @ id @ X134 @ id)) = $true)) | ~ ! [X136 : subst,X135 : term,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137)))) | ~ ! [X138 : term,X139 : subst,X140 : subst,X141 : subst] : (~ ($true = ((X129 @ X141 @ X138 @ (comp @ X140 @ X139)))) | (((X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) = $true)) | ~ ! [X142 : term] : ((((X129 @ id @ X142 @ id)) = $true) | ~ (((var @ (sub @ X142 @ id))) = $true)) | ~ ! [X143 : subst,X144 : term,X145 : subst,X146 : subst] : ((((X129 @ X145 @ X144 @ (comp @ X143 @ X146))) = $true) | ~ ($true = ((X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146))))))))) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X147 : term,X148 : (subst > term > subst > $o)] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ~ ! [X149 : (subst > term > term)] : (~ ! [X150 : term] : (~ ($true = ((X148 @ id @ X150 @ id))) | ($true = ((X148 @ id @ (X149 @ id @ X150) @ id)))) | (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) = $true) | ~ ! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152)))) | ~ ! [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) = $true) | ~ ($true = ((X148 @ id @ X154 @ id))))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem = $true) <=> ! [X155 : term,X156 : subst,X157 : (term > $o)] : (~ ! [X158 : term] : ((((X157 @ (lam @ X158))) = $true) | ~ ! [X159 : term] : (~ ($true = ((X157 @ X159))) | ($true = ((X157 @ (sub @ X158 @ (push @ X159 @ id))))))) | ~ ! [X160 : term,X161 : term] : ((((X157 @ (ap @ X160 @ X161))) = $true) | ~ ($true = ((X157 @ X160))) | ~ (((X157 @ X161)) = $true)) | ~ ! [X162 : term] : (~ ($true = ((var @ X162))) | (((X157 @ (sub @ X162 @ X156))) = $true)) | (((X157 @ (sub @ X155 @ X156))) = $true))) & ((hoaslamnotap = $true) <=> ! [X165 : term,X164 : term,X163 : (subst > term > term)] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ~ ! [X166 : subst,X167 : subst,X168 : term] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X163 @ X166 @ X168) @ X167))))) & (hoasinduction_lem2_lthm = $true) & (axassoc = $true) & ((laminj = $true) <=> ! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170))) & (substmonoid_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : (subst > term > subst > $o),X173 : term] : (~ ! [X174 : (subst > term > term)] : (~ ! [X175 : term] : (~ (((X172 @ id @ X175 @ id)) = $true) | ($true = ((X172 @ id @ (X174 @ id @ X175) @ id)))) | ~ ! [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) = ((sub @ (X174 @ X177 @ X176) @ X178))) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) | ($true = ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id))) | ~ ! [X179 : term] : (($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id))) | ~ (((X172 @ id @ X179 @ id)) = $true))) => ! [X180 : term,X181 : (subst > term > subst > $o)] : (~ ! [X182 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : subst,X183 : term,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) | ~ ! [X186 : term] : (($true = ((X181 @ id @ (X182 @ id @ X186) @ id))) | ~ (((X181 @ id @ X186 @ id)) = $true))) | ~ ! [X187 : term] : ((((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)) = $true) | ~ (((X181 @ id @ X187 @ id)) = $true)) | (((X181 @ id @ (lam @ X180) @ id)) = $true))))) & (pushprop_lem0_gthm = $true) & (axvarshift = $true) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> (axidr = $true)) & ((! [X189 : (subst > term > subst > $o)] : ~ ! [X190 : (term > $o)] : ~ ! [X191 : term] : (((X190 @ X191)) = ((X189 @ id @ X191 @ id))) => (! [X192 : term,X193 : (term > $o)] : ((((X193 @ X192)) = $true) | ~ ! [X194 : term] : ((((X193 @ (lam @ X194))) = $true) | ~ ! [X195 : term] : (($true = ((X193 @ (sub @ X194 @ (push @ X195 @ id))))) | ~ (((X193 @ X195)) = $true))) | ~ ! [X196 : term] : (($true = ((X193 @ X196))) | ~ (((var @ X196)) = $true)) | ~ ! [X197 : term,X198 : term] : ((((X193 @ (ap @ X198 @ X197))) = $true) | ~ (((X193 @ X197)) = $true) | ~ (((X193 @ X198)) = $true))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => (! [X200 : (subst > term > subst > $o),X201 : (term > $o),X202 : term] : (~ ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203))) | ~ ! [X204 : (subst > term > term)] : (($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ~ ! [X206 : subst,X205 : term,X207 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X204 @ X206 @ X205) @ X207))) | ~ ! [X208 : term] : (~ ($true = ((X200 @ id @ X208 @ id))) | ($true = ((X200 @ id @ (X204 @ id @ X208) @ id))))) | (((X201 @ (lam @ X202))) = $true) | ~ ! [X209 : term] : (~ ($true = ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id))))))) => ! [X210 : (subst > term > subst > $o),X211 : term] : (($true = ((X210 @ id @ X211 @ id))) | ~ ! [X212 : term,X213 : term] : (~ ($true = ((X210 @ id @ X212 @ id))) | (((X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id)) = $true) | ~ (((X210 @ id @ X213 @ id)) = $true)) | ~ ! [X214 : (subst > term > term)] : (($true = ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id))) | ~ ! [X215 : term] : ((((X210 @ id @ (X214 @ id @ X215) @ id)) = $true) | ~ (((X210 @ id @ X215 @ id)) = $true)) | ~ ! [X217 : subst,X218 : term,X216 : subst] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X222 : term] : ? [X223 : d_term] : (((d2term @ X223)) = X222) & ((axidl = $true) <=> ! [X224 : subst] : (((comp @ id @ X224)) = X224)) & (pushprop_lthm_orig = $true) & (! [X225 : term,X226 : (term > $o),X227 : subst] : ~ ! [X228 : (term > $o)] : ~ ! [X229 : term] : (((X228 @ X229)) = ((X226 @ (sub @ X229 @ (push @ X225 @ X227))))) <=> (pushprop_lem0 = $true)) & ! [X230 : d_subst,X231 : d_subst] : ((((d2subst @ X230)) = ((d2subst @ X231))) => (X230 = X231)) & (pushprop_lem2v2_gthm = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & ((! [X232 : term] : (((sub @ X232 @ id)) = X232) => ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : (~ ! [X236 : subst,X237 : subst,X238 : subst,X239 : term] : (($true = ((X233 @ X236 @ X239 @ (comp @ X237 @ X238)))) | ~ (((X233 @ (comp @ X236 @ X237) @ (sub @ X239 @ X237) @ X238)) = $true)) | ~ ! [X240 : term] : (((X234 @ X240)) = ((X233 @ id @ X240 @ id))) | ~ ! [X241 : term] : ((((X234 @ (sub @ X235 @ (push @ X241 @ id)))) = $true) | ~ (((X234 @ X241)) = $true)) | (((X234 @ (lam @ X235))) = $true) | ~ ! [X242 : subst,X243 : term,X244 : subst,X245 : subst] : ((((X233 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244) @ X245)) = $true) | ~ ($true = ((X233 @ X242 @ X243 @ (comp @ X244 @ X245))))) | ~ ! [X246 : (subst > term > term)] : (~ ! [X247 : term] : (~ (((X233 @ id @ X247 @ id)) = $true) | (((X233 @ id @ (X246 @ id @ X247) @ id)) = $true)) | (((X233 @ id @ (lam @ (X246 @ sh @ one)) @ id)) = $true) | ~ ! [X248 : term,X249 : subst,X250 : subst] : (((sub @ (X246 @ X250 @ X248) @ X249)) = ((X246 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o),X254 : term] : (~ ($true = ((X251 @ X252))) | ~ ! [X255 : subst,X256 : subst,X257 : subst,X258 : term] : (~ ($true = ((X253 @ X256 @ X258 @ (comp @ X257 @ X255)))) | ($true = ((X253 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257) @ X255)))) | ~ ! [X259 : term,X260 : term] : (~ ($true = ((X253 @ id @ X260 @ id))) | ~ ($true = ((X253 @ id @ X259 @ id))) | ($true = ((X253 @ id @ (ap @ (sub @ X260 @ id) @ X259) @ id)))) | ~ ! [X261 : term] : (((X253 @ id @ X261 @ id)) = ((X251 @ X261))) | (((X251 @ (ap @ X252 @ X254))) = $true) | ~ ! [X262 : subst,X263 : term,X264 : subst,X265 : subst] : ((((X253 @ X262 @ X263 @ (comp @ X264 @ X265))) = $true) | ~ ($true = ((X253 @ (comp @ X262 @ X264) @ (sub @ X263 @ X264) @ X265)))) | ~ (((X251 @ X254)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & (! [X266 : term] : ~ ! [X267 : (subst > term > term)] : (((sub @ X266 @ (push @ one @ sh))) != ((X267 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem1v2 = $true) & ((hoasapinj1_lthm = $true) <=> (! [X268 : term] : (((sub @ X268 @ id)) = X268) => (! [X269 : term,X270 : term,X271 : term,X272 : term] : ((((ap @ X271 @ X269)) != ((ap @ X270 @ X272))) | (X270 = X271)) => ! [X273 : term,X274 : term,X275 : term,X276 : term] : ((((ap @ (sub @ X276 @ id) @ X274)) != ((ap @ (sub @ X275 @ id) @ X273))) | (X275 = X276))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslaminj_lthm = $true) <=> (! [X277 : subst,X278 : term] : (((sub @ one @ (push @ X278 @ X277))) = X278) => (! [X279 : term,X280 : subst] : (((comp @ sh @ (push @ X279 @ X280))) = X280) => (! [X281 : term,X282 : term] : ((((lam @ X282)) != ((lam @ X281))) | (X281 = X282)) => ! [X283 : subst,X284 : (subst > term > term),X285 : term,X286 : (subst > term > term)] : ((((X286 @ X283 @ X285)) = ((X284 @ X283 @ X285))) | ~ ! [X287 : term,X288 : subst,X289 : subst] : (((sub @ (X286 @ X288 @ X287) @ X289)) = ((X286 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289)))) | (((lam @ (X284 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))) | ~ ! [X290 : term,X291 : subst,X292 : subst] : (((sub @ (X284 @ X291 @ X290) @ X292)) = ((X284 @ (comp @ X291 @ X292) @ (sub @ X290 @ X292))))))))) & (pushprop_gthm = $true) & ((shinj = $true) <=> ! [X293 : term,X294 : term] : ((((sub @ X293 @ sh)) != ((sub @ X294 @ sh))) | (X293 = X294))) & (! [X295 : subst] : (((push @ (sub @ one @ X295) @ (comp @ sh @ X295))) = X295) <=> (axscons = $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X296 : term,X297 : (subst > term > subst > $o)] : (($true = ((X297 @ id @ (lam @ (sub @ X296 @ (push @ one @ sh))) @ id))) | ~ ! [X298 : term] : (~ (((X297 @ id @ X298 @ id)) = $true) | (((X297 @ id @ (sub @ X296 @ (push @ X298 @ id)) @ id)) = $true)) | ~ ! [X299 : term,X300 : (subst > term > term)] : (~ ! [X301 : term,X302 : subst,X303 : subst] : (((sub @ X299 @ (push @ (sub @ X301 @ X303) @ (comp @ X302 @ X303)))) = ((X300 @ (comp @ X302 @ X303) @ (sub @ X301 @ X303)))) | (((X297 @ id @ (lam @ (X300 @ sh @ one)) @ id)) = $true) | ~ ! [X304 : term] : (($true = ((X297 @ id @ (X300 @ id @ X304) @ id))) | ~ (((X297 @ id @ X304 @ id)) = $true)) | ~ ! [X305 : subst,X306 : subst,X307 : term] : (((sub @ (X300 @ X306 @ X307) @ X305)) = ((sub @ (sub @ X299 @ (push @ X307 @ X306)) @ X305))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X308 : (term > $o),X309 : (subst > term > subst > $o),X310 : term] : (($true = ((X308 @ (lam @ X310)))) | ~ ! [X311 : (subst > term > term)] : (~ ! [X312 : subst,X313 : term,X314 : subst] : (((sub @ (X311 @ X312 @ X313) @ X314)) = ((X311 @ (comp @ X312 @ X314) @ (sub @ X313 @ X314)))) | ($true = ((X309 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ~ ! [X315 : term] : (($true = ((X309 @ id @ (X311 @ id @ X315) @ id))) | ~ (((X309 @ id @ X315 @ id)) = $true))) | ~ ! [X316 : term] : (((X309 @ id @ X316 @ id)) = ((X308 @ X316))) | ~ ! [X317 : term,X318 : subst,X319 : subst,X320 : subst] : (($true = ((X309 @ X320 @ X317 @ (comp @ X318 @ X319)))) | ~ ($true = ((X309 @ (comp @ X320 @ X318) @ (sub @ X317 @ X318) @ X319)))) | ~ ! [X321 : term] : (~ ($true = ((X308 @ X321))) | (((X308 @ (sub @ X310 @ (push @ X321 @ id)))) = $true)) | ~ ! [X322 : term,X323 : subst,X324 : subst,X325 : subst] : (~ ($true = ((X309 @ X324 @ X322 @ (comp @ X325 @ X323)))) | ($true = ((X309 @ (comp @ X324 @ X325) @ (sub @ X322 @ X325) @ X323)))))) & ((! [X326 : (subst > term > subst > $o)] : ~ ! [X327 : (term > $o)] : ~ ! [X328 : term] : (((X327 @ X328)) = ((X326 @ id @ X328 @ id))) => (! [X329 : (term > $o),X330 : term] : (~ ! [X331 : term] : ((((X329 @ (lam @ X331))) = $true) | ~ ! [X332 : term] : (~ ($true = ((X329 @ X332))) | (((X329 @ (sub @ X331 @ (push @ X332 @ id)))) = $true))) | ~ ! [X333 : term] : ((((X329 @ X333)) = $true) | ~ ($true = ((var @ X333)))) | ~ ! [X334 : term,X335 : term] : (~ ($true = ((X329 @ X335))) | ~ ($true = ((X329 @ X334))) | ($true = ((X329 @ (ap @ X335 @ X334))))) | (((X329 @ X330)) = $true)) => (! [X336 : term] : (((sub @ X336 @ id)) = X336) => (! [X337 : (term > $o),X338 : term,X339 : (subst > term > subst > $o)] : ((((X337 @ (lam @ X338))) = $true) | ~ ! [X340 : term] : (((X337 @ X340)) = ((X339 @ id @ X340 @ id))) | ~ ! [X341 : term] : ((((X337 @ (sub @ X338 @ (push @ X341 @ id)))) = $true) | ~ ($true = ((X337 @ X341)))) | ~ ! [X342 : (subst > term > term)] : (~ ! [X343 : subst,X344 : term,X345 : subst] : (((sub @ (X342 @ X343 @ X344) @ X345)) = ((X342 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345)))) | (((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id)) = $true) | ~ ! [X346 : term] : ((((X339 @ id @ (X342 @ id @ X346) @ id)) = $true) | ~ ($true = ((X339 @ id @ X346 @ id)))))) => ! [X347 : (subst > term > subst > $o),X348 : term] : (~ ! [X349 : term,X350 : term] : ((((X347 @ id @ (ap @ (sub @ X349 @ id) @ X350) @ id)) = $true) | ~ ($true = ((X347 @ id @ X350 @ id))) | ~ ($true = ((X347 @ id @ X349 @ id)))) | ($true = ((X347 @ id @ X348 @ id))) | ~ ! [X351 : subst,X352 : term,X353 : subst,X354 : subst] : (~ (((X347 @ (comp @ X354 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true) | ($true = ((X347 @ X354 @ X352 @ (comp @ X351 @ X353))))) | ~ ! [X355 : (subst > term > term)] : (~ ! [X356 : subst,X357 : term,X358 : subst] : (((sub @ (X355 @ X358 @ X357) @ X356)) = ((X355 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356)))) | ~ ! [X359 : term] : (~ (((X347 @ id @ X359 @ id)) = $true) | (((X347 @ id @ (X355 @ id @ X359) @ id)) = $true)) | (((X347 @ id @ (lam @ (X355 @ sh @ one)) @ id)) = $true)) | ~ ! [X360 : subst,X361 : term,X362 : subst,X363 : subst] : ((((X347 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362)) = $true) | ~ ($true = ((X347 @ X363 @ X361 @ (comp @ X360 @ X362))))) | ~ ! [X364 : term] : (~ (((var @ (sub @ X364 @ id))) = $true) | (((X347 @ id @ X364 @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = sh) & (axmap = $true) & (! [X370 : (term > $o),X371 : (subst > term > subst > $o),X372 : term] : (~ ! [X373 : term] : ((((X370 @ (sub @ X372 @ (push @ X373 @ id)))) = $true) | ~ ($true = ((X370 @ X373)))) | ~ ! [X374 : term] : (((X371 @ id @ X374 @ id)) = ((X370 @ X374))) | (((X370 @ (lam @ X372))) = $true) | ~ ! [X375 : (subst > term > term)] : (($true = ((X371 @ id @ (lam @ (X375 @ sh @ one)) @ id))) | ~ ! [X376 : term] : (($true = ((X371 @ id @ (X375 @ id @ X376) @ id))) | ~ ($true = ((X371 @ id @ X376 @ id)))) | ~ ! [X377 : term,X378 : subst,X379 : subst] : (((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))) = ((sub @ (X375 @ X378 @ X377) @ X379))))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X380 : term,X381 : (subst > term > subst > $o),X382 : term] : (~ (((X381 @ id @ X382 @ id)) = $true) | ~ ! [X383 : term,X384 : subst,X385 : subst,X386 : subst] : (($true = ((X381 @ X385 @ X383 @ (comp @ X386 @ X384)))) | ~ (((X381 @ (comp @ X385 @ X386) @ (sub @ X383 @ X386) @ X384)) = $true)) | ~ ! [X387 : term,X388 : term] : (~ (((X381 @ id @ X387 @ id)) = $true) | ~ ($true = ((X381 @ id @ X388 @ id))) | ($true = ((X381 @ id @ (ap @ (sub @ X387 @ id) @ X388) @ id)))) | ($true = ((X381 @ id @ (ap @ X382 @ X380) @ id))) | ~ ! [X389 : term,X390 : subst,X391 : subst,X392 : subst] : (~ ($true = ((X381 @ X392 @ X389 @ (comp @ X391 @ X390)))) | (((X381 @ (comp @ X392 @ X391) @ (sub @ X389 @ X391) @ X390)) = $true)) | ~ (((X381 @ id @ X380 @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & ~ (lamnotap = $true) & ((axvarcons = $true) <=> ! [X393 : subst,X394 : term] : (((sub @ one @ (push @ X394 @ X393))) = X394)) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar = $true) & ((induction2_lthm = $true) <=> (! [X395 : term] : (((sub @ X395 @ id)) = X395) => (! [X396 : term,X397 : subst,X398 : (term > $o)] : (~ ! [X399 : term] : (($true = ((X398 @ (lam @ X399)))) | ~ ! [X400 : term] : ((((X398 @ (sub @ X399 @ (push @ X400 @ id)))) = $true) | ~ (((X398 @ X400)) = $true))) | ~ ! [X401 : term] : (~ (((var @ X401)) = $true) | ($true = ((X398 @ (sub @ X401 @ X397))))) | ($true = ((X398 @ (sub @ X396 @ X397)))) | ~ ! [X402 : term,X403 : term] : (($true = ((X398 @ (ap @ X402 @ X403)))) | ~ (((X398 @ X402)) = $true) | ~ ($true = ((X398 @ X403))))) => ! [X404 : term,X405 : (term > $o)] : (~ ! [X406 : term] : (~ ! [X407 : term] : (~ (((X405 @ X407)) = $true) | (((X405 @ (sub @ X406 @ (push @ X407 @ id)))) = $true)) | ($true = ((X405 @ (lam @ X406))))) | ~ ! [X408 : term] : ((((X405 @ X408)) = $true) | ~ (((var @ X408)) = $true)) | ~ ! [X409 : term,X410 : term] : (~ (((X405 @ X409)) = $true) | ~ ($true = ((X405 @ X410))) | (((X405 @ (ap @ X410 @ X409))) = $true)) | ($true = ((X405 @ X404))))))) & (! [X411 : term,X412 : (subst > term > term),X413 : subst,X414 : (subst > term > term)] : (~ ! [X415 : subst,X416 : subst,X417 : term] : (((X412 @ (comp @ X415 @ X416) @ (sub @ X417 @ X416))) = ((sub @ (X412 @ X415 @ X417) @ X416))) | (((lam @ (X412 @ sh @ one))) != ((lam @ (X414 @ sh @ one)))) | ~ ! [X418 : term,X419 : subst,X420 : subst] : (((sub @ (X414 @ X419 @ X418) @ X420)) = ((X414 @ (comp @ X419 @ X420) @ (sub @ X418 @ X420)))) | (((X414 @ X413 @ X411)) = ((X412 @ X413 @ X411)))) <=> (hoaslaminj = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X421 : term,X422 : (term > $o),X423 : subst,X424 : (term > $o)] : (~ ! [X425 : term] : (((X424 @ X425)) = ((X422 @ (sub @ X425 @ (push @ X421 @ X423))))) | ~ ($true = ((X422 @ X421))) | ($true = ((X424 @ one))))) & (axclos = $true) & ((hoasinduction = $true) <=> ! [X426 : term,X427 : (subst > term > subst > $o)] : (~ ! [X428 : term,X429 : subst,X430 : subst,X431 : subst] : ((((X427 @ (comp @ X431 @ X430) @ (sub @ X428 @ X430) @ X429)) = $true) | ~ ($true = ((X427 @ X431 @ X428 @ (comp @ X430 @ X429))))) | ~ ! [X432 : term] : (~ ($true = ((var @ (sub @ X432 @ id)))) | (((X427 @ id @ X432 @ id)) = $true)) | (((X427 @ id @ X426 @ id)) = $true) | ~ ! [X433 : term,X434 : term] : (($true = ((X427 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id))) | ~ ($true = ((X427 @ id @ X434 @ id))) | ~ ($true = ((X427 @ id @ X433 @ id)))) | ~ ! [X435 : subst,X436 : subst,X437 : term,X438 : subst] : ((((X427 @ X435 @ X437 @ (comp @ X438 @ X436))) = $true) | ~ (((X427 @ (comp @ X435 @ X438) @ (sub @ X437 @ X438) @ X436)) = $true)) | ~ ! [X439 : (subst > term > term)] : (($true = ((X427 @ id @ (lam @ (X439 @ sh @ one)) @ id))) | ~ ! [X440 : term] : (~ (((X427 @ id @ X440 @ id)) = $true) | (((X427 @ id @ (X439 @ id @ X440) @ id)) = $true)) | ~ ! [X441 : term,X442 : subst,X443 : subst] : (((X439 @ (comp @ X442 @ X443) @ (sub @ X441 @ X443))) = ((sub @ (X439 @ X442 @ X441) @ X443)))))) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X444 : subst,X445 : (term > $o),X446 : term] : ~ ! [X447 : (term > $o)] : ~ ! [X448 : term] : (((X447 @ X448)) = ((X445 @ (sub @ X448 @ (push @ X446 @ X444))))) <=> (pushprop_lem0_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X449 : term] : ~ ! [X450 : (subst > term > term)] : (((X450 @ sh @ one)) != ((sub @ X449 @ (push @ one @ sh))))) & ! [X451 : d_term] : (d_one = X451) & (hoasapnotvar = $true) & (! [X452 : (subst > term > subst > $o)] : ~ ! [X453 : (term > $o)] : ~ ! [X454 : term] : (((X453 @ X454)) = ((X452 @ id @ X454 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X455 : term] : ~ ! [X456 : (subst > term > term)] : ~ ! [X457 : term,X458 : subst] : (((X456 @ X458 @ X457)) = ((sub @ X455 @ (push @ X457 @ X458))))) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X459 : term,X460 : (subst > term > subst > $o)] : (~ ! [X461 : subst,X462 : subst,X463 : term,X464 : subst] : (($true = ((X460 @ X461 @ X463 @ (comp @ X464 @ X462)))) | ~ (((X460 @ (comp @ X461 @ X464) @ (sub @ X463 @ X464) @ X462)) = $true)) | ~ ! [X465 : term] : (($true = ((X460 @ id @ (sub @ X459 @ (push @ X465 @ id)) @ id))) | ~ (((X460 @ id @ X465 @ id)) = $true)) | ~ ! [X466 : (subst > term > term)] : (~ ! [X467 : term] : ((((X460 @ id @ (X466 @ id @ X467) @ id)) = $true) | ~ (((X460 @ id @ X467 @ id)) = $true)) | ~ ! [X468 : subst,X469 : term,X470 : subst] : (((sub @ (X466 @ X468 @ X469) @ X470)) = ((X466 @ (comp @ X468 @ X470) @ (sub @ X469 @ X470)))) | ($true = ((X460 @ id @ (lam @ (X466 @ sh @ one)) @ id)))) | (((X460 @ id @ (lam @ X459) @ id)) = $true) | ~ ! [X471 : subst,X472 : subst,X473 : subst,X474 : term] : ((((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473)) = $true) | ~ ($true = ((X460 @ X471 @ X474 @ (comp @ X472 @ X473))))))) & ((axvarid = $true) <=> ! [X475 : term] : (((sub @ X475 @ id)) = X475)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((induction2lem_lthm = $true) <=> (! [X478 : term,X479 : subst] : (((sub @ one @ (push @ X478 @ X479))) = X478) => (! [X480 : subst,X481 : term] : (((comp @ sh @ (push @ X481 @ X480))) = X480) => (! [X482 : subst] : (((comp @ X482 @ id)) = X482) => (! [X483 : term,X484 : (term > $o)] : (~ ! [X485 : term,X486 : term] : (~ (((X484 @ X485)) = $true) | ~ (((X484 @ X486)) = $true) | ($true = ((X484 @ (ap @ X486 @ X485))))) | (((X484 @ X483)) = $true) | ~ ! [X487 : term] : ((((X484 @ (lam @ X487))) = $true) | ~ (((X484 @ X487)) = $true)) | ~ ! [X488 : term] : (~ (((var @ X488)) = $true) | (((X484 @ X488)) = $true))) => ! [X489 : term,X490 : subst,X491 : (term > $o)] : (~ ! [X492 : term] : ((((X491 @ (sub @ X492 @ X490))) = $true) | ~ ($true = ((var @ X492)))) | ($true = ((X491 @ (sub @ X489 @ X490)))) | ~ ! [X493 : term] : ((((X491 @ (lam @ X493))) = $true) | ~ ! [X494 : term] : ((((X491 @ (sub @ X493 @ (push @ X494 @ id)))) = $true) | ~ (((X491 @ X494)) = $true))) | ~ ! [X495 : term,X496 : term] : (~ ($true = ((X491 @ X496))) | ~ (((X491 @ X495)) = $true) | (((X491 @ (ap @ X496 @ X495))) = $true)))))))) & ((! [X497 : term,X498 : term,X499 : term,X500 : term] : ((X497 = X500) | (((ap @ X499 @ X500)) != ((ap @ X498 @ X497)))) => ! [X501 : term,X502 : term,X503 : term,X504 : term] : ((X501 = X503) | (((ap @ (sub @ X504 @ id) @ X503)) != ((ap @ (sub @ X502 @ id) @ X501))))) <=> (hoasapinj2_lthm = $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ~ (ulamvar1 = $true) & (hoaslamnotvar_lthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (axapp = $true) & (! [X505 : term,X506 : (subst > term > subst > $o)] : (($true = ((X506 @ id @ X505 @ id))) | ~ ! [X507 : term,X508 : term] : (~ ($true = ((X506 @ id @ X508 @ id))) | ~ ($true = ((X506 @ id @ X507 @ id))) | (((X506 @ id @ (ap @ (sub @ X508 @ id) @ X507) @ id)) = $true)) | ~ ! [X509 : (subst > term > term)] : (~ ! [X510 : subst,X511 : subst,X512 : term] : (((X509 @ (comp @ X510 @ X511) @ (sub @ X512 @ X511))) = ((sub @ (X509 @ X510 @ X512) @ X511))) | ~ ! [X513 : term] : ((((X506 @ id @ (X509 @ id @ X513) @ id)) = $true) | ~ (((X506 @ id @ X513 @ id)) = $true)) | ($true = ((X506 @ id @ (lam @ (X509 @ sh @ one)) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & ((apinj1 = $true) <=> ! [X514 : term,X515 : term,X516 : term,X517 : term] : ((((ap @ X515 @ X516)) != ((ap @ X517 @ X514))) | (X515 = X517))) & ((hoasapinj2 = $true) <=> ! [X518 : term,X519 : term,X520 : term,X521 : term] : ((((ap @ (sub @ X521 @ id) @ X519)) != ((ap @ (sub @ X520 @ id) @ X518))) | (X518 = X519))) & (pushprop = $true) & (! [X522 : (term > $o),X523 : term] : (~ ! [X524 : term] : (~ (((X522 @ X524)) = $true) | (((X522 @ (lam @ X524))) = $true)) | ~ ! [X525 : term] : (~ ($true = ((var @ X525))) | (((X522 @ X525)) = $true)) | (((X522 @ X523)) = $true) | ~ ! [X526 : term,X527 : term] : (~ ($true = ((X522 @ X527))) | ($true = ((X522 @ (ap @ X526 @ X527)))) | ~ (((X522 @ X526)) = $true))) <=> (induction = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X528 : (subst > term > subst > $o),X529 : term] : (($true = ((X528 @ id @ (lam @ X529) @ id))) | ~ ! [X530 : (subst > term > term)] : (~ ! [X531 : term] : (~ ($true = ((X528 @ id @ X531 @ id))) | ($true = ((X528 @ id @ (X530 @ id @ X531) @ id)))) | ($true = ((X528 @ id @ (lam @ (X530 @ sh @ one)) @ id))) | ~ ! [X532 : subst,X533 : subst,X534 : term] : (((X530 @ (comp @ X532 @ X533) @ (sub @ X534 @ X533))) = ((sub @ (X530 @ X532 @ X534) @ X533)))) | ~ ! [X535 : term] : (($true = ((X528 @ id @ (sub @ X529 @ (push @ X535 @ id)) @ id))) | ~ ($true = ((X528 @ id @ X535 @ id)))))) & ((termmset_lthm = $true) <=> (! [X536 : term] : (((sub @ X536 @ id)) = X536) => ! [X537 : term] : (((sub @ X537 @ id)) = X537))) & ! [X538 : subst] : ? [X539 : d_subst] : (((d2subst @ X539)) = X538) & (ulamvarind = $true) & ((hoasapinj1 = $true) <=> ! [X540 : term,X541 : term,X542 : term,X543 : term] : ((((ap @ (sub @ X541 @ id) @ X543)) != ((ap @ (sub @ X540 @ id) @ X542))) | (X540 = X541))) & ((apinj2 = $true) <=> ! [X544 : term,X545 : term,X546 : term,X547 : term] : ((((ap @ X546 @ X547)) != ((ap @ X545 @ X544))) | (X544 = X547))) & (termmset_gthm = $true) & ! [X548 : d_term,X549 : d_term] : ((((d2term @ X548)) = ((d2term @ X549))) => (X548 = X549)) & (pushprop_lem3v2_lthm = $true)), 26.09/4.24 inference(fool_elimination,[],[f6])). 26.09/4.24 thf(f8,plain,( 26.09/4.24 ~((hoasinduction_lem3a = $true) <=> ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : term,X2 : subst,X3 : subst] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2)))) => (! [X5 : term] : ((((X0 @ id @ X5 @ id)) = $true) => ($true = ((X0 @ id @ (X1 @ id @ X5) @ id)))) => ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))))) => ! [X6 : term] : (! [X7 : term] : (($true = ((X0 @ id @ X7 @ id))) => (((X0 @ id @ (sub @ X6 @ (push @ X7 @ id)) @ id)) = $true)) => (((X0 @ id @ (lam @ X6) @ id)) = $true))))), 26.09/4.24 inference(rectify,[],[f5])). 26.09/4.24 thf(f9,plain,( 26.09/4.24 (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X0 : term] : ~ ! [X1 : (subst > term > term)] : ~ ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2))))) & ((induction2 = $true) <=> ! [X4 : (term > $o),X5 : term] : (($true = ((X4 @ X5))) | ~ ! [X6 : term,X7 : term] : (~ ($true = ((X4 @ X6))) | (((X4 @ (ap @ X6 @ X7))) = $true) | ~ ($true = ((X4 @ X7)))) | ~ ! [X8 : term] : ((((X4 @ X8)) = $true) | ~ (((var @ X8)) = $true)) | ~ ! [X9 : term] : (~ ! [X10 : term] : (~ (((X4 @ X10)) = $true) | ($true = ((X4 @ (sub @ X9 @ (push @ X10 @ id)))))) | ($true = ((X4 @ (lam @ X9))))))) & (hoasinduction_lem2v2_gthm = $true) & ((! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X14 : term] : (~ ($true = ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X15 : (subst > term > term)] : (~ ! [X18 : subst,X16 : term,X17 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) = ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ~ ! [X19 : term] : (~ ($true = ((X12 @ id @ X19 @ id))) | ($true = ((X12 @ id @ (X15 @ id @ X19) @ id)))))) => ! [X20 : term,X21 : (subst > term > subst > $o)] : (~ ! [X22 : term] : (($true = ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id))) | ~ ($true = ((X21 @ id @ X22 @ id)))) | ($true = ((X21 @ id @ (lam @ X20) @ id))) | ~ ! [X23 : term,X24 : subst,X25 : subst,X26 : subst] : (~ (((X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25)) = $true) | ($true = ((X21 @ X26 @ X23 @ (comp @ X24 @ X25))))) | ~ ! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : ((((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30)) = $true) | ~ (((X21 @ X27 @ X28 @ (comp @ X29 @ X30))) = $true)) | ~ ! [X31 : (subst > term > term)] : (~ ! [X32 : term] : (($true = ((X21 @ id @ (X31 @ id @ X32) @ id))) | ~ (((X21 @ id @ X32 @ id)) = $true)) | ~ ! [X34 : term,X33 : subst,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35)))) | (((X21 @ id @ (lam @ (X31 @ sh @ one)) @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) <=> (axshiftcons = $true)) & (induction2_gthm = $true) & (hoaslaminj_gthm = $true) & ! [X38 : d_subst] : (d_id = X38) & ((pushprop_lem1v2_lthm = $true) <=> (! [X40 : term,X39 : subst] : (((sub @ one @ (push @ X40 @ X39))) = X40) => ! [X41 : (term > $o),X42 : term,X43 : (term > $o),X44 : subst] : (~ ! [X45 : term] : (((X41 @ X45)) = ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true) | ~ (((X43 @ X42)) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X47 : subst,X46 : term] : (((sub @ one @ (push @ X46 @ X47))) = X46) => (! [X48 : term,X49 : subst] : (((comp @ sh @ (push @ X48 @ X49))) = X49) => ! [X50 : subst,X51 : term,X52 : (term > $o),X53 : term,X54 : (term > $o)] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ~ ($true = ((X52 @ X51))))))) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> (termmset = $true)) & (hoasapinj2_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1 = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ((pushprop_lem1 = $true) <=> ! [X56 : term,X57 : (term > $o),X58 : term,X59 : (term > $o),X60 : subst] : (~ ($true = ((X59 @ X58))) | ($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))))) & (! [X61 : (subst > term > subst > $o)] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2 = $true) & ((! [X64 : subst] : (((comp @ id @ X64)) = X64) => (! [X65 : subst] : (((comp @ X65 @ id)) = X65) => (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)))) <=> (substmonoid_lthm = $true)) & ((! [X68 : term] : ~ ! [X69 : (subst > term > term)] : ~ ! [X71 : subst,X70 : term] : (((X69 @ X71 @ X70)) = ((sub @ X68 @ (push @ X70 @ X71)))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => ! [X73 : (term > $o),X74 : (subst > term > subst > $o),X75 : term] : (~ ! [X76 : (subst > term > term)] : (~ ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) | ($true = ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) | ~ ! [X80 : term] : (~ ($true = ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id))))) | ~ ! [X81 : term] : (~ ($true = ((X73 @ X81))) | ($true = ((X73 @ (sub @ X75 @ (push @ X81 @ id)))))) | ($true = ((X73 @ (lam @ X75)))) | ~ ! [X82 : term] : (((X74 @ id @ X82 @ id)) = ((X73 @ X82)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X83 : term,X84 : (subst > term > subst > $o)] : (~ ! [X85 : term] : (($true = ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) | ~ (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ~ ! [X86 : (subst > term > term)] : (~ ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))) | ~ ! [X90 : term] : ((((X84 @ id @ (X86 @ id @ X90) @ id)) = $true) | ~ (((X84 @ id @ X90 @ id)) = $true)) | (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true)))) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) <=> (substmonoid = $true)) & (ulamvarsh = $true) & ((hoasinduction_lthm = $true) <=> (! [X93 : (term > $o),X94 : term] : (~ ! [X95 : term] : (($true = ((X93 @ (lam @ X95)))) | ~ ! [X96 : term] : ((((X93 @ (sub @ X95 @ (push @ X96 @ id)))) = $true) | ~ ($true = ((X93 @ X96))))) | ($true = ((X93 @ X94))) | ~ ! [X97 : term] : (($true = ((X93 @ X97))) | ~ (((var @ X97)) = $true)) | ~ ! [X98 : term,X99 : term] : (~ (((X93 @ X98)) = $true) | ($true = ((X93 @ (ap @ X98 @ X99)))) | ~ ($true = ((X93 @ X99))))) => (! [X100 : term,X101 : (subst > term > subst > $o),X102 : term] : (~ (((X101 @ id @ X102 @ id)) = $true) | ~ (((X101 @ id @ X100 @ id)) = $true) | ~ ! [X103 : subst,X104 : subst,X105 : subst,X106 : term] : (($true = ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)))) | ~ ($true = ((X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)))) | ($true = ((X101 @ id @ (ap @ X102 @ X100) @ id))) | ~ ! [X107 : subst,X108 : subst,X109 : subst,X110 : term] : (($true = ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108))) | ~ (((X101 @ X107 @ X110 @ (comp @ X109 @ X108))) = $true)) | ~ ! [X111 : term,X112 : term] : (~ (((X101 @ id @ X112 @ id)) = $true) | ~ ($true = ((X101 @ id @ X111 @ id))) | ($true = ((X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id))))) => (! [X113 : (subst > term > subst > $o),X114 : term] : (~ ! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ~ ($true = ((X113 @ id @ X115 @ id)))) | ~ ! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ~ ($true = ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ($true = ((X113 @ id @ (lam @ X114) @ id))) | ~ ! [X120 : (subst > term > term)] : (~ ! [X122 : subst,X123 : subst,X121 : term] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X120 @ X123 @ X121) @ X122))) | ($true = ((X113 @ id @ (lam @ (X120 @ sh @ one)) @ id))) | ~ ! [X124 : term] : (~ (((X113 @ id @ X124 @ id)) = $true) | ($true = ((X113 @ id @ (X120 @ id @ X124) @ id))))) | ~ ! [X125 : subst,X126 : term,X127 : subst,X128 : subst] : ((((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true) | ~ ($true = ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))))) => ! [X129 : (subst > term > subst > $o),X130 : term] : ((((X129 @ id @ X130 @ id)) = $true) | ~ ! [X131 : term,X132 : term] : (($true = ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id))) | ~ ($true = ((X129 @ id @ X132 @ id))) | ~ ($true = ((X129 @ id @ X131 @ id)))) | ~ ! [X133 : (subst > term > term)] : (($true = ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id))) | ~ ! [X134 : term] : (($true = ((X129 @ id @ (X133 @ id @ X134) @ id))) | ~ (((X129 @ id @ X134 @ id)) = $true)) | ~ ! [X136 : subst,X135 : term,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137)))) | ~ ! [X138 : term,X139 : subst,X140 : subst,X141 : subst] : (~ ($true = ((X129 @ X141 @ X138 @ (comp @ X140 @ X139)))) | (((X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) = $true)) | ~ ! [X142 : term] : ((((X129 @ id @ X142 @ id)) = $true) | ~ (((var @ (sub @ X142 @ id))) = $true)) | ~ ! [X143 : subst,X144 : term,X145 : subst,X146 : subst] : ((((X129 @ X145 @ X144 @ (comp @ X143 @ X146))) = $true) | ~ ($true = ((X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146))))))))) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X147 : term,X148 : (subst > term > subst > $o)] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ~ ! [X149 : (subst > term > term)] : (~ ! [X150 : term] : (~ ($true = ((X148 @ id @ X150 @ id))) | ($true = ((X148 @ id @ (X149 @ id @ X150) @ id)))) | (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) = $true) | ~ ! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152)))) | ~ ! [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) = $true) | ~ ($true = ((X148 @ id @ X154 @ id))))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem = $true) <=> ! [X155 : term,X156 : subst,X157 : (term > $o)] : (~ ! [X158 : term] : ((((X157 @ (lam @ X158))) = $true) | ~ ! [X159 : term] : (~ ($true = ((X157 @ X159))) | ($true = ((X157 @ (sub @ X158 @ (push @ X159 @ id))))))) | ~ ! [X160 : term,X161 : term] : ((((X157 @ (ap @ X160 @ X161))) = $true) | ~ ($true = ((X157 @ X160))) | ~ (((X157 @ X161)) = $true)) | ~ ! [X162 : term] : (~ ($true = ((var @ X162))) | (((X157 @ (sub @ X162 @ X156))) = $true)) | (((X157 @ (sub @ X155 @ X156))) = $true))) & ((hoaslamnotap = $true) <=> ! [X165 : term,X164 : term,X163 : (subst > term > term)] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ~ ! [X166 : subst,X167 : subst,X168 : term] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X163 @ X166 @ X168) @ X167))))) & (hoasinduction_lem2_lthm = $true) & (axassoc = $true) & ((laminj = $true) <=> ! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170))) & (substmonoid_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : (subst > term > subst > $o),X173 : term] : (~ ! [X174 : (subst > term > term)] : (~ ! [X175 : term] : (~ (((X172 @ id @ X175 @ id)) = $true) | ($true = ((X172 @ id @ (X174 @ id @ X175) @ id)))) | ~ ! [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) = ((sub @ (X174 @ X177 @ X176) @ X178))) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) | ($true = ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id))) | ~ ! [X179 : term] : (($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id))) | ~ (((X172 @ id @ X179 @ id)) = $true))) => ! [X180 : term,X181 : (subst > term > subst > $o)] : (~ ! [X182 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : subst,X183 : term,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) | ~ ! [X186 : term] : (($true = ((X181 @ id @ (X182 @ id @ X186) @ id))) | ~ (((X181 @ id @ X186 @ id)) = $true))) | ~ ! [X187 : term] : ((((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)) = $true) | ~ (((X181 @ id @ X187 @ id)) = $true)) | (((X181 @ id @ (lam @ X180) @ id)) = $true))))) & (pushprop_lem0_gthm = $true) & (axvarshift = $true) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> (axidr = $true)) & ((! [X189 : (subst > term > subst > $o)] : ~ ! [X190 : (term > $o)] : ~ ! [X191 : term] : (((X190 @ X191)) = ((X189 @ id @ X191 @ id))) => (! [X192 : term,X193 : (term > $o)] : ((((X193 @ X192)) = $true) | ~ ! [X194 : term] : ((((X193 @ (lam @ X194))) = $true) | ~ ! [X195 : term] : (($true = ((X193 @ (sub @ X194 @ (push @ X195 @ id))))) | ~ (((X193 @ X195)) = $true))) | ~ ! [X196 : term] : (($true = ((X193 @ X196))) | ~ (((var @ X196)) = $true)) | ~ ! [X197 : term,X198 : term] : ((((X193 @ (ap @ X198 @ X197))) = $true) | ~ (((X193 @ X197)) = $true) | ~ (((X193 @ X198)) = $true))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => (! [X200 : (subst > term > subst > $o),X201 : (term > $o),X202 : term] : (~ ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203))) | ~ ! [X204 : (subst > term > term)] : (($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ~ ! [X206 : subst,X205 : term,X207 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X204 @ X206 @ X205) @ X207))) | ~ ! [X208 : term] : (~ ($true = ((X200 @ id @ X208 @ id))) | ($true = ((X200 @ id @ (X204 @ id @ X208) @ id))))) | (((X201 @ (lam @ X202))) = $true) | ~ ! [X209 : term] : (~ ($true = ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id))))))) => ! [X210 : (subst > term > subst > $o),X211 : term] : (($true = ((X210 @ id @ X211 @ id))) | ~ ! [X212 : term,X213 : term] : (~ ($true = ((X210 @ id @ X212 @ id))) | (((X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id)) = $true) | ~ (((X210 @ id @ X213 @ id)) = $true)) | ~ ! [X214 : (subst > term > term)] : (($true = ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id))) | ~ ! [X215 : term] : ((((X210 @ id @ (X214 @ id @ X215) @ id)) = $true) | ~ (((X210 @ id @ X215 @ id)) = $true)) | ~ ! [X217 : subst,X218 : term,X216 : subst] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & (! [X221 : subst] : (((comp @ id @ X221)) = X221) <=> (axidl = $true)) & (pushprop_lthm_orig = $true) & ((pushprop_lem0 = $true) <=> ! [X222 : term,X224 : subst,X223 : (term > $o)] : ~ ! [X225 : (term > $o)] : ~ ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226)))) & ! [X227 : d_subst,X228 : d_subst] : ((((d2subst @ X227)) = ((d2subst @ X228))) => (X227 = X228)) & (pushprop_lem2v2_gthm = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = id) & (apnotvar = $true) & ((! [X229 : term] : (((sub @ X229 @ id)) = X229) => ! [X230 : (subst > term > subst > $o),X231 : (term > $o),X232 : term] : (~ ! [X233 : subst,X234 : subst,X235 : subst,X236 : term] : ((((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) = $true) | ~ ($true = ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235)))) | ~ ! [X237 : term] : (((X230 @ id @ X237 @ id)) = ((X231 @ X237))) | ~ ! [X238 : term] : ((((X231 @ (sub @ X232 @ (push @ X238 @ id)))) = $true) | ~ (((X231 @ X238)) = $true)) | ($true = ((X231 @ (lam @ X232)))) | ~ ! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : (($true = ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) | ~ ($true = ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ~ ! [X243 : (subst > term > term)] : (~ ! [X244 : term] : (~ (((X230 @ id @ X244 @ id)) = $true) | ($true = ((X230 @ id @ (X243 @ id @ X244) @ id)))) | ($true = ((X230 @ id @ (lam @ (X243 @ sh @ one)) @ id))) | ~ ! [X247 : subst,X246 : subst,X245 : term] : (((sub @ (X243 @ X247 @ X245) @ X246)) = ((X243 @ (comp @ X247 @ X246) @ (sub @ X245 @ X246))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X248 : (term > $o),X249 : term,X250 : (subst > term > subst > $o),X251 : term] : (~ ($true = ((X248 @ X249))) | ~ ! [X252 : subst,X253 : subst,X254 : subst,X255 : term] : (~ ($true = ((X250 @ X253 @ X255 @ (comp @ X254 @ X252)))) | ($true = ((X250 @ (comp @ X253 @ X254) @ (sub @ X255 @ X254) @ X252)))) | ~ ! [X256 : term,X257 : term] : (~ ($true = ((X250 @ id @ X257 @ id))) | ~ (((X250 @ id @ X256 @ id)) = $true) | ($true = ((X250 @ id @ (ap @ (sub @ X257 @ id) @ X256) @ id)))) | ~ ! [X258 : term] : (((X248 @ X258)) = ((X250 @ id @ X258 @ id))) | ($true = ((X248 @ (ap @ X249 @ X251)))) | ~ ! [X259 : subst,X260 : term,X261 : subst,X262 : subst] : ((((X250 @ X259 @ X260 @ (comp @ X261 @ X262))) = $true) | ~ (((X250 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)) = $true)) | ~ ($true = ((X248 @ X251)))) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X263 : term] : ~ ! [X264 : (subst > term > term)] : (((X264 @ sh @ one)) != ((sub @ X263 @ (push @ one @ sh))))) & (hoasinduction_lem1v2 = $true) & ((hoasapinj1_lthm = $true) <=> (! [X265 : term] : (((sub @ X265 @ id)) = X265) => (! [X268 : term,X267 : term,X266 : term,X269 : term] : ((X267 = X268) | (((ap @ X267 @ X269)) != ((ap @ X268 @ X266)))) => ! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X275 : term,X274 : subst] : (((sub @ one @ (push @ X275 @ X274))) = X275) => (! [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) = X277) => (! [X278 : term,X279 : term] : ((X278 = X279) | (((lam @ X279)) != ((lam @ X278)))) => ! [X280 : subst,X281 : (subst > term > term),X283 : (subst > term > term),X282 : term] : ((((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one)))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ~ ! [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) = ((sub @ (X281 @ X288 @ X287) @ X289))) | ~ ! [X285 : subst,X286 : subst,X284 : term] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) = ((sub @ (X283 @ X285 @ X284) @ X286))))))) <=> (hoaslaminj_lthm = $true)) & (pushprop_gthm = $true) & (! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) <=> (shinj = $true)) & (! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) <=> (axscons = $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X293 : term,X294 : (subst > term > subst > $o)] : ((((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X295 : term] : (~ (((X294 @ id @ X295 @ id)) = $true) | ($true = ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id)))) | ~ ! [X296 : term,X297 : (subst > term > term)] : (~ ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ~ ! [X301 : term] : ((((X294 @ id @ (X297 @ id @ X301) @ id)) = $true) | ~ (((X294 @ id @ X301 @ id)) = $true)) | ~ ! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X305 : (term > $o),X306 : (subst > term > subst > $o),X307 : term] : ((((X305 @ (lam @ X307))) = $true) | ~ ! [X308 : (subst > term > term)] : (~ ! [X309 : subst,X311 : subst,X310 : term] : (((sub @ (X308 @ X309 @ X310) @ X311)) = ((X308 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311)))) | ($true = ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) | ~ ! [X312 : term] : ((((X306 @ id @ (X308 @ id @ X312) @ id)) = $true) | ~ ($true = ((X306 @ id @ X312 @ id))))) | ~ ! [X313 : term] : (((X305 @ X313)) = ((X306 @ id @ X313 @ id))) | ~ ! [X314 : term,X315 : subst,X316 : subst,X317 : subst] : (($true = ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) | ~ (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) = $true)) | ~ ! [X318 : term] : (~ ($true = ((X305 @ X318))) | ($true = ((X305 @ (sub @ X307 @ (push @ X318 @ id)))))) | ~ ! [X319 : term,X320 : subst,X321 : subst,X322 : subst] : (~ (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) = $true) | (((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) = $true)))) & ((! [X323 : (subst > term > subst > $o)] : ~ ! [X324 : (term > $o)] : ~ ! [X325 : term] : (((X324 @ X325)) = ((X323 @ id @ X325 @ id))) => (! [X326 : (term > $o),X327 : term] : (~ ! [X328 : term] : (($true = ((X326 @ (lam @ X328)))) | ~ ! [X329 : term] : (~ (((X326 @ X329)) = $true) | ($true = ((X326 @ (sub @ X328 @ (push @ X329 @ id))))))) | ~ ! [X330 : term] : (($true = ((X326 @ X330))) | ~ (((var @ X330)) = $true)) | ~ ! [X331 : term,X332 : term] : (~ ($true = ((X326 @ X332))) | ~ ($true = ((X326 @ X331))) | (((X326 @ (ap @ X332 @ X331))) = $true)) | (((X326 @ X327)) = $true)) => (! [X333 : term] : (((sub @ X333 @ id)) = X333) => (! [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) = $true) | ~ ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id))) | ~ ! [X338 : term] : ((((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true) | ~ (((X334 @ X338)) = $true)) | ~ ! [X339 : (subst > term > term)] : (~ ! [X342 : subst,X341 : term,X340 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) = ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) | ~ ! [X343 : term] : (($true = ((X336 @ id @ (X339 @ id @ X343) @ id))) | ~ (((X336 @ id @ X343 @ id)) = $true)))) => ! [X344 : (subst > term > subst > $o),X345 : term] : (~ ! [X346 : term,X347 : term] : ((((X344 @ id @ (ap @ (sub @ X346 @ id) @ X347) @ id)) = $true) | ~ (((X344 @ id @ X347 @ id)) = $true) | ~ (((X344 @ id @ X346 @ id)) = $true)) | (((X344 @ id @ X345 @ id)) = $true) | ~ ! [X348 : subst,X349 : term,X350 : subst,X351 : subst] : (~ (((X344 @ (comp @ X351 @ X348) @ (sub @ X349 @ X348) @ X350)) = $true) | (((X344 @ X351 @ X349 @ (comp @ X348 @ X350))) = $true)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : subst,X355 : subst,X354 : term] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) | ~ ! [X356 : term] : (~ (((X344 @ id @ X356 @ id)) = $true) | ($true = ((X344 @ id @ (X352 @ id @ X356) @ id)))) | ($true = ((X344 @ id @ (lam @ (X352 @ sh @ one)) @ id)))) | ~ ! [X357 : subst,X358 : term,X359 : subst,X360 : subst] : ((((X344 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359)) = $true) | ~ (((X344 @ X360 @ X358 @ (comp @ X357 @ X359))) = $true)) | ~ ! [X361 : term] : (~ ($true = ((var @ (sub @ X361 @ id)))) | (((X344 @ id @ X361 @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = sh) & (axmap = $true) & (! [X362 : (term > $o),X363 : (subst > term > subst > $o),X364 : term] : (~ ! [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) = $true) | ~ (((X362 @ X365)) = $true)) | ~ ! [X366 : term] : (((X362 @ X366)) = ((X363 @ id @ X366 @ id))) | (((X362 @ (lam @ X364))) = $true) | ~ ! [X367 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) | ~ ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | ~ (((X363 @ id @ X368 @ id)) = $true)) | ~ ! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X372 : term,X373 : (subst > term > subst > $o),X374 : term] : (~ ($true = ((X373 @ id @ X374 @ id))) | ~ ! [X375 : term,X376 : subst,X377 : subst,X378 : subst] : (($true = ((X373 @ X377 @ X375 @ (comp @ X378 @ X376)))) | ~ (((X373 @ (comp @ X377 @ X378) @ (sub @ X375 @ X378) @ X376)) = $true)) | ~ ! [X379 : term,X380 : term] : (~ (((X373 @ id @ X379 @ id)) = $true) | ~ ($true = ((X373 @ id @ X380 @ id))) | ($true = ((X373 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id)))) | ($true = ((X373 @ id @ (ap @ X374 @ X372) @ id))) | ~ ! [X381 : term,X382 : subst,X383 : subst,X384 : subst] : (~ ($true = ((X373 @ X384 @ X381 @ (comp @ X383 @ X382)))) | (((X373 @ (comp @ X384 @ X383) @ (sub @ X381 @ X383) @ X382)) = $true)) | ~ (((X373 @ id @ X372 @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_gthm = $true) & (hoasapnotvar_lthm = $true) & ~ (lamnotap = $true) & ((axvarcons = $true) <=> ! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386)) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar = $true) & ((induction2_lthm = $true) <=> (! [X387 : term] : (((sub @ X387 @ id)) = X387) => (! [X388 : term,X389 : subst,X390 : (term > $o)] : (~ ! [X391 : term] : (($true = ((X390 @ (lam @ X391)))) | ~ ! [X392 : term] : (($true = ((X390 @ (sub @ X391 @ (push @ X392 @ id))))) | ~ (((X390 @ X392)) = $true))) | ~ ! [X393 : term] : (~ ($true = ((var @ X393))) | ($true = ((X390 @ (sub @ X393 @ X389))))) | ($true = ((X390 @ (sub @ X388 @ X389)))) | ~ ! [X394 : term,X395 : term] : (($true = ((X390 @ (ap @ X394 @ X395)))) | ~ (((X390 @ X394)) = $true) | ~ (((X390 @ X395)) = $true))) => ! [X396 : term,X397 : (term > $o)] : (~ ! [X398 : term] : (~ ! [X399 : term] : (~ (((X397 @ X399)) = $true) | ($true = ((X397 @ (sub @ X398 @ (push @ X399 @ id)))))) | (((X397 @ (lam @ X398))) = $true)) | ~ ! [X400 : term] : (($true = ((X397 @ X400))) | ~ ($true = ((var @ X400)))) | ~ ! [X401 : term,X402 : term] : (~ (((X397 @ X401)) = $true) | ~ (((X397 @ X402)) = $true) | (((X397 @ (ap @ X402 @ X401))) = $true)) | ($true = ((X397 @ X396))))))) & (! [X406 : (subst > term > term),X403 : term,X404 : (subst > term > term),X405 : subst] : (~ ! [X410 : term,X411 : subst,X412 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) = ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ~ ! [X408 : subst,X407 : subst,X409 : term] : (((sub @ (X404 @ X407 @ X409) @ X408)) = ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408))))) <=> (hoaslaminj = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X413 : term,X414 : (term > $o),X415 : subst,X416 : (term > $o)] : (~ ! [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) = ((X416 @ X417))) | ~ ($true = ((X414 @ X413))) | (((X416 @ one)) = $true))) & (axclos = $true) & ((hoasinduction = $true) <=> ! [X418 : term,X419 : (subst > term > subst > $o)] : (~ ! [X420 : term,X421 : subst,X422 : subst,X423 : subst] : (($true = ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) | ~ (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) = $true)) | ~ ! [X424 : term] : (~ (((var @ (sub @ X424 @ id))) = $true) | ($true = ((X419 @ id @ X424 @ id)))) | ($true = ((X419 @ id @ X418 @ id))) | ~ ! [X425 : term,X426 : term] : ((((X419 @ id @ (ap @ (sub @ X425 @ id) @ X426) @ id)) = $true) | ~ (((X419 @ id @ X426 @ id)) = $true) | ~ ($true = ((X419 @ id @ X425 @ id)))) | ~ ! [X427 : subst,X428 : subst,X429 : term,X430 : subst] : (($true = ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) | ~ ($true = ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) | ~ ! [X431 : (subst > term > term)] : (($true = ((X419 @ id @ (lam @ (X431 @ sh @ one)) @ id))) | ~ ! [X432 : term] : (~ (((X419 @ id @ X432 @ id)) = $true) | ($true = ((X419 @ id @ (X431 @ id @ X432) @ id)))) | ~ ! [X434 : subst,X433 : term,X435 : subst] : (((sub @ (X431 @ X434 @ X433) @ X435)) = ((X431 @ (comp @ X434 @ X435) @ (sub @ X433 @ X435))))))) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X438 : term,X436 : subst,X437 : (term > $o)] : ~ ! [X439 : (term > $o)] : ~ ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) <=> (pushprop_lem0_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X441 : term] : ~ ! [X442 : (subst > term > term)] : (((X442 @ sh @ one)) != ((sub @ X441 @ (push @ one @ sh))))) & ! [X443 : d_term] : (d_one = X443) & (hoasapnotvar = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X444 : (subst > term > subst > $o)] : ~ ! [X445 : (term > $o)] : ~ ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446)))) & (! [X447 : term] : ~ ! [X448 : (subst > term > term)] : ~ ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X451 : term,X452 : (subst > term > subst > $o)] : (~ ! [X453 : subst,X454 : subst,X455 : term,X456 : subst] : ((((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) = $true) | ~ (((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) = $true)) | ~ ! [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) = $true) | ~ ($true = ((X452 @ id @ X457 @ id)))) | ~ ! [X458 : (subst > term > term)] : (~ ! [X459 : term] : (($true = ((X452 @ id @ (X458 @ id @ X459) @ id))) | ~ (((X452 @ id @ X459 @ id)) = $true)) | ~ ! [X461 : term,X462 : subst,X460 : subst] : (((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X458 @ X460 @ X461) @ X462))) | (((X452 @ id @ (lam @ (X458 @ sh @ one)) @ id)) = $true)) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ~ ! [X463 : subst,X464 : subst,X465 : subst,X466 : term] : (($true = ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))) | ~ (((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) = $true)))) & ((axvarid = $true) <=> ! [X467 : term] : (((sub @ X467 @ id)) = X467)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((induction2lem_lthm = $true) <=> (! [X468 : term,X469 : subst] : (((sub @ one @ (push @ X468 @ X469))) = X468) => (! [X471 : term,X470 : subst] : (((comp @ sh @ (push @ X471 @ X470))) = X470) => (! [X472 : subst] : (((comp @ X472 @ id)) = X472) => (! [X473 : term,X474 : (term > $o)] : (~ ! [X475 : term,X476 : term] : (~ (((X474 @ X475)) = $true) | ~ (((X474 @ X476)) = $true) | (((X474 @ (ap @ X476 @ X475))) = $true)) | (((X474 @ X473)) = $true) | ~ ! [X477 : term] : ((((X474 @ (lam @ X477))) = $true) | ~ (((X474 @ X477)) = $true)) | ~ ! [X478 : term] : (~ (((var @ X478)) = $true) | (((X474 @ X478)) = $true))) => ! [X479 : term,X480 : subst,X481 : (term > $o)] : (~ ! [X482 : term] : (($true = ((X481 @ (sub @ X482 @ X480)))) | ~ ($true = ((var @ X482)))) | ($true = ((X481 @ (sub @ X479 @ X480)))) | ~ ! [X483 : term] : ((((X481 @ (lam @ X483))) = $true) | ~ ! [X484 : term] : (($true = ((X481 @ (sub @ X483 @ (push @ X484 @ id))))) | ~ (((X481 @ X484)) = $true))) | ~ ! [X485 : term,X486 : term] : (~ (((X481 @ X486)) = $true) | ~ ($true = ((X481 @ X485))) | ($true = ((X481 @ (ap @ X486 @ X485))))))))))) & ((! [X488 : term,X487 : term,X490 : term,X489 : term] : ((X487 = X490) | (((ap @ X488 @ X487)) != ((ap @ X489 @ X490)))) => ! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491))))) <=> (hoasapinj2_lthm = $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ~ (ulamvar1 = $true) & (hoaslamnotvar_lthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (axapp = $true) & (! [X495 : term,X496 : (subst > term > subst > $o)] : (($true = ((X496 @ id @ X495 @ id))) | ~ ! [X497 : term,X498 : term] : (~ ($true = ((X496 @ id @ X498 @ id))) | ~ (((X496 @ id @ X497 @ id)) = $true) | (((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) = $true)) | ~ ! [X499 : (subst > term > term)] : (~ ! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501))) | ~ ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ~ ($true = ((X496 @ id @ X503 @ id)))) | ($true = ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & ((apinj1 = $true) <=> ! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507))) & ((hoasapinj2 = $true) <=> ! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509))) & (pushprop = $true) & (! [X512 : (term > $o),X513 : term] : (~ ! [X514 : term] : (~ ($true = ((X512 @ X514))) | (((X512 @ (lam @ X514))) = $true)) | ~ ! [X515 : term] : (~ (((var @ X515)) = $true) | (((X512 @ X515)) = $true)) | ($true = ((X512 @ X513))) | ~ ! [X516 : term,X517 : term] : (~ (((X512 @ X517)) = $true) | ($true = ((X512 @ (ap @ X516 @ X517)))) | ~ (((X512 @ X516)) = $true))) <=> (induction = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X518 : (subst > term > subst > $o),X519 : term] : (($true = ((X518 @ id @ (lam @ X519) @ id))) | ~ ! [X520 : (subst > term > term)] : (~ ! [X521 : term] : (~ ($true = ((X518 @ id @ X521 @ id))) | (((X518 @ id @ (X520 @ id @ X521) @ id)) = $true)) | ($true = ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) | ~ ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523)))) | ~ ! [X525 : term] : (($true = ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id))) | ~ (((X518 @ id @ X525 @ id)) = $true)))) & ((! [X526 : term] : (((sub @ X526 @ id)) = X526) => ! [X527 : term] : (((sub @ X527 @ id)) = X527)) <=> (termmset_lthm = $true)) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & (ulamvarind = $true) & ((hoasapinj1 = $true) <=> ! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533))))) & (! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) <=> (apinj2 = $true)) & (termmset_gthm = $true) & ! [X538 : d_term,X539 : d_term] : ((((d2term @ X538)) = ((d2term @ X539))) => (X538 = X539)) & (pushprop_lem3v2_lthm = $true)), 26.09/4.24 inference(rectify,[],[f7])). 26.09/4.24 thf(f10,plain,( 26.09/4.24 (! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) <=> (apinj2 = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X305 : (term > $o),X307 : term,X306 : (subst > term > subst > $o)] : (~ ! [X317 : subst,X316 : subst,X314 : term,X315 : subst] : (($true = ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) | (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) != $true)) | ~ ! [X313 : term] : (((X305 @ X313)) = ((X306 @ id @ X313 @ id))) | (((X305 @ (lam @ X307))) = $true) | ~ ! [X320 : subst,X321 : subst,X319 : term,X322 : subst] : ((((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) != $true) | (((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) = $true)) | ~ ! [X318 : term] : (($true = ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) | ($true != ((X305 @ X318)))) | ~ ! [X308 : (subst > term > term)] : (($true = ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) | ~ ! [X309 : subst,X311 : subst,X310 : term] : (((sub @ (X308 @ X309 @ X310) @ X311)) = ((X308 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311)))) | ~ ! [X312 : term] : ((((X306 @ id @ (X308 @ id @ X312) @ id)) = $true) | ($true != ((X306 @ id @ X312 @ id))))))) & ! [X227 : d_subst,X228 : d_subst] : ((((d2subst @ X227)) = ((d2subst @ X228))) => (X227 = X228)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X441 : term] : ~ ! [X442 : (subst > term > term)] : (((X442 @ sh @ one)) != ((sub @ X441 @ (push @ one @ sh))))) & ! [X38 : d_subst] : (d_id = X38) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X229 : term] : (((sub @ X229 @ id)) = X229) => ! [X231 : (term > $o),X230 : (subst > term > subst > $o),X232 : term] : (~ ! [X238 : term] : ((((X231 @ X238)) != $true) | (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) = $true)) | ~ ! [X242 : subst,X241 : subst,X240 : term,X239 : subst] : (($true = ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) | ($true != ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ($true = ((X231 @ (lam @ X232)))) | ~ ! [X234 : subst,X235 : subst,X236 : term,X233 : subst] : (($true != ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) | (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) = $true)) | ~ ! [X243 : (subst > term > term)] : (~ ! [X247 : subst,X246 : subst,X245 : term] : (((sub @ (X243 @ X247 @ X245) @ X246)) = ((X243 @ (comp @ X247 @ X246) @ (sub @ X245 @ X246)))) | ($true = ((X230 @ id @ (lam @ (X243 @ sh @ one)) @ id))) | ~ ! [X244 : term] : ((((X230 @ id @ X244 @ id)) != $true) | ($true = ((X230 @ id @ (X243 @ id @ X244) @ id))))) | ~ ! [X237 : term] : (((X230 @ id @ X237 @ id)) = ((X231 @ X237)))))) & (! [X4 : (term > $o),X5 : term] : (~ ! [X9 : term] : (($true = ((X4 @ (lam @ X9)))) | ~ ! [X10 : term] : ((((X4 @ X10)) != $true) | ($true = ((X4 @ (sub @ X9 @ (push @ X10 @ id))))))) | ~ ! [X8 : term] : ((((X4 @ X8)) = $true) | (((var @ X8)) != $true)) | ($true = ((X4 @ X5))) | ~ ! [X7 : term,X6 : term] : (($true != ((X4 @ X7))) | ($true != ((X4 @ X6))) | (((X4 @ (ap @ X6 @ X7))) = $true))) <=> (induction2 = $true)) & ((hoasapinj2 = $true) <=> ! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509))) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> (axidr = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & ((induction = $true) <=> ! [X512 : (term > $o),X513 : term] : (~ ! [X517 : term,X516 : term] : ((((X512 @ X517)) != $true) | (((X512 @ X516)) != $true) | ($true = ((X512 @ (ap @ X516 @ X517))))) | ~ ! [X515 : term] : ((((X512 @ X515)) = $true) | (((var @ X515)) != $true)) | ~ ! [X514 : term] : ((((X512 @ (lam @ X514))) = $true) | ($true != ((X512 @ X514)))) | ($true = ((X512 @ X513))))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_gthm = $true) & ((! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X15 : (subst > term > term)] : (~ ! [X19 : term] : (($true != ((X12 @ id @ X19 @ id))) | ($true = ((X12 @ id @ (X15 @ id @ X19) @ id)))) | ~ ! [X18 : subst,X16 : term,X17 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) = ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true)) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X14 : term] : (($true != ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id))))) => ! [X20 : term,X21 : (subst > term > subst > $o)] : (~ ! [X31 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X31 @ sh @ one)) @ id)) = $true) | ~ ! [X32 : term] : (($true = ((X21 @ id @ (X31 @ id @ X32) @ id))) | (((X21 @ id @ X32 @ id)) != $true)) | ~ ! [X34 : term,X33 : subst,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35))))) | ($true = ((X21 @ id @ (lam @ X20) @ id))) | ~ ! [X22 : term] : (($true != ((X21 @ id @ X22 @ id))) | ($true = ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)))) | ~ ! [X26 : subst,X25 : subst,X24 : subst,X23 : term] : (($true = ((X21 @ X26 @ X23 @ (comp @ X24 @ X25)))) | (((X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25)) != $true)) | ~ ! [X27 : subst,X28 : term,X30 : subst,X29 : subst] : ((((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30)) = $true) | (((X21 @ X27 @ X28 @ (comp @ X29 @ X30))) != $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (induction2_gthm = $true) & ((! [X468 : term,X469 : subst] : (((sub @ one @ (push @ X468 @ X469))) = X468) => (! [X471 : term,X470 : subst] : (((comp @ sh @ (push @ X471 @ X470))) = X470) => (! [X472 : subst] : (((comp @ X472 @ id)) = X472) => (! [X474 : (term > $o),X473 : term] : (~ ! [X477 : term] : ((((X474 @ X477)) != $true) | (((X474 @ (lam @ X477))) = $true)) | ~ ! [X476 : term,X475 : term] : ((((X474 @ X476)) != $true) | (((X474 @ X475)) != $true) | (((X474 @ (ap @ X476 @ X475))) = $true)) | ~ ! [X478 : term] : ((((X474 @ X478)) = $true) | (((var @ X478)) != $true)) | (((X474 @ X473)) = $true)) => ! [X481 : (term > $o),X479 : term,X480 : subst] : (~ ! [X485 : term,X486 : term] : ((((X481 @ X486)) != $true) | ($true = ((X481 @ (ap @ X486 @ X485)))) | ($true != ((X481 @ X485)))) | ($true = ((X481 @ (sub @ X479 @ X480)))) | ~ ! [X483 : term] : (~ ! [X484 : term] : ((((X481 @ X484)) != $true) | ($true = ((X481 @ (sub @ X483 @ (push @ X484 @ id)))))) | (((X481 @ (lam @ X483))) = $true)) | ~ ! [X482 : term] : (($true != ((var @ X482))) | ($true = ((X481 @ (sub @ X482 @ X480)))))))))) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X68 : term] : ~ ! [X69 : (subst > term > term)] : ~ ! [X71 : subst,X70 : term] : (((X69 @ X71 @ X70)) = ((sub @ X68 @ (push @ X70 @ X71)))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => ! [X75 : term,X73 : (term > $o),X74 : (subst > term > subst > $o)] : (~ ! [X76 : (subst > term > term)] : (~ ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) | ($true = ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) | ~ ! [X80 : term] : (($true != ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id))))) | ($true = ((X73 @ (lam @ X75)))) | ~ ! [X82 : term] : (((X74 @ id @ X82 @ id)) = ((X73 @ X82))) | ~ ! [X81 : term] : (($true = ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) | ($true != ((X73 @ X81)))))))) & (lamnotvar = $true) & (termmset_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2_lthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (one = ((d2term @ d_one))) & (axclos = $true) & (hoaslamnotvar = $true) & (ulamvarind = $true) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & ((pushprop_lem0 = $true) <=> ! [X222 : term,X224 : subst,X223 : (term > $o)] : ~ ! [X225 : (term > $o)] : ~ ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226)))) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction = $true) <=> ! [X418 : term,X419 : (subst > term > subst > $o)] : (~ ! [X424 : term] : (($true = ((X419 @ id @ X424 @ id))) | (((var @ (sub @ X424 @ id))) != $true)) | ~ ! [X422 : subst,X420 : term,X421 : subst,X423 : subst] : ((((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) != $true) | ($true = ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421)))) | ($true = ((X419 @ id @ X418 @ id))) | ~ ! [X427 : subst,X428 : subst,X430 : subst,X429 : term] : (($true != ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428))) | ($true = ((X419 @ X427 @ X429 @ (comp @ X430 @ X428))))) | ~ ! [X426 : term,X425 : term] : ((((X419 @ id @ X426 @ id)) != $true) | (((X419 @ id @ (ap @ (sub @ X425 @ id) @ X426) @ id)) = $true) | ($true != ((X419 @ id @ X425 @ id)))) | ~ ! [X431 : (subst > term > term)] : (($true = ((X419 @ id @ (lam @ (X431 @ sh @ one)) @ id))) | ~ ! [X434 : subst,X433 : term,X435 : subst] : (((sub @ (X431 @ X434 @ X433) @ X435)) = ((X431 @ (comp @ X434 @ X435) @ (sub @ X433 @ X435)))) | ~ ! [X432 : term] : (($true = ((X419 @ id @ (X431 @ id @ X432) @ id))) | (((X419 @ id @ X432 @ id)) != $true))))) & (! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) <=> (axscons = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X364 : term,X362 : (term > $o),X363 : (subst > term > subst > $o)] : (~ ! [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) = $true) | (((X362 @ X365)) != $true)) | ~ ! [X367 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) | ~ ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | (((X363 @ id @ X368 @ id)) != $true)) | ~ ! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371)))) | ~ ! [X366 : term] : (((X362 @ X366)) = ((X363 @ id @ X366 @ id))) | (((X362 @ (lam @ X364))) = $true))) & ((apinj1 = $true) <=> ! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X444 : (subst > term > subst > $o)] : ~ ! [X445 : (term > $o)] : ~ ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446)))) & ((! [X189 : (subst > term > subst > $o)] : ~ ! [X190 : (term > $o)] : ~ ! [X191 : term] : (((X190 @ X191)) = ((X189 @ id @ X191 @ id))) => (! [X193 : (term > $o),X192 : term] : (~ ! [X196 : term] : (($true = ((X193 @ X196))) | (((var @ X196)) != $true)) | ~ ! [X194 : term] : (~ ! [X195 : term] : ((((X193 @ X195)) != $true) | ($true = ((X193 @ (sub @ X194 @ (push @ X195 @ id)))))) | (((X193 @ (lam @ X194))) = $true)) | (((X193 @ X192)) = $true) | ~ ! [X198 : term,X197 : term] : ((((X193 @ X198)) != $true) | (((X193 @ X197)) != $true) | (((X193 @ (ap @ X198 @ X197))) = $true))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => (! [X201 : (term > $o),X202 : term,X200 : (subst > term > subst > $o)] : ((((X201 @ (lam @ X202))) = $true) | ~ ! [X209 : term] : (($true != ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) | ~ ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203))) | ~ ! [X204 : (subst > term > term)] : (($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ~ ! [X208 : term] : (($true != ((X200 @ id @ X208 @ id))) | ($true = ((X200 @ id @ (X204 @ id @ X208) @ id)))) | ~ ! [X206 : subst,X205 : term,X207 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X204 @ X206 @ X205) @ X207))))) => ! [X211 : term,X210 : (subst > term > subst > $o)] : (($true = ((X210 @ id @ X211 @ id))) | ~ ! [X214 : (subst > term > term)] : (($true = ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id))) | ~ ! [X217 : subst,X218 : term,X216 : subst] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))) | ~ ! [X215 : term] : ((((X210 @ id @ (X214 @ id @ X215) @ id)) = $true) | (((X210 @ id @ X215 @ id)) != $true))) | ~ ! [X212 : term,X213 : term] : (($true != ((X210 @ id @ X212 @ id))) | (((X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id)) = $true) | (((X210 @ id @ X213 @ id)) != $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X64 : subst] : (((comp @ id @ X64)) = X64) => (! [X65 : subst] : (((comp @ X65 @ id)) = X65) => (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X248 : (term > $o),X249 : term,X250 : (subst > term > subst > $o),X251 : term] : (($true = ((X248 @ (ap @ X249 @ X251)))) | ~ ! [X256 : term,X257 : term] : (($true = ((X250 @ id @ (ap @ (sub @ X257 @ id) @ X256) @ id))) | (((X250 @ id @ X256 @ id)) != $true) | ($true != ((X250 @ id @ X257 @ id)))) | ($true != ((X248 @ X251))) | ~ ! [X258 : term] : (((X248 @ X258)) = ((X250 @ id @ X258 @ id))) | ~ ! [X261 : subst,X259 : subst,X262 : subst,X260 : term] : ((((X250 @ X259 @ X260 @ (comp @ X261 @ X262))) = $true) | (((X250 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)) != $true)) | ($true != ((X248 @ X249))) | ~ ! [X255 : term,X253 : subst,X254 : subst,X252 : subst] : (($true = ((X250 @ (comp @ X253 @ X254) @ (sub @ X255 @ X254) @ X252))) | ($true != ((X250 @ X253 @ X255 @ (comp @ X254 @ X252))))))) & ((hoasapinj1 = $true) <=> ! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533))))) & ((! [X488 : term,X487 : term,X490 : term,X489 : term] : ((X487 = X490) | (((ap @ X488 @ X487)) != ((ap @ X489 @ X490)))) => ! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491))))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (axvarshift = $true) & (! [X148 : (subst > term > subst > $o),X147 : term] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ~ ! [X154 : term] : (($true != ((X148 @ id @ X154 @ id))) | (((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) = $true)) | ~ ! [X149 : (subst > term > term)] : ((((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) = $true) | ~ ! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152))) | ~ ! [X150 : term] : (($true = ((X148 @ id @ (X149 @ id @ X150) @ id))) | ($true != ((X148 @ id @ X150 @ id)))))) <=> (hoasinduction_lem3aa = $true)) & (axassoc = $true) & (! [X447 : term] : ~ ! [X448 : (subst > term > term)] : ~ ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((! [X275 : term,X274 : subst] : (((sub @ one @ (push @ X275 @ X274))) = X275) => (! [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) = X277) => (! [X278 : term,X279 : term] : ((X278 = X279) | (((lam @ X279)) != ((lam @ X278)))) => ! [X280 : subst,X281 : (subst > term > term),X283 : (subst > term > term),X282 : term] : ((((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one)))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ~ ! [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) = ((sub @ (X281 @ X288 @ X287) @ X289))) | ~ ! [X285 : subst,X286 : subst,X284 : term] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) = ((sub @ (X283 @ X285 @ X284) @ X286))))))) <=> (hoaslaminj_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (lamnotap != $true) & ((laminj = $true) <=> ! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170))) & (substmonoid_gthm = $true) & (induction2lem_gthm = $true) & (! [X495 : term,X496 : (subst > term > subst > $o)] : (~ ! [X498 : term,X497 : term] : (($true != ((X496 @ id @ X498 @ id))) | (((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) = $true) | (((X496 @ id @ X497 @ id)) != $true)) | ~ ! [X499 : (subst > term > term)] : (($true = ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id))) | ~ ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ($true != ((X496 @ id @ X503 @ id)))) | ~ ! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501)))) | ($true = ((X496 @ id @ X495 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (((var @ (d2term @ d_one))) != $true) & ((induction2_lthm = $true) <=> (! [X387 : term] : (((sub @ X387 @ id)) = X387) => (! [X390 : (term > $o),X389 : subst,X388 : term] : (($true = ((X390 @ (sub @ X388 @ X389)))) | ~ ! [X393 : term] : (($true != ((var @ X393))) | ($true = ((X390 @ (sub @ X393 @ X389))))) | ~ ! [X391 : term] : (~ ! [X392 : term] : ((((X390 @ X392)) != $true) | ($true = ((X390 @ (sub @ X391 @ (push @ X392 @ id)))))) | ($true = ((X390 @ (lam @ X391))))) | ~ ! [X394 : term,X395 : term] : (($true = ((X390 @ (ap @ X394 @ X395)))) | (((X390 @ X394)) != $true) | (((X390 @ X395)) != $true))) => ! [X396 : term,X397 : (term > $o)] : (($true = ((X397 @ X396))) | ~ ! [X400 : term] : (($true != ((var @ X400))) | ($true = ((X397 @ X400)))) | ~ ! [X402 : term,X401 : term] : ((((X397 @ X401)) != $true) | (((X397 @ X402)) != $true) | (((X397 @ (ap @ X402 @ X401))) = $true)) | ~ ! [X398 : term] : ((((X397 @ (lam @ X398))) = $true) | ~ ! [X399 : term] : (($true = ((X397 @ (sub @ X398 @ (push @ X399 @ id))))) | (((X397 @ X399)) != $true))))))) & (! [X84 : (subst > term > subst > $o),X83 : term] : (~ ! [X86 : (subst > term > term)] : ((((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ~ ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))) | ~ ! [X90 : term] : ((((X84 @ id @ X90 @ id)) != $true) | (((X84 @ id @ (X86 @ id @ X90) @ id)) = $true))) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ~ ! [X85 : term] : (($true = ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) | (((X84 @ id @ X85 @ id)) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> (termmset = $true)) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & (! [X372 : term,X374 : term,X373 : (subst > term > subst > $o)] : (($true = ((X373 @ id @ (ap @ X374 @ X372) @ id))) | ~ ! [X379 : term,X380 : term] : ((((X373 @ id @ X379 @ id)) != $true) | ($true = ((X373 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id))) | ($true != ((X373 @ id @ X380 @ id)))) | ~ ! [X383 : subst,X382 : subst,X384 : subst,X381 : term] : (($true != ((X373 @ X384 @ X381 @ (comp @ X383 @ X382)))) | (((X373 @ (comp @ X384 @ X383) @ (sub @ X381 @ X383) @ X382)) = $true)) | ~ ! [X377 : subst,X378 : subst,X376 : subst,X375 : term] : ((((X373 @ (comp @ X377 @ X378) @ (sub @ X375 @ X378) @ X376)) != $true) | ($true = ((X373 @ X377 @ X375 @ (comp @ X378 @ X376))))) | (((X373 @ id @ X372 @ id)) != $true) | ($true != ((X373 @ id @ X374 @ id)))) <=> (hoasinduction_lem2 = $true)) & ((! [X526 : term] : (((sub @ X526 @ id)) = X526) => ! [X527 : term] : (((sub @ X527 @ id)) = X527)) <=> (termmset_lthm = $true)) & ((induction2lem = $true) <=> ! [X155 : term,X156 : subst,X157 : (term > $o)] : (~ ! [X162 : term] : (($true != ((var @ X162))) | (((X157 @ (sub @ X162 @ X156))) = $true)) | ~ ! [X161 : term,X160 : term] : ((((X157 @ X161)) != $true) | (((X157 @ (ap @ X160 @ X161))) = $true) | ($true != ((X157 @ X160)))) | ~ ! [X158 : term] : (~ ! [X159 : term] : (($true = ((X157 @ (sub @ X158 @ (push @ X159 @ id))))) | ($true != ((X157 @ X159)))) | (((X157 @ (lam @ X158))) = $true)) | (((X157 @ (sub @ X155 @ X156))) = $true))) & (hoasinduction_lem1 = $true) & (! [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) | ($true != ((X59 @ X58)))) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem3_gthm = $true) & ! [X443 : d_term] : (d_one = X443) & (axabs = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (axapp = $true) & (! [X293 : term,X294 : (subst > term > subst > $o)] : (~ ! [X296 : term,X297 : (subst > term > term)] : (~ ! [X301 : term] : ((((X294 @ id @ X301 @ id)) != $true) | (((X294 @ id @ (X297 @ id @ X301) @ id)) = $true)) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ~ ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) | ~ ! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302)))) | ~ ! [X295 : term] : ((((X294 @ id @ X295 @ id)) != $true) | ($true = ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id)))) | (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : (subst > term > subst > $o),X173 : term] : (($true = ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id))) | ~ ! [X179 : term] : ((((X172 @ id @ X179 @ id)) != $true) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) | ~ ! [X174 : (subst > term > term)] : ((((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true) | ~ ! [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) = ((sub @ (X174 @ X177 @ X176) @ X178))) | ~ ! [X175 : term] : (($true = ((X172 @ id @ (X174 @ id @ X175) @ id))) | (((X172 @ id @ X175 @ id)) != $true)))) => ! [X180 : term,X181 : (subst > term > subst > $o)] : (~ ! [X182 : (subst > term > term)] : (~ ! [X184 : subst,X183 : term,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) | (((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ~ ! [X186 : term] : (($true = ((X181 @ id @ (X182 @ id @ X186) @ id))) | (((X181 @ id @ X186 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true) | ~ ! [X187 : term] : ((((X181 @ id @ X187 @ id)) != $true) | (((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)) = $true))))) <=> (hoasinduction_lem3a_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X40 : term,X39 : subst] : (((sub @ one @ (push @ X40 @ X39))) = X40) => ! [X41 : (term > $o),X43 : (term > $o),X44 : subst,X42 : term] : ((((X41 @ one)) = $true) | ~ ! [X45 : term] : (((X41 @ X45)) = ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X43 @ X42)) != $true)))) & (hoasapinj1_gthm = $true) & (! [X519 : term,X518 : (subst > term > subst > $o)] : (~ ! [X525 : term] : ((((X518 @ id @ X525 @ id)) != $true) | ($true = ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) | ($true = ((X518 @ id @ (lam @ X519) @ id))) | ~ ! [X520 : (subst > term > term)] : (~ ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523))) | ($true = ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) | ~ ! [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) = $true) | ($true != ((X518 @ id @ X521 @ id)))))) <=> (hoasinduction_lem3a = $true)) & (ulamvar1 != $true) & ((! [X323 : (subst > term > subst > $o)] : ~ ! [X324 : (term > $o)] : ~ ! [X325 : term] : (((X324 @ X325)) = ((X323 @ id @ X325 @ id))) => (! [X327 : term,X326 : (term > $o)] : (~ ! [X330 : term] : ((((var @ X330)) != $true) | ($true = ((X326 @ X330)))) | (((X326 @ X327)) = $true) | ~ ! [X332 : term,X331 : term] : (($true != ((X326 @ X332))) | ($true != ((X326 @ X331))) | (((X326 @ (ap @ X332 @ X331))) = $true)) | ~ ! [X328 : term] : (~ ! [X329 : term] : (($true = ((X326 @ (sub @ X328 @ (push @ X329 @ id))))) | (((X326 @ X329)) != $true)) | ($true = ((X326 @ (lam @ X328)))))) => (! [X333 : term] : (((sub @ X333 @ id)) = X333) => (! [X336 : (subst > term > subst > $o),X335 : term,X334 : (term > $o)] : ((((X334 @ (lam @ X335))) = $true) | ~ ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id))) | ~ ! [X338 : term] : ((((X334 @ X338)) != $true) | (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true)) | ~ ! [X339 : (subst > term > term)] : (~ ! [X343 : term] : ((((X336 @ id @ X343 @ id)) != $true) | ($true = ((X336 @ id @ (X339 @ id @ X343) @ id)))) | ~ ! [X342 : subst,X341 : term,X340 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) = ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))))) => ! [X345 : term,X344 : (subst > term > subst > $o)] : (~ ! [X361 : term] : (($true != ((var @ (sub @ X361 @ id)))) | (((X344 @ id @ X361 @ id)) = $true)) | ~ ! [X360 : subst,X359 : subst,X358 : term,X357 : subst] : ((((X344 @ X360 @ X358 @ (comp @ X357 @ X359))) != $true) | (((X344 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359)) = $true)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : subst,X355 : subst,X354 : term] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) | ($true = ((X344 @ id @ (lam @ (X352 @ sh @ one)) @ id))) | ~ ! [X356 : term] : (($true = ((X344 @ id @ (X352 @ id @ X356) @ id))) | (((X344 @ id @ X356 @ id)) != $true))) | ~ ! [X347 : term,X346 : term] : ((((X344 @ id @ X347 @ id)) != $true) | (((X344 @ id @ (ap @ (sub @ X346 @ id) @ X347) @ id)) = $true) | (((X344 @ id @ X346 @ id)) != $true)) | (((X344 @ id @ X345 @ id)) = $true) | ~ ! [X351 : subst,X349 : term,X348 : subst,X350 : subst] : ((((X344 @ (comp @ X351 @ X348) @ (sub @ X349 @ X348) @ X350)) != $true) | (((X344 @ X351 @ X349 @ (comp @ X348 @ X350))) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X61 : (subst > term > subst > $o)] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_gthm = $true) & (hoasapnotvar_gthm = $true) & (! [X406 : (subst > term > term),X403 : term,X404 : (subst > term > term),X405 : subst] : (~ ! [X410 : term,X411 : subst,X412 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) = ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ~ ! [X408 : subst,X407 : subst,X409 : term] : (((sub @ (X404 @ X407 @ X409) @ X408)) = ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408))))) <=> (hoaslaminj = $true)) & ((axvarid = $true) <=> ! [X467 : term] : (((sub @ X467 @ id)) = X467)) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = id) & (pushprop = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X451 : term,X452 : (subst > term > subst > $o)] : (~ ! [X457 : term] : (($true != ((X452 @ id @ X457 @ id))) | (((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) = $true)) | ~ ! [X454 : subst,X456 : subst,X455 : term,X453 : subst] : ((((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) = $true) | (((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) != $true)) | ~ ! [X458 : (subst > term > term)] : (~ ! [X461 : term,X462 : subst,X460 : subst] : (((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X458 @ X460 @ X461) @ X462))) | (((X452 @ id @ (lam @ (X458 @ sh @ one)) @ id)) = $true) | ~ ! [X459 : term] : (($true = ((X452 @ id @ (X458 @ id @ X459) @ id))) | (((X452 @ id @ X459 @ id)) != $true))) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ~ ! [X464 : subst,X463 : subst,X466 : term,X465 : subst] : (($true = ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))) | (((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) != $true))) <=> (hoasinduction_lem3 = $true)) & (hoaslamnotvar_lthm = $true) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) <=> (substmonoid = $true)) & (((d2subst @ d_id)) = sh) & ((hoaslamnotap = $true) <=> ! [X165 : term,X164 : term,X163 : (subst > term > term)] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ~ ! [X166 : subst,X167 : subst,X168 : term] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X163 @ X166 @ X168) @ X167))))) & (! [X413 : term,X416 : (term > $o),X415 : subst,X414 : (term > $o)] : (~ ! [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) = ((X416 @ X417))) | (((X416 @ one)) = $true) | ($true != ((X414 @ X413)))) <=> (pushprop_lem1v2 = $true)) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X438 : term,X436 : subst,X437 : (term > $o)] : ~ ! [X439 : (term > $o)] : ~ ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X265 : term] : (((sub @ X265 @ id)) = X265) => (! [X268 : term,X267 : term,X266 : term,X269 : term] : ((X267 = X268) | (((ap @ X267 @ X269)) != ((ap @ X268 @ X266)))) => ! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271))))))) & (pushprop_lem0_gthm = $true) & (! [X221 : subst] : (((comp @ id @ X221)) = X221) <=> (axidl = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3b = $true) <=> ! [X263 : term] : ~ ! [X264 : (subst > term > term)] : (((X264 @ sh @ one)) != ((sub @ X263 @ (push @ one @ sh))))) & (hoasapinj2_gthm = $true) & ((axvarcons = $true) <=> ! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386)) & ((! [X94 : term,X93 : (term > $o)] : (~ ! [X99 : term,X98 : term] : ((((X93 @ X98)) != $true) | ($true != ((X93 @ X99))) | ($true = ((X93 @ (ap @ X98 @ X99))))) | ~ ! [X95 : term] : (($true = ((X93 @ (lam @ X95)))) | ~ ! [X96 : term] : ((((X93 @ (sub @ X95 @ (push @ X96 @ id)))) = $true) | ($true != ((X93 @ X96))))) | ($true = ((X93 @ X94))) | ~ ! [X97 : term] : (($true = ((X93 @ X97))) | (((var @ X97)) != $true))) => (! [X102 : term,X100 : term,X101 : (subst > term > subst > $o)] : (~ ! [X108 : subst,X109 : subst,X107 : subst,X110 : term] : ((((X101 @ X107 @ X110 @ (comp @ X109 @ X108))) != $true) | ($true = ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108)))) | (((X101 @ id @ X102 @ id)) != $true) | ($true = ((X101 @ id @ (ap @ X102 @ X100) @ id))) | ~ ! [X112 : term,X111 : term] : ((((X101 @ id @ X112 @ id)) != $true) | ($true != ((X101 @ id @ X111 @ id))) | ($true = ((X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id)))) | ~ ! [X105 : subst,X103 : subst,X106 : term,X104 : subst] : (($true = ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)))) | ($true != ((X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)))) | (((X101 @ id @ X100 @ id)) != $true)) => (! [X114 : term,X113 : (subst > term > subst > $o)] : (~ ! [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true != ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ~ ! [X120 : (subst > term > term)] : (($true = ((X113 @ id @ (lam @ (X120 @ sh @ one)) @ id))) | ~ ! [X122 : subst,X123 : subst,X121 : term] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X120 @ X123 @ X121) @ X122))) | ~ ! [X124 : term] : (($true = ((X113 @ id @ (X120 @ id @ X124) @ id))) | (((X113 @ id @ X124 @ id)) != $true))) | ($true = ((X113 @ id @ (lam @ X114) @ id))) | ~ ! [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true != ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) | (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true)) | ~ ! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ($true != ((X113 @ id @ X115 @ id))))) => ! [X130 : term,X129 : (subst > term > subst > $o)] : ((((X129 @ id @ X130 @ id)) = $true) | ~ ! [X143 : subst,X144 : term,X145 : subst,X146 : subst] : ((((X129 @ X145 @ X144 @ (comp @ X143 @ X146))) = $true) | ($true != ((X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146)))) | ~ ! [X142 : term] : ((((var @ (sub @ X142 @ id))) != $true) | (((X129 @ id @ X142 @ id)) = $true)) | ~ ! [X131 : term,X132 : term] : (($true = ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id))) | ($true != ((X129 @ id @ X131 @ id))) | ($true != ((X129 @ id @ X132 @ id)))) | ~ ! [X138 : term,X140 : subst,X139 : subst,X141 : subst] : (($true != ((X129 @ X141 @ X138 @ (comp @ X140 @ X139)))) | (((X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) = $true)) | ~ ! [X133 : (subst > term > term)] : (~ ! [X134 : term] : (($true = ((X129 @ id @ (X133 @ id @ X134) @ id))) | (((X129 @ id @ X134 @ id)) != $true)) | ~ ! [X136 : subst,X135 : term,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137))) | ($true = ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)))))))) <=> (hoasinduction_lthm = $true)) & (pushprop_lem3v2 = $true) & (apnotvar = $true) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) <=> (axshiftcons = $true)) & (! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) <=> (shinj = $true)) & (pushprop_lem1v2_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X47 : subst,X46 : term] : (((sub @ one @ (push @ X46 @ X47))) = X46) => (! [X48 : term,X49 : subst] : (((comp @ sh @ (push @ X48 @ X49))) = X49) => ! [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ($true != ((X52 @ X51))))))) & (hoasapnotvar = $true) & ! [X538 : d_term,X539 : d_term] : ((((d2term @ X538)) = ((d2term @ X539))) => (X538 = X539)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X0 : term] : ~ ! [X1 : (subst > term > term)] : ~ ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2)))))), 26.09/4.24 inference(flattening,[],[f9])). 26.09/4.24 thf(f11,plain,( 26.09/4.24 (! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) <=> (apinj2 = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (? [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) != $true) & (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) = $true)) | ? [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true != ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) & (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) = $true)) | ? [X308 : (subst > term > term)] : (! [X312 : term] : ((((X306 @ id @ (X308 @ id @ X312) @ id)) = $true) | ($true != ((X306 @ id @ X312 @ id)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) & ! [X309 : subst,X311 : subst,X310 : term] : (((sub @ (X308 @ X309 @ X310) @ X311)) = ((X308 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311))))) | ? [X318 : term] : (($true != ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) & ($true = ((X305 @ X318)))) | (((X305 @ (lam @ X307))) = $true) | ? [X313 : term] : (((X305 @ X313)) != ((X306 @ id @ X313 @ id))))) & ! [X228 : d_subst,X227 : d_subst] : ((((d2subst @ X227)) != ((d2subst @ X228))) | (X227 = X228)) & (! [X441 : term] : ? [X442 : (subst > term > term)] : (((X442 @ sh @ one)) = ((sub @ X441 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ! [X38 : d_subst] : (d_id = X38) & ((? [X229 : term] : (((sub @ X229 @ id)) != X229) | ! [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (? [X243 : (subst > term > term)] : (! [X244 : term] : ((((X230 @ id @ X244 @ id)) != $true) | ($true = ((X230 @ id @ (X243 @ id @ X244) @ id)))) & ($true != ((X230 @ id @ (lam @ (X243 @ sh @ one)) @ id))) & ! [X247 : subst,X246 : subst,X245 : term] : (((sub @ (X243 @ X247 @ X245) @ X246)) = ((X243 @ (comp @ X247 @ X246) @ (sub @ X245 @ X246))))) | ? [X237 : term] : (((X230 @ id @ X237 @ id)) != ((X231 @ X237))) | ? [X238 : term] : ((((X231 @ X238)) = $true) & (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) != $true)) | ? [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true != ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) & ($true = ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ? [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true = ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) & (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) != $true)) | ($true = ((X231 @ (lam @ X232)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((induction2 = $true) <=> ! [X5 : term,X4 : (term > $o)] : (? [X6 : term,X7 : term] : ((((X4 @ (ap @ X6 @ X7))) != $true) & ($true = ((X4 @ X6))) & ($true = ((X4 @ X7)))) | ? [X8 : term] : ((((var @ X8)) = $true) & (((X4 @ X8)) != $true)) | ? [X9 : term] : (! [X10 : term] : ((((X4 @ X10)) != $true) | ($true = ((X4 @ (sub @ X9 @ (push @ X10 @ id)))))) & ($true != ((X4 @ (lam @ X9))))) | ($true = ((X4 @ X5))))) & ((hoasapinj2 = $true) <=> ! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509))) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> (axidr = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (! [X512 : (term > $o),X513 : term] : (($true = ((X512 @ X513))) | ? [X515 : term] : ((((X512 @ X515)) != $true) & (((var @ X515)) = $true)) | ? [X514 : term] : (($true = ((X512 @ X514))) & (((X512 @ (lam @ X514))) != $true)) | ? [X517 : term,X516 : term] : ((((X512 @ X517)) = $true) & ($true != ((X512 @ (ap @ X516 @ X517)))) & (((X512 @ X516)) = $true))) <=> (induction = $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_gthm = $true) & (((! [X20 : term,X21 : (subst > term > subst > $o)] : (? [X26 : subst,X23 : term,X25 : subst,X24 : subst] : (($true != ((X21 @ X26 @ X23 @ (comp @ X24 @ X25)))) & (((X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25)) = $true)) | ($true = ((X21 @ id @ (lam @ X20) @ id))) | ? [X29 : subst,X28 : term,X27 : subst,X30 : subst] : ((((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30)) != $true) & (((X21 @ X27 @ X28 @ (comp @ X29 @ X30))) = $true)) | ? [X22 : term] : (($true != ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id))) & ($true = ((X21 @ id @ X22 @ id)))) | ? [X31 : (subst > term > term)] : (! [X32 : term] : (($true = ((X21 @ id @ (X31 @ id @ X32) @ id))) | (((X21 @ id @ X32 @ id)) != $true)) & (((X21 @ id @ (lam @ (X31 @ sh @ one)) @ id)) != $true) & ! [X34 : term,X33 : subst,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35)))))) | ? [X12 : (subst > term > subst > $o),X13 : term] : (! [X15 : (subst > term > term)] : (? [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) != ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : (($true = ((X12 @ id @ X19 @ id))) & ($true != ((X12 @ id @ (X15 @ id @ X19) @ id))))) & ! [X14 : term] : (($true != ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) & (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) != $true))) | ? [X11 : term] : (((sub @ X11 @ id)) != X11)) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (induction2_gthm = $true) & (((((! [X480 : subst,X479 : term,X481 : (term > $o)] : (? [X482 : term] : (($true != ((X481 @ (sub @ X482 @ X480)))) & ($true = ((var @ X482)))) | ($true = ((X481 @ (sub @ X479 @ X480)))) | ? [X485 : term,X486 : term] : ((((X481 @ X486)) = $true) & ($true != ((X481 @ (ap @ X486 @ X485)))) & ($true = ((X481 @ X485)))) | ? [X483 : term] : ((((X481 @ (lam @ X483))) != $true) & ! [X484 : term] : ((((X481 @ X484)) != $true) | ($true = ((X481 @ (sub @ X483 @ (push @ X484 @ id)))))))) | ? [X474 : (term > $o),X473 : term] : ((((X474 @ X473)) != $true) & ! [X478 : term] : ((((X474 @ X478)) = $true) | (((var @ X478)) != $true)) & ! [X477 : term] : ((((X474 @ X477)) != $true) | (((X474 @ (lam @ X477))) = $true)) & ! [X476 : term,X475 : term] : ((((X474 @ X476)) != $true) | (((X474 @ X475)) != $true) | (((X474 @ (ap @ X476 @ X475))) = $true)))) | ? [X472 : subst] : (((comp @ X472 @ id)) != X472)) | ? [X470 : subst,X471 : term] : (((comp @ sh @ (push @ X471 @ X470))) != X470)) | ? [X469 : subst,X468 : term] : (((sub @ one @ (push @ X468 @ X469))) != X468)) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (? [X81 : term] : (($true != ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) & ($true = ((X73 @ X81)))) | ($true = ((X73 @ (lam @ X75)))) | ? [X82 : term] : (((X74 @ id @ X82 @ id)) != ((X73 @ X82))) | ? [X76 : (subst > term > term)] : (($true != ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) & ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) & ! [X80 : term] : (($true != ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id)))))) | ? [X72 : term] : (((sub @ X72 @ id)) != X72)) | ? [X68 : term] : ! [X69 : (subst > term > term)] : ? [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) != ((sub @ X68 @ (push @ X70 @ X71)))))) & (lamnotvar = $true) & (termmset_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2_lthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (one = ((d2term @ d_one))) & (axclos = $true) & (hoaslamnotvar = $true) & (ulamvarind = $true) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & ((pushprop_lem0 = $true) <=> ! [X224 : subst,X222 : term,X223 : (term > $o)] : ? [X225 : (term > $o)] : ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226)))) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X419 : (subst > term > subst > $o),X418 : term] : (? [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true != ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) & ($true = ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) | ? [X426 : term,X425 : term] : ((((X419 @ id @ (ap @ (sub @ X425 @ id) @ X426) @ id)) != $true) & (((X419 @ id @ X426 @ id)) = $true) & ($true = ((X419 @ id @ X425 @ id)))) | ? [X431 : (subst > term > term)] : (! [X434 : subst,X433 : term,X435 : subst] : (((sub @ (X431 @ X434 @ X433) @ X435)) = ((X431 @ (comp @ X434 @ X435) @ (sub @ X433 @ X435)))) & ($true != ((X419 @ id @ (lam @ (X431 @ sh @ one)) @ id))) & ! [X432 : term] : (($true = ((X419 @ id @ (X431 @ id @ X432) @ id))) | (((X419 @ id @ X432 @ id)) != $true))) | ? [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true != ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) & (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) = $true)) | ($true = ((X419 @ id @ X418 @ id))) | ? [X424 : term] : ((((var @ (sub @ X424 @ id))) = $true) & ($true != ((X419 @ id @ X424 @ id))))) <=> (hoasinduction = $true)) & (! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) <=> (axscons = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (? [X366 : term] : (((X362 @ X366)) != ((X363 @ id @ X366 @ id))) | ? [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) != $true) & (((X362 @ X365)) = $true)) | ? [X367 : (subst > term > term)] : (! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) & ($true != ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | (((X363 @ id @ X368 @ id)) != $true))) | (((X362 @ (lam @ X364))) = $true))) & ((apinj1 = $true) <=> ! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem3b_gthm = $true) & (! [X444 : (subst > term > subst > $o)] : ? [X445 : (term > $o)] : ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446))) <=> (hoasinduction_lem0_lthm = $true)) & (((((! [X211 : term,X210 : (subst > term > subst > $o)] : (? [X213 : term,X212 : term] : (($true = ((X210 @ id @ X212 @ id))) & (((X210 @ id @ X213 @ id)) = $true) & (((X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id)) != $true)) | ? [X214 : (subst > term > term)] : (! [X217 : subst,X218 : term,X216 : subst] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))) & ! [X215 : term] : ((((X210 @ id @ (X214 @ id @ X215) @ id)) = $true) | (((X210 @ id @ X215 @ id)) != $true)) & ($true != ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id)))) | ($true = ((X210 @ id @ X211 @ id)))) | ? [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) != $true) & ! [X204 : (subst > term > term)] : (? [X208 : term] : (($true != ((X200 @ id @ (X204 @ id @ X208) @ id))) & ($true = ((X200 @ id @ X208 @ id)))) | ($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ? [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X204 @ X206 @ X205) @ X207)))) & ! [X209 : term] : (($true != ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) & ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203))))) | ? [X199 : term] : (((sub @ X199 @ id)) != X199)) | ? [X192 : term,X193 : (term > $o)] : (! [X194 : term] : (? [X195 : term] : ((((X193 @ X195)) = $true) & ($true != ((X193 @ (sub @ X194 @ (push @ X195 @ id)))))) | (((X193 @ (lam @ X194))) = $true)) & ! [X196 : term] : (($true = ((X193 @ X196))) | (((var @ X196)) != $true)) & ! [X198 : term,X197 : term] : ((((X193 @ X198)) != $true) | (((X193 @ X197)) != $true) | (((X193 @ (ap @ X198 @ X197))) = $true)) & (((X193 @ X192)) != $true))) | ? [X189 : (subst > term > subst > $o)] : ! [X190 : (term > $o)] : ? [X191 : term] : (((X190 @ X191)) != ((X189 @ id @ X191 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((((! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)) | ? [X65 : subst] : (((comp @ X65 @ id)) != X65)) | ? [X64 : subst] : (((comp @ id @ X64)) != X64)) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X250 : (subst > term > subst > $o),X251 : term,X249 : term,X248 : (term > $o)] : (($true != ((X248 @ X251))) | ? [X258 : term] : (((X248 @ X258)) != ((X250 @ id @ X258 @ id))) | ? [X256 : term,X257 : term] : (($true = ((X250 @ id @ X257 @ id))) & ($true != ((X250 @ id @ (ap @ (sub @ X257 @ id) @ X256) @ id))) & (((X250 @ id @ X256 @ id)) = $true)) | ($true != ((X248 @ X249))) | ? [X255 : term,X252 : subst,X254 : subst,X253 : subst] : (($true = ((X250 @ X253 @ X255 @ (comp @ X254 @ X252)))) & ($true != ((X250 @ (comp @ X253 @ X254) @ (sub @ X255 @ X254) @ X252)))) | ($true = ((X248 @ (ap @ X249 @ X251)))) | ? [X262 : subst,X260 : term,X261 : subst,X259 : subst] : ((((X250 @ X259 @ X260 @ (comp @ X261 @ X262))) != $true) & (((X250 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)) = $true)))) & ((hoasapinj1 = $true) <=> ! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533))))) & ((! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491)))) | ? [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) = ((ap @ X489 @ X490))) & (X487 != X490))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (axvarshift = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X148 : (subst > term > subst > $o),X147 : term] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ? [X149 : (subst > term > term)] : (! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152))) & (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) != $true) & ! [X150 : term] : (($true = ((X148 @ id @ (X149 @ id @ X150) @ id))) | ($true != ((X148 @ id @ X150 @ id))))) | ? [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) != $true) & ($true = ((X148 @ id @ X154 @ id)))))) & (axassoc = $true) & (! [X447 : term] : ? [X448 : (subst > term > term)] : ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((((! [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (? [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) != ((sub @ (X281 @ X288 @ X287) @ X289))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ? [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) != ((sub @ (X283 @ X285 @ X284) @ X286))) | (((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one))))) | ? [X279 : term,X278 : term] : ((((lam @ X279)) = ((lam @ X278))) & (X278 != X279))) | ? [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) != X277)) | ? [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) != X275)) <=> (hoaslaminj_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (lamnotap != $true) & ((laminj = $true) <=> ! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170))) & (substmonoid_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X496 : (subst > term > subst > $o),X495 : term] : (? [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) != $true) & ($true = ((X496 @ id @ X498 @ id))) & (((X496 @ id @ X497 @ id)) = $true)) | ? [X499 : (subst > term > term)] : (! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501))) & ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ($true != ((X496 @ id @ X503 @ id)))) & ($true != ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) | ($true = ((X496 @ id @ X495 @ id))))) & (((var @ (d2term @ d_one))) != $true) & ((induction2_lthm = $true) <=> ((! [X397 : (term > $o),X396 : term] : (? [X398 : term] : (! [X399 : term] : (($true = ((X397 @ (sub @ X398 @ (push @ X399 @ id))))) | (((X397 @ X399)) != $true)) & (((X397 @ (lam @ X398))) != $true)) | ? [X400 : term] : (($true = ((var @ X400))) & ($true != ((X397 @ X400)))) | ? [X402 : term,X401 : term] : ((((X397 @ (ap @ X402 @ X401))) != $true) & (((X397 @ X402)) = $true) & (((X397 @ X401)) = $true)) | ($true = ((X397 @ X396)))) | ? [X390 : (term > $o),X388 : term,X389 : subst] : (($true != ((X390 @ (sub @ X388 @ X389)))) & ! [X391 : term] : (? [X392 : term] : ((((X390 @ X392)) = $true) & ($true != ((X390 @ (sub @ X391 @ (push @ X392 @ id)))))) | ($true = ((X390 @ (lam @ X391))))) & ! [X393 : term] : (($true != ((var @ X393))) | ($true = ((X390 @ (sub @ X393 @ X389))))) & ! [X394 : term,X395 : term] : (($true = ((X390 @ (ap @ X394 @ X395)))) | (((X390 @ X394)) != $true) | (((X390 @ X395)) != $true)))) | ? [X387 : term] : (((sub @ X387 @ id)) != X387))) & (! [X84 : (subst > term > subst > $o),X83 : term] : (? [X85 : term] : (($true != ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) & (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ? [X86 : (subst > term > term)] : (! [X90 : term] : ((((X84 @ id @ X90 @ id)) != $true) | (((X84 @ id @ (X86 @ id @ X90) @ id)) = $true)) & (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> (termmset = $true)) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & (! [X372 : term,X374 : term,X373 : (subst > term > subst > $o)] : (? [X377 : subst,X376 : subst,X375 : term,X378 : subst] : (($true != ((X373 @ X377 @ X375 @ (comp @ X378 @ X376)))) & (((X373 @ (comp @ X377 @ X378) @ (sub @ X375 @ X378) @ X376)) = $true)) | ($true = ((X373 @ id @ (ap @ X374 @ X372) @ id))) | ? [X382 : subst,X381 : term,X383 : subst,X384 : subst] : (($true = ((X373 @ X384 @ X381 @ (comp @ X383 @ X382)))) & (((X373 @ (comp @ X384 @ X383) @ (sub @ X381 @ X383) @ X382)) != $true)) | ? [X379 : term,X380 : term] : (($true = ((X373 @ id @ X380 @ id))) & (((X373 @ id @ X379 @ id)) = $true) & ($true != ((X373 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id)))) | (((X373 @ id @ X372 @ id)) != $true) | ($true != ((X373 @ id @ X374 @ id)))) <=> (hoasinduction_lem2 = $true)) & ((! [X527 : term] : (((sub @ X527 @ id)) = X527) | ? [X526 : term] : (((sub @ X526 @ id)) != X526)) <=> (termmset_lthm = $true)) & (! [X157 : (term > $o),X156 : subst,X155 : term] : (? [X161 : term,X160 : term] : (($true = ((X157 @ X160))) & (((X157 @ (ap @ X160 @ X161))) != $true) & (((X157 @ X161)) = $true)) | ? [X162 : term] : (($true = ((var @ X162))) & (((X157 @ (sub @ X162 @ X156))) != $true)) | ? [X158 : term] : (! [X159 : term] : (($true = ((X157 @ (sub @ X158 @ (push @ X159 @ id))))) | ($true != ((X157 @ X159)))) & (((X157 @ (lam @ X158))) != $true)) | (((X157 @ (sub @ X155 @ X156))) = $true)) <=> (induction2lem = $true)) & (hoasinduction_lem1 = $true) & (! [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) | ($true != ((X59 @ X58)))) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem3_gthm = $true) & ! [X443 : d_term] : (d_one = X443) & (axabs = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X294 : (subst > term > subst > $o),X293 : term] : (? [X296 : term,X297 : (subst > term > term)] : (! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) & ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) & ! [X301 : term] : ((((X294 @ id @ X301 @ id)) != $true) | (((X294 @ id @ (X297 @ id @ X301) @ id)) = $true)) & (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true)) | (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true) | ? [X295 : term] : (($true != ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) & (((X294 @ id @ X295 @ id)) = $true)))) & (((! [X180 : term,X181 : (subst > term > subst > $o)] : (? [X187 : term] : ((((X181 @ id @ X187 @ id)) = $true) & (((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)) != $true)) | ? [X182 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id)) != $true) & ! [X184 : subst,X183 : term,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) & ! [X186 : term] : (($true = ((X181 @ id @ (X182 @ id @ X186) @ id))) | (((X181 @ id @ X186 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true)) | ? [X172 : (subst > term > subst > $o),X173 : term] : (! [X174 : (subst > term > term)] : (? [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) != ((sub @ (X174 @ X177 @ X176) @ X178))) | ? [X175 : term] : (($true != ((X172 @ id @ (X174 @ id @ X175) @ id))) & (((X172 @ id @ X175 @ id)) = $true)) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) & ! [X179 : term] : ((((X172 @ id @ X179 @ id)) != $true) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) & ($true != ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id))))) | ? [X171 : term] : (((sub @ X171 @ id)) != X171)) <=> (hoasinduction_lem3a_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) != X40) | ! [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) != $true) | ? [X45 : term] : (((X41 @ X45)) != ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true)))) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X518 : (subst > term > subst > $o),X519 : term] : (($true = ((X518 @ id @ (lam @ X519) @ id))) | ? [X525 : term] : ((((X518 @ id @ X525 @ id)) = $true) & ($true != ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) | ? [X520 : (subst > term > term)] : (! [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) = $true) | ($true != ((X518 @ id @ X521 @ id)))) & ($true != ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) & ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523)))))) & (ulamvar1 != $true) & (((((! [X345 : term,X344 : (subst > term > subst > $o)] : (? [X347 : term,X346 : term] : ((((X344 @ id @ (ap @ (sub @ X346 @ id) @ X347) @ id)) != $true) & (((X344 @ id @ X347 @ id)) = $true) & (((X344 @ id @ X346 @ id)) = $true)) | ? [X361 : term] : (($true = ((var @ (sub @ X361 @ id)))) & (((X344 @ id @ X361 @ id)) != $true)) | ? [X349 : term,X351 : subst,X348 : subst,X350 : subst] : ((((X344 @ X351 @ X349 @ (comp @ X348 @ X350))) != $true) & (((X344 @ (comp @ X351 @ X348) @ (sub @ X349 @ X348) @ X350)) = $true)) | ? [X358 : term,X357 : subst,X360 : subst,X359 : subst] : ((((X344 @ X360 @ X358 @ (comp @ X357 @ X359))) = $true) & (((X344 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359)) != $true)) | (((X344 @ id @ X345 @ id)) = $true) | ? [X352 : (subst > term > term)] : (! [X353 : subst,X355 : subst,X354 : term] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) & ! [X356 : term] : (($true = ((X344 @ id @ (X352 @ id @ X356) @ id))) | (((X344 @ id @ X356 @ id)) != $true)) & ($true != ((X344 @ id @ (lam @ (X352 @ sh @ one)) @ id))))) | ? [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) != $true) & ! [X339 : (subst > term > term)] : (? [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) != ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) | ? [X343 : term] : (($true != ((X336 @ id @ (X339 @ id @ X343) @ id))) & (((X336 @ id @ X343 @ id)) = $true))) & ! [X338 : term] : ((((X334 @ X338)) != $true) | (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true)) & ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id))))) | ? [X333 : term] : (((sub @ X333 @ id)) != X333)) | ? [X327 : term,X326 : (term > $o)] : (! [X330 : term] : ((((var @ X330)) != $true) | ($true = ((X326 @ X330)))) & (((X326 @ X327)) != $true) & ! [X328 : term] : (? [X329 : term] : ((((X326 @ X329)) = $true) & ($true != ((X326 @ (sub @ X328 @ (push @ X329 @ id)))))) | ($true = ((X326 @ (lam @ X328))))) & ! [X332 : term,X331 : term] : (($true != ((X326 @ X332))) | ($true != ((X326 @ X331))) | (((X326 @ (ap @ X332 @ X331))) = $true)))) | ? [X323 : (subst > term > subst > $o)] : ! [X324 : (term > $o)] : ? [X325 : term] : (((X324 @ X325)) != ((X323 @ id @ X325 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X61 : (subst > term > subst > $o)] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id)))) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_gthm = $true) & (hoasapnotvar_gthm = $true) & ((hoaslaminj = $true) <=> ! [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (? [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) != ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ? [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) != ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408)))))) & ((axvarid = $true) <=> ! [X467 : term] : (((sub @ X467 @ id)) = X467)) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = id) & (pushprop = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X451 : term,X452 : (subst > term > subst > $o)] : (? [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) != $true) & ($true = ((X452 @ id @ X457 @ id)))) | ? [X458 : (subst > term > term)] : ((((X452 @ id @ (lam @ (X458 @ sh @ one)) @ id)) != $true) & ! [X459 : term] : (($true = ((X452 @ id @ (X458 @ id @ X459) @ id))) | (((X452 @ id @ X459 @ id)) != $true)) & ! [X461 : term,X462 : subst,X460 : subst] : (((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X458 @ X460 @ X461) @ X462)))) | ? [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) = $true) & (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) != $true)) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ? [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) = $true) & ($true != ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))))) <=> (hoasinduction_lem3 = $true)) & (hoaslamnotvar_lthm = $true) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) <=> (substmonoid = $true)) & (((d2subst @ d_id)) = sh) & ((hoaslamnotap = $true) <=> ! [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ? [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) != ((sub @ (X163 @ X166 @ X168) @ X167))))) & ((pushprop_lem1v2 = $true) <=> ! [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (? [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) != ((X416 @ X417))) | ($true != ((X414 @ X413))) | (((X416 @ one)) = $true))) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X436 : subst,X437 : (term > $o),X438 : term] : ? [X439 : (term > $o)] : ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271)))) | ? [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) = ((ap @ X268 @ X266))) & (X267 != X268))) | ? [X265 : term] : (((sub @ X265 @ id)) != X265))) & (pushprop_lem0_gthm = $true) & (! [X221 : subst] : (((comp @ id @ X221)) = X221) <=> (axidl = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3b = $true) <=> ! [X263 : term] : ? [X264 : (subst > term > term)] : (((X264 @ sh @ one)) = ((sub @ X263 @ (push @ one @ sh))))) & (hoasapinj2_gthm = $true) & ((axvarcons = $true) <=> ! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386)) & ((((! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X142 : term] : ((((var @ (sub @ X142 @ id))) = $true) & (((X129 @ id @ X142 @ id)) != $true)) | ? [X133 : (subst > term > term)] : (! [X136 : subst,X135 : term,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137))) & ($true != ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id))) & ! [X134 : term] : (($true = ((X129 @ id @ (X133 @ id @ X134) @ id))) | (((X129 @ id @ X134 @ id)) != $true))) | ? [X140 : subst,X138 : term,X141 : subst,X139 : subst] : (($true = ((X129 @ X141 @ X138 @ (comp @ X140 @ X139)))) & (((X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | ? [X146 : subst,X144 : term,X145 : subst,X143 : subst] : (($true = ((X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146))) & (((X129 @ X145 @ X144 @ (comp @ X143 @ X146))) != $true)) | ? [X131 : term,X132 : term] : (($true = ((X129 @ id @ X132 @ id))) & ($true = ((X129 @ id @ X131 @ id))) & ($true != ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id))))) | ? [X114 : term,X113 : (subst > term > subst > $o)] : (! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ($true != ((X113 @ id @ X115 @ id)))) & ! [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true != ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) & ($true != ((X113 @ id @ (lam @ X114) @ id))) & ! [X120 : (subst > term > term)] : (($true = ((X113 @ id @ (lam @ (X120 @ sh @ one)) @ id))) | ? [X123 : subst,X122 : subst,X121 : term] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) != ((sub @ (X120 @ X123 @ X121) @ X122))) | ? [X124 : term] : (($true != ((X113 @ id @ (X120 @ id @ X124) @ id))) & (((X113 @ id @ X124 @ id)) = $true))) & ! [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true != ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) | (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true)))) | ? [X101 : (subst > term > subst > $o),X102 : term,X100 : term] : (($true != ((X101 @ id @ (ap @ X102 @ X100) @ id))) & ! [X105 : subst,X103 : subst,X106 : term,X104 : subst] : (($true = ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)))) | ($true != ((X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)))) & (((X101 @ id @ X102 @ id)) = $true) & (((X101 @ id @ X100 @ id)) = $true) & ! [X112 : term,X111 : term] : ((((X101 @ id @ X112 @ id)) != $true) | ($true != ((X101 @ id @ X111 @ id))) | ($true = ((X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id)))) & ! [X108 : subst,X109 : subst,X107 : subst,X110 : term] : ((((X101 @ X107 @ X110 @ (comp @ X109 @ X108))) != $true) | ($true = ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108)))))) | ? [X93 : (term > $o),X94 : term] : (! [X99 : term,X98 : term] : ((((X93 @ X98)) != $true) | ($true != ((X93 @ X99))) | ($true = ((X93 @ (ap @ X98 @ X99))))) & ! [X95 : term] : (? [X96 : term] : ((((X93 @ (sub @ X95 @ (push @ X96 @ id)))) != $true) & ($true = ((X93 @ X96)))) | ($true = ((X93 @ (lam @ X95))))) & ! [X97 : term] : (($true = ((X93 @ X97))) | (((var @ X97)) != $true)) & ($true != ((X93 @ X94))))) <=> (hoasinduction_lthm = $true)) & (pushprop_lem3v2 = $true) & (apnotvar = $true) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) <=> (axshiftcons = $true)) & (! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) <=> (shinj = $true)) & (pushprop_lem1v2_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ($true != ((X52 @ X51)))) | ? [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) != X49)) | ? [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) != X46))) & (hoasapnotvar = $true) & ! [X538 : d_term,X539 : d_term] : ((X538 = X539) | (((d2term @ X538)) != ((d2term @ X539)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X0 : term] : ? [X1 : (subst > term > term)] : ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2)))))), 26.09/4.24 inference(ennf_transformation,[],[f10])). 26.09/4.24 thf(f12,plain,( 26.09/4.24 (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) <=> ! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386)) & (hoasapnotvar_lthm = $true) & ((hoaslaminj = $true) <=> ! [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (? [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) != ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ? [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) != ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408)))))) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X250 : (subst > term > subst > $o),X251 : term,X249 : term,X248 : (term > $o)] : (($true != ((X248 @ X251))) | ? [X258 : term] : (((X248 @ X258)) != ((X250 @ id @ X258 @ id))) | ? [X256 : term,X257 : term] : (($true = ((X250 @ id @ X257 @ id))) & ($true != ((X250 @ id @ (ap @ (sub @ X257 @ id) @ X256) @ id))) & (((X250 @ id @ X256 @ id)) = $true)) | ($true != ((X248 @ X249))) | ? [X255 : term,X252 : subst,X254 : subst,X253 : subst] : (($true = ((X250 @ X253 @ X255 @ (comp @ X254 @ X252)))) & ($true != ((X250 @ (comp @ X253 @ X254) @ (sub @ X255 @ X254) @ X252)))) | ($true = ((X248 @ (ap @ X249 @ X251)))) | ? [X262 : subst,X260 : term,X261 : subst,X259 : subst] : ((((X250 @ X259 @ X260 @ (comp @ X261 @ X262))) != $true) & (((X250 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)) = $true)))) & (! [X221 : subst] : (((comp @ id @ X221)) = X221) <=> (axidl = $true)) & (hoaslamnotvar_lthm = $true) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & (! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) <=> (shinj = $true)) & (! [X444 : (subst > term > subst > $o)] : ? [X445 : (term > $o)] : ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446))) <=> (hoasinduction_lem0_lthm = $true)) & (axclos = $true) & (substmonoid_gthm = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (! [X157 : (term > $o),X156 : subst,X155 : term] : (? [X161 : term,X160 : term] : (($true = ((X157 @ X160))) & (((X157 @ (ap @ X160 @ X161))) != $true) & (((X157 @ X161)) = $true)) | ? [X162 : term] : (($true = ((var @ X162))) & (((X157 @ (sub @ X162 @ X156))) != $true)) | ? [X158 : term] : (! [X159 : term] : (($true = ((X157 @ (sub @ X158 @ (push @ X159 @ id))))) | ($true != ((X157 @ X159)))) & (((X157 @ (lam @ X158))) != $true)) | (((X157 @ (sub @ X155 @ X156))) = $true)) <=> (induction2lem = $true)) & (lamnotvar = $true) & (axabs = $true) & ! [X538 : d_term,X539 : d_term] : ((X538 = X539) | (((d2term @ X538)) != ((d2term @ X539)))) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) <=> (axshiftcons = $true)) & ((hoaslamnotap = $true) <=> ! [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ? [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) != ((sub @ (X163 @ X166 @ X168) @ X167))))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (axvarshift = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (hoasinduction_gthm = $true) & (! [X447 : term] : ? [X448 : (subst > term > term)] : ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X189 : (subst > term > subst > $o)] : ! [X190 : (term > $o)] : ? [X191 : term] : (((X190 @ X191)) != ((X189 @ id @ X191 @ id))) | ? [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) != $true) & ! [X204 : (subst > term > term)] : (? [X208 : term] : (($true != ((X200 @ id @ (X204 @ id @ X208) @ id))) & ($true = ((X200 @ id @ X208 @ id)))) | ($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ? [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X204 @ X206 @ X205) @ X207)))) & ! [X209 : term] : (($true != ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) & ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203)))) | ? [X199 : term] : (((sub @ X199 @ id)) != X199) | ! [X211 : term,X210 : (subst > term > subst > $o)] : (? [X213 : term,X212 : term] : (($true = ((X210 @ id @ X212 @ id))) & (((X210 @ id @ X213 @ id)) = $true) & (((X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id)) != $true)) | ? [X214 : (subst > term > term)] : (! [X217 : subst,X218 : term,X216 : subst] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))) & ! [X215 : term] : ((((X210 @ id @ (X214 @ id @ X215) @ id)) = $true) | (((X210 @ id @ X215 @ id)) != $true)) & ($true != ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id)))) | ($true = ((X210 @ id @ X211 @ id)))) | ? [X192 : term,X193 : (term > $o)] : (! [X194 : term] : (? [X195 : term] : ((((X193 @ X195)) = $true) & ($true != ((X193 @ (sub @ X194 @ (push @ X195 @ id)))))) | (((X193 @ (lam @ X194))) = $true)) & ! [X196 : term] : (($true = ((X193 @ X196))) | (((var @ X196)) != $true)) & ! [X198 : term,X197 : term] : ((((X193 @ X198)) != $true) | (((X193 @ X197)) != $true) | (((X193 @ (ap @ X198 @ X197))) = $true)) & (((X193 @ X192)) != $true)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X496 : (subst > term > subst > $o),X495 : term] : (? [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) != $true) & ($true = ((X496 @ id @ X498 @ id))) & (((X496 @ id @ X497 @ id)) = $true)) | ? [X499 : (subst > term > term)] : (! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501))) & ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ($true != ((X496 @ id @ X503 @ id)))) & ($true != ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) | ($true = ((X496 @ id @ X495 @ id))))) & ! [X228 : d_subst,X227 : d_subst] : ((((d2subst @ X227)) != ((d2subst @ X228))) | (X227 = X228)) & ((pushprop_lem1v2 = $true) <=> ! [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (? [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) != ((X416 @ X417))) | ($true != ((X414 @ X413))) | (((X416 @ one)) = $true))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (? [X81 : term] : (($true != ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) & ($true = ((X73 @ X81)))) | ($true = ((X73 @ (lam @ X75)))) | ? [X82 : term] : (((X74 @ id @ X82 @ id)) != ((X73 @ X82))) | ? [X76 : (subst > term > term)] : (($true != ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) & ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) & ! [X80 : term] : (($true != ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id)))))) | ? [X68 : term] : ! [X69 : (subst > term > term)] : ? [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) != ((sub @ X68 @ (push @ X70 @ X71)))) | ? [X72 : term] : (((sub @ X72 @ id)) != X72))) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & ((! [X527 : term] : (((sub @ X527 @ id)) = X527) | ? [X526 : term] : (((sub @ X526 @ id)) != X526)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X180 : term,X181 : (subst > term > subst > $o)] : (? [X187 : term] : ((((X181 @ id @ X187 @ id)) = $true) & (((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)) != $true)) | ? [X182 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id)) != $true) & ! [X184 : subst,X183 : term,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) & ! [X186 : term] : (($true = ((X181 @ id @ (X182 @ id @ X186) @ id))) | (((X181 @ id @ X186 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true)) | ? [X172 : (subst > term > subst > $o),X173 : term] : (! [X174 : (subst > term > term)] : (? [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) != ((sub @ (X174 @ X177 @ X176) @ X178))) | ? [X175 : term] : (($true != ((X172 @ id @ (X174 @ id @ X175) @ id))) & (((X172 @ id @ X175 @ id)) = $true)) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) & ! [X179 : term] : ((((X172 @ id @ X179 @ id)) != $true) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) & ($true != ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id)))) | ? [X171 : term] : (((sub @ X171 @ id)) != X171))) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> (termmset = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (? [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) != X40) | ! [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) != $true) | ? [X45 : term] : (((X41 @ X45)) != ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true)))) & (! [X372 : term,X374 : term,X373 : (subst > term > subst > $o)] : (? [X377 : subst,X376 : subst,X375 : term,X378 : subst] : (($true != ((X373 @ X377 @ X375 @ (comp @ X378 @ X376)))) & (((X373 @ (comp @ X377 @ X378) @ (sub @ X375 @ X378) @ X376)) = $true)) | ($true = ((X373 @ id @ (ap @ X374 @ X372) @ id))) | ? [X382 : subst,X381 : term,X383 : subst,X384 : subst] : (($true = ((X373 @ X384 @ X381 @ (comp @ X383 @ X382)))) & (((X373 @ (comp @ X384 @ X383) @ (sub @ X381 @ X383) @ X382)) != $true)) | ? [X379 : term,X380 : term] : (($true = ((X373 @ id @ X380 @ id))) & (((X373 @ id @ X379 @ id)) = $true) & ($true != ((X373 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id)))) | (((X373 @ id @ X372 @ id)) != $true) | ($true != ((X373 @ id @ X374 @ id)))) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X263 : term] : ? [X264 : (subst > term > term)] : (((X264 @ sh @ one)) = ((sub @ X263 @ (push @ one @ sh))))) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> (axidr = $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X61 : (subst > term > subst > $o)] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id)))) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) <=> ! [X5 : term,X4 : (term > $o)] : (? [X6 : term,X7 : term] : ((((X4 @ (ap @ X6 @ X7))) != $true) & ($true = ((X4 @ X6))) & ($true = ((X4 @ X7)))) | ? [X8 : term] : ((((var @ X8)) = $true) & (((X4 @ X8)) != $true)) | ? [X9 : term] : (! [X10 : term] : ((((X4 @ X10)) != $true) | ($true = ((X4 @ (sub @ X9 @ (push @ X10 @ id)))))) & ($true != ((X4 @ (lam @ X9))))) | ($true = ((X4 @ X5))))) & (pushprop_gthm = $true) & (one = ((d2term @ d_one))) & (! [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) | ($true != ((X59 @ X58)))) <=> (pushprop_lem1 = $true)) & (induction2_gthm = $true) & (axmap = $true) & ! [X443 : d_term] : (d_one = X443) & ((hoasapinj1 = $true) <=> ! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533))))) & ((hoasapinj2 = $true) <=> ! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X11 : term] : (((sub @ X11 @ id)) != X11) | ! [X20 : term,X21 : (subst > term > subst > $o)] : (? [X26 : subst,X23 : term,X25 : subst,X24 : subst] : (($true != ((X21 @ X26 @ X23 @ (comp @ X24 @ X25)))) & (((X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25)) = $true)) | ($true = ((X21 @ id @ (lam @ X20) @ id))) | ? [X29 : subst,X28 : term,X27 : subst,X30 : subst] : ((((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30)) != $true) & (((X21 @ X27 @ X28 @ (comp @ X29 @ X30))) = $true)) | ? [X22 : term] : (($true != ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id))) & ($true = ((X21 @ id @ X22 @ id)))) | ? [X31 : (subst > term > term)] : (! [X32 : term] : (($true = ((X21 @ id @ (X31 @ id @ X32) @ id))) | (((X21 @ id @ X32 @ id)) != $true)) & (((X21 @ id @ (lam @ (X31 @ sh @ one)) @ id)) != $true) & ! [X34 : term,X33 : subst,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35)))))) | ? [X12 : (subst > term > subst > $o),X13 : term] : (! [X15 : (subst > term > term)] : (? [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) != ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : (($true = ((X12 @ id @ X19 @ id))) & ($true != ((X12 @ id @ (X15 @ id @ X19) @ id))))) & ! [X14 : term] : (($true != ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) & (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) != $true)))) & (((var @ (d2term @ d_one))) != $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((induction2_lthm = $true) <=> (! [X397 : (term > $o),X396 : term] : (? [X398 : term] : (! [X399 : term] : (($true = ((X397 @ (sub @ X398 @ (push @ X399 @ id))))) | (((X397 @ X399)) != $true)) & (((X397 @ (lam @ X398))) != $true)) | ? [X400 : term] : (($true = ((var @ X400))) & ($true != ((X397 @ X400)))) | ? [X402 : term,X401 : term] : ((((X397 @ (ap @ X402 @ X401))) != $true) & (((X397 @ X402)) = $true) & (((X397 @ X401)) = $true)) | ($true = ((X397 @ X396)))) | ? [X390 : (term > $o),X388 : term,X389 : subst] : (($true != ((X390 @ (sub @ X388 @ X389)))) & ! [X391 : term] : (? [X392 : term] : ((((X390 @ X392)) = $true) & ($true != ((X390 @ (sub @ X391 @ (push @ X392 @ id)))))) | ($true = ((X390 @ (lam @ X391))))) & ! [X393 : term] : (($true != ((var @ X393))) | ($true = ((X390 @ (sub @ X393 @ X389))))) & ! [X394 : term,X395 : term] : (($true = ((X390 @ (ap @ X394 @ X395)))) | (((X390 @ X394)) != $true) | (((X390 @ X395)) != $true))) | ? [X387 : term] : (((sub @ X387 @ id)) != X387))) & (! [X441 : term] : ? [X442 : (subst > term > term)] : (((X442 @ sh @ one)) = ((sub @ X441 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491)))) | ? [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) = ((ap @ X489 @ X490))) & (X487 != X490))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X518 : (subst > term > subst > $o),X519 : term] : (($true = ((X518 @ id @ (lam @ X519) @ id))) | ? [X525 : term] : ((((X518 @ id @ X525 @ id)) = $true) & ($true != ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) | ? [X520 : (subst > term > term)] : (! [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) = $true) | ($true != ((X518 @ id @ X521 @ id)))) & ($true != ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) & ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523)))))) & (pushprop = $true) & (pushprop_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((substmonoid_lthm = $true) <=> (? [X65 : subst] : (((comp @ X65 @ id)) != X65) | (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)) | ? [X64 : subst] : (((comp @ id @ X64)) != X64))) & ((apinj1 = $true) <=> ! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507))) & (ulamvarind = $true) & (pushprop_lthm_orig = $true) & (! [X84 : (subst > term > subst > $o),X83 : term] : (? [X85 : term] : (($true != ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) & (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ? [X86 : (subst > term > term)] : (! [X90 : term] : ((((X84 @ id @ X90 @ id)) != $true) | (((X84 @ id @ (X86 @ id @ X90) @ id)) = $true)) & (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X294 : (subst > term > subst > $o),X293 : term] : (? [X296 : term,X297 : (subst > term > term)] : (! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) & ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) & ! [X301 : term] : ((((X294 @ id @ X301 @ id)) != $true) | (((X294 @ id @ (X297 @ id @ X301) @ id)) = $true)) & (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true)) | (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true) | ? [X295 : term] : (($true != ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) & (((X294 @ id @ X295 @ id)) = $true)))) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (! [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (? [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) != ((sub @ (X281 @ X288 @ X287) @ X289))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ? [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) != ((sub @ (X283 @ X285 @ X284) @ X286))) | (((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one))))) | ? [X279 : term,X278 : term] : ((((lam @ X279)) = ((lam @ X278))) & (X278 != X279)) | ? [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) != X275) | ? [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) != X277))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X451 : term,X452 : (subst > term > subst > $o)] : (? [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) != $true) & ($true = ((X452 @ id @ X457 @ id)))) | ? [X458 : (subst > term > term)] : ((((X452 @ id @ (lam @ (X458 @ sh @ one)) @ id)) != $true) & ! [X459 : term] : (($true = ((X452 @ id @ (X458 @ id @ X459) @ id))) | (((X452 @ id @ X459 @ id)) != $true)) & ! [X461 : term,X462 : subst,X460 : subst] : (((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X458 @ X460 @ X461) @ X462)))) | ? [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) = $true) & (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) != $true)) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ? [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) = $true) & ($true != ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem1_gthm = $true) & ((? [X470 : subst,X471 : term] : (((comp @ sh @ (push @ X471 @ X470))) != X470) | ? [X474 : (term > $o),X473 : term] : ((((X474 @ X473)) != $true) & ! [X478 : term] : ((((X474 @ X478)) = $true) | (((var @ X478)) != $true)) & ! [X477 : term] : ((((X474 @ X477)) != $true) | (((X474 @ (lam @ X477))) = $true)) & ! [X476 : term,X475 : term] : ((((X474 @ X476)) != $true) | (((X474 @ X475)) != $true) | (((X474 @ (ap @ X476 @ X475))) = $true))) | ? [X469 : subst,X468 : term] : (((sub @ one @ (push @ X468 @ X469))) != X468) | ! [X480 : subst,X479 : term,X481 : (term > $o)] : (? [X482 : term] : (($true != ((X481 @ (sub @ X482 @ X480)))) & ($true = ((var @ X482)))) | ($true = ((X481 @ (sub @ X479 @ X480)))) | ? [X485 : term,X486 : term] : ((((X481 @ X486)) = $true) & ($true != ((X481 @ (ap @ X486 @ X485)))) & ($true = ((X481 @ X485)))) | ? [X483 : term] : ((((X481 @ (lam @ X483))) != $true) & ! [X484 : term] : ((((X481 @ X484)) != $true) | ($true = ((X481 @ (sub @ X483 @ (push @ X484 @ id)))))))) | ? [X472 : subst] : (((comp @ X472 @ id)) != X472)) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = id) & ((axvarid = $true) <=> ! [X467 : term] : (((sub @ X467 @ id)) = X467)) & (! [X436 : subst,X437 : (term > $o),X438 : term] : ? [X439 : (term > $o)] : ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) <=> (pushprop_lem0_lthm = $true)) & (! [X419 : (subst > term > subst > $o),X418 : term] : (? [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true != ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) & ($true = ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) | ? [X426 : term,X425 : term] : ((((X419 @ id @ (ap @ (sub @ X425 @ id) @ X426) @ id)) != $true) & (((X419 @ id @ X426 @ id)) = $true) & ($true = ((X419 @ id @ X425 @ id)))) | ? [X431 : (subst > term > term)] : (! [X434 : subst,X433 : term,X435 : subst] : (((sub @ (X431 @ X434 @ X433) @ X435)) = ((X431 @ (comp @ X434 @ X435) @ (sub @ X433 @ X435)))) & ($true != ((X419 @ id @ (lam @ (X431 @ sh @ one)) @ id))) & ! [X432 : term] : (($true = ((X419 @ id @ (X431 @ id @ X432) @ id))) | (((X419 @ id @ X432 @ id)) != $true))) | ? [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true != ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) & (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) = $true)) | ($true = ((X419 @ id @ X418 @ id))) | ? [X424 : term] : ((((var @ (sub @ X424 @ id))) = $true) & ($true != ((X419 @ id @ X424 @ id))))) <=> (hoasinduction = $true)) & (hoasapinj2_gthm = $true) & (! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) <=> (axscons = $true)) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((laminj = $true) <=> ! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170))) & (lamnotap != $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (? [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) != $true) & (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) = $true)) | ? [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true != ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) & (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) = $true)) | ? [X308 : (subst > term > term)] : (! [X312 : term] : ((((X306 @ id @ (X308 @ id @ X312) @ id)) = $true) | ($true != ((X306 @ id @ X312 @ id)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) & ! [X309 : subst,X311 : subst,X310 : term] : (((sub @ (X308 @ X309 @ X310) @ X311)) = ((X308 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311))))) | ? [X318 : term] : (($true != ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) & ($true = ((X305 @ X318)))) | (((X305 @ (lam @ X307))) = $true) | ? [X313 : term] : (((X305 @ X313)) != ((X306 @ id @ X313 @ id))))) & (! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) <=> (apinj2 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (? [X366 : term] : (((X362 @ X366)) != ((X363 @ id @ X366 @ id))) | ? [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) != $true) & (((X362 @ X365)) = $true)) | ? [X367 : (subst > term > term)] : (! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) & ($true != ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | (((X363 @ id @ X368 @ id)) != $true))) | (((X362 @ (lam @ X364))) = $true))) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X148 : (subst > term > subst > $o),X147 : term] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ? [X149 : (subst > term > term)] : (! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152))) & (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) != $true) & ! [X150 : term] : (($true = ((X148 @ id @ (X149 @ id @ X150) @ id))) | ($true != ((X148 @ id @ X150 @ id))))) | ? [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) != $true) & ($true = ((X148 @ id @ X154 @ id)))))) & (hoasinduction_lem3a_gthm = $true) & (ulamvarsh = $true) & ((pushprop_lem0 = $true) <=> ! [X224 : subst,X222 : term,X223 : (term > $o)] : ? [X225 : (term > $o)] : ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226)))) & ! [X38 : d_subst] : (d_id = X38) & ((? [X229 : term] : (((sub @ X229 @ id)) != X229) | ! [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (? [X243 : (subst > term > term)] : (! [X244 : term] : ((((X230 @ id @ X244 @ id)) != $true) | ($true = ((X230 @ id @ (X243 @ id @ X244) @ id)))) & ($true != ((X230 @ id @ (lam @ (X243 @ sh @ one)) @ id))) & ! [X247 : subst,X246 : subst,X245 : term] : (((sub @ (X243 @ X247 @ X245) @ X246)) = ((X243 @ (comp @ X247 @ X246) @ (sub @ X245 @ X246))))) | ? [X237 : term] : (((X230 @ id @ X237 @ id)) != ((X231 @ X237))) | ? [X238 : term] : ((((X231 @ X238)) = $true) & (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) != $true)) | ? [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true != ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) & ($true = ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ? [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true = ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) & (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) != $true)) | ($true = ((X231 @ (lam @ X232)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_lthm = $true) <=> (? [X114 : term,X113 : (subst > term > subst > $o)] : (! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ($true != ((X113 @ id @ X115 @ id)))) & ! [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true != ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) & ($true != ((X113 @ id @ (lam @ X114) @ id))) & ! [X120 : (subst > term > term)] : (($true = ((X113 @ id @ (lam @ (X120 @ sh @ one)) @ id))) | ? [X123 : subst,X122 : subst,X121 : term] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) != ((sub @ (X120 @ X123 @ X121) @ X122))) | ? [X124 : term] : (($true != ((X113 @ id @ (X120 @ id @ X124) @ id))) & (((X113 @ id @ X124 @ id)) = $true))) & ! [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true != ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) | (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true))) | ? [X93 : (term > $o),X94 : term] : (! [X99 : term,X98 : term] : ((((X93 @ X98)) != $true) | ($true != ((X93 @ X99))) | ($true = ((X93 @ (ap @ X98 @ X99))))) & ! [X95 : term] : (? [X96 : term] : ((((X93 @ (sub @ X95 @ (push @ X96 @ id)))) != $true) & ($true = ((X93 @ X96)))) | ($true = ((X93 @ (lam @ X95))))) & ! [X97 : term] : (($true = ((X93 @ X97))) | (((var @ X97)) != $true)) & ($true != ((X93 @ X94)))) | ? [X101 : (subst > term > subst > $o),X102 : term,X100 : term] : (($true != ((X101 @ id @ (ap @ X102 @ X100) @ id))) & ! [X105 : subst,X103 : subst,X106 : term,X104 : subst] : (($true = ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)))) | ($true != ((X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)))) & (((X101 @ id @ X102 @ id)) = $true) & (((X101 @ id @ X100 @ id)) = $true) & ! [X112 : term,X111 : term] : ((((X101 @ id @ X112 @ id)) != $true) | ($true != ((X101 @ id @ X111 @ id))) | ($true = ((X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id)))) & ! [X108 : subst,X109 : subst,X107 : subst,X110 : term] : ((((X101 @ X107 @ X110 @ (comp @ X109 @ X108))) != $true) | ($true = ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108))))) | ! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X142 : term] : ((((var @ (sub @ X142 @ id))) = $true) & (((X129 @ id @ X142 @ id)) != $true)) | ? [X133 : (subst > term > term)] : (! [X136 : subst,X135 : term,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137))) & ($true != ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id))) & ! [X134 : term] : (($true = ((X129 @ id @ (X133 @ id @ X134) @ id))) | (((X129 @ id @ X134 @ id)) != $true))) | ? [X140 : subst,X138 : term,X141 : subst,X139 : subst] : (($true = ((X129 @ X141 @ X138 @ (comp @ X140 @ X139)))) & (((X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | ? [X146 : subst,X144 : term,X145 : subst,X143 : subst] : (($true = ((X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146))) & (((X129 @ X145 @ X144 @ (comp @ X143 @ X146))) != $true)) | ? [X131 : term,X132 : term] : (($true = ((X129 @ id @ X132 @ id))) & ($true = ((X129 @ id @ X131 @ id))) & ($true != ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id))))))) & ((hoasinduction_lthm_3 = $true) <=> (? [X333 : term] : (((sub @ X333 @ id)) != X333) | ? [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) != $true) & ! [X339 : (subst > term > term)] : (? [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) != ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) | ? [X343 : term] : (($true != ((X336 @ id @ (X339 @ id @ X343) @ id))) & (((X336 @ id @ X343 @ id)) = $true))) & ! [X338 : term] : ((((X334 @ X338)) != $true) | (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true)) & ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id)))) | ? [X323 : (subst > term > subst > $o)] : ! [X324 : (term > $o)] : ? [X325 : term] : (((X324 @ X325)) != ((X323 @ id @ X325 @ id))) | ! [X345 : term,X344 : (subst > term > subst > $o)] : (? [X347 : term,X346 : term] : ((((X344 @ id @ (ap @ (sub @ X346 @ id) @ X347) @ id)) != $true) & (((X344 @ id @ X347 @ id)) = $true) & (((X344 @ id @ X346 @ id)) = $true)) | ? [X361 : term] : (($true = ((var @ (sub @ X361 @ id)))) & (((X344 @ id @ X361 @ id)) != $true)) | ? [X349 : term,X351 : subst,X348 : subst,X350 : subst] : ((((X344 @ X351 @ X349 @ (comp @ X348 @ X350))) != $true) & (((X344 @ (comp @ X351 @ X348) @ (sub @ X349 @ X348) @ X350)) = $true)) | ? [X358 : term,X357 : subst,X360 : subst,X359 : subst] : ((((X344 @ X360 @ X358 @ (comp @ X357 @ X359))) = $true) & (((X344 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359)) != $true)) | (((X344 @ id @ X345 @ id)) = $true) | ? [X352 : (subst > term > term)] : (! [X353 : subst,X355 : subst,X354 : term] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) & ! [X356 : term] : (($true = ((X344 @ id @ (X352 @ id @ X356) @ id))) | (((X344 @ id @ X356 @ id)) != $true)) & ($true != ((X344 @ id @ (lam @ (X352 @ sh @ one)) @ id))))) | ? [X327 : term,X326 : (term > $o)] : (! [X330 : term] : ((((var @ X330)) != $true) | ($true = ((X326 @ X330)))) & (((X326 @ X327)) != $true) & ! [X328 : term] : (? [X329 : term] : ((((X326 @ X329)) = $true) & ($true != ((X326 @ (sub @ X328 @ (push @ X329 @ id)))))) | ($true = ((X326 @ (lam @ X328))))) & ! [X332 : term,X331 : term] : (($true != ((X326 @ X332))) | ($true != ((X326 @ X331))) | (((X326 @ (ap @ X332 @ X331))) = $true))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & ((hoasinduction_lem3v2_f = $true) <=> ! [X0 : term] : ? [X1 : (subst > term > term)] : ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2))))) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) <=> (substmonoid = $true)) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X512 : (term > $o),X513 : term] : (($true = ((X512 @ X513))) | ? [X515 : term] : ((((X512 @ X515)) != $true) & (((var @ X515)) = $true)) | ? [X514 : term] : (($true = ((X512 @ X514))) & (((X512 @ (lam @ X514))) != $true)) | ? [X517 : term,X516 : term] : ((((X512 @ X517)) = $true) & ($true != ((X512 @ (ap @ X516 @ X517)))) & (((X512 @ X516)) = $true))) <=> (induction = $true)) & ((pushprop_lem1_lthm = $true) <=> (? [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) != X46) | ? [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) != X49) | ! [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ($true != ((X52 @ X51)))))) & ((! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271)))) | ? [X265 : term] : (((sub @ X265 @ id)) != X265) | ? [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) = ((ap @ X268 @ X266))) & (X267 != X268))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem2_lthm = $true)), 26.09/4.24 inference(flattening,[],[f11])). 26.09/4.24 thf(f13,plain,( 26.09/4.24 (hoasinduction_lem3a = $true) <~> ! [X0 : (subst > term > subst > $o)] : (! [X6 : term] : (? [X7 : term] : ((((X0 @ id @ (sub @ X6 @ (push @ X7 @ id)) @ id)) != $true) & ($true = ((X0 @ id @ X7 @ id)))) | (((X0 @ id @ (lam @ X6) @ id)) = $true)) | ? [X1 : (subst > term > term)] : ((($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) & ! [X5 : term] : (($true = ((X0 @ id @ (X1 @ id @ X5) @ id))) | (((X0 @ id @ X5 @ id)) != $true))) & ! [X4 : term,X2 : subst,X3 : subst] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2))))))), 26.09/4.24 inference(ennf_transformation,[],[f8])). 26.09/4.24 thf(f14,plain,( 26.09/4.24 ! [X0 : (subst > term > subst > $o)] : (? [X1 : (subst > term > term)] : (! [X5 : term] : (($true = ((X0 @ id @ (X1 @ id @ X5) @ id))) | (((X0 @ id @ X5 @ id)) != $true)) & ($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) & ! [X4 : term,X2 : subst,X3 : subst] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2))))) | ! [X6 : term] : (? [X7 : term] : ((((X0 @ id @ (sub @ X6 @ (push @ X7 @ id)) @ id)) != $true) & ($true = ((X0 @ id @ X7 @ id)))) | (((X0 @ id @ (lam @ X6) @ id)) = $true))) <~> (hoasinduction_lem3a = $true)), 26.09/4.24 inference(flattening,[],[f13])). 26.09/4.24 thf(f15,definition,( 26.09/4.24 ! [X344 : (subst > term > subst > $o)] : ((((sP0 @ X344)) = $true) <=> ? [X352 : (subst > term > term)] : (! [X353 : subst,X355 : subst,X354 : term] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) & ! [X356 : term] : (($true = ((X344 @ id @ (X352 @ id @ X356) @ id))) | (((X344 @ id @ X356 @ id)) != $true)) & ($true != ((X344 @ id @ (lam @ (X352 @ sh @ one)) @ id)))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f16,definition,( 26.09/4.24 ! [X344 : (subst > term > subst > $o)] : (($true = ((sP1 @ X344))) <=> ? [X347 : term,X346 : term] : ((((X344 @ id @ (ap @ (sub @ X346 @ id) @ X347) @ id)) != $true) & (((X344 @ id @ X347 @ id)) = $true) & (((X344 @ id @ X346 @ id)) = $true)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f17,definition,( 26.09/4.24 (sP2 = $true) <=> ? [X327 : term,X326 : (term > $o)] : (! [X330 : term] : ((((var @ X330)) != $true) | ($true = ((X326 @ X330)))) & (((X326 @ X327)) != $true) & ! [X328 : term] : (? [X329 : term] : ((((X326 @ X329)) = $true) & ($true != ((X326 @ (sub @ X328 @ (push @ X329 @ id)))))) | ($true = ((X326 @ (lam @ X328))))) & ! [X332 : term,X331 : term] : (($true != ((X326 @ X332))) | ($true != ((X326 @ X331))) | (((X326 @ (ap @ X332 @ X331))) = $true)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f18,definition,( 26.09/4.24 ($true = sP3) <=> ! [X345 : term,X344 : (subst > term > subst > $o)] : (($true = ((sP1 @ X344))) | ? [X361 : term] : (($true = ((var @ (sub @ X361 @ id)))) & (((X344 @ id @ X361 @ id)) != $true)) | ? [X349 : term,X351 : subst,X348 : subst,X350 : subst] : ((((X344 @ X351 @ X349 @ (comp @ X348 @ X350))) != $true) & (((X344 @ (comp @ X351 @ X348) @ (sub @ X349 @ X348) @ X350)) = $true)) | ? [X358 : term,X357 : subst,X360 : subst,X359 : subst] : ((((X344 @ X360 @ X358 @ (comp @ X357 @ X359))) = $true) & (((X344 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359)) != $true)) | (((X344 @ id @ X345 @ id)) = $true) | (((sP0 @ X344)) = $true))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f19,definition,( 26.09/4.24 ! [X129 : (subst > term > subst > $o)] : (($true = ((sP4 @ X129))) <=> ? [X131 : term,X132 : term] : (($true = ((X129 @ id @ X132 @ id))) & ($true = ((X129 @ id @ X131 @ id))) & ($true != ((X129 @ id @ (ap @ (sub @ X131 @ id) @ X132) @ id)))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f20,definition,( 26.09/4.24 ! [X129 : (subst > term > subst > $o)] : (($true = ((sP5 @ X129))) <=> ? [X133 : (subst > term > term)] : (! [X136 : subst,X135 : term,X137 : subst] : (((X133 @ (comp @ X136 @ X137) @ (sub @ X135 @ X137))) = ((sub @ (X133 @ X136 @ X135) @ X137))) & ($true != ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id))) & ! [X134 : term] : (($true = ((X129 @ id @ (X133 @ id @ X134) @ id))) | (((X129 @ id @ X134 @ id)) != $true))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f21,definition,( 26.09/4.24 ! [X113 : (subst > term > subst > $o)] : ((((sP6 @ X113)) = $true) <=> ! [X120 : (subst > term > term)] : (($true = ((X113 @ id @ (lam @ (X120 @ sh @ one)) @ id))) | ? [X123 : subst,X122 : subst,X121 : term] : (((X120 @ (comp @ X123 @ X122) @ (sub @ X121 @ X122))) != ((sub @ (X120 @ X123 @ X121) @ X122))) | ? [X124 : term] : (($true != ((X113 @ id @ (X120 @ id @ X124) @ id))) & (((X113 @ id @ X124 @ id)) = $true))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f22,definition,( 26.09/4.24 (sP7 = $true) <=> ? [X101 : (subst > term > subst > $o),X102 : term,X100 : term] : (($true != ((X101 @ id @ (ap @ X102 @ X100) @ id))) & ! [X105 : subst,X103 : subst,X106 : term,X104 : subst] : (($true = ((X101 @ X103 @ X106 @ (comp @ X105 @ X104)))) | ($true != ((X101 @ (comp @ X103 @ X105) @ (sub @ X106 @ X105) @ X104)))) & (((X101 @ id @ X102 @ id)) = $true) & (((X101 @ id @ X100 @ id)) = $true) & ! [X112 : term,X111 : term] : ((((X101 @ id @ X112 @ id)) != $true) | ($true != ((X101 @ id @ X111 @ id))) | ($true = ((X101 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id)))) & ! [X108 : subst,X109 : subst,X107 : subst,X110 : term] : ((((X101 @ X107 @ X110 @ (comp @ X109 @ X108))) != $true) | ($true = ((X101 @ (comp @ X107 @ X109) @ (sub @ X110 @ X109) @ X108)))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f23,definition,( 26.09/4.24 ($true = sP8) <=> ? [X93 : (term > $o),X94 : term] : (! [X99 : term,X98 : term] : ((((X93 @ X98)) != $true) | ($true != ((X93 @ X99))) | ($true = ((X93 @ (ap @ X98 @ X99))))) & ! [X95 : term] : (? [X96 : term] : ((((X93 @ (sub @ X95 @ (push @ X96 @ id)))) != $true) & ($true = ((X93 @ X96)))) | ($true = ((X93 @ (lam @ X95))))) & ! [X97 : term] : (($true = ((X93 @ X97))) | (((var @ X97)) != $true)) & ($true != ((X93 @ X94))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f24,definition,( 26.09/4.24 ($true = sP9) <=> ! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X142 : term] : ((((var @ (sub @ X142 @ id))) = $true) & (((X129 @ id @ X142 @ id)) != $true)) | ($true = ((sP5 @ X129))) | ? [X140 : subst,X138 : term,X141 : subst,X139 : subst] : (($true = ((X129 @ X141 @ X138 @ (comp @ X140 @ X139)))) & (((X129 @ (comp @ X141 @ X140) @ (sub @ X138 @ X140) @ X139)) != $true)) | (((X129 @ id @ X130 @ id)) = $true) | ? [X146 : subst,X144 : term,X145 : subst,X143 : subst] : (($true = ((X129 @ (comp @ X145 @ X143) @ (sub @ X144 @ X143) @ X146))) & (((X129 @ X145 @ X144 @ (comp @ X143 @ X146))) != $true)) | ($true = ((sP4 @ X129))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f25,definition,( 26.09/4.24 ! [X230 : (subst > term > subst > $o)] : (($true = ((sP10 @ X230))) <=> ? [X243 : (subst > term > term)] : (! [X244 : term] : ((((X230 @ id @ X244 @ id)) != $true) | ($true = ((X230 @ id @ (X243 @ id @ X244) @ id)))) & ($true != ((X230 @ id @ (lam @ (X243 @ sh @ one)) @ id))) & ! [X247 : subst,X246 : subst,X245 : term] : (((sub @ (X243 @ X247 @ X245) @ X246)) = ((X243 @ (comp @ X247 @ X246) @ (sub @ X245 @ X246))))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f26,definition,( 26.09/4.24 ! [X306 : (subst > term > subst > $o)] : (($true = ((sP11 @ X306))) <=> ? [X308 : (subst > term > term)] : (! [X312 : term] : ((((X306 @ id @ (X308 @ id @ X312) @ id)) = $true) | ($true != ((X306 @ id @ X312 @ id)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) & ! [X309 : subst,X311 : subst,X310 : term] : (((sub @ (X308 @ X309 @ X310) @ X311)) = ((X308 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311))))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f27,definition,( 26.09/4.24 ! [X419 : (subst > term > subst > $o)] : (($true = ((sP12 @ X419))) <=> ? [X431 : (subst > term > term)] : (! [X434 : subst,X433 : term,X435 : subst] : (((sub @ (X431 @ X434 @ X433) @ X435)) = ((X431 @ (comp @ X434 @ X435) @ (sub @ X433 @ X435)))) & ($true != ((X419 @ id @ (lam @ (X431 @ sh @ one)) @ id))) & ! [X432 : term] : (($true = ((X419 @ id @ (X431 @ id @ X432) @ id))) | (((X419 @ id @ X432 @ id)) != $true))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f28,definition,( 26.09/4.24 ! [X419 : (subst > term > subst > $o)] : (($true = ((sP13 @ X419))) <=> ? [X426 : term,X425 : term] : ((((X419 @ id @ (ap @ (sub @ X425 @ id) @ X426) @ id)) != $true) & (((X419 @ id @ X426 @ id)) = $true) & ($true = ((X419 @ id @ X425 @ id)))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f29,definition,( 26.09/4.24 (sP14 = $true) <=> ? [X474 : (term > $o),X473 : term] : ((((X474 @ X473)) != $true) & ! [X478 : term] : ((((X474 @ X478)) = $true) | (((var @ X478)) != $true)) & ! [X477 : term] : ((((X474 @ X477)) != $true) | (((X474 @ (lam @ X477))) = $true)) & ! [X476 : term,X475 : term] : ((((X474 @ X476)) != $true) | (((X474 @ X475)) != $true) | (((X474 @ (ap @ X476 @ X475))) = $true)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f30,definition,( 26.09/4.24 ($true = sP15) <=> (? [X470 : subst,X471 : term] : (((comp @ sh @ (push @ X471 @ X470))) != X470) | (sP14 = $true) | ? [X469 : subst,X468 : term] : (((sub @ one @ (push @ X468 @ X469))) != X468) | ! [X480 : subst,X479 : term,X481 : (term > $o)] : (? [X482 : term] : (($true != ((X481 @ (sub @ X482 @ X480)))) & ($true = ((var @ X482)))) | ($true = ((X481 @ (sub @ X479 @ X480)))) | ? [X485 : term,X486 : term] : ((((X481 @ X486)) = $true) & ($true != ((X481 @ (ap @ X486 @ X485)))) & ($true = ((X481 @ X485)))) | ? [X483 : term] : ((((X481 @ (lam @ X483))) != $true) & ! [X484 : term] : ((((X481 @ X484)) != $true) | ($true = ((X481 @ (sub @ X483 @ (push @ X484 @ id)))))))) | ? [X472 : subst] : (((comp @ X472 @ id)) != X472))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f31,definition,( 26.09/4.24 ! [X452 : (subst > term > subst > $o)] : ((((sP16 @ X452)) = $true) <=> ? [X458 : (subst > term > term)] : ((((X452 @ id @ (lam @ (X458 @ sh @ one)) @ id)) != $true) & ! [X459 : term] : (($true = ((X452 @ id @ (X458 @ id @ X459) @ id))) | (((X452 @ id @ X459 @ id)) != $true)) & ! [X461 : term,X462 : subst,X460 : subst] : (((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X458 @ X460 @ X461) @ X462)))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f32,definition,( 26.09/4.24 ($true = sP17) <=> ? [X390 : (term > $o),X388 : term,X389 : subst] : (($true != ((X390 @ (sub @ X388 @ X389)))) & ! [X391 : term] : (? [X392 : term] : ((((X390 @ X392)) = $true) & ($true != ((X390 @ (sub @ X391 @ (push @ X392 @ id)))))) | ($true = ((X390 @ (lam @ X391))))) & ! [X393 : term] : (($true != ((var @ X393))) | ($true = ((X390 @ (sub @ X393 @ X389))))) & ! [X394 : term,X395 : term] : (($true = ((X390 @ (ap @ X394 @ X395)))) | (((X390 @ X394)) != $true) | (((X390 @ X395)) != $true)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f33,definition,( 26.09/4.24 (sP18 = $true) <=> (! [X397 : (term > $o),X396 : term] : (? [X398 : term] : (! [X399 : term] : (($true = ((X397 @ (sub @ X398 @ (push @ X399 @ id))))) | (((X397 @ X399)) != $true)) & (((X397 @ (lam @ X398))) != $true)) | ? [X400 : term] : (($true = ((var @ X400))) & ($true != ((X397 @ X400)))) | ? [X402 : term,X401 : term] : ((((X397 @ (ap @ X402 @ X401))) != $true) & (((X397 @ X402)) = $true) & (((X397 @ X401)) = $true)) | ($true = ((X397 @ X396)))) | ($true = sP17) | ? [X387 : term] : (((sub @ X387 @ id)) != X387))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f34,definition,( 26.09/4.24 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP19 @ X21))) <=> ? [X31 : (subst > term > term)] : (! [X32 : term] : (($true = ((X21 @ id @ (X31 @ id @ X32) @ id))) | (((X21 @ id @ X32 @ id)) != $true)) & (((X21 @ id @ (lam @ (X31 @ sh @ one)) @ id)) != $true) & ! [X34 : term,X33 : subst,X35 : subst] : (((sub @ (X31 @ X33 @ X34) @ X35)) = ((X31 @ (comp @ X33 @ X35) @ (sub @ X34 @ X35))))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f35,definition,( 26.09/4.24 ($true = sP20) <=> ! [X20 : term,X21 : (subst > term > subst > $o)] : (? [X26 : subst,X23 : term,X25 : subst,X24 : subst] : (($true != ((X21 @ X26 @ X23 @ (comp @ X24 @ X25)))) & (((X21 @ (comp @ X26 @ X24) @ (sub @ X23 @ X24) @ X25)) = $true)) | ($true = ((X21 @ id @ (lam @ X20) @ id))) | ? [X29 : subst,X28 : term,X27 : subst,X30 : subst] : ((((X21 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29) @ X30)) != $true) & (((X21 @ X27 @ X28 @ (comp @ X29 @ X30))) = $true)) | ? [X22 : term] : (($true != ((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id))) & ($true = ((X21 @ id @ X22 @ id)))) | ($true = ((sP19 @ X21))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f36,definition,( 26.09/4.24 (sP21 = $true) <=> ! [X5 : term,X4 : (term > $o)] : (? [X6 : term,X7 : term] : ((((X4 @ (ap @ X6 @ X7))) != $true) & ($true = ((X4 @ X6))) & ($true = ((X4 @ X7)))) | ? [X8 : term] : ((((var @ X8)) = $true) & (((X4 @ X8)) != $true)) | ? [X9 : term] : (! [X10 : term] : ((((X4 @ X10)) != $true) | ($true = ((X4 @ (sub @ X9 @ (push @ X10 @ id)))))) & ($true != ((X4 @ (lam @ X9))))) | ($true = ((X4 @ X5))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f37,definition,( 26.09/4.24 ($true = sP22) <=> ! [X372 : term,X374 : term,X373 : (subst > term > subst > $o)] : (? [X377 : subst,X376 : subst,X375 : term,X378 : subst] : (($true != ((X373 @ X377 @ X375 @ (comp @ X378 @ X376)))) & (((X373 @ (comp @ X377 @ X378) @ (sub @ X375 @ X378) @ X376)) = $true)) | ($true = ((X373 @ id @ (ap @ X374 @ X372) @ id))) | ? [X382 : subst,X381 : term,X383 : subst,X384 : subst] : (($true = ((X373 @ X384 @ X381 @ (comp @ X383 @ X382)))) & (((X373 @ (comp @ X384 @ X383) @ (sub @ X381 @ X383) @ X382)) != $true)) | ? [X379 : term,X380 : term] : (($true = ((X373 @ id @ X380 @ id))) & (((X373 @ id @ X379 @ id)) = $true) & ($true != ((X373 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id)))) | (((X373 @ id @ X372 @ id)) != $true) | ($true != ((X373 @ id @ X374 @ id))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f38,definition,( 26.09/4.24 ($true = sP23) <=> ! [X180 : term,X181 : (subst > term > subst > $o)] : (? [X187 : term] : ((((X181 @ id @ X187 @ id)) = $true) & (((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)) != $true)) | ? [X182 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id)) != $true) & ! [X184 : subst,X183 : term,X185 : subst] : (((sub @ (X182 @ X184 @ X183) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X183 @ X185)))) & ! [X186 : term] : (($true = ((X181 @ id @ (X182 @ id @ X186) @ id))) | (((X181 @ id @ X186 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f39,definition,( 26.09/4.24 ($true = sP24) <=> ? [X192 : term,X193 : (term > $o)] : (! [X194 : term] : (? [X195 : term] : ((((X193 @ X195)) = $true) & ($true != ((X193 @ (sub @ X194 @ (push @ X195 @ id)))))) | (((X193 @ (lam @ X194))) = $true)) & ! [X196 : term] : (($true = ((X193 @ X196))) | (((var @ X196)) != $true)) & ! [X198 : term,X197 : term] : ((((X193 @ X198)) != $true) | (((X193 @ X197)) != $true) | (((X193 @ (ap @ X198 @ X197))) = $true)) & (((X193 @ X192)) != $true))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f40,definition,( 26.09/4.24 (sP25 = $true) <=> ! [X211 : term,X210 : (subst > term > subst > $o)] : (? [X213 : term,X212 : term] : (($true = ((X210 @ id @ X212 @ id))) & (((X210 @ id @ X213 @ id)) = $true) & (((X210 @ id @ (ap @ (sub @ X212 @ id) @ X213) @ id)) != $true)) | ? [X214 : (subst > term > term)] : (! [X217 : subst,X218 : term,X216 : subst] : (((sub @ (X214 @ X217 @ X218) @ X216)) = ((X214 @ (comp @ X217 @ X216) @ (sub @ X218 @ X216)))) & ! [X215 : term] : ((((X210 @ id @ (X214 @ id @ X215) @ id)) = $true) | (((X210 @ id @ X215 @ id)) != $true)) & ($true != ((X210 @ id @ (lam @ (X214 @ sh @ one)) @ id)))) | ($true = ((X210 @ id @ X211 @ id))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f41,definition,( 26.09/4.24 (sP26 = $true) <=> ! [X157 : (term > $o),X156 : subst,X155 : term] : (? [X161 : term,X160 : term] : (($true = ((X157 @ X160))) & (((X157 @ (ap @ X160 @ X161))) != $true) & (((X157 @ X161)) = $true)) | ? [X162 : term] : (($true = ((var @ X162))) & (((X157 @ (sub @ X162 @ X156))) != $true)) | ? [X158 : term] : (! [X159 : term] : (($true = ((X157 @ (sub @ X158 @ (push @ X159 @ id))))) | ($true != ((X157 @ X159)))) & (((X157 @ (lam @ X158))) != $true)) | (((X157 @ (sub @ X155 @ X156))) = $true))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f42,definition,( 26.09/4.24 ($true = sP27) <=> ! [X250 : (subst > term > subst > $o),X251 : term,X249 : term,X248 : (term > $o)] : (($true != ((X248 @ X251))) | ? [X258 : term] : (((X248 @ X258)) != ((X250 @ id @ X258 @ id))) | ? [X256 : term,X257 : term] : (($true = ((X250 @ id @ X257 @ id))) & ($true != ((X250 @ id @ (ap @ (sub @ X257 @ id) @ X256) @ id))) & (((X250 @ id @ X256 @ id)) = $true)) | ($true != ((X248 @ X249))) | ? [X255 : term,X252 : subst,X254 : subst,X253 : subst] : (($true = ((X250 @ X253 @ X255 @ (comp @ X254 @ X252)))) & ($true != ((X250 @ (comp @ X253 @ X254) @ (sub @ X255 @ X254) @ X252)))) | ($true = ((X248 @ (ap @ X249 @ X251)))) | ? [X262 : subst,X260 : term,X261 : subst,X259 : subst] : ((((X250 @ X259 @ X260 @ (comp @ X261 @ X262))) != $true) & (((X250 @ (comp @ X259 @ X261) @ (sub @ X260 @ X261) @ X262)) = $true)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 26.09/4.24 thf(f43,plain,( 26.09/4.24 (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) <=> ! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386)) & (hoasapnotvar_lthm = $true) & ((hoaslaminj = $true) <=> ! [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (? [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) != ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ? [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) != ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408)))))) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP27)) & (! [X221 : subst] : (((comp @ id @ X221)) = X221) <=> (axidl = $true)) & (hoaslamnotvar_lthm = $true) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & (! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) <=> (shinj = $true)) & (! [X444 : (subst > term > subst > $o)] : ? [X445 : (term > $o)] : ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446))) <=> (hoasinduction_lem0_lthm = $true)) & (axclos = $true) & (substmonoid_gthm = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((sP26 = $true) <=> (induction2lem = $true)) & (lamnotvar = $true) & (axabs = $true) & ! [X538 : d_term,X539 : d_term] : ((X538 = X539) | (((d2term @ X538)) != ((d2term @ X539)))) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) <=> (axshiftcons = $true)) & ((hoaslamnotap = $true) <=> ! [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ? [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) != ((sub @ (X163 @ X166 @ X168) @ X167))))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (axvarshift = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (hoasinduction_gthm = $true) & (! [X447 : term] : ? [X448 : (subst > term > term)] : ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X189 : (subst > term > subst > $o)] : ! [X190 : (term > $o)] : ? [X191 : term] : (((X190 @ X191)) != ((X189 @ id @ X191 @ id))) | ? [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) != $true) & ! [X204 : (subst > term > term)] : (? [X208 : term] : (($true != ((X200 @ id @ (X204 @ id @ X208) @ id))) & ($true = ((X200 @ id @ X208 @ id)))) | ($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ? [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X204 @ X206 @ X205) @ X207)))) & ! [X209 : term] : (($true != ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) & ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203)))) | ? [X199 : term] : (((sub @ X199 @ id)) != X199) | (sP25 = $true) | ($true = sP24))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X496 : (subst > term > subst > $o),X495 : term] : (? [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) != $true) & ($true = ((X496 @ id @ X498 @ id))) & (((X496 @ id @ X497 @ id)) = $true)) | ? [X499 : (subst > term > term)] : (! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501))) & ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ($true != ((X496 @ id @ X503 @ id)))) & ($true != ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) | ($true = ((X496 @ id @ X495 @ id))))) & ! [X228 : d_subst,X227 : d_subst] : ((((d2subst @ X227)) != ((d2subst @ X228))) | (X227 = X228)) & ((pushprop_lem1v2 = $true) <=> ! [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (? [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) != ((X416 @ X417))) | ($true != ((X414 @ X413))) | (((X416 @ one)) = $true))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (? [X81 : term] : (($true != ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) & ($true = ((X73 @ X81)))) | ($true = ((X73 @ (lam @ X75)))) | ? [X82 : term] : (((X74 @ id @ X82 @ id)) != ((X73 @ X82))) | ? [X76 : (subst > term > term)] : (($true != ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) & ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) & ! [X80 : term] : (($true != ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id)))))) | ? [X68 : term] : ! [X69 : (subst > term > term)] : ? [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) != ((sub @ X68 @ (push @ X70 @ X71)))) | ? [X72 : term] : (((sub @ X72 @ id)) != X72))) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & ((! [X527 : term] : (((sub @ X527 @ id)) = X527) | ? [X526 : term] : (((sub @ X526 @ id)) != X526)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (($true = sP23) | ? [X172 : (subst > term > subst > $o),X173 : term] : (! [X174 : (subst > term > term)] : (? [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) != ((sub @ (X174 @ X177 @ X176) @ X178))) | ? [X175 : term] : (($true != ((X172 @ id @ (X174 @ id @ X175) @ id))) & (((X172 @ id @ X175 @ id)) = $true)) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) & ! [X179 : term] : ((((X172 @ id @ X179 @ id)) != $true) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) & ($true != ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id)))) | ? [X171 : term] : (((sub @ X171 @ id)) != X171))) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) <=> (termmset = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (? [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) != X40) | ! [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) != $true) | ? [X45 : term] : (((X41 @ X45)) != ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true)))) & (($true = sP22) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X263 : term] : ? [X264 : (subst > term > term)] : (((X264 @ sh @ one)) = ((sub @ X263 @ (push @ one @ sh))))) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) <=> (axidr = $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X61 : (subst > term > subst > $o)] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id)))) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) <=> (sP21 = $true)) & (pushprop_gthm = $true) & (one = ((d2term @ d_one))) & (! [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) | ($true != ((X59 @ X58)))) <=> (pushprop_lem1 = $true)) & (induction2_gthm = $true) & (axmap = $true) & ! [X443 : d_term] : (d_one = X443) & ((hoasapinj1 = $true) <=> ! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533))))) & ((hoasapinj2 = $true) <=> ! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X11 : term] : (((sub @ X11 @ id)) != X11) | ($true = sP20) | ? [X12 : (subst > term > subst > $o),X13 : term] : (! [X15 : (subst > term > term)] : (? [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) != ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : (($true = ((X12 @ id @ X19 @ id))) & ($true != ((X12 @ id @ (X15 @ id @ X19) @ id))))) & ! [X14 : term] : (($true != ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) & (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) != $true)))) & (((var @ (d2term @ d_one))) != $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((induction2_lthm = $true) <=> (sP18 = $true)) & (! [X441 : term] : ? [X442 : (subst > term > term)] : (((X442 @ sh @ one)) = ((sub @ X441 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491)))) | ? [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) = ((ap @ X489 @ X490))) & (X487 != X490))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X518 : (subst > term > subst > $o),X519 : term] : (($true = ((X518 @ id @ (lam @ X519) @ id))) | ? [X525 : term] : ((((X518 @ id @ X525 @ id)) = $true) & ($true != ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) | ? [X520 : (subst > term > term)] : (! [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) = $true) | ($true != ((X518 @ id @ X521 @ id)))) & ($true != ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) & ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523)))))) & (pushprop = $true) & (pushprop_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((substmonoid_lthm = $true) <=> (? [X65 : subst] : (((comp @ X65 @ id)) != X65) | (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)) | ? [X64 : subst] : (((comp @ id @ X64)) != X64))) & ((apinj1 = $true) <=> ! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507))) & (ulamvarind = $true) & (pushprop_lthm_orig = $true) & (! [X84 : (subst > term > subst > $o),X83 : term] : (? [X85 : term] : (($true != ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) & (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ? [X86 : (subst > term > term)] : (! [X90 : term] : ((((X84 @ id @ X90 @ id)) != $true) | (((X84 @ id @ (X86 @ id @ X90) @ id)) = $true)) & (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X294 : (subst > term > subst > $o),X293 : term] : (? [X296 : term,X297 : (subst > term > term)] : (! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) & ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) & ! [X301 : term] : ((((X294 @ id @ X301 @ id)) != $true) | (((X294 @ id @ (X297 @ id @ X301) @ id)) = $true)) & (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true)) | (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true) | ? [X295 : term] : (($true != ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) & (((X294 @ id @ X295 @ id)) = $true)))) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (! [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (? [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) != ((sub @ (X281 @ X288 @ X287) @ X289))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ? [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) != ((sub @ (X283 @ X285 @ X284) @ X286))) | (((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one))))) | ? [X279 : term,X278 : term] : ((((lam @ X279)) = ((lam @ X278))) & (X278 != X279)) | ? [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) != X275) | ? [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) != X277))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X451 : term,X452 : (subst > term > subst > $o)] : (? [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) != $true) & ($true = ((X452 @ id @ X457 @ id)))) | (((sP16 @ X452)) = $true) | ? [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) = $true) & (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) != $true)) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ? [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) = $true) & ($true != ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem1_gthm = $true) & (($true = sP15) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = id) & ((axvarid = $true) <=> ! [X467 : term] : (((sub @ X467 @ id)) = X467)) & (! [X436 : subst,X437 : (term > $o),X438 : term] : ? [X439 : (term > $o)] : ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) <=> (pushprop_lem0_lthm = $true)) & (! [X419 : (subst > term > subst > $o),X418 : term] : (? [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true != ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) & ($true = ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) | ($true = ((sP13 @ X419))) | ($true = ((sP12 @ X419))) | ? [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true != ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) & (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) = $true)) | ($true = ((X419 @ id @ X418 @ id))) | ? [X424 : term] : ((((var @ (sub @ X424 @ id))) = $true) & ($true != ((X419 @ id @ X424 @ id))))) <=> (hoasinduction = $true)) & (hoasapinj2_gthm = $true) & (! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) <=> (axscons = $true)) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((laminj = $true) <=> ! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170))) & (lamnotap != $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (? [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) != $true) & (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) = $true)) | ? [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true != ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) & (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) = $true)) | ($true = ((sP11 @ X306))) | ? [X318 : term] : (($true != ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) & ($true = ((X305 @ X318)))) | (((X305 @ (lam @ X307))) = $true) | ? [X313 : term] : (((X305 @ X313)) != ((X306 @ id @ X313 @ id))))) & (! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) <=> (apinj2 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (? [X366 : term] : (((X362 @ X366)) != ((X363 @ id @ X366 @ id))) | ? [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) != $true) & (((X362 @ X365)) = $true)) | ? [X367 : (subst > term > term)] : (! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) & ($true != ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | (((X363 @ id @ X368 @ id)) != $true))) | (((X362 @ (lam @ X364))) = $true))) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X148 : (subst > term > subst > $o),X147 : term] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ? [X149 : (subst > term > term)] : (! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152))) & (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) != $true) & ! [X150 : term] : (($true = ((X148 @ id @ (X149 @ id @ X150) @ id))) | ($true != ((X148 @ id @ X150 @ id))))) | ? [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) != $true) & ($true = ((X148 @ id @ X154 @ id)))))) & (hoasinduction_lem3a_gthm = $true) & (ulamvarsh = $true) & ((pushprop_lem0 = $true) <=> ! [X224 : subst,X222 : term,X223 : (term > $o)] : ? [X225 : (term > $o)] : ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226)))) & ! [X38 : d_subst] : (d_id = X38) & ((? [X229 : term] : (((sub @ X229 @ id)) != X229) | ! [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (($true = ((sP10 @ X230))) | ? [X237 : term] : (((X230 @ id @ X237 @ id)) != ((X231 @ X237))) | ? [X238 : term] : ((((X231 @ X238)) = $true) & (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) != $true)) | ? [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true != ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) & ($true = ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ? [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true = ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) & (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) != $true)) | ($true = ((X231 @ (lam @ X232)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_lthm = $true) <=> (? [X114 : term,X113 : (subst > term > subst > $o)] : (! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ($true != ((X113 @ id @ X115 @ id)))) & ! [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true != ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) & ($true != ((X113 @ id @ (lam @ X114) @ id))) & (((sP6 @ X113)) = $true) & ! [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true != ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) | (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true))) | ($true = sP8) | (sP7 = $true) | ($true = sP9))) & ((hoasinduction_lthm_3 = $true) <=> (? [X333 : term] : (((sub @ X333 @ id)) != X333) | ? [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) != $true) & ! [X339 : (subst > term > term)] : (? [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) != ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) | ? [X343 : term] : (($true != ((X336 @ id @ (X339 @ id @ X343) @ id))) & (((X336 @ id @ X343 @ id)) = $true))) & ! [X338 : term] : ((((X334 @ X338)) != $true) | (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true)) & ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id)))) | ? [X323 : (subst > term > subst > $o)] : ! [X324 : (term > $o)] : ? [X325 : term] : (((X324 @ X325)) != ((X323 @ id @ X325 @ id))) | ($true = sP3) | (sP2 = $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & ((hoasinduction_lem3v2_f = $true) <=> ! [X0 : term] : ? [X1 : (subst > term > term)] : ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2))))) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) <=> (substmonoid = $true)) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X512 : (term > $o),X513 : term] : (($true = ((X512 @ X513))) | ? [X515 : term] : ((((X512 @ X515)) != $true) & (((var @ X515)) = $true)) | ? [X514 : term] : (($true = ((X512 @ X514))) & (((X512 @ (lam @ X514))) != $true)) | ? [X517 : term,X516 : term] : ((((X512 @ X517)) = $true) & ($true != ((X512 @ (ap @ X516 @ X517)))) & (((X512 @ X516)) = $true))) <=> (induction = $true)) & ((pushprop_lem1_lthm = $true) <=> (? [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) != X46) | ? [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) != X49) | ! [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ($true != ((X52 @ X51)))))) & ((! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271)))) | ? [X265 : term] : (((sub @ X265 @ id)) != X265) | ? [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) = ((ap @ X268 @ X266))) & (X267 != X268))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem2_lthm = $true)), 26.09/4.24 inference(definition_folding,[],[f12,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15])). 26.09/4.24 thf(f44,plain,( 26.09/4.24 ((hoasinduction_lem3a != $true) | ? [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (? [X5 : term] : (($true != ((X0 @ id @ (X1 @ id @ X5) @ id))) & (((X0 @ id @ X5 @ id)) = $true)) | ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | ? [X4 : term,X2 : subst,X3 : subst] : (((sub @ (X1 @ X3 @ X4) @ X2)) != ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2))))) & ? [X6 : term] : (! [X7 : term] : ((((X0 @ id @ (sub @ X6 @ (push @ X7 @ id)) @ id)) = $true) | ($true != ((X0 @ id @ X7 @ id)))) & (((X0 @ id @ (lam @ X6) @ id)) != $true)))) & ((hoasinduction_lem3a = $true) | ! [X0 : (subst > term > subst > $o)] : (? [X1 : (subst > term > term)] : (! [X5 : term] : (($true = ((X0 @ id @ (X1 @ id @ X5) @ id))) | (((X0 @ id @ X5 @ id)) != $true)) & ($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) & ! [X4 : term,X2 : subst,X3 : subst] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2))))) | ! [X6 : term] : (? [X7 : term] : ((((X0 @ id @ (sub @ X6 @ (push @ X7 @ id)) @ id)) != $true) & ($true = ((X0 @ id @ X7 @ id)))) | (((X0 @ id @ (lam @ X6) @ id)) = $true))))), 26.09/4.24 inference(nnf_transformation,[],[f14])). 26.09/4.24 thf(f45,plain,( 26.09/4.24 ((hoasinduction_lem3a != $true) | ? [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (? [X2 : term] : (($true != ((X0 @ id @ (X1 @ id @ X2) @ id))) & (((X0 @ id @ X2 @ id)) = $true)) | ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | ? [X3 : term,X4 : subst,X5 : subst] : (((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4))) != ((sub @ (X1 @ X5 @ X3) @ X4)))) & ? [X6 : term] : (! [X7 : term] : ((((X0 @ id @ (sub @ X6 @ (push @ X7 @ id)) @ id)) = $true) | ($true != ((X0 @ id @ X7 @ id)))) & (((X0 @ id @ (lam @ X6) @ id)) != $true)))) & ((hoasinduction_lem3a = $true) | ! [X8 : (subst > term > subst > $o)] : (? [X9 : (subst > term > term)] : (! [X10 : term] : (($true = ((X8 @ id @ (X9 @ id @ X10) @ id))) | (((X8 @ id @ X10 @ id)) != $true)) & (((X8 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X9 @ Y0 @ Y1))))) @ id)) != $true) & ! [X11 : term,X12 : subst,X13 : subst] : (((sub @ (X9 @ X13 @ X11) @ X12)) = ((X9 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) | ! [X14 : term] : (? [X15 : term] : (($true != ((X8 @ id @ (sub @ X14 @ (push @ X15 @ id)) @ id))) & (((X8 @ id @ X15 @ id)) = $true)) | ($true = ((X8 @ id @ (lam @ X14) @ id))))))), 26.09/4.24 inference(rectify,[],[f44])). 26.09/4.24 thf(f46,plain,( 26.09/4.24 ((hoasinduction_lem3a != $true) | (! [X1 : (subst > term > term)] : ((($true != ((sK28 @ id @ (X1 @ id @ (sK29 @ X1)) @ id))) & ($true = ((sK28 @ id @ (sK29 @ X1) @ id)))) | (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1)))))) & (! [X7 : term] : (($true = ((sK28 @ id @ (sub @ sK33 @ (push @ X7 @ id)) @ id))) | (((sK28 @ id @ X7 @ id)) != $true)) & (((sK28 @ id @ (lam @ sK33) @ id)) != $true)))) & ((hoasinduction_lem3a = $true) | ! [X8 : (subst > term > subst > $o)] : ((! [X10 : term] : ((((X8 @ id @ (sK34 @ X8 @ id @ X10) @ id)) = $true) | (((X8 @ id @ X10 @ id)) != $true)) & ($true != ((X8 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK34 @ X8 @ Y0 @ Y1))))) @ id))) & ! [X11 : term,X12 : subst,X13 : subst] : (((sub @ (sK34 @ X8 @ X13 @ X11) @ X12)) = ((sK34 @ X8 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) | ! [X14 : term] : ((($true != ((X8 @ id @ (sub @ X14 @ (push @ (sK35 @ X14 @ X8) @ id)) @ id))) & (((X8 @ id @ (sK35 @ X14 @ X8) @ id)) = $true)) | ($true = ((X8 @ id @ (lam @ X14) @ id))))))), 26.09/4.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK28,vAPP,vAPP,vAPP,vAPP,sK33,vAPP,vAPP]),skolemize(X0,sK28),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X6,sK33),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8)],[f45])). 26.09/4.24 thf(f133,plain,( 26.09/4.24 (hoasinduction_lem3b_gthm = $true) & (((axvarcons = $true) | ? [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) != X386)) & (! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386) | (axvarcons != $true))) & (hoasapnotvar_lthm = $true) & (((hoaslaminj = $true) | ? [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (! [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) = ((sub @ (X406 @ X411 @ X410) @ X412))) & (((X406 @ X405 @ X403)) != ((X404 @ X405 @ X403))) & (((lam @ (X404 @ sh @ one))) = ((lam @ (X406 @ sh @ one)))) & ! [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) = ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408)))))) & (! [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (? [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) != ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ? [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) != ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408))))) | (hoaslaminj != $true))) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction_lem2v2 != $true))) & ((! [X221 : subst] : (((comp @ id @ X221)) = X221) | (axidl != $true)) & ((axidl = $true) | ? [X221 : subst] : (((comp @ id @ X221)) != X221))) & (hoaslamnotvar_lthm = $true) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & ((! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X291 : term,X290 : term] : ((X290 != X291) & (((sub @ X291 @ sh)) = ((sub @ X290 @ sh)))))) & ((! [X444 : (subst > term > subst > $o)] : ? [X445 : (term > $o)] : ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X444 : (subst > term > subst > $o)] : ! [X445 : (term > $o)] : ? [X446 : term] : (((X444 @ id @ X446 @ id)) != ((X445 @ X446))))) & (axclos = $true) & (substmonoid_gthm = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((sP26 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP26 != $true))) & (lamnotvar = $true) & (axabs = $true) & ! [X538 : d_term,X539 : d_term] : ((X538 = X539) | (((d2term @ X538)) != ((d2term @ X539)))) & ((! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) != X37))) & (((hoaslamnotap = $true) | ? [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) = ((lam @ (X163 @ sh @ one)))) & ! [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X163 @ X166 @ X168) @ X167))))) & (! [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ? [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) != ((sub @ (X163 @ X166 @ X168) @ X167)))) | (hoaslamnotap != $true))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (axvarshift = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (hoasinduction_gthm = $true) & ((! [X447 : term] : ? [X448 : (subst > term > term)] : ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X447 : term] : ! [X448 : (subst > term > term)] : ? [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) != ((X448 @ X450 @ X449))))) & (((hoasinduction_no_psi_cond_lthm = $true) | (! [X189 : (subst > term > subst > $o)] : ? [X190 : (term > $o)] : ! [X191 : term] : (((X190 @ X191)) = ((X189 @ id @ X191 @ id))) & ! [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) = $true) | ? [X204 : (subst > term > term)] : (! [X208 : term] : (($true = ((X200 @ id @ (X204 @ id @ X208) @ id))) | ($true != ((X200 @ id @ X208 @ id)))) & ($true != ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) & ! [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X204 @ X206 @ X205) @ X207)))) | ? [X209 : term] : (($true = ((X201 @ X209))) & ($true != ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) | ? [X203 : term] : (((X200 @ id @ X203 @ id)) != ((X201 @ X203)))) & ! [X199 : term] : (((sub @ X199 @ id)) = X199) & (sP25 != $true) & ($true != sP24))) & ((? [X189 : (subst > term > subst > $o)] : ! [X190 : (term > $o)] : ? [X191 : term] : (((X190 @ X191)) != ((X189 @ id @ X191 @ id))) | ? [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) != $true) & ! [X204 : (subst > term > term)] : (? [X208 : term] : (($true != ((X200 @ id @ (X204 @ id @ X208) @ id))) & ($true = ((X200 @ id @ X208 @ id)))) | ($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ? [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X204 @ X206 @ X205) @ X207)))) & ! [X209 : term] : (($true != ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) & ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203)))) | ? [X199 : term] : (((sub @ X199 @ id)) != X199) | (sP25 = $true) | ($true = sP24)) | (hoasinduction_no_psi_cond_lthm != $true))) & (((hoasinduction_no_psi_cond = $true) | ? [X496 : (subst > term > subst > $o),X495 : term] : (! [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) = $true) | ($true != ((X496 @ id @ X498 @ id))) | (((X496 @ id @ X497 @ id)) != $true)) & ! [X499 : (subst > term > term)] : (? [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) != ((sub @ (X499 @ X500 @ X502) @ X501))) | ? [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) != $true) & ($true = ((X496 @ id @ X503 @ id)))) | ($true = ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) & ($true != ((X496 @ id @ X495 @ id))))) & (! [X496 : (subst > term > subst > $o),X495 : term] : (? [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) != $true) & ($true = ((X496 @ id @ X498 @ id))) & (((X496 @ id @ X497 @ id)) = $true)) | ? [X499 : (subst > term > term)] : (! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501))) & ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ($true != ((X496 @ id @ X503 @ id)))) & ($true != ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) | ($true = ((X496 @ id @ X495 @ id)))) | (hoasinduction_no_psi_cond != $true))) & ! [X228 : d_subst,X227 : d_subst] : ((((d2subst @ X227)) != ((d2subst @ X228))) | (X227 = X228)) & (((pushprop_lem1v2 = $true) | ? [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (! [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) = ((X416 @ X417))) & ($true = ((X414 @ X413))) & (((X416 @ one)) != $true))) & (! [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (? [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) != ((X416 @ X417))) | ($true != ((X414 @ X413))) | (((X416 @ one)) = $true)) | (pushprop_lem1v2 != $true))) & (((hoasinduction_lem3v2a_lthm = $true) | (? [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (! [X81 : term] : (($true = ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) | ($true != ((X73 @ X81)))) & ($true != ((X73 @ (lam @ X75)))) & ! [X82 : term] : (((X74 @ id @ X82 @ id)) = ((X73 @ X82))) & ! [X76 : (subst > term > term)] : (($true = ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) | ? [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) != ((sub @ (X76 @ X77 @ X79) @ X78))) | ? [X80 : term] : (($true = ((X74 @ id @ X80 @ id))) & ($true != ((X74 @ id @ (X76 @ id @ X80) @ id)))))) & ! [X68 : term] : ? [X69 : (subst > term > term)] : ! [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) = ((sub @ X68 @ (push @ X70 @ X71)))) & ! [X72 : term] : (((sub @ X72 @ id)) = X72))) & ((! [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (? [X81 : term] : (($true != ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) & ($true = ((X73 @ X81)))) | ($true = ((X73 @ (lam @ X75)))) | ? [X82 : term] : (((X74 @ id @ X82 @ id)) != ((X73 @ X82))) | ? [X76 : (subst > term > term)] : (($true != ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) & ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) & ! [X80 : term] : (($true != ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id)))))) | ? [X68 : term] : ! [X69 : (subst > term > term)] : ? [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) != ((sub @ X68 @ (push @ X70 @ X71)))) | ? [X72 : term] : (((sub @ X72 @ id)) != X72)) | (hoasinduction_lem3v2a_lthm != $true))) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (((! [X527 : term] : (((sub @ X527 @ id)) = X527) | ? [X526 : term] : (((sub @ X526 @ id)) != X526)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X527 : term] : (((sub @ X527 @ id)) != X527) & ! [X526 : term] : (((sub @ X526 @ id)) = X526)))) & (((hoasinduction_lem3a_lthm = $true) | (($true != sP23) & ! [X172 : (subst > term > subst > $o),X173 : term] : (? [X174 : (subst > term > term)] : (! [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) = ((sub @ (X174 @ X177 @ X176) @ X178))) & ! [X175 : term] : (($true = ((X172 @ id @ (X174 @ id @ X175) @ id))) | (((X172 @ id @ X175 @ id)) != $true)) & (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) != $true)) | ? [X179 : term] : ((((X172 @ id @ X179 @ id)) = $true) & ($true != ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) | ($true = ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id)))) & ! [X171 : term] : (((sub @ X171 @ id)) = X171))) & ((($true = sP23) | ? [X172 : (subst > term > subst > $o),X173 : term] : (! [X174 : (subst > term > term)] : (? [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) != ((sub @ (X174 @ X177 @ X176) @ X178))) | ? [X175 : term] : (($true != ((X172 @ id @ (X174 @ id @ X175) @ id))) & (((X172 @ id @ X175 @ id)) = $true)) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) & ! [X179 : term] : ((((X172 @ id @ X179 @ id)) != $true) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) & ($true != ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id)))) | ? [X171 : term] : (((sub @ X171 @ id)) != X171)) | (hoasinduction_lem3a_lthm != $true))) & ((! [X55 : term] : (((sub @ X55 @ id)) = X55) | (termmset != $true)) & ((termmset = $true) | ? [X55 : term] : (((sub @ X55 @ id)) != X55))) & (((pushprop_lem1v2_lthm = $true) | (! [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) = X40) & ? [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) = $true) & ! [X45 : term] : (((X41 @ X45)) = ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) & (((X41 @ one)) != $true)))) & ((? [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) != X40) | ! [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) != $true) | ? [X45 : term] : (((X41 @ X45)) != ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true))) | (pushprop_lem1v2_lthm != $true))) & ((($true = sP22) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP22))) & (((hoasinduction_lem3b = $true) | ? [X263 : term] : ! [X264 : (subst > term > term)] : (((X264 @ sh @ one)) != ((sub @ X263 @ (push @ one @ sh))))) & (! [X263 : term] : ? [X264 : (subst > term > term)] : (((X264 @ sh @ one)) = ((sub @ X263 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & ((! [X188 : subst] : (((comp @ X188 @ id)) = X188) | (axidr != $true)) & ((axidr = $true) | ? [X188 : subst] : (((comp @ X188 @ id)) != X188))) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (((hoasinduction_lem0 = $true) | ? [X61 : (subst > term > subst > $o)] : ! [X62 : (term > $o)] : ? [X63 : term] : (((X62 @ X63)) != ((X61 @ id @ X63 @ id)))) & (! [X61 : (subst > term > subst > $o)] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id))) | (hoasinduction_lem0 != $true))) & (hoaslamnotvar_gthm = $true) & (((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true))) & (pushprop_gthm = $true) & (one = ((d2term @ d_one))) & ((! [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) | ($true != ((X59 @ X58)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true != ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) & ($true = ((X59 @ X58)))))) & (induction2_gthm = $true) & (axmap = $true) & ! [X443 : d_term] : (d_one = X443) & (((hoasapinj1 = $true) | ? [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 != X531) & (((ap @ (sub @ X530 @ id) @ X532)) = ((ap @ (sub @ X531 @ id) @ X533))))) & (! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533)))) | (hoasapinj1 != $true))) & (((hoasapinj2 = $true) | ? [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) = ((ap @ (sub @ X511 @ id) @ X509))) & (X508 != X509))) & (! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509)) | (hoasapinj2 != $true))) & (((hoasinduction_lem3_lthm = $true) | (! [X11 : term] : (((sub @ X11 @ id)) = X11) & ($true != sP20) & ! [X12 : (subst > term > subst > $o),X13 : term] : (? [X15 : (subst > term > term)] : (! [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) = ((sub @ (X15 @ X17 @ X16) @ X18))) & (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) != $true) & ! [X19 : term] : (($true != ((X12 @ id @ X19 @ id))) | ($true = ((X12 @ id @ (X15 @ id @ X19) @ id))))) | ? [X14 : term] : (($true = ((X12 @ id @ X14 @ id))) & ($true != ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true)))) & ((? [X11 : term] : (((sub @ X11 @ id)) != X11) | ($true = sP20) | ? [X12 : (subst > term > subst > $o),X13 : term] : (! [X15 : (subst > term > term)] : (? [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) != ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : (($true = ((X12 @ id @ X19 @ id))) & ($true != ((X12 @ id @ (X15 @ id @ X19) @ id))))) & ! [X14 : term] : (($true != ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) & (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) != $true))) | (hoasinduction_lem3_lthm != $true))) & (((var @ (d2term @ d_one))) != $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (((induction2_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (induction2_lthm != $true))) & ((! [X441 : term] : ? [X442 : (subst > term > term)] : (((X442 @ sh @ one)) = ((sub @ X441 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X441 : term] : ! [X442 : (subst > term > term)] : (((X442 @ sh @ one)) != ((sub @ X441 @ (push @ one @ sh)))))) & (((! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491)))) | ? [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) = ((ap @ X489 @ X490))) & (X487 != X490))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 != X493) & (((ap @ (sub @ X494 @ id) @ X493)) = ((ap @ (sub @ X492 @ id) @ X491)))) & ! [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) != ((ap @ X489 @ X490))) | (X487 = X490))))) & (((hoasinduction_lem3a = $true) | ? [X518 : (subst > term > subst > $o),X519 : term] : (($true != ((X518 @ id @ (lam @ X519) @ id))) & ! [X525 : term] : ((((X518 @ id @ X525 @ id)) != $true) | ($true = ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) & ! [X520 : (subst > term > term)] : (? [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) != $true) & ($true = ((X518 @ id @ X521 @ id)))) | ($true = ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) | ? [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) != ((sub @ (X520 @ X522 @ X524) @ X523)))))) & (! [X518 : (subst > term > subst > $o),X519 : term] : (($true = ((X518 @ id @ (lam @ X519) @ id))) | ? [X525 : term] : ((((X518 @ id @ X525 @ id)) = $true) & ($true != ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) | ? [X520 : (subst > term > term)] : (! [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) = $true) | ($true != ((X518 @ id @ X521 @ id)))) & ($true != ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) & ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523))))) | (hoasinduction_lem3a != $true))) & (pushprop = $true) & (pushprop_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((substmonoid_lthm = $true) | (! [X65 : subst] : (((comp @ X65 @ id)) = X65) & (? [X66 : subst] : (((comp @ id @ X66)) != X66) | ? [X67 : subst] : (((comp @ X67 @ id)) != X67)) & ! [X64 : subst] : (((comp @ id @ X64)) = X64))) & ((? [X65 : subst] : (((comp @ X65 @ id)) != X65) | (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)) | ? [X64 : subst] : (((comp @ id @ X64)) != X64)) | (substmonoid_lthm != $true))) & (((apinj1 = $true) | ? [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) = ((ap @ X505 @ X506))) & (X505 != X507))) & (! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507)) | (apinj1 != $true))) & (ulamvarind = $true) & (pushprop_lthm_orig = $true) & ((! [X84 : (subst > term > subst > $o),X83 : term] : (? [X85 : term] : (($true != ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) & (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ? [X86 : (subst > term > term)] : (! [X90 : term] : ((((X84 @ id @ X90 @ id)) != $true) | (((X84 @ id @ (X86 @ id @ X90) @ id)) = $true)) & (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X84 : (subst > term > subst > $o),X83 : term] : (! [X85 : term] : (($true = ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) | (((X84 @ id @ X85 @ id)) != $true)) & ($true != ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) & ! [X86 : (subst > term > term)] : (? [X90 : term] : ((((X84 @ id @ X90 @ id)) = $true) & (((X84 @ id @ (X86 @ id @ X90) @ id)) != $true)) | (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ? [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) != ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))))))) & (((hoasinduction_lem3aaa = $true) | ? [X294 : (subst > term > subst > $o),X293 : term] : (! [X296 : term,X297 : (subst > term > term)] : (? [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) != ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) | ? [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) != ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) | ? [X301 : term] : ((((X294 @ id @ X301 @ id)) = $true) & (((X294 @ id @ (X297 @ id @ X301) @ id)) != $true)) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)) & (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) != $true) & ! [X295 : term] : (($true = ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) | (((X294 @ id @ X295 @ id)) != $true)))) & (! [X294 : (subst > term > subst > $o),X293 : term] : (? [X296 : term,X297 : (subst > term > term)] : (! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) & ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) & ! [X301 : term] : ((((X294 @ id @ X301 @ id)) != $true) | (((X294 @ id @ (X297 @ id @ X301) @ id)) = $true)) & (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true)) | (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true) | ? [X295 : term] : (($true != ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) & (((X294 @ id @ X295 @ id)) = $true))) | (hoasinduction_lem3aaa != $true))) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & (((hoaslaminj_lthm = $true) | (? [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (! [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) = ((sub @ (X281 @ X288 @ X287) @ X289))) & (((X283 @ X280 @ X282)) != ((X281 @ X280 @ X282))) & ! [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) = ((sub @ (X283 @ X285 @ X284) @ X286))) & (((lam @ (X283 @ sh @ one))) = ((lam @ (X281 @ sh @ one))))) & ! [X279 : term,X278 : term] : ((((lam @ X279)) != ((lam @ X278))) | (X278 = X279)) & ! [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) = X275) & ! [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) = X277))) & ((! [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (? [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) != ((sub @ (X281 @ X288 @ X287) @ X289))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ? [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) != ((sub @ (X283 @ X285 @ X284) @ X286))) | (((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one))))) | ? [X279 : term,X278 : term] : ((((lam @ X279)) = ((lam @ X278))) & (X278 != X279)) | ? [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) != X275) | ? [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) != X277)) | (hoaslaminj_lthm != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((! [X451 : term,X452 : (subst > term > subst > $o)] : (? [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) != $true) & ($true = ((X452 @ id @ X457 @ id)))) | (((sP16 @ X452)) = $true) | ? [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) = $true) & (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) != $true)) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ? [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) = $true) & ($true != ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ? [X451 : term,X452 : (subst > term > subst > $o)] : (! [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) = $true) | ($true != ((X452 @ id @ X457 @ id)))) & (((sP16 @ X452)) != $true) & ! [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) != $true) | (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) = $true)) & (((X452 @ id @ (lam @ X451) @ id)) != $true) & ! [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) != $true) | ($true = ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))))))) & (pushprop_lem1_gthm = $true) & ((($true = sP15) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP15))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = id) & (((axvarid = $true) | ? [X467 : term] : (((sub @ X467 @ id)) != X467)) & (! [X467 : term] : (((sub @ X467 @ id)) = X467) | (axvarid != $true))) & ((! [X436 : subst,X437 : (term > $o),X438 : term] : ? [X439 : (term > $o)] : ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X436 : subst,X437 : (term > $o),X438 : term] : ! [X439 : (term > $o)] : ? [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) != ((X439 @ X440))))) & ((! [X419 : (subst > term > subst > $o),X418 : term] : (? [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true != ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) & ($true = ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) | ($true = ((sP13 @ X419))) | ($true = ((sP12 @ X419))) | ? [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true != ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) & (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) = $true)) | ($true = ((X419 @ id @ X418 @ id))) | ? [X424 : term] : ((((var @ (sub @ X424 @ id))) = $true) & ($true != ((X419 @ id @ X424 @ id))))) | (hoasinduction != $true)) & ((hoasinduction = $true) | ? [X419 : (subst > term > subst > $o),X418 : term] : (! [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true = ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) | ($true != ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) & ($true != ((sP13 @ X419))) & ($true != ((sP12 @ X419))) & ! [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true = ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) | (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) != $true)) & ($true != ((X419 @ id @ X418 @ id))) & ! [X424 : term] : ((((var @ (sub @ X424 @ id))) != $true) | ($true = ((X419 @ id @ X424 @ id))))))) & (hoasapinj2_gthm = $true) & ((! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) | (axscons != $true)) & ((axscons = $true) | ? [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) != X292))) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & (((laminj = $true) | ? [X170 : term,X169 : term] : ((((lam @ X169)) = ((lam @ X170))) & (X169 != X170))) & (! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170)) | (laminj != $true))) & (lamnotap != $true) & (hoasinduction_lem1_gthm = $true) & (((hoasinduction_lem3v2 = $true) | ? [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (! [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) = $true) | (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) != $true)) & ! [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true = ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) | (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) != $true)) & ($true != ((sP11 @ X306))) & ! [X318 : term] : (($true = ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) | ($true != ((X305 @ X318)))) & (((X305 @ (lam @ X307))) != $true) & ! [X313 : term] : (((X305 @ X313)) = ((X306 @ id @ X313 @ id))))) & (! [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (? [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) != $true) & (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) = $true)) | ? [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true != ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) & (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) = $true)) | ($true = ((sP11 @ X306))) | ? [X318 : term] : (($true != ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) & ($true = ((X305 @ X318)))) | (((X305 @ (lam @ X307))) = $true) | ? [X313 : term] : (((X305 @ X313)) != ((X306 @ id @ X313 @ id)))) | (hoasinduction_lem3v2 != $true))) & ((! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 != X537) & (((ap @ X536 @ X537)) = ((ap @ X535 @ X534)))))) & (((hoasinduction_lem3v2a = $true) | ? [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (! [X366 : term] : (((X362 @ X366)) = ((X363 @ id @ X366 @ id))) & ! [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) = $true) | (((X362 @ X365)) != $true)) & ! [X367 : (subst > term > term)] : (? [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) != ((sub @ (X367 @ X370 @ X369) @ X371))) | ($true = ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) | ? [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) != $true) & (((X363 @ id @ X368 @ id)) = $true))) & (((X362 @ (lam @ X364))) != $true))) & (! [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (? [X366 : term] : (((X362 @ X366)) != ((X363 @ id @ X366 @ id))) | ? [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) != $true) & (((X362 @ X365)) = $true)) | ? [X367 : (subst > term > term)] : (! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) & ($true != ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | (((X363 @ id @ X368 @ id)) != $true))) | (((X362 @ (lam @ X364))) = $true)) | (hoasinduction_lem3v2a != $true))) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & (((hoasinduction_lem3aa = $true) | ? [X148 : (subst > term > subst > $o),X147 : term] : (($true != ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) & ! [X149 : (subst > term > term)] : (? [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) != ((sub @ (X149 @ X153 @ X151) @ X152))) | (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) = $true) | ? [X150 : term] : (($true != ((X148 @ id @ (X149 @ id @ X150) @ id))) & ($true = ((X148 @ id @ X150 @ id))))) & ! [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) = $true) | ($true != ((X148 @ id @ X154 @ id)))))) & (! [X148 : (subst > term > subst > $o),X147 : term] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ? [X149 : (subst > term > term)] : (! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152))) & (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) != $true) & ! [X150 : term] : (($true = ((X148 @ id @ (X149 @ id @ X150) @ id))) | ($true != ((X148 @ id @ X150 @ id))))) | ? [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) != $true) & ($true = ((X148 @ id @ X154 @ id))))) | (hoasinduction_lem3aa != $true))) & (hoasinduction_lem3a_gthm = $true) & (ulamvarsh = $true) & (((pushprop_lem0 = $true) | ? [X224 : subst,X222 : term,X223 : (term > $o)] : ! [X225 : (term > $o)] : ? [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) != ((X225 @ X226)))) & (! [X224 : subst,X222 : term,X223 : (term > $o)] : ? [X225 : (term > $o)] : ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226))) | (pushprop_lem0 != $true))) & ! [X38 : d_subst] : (d_id = X38) & (((? [X229 : term] : (((sub @ X229 @ id)) != X229) | ! [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (($true = ((sP10 @ X230))) | ? [X237 : term] : (((X230 @ id @ X237 @ id)) != ((X231 @ X237))) | ? [X238 : term] : ((((X231 @ X238)) = $true) & (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) != $true)) | ? [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true != ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) & ($true = ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ? [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true = ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) & (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) != $true)) | ($true = ((X231 @ (lam @ X232)))))) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (! [X229 : term] : (((sub @ X229 @ id)) = X229) & ? [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (($true != ((sP10 @ X230))) & ! [X237 : term] : (((X230 @ id @ X237 @ id)) = ((X231 @ X237))) & ! [X238 : term] : ((((X231 @ X238)) != $true) | (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) = $true)) & ! [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true = ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) | ($true != ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) & ! [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true != ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) | (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) = $true)) & ($true != ((X231 @ (lam @ X232)))))))) & (((hoasinduction_lthm = $true) | (! [X114 : term,X113 : (subst > term > subst > $o)] : (? [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) != $true) & ($true = ((X113 @ id @ X115 @ id)))) | ? [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) != $true) & ($true = ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ($true = ((X113 @ id @ (lam @ X114) @ id))) | (((sP6 @ X113)) != $true) | ? [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true = ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) & (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) != $true))) & ($true != sP8) & (sP7 != $true) & ($true != sP9))) & ((? [X114 : term,X113 : (subst > term > subst > $o)] : (! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ($true != ((X113 @ id @ X115 @ id)))) & ! [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true != ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) & ($true != ((X113 @ id @ (lam @ X114) @ id))) & (((sP6 @ X113)) = $true) & ! [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true != ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) | (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true))) | ($true = sP8) | (sP7 = $true) | ($true = sP9)) | (hoasinduction_lthm != $true))) & (((hoasinduction_lthm_3 = $true) | (! [X333 : term] : (((sub @ X333 @ id)) = X333) & ! [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) = $true) | ? [X339 : (subst > term > term)] : (! [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) = ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) & ($true != ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) & ! [X343 : term] : (($true = ((X336 @ id @ (X339 @ id @ X343) @ id))) | (((X336 @ id @ X343 @ id)) != $true))) | ? [X338 : term] : ((((X334 @ X338)) = $true) & (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) != $true)) | ? [X337 : term] : (((X334 @ X337)) != ((X336 @ id @ X337 @ id)))) & ! [X323 : (subst > term > subst > $o)] : ? [X324 : (term > $o)] : ! [X325 : term] : (((X324 @ X325)) = ((X323 @ id @ X325 @ id))) & ($true != sP3) & (sP2 != $true))) & ((? [X333 : term] : (((sub @ X333 @ id)) != X333) | ? [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) != $true) & ! [X339 : (subst > term > term)] : (? [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) != ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) | ? [X343 : term] : (($true != ((X336 @ id @ (X339 @ id @ X343) @ id))) & (((X336 @ id @ X343 @ id)) = $true))) & ! [X338 : term] : ((((X334 @ X338)) != $true) | (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true)) & ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id)))) | ? [X323 : (subst > term > subst > $o)] : ! [X324 : (term > $o)] : ? [X325 : term] : (((X324 @ X325)) != ((X323 @ id @ X325 @ id))) | ($true = sP3) | (sP2 = $true)) | (hoasinduction_lthm_3 != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & (((hoasinduction_lem3v2_f = $true) | ? [X0 : term] : ! [X1 : (subst > term > term)] : ? [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) != ((sub @ X0 @ (push @ X3 @ X2))))) & (! [X0 : term] : ? [X1 : (subst > term > term)] : ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2)))) | (hoasinduction_lem3v2_f != $true))) & (((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X91 : subst] : (((comp @ id @ X91)) != X91) | ? [X92 : subst] : (((comp @ X92 @ id)) != X92)))) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & ((! [X512 : (term > $o),X513 : term] : (($true = ((X512 @ X513))) | ? [X515 : term] : ((((X512 @ X515)) != $true) & (((var @ X515)) = $true)) | ? [X514 : term] : (($true = ((X512 @ X514))) & (((X512 @ (lam @ X514))) != $true)) | ? [X517 : term,X516 : term] : ((((X512 @ X517)) = $true) & ($true != ((X512 @ (ap @ X516 @ X517)))) & (((X512 @ X516)) = $true))) | (induction != $true)) & ((induction = $true) | ? [X512 : (term > $o),X513 : term] : (($true != ((X512 @ X513))) & ! [X515 : term] : ((((X512 @ X515)) = $true) | (((var @ X515)) != $true)) & ! [X514 : term] : (($true != ((X512 @ X514))) | (((X512 @ (lam @ X514))) = $true)) & ! [X517 : term,X516 : term] : ((((X512 @ X517)) != $true) | ($true = ((X512 @ (ap @ X516 @ X517)))) | (((X512 @ X516)) != $true))))) & (((pushprop_lem1_lthm = $true) | (! [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) = X46) & ! [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) = X49) & ? [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true != ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) & ($true = ((X52 @ X51)))))) & ((? [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) != X46) | ? [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) != X49) | ! [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ($true != ((X52 @ X51))))) | (pushprop_lem1_lthm != $true))) & (((! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271)))) | ? [X265 : term] : (((sub @ X265 @ id)) != X265) | ? [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) = ((ap @ X268 @ X266))) & (X267 != X268))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 != X273) & (((ap @ (sub @ X272 @ id) @ X270)) = ((ap @ (sub @ X273 @ id) @ X271)))) & ! [X265 : term] : (((sub @ X265 @ id)) = X265) & ! [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) != ((ap @ X268 @ X266))) | (X267 = X268))))) & (hoasinduction_lem2_lthm = $true)), 26.09/4.24 inference(nnf_transformation,[],[f43])). 