0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.15/0.41 % Computer : n029.cluster.edu 0.15/0.41 % Model : x86_64 x86_64 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.41 % Memory : 8046.5625MB 0.15/0.41 % OS : Linux 6.8.0-71-generic 0.15/0.41 % CPULimit : 1440 0.15/0.41 % WCLimit : 180 0.15/0.41 % DateTime : Mon Jul 27 13:28:46 UTC 2026 0.15/0.41 % CPUTime : 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.15/0.45 Running higher-order theorem proving 0.20/0.49 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 1.14/0.72 % (2898188)Detected a higher-order problem, will run a greedy HOL sequence. 1.14/0.72 % (2898194)lrs+10_16_si=on:nwc=1.5:random_seed=4208505403:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 1.14/0.72 % (2898195)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3436467135:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 1.14/0.72 % (2898195)Instruction limit reached! 1.14/0.72 % (2898195)------------------------------ 1.14/0.72 % (2898195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.72 % (2898195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.72 % (2898195)CaDiCaL version: 2.1.3 1.14/0.72 % (2898195)Termination reason: Instruction limit 1.14/0.72 % (2898195)Termination phase: shuffling 1.14/0.72 % (2898195)Time elapsed: 0.004 s 1.14/0.72 % (2898195)Peak memory usage: 10 MB 1.14/0.72 % (2898195)Instructions burned: 9 (million) 1.14/0.72 % (2898194)Instruction limit reached! 1.14/0.72 % (2898194)------------------------------ 1.14/0.72 % (2898194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.72 % (2898194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.72 % (2898194)CaDiCaL version: 2.1.3 1.14/0.72 % (2898194)Termination reason: Instruction limit 1.14/0.72 % (2898194)Termination phase: shuffling 1.14/0.72 % (2898194)Time elapsed: 0.008 s 1.14/0.72 % (2898194)Peak memory usage: 10 MB 1.14/0.72 % (2898194)Instructions burned: 19 (million) 1.14/0.72 % (2898199)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 1.14/0.72 % (2898199)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 1.14/0.72 % (2898196)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=1702980150: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) 1.14/0.72 % (2898197)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3923549042:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 1.14/0.72 % (2898199)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=2035220904:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 1.14/0.72 % (2898198)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=255166136:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 1.14/0.72 % (2898193)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1229325243:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 1.14/0.72 % (2898202)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=952508688:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 1.14/0.72 % (2898202)Instruction limit reached! 1.14/0.72 % (2898202)------------------------------ 1.14/0.72 % (2898202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.72 % (2898202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.72 % (2898202)CaDiCaL version: 2.1.3 1.14/0.72 % (2898202)Termination reason: Instruction limit 1.14/0.72 % (2898202)Termination phase: shuffling 1.14/0.72 % (2898202)Time elapsed: 0.002 s 1.14/0.72 % (2898202)Peak memory usage: 9 MB 1.14/0.72 % (2898202)Instructions burned: 4 (million) 1.14/0.72 % (2898197)Instruction limit reached! 1.14/0.72 % (2898197)------------------------------ 1.14/0.72 % (2898197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.72 % (2898197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.72 % (2898197)CaDiCaL version: 2.1.3 1.14/0.72 % (2898197)Termination reason: Instruction limit 1.14/0.72 % (2898197)Termination phase: shuffling 1.14/0.72 % (2898197)Time elapsed: 0.020 s 1.14/0.72 % (2898197)Peak memory usage: 10 MB 1.14/0.72 % (2898197)Instructions burned: 24 (million) 1.14/0.72 % (2898203)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=25550327:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 1.14/0.78 % (2898203)Instruction limit reached! 1.14/0.78 % (2898203)------------------------------ 1.14/0.78 % (2898203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.78 % (2898203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.78 % (2898203)CaDiCaL version: 2.1.3 1.14/0.78 % (2898203)Termination reason: Instruction limit 1.14/0.78 % (2898203)Termination phase: shuffling 1.14/0.78 % (2898203)Time elapsed: 0.005 s 1.14/0.78 % (2898203)Peak memory usage: 10 MB 1.14/0.78 % (2898203)Instructions burned: 6 (million) 1.14/0.78 % (2898210)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 1.14/0.78 % (2898211)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=525630900:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 1.14/0.78 % (2898210)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=925223562:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 1.14/0.78 % (2898211)Instruction limit reached! 1.14/0.78 % (2898211)------------------------------ 1.14/0.78 % (2898211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.78 % (2898211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.78 % (2898211)CaDiCaL version: 2.1.3 1.14/0.78 % (2898211)Termination reason: Instruction limit 1.14/0.78 % (2898211)Termination phase: shuffling 1.14/0.78 % (2898211)Time elapsed: 0.006 s 1.14/0.78 % (2898211)Peak memory usage: 10 MB 1.14/0.78 % (2898211)Instructions burned: 13 (million) 1.14/0.78 % (2898210)Instruction limit reached! 1.14/0.78 % (2898210)------------------------------ 1.14/0.78 % (2898210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.78 % (2898210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.78 % (2898210)CaDiCaL version: 2.1.3 1.14/0.78 % (2898210)Termination reason: Instruction limit 1.14/0.78 % (2898210)Termination phase: shuffling 1.14/0.78 % (2898210)Time elapsed: 0.006 s 1.14/0.78 % (2898210)Peak memory usage: 9 MB 1.14/0.78 % (2898210)Instructions burned: 7 (million) 1.14/0.78 % (2898198)Instruction limit reached! 1.14/0.78 % (2898198)------------------------------ 1.14/0.78 % (2898198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.78 % (2898198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.78 % (2898198)CaDiCaL version: 2.1.3 1.14/0.78 % (2898198)Termination reason: Instruction limit 1.14/0.78 % (2898198)Termination phase: Preprocessing 3 1.14/0.78 % (2898198)Time elapsed: 0.062 s 1.14/0.78 % (2898198)Peak memory usage: 12 MB 1.14/0.78 % (2898198)Instructions burned: 75 (million) 1.14/0.78 % (2898213)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 1.14/0.78 % (2898213)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 1.14/0.78 % (2898216)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=1060601449:i=86:piset=equals:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/86Mi) 1.14/0.78 % (2898213)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2821700467:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 1.14/0.78 % (2898217)lrs+10_1_si=on:cs=on:random_seed=1750556338:i=8:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/8Mi) 1.14/0.78 % (2898193)Instruction limit reached! 1.14/0.78 % (2898193)------------------------------ 1.14/0.78 % (2898193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.14/0.78 % (2898193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.14/0.78 % (2898193)CaDiCaL version: 2.1.3 1.14/0.78 % (2898193)Termination reason: Instruction limit 1.14/0.78 % (2898193)Termination phase: Preprocessing 3 1.14/0.78 % (2898193)Time elapsed: 0.085 s 1.14/0.78 % (2898193)Peak memory usage: 12 MB 1.14/0.78 % (2898193)Instructions burned: 87 (million) 1.14/0.78 % (2898217)Instruction limit reached! 1.54/0.84 % (2898217)------------------------------ 1.54/0.84 % (2898217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.54/0.84 % (2898217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.54/0.84 % (2898217)CaDiCaL version: 2.1.3 1.54/0.84 % (2898217)Termination reason: Instruction limit 1.54/0.84 % (2898217)Termination phase: shuffling 1.54/0.84 % (2898217)Time elapsed: 0.004 s 1.54/0.84 % (2898217)Peak memory usage: 9 MB 1.54/0.84 % (2898217)Instructions burned: 9 (million) 1.54/0.84 % (2898218)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 1.54/0.84 % (2898218)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=30333713:i=2:add=on:rtra=on_1798 on theBenchmark for (1798ds/2Mi) 1.54/0.84 % (2898218)Instruction limit reached! 1.54/0.84 % (2898218)------------------------------ 1.54/0.84 % (2898218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.54/0.84 % (2898218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.54/0.84 % (2898218)CaDiCaL version: 2.1.3 1.54/0.84 % (2898218)Termination reason: Instruction limit 1.54/0.84 % (2898218)Termination phase: shuffling 1.54/0.84 % (2898218)Time elapsed: 0.002 s 1.54/0.84 % (2898218)Peak memory usage: 9 MB 1.54/0.84 % (2898218)Instructions burned: 2 (million) 1.54/0.84 % (2898213)Instruction limit reached! 1.54/0.84 % (2898213)------------------------------ 1.54/0.84 % (2898213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.54/0.84 % (2898213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.54/0.84 % (2898213)CaDiCaL version: 2.1.3 1.54/0.84 % (2898213)Termination reason: Instruction limit 1.54/0.84 % (2898213)Termination phase: shuffling 1.54/0.84 % (2898213)Time elapsed: 0.029 s 1.54/0.84 % (2898213)Peak memory usage: 10 MB 1.54/0.84 % (2898213)Instructions burned: 30 (million) 1.54/0.84 % (2898223)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=337911988:st=2:i=249:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/249Mi) 1.54/0.84 % (2898216)Instruction limit reached! 1.54/0.84 % (2898216)------------------------------ 1.54/0.84 % (2898216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.54/0.84 % (2898216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.54/0.84 % (2898216)CaDiCaL version: 2.1.3 1.54/0.84 % (2898216)Termination reason: Instruction limit 1.54/0.84 % (2898216)Termination phase: Saturation 1.54/0.84 % (2898216)Time elapsed: 0.034 s 1.54/0.84 % (2898216)Peak memory usage: 12 MB 1.54/0.84 % (2898216)Instructions burned: 88 (million) 1.54/0.84 % (2898199)Instruction limit reached! 1.54/0.84 % (2898199)------------------------------ 1.54/0.84 % (2898199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.54/0.84 % (2898199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.54/0.84 % (2898199)CaDiCaL version: 2.1.3 1.54/0.84 % (2898199)Termination reason: Instruction limit 1.54/0.84 % (2898199)Termination phase: Property scanning 1.54/0.84 % (2898199)Time elapsed: 0.122 s 1.54/0.84 % (2898199)Peak memory usage: 13 MB 1.54/0.84 % (2898199)Instructions burned: 157 (million) 1.54/0.84 % (2898225)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3512583600:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/25Mi) 1.54/0.84 % (2898222)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4273808444:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/38Mi) 1.54/0.84 % (2898229)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3755632639:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 1.54/0.84 % (2898229)Instruction limit reached! 1.54/0.84 % (2898229)------------------------------ 1.54/0.84 % (2898229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.54/0.84 % (2898229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.54/0.84 % (2898229)CaDiCaL version: 2.1.3 1.54/0.84 % (2898229)Termination reason: Instruction limit 1.54/0.84 % (2898229)Termination phase: shuffling 1.54/0.84 % (2898229)Time elapsed: 0.007 s 1.54/0.84 % (2898229)Peak memory usage: 10 MB 1.88/0.95 % (2898229)Instructions burned: 16 (million) 1.88/0.95 % (2898225)Instruction limit reached! 1.88/0.95 % (2898225)------------------------------ 1.88/0.95 % (2898225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.88/0.95 % (2898225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.88/0.95 % (2898225)CaDiCaL version: 2.1.3 1.88/0.95 % (2898225)Termination reason: Instruction limit 1.88/0.95 % (2898225)Termination phase: Property scanning 1.88/0.95 % (2898225)Time elapsed: 0.021 s 1.88/0.95 % (2898225)Peak memory usage: 10 MB 1.88/0.95 % (2898225)Instructions burned: 26 (million) 1.88/0.95 % (2898228)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1968677915:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 1.88/0.95 % (2898222)Instruction limit reached! 1.88/0.95 % (2898222)------------------------------ 1.88/0.95 % (2898222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.88/0.95 % (2898222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.88/0.95 % (2898222)CaDiCaL version: 2.1.3 1.88/0.95 % (2898222)Termination reason: Instruction limit 1.88/0.95 % (2898222)Termination phase: Preprocessing 3 1.88/0.95 % (2898222)Time elapsed: 0.030 s 1.88/0.95 % (2898222)Peak memory usage: 11 MB 1.88/0.95 % (2898222)Instructions burned: 38 (million) 1.88/0.95 % (2898233)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2807097845:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1797 on theBenchmark for (1797ds/2Mi) 1.88/0.95 % (2898233)Instruction limit reached! 1.88/0.95 % (2898233)------------------------------ 1.88/0.95 % (2898233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.88/0.95 % (2898233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.88/0.95 % (2898233)CaDiCaL version: 2.1.3 1.88/0.95 % (2898233)Termination reason: Instruction limit 1.88/0.95 % (2898233)Termination phase: shuffling 1.88/0.95 % (2898233)Time elapsed: 0.003 s 1.88/0.95 % (2898233)Peak memory usage: 9 MB 1.88/0.95 % (2898233)Instructions burned: 2 (million) 1.88/0.95 % (2898226)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1625795468:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 1.88/0.95 % (2898234)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1449209463:i=26:ep=R:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/26Mi) 1.88/0.95 % (2898226)Instruction limit reached! 1.88/0.95 % (2898226)------------------------------ 1.88/0.95 % (2898226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.88/0.95 % (2898226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.88/0.95 % (2898226)CaDiCaL version: 2.1.3 1.88/0.95 % (2898226)Termination reason: Instruction limit 1.88/0.95 % (2898226)Termination phase: shuffling 1.88/0.95 % (2898226)Time elapsed: 0.012 s 1.88/0.95 % (2898226)Peak memory usage: 10 MB 1.88/0.95 % (2898226)Instructions burned: 14 (million) 1.88/0.95 % (2898234)Instruction limit reached! 1.88/0.95 % (2898234)------------------------------ 1.88/0.95 % (2898234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.88/0.95 % (2898234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.88/0.95 % (2898234)CaDiCaL version: 2.1.3 1.88/0.95 % (2898234)Termination reason: Instruction limit 1.88/0.95 % (2898234)Termination phase: shuffling 1.88/0.95 % (2898234)Time elapsed: 0.011 s 1.88/0.95 % (2898234)Peak memory usage: 10 MB 1.88/0.95 % (2898234)Instructions burned: 27 (million) 1.88/0.95 % (2898236)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1009366677:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1797 on theBenchmark for (1797ds/23Mi) 1.88/0.95 % (2898236)Instruction limit reached! 1.88/0.95 % (2898236)------------------------------ 1.88/0.95 % (2898236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.88/0.95 % (2898236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.88/0.95 % (2898236)CaDiCaL version: 2.1.3 1.88/0.95 % (2898236)Termination reason: Instruction limit 1.88/0.95 % (2898236)Termination phase: Property scanning 1.88/0.95 % (2898236)Time elapsed: 0.019 s 1.88/0.95 % (2898236)Peak memory usage: 10 MB 1.88/0.95 % (2898236)Instructions burned: 25 (million) 3.36/1.05 % (2898238)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4012563122:cond=on:i=60:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/60Mi) 3.36/1.05 % (2898241)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 3.36/1.05 % (2898241)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 3.36/1.05 % (2898242)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 3.36/1.05 % (2898241)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=4085810546:i=14:add=off:nm=40:rtra=on:rawr=on_1797 on theBenchmark for (1797ds/14Mi) 3.36/1.05 % (2898241)Instruction limit reached! 3.36/1.05 % (2898241)------------------------------ 3.36/1.05 % (2898241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.36/1.05 % (2898241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.36/1.05 % (2898241)CaDiCaL version: 2.1.3 3.36/1.05 % (2898241)Termination reason: Instruction limit 3.36/1.05 % (2898241)Termination phase: shuffling 3.36/1.05 % (2898241)Time elapsed: 0.007 s 3.36/1.05 % (2898241)Peak memory usage: 10 MB 3.36/1.05 % (2898241)Instructions burned: 15 (million) 3.36/1.05 % (2898242)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=4087948089:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1797 on theBenchmark for (1797ds/8Mi) 3.36/1.05 % (2898242)Instruction limit reached! 3.36/1.05 % (2898242)------------------------------ 3.36/1.05 % (2898242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.36/1.05 % (2898242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.36/1.05 % (2898242)CaDiCaL version: 2.1.3 3.36/1.05 % (2898242)Termination reason: Instruction limit 3.36/1.05 % (2898242)Termination phase: shuffling 3.36/1.05 % (2898242)Time elapsed: 0.012 s 3.36/1.05 % (2898242)Peak memory usage: 9 MB 3.36/1.05 % (2898242)Instructions burned: 10 (million) 3.36/1.05 % (2898245)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=761676212:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1797 on theBenchmark for (1797ds/31Mi) 3.36/1.05 % (2898248)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4094569193:i=7:hud=5:bd=preordered:rtra=on:bet=on_1797 on theBenchmark for (1797ds/7Mi) 3.36/1.05 % (2898248)Instruction limit reached! 3.36/1.05 % (2898248)------------------------------ 3.36/1.05 % (2898248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.36/1.05 % (2898248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.36/1.05 % (2898248)CaDiCaL version: 2.1.3 3.36/1.05 % (2898248)Termination reason: Instruction limit 3.36/1.05 % (2898248)Termination phase: shuffling 3.36/1.05 % (2898248)Time elapsed: 0.004 s 3.36/1.05 % (2898248)Peak memory usage: 9 MB 3.36/1.05 % (2898248)Instructions burned: 9 (million) 3.36/1.05 % (2898238)Instruction limit reached! 3.36/1.05 % (2898238)------------------------------ 3.36/1.05 % (2898238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.36/1.05 % (2898238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.36/1.05 % (2898238)CaDiCaL version: 2.1.3 3.36/1.05 % (2898238)Termination reason: Instruction limit 3.36/1.05 % (2898238)Termination phase: Preprocessing 3 3.36/1.05 % (2898238)Time elapsed: 0.050 s 3.36/1.05 % (2898238)Peak memory usage: 11 MB 3.36/1.05 % (2898238)Instructions burned: 60 (million) 3.36/1.05 % (2898249)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1243098457:i=23:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/23Mi) 3.36/1.05 % (2898245)Instruction limit reached! 3.36/1.05 % (2898245)------------------------------ 3.36/1.05 % (2898245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.36/1.05 % (2898245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.36/1.05 % (2898245)CaDiCaL version: 2.1.3 3.89/1.16 % (2898245)Termination reason: Instruction limit 3.89/1.16 % (2898245)Termination phase: shuffling 3.89/1.16 % (2898245)Time elapsed: 0.023 s 3.89/1.16 % (2898245)Peak memory usage: 10 MB 3.89/1.16 % (2898245)Instructions burned: 31 (million) 3.89/1.16 % (2898249)Instruction limit reached! 3.89/1.16 % (2898249)------------------------------ 3.89/1.16 % (2898249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.89/1.16 % (2898249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.89/1.16 % (2898249)CaDiCaL version: 2.1.3 3.89/1.16 % (2898249)Termination reason: Instruction limit 3.89/1.16 % (2898249)Termination phase: shuffling 3.89/1.16 % (2898249)Time elapsed: 0.015 s 3.89/1.16 % (2898249)Peak memory usage: 10 MB 3.89/1.16 % (2898249)Instructions burned: 25 (million) 3.89/1.16 % (2898253)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2164373300:i=1240:rtra=on:ixr=off_1796 on theBenchmark for (1796ds/1240Mi) 3.89/1.16 % (2898252)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=694569258:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1796 on theBenchmark for (1796ds/20Mi) 3.89/1.16 % (2898256)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2430076788:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1796 on theBenchmark for (1796ds/193Mi) 3.89/1.16 % (2898252)Instruction limit reached! 3.89/1.16 % (2898252)------------------------------ 3.89/1.16 % (2898252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.89/1.16 % (2898252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.89/1.16 % (2898252)CaDiCaL version: 2.1.3 3.89/1.16 % (2898252)Termination reason: Instruction limit 3.89/1.16 % (2898252)Termination phase: shuffling 3.89/1.16 % (2898252)Time elapsed: 0.009 s 3.89/1.16 % (2898252)Peak memory usage: 10 MB 3.89/1.16 % (2898252)Instructions burned: 21 (million) 3.89/1.16 % (2898255)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3736561669:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1796 on theBenchmark for (1796ds/143Mi) 3.89/1.16 % (2898223)Instruction limit reached! 3.89/1.16 % (2898223)------------------------------ 3.89/1.16 % (2898223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.89/1.16 % (2898223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.89/1.16 % (2898223)CaDiCaL version: 2.1.3 3.89/1.16 % (2898223)Termination reason: Instruction limit 3.89/1.16 % (2898223)Termination phase: Saturation 3.89/1.16 % (2898223)Time elapsed: 0.221 s 3.89/1.16 % (2898223)Peak memory usage: 14 MB 3.89/1.16 % (2898223)Instructions burned: 249 (million) 3.89/1.16 % (2898260)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4109955468:i=42:hud=10:rtra=on_1796 on theBenchmark for (1796ds/42Mi) 3.89/1.16 % (2898262)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 3.89/1.16 % (2898262)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=402943436:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1795 on theBenchmark for (1795ds/7Mi) 3.89/1.16 % (2898262)Instruction limit reached! 3.89/1.16 % (2898262)------------------------------ 3.89/1.16 % (2898262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.89/1.16 % (2898262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.89/1.16 % (2898262)CaDiCaL version: 2.1.3 3.89/1.16 % (2898262)Termination reason: Instruction limit 3.89/1.16 % (2898262)Termination phase: shuffling 3.89/1.16 % (2898262)Time elapsed: 0.004 s 3.89/1.16 % (2898262)Peak memory usage: 10 MB 3.89/1.16 % (2898262)Instructions burned: 7 (million) 3.89/1.16 % (2898260)Instruction limit reached! 3.89/1.16 % (2898260)------------------------------ 3.89/1.16 % (2898260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.89/1.16 % (2898260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.89/1.16 % (2898260)CaDiCaL version: 2.1.3 3.89/1.16 % (2898260)Termination reason: Instruction limit 3.89/1.16 % (2898260)Termination phase: Preprocessing 1 3.89/1.16 % (2898260)Time elapsed: 0.035 s 3.89/1.16 % (2898260)Peak memory usage: 11 MB 3.89/1.16 % (2898260)Instructions burned: 42 (million) 3.89/1.16 % (2898256)Instruction limit reached! 3.89/1.16 % (2898256)------------------------------ 3.89/1.16 % (2898256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.09/1.29 % (2898256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.09/1.29 % (2898256)CaDiCaL version: 2.1.3 4.09/1.29 % (2898256)Termination reason: Instruction limit 4.09/1.29 % (2898256)Termination phase: Property scanning 4.09/1.29 % (2898256)Time elapsed: 0.085 s 4.09/1.29 % (2898256)Peak memory usage: 13 MB 4.09/1.29 % (2898256)Instructions burned: 193 (million) 4.09/1.29 % (2898265)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=791702519:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1795 on theBenchmark for (1795ds/181Mi) 4.09/1.29 % (2898267)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 4.09/1.29 % (2898267)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1009275698:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1795 on theBenchmark for (1795ds/6Mi) 4.09/1.29 % (2898267)Instruction limit reached! 4.09/1.29 % (2898267)------------------------------ 4.09/1.29 % (2898267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.09/1.29 % (2898267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.09/1.29 % (2898267)CaDiCaL version: 2.1.3 4.09/1.29 % (2898267)Termination reason: Instruction limit 4.09/1.29 % (2898267)Termination phase: shuffling 4.09/1.29 % (2898267)Time elapsed: 0.003 s 4.09/1.29 % (2898267)Peak memory usage: 10 MB 4.09/1.29 % (2898267)Instructions burned: 6 (million) 4.09/1.29 % (2898228)Instruction limit reached! 4.09/1.29 % (2898228)------------------------------ 4.09/1.29 % (2898228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.09/1.29 % (2898228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.09/1.29 % (2898228)CaDiCaL version: 2.1.3 4.09/1.29 % (2898228)Termination reason: Instruction limit 4.09/1.29 % (2898228)Termination phase: Saturation 4.09/1.29 % (2898228)Time elapsed: 0.255 s 4.09/1.29 % (2898228)Peak memory usage: 15 MB 4.09/1.29 % (2898228)Instructions burned: 327 (million) 4.09/1.29 % (2898266)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=3771441827:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1795 on theBenchmark for (1795ds/169Mi) 4.09/1.29 % (2898255)Instruction limit reached! 4.09/1.29 % (2898255)------------------------------ 4.09/1.29 % (2898255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.09/1.29 % (2898255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.09/1.29 % (2898255)CaDiCaL version: 2.1.3 4.09/1.29 % (2898255)Termination reason: Instruction limit 4.09/1.29 % (2898255)Termination phase: Function definition elimination 4.09/1.29 % (2898255)Time elapsed: 0.113 s 4.09/1.29 % (2898255)Peak memory usage: 13 MB 4.09/1.29 % (2898255)Instructions burned: 143 (million) 4.09/1.29 % (2898270)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3867389910:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1795 on theBenchmark for (1795ds/22Mi) 4.09/1.29 % (2898270)Instruction limit reached! 4.09/1.29 % (2898270)------------------------------ 4.09/1.29 % (2898270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.09/1.29 % (2898270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.09/1.29 % (2898270)CaDiCaL version: 2.1.3 4.09/1.29 % (2898270)Termination reason: Instruction limit 4.09/1.29 % (2898270)Termination phase: shuffling 4.09/1.29 % (2898270)Time elapsed: 0.019 s 4.09/1.29 % (2898270)Peak memory usage: 10 MB 4.09/1.29 % (2898270)Instructions burned: 22 (million) 4.09/1.29 % (2898271)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3899686869:i=19:add=on:rtra=on_1795 on theBenchmark for (1795ds/19Mi) 4.09/1.29 % (2898273)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=755450368:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1795 on theBenchmark for (1795ds/316Mi) 4.09/1.29 % (2898271)Instruction limit reached! 4.09/1.29 % (2898271)------------------------------ 4.09/1.29 % (2898271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.98/1.44 % (2898271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.98/1.44 % (2898271)CaDiCaL version: 2.1.3 4.98/1.44 % (2898271)Termination reason: Instruction limit 4.98/1.44 % (2898271)Termination phase: shuffling 4.98/1.44 % (2898271)Time elapsed: 0.009 s 4.98/1.44 % (2898271)Peak memory usage: 10 MB 4.98/1.44 % (2898271)Instructions burned: 20 (million) 4.98/1.44 % (2898278)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=1062498781:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1794 on theBenchmark for (1794ds/45Mi) 4.98/1.44 % (2898275)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=491440207:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1794 on theBenchmark for (1794ds/853Mi) 4.98/1.44 % (2898278)Instruction limit reached! 4.98/1.44 % (2898278)------------------------------ 4.98/1.44 % (2898278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.98/1.44 % (2898278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.98/1.44 % (2898278)CaDiCaL version: 2.1.3 4.98/1.44 % (2898278)Termination reason: Instruction limit 4.98/1.44 % (2898278)Termination phase: SInE selection 4.98/1.44 % (2898278)Time elapsed: 0.020 s 4.98/1.44 % (2898278)Peak memory usage: 10 MB 4.98/1.44 % (2898278)Instructions burned: 47 (million) 4.98/1.44 % (2898265)Instruction limit reached! 4.98/1.44 % (2898265)------------------------------ 4.98/1.44 % (2898265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.98/1.44 % (2898265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.98/1.44 % (2898265)CaDiCaL version: 2.1.3 4.98/1.44 % (2898265)Termination reason: Instruction limit 4.98/1.44 % (2898265)Termination phase: Saturation 4.98/1.44 % (2898265)Time elapsed: 0.122 s 4.98/1.44 % (2898265)Peak memory usage: 15 MB 4.98/1.44 % (2898265)Instructions burned: 181 (million) 4.98/1.44 % (2898281)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1092553568:i=480:rtra=on_1794 on theBenchmark for (1794ds/480Mi) 4.98/1.44 % (2898282)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1571051268:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1794 on theBenchmark for (1794ds/21Mi) 4.98/1.44 % (2898196)Instruction limit reached! 4.98/1.44 % (2898196)------------------------------ 4.98/1.44 % (2898196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.98/1.44 % (2898196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.98/1.44 % (2898196)CaDiCaL version: 2.1.3 4.98/1.44 % (2898196)Termination reason: Instruction limit 4.98/1.44 % (2898196)Termination phase: Saturation 4.98/1.44 % (2898196)Time elapsed: 0.562 s 4.98/1.44 % (2898196)Peak memory usage: 18 MB 4.98/1.44 % (2898196)Instructions burned: 634 (million) 4.98/1.44 % (2898266)Instruction limit reached! 4.98/1.44 % (2898266)------------------------------ 4.98/1.44 % (2898266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.98/1.44 % (2898266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.98/1.44 % (2898266)CaDiCaL version: 2.1.3 4.98/1.44 % (2898266)Termination reason: Instruction limit 4.98/1.44 % (2898266)Termination phase: Property scanning 4.98/1.44 % (2898266)Time elapsed: 0.130 s 4.98/1.44 % (2898266)Peak memory usage: 13 MB 4.98/1.44 % (2898266)Instructions burned: 170 (million) 4.98/1.44 % (2898282)Instruction limit reached! 4.98/1.44 % (2898282)------------------------------ 4.98/1.44 % (2898282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.98/1.44 % (2898282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.98/1.44 % (2898282)CaDiCaL version: 2.1.3 4.98/1.44 % (2898282)Termination reason: Instruction limit 4.98/1.44 % (2898282)Termination phase: shuffling 4.98/1.44 % (2898282)Time elapsed: 0.010 s 4.98/1.44 % (2898282)Peak memory usage: 10 MB 4.98/1.44 % (2898282)Instructions burned: 21 (million) 4.98/1.44 % (2898285)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 4.98/1.44 % (2898285)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3724238597:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1793 on theBenchmark for (1793ds/200Mi) 5.75/1.62 % (2898286)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2577035933:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1793 on theBenchmark for (1793ds/13Mi) 5.75/1.62 % (2898286)Instruction limit reached! 5.75/1.62 % (2898286)------------------------------ 5.75/1.62 % (2898286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.75/1.62 % (2898286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.75/1.62 % (2898286)CaDiCaL version: 2.1.3 5.75/1.62 % (2898286)Termination reason: Instruction limit 5.75/1.62 % (2898286)Termination phase: shuffling 5.75/1.62 % (2898286)Time elapsed: 0.011 s 5.75/1.62 % (2898286)Peak memory usage: 10 MB 5.75/1.62 % (2898286)Instructions burned: 14 (million) 5.75/1.62 % (2898287)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=2242144483:i=66:s2at=3:nm=2:rtra=on:rawr=on_1793 on theBenchmark for (1793ds/66Mi) 5.75/1.62 % (2898290)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1031717855:i=51:fsr=off:rtra=on_1793 on theBenchmark for (1793ds/51Mi) 5.75/1.62 % (2898290)Instruction limit reached! 5.75/1.62 % (2898290)------------------------------ 5.75/1.62 % (2898290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.75/1.62 % (2898290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.75/1.62 % (2898290)CaDiCaL version: 2.1.3 5.75/1.62 % (2898290)Termination reason: Instruction limit 5.75/1.62 % (2898290)Termination phase: Preprocessing 3 5.75/1.62 % (2898290)Time elapsed: 0.022 s 5.75/1.62 % (2898290)Peak memory usage: 11 MB 5.75/1.62 % (2898290)Instructions burned: 51 (million) 5.75/1.62 % (2898287)Instruction limit reached! 5.75/1.62 % (2898287)------------------------------ 5.75/1.62 % (2898287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.75/1.62 % (2898287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.75/1.62 % (2898287)CaDiCaL version: 2.1.3 5.75/1.62 % (2898287)Termination reason: Instruction limit 5.75/1.62 % (2898287)Termination phase: SInE selection 5.75/1.62 % (2898287)Time elapsed: 0.049 s 5.75/1.62 % (2898287)Peak memory usage: 11 MB 5.75/1.62 % (2898287)Instructions burned: 66 (million) 5.75/1.62 % (2898285)Instruction limit reached! 5.75/1.62 % (2898285)------------------------------ 5.75/1.62 % (2898285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.75/1.62 % (2898285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.75/1.62 % (2898285)CaDiCaL version: 2.1.3 5.75/1.62 % (2898285)Termination reason: Instruction limit 5.75/1.62 % (2898285)Termination phase: Saturation 5.75/1.62 % (2898285)Time elapsed: 0.097 s 5.75/1.62 % (2898285)Peak memory usage: 13 MB 5.75/1.62 % (2898285)Instructions burned: 201 (million) 5.75/1.62 % (2898293)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2745310558:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1792 on theBenchmark for (1792ds/31Mi) 5.75/1.62 % (2898295)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=2153202791:cond=on:i=34:hud=10:nm=10:rtra=on_1792 on theBenchmark for (1792ds/34Mi) 5.75/1.62 % (2898294)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4110202389:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1792 on theBenchmark for (1792ds/137Mi) 5.75/1.62 % (2898281)Refutation not found, incomplete strategy 5.75/1.62 % (2898281)------------------------------ 5.75/1.62 % (2898281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.75/1.62 % (2898281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.75/1.62 % (2898281)CaDiCaL version: 2.1.3 5.75/1.62 % (2898281)Termination reason: Refutation not found, incomplete strategy 5.75/1.62 % (2898281)Time elapsed: 0.179 s 5.75/1.62 % (2898281)Peak memory usage: 16 MB 5.75/1.62 % (2898281)Instructions burned: 278 (million) 5.75/1.62 % (2898281)------------------------------ 5.75/1.62 % (2898281)------------------------------ 5.75/1.62 % (2898295)Instruction limit reached! 5.75/1.62 % (2898295)------------------------------ 5.75/1.62 % (2898295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.08/1.81 % (2898295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.08/1.81 % (2898295)CaDiCaL version: 2.1.3 7.08/1.81 % (2898295)Termination reason: Instruction limit 7.08/1.81 % (2898295)Termination phase: Property scanning 7.08/1.81 % (2898295)Time elapsed: 0.016 s 7.08/1.81 % (2898295)Peak memory usage: 10 MB 7.08/1.81 % (2898295)Instructions burned: 35 (million) 7.08/1.81 % (2898273)Instruction limit reached! 7.08/1.81 % (2898273)------------------------------ 7.08/1.81 % (2898273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.08/1.81 % (2898273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.08/1.81 % (2898273)CaDiCaL version: 2.1.3 7.08/1.81 % (2898273)Termination reason: Instruction limit 7.08/1.81 % (2898273)Termination phase: Saturation 7.08/1.81 % (2898273)Time elapsed: 0.259 s 7.08/1.81 % (2898273)Peak memory usage: 15 MB 7.08/1.81 % (2898273)Instructions burned: 316 (million) 7.08/1.81 % (2898293)Instruction limit reached! 7.08/1.81 % (2898293)------------------------------ 7.08/1.81 % (2898293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.08/1.81 % (2898293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.08/1.81 % (2898293)CaDiCaL version: 2.1.3 7.08/1.81 % (2898293)Termination reason: Instruction limit 7.08/1.81 % (2898293)Termination phase: shuffling 7.08/1.81 % (2898293)Time elapsed: 0.034 s 7.08/1.81 % (2898293)Peak memory usage: 10 MB 7.08/1.81 % (2898293)Instructions burned: 31 (million) 7.08/1.81 % (2898253)Instruction limit reached! 7.08/1.81 % (2898253)------------------------------ 7.08/1.81 % (2898253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.08/1.81 % (2898253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.08/1.81 % (2898253)CaDiCaL version: 2.1.3 7.08/1.81 % (2898253)Termination reason: Instruction limit 7.08/1.81 % (2898253)Termination phase: Saturation 7.08/1.81 % (2898253)Time elapsed: 0.456 s 7.08/1.81 % (2898253)Peak memory usage: 12 MB 7.08/1.81 % (2898253)Instructions burned: 1243 (million) 7.08/1.81 % (2898300)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 7.08/1.81 % (2898299)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1600566253:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1792 on theBenchmark for (1792ds/67Mi) 7.08/1.81 % (2898300)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2220415892:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1792 on theBenchmark for (1792ds/180Mi) 7.08/1.81 % (2898301)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1896109239:st=2:i=246:sd=3:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/246Mi) 7.08/1.81 % (2898303)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2749501928:i=427:sd=1:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/427Mi) 7.08/1.81 % (2898302)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=754242910:cond=on:i=96:bd=all:rtra=on_1791 on theBenchmark for (1791ds/96Mi) 7.08/1.81 % (2898299)Instruction limit reached! 7.08/1.81 % (2898299)------------------------------ 7.08/1.81 % (2898299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.08/1.81 % (2898299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.08/1.81 % (2898299)CaDiCaL version: 2.1.3 7.08/1.81 % (2898299)Termination reason: Instruction limit 7.08/1.81 % (2898299)Termination phase: Preprocessing 3 7.08/1.81 % (2898299)Time elapsed: 0.056 s 7.08/1.81 % (2898299)Peak memory usage: 11 MB 7.08/1.81 % (2898299)Instructions burned: 67 (million) 7.08/1.81 % (2898294)Instruction limit reached! 7.08/1.81 % (2898294)------------------------------ 7.08/1.81 % (2898294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.08/1.81 % (2898294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.08/1.81 % (2898294)CaDiCaL version: 2.1.3 7.08/1.81 % (2898294)Termination reason: Instruction limit 7.08/1.81 % (2898294)Termination phase: Property scanning 7.08/1.81 % (2898294)Time elapsed: 0.150 s 7.08/1.81 % (2898294)Peak memory usage: 13 MB 7.08/1.81 % (2898294)Instructions burned: 137 (million) 7.08/1.81 % (2898300)Instruction limit reached! 7.08/1.81 % (2898300)------------------------------ 7.08/1.81 % (2898300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.97 % (2898300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.97 % (2898300)CaDiCaL version: 2.1.3 7.52/1.97 % (2898300)Termination reason: Instruction limit 7.52/1.97 % (2898300)Termination phase: Saturation 7.52/1.97 % (2898300)Time elapsed: 0.111 s 7.52/1.97 % (2898300)Peak memory usage: 12 MB 7.52/1.97 % (2898300)Instructions burned: 181 (million) 7.52/1.97 % (2898310)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=136447197:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1790 on theBenchmark for (1790ds/515Mi) 7.52/1.97 % (2898302)Instruction limit reached! 7.52/1.97 % (2898302)------------------------------ 7.52/1.97 % (2898302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.97 % (2898302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.97 % (2898302)CaDiCaL version: 2.1.3 7.52/1.97 % (2898302)Termination reason: Instruction limit 7.52/1.97 % (2898302)Termination phase: Property scanning 7.52/1.97 % (2898302)Time elapsed: 0.081 s 7.52/1.97 % (2898302)Peak memory usage: 13 MB 7.52/1.97 % (2898302)Instructions burned: 97 (million) 7.52/1.97 % (2898309)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3168342568:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/874Mi) 7.52/1.97 % (2898311)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1674867510:st=1.5:i=130:rtra=on:ss=axioms_1790 on theBenchmark for (1790ds/130Mi) 7.52/1.97 % (2898313)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3657267180:i=44:ep=R:rtra=on:ntd=on_1790 on theBenchmark for (1790ds/44Mi) 7.52/1.97 % (2898313)Instruction limit reached! 7.52/1.97 % (2898313)------------------------------ 7.52/1.97 % (2898313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.97 % (2898313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.97 % (2898313)CaDiCaL version: 2.1.3 7.52/1.97 % (2898313)Termination reason: Instruction limit 7.52/1.97 % (2898313)Termination phase: Property scanning 7.52/1.97 % (2898313)Time elapsed: 0.034 s 7.52/1.97 % (2898313)Peak memory usage: 10 MB 7.52/1.97 % (2898313)Instructions burned: 44 (million) 7.52/1.97 % (2898303)Instruction limit reached! 7.52/1.97 % (2898303)------------------------------ 7.52/1.97 % (2898303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.97 % (2898303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.97 % (2898303)CaDiCaL version: 2.1.3 7.52/1.97 % (2898303)Termination reason: Instruction limit 7.52/1.97 % (2898303)Termination phase: Saturation 7.52/1.97 % (2898303)Time elapsed: 0.171 s 7.52/1.97 % (2898303)Peak memory usage: 14 MB 7.52/1.97 % (2898303)Instructions burned: 429 (million) 7.52/1.97 % (2898318)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3669210115:i=450:rtra=on:ixr=off:ntd=on_1789 on theBenchmark for (1789ds/450Mi) 7.52/1.97 % (2898317)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4081718382:s2a=on:i=571:nm=16:rtra=on_1789 on theBenchmark for (1789ds/571Mi) 7.52/1.97 % (2898301)Instruction limit reached! 7.52/1.97 % (2898301)------------------------------ 7.52/1.97 % (2898301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.97 % (2898301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.97 % (2898301)CaDiCaL version: 2.1.3 7.52/1.97 % (2898301)Termination reason: Instruction limit 7.52/1.97 % (2898301)Termination phase: Saturation 7.52/1.97 % (2898301)Time elapsed: 0.235 s 7.52/1.97 % (2898301)Peak memory usage: 15 MB 7.52/1.97 % (2898301)Instructions burned: 247 (million) 7.52/1.97 % (2898311)Instruction limit reached! 7.52/1.97 % (2898311)------------------------------ 7.52/1.97 % (2898311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.52/1.97 % (2898311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.52/1.97 % (2898311)CaDiCaL version: 2.1.3 7.52/1.97 % (2898311)Termination reason: Instruction limit 7.52/1.97 % (2898311)Termination phase: Saturation 7.52/1.97 % (2898311)Time elapsed: 0.104 s 7.52/1.97 % (2898311)Peak memory usage: 13 MB 7.52/1.97 % (2898311)Instructions burned: 130 (million) 7.52/1.97 % (2898322)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=223030107:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1788 on theBenchmark for (1788ds/65Mi) 9.60/2.14 % (2898321)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3350596307:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/95Mi) 9.60/2.14 % (2898322)Instruction limit reached! 9.60/2.14 % (2898322)------------------------------ 9.60/2.14 % (2898322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 9.60/2.14 % (2898322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 9.60/2.14 % (2898322)CaDiCaL version: 2.1.3 9.60/2.14 % (2898322)Termination reason: Instruction limit 9.60/2.14 % (2898322)Termination phase: Property scanning 9.60/2.14 % (2898322)Time elapsed: 0.029 s 9.60/2.14 % (2898322)Peak memory usage: 11 MB 9.60/2.14 % (2898322)Instructions burned: 67 (million) 9.60/2.14 % (2898325)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=3115894493: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_1788 on theBenchmark for (1788ds/105Mi) 9.60/2.14 % (2898321)Instruction limit reached! 9.60/2.14 % (2898321)------------------------------ 9.60/2.14 % (2898321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 9.60/2.14 % (2898321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 9.60/2.14 % (2898321)CaDiCaL version: 2.1.3 9.60/2.14 % (2898321)Termination reason: Instruction limit 9.60/2.14 % (2898321)Termination phase: Property scanning 9.60/2.14 % (2898321)Time elapsed: 0.076 s 9.60/2.14 % (2898321)Peak memory usage: 13 MB 9.60/2.14 % (2898321)Instructions burned: 95 (million) 9.60/2.14 % (2898325)Instruction limit reached! 9.60/2.14 % (2898325)------------------------------ 9.60/2.14 % (2898325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 9.60/2.14 % (2898325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 9.60/2.14 % (2898325)CaDiCaL version: 2.1.3 9.60/2.14 % (2898325)Termination reason: Instruction limit 9.60/2.14 % (2898325)Termination phase: Saturation 9.60/2.14 % (2898325)Time elapsed: 0.045 s 9.60/2.14 % (2898325)Peak memory usage: 12 MB 9.60/2.14 % (2898325)Instructions burned: 106 (million) 9.60/2.14 % (2898328)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2796423365:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1787 on theBenchmark for (1787ds/375Mi) 9.60/2.14 % (2898327)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=1394145676:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1787 on theBenchmark for (1787ds/5755Mi) 9.60/2.14 % (2898275)Instruction limit reached! 9.60/2.14 % (2898275)------------------------------ 9.60/2.14 % (2898275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 9.60/2.14 % (2898275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 9.60/2.14 % (2898275)CaDiCaL version: 2.1.3 9.60/2.14 % (2898275)Termination reason: Instruction limit 9.60/2.14 % (2898275)Termination phase: Saturation 9.60/2.14 % (2898275)Time elapsed: 0.691 s 9.60/2.14 % (2898275)Peak memory usage: 19 MB 9.60/2.14 % (2898275)Instructions burned: 853 (million) 9.60/2.14 % (2898318)Instruction limit reached! 9.60/2.14 % (2898318)------------------------------ 9.60/2.14 % (2898318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 9.60/2.14 % (2898318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 9.60/2.14 % (2898318)CaDiCaL version: 2.1.3 9.60/2.14 % (2898318)Termination reason: Instruction limit 9.60/2.14 % (2898318)Termination phase: Saturation 9.60/2.14 % (2898318)Time elapsed: 0.192 s 9.60/2.14 % (2898318)Peak memory usage: 16 MB 9.60/2.14 % (2898318)Instructions burned: 451 (million) 9.60/2.14 % (2898331)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4119802407:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1787 on theBenchmark for (1787ds/495Mi) 9.60/2.14 % (2898332)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=1819337846:cond=on:i=34:hud=10:nm=10:rtra=on_1787 on theBenchmark for (1787ds/34Mi) 10.69/2.34 % (2898310)Instruction limit reached! 10.69/2.34 % (2898310)------------------------------ 10.69/2.34 % (2898310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898310)CaDiCaL version: 2.1.3 10.69/2.34 % (2898310)Termination reason: Instruction limit 10.69/2.34 % (2898310)Termination phase: Saturation 10.69/2.34 % (2898310)Time elapsed: 0.365 s 10.69/2.34 % (2898310)Peak memory usage: 18 MB 10.69/2.34 % (2898310)Instructions burned: 515 (million) 10.69/2.34 % (2898332)Instruction limit reached! 10.69/2.34 % (2898332)------------------------------ 10.69/2.34 % (2898332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898332)CaDiCaL version: 2.1.3 10.69/2.34 % (2898332)Termination reason: Instruction limit 10.69/2.34 % (2898332)Termination phase: Property scanning 10.69/2.34 % (2898332)Time elapsed: 0.028 s 10.69/2.34 % (2898332)Peak memory usage: 10 MB 10.69/2.34 % (2898332)Instructions burned: 34 (million) 10.69/2.34 % (2898335)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4051686569:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1786 on theBenchmark for (1786ds/91Mi) 10.69/2.34 % (2898336)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=1327177970:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1786 on theBenchmark for (1786ds/66Mi) 10.69/2.34 % (2898336)Instruction limit reached! 10.69/2.34 % (2898336)------------------------------ 10.69/2.34 % (2898336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898336)CaDiCaL version: 2.1.3 10.69/2.34 % (2898336)Termination reason: Instruction limit 10.69/2.34 % (2898336)Termination phase: Saturation 10.69/2.34 % (2898336)Time elapsed: 0.028 s 10.69/2.34 % (2898336)Peak memory usage: 12 MB 10.69/2.34 % (2898336)Instructions burned: 68 (million) 10.69/2.34 % (2898339)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3293619367:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1785 on theBenchmark for (1785ds/22Mi) 10.69/2.34 % (2898328)Instruction limit reached! 10.69/2.34 % (2898328)------------------------------ 10.69/2.34 % (2898328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898328)CaDiCaL version: 2.1.3 10.69/2.34 % (2898328)Termination reason: Instruction limit 10.69/2.34 % (2898328)Termination phase: Saturation 10.69/2.34 % (2898328)Time elapsed: 0.214 s 10.69/2.34 % (2898328)Peak memory usage: 16 MB 10.69/2.34 % (2898328)Instructions burned: 376 (million) 10.69/2.34 % (2898339)Instruction limit reached! 10.69/2.34 % (2898339)------------------------------ 10.69/2.34 % (2898339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898339)CaDiCaL version: 2.1.3 10.69/2.34 % (2898339)Termination reason: Instruction limit 10.69/2.34 % (2898339)Termination phase: shuffling 10.69/2.34 % (2898339)Time elapsed: 0.010 s 10.69/2.34 % (2898339)Peak memory usage: 10 MB 10.69/2.34 % (2898339)Instructions burned: 24 (million) 10.69/2.34 % (2898335)Instruction limit reached! 10.69/2.34 % (2898335)------------------------------ 10.69/2.34 % (2898335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898335)CaDiCaL version: 2.1.3 10.69/2.34 % (2898335)Termination reason: Instruction limit 10.69/2.34 % (2898335)Termination phase: Preprocessing 3 10.69/2.34 % (2898335)Time elapsed: 0.076 s 10.69/2.34 % (2898335)Peak memory usage: 12 MB 10.69/2.34 % (2898335)Instructions burned: 91 (million) 10.69/2.34 % (2898317)Refutation not found, incomplete strategy 10.69/2.34 % (2898317)------------------------------ 10.69/2.34 % (2898317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 10.69/2.34 % (2898317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 10.69/2.34 % (2898317)CaDiCaL version: 2.1.3 10.69/2.34 % (2898317)Termination reason: Refutation not found, incomplete strategy 12.83/2.71 % (2898317)Time elapsed: 0.389 s 12.83/2.71 % (2898317)Peak memory usage: 17 MB 12.83/2.71 % (2898317)Instructions burned: 453 (million) 12.83/2.71 % (2898317)------------------------------ 12.83/2.71 % (2898317)------------------------------ 12.83/2.71 % (2898341)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=1548514076:i=338:bd=all:ins=4:rtra=on_1785 on theBenchmark for (1785ds/338Mi) 12.83/2.71 % (2898343)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 12.83/2.71 % (2898343)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=3377645664:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1785 on theBenchmark for (1785ds/137Mi) 12.83/2.71 % (2898342)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2336202404:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1785 on theBenchmark for (1785ds/28Mi) 12.83/2.71 % (2898344)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=3327376724:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1785 on theBenchmark for (1785ds/340Mi) 12.83/2.71 % (2898342)Instruction limit reached! 12.83/2.71 % (2898342)------------------------------ 12.83/2.71 % (2898342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.71 % (2898342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.71 % (2898342)CaDiCaL version: 2.1.3 12.83/2.71 % (2898342)Termination reason: Instruction limit 12.83/2.71 % (2898342)Termination phase: Property scanning 12.83/2.71 % (2898342)Time elapsed: 0.023 s 12.83/2.71 % (2898342)Peak memory usage: 10 MB 12.83/2.71 % (2898342)Instructions burned: 29 (million) 12.83/2.71 % (2898309)Instruction limit reached! 12.83/2.71 % (2898309)------------------------------ 12.83/2.71 % (2898309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.71 % (2898309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.71 % (2898309)CaDiCaL version: 2.1.3 12.83/2.71 % (2898309)Termination reason: Instruction limit 12.83/2.71 % (2898309)Termination phase: Saturation 12.83/2.71 % (2898309)Time elapsed: 0.577 s 12.83/2.71 % (2898309)Peak memory usage: 19 MB 12.83/2.71 % (2898309)Instructions burned: 875 (million) 12.83/2.71 % (2898349)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=2324097289:i=227:sd=1:bd=all:rtra=on:ss=axioms_1784 on theBenchmark for (1784ds/227Mi) 12.83/2.71 % (2898343)Instruction limit reached! 12.83/2.71 % (2898343)------------------------------ 12.83/2.71 % (2898343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.71 % (2898343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.71 % (2898343)CaDiCaL version: 2.1.3 12.83/2.71 % (2898343)Termination reason: Instruction limit 12.83/2.71 % (2898343)Termination phase: Saturation 12.83/2.71 % (2898343)Time elapsed: 0.063 s 12.83/2.71 % (2898343)Peak memory usage: 12 MB 12.83/2.71 % (2898343)Instructions burned: 137 (million) 12.83/2.71 % (2898350)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 12.83/2.71 % (2898352)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=566202524:i=116:ep=RSTC:rtra=on:ntd=on_1784 on theBenchmark for (1784ds/116Mi) 12.83/2.71 % (2898350)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=1178338200:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1784 on theBenchmark for (1784ds/373Mi) 12.83/2.71 % (2898341)Instruction limit reached! 12.83/2.71 % (2898341)------------------------------ 12.83/2.71 % (2898341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.83/2.71 % (2898341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.83/2.71 % (2898341)CaDiCaL version: 2.1.3 12.83/2.71 % (2898341)Termination reason: Instruction limit 12.83/2.71 % (2898341)Termination phase: Saturation 12.83/2.71 % (2898341)Time elapsed: 0.139 s 12.83/2.71 % (2898341)Peak memory usage: 18 MB 12.83/2.71 % (2898341)Instructions burned: 340 (million) 12.83/2.71 % (2898352)Instruction limit reached! 12.83/2.71 % (2898352)------------------------------ 12.83/2.71 % (2898352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.37/3.02 % (2898352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.37/3.02 % (2898352)CaDiCaL version: 2.1.3 13.37/3.02 % (2898352)Termination reason: Instruction limit 13.37/3.02 % (2898352)Termination phase: Property scanning 13.37/3.02 % (2898352)Time elapsed: 0.054 s 13.37/3.02 % (2898352)Peak memory usage: 13 MB 13.37/3.02 % (2898352)Instructions burned: 116 (million) 13.37/3.02 % (2898356)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=559599647:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1783 on theBenchmark for (1783ds/270Mi) 13.37/3.02 % (2898349)Instruction limit reached! 13.37/3.02 % (2898349)------------------------------ 13.37/3.02 % (2898349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.37/3.02 % (2898349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.37/3.02 % (2898349)CaDiCaL version: 2.1.3 13.37/3.02 % (2898349)Termination reason: Instruction limit 13.37/3.02 % (2898349)Termination phase: Saturation 13.37/3.02 % (2898349)Time elapsed: 0.106 s 13.37/3.02 % (2898349)Peak memory usage: 14 MB 13.37/3.02 % (2898349)Instructions burned: 228 (million) 13.37/3.02 % (2898355)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1207406049:i=575:rtra=on_1783 on theBenchmark for (1783ds/575Mi) 13.37/3.02 % (2898359)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=1611344566: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_1783 on theBenchmark for (1783ds/9840Mi) 13.37/3.02 % (2898331)Instruction limit reached! 13.37/3.02 % (2898331)------------------------------ 13.37/3.02 % (2898331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.37/3.02 % (2898331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.37/3.02 % (2898331)CaDiCaL version: 2.1.3 13.37/3.02 % (2898331)Termination reason: Instruction limit 13.37/3.02 % (2898331)Termination phase: Saturation 13.37/3.02 % (2898331)Time elapsed: 0.397 s 13.37/3.02 % (2898331)Peak memory usage: 16 MB 13.37/3.02 % (2898331)Instructions burned: 496 (million) 13.37/3.02 % (2898361)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=603307787:i=421:rtra=on:ss=axioms_1783 on theBenchmark for (1783ds/421Mi) 13.37/3.02 % (2898344)Instruction limit reached! 13.37/3.02 % (2898344)------------------------------ 13.37/3.02 % (2898344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.37/3.02 % (2898344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.37/3.02 % (2898344)CaDiCaL version: 2.1.3 13.37/3.02 % (2898344)Termination reason: Instruction limit 13.37/3.02 % (2898344)Termination phase: Saturation 13.37/3.02 % (2898344)Time elapsed: 0.258 s 13.37/3.02 % (2898344)Peak memory usage: 16 MB 13.37/3.02 % (2898344)Instructions burned: 341 (million) 13.37/3.02 % (2898350)Instruction limit reached! 13.37/3.02 % (2898350)------------------------------ 13.37/3.02 % (2898350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.37/3.02 % (2898350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.37/3.02 % (2898350)CaDiCaL version: 2.1.3 13.37/3.02 % (2898350)Termination reason: Instruction limit 13.37/3.02 % (2898350)Termination phase: Saturation 13.37/3.02 % (2898350)Time elapsed: 0.241 s 13.37/3.02 % (2898350)Peak memory usage: 15 MB 13.37/3.02 % (2898350)Instructions burned: 374 (million) 13.37/3.02 % (2898363)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 13.37/3.02 % (2898356)Instruction limit reached! 13.37/3.02 % (2898356)------------------------------ 13.37/3.02 % (2898356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.37/3.02 % (2898356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.37/3.02 % (2898356)CaDiCaL version: 2.1.3 13.37/3.02 % (2898356)Termination reason: Instruction limit 13.37/3.02 % (2898356)Termination phase: Saturation 13.37/3.02 % (2898356)Time elapsed: 0.168 s 13.37/3.02 % (2898356)Peak memory usage: 12 MB 13.37/3.02 % (2898356)Instructions burned: 271 (million) 13.37/3.02 % (2898363)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=3168557163:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1782 on theBenchmark for (1782ds/270Mi) 17.40/3.35 % (2898364)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2284163493:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1781 on theBenchmark for (1781ds/31Mi) 17.40/3.35 % (2898364)Instruction limit reached! 17.40/3.35 % (2898364)------------------------------ 17.40/3.35 % (2898364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.40/3.35 % (2898364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.40/3.35 % (2898364)CaDiCaL version: 2.1.3 17.40/3.35 % (2898364)Termination reason: Instruction limit 17.40/3.35 % (2898364)Termination phase: Property scanning 17.40/3.35 % (2898364)Time elapsed: 0.013 s 17.40/3.35 % (2898364)Peak memory usage: 10 MB 17.40/3.35 % (2898364)Instructions burned: 33 (million) 17.40/3.35 % (2898365)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 17.40/3.35 % (2898365)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 17.40/3.35 % (2898365)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=1155822734:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1781 on theBenchmark for (1781ds/1440Mi) 17.40/3.35 % (2898368)dis+10_2_sil=128000:si=on:random_seed=311917046:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1781 on theBenchmark for (1781ds/339Mi) 17.40/3.35 % (2898368)Instruction limit reached! 17.40/3.35 % (2898368)------------------------------ 17.40/3.35 % (2898368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.40/3.35 % (2898368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.40/3.35 % (2898368)CaDiCaL version: 2.1.3 17.40/3.35 % (2898368)Termination reason: Instruction limit 17.40/3.35 % (2898368)Termination phase: Saturation 17.40/3.35 % (2898368)Time elapsed: 0.138 s 17.40/3.35 % (2898368)Peak memory usage: 14 MB 17.40/3.35 % (2898368)Instructions burned: 341 (million) 17.40/3.35 % (2898361)Instruction limit reached! 17.40/3.35 % (2898361)------------------------------ 17.40/3.35 % (2898361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.40/3.35 % (2898361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.40/3.35 % (2898361)CaDiCaL version: 2.1.3 17.40/3.35 % (2898361)Termination reason: Instruction limit 17.40/3.35 % (2898361)Termination phase: Saturation 17.40/3.35 % (2898361)Time elapsed: 0.390 s 17.40/3.35 % (2898361)Peak memory usage: 16 MB 17.40/3.35 % (2898361)Instructions burned: 422 (million) 17.40/3.35 % (2898363)Instruction limit reached! 17.40/3.35 % (2898363)------------------------------ 17.40/3.35 % (2898363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.40/3.35 % (2898363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.40/3.35 % (2898363)CaDiCaL version: 2.1.3 17.40/3.35 % (2898363)Termination reason: Instruction limit 17.40/3.35 % (2898363)Termination phase: Saturation 17.40/3.35 % (2898363)Time elapsed: 0.280 s 17.40/3.35 % (2898363)Peak memory usage: 15 MB 17.40/3.35 % (2898363)Instructions burned: 270 (million) 17.40/3.35 % (2898371)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2961912410:i=111:add=on:fgj=on:rtra=on:fdi=1024_1778 on theBenchmark for (1778ds/111Mi) 17.40/3.35 % (2898355)Instruction limit reached! 17.40/3.35 % (2898355)------------------------------ 17.40/3.35 % (2898355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 17.40/3.35 % (2898355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 17.40/3.35 % (2898355)CaDiCaL version: 2.1.3 17.40/3.35 % (2898355)Termination reason: Instruction limit 17.40/3.35 % (2898355)Termination phase: Saturation 17.40/3.35 % (2898355)Time elapsed: 0.479 s 17.40/3.35 % (2898355)Peak memory usage: 19 MB 17.40/3.35 % (2898355)Instructions burned: 575 (million) 17.40/3.35 % (2898373)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=3095815436:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1778 on theBenchmark for (1778ds/136Mi) 19.32/3.69 % (2898372)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=3767074391:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1778 on theBenchmark for (1778ds/122Mi) 19.32/3.69 % (2898375)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3659162526:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1778 on theBenchmark for (1778ds/232Mi) 19.32/3.69 % (2898371)Instruction limit reached! 19.32/3.69 % (2898371)------------------------------ 19.32/3.69 % (2898371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 19.32/3.69 % (2898371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 19.32/3.69 % (2898371)CaDiCaL version: 2.1.3 19.32/3.69 % (2898371)Termination reason: Instruction limit 19.32/3.69 % (2898371)Termination phase: Property scanning 19.32/3.69 % (2898371)Time elapsed: 0.126 s 19.32/3.69 % (2898371)Peak memory usage: 13 MB 19.32/3.69 % (2898371)Instructions burned: 113 (million) 19.32/3.69 % (2898372)Instruction limit reached! 19.32/3.69 % (2898372)------------------------------ 19.32/3.69 % (2898372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 19.32/3.69 % (2898372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 19.32/3.69 % (2898372)CaDiCaL version: 2.1.3 19.32/3.69 % (2898372)Termination reason: Instruction limit 19.32/3.69 % (2898372)Termination phase: Property scanning 19.32/3.69 % (2898372)Time elapsed: 0.095 s 19.32/3.69 % (2898372)Peak memory usage: 12 MB 19.32/3.69 % (2898372)Instructions burned: 122 (million) 19.32/3.69 % (2898379)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=153681727:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1777 on theBenchmark for (1777ds/1254Mi) 19.32/3.69 % (2898373)Instruction limit reached! 19.32/3.69 % (2898373)------------------------------ 19.32/3.69 % (2898373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 19.32/3.69 % (2898373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 19.32/3.69 % (2898373)CaDiCaL version: 2.1.3 19.32/3.69 % (2898373)Termination reason: Instruction limit 19.32/3.69 % (2898373)Termination phase: Property scanning 19.32/3.69 % (2898373)Time elapsed: 0.113 s 19.32/3.69 % (2898373)Peak memory usage: 16 MB 19.32/3.69 % (2898373)Instructions burned: 137 (million) 19.32/3.69 % (2898382)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4189959646:i=619:add=on:rtra=on_1776 on theBenchmark for (1776ds/619Mi) 19.32/3.69 % (2898380)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 19.32/3.69 % (2898380)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=3008821628:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1776 on theBenchmark for (1776ds/281Mi) 19.32/3.69 % (2898375)Instruction limit reached! 19.32/3.69 % (2898375)------------------------------ 19.32/3.69 % (2898375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 19.32/3.69 % (2898375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 19.32/3.69 % (2898375)CaDiCaL version: 2.1.3 19.32/3.69 % (2898375)Termination reason: Instruction limit 19.32/3.69 % (2898375)Termination phase: Saturation 19.32/3.69 % (2898375)Time elapsed: 0.185 s 19.32/3.69 % (2898375)Peak memory usage: 14 MB 19.32/3.69 % (2898375)Instructions burned: 232 (million) 19.32/3.69 % (2898385)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=387300832:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1775 on theBenchmark for (1775ds/865Mi) 19.32/3.69 % (2898379)Refutation not found, incomplete strategy 19.32/3.69 % (2898379)------------------------------ 19.32/3.69 % (2898379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 19.32/3.69 % (2898379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 19.32/3.69 % (2898379)CaDiCaL version: 2.1.3 19.32/3.69 % (2898379)Termination reason: Refutation not found, incomplete strategy 19.32/3.69 % (2898379)Time elapsed: 0.197 s 19.32/3.69 % (2898379)Peak memory usage: 16 MB 19.32/3.69 % (2898379)Instructions burned: 223 (million) 20.54/3.97 % (2898379)------------------------------ 20.54/3.97 % (2898379)------------------------------ 20.54/3.97 % (2898387)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3844605386:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1774 on theBenchmark for (1774ds/212Mi) 20.54/3.97 % (2898380)Instruction limit reached! 20.54/3.97 % (2898380)------------------------------ 20.54/3.97 % (2898380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.54/3.97 % (2898380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.54/3.97 % (2898380)CaDiCaL version: 2.1.3 20.54/3.97 % (2898380)Termination reason: Instruction limit 20.54/3.97 % (2898380)Termination phase: Saturation 20.54/3.97 % (2898380)Time elapsed: 0.203 s 20.54/3.97 % (2898380)Peak memory usage: 12 MB 20.54/3.97 % (2898380)Instructions burned: 282 (million) 20.54/3.97 % (2898389)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=1443015197:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1774 on theBenchmark for (1774ds/130Mi) 20.54/3.97 % (2898382)Instruction limit reached! 20.54/3.97 % (2898382)------------------------------ 20.54/3.97 % (2898382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.54/3.97 % (2898382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.54/3.97 % (2898382)CaDiCaL version: 2.1.3 20.54/3.97 % (2898382)Termination reason: Instruction limit 20.54/3.97 % (2898382)Termination phase: Saturation 20.54/3.97 % (2898382)Time elapsed: 0.323 s 20.54/3.97 % (2898382)Peak memory usage: 18 MB 20.54/3.97 % (2898382)Instructions burned: 621 (million) 20.54/3.97 % (2898387)Instruction limit reached! 20.54/3.97 % (2898387)------------------------------ 20.54/3.97 % (2898387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.54/3.97 % (2898387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.54/3.97 % (2898387)CaDiCaL version: 2.1.3 20.54/3.97 % (2898387)Termination reason: Instruction limit 20.54/3.97 % (2898387)Termination phase: Saturation 20.54/3.97 % (2898387)Time elapsed: 0.108 s 20.54/3.97 % (2898387)Peak memory usage: 14 MB 20.54/3.97 % (2898387)Instructions burned: 214 (million) 20.54/3.97 % (2898391)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2366994641:st=1.5:i=346:rtra=on:ss=axioms_1773 on theBenchmark for (1773ds/346Mi) 20.54/3.97 % (2898392)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=2080557929:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_1773 on theBenchmark for (1773ds/152Mi) 20.54/3.97 % (2898389)Instruction limit reached! 20.54/3.97 % (2898389)------------------------------ 20.54/3.97 % (2898389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.54/3.97 % (2898389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.54/3.97 % (2898389)CaDiCaL version: 2.1.3 20.54/3.97 % (2898389)Termination reason: Instruction limit 20.54/3.97 % (2898389)Termination phase: Property scanning 20.54/3.97 % (2898389)Time elapsed: 0.100 s 20.54/3.97 % (2898389)Peak memory usage: 13 MB 20.54/3.97 % (2898389)Instructions burned: 130 (million) 20.54/3.97 % (2898395)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=768875349:i=75:ep=R:rtra=on:ntd=on_1772 on theBenchmark for (1772ds/75Mi) 20.54/3.97 % (2898391)Refutation not found, incomplete strategy 20.54/3.97 % (2898391)------------------------------ 20.54/3.97 % (2898391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.54/3.97 % (2898391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.54/3.97 % (2898391)CaDiCaL version: 2.1.3 20.54/3.97 % (2898391)Termination reason: Refutation not found, incomplete strategy 20.54/3.97 % (2898391)Time elapsed: 0.138 s 20.54/3.97 % (2898391)Peak memory usage: 13 MB 20.54/3.97 % (2898391)Instructions burned: 190 (million) 20.54/3.97 % (2898391)------------------------------ 20.54/3.97 % (2898391)------------------------------ 20.54/3.97 % (2898392)Instruction limit reached! 20.54/3.97 % (2898392)------------------------------ 20.54/3.97 % (2898392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.54/3.97 % (2898392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.54/3.97 % (2898392)CaDiCaL version: 2.1.3 20.54/3.97 % (2898392)Termination reason: Instruction limit 20.54/3.97 % (2898392)Termination phase: Inequality splitting 20.54/3.97 % (2898392)Time elapsed: 0.125 s 20.54/3.97 % (2898392)Peak memory usage: 13 MB 24.01/4.33 % (2898392)Instructions burned: 152 (million) 24.01/4.33 % (2898395)Instruction limit reached! 24.01/4.33 % (2898395)------------------------------ 24.01/4.33 % (2898395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.01/4.33 % (2898395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.01/4.33 % (2898395)CaDiCaL version: 2.1.3 24.01/4.33 % (2898395)Termination reason: Instruction limit 24.01/4.33 % (2898395)Termination phase: Property scanning 24.01/4.33 % (2898395)Time elapsed: 0.055 s 24.01/4.33 % (2898395)Peak memory usage: 10 MB 24.01/4.33 % (2898395)Instructions burned: 76 (million) 24.01/4.33 % (2898397)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=3932631318:st=2.5:i=387:sd=2:rtra=on:ss=axioms_1771 on theBenchmark for (1771ds/387Mi) 24.01/4.33 % (2898398)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=854925224:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_1771 on theBenchmark for (1771ds/148Mi) 24.01/4.33 % (2898399)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3558667718:i=161:piset=and:rtra=on:ntd=on_1771 on theBenchmark for (1771ds/161Mi) 24.01/4.33 % (2898398)Instruction limit reached! 24.01/4.33 % (2898398)------------------------------ 24.01/4.33 % (2898398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.01/4.33 % (2898398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.01/4.33 % (2898398)CaDiCaL version: 2.1.3 24.01/4.33 % (2898398)Termination reason: Instruction limit 24.01/4.33 % (2898398)Termination phase: Saturation 24.01/4.33 % (2898398)Time elapsed: 0.138 s 24.01/4.33 % (2898398)Peak memory usage: 12 MB 24.01/4.33 % (2898398)Instructions burned: 149 (million) 24.01/4.33 % (2898399)Instruction limit reached! 24.01/4.33 % (2898399)------------------------------ 24.01/4.33 % (2898399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.01/4.33 % (2898399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.01/4.33 % (2898399)CaDiCaL version: 2.1.3 24.01/4.33 % (2898399)Termination reason: Instruction limit 24.01/4.33 % (2898399)Termination phase: Property scanning 24.01/4.33 % (2898399)Time elapsed: 0.146 s 24.01/4.33 % (2898399)Peak memory usage: 13 MB 24.01/4.33 % (2898399)Instructions burned: 161 (million) 24.01/4.33 % (2898365)Instruction limit reached! 24.01/4.33 % (2898365)------------------------------ 24.01/4.33 % (2898365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.01/4.33 % (2898365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.01/4.33 % (2898365)CaDiCaL version: 2.1.3 24.01/4.33 % (2898365)Termination reason: Instruction limit 24.01/4.33 % (2898365)Termination phase: Saturation 24.01/4.33 % (2898365)Time elapsed: 1.200 s 24.01/4.33 % (2898365)Peak memory usage: 22 MB 24.01/4.33 % (2898365)Instructions burned: 1440 (million) 24.01/4.33 % (2898403)lrs+10_1_sil=128000:si=on:random_seed=3889827000:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_1769 on theBenchmark for (1769ds/888Mi) 24.01/4.33 % (2898404)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=2138171624:i=136:add=on:ins=4:rtra=on:sup=off_1769 on theBenchmark for (1769ds/136Mi) 24.01/4.33 % (2898405)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=4124929981:i=88:s2at=3:nm=2:rtra=on:rawr=on_1768 on theBenchmark for (1768ds/88Mi) 24.01/4.33 % (2898385)Instruction limit reached! 24.01/4.33 % (2898385)------------------------------ 24.01/4.33 % (2898385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.01/4.33 % (2898385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.01/4.33 % (2898385)CaDiCaL version: 2.1.3 24.01/4.33 % (2898385)Termination reason: Instruction limit 24.01/4.33 % (2898385)Termination phase: Saturation 24.01/4.33 % (2898385)Time elapsed: 0.680 s 24.01/4.33 % (2898385)Peak memory usage: 19 MB 24.01/4.33 % (2898385)Instructions burned: 865 (million) 24.01/4.33 % (2898397)Instruction limit reached! 24.01/4.33 % (2898397)------------------------------ 24.01/4.33 % (2898397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.01/4.33 % (2898397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.77/4.65 % (2898397)CaDiCaL version: 2.1.3 25.77/4.65 % (2898397)Termination reason: Instruction limit 25.77/4.65 % (2898397)Termination phase: Saturation 25.77/4.65 % (2898397)Time elapsed: 0.282 s 25.77/4.65 % (2898397)Peak memory usage: 13 MB 25.77/4.65 % (2898397)Instructions burned: 388 (million) 25.77/4.65 % (2898409)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2962668153:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_1768 on theBenchmark for (1768ds/93Mi) 25.77/4.65 % (2898405)Instruction limit reached! 25.77/4.65 % (2898405)------------------------------ 25.77/4.65 % (2898405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.77/4.65 % (2898405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.77/4.65 % (2898405)CaDiCaL version: 2.1.3 25.77/4.65 % (2898405)Termination reason: Instruction limit 25.77/4.65 % (2898405)Termination phase: Property scanning 25.77/4.65 % (2898405)Time elapsed: 0.075 s 25.77/4.65 % (2898405)Peak memory usage: 11 MB 25.77/4.65 % (2898405)Instructions burned: 88 (million) 25.77/4.65 % (2898410)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=378061119:i=2186:rtra=on:ixr=off_1768 on theBenchmark for (1768ds/2186Mi) 25.77/4.65 % (2898404)Instruction limit reached! 25.77/4.65 % (2898404)------------------------------ 25.77/4.65 % (2898404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.77/4.65 % (2898404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.77/4.65 % (2898404)CaDiCaL version: 2.1.3 25.77/4.65 % (2898404)Termination reason: Instruction limit 25.77/4.65 % (2898404)Termination phase: Property scanning 25.77/4.65 % (2898404)Time elapsed: 0.111 s 25.77/4.65 % (2898404)Peak memory usage: 12 MB 25.77/4.65 % (2898404)Instructions burned: 137 (million) 25.77/4.65 % (2898412)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=25762548:s2a=on:i=240:rtra=on:ntd=on_1767 on theBenchmark for (1767ds/240Mi) 25.77/4.65 % (2898409)Instruction limit reached! 25.77/4.65 % (2898409)------------------------------ 25.77/4.65 % (2898409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.77/4.65 % (2898409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.77/4.65 % (2898409)CaDiCaL version: 2.1.3 25.77/4.65 % (2898409)Termination reason: Instruction limit 25.77/4.65 % (2898409)Termination phase: Saturation 25.77/4.65 % (2898409)Time elapsed: 0.069 s 25.77/4.65 % (2898409)Peak memory usage: 12 MB 25.77/4.65 % (2898409)Instructions burned: 95 (million) 25.77/4.65 % (2898415)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=3707438660:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_1767 on theBenchmark for (1767ds/805Mi) 25.77/4.65 % (2898416)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on 25.77/4.65 % (2898416)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=2136144008:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_1767 on theBenchmark for (1767ds/391Mi) 25.77/4.65 % (2898412)Instruction limit reached! 25.77/4.65 % (2898412)------------------------------ 25.77/4.65 % (2898412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.77/4.65 % (2898412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.77/4.65 % (2898412)CaDiCaL version: 2.1.3 25.77/4.65 % (2898412)Termination reason: Instruction limit 25.77/4.65 % (2898412)Termination phase: Saturation 25.77/4.65 % (2898412)Time elapsed: 0.192 s 25.77/4.65 % (2898412)Peak memory usage: 15 MB 25.77/4.65 % (2898412)Instructions burned: 241 (million) 25.77/4.65 % (2898423)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=831992186:i=355:av=off:fsr=off:rtra=on:ixr=off_1765 on theBenchmark for (1765ds/355Mi) 25.77/4.65 % (2898416)Instruction limit reached! 25.77/4.65 % (2898416)------------------------------ 25.77/4.65 % (2898416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 25.77/4.65 % (2898416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 25.77/4.65 % (2898416)CaDiCaL version: 2.1.3 25.77/4.65 % (2898416)Termination reason: Instruction limit 25.77/4.65 % (2898416)Termination phase: Saturation 25.77/4.65 % (2898416)Time elapsed: 0.179 s 26.86/4.85 % (2898416)Peak memory usage: 13 MB 26.86/4.85 % (2898416)Instructions burned: 394 (million) 26.86/4.85 % (2898425)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=645243097:lrd=on:i=314:sd=1:rtra=on:ss=axioms_1765 on theBenchmark for (1765ds/314Mi) 26.86/4.85 % (2898425)Refutation not found, incomplete strategy 26.86/4.85 % (2898425)------------------------------ 26.86/4.85 % (2898425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.86/4.85 % (2898425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.86/4.85 % (2898425)CaDiCaL version: 2.1.3 26.86/4.85 % (2898425)Termination reason: Refutation not found, incomplete strategy 26.86/4.85 % (2898425)Time elapsed: 0.145 s 26.86/4.85 % (2898425)Peak memory usage: 15 MB 26.86/4.85 % (2898425)Instructions burned: 315 (million) 26.86/4.85 % (2898425)------------------------------ 26.86/4.85 % (2898425)------------------------------ 26.86/4.85 % (2898427)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=3660935332:s2a=on:i=251:fsr=off:rtra=on_1763 on theBenchmark for (1763ds/251Mi) 26.86/4.85 % (2898423)Instruction limit reached! 26.86/4.85 % (2898423)------------------------------ 26.86/4.85 % (2898423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.86/4.85 % (2898423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.86/4.85 % (2898423)CaDiCaL version: 2.1.3 26.86/4.85 % (2898423)Termination reason: Instruction limit 26.86/4.85 % (2898423)Termination phase: Saturation 26.86/4.85 % (2898423)Time elapsed: 0.236 s 26.86/4.85 % (2898423)Peak memory usage: 15 MB 26.86/4.85 % (2898423)Instructions burned: 357 (million) 26.86/4.85 % (2898429)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=769807098: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_1763 on theBenchmark for (1763ds/2470Mi) 26.86/4.85 % (2898415)Instruction limit reached! 26.86/4.85 % (2898415)------------------------------ 26.86/4.85 % (2898415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.86/4.85 % (2898415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.86/4.85 % (2898415)CaDiCaL version: 2.1.3 26.86/4.85 % (2898415)Termination reason: Instruction limit 26.86/4.85 % (2898415)Termination phase: Saturation 26.86/4.85 % (2898415)Time elapsed: 0.455 s 26.86/4.85 % (2898415)Peak memory usage: 18 MB 26.86/4.85 % (2898415)Instructions burned: 805 (million) 26.86/4.85 % (2898403)Instruction limit reached! 26.86/4.85 % (2898403)------------------------------ 26.86/4.85 % (2898403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.86/4.85 % (2898403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.86/4.85 % (2898403)CaDiCaL version: 2.1.3 26.86/4.85 % (2898403)Termination reason: Instruction limit 26.86/4.85 % (2898403)Termination phase: Saturation 26.86/4.85 % (2898403)Time elapsed: 0.637 s 26.86/4.85 % (2898403)Peak memory usage: 18 MB 26.86/4.85 % (2898403)Instructions burned: 888 (million) 26.86/4.85 % (2898431)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=3261670598:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_1762 on theBenchmark for (1762ds/673Mi) 26.86/4.85 % (2898432)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=729911362:i=116:ep=RSTC:rtra=on:ntd=on_1762 on theBenchmark for (1762ds/116Mi) 26.86/4.85 % (2898427)Instruction limit reached! 26.86/4.85 % (2898427)------------------------------ 26.86/4.85 % (2898427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.86/4.85 % (2898427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 26.86/4.85 % (2898427)CaDiCaL version: 2.1.3 26.86/4.85 % (2898427)Termination reason: Instruction limit 26.86/4.85 % (2898427)Termination phase: Saturation 26.86/4.85 % (2898427)Time elapsed: 0.168 s 26.86/4.85 % (2898427)Peak memory usage: 14 MB 26.86/4.85 % (2898427)Instructions burned: 252 (million) 26.86/4.85 % (2898432)Instruction limit reached! 26.86/4.85 % (2898432)------------------------------ 26.86/4.85 % (2898432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 26.86/4.85 % (2898432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 30.86/5.31 % (2898432)CaDiCaL version: 2.1.3 30.86/5.31 % (2898432)Termination reason: Instruction limit 30.86/5.31 % (2898432)Termination phase: Property scanning 30.86/5.31 % (2898432)Time elapsed: 0.054 s 30.86/5.31 % (2898432)Peak memory usage: 13 MB 30.86/5.31 % (2898432)Instructions burned: 121 (million) 30.86/5.31 % (2898435)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=459257450:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1761 on theBenchmark for (1761ds/270Mi) 30.86/5.31 % (2898436)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=3027868415: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_1761 on theBenchmark for (1761ds/30Mi) 30.86/5.31 % (2898436)Instruction limit reached! 30.86/5.31 % (2898436)------------------------------ 30.86/5.31 % (2898436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 30.86/5.31 % (2898436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 30.86/5.31 % (2898436)CaDiCaL version: 2.1.3 30.86/5.31 % (2898436)Termination reason: Instruction limit 30.86/5.31 % (2898436)Termination phase: shuffling 30.86/5.31 % (2898436)Time elapsed: 0.013 s 30.86/5.31 % (2898436)Peak memory usage: 10 MB 30.86/5.31 % (2898436)Instructions burned: 30 (million) 30.86/5.31 % (2898439)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off 30.86/5.31 % (2898439)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=1102647705:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_1761 on theBenchmark for (1761ds/39Mi) 30.86/5.31 % (2898439)Instruction limit reached! 30.86/5.31 % (2898439)------------------------------ 30.86/5.31 % (2898439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 30.86/5.31 % (2898439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 30.86/5.31 % (2898439)CaDiCaL version: 2.1.3 30.86/5.31 % (2898439)Termination reason: Instruction limit 30.86/5.31 % (2898439)Termination phase: Property scanning 30.86/5.31 % (2898439)Time elapsed: 0.018 s 30.86/5.31 % (2898439)Peak memory usage: 10 MB 30.86/5.31 % (2898439)Instructions burned: 41 (million) 30.86/5.31 % (2898441)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=430827235:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1760 on theBenchmark for (1760ds/365Mi) 30.86/5.31 % (2898435)Instruction limit reached! 30.86/5.31 % (2898435)------------------------------ 30.86/5.31 % (2898435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 30.86/5.31 % (2898435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 30.86/5.31 % (2898435)CaDiCaL version: 2.1.3 30.86/5.31 % (2898435)Termination reason: Instruction limit 30.86/5.31 % (2898435)Termination phase: Saturation 30.86/5.31 % (2898435)Time elapsed: 0.159 s 30.86/5.31 % (2898435)Peak memory usage: 12 MB 30.86/5.31 % (2898435)Instructions burned: 270 (million) 30.86/5.31 % (2898443)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3480394731:i=158:av=off:rtra=on_1759 on theBenchmark for (1759ds/158Mi) 30.86/5.31 % (2898431)Instruction limit reached! 30.86/5.31 % (2898431)------------------------------ 30.86/5.31 % (2898431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 30.86/5.31 % (2898431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 30.86/5.31 % (2898431)CaDiCaL version: 2.1.3 30.86/5.31 % (2898431)Termination reason: Instruction limit 30.86/5.31 % (2898431)Termination phase: Saturation 30.86/5.31 % (2898431)Time elapsed: 0.309 s 30.86/5.31 % (2898431)Peak memory usage: 18 MB 30.86/5.31 % (2898431)Instructions burned: 674 (million) 30.86/5.31 % (2898445)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 30.86/5.31 % (2898445)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=4044414725:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_1759 on theBenchmark for (1759ds/252Mi) 30.86/5.31 % (2898441)Instruction limit reached! 30.86/5.31 % (2898441)------------------------------ 30.86/5.31 % (2898441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 31.74/5.49 % (2898441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 31.74/5.49 % (2898441)CaDiCaL version: 2.1.3 31.74/5.49 % (2898441)Termination reason: Instruction limit 31.74/5.49 % (2898441)Termination phase: Saturation 31.74/5.49 % (2898441)Time elapsed: 0.227 s 31.74/5.49 % (2898441)Peak memory usage: 16 MB 31.74/5.49 % (2898441)Instructions burned: 366 (million) 31.74/5.49 % (2898447)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2094254750:i=213:rtra=on:ss=axioms_1758 on theBenchmark for (1758ds/213Mi) 31.74/5.49 % (2898443)Instruction limit reached! 31.74/5.49 % (2898443)------------------------------ 31.74/5.49 % (2898443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 31.74/5.49 % (2898443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 31.74/5.49 % (2898443)CaDiCaL version: 2.1.3 31.74/5.49 % (2898443)Termination reason: Instruction limit 31.74/5.49 % (2898443)Termination phase: Saturation 31.74/5.49 % (2898443)Time elapsed: 0.132 s 31.74/5.49 % (2898443)Peak memory usage: 14 MB 31.74/5.49 % (2898443)Instructions burned: 159 (million) 31.74/5.49 % (2898447)Refutation not found, incomplete strategy 31.74/5.49 % (2898447)------------------------------ 31.74/5.49 % (2898447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 31.74/5.49 % (2898447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 31.74/5.49 % (2898447)CaDiCaL version: 2.1.3 31.74/5.49 % (2898447)Termination reason: Refutation not found, incomplete strategy 31.74/5.49 % (2898447)Time elapsed: 0.018 s 31.74/5.49 % (2898447)Peak memory usage: 13 MB 31.74/5.49 % (2898447)Instructions burned: 41 (million) 31.74/5.49 % (2898447)------------------------------ 31.74/5.49 % (2898447)------------------------------ 31.74/5.49 % (2898445)Instruction limit reached! 31.74/5.49 % (2898445)------------------------------ 31.74/5.49 % (2898445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 31.74/5.49 % (2898445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 31.74/5.49 % (2898445)CaDiCaL version: 2.1.3 31.74/5.49 % (2898445)Termination reason: Instruction limit 31.74/5.49 % (2898445)Termination phase: Saturation 31.74/5.49 % (2898445)Time elapsed: 0.110 s 31.74/5.49 % (2898445)Peak memory usage: 15 MB 31.74/5.49 % (2898445)Instructions burned: 252 (million) 31.74/5.49 % (2898450)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=4161898658:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_1758 on theBenchmark for (1758ds/763Mi) 31.74/5.49 % (2898451)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on 31.74/5.49 % (2898451)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=2213445864:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_1757 on theBenchmark for (1757ds/237Mi) 31.74/5.49 % (2898449)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=3607309910:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_1758 on theBenchmark for (1758ds/160Mi) 31.74/5.49 % (2898451)Instruction limit reached! 31.74/5.49 % (2898451)------------------------------ 31.74/5.49 % (2898451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 31.74/5.49 % (2898451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 31.74/5.49 % (2898451)CaDiCaL version: 2.1.3 31.74/5.49 % (2898451)Termination reason: Instruction limit 31.74/5.49 % (2898451)Termination phase: Saturation 31.74/5.49 % (2898451)Time elapsed: 0.107 s 31.74/5.49 % (2898451)Peak memory usage: 15 MB 31.74/5.49 % (2898451)Instructions burned: 237 (million) 31.74/5.49 % (2898449)Instruction limit reached! 31.74/5.49 % (2898449)------------------------------ 31.74/5.49 % (2898449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 31.74/5.49 % (2898449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 31.74/5.49 % (2898449)CaDiCaL version: 2.1.3 31.74/5.49 % (2898449)Termination reason: Instruction limit 31.74/5.49 % (2898449)Termination phase: Function definition elimination 31.74/5.49 % (2898449)Time elapsed: 0.124 s 31.74/5.49 % (2898449)Peak memory usage: 12 MB 31.74/5.49 % (2898449)Instructions burned: 160 (million) 32.78/5.70 % (2898455)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=935478780:s2a=on:i=386:rtra=on:ntd=on_1756 on theBenchmark for (1756ds/386Mi) 32.78/5.70 % (2898456)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=3393339021:i=300:piset=and:nm=32:rtra=on_1756 on theBenchmark for (1756ds/300Mi) 32.78/5.70 % (2898455)Instruction limit reached! 32.78/5.70 % (2898455)------------------------------ 32.78/5.70 % (2898455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.78/5.70 % (2898455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.78/5.70 % (2898455)CaDiCaL version: 2.1.3 32.78/5.70 % (2898455)Termination reason: Instruction limit 32.78/5.70 % (2898455)Termination phase: Saturation 32.78/5.70 % (2898455)Time elapsed: 0.158 s 32.78/5.70 % (2898455)Peak memory usage: 12 MB 32.78/5.70 % (2898455)Instructions burned: 387 (million) 32.78/5.70 % (2898459)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=2557356467:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_1754 on theBenchmark for (1754ds/567Mi) 32.78/5.70 % (2898456)Instruction limit reached! 32.78/5.70 % (2898456)------------------------------ 32.78/5.70 % (2898456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.78/5.70 % (2898456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.78/5.70 % (2898456)CaDiCaL version: 2.1.3 32.78/5.70 % (2898456)Termination reason: Instruction limit 32.78/5.70 % (2898456)Termination phase: Property scanning 32.78/5.70 % (2898456)Time elapsed: 0.211 s 32.78/5.70 % (2898456)Peak memory usage: 13 MB 32.78/5.70 % (2898456)Instructions burned: 300 (million) 32.78/5.70 % (2898450)Instruction limit reached! 32.78/5.70 % (2898450)------------------------------ 32.78/5.70 % (2898450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.78/5.70 % (2898450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.78/5.70 % (2898450)CaDiCaL version: 2.1.3 32.78/5.70 % (2898450)Termination reason: Instruction limit 32.78/5.70 % (2898450)Termination phase: Saturation 32.78/5.70 % (2898450)Time elapsed: 0.373 s 32.78/5.70 % (2898450)Peak memory usage: 17 MB 32.78/5.70 % (2898450)Instructions burned: 765 (million) 32.78/5.70 % (2898461)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=2342530827:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_1754 on theBenchmark for (1754ds/379Mi) 32.78/5.70 % (2898462)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=2630274305:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_1754 on theBenchmark for (1754ds/429Mi) 32.78/5.70 % (2898459)Instruction limit reached! 32.78/5.70 % (2898459)------------------------------ 32.78/5.70 % (2898459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.78/5.70 % (2898459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.78/5.70 % (2898459)CaDiCaL version: 2.1.3 32.78/5.70 % (2898459)Termination reason: Instruction limit 32.78/5.70 % (2898459)Termination phase: Saturation 32.78/5.70 % (2898459)Time elapsed: 0.231 s 32.78/5.70 % (2898459)Peak memory usage: 12 MB 32.78/5.70 % (2898459)Instructions burned: 570 (million) 32.78/5.70 % (2898429)Instruction limit reached! 32.78/5.70 % (2898429)------------------------------ 32.78/5.70 % (2898429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.78/5.70 % (2898429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 32.78/5.70 % (2898429)CaDiCaL version: 2.1.3 32.78/5.70 % (2898429)Termination reason: Instruction limit 32.78/5.70 % (2898429)Termination phase: Saturation 32.78/5.70 % (2898429)Time elapsed: 1.055 s 32.78/5.70 % (2898429)Peak memory usage: 17 MB 32.78/5.70 % (2898429)Instructions burned: 2470 (million) 32.78/5.70 % (2898465)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=3629769022:i=478:bd=all:rtra=on_1752 on theBenchmark for (1752ds/478Mi) 32.78/5.70 % (2898466)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3972640601:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1752 on theBenchmark for (1752ds/445Mi) 32.78/5.70 % (2898462)Instruction limit reached! 32.78/5.70 % (2898462)------------------------------ 32.78/5.70 % (2898462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 32.78/5.70 % (2898462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.19/5.99 % (2898462)CaDiCaL version: 2.1.3 34.19/5.99 % (2898462)Termination reason: Instruction limit 34.19/5.99 % (2898462)Termination phase: Saturation 34.19/5.99 % (2898462)Time elapsed: 0.199 s 34.19/5.99 % (2898462)Peak memory usage: 17 MB 34.19/5.99 % (2898462)Instructions burned: 430 (million) 34.19/5.99 % (2898469)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3619964651:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_1751 on theBenchmark for (1751ds/71Mi) 34.19/5.99 % (2898469)Instruction limit reached! 34.19/5.99 % (2898469)------------------------------ 34.19/5.99 % (2898469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.19/5.99 % (2898469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.19/5.99 % (2898469)CaDiCaL version: 2.1.3 34.19/5.99 % (2898469)Termination reason: Instruction limit 34.19/5.99 % (2898469)Termination phase: Property scanning 34.19/5.99 % (2898469)Time elapsed: 0.030 s 34.19/5.99 % (2898469)Peak memory usage: 11 MB 34.19/5.99 % (2898469)Instructions burned: 72 (million) 34.19/5.99 % (2898410)Instruction limit reached! 34.19/5.99 % (2898410)------------------------------ 34.19/5.99 % (2898410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.19/5.99 % (2898410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.19/5.99 % (2898410)CaDiCaL version: 2.1.3 34.19/5.99 % (2898410)Termination reason: Instruction limit 34.19/5.99 % (2898410)Termination phase: Saturation 34.19/5.99 % (2898410)Time elapsed: 1.641 s 34.19/5.99 % (2898410)Peak memory usage: 15 MB 34.19/5.99 % (2898410)Instructions burned: 2187 (million) 34.19/5.99 % (2898461)Instruction limit reached! 34.19/5.99 % (2898461)------------------------------ 34.19/5.99 % (2898461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.19/5.99 % (2898461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.19/5.99 % (2898461)CaDiCaL version: 2.1.3 34.19/5.99 % (2898461)Termination reason: Instruction limit 34.19/5.99 % (2898461)Termination phase: Saturation 34.19/5.99 % (2898461)Time elapsed: 0.283 s 34.19/5.99 % (2898461)Peak memory usage: 16 MB 34.19/5.99 % (2898461)Instructions burned: 380 (million) 34.19/5.99 % (2898471)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3029643556:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_1751 on theBenchmark for (1751ds/302Mi) 34.19/5.99 % (2898472)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=1262904939:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_1751 on theBenchmark for (1751ds/4980Mi) 34.19/5.99 % (2898474)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 34.19/5.99 % (2898474)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 34.19/5.99 % (2898474)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2203921271:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1751 on theBenchmark for (1751ds/100Mi) 34.19/5.99 % (2898472)Refutation not found, incomplete strategy 34.19/5.99 % (2898472)------------------------------ 34.19/5.99 % (2898472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.19/5.99 % (2898472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.19/5.99 % (2898472)CaDiCaL version: 2.1.3 34.19/5.99 % (2898472)Termination reason: Refutation not found, incomplete strategy 34.19/5.99 % (2898472)Time elapsed: 0.039 s 34.19/5.99 % (2898472)Peak memory usage: 12 MB 34.19/5.99 % (2898472)Instructions burned: 42 (million) 34.19/5.99 % (2898472)------------------------------ 34.19/5.99 % (2898472)------------------------------ 34.19/5.99 % (2898474)Instruction limit reached! 34.19/5.99 % (2898474)------------------------------ 34.19/5.99 % (2898474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 34.19/5.99 % (2898474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 34.19/5.99 % (2898474)CaDiCaL version: 2.1.3 34.19/5.99 % (2898474)Termination reason: Instruction limit 34.19/5.99 % (2898474)Termination phase: Twee Goal Transformation 34.19/5.99 % (2898474)Time elapsed: 0.050 s 34.19/5.99 % (2898474)Peak memory usage: 11 MB 34.19/5.99 % (2898474)Instructions burned: 100 (million) 36.84/6.23 % (2898477)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=1280124755:i=76:piset=equals:rtra=on:ntd=on_1750 on theBenchmark for (1750ds/76Mi) 36.84/6.23 % (2898478)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=1140160562:i=289:rtra=on_1750 on theBenchmark for (1750ds/289Mi) 36.84/6.23 % (2898466)Instruction limit reached! 36.84/6.23 % (2898466)------------------------------ 36.84/6.23 % (2898466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 36.84/6.23 % (2898466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 36.84/6.23 % (2898466)CaDiCaL version: 2.1.3 36.84/6.23 % (2898466)Termination reason: Instruction limit 36.84/6.23 % (2898466)Termination phase: Saturation 36.84/6.23 % (2898466)Time elapsed: 0.256 s 36.84/6.23 % (2898466)Peak memory usage: 16 MB 36.84/6.23 % (2898466)Instructions burned: 445 (million) 36.84/6.23 % (2898481)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=686542706:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_1749 on theBenchmark for (1749ds/493Mi) 36.84/6.23 % (2898477)Instruction limit reached! 36.84/6.23 % (2898477)------------------------------ 36.84/6.23 % (2898477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 36.84/6.23 % (2898477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 36.84/6.23 % (2898477)CaDiCaL version: 2.1.3 36.84/6.23 % (2898477)Termination reason: Instruction limit 36.84/6.23 % (2898477)Termination phase: Property scanning 36.84/6.23 % (2898477)Time elapsed: 0.063 s 36.84/6.23 % (2898477)Peak memory usage: 11 MB 36.84/6.23 % (2898477)Instructions burned: 77 (million) 36.84/6.23 % (2898471)Instruction limit reached! 36.84/6.23 % (2898471)------------------------------ 36.84/6.23 % (2898471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 36.84/6.23 % (2898471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 36.84/6.23 % (2898471)CaDiCaL version: 2.1.3 36.84/6.23 % (2898471)Termination reason: Instruction limit 36.84/6.23 % (2898471)Termination phase: Saturation 36.84/6.23 % (2898471)Time elapsed: 0.197 s 36.84/6.23 % (2898471)Peak memory usage: 16 MB 36.84/6.23 % (2898471)Instructions burned: 303 (million) 36.84/6.23 % (2898484)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 36.84/6.23 % (2898483)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=476300323:cond=on:i=34:hud=10:nm=10:rtra=on_1749 on theBenchmark for (1749ds/34Mi) 36.84/6.23 % (2898484)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=3804911108:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_1749 on theBenchmark for (1749ds/372Mi) 36.84/6.23 % (2898465)Instruction limit reached! 36.84/6.23 % (2898465)------------------------------ 36.84/6.23 % (2898465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 36.84/6.23 % (2898465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 36.84/6.23 % (2898465)CaDiCaL version: 2.1.3 36.84/6.23 % (2898465)Termination reason: Instruction limit 36.84/6.23 % (2898465)Termination phase: Saturation 36.84/6.23 % (2898465)Time elapsed: 0.357 s 36.84/6.23 % (2898465)Peak memory usage: 17 MB 36.84/6.23 % (2898465)Instructions burned: 479 (million) 36.84/6.23 % (2898483)Instruction limit reached! 36.84/6.23 % (2898483)------------------------------ 36.84/6.23 % (2898483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 36.84/6.23 % (2898483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 36.84/6.23 % (2898483)CaDiCaL version: 2.1.3 36.84/6.23 % (2898483)Termination reason: Instruction limit 36.84/6.23 % (2898483)Termination phase: Property scanning 36.84/6.23 % (2898483)Time elapsed: 0.027 s 36.84/6.23 % (2898483)Peak memory usage: 10 MB 36.84/6.23 % (2898483)Instructions burned: 36 (million) 36.84/6.23 % (2898488)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2481825652:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1748 on theBenchmark for (1748ds/647Mi) 36.84/6.23 % (2898487)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=1876304485:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_1748 on theBenchmark for (1748ds/670Mi) 37.89/6.51 % (2898478)Instruction limit reached! 37.89/6.51 % (2898478)------------------------------ 37.89/6.51 % (2898478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 37.89/6.51 % (2898478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 37.89/6.51 % (2898478)CaDiCaL version: 2.1.3 37.89/6.51 % (2898478)Termination reason: Instruction limit 37.89/6.51 % (2898478)Termination phase: Saturation 37.89/6.51 % (2898478)Time elapsed: 0.242 s 37.89/6.51 % (2898478)Peak memory usage: 15 MB 37.89/6.51 % (2898478)Instructions burned: 289 (million) 37.89/6.51 % (2898491)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=1179826162:i=857:add=off:kws=frequency:rtra=on:ntd=on_1747 on theBenchmark for (1747ds/857Mi) 37.89/6.51 % (2898484)Instruction limit reached! 37.89/6.51 % (2898484)------------------------------ 37.89/6.51 % (2898484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 37.89/6.51 % (2898484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 37.89/6.51 % (2898484)CaDiCaL version: 2.1.3 37.89/6.51 % (2898484)Termination reason: Instruction limit 37.89/6.51 % (2898484)Termination phase: Saturation 37.89/6.51 % (2898484)Time elapsed: 0.200 s 37.89/6.51 % (2898484)Peak memory usage: 16 MB 37.89/6.51 % (2898484)Instructions burned: 373 (million) 37.89/6.51 % (2898493)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=3883437956:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_1746 on theBenchmark for (1746ds/693Mi) 37.89/6.51 % (2898359)Instruction limit reached! 37.89/6.51 % (2898359)------------------------------ 37.89/6.51 % (2898359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 37.89/6.51 % (2898359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 37.89/6.51 % (2898359)CaDiCaL version: 2.1.3 37.89/6.51 % (2898359)Termination reason: Instruction limit 37.89/6.51 % (2898359)Termination phase: Saturation 37.89/6.51 % (2898359)Time elapsed: 3.683 s 37.89/6.51 % (2898359)Peak memory usage: 57 MB 37.89/6.51 % (2898359)Instructions burned: 9841 (million) 37.89/6.51 % (2898327)Instruction limit reached! 37.89/6.51 % (2898327)------------------------------ 37.89/6.51 % (2898327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 37.89/6.51 % (2898327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 37.89/6.51 % (2898327)CaDiCaL version: 2.1.3 37.89/6.51 % (2898327)Termination reason: Instruction limit 37.89/6.51 % (2898327)Termination phase: Saturation 37.89/6.51 % (2898327)Time elapsed: 4.152 s 37.89/6.51 % (2898327)Peak memory usage: 31 MB 37.89/6.51 % (2898327)Instructions burned: 5756 (million) 37.89/6.51 % (2898495)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=3058686620:i=285:hud=10:bd=all:rtra=on:ss=axioms_1746 on theBenchmark for (1746ds/285Mi) 37.89/6.51 % (2898496)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on 37.89/6.51 % (2898496)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=2292084313:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_1745 on theBenchmark for (1745ds/52Mi) 37.89/6.51 % (2898496)Instruction limit reached! 37.89/6.51 % (2898496)------------------------------ 37.89/6.51 % (2898496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 37.89/6.51 % (2898496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 37.89/6.51 % (2898496)CaDiCaL version: 2.1.3 37.89/6.51 % (2898496)Termination reason: Instruction limit 37.89/6.51 % (2898496)Termination phase: Preprocessing 3 37.89/6.51 % (2898496)Time elapsed: 0.024 s 37.89/6.51 % (2898496)Peak memory usage: 11 MB 37.89/6.51 % (2898496)Instructions burned: 54 (million) 37.89/6.51 % (2898499)dis+10_1_si=on:random_seed=11453982:i=407:sd=4:rtra=on:ss=axioms:sgt=20_1745 on theBenchmark for (1745ds/407Mi) 37.89/6.51 % (2898488)Instruction limit reached! 37.89/6.51 % (2898488)------------------------------ 37.89/6.51 % (2898488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 39.42/6.88 % (2898488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 39.42/6.88 % (2898488)CaDiCaL version: 2.1.3 39.42/6.88 % (2898488)Termination reason: Instruction limit 39.42/6.88 % (2898488)Termination phase: Saturation 39.42/6.88 % (2898488)Time elapsed: 0.317 s 39.42/6.88 % (2898488)Peak memory usage: 18 MB 39.42/6.88 % (2898488)Instructions burned: 648 (million) 39.42/6.88 % (2898501)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=803678484:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_1745 on theBenchmark for (1745ds/2240Mi) 39.42/6.88 % (2898481)Instruction limit reached! 39.42/6.88 % (2898481)------------------------------ 39.42/6.88 % (2898481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 39.42/6.88 % (2898481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 39.42/6.88 % (2898481)CaDiCaL version: 2.1.3 39.42/6.88 % (2898481)Termination reason: Instruction limit 39.42/6.88 % (2898481)Termination phase: Saturation 39.42/6.88 % (2898481)Time elapsed: 0.452 s 39.42/6.88 % (2898481)Peak memory usage: 15 MB 39.42/6.88 % (2898481)Instructions burned: 493 (million) 39.42/6.88 % (2898495)Instruction limit reached! 39.42/6.88 % (2898495)------------------------------ 39.42/6.88 % (2898495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 39.42/6.88 % (2898495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 39.42/6.88 % (2898495)CaDiCaL version: 2.1.3 39.42/6.88 % (2898495)Termination reason: Instruction limit 39.42/6.88 % (2898495)Termination phase: Saturation 39.42/6.88 % (2898495)Time elapsed: 0.125 s 39.42/6.88 % (2898495)Peak memory usage: 15 MB 39.42/6.88 % (2898495)Instructions burned: 286 (million) 39.42/6.88 % (2898504)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=1473143276:s2a=on:i=1142:s2at=3:bd=all:rtra=on_1744 on theBenchmark for (1744ds/1142Mi) 39.42/6.88 % (2898503)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=3940648787:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_1744 on theBenchmark for (1744ds/336Mi) 39.42/6.88 % (2898499)Instruction limit reached! 39.42/6.88 % (2898499)------------------------------ 39.42/6.88 % (2898499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 39.42/6.88 % (2898499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 39.42/6.88 % (2898499)CaDiCaL version: 2.1.3 39.42/6.88 % (2898499)Termination reason: Instruction limit 39.42/6.88 % (2898499)Termination phase: Saturation 39.42/6.88 % (2898499)Time elapsed: 0.184 s 39.42/6.88 % (2898499)Peak memory usage: 17 MB 39.42/6.88 % (2898499)Instructions burned: 408 (million) 39.42/6.88 % (2898507)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=663683509:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_1743 on theBenchmark for (1743ds/376Mi) 39.42/6.88 % (2898491)Instruction limit reached! 39.42/6.88 % (2898491)------------------------------ 39.42/6.88 % (2898491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 39.42/6.88 % (2898491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 39.42/6.88 % (2898491)CaDiCaL version: 2.1.3 39.42/6.88 % (2898491)Termination reason: Instruction limit 39.42/6.88 % (2898491)Termination phase: Saturation 39.42/6.88 % (2898491)Time elapsed: 0.379 s 39.42/6.88 % (2898491)Peak memory usage: 17 MB 39.42/6.88 % (2898491)Instructions burned: 858 (million) 39.42/6.88 % (2898503)Instruction limit reached! 39.42/6.88 % (2898503)------------------------------ 39.42/6.88 % (2898503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 39.42/6.88 % (2898503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 39.42/6.88 % (2898503)CaDiCaL version: 2.1.3 39.42/6.88 % (2898503)Termination reason: Instruction limit 39.42/6.88 % (2898503)Termination phase: Saturation 39.42/6.88 % (2898503)Time elapsed: 0.157 s 39.42/6.88 % (2898503)Peak memory usage: 16 MB 39.42/6.88 % (2898503)Instructions burned: 338 (million) 39.42/6.88 % (2898510)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on 39.42/6.88 % (2898510)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=1496342521: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_1742 on theBenchmark for (1742ds/959Mi) 42.59/7.06 % (2898509)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=1309475828:i=766:bd=all:rtra=on_1743 on theBenchmark for (1743ds/766Mi) 42.59/7.06 % (2898487)Instruction limit reached! 42.59/7.06 % (2898487)------------------------------ 42.59/7.06 % (2898487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.59/7.06 % (2898487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.59/7.06 % (2898487)CaDiCaL version: 2.1.3 42.59/7.06 % (2898487)Termination reason: Instruction limit 42.59/7.06 % (2898487)Termination phase: Saturation 42.59/7.06 % (2898487)Time elapsed: 0.563 s 42.59/7.06 % (2898487)Peak memory usage: 17 MB 42.59/7.06 % (2898487)Instructions burned: 670 (million) 42.59/7.06 % (2898513)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=3996118925:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_1742 on theBenchmark for (1742ds/6359Mi) 42.59/7.06 % (2898493)Instruction limit reached! 42.59/7.06 % (2898493)------------------------------ 42.59/7.06 % (2898493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.59/7.06 % (2898493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.59/7.06 % (2898493)CaDiCaL version: 2.1.3 42.59/7.06 % (2898493)Termination reason: Instruction limit 42.59/7.06 % (2898493)Termination phase: Saturation 42.59/7.06 % (2898493)Time elapsed: 0.487 s 42.59/7.06 % (2898493)Peak memory usage: 13 MB 42.59/7.06 % (2898493)Instructions burned: 693 (million) 42.59/7.06 % (2898515)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1984641818:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1741 on theBenchmark for (1741ds/35Mi) 42.59/7.06 % (2898515)Instruction limit reached! 42.59/7.06 % (2898515)------------------------------ 42.59/7.06 % (2898515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.59/7.06 % (2898515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.59/7.06 % (2898515)CaDiCaL version: 2.1.3 42.59/7.06 % (2898515)Termination reason: Instruction limit 42.59/7.06 % (2898515)Termination phase: SInE selection 42.59/7.06 % (2898515)Time elapsed: 0.029 s 42.59/7.06 % (2898515)Peak memory usage: 10 MB 42.59/7.06 % (2898515)Instructions burned: 36 (million) 42.59/7.06 % (2898517)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=272900228:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_1740 on theBenchmark for (1740ds/53Mi) 42.59/7.06 % (2898517)Instruction limit reached! 42.59/7.06 % (2898517)------------------------------ 42.59/7.06 % (2898517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.59/7.06 % (2898517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.59/7.06 % (2898517)CaDiCaL version: 2.1.3 42.59/7.06 % (2898517)Termination reason: Instruction limit 42.59/7.06 % (2898517)Termination phase: Property scanning 42.59/7.06 % (2898517)Time elapsed: 0.022 s 42.59/7.06 % (2898517)Peak memory usage: 10 MB 42.59/7.06 % (2898517)Instructions burned: 53 (million) 42.59/7.06 % (2898507)Instruction limit reached! 42.59/7.06 % (2898507)------------------------------ 42.59/7.06 % (2898507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.59/7.06 % (2898507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.59/7.06 % (2898507)CaDiCaL version: 2.1.3 42.59/7.06 % (2898507)Termination reason: Instruction limit 42.59/7.06 % (2898507)Termination phase: Saturation 42.59/7.06 % (2898507)Time elapsed: 0.297 s 42.59/7.06 % (2898507)Peak memory usage: 17 MB 42.59/7.06 % (2898507)Instructions burned: 377 (million) 42.59/7.06 % (2898504)Refutation not found, incomplete strategy 42.59/7.06 % (2898504)------------------------------ 42.59/7.06 % (2898504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 42.59/7.06 % (2898504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 42.59/7.06 % (2898504)CaDiCaL version: 2.1.3 42.59/7.06 % (2898504)Termination reason: Refutation not found, incomplete strategy 42.59/7.06 % (2898504)Time elapsed: 0.454 s 42.59/7.06 % (2898504)Peak memory usage: 19 MB 42.59/7.06 % (2898504)Instructions burned: 862 (million) 42.59/7.06 % (2898519)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=277899198:s2a=on:i=876:s2at=6:nm=2:rtra=on_1740 on theBenchmark for (1740ds/876Mi) 43.62/7.26 % (2898504)------------------------------ 43.62/7.26 % (2898504)------------------------------ 43.62/7.26 % (2898520)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1198262729:i=57:ep=R:rtra=on:ntd=on_1740 on theBenchmark for (1740ds/57Mi) 43.62/7.26 % (2898522)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 43.62/7.26 % (2898522)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3351541229:i=306:bd=all:rtra=on_1739 on theBenchmark for (1739ds/306Mi) 43.62/7.26 % (2898520)Instruction limit reached! 43.62/7.26 % (2898520)------------------------------ 43.62/7.26 % (2898520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 43.62/7.26 % (2898520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 43.62/7.26 % (2898520)CaDiCaL version: 2.1.3 43.62/7.26 % (2898520)Termination reason: Instruction limit 43.62/7.26 % (2898520)Termination phase: Property scanning 43.62/7.26 % (2898520)Time elapsed: 0.025 s 43.62/7.26 % (2898520)Peak memory usage: 11 MB 43.62/7.26 % (2898520)Instructions burned: 59 (million) 43.62/7.26 % (2898525)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=4259665338:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_1739 on theBenchmark for (1739ds/262Mi) 43.62/7.26 % (2898509)Instruction limit reached! 43.62/7.26 % (2898509)------------------------------ 43.62/7.26 % (2898509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 43.62/7.26 % (2898509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 43.62/7.26 % (2898509)CaDiCaL version: 2.1.3 43.62/7.26 % (2898509)Termination reason: Instruction limit 43.62/7.26 % (2898509)Termination phase: Saturation 43.62/7.26 % (2898509)Time elapsed: 0.415 s 43.62/7.26 % (2898509)Peak memory usage: 20 MB 43.62/7.26 % (2898509)Instructions burned: 767 (million) 43.62/7.26 % (2898522)Instruction limit reached! 43.62/7.26 % (2898522)------------------------------ 43.62/7.26 % (2898522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 43.62/7.26 % (2898522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 43.62/7.26 % (2898522)CaDiCaL version: 2.1.3 43.62/7.26 % (2898522)Termination reason: Instruction limit 43.62/7.26 % (2898522)Termination phase: Saturation 43.62/7.26 % (2898522)Time elapsed: 0.141 s 43.62/7.26 % (2898522)Peak memory usage: 16 MB 43.62/7.26 % (2898522)Instructions burned: 306 (million) 43.62/7.26 % (2898527)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on 43.62/7.26 % (2898528)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=3027043392:s2a=on:i=381:rtra=on_1738 on theBenchmark for (1738ds/381Mi) 43.62/7.26 % (2898527)ott+1002_16_sil=128000:si=on:random_seed=4039350076:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_1738 on theBenchmark for (1738ds/409Mi) 43.62/7.26 % (2898525)Instruction limit reached! 43.62/7.26 % (2898525)------------------------------ 43.62/7.26 % (2898525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 43.62/7.26 % (2898525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 43.62/7.26 % (2898525)CaDiCaL version: 2.1.3 43.62/7.26 % (2898525)Termination reason: Instruction limit 43.62/7.26 % (2898525)Termination phase: Saturation 43.62/7.26 % (2898525)Time elapsed: 0.139 s 43.62/7.26 % (2898525)Peak memory usage: 15 MB 43.62/7.26 % (2898525)Instructions burned: 262 (million) 43.62/7.26 % (2898531)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=606435503:cond=on:i=324:rtra=on:ntd=on_1737 on theBenchmark for (1737ds/324Mi) 43.62/7.26 % (2898528)Instruction limit reached! 43.62/7.26 % (2898528)------------------------------ 43.62/7.26 % (2898528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 43.62/7.26 % (2898528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 43.62/7.26 % (2898528)CaDiCaL version: 2.1.3 43.62/7.26 % (2898528)Termination reason: Instruction limit 43.62/7.26 % (2898528)Termination phase: Saturation 43.62/7.26 % (2898528)Time elapsed: 0.167 s 43.62/7.26 % (2898528)Peak memory usage: 16 MB 43.62/7.26 % (2898528)Instructions burned: 382 (million) 43.62/7.26 % (2898531)Instruction limit reached! 44.71/7.40 % (2898531)------------------------------ 44.71/7.40 % (2898531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 44.71/7.40 % (2898531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 44.71/7.40 % (2898531)CaDiCaL version: 2.1.3 44.71/7.40 % (2898531)Termination reason: Instruction limit 44.71/7.40 % (2898531)Termination phase: Saturation 44.71/7.40 % (2898531)Time elapsed: 0.155 s 44.71/7.40 % (2898531)Peak memory usage: 16 MB 44.71/7.40 % (2898531)Instructions burned: 325 (million) 44.71/7.40 % (2898533)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=3609851314:i=240:kws=inv_precedence:rtra=on_1736 on theBenchmark for (1736ds/240Mi) 44.71/7.40 % (2898534)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 44.71/7.40 % (2898527)Instruction limit reached! 44.71/7.40 % (2898527)------------------------------ 44.71/7.40 % (2898527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 44.71/7.40 % (2898527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 44.71/7.40 % (2898527)CaDiCaL version: 2.1.3 44.71/7.40 % (2898527)Termination reason: Instruction limit 44.71/7.40 % (2898527)Termination phase: Saturation 44.71/7.40 % (2898527)Time elapsed: 0.231 s 44.71/7.40 % (2898527)Peak memory usage: 16 MB 44.71/7.40 % (2898527)Instructions burned: 410 (million) 44.71/7.40 % (2898534)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=13612558:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_1736 on theBenchmark for (1736ds/124Mi) 44.71/7.40 % (2898536)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=1397574303:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_1735 on theBenchmark for (1735ds/223Mi) 44.71/7.40 % (2898510)Instruction limit reached! 44.71/7.40 % (2898510)------------------------------ 44.71/7.40 % (2898510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 44.71/7.40 % (2898510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 44.71/7.40 % (2898510)CaDiCaL version: 2.1.3 44.71/7.40 % (2898510)Termination reason: Instruction limit 44.71/7.40 % (2898510)Termination phase: Saturation 44.71/7.40 % (2898510)Time elapsed: 0.733 s 44.71/7.40 % (2898510)Peak memory usage: 20 MB 44.71/7.40 % (2898510)Instructions burned: 959 (million) 44.71/7.40 % (2898539)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1946149693:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_1735 on theBenchmark for (1735ds/282Mi) 44.71/7.40 % (2898533)Instruction limit reached! 44.71/7.40 % (2898533)------------------------------ 44.71/7.40 % (2898533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 44.71/7.40 % (2898533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 44.71/7.40 % (2898533)CaDiCaL version: 2.1.3 44.71/7.40 % (2898533)Termination reason: Instruction limit 44.71/7.40 % (2898533)Termination phase: Saturation 44.71/7.40 % (2898533)Time elapsed: 0.109 s 44.71/7.40 % (2898533)Peak memory usage: 15 MB 44.71/7.40 % (2898533)Instructions burned: 240 (million) 44.71/7.40 % (2898534)Instruction limit reached! 44.71/7.40 % (2898534)------------------------------ 44.71/7.40 % (2898534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 44.71/7.40 % (2898534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 44.71/7.40 % (2898534)CaDiCaL version: 2.1.3 44.71/7.40 % (2898534)Termination reason: Instruction limit 44.71/7.40 % (2898534)Termination phase: Property scanning 44.71/7.40 % (2898534)Time elapsed: 0.102 s 44.71/7.40 % (2898534)Peak memory usage: 12 MB 44.71/7.40 % (2898534)Instructions burned: 124 (million) 44.71/7.40 % (2898541)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=3472749399:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_1735 on theBenchmark for (1735ds/464Mi) 44.71/7.40 % (2898536)Instruction limit reached! 