26.09/4.24 thf(f134,plain,( 26.09/4.24 (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) | ? [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) != X386)) & (! [X386 : term,X385 : subst] : (((sub @ one @ (push @ X386 @ X385))) = X386) | (axvarcons != $true)) & (hoasapnotvar_lthm = $true) & ((hoaslaminj = $true) | ? [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (! [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) = ((sub @ (X406 @ X411 @ X410) @ X412))) & (((X406 @ X405 @ X403)) != ((X404 @ X405 @ X403))) & (((lam @ (X404 @ sh @ one))) = ((lam @ (X406 @ sh @ one)))) & ! [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) = ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408)))))) & (! [X403 : term,X405 : subst,X404 : (subst > term > term),X406 : (subst > term > term)] : (? [X412 : subst,X410 : term,X411 : subst] : (((X406 @ (comp @ X411 @ X412) @ (sub @ X410 @ X412))) != ((sub @ (X406 @ X411 @ X410) @ X412))) | (((X406 @ X405 @ X403)) = ((X404 @ X405 @ X403))) | (((lam @ (X404 @ sh @ one))) != ((lam @ (X406 @ sh @ one)))) | ? [X408 : subst,X409 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X409) @ X408)) != ((X404 @ (comp @ X407 @ X408) @ (sub @ X409 @ X408))))) | (hoaslaminj != $true)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction_lem2v2 != $true)) & (! [X221 : subst] : (((comp @ id @ X221)) = X221) | (axidl != $true)) & ((axidl = $true) | ? [X221 : subst] : (((comp @ id @ X221)) != X221)) & (hoaslamnotvar_lthm = $true) & ! [X528 : subst] : ? [X529 : d_subst] : (((d2subst @ X529)) = X528) & (! [X291 : term,X290 : term] : ((X290 = X291) | (((sub @ X291 @ sh)) != ((sub @ X290 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X291 : term,X290 : term] : ((X290 != X291) & (((sub @ X291 @ sh)) = ((sub @ X290 @ sh))))) & (! [X444 : (subst > term > subst > $o)] : ? [X445 : (term > $o)] : ! [X446 : term] : (((X444 @ id @ X446 @ id)) = ((X445 @ X446))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X444 : (subst > term > subst > $o)] : ! [X445 : (term > $o)] : ? [X446 : term] : (((X444 @ id @ X446 @ id)) != ((X445 @ X446)))) & (axclos = $true) & (substmonoid_gthm = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((sP26 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP26 != $true)) & (lamnotvar = $true) & (axabs = $true) & ! [X538 : d_term,X539 : d_term] : ((X538 = X539) | (((d2term @ X538)) != ((d2term @ X539)))) & (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) != X37)) & ((hoaslamnotap = $true) | ? [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) = ((lam @ (X163 @ sh @ one)))) & ! [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X163 @ X166 @ X168) @ X167))))) & (! [X164 : term,X163 : (subst > term > term),X165 : term] : ((((ap @ (sub @ X165 @ id) @ X164)) != ((lam @ (X163 @ sh @ one)))) | ? [X168 : term,X166 : subst,X167 : subst] : (((X163 @ (comp @ X166 @ X167) @ (sub @ X168 @ X167))) != ((sub @ (X163 @ X166 @ X168) @ X167)))) | (hoaslamnotap != $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (axvarshift = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (hoasinduction_gthm = $true) & (! [X447 : term] : ? [X448 : (subst > term > term)] : ! [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) = ((X448 @ X450 @ X449))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X447 : term] : ! [X448 : (subst > term > term)] : ? [X449 : term,X450 : subst] : (((sub @ X447 @ (push @ X449 @ X450))) != ((X448 @ X450 @ X449)))) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X189 : (subst > term > subst > $o)] : ? [X190 : (term > $o)] : ! [X191 : term] : (((X190 @ X191)) = ((X189 @ id @ X191 @ id))) & ! [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) = $true) | ? [X204 : (subst > term > term)] : (! [X208 : term] : (($true = ((X200 @ id @ (X204 @ id @ X208) @ id))) | ($true != ((X200 @ id @ X208 @ id)))) & ($true != ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) & ! [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X204 @ X206 @ X205) @ X207)))) | ? [X209 : term] : (($true = ((X201 @ X209))) & ($true != ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) | ? [X203 : term] : (((X200 @ id @ X203 @ id)) != ((X201 @ X203)))) & ! [X199 : term] : (((sub @ X199 @ id)) = X199) & (sP25 != $true) & ($true != sP24))) & (? [X189 : (subst > term > subst > $o)] : ! [X190 : (term > $o)] : ? [X191 : term] : (((X190 @ X191)) != ((X189 @ id @ X191 @ id))) | ? [X200 : (subst > term > subst > $o),X202 : term,X201 : (term > $o)] : ((((X201 @ (lam @ X202))) != $true) & ! [X204 : (subst > term > term)] : (? [X208 : term] : (($true != ((X200 @ id @ (X204 @ id @ X208) @ id))) & ($true = ((X200 @ id @ X208 @ id)))) | ($true = ((X200 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ? [X207 : subst,X205 : term,X206 : subst] : (((X204 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X204 @ X206 @ X205) @ X207)))) & ! [X209 : term] : (($true != ((X201 @ X209))) | ($true = ((X201 @ (sub @ X202 @ (push @ X209 @ id)))))) & ! [X203 : term] : (((X200 @ id @ X203 @ id)) = ((X201 @ X203)))) | ? [X199 : term] : (((sub @ X199 @ id)) != X199) | (sP25 = $true) | ($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X496 : (subst > term > subst > $o),X495 : term] : (! [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) = $true) | ($true != ((X496 @ id @ X498 @ id))) | (((X496 @ id @ X497 @ id)) != $true)) & ! [X499 : (subst > term > term)] : (? [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) != ((sub @ (X499 @ X500 @ X502) @ X501))) | ? [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) != $true) & ($true = ((X496 @ id @ X503 @ id)))) | ($true = ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) & ($true != ((X496 @ id @ X495 @ id))))) & (! [X496 : (subst > term > subst > $o),X495 : term] : (? [X498 : term,X497 : term] : ((((X496 @ id @ (ap @ (sub @ X498 @ id) @ X497) @ id)) != $true) & ($true = ((X496 @ id @ X498 @ id))) & (((X496 @ id @ X497 @ id)) = $true)) | ? [X499 : (subst > term > term)] : (! [X502 : term,X501 : subst,X500 : subst] : (((X499 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501))) = ((sub @ (X499 @ X500 @ X502) @ X501))) & ! [X503 : term] : ((((X496 @ id @ (X499 @ id @ X503) @ id)) = $true) | ($true != ((X496 @ id @ X503 @ id)))) & ($true != ((X496 @ id @ (lam @ (X499 @ sh @ one)) @ id)))) | ($true = ((X496 @ id @ X495 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ! [X228 : d_subst,X227 : d_subst] : ((((d2subst @ X227)) != ((d2subst @ X228))) | (X227 = X228)) & ((pushprop_lem1v2 = $true) | ? [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (! [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) = ((X416 @ X417))) & ($true = ((X414 @ X413))) & (((X416 @ one)) != $true))) & (! [X413 : term,X415 : subst,X416 : (term > $o),X414 : (term > $o)] : (? [X417 : term] : (((X414 @ (sub @ X417 @ (push @ X413 @ X415)))) != ((X416 @ X417))) | ($true != ((X414 @ X413))) | (((X416 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (? [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (! [X81 : term] : (($true = ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) | ($true != ((X73 @ X81)))) & ($true != ((X73 @ (lam @ X75)))) & ! [X82 : term] : (((X74 @ id @ X82 @ id)) = ((X73 @ X82))) & ! [X76 : (subst > term > term)] : (($true = ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) | ? [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) != ((sub @ (X76 @ X77 @ X79) @ X78))) | ? [X80 : term] : (($true = ((X74 @ id @ X80 @ id))) & ($true != ((X74 @ id @ (X76 @ id @ X80) @ id)))))) & ! [X68 : term] : ? [X69 : (subst > term > term)] : ! [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) = ((sub @ X68 @ (push @ X70 @ X71)))) & ! [X72 : term] : (((sub @ X72 @ id)) = X72))) & (! [X74 : (subst > term > subst > $o),X73 : (term > $o),X75 : term] : (? [X81 : term] : (($true != ((X73 @ (sub @ X75 @ (push @ X81 @ id))))) & ($true = ((X73 @ X81)))) | ($true = ((X73 @ (lam @ X75)))) | ? [X82 : term] : (((X74 @ id @ X82 @ id)) != ((X73 @ X82))) | ? [X76 : (subst > term > term)] : (($true != ((X74 @ id @ (lam @ (X76 @ sh @ one)) @ id))) & ! [X77 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X77 @ X78) @ (sub @ X79 @ X78))) = ((sub @ (X76 @ X77 @ X79) @ X78))) & ! [X80 : term] : (($true != ((X74 @ id @ X80 @ id))) | ($true = ((X74 @ id @ (X76 @ id @ X80) @ id)))))) | ? [X68 : term] : ! [X69 : (subst > term > term)] : ? [X70 : term,X71 : subst] : (((X69 @ X71 @ X70)) != ((sub @ X68 @ (push @ X70 @ X71)))) | ? [X72 : term] : (((sub @ X72 @ id)) != X72) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (! [X527 : term] : (((sub @ X527 @ id)) = X527) | ? [X526 : term] : (((sub @ X526 @ id)) != X526) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X527 : term] : (((sub @ X527 @ id)) != X527) & ! [X526 : term] : (((sub @ X526 @ id)) = X526))) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP23) & ! [X172 : (subst > term > subst > $o),X173 : term] : (? [X174 : (subst > term > term)] : (! [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) = ((sub @ (X174 @ X177 @ X176) @ X178))) & ! [X175 : term] : (($true = ((X172 @ id @ (X174 @ id @ X175) @ id))) | (((X172 @ id @ X175 @ id)) != $true)) & (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) != $true)) | ? [X179 : term] : ((((X172 @ id @ X179 @ id)) = $true) & ($true != ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) | ($true = ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id)))) & ! [X171 : term] : (((sub @ X171 @ id)) = X171))) & (($true = sP23) | ? [X172 : (subst > term > subst > $o),X173 : term] : (! [X174 : (subst > term > term)] : (? [X176 : term,X178 : subst,X177 : subst] : (((X174 @ (comp @ X177 @ X178) @ (sub @ X176 @ X178))) != ((sub @ (X174 @ X177 @ X176) @ X178))) | ? [X175 : term] : (($true != ((X172 @ id @ (X174 @ id @ X175) @ id))) & (((X172 @ id @ X175 @ id)) = $true)) | (((X172 @ id @ (lam @ (X174 @ sh @ one)) @ id)) = $true)) & ! [X179 : term] : ((((X172 @ id @ X179 @ id)) != $true) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X179 @ id)) @ id)))) & ($true != ((X172 @ id @ (lam @ (sub @ X173 @ (push @ one @ sh))) @ id)))) | ? [X171 : term] : (((sub @ X171 @ id)) != X171) | (hoasinduction_lem3a_lthm != $true)) & (! [X55 : term] : (((sub @ X55 @ id)) = X55) | (termmset != $true)) & ((termmset = $true) | ? [X55 : term] : (((sub @ X55 @ id)) != X55)) & ((pushprop_lem1v2_lthm = $true) | (! [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) = X40) & ? [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) = $true) & ! [X45 : term] : (((X41 @ X45)) = ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) & (((X41 @ one)) != $true)))) & (? [X39 : subst,X40 : term] : (((sub @ one @ (push @ X40 @ X39))) != X40) | ! [X42 : term,X43 : (term > $o),X44 : subst,X41 : (term > $o)] : ((((X43 @ X42)) != $true) | ? [X45 : term] : (((X41 @ X45)) != ((X43 @ (sub @ X45 @ (push @ X42 @ X44))))) | (((X41 @ one)) = $true)) | (pushprop_lem1v2_lthm != $true)) & (($true = sP22) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP22)) & ((hoasinduction_lem3b = $true) | ? [X263 : term] : ! [X264 : (subst > term > term)] : (((X264 @ sh @ one)) != ((sub @ X263 @ (push @ one @ sh))))) & (! [X263 : term] : ? [X264 : (subst > term > term)] : (((X264 @ sh @ one)) = ((sub @ X263 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (! [X188 : subst] : (((comp @ X188 @ id)) = X188) | (axidr != $true)) & ((axidr = $true) | ? [X188 : subst] : (((comp @ X188 @ id)) != X188)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem0 = $true) | ? [X61 : (subst > term > subst > $o)] : ! [X62 : (term > $o)] : ? [X63 : term] : (((X62 @ X63)) != ((X61 @ id @ X63 @ id)))) & (! [X61 : (subst > term > subst > $o)] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X61 @ id @ X63 @ id))) | (hoasinduction_lem0 != $true)) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true)) & (pushprop_gthm = $true) & (one = ((d2term @ d_one))) & (! [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true = ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) | ($true != ((X59 @ X58)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X56 : term,X58 : term,X59 : (term > $o),X57 : (term > $o),X60 : subst] : (($true != ((X57 @ (sub @ X58 @ (push @ X56 @ X60))))) & ($true = ((X59 @ X58))))) & (induction2_gthm = $true) & (axmap = $true) & ! [X443 : d_term] : (d_one = X443) & ((hoasapinj1 = $true) | ? [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 != X531) & (((ap @ (sub @ X530 @ id) @ X532)) = ((ap @ (sub @ X531 @ id) @ X533))))) & (! [X530 : term,X531 : term,X533 : term,X532 : term] : ((X530 = X531) | (((ap @ (sub @ X530 @ id) @ X532)) != ((ap @ (sub @ X531 @ id) @ X533)))) | (hoasapinj1 != $true)) & ((hoasapinj2 = $true) | ? [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) = ((ap @ (sub @ X511 @ id) @ X509))) & (X508 != X509))) & (! [X511 : term,X508 : term,X509 : term,X510 : term] : ((((ap @ (sub @ X510 @ id) @ X508)) != ((ap @ (sub @ X511 @ id) @ X509))) | (X508 = X509)) | (hoasapinj2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X11 : term] : (((sub @ X11 @ id)) = X11) & ($true != sP20) & ! [X12 : (subst > term > subst > $o),X13 : term] : (? [X15 : (subst > term > term)] : (! [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) = ((sub @ (X15 @ X17 @ X16) @ X18))) & (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) != $true) & ! [X19 : term] : (($true != ((X12 @ id @ X19 @ id))) | ($true = ((X12 @ id @ (X15 @ id @ X19) @ id))))) | ? [X14 : term] : (($true = ((X12 @ id @ X14 @ id))) & ($true != ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true)))) & (? [X11 : term] : (((sub @ X11 @ id)) != X11) | ($true = sP20) | ? [X12 : (subst > term > subst > $o),X13 : term] : (! [X15 : (subst > term > term)] : (? [X17 : subst,X16 : term,X18 : subst] : (((X15 @ (comp @ X17 @ X18) @ (sub @ X16 @ X18))) != ((sub @ (X15 @ X17 @ X16) @ X18))) | (((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : (($true = ((X12 @ id @ X19 @ id))) & ($true != ((X12 @ id @ (X15 @ id @ X19) @ id))))) & ! [X14 : term] : (($true != ((X12 @ id @ X14 @ id))) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)))) & (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) != $true)) | (hoasinduction_lem3_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((induction2_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (induction2_lthm != $true)) & (! [X441 : term] : ? [X442 : (subst > term > term)] : (((X442 @ sh @ one)) = ((sub @ X441 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X441 : term] : ! [X442 : (subst > term > term)] : (((X442 @ sh @ one)) != ((sub @ X441 @ (push @ one @ sh))))) & (! [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 = X493) | (((ap @ (sub @ X494 @ id) @ X493)) != ((ap @ (sub @ X492 @ id) @ X491)))) | ? [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) = ((ap @ X489 @ X490))) & (X487 != X490)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X492 : term,X494 : term,X493 : term,X491 : term] : ((X491 != X493) & (((ap @ (sub @ X494 @ id) @ X493)) = ((ap @ (sub @ X492 @ id) @ X491)))) & ! [X490 : term,X487 : term,X488 : term,X489 : term] : ((((ap @ X488 @ X487)) != ((ap @ X489 @ X490))) | (X487 = X490)))) & ((hoasinduction_lem3a = $true) | ? [X518 : (subst > term > subst > $o),X519 : term] : (($true != ((X518 @ id @ (lam @ X519) @ id))) & ! [X525 : term] : ((((X518 @ id @ X525 @ id)) != $true) | ($true = ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) & ! [X520 : (subst > term > term)] : (? [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) != $true) & ($true = ((X518 @ id @ X521 @ id)))) | ($true = ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) | ? [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) != ((sub @ (X520 @ X522 @ X524) @ X523)))))) & (! [X518 : (subst > term > subst > $o),X519 : term] : (($true = ((X518 @ id @ (lam @ X519) @ id))) | ? [X525 : term] : ((((X518 @ id @ X525 @ id)) = $true) & ($true != ((X518 @ id @ (sub @ X519 @ (push @ X525 @ id)) @ id)))) | ? [X520 : (subst > term > term)] : (! [X521 : term] : ((((X518 @ id @ (X520 @ id @ X521) @ id)) = $true) | ($true != ((X518 @ id @ X521 @ id)))) & ($true != ((X518 @ id @ (lam @ (X520 @ sh @ one)) @ id))) & ! [X524 : term,X522 : subst,X523 : subst] : (((X520 @ (comp @ X522 @ X523) @ (sub @ X524 @ X523))) = ((sub @ (X520 @ X522 @ X524) @ X523))))) | (hoasinduction_lem3a != $true)) & (pushprop = $true) & (pushprop_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((substmonoid_lthm = $true) | (! [X65 : subst] : (((comp @ X65 @ id)) = X65) & (? [X66 : subst] : (((comp @ id @ X66)) != X66) | ? [X67 : subst] : (((comp @ X67 @ id)) != X67)) & ! [X64 : subst] : (((comp @ id @ X64)) = X64))) & (? [X65 : subst] : (((comp @ X65 @ id)) != X65) | (! [X66 : subst] : (((comp @ id @ X66)) = X66) & ! [X67 : subst] : (((comp @ X67 @ id)) = X67)) | ? [X64 : subst] : (((comp @ id @ X64)) != X64) | (substmonoid_lthm != $true)) & ((apinj1 = $true) | ? [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) = ((ap @ X505 @ X506))) & (X505 != X507))) & (! [X505 : term,X504 : term,X506 : term,X507 : term] : ((((ap @ X507 @ X504)) != ((ap @ X505 @ X506))) | (X505 = X507)) | (apinj1 != $true)) & (ulamvarind = $true) & (pushprop_lthm_orig = $true) & (! [X84 : (subst > term > subst > $o),X83 : term] : (? [X85 : term] : (($true != ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) & (((X84 @ id @ X85 @ id)) = $true)) | ($true = ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) | ? [X86 : (subst > term > term)] : (! [X90 : term] : ((((X84 @ id @ X90 @ id)) != $true) | (((X84 @ id @ (X86 @ id @ X90) @ id)) = $true)) & (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) = ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87)))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X84 : (subst > term > subst > $o),X83 : term] : (! [X85 : term] : (($true = ((X84 @ id @ (sub @ X83 @ (push @ X85 @ id)) @ id))) | (((X84 @ id @ X85 @ id)) != $true)) & ($true != ((X84 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id))) & ! [X86 : (subst > term > term)] : (? [X90 : term] : ((((X84 @ id @ X90 @ id)) = $true) & (((X84 @ id @ (X86 @ id @ X90) @ id)) != $true)) | (((X84 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ? [X87 : subst,X88 : term,X89 : subst] : (((sub @ (X86 @ X89 @ X88) @ X87)) != ((X86 @ (comp @ X89 @ X87) @ (sub @ X88 @ X87))))))) & ((hoasinduction_lem3aaa = $true) | ? [X294 : (subst > term > subst > $o),X293 : term] : (! [X296 : term,X297 : (subst > term > term)] : (? [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) != ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) | ? [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) != ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) | ? [X301 : term] : ((((X294 @ id @ X301 @ id)) = $true) & (((X294 @ id @ (X297 @ id @ X301) @ id)) != $true)) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)) & (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) != $true) & ! [X295 : term] : (($true = ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) | (((X294 @ id @ X295 @ id)) != $true)))) & (! [X294 : (subst > term > subst > $o),X293 : term] : (? [X296 : term,X297 : (subst > term > term)] : (! [X303 : subst,X302 : subst,X304 : term] : (((sub @ (X297 @ X303 @ X304) @ X302)) = ((sub @ (sub @ X296 @ (push @ X304 @ X303)) @ X302))) & ! [X298 : term,X300 : subst,X299 : subst] : (((X297 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ X296 @ (push @ (sub @ X298 @ X300) @ (comp @ X299 @ X300))))) & ! [X301 : term] : ((((X294 @ id @ X301 @ id)) != $true) | (((X294 @ id @ (X297 @ id @ X301) @ id)) = $true)) & (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true)) | (((X294 @ id @ (lam @ (sub @ X293 @ (push @ one @ sh))) @ id)) = $true) | ? [X295 : term] : (($true != ((X294 @ id @ (sub @ X293 @ (push @ X295 @ id)) @ id))) & (((X294 @ id @ X295 @ id)) = $true))) | (hoasinduction_lem3aaa != $true)) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) | (? [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (! [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) = ((sub @ (X281 @ X288 @ X287) @ X289))) & (((X283 @ X280 @ X282)) != ((X281 @ X280 @ X282))) & ! [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) = ((sub @ (X283 @ X285 @ X284) @ X286))) & (((lam @ (X283 @ sh @ one))) = ((lam @ (X281 @ sh @ one))))) & ! [X279 : term,X278 : term] : ((((lam @ X279)) != ((lam @ X278))) | (X278 = X279)) & ! [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) = X275) & ! [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) = X277))) & (! [X282 : term,X280 : subst,X283 : (subst > term > term),X281 : (subst > term > term)] : (? [X288 : subst,X287 : term,X289 : subst] : (((X281 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289))) != ((sub @ (X281 @ X288 @ X287) @ X289))) | (((X283 @ X280 @ X282)) = ((X281 @ X280 @ X282))) | ? [X284 : term,X285 : subst,X286 : subst] : (((X283 @ (comp @ X285 @ X286) @ (sub @ X284 @ X286))) != ((sub @ (X283 @ X285 @ X284) @ X286))) | (((lam @ (X283 @ sh @ one))) != ((lam @ (X281 @ sh @ one))))) | ? [X279 : term,X278 : term] : ((((lam @ X279)) = ((lam @ X278))) & (X278 != X279)) | ? [X274 : subst,X275 : term] : (((sub @ one @ (push @ X275 @ X274))) != X275) | ? [X277 : subst,X276 : term] : (((comp @ sh @ (push @ X276 @ X277))) != X277) | (hoaslaminj_lthm != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X451 : term,X452 : (subst > term > subst > $o)] : (? [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) != $true) & ($true = ((X452 @ id @ X457 @ id)))) | (((sP16 @ X452)) = $true) | ? [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) = $true) & (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) != $true)) | (((X452 @ id @ (lam @ X451) @ id)) = $true) | ? [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) = $true) & ($true != ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465))))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ? [X451 : term,X452 : (subst > term > subst > $o)] : (! [X457 : term] : ((((X452 @ id @ (sub @ X451 @ (push @ X457 @ id)) @ id)) = $true) | ($true != ((X452 @ id @ X457 @ id)))) & (((sP16 @ X452)) != $true) & ! [X453 : subst,X455 : term,X456 : subst,X454 : subst] : ((((X452 @ (comp @ X453 @ X456) @ (sub @ X455 @ X456) @ X454)) != $true) | (((X452 @ X453 @ X455 @ (comp @ X456 @ X454))) = $true)) & (((X452 @ id @ (lam @ X451) @ id)) != $true) & ! [X466 : term,X463 : subst,X464 : subst,X465 : subst] : ((((X452 @ X463 @ X466 @ (comp @ X464 @ X465))) != $true) | ($true = ((X452 @ (comp @ X463 @ X464) @ (sub @ X466 @ X464) @ X465)))))) & (pushprop_lem1_gthm = $true) & (($true = sP15) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP15)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = id) & ((axvarid = $true) | ? [X467 : term] : (((sub @ X467 @ id)) != X467)) & (! [X467 : term] : (((sub @ X467 @ id)) = X467) | (axvarid != $true)) & (! [X436 : subst,X437 : (term > $o),X438 : term] : ? [X439 : (term > $o)] : ! [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) = ((X439 @ X440))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X436 : subst,X437 : (term > $o),X438 : term] : ! [X439 : (term > $o)] : ? [X440 : term] : (((X437 @ (sub @ X440 @ (push @ X438 @ X436)))) != ((X439 @ X440)))) & (! [X419 : (subst > term > subst > $o),X418 : term] : (? [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true != ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) & ($true = ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) | ($true = ((sP13 @ X419))) | ($true = ((sP12 @ X419))) | ? [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true != ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) & (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) = $true)) | ($true = ((X419 @ id @ X418 @ id))) | ? [X424 : term] : ((((var @ (sub @ X424 @ id))) = $true) & ($true != ((X419 @ id @ X424 @ id))))) | (hoasinduction != $true)) & ((hoasinduction = $true) | ? [X419 : (subst > term > subst > $o),X418 : term] : (! [X428 : subst,X429 : term,X427 : subst,X430 : subst] : (($true = ((X419 @ X427 @ X429 @ (comp @ X430 @ X428)))) | ($true != ((X419 @ (comp @ X427 @ X430) @ (sub @ X429 @ X430) @ X428)))) & ($true != ((sP13 @ X419))) & ($true != ((sP12 @ X419))) & ! [X423 : subst,X421 : subst,X420 : term,X422 : subst] : (($true = ((X419 @ (comp @ X423 @ X422) @ (sub @ X420 @ X422) @ X421))) | (((X419 @ X423 @ X420 @ (comp @ X422 @ X421))) != $true)) & ($true != ((X419 @ id @ X418 @ id))) & ! [X424 : term] : ((((var @ (sub @ X424 @ id))) != $true) | ($true = ((X419 @ id @ X424 @ id)))))) & (hoasapinj2_gthm = $true) & (! [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) = X292) | (axscons != $true)) & ((axscons = $true) | ? [X292 : subst] : (((push @ (sub @ one @ X292) @ (comp @ sh @ X292))) != X292)) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((laminj = $true) | ? [X170 : term,X169 : term] : ((((lam @ X169)) = ((lam @ X170))) & (X169 != X170))) & (! [X170 : term,X169 : term] : ((((lam @ X169)) != ((lam @ X170))) | (X169 = X170)) | (laminj != $true)) & (lamnotap != $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ? [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (! [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) = $true) | (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) != $true)) & ! [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true = ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) | (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) != $true)) & ($true != ((sP11 @ X306))) & ! [X318 : term] : (($true = ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) | ($true != ((X305 @ X318)))) & (((X305 @ (lam @ X307))) != $true) & ! [X313 : term] : (((X305 @ X313)) = ((X306 @ id @ X313 @ id))))) & (! [X307 : term,X305 : (term > $o),X306 : (subst > term > subst > $o)] : (? [X322 : subst,X320 : subst,X321 : subst,X319 : term] : ((((X306 @ (comp @ X321 @ X322) @ (sub @ X319 @ X322) @ X320)) != $true) & (((X306 @ X321 @ X319 @ (comp @ X322 @ X320))) = $true)) | ? [X314 : term,X317 : subst,X316 : subst,X315 : subst] : (($true != ((X306 @ X317 @ X314 @ (comp @ X315 @ X316)))) & (((X306 @ (comp @ X317 @ X315) @ (sub @ X314 @ X315) @ X316)) = $true)) | ($true = ((sP11 @ X306))) | ? [X318 : term] : (($true != ((X305 @ (sub @ X307 @ (push @ X318 @ id))))) & ($true = ((X305 @ X318)))) | (((X305 @ (lam @ X307))) = $true) | ? [X313 : term] : (((X305 @ X313)) != ((X306 @ id @ X313 @ id)))) | (hoasinduction_lem3v2 != $true)) & (! [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 = X537) | (((ap @ X536 @ X537)) != ((ap @ X535 @ X534)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X537 : term,X536 : term,X534 : term,X535 : term] : ((X534 != X537) & (((ap @ X536 @ X537)) = ((ap @ X535 @ X534))))) & ((hoasinduction_lem3v2a = $true) | ? [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (! [X366 : term] : (((X362 @ X366)) = ((X363 @ id @ X366 @ id))) & ! [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) = $true) | (((X362 @ X365)) != $true)) & ! [X367 : (subst > term > term)] : (? [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) != ((sub @ (X367 @ X370 @ X369) @ X371))) | ($true = ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) | ? [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) != $true) & (((X363 @ id @ X368 @ id)) = $true))) & (((X362 @ (lam @ X364))) != $true))) & (! [X363 : (subst > term > subst > $o),X364 : term,X362 : (term > $o)] : (? [X366 : term] : (((X362 @ X366)) != ((X363 @ id @ X366 @ id))) | ? [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) != $true) & (((X362 @ X365)) = $true)) | ? [X367 : (subst > term > term)] : (! [X370 : subst,X369 : term,X371 : subst] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) & ($true != ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X368 : term] : ((((X363 @ id @ (X367 @ id @ X368) @ id)) = $true) | (((X363 @ id @ X368 @ id)) != $true))) | (((X362 @ (lam @ X364))) = $true)) | (hoasinduction_lem3v2a != $true)) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & ((hoasinduction_lem3aa = $true) | ? [X148 : (subst > term > subst > $o),X147 : term] : (($true != ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) & ! [X149 : (subst > term > term)] : (? [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) != ((sub @ (X149 @ X153 @ X151) @ X152))) | (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) = $true) | ? [X150 : term] : (($true != ((X148 @ id @ (X149 @ id @ X150) @ id))) & ($true = ((X148 @ id @ X150 @ id))))) & ! [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) = $true) | ($true != ((X148 @ id @ X154 @ id)))))) & (! [X148 : (subst > term > subst > $o),X147 : term] : (($true = ((X148 @ id @ (lam @ (sub @ X147 @ (push @ one @ sh))) @ id))) | ? [X149 : (subst > term > term)] : (! [X151 : term,X153 : subst,X152 : subst] : (((X149 @ (comp @ X153 @ X152) @ (sub @ X151 @ X152))) = ((sub @ (X149 @ X153 @ X151) @ X152))) & (((X148 @ id @ (lam @ (X149 @ sh @ one)) @ id)) != $true) & ! [X150 : term] : (($true = ((X148 @ id @ (X149 @ id @ X150) @ id))) | ($true != ((X148 @ id @ X150 @ id))))) | ? [X154 : term] : ((((X148 @ id @ (sub @ X147 @ (push @ X154 @ id)) @ id)) != $true) & ($true = ((X148 @ id @ X154 @ id))))) | (hoasinduction_lem3aa != $true)) & (hoasinduction_lem3a_gthm = $true) & (ulamvarsh = $true) & ((pushprop_lem0 = $true) | ? [X224 : subst,X222 : term,X223 : (term > $o)] : ! [X225 : (term > $o)] : ? [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) != ((X225 @ X226)))) & (! [X224 : subst,X222 : term,X223 : (term > $o)] : ? [X225 : (term > $o)] : ! [X226 : term] : (((X223 @ (sub @ X226 @ (push @ X222 @ X224)))) = ((X225 @ X226))) | (pushprop_lem0 != $true)) & ! [X38 : d_subst] : (d_id = X38) & (? [X229 : term] : (((sub @ X229 @ id)) != X229) | ! [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (($true = ((sP10 @ X230))) | ? [X237 : term] : (((X230 @ id @ X237 @ id)) != ((X231 @ X237))) | ? [X238 : term] : ((((X231 @ X238)) = $true) & (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) != $true)) | ? [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true != ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) & ($true = ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) | ? [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true = ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) & (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) != $true)) | ($true = ((X231 @ (lam @ X232))))) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (! [X229 : term] : (((sub @ X229 @ id)) = X229) & ? [X231 : (term > $o),X232 : term,X230 : (subst > term > subst > $o)] : (($true != ((sP10 @ X230))) & ! [X237 : term] : (((X230 @ id @ X237 @ id)) = ((X231 @ X237))) & ! [X238 : term] : ((((X231 @ X238)) != $true) | (((X231 @ (sub @ X232 @ (push @ X238 @ id)))) = $true)) & ! [X242 : subst,X240 : term,X241 : subst,X239 : subst] : (($true = ((X230 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241) @ X242))) | ($true != ((X230 @ X239 @ X240 @ (comp @ X241 @ X242))))) & ! [X236 : term,X234 : subst,X233 : subst,X235 : subst] : (($true != ((X230 @ (comp @ X233 @ X234) @ (sub @ X236 @ X234) @ X235))) | (((X230 @ X233 @ X236 @ (comp @ X234 @ X235))) = $true)) & ($true != ((X231 @ (lam @ X232))))))) & ((hoasinduction_lthm = $true) | (! [X114 : term,X113 : (subst > term > subst > $o)] : (? [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) != $true) & ($true = ((X113 @ id @ X115 @ id)))) | ? [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) != $true) & ($true = ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ($true = ((X113 @ id @ (lam @ X114) @ id))) | (((sP6 @ X113)) != $true) | ? [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true = ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) & (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) != $true))) & ($true != sP8) & (sP7 != $true) & ($true != sP9))) & (? [X114 : term,X113 : (subst > term > subst > $o)] : (! [X115 : term] : ((((X113 @ id @ (sub @ X114 @ (push @ X115 @ id)) @ id)) = $true) | ($true != ((X113 @ id @ X115 @ id)))) & ! [X118 : subst,X119 : term,X117 : subst,X116 : subst] : ((((X113 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true != ((X113 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) & ($true != ((X113 @ id @ (lam @ X114) @ id))) & (((sP6 @ X113)) = $true) & ! [X127 : subst,X125 : subst,X126 : term,X128 : subst] : (($true != ((X113 @ X127 @ X126 @ (comp @ X128 @ X125)))) | (((X113 @ (comp @ X127 @ X128) @ (sub @ X126 @ X128) @ X125)) = $true))) | ($true = sP8) | (sP7 = $true) | ($true = sP9) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X333 : term] : (((sub @ X333 @ id)) = X333) & ! [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) = $true) | ? [X339 : (subst > term > term)] : (! [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) = ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) & ($true != ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) & ! [X343 : term] : (($true = ((X336 @ id @ (X339 @ id @ X343) @ id))) | (((X336 @ id @ X343 @ id)) != $true))) | ? [X338 : term] : ((((X334 @ X338)) = $true) & (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) != $true)) | ? [X337 : term] : (((X334 @ X337)) != ((X336 @ id @ X337 @ id)))) & ! [X323 : (subst > term > subst > $o)] : ? [X324 : (term > $o)] : ! [X325 : term] : (((X324 @ X325)) = ((X323 @ id @ X325 @ id))) & ($true != sP3) & (sP2 != $true))) & (? [X333 : term] : (((sub @ X333 @ id)) != X333) | ? [X334 : (term > $o),X335 : term,X336 : (subst > term > subst > $o)] : ((((X334 @ (lam @ X335))) != $true) & ! [X339 : (subst > term > term)] : (? [X340 : subst,X341 : term,X342 : subst] : (((sub @ (X339 @ X340 @ X341) @ X342)) != ((X339 @ (comp @ X340 @ X342) @ (sub @ X341 @ X342)))) | ($true = ((X336 @ id @ (lam @ (X339 @ sh @ one)) @ id))) | ? [X343 : term] : (($true != ((X336 @ id @ (X339 @ id @ X343) @ id))) & (((X336 @ id @ X343 @ id)) = $true))) & ! [X338 : term] : ((((X334 @ X338)) != $true) | (((X334 @ (sub @ X335 @ (push @ X338 @ id)))) = $true)) & ! [X337 : term] : (((X334 @ X337)) = ((X336 @ id @ X337 @ id)))) | ? [X323 : (subst > term > subst > $o)] : ! [X324 : (term > $o)] : ? [X325 : term] : (((X324 @ X325)) != ((X323 @ id @ X325 @ id))) | ($true = sP3) | (sP2 = $true) | (hoasinduction_lthm_3 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X219 : term] : ? [X220 : d_term] : (((d2term @ X220)) = X219) & ((hoasinduction_lem3v2_f = $true) | ? [X0 : term] : ! [X1 : (subst > term > term)] : ? [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) != ((sub @ X0 @ (push @ X3 @ X2))))) & (! [X0 : term] : ? [X1 : (subst > term > term)] : ! [X3 : term,X2 : subst] : (((X1 @ X2 @ X3)) = ((sub @ X0 @ (push @ X3 @ X2)))) | (hoasinduction_lem3v2_f != $true)) & ((! [X91 : subst] : (((comp @ id @ X91)) = X91) & ! [X92 : subst] : (((comp @ X92 @ id)) = X92)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X91 : subst] : (((comp @ id @ X91)) != X91) | ? [X92 : subst] : (((comp @ X92 @ id)) != X92)) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X512 : (term > $o),X513 : term] : (($true = ((X512 @ X513))) | ? [X515 : term] : ((((X512 @ X515)) != $true) & (((var @ X515)) = $true)) | ? [X514 : term] : (($true = ((X512 @ X514))) & (((X512 @ (lam @ X514))) != $true)) | ? [X517 : term,X516 : term] : ((((X512 @ X517)) = $true) & ($true != ((X512 @ (ap @ X516 @ X517)))) & (((X512 @ X516)) = $true))) | (induction != $true)) & ((induction = $true) | ? [X512 : (term > $o),X513 : term] : (($true != ((X512 @ X513))) & ! [X515 : term] : ((((X512 @ X515)) = $true) | (((var @ X515)) != $true)) & ! [X514 : term] : (($true != ((X512 @ X514))) | (((X512 @ (lam @ X514))) = $true)) & ! [X517 : term,X516 : term] : ((((X512 @ X517)) != $true) | ($true = ((X512 @ (ap @ X516 @ X517)))) | (((X512 @ X516)) != $true)))) & ((pushprop_lem1_lthm = $true) | (! [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) = X46) & ! [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) = X49) & ? [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true != ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) & ($true = ((X52 @ X51)))))) & (? [X46 : term,X47 : subst] : (((sub @ one @ (push @ X46 @ X47))) != X46) | ? [X49 : subst,X48 : term] : (((comp @ sh @ (push @ X48 @ X49))) != X49) | ! [X54 : (term > $o),X52 : (term > $o),X50 : subst,X53 : term,X51 : term] : (($true = ((X54 @ (sub @ X51 @ (push @ X53 @ X50))))) | ($true != ((X52 @ X51)))) | (pushprop_lem1_lthm != $true)) & (! [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 = X273) | (((ap @ (sub @ X272 @ id) @ X270)) != ((ap @ (sub @ X273 @ id) @ X271)))) | ? [X265 : term] : (((sub @ X265 @ id)) != X265) | ? [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) = ((ap @ X268 @ X266))) & (X267 != X268)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X270 : term,X271 : term,X273 : term,X272 : term] : ((X272 != X273) & (((ap @ (sub @ X272 @ id) @ X270)) = ((ap @ (sub @ X273 @ id) @ X271)))) & ! [X265 : term] : (((sub @ X265 @ id)) = X265) & ! [X269 : term,X267 : term,X266 : term,X268 : term] : ((((ap @ X267 @ X269)) != ((ap @ X268 @ X266))) | (X267 = X268)))) & (hoasinduction_lem2_lthm = $true)), 26.09/4.24 inference(flattening,[],[f133])). 26.09/4.24 thf(f135,plain,( 26.09/4.24 (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) | ? [X0 : term,X1 : subst] : (((sub @ one @ (push @ X0 @ X1))) != X0)) & (! [X2 : term,X3 : subst] : (((sub @ one @ (push @ X2 @ X3))) = X2) | (axvarcons != $true)) & (hoasapnotvar_lthm = $true) & ((hoaslaminj = $true) | ? [X4 : term,X5 : subst,X6 : (subst > term > term),X7 : (subst > term > term)] : (! [X8 : subst,X9 : term,X10 : subst] : (((X7 @ (comp @ X10 @ X8) @ (sub @ X9 @ X8))) = ((sub @ (X7 @ X10 @ X9) @ X8))) & (((X7 @ X5 @ X4)) != ((X6 @ X5 @ X4))) & (((lam @ (X6 @ sh @ one))) = ((lam @ (X7 @ sh @ one)))) & ! [X11 : subst,X12 : term,X13 : subst] : (((X6 @ (comp @ X13 @ X11) @ (sub @ X12 @ X11))) = ((sub @ (X6 @ X13 @ X12) @ X11))))) & (! [X14 : term,X15 : subst,X16 : (subst > term > term),X17 : (subst > term > term)] : (? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X17 @ X20 @ X19) @ X18)) != ((X17 @ (comp @ X20 @ X18) @ (sub @ X19 @ X18)))) | (((X16 @ X15 @ X14)) = ((X17 @ X15 @ X14))) | (((lam @ (X16 @ sh @ one))) != ((lam @ (X17 @ sh @ one)))) | ? [X21 : subst,X22 : term,X23 : subst] : (((X16 @ (comp @ X23 @ X21) @ (sub @ X22 @ X21))) != ((sub @ (X16 @ X23 @ X22) @ X21)))) | (hoaslaminj != $true)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction_lem2v2 != $true)) & (! [X24 : subst] : (((comp @ id @ X24)) = X24) | (axidl != $true)) & ((axidl = $true) | ? [X25 : subst] : (((comp @ id @ X25)) != X25)) & (hoaslamnotvar_lthm = $true) & ! [X26 : subst] : ? [X27 : d_subst] : (((d2subst @ X27)) = X26) & (! [X28 : term,X29 : term] : ((X28 = X29) | (((sub @ X29 @ sh)) != ((sub @ X28 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X30 : term,X31 : term] : ((X30 != X31) & (((sub @ X31 @ sh)) = ((sub @ X30 @ sh))))) & (! [X32 : (subst > term > subst > $o)] : ? [X33 : (term > $o)] : ! [X34 : term] : (((X33 @ X34)) = ((X32 @ id @ X34 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X35 : (subst > term > subst > $o)] : ! [X36 : (term > $o)] : ? [X37 : term] : (((X35 @ id @ X37 @ id)) != ((X36 @ X37)))) & (axclos = $true) & (substmonoid_gthm = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((sP26 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP26 != $true)) & (lamnotvar = $true) & (axabs = $true) & ! [X38 : d_term,X39 : d_term] : ((X38 = X39) | (((d2term @ X39)) != ((d2term @ X38)))) & (! [X40 : term,X41 : subst] : (((comp @ sh @ (push @ X40 @ X41))) = X41) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X42 : term,X43 : subst] : (((comp @ sh @ (push @ X42 @ X43))) != X43)) & ((hoaslamnotap = $true) | ? [X44 : term,X45 : (subst > term > term),X46 : term] : ((((lam @ (X45 @ sh @ one))) = ((ap @ (sub @ X46 @ id) @ X44))) & ! [X47 : term,X48 : subst,X49 : subst] : (((sub @ (X45 @ X48 @ X47) @ X49)) = ((X45 @ (comp @ X48 @ X49) @ (sub @ X47 @ X49)))))) & (! [X50 : term,X51 : (subst > term > term),X52 : term] : ((((lam @ (X51 @ sh @ one))) != ((ap @ (sub @ X52 @ id) @ X50))) | ? [X53 : term,X54 : subst,X55 : subst] : (((sub @ (X51 @ X54 @ X53) @ X55)) != ((X51 @ (comp @ X54 @ X55) @ (sub @ X53 @ X55))))) | (hoaslamnotap != $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (axvarshift = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (hoasinduction_gthm = $true) & (! [X56 : term] : ? [X57 : (subst > term > term)] : ! [X58 : term,X59 : subst] : (((X57 @ X59 @ X58)) = ((sub @ X56 @ (push @ X58 @ X59)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X60 : term] : ! [X61 : (subst > term > term)] : ? [X62 : term,X63 : subst] : (((sub @ X60 @ (push @ X62 @ X63))) != ((X61 @ X63 @ X62)))) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X64 : (subst > term > subst > $o)] : ? [X65 : (term > $o)] : ! [X66 : term] : (((X64 @ id @ X66 @ id)) = ((X65 @ X66))) & ! [X67 : (subst > term > subst > $o),X68 : term,X69 : (term > $o)] : ((((X69 @ (lam @ X68))) = $true) | ? [X70 : (subst > term > term)] : (! [X71 : term] : (($true = ((X67 @ id @ (X70 @ id @ X71) @ id))) | (((X67 @ id @ X71 @ id)) != $true)) & ($true != ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id))) & ! [X72 : subst,X73 : term,X74 : subst] : (((sub @ (X70 @ X74 @ X73) @ X72)) = ((X70 @ (comp @ X74 @ X72) @ (sub @ X73 @ X72))))) | ? [X75 : term] : ((((X69 @ X75)) = $true) & (((X69 @ (sub @ X68 @ (push @ X75 @ id)))) != $true)) | ? [X76 : term] : (((X69 @ X76)) != ((X67 @ id @ X76 @ id)))) & ! [X77 : term] : (((sub @ X77 @ id)) = X77) & (sP25 != $true) & ($true != sP24))) & (? [X78 : (subst > term > subst > $o)] : ! [X79 : (term > $o)] : ? [X80 : term] : (((X78 @ id @ X80 @ id)) != ((X79 @ X80))) | ? [X81 : (subst > term > subst > $o),X82 : term,X83 : (term > $o)] : ((((X83 @ (lam @ X82))) != $true) & ! [X84 : (subst > term > term)] : (? [X85 : term] : (($true != ((X81 @ id @ (X84 @ id @ X85) @ id))) & (((X81 @ id @ X85 @ id)) = $true)) | ($true = ((X81 @ id @ (lam @ (X84 @ sh @ one)) @ id))) | ? [X86 : subst,X87 : term,X88 : subst] : (((sub @ (X84 @ X88 @ X87) @ X86)) != ((X84 @ (comp @ X88 @ X86) @ (sub @ X87 @ X86))))) & ! [X89 : term] : ((((X83 @ X89)) != $true) | ($true = ((X83 @ (sub @ X82 @ (push @ X89 @ id)))))) & ! [X90 : term] : (((X81 @ id @ X90 @ id)) = ((X83 @ X90)))) | ? [X91 : term] : (((sub @ X91 @ id)) != X91) | (sP25 = $true) | ($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X92 : (subst > term > subst > $o),X93 : term] : (! [X94 : term,X95 : term] : ((((X92 @ id @ (ap @ (sub @ X94 @ id) @ X95) @ id)) = $true) | (((X92 @ id @ X94 @ id)) != $true) | ($true != ((X92 @ id @ X95 @ id)))) & ! [X96 : (subst > term > term)] : (? [X97 : term,X98 : subst,X99 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) != ((sub @ (X96 @ X99 @ X97) @ X98))) | ? [X100 : term] : (($true != ((X92 @ id @ (X96 @ id @ X100) @ id))) & (((X92 @ id @ X100 @ id)) = $true)) | ($true = ((X92 @ id @ (lam @ (X96 @ sh @ one)) @ id)))) & ($true != ((X92 @ id @ X93 @ id))))) & (! [X101 : (subst > term > subst > $o),X102 : term] : (? [X103 : term,X104 : term] : (($true != ((X101 @ id @ (ap @ (sub @ X103 @ id) @ X104) @ id))) & ($true = ((X101 @ id @ X103 @ id))) & ($true = ((X101 @ id @ X104 @ id)))) | ? [X105 : (subst > term > term)] : (! [X106 : term,X107 : subst,X108 : subst] : (((X105 @ (comp @ X108 @ X107) @ (sub @ X106 @ X107))) = ((sub @ (X105 @ X108 @ X106) @ X107))) & ! [X109 : term] : (($true = ((X101 @ id @ (X105 @ id @ X109) @ id))) | ($true != ((X101 @ id @ X109 @ id)))) & ($true != ((X101 @ id @ (lam @ (X105 @ sh @ one)) @ id)))) | (((X101 @ id @ X102 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ! [X110 : d_subst,X111 : d_subst] : ((((d2subst @ X111)) != ((d2subst @ X110))) | (X110 = X111)) & ((pushprop_lem1v2 = $true) | ? [X112 : term,X113 : subst,X114 : (term > $o),X115 : (term > $o)] : (! [X116 : term] : (((X114 @ X116)) = ((X115 @ (sub @ X116 @ (push @ X112 @ X113))))) & ($true = ((X115 @ X112))) & (((X114 @ one)) != $true))) & (! [X117 : term,X118 : subst,X119 : (term > $o),X120 : (term > $o)] : (? [X121 : term] : (((X120 @ (sub @ X121 @ (push @ X117 @ X118)))) != ((X119 @ X121))) | (((X120 @ X117)) != $true) | ($true = ((X119 @ one)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (? [X122 : (subst > term > subst > $o),X123 : (term > $o),X124 : term] : (! [X125 : term] : (($true = ((X123 @ (sub @ X124 @ (push @ X125 @ id))))) | (((X123 @ X125)) != $true)) & (((X123 @ (lam @ X124))) != $true) & ! [X126 : term] : (((X122 @ id @ X126 @ id)) = ((X123 @ X126))) & ! [X127 : (subst > term > term)] : ((((X122 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ? [X128 : subst,X129 : term,X130 : subst] : (((sub @ (X127 @ X128 @ X129) @ X130)) != ((X127 @ (comp @ X128 @ X130) @ (sub @ X129 @ X130)))) | ? [X131 : term] : (($true = ((X122 @ id @ X131 @ id))) & ($true != ((X122 @ id @ (X127 @ id @ X131) @ id)))))) & ! [X132 : term] : ? [X133 : (subst > term > term)] : ! [X134 : term,X135 : subst] : (((X133 @ X135 @ X134)) = ((sub @ X132 @ (push @ X134 @ X135)))) & ! [X136 : term] : (((sub @ X136 @ id)) = X136))) & (! [X137 : (subst > term > subst > $o),X138 : (term > $o),X139 : term] : (? [X140 : term] : (($true != ((X138 @ (sub @ X139 @ (push @ X140 @ id))))) & (((X138 @ X140)) = $true)) | ($true = ((X138 @ (lam @ X139)))) | ? [X141 : term] : (((X137 @ id @ X141 @ id)) != ((X138 @ X141))) | ? [X142 : (subst > term > term)] : ((((X137 @ id @ (lam @ (X142 @ sh @ one)) @ id)) != $true) & ! [X143 : subst,X144 : term,X145 : subst] : (((X142 @ (comp @ X143 @ X145) @ (sub @ X144 @ X145))) = ((sub @ (X142 @ X143 @ X144) @ X145))) & ! [X146 : term] : ((((X137 @ id @ X146 @ id)) != $true) | ($true = ((X137 @ id @ (X142 @ id @ X146) @ id)))))) | ? [X147 : term] : ! [X148 : (subst > term > term)] : ? [X149 : term,X150 : subst] : (((sub @ X147 @ (push @ X149 @ X150))) != ((X148 @ X150 @ X149))) | ? [X151 : term] : (((sub @ X151 @ id)) != X151) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (! [X152 : term] : (((sub @ X152 @ id)) = X152) | ? [X153 : term] : (((sub @ X153 @ id)) != X153) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X154 : term] : (((sub @ X154 @ id)) != X154) & ! [X155 : term] : (((sub @ X155 @ id)) = X155))) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP23) & ! [X156 : (subst > term > subst > $o),X157 : term] : (? [X158 : (subst > term > term)] : (! [X159 : term,X160 : subst,X161 : subst] : (((sub @ (X158 @ X161 @ X159) @ X160)) = ((X158 @ (comp @ X161 @ X160) @ (sub @ X159 @ X160)))) & ! [X162 : term] : (($true = ((X156 @ id @ (X158 @ id @ X162) @ id))) | ($true != ((X156 @ id @ X162 @ id)))) & ($true != ((X156 @ id @ (lam @ (X158 @ sh @ one)) @ id)))) | ? [X163 : term] : ((((X156 @ id @ X163 @ id)) = $true) & ($true != ((X156 @ id @ (sub @ X157 @ (push @ X163 @ id)) @ id)))) | ($true = ((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id)))) & ! [X164 : term] : (((sub @ X164 @ id)) = X164))) & (($true = sP23) | ? [X165 : (subst > term > subst > $o),X166 : term] : (! [X167 : (subst > term > term)] : (? [X168 : term,X169 : subst,X170 : subst] : (((sub @ (X167 @ X170 @ X168) @ X169)) != ((X167 @ (comp @ X170 @ X169) @ (sub @ X168 @ X169)))) | ? [X171 : term] : (($true != ((X165 @ id @ (X167 @ id @ X171) @ id))) & (((X165 @ id @ X171 @ id)) = $true)) | (((X165 @ id @ (lam @ (X167 @ sh @ one)) @ id)) = $true)) & ! [X172 : term] : (($true != ((X165 @ id @ X172 @ id))) | (((X165 @ id @ (sub @ X166 @ (push @ X172 @ id)) @ id)) = $true)) & (((X165 @ id @ (lam @ (sub @ X166 @ (push @ one @ sh))) @ id)) != $true)) | ? [X173 : term] : (((sub @ X173 @ id)) != X173) | (hoasinduction_lem3a_lthm != $true)) & (! [X174 : term] : (((sub @ X174 @ id)) = X174) | (termmset != $true)) & ((termmset = $true) | ? [X175 : term] : (((sub @ X175 @ id)) != X175)) & ((pushprop_lem1v2_lthm = $true) | (! [X176 : subst,X177 : term] : (((sub @ one @ (push @ X177 @ X176))) = X177) & ? [X178 : term,X179 : (term > $o),X180 : subst,X181 : (term > $o)] : ((((X179 @ X178)) = $true) & ! [X182 : term] : (((X179 @ (sub @ X182 @ (push @ X178 @ X180)))) = ((X181 @ X182))) & (((X181 @ one)) != $true)))) & (? [X183 : subst,X184 : term] : (((sub @ one @ (push @ X184 @ X183))) != X184) | ! [X185 : term,X186 : (term > $o),X187 : subst,X188 : (term > $o)] : ((((X186 @ X185)) != $true) | ? [X189 : term] : (((X188 @ X189)) != ((X186 @ (sub @ X189 @ (push @ X185 @ X187))))) | (((X188 @ one)) = $true)) | (pushprop_lem1v2_lthm != $true)) & (($true = sP22) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP22)) & ((hoasinduction_lem3b = $true) | ? [X190 : term] : ! [X191 : (subst > term > term)] : (((X191 @ sh @ one)) != ((sub @ X190 @ (push @ one @ sh))))) & (! [X192 : term] : ? [X193 : (subst > term > term)] : (((X193 @ sh @ one)) = ((sub @ X192 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) | (axidr != $true)) & ((axidr = $true) | ? [X195 : subst] : (((comp @ X195 @ id)) != X195)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem0 = $true) | ? [X196 : (subst > term > subst > $o)] : ! [X197 : (term > $o)] : ? [X198 : term] : (((X197 @ X198)) != ((X196 @ id @ X198 @ id)))) & (! [X199 : (subst > term > subst > $o)] : ? [X200 : (term > $o)] : ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id))) | (hoasinduction_lem0 != $true)) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true)) & (pushprop_gthm = $true) & (one = ((d2term @ d_one))) & (! [X202 : term,X203 : term,X204 : (term > $o),X205 : (term > $o),X206 : subst] : (($true = ((X205 @ (sub @ X203 @ (push @ X202 @ X206))))) | (((X204 @ X203)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X207 : term,X208 : term,X209 : (term > $o),X210 : (term > $o),X211 : subst] : (($true != ((X210 @ (sub @ X208 @ (push @ X207 @ X211))))) & ($true = ((X209 @ X208))))) & (induction2_gthm = $true) & (axmap = $true) & ! [X212 : d_term] : (d_one = X212) & ((hoasapinj1 = $true) | ? [X213 : term,X214 : term,X215 : term,X216 : term] : ((X213 != X214) & (((ap @ (sub @ X214 @ id) @ X215)) = ((ap @ (sub @ X213 @ id) @ X216))))) & (! [X217 : term,X218 : term,X219 : term,X220 : term] : ((X217 = X218) | (((ap @ (sub @ X217 @ id) @ X220)) != ((ap @ (sub @ X218 @ id) @ X219)))) | (hoasapinj1 != $true)) & ((hoasapinj2 = $true) | ? [X221 : term,X222 : term,X223 : term,X224 : term] : ((((ap @ (sub @ X224 @ id) @ X222)) = ((ap @ (sub @ X221 @ id) @ X223))) & (X222 != X223))) & (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((((ap @ (sub @ X225 @ id) @ X227)) != ((ap @ (sub @ X228 @ id) @ X226))) | (X226 = X227)) | (hoasapinj2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X229 : term] : (((sub @ X229 @ id)) = X229) & ($true != sP20) & ! [X230 : (subst > term > subst > $o),X231 : term] : (? [X232 : (subst > term > term)] : (! [X233 : subst,X234 : term,X235 : subst] : (((X232 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235))) = ((sub @ (X232 @ X233 @ X234) @ X235))) & ($true != ((X230 @ id @ (lam @ (X232 @ sh @ one)) @ id))) & ! [X236 : term] : (($true != ((X230 @ id @ X236 @ id))) | ($true = ((X230 @ id @ (X232 @ id @ X236) @ id))))) | ? [X237 : term] : ((((X230 @ id @ X237 @ id)) = $true) & (((X230 @ id @ (sub @ X231 @ (push @ X237 @ id)) @ id)) != $true)) | (((X230 @ id @ (lam @ (sub @ X231 @ (push @ one @ sh))) @ id)) = $true)))) & (? [X238 : term] : (((sub @ X238 @ id)) != X238) | ($true = sP20) | ? [X239 : (subst > term > subst > $o),X240 : term] : (! [X241 : (subst > term > term)] : (? [X242 : subst,X243 : term,X244 : subst] : (((sub @ (X241 @ X242 @ X243) @ X244)) != ((X241 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ($true = ((X239 @ id @ (lam @ (X241 @ sh @ one)) @ id))) | ? [X245 : term] : (($true = ((X239 @ id @ X245 @ id))) & (((X239 @ id @ (X241 @ id @ X245) @ id)) != $true))) & ! [X246 : term] : (($true != ((X239 @ id @ X246 @ id))) | ($true = ((X239 @ id @ (sub @ X240 @ (push @ X246 @ id)) @ id)))) & ($true != ((X239 @ id @ (lam @ (sub @ X240 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((induction2_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (induction2_lthm != $true)) & (! [X247 : term] : ? [X248 : (subst > term > term)] : (((sub @ X247 @ (push @ one @ sh))) = ((X248 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X249 : term] : ! [X250 : (subst > term > term)] : (((sub @ X249 @ (push @ one @ sh))) != ((X250 @ sh @ one)))) & (! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X253 = X254) | (((ap @ (sub @ X251 @ id) @ X254)) != ((ap @ (sub @ X252 @ id) @ X253)))) | ? [X255 : term,X256 : term,X257 : term,X258 : term] : ((((ap @ X257 @ X256)) = ((ap @ X258 @ X255))) & (X255 != X256)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X259 : term,X260 : term,X261 : term,X262 : term] : ((X261 != X262) & (((ap @ (sub @ X259 @ id) @ X262)) = ((ap @ (sub @ X260 @ id) @ X261)))) & ! [X263 : term,X264 : term,X265 : term,X266 : term] : ((((ap @ X265 @ X264)) != ((ap @ X266 @ X263))) | (X263 = X264)))) & ((hoasinduction_lem3a = $true) | ? [X267 : (subst > term > subst > $o),X268 : term] : ((((X267 @ id @ (lam @ X268) @ id)) != $true) & ! [X269 : term] : ((((X267 @ id @ X269 @ id)) != $true) | ($true = ((X267 @ id @ (sub @ X268 @ (push @ X269 @ id)) @ id)))) & ! [X270 : (subst > term > term)] : (? [X271 : term] : (($true != ((X267 @ id @ (X270 @ id @ X271) @ id))) & ($true = ((X267 @ id @ X271 @ id)))) | ($true = ((X267 @ id @ (lam @ (X270 @ sh @ one)) @ id))) | ? [X272 : term,X273 : subst,X274 : subst] : (((sub @ (X270 @ X273 @ X272) @ X274)) != ((X270 @ (comp @ X273 @ X274) @ (sub @ X272 @ X274))))))) & (! [X275 : (subst > term > subst > $o),X276 : term] : (($true = ((X275 @ id @ (lam @ X276) @ id))) | ? [X277 : term] : ((((X275 @ id @ X277 @ id)) = $true) & ($true != ((X275 @ id @ (sub @ X276 @ (push @ X277 @ id)) @ id)))) | ? [X278 : (subst > term > term)] : (! [X279 : term] : ((((X275 @ id @ (X278 @ id @ X279) @ id)) = $true) | ($true != ((X275 @ id @ X279 @ id)))) & ($true != ((X275 @ id @ (lam @ (X278 @ sh @ one)) @ id))) & ! [X280 : term,X281 : subst,X282 : subst] : (((sub @ (X278 @ X281 @ X280) @ X282)) = ((X278 @ (comp @ X281 @ X282) @ (sub @ X280 @ X282)))))) | (hoasinduction_lem3a != $true)) & (pushprop = $true) & (pushprop_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((substmonoid_lthm = $true) | (! [X283 : subst] : (((comp @ X283 @ id)) = X283) & (? [X284 : subst] : (((comp @ id @ X284)) != X284) | ? [X285 : subst] : (((comp @ X285 @ id)) != X285)) & ! [X286 : subst] : (((comp @ id @ X286)) = X286))) & (? [X287 : subst] : (((comp @ X287 @ id)) != X287) | (! [X288 : subst] : (((comp @ id @ X288)) = X288) & ! [X289 : subst] : (((comp @ X289 @ id)) = X289)) | ? [X290 : subst] : (((comp @ id @ X290)) != X290) | (substmonoid_lthm != $true)) & ((apinj1 = $true) | ? [X291 : term,X292 : term,X293 : term,X294 : term] : ((((ap @ X294 @ X292)) = ((ap @ X291 @ X293))) & (X291 != X294))) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : ((((ap @ X298 @ X296)) != ((ap @ X295 @ X297))) | (X295 = X298)) | (apinj1 != $true)) & (ulamvarind = $true) & (pushprop_lthm_orig = $true) & (! [X299 : (subst > term > subst > $o),X300 : term] : (? [X301 : term] : (($true != ((X299 @ id @ (sub @ X300 @ (push @ X301 @ id)) @ id))) & (((X299 @ id @ X301 @ id)) = $true)) | (((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id)) = $true) | ? [X302 : (subst > term > term)] : (! [X303 : term] : (($true != ((X299 @ id @ X303 @ id))) | (((X299 @ id @ (X302 @ id @ X303) @ id)) = $true)) & ($true != ((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id))) & ! [X304 : subst,X305 : term,X306 : subst] : (((sub @ (X302 @ X306 @ X305) @ X304)) = ((X302 @ (comp @ X306 @ X304) @ (sub @ X305 @ X304)))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X307 : (subst > term > subst > $o),X308 : term] : (! [X309 : term] : ((((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id)) = $true) | (((X307 @ id @ X309 @ id)) != $true)) & (((X307 @ id @ (lam @ (sub @ X308 @ (push @ one @ sh))) @ id)) != $true) & ! [X310 : (subst > term > term)] : (? [X311 : term] : (($true = ((X307 @ id @ X311 @ id))) & ($true != ((X307 @ id @ (X310 @ id @ X311) @ id)))) | ($true = ((X307 @ id @ (lam @ (X310 @ sh @ one)) @ id))) | ? [X312 : subst,X313 : term,X314 : subst] : (((sub @ (X310 @ X314 @ X313) @ X312)) != ((X310 @ (comp @ X314 @ X312) @ (sub @ X313 @ X312))))))) & ((hoasinduction_lem3aaa = $true) | ? [X315 : (subst > term > subst > $o),X316 : term] : (! [X317 : term,X318 : (subst > term > term)] : (? [X319 : subst,X320 : subst,X321 : term] : (((sub @ (sub @ X317 @ (push @ X321 @ X319)) @ X320)) != ((sub @ (X318 @ X319 @ X321) @ X320))) | ? [X322 : term,X323 : subst,X324 : subst] : (((sub @ X317 @ (push @ (sub @ X322 @ X323) @ (comp @ X324 @ X323)))) != ((X318 @ (comp @ X324 @ X323) @ (sub @ X322 @ X323)))) | ? [X325 : term] : (($true = ((X315 @ id @ X325 @ id))) & (((X315 @ id @ (X318 @ id @ X325) @ id)) != $true)) | (((X315 @ id @ (lam @ (X318 @ sh @ one)) @ id)) = $true)) & (((X315 @ id @ (lam @ (sub @ X316 @ (push @ one @ sh))) @ id)) != $true) & ! [X326 : term] : ((((X315 @ id @ (sub @ X316 @ (push @ X326 @ id)) @ id)) = $true) | ($true != ((X315 @ id @ X326 @ id)))))) & (! [X327 : (subst > term > subst > $o),X328 : term] : (? [X329 : term,X330 : (subst > term > term)] : (! [X331 : subst,X332 : subst,X333 : term] : (((sub @ (sub @ X329 @ (push @ X333 @ X331)) @ X332)) = ((sub @ (X330 @ X331 @ X333) @ X332))) & ! [X334 : term,X335 : subst,X336 : subst] : (((X330 @ (comp @ X336 @ X335) @ (sub @ X334 @ X335))) = ((sub @ X329 @ (push @ (sub @ X334 @ X335) @ (comp @ X336 @ X335))))) & ! [X337 : term] : ((((X327 @ id @ X337 @ id)) != $true) | ($true = ((X327 @ id @ (X330 @ id @ X337) @ id)))) & ($true != ((X327 @ id @ (lam @ (X330 @ sh @ one)) @ id)))) | (((X327 @ id @ (lam @ (sub @ X328 @ (push @ one @ sh))) @ id)) = $true) | ? [X338 : term] : (($true != ((X327 @ id @ (sub @ X328 @ (push @ X338 @ id)) @ id))) & ($true = ((X327 @ id @ X338 @ id))))) | (hoasinduction_lem3aaa != $true)) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) | (? [X339 : term,X340 : subst,X341 : (subst > term > term),X342 : (subst > term > term)] : (! [X343 : subst,X344 : term,X345 : subst] : (((sub @ (X342 @ X343 @ X344) @ X345)) = ((X342 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345)))) & (((X341 @ X340 @ X339)) != ((X342 @ X340 @ X339))) & ! [X346 : term,X347 : subst,X348 : subst] : (((sub @ (X341 @ X347 @ X346) @ X348)) = ((X341 @ (comp @ X347 @ X348) @ (sub @ X346 @ X348)))) & (((lam @ (X342 @ sh @ one))) = ((lam @ (X341 @ sh @ one))))) & ! [X349 : term,X350 : term] : ((((lam @ X350)) != ((lam @ X349))) | (X349 = X350)) & ! [X351 : subst,X352 : term] : (((sub @ one @ (push @ X352 @ X351))) = X352) & ! [X353 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X353))) = X353))) & (! [X355 : term,X356 : subst,X357 : (subst > term > term),X358 : (subst > term > term)] : (? [X359 : subst,X360 : term,X361 : subst] : (((sub @ (X358 @ X359 @ X360) @ X361)) != ((X358 @ (comp @ X359 @ X361) @ (sub @ X360 @ X361)))) | (((X357 @ X356 @ X355)) = ((X358 @ X356 @ X355))) | ? [X362 : term,X363 : subst,X364 : subst] : (((sub @ (X357 @ X363 @ X362) @ X364)) != ((X357 @ (comp @ X363 @ X364) @ (sub @ X362 @ X364)))) | (((lam @ (X357 @ sh @ one))) != ((lam @ (X358 @ sh @ one))))) | ? [X365 : term,X366 : term] : ((((lam @ X365)) = ((lam @ X366))) & (X365 != X366)) | ? [X367 : subst,X368 : term] : (((sub @ one @ (push @ X368 @ X367))) != X368) | ? [X369 : subst,X370 : term] : (((comp @ sh @ (push @ X370 @ X369))) != X369) | (hoaslaminj_lthm != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X371 : term,X372 : (subst > term > subst > $o)] : (? [X373 : term] : ((((X372 @ id @ (sub @ X371 @ (push @ X373 @ id)) @ id)) != $true) & ($true = ((X372 @ id @ X373 @ id)))) | (((sP16 @ X372)) = $true) | ? [X374 : subst,X375 : term,X376 : subst,X377 : subst] : ((((X372 @ (comp @ X374 @ X376) @ (sub @ X375 @ X376) @ X377)) = $true) & ($true != ((X372 @ X374 @ X375 @ (comp @ X376 @ X377))))) | (((X372 @ id @ (lam @ X371) @ id)) = $true) | ? [X378 : term,X379 : subst,X380 : subst,X381 : subst] : ((((X372 @ X379 @ X378 @ (comp @ X380 @ X381))) = $true) & (((X372 @ (comp @ X379 @ X380) @ (sub @ X378 @ X380) @ X381)) != $true))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ? [X382 : term,X383 : (subst > term > subst > $o)] : (! [X384 : term] : ((((X383 @ id @ (sub @ X382 @ (push @ X384 @ id)) @ id)) = $true) | ($true != ((X383 @ id @ X384 @ id)))) & (((sP16 @ X383)) != $true) & ! [X385 : subst,X386 : term,X387 : subst,X388 : subst] : (($true != ((X383 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X388))) | ($true = ((X383 @ X385 @ X386 @ (comp @ X387 @ X388))))) & (((X383 @ id @ (lam @ X382) @ id)) != $true) & ! [X389 : term,X390 : subst,X391 : subst,X392 : subst] : (($true != ((X383 @ X390 @ X389 @ (comp @ X391 @ X392)))) | (((X383 @ (comp @ X390 @ X391) @ (sub @ X389 @ X391) @ X392)) = $true)))) & (pushprop_lem1_gthm = $true) & (($true = sP15) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP15)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = id) & ((axvarid = $true) | ? [X393 : term] : (((sub @ X393 @ id)) != X393)) & (! [X394 : term] : (((sub @ X394 @ id)) = X394) | (axvarid != $true)) & (! [X395 : subst,X396 : (term > $o),X397 : term] : ? [X398 : (term > $o)] : ! [X399 : term] : (((X398 @ X399)) = ((X396 @ (sub @ X399 @ (push @ X397 @ X395))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X400 : subst,X401 : (term > $o),X402 : term] : ! [X403 : (term > $o)] : ? [X404 : term] : (((X403 @ X404)) != ((X401 @ (sub @ X404 @ (push @ X402 @ X400)))))) & (! [X405 : (subst > term > subst > $o),X406 : term] : (? [X407 : subst,X408 : term,X409 : subst,X410 : subst] : ((((X405 @ X409 @ X408 @ (comp @ X410 @ X407))) != $true) & (((X405 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410) @ X407)) = $true)) | ($true = ((sP13 @ X405))) | ($true = ((sP12 @ X405))) | ? [X411 : subst,X412 : subst,X413 : term,X414 : subst] : (($true != ((X405 @ (comp @ X411 @ X414) @ (sub @ X413 @ X414) @ X412))) & ($true = ((X405 @ X411 @ X413 @ (comp @ X414 @ X412))))) | ($true = ((X405 @ id @ X406 @ id))) | ? [X415 : term] : (($true = ((var @ (sub @ X415 @ id)))) & (((X405 @ id @ X415 @ id)) != $true))) | (hoasinduction != $true)) & ((hoasinduction = $true) | ? [X416 : (subst > term > subst > $o),X417 : term] : (! [X418 : subst,X419 : term,X420 : subst,X421 : subst] : (($true = ((X416 @ X420 @ X419 @ (comp @ X421 @ X418)))) | (((X416 @ (comp @ X420 @ X421) @ (sub @ X419 @ X421) @ X418)) != $true)) & (((sP13 @ X416)) != $true) & (((sP12 @ X416)) != $true) & ! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : ((((X416 @ (comp @ X422 @ X425) @ (sub @ X424 @ X425) @ X423)) = $true) | (((X416 @ X422 @ X424 @ (comp @ X425 @ X423))) != $true)) & (((X416 @ id @ X417 @ id)) != $true) & ! [X426 : term] : (($true != ((var @ (sub @ X426 @ id)))) | ($true = ((X416 @ id @ X426 @ id)))))) & (hoasapinj2_gthm = $true) & (! [X427 : subst] : (((push @ (sub @ one @ X427) @ (comp @ sh @ X427))) = X427) | (axscons != $true)) & ((axscons = $true) | ? [X428 : subst] : (((push @ (sub @ one @ X428) @ (comp @ sh @ X428))) != X428)) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((laminj = $true) | ? [X429 : term,X430 : term] : ((((lam @ X429)) = ((lam @ X430))) & (X429 != X430))) & (! [X431 : term,X432 : term] : ((((lam @ X432)) != ((lam @ X431))) | (X431 = X432)) | (laminj != $true)) & (lamnotap != $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ? [X433 : term,X434 : (term > $o),X435 : (subst > term > subst > $o)] : (! [X436 : subst,X437 : subst,X438 : subst,X439 : term] : (($true = ((X435 @ (comp @ X438 @ X436) @ (sub @ X439 @ X436) @ X437))) | ($true != ((X435 @ X438 @ X439 @ (comp @ X436 @ X437))))) & ! [X440 : term,X441 : subst,X442 : subst,X443 : subst] : ((((X435 @ X441 @ X440 @ (comp @ X443 @ X442))) = $true) | (((X435 @ (comp @ X441 @ X443) @ (sub @ X440 @ X443) @ X442)) != $true)) & ($true != ((sP11 @ X435))) & ! [X444 : term] : (($true = ((X434 @ (sub @ X433 @ (push @ X444 @ id))))) | (((X434 @ X444)) != $true)) & (((X434 @ (lam @ X433))) != $true) & ! [X445 : term] : (((X435 @ id @ X445 @ id)) = ((X434 @ X445))))) & (! [X446 : term,X447 : (term > $o),X448 : (subst > term > subst > $o)] : (? [X449 : subst,X450 : subst,X451 : subst,X452 : term] : (($true != ((X448 @ (comp @ X451 @ X449) @ (sub @ X452 @ X449) @ X450))) & (((X448 @ X451 @ X452 @ (comp @ X449 @ X450))) = $true)) | ? [X453 : term,X454 : subst,X455 : subst,X456 : subst] : ((((X448 @ X454 @ X453 @ (comp @ X456 @ X455))) != $true) & ($true = ((X448 @ (comp @ X454 @ X456) @ (sub @ X453 @ X456) @ X455)))) | (((sP11 @ X448)) = $true) | ? [X457 : term] : (($true != ((X447 @ (sub @ X446 @ (push @ X457 @ id))))) & ($true = ((X447 @ X457)))) | (((X447 @ (lam @ X446))) = $true) | ? [X458 : term] : (((X448 @ id @ X458 @ id)) != ((X447 @ X458)))) | (hoasinduction_lem3v2 != $true)) & (! [X459 : term,X460 : term,X461 : term,X462 : term] : ((X459 = X461) | (((ap @ X460 @ X459)) != ((ap @ X462 @ X461)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X463 : term,X464 : term,X465 : term,X466 : term] : ((X463 != X465) & (((ap @ X466 @ X465)) = ((ap @ X464 @ X463))))) & ((hoasinduction_lem3v2a = $true) | ? [X467 : (subst > term > subst > $o),X468 : term,X469 : (term > $o)] : (! [X470 : term] : (((X467 @ id @ X470 @ id)) = ((X469 @ X470))) & ! [X471 : term] : (($true = ((X469 @ (sub @ X468 @ (push @ X471 @ id))))) | (((X469 @ X471)) != $true)) & ! [X472 : (subst > term > term)] : (? [X473 : subst,X474 : term,X475 : subst] : (((sub @ (X472 @ X473 @ X474) @ X475)) != ((X472 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475)))) | (((X467 @ id @ (lam @ (X472 @ sh @ one)) @ id)) = $true) | ? [X476 : term] : ((((X467 @ id @ (X472 @ id @ X476) @ id)) != $true) & ($true = ((X467 @ id @ X476 @ id))))) & (((X469 @ (lam @ X468))) != $true))) & (! [X477 : (subst > term > subst > $o),X478 : term,X479 : (term > $o)] : (? [X480 : term] : (((X479 @ X480)) != ((X477 @ id @ X480 @ id))) | ? [X481 : term] : (($true != ((X479 @ (sub @ X478 @ (push @ X481 @ id))))) & (((X479 @ X481)) = $true)) | ? [X482 : (subst > term > term)] : (! [X483 : subst,X484 : term,X485 : subst] : (((X482 @ (comp @ X483 @ X485) @ (sub @ X484 @ X485))) = ((sub @ (X482 @ X483 @ X484) @ X485))) & (((X477 @ id @ (lam @ (X482 @ sh @ one)) @ id)) != $true) & ! [X486 : term] : ((((X477 @ id @ (X482 @ id @ X486) @ id)) = $true) | ($true != ((X477 @ id @ X486 @ id))))) | (((X479 @ (lam @ X478))) = $true)) | (hoasinduction_lem3v2a != $true)) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & ((hoasinduction_lem3aa = $true) | ? [X487 : (subst > term > subst > $o),X488 : term] : ((((X487 @ id @ (lam @ (sub @ X488 @ (push @ one @ sh))) @ id)) != $true) & ! [X489 : (subst > term > term)] : (? [X490 : term,X491 : subst,X492 : subst] : (((sub @ (X489 @ X491 @ X490) @ X492)) != ((X489 @ (comp @ X491 @ X492) @ (sub @ X490 @ X492)))) | ($true = ((X487 @ id @ (lam @ (X489 @ sh @ one)) @ id))) | ? [X493 : term] : (($true != ((X487 @ id @ (X489 @ id @ X493) @ id))) & (((X487 @ id @ X493 @ id)) = $true))) & ! [X494 : term] : ((((X487 @ id @ (sub @ X488 @ (push @ X494 @ id)) @ id)) = $true) | ($true != ((X487 @ id @ X494 @ id)))))) & (! [X495 : (subst > term > subst > $o),X496 : term] : (($true = ((X495 @ id @ (lam @ (sub @ X496 @ (push @ one @ sh))) @ id))) | ? [X497 : (subst > term > term)] : (! [X498 : term,X499 : subst,X500 : subst] : (((X497 @ (comp @ X499 @ X500) @ (sub @ X498 @ X500))) = ((sub @ (X497 @ X499 @ X498) @ X500))) & (((X495 @ id @ (lam @ (X497 @ sh @ one)) @ id)) != $true) & ! [X501 : term] : (($true = ((X495 @ id @ (X497 @ id @ X501) @ id))) | ($true != ((X495 @ id @ X501 @ id))))) | ? [X502 : term] : (($true != ((X495 @ id @ (sub @ X496 @ (push @ X502 @ id)) @ id))) & ($true = ((X495 @ id @ X502 @ id))))) | (hoasinduction_lem3aa != $true)) & (hoasinduction_lem3a_gthm = $true) & (ulamvarsh = $true) & ((pushprop_lem0 = $true) | ? [X503 : subst,X504 : term,X505 : (term > $o)] : ! [X506 : (term > $o)] : ? [X507 : term] : (((X505 @ (sub @ X507 @ (push @ X504 @ X503)))) != ((X506 @ X507)))) & (! [X508 : subst,X509 : term,X510 : (term > $o)] : ? [X511 : (term > $o)] : ! [X512 : term] : (((X510 @ (sub @ X512 @ (push @ X509 @ X508)))) = ((X511 @ X512))) | (pushprop_lem0 != $true)) & ! [X513 : d_subst] : (d_id = X513) & (? [X514 : term] : (((sub @ X514 @ id)) != X514) | ! [X515 : (term > $o),X516 : term,X517 : (subst > term > subst > $o)] : ((((sP10 @ X517)) = $true) | ? [X518 : term] : (((X517 @ id @ X518 @ id)) != ((X515 @ X518))) | ? [X519 : term] : ((((X515 @ X519)) = $true) & (((X515 @ (sub @ X516 @ (push @ X519 @ id)))) != $true)) | ? [X520 : subst,X521 : term,X522 : subst,X523 : subst] : (($true != ((X517 @ (comp @ X523 @ X522) @ (sub @ X521 @ X522) @ X520))) & ($true = ((X517 @ X523 @ X521 @ (comp @ X522 @ X520))))) | ? [X524 : term,X525 : subst,X526 : subst,X527 : subst] : ((((X517 @ (comp @ X526 @ X525) @ (sub @ X524 @ X525) @ X527)) = $true) & ($true != ((X517 @ X526 @ X524 @ (comp @ X525 @ X527))))) | ($true = ((X515 @ (lam @ X516))))) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (! [X528 : term] : (((sub @ X528 @ id)) = X528) & ? [X529 : (term > $o),X530 : term,X531 : (subst > term > subst > $o)] : ((((sP10 @ X531)) != $true) & ! [X532 : term] : (((X531 @ id @ X532 @ id)) = ((X529 @ X532))) & ! [X533 : term] : ((((X529 @ X533)) != $true) | (((X529 @ (sub @ X530 @ (push @ X533 @ id)))) = $true)) & ! [X534 : subst,X535 : term,X536 : subst,X537 : subst] : ((((X531 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) = $true) | ($true != ((X531 @ X537 @ X535 @ (comp @ X536 @ X534))))) & ! [X538 : term,X539 : subst,X540 : subst,X541 : subst] : ((((X531 @ (comp @ X540 @ X539) @ (sub @ X538 @ X539) @ X541)) != $true) | (((X531 @ X540 @ X538 @ (comp @ X539 @ X541))) = $true)) & (((X529 @ (lam @ X530))) != $true)))) & ((hoasinduction_lthm = $true) | (! [X542 : term,X543 : (subst > term > subst > $o)] : (? [X544 : term] : (($true != ((X543 @ id @ (sub @ X542 @ (push @ X544 @ id)) @ id))) & (((X543 @ id @ X544 @ id)) = $true)) | ? [X545 : subst,X546 : term,X547 : subst,X548 : subst] : (($true != ((X543 @ X545 @ X546 @ (comp @ X547 @ X548)))) & (((X543 @ (comp @ X545 @ X547) @ (sub @ X546 @ X547) @ X548)) = $true)) | (((X543 @ id @ (lam @ X542) @ id)) = $true) | (((sP6 @ X543)) != $true) | ? [X549 : subst,X550 : subst,X551 : term,X552 : subst] : (($true = ((X543 @ X549 @ X551 @ (comp @ X552 @ X550)))) & (((X543 @ (comp @ X549 @ X552) @ (sub @ X551 @ X552) @ X550)) != $true))) & ($true != sP8) & (sP7 != $true) & ($true != sP9))) & (? [X553 : term,X554 : (subst > term > subst > $o)] : (! [X555 : term] : ((((X554 @ id @ (sub @ X553 @ (push @ X555 @ id)) @ id)) = $true) | ($true != ((X554 @ id @ X555 @ id)))) & ! [X556 : subst,X557 : term,X558 : subst,X559 : subst] : (($true = ((X554 @ X556 @ X557 @ (comp @ X558 @ X559)))) | (((X554 @ (comp @ X556 @ X558) @ (sub @ X557 @ X558) @ X559)) != $true)) & (((X554 @ id @ (lam @ X553) @ id)) != $true) & (((sP6 @ X554)) = $true) & ! [X560 : subst,X561 : subst,X562 : term,X563 : subst] : (($true != ((X554 @ X560 @ X562 @ (comp @ X563 @ X561)))) | ($true = ((X554 @ (comp @ X560 @ X563) @ (sub @ X562 @ X563) @ X561))))) | ($true = sP8) | (sP7 = $true) | ($true = sP9) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X564 : term] : (((sub @ X564 @ id)) = X564) & ! [X565 : (term > $o),X566 : term,X567 : (subst > term > subst > $o)] : ((((X565 @ (lam @ X566))) = $true) | ? [X568 : (subst > term > term)] : (! [X569 : subst,X570 : term,X571 : subst] : (((X568 @ (comp @ X569 @ X571) @ (sub @ X570 @ X571))) = ((sub @ (X568 @ X569 @ X570) @ X571))) & ($true != ((X567 @ id @ (lam @ (X568 @ sh @ one)) @ id))) & ! [X572 : term] : (($true = ((X567 @ id @ (X568 @ id @ X572) @ id))) | ($true != ((X567 @ id @ X572 @ id))))) | ? [X573 : term] : (($true = ((X565 @ X573))) & ($true != ((X565 @ (sub @ X566 @ (push @ X573 @ id)))))) | ? [X574 : term] : (((X567 @ id @ X574 @ id)) != ((X565 @ X574)))) & ! [X575 : (subst > term > subst > $o)] : ? [X576 : (term > $o)] : ! [X577 : term] : (((X576 @ X577)) = ((X575 @ id @ X577 @ id))) & ($true != sP3) & (sP2 != $true))) & (? [X578 : term] : (((sub @ X578 @ id)) != X578) | ? [X579 : (term > $o),X580 : term,X581 : (subst > term > subst > $o)] : ((((X579 @ (lam @ X580))) != $true) & ! [X582 : (subst > term > term)] : (? [X583 : subst,X584 : term,X585 : subst] : (((X582 @ (comp @ X583 @ X585) @ (sub @ X584 @ X585))) != ((sub @ (X582 @ X583 @ X584) @ X585))) | (((X581 @ id @ (lam @ (X582 @ sh @ one)) @ id)) = $true) | ? [X586 : term] : (($true != ((X581 @ id @ (X582 @ id @ X586) @ id))) & ($true = ((X581 @ id @ X586 @ id))))) & ! [X587 : term] : (($true != ((X579 @ X587))) | (((X579 @ (sub @ X580 @ (push @ X587 @ id)))) = $true)) & ! [X588 : term] : (((X581 @ id @ X588 @ id)) = ((X579 @ X588)))) | ? [X589 : (subst > term > subst > $o)] : ! [X590 : (term > $o)] : ? [X591 : term] : (((X590 @ X591)) != ((X589 @ id @ X591 @ id))) | ($true = sP3) | (sP2 = $true) | (hoasinduction_lthm_3 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X592 : term] : ? [X593 : d_term] : (((d2term @ X593)) = X592) & ((hoasinduction_lem3v2_f = $true) | ? [X594 : term] : ! [X595 : (subst > term > term)] : ? [X596 : term,X597 : subst] : (((X595 @ X597 @ X596)) != ((sub @ X594 @ (push @ X596 @ X597))))) & (! [X598 : term] : ? [X599 : (subst > term > term)] : ! [X600 : term,X601 : subst] : (((X599 @ X601 @ X600)) = ((sub @ X598 @ (push @ X600 @ X601)))) | (hoasinduction_lem3v2_f != $true)) & ((! [X602 : subst] : (((comp @ id @ X602)) = X602) & ! [X603 : subst] : (((comp @ X603 @ id)) = X603)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X604 : subst] : (((comp @ id @ X604)) != X604) | ? [X605 : subst] : (((comp @ X605 @ id)) != X605)) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X606 : (term > $o),X607 : term] : (($true = ((X606 @ X607))) | ? [X608 : term] : ((((X606 @ X608)) != $true) & (((var @ X608)) = $true)) | ? [X609 : term] : ((((X606 @ X609)) = $true) & ($true != ((X606 @ (lam @ X609))))) | ? [X610 : term,X611 : term] : (($true = ((X606 @ X610))) & (((X606 @ (ap @ X611 @ X610))) != $true) & (((X606 @ X611)) = $true))) | (induction != $true)) & ((induction = $true) | ? [X612 : (term > $o),X613 : term] : (($true != ((X612 @ X613))) & ! [X614 : term] : (($true = ((X612 @ X614))) | (((var @ X614)) != $true)) & ! [X615 : term] : ((((X612 @ X615)) != $true) | (((X612 @ (lam @ X615))) = $true)) & ! [X616 : term,X617 : term] : (($true != ((X612 @ X616))) | ($true = ((X612 @ (ap @ X617 @ X616)))) | ($true != ((X612 @ X617)))))) & ((pushprop_lem1_lthm = $true) | (! [X618 : term,X619 : subst] : (((sub @ one @ (push @ X618 @ X619))) = X618) & ! [X620 : subst,X621 : term] : (((comp @ sh @ (push @ X621 @ X620))) = X620) & ? [X622 : (term > $o),X623 : (term > $o),X624 : subst,X625 : term,X626 : term] : ((((X622 @ (sub @ X626 @ (push @ X625 @ X624)))) != $true) & (((X623 @ X626)) = $true)))) & (? [X627 : term,X628 : subst] : (((sub @ one @ (push @ X627 @ X628))) != X627) | ? [X629 : subst,X630 : term] : (((comp @ sh @ (push @ X630 @ X629))) != X629) | ! [X631 : (term > $o),X632 : (term > $o),X633 : subst,X634 : term,X635 : term] : (($true = ((X631 @ (sub @ X635 @ (push @ X634 @ X633))))) | ($true != ((X632 @ X635)))) | (pushprop_lem1_lthm != $true)) & (! [X636 : term,X637 : term,X638 : term,X639 : term] : ((X638 = X639) | (((ap @ (sub @ X639 @ id) @ X636)) != ((ap @ (sub @ X638 @ id) @ X637)))) | ? [X640 : term] : (((sub @ X640 @ id)) != X640) | ? [X641 : term,X642 : term,X643 : term,X644 : term] : ((((ap @ X642 @ X641)) = ((ap @ X644 @ X643))) & (X642 != X644)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X645 : term,X646 : term,X647 : term,X648 : term] : ((X647 != X648) & (((ap @ (sub @ X648 @ id) @ X645)) = ((ap @ (sub @ X647 @ id) @ X646)))) & ! [X649 : term] : (((sub @ X649 @ id)) = X649) & ! [X650 : term,X651 : term,X652 : term,X653 : term] : ((((ap @ X653 @ X652)) != ((ap @ X651 @ X650))) | (X651 = X653)))) & (hoasinduction_lem2_lthm = $true)), 26.09/4.24 inference(rectify,[],[f134])). 26.09/4.24 thf(f136,plain,( 26.09/4.24 (hoasinduction_lem3b_gthm = $true) & ((axvarcons = $true) | (sK244 != ((sub @ one @ (push @ sK244 @ sK245))))) & (! [X2 : term,X3 : subst] : (((sub @ one @ (push @ X2 @ X3))) = X2) | (axvarcons != $true)) & (hoasapnotvar_lthm = $true) & ((hoaslaminj = $true) | (! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (sK249 @ X10 @ X9) @ X8)) = ((sK249 @ (comp @ X10 @ X8) @ (sub @ X9 @ X8)))) & (((sK249 @ sK247 @ sK246)) != ((sK248 @ sK247 @ sK246))) & (((lam @ (sK248 @ sh @ one))) = ((lam @ (sK249 @ sh @ one)))) & ! [X11 : subst,X12 : term,X13 : subst] : (((sK248 @ (comp @ X13 @ X11) @ (sub @ X12 @ X11))) = ((sub @ (sK248 @ X13 @ X12) @ X11))))) & (! [X14 : term,X15 : subst,X16 : (subst > term > term),X17 : (subst > term > term)] : ((((X17 @ (comp @ (sK252 @ X17) @ (sK250 @ X17)) @ (sub @ (sK251 @ X17) @ (sK250 @ X17)))) != ((sub @ (X17 @ (sK252 @ X17) @ (sK251 @ X17)) @ (sK250 @ X17)))) | (((X16 @ X15 @ X14)) = ((X17 @ X15 @ X14))) | (((lam @ (X16 @ sh @ one))) != ((lam @ (X17 @ sh @ one)))) | (((X16 @ (comp @ (sK255 @ X16) @ (sK253 @ X16)) @ (sub @ (sK254 @ X16) @ (sK253 @ X16)))) != ((sub @ (X16 @ (sK255 @ X16) @ (sK254 @ X16)) @ (sK253 @ X16))))) | (hoaslaminj != $true)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction_lem2v2 != $true)) & (! [X24 : subst] : (((comp @ id @ X24)) = X24) | (axidl != $true)) & ((axidl = $true) | (sK256 != ((comp @ id @ sK256)))) & (hoaslamnotvar_lthm = $true) & ! [X26 : subst] : (((d2subst @ (sK257 @ X26))) = X26) & (! [X28 : term,X29 : term] : ((X28 = X29) | (((sub @ X29 @ sh)) != ((sub @ X28 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ((sK258 != sK259) & (((sub @ sK259 @ sh)) = ((sub @ sK258 @ sh))))) & (! [X32 : (subst > term > subst > $o)] : ! [X34 : term] : (((sK260 @ X32 @ X34)) = ((X32 @ id @ X34 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X36 : (term > $o)] : (((X36 @ (sK262 @ X36))) != ((sK261 @ id @ (sK262 @ X36) @ id)))) & (axclos = $true) & (substmonoid_gthm = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((sP26 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP26 != $true)) & (lamnotvar = $true) & (axabs = $true) & ! [X38 : d_term,X39 : d_term] : ((X38 = X39) | (((d2term @ X39)) != ((d2term @ X38)))) & (! [X40 : term,X41 : subst] : (((comp @ sh @ (push @ X40 @ X41))) = X41) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK264 != ((comp @ sh @ (push @ sK263 @ sK264))))) & ((hoaslamnotap = $true) | ((((ap @ (sub @ sK267 @ id) @ sK265)) = ((lam @ (sK266 @ sh @ one)))) & ! [X47 : term,X48 : subst,X49 : subst] : (((sub @ (sK266 @ X48 @ X47) @ X49)) = ((sK266 @ (comp @ X48 @ X49) @ (sub @ X47 @ X49)))))) & (! [X50 : term,X51 : (subst > term > term),X52 : term] : ((((lam @ (X51 @ sh @ one))) != ((ap @ (sub @ X52 @ id) @ X50))) | (((X51 @ (comp @ (sK269 @ X51) @ (sK270 @ X51)) @ (sub @ (sK268 @ X51) @ (sK270 @ X51)))) != ((sub @ (X51 @ (sK269 @ X51) @ (sK268 @ X51)) @ (sK270 @ X51))))) | (hoaslamnotap != $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (axvarshift = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (hoasinduction_gthm = $true) & (! [X56 : term] : ! [X58 : term,X59 : subst] : (((sK271 @ X56 @ X59 @ X58)) = ((sub @ X56 @ (push @ X58 @ X59)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X61 : (subst > term > term)] : (((sub @ sK272 @ (push @ (sK273 @ X61) @ (sK274 @ X61)))) != ((X61 @ (sK274 @ X61) @ (sK273 @ X61))))) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X64 : (subst > term > subst > $o)] : ! [X66 : term] : (((X64 @ id @ X66 @ id)) = ((sK275 @ X64 @ X66))) & ! [X67 : (subst > term > subst > $o),X68 : term,X69 : (term > $o)] : ((((X69 @ (lam @ X68))) = $true) | (! [X71 : term] : ((((X67 @ id @ (sK276 @ X67 @ id @ X71) @ id)) = $true) | (((X67 @ id @ X71 @ id)) != $true)) & (((X67 @ id @ (lam @ (sK276 @ X67 @ sh @ one)) @ id)) != $true) & ! [X72 : subst,X73 : term,X74 : subst] : (((sK276 @ X67 @ (comp @ X74 @ X72) @ (sub @ X73 @ X72))) = ((sub @ (sK276 @ X67 @ X74 @ X73) @ X72)))) | ((((X69 @ (sK277 @ X69 @ X68))) = $true) & ($true != ((X69 @ (sub @ X68 @ (push @ (sK277 @ X69 @ X68) @ id)))))) | (((X69 @ (sK278 @ X69 @ X67))) != ((X67 @ id @ (sK278 @ X69 @ X67) @ id)))) & ! [X77 : term] : (((sub @ X77 @ id)) = X77) & (sP25 != $true) & ($true != sP24))) & (! [X79 : (term > $o)] : (((X79 @ (sK280 @ X79))) != ((sK279 @ id @ (sK280 @ X79) @ id))) | (($true != ((sK283 @ (lam @ sK282)))) & ! [X84 : (subst > term > term)] : (((((sK281 @ id @ (X84 @ id @ (sK284 @ X84)) @ id)) != $true) & (((sK281 @ id @ (sK284 @ X84) @ id)) = $true)) | (((sK281 @ id @ (lam @ (X84 @ sh @ one)) @ id)) = $true) | (((sub @ (X84 @ (sK287 @ X84) @ (sK286 @ X84)) @ (sK285 @ X84))) != ((X84 @ (comp @ (sK287 @ X84) @ (sK285 @ X84)) @ (sub @ (sK286 @ X84) @ (sK285 @ X84)))))) & ! [X89 : term] : (($true != ((sK283 @ X89))) | ($true = ((sK283 @ (sub @ sK282 @ (push @ X89 @ id)))))) & ! [X90 : term] : (((sK281 @ id @ X90 @ id)) = ((sK283 @ X90)))) | (sK288 != ((sub @ sK288 @ id))) | (sP25 = $true) | ($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X94 : term,X95 : term] : ((((sK289 @ id @ (ap @ (sub @ X94 @ id) @ X95) @ id)) = $true) | (((sK289 @ id @ X94 @ id)) != $true) | ($true != ((sK289 @ id @ X95 @ id)))) & ! [X96 : (subst > term > term)] : ((((sub @ (X96 @ (sK293 @ X96) @ (sK291 @ X96)) @ (sK292 @ X96))) != ((X96 @ (comp @ (sK293 @ X96) @ (sK292 @ X96)) @ (sub @ (sK291 @ X96) @ (sK292 @ X96))))) | ((((sK289 @ id @ (X96 @ id @ (sK294 @ X96)) @ id)) != $true) & (((sK289 @ id @ (sK294 @ X96) @ id)) = $true)) | ($true = ((sK289 @ id @ (lam @ (X96 @ sh @ one)) @ id)))) & ($true != ((sK289 @ id @ sK290 @ id))))) & (! [X101 : (subst > term > subst > $o),X102 : term] : ((($true != ((X101 @ id @ (ap @ (sub @ (sK295 @ X101) @ id) @ (sK296 @ X101)) @ id))) & (((X101 @ id @ (sK295 @ X101) @ id)) = $true) & (((X101 @ id @ (sK296 @ X101) @ id)) = $true)) | (! [X106 : term,X107 : subst,X108 : subst] : (((sub @ (sK297 @ X101 @ X108 @ X106) @ X107)) = ((sK297 @ X101 @ (comp @ X108 @ X107) @ (sub @ X106 @ X107)))) & ! [X109 : term] : ((((X101 @ id @ (sK297 @ X101 @ id @ X109) @ id)) = $true) | ($true != ((X101 @ id @ X109 @ id)))) & (((X101 @ id @ (lam @ (sK297 @ X101 @ sh @ one)) @ id)) != $true)) | (((X101 @ id @ X102 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ! [X110 : d_subst,X111 : d_subst] : ((((d2subst @ X111)) != ((d2subst @ X110))) | (X110 = X111)) & ((pushprop_lem1v2 = $true) | (! [X116 : term] : (((sK301 @ (sub @ X116 @ (push @ sK298 @ sK299)))) = ((sK300 @ X116))) & (((sK301 @ sK298)) = $true) & (((sK300 @ one)) != $true))) & (! [X117 : term,X118 : subst,X119 : (term > $o),X120 : (term > $o)] : ((((X119 @ (sK302 @ X120 @ X119 @ X118 @ X117))) != ((X120 @ (sub @ (sK302 @ X120 @ X119 @ X118 @ X117) @ (push @ X117 @ X118))))) | (((X120 @ X117)) != $true) | ($true = ((X119 @ one)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ((! [X125 : term] : ((((sK304 @ (sub @ sK305 @ (push @ X125 @ id)))) = $true) | ($true != ((sK304 @ X125)))) & (((sK304 @ (lam @ sK305))) != $true) & ! [X126 : term] : (((sK303 @ id @ X126 @ id)) = ((sK304 @ X126))) & ! [X127 : (subst > term > term)] : ((((sK303 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | (((sub @ (X127 @ (sK306 @ X127) @ (sK307 @ X127)) @ (sK308 @ X127))) != ((X127 @ (comp @ (sK306 @ X127) @ (sK308 @ X127)) @ (sub @ (sK307 @ X127) @ (sK308 @ X127))))) | (($true = ((sK303 @ id @ (sK309 @ X127) @ id))) & ($true != ((sK303 @ id @ (X127 @ id @ (sK309 @ X127)) @ id)))))) & ! [X132 : term] : ! [X134 : term,X135 : subst] : (((sK310 @ X132 @ X135 @ X134)) = ((sub @ X132 @ (push @ X134 @ X135)))) & ! [X136 : term] : (((sub @ X136 @ id)) = X136))) & (! [X137 : (subst > term > subst > $o),X138 : (term > $o),X139 : term] : ((($true != ((X138 @ (sub @ X139 @ (push @ (sK311 @ X139 @ X138) @ id))))) & ($true = ((X138 @ (sK311 @ X139 @ X138))))) | ($true = ((X138 @ (lam @ X139)))) | (((X138 @ (sK312 @ X138 @ X137))) != ((X137 @ id @ (sK312 @ X138 @ X137) @ id))) | ((((X137 @ id @ (lam @ (sK313 @ X137 @ sh @ one)) @ id)) != $true) & ! [X143 : subst,X144 : term,X145 : subst] : (((sub @ (sK313 @ X137 @ X143 @ X144) @ X145)) = ((sK313 @ X137 @ (comp @ X143 @ X145) @ (sub @ X144 @ X145)))) & ! [X146 : term] : ((((X137 @ id @ X146 @ id)) != $true) | ($true = ((X137 @ id @ (sK313 @ X137 @ id @ X146) @ id)))))) | ! [X148 : (subst > term > term)] : (((X148 @ (sK316 @ X148) @ (sK315 @ X148))) != ((sub @ sK314 @ (push @ (sK315 @ X148) @ (sK316 @ X148))))) | (((sub @ sK317 @ id)) != sK317) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (! [X152 : term] : (((sub @ X152 @ id)) = X152) | (sK318 != ((sub @ sK318 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK319 @ id)) != sK319) & ! [X155 : term] : (((sub @ X155 @ id)) = X155))) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP23) & ! [X156 : (subst > term > subst > $o),X157 : term] : ((! [X159 : term,X160 : subst,X161 : subst] : (((sK320 @ X156 @ (comp @ X161 @ X160) @ (sub @ X159 @ X160))) = ((sub @ (sK320 @ X156 @ X161 @ X159) @ X160))) & ! [X162 : term] : (($true = ((X156 @ id @ (sK320 @ X156 @ id @ X162) @ id))) | ($true != ((X156 @ id @ X162 @ id)))) & ($true != ((X156 @ id @ (lam @ (sK320 @ X156 @ sh @ one)) @ id)))) | (($true = ((X156 @ id @ (sK321 @ X157 @ X156) @ id))) & (((X156 @ id @ (sub @ X157 @ (push @ (sK321 @ X157 @ X156) @ id)) @ id)) != $true)) | ($true = ((X156 @ id @ (lam @ (sub @ X157 @ (push @ one @ sh))) @ id)))) & ! [X164 : term] : (((sub @ X164 @ id)) = X164))) & (($true = sP23) | (! [X167 : (subst > term > term)] : ((((sub @ (X167 @ (sK326 @ X167) @ (sK324 @ X167)) @ (sK325 @ X167))) != ((X167 @ (comp @ (sK326 @ X167) @ (sK325 @ X167)) @ (sub @ (sK324 @ X167) @ (sK325 @ X167))))) | (($true != ((sK322 @ id @ (X167 @ id @ (sK327 @ X167)) @ id))) & (((sK322 @ id @ (sK327 @ X167) @ id)) = $true)) | ($true = ((sK322 @ id @ (lam @ (X167 @ sh @ one)) @ id)))) & ! [X172 : term] : (($true != ((sK322 @ id @ X172 @ id))) | (((sK322 @ id @ (sub @ sK323 @ (push @ X172 @ id)) @ id)) = $true)) & (((sK322 @ id @ (lam @ (sub @ sK323 @ (push @ one @ sh))) @ id)) != $true)) | (((sub @ sK328 @ id)) != sK328) | (hoasinduction_lem3a_lthm != $true)) & (! [X174 : term] : (((sub @ X174 @ id)) = X174) | (termmset != $true)) & ((termmset = $true) | (sK329 != ((sub @ sK329 @ id)))) & ((pushprop_lem1v2_lthm = $true) | (! [X176 : subst,X177 : term] : (((sub @ one @ (push @ X177 @ X176))) = X177) & ((((sK331 @ sK330)) = $true) & ! [X182 : term] : (((sK333 @ X182)) = ((sK331 @ (sub @ X182 @ (push @ sK330 @ sK332))))) & (((sK333 @ one)) != $true)))) & ((((sub @ one @ (push @ sK335 @ sK334))) != sK335) | ! [X185 : term,X186 : (term > $o),X187 : subst,X188 : (term > $o)] : ((((X186 @ X185)) != $true) | (((X188 @ (sK336 @ X188 @ X187 @ X186 @ X185))) != ((X186 @ (sub @ (sK336 @ X188 @ X187 @ X186 @ X185) @ (push @ X185 @ X187))))) | (((X188 @ one)) = $true)) | (pushprop_lem1v2_lthm != $true)) & (($true = sP22) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP22)) & ((hoasinduction_lem3b = $true) | ! [X191 : (subst > term > term)] : (((sub @ sK337 @ (push @ one @ sh))) != ((X191 @ sh @ one)))) & (! [X192 : term] : (((sK338 @ X192 @ sh @ one)) = ((sub @ X192 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) | (axidr != $true)) & ((axidr = $true) | (sK339 != ((comp @ sK339 @ id)))) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem0 = $true) | ! [X197 : (term > $o)] : (((sK340 @ id @ (sK341 @ X197) @ id)) != ((X197 @ (sK341 @ X197))))) & (! [X199 : (subst > term > subst > $o)] : ! [X201 : term] : (((X199 @ id @ X201 @ id)) = ((sK342 @ X199 @ X201))) | (hoasinduction_lem0 != $true)) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2 != $true)) & (pushprop_gthm = $true) & (one = ((d2term @ d_one))) & (! [X202 : term,X203 : term,X204 : (term > $o),X205 : (term > $o),X206 : subst] : (($true = ((X205 @ (sub @ X203 @ (push @ X202 @ X206))))) | (((X204 @ X203)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK346 @ (sub @ sK344 @ (push @ sK343 @ sK347)))) != $true) & ($true = ((sK345 @ sK344))))) & (induction2_gthm = $true) & (axmap = $true) & ! [X212 : d_term] : (d_one = X212) & ((hoasapinj1 = $true) | ((sK348 != sK349) & (((ap @ (sub @ sK349 @ id) @ sK350)) = ((ap @ (sub @ sK348 @ id) @ sK351))))) & (! [X217 : term,X218 : term,X219 : term,X220 : term] : ((X217 = X218) | (((ap @ (sub @ X217 @ id) @ X220)) != ((ap @ (sub @ X218 @ id) @ X219)))) | (hoasapinj1 != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK352 @ id) @ sK354)) = ((ap @ (sub @ sK355 @ id) @ sK353))) & (sK354 != sK353))) & (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((((ap @ (sub @ X225 @ id) @ X227)) != ((ap @ (sub @ X228 @ id) @ X226))) | (X226 = X227)) | (hoasapinj2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X229 : term] : (((sub @ X229 @ id)) = X229) & ($true != sP20) & ! [X230 : (subst > term > subst > $o),X231 : term] : ((! [X233 : subst,X234 : term,X235 : subst] : (((sK356 @ X230 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235))) = ((sub @ (sK356 @ X230 @ X233 @ X234) @ X235))) & ($true != ((X230 @ id @ (lam @ (sK356 @ X230 @ sh @ one)) @ id))) & ! [X236 : term] : (($true != ((X230 @ id @ X236 @ id))) | ($true = ((X230 @ id @ (sK356 @ X230 @ id @ X236) @ id))))) | (($true = ((X230 @ id @ (sK357 @ X231 @ X230) @ id))) & (((X230 @ id @ (sub @ X231 @ (push @ (sK357 @ X231 @ X230) @ id)) @ id)) != $true)) | (((X230 @ id @ (lam @ (sub @ X231 @ (push @ one @ sh))) @ id)) = $true)))) & ((sK358 != ((sub @ sK358 @ id))) | ($true = sP20) | (! [X241 : (subst > term > term)] : ((((sub @ (X241 @ (sK361 @ X241) @ (sK362 @ X241)) @ (sK363 @ X241))) != ((X241 @ (comp @ (sK361 @ X241) @ (sK363 @ X241)) @ (sub @ (sK362 @ X241) @ (sK363 @ X241))))) | (((sK359 @ id @ (lam @ (X241 @ sh @ one)) @ id)) = $true) | (($true = ((sK359 @ id @ (sK364 @ X241) @ id))) & ($true != ((sK359 @ id @ (X241 @ id @ (sK364 @ X241)) @ id))))) & ! [X246 : term] : (($true != ((sK359 @ id @ X246 @ id))) | (((sK359 @ id @ (sub @ sK360 @ (push @ X246 @ id)) @ id)) = $true)) & ($true != ((sK359 @ id @ (lam @ (sub @ sK360 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((induction2_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (induction2_lthm != $true)) & (! [X247 : term] : (((sK365 @ X247 @ sh @ one)) = ((sub @ X247 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X250 : (subst > term > term)] : (((sub @ sK366 @ (push @ one @ sh))) != ((X250 @ sh @ one)))) & (! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X253 = X254) | (((ap @ (sub @ X251 @ id) @ X254)) != ((ap @ (sub @ X252 @ id) @ X253)))) | ((((ap @ sK370 @ sK367)) = ((ap @ sK369 @ sK368))) & (sK368 != sK367)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((sK373 != sK374) & (((ap @ (sub @ sK371 @ id) @ sK374)) = ((ap @ (sub @ sK372 @ id) @ sK373)))) & ! [X263 : term,X264 : term,X265 : term,X266 : term] : ((((ap @ X265 @ X264)) != ((ap @ X266 @ X263))) | (X263 = X264)))) & ((hoasinduction_lem3a = $true) | ((((sK375 @ id @ (lam @ sK376) @ id)) != $true) & ! [X269 : term] : (($true != ((sK375 @ id @ X269 @ id))) | (((sK375 @ id @ (sub @ sK376 @ (push @ X269 @ id)) @ id)) = $true)) & ! [X270 : (subst > term > term)] : (((((sK375 @ id @ (X270 @ id @ (sK377 @ X270)) @ id)) != $true) & ($true = ((sK375 @ id @ (sK377 @ X270) @ id)))) | (((sK375 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true) | (((sub @ (X270 @ (sK379 @ X270) @ (sK378 @ X270)) @ (sK380 @ X270))) != ((X270 @ (comp @ (sK379 @ X270) @ (sK380 @ X270)) @ (sub @ (sK378 @ X270) @ (sK380 @ X270)))))))) & (! [X275 : (subst > term > subst > $o),X276 : term] : (($true = ((X275 @ id @ (lam @ X276) @ id))) | (($true = ((X275 @ id @ (sK381 @ X276 @ X275) @ id))) & ($true != ((X275 @ id @ (sub @ X276 @ (push @ (sK381 @ X276 @ X275) @ id)) @ id)))) | (! [X279 : term] : ((((X275 @ id @ (sK382 @ X275 @ id @ X279) @ id)) = $true) | ($true != ((X275 @ id @ X279 @ id)))) & ($true != ((X275 @ id @ (lam @ (sK382 @ X275 @ sh @ one)) @ id))) & ! [X280 : term,X281 : subst,X282 : subst] : (((sK382 @ X275 @ (comp @ X281 @ X282) @ (sub @ X280 @ X282))) = ((sub @ (sK382 @ X275 @ X281 @ X280) @ X282))))) | (hoasinduction_lem3a != $true)) & (pushprop = $true) & (pushprop_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((substmonoid_lthm = $true) | (! [X283 : subst] : (((comp @ X283 @ id)) = X283) & ((((comp @ id @ sK383)) != sK383) | (((comp @ sK384 @ id)) != sK384)) & ! [X286 : subst] : (((comp @ id @ X286)) = X286))) & ((sK385 != ((comp @ sK385 @ id))) | (! [X288 : subst] : (((comp @ id @ X288)) = X288) & ! [X289 : subst] : (((comp @ X289 @ id)) = X289)) | (((comp @ id @ sK386)) != sK386) | (substmonoid_lthm != $true)) & ((apinj1 = $true) | ((((ap @ sK390 @ sK388)) = ((ap @ sK387 @ sK389))) & (sK387 != sK390))) & (! [X295 : term,X296 : term,X297 : term,X298 : term] : ((((ap @ X298 @ X296)) != ((ap @ X295 @ X297))) | (X295 = X298)) | (apinj1 != $true)) & (ulamvarind = $true) & (pushprop_lthm_orig = $true) & (! [X299 : (subst > term > subst > $o),X300 : term] : (((((X299 @ id @ (sub @ X300 @ (push @ (sK391 @ X300 @ X299) @ id)) @ id)) != $true) & ($true = ((X299 @ id @ (sK391 @ X300 @ X299) @ id)))) | (((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id)) = $true) | (! [X303 : term] : (($true != ((X299 @ id @ X303 @ id))) | ($true = ((X299 @ id @ (sK392 @ X299 @ id @ X303) @ id)))) & ($true != ((X299 @ id @ (lam @ (sK392 @ X299 @ sh @ one)) @ id))) & ! [X304 : subst,X305 : term,X306 : subst] : (((sK392 @ X299 @ (comp @ X306 @ X304) @ (sub @ X305 @ X304))) = ((sub @ (sK392 @ X299 @ X306 @ X305) @ X304))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (! [X309 : term] : (($true = ((sK393 @ id @ (sub @ sK394 @ (push @ X309 @ id)) @ id))) | (((sK393 @ id @ X309 @ id)) != $true)) & (((sK393 @ id @ (lam @ (sub @ sK394 @ (push @ one @ sh))) @ id)) != $true) & ! [X310 : (subst > term > term)] : ((($true = ((sK393 @ id @ (sK395 @ X310) @ id))) & ($true != ((sK393 @ id @ (X310 @ id @ (sK395 @ X310)) @ id)))) | (((sK393 @ id @ (lam @ (X310 @ sh @ one)) @ id)) = $true) | (((sub @ (X310 @ (sK398 @ X310) @ (sK397 @ X310)) @ (sK396 @ X310))) != ((X310 @ (comp @ (sK398 @ X310) @ (sK396 @ X310)) @ (sub @ (sK397 @ X310) @ (sK396 @ X310)))))))) & ((hoasinduction_lem3aaa = $true) | (! [X317 : term,X318 : (subst > term > term)] : ((((sub @ (X318 @ (sK401 @ X318 @ X317) @ (sK403 @ X318 @ X317)) @ (sK402 @ X318 @ X317))) != ((sub @ (sub @ X317 @ (push @ (sK403 @ X318 @ X317) @ (sK401 @ X318 @ X317))) @ (sK402 @ X318 @ X317)))) | (((X318 @ (comp @ (sK406 @ X318 @ X317) @ (sK405 @ X318 @ X317)) @ (sub @ (sK404 @ X318 @ X317) @ (sK405 @ X318 @ X317)))) != ((sub @ X317 @ (push @ (sub @ (sK404 @ X318 @ X317) @ (sK405 @ X318 @ X317)) @ (comp @ (sK406 @ X318 @ X317) @ (sK405 @ X318 @ X317)))))) | (($true = ((sK399 @ id @ (sK407 @ X318) @ id))) & (((sK399 @ id @ (X318 @ id @ (sK407 @ X318)) @ id)) != $true)) | ($true = ((sK399 @ id @ (lam @ (X318 @ sh @ one)) @ id)))) & (((sK399 @ id @ (lam @ (sub @ sK400 @ (push @ one @ sh))) @ id)) != $true) & ! [X326 : term] : ((((sK399 @ id @ (sub @ sK400 @ (push @ X326 @ id)) @ id)) = $true) | ($true != ((sK399 @ id @ X326 @ id)))))) & (! [X327 : (subst > term > subst > $o),X328 : term] : ((! [X331 : subst,X332 : subst,X333 : term] : (((sub @ (sub @ (sK408 @ X327) @ (push @ X333 @ X331)) @ X332)) = ((sub @ (sK409 @ X327 @ X331 @ X333) @ X332))) & ! [X334 : term,X335 : subst,X336 : subst] : (((sK409 @ X327 @ (comp @ X336 @ X335) @ (sub @ X334 @ X335))) = ((sub @ (sK408 @ X327) @ (push @ (sub @ X334 @ X335) @ (comp @ X336 @ X335))))) & ! [X337 : term] : ((((X327 @ id @ X337 @ id)) != $true) | ($true = ((X327 @ id @ (sK409 @ X327 @ id @ X337) @ id)))) & ($true != ((X327 @ id @ (lam @ (sK409 @ X327 @ sh @ one)) @ id)))) | (((X327 @ id @ (lam @ (sub @ X328 @ (push @ one @ sh))) @ id)) = $true) | ((((X327 @ id @ (sub @ X328 @ (push @ (sK410 @ X328 @ X327) @ id)) @ id)) != $true) & ($true = ((X327 @ id @ (sK410 @ X328 @ X327) @ id))))) | (hoasinduction_lem3aaa != $true)) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) | ((! [X343 : subst,X344 : term,X345 : subst] : (((sub @ (sK414 @ X343 @ X344) @ X345)) = ((sK414 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345)))) & (((sK414 @ sK412 @ sK411)) != ((sK413 @ sK412 @ sK411))) & ! [X346 : term,X347 : subst,X348 : subst] : (((sK413 @ (comp @ X347 @ X348) @ (sub @ X346 @ X348))) = ((sub @ (sK413 @ X347 @ X346) @ X348))) & (((lam @ (sK413 @ sh @ one))) = ((lam @ (sK414 @ sh @ one))))) & ! [X349 : term,X350 : term] : ((((lam @ X350)) != ((lam @ X349))) | (X349 = X350)) & ! [X351 : subst,X352 : term] : (((sub @ one @ (push @ X352 @ X351))) = X352) & ! [X353 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X353))) = X353))) & (! [X355 : term,X356 : subst,X357 : (subst > term > term),X358 : (subst > term > term)] : ((((sub @ (X358 @ (sK415 @ X358) @ (sK416 @ X358)) @ (sK417 @ X358))) != ((X358 @ (comp @ (sK415 @ X358) @ (sK417 @ X358)) @ (sub @ (sK416 @ X358) @ (sK417 @ X358))))) | (((X357 @ X356 @ X355)) = ((X358 @ X356 @ X355))) | (((X357 @ (comp @ (sK419 @ X357) @ (sK420 @ X357)) @ (sub @ (sK418 @ X357) @ (sK420 @ X357)))) != ((sub @ (X357 @ (sK419 @ X357) @ (sK418 @ X357)) @ (sK420 @ X357)))) | (((lam @ (X357 @ sh @ one))) != ((lam @ (X358 @ sh @ one))))) | ((((lam @ sK422)) = ((lam @ sK421))) & (sK421 != sK422)) | (sK424 != ((sub @ one @ (push @ sK424 @ sK423)))) | (sK425 != ((comp @ sh @ (push @ sK426 @ sK425)))) | (hoaslaminj_lthm != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X371 : term,X372 : (subst > term > subst > $o)] : ((($true != ((X372 @ id @ (sub @ X371 @ (push @ (sK427 @ X372 @ X371) @ id)) @ id))) & (((X372 @ id @ (sK427 @ X372 @ X371) @ id)) = $true)) | (((sP16 @ X372)) = $true) | (($true = ((X372 @ (comp @ (sK428 @ X372) @ (sK430 @ X372)) @ (sub @ (sK429 @ X372) @ (sK430 @ X372)) @ (sK431 @ X372)))) & (((X372 @ (sK428 @ X372) @ (sK429 @ X372) @ (comp @ (sK430 @ X372) @ (sK431 @ X372)))) != $true)) | (((X372 @ id @ (lam @ X371) @ id)) = $true) | (($true = ((X372 @ (sK433 @ X372) @ (sK432 @ X372) @ (comp @ (sK434 @ X372) @ (sK435 @ X372))))) & (((X372 @ (comp @ (sK433 @ X372) @ (sK434 @ X372)) @ (sub @ (sK432 @ X372) @ (sK434 @ X372)) @ (sK435 @ X372))) != $true))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (! [X384 : term] : (($true = ((sK437 @ id @ (sub @ sK436 @ (push @ X384 @ id)) @ id))) | ($true != ((sK437 @ id @ X384 @ id)))) & (((sP16 @ sK437)) != $true) & ! [X385 : subst,X386 : term,X387 : subst,X388 : subst] : (($true != ((sK437 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X388))) | (((sK437 @ X385 @ X386 @ (comp @ X387 @ X388))) = $true)) & (((sK437 @ id @ (lam @ sK436) @ id)) != $true) & ! [X389 : term,X390 : subst,X391 : subst,X392 : subst] : ((((sK437 @ X390 @ X389 @ (comp @ X391 @ X392))) != $true) | ($true = ((sK437 @ (comp @ X390 @ X391) @ (sub @ X389 @ X391) @ X392)))))) & (pushprop_lem1_gthm = $true) & (($true = sP15) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP15)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = id) & ((axvarid = $true) | (sK438 != ((sub @ sK438 @ id)))) & (! [X394 : term] : (((sub @ X394 @ id)) = X394) | (axvarid != $true)) & (! [X395 : subst,X396 : (term > $o),X397 : term] : ! [X399 : term] : (((X396 @ (sub @ X399 @ (push @ X397 @ X395)))) = ((sK439 @ X397 @ X396 @ X395 @ X399))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X403 : (term > $o)] : (((sK441 @ (sub @ (sK443 @ X403) @ (push @ sK442 @ sK440)))) != ((X403 @ (sK443 @ X403))))) & (! [X405 : (subst > term > subst > $o),X406 : term] : (((((X405 @ (sK446 @ X405) @ (sK445 @ X405) @ (comp @ (sK447 @ X405) @ (sK444 @ X405)))) != $true) & (((X405 @ (comp @ (sK446 @ X405) @ (sK447 @ X405)) @ (sub @ (sK445 @ X405) @ (sK447 @ X405)) @ (sK444 @ X405))) = $true)) | ($true = ((sP13 @ X405))) | ($true = ((sP12 @ X405))) | (($true != ((X405 @ (comp @ (sK448 @ X405) @ (sK451 @ X405)) @ (sub @ (sK450 @ X405) @ (sK451 @ X405)) @ (sK449 @ X405)))) & (((X405 @ (sK448 @ X405) @ (sK450 @ X405) @ (comp @ (sK451 @ X405) @ (sK449 @ X405)))) = $true)) | ($true = ((X405 @ id @ X406 @ id))) | ((((var @ (sub @ (sK452 @ X405) @ id))) = $true) & ($true != ((X405 @ id @ (sK452 @ X405) @ id))))) | (hoasinduction != $true)) & ((hoasinduction = $true) | (! [X418 : subst,X419 : term,X420 : subst,X421 : subst] : ((((sK453 @ X420 @ X419 @ (comp @ X421 @ X418))) = $true) | (((sK453 @ (comp @ X420 @ X421) @ (sub @ X419 @ X421) @ X418)) != $true)) & ($true != ((sP13 @ sK453))) & (((sP12 @ sK453)) != $true) & ! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : ((((sK453 @ (comp @ X422 @ X425) @ (sub @ X424 @ X425) @ X423)) = $true) | (((sK453 @ X422 @ X424 @ (comp @ X425 @ X423))) != $true)) & ($true != ((sK453 @ id @ sK454 @ id))) & ! [X426 : term] : (($true != ((var @ (sub @ X426 @ id)))) | (((sK453 @ id @ X426 @ id)) = $true)))) & (hoasapinj2_gthm = $true) & (! [X427 : subst] : (((push @ (sub @ one @ X427) @ (comp @ sh @ X427))) = X427) | (axscons != $true)) & ((axscons = $true) | (sK455 != ((push @ (sub @ one @ sK455) @ (comp @ sh @ sK455))))) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & ((laminj = $true) | ((((lam @ sK457)) = ((lam @ sK456))) & (sK456 != sK457))) & (! [X431 : term,X432 : term] : ((((lam @ X432)) != ((lam @ X431))) | (X431 = X432)) | (laminj != $true)) & (lamnotap != $true) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2 = $true) | (! [X436 : subst,X437 : subst,X438 : subst,X439 : term] : ((((sK460 @ (comp @ X438 @ X436) @ (sub @ X439 @ X436) @ X437)) = $true) | (((sK460 @ X438 @ X439 @ (comp @ X436 @ X437))) != $true)) & ! [X440 : term,X441 : subst,X442 : subst,X443 : subst] : ((((sK460 @ X441 @ X440 @ (comp @ X443 @ X442))) = $true) | ($true != ((sK460 @ (comp @ X441 @ X443) @ (sub @ X440 @ X443) @ X442)))) & (((sP11 @ sK460)) != $true) & ! [X444 : term] : ((((sK459 @ (sub @ sK458 @ (push @ X444 @ id)))) = $true) | ($true != ((sK459 @ X444)))) & ($true != ((sK459 @ (lam @ sK458)))) & ! [X445 : term] : (((sK459 @ X445)) = ((sK460 @ id @ X445 @ id))))) & (! [X446 : term,X447 : (term > $o),X448 : (subst > term > subst > $o)] : ((($true != ((X448 @ (comp @ (sK463 @ X448) @ (sK461 @ X448)) @ (sub @ (sK464 @ X448) @ (sK461 @ X448)) @ (sK462 @ X448)))) & ($true = ((X448 @ (sK463 @ X448) @ (sK464 @ X448) @ (comp @ (sK461 @ X448) @ (sK462 @ X448)))))) | (($true != ((X448 @ (sK466 @ X448) @ (sK465 @ X448) @ (comp @ (sK468 @ X448) @ (sK467 @ X448))))) & ($true = ((X448 @ (comp @ (sK466 @ X448) @ (sK468 @ X448)) @ (sub @ (sK465 @ X448) @ (sK468 @ X448)) @ (sK467 @ X448))))) | (((sP11 @ X448)) = $true) | ((((X447 @ (sub @ X446 @ (push @ (sK469 @ X447 @ X446) @ id)))) != $true) & (((X447 @ (sK469 @ X447 @ X446))) = $true)) | (((X447 @ (lam @ X446))) = $true) | (((X447 @ (sK470 @ X448 @ X447))) != ((X448 @ id @ (sK470 @ X448 @ X447) @ id)))) | (hoasinduction_lem3v2 != $true)) & (! [X459 : term,X460 : term,X461 : term,X462 : term] : ((X459 = X461) | (((ap @ X460 @ X459)) != ((ap @ X462 @ X461)))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK471 != sK473) & (((ap @ sK474 @ sK473)) = ((ap @ sK472 @ sK471))))) & ((hoasinduction_lem3v2a = $true) | (! [X470 : term] : (((sK475 @ id @ X470 @ id)) = ((sK477 @ X470))) & ! [X471 : term] : (($true = ((sK477 @ (sub @ sK476 @ (push @ X471 @ id))))) | ($true != ((sK477 @ X471)))) & ! [X472 : (subst > term > term)] : ((((sub @ (X472 @ (sK478 @ X472) @ (sK479 @ X472)) @ (sK480 @ X472))) != ((X472 @ (comp @ (sK478 @ X472) @ (sK480 @ X472)) @ (sub @ (sK479 @ X472) @ (sK480 @ X472))))) | ($true = ((sK475 @ id @ (lam @ (X472 @ sh @ one)) @ id))) | (($true != ((sK475 @ id @ (X472 @ id @ (sK481 @ X472)) @ id))) & (((sK475 @ id @ (sK481 @ X472) @ id)) = $true))) & ($true != ((sK477 @ (lam @ sK476)))))) & (! [X477 : (subst > term > subst > $o),X478 : term,X479 : (term > $o)] : ((((X479 @ (sK482 @ X479 @ X477))) != ((X477 @ id @ (sK482 @ X479 @ X477) @ id))) | ((((X479 @ (sub @ X478 @ (push @ (sK483 @ X479 @ X478) @ id)))) != $true) & (((X479 @ (sK483 @ X479 @ X478))) = $true)) | (! [X483 : subst,X484 : term,X485 : subst] : (((sK484 @ X477 @ (comp @ X483 @ X485) @ (sub @ X484 @ X485))) = ((sub @ (sK484 @ X477 @ X483 @ X484) @ X485))) & ($true != ((X477 @ id @ (lam @ (sK484 @ X477 @ sh @ one)) @ id))) & ! [X486 : term] : (($true = ((X477 @ id @ (sK484 @ X477 @ id @ X486) @ id))) | ($true != ((X477 @ id @ X486 @ id))))) | (((X479 @ (lam @ X478))) = $true)) | (hoasinduction_lem3v2a != $true)) & (axassoc = $true) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & ((hoasinduction_lem3aa = $true) | ((((sK485 @ id @ (lam @ (sub @ sK486 @ (push @ one @ sh))) @ id)) != $true) & ! [X489 : (subst > term > term)] : ((((X489 @ (comp @ (sK488 @ X489) @ (sK489 @ X489)) @ (sub @ (sK487 @ X489) @ (sK489 @ X489)))) != ((sub @ (X489 @ (sK488 @ X489) @ (sK487 @ X489)) @ (sK489 @ X489)))) | ($true = ((sK485 @ id @ (lam @ (X489 @ sh @ one)) @ id))) | (($true != ((sK485 @ id @ (X489 @ id @ (sK490 @ X489)) @ id))) & ($true = ((sK485 @ id @ (sK490 @ X489) @ id))))) & ! [X494 : term] : ((((sK485 @ id @ (sub @ sK486 @ (push @ X494 @ id)) @ id)) = $true) | ($true != ((sK485 @ id @ X494 @ id)))))) & (! [X495 : (subst > term > subst > $o),X496 : term] : (($true = ((X495 @ id @ (lam @ (sub @ X496 @ (push @ one @ sh))) @ id))) | (! [X498 : term,X499 : subst,X500 : subst] : (((sK491 @ X495 @ (comp @ X499 @ X500) @ (sub @ X498 @ X500))) = ((sub @ (sK491 @ X495 @ X499 @ X498) @ X500))) & ($true != ((X495 @ id @ (lam @ (sK491 @ X495 @ sh @ one)) @ id))) & ! [X501 : term] : (($true = ((X495 @ id @ (sK491 @ X495 @ id @ X501) @ id))) | ($true != ((X495 @ id @ X501 @ id))))) | (($true != ((X495 @ id @ (sub @ X496 @ (push @ (sK492 @ X496 @ X495) @ id)) @ id))) & (((X495 @ id @ (sK492 @ X496 @ X495) @ id)) = $true))) | (hoasinduction_lem3aa != $true)) & (hoasinduction_lem3a_gthm = $true) & (ulamvarsh = $true) & ((pushprop_lem0 = $true) | ! [X506 : (term > $o)] : (((X506 @ (sK496 @ X506))) != ((sK495 @ (sub @ (sK496 @ X506) @ (push @ sK494 @ sK493)))))) & (! [X508 : subst,X509 : term,X510 : (term > $o)] : ! [X512 : term] : (((X510 @ (sub @ X512 @ (push @ X509 @ X508)))) = ((sK497 @ X510 @ X509 @ X508 @ X512))) | (pushprop_lem0 != $true)) & ! [X513 : d_subst] : (d_id = X513) & ((sK498 != ((sub @ sK498 @ id))) | ! [X515 : (term > $o),X516 : term,X517 : (subst > term > subst > $o)] : ((((sP10 @ X517)) = $true) | (((X517 @ id @ (sK499 @ X517 @ X515) @ id)) != ((X515 @ (sK499 @ X517 @ X515)))) | (($true = ((X515 @ (sK500 @ X516 @ X515)))) & ($true != ((X515 @ (sub @ X516 @ (push @ (sK500 @ X516 @ X515) @ id)))))) | (($true != ((X517 @ (comp @ (sK504 @ X517) @ (sK503 @ X517)) @ (sub @ (sK502 @ X517) @ (sK503 @ X517)) @ (sK501 @ X517)))) & ($true = ((X517 @ (sK504 @ X517) @ (sK502 @ X517) @ (comp @ (sK503 @ X517) @ (sK501 @ X517)))))) | (($true = ((X517 @ (comp @ (sK507 @ X517) @ (sK506 @ X517)) @ (sub @ (sK505 @ X517) @ (sK506 @ X517)) @ (sK508 @ X517)))) & ($true != ((X517 @ (sK507 @ X517) @ (sK505 @ X517) @ (comp @ (sK506 @ X517) @ (sK508 @ X517)))))) | ($true = ((X515 @ (lam @ X516))))) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (! [X528 : term] : (((sub @ X528 @ id)) = X528) & ((((sP10 @ sK511)) != $true) & ! [X532 : term] : (((sK509 @ X532)) = ((sK511 @ id @ X532 @ id))) & ! [X533 : term] : (($true != ((sK509 @ X533))) | ($true = ((sK509 @ (sub @ sK510 @ (push @ X533 @ id)))))) & ! [X534 : subst,X535 : term,X536 : subst,X537 : subst] : ((((sK511 @ (comp @ X537 @ X536) @ (sub @ X535 @ X536) @ X534)) = $true) | (((sK511 @ X537 @ X535 @ (comp @ X536 @ X534))) != $true)) & ! [X538 : term,X539 : subst,X540 : subst,X541 : subst] : ((((sK511 @ (comp @ X540 @ X539) @ (sub @ X538 @ X539) @ X541)) != $true) | ($true = ((sK511 @ X540 @ X538 @ (comp @ X539 @ X541))))) & (((sK509 @ (lam @ sK510))) != $true)))) & ((hoasinduction_lthm = $true) | (! [X542 : term,X543 : (subst > term > subst > $o)] : (((((X543 @ id @ (sub @ X542 @ (push @ (sK512 @ X543 @ X542) @ id)) @ id)) != $true) & (((X543 @ id @ (sK512 @ X543 @ X542) @ id)) = $true)) | ((((X543 @ (sK513 @ X543) @ (sK514 @ X543) @ (comp @ (sK515 @ X543) @ (sK516 @ X543)))) != $true) & (((X543 @ (comp @ (sK513 @ X543) @ (sK515 @ X543)) @ (sub @ (sK514 @ X543) @ (sK515 @ X543)) @ (sK516 @ X543))) = $true)) | (((X543 @ id @ (lam @ X542) @ id)) = $true) | (((sP6 @ X543)) != $true) | (($true = ((X543 @ (sK517 @ X543) @ (sK519 @ X543) @ (comp @ (sK520 @ X543) @ (sK518 @ X543))))) & (((X543 @ (comp @ (sK517 @ X543) @ (sK520 @ X543)) @ (sub @ (sK519 @ X543) @ (sK520 @ X543)) @ (sK518 @ X543))) != $true))) & ($true != sP8) & (sP7 != $true) & ($true != sP9))) & ((! [X555 : term] : ((((sK522 @ id @ (sub @ sK521 @ (push @ X555 @ id)) @ id)) = $true) | (((sK522 @ id @ X555 @ id)) != $true)) & ! [X556 : subst,X557 : term,X558 : subst,X559 : subst] : ((((sK522 @ X556 @ X557 @ (comp @ X558 @ X559))) = $true) | ($true != ((sK522 @ (comp @ X556 @ X558) @ (sub @ X557 @ X558) @ X559)))) & ($true != ((sK522 @ id @ (lam @ sK521) @ id))) & ($true = ((sP6 @ sK522))) & ! [X560 : subst,X561 : subst,X562 : term,X563 : subst] : ((((sK522 @ X560 @ X562 @ (comp @ X563 @ X561))) != $true) | ($true = ((sK522 @ (comp @ X560 @ X563) @ (sub @ X562 @ X563) @ X561))))) | ($true = sP8) | (sP7 = $true) | ($true = sP9) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X564 : term] : (((sub @ X564 @ id)) = X564) & ! [X565 : (term > $o),X566 : term,X567 : (subst > term > subst > $o)] : ((((X565 @ (lam @ X566))) = $true) | (! [X569 : subst,X570 : term,X571 : subst] : (((sK523 @ X567 @ (comp @ X569 @ X571) @ (sub @ X570 @ X571))) = ((sub @ (sK523 @ X567 @ X569 @ X570) @ X571))) & (((X567 @ id @ (lam @ (sK523 @ X567 @ sh @ one)) @ id)) != $true) & ! [X572 : term] : (($true = ((X567 @ id @ (sK523 @ X567 @ id @ X572) @ id))) | ($true != ((X567 @ id @ X572 @ id))))) | (($true = ((X565 @ (sK524 @ X566 @ X565)))) & ($true != ((X565 @ (sub @ X566 @ (push @ (sK524 @ X566 @ X565) @ id)))))) | (((X567 @ id @ (sK525 @ X567 @ X565) @ id)) != ((X565 @ (sK525 @ X567 @ X565))))) & ! [X575 : (subst > term > subst > $o)] : ! [X577 : term] : (((sK526 @ X575 @ X577)) = ((X575 @ id @ X577 @ id))) & ($true != sP3) & (sP2 != $true))) & ((((sub @ sK527 @ id)) != sK527) | (($true != ((sK528 @ (lam @ sK529)))) & ! [X582 : (subst > term > term)] : ((((sub @ (X582 @ (sK531 @ X582) @ (sK532 @ X582)) @ (sK533 @ X582))) != ((X582 @ (comp @ (sK531 @ X582) @ (sK533 @ X582)) @ (sub @ (sK532 @ X582) @ (sK533 @ X582))))) | (((sK530 @ id @ (lam @ (X582 @ sh @ one)) @ id)) = $true) | ((((sK530 @ id @ (X582 @ id @ (sK534 @ X582)) @ id)) != $true) & ($true = ((sK530 @ id @ (sK534 @ X582) @ id))))) & ! [X587 : term] : ((((sK528 @ X587)) != $true) | (((sK528 @ (sub @ sK529 @ (push @ X587 @ id)))) = $true)) & ! [X588 : term] : (((sK530 @ id @ X588 @ id)) = ((sK528 @ X588)))) | ! [X590 : (term > $o)] : (((X590 @ (sK536 @ X590))) != ((sK535 @ id @ (sK536 @ X590) @ id))) | ($true = sP3) | (sP2 = $true) | (hoasinduction_lthm_3 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X592 : term] : (((d2term @ (sK537 @ X592))) = X592) & ((hoasinduction_lem3v2_f = $true) | ! [X595 : (subst > term > term)] : (((sub @ sK538 @ (push @ (sK539 @ X595) @ (sK540 @ X595)))) != ((X595 @ (sK540 @ X595) @ (sK539 @ X595))))) & (! [X598 : term] : ! [X600 : term,X601 : subst] : (((sub @ X598 @ (push @ X600 @ X601))) = ((sK541 @ X598 @ X601 @ X600))) | (hoasinduction_lem3v2_f != $true)) & ((! [X602 : subst] : (((comp @ id @ X602)) = X602) & ! [X603 : subst] : (((comp @ X603 @ id)) = X603)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ id @ sK542)) != sK542) | (sK543 != ((comp @ sK543 @ id)))) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X606 : (term > $o),X607 : term] : (($true = ((X606 @ X607))) | ((((X606 @ (sK544 @ X606))) != $true) & (((var @ (sK544 @ X606))) = $true)) | ((((X606 @ (sK545 @ X606))) = $true) & (((X606 @ (lam @ (sK545 @ X606)))) != $true)) | (($true = ((X606 @ (sK546 @ X606)))) & ($true != ((X606 @ (ap @ (sK547 @ X606) @ (sK546 @ X606))))) & (((X606 @ (sK547 @ X606))) = $true))) | (induction != $true)) & ((induction = $true) | ((((sK548 @ sK549)) != $true) & ! [X614 : term] : ((((sK548 @ X614)) = $true) | (((var @ X614)) != $true)) & ! [X615 : term] : ((((sK548 @ X615)) != $true) | (((sK548 @ (lam @ X615))) = $true)) & ! [X616 : term,X617 : term] : ((((sK548 @ X616)) != $true) | (((sK548 @ (ap @ X617 @ X616))) = $true) | ($true != ((sK548 @ X617)))))) & ((pushprop_lem1_lthm = $true) | (! [X618 : term,X619 : subst] : (((sub @ one @ (push @ X618 @ X619))) = X618) & ! [X620 : subst,X621 : term] : (((comp @ sh @ (push @ X621 @ X620))) = X620) & ((((sK550 @ (sub @ sK554 @ (push @ sK553 @ sK552)))) != $true) & (((sK551 @ sK554)) = $true)))) & ((sK555 != ((sub @ one @ (push @ sK555 @ sK556)))) | (sK557 != ((comp @ sh @ (push @ sK558 @ sK557)))) | ! [X631 : (term > $o),X632 : (term > $o),X633 : subst,X634 : term,X635 : term] : (($true = ((X631 @ (sub @ X635 @ (push @ X634 @ X633))))) | ($true != ((X632 @ X635)))) | (pushprop_lem1_lthm != $true)) & (! [X636 : term,X637 : term,X638 : term,X639 : term] : ((X638 = X639) | (((ap @ (sub @ X639 @ id) @ X636)) != ((ap @ (sub @ X638 @ id) @ X637)))) | (sK559 != ((sub @ sK559 @ id))) | ((((ap @ sK563 @ sK562)) = ((ap @ sK561 @ sK560))) & (sK563 != sK561)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (((sK566 != sK567) & (((ap @ (sub @ sK567 @ id) @ sK564)) = ((ap @ (sub @ sK566 @ id) @ sK565)))) & ! [X649 : term] : (((sub @ X649 @ id)) = X649) & ! [X650 : term,X651 : term,X652 : term,X653 : term] : ((((ap @ X653 @ X652)) != ((ap @ X651 @ X650))) | (X651 = X653)))) & (hoasinduction_lem2_lthm = $true)), 26.09/4.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK244,sK245,sK246,sK247,sK248,sK249,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK256,vAPP,sK258,sK259,vAPP,sK261,vAPP,sK263,sK264,sK265,sK266,sK267,vAPP,vAPP,vAPP,vAPP,sK272,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK279,vAPP,sK281,sK282,sK283,vAPP,vAPP,vAPP,vAPP,sK288,sK289,sK290,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK298,sK299,sK300,sK301,vAPP,sK303,sK304,sK305,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK314,vAPP,vAPP,sK317,sK318,sK319,vAPP,vAPP,sK322,sK323,vAPP,vAPP,vAPP,vAPP,sK328,sK329,sK330,sK331,sK332,sK333,sK334,sK335,vAPP,sK337,vAPP,sK339,sK340,vAPP,vAPP,sK343,sK344,sK345,sK346,sK347,sK348,sK349,sK350,sK351,sK352,sK353,sK354,sK355,vAPP,vAPP,sK358,sK359,sK360,vAPP,vAPP,vAPP,vAPP,vAPP,sK366,sK367,sK368,sK369,sK370,sK371,sK372,sK373,sK374,sK375,sK376,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK383,sK384,sK385,sK386,sK387,sK388,sK389,sK390,vAPP,vAPP,sK393,sK394,vAPP,vAPP,vAPP,vAPP,sK399,sK400,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK411,sK412,sK413,sK414,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK421,sK422,sK423,sK424,sK425,sK426,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK436,sK437,sK438,vAPP,sK440,sK441,sK442,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK453,sK454,sK455,sK456,sK457,sK458,sK459,sK460,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK471,sK472,sK473,sK474,sK475,sK476,sK477,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK485,sK486,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK493,sK494,sK495,vAPP,vAPP,sK498,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK509,sK510,sK511,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK521,sK522,vAPP,vAPP,vAPP,vAPP,sK527,sK528,sK529,sK530,vAPP,vAPP,vAPP,vAPP,sK535,vAPP,vAPP,sK538,vAPP,vAPP,vAPP,sK542,sK543,vAPP,vAPP,vAPP,vAPP,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567]),skolemize(X0,sK244),skolemize(X1,sK245),skolemize(X4,sK246),skolemize(X5,sK247),skolemize(X6,sK248),skolemize(X7,sK249),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X25,sK256),skolemize(X15,sK35 @ X14 @ X8),skolemize(X30,sK258),skolemize(X31,sK259),skolemize(X15,sK35 @ X14 @ X8),skolemize(X35,sK261),skolemize(X15,sK35 @ X14 @ X8),skolemize(X42,sK263),skolemize(X43,sK264),skolemize(X44,sK265),skolemize(X45,sK266),skolemize(X46,sK267),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X60,sK272),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X78,sK279),skolemize(X15,sK35 @ X14 @ X8),skolemize(X81,sK281),skolemize(X82,sK282),skolemize(X83,sK283),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X91,sK288),skolemize(X92,sK289),skolemize(X93,sK290),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X112,sK298),skolemize(X113,sK299),skolemize(X114,sK300),skolemize(X115,sK301),skolemize(X15,sK35 @ X14 @ X8),skolemize(X122,sK303),skolemize(X123,sK304),skolemize(X124,sK305),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X147,sK314),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X151,sK317),skolemize(X153,sK318),skolemize(X154,sK319),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X165,sK322),skolemize(X166,sK323),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X173,sK328),skolemize(X175,sK329),skolemize(X178,sK330),skolemize(X179,sK331),skolemize(X180,sK332),skolemize(X181,sK333),skolemize(X183,sK334),skolemize(X184,sK335),skolemize(X15,sK35 @ X14 @ X8),skolemize(X190,sK337),skolemize(X15,sK35 @ X14 @ X8),skolemize(X195,sK339),skolemize(X196,sK340),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X207,sK343),skolemize(X208,sK344),skolemize(X209,sK345),skolemize(X210,sK346),skolemize(X211,sK347),skolemize(X213,sK348),skolemize(X214,sK349),skolemize(X215,sK350),skolemize(X216,sK351),skolemize(X221,sK352),skolemize(X222,sK353),skolemize(X223,sK354),skolemize(X224,sK355),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X238,sK358),skolemize(X239,sK359),skolemize(X240,sK360),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X249,sK366),skolemize(X255,sK367),skolemize(X256,sK368),skolemize(X257,sK369),skolemize(X258,sK370),skolemize(X259,sK371),skolemize(X260,sK372),skolemize(X261,sK373),skolemize(X262,sK374),skolemize(X267,sK375),skolemize(X268,sK376),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X284,sK383),skolemize(X285,sK384),skolemize(X287,sK385),skolemize(X290,sK386),skolemize(X291,sK387),skolemize(X292,sK388),skolemize(X293,sK389),skolemize(X294,sK390),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X307,sK393),skolemize(X308,sK394),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X315,sK399),skolemize(X316,sK400),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X339,sK411),skolemize(X340,sK412),skolemize(X341,sK413),skolemize(X342,sK414),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X365,sK421),skolemize(X366,sK422),skolemize(X367,sK423),skolemize(X368,sK424),skolemize(X369,sK425),skolemize(X370,sK426),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X382,sK436),skolemize(X383,sK437),skolemize(X393,sK438),skolemize(X15,sK35 @ X14 @ X8),skolemize(X400,sK440),skolemize(X401,sK441),skolemize(X402,sK442),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X416,sK453),skolemize(X417,sK454),skolemize(X428,sK455),skolemize(X429,sK456),skolemize(X430,sK457),skolemize(X433,sK458),skolemize(X434,sK459),skolemize(X435,sK460),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X463,sK471),skolemize(X464,sK472),skolemize(X465,sK473),skolemize(X466,sK474),skolemize(X467,sK475),skolemize(X468,sK476),skolemize(X469,sK477),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X487,sK485),skolemize(X488,sK486),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X503,sK493),skolemize(X504,sK494),skolemize(X505,sK495),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X514,sK498),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X529,sK509),skolemize(X530,sK510),skolemize(X531,sK511),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X553,sK521),skolemize(X554,sK522),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X578,sK527),skolemize(X579,sK528),skolemize(X580,sK529),skolemize(X581,sK530),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X589,sK535),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X594,sK538),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X604,sK542),skolemize(X605,sK543),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X15,sK35 @ X14 @ X8),skolemize(X612,sK548),skolemize(X613,sK549),skolemize(X622,sK550),skolemize(X623,sK551),skolemize(X624,sK552),skolemize(X625,sK553),skolemize(X626,sK554),skolemize(X627,sK555),skolemize(X628,sK556),skolemize(X629,sK557),skolemize(X630,sK558),skolemize(X640,sK559),skolemize(X641,sK560),skolemize(X642,sK561),skolemize(X643,sK562),skolemize(X644,sK563),skolemize(X645,sK564),skolemize(X646,sK565),skolemize(X647,sK566),skolemize(X648,sK567)],[f135])). 26.09/4.24 thf(f143,plain,( 26.09/4.24 (hoasinduction_lem3a != $true) | (((sK28 @ id @ (lam @ sK33) @ id)) != $true)), 26.09/4.24 inference(cnf_transformation,[],[f46])). 26.09/4.24 thf(f145,plain,( 26.09/4.24 ( ! [X1 : (subst > term > term)] : (($true = ((sK28 @ id @ (sK29 @ X1) @ id))) | (hoasinduction_lem3a != $true) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))) | (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true)) )), 26.09/4.24 inference(cnf_transformation,[],[f46])). 26.09/4.24 thf(f146,plain,( 26.09/4.24 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3a != $true) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))) | ($true != ((sK28 @ id @ (X1 @ id @ (sK29 @ X1)) @ id))) | (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true)) )), 26.09/4.24 inference(cnf_transformation,[],[f46])). 26.09/4.24 thf(f512,plain,( 26.09/4.24 ( ! [X592 : term] : ((((d2term @ (sK537 @ X592))) = X592)) )), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f560,plain,( 26.09/4.24 ( ! [X513 : d_subst] : ((d_id = X513)) )), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f635,plain,( 26.09/4.24 (((d2subst @ d_id)) = id)), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f711,plain,( 26.09/4.24 ( ! [X270 : (subst > term > term)] : ((((sub @ (X270 @ (sK379 @ X270) @ (sK378 @ X270)) @ (sK380 @ X270))) != ((X270 @ (comp @ (sK379 @ X270) @ (sK380 @ X270)) @ (sub @ (sK378 @ X270) @ (sK380 @ X270))))) | (((sK375 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true) | (hoasinduction_lem3a = $true) | ($true = ((sK375 @ id @ (sK377 @ X270) @ id)))) )), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f714,plain,( 26.09/4.24 (hoasinduction_lem3a = $true) | (((sK375 @ id @ (lam @ sK376) @ id)) != $true)), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f745,plain,( 26.09/4.24 ( ! [X212 : d_term] : ((d_one = X212)) )), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f751,plain,( 26.09/4.24 (one = ((d2term @ d_one)))), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f867,plain,( 26.09/4.24 ( ! [X26 : subst] : ((((d2subst @ (sK257 @ X26))) = X26)) )), 26.09/4.24 inference(cnf_transformation,[],[f136])). 26.09/4.24 thf(f987,plain,( 26.09/4.24 ( ! [X1 : (subst > term > term)] : (($true = ((sK28 @ id @ (hoaslam @ id @ X1) @ id))) | ($true = ((sK28 @ id @ (sK29 @ X1) @ id))) | (hoasinduction_lem3a != $true) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1)))))) )), 26.09/4.24 inference(beta-eta_normalization,[],[f145])). 26.09/4.24 thf(f1015,plain,( 26.09/4.24 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3a != $true) | ($true = ((sK28 @ id @ (hoaslam @ id @ X1) @ id))) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))) | ($true != ((sK28 @ id @ (X1 @ id @ (sK29 @ X1)) @ id)))) )), 26.09/4.24 inference(beta-eta_normalization,[],[f146])). 26.09/4.24 thf(f1722,definition,( 26.09/4.24 spl568_159 <=> (hoasinduction_lem3a = $true)), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_159])],[avatar_definition])). 26.09/4.24 thf(f1726,definition,( 26.09/4.24 spl568_160 <=> (((sK28 @ id @ (lam @ sK33) @ id)) = $true)), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_160])],[avatar_definition])). 26.09/4.24 thf(f1728,plain,( 26.09/4.24 (((sK28 @ id @ (lam @ sK33) @ id)) != $true) | spl568_160), 26.09/4.24 inference(avatar_component_clause,[],[f1726])). 26.09/4.24 thf(f1729,plain,( 26.09/4.24 ~spl568_159 | ~spl568_160), 26.09/4.24 inference(avatar_split_clause,[],[f143,f1726,f1722])). 26.09/4.24 thf(f2041,definition,( 26.09/4.24 spl568_235 <=> (one = ((d2term @ d_one)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_235])],[avatar_definition])). 26.09/4.24 thf(f2043,plain,( 26.09/4.24 (one = ((d2term @ d_one))) | ~spl568_235), 26.09/4.24 inference(avatar_component_clause,[],[f2041])). 26.09/4.24 thf(f2044,plain,( 26.09/4.24 spl568_235), 26.09/4.24 inference(avatar_split_clause,[],[f751,f2041])). 26.09/4.24 thf(f2188,definition,( 26.09/4.24 spl568_269 <=> (((sK375 @ id @ (lam @ sK376) @ id)) = $true)), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_269])],[avatar_definition])). 26.09/4.24 thf(f2190,plain,( 26.09/4.24 (((sK375 @ id @ (lam @ sK376) @ id)) != $true) | spl568_269), 26.09/4.24 inference(avatar_component_clause,[],[f2188])). 26.09/4.24 thf(f2191,plain,( 26.09/4.24 ~spl568_269 | spl568_159), 26.09/4.24 inference(avatar_split_clause,[],[f714,f1722,f2188])). 26.09/4.24 thf(f2698,definition,( 26.09/4.24 spl568_390 <=> ! [X270 : (subst > term > term)] : ((((sub @ (X270 @ (sK379 @ X270) @ (sK378 @ X270)) @ (sK380 @ X270))) != ((X270 @ (comp @ (sK379 @ X270) @ (sK380 @ X270)) @ (sub @ (sK378 @ X270) @ (sK380 @ X270))))) | ($true = ((sK375 @ id @ (sK377 @ X270) @ id))) | (((sK375 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true))), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_390])],[avatar_definition])). 26.09/4.24 thf(f2699,plain,( 26.09/4.24 ( ! [X270 : (subst > term > term)] : ((((sK375 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true) | (((sub @ (X270 @ (sK379 @ X270) @ (sK378 @ X270)) @ (sK380 @ X270))) != ((X270 @ (comp @ (sK379 @ X270) @ (sK380 @ X270)) @ (sub @ (sK378 @ X270) @ (sK380 @ X270))))) | ($true = ((sK375 @ id @ (sK377 @ X270) @ id)))) ) | ~spl568_390), 26.09/4.24 inference(avatar_component_clause,[],[f2698])). 26.09/4.24 thf(f2700,plain,( 26.09/4.24 spl568_390 | spl568_159), 26.09/4.24 inference(avatar_split_clause,[],[f711,f1722,f2698])). 26.09/4.24 thf(f3241,definition,( 26.09/4.24 spl568_516 <=> ! [X1 : (subst > term > term)] : (($true = ((sK28 @ id @ (hoaslam @ id @ X1) @ id))) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))) | ($true = ((sK28 @ id @ (sK29 @ X1) @ id))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_516])],[avatar_definition])). 26.09/4.24 thf(f3242,plain,( 26.09/4.24 ( ! [X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))) | ($true = ((sK28 @ id @ (sK29 @ X1) @ id))) | ($true = ((sK28 @ id @ (hoaslam @ id @ X1) @ id)))) ) | ~spl568_516), 26.09/4.24 inference(avatar_component_clause,[],[f3241])). 26.09/4.24 thf(f3243,plain,( 26.09/4.24 ~spl568_159 | spl568_516), 26.09/4.24 inference(avatar_split_clause,[],[f987,f3241,f1722])). 26.09/4.24 thf(f3418,definition,( 26.09/4.24 spl568_556 <=> (((d2subst @ d_id)) = id)), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_556])],[avatar_definition])). 26.09/4.24 thf(f3420,plain,( 26.09/4.24 (((d2subst @ d_id)) = id) | ~spl568_556), 26.09/4.24 inference(avatar_component_clause,[],[f3418])). 26.09/4.24 thf(f3421,plain,( 26.09/4.24 spl568_556), 26.09/4.24 inference(avatar_split_clause,[],[f635,f3418])). 26.09/4.24 thf(f3756,definition,( 26.09/4.24 spl568_633 <=> ! [X1 : (subst > term > term)] : (($true = ((sK28 @ id @ (hoaslam @ id @ X1) @ id))) | ($true != ((sK28 @ id @ (X1 @ id @ (sK29 @ X1)) @ id))) | (((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))))), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_633])],[avatar_definition])). 26.09/4.24 thf(f3757,plain,( 26.09/4.24 ( ! [X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK32 @ X1) @ (sK30 @ X1)) @ (sK31 @ X1))) != ((X1 @ (comp @ (sK32 @ X1) @ (sK31 @ X1)) @ (sub @ (sK30 @ X1) @ (sK31 @ X1))))) | ($true = ((sK28 @ id @ (hoaslam @ id @ X1) @ id))) | ($true != ((sK28 @ id @ (X1 @ id @ (sK29 @ X1)) @ id)))) ) | ~spl568_633), 26.09/4.24 inference(avatar_component_clause,[],[f3756])). 26.09/4.24 thf(f3758,plain,( 26.09/4.24 ~spl568_159 | spl568_633), 26.09/4.24 inference(avatar_split_clause,[],[f1015,f3756,f1722])). 26.09/4.24 thf(f4534,definition,( 26.09/4.24 spl568_812 <=> (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true)), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_812])],[avatar_definition])). 26.09/4.24 thf(f4536,plain,( 26.09/4.24 (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | ~spl568_812), 26.09/4.24 inference(avatar_component_clause,[],[f4534])). 26.09/4.24 thf(f4538,definition,( 26.09/4.24 spl568_813 <=> (((sK28 @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true)), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_813])],[avatar_definition])). 26.09/4.24 thf(f4901,plain,( 26.09/4.24 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) ) | ~spl568_235), 26.09/4.24 inference(superposition,[],[f2043,f745])). 26.09/4.24 thf(f4908,plain,( 26.09/4.24 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) ) | ~spl568_556), 26.09/4.24 inference(superposition,[],[f3420,f560])). 26.09/4.24 thf(f5070,plain,( 26.09/4.24 (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | (((sK28 @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | (((sub @ ((^[Y0 : subst]: ((^[Y1 : term]: (Y1)))) @ (sK32 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))))) != (((^[Y0 : subst]: ((^[Y1 : term]: (Y1)))) @ (comp @ (sK32 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))) @ (sub @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))))))) | ~spl568_516), 26.09/4.24 inference(projection,[],[f3242])). 26.09/4.24 thf(f5075,plain,( 26.09/4.24 (((sub @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))))) != ((sub @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))))) | (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | (((sK28 @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | ~spl568_516), 26.09/4.24 inference(beta-eta_normalization,[],[f5070])). 26.09/4.24 thf(f5076,plain,( 26.09/4.24 (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | (((sK28 @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | ~spl568_516), 26.09/4.24 inference(trivial_inequality_removal,[],[f5075])). 26.09/4.24 thf(f5078,plain,( 26.09/4.24 spl568_812 | spl568_813 | ~spl568_516), 26.09/4.24 inference(avatar_split_clause,[],[f5076,f3241,f4538,f4534])). 26.09/4.24 thf(f5181,plain,( 26.09/4.24 (((sub @ ((^[Y0 : subst]: ((^[Y1 : term]: (Y1)))) @ (sK32 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))))) != (((^[Y0 : subst]: ((^[Y1 : term]: (Y1)))) @ (comp @ (sK32 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))) @ (sub @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))))))) | ($true != ((sK28 @ id @ ((^[Y0 : subst]: ((^[Y1 : term]: (Y1)))) @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))) @ id))) | (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | ~spl568_633), 26.09/4.24 inference(projection,[],[f3757])). 26.09/4.24 thf(f5188,plain,( 26.09/4.24 (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | (((sub @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))))) != ((sub @ (sK30 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ (sK31 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1)))))))) | (((sK28 @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) != $true) | ~spl568_633), 26.09/4.24 inference(beta-eta_normalization,[],[f5181])). 26.09/4.24 thf(f5189,plain,( 26.09/4.24 (((sK28 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) = $true) | (((sK28 @ id @ (sK29 @ (^[Y0 : subst]: ((^[Y1 : term]: (Y1))))) @ id)) != $true) | ~spl568_633), 26.09/4.24 inference(trivial_inequality_removal,[],[f5188])). 26.09/4.24 thf(f5190,plain,( 26.09/4.24 ~spl568_813 | spl568_812 | ~spl568_633), 26.09/4.24 inference(avatar_split_clause,[],[f5189,f3756,f4534,f4538])). 26.09/4.24 thf(f5503,plain,( 26.09/4.24 ( ! [X0 : term] : ((one = X0)) ) | ~spl568_235), 26.09/4.24 inference(superposition,[],[f4901,f512])). 26.09/4.24 thf(f5507,plain,( 26.09/4.24 ( ! [X0 : subst] : ((id = X0)) ) | ~spl568_556), 26.09/4.24 inference(superposition,[],[f4908,f867])). 26.09/4.24 thf(f5523,plain,( 26.09/4.24 ( ! [X0 : term,X1 : term] : ((X0 = X1)) ) | ~spl568_235), 26.09/4.24 inference(superposition,[],[f5503,f5503])). 26.09/4.24 thf(f5578,plain,( 26.09/4.24 ( ! [X0 : subst] : (($true != ((sK28 @ X0 @ (lam @ sK33) @ X0)))) ) | (spl568_160 | ~spl568_556)), 26.09/4.24 inference(superposition,[],[f1728,f5507])). 26.09/4.24 thf(f5582,plain,( 26.09/4.24 ( ! [X0 : subst] : (($true != ((sK375 @ X0 @ (lam @ sK376) @ X0)))) ) | (spl568_269 | ~spl568_556)), 26.09/4.24 inference(superposition,[],[f2190,f5507])). 26.09/4.24 thf(f5969,definition,( 26.09/4.24 spl568_917 <=> ($true = ((sK28 @ id @ one @ id)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_917])],[avatar_definition])). 26.09/4.24 thf(f5970,plain,( 26.09/4.24 ($true = ((sK28 @ id @ one @ id))) | ~spl568_917), 26.09/4.24 inference(avatar_component_clause,[],[f5969])). 26.09/4.24 thf(f5971,plain,( 26.09/4.24 ($true != ((sK28 @ id @ one @ id))) | spl568_917), 26.09/4.24 inference(avatar_component_clause,[],[f5969])). 26.09/4.24 thf(f6053,plain,( 26.09/4.24 ( ! [X0 : term] : ((((sK28 @ id @ X0 @ id)) != $true)) ) | (~spl568_235 | spl568_917)), 26.09/4.24 inference(superposition,[],[f5971,f5503])). 26.09/4.24 thf(f6135,plain,( 26.09/4.24 ($true != $true) | (~spl568_235 | ~spl568_812 | spl568_917)), 26.09/4.24 inference(superposition,[],[f6053,f4536])). 26.09/4.24 thf(f6141,plain,( 26.09/4.24 $false | (~spl568_235 | ~spl568_812 | spl568_917)), 26.09/4.24 inference(trivial_inequality_removal,[],[f6135])). 26.09/4.24 thf(f6142,plain,( 26.09/4.24 ~spl568_235 | ~spl568_812 | spl568_917), 26.09/4.24 inference(avatar_contradiction_clause,[],[f6141])). 26.09/4.24 thf(f6386,plain,( 26.09/4.24 ( ! [X0 : term] : ((((sK28 @ id @ X0 @ id)) = $true)) ) | (~spl568_235 | ~spl568_917)), 26.09/4.24 inference(superposition,[],[f5970,f5503])). 26.09/4.24 thf(f6408,plain,( 26.09/4.24 ($true != $true) | (spl568_160 | ~spl568_235 | ~spl568_556 | ~spl568_917)), 26.09/4.24 inference(superposition,[],[f5578,f6386])). 26.09/4.24 thf(f6431,plain,( 26.09/4.24 $false | (spl568_160 | ~spl568_235 | ~spl568_556 | ~spl568_917)), 26.09/4.24 inference(trivial_inequality_removal,[],[f6408])). 26.09/4.24 thf(f6432,plain,( 26.09/4.24 spl568_160 | ~spl568_235 | ~spl568_556 | ~spl568_917), 26.09/4.24 inference(avatar_contradiction_clause,[],[f6431])). 26.09/4.24 thf(f6952,definition,( 26.09/4.24 spl568_950 <=> ($true = ((sK375 @ id @ one @ id)))), 26.09/4.24 introduced(definition,[new_symbols(definition,[spl568_950])],[avatar_definition])). 26.09/4.24 thf(f6953,plain,( 26.09/4.24 ($true = ((sK375 @ id @ one @ id))) | ~spl568_950), 26.09/4.24 inference(avatar_component_clause,[],[f6952])). 26.09/4.24 thf(f6954,plain,( 26.09/4.24 ($true != ((sK375 @ id @ one @ id))) | spl568_950), 26.09/4.24 inference(avatar_component_clause,[],[f6952])). 26.09/4.24 thf(f8055,plain,( 26.09/4.24 ( ! [X0 : term] : (($true != ((sK375 @ id @ X0 @ id)))) ) | (~spl568_235 | spl568_950)), 26.09/4.24 inference(superposition,[],[f6954,f5503])). 26.09/4.24 thf(f37491,plain,( 26.09/4.24 ( ! [X270 : (subst > term > term)] : ((((sub @ (X270 @ (sK379 @ X270) @ (sK378 @ X270)) @ (sK380 @ X270))) != ((X270 @ (comp @ (sK379 @ X270) @ (sK380 @ X270)) @ (sub @ (sK378 @ X270) @ (sK380 @ X270))))) | (((sK375 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true)) ) | (~spl568_235 | ~spl568_390 | spl568_950)), 26.09/4.24 inference(forward_subsumption_resolution,[],[f2699,f8055])). 26.09/4.24 thf(f37492,plain,( 26.09/4.24 ( ! [X270 : (subst > term > term)] : ((((sK375 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true)) ) | (~spl568_235 | ~spl568_390 | spl568_950)), 26.09/4.24 inference(forward_subsumption_resolution,[],[f37491,f5523])). 26.09/4.24 thf(f37493,plain,( 26.09/4.24 $false | (~spl568_235 | ~spl568_390 | spl568_950)), 26.09/4.24 inference(forward_subsumption_resolution,[],[f37492,f8055])). 26.09/4.24 thf(f37494,plain,( 26.09/4.24 ~spl568_235 | ~spl568_390 | spl568_950), 26.09/4.24 inference(avatar_contradiction_clause,[],[f37493])). 26.09/4.24 thf(f37550,plain,( 26.09/4.24 ( ! [X0 : term] : (($true = ((sK375 @ id @ X0 @ id)))) ) | (~spl568_235 | ~spl568_950)), 26.09/4.24 inference(superposition,[],[f6953,f5503])). 26.09/4.24 thf(f37616,plain,( 26.09/4.24 ($true != $true) | (~spl568_235 | spl568_269 | ~spl568_556 | ~spl568_950)), 26.09/4.24 inference(superposition,[],[f5582,f37550])). 26.09/4.24 thf(f37631,plain,( 26.09/4.24 $false | (~spl568_235 | spl568_269 | ~spl568_556 | ~spl568_950)), 26.09/4.24 inference(trivial_inequality_removal,[],[f37616])). 26.09/4.24 thf(f37632,plain,( 26.09/4.24 ~spl568_235 | spl568_269 | ~spl568_556 | ~spl568_950), 26.09/4.24 inference(avatar_contradiction_clause,[],[f37631])). 26.09/4.24 cnf(s108, plain, ~spl568_159 | ~spl568_160, inference(sat_conversion,[],[f1729])). 26.09/4.24 cnf(s180, plain, spl568_235, inference(sat_conversion,[],[f2044])). 26.09/4.24 cnf(s213, plain, spl568_159 | ~spl568_269, inference(sat_conversion,[],[f2191])). 26.09/4.24 cnf(s328, plain, spl568_159 | spl568_390, inference(sat_conversion,[],[f2700])). 26.09/4.24 cnf(s463, plain, ~spl568_159 | spl568_516, inference(sat_conversion,[],[f3243])). 26.09/4.24 cnf(s506, plain, spl568_556, inference(sat_conversion,[],[f3421])). 26.09/4.24 cnf(s588, plain, ~spl568_159 | spl568_633, inference(sat_conversion,[],[f3758])). 26.09/4.24 cnf(s821, plain, ~spl568_516 | spl568_812 | spl568_813, inference(sat_conversion,[],[f5078])). 26.09/4.24 cnf(s832, plain, ~spl568_633 | spl568_812 | ~spl568_813, inference(sat_conversion,[],[f5190])). 26.09/4.24 cnf(s902, plain, ~spl568_235 | ~spl568_812 | spl568_917, inference(sat_conversion,[],[f6142])). 26.09/4.24 cnf(s924, plain, spl568_160 | ~spl568_235 | ~spl568_556 | ~spl568_917, inference(sat_conversion,[],[f6432])). 26.09/4.24 cnf(s1548, plain, ~spl568_235 | ~spl568_390 | spl568_950, inference(sat_conversion,[],[f37494])). 26.09/4.24 cnf(s1577, plain, ~spl568_235 | spl568_269 | ~spl568_556 | ~spl568_950, inference(sat_conversion,[],[f37632])). 26.09/4.24 cnf(s1681, plain, spl568_159, inference(rat,[],[s1577,s1548,s213,s328,s506,s180])). 26.09/4.24 cnf(s1683, plain, spl568_633, inference(rat,[],[s588,s1681])). 26.09/4.24 cnf(s1684, plain, spl568_516, inference(rat,[],[s463,s1681])). 26.09/4.24 cnf(s1691, plain, ~spl568_160, inference(rat,[],[s108,s1681])). 26.09/4.24 cnf(s1693, plain, ~spl568_917, inference(rat,[],[s924,s180,s506,s1691])). 26.09/4.24 cnf(s1694, plain, ~spl568_812, inference(rat,[],[s902,s180,s1693])). 26.09/4.24 cnf(s1695, plain, ~spl568_813, inference(rat,[],[s832,s1683,s1694])). 26.09/4.24 cnf(s1696, plain, $false, inference(rat,[],[s821,s1684,s1695,s1694])). 26.09/4.24 thf(f37652,plain,( 26.09/4.24 $false), 26.09/4.24 inference(avatar_sat_refutation,[],[s1696])). 26.09/4.24 % SZS output end Proof for theBenchmark 26.09/4.24 % (1095997)------------------------------ 26.09/4.24 % (1095997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.09/4.24 % (1095997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.09/4.24 % (1095997)CaDiCaL version: 2.1.3 26.09/4.24 % (1095997)Termination reason: Refutation 26.09/4.24 % (1095997)Time elapsed: 2.741 s 26.09/4.24 % (1095997)Peak memory usage: 35 MB 26.09/4.24 % (1095997)Instructions burned: 5085 (million) 26.09/4.24 % (1095827)Success in time 3.771 s 26.09/4.24 % Vampire exiting 26.09/4.24 EOF