44.71/7.40 % (2898536)------------------------------ 44.71/7.40 % (2898536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 44.71/7.40 % (2898536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 44.71/7.40 % (2898536)CaDiCaL version: 2.1.3 44.71/7.40 % (2898536)Termination reason: Instruction limit 44.71/7.40 % (2898536)Termination phase: Saturation 44.71/7.40 % (2898536)Time elapsed: 0.099 s 44.71/7.40 % (2898536)Peak memory usage: 14 MB 44.71/7.40 % (2898536)Instructions burned: 224 (million) 44.71/7.40 % (2898542)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=3350287164:i=88:s2at=3:nm=2:rtra=on:rawr=on_1734 on theBenchmark for (1734ds/88Mi) 45.65/7.85 % (2898544)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1507468952:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_1734 on theBenchmark for (1734ds/280Mi) 45.65/7.85 % (2898542)Instruction limit reached! 45.65/7.85 % (2898542)------------------------------ 45.65/7.85 % (2898542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.65/7.85 % (2898542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.65/7.85 % (2898542)CaDiCaL version: 2.1.3 45.65/7.85 % (2898542)Termination reason: Instruction limit 45.65/7.85 % (2898542)Termination phase: Property scanning 45.65/7.85 % (2898542)Time elapsed: 0.036 s 45.65/7.85 % (2898542)Peak memory usage: 11 MB 45.65/7.85 % (2898542)Instructions burned: 89 (million) 45.65/7.85 % (2898547)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 45.65/7.85 % (2898539)Instruction limit reached! 45.65/7.85 % (2898539)------------------------------ 45.65/7.85 % (2898539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.65/7.85 % (2898539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.65/7.85 % (2898539)CaDiCaL version: 2.1.3 45.65/7.85 % (2898539)Termination reason: Instruction limit 45.65/7.85 % (2898539)Termination phase: Saturation 45.65/7.85 % (2898539)Time elapsed: 0.127 s 45.65/7.85 % (2898539)Peak memory usage: 15 MB 45.65/7.85 % (2898539)Instructions burned: 282 (million) 45.65/7.85 % (2898547)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3996578694:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_1734 on theBenchmark for (1734ds/4386Mi) 45.65/7.85 % (2898549)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection 45.65/7.85 % (2898549)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off 45.65/7.85 % (2898549)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=930463792:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_1733 on theBenchmark for (1733ds/483Mi) 45.65/7.85 % (2898544)Instruction limit reached! 45.65/7.85 % (2898544)------------------------------ 45.65/7.85 % (2898544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.65/7.85 % (2898544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.65/7.85 % (2898544)CaDiCaL version: 2.1.3 45.65/7.85 % (2898544)Termination reason: Instruction limit 45.65/7.85 % (2898544)Termination phase: Saturation 45.65/7.85 % (2898544)Time elapsed: 0.117 s 45.65/7.85 % (2898544)Peak memory usage: 13 MB 45.65/7.85 % (2898544)Instructions burned: 280 (million) 45.65/7.85 % (2898551)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2919497235:i=73:rtra=on_1733 on theBenchmark for (1733ds/73Mi) 45.65/7.85 % (2898551)Instruction limit reached! 45.65/7.85 % (2898551)------------------------------ 45.65/7.85 % (2898551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.65/7.85 % (2898551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.65/7.85 % (2898551)CaDiCaL version: 2.1.3 45.65/7.85 % (2898551)Termination reason: Instruction limit 45.65/7.85 % (2898551)Termination phase: Preprocessing 3 45.65/7.85 % (2898551)Time elapsed: 0.033 s 45.65/7.85 % (2898551)Peak memory usage: 12 MB 45.65/7.85 % (2898551)Instructions burned: 74 (million) 45.65/7.85 % (2898553)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=854589125:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1732 on theBenchmark for (1732ds/176Mi) 45.65/7.85 % (2898519)Instruction limit reached! 45.65/7.85 % (2898519)------------------------------ 45.65/7.85 % (2898519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 45.65/7.85 % (2898519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 45.65/7.85 % (2898519)CaDiCaL version: 2.1.3 49.20/8.10 % (2898519)Termination reason: Instruction limit 49.20/8.10 % (2898519)Termination phase: Saturation 49.20/8.10 % (2898519)Time elapsed: 0.756 s 49.20/8.10 % (2898519)Peak memory usage: 17 MB 49.20/8.10 % (2898519)Instructions burned: 877 (million) 49.20/8.10 % (2898555)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off 49.20/8.10 % (2898555)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3843926554:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_1732 on theBenchmark for (1732ds/39Mi) 49.20/8.10 % (2898555)Instruction limit reached! 49.20/8.10 % (2898555)------------------------------ 49.20/8.10 % (2898555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.20/8.10 % (2898555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.20/8.10 % (2898555)CaDiCaL version: 2.1.3 49.20/8.10 % (2898555)Termination reason: Instruction limit 49.20/8.10 % (2898555)Termination phase: Property scanning 49.20/8.10 % (2898555)Time elapsed: 0.031 s 49.20/8.10 % (2898555)Peak memory usage: 10 MB 49.20/8.10 % (2898555)Instructions burned: 39 (million) 49.20/8.10 % (2898553)Instruction limit reached! 49.20/8.10 % (2898553)------------------------------ 49.20/8.10 % (2898553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.20/8.10 % (2898553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.20/8.10 % (2898553)CaDiCaL version: 2.1.3 49.20/8.10 % (2898553)Termination reason: Instruction limit 49.20/8.10 % (2898553)Termination phase: Saturation 49.20/8.10 % (2898553)Time elapsed: 0.078 s 49.20/8.10 % (2898553)Peak memory usage: 12 MB 49.20/8.10 % (2898553)Instructions burned: 177 (million) 49.20/8.10 % (2898501)Instruction limit reached! 49.20/8.10 % (2898501)------------------------------ 49.20/8.10 % (2898501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.20/8.10 % (2898501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.20/8.10 % (2898501)CaDiCaL version: 2.1.3 49.20/8.10 % (2898501)Termination reason: Instruction limit 49.20/8.10 % (2898501)Termination phase: Saturation 49.20/8.10 % (2898501)Time elapsed: 1.327 s 49.20/8.10 % (2898501)Peak memory usage: 23 MB 49.20/8.10 % (2898501)Instructions burned: 2242 (million) 49.20/8.10 % (2898549)Instruction limit reached! 49.20/8.10 % (2898549)------------------------------ 49.20/8.10 % (2898549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.20/8.10 % (2898549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.20/8.10 % (2898549)CaDiCaL version: 2.1.3 49.20/8.10 % (2898549)Termination reason: Instruction limit 49.20/8.10 % (2898549)Termination phase: Saturation 49.20/8.10 % (2898549)Time elapsed: 0.213 s 49.20/8.10 % (2898549)Peak memory usage: 17 MB 49.20/8.10 % (2898549)Instructions burned: 485 (million) 49.20/8.10 % (2898558)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 49.20/8.10 % (2898558)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=3667617379:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_1731 on theBenchmark for (1731ds/252Mi) 49.20/8.10 % (2898557)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3005230600:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1731 on theBenchmark for (1731ds/708Mi) 49.20/8.10 % (2898559)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=24193041:i=823:fsr=off:rtra=on_1731 on theBenchmark for (1731ds/823Mi) 49.20/8.10 % (2898541)Instruction limit reached! 49.20/8.10 % (2898541)------------------------------ 49.20/8.10 % (2898541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 49.20/8.10 % (2898541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 49.20/8.10 % (2898541)CaDiCaL version: 2.1.3 49.20/8.10 % (2898541)Termination reason: Instruction limit 49.20/8.10 % (2898541)Termination phase: Saturation 49.20/8.10 % (2898541)Time elapsed: 0.343 s 49.20/8.10 % (2898541)Peak memory usage: 17 MB 49.20/8.10 % (2898541)Instructions burned: 464 (million) 49.20/8.10 % (2898560)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100 49.20/8.10 % (2898560)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=2303606396:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_1731 on theBenchmark for (1731ds/16202Mi) 52.36/8.65 % (2898564)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=2086487868:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_1731 on theBenchmark for (1731ds/300Mi) 52.36/8.65 % (2898558)Instruction limit reached! 52.36/8.65 % (2898558)------------------------------ 52.36/8.65 % (2898558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 52.36/8.65 % (2898558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 52.36/8.65 % (2898558)CaDiCaL version: 2.1.3 52.36/8.65 % (2898558)Termination reason: Instruction limit 52.36/8.65 % (2898558)Termination phase: Saturation 52.36/8.65 % (2898558)Time elapsed: 0.112 s 52.36/8.65 % (2898558)Peak memory usage: 15 MB 52.36/8.65 % (2898558)Instructions burned: 253 (million) 52.36/8.65 % (2898567)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on 52.36/8.65 % (2898567)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on 52.36/8.65 % (2898567)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=1212136127:i=177:add=on:bd=preordered:rtra=on:rawr=on_1730 on theBenchmark for (1730ds/177Mi) 52.36/8.65 % (2898564)Instruction limit reached! 52.36/8.65 % (2898564)------------------------------ 52.36/8.65 % (2898564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 52.36/8.65 % (2898564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 52.36/8.65 % (2898564)CaDiCaL version: 2.1.3 52.36/8.65 % (2898564)Termination reason: Instruction limit 52.36/8.65 % (2898564)Termination phase: Saturation 52.36/8.65 % (2898564)Time elapsed: 0.114 s 52.36/8.65 % (2898564)Peak memory usage: 12 MB 52.36/8.65 % (2898564)Instructions burned: 301 (million) 52.36/8.65 % (2898569)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=4040871950:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_1729 on theBenchmark for (1729ds/715Mi) 52.36/8.65 % (2898567)Instruction limit reached! 52.36/8.65 % (2898567)------------------------------ 52.36/8.65 % (2898567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 52.36/8.65 % (2898567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 52.36/8.65 % (2898567)CaDiCaL version: 2.1.3 52.36/8.65 % (2898567)Termination reason: Instruction limit 52.36/8.65 % (2898567)Termination phase: Property scanning 52.36/8.65 % (2898567)Time elapsed: 0.081 s 52.36/8.65 % (2898567)Peak memory usage: 13 MB 52.36/8.65 % (2898567)Instructions burned: 179 (million) 52.36/8.65 % (2898571)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on 52.36/8.65 % (2898571)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on 52.36/8.65 % (2898571)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=1664169188:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1729 on theBenchmark for (1729ds/230Mi) 52.36/8.65 % (2898571)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use 52.36/8.65 % (2898571)Instruction limit reached! 52.36/8.65 % (2898571)------------------------------ 52.36/8.65 % (2898571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 52.36/8.65 % (2898571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 52.36/8.65 % (2898571)CaDiCaL version: 2.1.3 52.36/8.65 % (2898571)Termination reason: Instruction limit 52.36/8.65 % (2898571)Termination phase: Saturation 52.36/8.65 % (2898571)Time elapsed: 0.118 s 52.36/8.65 % (2898571)Peak memory usage: 16 MB 52.36/8.65 % (2898571)Instructions burned: 231 (million) 52.36/8.65 % (2898573)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=1101946148:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_1727 on theBenchmark for (1727ds/606Mi) 52.36/8.65 % (2898569)Instruction limit reached! 52.36/8.65 % (2898569)------------------------------ 52.36/8.65 % (2898569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898569)CaDiCaL version: 2.1.3 50.81/8.71 % (2898569)Termination reason: Instruction limit 50.81/8.71 % (2898569)Termination phase: Saturation 50.81/8.71 % (2898569)Time elapsed: 0.308 s 50.81/8.71 % (2898569)Peak memory usage: 15 MB 50.81/8.71 % (2898569)Instructions burned: 715 (million) 50.81/8.71 % (2898575)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs 50.81/8.71 % (2898575)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=1337983097:lrd=on:i=841:nm=0:rtra=on_1726 on theBenchmark for (1726ds/841Mi) 50.81/8.71 % (2898557)Instruction limit reached! 50.81/8.71 % (2898557)------------------------------ 50.81/8.71 % (2898557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898557)CaDiCaL version: 2.1.3 50.81/8.71 % (2898557)Termination reason: Instruction limit 50.81/8.71 % (2898557)Termination phase: Saturation 50.81/8.71 % (2898557)Time elapsed: 0.558 s 50.81/8.71 % (2898557)Peak memory usage: 17 MB 50.81/8.71 % (2898557)Instructions burned: 709 (million) 50.81/8.71 % (2898577)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1606038852:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1725 on theBenchmark for (1725ds/445Mi) 50.81/8.71 % (2898559)Instruction limit reached! 50.81/8.71 % (2898559)------------------------------ 50.81/8.71 % (2898559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898559)CaDiCaL version: 2.1.3 50.81/8.71 % (2898559)Termination reason: Instruction limit 50.81/8.71 % (2898559)Termination phase: Saturation 50.81/8.71 % (2898559)Time elapsed: 0.608 s 50.81/8.71 % (2898559)Peak memory usage: 13 MB 50.81/8.71 % (2898559)Instructions burned: 824 (million) 50.81/8.71 % (2898579)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3361207137:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_1725 on theBenchmark for (1725ds/71Mi) 50.81/8.71 % (2898573)Instruction limit reached! 50.81/8.71 % (2898573)------------------------------ 50.81/8.71 % (2898573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898573)CaDiCaL version: 2.1.3 50.81/8.71 % (2898573)Termination reason: Instruction limit 50.81/8.71 % (2898573)Termination phase: Saturation 50.81/8.71 % (2898573)Time elapsed: 0.291 s 50.81/8.71 % (2898573)Peak memory usage: 17 MB 50.81/8.71 % (2898573)Instructions burned: 608 (million) 50.81/8.71 % (2898579)Instruction limit reached! 50.81/8.71 % (2898579)------------------------------ 50.81/8.71 % (2898579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898579)CaDiCaL version: 2.1.3 50.81/8.71 % (2898579)Termination reason: Instruction limit 50.81/8.71 % (2898579)Termination phase: Property scanning 50.81/8.71 % (2898579)Time elapsed: 0.031 s 50.81/8.71 % (2898579)Peak memory usage: 11 MB 50.81/8.71 % (2898579)Instructions burned: 73 (million) 50.81/8.71 % (2898581)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 50.81/8.71 % (2898581)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 50.81/8.71 % (2898582)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on 50.81/8.71 % (2898581)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=609342062:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1724 on theBenchmark for (1724ds/100Mi) 50.81/8.71 % (2898582)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=3461355012:i=1352:add=on:aac=none:rtra=on_1724 on theBenchmark for (1724ds/1352Mi) 50.81/8.71 % (2898581)Instruction limit reached! 50.81/8.71 % (2898581)------------------------------ 50.81/8.71 % (2898581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898581)CaDiCaL version: 2.1.3 50.81/8.71 % (2898581)Termination reason: Instruction limit 50.81/8.71 % (2898581)Termination phase: Twee Goal Transformation 50.81/8.71 % (2898581)Time elapsed: 0.042 s 50.81/8.71 % (2898581)Peak memory usage: 11 MB 50.81/8.71 % (2898581)Instructions burned: 102 (million) 50.81/8.71 % (2898585)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=3390435737:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_1724 on theBenchmark for (1724ds/646Mi) 50.81/8.71 % (2898577)Instruction limit reached! 50.81/8.71 % (2898577)------------------------------ 50.81/8.71 % (2898577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898577)CaDiCaL version: 2.1.3 50.81/8.71 % (2898577)Termination reason: Instruction limit 50.81/8.71 % (2898577)Termination phase: Saturation 50.81/8.71 % (2898577)Time elapsed: 0.350 s 50.81/8.71 % (2898577)Peak memory usage: 15 MB 50.81/8.71 % (2898577)Instructions burned: 446 (million) 50.81/8.71 % (2898587)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=3195200359:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_1721 on theBenchmark for (1721ds/1924Mi) 50.81/8.71 % (2898575)Instruction limit reached! 50.81/8.71 % (2898575)------------------------------ 50.81/8.71 % (2898575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898575)CaDiCaL version: 2.1.3 50.81/8.71 % (2898575)Termination reason: Instruction limit 50.81/8.71 % (2898575)Termination phase: Property scanning 50.81/8.71 % (2898575)Time elapsed: 0.538 s 50.81/8.71 % (2898575)Peak memory usage: 16 MB 50.81/8.71 % (2898575)Instructions burned: 842 (million) 50.81/8.71 % (2898585)Instruction limit reached! 50.81/8.71 % (2898585)------------------------------ 50.81/8.71 % (2898585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898585)CaDiCaL version: 2.1.3 50.81/8.71 % (2898585)Termination reason: Instruction limit 50.81/8.71 % (2898585)Termination phase: Saturation 50.81/8.71 % (2898585)Time elapsed: 0.298 s 50.81/8.71 % (2898585)Peak memory usage: 17 MB 50.81/8.71 % (2898585)Instructions burned: 652 (million) 50.81/8.71 % (2898589)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=2999826471:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1720 on theBenchmark for (1720ds/984Mi) 50.81/8.71 % (2898590)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=2018295580:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_1720 on theBenchmark for (1720ds/592Mi) 50.81/8.71 % (2898547)Instruction limit reached! 50.81/8.71 % (2898547)------------------------------ 50.81/8.71 % (2898547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898547)CaDiCaL version: 2.1.3 50.81/8.71 % (2898547)Termination reason: Instruction limit 50.81/8.71 % (2898547)Termination phase: Saturation 50.81/8.71 % (2898547)Time elapsed: 1.475 s 50.81/8.71 % (2898547)Peak memory usage: 18 MB 50.81/8.71 % (2898547)Instructions burned: 4389 (million) 50.81/8.71 % (2898582)Instruction limit reached! 50.81/8.71 % (2898582)------------------------------ 50.81/8.71 % (2898582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.71 % (2898582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.71 % (2898582)CaDiCaL version: 2.1.3 50.81/8.71 % (2898582)Termination reason: Instruction limit 50.81/8.71 % (2898582)Termination phase: Saturation 50.81/8.71 % (2898582)Time elapsed: 0.579 s 50.81/8.71 % (2898582)Peak memory usage: 24 MB 50.81/8.71 % (2898582)Instructions burned: 1352 (million) 50.81/8.71 % (2898513) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2898188-2898513"... 50.81/8.71 % (2898593)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=1105477734:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_1719 on theBenchmark for (1719ds/872Mi) 50.81/8.71 % (2898594)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 50.81/8.71 % (2898594)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=2944814751:i=999:add=on:rtra=on_1718 on theBenchmark for (1718ds/999Mi) 50.81/8.71 % (2898513)...printing done. 50.81/8.71 % (2898513)Refutation found. Thanks to Tanya! 50.81/8.71 % SZS status Theorem for theBenchmark 50.81/8.71 % SZS output start Proof for theBenchmark 50.81/8.71 thf(type_def_5, type, term: $tType). 50.81/8.71 thf(type_def_6, type, subst: $tType). 50.81/8.71 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType). 50.81/8.71 thf(type_def_8, type, d_term: $tType). 50.81/8.71 thf(type_def_9, type, d_subst: $tType). 50.81/8.71 thf(func_def_0, type, one: term). 50.81/8.71 thf(func_def_1, type, ap: (term > term > term)). 50.81/8.71 thf(func_def_2, type, lam: (term > term)). 50.81/8.71 thf(func_def_3, type, sub: (term > subst > term)). 50.81/8.71 thf(func_def_4, type, id: subst). 50.81/8.71 thf(func_def_5, type, sh: subst). 50.81/8.71 thf(func_def_6, type, push: (term > subst > subst)). 50.81/8.71 thf(func_def_7, type, comp: (subst > subst > subst)). 50.81/8.71 thf(func_def_8, type, var: (term > $o)). 50.81/8.71 thf(func_def_9, type, pushprop_lem1v2: $o). 50.81/8.71 thf(func_def_10, type, pushprop_lem1_gthm: $o). 50.81/8.71 thf(func_def_11, type, axmap: $o). 50.81/8.71 thf(func_def_12, type, pushprop_lem0_gthm: $o). 50.81/8.71 thf(func_def_13, type, shinj: $o). 50.81/8.71 thf(func_def_14, type, hoasinduction_lem1v2: $o). 50.81/8.71 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o). 50.81/8.71 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)). 50.81/8.71 thf(func_def_17, type, induction2lem: $o). 50.81/8.71 thf(func_def_18, type, hoasinduction_lem3v2_f: $o). 50.81/8.71 thf(func_def_19, type, axvarshift: $o). 50.81/8.71 thf(func_def_20, type, hoasapinj2: $o). 50.81/8.71 thf(func_def_21, type, hoasapnotvar_gthm: $o). 50.81/8.71 thf(func_def_22, type, hoasapinj1: $o). 50.81/8.71 thf(func_def_23, type, ulamvar1: $o). 50.81/8.71 thf(func_def_24, type, induction2lem_lthm: $o). 50.81/8.71 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o). 50.81/8.71 thf(func_def_26, type, apnotvar: $o). 50.81/8.71 thf(func_def_27, type, pushprop_lthm_orig: $o). 50.81/8.71 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o). 50.81/8.71 thf(func_def_29, type, hoasinduction_lthm: $o). 50.81/8.71 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o). 50.81/8.71 thf(func_def_31, type, hoaslaminj: $o). 50.81/8.71 thf(func_def_32, type, hoasinduction_lem3aaa: $o). 50.81/8.71 thf(func_def_33, type, induction2lem_gthm: $o). 50.81/8.71 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o). 50.81/8.71 thf(func_def_35, type, hoasinduction_lem3: $o). 50.81/8.71 thf(func_def_36, type, hoasinduction_lem2: $o). 50.81/8.71 thf(func_def_37, type, termmset_lthm: $o). 50.81/8.71 thf(func_def_38, type, hoasinduction_lem1: $o). 50.81/8.71 thf(func_def_39, type, hoaslamnotap_lthm: $o). 50.81/8.71 thf(func_def_40, type, pushprop_lem1v2_lthm: $o). 50.81/8.71 thf(func_def_41, type, hoasapnotvar: $o). 50.81/8.71 thf(func_def_42, type, hoasinduction_lem0: $o). 50.81/8.71 thf(func_def_43, type, hoasinduction: $o). 50.81/8.71 thf(func_def_44, type, hoasinduction_gthm: $o). 50.81/8.71 thf(func_def_45, type, axapp: $o). 50.81/8.71 thf(func_def_46, type, hoaslamnotvar_lthm: $o). 50.81/8.71 thf(func_def_47, type, pushprop_lem3v2_lthm: $o). 50.81/8.71 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o). 50.81/8.71 thf(func_def_49, type, ulamvarind: $o). 50.81/8.71 thf(func_def_50, type, induction: $o). 50.81/8.71 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o). 50.81/8.71 thf(func_def_52, type, termmset_gthm: $o). 50.81/8.71 thf(func_def_53, type, hoasinduction_lem3aa: $o). 50.81/8.71 thf(func_def_54, type, pushprop_lem1v2_gthm: $o). 50.81/8.71 thf(func_def_55, type, hoaslamnotap_gthm: $o). 50.81/8.71 thf(func_def_56, type, hoaslamnotvar_gthm: $o). 50.81/8.71 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o). 50.81/8.71 thf(func_def_58, type, pushprop_lem2v2: $o). 50.81/8.71 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o). 50.81/8.71 thf(func_def_60, type, axclos: $o). 50.81/8.71 thf(func_def_61, type, axassoc: $o). 50.81/8.71 thf(func_def_62, type, hoasinduction_lem2v2: $o). 50.81/8.71 thf(func_def_63, type, pushprop_lthm: $o). 50.81/8.71 thf(func_def_64, type, apinj2: $o). 50.81/8.71 thf(func_def_65, type, apinj1: $o). 50.81/8.71 thf(func_def_66, type, hoasapinj2_lthm: $o). 50.81/8.71 thf(func_def_67, type, hoasinduction_lem3v2a: $o). 50.81/8.71 thf(func_def_68, type, hoasapinj1_lthm: $o). 50.81/8.71 thf(func_def_69, type, hoaslaminj_lthm: $o). 50.81/8.71 thf(func_def_70, type, axvarcons: $o). 50.81/8.71 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)). 50.81/8.71 thf(func_def_72, type, axscons: $o). 50.81/8.71 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o). 50.81/8.71 thf(func_def_74, type, axidr: $o). 50.81/8.71 thf(func_def_75, type, pushprop_lem1: $o). 50.81/8.71 thf(func_def_76, type, laminj: $o). 50.81/8.71 thf(func_def_77, type, hoasinduction_lem3_lthm: $o). 50.81/8.71 thf(func_def_78, type, pushprop_lem0: $o). 50.81/8.71 thf(func_def_79, type, pushprop_gthm: $o). 50.81/8.71 thf(func_def_80, type, axabs: $o). 50.81/8.71 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o). 50.81/8.71 thf(func_def_82, type, hoasinduction_lem2_lthm: $o). 50.81/8.71 thf(func_def_83, type, hoasapinj2_gthm: $o). 50.81/8.71 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)). 50.81/8.71 thf(func_def_85, type, hoasinduction_lem1_lthm: $o). 50.81/8.71 thf(func_def_86, type, lamnotap: $o). 50.81/8.71 thf(func_def_87, type, hoasapinj1_gthm: $o). 50.81/8.71 thf(func_def_88, type, hoaslamnotvar: $o). 50.81/8.71 thf(func_def_89, type, axidl: $o). 50.81/8.71 thf(func_def_90, type, hoaslaminj_gthm: $o). 50.81/8.71 thf(func_def_91, type, induction2_lthm: $o). 50.81/8.71 thf(func_def_92, type, hoasinduction_lem0_lthm: $o). 50.81/8.71 thf(func_def_93, type, substmonoid_lthm: $o). 50.81/8.71 thf(func_def_94, type, pushprop: $o). 50.81/8.71 thf(func_def_95, type, hoasinduction_lem3_gthm: $o). 50.81/8.71 thf(func_def_96, type, hoasinduction_lem2_gthm: $o). 50.81/8.71 thf(func_def_97, type, hoasinduction_lem3b: $o). 50.81/8.71 thf(func_def_98, type, substmonoid: $o). 50.81/8.71 thf(func_def_99, type, lamnotvar: $o). 50.81/8.71 thf(func_def_100, type, hoasinduction_lem3a: $o). 50.81/8.71 thf(func_def_101, type, hoasinduction_lem1_gthm: $o). 50.81/8.71 thf(func_def_102, type, hoasinduction_no_psi_cond: $o). 50.81/8.71 thf(func_def_103, type, induction2_gthm: $o). 50.81/8.71 thf(func_def_104, type, pushprop_lem2v2_lthm: $o). 50.81/8.71 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_106, type, hoaslamnotap: $o). 50.81/8.71 thf(func_def_107, type, substmonoid_gthm: $o). 50.81/8.71 thf(func_def_108, type, ulamvarsh: $o). 50.81/8.71 thf(func_def_109, type, induction2: $o). 50.81/8.71 thf(func_def_110, type, pushprop_lem3v2: $o). 50.81/8.71 thf(func_def_111, type, pushprop_lem2v2_gthm: $o). 50.81/8.71 thf(func_def_112, type, pushprop_lem1_lthm: $o). 50.81/8.71 thf(func_def_113, type, hoasinduction_lem3v2: $o). 50.81/8.71 thf(func_def_114, type, axshiftcons: $o). 50.81/8.71 thf(func_def_115, type, termmset: $o). 50.81/8.71 thf(func_def_116, type, pushprop_lem0_lthm: $o). 50.81/8.71 thf(func_def_117, type, hoasapnotvar_lthm: $o). 50.81/8.71 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o). 50.81/8.71 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)). 50.81/8.71 thf(func_def_120, type, axvarid: $o). 50.81/8.71 thf(func_def_121, type, hoasinduction_lthm_3: $o). 50.81/8.71 thf(func_def_122, type, d2term: (d_term > term)). 50.81/8.71 thf(func_def_123, type, d2subst: (d_subst > subst)). 50.81/8.71 thf(func_def_124, type, d_one: d_term). 50.81/8.71 thf(func_def_125, type, d_id: d_subst). 50.81/8.71 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)). 50.81/8.71 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)). 50.81/8.71 thf(func_def_131, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 50.81/8.71 thf(func_def_132, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 50.81/8.71 thf(func_def_133, type, db2: !>[X0: $tType]:(X0)). 50.81/8.71 thf(func_def_134, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 50.81/8.71 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)). 50.81/8.71 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)). 50.81/8.71 thf(func_def_137, type, sP0: ((term > $o) > $o)). 50.81/8.71 thf(func_def_138, type, sP1: ((term > $o) > $o)). 50.81/8.71 thf(func_def_139, type, sP2: $o). 50.81/8.71 thf(func_def_140, type, sP3: $o). 50.81/8.71 thf(func_def_141, type, sP4: ((term > $o) > $o)). 50.81/8.71 thf(func_def_142, type, sP5: $o). 50.81/8.71 thf(func_def_143, type, sP6: $o). 50.81/8.71 thf(func_def_144, type, sP7: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_145, type, sP8: $o). 50.81/8.71 thf(func_def_146, type, sP9: $o). 50.81/8.71 thf(func_def_147, type, sP10: $o). 50.81/8.71 thf(func_def_148, type, sP11: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_149, type, sP12: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_150, type, sP13: $o). 50.81/8.71 thf(func_def_151, type, sP14: $o). 50.81/8.71 thf(func_def_152, type, sP15: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_153, type, sP16: $o). 50.81/8.71 thf(func_def_154, type, sP17: ((term > $o) > $o)). 50.81/8.71 thf(func_def_155, type, sP18: $o). 50.81/8.71 thf(func_def_156, type, sP19: $o). 50.81/8.71 thf(func_def_157, type, sP20: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_158, type, sP21: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_159, type, sP22: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_160, type, sP23: ((term > $o) > $o)). 50.81/8.71 thf(func_def_161, type, sP24: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_162, type, sP25: $o). 50.81/8.71 thf(func_def_163, type, sP26: $o). 50.81/8.71 thf(func_def_164, type, sP27: $o). 50.81/8.71 thf(func_def_165, type, sP28: $o). 50.81/8.71 thf(func_def_166, type, sP29: $o). 50.81/8.71 thf(func_def_167, type, sP30: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_168, type, sP31: $o). 50.81/8.71 thf(func_def_169, type, sP32: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_170, type, sP33: $o). 50.81/8.71 thf(func_def_171, type, sP34: ((term > $o) > $o)). 50.81/8.71 thf(func_def_172, type, sP35: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_173, type, sP36: $o). 50.81/8.71 thf(func_def_174, type, sP37: $o). 50.81/8.71 thf(func_def_175, type, sP38: $o). 50.81/8.71 thf(func_def_176, type, sP39: ((term > $o) > $o)). 50.81/8.71 thf(func_def_177, type, sP40: $o). 50.81/8.71 thf(func_def_178, type, sP41: ((term > $o) > $o)). 50.81/8.71 thf(func_def_179, type, sP42: ((term > $o) > $o)). 50.81/8.71 thf(func_def_180, type, sP43: $o). 50.81/8.71 thf(func_def_181, type, sP44: $o). 50.81/8.71 thf(func_def_182, type, sP45: $o). 50.81/8.71 thf(func_def_183, type, sP46: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_184, type, sP47: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_185, type, sP48: ((term > $o) > $o)). 50.81/8.71 thf(func_def_186, type, sP49: $o). 50.81/8.71 thf(func_def_187, type, sP50: $o). 50.81/8.71 thf(func_def_188, type, sP51: $o). 50.81/8.71 thf(func_def_189, type, sP52: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_190, type, sP53: $o). 50.81/8.71 thf(func_def_191, type, sP54: $o). 50.81/8.71 thf(func_def_192, type, sP55: $o). 50.81/8.71 thf(func_def_193, type, sP56: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_194, type, sP57: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_195, type, sP58: $o). 50.81/8.71 thf(func_def_196, type, sP59: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_197, type, sP60: ((subst > term > subst > $o) > $o)). 50.81/8.71 thf(func_def_198, type, sP61: $o). 50.81/8.71 thf(func_def_199, type, sK62: term). 50.81/8.71 thf(func_def_200, type, sK63: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_201, type, sK64: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_202, type, sK65: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_203, type, sK66: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_204, type, sK67: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_205, type, sK68: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_206, type, sK69: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_207, type, sK70: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_208, type, sK71: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_209, type, sK72: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_210, type, sK73: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_211, type, sK74: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_212, type, sK75: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_213, type, sK76: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_214, type, sK77: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_215, type, sK78: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_216, type, sK79: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_217, type, sK80: term). 50.81/8.71 thf(func_def_218, type, sK81: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_219, type, sK82: (term > $o)). 50.81/8.71 thf(func_def_220, type, sK83: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_221, type, sK84: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_222, type, sK85: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_223, type, sK86: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_224, type, sK87: (term > subst > term > term)). 50.81/8.71 thf(func_def_225, type, sK88: term). 50.81/8.71 thf(func_def_226, type, sK89: ((term > $o) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_227, type, sK90: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_228, type, sK91: ((term > $o) > term > term)). 50.81/8.71 thf(func_def_229, type, sK92: term). 50.81/8.71 thf(func_def_230, type, sK93: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_231, type, sK94: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_232, type, sK95: (subst > term > term)). 50.81/8.71 thf(func_def_233, type, sK96: (subst > term > term)). 50.81/8.71 thf(func_def_234, type, sK97: subst). 50.81/8.71 thf(func_def_235, type, sK98: term). 50.81/8.71 thf(func_def_236, type, sK99: term). 50.81/8.71 thf(func_def_237, type, sK100: term). 50.81/8.71 thf(func_def_238, type, sK101: subst). 50.81/8.71 thf(func_def_239, type, sK102: term). 50.81/8.71 thf(func_def_240, type, sK103: subst). 50.81/8.71 thf(func_def_241, type, sK104: term). 50.81/8.71 thf(func_def_242, type, sK105: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_243, type, sK106: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_244, type, sK107: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_245, type, sK108: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_246, type, sK109: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_247, type, sK110: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_248, type, sK111: (term > $o)). 50.81/8.71 thf(func_def_249, type, sK112: term). 50.81/8.71 thf(func_def_250, type, sK113: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_251, type, sK114: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_252, type, sK115: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_253, type, sK116: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_254, type, sK117: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_255, type, sK118: ((subst > term > subst > $o) > (term > $o) > term)). 50.81/8.71 thf(func_def_256, type, sK119: (term > (term > $o) > term)). 50.81/8.71 thf(func_def_257, type, sK120: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_258, type, sK121: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_259, type, sK122: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_260, type, sK123: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_261, type, sK124: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_262, type, sK125: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_263, type, sK126: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_264, type, sK127: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_265, type, sK128: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_266, type, sK129: ((term > $o) > term)). 50.81/8.71 thf(func_def_267, type, sK130: ((term > $o) > term)). 50.81/8.71 thf(func_def_268, type, sK131: ((subst > term > subst > $o) > term > $o)). 50.81/8.71 thf(func_def_269, type, sK132: (term > $o)). 50.81/8.71 thf(func_def_270, type, sK133: term). 50.81/8.71 thf(func_def_271, type, sK134: (term > term)). 50.81/8.71 thf(func_def_272, type, sK135: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_273, type, sK136: ((term > $o) > term)). 50.81/8.71 thf(func_def_274, type, sK137: term). 50.81/8.71 thf(func_def_275, type, sK138: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_276, type, sK139: (term > (term > $o) > term)). 50.81/8.71 thf(func_def_277, type, sK140: ((subst > term > subst > $o) > (term > $o) > term)). 50.81/8.71 thf(func_def_278, type, sK141: (term > $o)). 50.81/8.71 thf(func_def_279, type, sK142: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_280, type, sK143: term). 50.81/8.71 thf(func_def_281, type, sK144: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_282, type, sK145: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_283, type, sK146: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_284, type, sK147: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_285, type, sK148: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_286, type, sK149: term). 50.81/8.71 thf(func_def_287, type, sK150: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_288, type, sK151: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_289, type, sK152: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_290, type, sK153: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_291, type, sK154: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_292, type, sK155: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_293, type, sK156: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_294, type, sK157: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_295, type, sK158: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_296, type, sK159: ((term > $o) > term)). 50.81/8.71 thf(func_def_297, type, sK160: ((term > $o) > term)). 50.81/8.71 thf(func_def_298, type, sK161: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_299, type, sK162: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_300, type, sK163: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_301, type, sK164: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_302, type, sK165: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_303, type, sK166: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_304, type, sK167: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_305, type, sK168: term). 50.81/8.71 thf(func_def_306, type, sK169: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_307, type, sK170: (term > (subst > term > term) > term)). 50.81/8.71 thf(func_def_308, type, sK171: (term > (subst > term > term) > subst)). 50.81/8.71 thf(func_def_309, type, sK172: (term > (subst > term > term) > subst)). 50.81/8.71 thf(func_def_310, type, sK173: (term > (subst > term > term) > subst)). 50.81/8.71 thf(func_def_311, type, sK174: (term > (subst > term > term) > subst)). 50.81/8.71 thf(func_def_312, type, sK175: (term > (subst > term > term) > term)). 50.81/8.71 thf(func_def_313, type, sK176: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_314, type, sK177: ((subst > term > subst > $o) > term > term)). 50.81/8.71 thf(func_def_315, type, sK178: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_317, type, sK180: ((term > $o) > term)). 50.81/8.71 thf(func_def_318, type, sK181: ((term > $o) > term)). 50.81/8.71 thf(func_def_319, type, sK182: subst). 50.81/8.71 thf(func_def_320, type, sK183: term). 50.81/8.71 thf(func_def_321, type, sK184: subst). 50.81/8.71 thf(func_def_322, type, sK185: term). 50.81/8.71 thf(func_def_323, type, sK186: (term > $o)). 50.81/8.71 thf(func_def_324, type, sK187: term). 50.81/8.71 thf(func_def_325, type, sK188: subst). 50.81/8.71 thf(func_def_326, type, sK189: (term > $o)). 50.81/8.71 thf(func_def_327, type, sK190: term). 50.81/8.71 thf(func_def_328, type, sK191: subst). 50.81/8.71 thf(func_def_329, type, sK192: (term > term)). 50.81/8.71 thf(func_def_330, type, sK193: (subst > (term > $o) > term)). 50.81/8.71 thf(func_def_331, type, sK194: ((term > $o) > term)). 50.81/8.71 thf(func_def_332, type, sK195: ((term > $o) > term)). 50.81/8.71 thf(func_def_333, type, sK196: ((term > $o) > term)). 50.81/8.71 thf(func_def_334, type, sK197: ((term > $o) > term)). 50.81/8.71 thf(func_def_335, type, sK198: ((term > $o) > term)). 50.81/8.71 thf(func_def_336, type, sK199: (term > $o)). 50.81/8.71 thf(func_def_337, type, sK200: term). 50.81/8.71 thf(func_def_338, type, sK201: subst). 50.81/8.71 thf(func_def_339, type, sK202: (term > term)). 50.81/8.71 thf(func_def_340, type, sK203: ((term > $o) > term)). 50.81/8.71 thf(func_def_341, type, sK204: (subst > (term > $o) > term)). 50.81/8.71 thf(func_def_342, type, sK205: ((term > $o) > term)). 50.81/8.71 thf(func_def_343, type, sK206: ((term > $o) > term)). 50.81/8.71 thf(func_def_344, type, sK207: term). 50.81/8.71 thf(func_def_345, type, sK208: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_346, type, sK209: ((subst > term > subst > $o) > term > $o)). 50.81/8.71 thf(func_def_347, type, sK210: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_348, type, sK211: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_349, type, sK212: term). 50.81/8.71 thf(func_def_350, type, sK213: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_351, type, sK214: ((term > $o) > term)). 50.81/8.71 thf(func_def_352, type, sK215: ((term > $o) > term)). 50.81/8.71 thf(func_def_353, type, sK216: ((term > $o) > term)). 50.81/8.71 thf(func_def_354, type, sK217: (term > $o)). 50.81/8.71 thf(func_def_355, type, sK218: term). 50.81/8.71 thf(func_def_356, type, sK219: (term > term)). 50.81/8.71 thf(func_def_357, type, sK220: ((term > $o) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_358, type, sK221: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_359, type, sK222: ((term > $o) > term > term)). 50.81/8.71 thf(func_def_360, type, sK223: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_361, type, sK224: term). 50.81/8.71 thf(func_def_362, type, sK225: (term > $o)). 50.81/8.71 thf(func_def_363, type, sK226: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_364, type, sK227: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_365, type, sK228: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_366, type, sK229: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_367, type, sK230: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_368, type, sK231: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_369, type, sK232: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_370, type, sK233: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_371, type, sK234: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_372, type, sK235: ((term > $o) > term)). 50.81/8.71 thf(func_def_373, type, sK236: ((term > $o) > term)). 50.81/8.71 thf(func_def_374, type, sK237: term). 50.81/8.71 thf(func_def_375, type, sK238: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_376, type, sK239: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_378, type, sK241: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_379, type, sK242: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_380, type, sK243: ((subst > term > subst > $o) > term > term)). 50.81/8.71 thf(func_def_381, type, sK244: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_382, type, sK245: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_383, type, sK246: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_384, type, sK247: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_385, type, sK248: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_386, type, sK249: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_387, type, sK250: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_388, type, sK251: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_389, type, sK252: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_390, type, sK253: term). 50.81/8.71 thf(func_def_391, type, sK254: (term > $o)). 50.81/8.71 thf(func_def_392, type, sK255: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_393, type, sK256: term). 50.81/8.71 thf(func_def_394, type, sK257: ((subst > term > subst > $o) > (term > $o) > term)). 50.81/8.71 thf(func_def_395, type, sK258: ((term > $o) > term > term)). 50.81/8.71 thf(func_def_396, type, sK259: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_398, type, sK261: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_399, type, sK262: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_400, type, sK263: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_401, type, sK264: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_402, type, sK265: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_403, type, sK266: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_404, type, sK267: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_405, type, sK268: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_406, type, sK269: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_407, type, sK270: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_408, type, sK271: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_409, type, sK272: term). 50.81/8.71 thf(func_def_410, type, sK273: (term > $o)). 50.81/8.71 thf(func_def_411, type, sK274: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_412, type, sK275: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_413, type, sK276: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_414, type, sK277: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_415, type, sK278: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_416, type, sK279: ((subst > term > subst > $o) > (term > $o) > term)). 50.81/8.71 thf(func_def_417, type, sK280: ((term > $o) > term > term)). 50.81/8.71 thf(func_def_418, type, sK281: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_419, type, sK282: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_420, type, sK283: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_421, type, sK284: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_422, type, sK285: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_423, type, sK286: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_424, type, sK287: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_425, type, sK288: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_426, type, sK289: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_427, type, sK290: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_428, type, sK291: term). 50.81/8.71 thf(func_def_429, type, sK292: term). 50.81/8.71 thf(func_def_430, type, sK293: ((term > $o) > term)). 50.81/8.71 thf(func_def_431, type, sK294: ((term > $o) > term)). 50.81/8.71 thf(func_def_432, type, sK295: term). 50.81/8.71 thf(func_def_433, type, sK296: (term > $o)). 50.81/8.71 thf(func_def_434, type, sK297: (term > term)). 50.81/8.71 thf(func_def_435, type, sK298: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_436, type, sK299: term). 50.81/8.71 thf(func_def_437, type, sK300: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_438, type, sK301: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_439, type, sK302: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_440, type, sK303: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_441, type, sK304: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_442, type, sK305: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_443, type, sK306: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_444, type, sK307: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_445, type, sK308: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_446, type, sK309: (term > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_447, type, sK310: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_448, type, sK311: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_449, type, sK312: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_450, type, sK313: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_451, type, sK314: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_452, type, sK315: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_453, type, sK316: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_454, type, sK317: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_455, type, sK318: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_456, type, sK319: term). 50.81/8.71 thf(func_def_457, type, sK320: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_458, type, sK321: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_459, type, sK322: ((term > $o) > term)). 50.81/8.71 thf(func_def_460, type, sK323: ((term > $o) > term)). 50.81/8.71 thf(func_def_461, type, sK324: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_462, type, sK325: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_463, type, sK326: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_464, type, sK327: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_465, type, sK328: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_466, type, sK329: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_467, type, sK330: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_468, type, sK331: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_469, type, sK332: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_470, type, sK333: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_471, type, sK334: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_472, type, sK335: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_473, type, sK336: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_474, type, sK337: term). 50.81/8.71 thf(func_def_475, type, sK338: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_476, type, sK339: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_477, type, sK340: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_478, type, sK341: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_479, type, sK342: (term > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_480, type, sK343: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_481, type, sK344: (term > $o)). 50.81/8.71 thf(func_def_482, type, sK345: term). 50.81/8.71 thf(func_def_483, type, sK346: (term > term)). 50.81/8.71 thf(func_def_484, type, sK347: ((term > $o) > term)). 50.81/8.71 thf(func_def_485, type, sK348: ((term > $o) > term)). 50.81/8.71 thf(func_def_486, type, sK349: ((term > $o) > term)). 50.81/8.71 thf(func_def_487, type, sK350: ((term > $o) > term)). 50.81/8.71 thf(func_def_488, type, sK351: (term > $o)). 50.81/8.71 thf(func_def_489, type, sK352: term). 50.81/8.71 thf(func_def_490, type, sK353: term). 50.81/8.71 thf(func_def_491, type, sK354: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_492, type, sK355: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_493, type, sK356: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_494, type, sK357: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_495, type, sK358: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_496, type, sK359: ((subst > term > subst > $o) > (term > $o) > term)). 50.81/8.71 thf(func_def_497, type, sK360: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_498, type, sK361: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_499, type, sK362: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_500, type, sK363: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_501, type, sK364: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_502, type, sK365: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_503, type, sK366: term). 50.81/8.71 thf(func_def_504, type, sK367: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_505, type, sK368: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_506, type, sK369: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_507, type, sK370: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_508, type, sK371: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_509, type, sK372: ((subst > term > subst > $o) > term > term)). 50.81/8.71 thf(func_def_510, type, sK373: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_511, type, sK374: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_512, type, sK375: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_513, type, sK376: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_514, type, sK377: term). 50.81/8.71 thf(func_def_515, type, sK378: ((subst > term > subst > $o) > term > term)). 50.81/8.71 thf(func_def_516, type, sK379: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_517, type, sK380: term). 50.81/8.71 thf(func_def_518, type, sK381: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_519, type, sK382: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_520, type, sK383: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_521, type, sK384: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_522, type, sK385: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_523, type, sK386: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_524, type, sK387: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_525, type, sK388: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_526, type, sK389: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_527, type, sK390: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_528, type, sK391: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_529, type, sK392: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_530, type, sK393: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_531, type, sK394: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_532, type, sK395: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_533, type, sK396: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_534, type, sK397: term). 50.81/8.71 thf(func_def_535, type, sK398: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_536, type, sK399: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_537, type, sK400: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_538, type, sK401: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_539, type, sK402: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_540, type, sK403: (term > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_541, type, sK404: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_542, type, sK405: term). 50.81/8.71 thf(func_def_543, type, sK406: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_544, type, sK407: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_545, type, sK408: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_546, type, sK409: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_547, type, sK410: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_548, type, sK411: (term > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_549, type, sK412: term). 50.81/8.71 thf(func_def_550, type, sK413: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_551, type, sK414: term). 50.81/8.71 thf(func_def_552, type, sK415: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_553, type, sK416: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_554, type, sK417: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_555, type, sK418: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_556, type, sK419: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_557, type, sK420: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_558, type, sK421: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_559, type, sK422: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_560, type, sK423: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_561, type, sK424: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_562, type, sK425: term). 50.81/8.71 thf(func_def_563, type, sK426: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_564, type, sK427: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_565, type, sK428: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_566, type, sK429: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_567, type, sK430: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_568, type, sK431: term). 50.81/8.71 thf(func_def_569, type, sK432: ((subst > term > subst > $o) > term > term)). 50.81/8.71 thf(func_def_570, type, sK433: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_571, type, sK434: (term > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_572, type, sK435: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_573, type, sK436: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_574, type, sK437: term). 50.81/8.71 thf(func_def_575, type, sK438: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_576, type, sK439: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_577, type, sK440: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_578, type, sK441: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_579, type, sK442: ((term > $o) > term)). 50.81/8.71 thf(func_def_580, type, sK443: ((term > $o) > term)). 50.81/8.71 thf(func_def_581, type, sK444: (subst > (term > $o) > term)). 50.81/8.71 thf(func_def_582, type, sK445: ((term > $o) > term)). 50.81/8.71 thf(func_def_583, type, sK446: (term > $o)). 50.81/8.71 thf(func_def_584, type, sK447: subst). 50.81/8.71 thf(func_def_585, type, sK448: term). 50.81/8.71 thf(func_def_586, type, sK449: (term > term)). 50.81/8.71 thf(func_def_587, type, sK450: term). 50.81/8.71 thf(func_def_588, type, sK451: term). 50.81/8.71 thf(func_def_589, type, sK452: (term > $o)). 50.81/8.71 thf(func_def_590, type, sK453: (term > term)). 50.81/8.71 thf(func_def_591, type, sK454: ((term > $o) > term)). 50.81/8.71 thf(func_def_592, type, sK455: ((term > $o) > term)). 50.81/8.71 thf(func_def_593, type, sK456: ((term > $o) > term)). 50.81/8.71 thf(func_def_594, type, sK457: ((term > $o) > term)). 50.81/8.71 thf(func_def_595, type, sK458: ((term > $o) > term)). 50.81/8.71 thf(func_def_596, type, sK459: ((term > $o) > term)). 50.81/8.71 thf(func_def_597, type, sK460: term). 50.81/8.71 thf(func_def_598, type, sK461: term). 50.81/8.71 thf(func_def_599, type, sK462: term). 50.81/8.71 thf(func_def_600, type, sK463: term). 50.81/8.71 thf(func_def_601, type, sK464: term). 50.81/8.71 thf(func_def_602, type, sK465: term). 50.81/8.71 thf(func_def_603, type, sK466: term). 50.81/8.71 thf(func_def_604, type, sK467: term). 50.81/8.71 thf(func_def_605, type, sK468: term). 50.81/8.71 thf(func_def_606, type, sK469: term). 50.81/8.71 thf(func_def_607, type, sK470: subst). 50.81/8.71 thf(func_def_608, type, sK471: subst). 50.81/8.71 thf(func_def_609, type, sK472: term). 50.81/8.71 thf(func_def_610, type, sK473: term). 50.81/8.71 thf(func_def_611, type, sK474: (term > $o)). 50.81/8.71 thf(func_def_612, type, sK475: (term > $o)). 50.81/8.71 thf(func_def_613, type, sK476: subst). 50.81/8.71 thf(func_def_614, type, sK477: term). 50.81/8.71 thf(func_def_615, type, sK478: term). 50.81/8.71 thf(func_def_616, type, sK479: term). 50.81/8.71 thf(func_def_617, type, sK480: term). 50.81/8.71 thf(func_def_618, type, sK481: term). 50.81/8.71 thf(func_def_619, type, sK482: ((subst > term > subst > $o) > term > $o)). 50.81/8.71 thf(func_def_620, type, sK483: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_621, type, sK484: ((term > $o) > term)). 50.81/8.71 thf(func_def_622, type, sK485: term). 50.81/8.71 thf(func_def_623, type, sK486: term). 50.81/8.71 thf(func_def_624, type, sK487: term). 50.81/8.71 thf(func_def_625, type, sK488: term). 50.81/8.71 thf(func_def_626, type, sK489: term). 50.81/8.71 thf(func_def_627, type, sK490: term). 50.81/8.71 thf(func_def_628, type, sK491: term). 50.81/8.71 thf(func_def_629, type, sK492: term). 50.81/8.71 thf(func_def_630, type, sK493: term). 50.81/8.71 thf(func_def_631, type, sK494: term). 50.81/8.71 thf(func_def_632, type, sK495: term). 50.81/8.71 thf(func_def_633, type, sK496: term). 50.81/8.71 thf(func_def_634, type, sK497: (term > d_term)). 50.81/8.71 thf(func_def_635, type, sK498: ((term > $o) > term > subst > term > $o)). 50.81/8.71 thf(func_def_636, type, sK499: subst). 50.81/8.71 thf(func_def_637, type, sK500: term). 50.81/8.71 thf(func_def_638, type, sK501: (term > $o)). 50.81/8.71 thf(func_def_639, type, sK502: ((term > $o) > term)). 50.81/8.71 thf(func_def_640, type, sK503: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_641, type, sK504: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_642, type, sK505: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_643, type, sK506: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_644, type, sK507: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_645, type, sK508: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_646, type, sK509: (subst > term > term)). 50.81/8.71 thf(func_def_647, type, sK510: (subst > term > term)). 50.81/8.71 thf(func_def_648, type, sK511: term). 50.81/8.71 thf(func_def_649, type, sK512: subst). 50.81/8.71 thf(func_def_650, type, sK513: term). 50.81/8.71 thf(func_def_651, type, sK514: term). 50.81/8.71 thf(func_def_652, type, sK515: subst). 50.81/8.71 thf(func_def_653, type, sK516: subst). 50.81/8.71 thf(func_def_654, type, sK517: (subst > d_subst)). 50.81/8.71 thf(func_def_655, type, sK518: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_656, type, sK519: ((term > $o) > term)). 50.81/8.71 thf(func_def_657, type, sK520: ((subst > term > subst > $o) > term > $o)). 50.81/8.71 thf(func_def_658, type, sK521: term). 50.81/8.71 thf(func_def_659, type, sK522: term). 50.81/8.71 thf(func_def_660, type, sK523: term). 50.81/8.71 thf(func_def_661, type, sK524: term). 50.81/8.71 thf(func_def_662, type, sK525: term). 50.81/8.71 thf(func_def_663, type, sK526: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_664, type, sK527: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_665, type, sK528: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_666, type, sK529: term). 50.81/8.71 thf(func_def_667, type, sK530: term). 50.81/8.71 thf(func_def_668, type, sK531: (term > subst > term > term)). 50.81/8.71 thf(func_def_669, type, sK532: subst). 50.81/8.71 thf(func_def_670, type, sK533: term). 50.81/8.71 thf(func_def_671, type, sK534: (term > $o)). 50.81/8.71 thf(func_def_672, type, sK535: (term > $o)). 50.81/8.71 thf(func_def_673, type, sK536: ((term > $o) > (term > $o) > term > subst > term)). 50.81/8.71 thf(func_def_674, type, sK537: term). 50.81/8.71 thf(func_def_675, type, sK538: subst). 50.81/8.71 thf(func_def_676, type, sK539: term). 50.81/8.71 thf(func_def_677, type, sK540: term). 50.81/8.71 thf(func_def_678, type, sK541: subst). 50.81/8.71 thf(func_def_679, type, sK542: term). 50.81/8.71 thf(func_def_680, type, sK543: term). 50.81/8.71 thf(func_def_681, type, sK544: (term > $o)). 50.81/8.71 thf(func_def_682, type, sK545: (term > $o)). 50.81/8.71 thf(func_def_683, type, sK546: subst). 50.81/8.71 thf(func_def_684, type, sK547: (subst > (term > $o) > (term > $o) > term > term)). 50.81/8.71 thf(func_def_685, type, sK548: term). 50.81/8.71 thf(func_def_686, type, sK549: (term > subst > term > term)). 50.81/8.71 thf(func_def_687, type, sK550: term). 50.81/8.71 thf(func_def_688, type, sK551: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_689, type, sK552: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_690, type, sK553: (term > subst > term > term)). 50.81/8.71 thf(func_def_691, type, sK554: subst). 50.81/8.71 thf(func_def_692, type, sK555: term). 50.81/8.71 thf(func_def_693, type, sK556: term). 50.81/8.71 thf(func_def_694, type, sK557: subst). 50.81/8.71 thf(func_def_695, type, sK558: (term > $o)). 50.81/8.71 thf(func_def_696, type, sK559: term). 50.81/8.71 thf(func_def_697, type, sK560: (term > $o)). 50.81/8.71 thf(func_def_698, type, sK561: subst). 50.81/8.71 thf(func_def_699, type, sK562: (subst > term > term)). 50.81/8.71 thf(func_def_700, type, sK563: term). 50.81/8.71 thf(func_def_701, type, sK564: term). 50.81/8.71 thf(func_def_702, type, sK565: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_703, type, sK566: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_704, type, sK567: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_705, type, sK568: term). 50.81/8.71 thf(func_def_706, type, sK569: subst). 50.81/8.71 thf(func_def_707, type, sK570: term). 50.81/8.71 thf(func_def_708, type, sK571: term). 50.81/8.71 thf(func_def_709, type, sK572: term). 50.81/8.71 thf(func_def_710, type, sK573: term). 50.81/8.71 thf(func_def_711, type, sK574: term). 50.81/8.71 thf(func_def_712, type, sK575: term). 50.81/8.71 thf(func_def_713, type, sK576: term). 50.81/8.71 thf(func_def_714, type, sK577: (term > $o)). 50.81/8.71 thf(func_def_715, type, sK578: ((term > $o) > term)). 50.81/8.71 thf(func_def_716, type, sK579: ((term > $o) > term)). 50.81/8.71 thf(func_def_717, type, sK580: (term > subst > term > term)). 50.81/8.71 thf(func_def_718, type, sK581: term). 50.81/8.71 thf(func_def_719, type, sK582: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_720, type, sK583: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_721, type, sK584: subst). 50.81/8.71 thf(func_def_722, type, sK585: subst). 50.81/8.71 thf(func_def_723, type, sK586: subst). 50.81/8.71 thf(func_def_724, type, sK587: subst). 50.81/8.71 thf(func_def_725, type, sK588: subst). 50.81/8.71 thf(func_def_726, type, sK589: (term > $o)). 50.81/8.71 thf(func_def_727, type, sK590: term). 50.81/8.71 thf(func_def_728, type, sK591: subst). 50.81/8.71 thf(func_def_729, type, sK592: ((term > $o) > term)). 50.81/8.71 thf(func_def_730, type, sK593: (subst > term > (term > $o) > term > $o)). 50.81/8.71 thf(func_def_731, type, sK594: (subst > term > subst > $o)). 50.81/8.71 thf(func_def_732, type, sK595: term). 50.81/8.71 thf(func_def_733, type, sK596: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_734, type, sK597: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_735, type, sK598: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_736, type, sK599: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_737, type, sK600: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_738, type, sK601: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_739, type, sK602: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_740, type, sK603: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_741, type, sK604: ((subst > term > subst > $o) > subst)). 50.81/8.71 thf(func_def_742, type, sK605: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_743, type, sK606: ((subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_744, type, sK607: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_745, type, sK608: ((subst > term > term) > term)). 50.81/8.71 thf(func_def_746, type, sK609: ((subst > term > term) > subst)). 50.81/8.71 thf(func_def_747, type, sK610: ((subst > term > term) > (subst > term > subst > $o) > term)). 50.81/8.71 thf(func_def_748, type, sK611: ((subst > term > subst > $o) > subst > term > term)). 50.81/8.71 thf(func_def_749, type, vNOT: ($o > $o)). 50.81/8.71 thf(f1,axiom,( 50.81/8.71 (substmonoid_lthm <=> (! [X9 : subst] : (X9 = ((comp @ id @ X9))) => (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) => (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) & ! [X9 : subst] : (X9 = ((comp @ id @ X9))))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2 & (! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) <=> axvarcons) & pushprop_lem1_gthm & (! [X13 : term,X32 : term,X8 : term,X33 : term] : ((X8 = X13) | (((ap @ (sub @ X8 @ id) @ X32)) != ((ap @ (sub @ X13 @ id) @ X33)))) <=> hoasapinj1) & hoasinduction_lem2_gthm & (! [X10 : (subst > term > subst > $o),X40 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X40) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (sub @ X40 @ (push @ X13 @ id)) @ id) | ~(X10 @ id @ X13 @ id))) <=> hoasinduction_lem3a) & (! [X21 : term,X10 : (term > $o)] : (~ ! [X8 : term] : ((X10 @ X8) | ~(var @ X8)) | ~ ! [X8 : term] : ((X10 @ (lam @ X8)) | ~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13))) | ~ ! [X13 : term,X8 : term] : (~(X10 @ X13) | ~(X10 @ X8) | (X10 @ (ap @ X8 @ X13))) | (X10 @ X21)) <=> induction2) & pushprop_lem3v2 & axassoc & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X13 : term,X8 : term] : ((((sub @ X8 @ sh)) != ((sub @ X13 @ sh))) | (X8 = X13)) <=> shinj) & (! [X8 : term,X9 : subst,X11 : (term > $o),X10 : (term > $o)] : (~(X10 @ X8) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) | (X11 @ one)) <=> pushprop_lem1v2) & (hoasinduction_lem3v2a_lthm <=> (! [X13 : term] : ~ ! [X14 : (subst > term > term)] : ~ ! [X8 : term,X9 : subst] : (((sub @ X13 @ (push @ X8 @ X9))) = ((X14 @ X9 @ X8))) => (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => ! [X10 : (subst > term > subst > $o),X36 : term,X11 : (term > $o)] : (~ ! [X13 : term] : (~(X11 @ X13) | (X11 @ (sub @ X36 @ (push @ X13 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | (X11 @ (lam @ X36)))))) & (hoasapinj2 <=> ! [X32 : term,X33 : term,X13 : term,X8 : term] : ((X32 = X33) | (((ap @ (sub @ X8 @ id) @ X32)) != ((ap @ (sub @ X13 @ id) @ X33))))) & pushprop_lthm & hoasapinj1_gthm & (laminj <=> ! [X8 : term,X13 : term] : ((X8 = X13) | (((lam @ X8)) != ((lam @ X13))))) & (! [X13 : term] : ~ ! [X14 : (subst > term > term)] : (((X14 @ sh @ one)) != ((sub @ X13 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & (one = ((d2term @ d_one))) & axapp & hoasapinj2_gthm & (axshiftcons <=> ! [X8 : term,X9 : subst] : (X9 = ((comp @ sh @ (push @ X8 @ X9))))) & (! [X8 : term,X33 : term,X13 : term,X32 : term] : ((X8 = X13) | (((ap @ X8 @ X32)) != ((ap @ X13 @ X33)))) <=> apinj1) & ~lamnotap & hoasapnotvar_gthm & (! [X8 : term] : (X8 = ((sub @ X8 @ id))) <=> axvarid) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X8 : term] : (~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13)) | (X10 @ (lam @ X8))) | (X10 @ X21) | ~ ! [X8 : term,X13 : term] : (~(X10 @ X8) | (X10 @ (ap @ X8 @ X13)) | ~(X10 @ X13)) | ~ ! [X8 : term] : (~(var @ X8) | (X10 @ X8))) => (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X11 : (term > $o),X36 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : (subst > term > term)] : ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | ~ ! [X9 : subst,X8 : term,X16 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))) | ~ ! [X13 : term] : (~(X11 @ X13) | (X11 @ (sub @ X36 @ (push @ X13 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X36))) => ! [X10 : (subst > term > subst > $o),X35 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | ~ ! [X13 : term,X8 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X8 @ id) | (X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id)) | (X10 @ id @ X35 @ id))))))) & (hoasinduction_lem3_lthm <=> (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X13 @ id)) @ id)) | ~ ! [X14 : (subst > term > term)] : ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | ~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id))) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X18 : term] : (~ ! [X13 : term] : ((X10 @ id @ (sub @ X18 @ (push @ X13 @ id)) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X16 : subst,X8 : term,X17 : subst,X9 : subst] : ((X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | ~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | (X10 @ id @ (lam @ X18) @ id) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X9 : subst,X8 : term,X16 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))) | ~ ! [X9 : subst,X8 : term,X16 : subst,X17 : subst] : (~(X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | (X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)))))) & (termmset_lthm <=> (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => ! [X8 : term] : (X8 = ((sub @ X8 @ id))))) & (induction <=> ! [X46 : term,X10 : (term > $o)] : (~ ! [X8 : term] : ((X10 @ (lam @ X8)) | ~(X10 @ X8)) | (X10 @ X46) | ~ ! [X8 : term,X13 : term] : ((X10 @ (ap @ X8 @ X13)) | ~(X10 @ X13) | ~(X10 @ X8)) | ~ ! [X8 : term] : (~(var @ X8) | (X10 @ X8)))) & (sh = ((d2subst @ d_id))) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & ulamvarind & (hoasinduction_lthm <=> (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term,X8 : term] : (~(X10 @ X13) | ~(X10 @ X8) | (X10 @ (ap @ X8 @ X13))) | ~ ! [X8 : term] : ((X10 @ (lam @ X8)) | ~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13))) | ~ ! [X8 : term] : (~(var @ X8) | (X10 @ X8)) | (X10 @ X21)) => (! [X19 : term,X10 : (subst > term > subst > $o),X20 : term] : (~ ! [X8 : term,X17 : subst,X16 : subst,X9 : subst] : ((X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | ~(X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~(X10 @ id @ X20 @ id) | (X10 @ id @ (ap @ X19 @ X20) @ id) | ~ ! [X8 : term,X16 : subst,X9 : subst,X17 : subst] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~ ! [X8 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id) | ~(X10 @ id @ X8 @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X19 @ id)) => (! [X18 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X18) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X18 @ (push @ X13 @ id)) @ id)) | ~ ! [X17 : subst,X8 : term,X16 : subst,X9 : subst] : (~(X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | (X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X9 : subst,X16 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))) | ~ ! [X17 : subst,X16 : subst,X8 : term,X9 : subst] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16)))) => ! [X10 : (subst > term > subst > $o),X15 : term] : (~ ! [X8 : term] : ((X10 @ id @ X8 @ id) | ~(var @ (sub @ X8 @ id))) | ~ ! [X8 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X8 @ id) | (X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id)) | (X10 @ id @ X15 @ id) | ~ ! [X8 : term,X17 : subst,X9 : subst,X16 : subst] : (~(X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | (X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X16 : subst,X8 : term,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | ~ ! [X9 : subst,X17 : subst,X16 : subst,X8 : term] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16)))))))) & hoasinduction_lem1_gthm & ! [X47 : d_term] : (X47 = d_one) & hoasinduction_lem3v2_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lthm_orig & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X15 : term] : ((X10 @ id @ X15 @ id) | ~ ! [X8 : term] : ((X10 @ id @ X8 @ id) | ~(var @ (sub @ X8 @ id))) | ~ ! [X8 : term,X17 : subst,X16 : subst,X9 : subst] : (~(X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | (X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X13 : term,X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X8 : term,X16 : subst,X17 : subst,X9 : subst] : ((X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | ~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | ~ ! [X8 : term,X9 : subst,X16 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) & termmset_gthm & (induction2lem <=> ! [X10 : (term > $o),X42 : subst,X41 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ (sub @ X13 @ X42))) | ~ ! [X8 : term] : ((X10 @ (lam @ X8)) | ~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13))) | ~ ! [X13 : term,X8 : term] : ((X10 @ (ap @ X8 @ X13)) | ~(X10 @ X8) | ~(X10 @ X13)) | (X10 @ (sub @ X41 @ X42)))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X42 : subst,X10 : (term > $o),X41 : term] : (~ ! [X8 : term] : (~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13)) | (X10 @ (lam @ X8))) | ~ ! [X13 : term] : ((X10 @ (sub @ X13 @ X42)) | ~(var @ X13)) | ~ ! [X8 : term,X13 : term] : ((X10 @ (ap @ X8 @ X13)) | ~(X10 @ X13) | ~(X10 @ X8)) | (X10 @ (sub @ X41 @ X42))) => ! [X10 : (term > $o),X21 : term] : (~ ! [X8 : term] : ((X10 @ X8) | ~(var @ X8)) | (X10 @ X21) | ~ ! [X8 : term] : (~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13)) | (X10 @ (lam @ X8))) | ~ ! [X8 : term,X13 : term] : ((X10 @ (ap @ X8 @ X13)) | ~(X10 @ X8) | ~(X10 @ X13))))) <=> induction2_lthm) & (pushprop_p_and_p_prime = (^[X8 : term, X9 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9)))))))) & ulamvarsh & (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) <=> axidr) & ~ulamvar1 & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & ! [X4 : d_subst,X5 : d_subst] : ((((d2subst @ X4)) = ((d2subst @ X5))) => (X4 = X5)) & hoaslamnotvar & hoasinduction_lem1v2_gthm & ((! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => ! [X8 : term,X10 : (term > $o),X11 : (term > $o),X9 : subst] : (~(X10 @ X8) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & (hoasinduction_lem3 <=> ! [X18 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X18 @ (push @ X13 @ id)) @ id)) | (X10 @ id @ (lam @ X18) @ id) | ~ ! [X17 : subst,X16 : subst,X8 : term,X9 : subst] : (~(X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | (X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | ~ ! [X16 : subst,X8 : term,X17 : subst,X9 : subst] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16))))) & hoasinduction_lem1v2 & axabs & pushprop_lem3v2_lthm & (hoaslaminj_lthm <=> (! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => (! [X8 : term,X9 : subst] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) => (! [X8 : term,X13 : term] : ((((lam @ X8)) != ((lam @ X13))) | (X8 = X13)) => ! [X44 : subst,X14 : (subst > term > term),X45 : term,X43 : (subst > term > term)] : (~ ! [X9 : subst,X16 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | ~ ! [X16 : subst,X8 : term,X9 : subst] : (((sub @ (X43 @ X9 @ X8) @ X16)) = ((X43 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (((lam @ (X14 @ sh @ one))) != ((lam @ (X43 @ sh @ one)))) | (((X14 @ X44 @ X45)) = ((X43 @ X44 @ X45)))))))) & apnotvar & (! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X13 @ id)) @ id)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & induction2_gthm & ~(var @ (d2term @ d_one)) & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X20 : term,X19 : term] : (~(X10 @ id @ X19 @ id) | ~ ! [X9 : subst,X8 : term,X17 : subst,X16 : subst] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~ ! [X13 : term,X8 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X8 @ id) | (X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id)) | (X10 @ id @ (ap @ X19 @ X20) @ id) | ~ ! [X8 : term,X17 : subst,X16 : subst,X9 : subst] : ((X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | ~(X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~(X10 @ id @ X20 @ id))) & pushprop & hoaslamnotvar_lthm & hoasinduction_lem1_lthm & ! [X0 : d_term,X1 : d_term] : ((((d2term @ X0)) = ((d2term @ X1))) => (X0 = X1)) & (hoasinduction_lem3a_lthm <=> (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X16 : subst,X9 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X13 @ id)) @ id))) => ! [X40 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X40 @ (push @ X13 @ id)) @ id)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X9 : subst,X8 : term,X16 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id))) | (X10 @ id @ (lam @ X40) @ id))))) & pushprop_lem0_gthm & hoasinduction_lem2_lthm & hoasinduction_lem3a_gthm & hoasinduction_lem3b_gthm & hoasapnotvar_lthm & (axscons <=> ! [X9 : subst] : (X9 = ((push @ (sub @ one @ X9) @ (comp @ sh @ X9))))) & (! [X44 : subst,X43 : (subst > term > term),X14 : (subst > term > term),X45 : term] : ((((lam @ (X14 @ sh @ one))) != ((lam @ (X43 @ sh @ one)))) | ~ ! [X8 : term,X9 : subst,X16 : subst] : (((sub @ (X43 @ X9 @ X8) @ X16)) = ((X43 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (((X14 @ X44 @ X45)) = ((X43 @ X44 @ X45))) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))) <=> hoaslaminj) & (axidl <=> ! [X9 : subst] : (X9 = ((comp @ id @ X9)))) & ! [X2 : subst] : ? [X3 : d_subst] : (X2 = ((d2subst @ X3))) & (hoasapinj1_lthm <=> (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X33 : term,X13 : term,X8 : term,X32 : term] : ((X8 = X13) | (((ap @ X8 @ X32)) != ((ap @ X13 @ X33)))) => ! [X33 : term,X32 : term,X8 : term,X13 : term] : ((X8 = X13) | (((ap @ (sub @ X8 @ id) @ X32)) != ((ap @ (sub @ X13 @ id) @ X33))))))) & (! [X36 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X36)) | ~ ! [X13 : term] : ((X11 @ (sub @ X36 @ (push @ X13 @ id))) | ~(X11 @ X13)) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term,X9 : subst,X16 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)))) <=> hoasinduction_lem3v2a) & (! [X30 : term,X31 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X8 : term] : ((X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X8 @ id)) | ~ ! [X17 : subst,X9 : subst,X16 : subst,X8 : term] : ((X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | ~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X8 : term,X17 : subst,X16 : subst,X9 : subst] : ((X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | ~(X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~(X11 @ X30) | (X11 @ (ap @ X30 @ X31)) | ~(X11 @ X31)) <=> hoasinduction_lem2v2) & hoasinduction_lem3_gthm & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & ! [X3 : d_subst] : (X3 = d_id) & (hoasinduction_lem3v2 <=> ! [X10 : (subst > term > subst > $o),X37 : term,X11 : (term > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | ~ ! [X9 : subst,X16 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | ~ ! [X9 : subst,X8 : term,X17 : subst,X16 : subst] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~ ! [X8 : term,X17 : subst,X9 : subst,X16 : subst] : ((X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | ~(X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | (X11 @ (lam @ X37)) | ~ ! [X13 : term] : (~(X11 @ X13) | (X11 @ (sub @ X37 @ (push @ X13 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (! [X10 : (term > $o),X9 : subst,X8 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> pushprop_lem0_lthm) & (induction2lem_lthm <=> (! [X9 : subst,X8 : term] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => (! [X8 : term,X9 : subst] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) => (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) => (! [X46 : term,X10 : (term > $o)] : (~ ! [X8 : term] : (~(var @ X8) | (X10 @ X8)) | (X10 @ X46) | ~ ! [X8 : term,X13 : term] : (~(X10 @ X8) | ~(X10 @ X13) | (X10 @ (ap @ X8 @ X13))) | ~ ! [X8 : term] : (~(X10 @ X8) | (X10 @ (lam @ X8)))) => ! [X42 : subst,X10 : (term > $o),X41 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ (sub @ X13 @ X42))) | (X10 @ (sub @ X41 @ X42)) | ~ ! [X8 : term] : ((X10 @ (lam @ X8)) | ~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13))) | ~ ! [X8 : term,X13 : term] : ((X10 @ (ap @ X8 @ X13)) | ~(X10 @ X13) | ~(X10 @ X8)))))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoaslam = (^[X6 : subst, X7 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lem2v2_gthm & axclos & (hoasapinj2_lthm <=> (! [X32 : term,X8 : term,X13 : term,X33 : term] : ((X32 = X33) | (((ap @ X8 @ X32)) != ((ap @ X13 @ X33)))) => ! [X8 : term,X13 : term,X32 : term,X33 : term] : ((X32 = X33) | (((ap @ (sub @ X8 @ id) @ X32)) != ((ap @ (sub @ X13 @ id) @ X33)))))) & lamnotvar & induction2lem_gthm & (! [X17 : (term > $o),X8 : term,X13 : term,X10 : (term > $o),X9 : subst] : ((X17 @ (sub @ X8 @ (push @ X13 @ X9))) | ~(X10 @ X8)) <=> pushprop_lem1) & (! [X14 : (subst > term > term),X39 : term,X38 : term] : ((((lam @ (X14 @ sh @ one))) != ((ap @ (sub @ X38 @ id) @ X39))) | ~ ! [X16 : subst,X9 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))) <=> hoaslamnotap) & (hoasinduction_lem3b <=> ! [X13 : term] : ~ ! [X14 : (subst > term > term)] : (((X14 @ sh @ one)) != ((sub @ X13 @ (push @ one @ sh))))) & hoaslamnotap_lthm & ((! [X8 : term] : (X8 = ((sub @ X8 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X37 : term] : (~ ! [X8 : term,X16 : subst,X9 : subst,X17 : subst] : ((X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | ~(X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | (X11 @ (lam @ X37)) | ~ ! [X13 : term] : (~(X11 @ X13) | (X11 @ (sub @ X37 @ (push @ X13 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X9 : subst,X17 : subst,X8 : term,X16 : subst] : ((X10 @ X9 @ X8 @ (comp @ X17 @ X16)) | ~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16)) | ~ ! [X14 : (subst > term > term)] : ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))))) <=> hoasinduction_lem3v2_lthm) & (! [X10 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : term,X14 : (subst > term > term)] : (~ ! [X24 : subst,X26 : subst,X25 : term] : (((X14 @ (comp @ X24 @ X26) @ (sub @ X25 @ X26))) = ((sub @ X23 @ (push @ (sub @ X25 @ X26) @ (comp @ X24 @ X26))))) | ~ ! [X28 : term,X27 : subst,X29 : subst] : (((sub @ (X14 @ X27 @ X28) @ X29)) = ((sub @ (sub @ X23 @ (push @ X28 @ X27)) @ X29))) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id))) | (X10 @ id @ (lam @ (sub @ X22 @ (push @ one @ sh))) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (sub @ X22 @ (push @ X13 @ id)) @ id) | ~(X10 @ id @ X13 @ id))) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X13 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X9 : subst,X16 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))))) & (apinj2 <=> ! [X8 : term,X32 : term,X33 : term,X13 : term] : ((((ap @ X8 @ X32)) != ((ap @ X13 @ X33))) | (X32 = X33))) & (termmset <=> ! [X8 : term] : (X8 = ((sub @ X8 @ id)))) & hoaslaminj_gthm & (substmonoid <=> (! [X9 : subst] : (X9 = ((comp @ id @ X9))) & ! [X9 : subst] : (X9 = ((comp @ X9 @ id))))) & hoasinduction_lem2v2_gthm & axmap & hoasinduction_lem1 & hoaslamnotap_gthm & axvarshift & substmonoid_gthm & (pushprop_lem0 <=> ! [X8 : term,X9 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9)))))) & hoasinduction_gthm & pushprop_gthm & pushprop_lem2v2_lthm & (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X8 : term,X13 : term] : ((X10 @ (ap @ X8 @ X13)) | ~(X10 @ X13) | ~(X10 @ X8)) | ~ ! [X8 : term] : ((X10 @ X8) | ~(var @ X8)) | ~ ! [X8 : term] : (~ ! [X13 : term] : ((X10 @ (sub @ X8 @ (push @ X13 @ id))) | ~(X10 @ X13)) | (X10 @ (lam @ X8)))) => (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X10 : (subst > term > subst > $o),X36 : term,X11 : (term > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X8 : term,X9 : subst,X16 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16)))) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | (X10 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | (X11 @ (lam @ X36)) | ~ ! [X13 : term] : (~(X11 @ X13) | (X11 @ (sub @ X36 @ (push @ X13 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X15 : term,X10 : (subst > term > subst > $o)] : (~ ! [X9 : subst,X8 : term,X17 : subst,X16 : subst] : ((X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | ~(X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~ ! [X8 : term,X16 : subst,X9 : subst,X17 : subst] : (~(X10 @ (comp @ X9 @ X17) @ (sub @ X8 @ X17) @ X16) | (X10 @ X9 @ X8 @ (comp @ X17 @ X16))) | ~ ! [X8 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id) | ~(X10 @ id @ X8 @ id)) | ~ ! [X8 : term] : (~(var @ (sub @ X8 @ id)) | (X10 @ id @ X8 @ id)) | (X10 @ id @ X15 @ id) | ~ ! [X14 : (subst > term > term)] : ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X10 @ id @ (X14 @ id @ X8) @ id) | ~(X10 @ id @ X8 @ id)) | ~ ! [X16 : subst,X9 : subst,X8 : term] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))))))))) & (hoasinduction_no_psi_cond <=> ! [X35 : term,X10 : (subst > term > subst > $o)] : (~ ! [X8 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X8 @ id) @ X13) @ id) | ~(X10 @ id @ X8 @ id)) | (X10 @ id @ X35 @ id) | ~ ! [X14 : (subst > term > term)] : ((X10 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X8 : term] : (~(X10 @ id @ X8 @ id) | (X10 @ id @ (X14 @ id @ X8) @ id)) | ~ ! [X8 : term,X16 : subst,X9 : subst] : (((sub @ (X14 @ X9 @ X8) @ X16)) = ((X14 @ (comp @ X9 @ X16) @ (sub @ X8 @ X16))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (id = ((d2subst @ d_id))) & (pushprop_lem1_lthm <=> (! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => (! [X8 : term,X9 : subst] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) => ! [X9 : subst,X8 : term,X13 : term,X17 : (term > $o),X10 : (term > $o)] : ((X17 @ (sub @ X8 @ (push @ X13 @ X9))) | ~(X10 @ X8))))) & ! [X48 : term] : ? [X47 : d_term] : (X48 = ((d2term @ X47))) & (! [X13 : term] : ~ ! [X14 : (subst > term > term)] : ~ ! [X9 : subst,X8 : term] : (((sub @ X13 @ (push @ X8 @ X9))) = ((X14 @ X9 @ X8))) <=> hoasinduction_lem3v2_f) & hoasapnotvar & (hoasinduction_lem3v2_f_lthm <=> ! [X13 : term] : ~ ! [X14 : (subst > term > term)] : ~ ! [X9 : subst,X8 : term] : (((sub @ X13 @ (push @ X8 @ X9))) = ((X14 @ X9 @ X8))))), 50.81/8.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)). 50.81/8.71 thf(f2,conjecture,( 50.81/8.71 (! [X0 : (subst > term > subst > $o)] : (! [X3 : subst,X4 : subst,X2 : term,X1 : subst] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X1 : subst,X3 : subst,X4 : subst,X2 : term] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => (! [X6 : term,X2 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X6 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X6) @ id))) => (! [X5 : (subst > term > term)] : (! [X3 : subst,X2 : term,X1 : subst] : (((sub @ (X5 @ X1 @ X2) @ X3)) = ((X5 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X5 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X5 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (X0 @ id @ X2 @ id)))))) = hoasinduction)), 50.81/8.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction)). 50.81/8.71 thf(f3,negated_conjecture,( 50.81/8.71 ~ (! [X0 : (subst > term > subst > $o)] : (! [X3 : subst,X4 : subst,X2 : term,X1 : subst] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X1 : subst,X3 : subst,X4 : subst,X2 : term] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => (! [X6 : term,X2 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X6 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X6) @ id))) => (! [X5 : (subst > term > term)] : (! [X3 : subst,X2 : term,X1 : subst] : (((sub @ (X5 @ X1 @ X2) @ X3)) = ((X5 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X5 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X5 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (X0 @ id @ X2 @ id)))))) = hoasinduction)), 50.81/8.71 inference(negated_conjecture,[status(cth)],[f2])). 50.81/8.71 thf(f4,plain,( 50.81/8.71 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : term,X4 : subst] : ((X0 @ X4 @ X3 @ (comp @ X2 @ X1)) => (X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) => (! [X5 : subst,X6 : subst,X7 : subst,X8 : term] : ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6) => (X0 @ X5 @ X8 @ (comp @ X7 @ X6))) => (! [X9 : term] : ((hoasvar @ id @ X9 @ id) => (X0 @ id @ X9 @ id)) => (! [X10 : term,X11 : term] : ((X0 @ id @ X11 @ id) => ((X0 @ id @ X10 @ id) => (X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id))) => (! [X12 : (subst > term > term)] : (! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))) => (! [X16 : term] : ((X0 @ id @ X16 @ id) => (X0 @ id @ (X12 @ id @ X16) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X17 : subst, X18 : term] : ((X12 @ X17 @ X18)))) @ id))) => ! [X19 : term] : (X0 @ id @ X19 @ id)))))) = hoasinduction)), 50.81/8.71 inference(rectify,[],[f3])). 50.81/8.71 thf(f5,plain,( 50.81/8.71 ~(! [X0 : (subst > term > subst > $o)] : (! [X4 : subst,X1 : subst,X3 : term,X2 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) => (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) = $true)) => (! [X6 : subst,X8 : term,X7 : subst,X5 : subst] : (($true = ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6))) => (((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) = $true)) => (! [X9 : term] : ((((hoasvar @ id @ X9 @ id)) = $true) => ($true = ((X0 @ id @ X9 @ id)))) => (! [X11 : term,X10 : term] : (($true = ((X0 @ id @ X11 @ id))) => ((((X0 @ id @ X10 @ id)) = $true) => (((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)) = $true))) => (! [X12 : (subst > term > term)] : (! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))) => (! [X16 : term] : ((((X0 @ id @ X16 @ id)) = $true) => (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) = $true))) => ! [X19 : term] : (((X0 @ id @ X19 @ id)) = $true)))))) <=> (hoasinduction = $true))), 50.81/8.71 inference(fool_elimination,[],[f4])). 50.81/8.71 thf(f6,plain,( 50.81/8.71 (substmonoid_lthm <=> (! [X0 : subst] : (((comp @ id @ X0)) = X0) => (! [X1 : subst] : (((comp @ X1 @ id)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2 & (! [X4 : term,X5 : subst] : (((sub @ one @ (push @ X4 @ X5))) = X4) <=> axvarcons) & pushprop_lem1_gthm & (! [X6 : term,X7 : term,X8 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7)))) <=> hoasapinj1) & hoasinduction_lem2_gthm & (! [X10 : (subst > term > subst > $o),X11 : term] : (~ ! [X12 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X12 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : term,X15 : subst,X16 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15)))) | (X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X11) @ id) | ~ ! [X17 : term] : ((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id) | ~(X10 @ id @ X17 @ id))) <=> hoasinduction_lem3a) & (! [X18 : term,X19 : (term > $o)] : (~ ! [X20 : term] : ((X19 @ X20) | ~(var @ X20)) | ~ ! [X21 : term] : ((X19 @ (lam @ X21)) | ~ ! [X22 : term] : ((X19 @ (sub @ X21 @ (push @ X22 @ id))) | ~(X19 @ X22))) | ~ ! [X23 : term,X24 : term] : (~(X19 @ X23) | ~(X19 @ X24) | (X19 @ (ap @ X24 @ X23))) | (X19 @ X18)) <=> induction2) & pushprop_lem3v2 & axassoc & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26)) <=> shinj) & (! [X27 : term,X28 : subst,X29 : (term > $o),X30 : (term > $o)] : (~(X30 @ X27) | ~ ! [X31 : term] : (((X29 @ X31)) = ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))) | (X29 @ one)) <=> pushprop_lem1v2) & (hoasinduction_lem3v2a_lthm <=> (! [X32 : term] : ~ ! [X33 : (subst > term > term)] : ~ ! [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) = ((X33 @ X35 @ X34))) => (! [X36 : term] : (((sub @ X36 @ id)) = X36) => ! [X37 : (subst > term > subst > $o),X38 : term,X39 : (term > $o)] : (~ ! [X40 : term] : (~(X39 @ X40) | (X39 @ (sub @ X38 @ (push @ X40 @ id)))) | ~ ! [X41 : term] : (((X37 @ id @ X41 @ id)) = ((X39 @ X41))) | ~ ! [X42 : (subst > term > term)] : (~ ! [X43 : term] : (~(X37 @ id @ X43 @ id) | (X37 @ id @ (X42 @ id @ X43) @ id)) | ~ ! [X44 : term,X45 : subst,X46 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45))) | (X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) | (X39 @ (lam @ X38)))))) & (hoasapinj2 <=> ! [X47 : term,X48 : term,X49 : term,X50 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & pushprop_lthm & hoasapinj1_gthm & (laminj <=> ! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51))))) & (! [X53 : term] : ~ ! [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) != ((X54 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & (one = ((d2term @ d_one))) & axapp & hoasapinj2_gthm & (axshiftcons <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & (! [X57 : term,X58 : term,X59 : term,X60 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> apinj1) & ~lamnotap & hoasapnotvar_gthm & (! [X61 : term] : (((sub @ X61 @ id)) = X61) <=> axvarid) & (hoasinduction_no_psi_cond_lthm <=> (! [X62 : (subst > term > subst > $o)] : ~ ! [X63 : (term > $o)] : ~ ! [X64 : term] : (((X63 @ X64)) = ((X62 @ id @ X64 @ id))) => (! [X65 : term,X66 : (term > $o)] : (~ ! [X67 : term] : (~ ! [X68 : term] : ((X66 @ (sub @ X67 @ (push @ X68 @ id))) | ~(X66 @ X68)) | (X66 @ (lam @ X67))) | (X66 @ X65) | ~ ! [X69 : term,X70 : term] : (~(X66 @ X69) | (X66 @ (ap @ X69 @ X70)) | ~(X66 @ X70)) | ~ ! [X71 : term] : (~(var @ X71) | (X66 @ X71))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => (! [X73 : (term > $o),X74 : term,X75 : (subst > term > subst > $o)] : (~ ! [X76 : (subst > term > term)] : ((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id) | ~ ! [X77 : term] : (~(X75 @ id @ X77 @ id) | (X75 @ id @ (X76 @ id @ X77) @ id)) | ~ ! [X78 : subst,X79 : term,X80 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) = ((sub @ (X76 @ X78 @ X79) @ X80)))) | ~ ! [X81 : term] : (~(X73 @ X81) | (X73 @ (sub @ X74 @ (push @ X81 @ id)))) | ~ ! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) | (X73 @ (lam @ X74))) => ! [X83 : (subst > term > subst > $o),X84 : term] : (~ ! [X85 : (subst > term > term)] : (~ ! [X86 : term] : (~(X83 @ id @ X86 @ id) | (X83 @ id @ (X85 @ id @ X86) @ id)) | ~ ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88)))) | (X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) | ~ ! [X90 : term,X91 : term] : (~(X83 @ id @ X90 @ id) | ~(X83 @ id @ X91 @ id) | (X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id)) | (X83 @ id @ X84 @ id))))))) & (hoasinduction_lem3_lthm <=> (! [X92 : term] : (((sub @ X92 @ id)) = X92) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X95 : term] : (~(X94 @ id @ X95 @ id) | (X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id)) | ~ ! [X96 : (subst > term > term)] : ((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id) | ~ ! [X97 : term,X98 : subst,X99 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X96 @ X99 @ X97) @ X98))) | ~ ! [X100 : term] : (~(X94 @ id @ X100 @ id) | (X94 @ id @ (X96 @ id @ X100) @ id))) | (X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) => ! [X101 : (subst > term > subst > $o),X102 : term] : (~ ! [X103 : term] : ((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id) | ~(X101 @ id @ X103 @ id)) | ~ ! [X104 : subst,X105 : term,X106 : subst,X107 : subst] : ((X101 @ X107 @ X105 @ (comp @ X106 @ X104)) | ~(X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) | (X101 @ id @ (lam @ X102) @ id) | ~ ! [X108 : (subst > term > term)] : (~ ! [X109 : term] : (~(X101 @ id @ X109 @ id) | (X101 @ id @ (X108 @ id @ X109) @ id)) | (X101 @ id @ (lam @ (X108 @ sh @ one)) @ id) | ~ ! [X110 : subst,X111 : term,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112))))) | ~ ! [X113 : subst,X114 : term,X115 : subst,X116 : subst] : (~(X101 @ X113 @ X114 @ (comp @ X116 @ X115)) | (X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115)))))) & (termmset_lthm <=> (! [X117 : term] : (((sub @ X117 @ id)) = X117) => ! [X118 : term] : (((sub @ X118 @ id)) = X118))) & (induction <=> ! [X119 : term,X120 : (term > $o)] : (~ ! [X121 : term] : ((X120 @ (lam @ X121)) | ~(X120 @ X121)) | (X120 @ X119) | ~ ! [X122 : term,X123 : term] : ((X120 @ (ap @ X122 @ X123)) | ~(X120 @ X123) | ~(X120 @ X122)) | ~ ! [X124 : term] : (~(var @ X124) | (X120 @ X124)))) & (sh = ((d2subst @ d_id))) & (hoasinduction_lem0_lthm <=> ! [X125 : (subst > term > subst > $o)] : ~ ! [X126 : (term > $o)] : ~ ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id)))) & ulamvarind & (hoasinduction_lthm <=> (! [X128 : term,X129 : (term > $o)] : (~ ! [X130 : term,X131 : term] : (~(X129 @ X130) | ~(X129 @ X131) | (X129 @ (ap @ X131 @ X130))) | ~ ! [X132 : term] : ((X129 @ (lam @ X132)) | ~ ! [X133 : term] : ((X129 @ (sub @ X132 @ (push @ X133 @ id))) | ~(X129 @ X133))) | ~ ! [X134 : term] : (~(var @ X134) | (X129 @ X134)) | (X129 @ X128)) => (! [X135 : term,X136 : (subst > term > subst > $o),X137 : term] : (~ ! [X138 : term,X139 : subst,X140 : subst,X141 : subst] : ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140) | ~(X136 @ X141 @ X138 @ (comp @ X139 @ X140))) | ~(X136 @ id @ X137 @ id) | (X136 @ id @ (ap @ X135 @ X137) @ id) | ~ ! [X142 : term,X143 : subst,X144 : subst,X145 : subst] : (~(X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143) | (X136 @ X144 @ X142 @ (comp @ X145 @ X143))) | ~ ! [X146 : term,X147 : term] : ((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id) | ~(X136 @ id @ X146 @ id) | ~(X136 @ id @ X147 @ id)) | ~(X136 @ id @ X135 @ id)) => (! [X148 : term,X149 : (subst > term > subst > $o)] : ((X149 @ id @ (lam @ X148) @ id) | ~ ! [X150 : term] : (~(X149 @ id @ X150 @ id) | (X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) | ~ ! [X151 : subst,X152 : term,X153 : subst,X154 : subst] : (~(X149 @ X154 @ X152 @ (comp @ X151 @ X153)) | (X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153)) | ~ ! [X155 : (subst > term > term)] : (~ ! [X156 : term] : (~(X149 @ id @ X156 @ id) | (X149 @ id @ (X155 @ id @ X156) @ id)) | (X149 @ id @ (lam @ (X155 @ sh @ one)) @ id) | ~ ! [X157 : subst,X158 : subst,X159 : term] : (((sub @ (X155 @ X157 @ X159) @ X158)) = ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158))))) | ~ ! [X160 : subst,X161 : subst,X162 : term,X163 : subst] : (~(X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161) | (X149 @ X163 @ X162 @ (comp @ X160 @ X161)))) => ! [X164 : (subst > term > subst > $o),X165 : term] : (~ ! [X166 : term] : ((X164 @ id @ X166 @ id) | ~(var @ (sub @ X166 @ id))) | ~ ! [X167 : term,X168 : term] : (~(X164 @ id @ X168 @ id) | ~(X164 @ id @ X167 @ id) | (X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id)) | (X164 @ id @ X165 @ id) | ~ ! [X169 : term,X170 : subst,X171 : subst,X172 : subst] : (~(X164 @ X171 @ X169 @ (comp @ X170 @ X172)) | (X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X174 : subst,X175 : term,X176 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174))) | ~ ! [X177 : term] : ((X164 @ id @ (X173 @ id @ X177) @ id) | ~(X164 @ id @ X177 @ id)) | (X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) | ~ ! [X178 : subst,X179 : subst,X180 : subst,X181 : term] : (~(X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180) | (X164 @ X178 @ X181 @ (comp @ X179 @ X180)))))))) & hoasinduction_lem1_gthm & ! [X182 : d_term] : (d_one = X182) & hoasinduction_lem3v2_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lthm_orig & (hoasinduction <=> ! [X183 : (subst > term > subst > $o),X184 : term] : ((X183 @ id @ X184 @ id) | ~ ! [X185 : term] : ((X183 @ id @ X185 @ id) | ~(var @ (sub @ X185 @ id))) | ~ ! [X186 : term,X187 : subst,X188 : subst,X189 : subst] : (~(X183 @ X189 @ X186 @ (comp @ X187 @ X188)) | (X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) | ~ ! [X190 : term,X191 : term] : (~(X183 @ id @ X191 @ id) | (X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id) | ~(X183 @ id @ X190 @ id)) | ~ ! [X192 : term,X193 : subst,X194 : subst,X195 : subst] : ((X183 @ X195 @ X192 @ (comp @ X194 @ X193)) | ~(X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) | ~ ! [X196 : (subst > term > term)] : (~ ! [X197 : term] : ((X183 @ id @ (X196 @ id @ X197) @ id) | ~(X183 @ id @ X197 @ id)) | ~ ! [X198 : term,X199 : subst,X200 : subst] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200)))) | (X183 @ id @ (lam @ (X196 @ sh @ one)) @ id)))) & termmset_gthm & (induction2lem <=> ! [X201 : (term > $o),X202 : subst,X203 : term] : (~ ! [X204 : term] : (~(var @ X204) | (X201 @ (sub @ X204 @ X202))) | ~ ! [X205 : term] : ((X201 @ (lam @ X205)) | ~ ! [X206 : term] : ((X201 @ (sub @ X205 @ (push @ X206 @ id))) | ~(X201 @ X206))) | ~ ! [X207 : term,X208 : term] : ((X201 @ (ap @ X208 @ X207)) | ~(X201 @ X208) | ~(X201 @ X207)) | (X201 @ (sub @ X203 @ X202)))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((! [X209 : term] : (((sub @ X209 @ id)) = X209) => (! [X210 : subst,X211 : (term > $o),X212 : term] : (~ ! [X213 : term] : (~ ! [X214 : term] : ((X211 @ (sub @ X213 @ (push @ X214 @ id))) | ~(X211 @ X214)) | (X211 @ (lam @ X213))) | ~ ! [X215 : term] : ((X211 @ (sub @ X215 @ X210)) | ~(var @ X215)) | ~ ! [X216 : term,X217 : term] : ((X211 @ (ap @ X216 @ X217)) | ~(X211 @ X217) | ~(X211 @ X216)) | (X211 @ (sub @ X212 @ X210))) => ! [X218 : (term > $o),X219 : term] : (~ ! [X220 : term] : ((X218 @ X220) | ~(var @ X220)) | (X218 @ X219) | ~ ! [X221 : term] : (~ ! [X222 : term] : ((X218 @ (sub @ X221 @ (push @ X222 @ id))) | ~(X218 @ X222)) | (X218 @ (lam @ X221))) | ~ ! [X223 : term,X224 : term] : ((X218 @ (ap @ X223 @ X224)) | ~(X218 @ X223) | ~(X218 @ X224))))) <=> induction2_lthm) & (pushprop_p_and_p_prime = (^[X225 : term, X226 : subst, X227 : (term > $o), X228 : (term > $o)] : (! [X229 : term] : (((X228 @ X229)) = ((X227 @ (sub @ X229 @ (push @ X225 @ X226)))))))) & ulamvarsh & (! [X230 : subst] : (((comp @ X230 @ id)) = X230) <=> axidr) & ~ulamvar1 & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & ! [X231 : d_subst,X232 : d_subst] : ((((d2subst @ X231)) = ((d2subst @ X232))) => (X231 = X232)) & hoaslamnotvar & hoasinduction_lem1v2_gthm & ((! [X233 : term,X234 : subst] : (((sub @ one @ (push @ X233 @ X234))) = X233) => ! [X235 : term,X236 : (term > $o),X237 : (term > $o),X238 : subst] : (~(X236 @ X235) | ~ ! [X239 : term] : (((X237 @ X239)) = ((X236 @ (sub @ X239 @ (push @ X235 @ X238))))) | (X237 @ one))) <=> pushprop_lem1v2_lthm) & (hoasinduction_lem3 <=> ! [X240 : term,X241 : (subst > term > subst > $o)] : (~ ! [X242 : term] : (~(X241 @ id @ X242 @ id) | (X241 @ id @ (sub @ X240 @ (push @ X242 @ id)) @ id)) | (X241 @ id @ (lam @ X240) @ id) | ~ ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (~(X241 @ X246 @ X245 @ (comp @ X243 @ X244)) | (X241 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) | ~ ! [X247 : (subst > term > term)] : (~ ! [X248 : term,X249 : subst,X250 : subst] : (((X247 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249))) = ((sub @ (X247 @ X250 @ X248) @ X249))) | ~ ! [X251 : term] : ((X241 @ id @ (X247 @ id @ X251) @ id) | ~(X241 @ id @ X251 @ id)) | (X241 @ id @ (lam @ (X247 @ sh @ one)) @ id)) | ~ ! [X252 : subst,X253 : term,X254 : subst,X255 : subst] : (~(X241 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254) @ X252) | (X241 @ X255 @ X253 @ (comp @ X254 @ X252))))) & hoasinduction_lem1v2 & axabs & pushprop_lem3v2_lthm & (hoaslaminj_lthm <=> (! [X256 : term,X257 : subst] : (((sub @ one @ (push @ X256 @ X257))) = X256) => (! [X258 : term,X259 : subst] : (((comp @ sh @ (push @ X258 @ X259))) = X259) => (! [X260 : term,X261 : term] : ((((lam @ X260)) != ((lam @ X261))) | (X260 = X261)) => ! [X262 : subst,X263 : (subst > term > term),X264 : term,X265 : (subst > term > term)] : (~ ! [X266 : subst,X267 : subst,X268 : term] : (((X263 @ (comp @ X266 @ X267) @ (sub @ X268 @ X267))) = ((sub @ (X263 @ X266 @ X268) @ X267))) | ~ ! [X269 : subst,X270 : term,X271 : subst] : (((X265 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269))) = ((sub @ (X265 @ X271 @ X270) @ X269))) | (((lam @ (X263 @ sh @ one))) != ((lam @ (X265 @ sh @ one)))) | (((X265 @ X262 @ X264)) = ((X263 @ X262 @ X264)))))))) & apnotvar & (! [X272 : (subst > term > subst > $o),X273 : term] : (~ ! [X274 : term] : (~(X272 @ id @ X274 @ id) | (X272 @ id @ (sub @ X273 @ (push @ X274 @ id)) @ id)) | ~ ! [X275 : (subst > term > term)] : (~ ! [X276 : term] : (~(X272 @ id @ X276 @ id) | (X272 @ id @ (X275 @ id @ X276) @ id)) | ~ ! [X277 : term,X278 : subst,X279 : subst] : (((sub @ (X275 @ X279 @ X277) @ X278)) = ((X275 @ (comp @ X279 @ X278) @ (sub @ X277 @ X278)))) | (X272 @ id @ (lam @ (X275 @ sh @ one)) @ id)) | (X272 @ id @ (lam @ (sub @ X273 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & induction2_gthm & ~(var @ (d2term @ d_one)) & (hoasinduction_lem2 <=> ! [X280 : (subst > term > subst > $o),X281 : term,X282 : term] : (~(X280 @ id @ X282 @ id) | ~ ! [X283 : subst,X284 : term,X285 : subst,X286 : subst] : (~(X280 @ (comp @ X283 @ X285) @ (sub @ X284 @ X285) @ X286) | (X280 @ X283 @ X284 @ (comp @ X285 @ X286))) | ~ ! [X287 : term,X288 : term] : (~(X280 @ id @ X287 @ id) | ~(X280 @ id @ X288 @ id) | (X280 @ id @ (ap @ (sub @ X288 @ id) @ X287) @ id)) | (X280 @ id @ (ap @ X282 @ X281) @ id) | ~ ! [X289 : term,X290 : subst,X291 : subst,X292 : subst] : ((X280 @ (comp @ X292 @ X290) @ (sub @ X289 @ X290) @ X291) | ~(X280 @ X292 @ X289 @ (comp @ X290 @ X291))) | ~(X280 @ id @ X281 @ id))) & pushprop & hoaslamnotvar_lthm & hoasinduction_lem1_lthm & ! [X293 : d_term,X294 : d_term] : ((((d2term @ X294)) = ((d2term @ X293))) => (X293 = X294)) & (hoasinduction_lem3a_lthm <=> (! [X295 : term] : (((sub @ X295 @ id)) = X295) => (! [X296 : (subst > term > subst > $o),X297 : term] : (~ ! [X298 : (subst > term > term)] : (~ ! [X299 : subst,X300 : subst,X301 : term] : (((sub @ (X298 @ X300 @ X301) @ X299)) = ((X298 @ (comp @ X300 @ X299) @ (sub @ X301 @ X299)))) | ~ ! [X302 : term] : ((X296 @ id @ (X298 @ id @ X302) @ id) | ~(X296 @ id @ X302 @ id)) | (X296 @ id @ (lam @ (X298 @ sh @ one)) @ id)) | (X296 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id) | ~ ! [X303 : term] : (~(X296 @ id @ X303 @ id) | (X296 @ id @ (sub @ X297 @ (push @ X303 @ id)) @ id))) => ! [X304 : term,X305 : (subst > term > subst > $o)] : (~ ! [X306 : term] : (~(X305 @ id @ X306 @ id) | (X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id)) | ~ ! [X307 : (subst > term > term)] : (~ ! [X308 : subst,X309 : term,X310 : subst] : (((sub @ (X307 @ X308 @ X309) @ X310)) = ((X307 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310)))) | (X305 @ id @ (lam @ (X307 @ sh @ one)) @ id) | ~ ! [X311 : term] : (~(X305 @ id @ X311 @ id) | (X305 @ id @ (X307 @ id @ X311) @ id))) | (X305 @ id @ (lam @ X304) @ id))))) & pushprop_lem0_gthm & hoasinduction_lem2_lthm & hoasinduction_lem3a_gthm & hoasinduction_lem3b_gthm & hoasapnotvar_lthm & (axscons <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & (! [X313 : subst,X314 : (subst > term > term),X315 : (subst > term > term),X316 : term] : ((((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ~ ! [X317 : term,X318 : subst,X319 : subst] : (((X314 @ (comp @ X318 @ X319) @ (sub @ X317 @ X319))) = ((sub @ (X314 @ X318 @ X317) @ X319))) | (((X314 @ X313 @ X316)) = ((X315 @ X313 @ X316))) | ~ ! [X320 : term,X321 : subst,X322 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X315 @ X322 @ X320) @ X321)))) <=> hoaslaminj) & (axidl <=> ! [X323 : subst] : (((comp @ id @ X323)) = X323)) & ! [X324 : subst] : ? [X325 : d_subst] : (((d2subst @ X325)) = X324) & (hoasapinj1_lthm <=> (! [X326 : term] : (((sub @ X326 @ id)) = X326) => (! [X327 : term,X328 : term,X329 : term,X330 : term] : ((X328 = X329) | (((ap @ X328 @ X327)) != ((ap @ X329 @ X330)))) => ! [X331 : term,X332 : term,X333 : term,X334 : term] : ((X333 = X334) | (((ap @ (sub @ X334 @ id) @ X331)) != ((ap @ (sub @ X333 @ id) @ X332))))))) & (! [X335 : term,X336 : (term > $o),X337 : (subst > term > subst > $o)] : (~ ! [X338 : term] : (((X337 @ id @ X338 @ id)) = ((X336 @ X338))) | (X336 @ (lam @ X335)) | ~ ! [X339 : term] : ((X336 @ (sub @ X335 @ (push @ X339 @ id))) | ~(X336 @ X339)) | ~ ! [X340 : (subst > term > term)] : (~ ! [X341 : term,X342 : subst,X343 : subst] : (((X340 @ (comp @ X342 @ X343) @ (sub @ X341 @ X343))) = ((sub @ (X340 @ X342 @ X341) @ X343))) | (X337 @ id @ (lam @ (X340 @ sh @ one)) @ id) | ~ ! [X344 : term] : ((X337 @ id @ (X340 @ id @ X344) @ id) | ~(X337 @ id @ X344 @ id)))) <=> hoasinduction_lem3v2a) & (! [X345 : term,X346 : term,X347 : (term > $o),X348 : (subst > term > subst > $o)] : (~ ! [X349 : term] : (((X348 @ id @ X349 @ id)) = ((X347 @ X349))) | ~ ! [X350 : term,X351 : term] : ((X348 @ id @ (ap @ (sub @ X351 @ id) @ X350) @ id) | ~(X348 @ id @ X350 @ id) | ~(X348 @ id @ X351 @ id)) | ~ ! [X352 : subst,X353 : subst,X354 : subst,X355 : term] : ((X348 @ X353 @ X355 @ (comp @ X352 @ X354)) | ~(X348 @ (comp @ X353 @ X352) @ (sub @ X355 @ X352) @ X354)) | ~ ! [X356 : term,X357 : subst,X358 : subst,X359 : subst] : ((X348 @ (comp @ X359 @ X357) @ (sub @ X356 @ X357) @ X358) | ~(X348 @ X359 @ X356 @ (comp @ X357 @ X358))) | ~(X347 @ X345) | (X347 @ (ap @ X345 @ X346)) | ~(X347 @ X346)) <=> hoasinduction_lem2v2) & hoasinduction_lem3_gthm & ((^[X360 : (subst > term > subst > $o), X361 : (term > $o)] : (! [X362 : term] : (((X361 @ X362)) = ((X360 @ id @ X362 @ id))))) = hoasinduction_p_and_p_prime) & ! [X363 : d_subst] : (d_id = X363) & (hoasinduction_lem3v2 <=> ! [X364 : (subst > term > subst > $o),X365 : term,X366 : (term > $o)] : (~ ! [X367 : (subst > term > term)] : (~ ! [X368 : term] : (~(X364 @ id @ X368 @ id) | (X364 @ id @ (X367 @ id @ X368) @ id)) | ~ ! [X369 : subst,X370 : subst,X371 : term] : (((X367 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370))) = ((sub @ (X367 @ X369 @ X371) @ X370))) | (X364 @ id @ (lam @ (X367 @ sh @ one)) @ id)) | ~ ! [X372 : subst,X373 : term,X374 : subst,X375 : subst] : (~(X364 @ (comp @ X372 @ X374) @ (sub @ X373 @ X374) @ X375) | (X364 @ X372 @ X373 @ (comp @ X374 @ X375))) | ~ ! [X376 : term,X377 : subst,X378 : subst,X379 : subst] : ((X364 @ (comp @ X378 @ X377) @ (sub @ X376 @ X377) @ X379) | ~(X364 @ X378 @ X376 @ (comp @ X377 @ X379))) | (X366 @ (lam @ X365)) | ~ ! [X380 : term] : (~(X366 @ X380) | (X366 @ (sub @ X365 @ (push @ X380 @ id)))) | ~ ! [X381 : term] : (((X366 @ X381)) = ((X364 @ id @ X381 @ id))))) & (! [X382 : (term > $o),X383 : subst,X384 : term] : ~ ! [X385 : (term > $o)] : ~ ! [X386 : term] : (((X385 @ X386)) = ((X382 @ (sub @ X386 @ (push @ X384 @ X383))))) <=> pushprop_lem0_lthm) & (induction2lem_lthm <=> (! [X387 : subst,X388 : term] : (((sub @ one @ (push @ X388 @ X387))) = X388) => (! [X389 : term,X390 : subst] : (((comp @ sh @ (push @ X389 @ X390))) = X390) => (! [X391 : subst] : (((comp @ X391 @ id)) = X391) => (! [X392 : term,X393 : (term > $o)] : (~ ! [X394 : term] : (~(var @ X394) | (X393 @ X394)) | (X393 @ X392) | ~ ! [X395 : term,X396 : term] : (~(X393 @ X395) | ~(X393 @ X396) | (X393 @ (ap @ X395 @ X396))) | ~ ! [X397 : term] : (~(X393 @ X397) | (X393 @ (lam @ X397)))) => ! [X398 : subst,X399 : (term > $o),X400 : term] : (~ ! [X401 : term] : (~(var @ X401) | (X399 @ (sub @ X401 @ X398))) | (X399 @ (sub @ X400 @ X398)) | ~ ! [X402 : term] : ((X399 @ (lam @ X402)) | ~ ! [X403 : term] : ((X399 @ (sub @ X402 @ (push @ X403 @ id))) | ~(X399 @ X403))) | ~ ! [X404 : term,X405 : term] : ((X399 @ (ap @ X404 @ X405)) | ~(X399 @ X405) | ~(X399 @ X404)))))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoaslam = (^[X406 : subst, X407 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lem2v2_gthm & axclos & (hoasapinj2_lthm <=> (! [X408 : term,X409 : term,X410 : term,X411 : term] : ((X408 = X411) | (((ap @ X410 @ X411)) != ((ap @ X409 @ X408)))) => ! [X412 : term,X413 : term,X414 : term,X415 : term] : ((X414 = X415) | (((ap @ (sub @ X413 @ id) @ X415)) != ((ap @ (sub @ X412 @ id) @ X414)))))) & lamnotvar & induction2lem_gthm & (! [X416 : (term > $o),X417 : term,X418 : term,X419 : (term > $o),X420 : subst] : ((X416 @ (sub @ X417 @ (push @ X418 @ X420))) | ~(X419 @ X417)) <=> pushprop_lem1) & (! [X421 : (subst > term > term),X422 : term,X423 : term] : ((((ap @ (sub @ X423 @ id) @ X422)) != ((lam @ (X421 @ sh @ one)))) | ~ ! [X424 : subst,X425 : subst,X426 : term] : (((sub @ (X421 @ X425 @ X426) @ X424)) = ((X421 @ (comp @ X425 @ X424) @ (sub @ X426 @ X424))))) <=> hoaslamnotap) & (hoasinduction_lem3b <=> ! [X427 : term] : ~ ! [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) != ((X428 @ sh @ one)))) & hoaslamnotap_lthm & ((! [X429 : term] : (((sub @ X429 @ id)) = X429) => ! [X430 : (subst > term > subst > $o),X431 : (term > $o),X432 : term] : (~ ! [X433 : term,X434 : subst,X435 : subst,X436 : subst] : ((X430 @ (comp @ X435 @ X436) @ (sub @ X433 @ X436) @ X434) | ~(X430 @ X435 @ X433 @ (comp @ X436 @ X434))) | (X431 @ (lam @ X432)) | ~ ! [X437 : term] : (~(X431 @ X437) | (X431 @ (sub @ X432 @ (push @ X437 @ id)))) | ~ ! [X438 : term] : (((X431 @ X438)) = ((X430 @ id @ X438 @ id))) | ~ ! [X439 : subst,X440 : subst,X441 : term,X442 : subst] : ((X430 @ X439 @ X441 @ (comp @ X440 @ X442)) | ~(X430 @ (comp @ X439 @ X440) @ (sub @ X441 @ X440) @ X442)) | ~ ! [X443 : (subst > term > term)] : ((X430 @ id @ (lam @ (X443 @ sh @ one)) @ id) | ~ ! [X444 : term] : ((X430 @ id @ (X443 @ id @ X444) @ id) | ~(X430 @ id @ X444 @ id)) | ~ ! [X445 : term,X446 : subst,X447 : subst] : (((X443 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X443 @ X447 @ X445) @ X446)))))) <=> hoasinduction_lem3v2_lthm) & (! [X448 : (subst > term > subst > $o),X449 : term] : (~ ! [X450 : term,X451 : (subst > term > term)] : (~ ! [X452 : subst,X453 : subst,X454 : term] : (((sub @ X450 @ (push @ (sub @ X454 @ X453) @ (comp @ X452 @ X453)))) = ((X451 @ (comp @ X452 @ X453) @ (sub @ X454 @ X453)))) | ~ ! [X455 : term,X456 : subst,X457 : subst] : (((sub @ (sub @ X450 @ (push @ X455 @ X456)) @ X457)) = ((sub @ (X451 @ X456 @ X455) @ X457))) | (X448 @ id @ (lam @ (X451 @ sh @ one)) @ id) | ~ ! [X458 : term] : (~(X448 @ id @ X458 @ id) | (X448 @ id @ (X451 @ id @ X458) @ id))) | (X448 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id) | ~ ! [X459 : term] : ((X448 @ id @ (sub @ X449 @ (push @ X459 @ id)) @ id) | ~(X448 @ id @ X459 @ id))) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3aa <=> ! [X460 : (subst > term > subst > $o),X461 : term] : (~ ! [X462 : term] : (~(X460 @ id @ X462 @ id) | (X460 @ id @ (sub @ X461 @ (push @ X462 @ id)) @ id)) | (X460 @ id @ (lam @ (sub @ X461 @ (push @ one @ sh))) @ id) | ~ ! [X463 : (subst > term > term)] : (~ ! [X464 : term] : (~(X460 @ id @ X464 @ id) | (X460 @ id @ (X463 @ id @ X464) @ id)) | (X460 @ id @ (lam @ (X463 @ sh @ one)) @ id) | ~ ! [X465 : subst,X466 : subst,X467 : term] : (((X463 @ (comp @ X465 @ X466) @ (sub @ X467 @ X466))) = ((sub @ (X463 @ X465 @ X467) @ X466)))))) & (apinj2 <=> ! [X468 : term,X469 : term,X470 : term,X471 : term] : ((((ap @ X468 @ X469)) != ((ap @ X471 @ X470))) | (X469 = X470))) & (termmset <=> ! [X472 : term] : (((sub @ X472 @ id)) = X472)) & hoaslaminj_gthm & (substmonoid <=> (! [X473 : subst] : (((comp @ id @ X473)) = X473) & ! [X474 : subst] : (((comp @ X474 @ id)) = X474))) & hoasinduction_lem2v2_gthm & axmap & hoasinduction_lem1 & hoaslamnotap_gthm & axvarshift & substmonoid_gthm & (pushprop_lem0 <=> ! [X475 : term,X476 : subst,X477 : (term > $o)] : ~ ! [X478 : (term > $o)] : ~ ! [X479 : term] : (((X477 @ (sub @ X479 @ (push @ X475 @ X476)))) = ((X478 @ X479)))) & hoasinduction_gthm & pushprop_gthm & pushprop_lem2v2_lthm & (hoasinduction_lthm_3 <=> (! [X480 : (subst > term > subst > $o)] : ~ ! [X481 : (term > $o)] : ~ ! [X482 : term] : (((X480 @ id @ X482 @ id)) = ((X481 @ X482))) => (! [X483 : (term > $o),X484 : term] : ((X483 @ X484) | ~ ! [X485 : term,X486 : term] : ((X483 @ (ap @ X485 @ X486)) | ~(X483 @ X486) | ~(X483 @ X485)) | ~ ! [X487 : term] : ((X483 @ X487) | ~(var @ X487)) | ~ ! [X488 : term] : (~ ! [X489 : term] : ((X483 @ (sub @ X488 @ (push @ X489 @ id))) | ~(X483 @ X489)) | (X483 @ (lam @ X488)))) => (! [X490 : term] : (((sub @ X490 @ id)) = X490) => (! [X491 : (subst > term > subst > $o),X492 : term,X493 : (term > $o)] : (~ ! [X494 : (subst > term > term)] : (~ ! [X495 : term,X496 : subst,X497 : subst] : (((sub @ (X494 @ X496 @ X495) @ X497)) = ((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497)))) | ~ ! [X498 : term] : ((X491 @ id @ (X494 @ id @ X498) @ id) | ~(X491 @ id @ X498 @ id)) | (X491 @ id @ (lam @ (X494 @ sh @ one)) @ id)) | (X493 @ (lam @ X492)) | ~ ! [X499 : term] : (~(X493 @ X499) | (X493 @ (sub @ X492 @ (push @ X499 @ id)))) | ~ ! [X500 : term] : (((X493 @ X500)) = ((X491 @ id @ X500 @ id)))) => ! [X501 : term,X502 : (subst > term > subst > $o)] : (~ ! [X503 : subst,X504 : term,X505 : subst,X506 : subst] : ((X502 @ (comp @ X503 @ X505) @ (sub @ X504 @ X505) @ X506) | ~(X502 @ X503 @ X504 @ (comp @ X505 @ X506))) | ~ ! [X507 : term,X508 : subst,X509 : subst,X510 : subst] : (~(X502 @ (comp @ X509 @ X510) @ (sub @ X507 @ X510) @ X508) | (X502 @ X509 @ X507 @ (comp @ X510 @ X508))) | ~ ! [X511 : term,X512 : term] : (~(X502 @ id @ X512 @ id) | (X502 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id) | ~(X502 @ id @ X511 @ id)) | ~ ! [X513 : term] : (~(var @ (sub @ X513 @ id)) | (X502 @ id @ X513 @ id)) | (X502 @ id @ X501 @ id) | ~ ! [X514 : (subst > term > term)] : ((X502 @ id @ (lam @ (X514 @ sh @ one)) @ id) | ~ ! [X515 : term] : ((X502 @ id @ (X514 @ id @ X515) @ id) | ~(X502 @ id @ X515 @ id)) | ~ ! [X516 : subst,X517 : subst,X518 : term] : (((X514 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516))) = ((sub @ (X514 @ X517 @ X518) @ X516)))))))))) & (hoasinduction_no_psi_cond <=> ! [X519 : term,X520 : (subst > term > subst > $o)] : (~ ! [X521 : term,X522 : term] : (~(X520 @ id @ X522 @ id) | (X520 @ id @ (ap @ (sub @ X521 @ id) @ X522) @ id) | ~(X520 @ id @ X521 @ id)) | (X520 @ id @ X519 @ id) | ~ ! [X523 : (subst > term > term)] : ((X520 @ id @ (lam @ (X523 @ sh @ one)) @ id) | ~ ! [X524 : term] : (~(X520 @ id @ X524 @ id) | (X520 @ id @ (X523 @ id @ X524) @ id)) | ~ ! [X525 : term,X526 : subst,X527 : subst] : (((X523 @ (comp @ X527 @ X526) @ (sub @ X525 @ X526))) = ((sub @ (X523 @ X527 @ X525) @ X526)))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem0 <=> ! [X528 : (subst > term > subst > $o)] : ~ ! [X529 : (term > $o)] : ~ ! [X530 : term] : (((X528 @ id @ X530 @ id)) = ((X529 @ X530)))) & (id = ((d2subst @ d_id))) & (pushprop_lem1_lthm <=> (! [X531 : term,X532 : subst] : (((sub @ one @ (push @ X531 @ X532))) = X531) => (! [X533 : term,X534 : subst] : (((comp @ sh @ (push @ X533 @ X534))) = X534) => ! [X535 : subst,X536 : term,X537 : term,X538 : (term > $o),X539 : (term > $o)] : ((X538 @ (sub @ X536 @ (push @ X537 @ X535))) | ~(X539 @ X536))))) & ! [X540 : term] : ? [X541 : d_term] : (((d2term @ X541)) = X540) & (! [X542 : term] : ~ ! [X543 : (subst > term > term)] : ~ ! [X544 : subst,X545 : term] : (((sub @ X542 @ (push @ X545 @ X544))) = ((X543 @ X544 @ X545))) <=> hoasinduction_lem3v2_f) & hoasapnotvar & (hoasinduction_lem3v2_f_lthm <=> ! [X546 : term] : ~ ! [X547 : (subst > term > term)] : ~ ! [X548 : subst,X549 : term] : (((X547 @ X548 @ X549)) = ((sub @ X546 @ (push @ X549 @ X548)))))), 50.81/8.71 inference(rectify,[],[f1])). 50.81/8.71 thf(f7,plain,( 50.81/8.71 ((substmonoid_lthm = $true) <=> (! [X0 : subst] : (((comp @ id @ X0)) = X0) => (! [X1 : subst] : (((comp @ X1 @ id)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2 = $true) & ((axvarcons = $true) <=> ! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4)) & (pushprop_lem1_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7))))) & (hoasinduction_lem2_gthm = $true) & (! [X10 : (subst > term > subst > $o),X11 : term] : (~ ! [X12 : (subst > term > term)] : (~ ! [X13 : term] : ((((X10 @ id @ (X12 @ id @ X13) @ id)) = $true) | ~ (((X10 @ id @ X13 @ id)) = $true)) | ~ ! [X16 : subst,X14 : term,X15 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15)))) | (((X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) = $true)) | (((X10 @ id @ (lam @ X11) @ id)) = $true) | ~ ! [X17 : term] : ((((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) = $true) | ~ ($true = ((X10 @ id @ X17 @ id))))) <=> (hoasinduction_lem3a = $true)) & (! [X18 : term,X19 : (term > $o)] : (~ ! [X20 : term] : ((((X19 @ X20)) = $true) | ~ ($true = ((var @ X20)))) | ~ ! [X21 : term] : ((((X19 @ (lam @ X21))) = $true) | ~ ! [X22 : term] : ((((X19 @ (sub @ X21 @ (push @ X22 @ id)))) = $true) | ~ (((X19 @ X22)) = $true))) | ~ ! [X23 : term,X24 : term] : (~ ($true = ((X19 @ X23))) | ~ (((X19 @ X24)) = $true) | (((X19 @ (ap @ X24 @ X23))) = $true)) | (((X19 @ X18)) = $true)) <=> (induction2 = $true)) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((shinj = $true) <=> ! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26))) & (! [X27 : term,X28 : subst,X29 : (term > $o),X30 : (term > $o)] : (~ ($true = ((X30 @ X27))) | ~ ! [X31 : term] : (((X29 @ X31)) = ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))) | ($true = ((X29 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X32 : term] : ~ ! [X33 : (subst > term > term)] : ~ ! [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) = ((X33 @ X35 @ X34))) => (! [X36 : term] : (((sub @ X36 @ id)) = X36) => ! [X37 : (subst > term > subst > $o),X38 : term,X39 : (term > $o)] : (~ ! [X40 : term] : (~ ($true = ((X39 @ X40))) | (((X39 @ (sub @ X38 @ (push @ X40 @ id)))) = $true)) | ~ ! [X41 : term] : (((X37 @ id @ X41 @ id)) = ((X39 @ X41))) | ~ ! [X42 : (subst > term > term)] : (~ ! [X43 : term] : (~ (((X37 @ id @ X43 @ id)) = $true) | ($true = ((X37 @ id @ (X42 @ id @ X43) @ id)))) | ~ ! [X44 : term,X46 : subst,X45 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45))) | (((X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) = $true)) | (((X39 @ (lam @ X38))) = $true))))) & ((hoasapinj2 = $true) <=> ! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & (pushprop_lthm = $true) & (hoasapinj1_gthm = $true) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) <=> (laminj = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X53 : term] : ~ ! [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) != ((X54 @ sh @ one)))) & (((d2term @ d_one)) = one) & (axapp = $true) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> (apinj1 = $true)) & ~ (lamnotap = $true) & (hoasapnotvar_gthm = $true) & ((axvarid = $true) <=> ! [X61 : term] : (((sub @ X61 @ id)) = X61)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X62 : (subst > term > subst > $o)] : ~ ! [X63 : (term > $o)] : ~ ! [X64 : term] : (((X63 @ X64)) = ((X62 @ id @ X64 @ id))) => (! [X65 : term,X66 : (term > $o)] : (~ ! [X67 : term] : (~ ! [X68 : term] : ((((X66 @ (sub @ X67 @ (push @ X68 @ id)))) = $true) | ~ (((X66 @ X68)) = $true)) | ($true = ((X66 @ (lam @ X67))))) | (((X66 @ X65)) = $true) | ~ ! [X69 : term,X70 : term] : (~ ($true = ((X66 @ X69))) | (((X66 @ (ap @ X69 @ X70))) = $true) | ~ (((X66 @ X70)) = $true)) | ~ ! [X71 : term] : (~ (((var @ X71)) = $true) | ($true = ((X66 @ X71))))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => (! [X73 : (term > $o),X74 : term,X75 : (subst > term > subst > $o)] : (~ ! [X76 : (subst > term > term)] : ((((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ~ ! [X77 : term] : (~ (((X75 @ id @ X77 @ id)) = $true) | (((X75 @ id @ (X76 @ id @ X77) @ id)) = $true)) | ~ ! [X80 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) = ((sub @ (X76 @ X78 @ X79) @ X80)))) | ~ ! [X81 : term] : (~ (((X73 @ X81)) = $true) | ($true = ((X73 @ (sub @ X74 @ (push @ X81 @ id)))))) | ~ ! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) | (((X73 @ (lam @ X74))) = $true)) => ! [X83 : (subst > term > subst > $o),X84 : term] : (~ ! [X85 : (subst > term > term)] : (~ ! [X86 : term] : (~ (((X83 @ id @ X86 @ id)) = $true) | (((X83 @ id @ (X85 @ id @ X86) @ id)) = $true)) | ~ ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88)))) | (((X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) = $true)) | ~ ! [X90 : term,X91 : term] : (~ (((X83 @ id @ X90 @ id)) = $true) | ~ (((X83 @ id @ X91 @ id)) = $true) | ($true = ((X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id)))) | ($true = ((X83 @ id @ X84 @ id))))))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X92 : term] : (((sub @ X92 @ id)) = X92) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X95 : term] : (~ (((X94 @ id @ X95 @ id)) = $true) | ($true = ((X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id)))) | ~ ! [X96 : (subst > term > term)] : ((((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true) | ~ ! [X97 : term,X99 : subst,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X96 @ X99 @ X97) @ X98))) | ~ ! [X100 : term] : (~ ($true = ((X94 @ id @ X100 @ id))) | (((X94 @ id @ (X96 @ id @ X100) @ id)) = $true))) | (((X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true)) => ! [X101 : (subst > term > subst > $o),X102 : term] : (~ ! [X103 : term] : ((((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id)) = $true) | ~ ($true = ((X101 @ id @ X103 @ id)))) | ~ ! [X104 : subst,X105 : term,X106 : subst,X107 : subst] : (($true = ((X101 @ X107 @ X105 @ (comp @ X106 @ X104)))) | ~ (((X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) = $true)) | (((X101 @ id @ (lam @ X102) @ id)) = $true) | ~ ! [X108 : (subst > term > term)] : (~ ! [X109 : term] : (~ (((X101 @ id @ X109 @ id)) = $true) | (((X101 @ id @ (X108 @ id @ X109) @ id)) = $true)) | (((X101 @ id @ (lam @ (X108 @ sh @ one)) @ id)) = $true) | ~ ! [X111 : term,X110 : subst,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112))))) | ~ ! [X113 : subst,X114 : term,X115 : subst,X116 : subst] : (~ (((X101 @ X113 @ X114 @ (comp @ X116 @ X115))) = $true) | ($true = ((X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115)))))))) & ((termmset_lthm = $true) <=> (! [X117 : term] : (((sub @ X117 @ id)) = X117) => ! [X118 : term] : (((sub @ X118 @ id)) = X118))) & ((induction = $true) <=> ! [X119 : term,X120 : (term > $o)] : (~ ! [X121 : term] : ((((X120 @ (lam @ X121))) = $true) | ~ ($true = ((X120 @ X121)))) | (((X120 @ X119)) = $true) | ~ ! [X122 : term,X123 : term] : (($true = ((X120 @ (ap @ X122 @ X123)))) | ~ (((X120 @ X123)) = $true) | ~ (((X120 @ X122)) = $true)) | ~ ! [X124 : term] : (~ (((var @ X124)) = $true) | (((X120 @ X124)) = $true)))) & (((d2subst @ d_id)) = sh) & (! [X125 : (subst > term > subst > $o)] : ~ ! [X126 : (term > $o)] : ~ ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (ulamvarind = $true) & ((hoasinduction_lthm = $true) <=> (! [X128 : term,X129 : (term > $o)] : (~ ! [X130 : term,X131 : term] : (~ ($true = ((X129 @ X130))) | ~ (((X129 @ X131)) = $true) | (((X129 @ (ap @ X131 @ X130))) = $true)) | ~ ! [X132 : term] : ((((X129 @ (lam @ X132))) = $true) | ~ ! [X133 : term] : ((((X129 @ (sub @ X132 @ (push @ X133 @ id)))) = $true) | ~ ($true = ((X129 @ X133))))) | ~ ! [X134 : term] : (~ (((var @ X134)) = $true) | (((X129 @ X134)) = $true)) | ($true = ((X129 @ X128)))) => (! [X135 : term,X136 : (subst > term > subst > $o),X137 : term] : (~ ! [X138 : term,X139 : subst,X140 : subst,X141 : subst] : (($true = ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140))) | ~ (((X136 @ X141 @ X138 @ (comp @ X139 @ X140))) = $true)) | ~ (((X136 @ id @ X137 @ id)) = $true) | (((X136 @ id @ (ap @ X135 @ X137) @ id)) = $true) | ~ ! [X142 : term,X143 : subst,X144 : subst,X145 : subst] : (~ (((X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143)) = $true) | (((X136 @ X144 @ X142 @ (comp @ X145 @ X143))) = $true)) | ~ ! [X146 : term,X147 : term] : ((((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id)) = $true) | ~ (((X136 @ id @ X146 @ id)) = $true) | ~ (((X136 @ id @ X147 @ id)) = $true)) | ~ (((X136 @ id @ X135 @ id)) = $true)) => (! [X148 : term,X149 : (subst > term > subst > $o)] : (($true = ((X149 @ id @ (lam @ X148) @ id))) | ~ ! [X150 : term] : (~ ($true = ((X149 @ id @ X150 @ id))) | (((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true)) | ~ ! [X151 : subst,X152 : term,X153 : subst,X154 : subst] : (~ (((X149 @ X154 @ X152 @ (comp @ X151 @ X153))) = $true) | ($true = ((X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153)))) | ~ ! [X155 : (subst > term > term)] : (~ ! [X156 : term] : (~ (((X149 @ id @ X156 @ id)) = $true) | ($true = ((X149 @ id @ (X155 @ id @ X156) @ id)))) | (((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ~ ! [X158 : subst,X157 : subst,X159 : term] : (((sub @ (X155 @ X157 @ X159) @ X158)) = ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158))))) | ~ ! [X160 : subst,X161 : subst,X162 : term,X163 : subst] : (~ (((X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161)) = $true) | (((X149 @ X163 @ X162 @ (comp @ X160 @ X161))) = $true))) => ! [X164 : (subst > term > subst > $o),X165 : term] : (~ ! [X166 : term] : ((((X164 @ id @ X166 @ id)) = $true) | ~ ($true = ((var @ (sub @ X166 @ id))))) | ~ ! [X167 : term,X168 : term] : (~ ($true = ((X164 @ id @ X168 @ id))) | ~ ($true = ((X164 @ id @ X167 @ id))) | ($true = ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id)))) | (((X164 @ id @ X165 @ id)) = $true) | ~ ! [X169 : term,X170 : subst,X171 : subst,X172 : subst] : (~ ($true = ((X164 @ X171 @ X169 @ (comp @ X170 @ X172)))) | (((X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) = $true)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X176 : subst,X175 : term,X174 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174))) | ~ ! [X177 : term] : (($true = ((X164 @ id @ (X173 @ id @ X177) @ id))) | ~ (((X164 @ id @ X177 @ id)) = $true)) | (((X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true)) | ~ ! [X178 : subst,X179 : subst,X180 : subst,X181 : term] : (~ (((X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180)) = $true) | ($true = ((X164 @ X178 @ X181 @ (comp @ X179 @ X180)))))))))) & (hoasinduction_lem1_gthm = $true) & ! [X182 : d_term] : (d_one = X182) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction = $true) <=> ! [X183 : (subst > term > subst > $o),X184 : term] : ((((X183 @ id @ X184 @ id)) = $true) | ~ ! [X185 : term] : (($true = ((X183 @ id @ X185 @ id))) | ~ ($true = ((var @ (sub @ X185 @ id))))) | ~ ! [X186 : term,X187 : subst,X188 : subst,X189 : subst] : (~ (((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) = $true) | (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) = $true)) | ~ ! [X190 : term,X191 : term] : (~ ($true = ((X183 @ id @ X191 @ id))) | (((X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) = $true) | ~ ($true = ((X183 @ id @ X190 @ id)))) | ~ ! [X192 : term,X193 : subst,X194 : subst,X195 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) = $true) | ~ (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) = $true)) | ~ ! [X196 : (subst > term > term)] : (~ ! [X197 : term] : ((((X183 @ id @ (X196 @ id @ X197) @ id)) = $true) | ~ (((X183 @ id @ X197 @ id)) = $true)) | ~ ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200)))) | ($true = ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id)))))) & (termmset_gthm = $true) & ((induction2lem = $true) <=> ! [X201 : (term > $o),X202 : subst,X203 : term] : (~ ! [X204 : term] : (~ (((var @ X204)) = $true) | (((X201 @ (sub @ X204 @ X202))) = $true)) | ~ ! [X205 : term] : ((((X201 @ (lam @ X205))) = $true) | ~ ! [X206 : term] : ((((X201 @ (sub @ X205 @ (push @ X206 @ id)))) = $true) | ~ ($true = ((X201 @ X206))))) | ~ ! [X207 : term,X208 : term] : ((((X201 @ (ap @ X208 @ X207))) = $true) | ~ (((X201 @ X208)) = $true) | ~ (((X201 @ X207)) = $true)) | (((X201 @ (sub @ X203 @ X202))) = $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X209 : term] : (((sub @ X209 @ id)) = X209) => (! [X210 : subst,X211 : (term > $o),X212 : term] : (~ ! [X213 : term] : (~ ! [X214 : term] : (($true = ((X211 @ (sub @ X213 @ (push @ X214 @ id))))) | ~ (((X211 @ X214)) = $true)) | (((X211 @ (lam @ X213))) = $true)) | ~ ! [X215 : term] : (($true = ((X211 @ (sub @ X215 @ X210)))) | ~ ($true = ((var @ X215)))) | ~ ! [X216 : term,X217 : term] : (($true = ((X211 @ (ap @ X216 @ X217)))) | ~ (((X211 @ X217)) = $true) | ~ (((X211 @ X216)) = $true)) | (((X211 @ (sub @ X212 @ X210))) = $true)) => ! [X218 : (term > $o),X219 : term] : (~ ! [X220 : term] : (($true = ((X218 @ X220))) | ~ (((var @ X220)) = $true)) | (((X218 @ X219)) = $true) | ~ ! [X221 : term] : (~ ! [X222 : term] : ((((X218 @ (sub @ X221 @ (push @ X222 @ id)))) = $true) | ~ ($true = ((X218 @ X222)))) | (((X218 @ (lam @ X221))) = $true)) | ~ ! [X223 : term,X224 : term] : ((((X218 @ (ap @ X223 @ X224))) = $true) | ~ ($true = ((X218 @ X223))) | ~ (((X218 @ X224)) = $true))))) <=> (induction2_lthm = $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)))))))))))))) & (ulamvarsh = $true) & (! [X230 : subst] : (((comp @ X230 @ id)) = X230) <=> (axidr = $true)) & ~ (ulamvar1 = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X231 : d_subst,X232 : d_subst] : ((((d2subst @ X231)) = ((d2subst @ X232))) => (X231 = X232)) & (hoaslamnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X233 : term,X234 : subst] : (((sub @ one @ (push @ X233 @ X234))) = X233) => ! [X235 : term,X236 : (term > $o),X237 : (term > $o),X238 : subst] : (~ ($true = ((X236 @ X235))) | ~ ! [X239 : term] : (((X237 @ X239)) = ((X236 @ (sub @ X239 @ (push @ X235 @ X238))))) | (((X237 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X240 : term,X241 : (subst > term > subst > $o)] : (~ ! [X242 : term] : (~ (((X241 @ id @ X242 @ id)) = $true) | ($true = ((X241 @ id @ (sub @ X240 @ (push @ X242 @ id)) @ id)))) | ($true = ((X241 @ id @ (lam @ X240) @ id))) | ~ ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (~ (((X241 @ X246 @ X245 @ (comp @ X243 @ X244))) = $true) | (((X241 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) = $true)) | ~ ! [X247 : (subst > term > term)] : (~ ! [X248 : term,X249 : subst,X250 : subst] : (((X247 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249))) = ((sub @ (X247 @ X250 @ X248) @ X249))) | ~ ! [X251 : term] : ((((X241 @ id @ (X247 @ id @ X251) @ id)) = $true) | ~ ($true = ((X241 @ id @ X251 @ id)))) | (((X241 @ id @ (lam @ (X247 @ sh @ one)) @ id)) = $true)) | ~ ! [X252 : subst,X253 : term,X254 : subst,X255 : subst] : (~ (((X241 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254) @ X252)) = $true) | (((X241 @ X255 @ X253 @ (comp @ X254 @ X252))) = $true)))) & (hoasinduction_lem1v2 = $true) & (axabs = $true) & (pushprop_lem3v2_lthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X256 : term,X257 : subst] : (((sub @ one @ (push @ X256 @ X257))) = X256) => (! [X258 : term,X259 : subst] : (((comp @ sh @ (push @ X258 @ X259))) = X259) => (! [X260 : term,X261 : term] : ((((lam @ X260)) != ((lam @ X261))) | (X260 = X261)) => ! [X262 : subst,X263 : (subst > term > term),X264 : term,X265 : (subst > term > term)] : (~ ! [X266 : subst,X267 : subst,X268 : term] : (((X263 @ (comp @ X266 @ X267) @ (sub @ X268 @ X267))) = ((sub @ (X263 @ X266 @ X268) @ X267))) | ~ ! [X269 : subst,X270 : term,X271 : subst] : (((X265 @ (comp @ X271 @ X269) @ (sub @ X270 @ X269))) = ((sub @ (X265 @ X271 @ X270) @ X269))) | (((lam @ (X263 @ sh @ one))) != ((lam @ (X265 @ sh @ one)))) | (((X265 @ X262 @ X264)) = ((X263 @ X262 @ X264)))))))) & (apnotvar = $true) & (! [X272 : (subst > term > subst > $o),X273 : term] : (~ ! [X274 : term] : (~ (((X272 @ id @ X274 @ id)) = $true) | (((X272 @ id @ (sub @ X273 @ (push @ X274 @ id)) @ id)) = $true)) | ~ ! [X275 : (subst > term > term)] : (~ ! [X276 : term] : (~ (((X272 @ id @ X276 @ id)) = $true) | (((X272 @ id @ (X275 @ id @ X276) @ id)) = $true)) | ~ ! [X277 : term,X278 : subst,X279 : subst] : (((sub @ (X275 @ X279 @ X277) @ X278)) = ((X275 @ (comp @ X279 @ X278) @ (sub @ X277 @ X278)))) | (((X272 @ id @ (lam @ (X275 @ sh @ one)) @ id)) = $true)) | (((X272 @ id @ (lam @ (sub @ X273 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (induction2_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((hoasinduction_lem2 = $true) <=> ! [X280 : (subst > term > subst > $o),X281 : term,X282 : term] : (~ (((X280 @ id @ X282 @ id)) = $true) | ~ ! [X283 : subst,X284 : term,X285 : subst,X286 : subst] : (~ ($true = ((X280 @ (comp @ X283 @ X285) @ (sub @ X284 @ X285) @ X286))) | (((X280 @ X283 @ X284 @ (comp @ X285 @ X286))) = $true)) | ~ ! [X287 : term,X288 : term] : (~ ($true = ((X280 @ id @ X287 @ id))) | ~ (((X280 @ id @ X288 @ id)) = $true) | (((X280 @ id @ (ap @ (sub @ X288 @ id) @ X287) @ id)) = $true)) | ($true = ((X280 @ id @ (ap @ X282 @ X281) @ id))) | ~ ! [X289 : term,X290 : subst,X291 : subst,X292 : subst] : (($true = ((X280 @ (comp @ X292 @ X290) @ (sub @ X289 @ X290) @ X291))) | ~ (((X280 @ X292 @ X289 @ (comp @ X290 @ X291))) = $true)) | ~ (((X280 @ id @ X281 @ id)) = $true))) & (pushprop = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1_lthm = $true) & ! [X293 : d_term,X294 : d_term] : ((((d2term @ X294)) = ((d2term @ X293))) => (X293 = X294)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X295 : term] : (((sub @ X295 @ id)) = X295) => (! [X296 : (subst > term > subst > $o),X297 : term] : (~ ! [X298 : (subst > term > term)] : (~ ! [X299 : subst,X300 : subst,X301 : term] : (((sub @ (X298 @ X300 @ X301) @ X299)) = ((X298 @ (comp @ X300 @ X299) @ (sub @ X301 @ X299)))) | ~ ! [X302 : term] : (($true = ((X296 @ id @ (X298 @ id @ X302) @ id))) | ~ (((X296 @ id @ X302 @ id)) = $true)) | (((X296 @ id @ (lam @ (X298 @ sh @ one)) @ id)) = $true)) | ($true = ((X296 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id))) | ~ ! [X303 : term] : (~ (((X296 @ id @ X303 @ id)) = $true) | (((X296 @ id @ (sub @ X297 @ (push @ X303 @ id)) @ id)) = $true))) => ! [X304 : term,X305 : (subst > term > subst > $o)] : (~ ! [X306 : term] : (~ ($true = ((X305 @ id @ X306 @ id))) | (((X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id)) = $true)) | ~ ! [X307 : (subst > term > term)] : (~ ! [X308 : subst,X309 : term,X310 : subst] : (((sub @ (X307 @ X308 @ X309) @ X310)) = ((X307 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310)))) | (((X305 @ id @ (lam @ (X307 @ sh @ one)) @ id)) = $true) | ~ ! [X311 : term] : (~ (((X305 @ id @ X311 @ id)) = $true) | (((X305 @ id @ (X307 @ id @ X311) @ id)) = $true))) | (((X305 @ id @ (lam @ X304) @ id)) = $true))))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasapnotvar_lthm = $true) & ((axscons = $true) <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & (! [X313 : subst,X314 : (subst > term > term),X315 : (subst > term > term),X316 : term] : ((((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ~ ! [X317 : term,X318 : subst,X319 : subst] : (((X314 @ (comp @ X318 @ X319) @ (sub @ X317 @ X319))) = ((sub @ (X314 @ X318 @ X317) @ X319))) | (((X314 @ X313 @ X316)) = ((X315 @ X313 @ X316))) | ~ ! [X320 : term,X321 : subst,X322 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X315 @ X322 @ X320) @ X321)))) <=> (hoaslaminj = $true)) & ((axidl = $true) <=> ! [X323 : subst] : (((comp @ id @ X323)) = X323)) & ! [X324 : subst] : ? [X325 : d_subst] : (((d2subst @ X325)) = X324) & ((hoasapinj1_lthm = $true) <=> (! [X326 : term] : (((sub @ X326 @ id)) = X326) => (! [X327 : term,X328 : term,X329 : term,X330 : term] : ((X328 = X329) | (((ap @ X328 @ X327)) != ((ap @ X329 @ X330)))) => ! [X331 : term,X332 : term,X333 : term,X334 : term] : ((X333 = X334) | (((ap @ (sub @ X334 @ id) @ X331)) != ((ap @ (sub @ X333 @ id) @ X332))))))) & (! [X335 : term,X336 : (term > $o),X337 : (subst > term > subst > $o)] : (~ ! [X338 : term] : (((X337 @ id @ X338 @ id)) = ((X336 @ X338))) | (((X336 @ (lam @ X335))) = $true) | ~ ! [X339 : term] : (($true = ((X336 @ (sub @ X335 @ (push @ X339 @ id))))) | ~ (((X336 @ X339)) = $true)) | ~ ! [X340 : (subst > term > term)] : (~ ! [X341 : term,X342 : subst,X343 : subst] : (((X340 @ (comp @ X342 @ X343) @ (sub @ X341 @ X343))) = ((sub @ (X340 @ X342 @ X341) @ X343))) | ($true = ((X337 @ id @ (lam @ (X340 @ sh @ one)) @ id))) | ~ ! [X344 : term] : ((((X337 @ id @ (X340 @ id @ X344) @ id)) = $true) | ~ (((X337 @ id @ X344 @ id)) = $true)))) <=> (hoasinduction_lem3v2a = $true)) & (! [X345 : term,X346 : term,X347 : (term > $o),X348 : (subst > term > subst > $o)] : (~ ! [X349 : term] : (((X348 @ id @ X349 @ id)) = ((X347 @ X349))) | ~ ! [X350 : term,X351 : term] : (($true = ((X348 @ id @ (ap @ (sub @ X351 @ id) @ X350) @ id))) | ~ ($true = ((X348 @ id @ X350 @ id))) | ~ ($true = ((X348 @ id @ X351 @ id)))) | ~ ! [X352 : subst,X353 : subst,X354 : subst,X355 : term] : ((((X348 @ X353 @ X355 @ (comp @ X352 @ X354))) = $true) | ~ ($true = ((X348 @ (comp @ X353 @ X352) @ (sub @ X355 @ X352) @ X354)))) | ~ ! [X356 : term,X357 : subst,X358 : subst,X359 : subst] : ((((X348 @ (comp @ X359 @ X357) @ (sub @ X356 @ X357) @ X358)) = $true) | ~ (((X348 @ X359 @ X356 @ (comp @ X357 @ X358))) = $true)) | ~ ($true = ((X347 @ X345))) | (((X347 @ (ap @ X345 @ X346))) = $true) | ~ (((X347 @ X346)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ! [X363 : d_subst] : (d_id = X363) & ((hoasinduction_lem3v2 = $true) <=> ! [X364 : (subst > term > subst > $o),X365 : term,X366 : (term > $o)] : (~ ! [X367 : (subst > term > term)] : (~ ! [X368 : term] : (~ ($true = ((X364 @ id @ X368 @ id))) | ($true = ((X364 @ id @ (X367 @ id @ X368) @ id)))) | ~ ! [X369 : subst,X370 : subst,X371 : term] : (((X367 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370))) = ((sub @ (X367 @ X369 @ X371) @ X370))) | ($true = ((X364 @ id @ (lam @ (X367 @ sh @ one)) @ id)))) | ~ ! [X372 : subst,X373 : term,X374 : subst,X375 : subst] : (~ (((X364 @ (comp @ X372 @ X374) @ (sub @ X373 @ X374) @ X375)) = $true) | (((X364 @ X372 @ X373 @ (comp @ X374 @ X375))) = $true)) | ~ ! [X376 : term,X377 : subst,X378 : subst,X379 : subst] : ((((X364 @ (comp @ X378 @ X377) @ (sub @ X376 @ X377) @ X379)) = $true) | ~ (((X364 @ X378 @ X376 @ (comp @ X377 @ X379))) = $true)) | (((X366 @ (lam @ X365))) = $true) | ~ ! [X380 : term] : (~ ($true = ((X366 @ X380))) | ($true = ((X366 @ (sub @ X365 @ (push @ X380 @ id)))))) | ~ ! [X381 : term] : (((X366 @ X381)) = ((X364 @ id @ X381 @ id))))) & (! [X382 : (term > $o),X383 : subst,X384 : term] : ~ ! [X385 : (term > $o)] : ~ ! [X386 : term] : (((X385 @ X386)) = ((X382 @ (sub @ X386 @ (push @ X384 @ X383))))) <=> (pushprop_lem0_lthm = $true)) & ((induction2lem_lthm = $true) <=> (! [X387 : subst,X388 : term] : (((sub @ one @ (push @ X388 @ X387))) = X388) => (! [X389 : term,X390 : subst] : (((comp @ sh @ (push @ X389 @ X390))) = X390) => (! [X391 : subst] : (((comp @ X391 @ id)) = X391) => (! [X392 : term,X393 : (term > $o)] : (~ ! [X394 : term] : (~ (((var @ X394)) = $true) | ($true = ((X393 @ X394)))) | ($true = ((X393 @ X392))) | ~ ! [X395 : term,X396 : term] : (~ (((X393 @ X395)) = $true) | ~ ($true = ((X393 @ X396))) | ($true = ((X393 @ (ap @ X395 @ X396))))) | ~ ! [X397 : term] : (~ ($true = ((X393 @ X397))) | (((X393 @ (lam @ X397))) = $true))) => ! [X398 : subst,X399 : (term > $o),X400 : term] : (~ ! [X401 : term] : (~ (((var @ X401)) = $true) | (((X399 @ (sub @ X401 @ X398))) = $true)) | (((X399 @ (sub @ X400 @ X398))) = $true) | ~ ! [X402 : term] : ((((X399 @ (lam @ X402))) = $true) | ~ ! [X403 : term] : ((((X399 @ (sub @ X402 @ (push @ X403 @ id)))) = $true) | ~ (((X399 @ X403)) = $true))) | ~ ! [X404 : term,X405 : term] : ((((X399 @ (ap @ X404 @ X405))) = $true) | ~ (((X399 @ X405)) = $true) | ~ (((X399 @ X404)) = $true)))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & ((hoasapinj2_lthm = $true) <=> (! [X408 : term,X409 : term,X410 : term,X411 : term] : ((X408 = X411) | (((ap @ X410 @ X411)) != ((ap @ X409 @ X408)))) => ! [X412 : term,X413 : term,X414 : term,X415 : term] : ((X414 = X415) | (((ap @ (sub @ X413 @ id) @ X415)) != ((ap @ (sub @ X412 @ id) @ X414)))))) & (lamnotvar = $true) & (induction2lem_gthm = $true) & (! [X416 : (term > $o),X417 : term,X418 : term,X419 : (term > $o),X420 : subst] : ((((X416 @ (sub @ X417 @ (push @ X418 @ X420)))) = $true) | ~ ($true = ((X419 @ X417)))) <=> (pushprop_lem1 = $true)) & (! [X421 : (subst > term > term),X422 : term,X423 : term] : ((((ap @ (sub @ X423 @ id) @ X422)) != ((lam @ (X421 @ sh @ one)))) | ~ ! [X424 : subst,X425 : subst,X426 : term] : (((sub @ (X421 @ X425 @ X426) @ X424)) = ((X421 @ (comp @ X425 @ X424) @ (sub @ X426 @ X424))))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X427 : term] : ~ ! [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) != ((X428 @ sh @ one)))) & (hoaslamnotap_lthm = $true) & ((! [X429 : term] : (((sub @ X429 @ id)) = X429) => ! [X430 : (subst > term > subst > $o),X431 : (term > $o),X432 : term] : (~ ! [X433 : term,X434 : subst,X435 : subst,X436 : subst] : ((((X430 @ (comp @ X435 @ X436) @ (sub @ X433 @ X436) @ X434)) = $true) | ~ ($true = ((X430 @ X435 @ X433 @ (comp @ X436 @ X434))))) | (((X431 @ (lam @ X432))) = $true) | ~ ! [X437 : term] : (~ (((X431 @ X437)) = $true) | ($true = ((X431 @ (sub @ X432 @ (push @ X437 @ id)))))) | ~ ! [X438 : term] : (((X431 @ X438)) = ((X430 @ id @ X438 @ id))) | ~ ! [X439 : subst,X440 : subst,X441 : term,X442 : subst] : ((((X430 @ X439 @ X441 @ (comp @ X440 @ X442))) = $true) | ~ ($true = ((X430 @ (comp @ X439 @ X440) @ (sub @ X441 @ X440) @ X442)))) | ~ ! [X443 : (subst > term > term)] : ((((X430 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true) | ~ ! [X444 : term] : (($true = ((X430 @ id @ (X443 @ id @ X444) @ id))) | ~ ($true = ((X430 @ id @ X444 @ id)))) | ~ ! [X445 : term,X446 : subst,X447 : subst] : (((X443 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X443 @ X447 @ X445) @ X446)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X448 : (subst > term > subst > $o),X449 : term] : (~ ! [X450 : term,X451 : (subst > term > term)] : (~ ! [X452 : subst,X453 : subst,X454 : term] : (((sub @ X450 @ (push @ (sub @ X454 @ X453) @ (comp @ X452 @ X453)))) = ((X451 @ (comp @ X452 @ X453) @ (sub @ X454 @ X453)))) | ~ ! [X455 : term,X456 : subst,X457 : subst] : (((sub @ (sub @ X450 @ (push @ X455 @ X456)) @ X457)) = ((sub @ (X451 @ X456 @ X455) @ X457))) | (((X448 @ id @ (lam @ (X451 @ sh @ one)) @ id)) = $true) | ~ ! [X458 : term] : (~ ($true = ((X448 @ id @ X458 @ id))) | (((X448 @ id @ (X451 @ id @ X458) @ id)) = $true))) | (((X448 @ id @ (lam @ (sub @ X449 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X459 : term] : (($true = ((X448 @ id @ (sub @ X449 @ (push @ X459 @ id)) @ id))) | ~ (((X448 @ id @ X459 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X460 : (subst > term > subst > $o),X461 : term] : (~ ! [X462 : term] : (~ (((X460 @ id @ X462 @ id)) = $true) | (((X460 @ id @ (sub @ X461 @ (push @ X462 @ id)) @ id)) = $true)) | (((X460 @ id @ (lam @ (sub @ X461 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X463 : (subst > term > term)] : (~ ! [X464 : term] : (~ (((X460 @ id @ X464 @ id)) = $true) | (((X460 @ id @ (X463 @ id @ X464) @ id)) = $true)) | ($true = ((X460 @ id @ (lam @ (X463 @ sh @ one)) @ id))) | ~ ! [X465 : subst,X466 : subst,X467 : term] : (((X463 @ (comp @ X465 @ X466) @ (sub @ X467 @ X466))) = ((sub @ (X463 @ X465 @ X467) @ X466)))))) & ((apinj2 = $true) <=> ! [X468 : term,X469 : term,X470 : term,X471 : term] : ((((ap @ X468 @ X469)) != ((ap @ X471 @ X470))) | (X469 = X470))) & ((termmset = $true) <=> ! [X472 : term] : (((sub @ X472 @ id)) = X472)) & (hoaslaminj_gthm = $true) & ((substmonoid = $true) <=> (! [X473 : subst] : (((comp @ id @ X473)) = X473) & ! [X474 : subst] : (((comp @ X474 @ id)) = X474))) & (hoasinduction_lem2v2_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & (hoaslamnotap_gthm = $true) & (axvarshift = $true) & (substmonoid_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X475 : term,X476 : subst,X477 : (term > $o)] : ~ ! [X478 : (term > $o)] : ~ ! [X479 : term] : (((X477 @ (sub @ X479 @ (push @ X475 @ X476)))) = ((X478 @ X479)))) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X480 : (subst > term > subst > $o)] : ~ ! [X481 : (term > $o)] : ~ ! [X482 : term] : (((X480 @ id @ X482 @ id)) = ((X481 @ X482))) => (! [X483 : (term > $o),X484 : term] : (($true = ((X483 @ X484))) | ~ ! [X485 : term,X486 : term] : (($true = ((X483 @ (ap @ X485 @ X486)))) | ~ ($true = ((X483 @ X486))) | ~ ($true = ((X483 @ X485)))) | ~ ! [X487 : term] : ((((X483 @ X487)) = $true) | ~ (((var @ X487)) = $true)) | ~ ! [X488 : term] : (~ ! [X489 : term] : (($true = ((X483 @ (sub @ X488 @ (push @ X489 @ id))))) | ~ (((X483 @ X489)) = $true)) | (((X483 @ (lam @ X488))) = $true))) => (! [X490 : term] : (((sub @ X490 @ id)) = X490) => (! [X491 : (subst > term > subst > $o),X492 : term,X493 : (term > $o)] : (~ ! [X494 : (subst > term > term)] : (~ ! [X495 : term,X496 : subst,X497 : subst] : (((sub @ (X494 @ X496 @ X495) @ X497)) = ((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497)))) | ~ ! [X498 : term] : ((((X491 @ id @ (X494 @ id @ X498) @ id)) = $true) | ~ (((X491 @ id @ X498 @ id)) = $true)) | (((X491 @ id @ (lam @ (X494 @ sh @ one)) @ id)) = $true)) | (((X493 @ (lam @ X492))) = $true) | ~ ! [X499 : term] : (~ ($true = ((X493 @ X499))) | (((X493 @ (sub @ X492 @ (push @ X499 @ id)))) = $true)) | ~ ! [X500 : term] : (((X493 @ X500)) = ((X491 @ id @ X500 @ id)))) => ! [X501 : term,X502 : (subst > term > subst > $o)] : (~ ! [X503 : subst,X504 : term,X505 : subst,X506 : subst] : ((((X502 @ (comp @ X503 @ X505) @ (sub @ X504 @ X505) @ X506)) = $true) | ~ (((X502 @ X503 @ X504 @ (comp @ X505 @ X506))) = $true)) | ~ ! [X507 : term,X508 : subst,X509 : subst,X510 : subst] : (~ (((X502 @ (comp @ X509 @ X510) @ (sub @ X507 @ X510) @ X508)) = $true) | (((X502 @ X509 @ X507 @ (comp @ X510 @ X508))) = $true)) | ~ ! [X511 : term,X512 : term] : (~ ($true = ((X502 @ id @ X512 @ id))) | (((X502 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) = $true) | ~ ($true = ((X502 @ id @ X511 @ id)))) | ~ ! [X513 : term] : (~ (((var @ (sub @ X513 @ id))) = $true) | ($true = ((X502 @ id @ X513 @ id)))) | (((X502 @ id @ X501 @ id)) = $true) | ~ ! [X514 : (subst > term > term)] : (($true = ((X502 @ id @ (lam @ (X514 @ sh @ one)) @ id))) | ~ ! [X515 : term] : ((((X502 @ id @ (X514 @ id @ X515) @ id)) = $true) | ~ (((X502 @ id @ X515 @ id)) = $true)) | ~ ! [X516 : subst,X517 : subst,X518 : term] : (((X514 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516))) = ((sub @ (X514 @ X517 @ X518) @ X516)))))))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X519 : term,X520 : (subst > term > subst > $o)] : (~ ! [X521 : term,X522 : term] : (~ (((X520 @ id @ X522 @ id)) = $true) | ($true = ((X520 @ id @ (ap @ (sub @ X521 @ id) @ X522) @ id))) | ~ (((X520 @ id @ X521 @ id)) = $true)) | ($true = ((X520 @ id @ X519 @ id))) | ~ ! [X523 : (subst > term > term)] : (($true = ((X520 @ id @ (lam @ (X523 @ sh @ one)) @ id))) | ~ ! [X524 : term] : (~ (((X520 @ id @ X524 @ id)) = $true) | (((X520 @ id @ (X523 @ id @ X524) @ id)) = $true)) | ~ ! [X525 : term,X526 : subst,X527 : subst] : (((X523 @ (comp @ X527 @ X526) @ (sub @ X525 @ X526))) = ((sub @ (X523 @ X527 @ X525) @ X526)))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem0 = $true) <=> ! [X528 : (subst > term > subst > $o)] : ~ ! [X529 : (term > $o)] : ~ ! [X530 : term] : (((X528 @ id @ X530 @ id)) = ((X529 @ X530)))) & (((d2subst @ d_id)) = id) & ((pushprop_lem1_lthm = $true) <=> (! [X531 : term,X532 : subst] : (((sub @ one @ (push @ X531 @ X532))) = X531) => (! [X533 : term,X534 : subst] : (((comp @ sh @ (push @ X533 @ X534))) = X534) => ! [X535 : subst,X536 : term,X537 : term,X538 : (term > $o),X539 : (term > $o)] : ((((X538 @ (sub @ X536 @ (push @ X537 @ X535)))) = $true) | ~ (((X539 @ X536)) = $true))))) & ! [X540 : term] : ? [X541 : d_term] : (((d2term @ X541)) = X540) & (! [X542 : term] : ~ ! [X543 : (subst > term > term)] : ~ ! [X544 : subst,X545 : term] : (((sub @ X542 @ (push @ X545 @ X544))) = ((X543 @ X544 @ X545))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X546 : term] : ~ ! [X547 : (subst > term > term)] : ~ ! [X548 : subst,X549 : term] : (((X547 @ X548 @ X549)) = ((sub @ X546 @ (push @ X549 @ X548)))))), 50.81/8.71 inference(fool_elimination,[],[f6])). 50.81/8.71 thf(f8,plain,( 50.81/8.71 ~((hoasinduction = $true) <=> ! [X0 : (subst > term > subst > $o)] : (! [X4 : subst,X1 : subst,X3 : term,X2 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) => (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) = $true)) => (! [X6 : subst,X8 : term,X7 : subst,X5 : subst] : (($true = ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6))) => (((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) = $true)) => (! [X9 : term] : ((((hoasvar @ id @ X9 @ id)) = $true) => ($true = ((X0 @ id @ X9 @ id)))) => (! [X11 : term,X10 : term] : (($true = ((X0 @ id @ X11 @ id))) => ((((X0 @ id @ X10 @ id)) = $true) => (((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)) = $true))) => (! [X12 : (subst > term > term)] : (! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))) => (! [X16 : term] : ((((X0 @ id @ X16 @ id)) = $true) => (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) = $true))) => ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true)))))))), 50.81/8.71 inference(rectify,[],[f5])). 50.81/8.71 thf(f9,plain,( 50.81/8.71 ((substmonoid_lthm = $true) <=> (! [X0 : subst] : (((comp @ id @ X0)) = X0) => (! [X1 : subst] : (((comp @ X1 @ id)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2 = $true) & ((axvarcons = $true) <=> ! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4)) & (pushprop_lem1_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7))))) & (hoasinduction_lem2_gthm = $true) & (! [X10 : (subst > term > subst > $o),X11 : term] : (~ ! [X12 : (subst > term > term)] : (~ ! [X13 : term] : ((((X10 @ id @ (X12 @ id @ X13) @ id)) = $true) | ~ (((X10 @ id @ X13 @ id)) = $true)) | ~ ! [X16 : subst,X14 : term,X15 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15)))) | (((X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) = $true)) | (((X10 @ id @ (lam @ X11) @ id)) = $true) | ~ ! [X17 : term] : ((((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) = $true) | ~ ($true = ((X10 @ id @ X17 @ id))))) <=> (hoasinduction_lem3a = $true)) & (! [X18 : term,X19 : (term > $o)] : (~ ! [X20 : term] : ((((X19 @ X20)) = $true) | ~ ($true = ((var @ X20)))) | ~ ! [X21 : term] : ((((X19 @ (lam @ X21))) = $true) | ~ ! [X22 : term] : ((((X19 @ (sub @ X21 @ (push @ X22 @ id)))) = $true) | ~ (((X19 @ X22)) = $true))) | ~ ! [X23 : term,X24 : term] : (~ ($true = ((X19 @ X23))) | ~ (((X19 @ X24)) = $true) | (((X19 @ (ap @ X24 @ X23))) = $true)) | (((X19 @ X18)) = $true)) <=> (induction2 = $true)) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((shinj = $true) <=> ! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26))) & (! [X27 : term,X28 : subst,X29 : (term > $o),X30 : (term > $o)] : (~ ($true = ((X30 @ X27))) | ~ ! [X31 : term] : (((X29 @ X31)) = ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))) | ($true = ((X29 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X32 : term] : ~ ! [X33 : (subst > term > term)] : ~ ! [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) = ((X33 @ X35 @ X34))) => (! [X36 : term] : (((sub @ X36 @ id)) = X36) => ! [X37 : (subst > term > subst > $o),X38 : term,X39 : (term > $o)] : (~ ! [X40 : term] : (~ ($true = ((X39 @ X40))) | (((X39 @ (sub @ X38 @ (push @ X40 @ id)))) = $true)) | ~ ! [X41 : term] : (((X37 @ id @ X41 @ id)) = ((X39 @ X41))) | ~ ! [X42 : (subst > term > term)] : (~ ! [X43 : term] : (~ (((X37 @ id @ X43 @ id)) = $true) | ($true = ((X37 @ id @ (X42 @ id @ X43) @ id)))) | ~ ! [X44 : term,X46 : subst,X45 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45))) | (((X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) = $true)) | (((X39 @ (lam @ X38))) = $true))))) & ((hoasapinj2 = $true) <=> ! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & (pushprop_lthm = $true) & (hoasapinj1_gthm = $true) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) <=> (laminj = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X53 : term] : ~ ! [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) != ((X54 @ sh @ one)))) & (((d2term @ d_one)) = one) & (axapp = $true) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> (apinj1 = $true)) & ~ (lamnotap = $true) & (hoasapnotvar_gthm = $true) & ((axvarid = $true) <=> ! [X61 : term] : (((sub @ X61 @ id)) = X61)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X62 : (subst > term > subst > $o)] : ~ ! [X63 : (term > $o)] : ~ ! [X64 : term] : (((X63 @ X64)) = ((X62 @ id @ X64 @ id))) => (! [X65 : term,X66 : (term > $o)] : (~ ! [X67 : term] : (~ ! [X68 : term] : ((((X66 @ (sub @ X67 @ (push @ X68 @ id)))) = $true) | ~ (((X66 @ X68)) = $true)) | ($true = ((X66 @ (lam @ X67))))) | (((X66 @ X65)) = $true) | ~ ! [X69 : term,X70 : term] : (~ ($true = ((X66 @ X69))) | (((X66 @ (ap @ X69 @ X70))) = $true) | ~ (((X66 @ X70)) = $true)) | ~ ! [X71 : term] : (~ (((var @ X71)) = $true) | ($true = ((X66 @ X71))))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => (! [X73 : (term > $o),X74 : term,X75 : (subst > term > subst > $o)] : (~ ! [X76 : (subst > term > term)] : ((((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ~ ! [X77 : term] : (~ (((X75 @ id @ X77 @ id)) = $true) | (((X75 @ id @ (X76 @ id @ X77) @ id)) = $true)) | ~ ! [X80 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) = ((sub @ (X76 @ X78 @ X79) @ X80)))) | ~ ! [X81 : term] : (~ (((X73 @ X81)) = $true) | ($true = ((X73 @ (sub @ X74 @ (push @ X81 @ id)))))) | ~ ! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) | (((X73 @ (lam @ X74))) = $true)) => ! [X83 : (subst > term > subst > $o),X84 : term] : (~ ! [X85 : (subst > term > term)] : (~ ! [X86 : term] : (~ (((X83 @ id @ X86 @ id)) = $true) | (((X83 @ id @ (X85 @ id @ X86) @ id)) = $true)) | ~ ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88)))) | (((X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) = $true)) | ~ ! [X90 : term,X91 : term] : (~ (((X83 @ id @ X90 @ id)) = $true) | ~ (((X83 @ id @ X91 @ id)) = $true) | ($true = ((X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id)))) | ($true = ((X83 @ id @ X84 @ id))))))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X92 : term] : (((sub @ X92 @ id)) = X92) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X95 : term] : (~ (((X94 @ id @ X95 @ id)) = $true) | ($true = ((X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id)))) | ~ ! [X96 : (subst > term > term)] : ((((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true) | ~ ! [X97 : term,X99 : subst,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X96 @ X99 @ X97) @ X98))) | ~ ! [X100 : term] : (~ ($true = ((X94 @ id @ X100 @ id))) | (((X94 @ id @ (X96 @ id @ X100) @ id)) = $true))) | (((X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true)) => ! [X101 : (subst > term > subst > $o),X102 : term] : (~ ! [X103 : term] : ((((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id)) = $true) | ~ ($true = ((X101 @ id @ X103 @ id)))) | ~ ! [X104 : subst,X105 : term,X106 : subst,X107 : subst] : (($true = ((X101 @ X107 @ X105 @ (comp @ X106 @ X104)))) | ~ (((X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) = $true)) | (((X101 @ id @ (lam @ X102) @ id)) = $true) | ~ ! [X108 : (subst > term > term)] : (~ ! [X109 : term] : (~ (((X101 @ id @ X109 @ id)) = $true) | (((X101 @ id @ (X108 @ id @ X109) @ id)) = $true)) | (((X101 @ id @ (lam @ (X108 @ sh @ one)) @ id)) = $true) | ~ ! [X111 : term,X110 : subst,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112))))) | ~ ! [X113 : subst,X114 : term,X115 : subst,X116 : subst] : (~ (((X101 @ X113 @ X114 @ (comp @ X116 @ X115))) = $true) | ($true = ((X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115)))))))) & ((termmset_lthm = $true) <=> (! [X117 : term] : (((sub @ X117 @ id)) = X117) => ! [X118 : term] : (((sub @ X118 @ id)) = X118))) & ((induction = $true) <=> ! [X119 : term,X120 : (term > $o)] : (~ ! [X121 : term] : ((((X120 @ (lam @ X121))) = $true) | ~ ($true = ((X120 @ X121)))) | (((X120 @ X119)) = $true) | ~ ! [X122 : term,X123 : term] : (($true = ((X120 @ (ap @ X122 @ X123)))) | ~ (((X120 @ X123)) = $true) | ~ (((X120 @ X122)) = $true)) | ~ ! [X124 : term] : (~ (((var @ X124)) = $true) | (((X120 @ X124)) = $true)))) & (((d2subst @ d_id)) = sh) & (! [X125 : (subst > term > subst > $o)] : ~ ! [X126 : (term > $o)] : ~ ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (ulamvarind = $true) & ((hoasinduction_lthm = $true) <=> (! [X128 : term,X129 : (term > $o)] : (~ ! [X130 : term,X131 : term] : (~ ($true = ((X129 @ X130))) | ~ (((X129 @ X131)) = $true) | (((X129 @ (ap @ X131 @ X130))) = $true)) | ~ ! [X132 : term] : ((((X129 @ (lam @ X132))) = $true) | ~ ! [X133 : term] : ((((X129 @ (sub @ X132 @ (push @ X133 @ id)))) = $true) | ~ ($true = ((X129 @ X133))))) | ~ ! [X134 : term] : (~ (((var @ X134)) = $true) | (((X129 @ X134)) = $true)) | ($true = ((X129 @ X128)))) => (! [X135 : term,X136 : (subst > term > subst > $o),X137 : term] : (~ ! [X138 : term,X139 : subst,X140 : subst,X141 : subst] : (($true = ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140))) | ~ (((X136 @ X141 @ X138 @ (comp @ X139 @ X140))) = $true)) | ~ (((X136 @ id @ X137 @ id)) = $true) | (((X136 @ id @ (ap @ X135 @ X137) @ id)) = $true) | ~ ! [X142 : term,X143 : subst,X144 : subst,X145 : subst] : (~ (((X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143)) = $true) | (((X136 @ X144 @ X142 @ (comp @ X145 @ X143))) = $true)) | ~ ! [X146 : term,X147 : term] : ((((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id)) = $true) | ~ (((X136 @ id @ X146 @ id)) = $true) | ~ (((X136 @ id @ X147 @ id)) = $true)) | ~ (((X136 @ id @ X135 @ id)) = $true)) => (! [X148 : term,X149 : (subst > term > subst > $o)] : (($true = ((X149 @ id @ (lam @ X148) @ id))) | ~ ! [X150 : term] : (~ ($true = ((X149 @ id @ X150 @ id))) | (((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true)) | ~ ! [X151 : subst,X152 : term,X153 : subst,X154 : subst] : (~ (((X149 @ X154 @ X152 @ (comp @ X151 @ X153))) = $true) | ($true = ((X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153)))) | ~ ! [X155 : (subst > term > term)] : (~ ! [X156 : term] : (~ (((X149 @ id @ X156 @ id)) = $true) | ($true = ((X149 @ id @ (X155 @ id @ X156) @ id)))) | (((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ~ ! [X158 : subst,X157 : subst,X159 : term] : (((sub @ (X155 @ X157 @ X159) @ X158)) = ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158))))) | ~ ! [X160 : subst,X161 : subst,X162 : term,X163 : subst] : (~ (((X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161)) = $true) | (((X149 @ X163 @ X162 @ (comp @ X160 @ X161))) = $true))) => ! [X164 : (subst > term > subst > $o),X165 : term] : (~ ! [X166 : term] : ((((X164 @ id @ X166 @ id)) = $true) | ~ ($true = ((var @ (sub @ X166 @ id))))) | ~ ! [X167 : term,X168 : term] : (~ ($true = ((X164 @ id @ X168 @ id))) | ~ ($true = ((X164 @ id @ X167 @ id))) | ($true = ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id)))) | (((X164 @ id @ X165 @ id)) = $true) | ~ ! [X169 : term,X170 : subst,X171 : subst,X172 : subst] : (~ ($true = ((X164 @ X171 @ X169 @ (comp @ X170 @ X172)))) | (((X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) = $true)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X176 : subst,X175 : term,X174 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174))) | ~ ! [X177 : term] : (($true = ((X164 @ id @ (X173 @ id @ X177) @ id))) | ~ (((X164 @ id @ X177 @ id)) = $true)) | (((X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true)) | ~ ! [X178 : subst,X179 : subst,X180 : subst,X181 : term] : (~ (((X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180)) = $true) | ($true = ((X164 @ X178 @ X181 @ (comp @ X179 @ X180)))))))))) & (hoasinduction_lem1_gthm = $true) & ! [X182 : d_term] : (d_one = X182) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction = $true) <=> ! [X183 : (subst > term > subst > $o),X184 : term] : ((((X183 @ id @ X184 @ id)) = $true) | ~ ! [X185 : term] : (($true = ((X183 @ id @ X185 @ id))) | ~ ($true = ((var @ (sub @ X185 @ id))))) | ~ ! [X186 : term,X187 : subst,X188 : subst,X189 : subst] : (~ (((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) = $true) | (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) = $true)) | ~ ! [X190 : term,X191 : term] : (~ ($true = ((X183 @ id @ X191 @ id))) | (((X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) = $true) | ~ ($true = ((X183 @ id @ X190 @ id)))) | ~ ! [X192 : term,X193 : subst,X194 : subst,X195 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) = $true) | ~ (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) = $true)) | ~ ! [X196 : (subst > term > term)] : (~ ! [X197 : term] : ((((X183 @ id @ (X196 @ id @ X197) @ id)) = $true) | ~ (((X183 @ id @ X197 @ id)) = $true)) | ~ ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200)))) | ($true = ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id)))))) & (termmset_gthm = $true) & ((induction2lem = $true) <=> ! [X201 : (term > $o),X202 : subst,X203 : term] : (~ ! [X204 : term] : (~ (((var @ X204)) = $true) | (((X201 @ (sub @ X204 @ X202))) = $true)) | ~ ! [X205 : term] : ((((X201 @ (lam @ X205))) = $true) | ~ ! [X206 : term] : ((((X201 @ (sub @ X205 @ (push @ X206 @ id)))) = $true) | ~ ($true = ((X201 @ X206))))) | ~ ! [X207 : term,X208 : term] : ((((X201 @ (ap @ X208 @ X207))) = $true) | ~ (((X201 @ X208)) = $true) | ~ (((X201 @ X207)) = $true)) | (((X201 @ (sub @ X203 @ X202))) = $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X209 : term] : (((sub @ X209 @ id)) = X209) => (! [X210 : subst,X211 : (term > $o),X212 : term] : (~ ! [X213 : term] : (~ ! [X214 : term] : (($true = ((X211 @ (sub @ X213 @ (push @ X214 @ id))))) | ~ (((X211 @ X214)) = $true)) | (((X211 @ (lam @ X213))) = $true)) | ~ ! [X215 : term] : (($true = ((X211 @ (sub @ X215 @ X210)))) | ~ ($true = ((var @ X215)))) | ~ ! [X216 : term,X217 : term] : (($true = ((X211 @ (ap @ X216 @ X217)))) | ~ (((X211 @ X217)) = $true) | ~ (((X211 @ X216)) = $true)) | (((X211 @ (sub @ X212 @ X210))) = $true)) => ! [X218 : (term > $o),X219 : term] : (~ ! [X220 : term] : (($true = ((X218 @ X220))) | ~ (((var @ X220)) = $true)) | (((X218 @ X219)) = $true) | ~ ! [X221 : term] : (~ ! [X222 : term] : ((((X218 @ (sub @ X221 @ (push @ X222 @ id)))) = $true) | ~ ($true = ((X218 @ X222)))) | (((X218 @ (lam @ X221))) = $true)) | ~ ! [X223 : term,X224 : term] : ((((X218 @ (ap @ X223 @ X224))) = $true) | ~ ($true = ((X218 @ X223))) | ~ (((X218 @ X224)) = $true))))) <=> (induction2_lthm = $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)))))))))))))) & (ulamvarsh = $true) & (! [X225 : subst] : (((comp @ X225 @ id)) = X225) <=> (axidr = $true)) & ~ (ulamvar1 = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X226 : d_subst,X227 : d_subst] : ((((d2subst @ X226)) = ((d2subst @ X227))) => (X226 = X227)) & (hoaslamnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X229 : subst,X228 : term] : (((sub @ one @ (push @ X228 @ X229))) = X228) => ! [X230 : term,X231 : (term > $o),X232 : (term > $o),X233 : subst] : (~ (((X231 @ X230)) = $true) | ~ ! [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) = ((X232 @ X234))) | (((X232 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X235 : term,X236 : (subst > term > subst > $o)] : (~ ! [X237 : term] : (~ ($true = ((X236 @ id @ X237 @ id))) | (((X236 @ id @ (sub @ X235 @ (push @ X237 @ id)) @ id)) = $true)) | ($true = ((X236 @ id @ (lam @ X235) @ id))) | ~ ! [X238 : subst,X239 : subst,X240 : term,X241 : subst] : (~ (((X236 @ X241 @ X240 @ (comp @ X238 @ X239))) = $true) | (((X236 @ (comp @ X241 @ X238) @ (sub @ X240 @ X238) @ X239)) = $true)) | ~ ! [X242 : (subst > term > term)] : (~ ! [X244 : subst,X243 : term,X245 : subst] : (((sub @ (X242 @ X245 @ X243) @ X244)) = ((X242 @ (comp @ X245 @ X244) @ (sub @ X243 @ X244)))) | ~ ! [X246 : term] : ((((X236 @ id @ (X242 @ id @ X246) @ id)) = $true) | ~ ($true = ((X236 @ id @ X246 @ id)))) | (((X236 @ id @ (lam @ (X242 @ sh @ one)) @ id)) = $true)) | ~ ! [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (~ (((X236 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249) @ X247)) = $true) | ($true = ((X236 @ X250 @ X248 @ (comp @ X249 @ X247))))))) & (hoasinduction_lem1v2 = $true) & (axabs = $true) & (pushprop_lem3v2_lthm = $true) & ((! [X251 : term,X252 : subst] : (((sub @ one @ (push @ X251 @ X252))) = X251) => (! [X253 : term,X254 : subst] : (((comp @ sh @ (push @ X253 @ X254))) = X254) => (! [X256 : term,X255 : term] : ((X255 = X256) | (((lam @ X256)) != ((lam @ X255)))) => ! [X257 : subst,X258 : (subst > term > term),X259 : term,X260 : (subst > term > term)] : ((((X258 @ X257 @ X259)) = ((X260 @ X257 @ X259))) | ~ ! [X263 : term,X261 : subst,X262 : subst] : (((X258 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262))) = ((sub @ (X258 @ X261 @ X263) @ X262))) | ~ ! [X264 : subst,X265 : term,X266 : subst] : (((sub @ (X260 @ X266 @ X265) @ X264)) = ((X260 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264)))) | (((lam @ (X258 @ sh @ one))) != ((lam @ (X260 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (apnotvar = $true) & (! [X267 : (subst > term > subst > $o),X268 : term] : (~ ! [X269 : term] : (~ (((X267 @ id @ X269 @ id)) = $true) | (((X267 @ id @ (sub @ X268 @ (push @ X269 @ id)) @ id)) = $true)) | ~ ! [X270 : (subst > term > term)] : (~ ! [X271 : term] : (~ ($true = ((X267 @ id @ X271 @ id))) | (((X267 @ id @ (X270 @ id @ X271) @ id)) = $true)) | ~ ! [X274 : subst,X272 : term,X273 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273)))) | (((X267 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true)) | (((X267 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (induction2_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((hoasinduction_lem2 = $true) <=> ! [X275 : (subst > term > subst > $o),X276 : term,X277 : term] : (~ ($true = ((X275 @ id @ X277 @ id))) | ~ ! [X278 : subst,X279 : term,X280 : subst,X281 : subst] : (~ (((X275 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280) @ X281)) = $true) | ($true = ((X275 @ X278 @ X279 @ (comp @ X280 @ X281))))) | ~ ! [X282 : term,X283 : term] : (~ ($true = ((X275 @ id @ X282 @ id))) | ~ (((X275 @ id @ X283 @ id)) = $true) | ($true = ((X275 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id)))) | ($true = ((X275 @ id @ (ap @ X277 @ X276) @ id))) | ~ ! [X284 : term,X285 : subst,X286 : subst,X287 : subst] : ((((X275 @ (comp @ X287 @ X285) @ (sub @ X284 @ X285) @ X286)) = $true) | ~ ($true = ((X275 @ X287 @ X284 @ (comp @ X285 @ X286))))) | ~ ($true = ((X275 @ id @ X276 @ id))))) & (pushprop = $true) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1_lthm = $true) & ! [X289 : d_term,X288 : d_term] : ((((d2term @ X288)) = ((d2term @ X289))) => (X288 = X289)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X290 : term] : (((sub @ X290 @ id)) = X290) => (! [X291 : (subst > term > subst > $o),X292 : term] : (~ ! [X293 : (subst > term > term)] : (~ ! [X295 : subst,X296 : term,X294 : subst] : (((sub @ (X293 @ X295 @ X296) @ X294)) = ((X293 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294)))) | ~ ! [X297 : term] : ((((X291 @ id @ (X293 @ id @ X297) @ id)) = $true) | ~ (((X291 @ id @ X297 @ id)) = $true)) | (((X291 @ id @ (lam @ (X293 @ sh @ one)) @ id)) = $true)) | (((X291 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X298 : term] : (~ (((X291 @ id @ X298 @ id)) = $true) | (((X291 @ id @ (sub @ X292 @ (push @ X298 @ id)) @ id)) = $true))) => ! [X299 : term,X300 : (subst > term > subst > $o)] : (~ ! [X301 : term] : (~ ($true = ((X300 @ id @ X301 @ id))) | (((X300 @ id @ (sub @ X299 @ (push @ X301 @ id)) @ id)) = $true)) | ~ ! [X302 : (subst > term > term)] : (~ ! [X305 : subst,X303 : subst,X304 : term] : (((sub @ (X302 @ X303 @ X304) @ X305)) = ((X302 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))) | (((X300 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ~ ! [X306 : term] : (~ (((X300 @ id @ X306 @ id)) = $true) | ($true = ((X300 @ id @ (X302 @ id @ X306) @ id))))) | (((X300 @ id @ (lam @ X299) @ id)) = $true))))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasapnotvar_lthm = $true) & ((axscons = $true) <=> ! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307)) & (! [X310 : (subst > term > term),X308 : subst,X309 : (subst > term > term),X311 : term] : (~ ! [X315 : term,X316 : subst,X317 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) = ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | (((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one)))) | ~ ! [X313 : subst,X312 : term,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) = ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314))))) <=> (hoaslaminj = $true)) & ((axidl = $true) <=> ! [X318 : subst] : (((comp @ id @ X318)) = X318)) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & ((hoasapinj1_lthm = $true) <=> (! [X321 : term] : (((sub @ X321 @ id)) = X321) => (! [X323 : term,X325 : term,X322 : term,X324 : term] : ((((ap @ X323 @ X322)) != ((ap @ X324 @ X325))) | (X323 = X324)) => ! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329))))) & (! [X330 : term,X331 : (term > $o),X332 : (subst > term > subst > $o)] : (~ ! [X333 : term] : (((X331 @ X333)) = ((X332 @ id @ X333 @ id))) | (((X331 @ (lam @ X330))) = $true) | ~ ! [X334 : term] : (($true = ((X331 @ (sub @ X330 @ (push @ X334 @ id))))) | ~ ($true = ((X331 @ X334)))) | ~ ! [X335 : (subst > term > term)] : (~ ! [X336 : term,X338 : subst,X337 : subst] : (((X335 @ (comp @ X337 @ X338) @ (sub @ X336 @ X338))) = ((sub @ (X335 @ X337 @ X336) @ X338))) | (((X332 @ id @ (lam @ (X335 @ sh @ one)) @ id)) = $true) | ~ ! [X339 : term] : (($true = ((X332 @ id @ (X335 @ id @ X339) @ id))) | ~ (((X332 @ id @ X339 @ id)) = $true)))) <=> (hoasinduction_lem3v2a = $true)) & (! [X340 : term,X341 : term,X342 : (term > $o),X343 : (subst > term > subst > $o)] : (~ ! [X344 : term] : (((X342 @ X344)) = ((X343 @ id @ X344 @ id))) | ~ ! [X345 : term,X346 : term] : ((((X343 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id)) = $true) | ~ (((X343 @ id @ X345 @ id)) = $true) | ~ ($true = ((X343 @ id @ X346 @ id)))) | ~ ! [X347 : subst,X348 : subst,X349 : subst,X350 : term] : ((((X343 @ X348 @ X350 @ (comp @ X347 @ X349))) = $true) | ~ (((X343 @ (comp @ X348 @ X347) @ (sub @ X350 @ X347) @ X349)) = $true)) | ~ ! [X351 : term,X352 : subst,X353 : subst,X354 : subst] : ((((X343 @ (comp @ X354 @ X352) @ (sub @ X351 @ X352) @ X353)) = $true) | ~ (((X343 @ X354 @ X351 @ (comp @ X352 @ X353))) = $true)) | ~ (((X342 @ X340)) = $true) | (((X342 @ (ap @ X340 @ X341))) = $true) | ~ (((X342 @ X341)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ! [X355 : d_subst] : (d_id = X355) & ((hoasinduction_lem3v2 = $true) <=> ! [X356 : (subst > term > subst > $o),X357 : term,X358 : (term > $o)] : (~ ! [X359 : (subst > term > term)] : (~ ! [X360 : term] : (~ (((X356 @ id @ X360 @ id)) = $true) | (((X356 @ id @ (X359 @ id @ X360) @ id)) = $true)) | ~ ! [X362 : subst,X363 : term,X361 : subst] : (((sub @ (X359 @ X361 @ X363) @ X362)) = ((X359 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362)))) | (((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id)) = $true)) | ~ ! [X364 : subst,X365 : term,X366 : subst,X367 : subst] : (~ ($true = ((X356 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X367))) | (((X356 @ X364 @ X365 @ (comp @ X366 @ X367))) = $true)) | ~ ! [X368 : term,X369 : subst,X370 : subst,X371 : subst] : ((((X356 @ (comp @ X370 @ X369) @ (sub @ X368 @ X369) @ X371)) = $true) | ~ (((X356 @ X370 @ X368 @ (comp @ X369 @ X371))) = $true)) | ($true = ((X358 @ (lam @ X357)))) | ~ ! [X372 : term] : (~ (((X358 @ X372)) = $true) | (((X358 @ (sub @ X357 @ (push @ X372 @ id)))) = $true)) | ~ ! [X373 : term] : (((X358 @ X373)) = ((X356 @ id @ X373 @ id))))) & ((pushprop_lem0_lthm = $true) <=> ! [X375 : subst,X374 : (term > $o),X376 : term] : ~ ! [X377 : (term > $o)] : ~ ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378)))) & ((induction2lem_lthm = $true) <=> (! [X379 : subst,X380 : term] : (((sub @ one @ (push @ X380 @ X379))) = X380) => (! [X382 : subst,X381 : term] : (((comp @ sh @ (push @ X381 @ X382))) = X382) => (! [X383 : subst] : (((comp @ X383 @ id)) = X383) => (! [X384 : term,X385 : (term > $o)] : (~ ! [X386 : term] : (~ (((var @ X386)) = $true) | ($true = ((X385 @ X386)))) | (((X385 @ X384)) = $true) | ~ ! [X387 : term,X388 : term] : (~ (((X385 @ X387)) = $true) | ~ (((X385 @ X388)) = $true) | (((X385 @ (ap @ X387 @ X388))) = $true)) | ~ ! [X389 : term] : (~ ($true = ((X385 @ X389))) | ($true = ((X385 @ (lam @ X389)))))) => ! [X390 : subst,X391 : (term > $o),X392 : term] : (~ ! [X393 : term] : (~ (((var @ X393)) = $true) | (((X391 @ (sub @ X393 @ X390))) = $true)) | (((X391 @ (sub @ X392 @ X390))) = $true) | ~ ! [X394 : term] : ((((X391 @ (lam @ X394))) = $true) | ~ ! [X395 : term] : ((((X391 @ (sub @ X394 @ (push @ X395 @ id)))) = $true) | ~ (((X391 @ X395)) = $true))) | ~ ! [X396 : term,X397 : term] : ((((X391 @ (ap @ X396 @ X397))) = $true) | ~ (((X391 @ X397)) = $true) | ~ (((X391 @ X396)) = $true)))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & ((hoasapinj2_lthm = $true) <=> (! [X401 : term,X400 : term,X399 : term,X398 : term] : ((((ap @ X400 @ X401)) != ((ap @ X399 @ X398))) | (X398 = X401)) => ! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))))) & (lamnotvar = $true) & (induction2lem_gthm = $true) & (! [X406 : (term > $o),X407 : term,X408 : term,X409 : (term > $o),X410 : subst] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | ~ (((X409 @ X407)) = $true)) <=> (pushprop_lem1 = $true)) & (! [X412 : term,X411 : (subst > term > term),X413 : term] : ((((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412))) | ~ ! [X414 : subst,X416 : term,X415 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) = ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414))))) <=> (hoaslamnotap = $true)) & (! [X417 : term] : ~ ! [X418 : (subst > term > term)] : (((X418 @ sh @ one)) != ((sub @ X417 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoaslamnotap_lthm = $true) & ((! [X419 : term] : (((sub @ X419 @ id)) = X419) => ! [X420 : (subst > term > subst > $o),X421 : (term > $o),X422 : term] : (~ ! [X423 : term,X424 : subst,X425 : subst,X426 : subst] : ((((X420 @ (comp @ X425 @ X426) @ (sub @ X423 @ X426) @ X424)) = $true) | ~ (((X420 @ X425 @ X423 @ (comp @ X426 @ X424))) = $true)) | (((X421 @ (lam @ X422))) = $true) | ~ ! [X427 : term] : (~ (((X421 @ X427)) = $true) | (((X421 @ (sub @ X422 @ (push @ X427 @ id)))) = $true)) | ~ ! [X428 : term] : (((X420 @ id @ X428 @ id)) = ((X421 @ X428))) | ~ ! [X429 : subst,X430 : subst,X431 : term,X432 : subst] : (($true = ((X420 @ X429 @ X431 @ (comp @ X430 @ X432)))) | ~ (((X420 @ (comp @ X429 @ X430) @ (sub @ X431 @ X430) @ X432)) = $true)) | ~ ! [X433 : (subst > term > term)] : ((((X420 @ id @ (lam @ (X433 @ sh @ one)) @ id)) = $true) | ~ ! [X434 : term] : (($true = ((X420 @ id @ (X433 @ id @ X434) @ id))) | ~ (((X420 @ id @ X434 @ id)) = $true)) | ~ ! [X437 : subst,X436 : subst,X435 : term] : (((X433 @ (comp @ X437 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X437 @ X435) @ X436)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X438 : (subst > term > subst > $o),X439 : term] : (~ ! [X440 : term,X441 : (subst > term > term)] : (~ ! [X444 : term,X443 : subst,X442 : subst] : (((X441 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443))) = ((sub @ X440 @ (push @ (sub @ X444 @ X443) @ (comp @ X442 @ X443))))) | ~ ! [X446 : subst,X447 : subst,X445 : term] : (((sub @ (sub @ X440 @ (push @ X445 @ X446)) @ X447)) = ((sub @ (X441 @ X446 @ X445) @ X447))) | (((X438 @ id @ (lam @ (X441 @ sh @ one)) @ id)) = $true) | ~ ! [X448 : term] : (~ (((X438 @ id @ X448 @ id)) = $true) | (((X438 @ id @ (X441 @ id @ X448) @ id)) = $true))) | (((X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X449 : term] : ((((X438 @ id @ (sub @ X439 @ (push @ X449 @ id)) @ id)) = $true) | ~ (((X438 @ id @ X449 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X450 : (subst > term > subst > $o),X451 : term] : (~ ! [X452 : term] : (~ ($true = ((X450 @ id @ X452 @ id))) | ($true = ((X450 @ id @ (sub @ X451 @ (push @ X452 @ id)) @ id)))) | (((X450 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X453 : (subst > term > term)] : (~ ! [X454 : term] : (~ (((X450 @ id @ X454 @ id)) = $true) | (((X450 @ id @ (X453 @ id @ X454) @ id)) = $true)) | (((X450 @ id @ (lam @ (X453 @ sh @ one)) @ id)) = $true) | ~ ! [X455 : subst,X456 : subst,X457 : term] : (((sub @ (X453 @ X455 @ X457) @ X456)) = ((X453 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456))))))) & (! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) <=> (apinj2 = $true)) & ((termmset = $true) <=> ! [X462 : term] : (((sub @ X462 @ id)) = X462)) & (hoaslaminj_gthm = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (hoasinduction_lem2v2_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & (hoaslamnotap_gthm = $true) & (axvarshift = $true) & (substmonoid_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X466 : subst,X465 : term,X467 : (term > $o)] : ~ ! [X468 : (term > $o)] : ~ ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469)))) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X470 : (subst > term > subst > $o)] : ~ ! [X471 : (term > $o)] : ~ ! [X472 : term] : (((X470 @ id @ X472 @ id)) = ((X471 @ X472))) => (! [X473 : (term > $o),X474 : term] : ((((X473 @ X474)) = $true) | ~ ! [X475 : term,X476 : term] : ((((X473 @ (ap @ X475 @ X476))) = $true) | ~ ($true = ((X473 @ X476))) | ~ (((X473 @ X475)) = $true)) | ~ ! [X477 : term] : ((((X473 @ X477)) = $true) | ~ ($true = ((var @ X477)))) | ~ ! [X478 : term] : (~ ! [X479 : term] : (($true = ((X473 @ (sub @ X478 @ (push @ X479 @ id))))) | ~ (((X473 @ X479)) = $true)) | (((X473 @ (lam @ X478))) = $true))) => (! [X480 : term] : (((sub @ X480 @ id)) = X480) => (! [X481 : (subst > term > subst > $o),X482 : term,X483 : (term > $o)] : (~ ! [X484 : (subst > term > term)] : (~ ! [X485 : term,X487 : subst,X486 : subst] : (((X484 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487))) = ((sub @ (X484 @ X486 @ X485) @ X487))) | ~ ! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ~ ($true = ((X481 @ id @ X488 @ id)))) | ($true = ((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id)))) | ($true = ((X483 @ (lam @ X482)))) | ~ ! [X489 : term] : (~ (((X483 @ X489)) = $true) | (((X483 @ (sub @ X482 @ (push @ X489 @ id)))) = $true)) | ~ ! [X490 : term] : (((X481 @ id @ X490 @ id)) = ((X483 @ X490)))) => ! [X491 : term,X492 : (subst > term > subst > $o)] : (~ ! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : ((((X492 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)) = $true) | ~ (((X492 @ X493 @ X494 @ (comp @ X495 @ X496))) = $true)) | ~ ! [X497 : term,X498 : subst,X499 : subst,X500 : subst] : (~ (((X492 @ (comp @ X499 @ X500) @ (sub @ X497 @ X500) @ X498)) = $true) | (((X492 @ X499 @ X497 @ (comp @ X500 @ X498))) = $true)) | ~ ! [X501 : term,X502 : term] : (~ (((X492 @ id @ X502 @ id)) = $true) | (((X492 @ id @ (ap @ (sub @ X501 @ id) @ X502) @ id)) = $true) | ~ (((X492 @ id @ X501 @ id)) = $true)) | ~ ! [X503 : term] : (~ ($true = ((var @ (sub @ X503 @ id)))) | (((X492 @ id @ X503 @ id)) = $true)) | (((X492 @ id @ X491 @ id)) = $true) | ~ ! [X504 : (subst > term > term)] : ((((X492 @ id @ (lam @ (X504 @ sh @ one)) @ id)) = $true) | ~ ! [X505 : term] : (($true = ((X492 @ id @ (X504 @ id @ X505) @ id))) | ~ (((X492 @ id @ X505 @ id)) = $true)) | ~ ! [X506 : subst,X507 : subst,X508 : term] : (((X504 @ (comp @ X507 @ X506) @ (sub @ X508 @ X506))) = ((sub @ (X504 @ X507 @ X508) @ X506)))))))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X509 : term,X510 : (subst > term > subst > $o)] : (~ ! [X511 : term,X512 : term] : (~ (((X510 @ id @ X512 @ id)) = $true) | (((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) = $true) | ~ (((X510 @ id @ X511 @ id)) = $true)) | ($true = ((X510 @ id @ X509 @ id))) | ~ ! [X513 : (subst > term > term)] : (($true = ((X510 @ id @ (lam @ (X513 @ sh @ one)) @ id))) | ~ ! [X514 : term] : (~ (((X510 @ id @ X514 @ id)) = $true) | (((X510 @ id @ (X513 @ id @ X514) @ id)) = $true)) | ~ ! [X515 : term,X516 : subst,X517 : subst] : (((sub @ (X513 @ X517 @ X515) @ X516)) = ((X513 @ (comp @ X517 @ X516) @ (sub @ X515 @ X516))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X518 : (subst > term > subst > $o)] : ~ ! [X519 : (term > $o)] : ~ ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2subst @ d_id)) = id) & ((pushprop_lem1_lthm = $true) <=> (! [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) = X521) => (! [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) = X524) => ! [X525 : subst,X526 : term,X527 : term,X528 : (term > $o),X529 : (term > $o)] : (($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525))))) | ~ ($true = ((X529 @ X526))))))) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & (! [X532 : term] : ~ ! [X533 : (subst > term > term)] : ~ ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X536 : term] : ~ ! [X537 : (subst > term > term)] : ~ ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539))))), 50.81/8.71 inference(rectify,[],[f7])). 50.81/8.71 thf(f10,plain,( 50.81/8.71 (hoasapinj2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X290 : term] : (((sub @ X290 @ id)) = X290) => (! [X291 : (subst > term > subst > $o),X292 : term] : (~ ! [X298 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X298 @ id)) @ id)) = $true) | (((X291 @ id @ X298 @ id)) != $true)) | ~ ! [X293 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X293 @ sh @ one)) @ id)) = $true) | ~ ! [X297 : term] : ((((X291 @ id @ X297 @ id)) != $true) | (((X291 @ id @ (X293 @ id @ X297) @ id)) = $true)) | ~ ! [X295 : subst,X296 : term,X294 : subst] : (((sub @ (X293 @ X295 @ X296) @ X294)) = ((X293 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))))) | (((X291 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id)) = $true)) => ! [X300 : (subst > term > subst > $o),X299 : term] : (~ ! [X302 : (subst > term > term)] : (~ ! [X305 : subst,X303 : subst,X304 : term] : (((sub @ (X302 @ X303 @ X304) @ X305)) = ((X302 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))) | (((X300 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ~ ! [X306 : term] : (($true = ((X300 @ id @ (X302 @ id @ X306) @ id))) | (((X300 @ id @ X306 @ id)) != $true))) | ~ ! [X301 : term] : (($true != ((X300 @ id @ X301 @ id))) | (((X300 @ id @ (sub @ X299 @ (push @ X301 @ id)) @ id)) = $true)) | (((X300 @ id @ (lam @ X299) @ id)) = $true))))) & ((shinj = $true) <=> ! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26))) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) <=> (! [X209 : term] : (((sub @ X209 @ id)) = X209) => (! [X210 : subst,X211 : (term > $o),X212 : term] : (~ ! [X215 : term] : (($true = ((X211 @ (sub @ X215 @ X210)))) | ($true != ((var @ X215)))) | (((X211 @ (sub @ X212 @ X210))) = $true) | ~ ! [X213 : term] : (~ ! [X214 : term] : ((((X211 @ X214)) != $true) | ($true = ((X211 @ (sub @ X213 @ (push @ X214 @ id)))))) | (((X211 @ (lam @ X213))) = $true)) | ~ ! [X217 : term,X216 : term] : (($true = ((X211 @ (ap @ X216 @ X217)))) | (((X211 @ X216)) != $true) | (((X211 @ X217)) != $true))) => ! [X219 : term,X218 : (term > $o)] : (~ ! [X223 : term,X224 : term] : ((((X218 @ (ap @ X223 @ X224))) = $true) | ($true != ((X218 @ X223))) | (((X218 @ X224)) != $true)) | (((X218 @ X219)) = $true) | ~ ! [X221 : term] : ((((X218 @ (lam @ X221))) = $true) | ~ ! [X222 : term] : (($true != ((X218 @ X222))) | (((X218 @ (sub @ X221 @ (push @ X222 @ id)))) = $true))) | ~ ! [X220 : term] : ((((var @ X220)) != $true) | ($true = ((X218 @ X220)))))))) & ((substmonoid_lthm = $true) <=> (! [X0 : subst] : (((comp @ id @ X0)) = X0) => (! [X1 : subst] : (((comp @ X1 @ id)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3))))) & (hoasinduction_lem3_gthm = $true) & ((axvarid = $true) <=> ! [X61 : term] : (((sub @ X61 @ id)) = X61)) & (! [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | (((X409 @ X407)) != $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X53 : term] : ~ ! [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) != ((X54 @ sh @ one)))) & (pushprop_lem0_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X375 : subst,X374 : (term > $o),X376 : term] : ~ ! [X377 : (term > $o)] : ~ ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378)))) & ((! [X62 : (subst > term > subst > $o)] : ~ ! [X63 : (term > $o)] : ~ ! [X64 : term] : (((X63 @ X64)) = ((X62 @ id @ X64 @ id))) => (! [X65 : term,X66 : (term > $o)] : (~ ! [X69 : term,X70 : term] : (($true != ((X66 @ X69))) | (((X66 @ X70)) != $true) | (((X66 @ (ap @ X69 @ X70))) = $true)) | (((X66 @ X65)) = $true) | ~ ! [X67 : term] : (~ ! [X68 : term] : ((((X66 @ X68)) != $true) | (((X66 @ (sub @ X67 @ (push @ X68 @ id)))) = $true)) | ($true = ((X66 @ (lam @ X67))))) | ~ ! [X71 : term] : (($true = ((X66 @ X71))) | (((var @ X71)) != $true))) => (! [X72 : term] : (((sub @ X72 @ id)) = X72) => (! [X75 : (subst > term > subst > $o),X74 : term,X73 : (term > $o)] : (~ ! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) | ~ ! [X76 : (subst > term > term)] : (~ ! [X80 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) = ((sub @ (X76 @ X78 @ X79) @ X80))) | ~ ! [X77 : term] : ((((X75 @ id @ X77 @ id)) != $true) | (((X75 @ id @ (X76 @ id @ X77) @ id)) = $true)) | (((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true)) | (((X73 @ (lam @ X74))) = $true) | ~ ! [X81 : term] : ((((X73 @ X81)) != $true) | ($true = ((X73 @ (sub @ X74 @ (push @ X81 @ id))))))) => ! [X83 : (subst > term > subst > $o),X84 : term] : (~ ! [X85 : (subst > term > term)] : ((((X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) = $true) | ~ ! [X86 : term] : ((((X83 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X83 @ id @ X86 @ id)) != $true)) | ~ ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88))))) | ~ ! [X91 : term,X90 : term] : ((((X83 @ id @ X90 @ id)) != $true) | ($true = ((X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id))) | (((X83 @ id @ X91 @ id)) != $true)) | ($true = ((X83 @ id @ X84 @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (pushprop = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axshiftcons = $true) <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & ((hoasinduction_lem3 = $true) <=> ! [X235 : term,X236 : (subst > term > subst > $o)] : (~ ! [X237 : term] : (($true != ((X236 @ id @ X237 @ id))) | (((X236 @ id @ (sub @ X235 @ (push @ X237 @ id)) @ id)) = $true)) | ~ ! [X240 : term,X241 : subst,X239 : subst,X238 : subst] : ((((X236 @ (comp @ X241 @ X238) @ (sub @ X240 @ X238) @ X239)) = $true) | (((X236 @ X241 @ X240 @ (comp @ X238 @ X239))) != $true)) | ~ ! [X249 : subst,X250 : subst,X248 : term,X247 : subst] : (($true = ((X236 @ X250 @ X248 @ (comp @ X249 @ X247)))) | (((X236 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249) @ X247)) != $true)) | ~ ! [X242 : (subst > term > term)] : (~ ! [X246 : term] : ((((X236 @ id @ (X242 @ id @ X246) @ id)) = $true) | ($true != ((X236 @ id @ X246 @ id)))) | ~ ! [X244 : subst,X243 : term,X245 : subst] : (((sub @ (X242 @ X245 @ X243) @ X244)) = ((X242 @ (comp @ X245 @ X244) @ (sub @ X243 @ X244)))) | (((X236 @ id @ (lam @ (X242 @ sh @ one)) @ id)) = $true)) | ($true = ((X236 @ id @ (lam @ X235) @ id))))) & ((! [X379 : subst,X380 : term] : (((sub @ one @ (push @ X380 @ X379))) = X380) => (! [X382 : subst,X381 : term] : (((comp @ sh @ (push @ X381 @ X382))) = X382) => (! [X383 : subst] : (((comp @ X383 @ id)) = X383) => (! [X384 : term,X385 : (term > $o)] : ((((X385 @ X384)) = $true) | ~ ! [X389 : term] : (($true = ((X385 @ (lam @ X389)))) | ($true != ((X385 @ X389)))) | ~ ! [X388 : term,X387 : term] : ((((X385 @ (ap @ X387 @ X388))) = $true) | (((X385 @ X388)) != $true) | (((X385 @ X387)) != $true)) | ~ ! [X386 : term] : ((((var @ X386)) != $true) | ($true = ((X385 @ X386))))) => ! [X392 : term,X390 : subst,X391 : (term > $o)] : (~ ! [X394 : term] : (~ ! [X395 : term] : ((((X391 @ (sub @ X394 @ (push @ X395 @ id)))) = $true) | (((X391 @ X395)) != $true)) | (((X391 @ (lam @ X394))) = $true)) | ~ ! [X396 : term,X397 : term] : ((((X391 @ X397)) != $true) | (((X391 @ (ap @ X396 @ X397))) = $true) | (((X391 @ X396)) != $true)) | (((X391 @ (sub @ X392 @ X390))) = $true) | ~ ! [X393 : term] : ((((var @ X393)) != $true) | (((X391 @ (sub @ X393 @ X390))) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoasapnotvar_lthm = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ! [X289 : d_term,X288 : d_term] : ((((d2term @ X288)) = ((d2term @ X289))) => (X288 = X289)) & ((pushprop_lem0 = $true) <=> ! [X466 : subst,X465 : term,X467 : (term > $o)] : ~ ! [X468 : (term > $o)] : ~ ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469)))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasapinj1 = $true) <=> ! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7))))) & (apnotvar = $true) & ((hoasapinj2_lthm = $true) <=> (! [X401 : term,X400 : term,X399 : term,X398 : term] : ((((ap @ X400 @ X401)) != ((ap @ X399 @ X398))) | (X398 = X401)) => ! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))))) & ((axscons = $true) <=> ! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307)) & (hoaslamnotap_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj2 = $true) <=> ! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axapp = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X343 : (subst > term > subst > $o),X340 : term,X342 : (term > $o),X341 : term] : (~ ! [X345 : term,X346 : term] : (($true != ((X343 @ id @ X346 @ id))) | (((X343 @ id @ X345 @ id)) != $true) | (((X343 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id)) = $true)) | ~ ! [X351 : term,X352 : subst,X354 : subst,X353 : subst] : ((((X343 @ (comp @ X354 @ X352) @ (sub @ X351 @ X352) @ X353)) = $true) | (((X343 @ X354 @ X351 @ (comp @ X352 @ X353))) != $true)) | (((X342 @ (ap @ X340 @ X341))) = $true) | (((X342 @ X341)) != $true) | ~ ! [X344 : term] : (((X342 @ X344)) = ((X343 @ id @ X344 @ id))) | ~ ! [X348 : subst,X347 : subst,X350 : term,X349 : subst] : ((((X343 @ (comp @ X348 @ X347) @ (sub @ X350 @ X347) @ X349)) != $true) | (((X343 @ X348 @ X350 @ (comp @ X347 @ X349))) = $true)) | (((X342 @ X340)) != $true))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X125 : (subst > term > subst > $o)] : ~ ! [X126 : (term > $o)] : ~ ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X536 : term] : ~ ! [X537 : (subst > term > term)] : ~ ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539)))) & ! [X226 : d_subst,X227 : d_subst] : ((((d2subst @ X226)) = ((d2subst @ X227))) => (X226 = X227)) & (ulamvarind = $true) & (((var @ (d2term @ d_one))) != $true) & ((! [X419 : term] : (((sub @ X419 @ id)) = X419) => ! [X421 : (term > $o),X420 : (subst > term > subst > $o),X422 : term] : (~ ! [X433 : (subst > term > term)] : (~ ! [X437 : subst,X436 : subst,X435 : term] : (((X433 @ (comp @ X437 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X437 @ X435) @ X436))) | (((X420 @ id @ (lam @ (X433 @ sh @ one)) @ id)) = $true) | ~ ! [X434 : term] : (($true = ((X420 @ id @ (X433 @ id @ X434) @ id))) | (((X420 @ id @ X434 @ id)) != $true))) | ~ ! [X428 : term] : (((X420 @ id @ X428 @ id)) = ((X421 @ X428))) | ~ ! [X427 : term] : ((((X421 @ (sub @ X422 @ (push @ X427 @ id)))) = $true) | (((X421 @ X427)) != $true)) | (((X421 @ (lam @ X422))) = $true) | ~ ! [X430 : subst,X432 : subst,X431 : term,X429 : subst] : ((((X420 @ (comp @ X429 @ X430) @ (sub @ X431 @ X430) @ X432)) != $true) | ($true = ((X420 @ X429 @ X431 @ (comp @ X430 @ X432))))) | ~ ! [X423 : term,X424 : subst,X426 : subst,X425 : subst] : ((((X420 @ X425 @ X423 @ (comp @ X426 @ X424))) != $true) | (((X420 @ (comp @ X425 @ X426) @ (sub @ X423 @ X426) @ X424)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X11 : term,X10 : (subst > term > subst > $o)] : ((((X10 @ id @ (lam @ X11) @ id)) = $true) | ~ ! [X17 : term] : (($true != ((X10 @ id @ X17 @ id))) | (((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) = $true)) | ~ ! [X12 : (subst > term > term)] : (~ ! [X16 : subst,X14 : term,X15 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15)))) | (((X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) = $true) | ~ ! [X13 : term] : ((((X10 @ id @ X13 @ id)) != $true) | (((X10 @ id @ (X12 @ id @ X13) @ id)) = $true)))) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lthm = $true) <=> (! [X128 : term,X129 : (term > $o)] : (~ ! [X130 : term,X131 : term] : ((((X129 @ X131)) != $true) | (((X129 @ (ap @ X131 @ X130))) = $true) | ($true != ((X129 @ X130)))) | ($true = ((X129 @ X128))) | ~ ! [X134 : term] : ((((var @ X134)) != $true) | (((X129 @ X134)) = $true)) | ~ ! [X132 : term] : ((((X129 @ (lam @ X132))) = $true) | ~ ! [X133 : term] : (($true != ((X129 @ X133))) | (((X129 @ (sub @ X132 @ (push @ X133 @ id)))) = $true)))) => (! [X137 : term,X135 : term,X136 : (subst > term > subst > $o)] : ((((X136 @ id @ X137 @ id)) != $true) | (((X136 @ id @ (ap @ X135 @ X137) @ id)) = $true) | ~ ! [X141 : subst,X138 : term,X139 : subst,X140 : subst] : ((((X136 @ X141 @ X138 @ (comp @ X139 @ X140))) != $true) | ($true = ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140)))) | ~ ! [X145 : subst,X143 : subst,X144 : subst,X142 : term] : ((((X136 @ X144 @ X142 @ (comp @ X145 @ X143))) = $true) | (((X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143)) != $true)) | ~ ! [X146 : term,X147 : term] : ((((X136 @ id @ X147 @ id)) != $true) | (((X136 @ id @ X146 @ id)) != $true) | (((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id)) = $true)) | (((X136 @ id @ X135 @ id)) != $true)) => (! [X148 : term,X149 : (subst > term > subst > $o)] : (~ ! [X155 : (subst > term > term)] : (~ ! [X156 : term] : (($true = ((X149 @ id @ (X155 @ id @ X156) @ id))) | (((X149 @ id @ X156 @ id)) != $true)) | (((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ~ ! [X158 : subst,X157 : subst,X159 : term] : (((sub @ (X155 @ X157 @ X159) @ X158)) = ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158))))) | ($true = ((X149 @ id @ (lam @ X148) @ id))) | ~ ! [X152 : term,X154 : subst,X151 : subst,X153 : subst] : (($true = ((X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153))) | (((X149 @ X154 @ X152 @ (comp @ X151 @ X153))) != $true)) | ~ ! [X150 : term] : ((((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true) | ($true != ((X149 @ id @ X150 @ id)))) | ~ ! [X163 : subst,X160 : subst,X161 : subst,X162 : term] : ((((X149 @ X163 @ X162 @ (comp @ X160 @ X161))) = $true) | (((X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161)) != $true))) => ! [X165 : term,X164 : (subst > term > subst > $o)] : ((((X164 @ id @ X165 @ id)) = $true) | ~ ! [X173 : (subst > term > term)] : (~ ! [X177 : term] : ((((X164 @ id @ X177 @ id)) != $true) | ($true = ((X164 @ id @ (X173 @ id @ X177) @ id)))) | (((X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ~ ! [X176 : subst,X175 : term,X174 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174)))) | ~ ! [X169 : term,X170 : subst,X172 : subst,X171 : subst] : (($true != ((X164 @ X171 @ X169 @ (comp @ X170 @ X172)))) | (((X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) = $true)) | ~ ! [X179 : subst,X180 : subst,X181 : term,X178 : subst] : (($true = ((X164 @ X178 @ X181 @ (comp @ X179 @ X180)))) | (((X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180)) != $true)) | ~ ! [X166 : term] : ((((X164 @ id @ X166 @ id)) = $true) | ($true != ((var @ (sub @ X166 @ id))))) | ~ ! [X168 : term,X167 : term] : (($true != ((X164 @ id @ X167 @ id))) | ($true = ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id))) | ($true != ((X164 @ id @ X168 @ id))))))))) & (! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) <=> (apinj2 = $true)) & ((! [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) = X521) => (! [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) = X524) => ! [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true != ((X529 @ X526))) | ($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))))) <=> (pushprop_lem1_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (! [X277 : term,X276 : term,X275 : (subst > term > subst > $o)] : (~ ! [X283 : term,X282 : term] : ((((X275 @ id @ X283 @ id)) != $true) | ($true != ((X275 @ id @ X282 @ id))) | ($true = ((X275 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id)))) | ($true = ((X275 @ id @ (ap @ X277 @ X276) @ id))) | ~ ! [X285 : subst,X287 : subst,X286 : subst,X284 : term] : ((((X275 @ (comp @ X287 @ X285) @ (sub @ X284 @ X285) @ X286)) = $true) | ($true != ((X275 @ X287 @ X284 @ (comp @ X285 @ X286))))) | ($true != ((X275 @ id @ X276 @ id))) | ~ ! [X280 : subst,X278 : subst,X279 : term,X281 : subst] : (($true = ((X275 @ X278 @ X279 @ (comp @ X280 @ X281)))) | (((X275 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280) @ X281)) != $true)) | ($true != ((X275 @ id @ X277 @ id)))) <=> (hoasinduction_lem2 = $true)) & (! [X518 : (subst > term > subst > $o)] : ~ ! [X519 : (term > $o)] : ~ ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X229 : subst,X228 : term] : (((sub @ one @ (push @ X228 @ X229))) = X228) => ! [X232 : (term > $o),X230 : term,X231 : (term > $o),X233 : subst] : ((((X232 @ one)) = $true) | ~ ! [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) = ((X232 @ X234))) | (((X231 @ X230)) != $true)))) & (induction2lem_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X331 : (term > $o),X332 : (subst > term > subst > $o),X330 : term] : (~ ! [X335 : (subst > term > term)] : (~ ! [X336 : term,X338 : subst,X337 : subst] : (((X335 @ (comp @ X337 @ X338) @ (sub @ X336 @ X338))) = ((sub @ (X335 @ X337 @ X336) @ X338))) | (((X332 @ id @ (lam @ (X335 @ sh @ one)) @ id)) = $true) | ~ ! [X339 : term] : ((((X332 @ id @ X339 @ id)) != $true) | ($true = ((X332 @ id @ (X335 @ id @ X339) @ id))))) | ~ ! [X333 : term] : (((X331 @ X333)) = ((X332 @ id @ X333 @ id))) | (((X331 @ (lam @ X330))) = $true) | ~ ! [X334 : term] : (($true = ((X331 @ (sub @ X330 @ (push @ X334 @ id))))) | ($true != ((X331 @ X334)))))) & (hoasinduction_lem1_gthm = $true) & ((axvarcons = $true) <=> ! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4)) & (termmset_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X225 : subst] : (((comp @ X225 @ id)) = X225) <=> (axidr = $true)) & (axclos = $true) & (ulamvarsh = $true) & ((hoasapinj1_lthm = $true) <=> (! [X321 : term] : (((sub @ X321 @ id)) = X321) => (! [X323 : term,X325 : term,X322 : term,X324 : term] : ((((ap @ X323 @ X322)) != ((ap @ X324 @ X325))) | (X323 = X324)) => ! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X470 : (subst > term > subst > $o)] : ~ ! [X471 : (term > $o)] : ~ ! [X472 : term] : (((X470 @ id @ X472 @ id)) = ((X471 @ X472))) => (! [X474 : term,X473 : (term > $o)] : (~ ! [X478 : term] : (~ ! [X479 : term] : (($true = ((X473 @ (sub @ X478 @ (push @ X479 @ id))))) | (((X473 @ X479)) != $true)) | (((X473 @ (lam @ X478))) = $true)) | (((X473 @ X474)) = $true) | ~ ! [X477 : term] : (($true != ((var @ X477))) | (((X473 @ X477)) = $true)) | ~ ! [X476 : term,X475 : term] : ((((X473 @ (ap @ X475 @ X476))) = $true) | ($true != ((X473 @ X476))) | (((X473 @ X475)) != $true))) => (! [X480 : term] : (((sub @ X480 @ id)) = X480) => (! [X483 : (term > $o),X481 : (subst > term > subst > $o),X482 : term] : (~ ! [X490 : term] : (((X481 @ id @ X490 @ id)) = ((X483 @ X490))) | ($true = ((X483 @ (lam @ X482)))) | ~ ! [X489 : term] : ((((X483 @ X489)) != $true) | (((X483 @ (sub @ X482 @ (push @ X489 @ id)))) = $true)) | ~ ! [X484 : (subst > term > term)] : (~ ! [X485 : term,X487 : subst,X486 : subst] : (((X484 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487))) = ((sub @ (X484 @ X486 @ X485) @ X487))) | ($true = ((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id))) | ~ ! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ($true != ((X481 @ id @ X488 @ id)))))) => ! [X491 : term,X492 : (subst > term > subst > $o)] : (~ ! [X501 : term,X502 : term] : ((((X492 @ id @ (ap @ (sub @ X501 @ id) @ X502) @ id)) = $true) | (((X492 @ id @ X501 @ id)) != $true) | (((X492 @ id @ X502 @ id)) != $true)) | ~ ! [X500 : subst,X497 : term,X498 : subst,X499 : subst] : ((((X492 @ (comp @ X499 @ X500) @ (sub @ X497 @ X500) @ X498)) != $true) | (((X492 @ X499 @ X497 @ (comp @ X500 @ X498))) = $true)) | (((X492 @ id @ X491 @ id)) = $true) | ~ ! [X503 : term] : ((((X492 @ id @ X503 @ id)) = $true) | ($true != ((var @ (sub @ X503 @ id))))) | ~ ! [X504 : (subst > term > term)] : ((((X492 @ id @ (lam @ (X504 @ sh @ one)) @ id)) = $true) | ~ ! [X505 : term] : (($true = ((X492 @ id @ (X504 @ id @ X505) @ id))) | (((X492 @ id @ X505 @ id)) != $true)) | ~ ! [X506 : subst,X507 : subst,X508 : term] : (((X504 @ (comp @ X507 @ X506) @ (sub @ X508 @ X506))) = ((sub @ (X504 @ X507 @ X508) @ X506)))) | ~ ! [X495 : subst,X494 : term,X493 : subst,X496 : subst] : ((((X492 @ X493 @ X494 @ (comp @ X495 @ X496))) != $true) | (((X492 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)) = $true)))))))) & (hoasapnotvar = $true) & ((! [X32 : term] : ~ ! [X33 : (subst > term > term)] : ~ ! [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) = ((X33 @ X35 @ X34))) => (! [X36 : term] : (((sub @ X36 @ id)) = X36) => ! [X37 : (subst > term > subst > $o),X38 : term,X39 : (term > $o)] : (~ ! [X41 : term] : (((X37 @ id @ X41 @ id)) = ((X39 @ X41))) | (((X39 @ (lam @ X38))) = $true) | ~ ! [X42 : (subst > term > term)] : ((((X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) = $true) | ~ ! [X43 : term] : (($true = ((X37 @ id @ (X42 @ id @ X43) @ id))) | (((X37 @ id @ X43 @ id)) != $true)) | ~ ! [X44 : term,X46 : subst,X45 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45)))) | ~ ! [X40 : term] : ((((X39 @ (sub @ X38 @ (push @ X40 @ id)))) = $true) | ($true != ((X39 @ X40))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((! [X92 : term] : (((sub @ X92 @ id)) = X92) => (! [X93 : term,X94 : (subst > term > subst > $o)] : ((((X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X96 : (subst > term > term)] : (~ ! [X100 : term] : (($true != ((X94 @ id @ X100 @ id))) | (((X94 @ id @ (X96 @ id @ X100) @ id)) = $true)) | ~ ! [X97 : term,X99 : subst,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X96 @ X99 @ X97) @ X98))) | (((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true)) | ~ ! [X95 : term] : (($true = ((X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id))) | (((X94 @ id @ X95 @ id)) != $true))) => ! [X102 : term,X101 : (subst > term > subst > $o)] : (~ ! [X114 : term,X113 : subst,X116 : subst,X115 : subst] : (($true = ((X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115))) | (((X101 @ X113 @ X114 @ (comp @ X116 @ X115))) != $true)) | ~ ! [X105 : term,X106 : subst,X104 : subst,X107 : subst] : ((((X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) != $true) | ($true = ((X101 @ X107 @ X105 @ (comp @ X106 @ X104))))) | (((X101 @ id @ (lam @ X102) @ id)) = $true) | ~ ! [X108 : (subst > term > term)] : ((((X101 @ id @ (lam @ (X108 @ sh @ one)) @ id)) = $true) | ~ ! [X111 : term,X110 : subst,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112)))) | ~ ! [X109 : term] : ((((X101 @ id @ (X108 @ id @ X109) @ id)) = $true) | (((X101 @ id @ X109 @ id)) != $true))) | ~ ! [X103 : term] : ((((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id)) = $true) | ($true != ((X101 @ id @ X103 @ id))))))) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = sh) & ((termmset_lthm = $true) <=> (! [X117 : term] : (((sub @ X117 @ id)) = X117) => ! [X118 : term] : (((sub @ X118 @ id)) = X118))) & ! [X182 : d_term] : (d_one = X182) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) <=> (laminj = $true)) & (axmap = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (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)))))))))))))) & ((axidl = $true) <=> ! [X318 : subst] : (((comp @ id @ X318)) = X318)) & (hoasinduction_lem3b_gthm = $true) & (((d2term @ d_one)) = one) & ! [X355 : d_subst] : (d_id = X355) & (! [X19 : (term > $o),X18 : term] : (~ ! [X24 : term,X23 : term] : ((((X19 @ (ap @ X24 @ X23))) = $true) | ($true != ((X19 @ X23))) | (((X19 @ X24)) != $true)) | ~ ! [X21 : term] : (~ ! [X22 : term] : ((((X19 @ (sub @ X21 @ (push @ X22 @ id)))) = $true) | (((X19 @ X22)) != $true)) | (((X19 @ (lam @ X21))) = $true)) | (((X19 @ X18)) = $true) | ~ ! [X20 : term] : ((((X19 @ X20)) = $true) | ($true != ((var @ X20))))) <=> (induction2 = $true)) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> (apinj1 = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X28 : subst,X29 : (term > $o),X30 : (term > $o),X27 : term] : (($true != ((X30 @ X27))) | ~ ! [X31 : term] : (((X29 @ X31)) = ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))) | ($true = ((X29 @ one)))) <=> (pushprop_lem1v2 = $true)) & (hoasapinj1_gthm = $true) & (! [X439 : term,X438 : (subst > term > subst > $o)] : (~ ! [X449 : term] : ((((X438 @ id @ (sub @ X439 @ (push @ X449 @ id)) @ id)) = $true) | (((X438 @ id @ X449 @ id)) != $true)) | (((X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X441 : (subst > term > term),X440 : term] : (~ ! [X448 : term] : ((((X438 @ id @ (X441 @ id @ X448) @ id)) = $true) | (((X438 @ id @ X448 @ id)) != $true)) | ~ ! [X444 : term,X443 : subst,X442 : subst] : (((X441 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443))) = ((sub @ X440 @ (push @ (sub @ X444 @ X443) @ (comp @ X442 @ X443))))) | ~ ! [X446 : subst,X447 : subst,X445 : term] : (((sub @ (sub @ X440 @ (push @ X445 @ X446)) @ X447)) = ((sub @ (X441 @ X446 @ X445) @ X447))) | (((X438 @ id @ (lam @ (X441 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (lamnotvar = $true) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X120 : (term > $o),X119 : term] : (~ ! [X121 : term] : (($true != ((X120 @ X121))) | (((X120 @ (lam @ X121))) = $true)) | ~ ! [X123 : term,X122 : term] : ((((X120 @ X122)) != $true) | (((X120 @ X123)) != $true) | ($true = ((X120 @ (ap @ X122 @ X123))))) | ~ ! [X124 : term] : ((((X120 @ X124)) = $true) | (((var @ X124)) != $true)) | (((X120 @ X119)) = $true)) <=> (induction = $true)) & (induction2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X451 : term,X450 : (subst > term > subst > $o)] : (~ ! [X452 : term] : (($true != ((X450 @ id @ X452 @ id))) | ($true = ((X450 @ id @ (sub @ X451 @ (push @ X452 @ id)) @ id)))) | ~ ! [X453 : (subst > term > term)] : (~ ! [X455 : subst,X456 : subst,X457 : term] : (((sub @ (X453 @ X455 @ X457) @ X456)) = ((X453 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456)))) | ~ ! [X454 : term] : ((((X450 @ id @ X454 @ id)) != $true) | (((X450 @ id @ (X453 @ id @ X454) @ id)) = $true)) | (((X450 @ id @ (lam @ (X453 @ sh @ one)) @ id)) = $true)) | (((X450 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & (! [X510 : (subst > term > subst > $o),X509 : term] : (~ ! [X513 : (subst > term > term)] : (~ ! [X514 : term] : ((((X510 @ id @ (X513 @ id @ X514) @ id)) = $true) | (((X510 @ id @ X514 @ id)) != $true)) | ~ ! [X515 : term,X516 : subst,X517 : subst] : (((sub @ (X513 @ X517 @ X515) @ X516)) = ((X513 @ (comp @ X517 @ X516) @ (sub @ X515 @ X516)))) | ($true = ((X510 @ id @ (lam @ (X513 @ sh @ one)) @ id)))) | ~ ! [X512 : term,X511 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) = $true) | (((X510 @ id @ X512 @ id)) != $true) | (((X510 @ id @ X511 @ id)) != $true)) | ($true = ((X510 @ id @ X509 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X268 : term,X267 : (subst > term > subst > $o)] : (~ ! [X270 : (subst > term > term)] : (~ ! [X274 : subst,X272 : term,X273 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273)))) | ~ ! [X271 : term] : ((((X267 @ id @ (X270 @ id @ X271) @ id)) = $true) | ($true != ((X267 @ id @ X271 @ id)))) | (((X267 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true)) | (((X267 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X269 : term] : ((((X267 @ id @ X269 @ id)) != $true) | (((X267 @ id @ (sub @ X268 @ (push @ X269 @ id)) @ id)) = $true)))) & (! [X417 : term] : ~ ! [X418 : (subst > term > term)] : (((X418 @ sh @ one)) != ((sub @ X417 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem2_lthm = $true) & (! [X412 : term,X411 : (subst > term > term),X413 : term] : ((((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412))) | ~ ! [X414 : subst,X416 : term,X415 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) = ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414))))) <=> (hoaslamnotap = $true)) & ((termmset = $true) <=> ! [X462 : term] : (((sub @ X462 @ id)) = X462)) & (((d2subst @ d_id)) = id) & (hoasapnotvar_gthm = $true) & (! [X357 : term,X358 : (term > $o),X356 : (subst > term > subst > $o)] : (($true = ((X358 @ (lam @ X357)))) | ~ ! [X359 : (subst > term > term)] : (~ ! [X362 : subst,X363 : term,X361 : subst] : (((sub @ (X359 @ X361 @ X363) @ X362)) = ((X359 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362)))) | ~ ! [X360 : term] : ((((X356 @ id @ (X359 @ id @ X360) @ id)) = $true) | (((X356 @ id @ X360 @ id)) != $true)) | (((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id)) = $true)) | ~ ! [X368 : term,X369 : subst,X371 : subst,X370 : subst] : ((((X356 @ (comp @ X370 @ X369) @ (sub @ X368 @ X369) @ X371)) = $true) | (((X356 @ X370 @ X368 @ (comp @ X369 @ X371))) != $true)) | ~ ! [X372 : term] : ((((X358 @ (sub @ X357 @ (push @ X372 @ id)))) = $true) | (((X358 @ X372)) != $true)) | ~ ! [X373 : term] : (((X358 @ X373)) = ((X356 @ id @ X373 @ id))) | ~ ! [X365 : term,X367 : subst,X364 : subst,X366 : subst] : (($true != ((X356 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X367))) | (((X356 @ X364 @ X365 @ (comp @ X366 @ X367))) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (! [X532 : term] : ~ ! [X533 : (subst > term > term)] : ~ ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535))) <=> (hoasinduction_lem3v2_f = $true)) & (lamnotap != $true) & (! [X310 : (subst > term > term),X308 : subst,X309 : (subst > term > term),X311 : term] : (~ ! [X315 : term,X316 : subst,X317 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) = ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | (((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one)))) | ~ ! [X313 : subst,X312 : term,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) = ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314))))) <=> (hoaslaminj = $true)) & (hoasinduction_lem2_gthm = $true) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & (hoasinduction_gthm = $true) & (! [X184 : term,X183 : (subst > term > subst > $o)] : ((((X183 @ id @ X184 @ id)) = $true) | ~ ! [X191 : term,X190 : term] : ((((X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) = $true) | ($true != ((X183 @ id @ X190 @ id))) | ($true != ((X183 @ id @ X191 @ id)))) | ~ ! [X185 : term] : (($true = ((X183 @ id @ X185 @ id))) | ($true != ((var @ (sub @ X185 @ id))))) | ~ ! [X192 : term,X194 : subst,X195 : subst,X193 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) = $true) | (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) != $true)) | ~ ! [X187 : subst,X189 : subst,X186 : term,X188 : subst] : ((((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) = $true) | (((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) != $true)) | ~ ! [X196 : (subst > term > term)] : (~ ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200)))) | ~ ! [X197 : term] : ((((X183 @ id @ X197 @ id)) != $true) | (((X183 @ id @ (X196 @ id @ X197) @ id)) = $true)) | ($true = ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id))))) <=> (hoasinduction = $true)) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X201 : (term > $o),X202 : subst,X203 : term] : (~ ! [X205 : term] : ((((X201 @ (lam @ X205))) = $true) | ~ ! [X206 : term] : ((((X201 @ (sub @ X205 @ (push @ X206 @ id)))) = $true) | ($true != ((X201 @ X206))))) | (((X201 @ (sub @ X203 @ X202))) = $true) | ~ ! [X204 : term] : ((((var @ X204)) != $true) | (((X201 @ (sub @ X204 @ X202))) = $true)) | ~ ! [X207 : term,X208 : term] : ((((X201 @ (ap @ X208 @ X207))) = $true) | (((X201 @ X207)) != $true) | (((X201 @ X208)) != $true))) <=> (induction2lem = $true)) & ((! [X251 : term,X252 : subst] : (((sub @ one @ (push @ X251 @ X252))) = X251) => (! [X253 : term,X254 : subst] : (((comp @ sh @ (push @ X253 @ X254))) = X254) => (! [X256 : term,X255 : term] : ((X255 = X256) | (((lam @ X256)) != ((lam @ X255)))) => ! [X257 : subst,X258 : (subst > term > term),X259 : term,X260 : (subst > term > term)] : ((((X258 @ X257 @ X259)) = ((X260 @ X257 @ X259))) | ~ ! [X263 : term,X261 : subst,X262 : subst] : (((X258 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262))) = ((sub @ (X258 @ X261 @ X263) @ X262))) | ~ ! [X264 : subst,X265 : term,X266 : subst] : (((sub @ (X260 @ X266 @ X265) @ X264)) = ((X260 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264)))) | (((lam @ (X258 @ sh @ one))) != ((lam @ (X260 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true)), 50.81/8.71 inference(flattening,[],[f9])). 50.81/8.71 thf(f11,plain,( 50.81/8.71 (hoasinduction = $true) <~> ! [X0 : (subst > term > subst > $o)] : (((((! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | ? [X12 : (subst > term > term)] : (((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true) & ! [X16 : term] : ((((X0 @ id @ (X12 @ id @ X16) @ id)) = $true) | (((X0 @ id @ X16 @ id)) != $true))) & ! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))))) | ? [X11 : term,X10 : term] : (((((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)) != $true) & (((X0 @ id @ X10 @ id)) = $true)) & ($true = ((X0 @ id @ X11 @ id))))) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true))) | ? [X7 : subst,X8 : term,X6 : subst,X5 : subst] : ((((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) != $true) & ($true = ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6))))) | ? [X3 : term,X1 : subst,X2 : subst,X4 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) != $true)))), 50.81/8.71 inference(ennf_transformation,[],[f8])). 50.81/8.71 thf(f12,plain,( 50.81/8.71 (hoasinduction = $true) <~> ! [X0 : (subst > term > subst > $o)] : (? [X7 : subst,X8 : term,X6 : subst,X5 : subst] : ((((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) != $true) & ($true = ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6)))) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true)) | ? [X3 : term,X1 : subst,X2 : subst,X4 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) != $true)) | ? [X10 : term,X11 : term] : (($true = ((X0 @ id @ X11 @ id))) & (((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)) != $true) & (((X0 @ id @ X10 @ id)) = $true)) | ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | ? [X12 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true) & ! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))) & ! [X16 : term] : ((((X0 @ id @ (X12 @ id @ X16) @ id)) = $true) | (((X0 @ id @ X16 @ id)) != $true))))), 50.81/8.71 inference(flattening,[],[f11])). 50.81/8.71 thf(f13,plain,( 50.81/8.71 (hoasapinj2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X299 : term,X300 : (subst > term > subst > $o)] : (? [X301 : term] : ((((X300 @ id @ (sub @ X299 @ (push @ X301 @ id)) @ id)) != $true) & ($true = ((X300 @ id @ X301 @ id)))) | (((X300 @ id @ (lam @ X299) @ id)) = $true) | ? [X302 : (subst > term > term)] : (! [X306 : term] : (($true = ((X300 @ id @ (X302 @ id @ X306) @ id))) | (((X300 @ id @ X306 @ id)) != $true)) & (((X300 @ id @ (lam @ (X302 @ sh @ one)) @ id)) != $true) & ! [X305 : subst,X303 : subst,X304 : term] : (((sub @ (X302 @ X303 @ X304) @ X305)) = ((X302 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))))) | ? [X291 : (subst > term > subst > $o),X292 : term] : (! [X298 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X298 @ id)) @ id)) = $true) | (((X291 @ id @ X298 @ id)) != $true)) & ! [X293 : (subst > term > term)] : (? [X297 : term] : ((((X291 @ id @ (X293 @ id @ X297) @ id)) != $true) & (((X291 @ id @ X297 @ id)) = $true)) | (((X291 @ id @ (lam @ (X293 @ sh @ one)) @ id)) = $true) | ? [X295 : subst,X296 : term,X294 : subst] : (((sub @ (X293 @ X295 @ X296) @ X294)) != ((X293 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))))) & (((X291 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id)) != $true))) | ? [X290 : term] : (((sub @ X290 @ id)) != X290))) & ((shinj = $true) <=> ! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26))) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) <=> ((! [X219 : term,X218 : (term > $o)] : (? [X224 : term,X223 : term] : (($true = ((X218 @ X223))) & (((X218 @ (ap @ X223 @ X224))) != $true) & (((X218 @ X224)) = $true)) | ? [X220 : term] : (($true != ((X218 @ X220))) & (((var @ X220)) = $true)) | (((X218 @ X219)) = $true) | ? [X221 : term] : (! [X222 : term] : (($true != ((X218 @ X222))) | (((X218 @ (sub @ X221 @ (push @ X222 @ id)))) = $true)) & (((X218 @ (lam @ X221))) != $true))) | ? [X211 : (term > $o),X210 : subst,X212 : term] : (! [X215 : term] : (($true = ((X211 @ (sub @ X215 @ X210)))) | ($true != ((var @ X215)))) & ! [X213 : term] : ((((X211 @ (lam @ X213))) = $true) | ? [X214 : term] : ((((X211 @ X214)) = $true) & ($true != ((X211 @ (sub @ X213 @ (push @ X214 @ id))))))) & (((X211 @ (sub @ X212 @ X210))) != $true) & ! [X217 : term,X216 : term] : (($true = ((X211 @ (ap @ X216 @ X217)))) | (((X211 @ X216)) != $true) | (((X211 @ X217)) != $true)))) | ? [X209 : term] : (((sub @ X209 @ id)) != X209))) & ((substmonoid_lthm = $true) <=> (((! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3)) | ? [X1 : subst] : (((comp @ X1 @ id)) != X1)) | ? [X0 : subst] : (((comp @ id @ X0)) != X0))) & (hoasinduction_lem3_gthm = $true) & ((axvarid = $true) <=> ! [X61 : term] : (((sub @ X61 @ id)) = X61)) & (! [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | (((X409 @ X407)) != $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X53 : term] : ? [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) = ((X54 @ sh @ one)))) & (pushprop_lem0_gthm = $true) & (! [X375 : subst,X376 : term,X374 : (term > $o)] : ? [X377 : (term > $o)] : ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378))) <=> (pushprop_lem0_lthm = $true)) & (((((! [X84 : term,X83 : (subst > term > subst > $o)] : (? [X90 : term,X91 : term] : ((((X83 @ id @ X91 @ id)) = $true) & ($true != ((X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id))) & (((X83 @ id @ X90 @ id)) = $true)) | ($true = ((X83 @ id @ X84 @ id))) | ? [X85 : (subst > term > term)] : ((((X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) != $true) & ! [X86 : term] : ((((X83 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X83 @ id @ X86 @ id)) != $true)) & ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88)))))) | ? [X75 : (subst > term > subst > $o),X74 : term,X73 : (term > $o)] : (! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) & (((X73 @ (lam @ X74))) != $true) & ! [X76 : (subst > term > term)] : (? [X77 : term] : ((((X75 @ id @ (X76 @ id @ X77) @ id)) != $true) & (((X75 @ id @ X77 @ id)) = $true)) | (((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ? [X80 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) != ((sub @ (X76 @ X78 @ X79) @ X80)))) & ! [X81 : term] : ((((X73 @ X81)) != $true) | ($true = ((X73 @ (sub @ X74 @ (push @ X81 @ id)))))))) | ? [X72 : term] : (((sub @ X72 @ id)) != X72)) | ? [X66 : (term > $o),X65 : term] : (! [X67 : term] : (($true = ((X66 @ (lam @ X67)))) | ? [X68 : term] : ((((X66 @ X68)) = $true) & (((X66 @ (sub @ X67 @ (push @ X68 @ id)))) != $true))) & ! [X69 : term,X70 : term] : (($true != ((X66 @ X69))) | (((X66 @ X70)) != $true) | (((X66 @ (ap @ X69 @ X70))) = $true)) & ! [X71 : term] : (($true = ((X66 @ X71))) | (((var @ X71)) != $true)) & (((X66 @ X65)) != $true))) | ? [X62 : (subst > term > subst > $o)] : ! [X63 : (term > $o)] : ? [X64 : term] : (((X63 @ X64)) != ((X62 @ id @ X64 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (pushprop = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axshiftcons = $true) <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & (! [X235 : term,X236 : (subst > term > subst > $o)] : (? [X241 : subst,X239 : subst,X238 : subst,X240 : term] : ((((X236 @ X241 @ X240 @ (comp @ X238 @ X239))) = $true) & (((X236 @ (comp @ X241 @ X238) @ (sub @ X240 @ X238) @ X239)) != $true)) | ($true = ((X236 @ id @ (lam @ X235) @ id))) | ? [X237 : term] : ((((X236 @ id @ (sub @ X235 @ (push @ X237 @ id)) @ id)) != $true) & ($true = ((X236 @ id @ X237 @ id)))) | ? [X242 : (subst > term > term)] : (! [X246 : term] : ((((X236 @ id @ (X242 @ id @ X246) @ id)) = $true) | ($true != ((X236 @ id @ X246 @ id)))) & (((X236 @ id @ (lam @ (X242 @ sh @ one)) @ id)) != $true) & ! [X244 : subst,X243 : term,X245 : subst] : (((sub @ (X242 @ X245 @ X243) @ X244)) = ((X242 @ (comp @ X245 @ X244) @ (sub @ X243 @ X244))))) | ? [X250 : subst,X247 : subst,X249 : subst,X248 : term] : (($true != ((X236 @ X250 @ X248 @ (comp @ X249 @ X247)))) & (((X236 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249) @ X247)) = $true))) <=> (hoasinduction_lem3 = $true)) & (((((! [X391 : (term > $o),X392 : term,X390 : subst] : ((((X391 @ (sub @ X392 @ X390))) = $true) | ? [X397 : term,X396 : term] : ((((X391 @ X397)) = $true) & (((X391 @ X396)) = $true) & (((X391 @ (ap @ X396 @ X397))) != $true)) | ? [X393 : term] : ((((var @ X393)) = $true) & (((X391 @ (sub @ X393 @ X390))) != $true)) | ? [X394 : term] : ((((X391 @ (lam @ X394))) != $true) & ! [X395 : term] : ((((X391 @ (sub @ X394 @ (push @ X395 @ id)))) = $true) | (((X391 @ X395)) != $true)))) | ? [X384 : term,X385 : (term > $o)] : ((((X385 @ X384)) != $true) & ! [X389 : term] : (($true = ((X385 @ (lam @ X389)))) | ($true != ((X385 @ X389)))) & ! [X388 : term,X387 : term] : ((((X385 @ (ap @ X387 @ X388))) = $true) | (((X385 @ X388)) != $true) | (((X385 @ X387)) != $true)) & ! [X386 : term] : ((((var @ X386)) != $true) | ($true = ((X385 @ X386)))))) | ? [X383 : subst] : (((comp @ X383 @ id)) != X383)) | ? [X381 : term,X382 : subst] : (((comp @ sh @ (push @ X381 @ X382))) != X382)) | ? [X380 : term,X379 : subst] : (((sub @ one @ (push @ X380 @ X379))) != X380)) <=> (induction2lem_lthm = $true)) & (hoasapnotvar_lthm = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ! [X288 : d_term,X289 : d_term] : ((X288 = X289) | (((d2term @ X288)) != ((d2term @ X289)))) & ((pushprop_lem0 = $true) <=> ! [X467 : (term > $o),X465 : term,X466 : subst] : ? [X468 : (term > $o)] : ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469)))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasapinj1 = $true) <=> ! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7))))) & (apnotvar = $true) & ((hoasapinj2_lthm = $true) <=> (! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))) | ? [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) = ((ap @ X399 @ X398))) & (X398 != X401)))) & ((axscons = $true) <=> ! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307)) & (hoaslamnotap_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj2 = $true) <=> ! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axapp = $true) & (! [X342 : (term > $o),X340 : term,X341 : term,X343 : (subst > term > subst > $o)] : ((((X342 @ (ap @ X340 @ X341))) = $true) | (((X342 @ X340)) != $true) | ? [X350 : term,X348 : subst,X347 : subst,X349 : subst] : ((((X343 @ (comp @ X348 @ X347) @ (sub @ X350 @ X347) @ X349)) = $true) & (((X343 @ X348 @ X350 @ (comp @ X347 @ X349))) != $true)) | ? [X345 : term,X346 : term] : ((((X343 @ id @ X345 @ id)) = $true) & ($true = ((X343 @ id @ X346 @ id))) & (((X343 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id)) != $true)) | ? [X344 : term] : (((X342 @ X344)) != ((X343 @ id @ X344 @ id))) | (((X342 @ X341)) != $true) | ? [X351 : term,X353 : subst,X354 : subst,X352 : subst] : ((((X343 @ (comp @ X354 @ X352) @ (sub @ X351 @ X352) @ X353)) != $true) & (((X343 @ X354 @ X351 @ (comp @ X352 @ X353))) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id)))) & (hoasinduction_lem1v2_gthm = $true) & (! [X536 : term] : ? [X537 : (subst > term > term)] : ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ! [X227 : d_subst,X226 : d_subst] : ((X226 = X227) | (((d2subst @ X226)) != ((d2subst @ X227)))) & (ulamvarind = $true) & (((var @ (d2term @ d_one))) != $true) & ((? [X419 : term] : (((sub @ X419 @ id)) != X419) | ! [X422 : term,X421 : (term > $o),X420 : (subst > term > subst > $o)] : (? [X433 : (subst > term > term)] : (! [X434 : term] : (($true = ((X420 @ id @ (X433 @ id @ X434) @ id))) | (((X420 @ id @ X434 @ id)) != $true)) & (((X420 @ id @ (lam @ (X433 @ sh @ one)) @ id)) != $true) & ! [X437 : subst,X436 : subst,X435 : term] : (((X433 @ (comp @ X437 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X437 @ X435) @ X436)))) | ? [X428 : term] : (((X420 @ id @ X428 @ id)) != ((X421 @ X428))) | ? [X427 : term] : ((((X421 @ (sub @ X422 @ (push @ X427 @ id)))) != $true) & (((X421 @ X427)) = $true)) | ? [X432 : subst,X430 : subst,X431 : term,X429 : subst] : ((((X420 @ (comp @ X429 @ X430) @ (sub @ X431 @ X430) @ X432)) = $true) & ($true != ((X420 @ X429 @ X431 @ (comp @ X430 @ X432))))) | ? [X423 : term,X425 : subst,X426 : subst,X424 : subst] : ((((X420 @ (comp @ X425 @ X426) @ (sub @ X423 @ X426) @ X424)) != $true) & (((X420 @ X425 @ X423 @ (comp @ X426 @ X424))) = $true)) | (((X421 @ (lam @ X422))) = $true))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X10 : (subst > term > subst > $o),X11 : term] : ((((X10 @ id @ (lam @ X11) @ id)) = $true) | ? [X12 : (subst > term > term)] : (! [X13 : term] : ((((X10 @ id @ X13 @ id)) != $true) | (((X10 @ id @ (X12 @ id @ X13) @ id)) = $true)) & (((X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) != $true) & ! [X16 : subst,X14 : term,X15 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15))))) | ? [X17 : term] : (($true = ((X10 @ id @ X17 @ id))) & (((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) != $true)))) & ((hoasinduction_lthm = $true) <=> (((! [X164 : (subst > term > subst > $o),X165 : term] : (? [X173 : (subst > term > term)] : (! [X177 : term] : ((((X164 @ id @ X177 @ id)) != $true) | ($true = ((X164 @ id @ (X173 @ id @ X177) @ id)))) & (((X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X176 : subst,X175 : term,X174 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174)))) | (((X164 @ id @ X165 @ id)) = $true) | ? [X166 : term] : (($true = ((var @ (sub @ X166 @ id)))) & (((X164 @ id @ X166 @ id)) != $true)) | ? [X171 : subst,X169 : term,X172 : subst,X170 : subst] : (($true = ((X164 @ X171 @ X169 @ (comp @ X170 @ X172)))) & (((X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) != $true)) | ? [X180 : subst,X178 : subst,X179 : subst,X181 : term] : (($true != ((X164 @ X178 @ X181 @ (comp @ X179 @ X180)))) & (((X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180)) = $true)) | ? [X168 : term,X167 : term] : (($true = ((X164 @ id @ X167 @ id))) & ($true != ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id))) & ($true = ((X164 @ id @ X168 @ id))))) | ? [X149 : (subst > term > subst > $o),X148 : term] : (($true != ((X149 @ id @ (lam @ X148) @ id))) & ! [X155 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ? [X159 : term,X158 : subst,X157 : subst] : (((sub @ (X155 @ X157 @ X159) @ X158)) != ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158)))) | ? [X156 : term] : (($true != ((X149 @ id @ (X155 @ id @ X156) @ id))) & (((X149 @ id @ X156 @ id)) = $true))) & ! [X150 : term] : ((((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true) | ($true != ((X149 @ id @ X150 @ id)))) & ! [X152 : term,X154 : subst,X151 : subst,X153 : subst] : (($true = ((X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153))) | (((X149 @ X154 @ X152 @ (comp @ X151 @ X153))) != $true)) & ! [X163 : subst,X160 : subst,X161 : subst,X162 : term] : ((((X149 @ X163 @ X162 @ (comp @ X160 @ X161))) = $true) | (((X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161)) != $true)))) | ? [X136 : (subst > term > subst > $o),X135 : term,X137 : term] : ((((X136 @ id @ (ap @ X135 @ X137) @ id)) != $true) & (((X136 @ id @ X135 @ id)) = $true) & ! [X146 : term,X147 : term] : ((((X136 @ id @ X147 @ id)) != $true) | (((X136 @ id @ X146 @ id)) != $true) | (((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id)) = $true)) & ! [X145 : subst,X143 : subst,X144 : subst,X142 : term] : ((((X136 @ X144 @ X142 @ (comp @ X145 @ X143))) = $true) | (((X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143)) != $true)) & ! [X141 : subst,X138 : term,X139 : subst,X140 : subst] : ((((X136 @ X141 @ X138 @ (comp @ X139 @ X140))) != $true) | ($true = ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140)))) & (((X136 @ id @ X137 @ id)) = $true))) | ? [X128 : term,X129 : (term > $o)] : (($true != ((X129 @ X128))) & ! [X132 : term] : ((((X129 @ (lam @ X132))) = $true) | ? [X133 : term] : ((((X129 @ (sub @ X132 @ (push @ X133 @ id)))) != $true) & ($true = ((X129 @ X133))))) & ! [X130 : term,X131 : term] : ((((X129 @ X131)) != $true) | (((X129 @ (ap @ X131 @ X130))) = $true) | ($true != ((X129 @ X130)))) & ! [X134 : term] : ((((var @ X134)) != $true) | (((X129 @ X134)) = $true))))) & (! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) <=> (apinj2 = $true)) & (((! [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true != ((X529 @ X526))) | ($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) | ? [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) != X524)) | ? [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) != X521)) <=> (pushprop_lem1_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X277 : term,X275 : (subst > term > subst > $o),X276 : term] : (($true != ((X275 @ id @ X277 @ id))) | ? [X282 : term,X283 : term] : ((((X275 @ id @ X283 @ id)) = $true) & ($true != ((X275 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id))) & ($true = ((X275 @ id @ X282 @ id)))) | ? [X279 : term,X280 : subst,X278 : subst,X281 : subst] : (($true != ((X275 @ X278 @ X279 @ (comp @ X280 @ X281)))) & (((X275 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280) @ X281)) = $true)) | ? [X284 : term,X287 : subst,X285 : subst,X286 : subst] : ((((X275 @ (comp @ X287 @ X285) @ (sub @ X284 @ X285) @ X286)) != $true) & ($true = ((X275 @ X287 @ X284 @ (comp @ X285 @ X286))))) | ($true != ((X275 @ id @ X276 @ id))) | ($true = ((X275 @ id @ (ap @ X277 @ X276) @ id))))) & (! [X518 : (subst > term > subst > $o)] : ? [X519 : (term > $o)] : ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) != $true) | ? [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) != ((X232 @ X234))) | (((X232 @ one)) = $true)) | ? [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) != X228))) & (induction2lem_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & (! [X330 : term,X331 : (term > $o),X332 : (subst > term > subst > $o)] : (? [X333 : term] : (((X331 @ X333)) != ((X332 @ id @ X333 @ id))) | ? [X334 : term] : (($true = ((X331 @ X334))) & ($true != ((X331 @ (sub @ X330 @ (push @ X334 @ id)))))) | ? [X335 : (subst > term > term)] : (! [X339 : term] : ((((X332 @ id @ X339 @ id)) != $true) | ($true = ((X332 @ id @ (X335 @ id @ X339) @ id)))) & ! [X336 : term,X338 : subst,X337 : subst] : (((X335 @ (comp @ X337 @ X338) @ (sub @ X336 @ X338))) = ((sub @ (X335 @ X337 @ X336) @ X338))) & (((X332 @ id @ (lam @ (X335 @ sh @ one)) @ id)) != $true)) | (((X331 @ (lam @ X330))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem1_gthm = $true) & ((axvarcons = $true) <=> ! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4)) & (termmset_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X225 : subst] : (((comp @ X225 @ id)) = X225) <=> (axidr = $true)) & (axclos = $true) & (ulamvarsh = $true) & ((hoasapinj1_lthm = $true) <=> ((! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329)) | ? [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) = ((ap @ X324 @ X325))) & (X323 != X324))) | ? [X321 : term] : (((sub @ X321 @ id)) != X321))) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X492 : (subst > term > subst > $o),X491 : term] : (? [X501 : term,X502 : term] : ((((X492 @ id @ (ap @ (sub @ X501 @ id) @ X502) @ id)) != $true) & (((X492 @ id @ X502 @ id)) = $true) & (((X492 @ id @ X501 @ id)) = $true)) | ? [X499 : subst,X500 : subst,X498 : subst,X497 : term] : ((((X492 @ (comp @ X499 @ X500) @ (sub @ X497 @ X500) @ X498)) = $true) & (((X492 @ X499 @ X497 @ (comp @ X500 @ X498))) != $true)) | ? [X504 : (subst > term > term)] : (! [X505 : term] : (($true = ((X492 @ id @ (X504 @ id @ X505) @ id))) | (((X492 @ id @ X505 @ id)) != $true)) & (((X492 @ id @ (lam @ (X504 @ sh @ one)) @ id)) != $true) & ! [X506 : subst,X507 : subst,X508 : term] : (((X504 @ (comp @ X507 @ X506) @ (sub @ X508 @ X506))) = ((sub @ (X504 @ X507 @ X508) @ X506)))) | ? [X493 : subst,X495 : subst,X496 : subst,X494 : term] : ((((X492 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)) != $true) & (((X492 @ X493 @ X494 @ (comp @ X495 @ X496))) = $true)) | ? [X503 : term] : ((((X492 @ id @ X503 @ id)) != $true) & ($true = ((var @ (sub @ X503 @ id))))) | (((X492 @ id @ X491 @ id)) = $true)) | ? [X483 : (term > $o),X481 : (subst > term > subst > $o),X482 : term] : (($true != ((X483 @ (lam @ X482)))) & ! [X484 : (subst > term > term)] : (? [X487 : subst,X485 : term,X486 : subst] : (((X484 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487))) != ((sub @ (X484 @ X486 @ X485) @ X487))) | ($true = ((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id))) | ? [X488 : term] : (($true = ((X481 @ id @ X488 @ id))) & ($true != ((X481 @ id @ (X484 @ id @ X488) @ id))))) & ! [X489 : term] : ((((X483 @ X489)) != $true) | (((X483 @ (sub @ X482 @ (push @ X489 @ id)))) = $true)) & ! [X490 : term] : (((X481 @ id @ X490 @ id)) = ((X483 @ X490))))) | ? [X480 : term] : (((sub @ X480 @ id)) != X480)) | ? [X473 : (term > $o),X474 : term] : ((((X473 @ X474)) != $true) & ! [X478 : term] : ((((X473 @ (lam @ X478))) = $true) | ? [X479 : term] : (($true != ((X473 @ (sub @ X478 @ (push @ X479 @ id))))) & (((X473 @ X479)) = $true))) & ! [X477 : term] : (($true != ((var @ X477))) | (((X473 @ X477)) = $true)) & ! [X476 : term,X475 : term] : ((((X473 @ (ap @ X475 @ X476))) = $true) | ($true != ((X473 @ X476))) | (((X473 @ X475)) != $true)))) | ? [X470 : (subst > term > subst > $o)] : ! [X471 : (term > $o)] : ? [X472 : term] : (((X470 @ id @ X472 @ id)) != ((X471 @ X472))))) & (hoasapnotvar = $true) & (((! [X38 : term,X37 : (subst > term > subst > $o),X39 : (term > $o)] : (? [X41 : term] : (((X37 @ id @ X41 @ id)) != ((X39 @ X41))) | (((X39 @ (lam @ X38))) = $true) | ? [X42 : (subst > term > term)] : (! [X43 : term] : (($true = ((X37 @ id @ (X42 @ id @ X43) @ id))) | (((X37 @ id @ X43 @ id)) != $true)) & (((X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) != $true) & ! [X44 : term,X46 : subst,X45 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45)))) | ? [X40 : term] : (($true = ((X39 @ X40))) & (((X39 @ (sub @ X38 @ (push @ X40 @ id)))) != $true))) | ? [X36 : term] : (((sub @ X36 @ id)) != X36)) | ? [X32 : term] : ! [X33 : (subst > term > term)] : ? [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) != ((X33 @ X35 @ X34)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (((! [X102 : term,X101 : (subst > term > subst > $o)] : (? [X106 : subst,X105 : term,X104 : subst,X107 : subst] : ((((X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) = $true) & ($true != ((X101 @ X107 @ X105 @ (comp @ X106 @ X104))))) | (((X101 @ id @ (lam @ X102) @ id)) = $true) | ? [X103 : term] : ((((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id)) != $true) & ($true = ((X101 @ id @ X103 @ id)))) | ? [X108 : (subst > term > term)] : (! [X111 : term,X110 : subst,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112)))) & ! [X109 : term] : ((((X101 @ id @ (X108 @ id @ X109) @ id)) = $true) | (((X101 @ id @ X109 @ id)) != $true)) & (((X101 @ id @ (lam @ (X108 @ sh @ one)) @ id)) != $true)) | ? [X116 : subst,X114 : term,X115 : subst,X113 : subst] : ((((X101 @ X113 @ X114 @ (comp @ X116 @ X115))) = $true) & ($true != ((X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115))))) | ? [X93 : term,X94 : (subst > term > subst > $o)] : (! [X95 : term] : (($true = ((X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id))) | (((X94 @ id @ X95 @ id)) != $true)) & (((X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true) & ! [X96 : (subst > term > term)] : (? [X100 : term] : (($true = ((X94 @ id @ X100 @ id))) & (((X94 @ id @ (X96 @ id @ X100) @ id)) != $true)) | ? [X97 : term,X98 : subst,X99 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) != ((sub @ (X96 @ X99 @ X97) @ X98))) | (((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true)))) | ? [X92 : term] : (((sub @ X92 @ id)) != X92)) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = sh) & ((termmset_lthm = $true) <=> (! [X118 : term] : (((sub @ X118 @ id)) = X118) | ? [X117 : term] : (((sub @ X117 @ id)) != X117))) & ! [X182 : d_term] : (d_one = X182) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) <=> (laminj = $true)) & (axmap = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (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)))))))))))))) & ((axidl = $true) <=> ! [X318 : subst] : (((comp @ id @ X318)) = X318)) & (hoasinduction_lem3b_gthm = $true) & (((d2term @ d_one)) = one) & ! [X355 : d_subst] : (d_id = X355) & ((induction2 = $true) <=> ! [X19 : (term > $o),X18 : term] : ((((X19 @ X18)) = $true) | ? [X21 : term] : (! [X22 : term] : ((((X19 @ (sub @ X21 @ (push @ X22 @ id)))) = $true) | (((X19 @ X22)) != $true)) & (((X19 @ (lam @ X21))) != $true)) | ? [X24 : term,X23 : term] : ((((X19 @ (ap @ X24 @ X23))) != $true) & (((X19 @ X24)) = $true) & ($true = ((X19 @ X23)))) | ? [X20 : term] : ((((X19 @ X20)) != $true) & ($true = ((var @ X20)))))) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> (apinj1 = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem1v2 = $true) <=> ! [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true != ((X30 @ X27))) | ($true = ((X29 @ one))) | ? [X31 : term] : (((X29 @ X31)) != ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))))) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X439 : term,X438 : (subst > term > subst > $o)] : (? [X449 : term] : ((((X438 @ id @ X449 @ id)) = $true) & (((X438 @ id @ (sub @ X439 @ (push @ X449 @ id)) @ id)) != $true)) | ? [X441 : (subst > term > term),X440 : term] : (! [X444 : term,X443 : subst,X442 : subst] : (((X441 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443))) = ((sub @ X440 @ (push @ (sub @ X444 @ X443) @ (comp @ X442 @ X443))))) & (((X438 @ id @ (lam @ (X441 @ sh @ one)) @ id)) != $true) & ! [X446 : subst,X447 : subst,X445 : term] : (((sub @ (sub @ X440 @ (push @ X445 @ X446)) @ X447)) = ((sub @ (X441 @ X446 @ X445) @ X447))) & ! [X448 : term] : ((((X438 @ id @ (X441 @ id @ X448) @ id)) = $true) | (((X438 @ id @ X448 @ id)) != $true))) | (((X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id)) = $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (lamnotvar = $true) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & ((induction = $true) <=> ! [X119 : term,X120 : (term > $o)] : (? [X121 : term] : (($true = ((X120 @ X121))) & (((X120 @ (lam @ X121))) != $true)) | ? [X124 : term] : ((((var @ X124)) = $true) & (((X120 @ X124)) != $true)) | ? [X123 : term,X122 : term] : ((((X120 @ X123)) = $true) & (((X120 @ X122)) = $true) & ($true != ((X120 @ (ap @ X122 @ X123))))) | (((X120 @ X119)) = $true))) & (induction2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X450 : (subst > term > subst > $o),X451 : term] : ((((X450 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id)) = $true) | ? [X453 : (subst > term > term)] : (! [X455 : subst,X456 : subst,X457 : term] : (((sub @ (X453 @ X455 @ X457) @ X456)) = ((X453 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456)))) & ! [X454 : term] : ((((X450 @ id @ X454 @ id)) != $true) | (((X450 @ id @ (X453 @ id @ X454) @ id)) = $true)) & (((X450 @ id @ (lam @ (X453 @ sh @ one)) @ id)) != $true)) | ? [X452 : term] : (($true != ((X450 @ id @ (sub @ X451 @ (push @ X452 @ id)) @ id))) & ($true = ((X450 @ id @ X452 @ id))))) <=> (hoasinduction_lem3aa = $true)) & (! [X510 : (subst > term > subst > $o),X509 : term] : (? [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) != $true) & (((X510 @ id @ X512 @ id)) = $true) & (((X510 @ id @ X511 @ id)) = $true)) | ? [X513 : (subst > term > term)] : (($true != ((X510 @ id @ (lam @ (X513 @ sh @ one)) @ id))) & ! [X515 : term,X516 : subst,X517 : subst] : (((sub @ (X513 @ X517 @ X515) @ X516)) = ((X513 @ (comp @ X517 @ X516) @ (sub @ X515 @ X516)))) & ! [X514 : term] : ((((X510 @ id @ (X513 @ id @ X514) @ id)) = $true) | (((X510 @ id @ X514 @ id)) != $true))) | ($true = ((X510 @ id @ X509 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X267 : (subst > term > subst > $o),X268 : term] : (? [X269 : term] : ((((X267 @ id @ X269 @ id)) = $true) & (((X267 @ id @ (sub @ X268 @ (push @ X269 @ id)) @ id)) != $true)) | (((X267 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id)) = $true) | ? [X270 : (subst > term > term)] : (! [X274 : subst,X272 : term,X273 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273)))) & ! [X271 : term] : ((((X267 @ id @ (X270 @ id @ X271) @ id)) = $true) | ($true != ((X267 @ id @ X271 @ id)))) & (((X267 @ id @ (lam @ (X270 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X417 : term] : ? [X418 : (subst > term > term)] : (((X418 @ sh @ one)) = ((sub @ X417 @ (push @ one @ sh))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem2_lthm = $true) & ((hoaslamnotap = $true) <=> ! [X411 : (subst > term > term),X412 : term,X413 : term] : (? [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) != ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) | (((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412))))) & ((termmset = $true) <=> ! [X462 : term] : (((sub @ X462 @ id)) = X462)) & (((d2subst @ d_id)) = id) & (hoasapnotvar_gthm = $true) & (! [X358 : (term > $o),X357 : term,X356 : (subst > term > subst > $o)] : (? [X359 : (subst > term > term)] : (! [X362 : subst,X363 : term,X361 : subst] : (((sub @ (X359 @ X361 @ X363) @ X362)) = ((X359 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362)))) & ! [X360 : term] : ((((X356 @ id @ (X359 @ id @ X360) @ id)) = $true) | (((X356 @ id @ X360 @ id)) != $true)) & (((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id)) != $true)) | ? [X371 : subst,X369 : subst,X370 : subst,X368 : term] : ((((X356 @ (comp @ X370 @ X369) @ (sub @ X368 @ X369) @ X371)) != $true) & (((X356 @ X370 @ X368 @ (comp @ X369 @ X371))) = $true)) | ($true = ((X358 @ (lam @ X357)))) | ? [X373 : term] : (((X358 @ X373)) != ((X356 @ id @ X373 @ id))) | ? [X372 : term] : ((((X358 @ X372)) = $true) & (((X358 @ (sub @ X357 @ (push @ X372 @ id)))) != $true)) | ? [X367 : subst,X366 : subst,X365 : term,X364 : subst] : (($true = ((X356 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X367))) & (((X356 @ X364 @ X365 @ (comp @ X366 @ X367))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X532 : term] : ? [X533 : (subst > term > term)] : ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535)))) & (lamnotap != $true) & (! [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | ? [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) != ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | ? [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) != ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))) <=> (hoaslaminj = $true)) & (hoasinduction_lem2_gthm = $true) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X184 : term,X183 : (subst > term > subst > $o)] : (? [X192 : term,X194 : subst,X195 : subst,X193 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) != $true) & (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) = $true)) | ? [X185 : term] : (($true != ((X183 @ id @ X185 @ id))) & ($true = ((var @ (sub @ X185 @ id))))) | ? [X186 : term,X187 : subst,X189 : subst,X188 : subst] : ((((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) = $true) & (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) != $true)) | ? [X190 : term,X191 : term] : (($true = ((X183 @ id @ X191 @ id))) & ($true = ((X183 @ id @ X190 @ id))) & (((X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) != $true)) | (((X183 @ id @ X184 @ id)) = $true) | ? [X196 : (subst > term > term)] : (($true != ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X197 : term] : ((((X183 @ id @ X197 @ id)) != $true) | (((X183 @ id @ (X196 @ id @ X197) @ id)) = $true)) & ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200))))))) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (! [X201 : (term > $o),X203 : term,X202 : subst] : (? [X205 : term] : ((((X201 @ (lam @ X205))) != $true) & ! [X206 : term] : ((((X201 @ (sub @ X205 @ (push @ X206 @ id)))) = $true) | ($true != ((X201 @ X206))))) | ? [X207 : term,X208 : term] : ((((X201 @ X207)) = $true) & (((X201 @ X208)) = $true) & (((X201 @ (ap @ X208 @ X207))) != $true)) | (((X201 @ (sub @ X203 @ X202))) = $true) | ? [X204 : term] : ((((var @ X204)) = $true) & (((X201 @ (sub @ X204 @ X202))) != $true))) <=> (induction2lem = $true)) & ((((! [X260 : (subst > term > term),X258 : (subst > term > term),X257 : subst,X259 : term] : ((((lam @ (X258 @ sh @ one))) != ((lam @ (X260 @ sh @ one)))) | (((X258 @ X257 @ X259)) = ((X260 @ X257 @ X259))) | ? [X263 : term,X261 : subst,X262 : subst] : (((X258 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262))) != ((sub @ (X258 @ X261 @ X263) @ X262))) | ? [X265 : term,X264 : subst,X266 : subst] : (((sub @ (X260 @ X266 @ X265) @ X264)) != ((X260 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264))))) | ? [X255 : term,X256 : term] : ((X255 != X256) & (((lam @ X256)) = ((lam @ X255))))) | ? [X254 : subst,X253 : term] : (((comp @ sh @ (push @ X253 @ X254))) != X254)) | ? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251)) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true)), 50.81/8.71 inference(ennf_transformation,[],[f10])). 50.81/8.71 thf(f14,plain,( 50.81/8.71 ((hoasinduction = $true) <=> ! [X184 : term,X183 : (subst > term > subst > $o)] : (? [X192 : term,X194 : subst,X195 : subst,X193 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) != $true) & (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) = $true)) | ? [X185 : term] : (($true != ((X183 @ id @ X185 @ id))) & ($true = ((var @ (sub @ X185 @ id))))) | ? [X186 : term,X187 : subst,X189 : subst,X188 : subst] : ((((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) = $true) & (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) != $true)) | ? [X190 : term,X191 : term] : (($true = ((X183 @ id @ X191 @ id))) & ($true = ((X183 @ id @ X190 @ id))) & (((X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) != $true)) | (((X183 @ id @ X184 @ id)) = $true) | ? [X196 : (subst > term > term)] : (($true != ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X197 : term] : ((((X183 @ id @ X197 @ id)) != $true) | (((X183 @ id @ (X196 @ id @ X197) @ id)) = $true)) & ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axclos = $true) & (axapp = $true) & (termmset_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2 = $true) & ((? [X36 : term] : (((sub @ X36 @ id)) != X36) | ! [X38 : term,X37 : (subst > term > subst > $o),X39 : (term > $o)] : (? [X41 : term] : (((X37 @ id @ X41 @ id)) != ((X39 @ X41))) | (((X39 @ (lam @ X38))) = $true) | ? [X42 : (subst > term > term)] : (! [X43 : term] : (($true = ((X37 @ id @ (X42 @ id @ X43) @ id))) | (((X37 @ id @ X43 @ id)) != $true)) & (((X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) != $true) & ! [X44 : term,X46 : subst,X45 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45)))) | ? [X40 : term] : (($true = ((X39 @ X40))) & (((X39 @ (sub @ X38 @ (push @ X40 @ id)))) != $true))) | ? [X32 : term] : ! [X33 : (subst > term > term)] : ? [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) != ((X33 @ X35 @ X34)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem0_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (? [X255 : term,X256 : term] : ((X255 != X256) & (((lam @ X256)) = ((lam @ X255)))) | ? [X254 : subst,X253 : term] : (((comp @ sh @ (push @ X253 @ X254))) != X254) | ? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251) | ! [X260 : (subst > term > term),X258 : (subst > term > term),X257 : subst,X259 : term] : ((((lam @ (X258 @ sh @ one))) != ((lam @ (X260 @ sh @ one)))) | (((X258 @ X257 @ X259)) = ((X260 @ X257 @ X259))) | ? [X263 : term,X261 : subst,X262 : subst] : (((X258 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262))) != ((sub @ (X258 @ X261 @ X263) @ X262))) | ? [X265 : term,X264 : subst,X266 : subst] : (((sub @ (X260 @ X266 @ X265) @ X264)) != ((X260 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264))))))) & (! [X358 : (term > $o),X357 : term,X356 : (subst > term > subst > $o)] : (? [X359 : (subst > term > term)] : (! [X362 : subst,X363 : term,X361 : subst] : (((sub @ (X359 @ X361 @ X363) @ X362)) = ((X359 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362)))) & ! [X360 : term] : ((((X356 @ id @ (X359 @ id @ X360) @ id)) = $true) | (((X356 @ id @ X360 @ id)) != $true)) & (((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id)) != $true)) | ? [X371 : subst,X369 : subst,X370 : subst,X368 : term] : ((((X356 @ (comp @ X370 @ X369) @ (sub @ X368 @ X369) @ X371)) != $true) & (((X356 @ X370 @ X368 @ (comp @ X369 @ X371))) = $true)) | ($true = ((X358 @ (lam @ X357)))) | ? [X373 : term] : (((X358 @ X373)) != ((X356 @ id @ X373 @ id))) | ? [X372 : term] : ((((X358 @ X372)) = $true) & (((X358 @ (sub @ X357 @ (push @ X372 @ id)))) != $true)) | ? [X367 : subst,X366 : subst,X365 : term,X364 : subst] : (($true = ((X356 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X367))) & (((X356 @ X364 @ X365 @ (comp @ X366 @ X367))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329)) | ? [X321 : term] : (((sub @ X321 @ id)) != X321) | ? [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) = ((ap @ X324 @ X325))) & (X323 != X324))) <=> (hoasapinj1_lthm = $true)) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & ((? [X483 : (term > $o),X481 : (subst > term > subst > $o),X482 : term] : (($true != ((X483 @ (lam @ X482)))) & ! [X484 : (subst > term > term)] : (? [X487 : subst,X485 : term,X486 : subst] : (((X484 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487))) != ((sub @ (X484 @ X486 @ X485) @ X487))) | ($true = ((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id))) | ? [X488 : term] : (($true = ((X481 @ id @ X488 @ id))) & ($true != ((X481 @ id @ (X484 @ id @ X488) @ id))))) & ! [X489 : term] : ((((X483 @ X489)) != $true) | (((X483 @ (sub @ X482 @ (push @ X489 @ id)))) = $true)) & ! [X490 : term] : (((X481 @ id @ X490 @ id)) = ((X483 @ X490)))) | ? [X473 : (term > $o),X474 : term] : ((((X473 @ X474)) != $true) & ! [X478 : term] : ((((X473 @ (lam @ X478))) = $true) | ? [X479 : term] : (($true != ((X473 @ (sub @ X478 @ (push @ X479 @ id))))) & (((X473 @ X479)) = $true))) & ! [X477 : term] : (($true != ((var @ X477))) | (((X473 @ X477)) = $true)) & ! [X476 : term,X475 : term] : ((((X473 @ (ap @ X475 @ X476))) = $true) | ($true != ((X473 @ X476))) | (((X473 @ X475)) != $true))) | ! [X492 : (subst > term > subst > $o),X491 : term] : (? [X501 : term,X502 : term] : ((((X492 @ id @ (ap @ (sub @ X501 @ id) @ X502) @ id)) != $true) & (((X492 @ id @ X502 @ id)) = $true) & (((X492 @ id @ X501 @ id)) = $true)) | ? [X499 : subst,X500 : subst,X498 : subst,X497 : term] : ((((X492 @ (comp @ X499 @ X500) @ (sub @ X497 @ X500) @ X498)) = $true) & (((X492 @ X499 @ X497 @ (comp @ X500 @ X498))) != $true)) | ? [X504 : (subst > term > term)] : (! [X505 : term] : (($true = ((X492 @ id @ (X504 @ id @ X505) @ id))) | (((X492 @ id @ X505 @ id)) != $true)) & (((X492 @ id @ (lam @ (X504 @ sh @ one)) @ id)) != $true) & ! [X506 : subst,X507 : subst,X508 : term] : (((X504 @ (comp @ X507 @ X506) @ (sub @ X508 @ X506))) = ((sub @ (X504 @ X507 @ X508) @ X506)))) | ? [X493 : subst,X495 : subst,X496 : subst,X494 : term] : ((((X492 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)) != $true) & (((X492 @ X493 @ X494 @ (comp @ X495 @ X496))) = $true)) | ? [X503 : term] : ((((X492 @ id @ X503 @ id)) != $true) & ($true = ((var @ (sub @ X503 @ id))))) | (((X492 @ id @ X491 @ id)) = $true)) | ? [X470 : (subst > term > subst > $o)] : ! [X471 : (term > $o)] : ? [X472 : term] : (((X470 @ id @ X472 @ id)) != ((X471 @ X472))) | ? [X480 : term] : (((sub @ X480 @ id)) != X480)) <=> (hoasinduction_lthm_3 = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & ((! [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true != ((X529 @ X526))) | ($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) | ? [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) != X521) | ? [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) != X524)) <=> (pushprop_lem1_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X439 : term,X438 : (subst > term > subst > $o)] : (? [X449 : term] : ((((X438 @ id @ X449 @ id)) = $true) & (((X438 @ id @ (sub @ X439 @ (push @ X449 @ id)) @ id)) != $true)) | ? [X441 : (subst > term > term),X440 : term] : (! [X444 : term,X443 : subst,X442 : subst] : (((X441 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443))) = ((sub @ X440 @ (push @ (sub @ X444 @ X443) @ (comp @ X442 @ X443))))) & (((X438 @ id @ (lam @ (X441 @ sh @ one)) @ id)) != $true) & ! [X446 : subst,X447 : subst,X445 : term] : (((sub @ (sub @ X440 @ (push @ X445 @ X446)) @ X447)) = ((sub @ (X441 @ X446 @ X445) @ X447))) & ! [X448 : term] : ((((X438 @ id @ (X441 @ id @ X448) @ id)) = $true) | (((X438 @ id @ X448 @ id)) != $true))) | (((X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id)) = $true))) & (hoasinduction_lem1_gthm = $true) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> (apinj1 = $true)) & (! [X518 : (subst > term > subst > $o)] : ? [X519 : (term > $o)] : ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))) | ? [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) = ((ap @ X399 @ X398))) & (X398 != X401)))) & (axassoc = $true) & (ulamvarsh = $true) & ((hoasapinj2 = $true) <=> ! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & (hoasinduction_lem1 = $true) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & ! [X288 : d_term,X289 : d_term] : ((X288 = X289) | (((d2term @ X288)) != ((d2term @ X289)))) & (hoasinduction_lem2_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X391 : (term > $o),X392 : term,X390 : subst] : ((((X391 @ (sub @ X392 @ X390))) = $true) | ? [X397 : term,X396 : term] : ((((X391 @ X397)) = $true) & (((X391 @ X396)) = $true) & (((X391 @ (ap @ X396 @ X397))) != $true)) | ? [X393 : term] : ((((var @ X393)) = $true) & (((X391 @ (sub @ X393 @ X390))) != $true)) | ? [X394 : term] : ((((X391 @ (lam @ X394))) != $true) & ! [X395 : term] : ((((X391 @ (sub @ X394 @ (push @ X395 @ id)))) = $true) | (((X391 @ X395)) != $true)))) | ? [X383 : subst] : (((comp @ X383 @ id)) != X383) | ? [X380 : term,X379 : subst] : (((sub @ one @ (push @ X380 @ X379))) != X380) | ? [X384 : term,X385 : (term > $o)] : ((((X385 @ X384)) != $true) & ! [X389 : term] : (($true = ((X385 @ (lam @ X389)))) | ($true != ((X385 @ X389)))) & ! [X388 : term,X387 : term] : ((((X385 @ (ap @ X387 @ X388))) = $true) | (((X385 @ X388)) != $true) | (((X385 @ X387)) != $true)) & ! [X386 : term] : ((((var @ X386)) != $true) | ($true = ((X385 @ X386))))) | ? [X381 : term,X382 : subst] : (((comp @ sh @ (push @ X381 @ X382))) != X382))) & (! [X201 : (term > $o),X203 : term,X202 : subst] : (? [X205 : term] : ((((X201 @ (lam @ X205))) != $true) & ! [X206 : term] : ((((X201 @ (sub @ X205 @ (push @ X206 @ id)))) = $true) | ($true != ((X201 @ X206))))) | ? [X207 : term,X208 : term] : ((((X201 @ X207)) = $true) & (((X201 @ X208)) = $true) & (((X201 @ (ap @ X208 @ X207))) != $true)) | (((X201 @ (sub @ X203 @ X202))) = $true) | ? [X204 : term] : ((((var @ X204)) = $true) & (((X201 @ (sub @ X204 @ X202))) != $true))) <=> (induction2lem = $true)) & (! [X375 : subst,X376 : term,X374 : (term > $o)] : ? [X377 : (term > $o)] : ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378))) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotvar_gthm = $true) & ! [X355 : d_subst] : (d_id = X355) & (hoasinduction_lem1v2 = $true) & (pushprop_lem1v2_gthm = $true) & (lamnotap != $true) & (induction2_gthm = $true) & (apnotvar = $true) & (axmap = $true) & (! [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | ? [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) != ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | ? [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) != ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))) <=> (hoaslaminj = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = id) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X84 : term,X83 : (subst > term > subst > $o)] : (? [X90 : term,X91 : term] : ((((X83 @ id @ X91 @ id)) = $true) & ($true != ((X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id))) & (((X83 @ id @ X90 @ id)) = $true)) | ($true = ((X83 @ id @ X84 @ id))) | ? [X85 : (subst > term > term)] : ((((X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) != $true) & ! [X86 : term] : ((((X83 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X83 @ id @ X86 @ id)) != $true)) & ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88)))))) | ? [X75 : (subst > term > subst > $o),X74 : term,X73 : (term > $o)] : (! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) & (((X73 @ (lam @ X74))) != $true) & ! [X76 : (subst > term > term)] : (? [X77 : term] : ((((X75 @ id @ (X76 @ id @ X77) @ id)) != $true) & (((X75 @ id @ X77 @ id)) = $true)) | (((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ? [X80 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) != ((sub @ (X76 @ X78 @ X79) @ X80)))) & ! [X81 : term] : ((((X73 @ X81)) != $true) | ($true = ((X73 @ (sub @ X74 @ (push @ X81 @ id))))))) | ? [X66 : (term > $o),X65 : term] : (! [X67 : term] : (($true = ((X66 @ (lam @ X67)))) | ? [X68 : term] : ((((X66 @ X68)) = $true) & (((X66 @ (sub @ X67 @ (push @ X68 @ id)))) != $true))) & ! [X69 : term,X70 : term] : (($true != ((X66 @ X69))) | (((X66 @ X70)) != $true) | (((X66 @ (ap @ X69 @ X70))) = $true)) & ! [X71 : term] : (($true = ((X66 @ X71))) | (((var @ X71)) != $true)) & (((X66 @ X65)) != $true)) | ? [X72 : term] : (((sub @ X72 @ id)) != X72) | ? [X62 : (subst > term > subst > $o)] : ! [X63 : (term > $o)] : ? [X64 : term] : (((X63 @ X64)) != ((X62 @ id @ X64 @ id))))) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) <=> (laminj = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X235 : term,X236 : (subst > term > subst > $o)] : (? [X241 : subst,X239 : subst,X238 : subst,X240 : term] : ((((X236 @ X241 @ X240 @ (comp @ X238 @ X239))) = $true) & (((X236 @ (comp @ X241 @ X238) @ (sub @ X240 @ X238) @ X239)) != $true)) | ($true = ((X236 @ id @ (lam @ X235) @ id))) | ? [X237 : term] : ((((X236 @ id @ (sub @ X235 @ (push @ X237 @ id)) @ id)) != $true) & ($true = ((X236 @ id @ X237 @ id)))) | ? [X242 : (subst > term > term)] : (! [X246 : term] : ((((X236 @ id @ (X242 @ id @ X246) @ id)) = $true) | ($true != ((X236 @ id @ X246 @ id)))) & (((X236 @ id @ (lam @ (X242 @ sh @ one)) @ id)) != $true) & ! [X244 : subst,X243 : term,X245 : subst] : (((sub @ (X242 @ X245 @ X243) @ X244)) = ((X242 @ (comp @ X245 @ X244) @ (sub @ X243 @ X244))))) | ? [X250 : subst,X247 : subst,X249 : subst,X248 : term] : (($true != ((X236 @ X250 @ X248 @ (comp @ X249 @ X247)))) & (((X236 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249) @ X247)) = $true))) <=> (hoasinduction_lem3 = $true)) & ((? [X419 : term] : (((sub @ X419 @ id)) != X419) | ! [X422 : term,X421 : (term > $o),X420 : (subst > term > subst > $o)] : (? [X433 : (subst > term > term)] : (! [X434 : term] : (($true = ((X420 @ id @ (X433 @ id @ X434) @ id))) | (((X420 @ id @ X434 @ id)) != $true)) & (((X420 @ id @ (lam @ (X433 @ sh @ one)) @ id)) != $true) & ! [X437 : subst,X436 : subst,X435 : term] : (((X433 @ (comp @ X437 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X437 @ X435) @ X436)))) | ? [X428 : term] : (((X420 @ id @ X428 @ id)) != ((X421 @ X428))) | ? [X427 : term] : ((((X421 @ (sub @ X422 @ (push @ X427 @ id)))) != $true) & (((X421 @ X427)) = $true)) | ? [X432 : subst,X430 : subst,X431 : term,X429 : subst] : ((((X420 @ (comp @ X429 @ X430) @ (sub @ X431 @ X430) @ X432)) = $true) & ($true != ((X420 @ X429 @ X431 @ (comp @ X430 @ X432))))) | ? [X423 : term,X425 : subst,X426 : subst,X424 : subst] : ((((X420 @ (comp @ X425 @ X426) @ (sub @ X423 @ X426) @ X424)) != $true) & (((X420 @ X425 @ X423 @ (comp @ X426 @ X424))) = $true)) | (((X421 @ (lam @ X422))) = $true))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X330 : term,X331 : (term > $o),X332 : (subst > term > subst > $o)] : (? [X333 : term] : (((X331 @ X333)) != ((X332 @ id @ X333 @ id))) | ? [X334 : term] : (($true = ((X331 @ X334))) & ($true != ((X331 @ (sub @ X330 @ (push @ X334 @ id)))))) | ? [X335 : (subst > term > term)] : (! [X339 : term] : ((((X332 @ id @ X339 @ id)) != $true) | ($true = ((X332 @ id @ (X335 @ id @ X339) @ id)))) & ! [X336 : term,X338 : subst,X337 : subst] : (((X335 @ (comp @ X337 @ X338) @ (sub @ X336 @ X338))) = ((sub @ (X335 @ X337 @ X336) @ X338))) & (((X332 @ id @ (lam @ (X335 @ sh @ one)) @ id)) != $true)) | (((X331 @ (lam @ X330))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & ((? [X136 : (subst > term > subst > $o),X135 : term,X137 : term] : ((((X136 @ id @ (ap @ X135 @ X137) @ id)) != $true) & (((X136 @ id @ X135 @ id)) = $true) & ! [X146 : term,X147 : term] : ((((X136 @ id @ X147 @ id)) != $true) | (((X136 @ id @ X146 @ id)) != $true) | (((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id)) = $true)) & ! [X145 : subst,X143 : subst,X144 : subst,X142 : term] : ((((X136 @ X144 @ X142 @ (comp @ X145 @ X143))) = $true) | (((X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143)) != $true)) & ! [X141 : subst,X138 : term,X139 : subst,X140 : subst] : ((((X136 @ X141 @ X138 @ (comp @ X139 @ X140))) != $true) | ($true = ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140)))) & (((X136 @ id @ X137 @ id)) = $true)) | ? [X128 : term,X129 : (term > $o)] : (($true != ((X129 @ X128))) & ! [X132 : term] : ((((X129 @ (lam @ X132))) = $true) | ? [X133 : term] : ((((X129 @ (sub @ X132 @ (push @ X133 @ id)))) != $true) & ($true = ((X129 @ X133))))) & ! [X130 : term,X131 : term] : ((((X129 @ X131)) != $true) | (((X129 @ (ap @ X131 @ X130))) = $true) | ($true != ((X129 @ X130)))) & ! [X134 : term] : ((((var @ X134)) != $true) | (((X129 @ X134)) = $true))) | ? [X149 : (subst > term > subst > $o),X148 : term] : (($true != ((X149 @ id @ (lam @ X148) @ id))) & ! [X155 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ? [X159 : term,X158 : subst,X157 : subst] : (((sub @ (X155 @ X157 @ X159) @ X158)) != ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158)))) | ? [X156 : term] : (($true != ((X149 @ id @ (X155 @ id @ X156) @ id))) & (((X149 @ id @ X156 @ id)) = $true))) & ! [X150 : term] : ((((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true) | ($true != ((X149 @ id @ X150 @ id)))) & ! [X152 : term,X154 : subst,X151 : subst,X153 : subst] : (($true = ((X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153))) | (((X149 @ X154 @ X152 @ (comp @ X151 @ X153))) != $true)) & ! [X163 : subst,X160 : subst,X161 : subst,X162 : term] : ((((X149 @ X163 @ X162 @ (comp @ X160 @ X161))) = $true) | (((X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161)) != $true))) | ! [X164 : (subst > term > subst > $o),X165 : term] : (? [X173 : (subst > term > term)] : (! [X177 : term] : ((((X164 @ id @ X177 @ id)) != $true) | ($true = ((X164 @ id @ (X173 @ id @ X177) @ id)))) & (((X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X176 : subst,X175 : term,X174 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174)))) | (((X164 @ id @ X165 @ id)) = $true) | ? [X166 : term] : (($true = ((var @ (sub @ X166 @ id)))) & (((X164 @ id @ X166 @ id)) != $true)) | ? [X171 : subst,X169 : term,X172 : subst,X170 : subst] : (($true = ((X164 @ X171 @ X169 @ (comp @ X170 @ X172)))) & (((X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) != $true)) | ? [X180 : subst,X178 : subst,X179 : subst,X181 : term] : (($true != ((X164 @ X178 @ X181 @ (comp @ X179 @ X180)))) & (((X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180)) = $true)) | ? [X168 : term,X167 : term] : (($true = ((X164 @ id @ X167 @ id))) & ($true != ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id))) & ($true = ((X164 @ id @ X168 @ id)))))) <=> (hoasinduction_lthm = $true)) & (! [X267 : (subst > term > subst > $o),X268 : term] : (? [X269 : term] : ((((X267 @ id @ X269 @ id)) = $true) & (((X267 @ id @ (sub @ X268 @ (push @ X269 @ id)) @ id)) != $true)) | (((X267 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id)) = $true) | ? [X270 : (subst > term > term)] : (! [X274 : subst,X272 : term,X273 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273)))) & ! [X271 : term] : ((((X267 @ id @ (X270 @ id @ X271) @ id)) = $true) | ($true != ((X267 @ id @ X271 @ id)))) & (((X267 @ id @ (lam @ (X270 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X182 : d_term] : (d_one = X182) & ((induction2 = $true) <=> ! [X19 : (term > $o),X18 : term] : ((((X19 @ X18)) = $true) | ? [X21 : term] : (! [X22 : term] : ((((X19 @ (sub @ X21 @ (push @ X22 @ id)))) = $true) | (((X19 @ X22)) != $true)) & (((X19 @ (lam @ X21))) != $true)) | ? [X24 : term,X23 : term] : ((((X19 @ (ap @ X24 @ X23))) != $true) & (((X19 @ X24)) = $true) & ($true = ((X19 @ X23)))) | ? [X20 : term] : ((((X19 @ X20)) != $true) & ($true = ((var @ X20)))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X342 : (term > $o),X340 : term,X341 : term,X343 : (subst > term > subst > $o)] : ((((X342 @ (ap @ X340 @ X341))) = $true) | (((X342 @ X340)) != $true) | ? [X350 : term,X348 : subst,X347 : subst,X349 : subst] : ((((X343 @ (comp @ X348 @ X347) @ (sub @ X350 @ X347) @ X349)) = $true) & (((X343 @ X348 @ X350 @ (comp @ X347 @ X349))) != $true)) | ? [X345 : term,X346 : term] : ((((X343 @ id @ X345 @ id)) = $true) & ($true = ((X343 @ id @ X346 @ id))) & (((X343 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id)) != $true)) | ? [X344 : term] : (((X342 @ X344)) != ((X343 @ id @ X344 @ id))) | (((X342 @ X341)) != $true) | ? [X351 : term,X353 : subst,X354 : subst,X352 : subst] : ((((X343 @ (comp @ X354 @ X352) @ (sub @ X351 @ X352) @ X353)) != $true) & (((X343 @ X354 @ X351 @ (comp @ X352 @ X353))) = $true))) <=> (hoasinduction_lem2v2 = $true)) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & ((hoasinduction_lem0_lthm = $true) <=> ! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id)))) & ((! [X102 : term,X101 : (subst > term > subst > $o)] : (? [X106 : subst,X105 : term,X104 : subst,X107 : subst] : ((((X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) = $true) & ($true != ((X101 @ X107 @ X105 @ (comp @ X106 @ X104))))) | (((X101 @ id @ (lam @ X102) @ id)) = $true) | ? [X103 : term] : ((((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id)) != $true) & ($true = ((X101 @ id @ X103 @ id)))) | ? [X108 : (subst > term > term)] : (! [X111 : term,X110 : subst,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112)))) & ! [X109 : term] : ((((X101 @ id @ (X108 @ id @ X109) @ id)) = $true) | (((X101 @ id @ X109 @ id)) != $true)) & (((X101 @ id @ (lam @ (X108 @ sh @ one)) @ id)) != $true)) | ? [X116 : subst,X114 : term,X115 : subst,X113 : subst] : ((((X101 @ X113 @ X114 @ (comp @ X116 @ X115))) = $true) & ($true != ((X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115))))) | ? [X93 : term,X94 : (subst > term > subst > $o)] : (! [X95 : term] : (($true = ((X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id))) | (((X94 @ id @ X95 @ id)) != $true)) & (((X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true) & ! [X96 : (subst > term > term)] : (? [X100 : term] : (($true = ((X94 @ id @ X100 @ id))) & (((X94 @ id @ (X96 @ id @ X100) @ id)) != $true)) | ? [X97 : term,X98 : subst,X99 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) != ((sub @ (X96 @ X99 @ X97) @ X98))) | (((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true))) | ? [X92 : term] : (((sub @ X92 @ id)) != X92)) <=> (hoasinduction_lem3_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) <=> ! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7))))) & (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)))))))))))))) & (hoaslamnotvar_lthm = $true) & ((axvarid = $true) <=> ! [X61 : term] : (((sub @ X61 @ id)) = X61)) & (! [X510 : (subst > term > subst > $o),X509 : term] : (? [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) != $true) & (((X510 @ id @ X512 @ id)) = $true) & (((X510 @ id @ X511 @ id)) = $true)) | ? [X513 : (subst > term > term)] : (($true != ((X510 @ id @ (lam @ (X513 @ sh @ one)) @ id))) & ! [X515 : term,X516 : subst,X517 : subst] : (((sub @ (X513 @ X517 @ X515) @ X516)) = ((X513 @ (comp @ X517 @ X516) @ (sub @ X515 @ X516)))) & ! [X514 : term] : ((((X510 @ id @ (X513 @ id @ X514) @ id)) = $true) | (((X510 @ id @ X514 @ id)) != $true))) | ($true = ((X510 @ id @ X509 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X450 : (subst > term > subst > $o),X451 : term] : ((((X450 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id)) = $true) | ? [X453 : (subst > term > term)] : (! [X455 : subst,X456 : subst,X457 : term] : (((sub @ (X453 @ X455 @ X457) @ X456)) = ((X453 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456)))) & ! [X454 : term] : ((((X450 @ id @ X454 @ id)) != $true) | (((X450 @ id @ (X453 @ id @ X454) @ id)) = $true)) & (((X450 @ id @ (lam @ (X453 @ sh @ one)) @ id)) != $true)) | ? [X452 : term] : (($true != ((X450 @ id @ (sub @ X451 @ (push @ X452 @ id)) @ id))) & ($true = ((X450 @ id @ X452 @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X10 : (subst > term > subst > $o),X11 : term] : ((((X10 @ id @ (lam @ X11) @ id)) = $true) | ? [X12 : (subst > term > term)] : (! [X13 : term] : ((((X10 @ id @ X13 @ id)) != $true) | (((X10 @ id @ (X12 @ id @ X13) @ id)) = $true)) & (((X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) != $true) & ! [X16 : subst,X14 : term,X15 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15))))) | ? [X17 : term] : (($true = ((X10 @ id @ X17 @ id))) & (((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) != $true)))) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & ((hoasinduction_lem3b = $true) <=> ! [X417 : term] : ? [X418 : (subst > term > term)] : (((X418 @ sh @ one)) = ((sub @ X417 @ (push @ one @ sh))))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) != $true) | ? [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) != ((X232 @ X234))) | (((X232 @ one)) = $true)) | ? [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) != X228))) & (hoasinduction_lem2_gthm = $true) & ((shinj = $true) <=> ! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26))) & (axabs = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lthm_orig = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) <=> ! [X277 : term,X275 : (subst > term > subst > $o),X276 : term] : (($true != ((X275 @ id @ X277 @ id))) | ? [X282 : term,X283 : term] : ((((X275 @ id @ X283 @ id)) = $true) & ($true != ((X275 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id))) & ($true = ((X275 @ id @ X282 @ id)))) | ? [X279 : term,X280 : subst,X278 : subst,X281 : subst] : (($true != ((X275 @ X278 @ X279 @ (comp @ X280 @ X281)))) & (((X275 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280) @ X281)) = $true)) | ? [X284 : term,X287 : subst,X285 : subst,X286 : subst] : ((((X275 @ (comp @ X287 @ X285) @ (sub @ X284 @ X285) @ X286)) != $true) & ($true = ((X275 @ X287 @ X284 @ (comp @ X285 @ X286))))) | ($true != ((X275 @ id @ X276 @ id))) | ($true = ((X275 @ id @ (ap @ X277 @ X276) @ id))))) & (ulamvar1 != $true) & ((axvarcons = $true) <=> ! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4)) & (hoasinduction_lem2v2_gthm = $true) & ((? [X291 : (subst > term > subst > $o),X292 : term] : (! [X298 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X298 @ id)) @ id)) = $true) | (((X291 @ id @ X298 @ id)) != $true)) & ! [X293 : (subst > term > term)] : (? [X297 : term] : ((((X291 @ id @ (X293 @ id @ X297) @ id)) != $true) & (((X291 @ id @ X297 @ id)) = $true)) | (((X291 @ id @ (lam @ (X293 @ sh @ one)) @ id)) = $true) | ? [X295 : subst,X296 : term,X294 : subst] : (((sub @ (X293 @ X295 @ X296) @ X294)) != ((X293 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))))) & (((X291 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id)) != $true)) | ? [X290 : term] : (((sub @ X290 @ id)) != X290) | ! [X299 : term,X300 : (subst > term > subst > $o)] : (? [X301 : term] : ((((X300 @ id @ (sub @ X299 @ (push @ X301 @ id)) @ id)) != $true) & ($true = ((X300 @ id @ X301 @ id)))) | (((X300 @ id @ (lam @ X299) @ id)) = $true) | ? [X302 : (subst > term > term)] : (! [X306 : term] : (($true = ((X300 @ id @ (X302 @ id @ X306) @ id))) | (((X300 @ id @ X306 @ id)) != $true)) & (((X300 @ id @ (lam @ (X302 @ sh @ one)) @ id)) != $true) & ! [X305 : subst,X303 : subst,X304 : term] : (((sub @ (X302 @ X303 @ X304) @ X305)) = ((X302 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true != ((X30 @ X27))) | ($true = ((X29 @ one))) | ? [X31 : term] : (((X29 @ X31)) != ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X53 : term] : ? [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) = ((X54 @ sh @ one)))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X532 : term] : ? [X533 : (subst > term > term)] : ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535)))) & ((axidl = $true) <=> ! [X318 : subst] : (((comp @ id @ X318)) = X318)) & ((termmset = $true) <=> ! [X462 : term] : (((sub @ X462 @ id)) = X462)) & (hoasinduction_gthm = $true) & (! [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | (((X409 @ X407)) != $true)) <=> (pushprop_lem1 = $true)) & (! [X225 : subst] : (((comp @ X225 @ id)) = X225) <=> (axidr = $true)) & ((hoaslamnotap = $true) <=> ! [X411 : (subst > term > term),X412 : term,X413 : term] : (? [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) != ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) | (((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412))))) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & ! [X227 : d_subst,X226 : d_subst] : ((X226 = X227) | (((d2subst @ X226)) != ((d2subst @ X227)))) & (! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) <=> (apinj2 = $true)) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3b_gthm = $true) & ((termmset_lthm = $true) <=> (! [X118 : term] : (((sub @ X118 @ id)) = X118) | ? [X117 : term] : (((sub @ X117 @ id)) != X117))) & ((induction = $true) <=> ! [X119 : term,X120 : (term > $o)] : (? [X121 : term] : (($true = ((X120 @ X121))) & (((X120 @ (lam @ X121))) != $true)) | ? [X124 : term] : ((((var @ X124)) = $true) & (((X120 @ X124)) != $true)) | ? [X123 : term,X122 : term] : ((((X120 @ X123)) = $true) & (((X120 @ X122)) = $true) & ($true != ((X120 @ (ap @ X122 @ X123))))) | (((X120 @ X119)) = $true))) & (hoaslamnotap_lthm = $true) & ((induction2_lthm = $true) <=> (! [X219 : term,X218 : (term > $o)] : (? [X224 : term,X223 : term] : (($true = ((X218 @ X223))) & (((X218 @ (ap @ X223 @ X224))) != $true) & (((X218 @ X224)) = $true)) | ? [X220 : term] : (($true != ((X218 @ X220))) & (((var @ X220)) = $true)) | (((X218 @ X219)) = $true) | ? [X221 : term] : (! [X222 : term] : (($true != ((X218 @ X222))) | (((X218 @ (sub @ X221 @ (push @ X222 @ id)))) = $true)) & (((X218 @ (lam @ X221))) != $true))) | ? [X211 : (term > $o),X210 : subst,X212 : term] : (! [X215 : term] : (($true = ((X211 @ (sub @ X215 @ X210)))) | ($true != ((var @ X215)))) & ! [X213 : term] : ((((X211 @ (lam @ X213))) = $true) | ? [X214 : term] : ((((X211 @ X214)) = $true) & ($true != ((X211 @ (sub @ X213 @ (push @ X214 @ id))))))) & (((X211 @ (sub @ X212 @ X210))) != $true) & ! [X217 : term,X216 : term] : (($true = ((X211 @ (ap @ X216 @ X217)))) | (((X211 @ X216)) != $true) | (((X211 @ X217)) != $true))) | ? [X209 : term] : (((sub @ X209 @ id)) != X209))) & (pushprop_lthm = $true) & (! [X536 : term] : ? [X537 : (subst > term > term)] : ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((substmonoid_lthm = $true) <=> ((! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3)) | ? [X0 : subst] : (((comp @ id @ X0)) != X0) | ? [X1 : subst] : (((comp @ X1 @ id)) != X1))) & ((axscons = $true) <=> ! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307)) & (ulamvarind = $true) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X467 : (term > $o),X465 : term,X466 : subst] : ? [X468 : (term > $o)] : ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469))))), 50.81/8.71 inference(flattening,[],[f13])). 50.81/8.71 thf(f15,definition,( 50.81/8.71 ! [X211 : (term > $o)] : ((((sP0 @ X211)) = $true) <=> ! [X217 : term,X216 : term] : (($true = ((X211 @ (ap @ X216 @ X217)))) | (((X211 @ X216)) != $true) | (((X211 @ X217)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f16,definition,( 50.81/8.71 ! [X218 : (term > $o)] : ((((sP1 @ X218)) = $true) <=> ? [X224 : term,X223 : term] : (($true = ((X218 @ X223))) & (((X218 @ (ap @ X223 @ X224))) != $true) & (((X218 @ X224)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f17,definition,( 50.81/8.71 (sP2 = $true) <=> ! [X219 : term,X218 : (term > $o)] : ((((sP1 @ X218)) = $true) | ? [X220 : term] : (($true != ((X218 @ X220))) & (((var @ X220)) = $true)) | (((X218 @ X219)) = $true) | ? [X221 : term] : (! [X222 : term] : (($true != ((X218 @ X222))) | (((X218 @ (sub @ X221 @ (push @ X222 @ id)))) = $true)) & (((X218 @ (lam @ X221))) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f18,definition,( 50.81/8.71 (sP3 = $true) <=> ((sP2 = $true) | ? [X211 : (term > $o),X210 : subst,X212 : term] : (! [X215 : term] : (($true = ((X211 @ (sub @ X215 @ X210)))) | ($true != ((var @ X215)))) & ! [X213 : term] : ((((X211 @ (lam @ X213))) = $true) | ? [X214 : term] : ((((X211 @ X214)) = $true) & ($true != ((X211 @ (sub @ X213 @ (push @ X214 @ id))))))) & (((X211 @ (sub @ X212 @ X210))) != $true) & (((sP0 @ X211)) = $true)) | ? [X209 : term] : (((sub @ X209 @ id)) != X209))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f19,definition,( 50.81/8.71 ! [X120 : (term > $o)] : ((((sP4 @ X120)) = $true) <=> ? [X123 : term,X122 : term] : ((((X120 @ X123)) = $true) & (((X120 @ X122)) = $true) & ($true != ((X120 @ (ap @ X122 @ X123))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f20,definition,( 50.81/8.71 (sP5 = $true) <=> ? [X291 : (subst > term > subst > $o),X292 : term] : (! [X298 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X298 @ id)) @ id)) = $true) | (((X291 @ id @ X298 @ id)) != $true)) & ! [X293 : (subst > term > term)] : (? [X297 : term] : ((((X291 @ id @ (X293 @ id @ X297) @ id)) != $true) & (((X291 @ id @ X297 @ id)) = $true)) | (((X291 @ id @ (lam @ (X293 @ sh @ one)) @ id)) = $true) | ? [X295 : subst,X296 : term,X294 : subst] : (((sub @ (X293 @ X295 @ X296) @ X294)) != ((X293 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))))) & (((X291 @ id @ (lam @ (sub @ X292 @ (push @ one @ sh))) @ id)) != $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f21,definition,( 50.81/8.71 ($true = sP6) <=> ((sP5 = $true) | ? [X290 : term] : (((sub @ X290 @ id)) != X290) | ! [X299 : term,X300 : (subst > term > subst > $o)] : (? [X301 : term] : ((((X300 @ id @ (sub @ X299 @ (push @ X301 @ id)) @ id)) != $true) & ($true = ((X300 @ id @ X301 @ id)))) | (((X300 @ id @ (lam @ X299) @ id)) = $true) | ? [X302 : (subst > term > term)] : (! [X306 : term] : (($true = ((X300 @ id @ (X302 @ id @ X306) @ id))) | (((X300 @ id @ X306 @ id)) != $true)) & (((X300 @ id @ (lam @ (X302 @ sh @ one)) @ id)) != $true) & ! [X305 : subst,X303 : subst,X304 : term] : (((sub @ (X302 @ X303 @ X304) @ X305)) = ((X302 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f22,definition,( 50.81/8.71 ! [X275 : (subst > term > subst > $o)] : ((((sP7 @ X275)) = $true) <=> ? [X282 : term,X283 : term] : ((((X275 @ id @ X283 @ id)) = $true) & ($true != ((X275 @ id @ (ap @ (sub @ X283 @ id) @ X282) @ id))) & ($true = ((X275 @ id @ X282 @ id)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f23,definition,( 50.81/8.71 (sP8 = $true) <=> ! [X277 : term,X275 : (subst > term > subst > $o),X276 : term] : (($true != ((X275 @ id @ X277 @ id))) | (((sP7 @ X275)) = $true) | ? [X279 : term,X280 : subst,X278 : subst,X281 : subst] : (($true != ((X275 @ X278 @ X279 @ (comp @ X280 @ X281)))) & (((X275 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280) @ X281)) = $true)) | ? [X284 : term,X287 : subst,X285 : subst,X286 : subst] : ((((X275 @ (comp @ X287 @ X285) @ (sub @ X284 @ X285) @ X286)) != $true) & ($true = ((X275 @ X287 @ X284 @ (comp @ X285 @ X286))))) | ($true != ((X275 @ id @ X276 @ id))) | ($true = ((X275 @ id @ (ap @ X277 @ X276) @ id))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f24,definition,( 50.81/8.71 (sP9 = $true) <=> ! [X10 : (subst > term > subst > $o),X11 : term] : ((((X10 @ id @ (lam @ X11) @ id)) = $true) | ? [X12 : (subst > term > term)] : (! [X13 : term] : ((((X10 @ id @ X13 @ id)) != $true) | (((X10 @ id @ (X12 @ id @ X13) @ id)) = $true)) & (((X10 @ id @ (lam @ (X12 @ sh @ one)) @ id)) != $true) & ! [X16 : subst,X14 : term,X15 : subst] : (((sub @ (X12 @ X16 @ X14) @ X15)) = ((X12 @ (comp @ X16 @ X15) @ (sub @ X14 @ X15))))) | ? [X17 : term] : (($true = ((X10 @ id @ X17 @ id))) & (((X10 @ id @ (sub @ X11 @ (push @ X17 @ id)) @ id)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f25,definition,( 50.81/8.71 (sP10 = $true) <=> ! [X450 : (subst > term > subst > $o),X451 : term] : ((((X450 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id)) = $true) | ? [X453 : (subst > term > term)] : (! [X455 : subst,X456 : subst,X457 : term] : (((sub @ (X453 @ X455 @ X457) @ X456)) = ((X453 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456)))) & ! [X454 : term] : ((((X450 @ id @ X454 @ id)) != $true) | (((X450 @ id @ (X453 @ id @ X454) @ id)) = $true)) & (((X450 @ id @ (lam @ (X453 @ sh @ one)) @ id)) != $true)) | ? [X452 : term] : (($true != ((X450 @ id @ (sub @ X451 @ (push @ X452 @ id)) @ id))) & ($true = ((X450 @ id @ X452 @ id)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f26,definition,( 50.81/8.71 ! [X510 : (subst > term > subst > $o)] : ((((sP11 @ X510)) = $true) <=> ? [X513 : (subst > term > term)] : (($true != ((X510 @ id @ (lam @ (X513 @ sh @ one)) @ id))) & ! [X515 : term,X516 : subst,X517 : subst] : (((sub @ (X513 @ X517 @ X515) @ X516)) = ((X513 @ (comp @ X517 @ X516) @ (sub @ X515 @ X516)))) & ! [X514 : term] : ((((X510 @ id @ (X513 @ id @ X514) @ id)) = $true) | (((X510 @ id @ X514 @ id)) != $true))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f27,definition,( 50.81/8.71 ! [X101 : (subst > term > subst > $o)] : ((((sP12 @ X101)) = $true) <=> ? [X108 : (subst > term > term)] : (! [X111 : term,X110 : subst,X112 : subst] : (((sub @ (X108 @ X110 @ X111) @ X112)) = ((X108 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112)))) & ! [X109 : term] : ((((X101 @ id @ (X108 @ id @ X109) @ id)) = $true) | (((X101 @ id @ X109 @ id)) != $true)) & (((X101 @ id @ (lam @ (X108 @ sh @ one)) @ id)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f28,definition,( 50.81/8.71 (sP13 = $true) <=> ? [X93 : term,X94 : (subst > term > subst > $o)] : (! [X95 : term] : (($true = ((X94 @ id @ (sub @ X93 @ (push @ X95 @ id)) @ id))) | (((X94 @ id @ X95 @ id)) != $true)) & (((X94 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true) & ! [X96 : (subst > term > term)] : (? [X100 : term] : (($true = ((X94 @ id @ X100 @ id))) & (((X94 @ id @ (X96 @ id @ X100) @ id)) != $true)) | ? [X97 : term,X98 : subst,X99 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) != ((sub @ (X96 @ X99 @ X97) @ X98))) | (((X94 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f29,definition,( 50.81/8.71 (sP14 = $true) <=> (! [X102 : term,X101 : (subst > term > subst > $o)] : (? [X106 : subst,X105 : term,X104 : subst,X107 : subst] : ((((X101 @ (comp @ X107 @ X106) @ (sub @ X105 @ X106) @ X104)) = $true) & ($true != ((X101 @ X107 @ X105 @ (comp @ X106 @ X104))))) | (((X101 @ id @ (lam @ X102) @ id)) = $true) | ? [X103 : term] : ((((X101 @ id @ (sub @ X102 @ (push @ X103 @ id)) @ id)) != $true) & ($true = ((X101 @ id @ X103 @ id)))) | (((sP12 @ X101)) = $true) | ? [X116 : subst,X114 : term,X115 : subst,X113 : subst] : ((((X101 @ X113 @ X114 @ (comp @ X116 @ X115))) = $true) & ($true != ((X101 @ (comp @ X113 @ X116) @ (sub @ X114 @ X116) @ X115))))) | (sP13 = $true) | ? [X92 : term] : (((sub @ X92 @ id)) != X92))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f30,definition,( 50.81/8.71 ! [X343 : (subst > term > subst > $o)] : (($true = ((sP15 @ X343))) <=> ? [X345 : term,X346 : term] : ((((X343 @ id @ X345 @ id)) = $true) & ($true = ((X343 @ id @ X346 @ id))) & (((X343 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f31,definition,( 50.81/8.71 ($true = sP16) <=> ! [X342 : (term > $o),X340 : term,X341 : term,X343 : (subst > term > subst > $o)] : ((((X342 @ (ap @ X340 @ X341))) = $true) | (((X342 @ X340)) != $true) | ? [X350 : term,X348 : subst,X347 : subst,X349 : subst] : ((((X343 @ (comp @ X348 @ X347) @ (sub @ X350 @ X347) @ X349)) = $true) & (((X343 @ X348 @ X350 @ (comp @ X347 @ X349))) != $true)) | ($true = ((sP15 @ X343))) | ? [X344 : term] : (((X342 @ X344)) != ((X343 @ id @ X344 @ id))) | (((X342 @ X341)) != $true) | ? [X351 : term,X353 : subst,X354 : subst,X352 : subst] : ((((X343 @ (comp @ X354 @ X352) @ (sub @ X351 @ X352) @ X353)) != $true) & (((X343 @ X354 @ X351 @ (comp @ X352 @ X353))) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f32,definition,( 50.81/8.71 ! [X19 : (term > $o)] : ((((sP17 @ X19)) = $true) <=> ? [X24 : term,X23 : term] : ((((X19 @ (ap @ X24 @ X23))) != $true) & (((X19 @ X24)) = $true) & ($true = ((X19 @ X23)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f33,definition,( 50.81/8.71 ($true = sP18) <=> ! [X19 : (term > $o),X18 : term] : ((((X19 @ X18)) = $true) | ? [X21 : term] : (! [X22 : term] : ((((X19 @ (sub @ X21 @ (push @ X22 @ id)))) = $true) | (((X19 @ X22)) != $true)) & (((X19 @ (lam @ X21))) != $true)) | (((sP17 @ X19)) = $true) | ? [X20 : term] : ((((X19 @ X20)) != $true) & ($true = ((var @ X20)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f34,definition,( 50.81/8.71 ($true = sP19) <=> ! [X267 : (subst > term > subst > $o),X268 : term] : (? [X269 : term] : ((((X267 @ id @ X269 @ id)) = $true) & (((X267 @ id @ (sub @ X268 @ (push @ X269 @ id)) @ id)) != $true)) | (((X267 @ id @ (lam @ (sub @ X268 @ (push @ one @ sh))) @ id)) = $true) | ? [X270 : (subst > term > term)] : (! [X274 : subst,X272 : term,X273 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273)))) & ! [X271 : term] : ((((X267 @ id @ (X270 @ id @ X271) @ id)) = $true) | ($true != ((X267 @ id @ X271 @ id)))) & (((X267 @ id @ (lam @ (X270 @ sh @ one)) @ id)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f35,definition,( 50.81/8.71 ! [X164 : (subst > term > subst > $o)] : ((((sP20 @ X164)) = $true) <=> ? [X168 : term,X167 : term] : (($true = ((X164 @ id @ X167 @ id))) & ($true != ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X168) @ id))) & ($true = ((X164 @ id @ X168 @ id)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f36,definition,( 50.81/8.71 ! [X164 : (subst > term > subst > $o)] : ((((sP21 @ X164)) = $true) <=> ? [X173 : (subst > term > term)] : (! [X177 : term] : ((((X164 @ id @ X177 @ id)) != $true) | ($true = ((X164 @ id @ (X173 @ id @ X177) @ id)))) & (((X164 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X176 : subst,X175 : term,X174 : subst] : (((X173 @ (comp @ X176 @ X174) @ (sub @ X175 @ X174))) = ((sub @ (X173 @ X176 @ X175) @ X174)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f37,definition,( 50.81/8.71 ! [X149 : (subst > term > subst > $o)] : (($true = ((sP22 @ X149))) <=> ! [X155 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ? [X159 : term,X158 : subst,X157 : subst] : (((sub @ (X155 @ X157 @ X159) @ X158)) != ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158)))) | ? [X156 : term] : (($true != ((X149 @ id @ (X155 @ id @ X156) @ id))) & (((X149 @ id @ X156 @ id)) = $true))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f38,definition,( 50.81/8.71 ! [X129 : (term > $o)] : ((((sP23 @ X129)) = $true) <=> ! [X130 : term,X131 : term] : ((((X129 @ X131)) != $true) | (((X129 @ (ap @ X131 @ X130))) = $true) | ($true != ((X129 @ X130)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f39,definition,( 50.81/8.71 ! [X136 : (subst > term > subst > $o)] : (($true = ((sP24 @ X136))) <=> ! [X146 : term,X147 : term] : ((((X136 @ id @ X147 @ id)) != $true) | (((X136 @ id @ X146 @ id)) != $true) | (((X136 @ id @ (ap @ (sub @ X146 @ id) @ X147) @ id)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f40,definition,( 50.81/8.71 (sP25 = $true) <=> ? [X149 : (subst > term > subst > $o),X148 : term] : (($true != ((X149 @ id @ (lam @ X148) @ id))) & ($true = ((sP22 @ X149))) & ! [X150 : term] : ((((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true) | ($true != ((X149 @ id @ X150 @ id)))) & ! [X152 : term,X154 : subst,X151 : subst,X153 : subst] : (($true = ((X149 @ (comp @ X154 @ X151) @ (sub @ X152 @ X151) @ X153))) | (((X149 @ X154 @ X152 @ (comp @ X151 @ X153))) != $true)) & ! [X163 : subst,X160 : subst,X161 : subst,X162 : term] : ((((X149 @ X163 @ X162 @ (comp @ X160 @ X161))) = $true) | (((X149 @ (comp @ X163 @ X160) @ (sub @ X162 @ X160) @ X161)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f41,definition,( 50.81/8.71 (sP26 = $true) <=> ! [X164 : (subst > term > subst > $o),X165 : term] : ((((sP21 @ X164)) = $true) | (((X164 @ id @ X165 @ id)) = $true) | ? [X166 : term] : (($true = ((var @ (sub @ X166 @ id)))) & (((X164 @ id @ X166 @ id)) != $true)) | ? [X171 : subst,X169 : term,X172 : subst,X170 : subst] : (($true = ((X164 @ X171 @ X169 @ (comp @ X170 @ X172)))) & (((X164 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170) @ X172)) != $true)) | ? [X180 : subst,X178 : subst,X179 : subst,X181 : term] : (($true != ((X164 @ X178 @ X181 @ (comp @ X179 @ X180)))) & (((X164 @ (comp @ X178 @ X179) @ (sub @ X181 @ X179) @ X180)) = $true)) | (((sP20 @ X164)) = $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f42,definition,( 50.81/8.71 ($true = sP27) <=> ? [X128 : term,X129 : (term > $o)] : (($true != ((X129 @ X128))) & ! [X132 : term] : ((((X129 @ (lam @ X132))) = $true) | ? [X133 : term] : ((((X129 @ (sub @ X132 @ (push @ X133 @ id)))) != $true) & ($true = ((X129 @ X133))))) & (((sP23 @ X129)) = $true) & ! [X134 : term] : ((((var @ X134)) != $true) | (((X129 @ X134)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f43,definition,( 50.81/8.71 ($true = sP28) <=> (? [X136 : (subst > term > subst > $o),X135 : term,X137 : term] : ((((X136 @ id @ (ap @ X135 @ X137) @ id)) != $true) & (((X136 @ id @ X135 @ id)) = $true) & ($true = ((sP24 @ X136))) & ! [X145 : subst,X143 : subst,X144 : subst,X142 : term] : ((((X136 @ X144 @ X142 @ (comp @ X145 @ X143))) = $true) | (((X136 @ (comp @ X144 @ X145) @ (sub @ X142 @ X145) @ X143)) != $true)) & ! [X141 : subst,X138 : term,X139 : subst,X140 : subst] : ((((X136 @ X141 @ X138 @ (comp @ X139 @ X140))) != $true) | ($true = ((X136 @ (comp @ X141 @ X139) @ (sub @ X138 @ X139) @ X140)))) & (((X136 @ id @ X137 @ id)) = $true)) | ($true = sP27) | (sP25 = $true) | (sP26 = $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f44,definition,( 50.81/8.71 (sP29 = $true) <=> ! [X330 : term,X331 : (term > $o),X332 : (subst > term > subst > $o)] : (? [X333 : term] : (((X331 @ X333)) != ((X332 @ id @ X333 @ id))) | ? [X334 : term] : (($true = ((X331 @ X334))) & ($true != ((X331 @ (sub @ X330 @ (push @ X334 @ id)))))) | ? [X335 : (subst > term > term)] : (! [X339 : term] : ((((X332 @ id @ X339 @ id)) != $true) | ($true = ((X332 @ id @ (X335 @ id @ X339) @ id)))) & ! [X336 : term,X338 : subst,X337 : subst] : (((X335 @ (comp @ X337 @ X338) @ (sub @ X336 @ X338))) = ((sub @ (X335 @ X337 @ X336) @ X338))) & (((X332 @ id @ (lam @ (X335 @ sh @ one)) @ id)) != $true)) | (((X331 @ (lam @ X330))) = $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f45,definition,( 50.81/8.71 ! [X420 : (subst > term > subst > $o)] : ((((sP30 @ X420)) = $true) <=> ? [X433 : (subst > term > term)] : (! [X434 : term] : (($true = ((X420 @ id @ (X433 @ id @ X434) @ id))) | (((X420 @ id @ X434 @ id)) != $true)) & (((X420 @ id @ (lam @ (X433 @ sh @ one)) @ id)) != $true) & ! [X437 : subst,X436 : subst,X435 : term] : (((X433 @ (comp @ X437 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X437 @ X435) @ X436)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f46,definition,( 50.81/8.71 (sP31 = $true) <=> (? [X419 : term] : (((sub @ X419 @ id)) != X419) | ! [X422 : term,X421 : (term > $o),X420 : (subst > term > subst > $o)] : ((((sP30 @ X420)) = $true) | ? [X428 : term] : (((X420 @ id @ X428 @ id)) != ((X421 @ X428))) | ? [X427 : term] : ((((X421 @ (sub @ X422 @ (push @ X427 @ id)))) != $true) & (((X421 @ X427)) = $true)) | ? [X432 : subst,X430 : subst,X431 : term,X429 : subst] : ((((X420 @ (comp @ X429 @ X430) @ (sub @ X431 @ X430) @ X432)) = $true) & ($true != ((X420 @ X429 @ X431 @ (comp @ X430 @ X432))))) | ? [X423 : term,X425 : subst,X426 : subst,X424 : subst] : ((((X420 @ (comp @ X425 @ X426) @ (sub @ X423 @ X426) @ X424)) != $true) & (((X420 @ X425 @ X423 @ (comp @ X426 @ X424))) = $true)) | (((X421 @ (lam @ X422))) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f47,definition,( 50.81/8.71 ! [X236 : (subst > term > subst > $o)] : ((((sP32 @ X236)) = $true) <=> ? [X242 : (subst > term > term)] : (! [X246 : term] : ((((X236 @ id @ (X242 @ id @ X246) @ id)) = $true) | ($true != ((X236 @ id @ X246 @ id)))) & (((X236 @ id @ (lam @ (X242 @ sh @ one)) @ id)) != $true) & ! [X244 : subst,X243 : term,X245 : subst] : (((sub @ (X242 @ X245 @ X243) @ X244)) = ((X242 @ (comp @ X245 @ X244) @ (sub @ X243 @ X244))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f48,definition,( 50.81/8.71 (sP33 = $true) <=> ! [X235 : term,X236 : (subst > term > subst > $o)] : (? [X241 : subst,X239 : subst,X238 : subst,X240 : term] : ((((X236 @ X241 @ X240 @ (comp @ X238 @ X239))) = $true) & (((X236 @ (comp @ X241 @ X238) @ (sub @ X240 @ X238) @ X239)) != $true)) | ($true = ((X236 @ id @ (lam @ X235) @ id))) | ? [X237 : term] : ((((X236 @ id @ (sub @ X235 @ (push @ X237 @ id)) @ id)) != $true) & ($true = ((X236 @ id @ X237 @ id)))) | (((sP32 @ X236)) = $true) | ? [X250 : subst,X247 : subst,X249 : subst,X248 : term] : (($true != ((X236 @ X250 @ X248 @ (comp @ X249 @ X247)))) & (((X236 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249) @ X247)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f49,definition,( 50.81/8.71 ! [X66 : (term > $o)] : ((((sP34 @ X66)) = $true) <=> ! [X69 : term,X70 : term] : (($true != ((X66 @ X69))) | (((X66 @ X70)) != $true) | (((X66 @ (ap @ X69 @ X70))) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f50,definition,( 50.81/8.71 ! [X83 : (subst > term > subst > $o)] : ((((sP35 @ X83)) = $true) <=> ? [X85 : (subst > term > term)] : ((((X83 @ id @ (lam @ (X85 @ sh @ one)) @ id)) != $true) & ! [X86 : term] : ((((X83 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X83 @ id @ X86 @ id)) != $true)) & ! [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X85 @ X89 @ X87) @ X88)) = ((X85 @ (comp @ X89 @ X88) @ (sub @ X87 @ X88))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f51,definition,( 50.81/8.71 ($true = sP36) <=> ? [X75 : (subst > term > subst > $o),X74 : term,X73 : (term > $o)] : (! [X82 : term] : (((X75 @ id @ X82 @ id)) = ((X73 @ X82))) & (((X73 @ (lam @ X74))) != $true) & ! [X76 : (subst > term > term)] : (? [X77 : term] : ((((X75 @ id @ (X76 @ id @ X77) @ id)) != $true) & (((X75 @ id @ X77 @ id)) = $true)) | (((X75 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ? [X80 : subst,X79 : term,X78 : subst] : (((X76 @ (comp @ X78 @ X80) @ (sub @ X79 @ X80))) != ((sub @ (X76 @ X78 @ X79) @ X80)))) & ! [X81 : term] : ((((X73 @ X81)) != $true) | ($true = ((X73 @ (sub @ X74 @ (push @ X81 @ id)))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f52,definition,( 50.81/8.71 (sP37 = $true) <=> ? [X66 : (term > $o),X65 : term] : (! [X67 : term] : (($true = ((X66 @ (lam @ X67)))) | ? [X68 : term] : ((((X66 @ X68)) = $true) & (((X66 @ (sub @ X67 @ (push @ X68 @ id)))) != $true))) & (((sP34 @ X66)) = $true) & ! [X71 : term] : (($true = ((X66 @ X71))) | (((var @ X71)) != $true)) & (((X66 @ X65)) != $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f53,definition,( 50.81/8.71 ($true = sP38) <=> (! [X84 : term,X83 : (subst > term > subst > $o)] : (? [X90 : term,X91 : term] : ((((X83 @ id @ X91 @ id)) = $true) & ($true != ((X83 @ id @ (ap @ (sub @ X91 @ id) @ X90) @ id))) & (((X83 @ id @ X90 @ id)) = $true)) | ($true = ((X83 @ id @ X84 @ id))) | (((sP35 @ X83)) = $true)) | ($true = sP36) | (sP37 = $true) | ? [X72 : term] : (((sub @ X72 @ id)) != X72) | ? [X62 : (subst > term > subst > $o)] : ! [X63 : (term > $o)] : ? [X64 : term] : (((X63 @ X64)) != ((X62 @ id @ X64 @ id))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f54,definition,( 50.81/8.71 ! [X201 : (term > $o)] : ((((sP39 @ X201)) = $true) <=> ? [X207 : term,X208 : term] : ((((X201 @ X207)) = $true) & (((X201 @ X208)) = $true) & (((X201 @ (ap @ X208 @ X207))) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f55,definition,( 50.81/8.71 (sP40 = $true) <=> ! [X201 : (term > $o),X203 : term,X202 : subst] : (? [X205 : term] : ((((X201 @ (lam @ X205))) != $true) & ! [X206 : term] : ((((X201 @ (sub @ X205 @ (push @ X206 @ id)))) = $true) | ($true != ((X201 @ X206))))) | (((sP39 @ X201)) = $true) | (((X201 @ (sub @ X203 @ X202))) = $true) | ? [X204 : term] : ((((var @ X204)) = $true) & (((X201 @ (sub @ X204 @ X202))) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f56,definition,( 50.81/8.71 ! [X385 : (term > $o)] : ((((sP41 @ X385)) = $true) <=> ! [X388 : term,X387 : term] : ((((X385 @ (ap @ X387 @ X388))) = $true) | (((X385 @ X388)) != $true) | (((X385 @ X387)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f57,definition,( 50.81/8.71 ! [X391 : (term > $o)] : ((((sP42 @ X391)) = $true) <=> ? [X397 : term,X396 : term] : ((((X391 @ X397)) = $true) & (((X391 @ X396)) = $true) & (((X391 @ (ap @ X396 @ X397))) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f58,definition,( 50.81/8.71 ($true = sP43) <=> ! [X391 : (term > $o),X392 : term,X390 : subst] : ((((X391 @ (sub @ X392 @ X390))) = $true) | (((sP42 @ X391)) = $true) | ? [X393 : term] : ((((var @ X393)) = $true) & (((X391 @ (sub @ X393 @ X390))) != $true)) | ? [X394 : term] : ((((X391 @ (lam @ X394))) != $true) & ! [X395 : term] : ((((X391 @ (sub @ X394 @ (push @ X395 @ id)))) = $true) | (((X391 @ X395)) != $true))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f59,definition,( 50.81/8.71 (sP44 = $true) <=> (($true = sP43) | ? [X383 : subst] : (((comp @ X383 @ id)) != X383) | ? [X380 : term,X379 : subst] : (((sub @ one @ (push @ X380 @ X379))) != X380) | ? [X384 : term,X385 : (term > $o)] : ((((X385 @ X384)) != $true) & ! [X389 : term] : (($true = ((X385 @ (lam @ X389)))) | ($true != ((X385 @ X389)))) & (((sP41 @ X385)) = $true) & ! [X386 : term] : ((((var @ X386)) != $true) | ($true = ((X385 @ X386))))) | ? [X381 : term,X382 : subst] : (((comp @ sh @ (push @ X381 @ X382))) != X382))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f60,definition,( 50.81/8.71 ($true = sP45) <=> ! [X439 : term,X438 : (subst > term > subst > $o)] : (? [X449 : term] : ((((X438 @ id @ X449 @ id)) = $true) & (((X438 @ id @ (sub @ X439 @ (push @ X449 @ id)) @ id)) != $true)) | ? [X441 : (subst > term > term),X440 : term] : (! [X444 : term,X443 : subst,X442 : subst] : (((X441 @ (comp @ X442 @ X443) @ (sub @ X444 @ X443))) = ((sub @ X440 @ (push @ (sub @ X444 @ X443) @ (comp @ X442 @ X443))))) & (((X438 @ id @ (lam @ (X441 @ sh @ one)) @ id)) != $true) & ! [X446 : subst,X447 : subst,X445 : term] : (((sub @ (sub @ X440 @ (push @ X445 @ X446)) @ X447)) = ((sub @ (X441 @ X446 @ X445) @ X447))) & ! [X448 : term] : ((((X438 @ id @ (X441 @ id @ X448) @ id)) = $true) | (((X438 @ id @ X448 @ id)) != $true))) | (((X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id)) = $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f61,definition,( 50.81/8.71 ! [X492 : (subst > term > subst > $o)] : (($true = ((sP46 @ X492))) <=> ? [X504 : (subst > term > term)] : (! [X505 : term] : (($true = ((X492 @ id @ (X504 @ id @ X505) @ id))) | (((X492 @ id @ X505 @ id)) != $true)) & (((X492 @ id @ (lam @ (X504 @ sh @ one)) @ id)) != $true) & ! [X506 : subst,X507 : subst,X508 : term] : (((X504 @ (comp @ X507 @ X506) @ (sub @ X508 @ X506))) = ((sub @ (X504 @ X507 @ X508) @ X506)))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f62,definition,( 50.81/8.71 ! [X492 : (subst > term > subst > $o)] : ((((sP47 @ X492)) = $true) <=> ? [X501 : term,X502 : term] : ((((X492 @ id @ (ap @ (sub @ X501 @ id) @ X502) @ id)) != $true) & (((X492 @ id @ X502 @ id)) = $true) & (((X492 @ id @ X501 @ id)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f63,definition,( 50.81/8.71 ! [X473 : (term > $o)] : (($true = ((sP48 @ X473))) <=> ! [X476 : term,X475 : term] : ((((X473 @ (ap @ X475 @ X476))) = $true) | ($true != ((X473 @ X476))) | (((X473 @ X475)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f64,definition,( 50.81/8.71 (sP49 = $true) <=> ! [X492 : (subst > term > subst > $o),X491 : term] : ((((sP47 @ X492)) = $true) | ? [X499 : subst,X500 : subst,X498 : subst,X497 : term] : ((((X492 @ (comp @ X499 @ X500) @ (sub @ X497 @ X500) @ X498)) = $true) & (((X492 @ X499 @ X497 @ (comp @ X500 @ X498))) != $true)) | ($true = ((sP46 @ X492))) | ? [X493 : subst,X495 : subst,X496 : subst,X494 : term] : ((((X492 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)) != $true) & (((X492 @ X493 @ X494 @ (comp @ X495 @ X496))) = $true)) | ? [X503 : term] : ((((X492 @ id @ X503 @ id)) != $true) & ($true = ((var @ (sub @ X503 @ id))))) | (((X492 @ id @ X491 @ id)) = $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f65,definition,( 50.81/8.71 ($true = sP50) <=> ? [X483 : (term > $o),X481 : (subst > term > subst > $o),X482 : term] : (($true != ((X483 @ (lam @ X482)))) & ! [X484 : (subst > term > term)] : (? [X487 : subst,X485 : term,X486 : subst] : (((X484 @ (comp @ X486 @ X487) @ (sub @ X485 @ X487))) != ((sub @ (X484 @ X486 @ X485) @ X487))) | ($true = ((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id))) | ? [X488 : term] : (($true = ((X481 @ id @ X488 @ id))) & ($true != ((X481 @ id @ (X484 @ id @ X488) @ id))))) & ! [X489 : term] : ((((X483 @ X489)) != $true) | (((X483 @ (sub @ X482 @ (push @ X489 @ id)))) = $true)) & ! [X490 : term] : (((X481 @ id @ X490 @ id)) = ((X483 @ X490))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f66,definition,( 50.81/8.71 (sP51 = $true) <=> (($true = sP50) | ? [X473 : (term > $o),X474 : term] : ((((X473 @ X474)) != $true) & ! [X478 : term] : ((((X473 @ (lam @ X478))) = $true) | ? [X479 : term] : (($true != ((X473 @ (sub @ X478 @ (push @ X479 @ id))))) & (((X473 @ X479)) = $true))) & ! [X477 : term] : (($true != ((var @ X477))) | (((X473 @ X477)) = $true)) & ($true = ((sP48 @ X473)))) | (sP49 = $true) | ? [X470 : (subst > term > subst > $o)] : ! [X471 : (term > $o)] : ? [X472 : term] : (((X470 @ id @ X472 @ id)) != ((X471 @ X472))) | ? [X480 : term] : (((sub @ X480 @ id)) != X480))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f67,definition,( 50.81/8.71 ! [X356 : (subst > term > subst > $o)] : ((((sP52 @ X356)) = $true) <=> ? [X359 : (subst > term > term)] : (! [X362 : subst,X363 : term,X361 : subst] : (((sub @ (X359 @ X361 @ X363) @ X362)) = ((X359 @ (comp @ X361 @ X362) @ (sub @ X363 @ X362)))) & ! [X360 : term] : ((((X356 @ id @ (X359 @ id @ X360) @ id)) = $true) | (((X356 @ id @ X360 @ id)) != $true)) & (((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f68,definition,( 50.81/8.71 (sP53 = $true) <=> ! [X358 : (term > $o),X357 : term,X356 : (subst > term > subst > $o)] : ((((sP52 @ X356)) = $true) | ? [X371 : subst,X369 : subst,X370 : subst,X368 : term] : ((((X356 @ (comp @ X370 @ X369) @ (sub @ X368 @ X369) @ X371)) != $true) & (((X356 @ X370 @ X368 @ (comp @ X369 @ X371))) = $true)) | ($true = ((X358 @ (lam @ X357)))) | ? [X373 : term] : (((X358 @ X373)) != ((X356 @ id @ X373 @ id))) | ? [X372 : term] : ((((X358 @ X372)) = $true) & (((X358 @ (sub @ X357 @ (push @ X372 @ id)))) != $true)) | ? [X367 : subst,X366 : subst,X365 : term,X364 : subst] : (($true = ((X356 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X367))) & (((X356 @ X364 @ X365 @ (comp @ X366 @ X367))) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f69,definition,( 50.81/8.71 (sP54 = $true) <=> (? [X255 : term,X256 : term] : ((X255 != X256) & (((lam @ X256)) = ((lam @ X255)))) | ? [X254 : subst,X253 : term] : (((comp @ sh @ (push @ X253 @ X254))) != X254) | ? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251) | ! [X260 : (subst > term > term),X258 : (subst > term > term),X257 : subst,X259 : term] : ((((lam @ (X258 @ sh @ one))) != ((lam @ (X260 @ sh @ one)))) | (((X258 @ X257 @ X259)) = ((X260 @ X257 @ X259))) | ? [X263 : term,X261 : subst,X262 : subst] : (((X258 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262))) != ((sub @ (X258 @ X261 @ X263) @ X262))) | ? [X265 : term,X264 : subst,X266 : subst] : (((sub @ (X260 @ X266 @ X265) @ X264)) != ((X260 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f70,definition,( 50.81/8.71 ($true = sP55) <=> (? [X36 : term] : (((sub @ X36 @ id)) != X36) | ! [X38 : term,X37 : (subst > term > subst > $o),X39 : (term > $o)] : (? [X41 : term] : (((X37 @ id @ X41 @ id)) != ((X39 @ X41))) | (((X39 @ (lam @ X38))) = $true) | ? [X42 : (subst > term > term)] : (! [X43 : term] : (($true = ((X37 @ id @ (X42 @ id @ X43) @ id))) | (((X37 @ id @ X43 @ id)) != $true)) & (((X37 @ id @ (lam @ (X42 @ sh @ one)) @ id)) != $true) & ! [X44 : term,X46 : subst,X45 : subst] : (((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45))) = ((sub @ (X42 @ X46 @ X44) @ X45)))) | ? [X40 : term] : (($true = ((X39 @ X40))) & (((X39 @ (sub @ X38 @ (push @ X40 @ id)))) != $true))) | ? [X32 : term] : ! [X33 : (subst > term > term)] : ? [X34 : term,X35 : subst] : (((sub @ X32 @ (push @ X34 @ X35))) != ((X33 @ X35 @ X34))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f71,definition,( 50.81/8.71 ! [X183 : (subst > term > subst > $o)] : ((((sP56 @ X183)) = $true) <=> ? [X196 : (subst > term > term)] : (($true != ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X197 : term] : ((((X183 @ id @ X197 @ id)) != $true) | (((X183 @ id @ (X196 @ id @ X197) @ id)) = $true)) & ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200))))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f72,definition,( 50.81/8.71 ! [X183 : (subst > term > subst > $o)] : (($true = ((sP57 @ X183))) <=> ? [X190 : term,X191 : term] : (($true = ((X183 @ id @ X191 @ id))) & ($true = ((X183 @ id @ X190 @ id))) & (((X183 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) != $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f73,definition,( 50.81/8.71 (sP58 = $true) <=> ! [X184 : term,X183 : (subst > term > subst > $o)] : (? [X192 : term,X194 : subst,X195 : subst,X193 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) != $true) & (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) = $true)) | ? [X185 : term] : (($true != ((X183 @ id @ X185 @ id))) & ($true = ((var @ (sub @ X185 @ id))))) | ? [X186 : term,X187 : subst,X189 : subst,X188 : subst] : ((((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) = $true) & (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) != $true)) | ($true = ((sP57 @ X183))) | (((X183 @ id @ X184 @ id)) = $true) | (((sP56 @ X183)) = $true))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f74,plain,( 50.81/8.71 ((hoasinduction = $true) <=> (sP58 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axclos = $true) & (axapp = $true) & (termmset_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2 = $true) & (($true = sP55) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem0_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (sP54 = $true)) & ((sP53 = $true) <=> (hoasinduction_lem3v2 = $true)) & ((! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329)) | ? [X321 : term] : (((sub @ X321 @ id)) != X321) | ? [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) = ((ap @ X324 @ X325))) & (X323 != X324))) <=> (hoasapinj1_lthm = $true)) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & ((sP51 = $true) <=> (hoasinduction_lthm_3 = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & ((! [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true != ((X529 @ X526))) | ($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) | ? [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) != X521) | ? [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) != X524)) <=> (pushprop_lem1_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP45)) & (hoasinduction_lem1_gthm = $true) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) <=> (apinj1 = $true)) & (! [X518 : (subst > term > subst > $o)] : ? [X519 : (term > $o)] : ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))) | ? [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) = ((ap @ X399 @ X398))) & (X398 != X401)))) & (axassoc = $true) & (ulamvarsh = $true) & ((hoasapinj2 = $true) <=> ! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47))))) & (hoasinduction_lem1 = $true) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & ! [X288 : d_term,X289 : d_term] : ((X288 = X289) | (((d2term @ X288)) != ((d2term @ X289)))) & (hoasinduction_lem2_lthm = $true) & ((induction2lem_lthm = $true) <=> (sP44 = $true)) & ((sP40 = $true) <=> (induction2lem = $true)) & (! [X375 : subst,X376 : term,X374 : (term > $o)] : ? [X377 : (term > $o)] : ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378))) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotvar_gthm = $true) & ! [X355 : d_subst] : (d_id = X355) & (hoasinduction_lem1v2 = $true) & (pushprop_lem1v2_gthm = $true) & (lamnotap != $true) & (induction2_gthm = $true) & (apnotvar = $true) & (axmap = $true) & (! [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | ? [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) != ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | ? [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) != ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))) <=> (hoaslaminj = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = id) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP38)) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) <=> (laminj = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP33 = $true) <=> (hoasinduction_lem3 = $true)) & ((sP31 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & ((sP29 = $true) <=> (hoasinduction_lem3v2a = $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & (($true = sP28) <=> (hoasinduction_lthm = $true)) & (($true = sP19) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X182 : d_term] : (d_one = X182) & ((induction2 = $true) <=> ($true = sP18)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP16) <=> (hoasinduction_lem2v2 = $true)) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & ((hoasinduction_lem0_lthm = $true) <=> ! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id)))) & ((sP14 = $true) <=> (hoasinduction_lem3_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) <=> ! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7))))) & (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)))))))))))))) & (hoaslamnotvar_lthm = $true) & ((axvarid = $true) <=> ! [X61 : term] : (((sub @ X61 @ id)) = X61)) & (! [X510 : (subst > term > subst > $o),X509 : term] : (? [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) != $true) & (((X510 @ id @ X512 @ id)) = $true) & (((X510 @ id @ X511 @ id)) = $true)) | (((sP11 @ X510)) = $true) | ($true = ((X510 @ id @ X509 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((sP10 = $true) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3a = $true) <=> (sP9 = $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & ((hoasinduction_lem3b = $true) <=> ! [X417 : term] : ? [X418 : (subst > term > term)] : (((X418 @ sh @ one)) = ((sub @ X417 @ (push @ one @ sh))))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) != $true) | ? [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) != ((X232 @ X234))) | (((X232 @ one)) = $true)) | ? [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) != X228))) & (hoasinduction_lem2_gthm = $true) & ((shinj = $true) <=> ! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26))) & (axabs = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lthm_orig = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) <=> (sP8 = $true)) & (ulamvar1 != $true) & ((axvarcons = $true) <=> ! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4)) & (hoasinduction_lem2v2_gthm = $true) & (($true = sP6) <=> (hoasinduction_lem3a_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true != ((X30 @ X27))) | ($true = ((X29 @ one))) | ? [X31 : term] : (((X29 @ X31)) != ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X53 : term] : ? [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) = ((X54 @ sh @ one)))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X532 : term] : ? [X533 : (subst > term > term)] : ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535)))) & ((axidl = $true) <=> ! [X318 : subst] : (((comp @ id @ X318)) = X318)) & ((termmset = $true) <=> ! [X462 : term] : (((sub @ X462 @ id)) = X462)) & (hoasinduction_gthm = $true) & (! [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | (((X409 @ X407)) != $true)) <=> (pushprop_lem1 = $true)) & (! [X225 : subst] : (((comp @ X225 @ id)) = X225) <=> (axidr = $true)) & ((hoaslamnotap = $true) <=> ! [X411 : (subst > term > term),X412 : term,X413 : term] : (? [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) != ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) | (((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412))))) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) <=> ! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56)) & ! [X227 : d_subst,X226 : d_subst] : ((X226 = X227) | (((d2subst @ X226)) != ((d2subst @ X227)))) & (! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) <=> (apinj2 = $true)) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3b_gthm = $true) & ((termmset_lthm = $true) <=> (! [X118 : term] : (((sub @ X118 @ id)) = X118) | ? [X117 : term] : (((sub @ X117 @ id)) != X117))) & ((induction = $true) <=> ! [X119 : term,X120 : (term > $o)] : (? [X121 : term] : (($true = ((X120 @ X121))) & (((X120 @ (lam @ X121))) != $true)) | ? [X124 : term] : ((((var @ X124)) = $true) & (((X120 @ X124)) != $true)) | (((sP4 @ X120)) = $true) | (((X120 @ X119)) = $true))) & (hoaslamnotap_lthm = $true) & ((induction2_lthm = $true) <=> (sP3 = $true)) & (pushprop_lthm = $true) & (! [X536 : term] : ? [X537 : (subst > term > term)] : ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((substmonoid_lthm = $true) <=> ((! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3)) | ? [X0 : subst] : (((comp @ id @ X0)) != X0) | ? [X1 : subst] : (((comp @ X1 @ id)) != X1))) & ((axscons = $true) <=> ! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307)) & (ulamvarind = $true) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X467 : (term > $o),X465 : term,X466 : subst] : ? [X468 : (term > $o)] : ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469))))), 50.81/8.71 inference(definition_folding,[],[f14,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,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])). 50.81/8.71 thf(f75,definition,( 50.81/8.71 ! [X0 : (subst > term > subst > $o)] : (($true = ((sP59 @ X0))) <=> ? [X12 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true) & ! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))) & ! [X16 : term] : ((((X0 @ id @ (X12 @ id @ X16) @ id)) = $true) | (((X0 @ id @ X16 @ id)) != $true))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f76,definition,( 50.81/8.71 ! [X0 : (subst > term > subst > $o)] : ((((sP60 @ X0)) = $true) <=> ? [X10 : term,X11 : term] : (($true = ((X0 @ id @ X11 @ id))) & (((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)) != $true) & (((X0 @ id @ X10 @ id)) = $true)))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f77,definition,( 50.81/8.71 (sP61 = $true) <=> ! [X0 : (subst > term > subst > $o)] : (? [X7 : subst,X8 : term,X6 : subst,X5 : subst] : ((((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) != $true) & ($true = ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6)))) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true)) | ? [X3 : term,X1 : subst,X2 : subst,X4 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) != $true)) | (((sP60 @ X0)) = $true) | ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | ($true = ((sP59 @ X0))))), 50.81/8.71 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 50.81/8.71 thf(f78,plain,( 50.81/8.71 (hoasinduction = $true) <~> (sP61 = $true)), 50.81/8.71 inference(definition_folding,[],[f12,f77,f76,f75])). 50.81/8.71 thf(f79,plain,( 50.81/8.71 ((sP58 = $true) | ? [X184 : term,X183 : (subst > term > subst > $o)] : (! [X192 : term,X194 : subst,X195 : subst,X193 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) = $true) | (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) != $true)) & ! [X185 : term] : (($true = ((X183 @ id @ X185 @ id))) | ($true != ((var @ (sub @ X185 @ id))))) & ! [X186 : term,X187 : subst,X189 : subst,X188 : subst] : ((((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) != $true) | (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) = $true)) & ($true != ((sP57 @ X183))) & (((X183 @ id @ X184 @ id)) != $true) & (((sP56 @ X183)) != $true))) & (! [X184 : term,X183 : (subst > term > subst > $o)] : (? [X192 : term,X194 : subst,X195 : subst,X193 : subst] : ((((X183 @ X195 @ X192 @ (comp @ X194 @ X193))) != $true) & (((X183 @ (comp @ X195 @ X194) @ (sub @ X192 @ X194) @ X193)) = $true)) | ? [X185 : term] : (($true != ((X183 @ id @ X185 @ id))) & ($true = ((var @ (sub @ X185 @ id))))) | ? [X186 : term,X187 : subst,X189 : subst,X188 : subst] : ((((X183 @ X189 @ X186 @ (comp @ X187 @ X188))) = $true) & (((X183 @ (comp @ X189 @ X187) @ (sub @ X186 @ X187) @ X188)) != $true)) | ($true = ((sP57 @ X183))) | (((X183 @ id @ X184 @ id)) = $true) | (((sP56 @ X183)) = $true)) | (sP58 != $true))), 50.81/8.71 inference(nnf_transformation,[],[f73])). 50.81/8.71 thf(f80,plain,( 50.81/8.71 ((sP58 = $true) | ? [X0 : term,X1 : (subst > term > subst > $o)] : (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : ((((X1 @ X4 @ X2 @ (comp @ X3 @ X5))) = $true) | (((X1 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5)) != $true)) & ! [X6 : term] : ((((X1 @ id @ X6 @ id)) = $true) | ($true != ((var @ (sub @ X6 @ id))))) & ! [X7 : term,X8 : subst,X9 : subst,X10 : subst] : ((((X1 @ X9 @ X7 @ (comp @ X8 @ X10))) != $true) | (((X1 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X10)) = $true)) & (((sP57 @ X1)) != $true) & (((X1 @ id @ X0 @ id)) != $true) & (((sP56 @ X1)) != $true))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : (? [X13 : term,X14 : subst,X15 : subst,X16 : subst] : ((((X12 @ X15 @ X13 @ (comp @ X14 @ X16))) != $true) & (((X12 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14) @ X16)) = $true)) | ? [X17 : term] : ((((X12 @ id @ X17 @ id)) != $true) & ($true = ((var @ (sub @ X17 @ id))))) | ? [X18 : term,X19 : subst,X20 : subst,X21 : subst] : ((((X12 @ X20 @ X18 @ (comp @ X19 @ X21))) = $true) & (((X12 @ (comp @ X20 @ X19) @ (sub @ X18 @ X19) @ X21)) != $true)) | ($true = ((sP57 @ X12))) | ($true = ((X12 @ id @ X11 @ id))) | (((sP56 @ X12)) = $true)) | (sP58 != $true))), 50.81/8.71 inference(rectify,[],[f79])). 50.81/8.71 thf(f81,plain,( 50.81/8.71 ((sP58 = $true) | (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : ((((sK63 @ X4 @ X2 @ (comp @ X3 @ X5))) = $true) | ($true != ((sK63 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3) @ X5)))) & ! [X6 : term] : ((((sK63 @ id @ X6 @ id)) = $true) | ($true != ((var @ (sub @ X6 @ id))))) & ! [X7 : term,X8 : subst,X9 : subst,X10 : subst] : ((((sK63 @ X9 @ X7 @ (comp @ X8 @ X10))) != $true) | (((sK63 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X10)) = $true)) & (((sP57 @ sK63)) != $true) & (((sK63 @ id @ sK62 @ id)) != $true) & (((sP56 @ sK63)) != $true))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : (((((X12 @ (sK66 @ X12) @ (sK64 @ X12) @ (comp @ (sK65 @ X12) @ (sK67 @ X12)))) != $true) & (((X12 @ (comp @ (sK66 @ X12) @ (sK65 @ X12)) @ (sub @ (sK64 @ X12) @ (sK65 @ X12)) @ (sK67 @ X12))) = $true)) | ((((X12 @ id @ (sK68 @ X12) @ id)) != $true) & (((var @ (sub @ (sK68 @ X12) @ id))) = $true)) | ((((X12 @ (sK71 @ X12) @ (sK69 @ X12) @ (comp @ (sK70 @ X12) @ (sK72 @ X12)))) = $true) & (((X12 @ (comp @ (sK71 @ X12) @ (sK70 @ X12)) @ (sub @ (sK69 @ X12) @ (sK70 @ X12)) @ (sK72 @ X12))) != $true)) | ($true = ((sP57 @ X12))) | ($true = ((X12 @ id @ X11 @ id))) | (((sP56 @ X12)) = $true)) | (sP58 != $true))), 50.81/8.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK62),skolemize(X1,sK63),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12)],[f80])). 50.81/8.71 thf(f85,plain,( 50.81/8.71 ! [X183 : (subst > term > subst > $o)] : (((((sP56 @ X183)) = $true) | ! [X196 : (subst > term > term)] : (($true = ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ? [X197 : term] : ((((X183 @ id @ X197 @ id)) = $true) & (((X183 @ id @ (X196 @ id @ X197) @ id)) != $true)) | ? [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) != ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200)))))) & (? [X196 : (subst > term > term)] : (($true != ((X183 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X197 : term] : ((((X183 @ id @ X197 @ id)) != $true) | (((X183 @ id @ (X196 @ id @ X197) @ id)) = $true)) & ! [X199 : subst,X200 : subst,X198 : term] : (((sub @ (X196 @ X199 @ X198) @ X200)) = ((X196 @ (comp @ X199 @ X200) @ (sub @ X198 @ X200))))) | (((sP56 @ X183)) != $true)))), 50.81/8.71 inference(nnf_transformation,[],[f71])). 50.81/8.71 thf(f86,plain,( 50.81/8.71 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP56 @ X0))) | ! [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ? [X2 : term] : ((((X0 @ id @ X2 @ id)) = $true) & ($true != ((X0 @ id @ (X1 @ id @ X2) @ id)))) | ? [X3 : subst,X4 : subst,X5 : term] : (((sub @ (X1 @ X3 @ X5) @ X4)) != ((X1 @ (comp @ X3 @ X4) @ (sub @ X5 @ X4)))))) & (? [X6 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) != $true) & ! [X7 : term] : ((((X0 @ id @ X7 @ id)) != $true) | (((X0 @ id @ (X6 @ id @ X7) @ id)) = $true)) & ! [X8 : subst,X9 : subst,X10 : term] : (((X6 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9))) = ((sub @ (X6 @ X8 @ X10) @ X9)))) | ($true != ((sP56 @ X0)))))), 50.81/8.71 inference(rectify,[],[f85])). 50.81/8.71 thf(f87,plain,( 50.81/8.71 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP56 @ X0))) | ! [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (($true = ((X0 @ id @ (sK75 @ X1 @ X0) @ id))) & (((X0 @ id @ (X1 @ id @ (sK75 @ X1 @ X0)) @ id)) != $true)) | (((X1 @ (comp @ (sK76 @ X1) @ (sK77 @ X1)) @ (sub @ (sK78 @ X1) @ (sK77 @ X1)))) != ((sub @ (X1 @ (sK76 @ X1) @ (sK78 @ X1)) @ (sK77 @ X1)))))) & ((($true != ((X0 @ id @ (lam @ (sK79 @ X0 @ sh @ one)) @ id))) & ! [X7 : term] : ((((X0 @ id @ X7 @ id)) != $true) | (((X0 @ id @ (sK79 @ X0 @ id @ X7) @ id)) = $true)) & ! [X8 : subst,X9 : subst,X10 : term] : (((sub @ (sK79 @ X0 @ X8 @ X10) @ X9)) = ((sK79 @ X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9))))) | ($true != ((sP56 @ X0)))))), 50.81/8.71 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12)],[f86])). 50.81/8.71 thf(f194,plain,( 50.81/8.71 ! [X149 : (subst > term > subst > $o)] : ((($true = ((sP22 @ X149))) | ? [X155 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) != $true) & ! [X159 : term,X158 : subst,X157 : subst] : (((sub @ (X155 @ X157 @ X159) @ X158)) = ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158)))) & ! [X156 : term] : (($true = ((X149 @ id @ (X155 @ id @ X156) @ id))) | (((X149 @ id @ X156 @ id)) != $true)))) & (! [X155 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X155 @ sh @ one)) @ id)) = $true) | ? [X159 : term,X158 : subst,X157 : subst] : (((sub @ (X155 @ X157 @ X159) @ X158)) != ((X155 @ (comp @ X157 @ X158) @ (sub @ X159 @ X158)))) | ? [X156 : term] : (($true != ((X149 @ id @ (X155 @ id @ X156) @ id))) & (((X149 @ id @ X156 @ id)) = $true))) | ($true != ((sP22 @ X149)))))), 50.81/8.71 inference(nnf_transformation,[],[f37])). 50.81/8.71 thf(f195,plain,( 50.81/8.71 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP22 @ X0))) | ? [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) != $true) & ! [X2 : term,X3 : subst,X4 : subst] : (((sub @ (X1 @ X4 @ X2) @ X3)) = ((X1 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3)))) & ! [X5 : term] : (($true = ((X0 @ id @ (X1 @ id @ X5) @ id))) | (((X0 @ id @ X5 @ id)) != $true)))) & (! [X6 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true) | ? [X7 : term,X8 : subst,X9 : subst] : (((sub @ (X6 @ X9 @ X7) @ X8)) != ((X6 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8)))) | ? [X10 : term] : ((((X0 @ id @ (X6 @ id @ X10) @ id)) != $true) & (((X0 @ id @ X10 @ id)) = $true))) | ($true != ((sP22 @ X0)))))), 50.81/8.71 inference(rectify,[],[f194])). 50.81/8.71 thf(f196,plain,( 50.81/8.71 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP22 @ X0))) | ((((X0 @ id @ (lam @ (sK324 @ X0 @ sh @ one)) @ id)) != $true) & ! [X2 : term,X3 : subst,X4 : subst] : (((sK324 @ X0 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3))) = ((sub @ (sK324 @ X0 @ X4 @ X2) @ X3))) & ! [X5 : term] : ((((X0 @ id @ (sK324 @ X0 @ id @ X5) @ id)) = $true) | (((X0 @ id @ X5 @ id)) != $true)))) & (! [X6 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true) | (((sub @ (X6 @ (sK327 @ X6) @ (sK325 @ X6)) @ (sK326 @ X6))) != ((X6 @ (comp @ (sK327 @ X6) @ (sK326 @ X6)) @ (sub @ (sK325 @ X6) @ (sK326 @ X6))))) | ((((X0 @ id @ (X6 @ id @ (sK328 @ X6 @ X0)) @ id)) != $true) & (((X0 @ id @ (sK328 @ X6 @ X0) @ id)) = $true))) | ($true != ((sP22 @ X0)))))), 50.81/8.71 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12)],[f195])). 50.81/8.71 thf(f266,plain,( 50.81/8.71 (((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axclos = $true) & (axapp = $true) & (termmset_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2 = $true) & ((($true = sP55) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP55))) & (pushprop_lem0_gthm = $true) & (((hoaslaminj_lthm = $true) | (sP54 != $true)) & ((sP54 = $true) | (hoaslaminj_lthm != $true))) & (((sP53 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP53 != $true))) & (((! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329)) | ? [X321 : term] : (((sub @ X321 @ id)) != X321) | ? [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) = ((ap @ X324 @ X325))) & (X323 != X324))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) = ((ap @ (sub @ X328 @ id) @ X327))) & (X328 != X329)) & ! [X321 : term] : (((sub @ X321 @ id)) = X321) & ! [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) != ((ap @ X324 @ X325))) | (X323 = X324))))) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & (((sP51 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP51 != $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((! [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true != ((X529 @ X526))) | ($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) | ? [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) != X521) | ? [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) != X524)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true = ((X529 @ X526))) & ($true != ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) & ! [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) = X521) & ! [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) = X524)))) & (((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true))) & (hoasinduction_lem1_gthm = $true) & ((! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 != X59) & (((ap @ X59 @ X58)) = ((ap @ X57 @ X60)))))) & ((! [X518 : (subst > term > subst > $o)] : ? [X519 : (term > $o)] : ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X518 : (subst > term > subst > $o)] : ! [X519 : (term > $o)] : ? [X520 : term] : (((X519 @ X520)) != ((X518 @ id @ X520 @ id))))) & (pushprop_lem3v2_lthm = $true) & (((hoasapinj2_lthm = $true) | (? [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 != X405) & (((ap @ (sub @ X403 @ id) @ X405)) = ((ap @ (sub @ X402 @ id) @ X404)))) & ! [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) != ((ap @ X399 @ X398))) | (X398 = X401)))) & ((! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))) | ? [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) = ((ap @ X399 @ X398))) & (X398 != X401))) | (hoasapinj2_lthm != $true))) & (axassoc = $true) & (ulamvarsh = $true) & (((hoasapinj2 = $true) | ? [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 != X48) & (((ap @ (sub @ X49 @ id) @ X48)) = ((ap @ (sub @ X50 @ id) @ X47))))) & (! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47)))) | (hoasapinj2 != $true))) & (hoasinduction_lem1 = $true) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & ! [X288 : d_term,X289 : d_term] : ((X288 = X289) | (((d2term @ X288)) != ((d2term @ X289)))) & (hoasinduction_lem2_lthm = $true) & (((induction2lem_lthm = $true) | (sP44 != $true)) & ((sP44 = $true) | (induction2lem_lthm != $true))) & (((sP40 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP40 != $true))) & ((! [X375 : subst,X376 : term,X374 : (term > $o)] : ? [X377 : (term > $o)] : ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X375 : subst,X376 : term,X374 : (term > $o)] : ! [X377 : (term > $o)] : ? [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) != ((X377 @ X378))))) & (hoaslamnotvar_gthm = $true) & ! [X355 : d_subst] : (d_id = X355) & (hoasinduction_lem1v2 = $true) & (pushprop_lem1v2_gthm = $true) & (lamnotap != $true) & (induction2_gthm = $true) & (apnotvar = $true) & (axmap = $true) & ((! [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | ? [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) != ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | ? [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) != ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) != ((X309 @ X308 @ X311))) & ! [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) = ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) & ! [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) = ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) & (((lam @ (X310 @ sh @ one))) = ((lam @ (X309 @ sh @ one))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = id) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_no_psi_cond_lthm != $true))) & ((! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) | (laminj != $true)) & ((laminj = $true) | ? [X51 : term,X52 : term] : ((X51 != X52) & (((lam @ X52)) = ((lam @ X51)))))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (((sP33 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP33 != $true))) & (((sP31 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP31 != $true))) & (((sP29 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP29 != $true))) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & (((substmonoid = $true) | (? [X464 : subst] : (((comp @ X464 @ id)) != X464) | ? [X463 : subst] : (((comp @ id @ X463)) != X463))) & ((! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463)) | (substmonoid != $true))) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & ((($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28))) & ((($true = sP19) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP19))) & ! [X182 : d_term] : (d_one = X182) & (((induction2 = $true) | ($true != sP18)) & (($true = sP18) | (induction2 != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((($true = sP16) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP16))) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & (((hoasinduction_lem0_lthm = $true) | ? [X125 : (subst > term > subst > $o)] : ! [X126 : (term > $o)] : ? [X127 : term] : (((X126 @ X127)) != ((X125 @ id @ X127 @ id)))) & (! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((sP14 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP14 != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasapinj1 = $true) | ? [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 != X8) & (((ap @ (sub @ X6 @ id) @ X9)) = ((ap @ (sub @ X8 @ id) @ X7))))) & (! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7)))) | (hoasapinj1 != $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)))))))))))))) & (hoaslamnotvar_lthm = $true) & (((axvarid = $true) | ? [X61 : term] : (((sub @ X61 @ id)) != X61)) & (! [X61 : term] : (((sub @ X61 @ id)) = X61) | (axvarid != $true))) & ((! [X510 : (subst > term > subst > $o),X509 : term] : (? [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) != $true) & (((X510 @ id @ X512 @ id)) = $true) & (((X510 @ id @ X511 @ id)) = $true)) | (((sP11 @ X510)) = $true) | ($true = ((X510 @ id @ X509 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X510 : (subst > term > subst > $o),X509 : term] : (! [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) = $true) | (((X510 @ id @ X512 @ id)) != $true) | (((X510 @ id @ X511 @ id)) != $true)) & (((sP11 @ X510)) != $true) & ($true != ((X510 @ id @ X509 @ id)))))) & (hoasinduction_lem3a_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (((sP10 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP10 != $true))) & (((hoasinduction_lem3a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a != $true))) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((hoasinduction_lem3b = $true) | ? [X417 : term] : ! [X418 : (subst > term > term)] : (((X418 @ sh @ one)) != ((sub @ X417 @ (push @ one @ sh))))) & (! [X417 : term] : ? [X418 : (subst > term > term)] : (((X418 @ sh @ one)) = ((sub @ X417 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (((pushprop_lem1v2_lthm = $true) | (? [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) = $true) & ! [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) = ((X232 @ X234))) & (((X232 @ one)) != $true)) & ! [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) = X228))) & ((! [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) != $true) | ? [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) != ((X232 @ X234))) | (((X232 @ one)) = $true)) | ? [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) != X228)) | (pushprop_lem1v2_lthm != $true))) & (hoasinduction_lem2_gthm = $true) & (((shinj = $true) | ? [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) = ((sub @ X26 @ sh))) & (X25 != X26))) & (! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26)) | (shinj != $true))) & (axabs = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lthm_orig = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((hoasinduction_lem2 = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem2 != $true))) & (ulamvar1 != $true) & (((axvarcons = $true) | ? [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) != X4)) & (! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4) | (axvarcons != $true))) & (hoasinduction_lem2v2_gthm = $true) & ((($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP6))) & (((pushprop_lem1v2 = $true) | ? [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true = ((X30 @ X27))) & ($true != ((X29 @ one))) & ! [X31 : term] : (((X29 @ X31)) = ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))))) & (! [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true != ((X30 @ X27))) | ($true = ((X29 @ one))) | ? [X31 : term] : (((X29 @ X31)) != ((X30 @ (sub @ X31 @ (push @ X27 @ X28)))))) | (pushprop_lem1v2 != $true))) & (pushprop_lem3v2 = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X53 : term] : ! [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) != ((X54 @ sh @ one)))) & (! [X53 : term] : ? [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) = ((X54 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (((hoasinduction_lem3v2_f = $true) | ? [X532 : term] : ! [X533 : (subst > term > term)] : ? [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) != ((X533 @ X534 @ X535)))) & (! [X532 : term] : ? [X533 : (subst > term > term)] : ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535))) | (hoasinduction_lem3v2_f != $true))) & (((axidl = $true) | ? [X318 : subst] : (((comp @ id @ X318)) != X318)) & (! [X318 : subst] : (((comp @ id @ X318)) = X318) | (axidl != $true))) & (((termmset = $true) | ? [X462 : term] : (((sub @ X462 @ id)) != X462)) & (! [X462 : term] : (((sub @ X462 @ id)) = X462) | (termmset != $true))) & (hoasinduction_gthm = $true) & ((! [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | (((X409 @ X407)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) != $true) & (((X409 @ X407)) = $true)))) & ((! [X225 : subst] : (((comp @ X225 @ id)) = X225) | (axidr != $true)) & ((axidr = $true) | ? [X225 : subst] : (((comp @ X225 @ id)) != X225))) & (((hoaslamnotap = $true) | ? [X411 : (subst > term > term),X412 : term,X413 : term] : (! [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) = ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) & (((lam @ (X411 @ sh @ one))) = ((ap @ (sub @ X413 @ id) @ X412))))) & (! [X411 : (subst > term > term),X412 : term,X413 : term] : (? [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) != ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) | (((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412)))) | (hoaslamnotap != $true))) & (hoasapinj2_gthm = $true) & (((axshiftcons = $true) | ? [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) != X56)) & (! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56) | (axshiftcons != $true))) & ! [X227 : d_subst,X226 : d_subst] : ((X226 = X227) | (((d2subst @ X226)) != ((d2subst @ X227)))) & ((! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) = ((ap @ X461 @ X460))) & (X459 != X460)))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3b_gthm = $true) & (((termmset_lthm = $true) | (? [X118 : term] : (((sub @ X118 @ id)) != X118) & ! [X117 : term] : (((sub @ X117 @ id)) = X117))) & ((! [X118 : term] : (((sub @ X118 @ id)) = X118) | ? [X117 : term] : (((sub @ X117 @ id)) != X117)) | (termmset_lthm != $true))) & (((induction = $true) | ? [X119 : term,X120 : (term > $o)] : (! [X121 : term] : (($true != ((X120 @ X121))) | (((X120 @ (lam @ X121))) = $true)) & ! [X124 : term] : ((((var @ X124)) != $true) | (((X120 @ X124)) = $true)) & (((sP4 @ X120)) != $true) & (((X120 @ X119)) != $true))) & (! [X119 : term,X120 : (term > $o)] : (? [X121 : term] : (($true = ((X120 @ X121))) & (((X120 @ (lam @ X121))) != $true)) | ? [X124 : term] : ((((var @ X124)) = $true) & (((X120 @ X124)) != $true)) | (((sP4 @ X120)) = $true) | (((X120 @ X119)) = $true)) | (induction != $true))) & (hoaslamnotap_lthm = $true) & (((induction2_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2_lthm != $true))) & (pushprop_lthm = $true) & ((! [X536 : term] : ? [X537 : (subst > term > term)] : ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X536 : term] : ! [X537 : (subst > term > term)] : ? [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) != ((X537 @ X538 @ X539))))) & (((substmonoid_lthm = $true) | ((? [X2 : subst] : (((comp @ X2 @ id)) != X2) | ? [X3 : subst] : (((comp @ id @ X3)) != X3)) & ! [X0 : subst] : (((comp @ id @ X0)) = X0) & ! [X1 : subst] : (((comp @ X1 @ id)) = X1))) & (((! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3)) | ? [X0 : subst] : (((comp @ id @ X0)) != X0) | ? [X1 : subst] : (((comp @ X1 @ id)) != X1)) | (substmonoid_lthm != $true))) & (((axscons = $true) | ? [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) != X307)) & (! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307) | (axscons != $true))) & (ulamvarind = $true) & (pushprop_lem2v2_lthm = $true) & (((pushprop_lem0 = $true) | ? [X467 : (term > $o),X465 : term,X466 : subst] : ! [X468 : (term > $o)] : ? [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) != ((X468 @ X469)))) & (! [X467 : (term > $o),X465 : term,X466 : subst] : ? [X468 : (term > $o)] : ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469))) | (pushprop_lem0 != $true)))), 50.81/8.71 inference(nnf_transformation,[],[f74])). 50.81/8.71 thf(f267,plain,( 50.81/8.71 ((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axclos = $true) & (axapp = $true) & (termmset_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2 = $true) & (($true = sP55) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP55)) & (pushprop_lem0_gthm = $true) & ((hoaslaminj_lthm = $true) | (sP54 != $true)) & ((sP54 = $true) | (hoaslaminj_lthm != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP53 != $true)) & (! [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) != ((ap @ (sub @ X328 @ id) @ X327))) | (X328 = X329)) | ? [X321 : term] : (((sub @ X321 @ id)) != X321) | ? [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) = ((ap @ X324 @ X325))) & (X323 != X324)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X328 : term,X327 : term,X329 : term,X326 : term] : ((((ap @ (sub @ X329 @ id) @ X326)) = ((ap @ (sub @ X328 @ id) @ X327))) & (X328 != X329)) & ! [X321 : term] : (((sub @ X321 @ id)) = X321) & ! [X322 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X323 @ X322)) != ((ap @ X324 @ X325))) | (X323 = X324)))) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & ((sP51 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP51 != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (! [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true != ((X529 @ X526))) | ($true = ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) | ? [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) != X521) | ? [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) != X524) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X526 : term,X529 : (term > $o),X528 : (term > $o),X525 : subst,X527 : term] : (($true = ((X529 @ X526))) & ($true != ((X528 @ (sub @ X526 @ (push @ X527 @ X525)))))) & ! [X521 : term,X522 : subst] : (((sub @ one @ (push @ X521 @ X522))) = X521) & ! [X524 : subst,X523 : term] : (((comp @ sh @ (push @ X523 @ X524))) = X524))) & ((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true)) & (hoasinduction_lem1_gthm = $true) & (! [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 = X59) | (((ap @ X59 @ X58)) != ((ap @ X57 @ X60)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X58 : term,X60 : term,X59 : term,X57 : term] : ((X57 != X59) & (((ap @ X59 @ X58)) = ((ap @ X57 @ X60))))) & (! [X518 : (subst > term > subst > $o)] : ? [X519 : (term > $o)] : ! [X520 : term] : (((X519 @ X520)) = ((X518 @ id @ X520 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X518 : (subst > term > subst > $o)] : ! [X519 : (term > $o)] : ? [X520 : term] : (((X519 @ X520)) != ((X518 @ id @ X520 @ id)))) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj2_lthm = $true) | (? [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 != X405) & (((ap @ (sub @ X403 @ id) @ X405)) = ((ap @ (sub @ X402 @ id) @ X404)))) & ! [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) != ((ap @ X399 @ X398))) | (X398 = X401)))) & (! [X403 : term,X402 : term,X405 : term,X404 : term] : ((X404 = X405) | (((ap @ (sub @ X403 @ id) @ X405)) != ((ap @ (sub @ X402 @ id) @ X404)))) | ? [X398 : term,X399 : term,X400 : term,X401 : term] : ((((ap @ X400 @ X401)) = ((ap @ X399 @ X398))) & (X398 != X401)) | (hoasapinj2_lthm != $true)) & (axassoc = $true) & (ulamvarsh = $true) & ((hoasapinj2 = $true) | ? [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 != X48) & (((ap @ (sub @ X49 @ id) @ X48)) = ((ap @ (sub @ X50 @ id) @ X47))))) & (! [X48 : term,X47 : term,X50 : term,X49 : term] : ((X47 = X48) | (((ap @ (sub @ X49 @ id) @ X48)) != ((ap @ (sub @ X50 @ id) @ X47)))) | (hoasapinj2 != $true)) & (hoasinduction_lem1 = $true) & ! [X530 : term] : ? [X531 : d_term] : (((d2term @ X531)) = X530) & ! [X288 : d_term,X289 : d_term] : ((X288 = X289) | (((d2term @ X288)) != ((d2term @ X289)))) & (hoasinduction_lem2_lthm = $true) & ((induction2lem_lthm = $true) | (sP44 != $true)) & ((sP44 = $true) | (induction2lem_lthm != $true)) & ((sP40 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP40 != $true)) & (! [X375 : subst,X376 : term,X374 : (term > $o)] : ? [X377 : (term > $o)] : ! [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) = ((X377 @ X378))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X375 : subst,X376 : term,X374 : (term > $o)] : ! [X377 : (term > $o)] : ? [X378 : term] : (((X374 @ (sub @ X378 @ (push @ X376 @ X375)))) != ((X377 @ X378)))) & (hoaslamnotvar_gthm = $true) & ! [X355 : d_subst] : (d_id = X355) & (hoasinduction_lem1v2 = $true) & (pushprop_lem1v2_gthm = $true) & (lamnotap != $true) & (induction2_gthm = $true) & (apnotvar = $true) & (axmap = $true) & (! [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) = ((X309 @ X308 @ X311))) | ? [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) != ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) | ? [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) != ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) | (((lam @ (X310 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X309 : (subst > term > term),X310 : (subst > term > term),X311 : term,X308 : subst] : ((((X310 @ X308 @ X311)) != ((X309 @ X308 @ X311))) & ! [X317 : subst,X315 : term,X316 : subst] : (((sub @ (X310 @ X317 @ X315) @ X316)) = ((X310 @ (comp @ X317 @ X316) @ (sub @ X315 @ X316)))) & ! [X312 : term,X313 : subst,X314 : subst] : (((sub @ (X309 @ X313 @ X312) @ X314)) = ((X309 @ (comp @ X313 @ X314) @ (sub @ X312 @ X314)))) & (((lam @ (X310 @ sh @ one))) = ((lam @ (X309 @ sh @ one)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = id) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X51 : term,X52 : term] : ((X51 = X52) | (((lam @ X52)) != ((lam @ X51)))) | (laminj != $true)) & ((laminj = $true) | ? [X51 : term,X52 : term] : ((X51 != X52) & (((lam @ X52)) = ((lam @ X51))))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP33 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP33 != $true)) & ((sP31 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP31 != $true)) & ((sP29 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP29 != $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ((substmonoid = $true) | ? [X464 : subst] : (((comp @ X464 @ id)) != X464) | ? [X463 : subst] : (((comp @ id @ X463)) != X463)) & ((! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463)) | (substmonoid != $true)) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & (($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28)) & (($true = sP19) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP19)) & ! [X182 : d_term] : (d_one = X182) & ((induction2 = $true) | ($true != sP18)) & (($true = sP18) | (induction2 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP16) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP16)) & ! [X319 : subst] : ? [X320 : d_subst] : (((d2subst @ X320)) = X319) & ((hoasinduction_lem0_lthm = $true) | ? [X125 : (subst > term > subst > $o)] : ! [X126 : (term > $o)] : ? [X127 : term] : (((X126 @ X127)) != ((X125 @ id @ X127 @ id)))) & (! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((sP14 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP14 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) | ? [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 != X8) & (((ap @ (sub @ X6 @ id) @ X9)) = ((ap @ (sub @ X8 @ id) @ X7))))) & (! [X7 : term,X8 : term,X6 : term,X9 : term] : ((X6 = X8) | (((ap @ (sub @ X6 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X7)))) | (hoasapinj1 != $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)))))))))))))) & (hoaslamnotvar_lthm = $true) & ((axvarid = $true) | ? [X61 : term] : (((sub @ X61 @ id)) != X61)) & (! [X61 : term] : (((sub @ X61 @ id)) = X61) | (axvarid != $true)) & (! [X510 : (subst > term > subst > $o),X509 : term] : (? [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) != $true) & (((X510 @ id @ X512 @ id)) = $true) & (((X510 @ id @ X511 @ id)) = $true)) | (((sP11 @ X510)) = $true) | ($true = ((X510 @ id @ X509 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X510 : (subst > term > subst > $o),X509 : term] : (! [X511 : term,X512 : term] : ((((X510 @ id @ (ap @ (sub @ X511 @ id) @ X512) @ id)) = $true) | (((X510 @ id @ X512 @ id)) != $true) | (((X510 @ id @ X511 @ id)) != $true)) & (((sP11 @ X510)) != $true) & ($true != ((X510 @ id @ X509 @ id))))) & (hoasinduction_lem3a_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((sP10 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP10 != $true)) & ((hoasinduction_lem3a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a != $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & ((hoasinduction_lem3b = $true) | ? [X417 : term] : ! [X418 : (subst > term > term)] : (((X418 @ sh @ one)) != ((sub @ X417 @ (push @ one @ sh))))) & (! [X417 : term] : ? [X418 : (subst > term > term)] : (((X418 @ sh @ one)) = ((sub @ X417 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) = $true) & ! [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) = ((X232 @ X234))) & (((X232 @ one)) != $true)) & ! [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) = X228))) & (! [X233 : subst,X230 : term,X231 : (term > $o),X232 : (term > $o)] : ((((X231 @ X230)) != $true) | ? [X234 : term] : (((X231 @ (sub @ X234 @ (push @ X230 @ X233)))) != ((X232 @ X234))) | (((X232 @ one)) = $true)) | ? [X228 : term,X229 : subst] : (((sub @ one @ (push @ X228 @ X229))) != X228) | (pushprop_lem1v2_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & ((shinj = $true) | ? [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) = ((sub @ X26 @ sh))) & (X25 != X26))) & (! [X25 : term,X26 : term] : ((((sub @ X25 @ sh)) != ((sub @ X26 @ sh))) | (X25 = X26)) | (shinj != $true)) & (axabs = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lthm_orig = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem2 != $true)) & (ulamvar1 != $true) & ((axvarcons = $true) | ? [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) != X4)) & (! [X5 : subst,X4 : term] : (((sub @ one @ (push @ X4 @ X5))) = X4) | (axvarcons != $true)) & (hoasinduction_lem2v2_gthm = $true) & (($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP6)) & ((pushprop_lem1v2 = $true) | ? [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true = ((X30 @ X27))) & ($true != ((X29 @ one))) & ! [X31 : term] : (((X29 @ X31)) = ((X30 @ (sub @ X31 @ (push @ X27 @ X28))))))) & (! [X27 : term,X29 : (term > $o),X30 : (term > $o),X28 : subst] : (($true != ((X30 @ X27))) | ($true = ((X29 @ one))) | ? [X31 : term] : (((X29 @ X31)) != ((X30 @ (sub @ X31 @ (push @ X27 @ X28)))))) | (pushprop_lem1v2 != $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X53 : term] : ! [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) != ((X54 @ sh @ one)))) & (! [X53 : term] : ? [X54 : (subst > term > term)] : (((sub @ X53 @ (push @ one @ sh))) = ((X54 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X532 : term] : ! [X533 : (subst > term > term)] : ? [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) != ((X533 @ X534 @ X535)))) & (! [X532 : term] : ? [X533 : (subst > term > term)] : ! [X535 : term,X534 : subst] : (((sub @ X532 @ (push @ X535 @ X534))) = ((X533 @ X534 @ X535))) | (hoasinduction_lem3v2_f != $true)) & ((axidl = $true) | ? [X318 : subst] : (((comp @ id @ X318)) != X318)) & (! [X318 : subst] : (((comp @ id @ X318)) = X318) | (axidl != $true)) & ((termmset = $true) | ? [X462 : term] : (((sub @ X462 @ id)) != X462)) & (! [X462 : term] : (((sub @ X462 @ id)) = X462) | (termmset != $true)) & (hoasinduction_gthm = $true) & (! [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) = $true) | (((X409 @ X407)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X408 : term,X410 : subst,X409 : (term > $o),X407 : term,X406 : (term > $o)] : ((((X406 @ (sub @ X407 @ (push @ X408 @ X410)))) != $true) & (((X409 @ X407)) = $true))) & (! [X225 : subst] : (((comp @ X225 @ id)) = X225) | (axidr != $true)) & ((axidr = $true) | ? [X225 : subst] : (((comp @ X225 @ id)) != X225)) & ((hoaslamnotap = $true) | ? [X411 : (subst > term > term),X412 : term,X413 : term] : (! [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) = ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) & (((lam @ (X411 @ sh @ one))) = ((ap @ (sub @ X413 @ id) @ X412))))) & (! [X411 : (subst > term > term),X412 : term,X413 : term] : (? [X416 : term,X415 : subst,X414 : subst] : (((sub @ (X411 @ X415 @ X416) @ X414)) != ((X411 @ (comp @ X415 @ X414) @ (sub @ X416 @ X414)))) | (((lam @ (X411 @ sh @ one))) != ((ap @ (sub @ X413 @ id) @ X412)))) | (hoaslamnotap != $true)) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) | ? [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) != X56)) & (! [X55 : term,X56 : subst] : (((comp @ sh @ (push @ X55 @ X56))) = X56) | (axshiftcons != $true)) & ! [X227 : d_subst,X226 : d_subst] : ((X226 = X227) | (((d2subst @ X226)) != ((d2subst @ X227)))) & (! [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) != ((ap @ X461 @ X460))) | (X459 = X460)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X459 : term,X460 : term,X461 : term,X458 : term] : ((((ap @ X458 @ X459)) = ((ap @ X461 @ X460))) & (X459 != X460))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3b_gthm = $true) & ((termmset_lthm = $true) | (? [X118 : term] : (((sub @ X118 @ id)) != X118) & ! [X117 : term] : (((sub @ X117 @ id)) = X117))) & (! [X118 : term] : (((sub @ X118 @ id)) = X118) | ? [X117 : term] : (((sub @ X117 @ id)) != X117) | (termmset_lthm != $true)) & ((induction = $true) | ? [X119 : term,X120 : (term > $o)] : (! [X121 : term] : (($true != ((X120 @ X121))) | (((X120 @ (lam @ X121))) = $true)) & ! [X124 : term] : ((((var @ X124)) != $true) | (((X120 @ X124)) = $true)) & (((sP4 @ X120)) != $true) & (((X120 @ X119)) != $true))) & (! [X119 : term,X120 : (term > $o)] : (? [X121 : term] : (($true = ((X120 @ X121))) & (((X120 @ (lam @ X121))) != $true)) | ? [X124 : term] : ((((var @ X124)) = $true) & (((X120 @ X124)) != $true)) | (((sP4 @ X120)) = $true) | (((X120 @ X119)) = $true)) | (induction != $true)) & (hoaslamnotap_lthm = $true) & ((induction2_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2_lthm != $true)) & (pushprop_lthm = $true) & (! [X536 : term] : ? [X537 : (subst > term > term)] : ! [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) = ((X537 @ X538 @ X539))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X536 : term] : ! [X537 : (subst > term > term)] : ? [X539 : term,X538 : subst] : (((sub @ X536 @ (push @ X539 @ X538))) != ((X537 @ X538 @ X539)))) & ((substmonoid_lthm = $true) | ((? [X2 : subst] : (((comp @ X2 @ id)) != X2) | ? [X3 : subst] : (((comp @ id @ X3)) != X3)) & ! [X0 : subst] : (((comp @ id @ X0)) = X0) & ! [X1 : subst] : (((comp @ X1 @ id)) = X1))) & ((! [X2 : subst] : (((comp @ X2 @ id)) = X2) & ! [X3 : subst] : (((comp @ id @ X3)) = X3)) | ? [X0 : subst] : (((comp @ id @ X0)) != X0) | ? [X1 : subst] : (((comp @ X1 @ id)) != X1) | (substmonoid_lthm != $true)) & ((axscons = $true) | ? [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) != X307)) & (! [X307 : subst] : (((push @ (sub @ one @ X307) @ (comp @ sh @ X307))) = X307) | (axscons != $true)) & (ulamvarind = $true) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem0 = $true) | ? [X467 : (term > $o),X465 : term,X466 : subst] : ! [X468 : (term > $o)] : ? [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) != ((X468 @ X469)))) & (! [X467 : (term > $o),X465 : term,X466 : subst] : ? [X468 : (term > $o)] : ! [X469 : term] : (((X467 @ (sub @ X469 @ (push @ X465 @ X466)))) = ((X468 @ X469))) | (pushprop_lem0 != $true))), 50.81/8.71 inference(flattening,[],[f266])). 50.81/8.71 thf(f268,plain,( 50.81/8.71 ((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axclos = $true) & (axapp = $true) & (termmset_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2 = $true) & (($true = sP55) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP55)) & (pushprop_lem0_gthm = $true) & ((hoaslaminj_lthm = $true) | (sP54 != $true)) & ((sP54 = $true) | (hoaslaminj_lthm != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP53 != $true)) & (! [X0 : term,X1 : term,X2 : term,X3 : term] : ((((ap @ (sub @ X2 @ id) @ X3)) != ((ap @ (sub @ X0 @ id) @ X1))) | (X0 = X2)) | ? [X4 : term] : (((sub @ X4 @ id)) != X4) | ? [X5 : term,X6 : term,X7 : term,X8 : term] : ((((ap @ X8 @ X5)) = ((ap @ X7 @ X6))) & (X7 != X8)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X9 : term,X10 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) = ((ap @ (sub @ X9 @ id) @ X10))) & (X9 != X11)) & ! [X13 : term] : (((sub @ X13 @ id)) = X13) & ! [X14 : term,X15 : term,X16 : term,X17 : term] : ((((ap @ X16 @ X15)) != ((ap @ X17 @ X14))) | (X16 = X17)))) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & ((sP51 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP51 != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (! [X18 : term,X19 : (term > $o),X20 : (term > $o),X21 : subst,X22 : term] : ((((X19 @ X18)) != $true) | ($true = ((X20 @ (sub @ X18 @ (push @ X22 @ X21)))))) | ? [X23 : term,X24 : subst] : (((sub @ one @ (push @ X23 @ X24))) != X23) | ? [X25 : subst,X26 : term] : (((comp @ sh @ (push @ X26 @ X25))) != X25) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X27 : term,X28 : (term > $o),X29 : (term > $o),X30 : subst,X31 : term] : ((((X28 @ X27)) = $true) & (((X29 @ (sub @ X27 @ (push @ X31 @ X30)))) != $true)) & ! [X32 : term,X33 : subst] : (((sub @ one @ (push @ X32 @ X33))) = X32) & ! [X34 : subst,X35 : term] : (((comp @ sh @ (push @ X35 @ X34))) = X34))) & ((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true)) & (hoasinduction_lem1_gthm = $true) & (! [X36 : term,X37 : term,X38 : term,X39 : term] : ((X38 = X39) | (((ap @ X39 @ X37)) != ((ap @ X38 @ X36)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X40 : term,X41 : term,X42 : term,X43 : term] : ((X42 != X43) & (((ap @ X43 @ X41)) = ((ap @ X42 @ X40))))) & (! [X44 : (subst > term > subst > $o)] : ? [X45 : (term > $o)] : ! [X46 : term] : (((X44 @ id @ X46 @ id)) = ((X45 @ X46))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X47 : (subst > term > subst > $o)] : ! [X48 : (term > $o)] : ? [X49 : term] : (((X47 @ id @ X49 @ id)) != ((X48 @ X49)))) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj2_lthm = $true) | (? [X50 : term,X51 : term,X52 : term,X53 : term] : ((X52 != X53) & (((ap @ (sub @ X51 @ id) @ X53)) = ((ap @ (sub @ X50 @ id) @ X52)))) & ! [X54 : term,X55 : term,X56 : term,X57 : term] : ((((ap @ X56 @ X57)) != ((ap @ X55 @ X54))) | (X54 = X57)))) & (! [X58 : term,X59 : term,X60 : term,X61 : term] : ((X60 = X61) | (((ap @ (sub @ X58 @ id) @ X60)) != ((ap @ (sub @ X59 @ id) @ X61)))) | ? [X62 : term,X63 : term,X64 : term,X65 : term] : ((((ap @ X63 @ X62)) = ((ap @ X64 @ X65))) & (X62 != X65)) | (hoasapinj2_lthm != $true)) & (axassoc = $true) & (ulamvarsh = $true) & ((hoasapinj2 = $true) | ? [X66 : term,X67 : term,X68 : term,X69 : term] : ((X66 != X67) & (((ap @ (sub @ X68 @ id) @ X67)) = ((ap @ (sub @ X69 @ id) @ X66))))) & (! [X70 : term,X71 : term,X72 : term,X73 : term] : ((X70 = X71) | (((ap @ (sub @ X73 @ id) @ X70)) != ((ap @ (sub @ X72 @ id) @ X71)))) | (hoasapinj2 != $true)) & (hoasinduction_lem1 = $true) & ! [X74 : term] : ? [X75 : d_term] : (((d2term @ X75)) = X74) & ! [X76 : d_term,X77 : d_term] : ((X76 = X77) | (((d2term @ X76)) != ((d2term @ X77)))) & (hoasinduction_lem2_lthm = $true) & ((induction2lem_lthm = $true) | (sP44 != $true)) & ((sP44 = $true) | (induction2lem_lthm != $true)) & ((sP40 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP40 != $true)) & (! [X78 : subst,X79 : term,X80 : (term > $o)] : ? [X81 : (term > $o)] : ! [X82 : term] : (((X81 @ X82)) = ((X80 @ (sub @ X82 @ (push @ X79 @ X78))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X83 : subst,X84 : term,X85 : (term > $o)] : ! [X86 : (term > $o)] : ? [X87 : term] : (((X86 @ X87)) != ((X85 @ (sub @ X87 @ (push @ X84 @ X83)))))) & (hoaslamnotvar_gthm = $true) & ! [X88 : d_subst] : (d_id = X88) & (hoasinduction_lem1v2 = $true) & (pushprop_lem1v2_gthm = $true) & (lamnotap != $true) & (induction2_gthm = $true) & (apnotvar = $true) & (axmap = $true) & (! [X89 : (subst > term > term),X90 : (subst > term > term),X91 : term,X92 : subst] : ((((X90 @ X92 @ X91)) = ((X89 @ X92 @ X91))) | ? [X93 : subst,X94 : term,X95 : subst] : (((sub @ (X90 @ X93 @ X94) @ X95)) != ((X90 @ (comp @ X93 @ X95) @ (sub @ X94 @ X95)))) | ? [X96 : term,X97 : subst,X98 : subst] : (((X89 @ (comp @ X97 @ X98) @ (sub @ X96 @ X98))) != ((sub @ (X89 @ X97 @ X96) @ X98))) | (((lam @ (X90 @ sh @ one))) != ((lam @ (X89 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X99 : (subst > term > term),X100 : (subst > term > term),X101 : term,X102 : subst] : ((((X100 @ X102 @ X101)) != ((X99 @ X102 @ X101))) & ! [X103 : subst,X104 : term,X105 : subst] : (((X100 @ (comp @ X103 @ X105) @ (sub @ X104 @ X105))) = ((sub @ (X100 @ X103 @ X104) @ X105))) & ! [X106 : term,X107 : subst,X108 : subst] : (((X99 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (X99 @ X107 @ X106) @ X108))) & (((lam @ (X99 @ sh @ one))) = ((lam @ (X100 @ sh @ one)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = id) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X109 : term,X110 : term] : ((X109 = X110) | (((lam @ X109)) != ((lam @ X110)))) | (laminj != $true)) & ((laminj = $true) | ? [X111 : term,X112 : term] : ((X111 != X112) & (((lam @ X112)) = ((lam @ X111))))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP33 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP33 != $true)) & ((sP31 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP31 != $true)) & ((sP29 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP29 != $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ((substmonoid = $true) | ? [X113 : subst] : (((comp @ X113 @ id)) != X113) | ? [X114 : subst] : (((comp @ id @ X114)) != X114)) & ((! [X115 : subst] : (((comp @ X115 @ id)) = X115) & ! [X116 : subst] : (((comp @ id @ X116)) = X116)) | (substmonoid != $true)) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & (($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28)) & (($true = sP19) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP19)) & ! [X117 : d_term] : (d_one = X117) & ((induction2 = $true) | ($true != sP18)) & (($true = sP18) | (induction2 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP16) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP16)) & ! [X118 : subst] : ? [X119 : d_subst] : (((d2subst @ X119)) = X118) & ((hoasinduction_lem0_lthm = $true) | ? [X120 : (subst > term > subst > $o)] : ! [X121 : (term > $o)] : ? [X122 : term] : (((X120 @ id @ X122 @ id)) != ((X121 @ X122)))) & (! [X123 : (subst > term > subst > $o)] : ? [X124 : (term > $o)] : ! [X125 : term] : (((X123 @ id @ X125 @ id)) = ((X124 @ X125))) | (hoasinduction_lem0_lthm != $true)) & ((sP14 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP14 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) | ? [X126 : term,X127 : term,X128 : term,X129 : term] : ((X127 != X128) & (((ap @ (sub @ X128 @ id) @ X129)) = ((ap @ (sub @ X127 @ id) @ X126))))) & (! [X130 : term,X131 : term,X132 : term,X133 : term] : ((X131 = X132) | (((ap @ (sub @ X132 @ id) @ X133)) != ((ap @ (sub @ X131 @ id) @ X130)))) | (hoasapinj1 != $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)))))))))))))) & (hoaslamnotvar_lthm = $true) & ((axvarid = $true) | ? [X134 : term] : (((sub @ X134 @ id)) != X134)) & (! [X135 : term] : (((sub @ X135 @ id)) = X135) | (axvarid != $true)) & (! [X136 : (subst > term > subst > $o),X137 : term] : (? [X138 : term,X139 : term] : ((((X136 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) != $true) & (((X136 @ id @ X139 @ id)) = $true) & ($true = ((X136 @ id @ X138 @ id)))) | (((sP11 @ X136)) = $true) | (((X136 @ id @ X137 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X140 : (subst > term > subst > $o),X141 : term] : (! [X142 : term,X143 : term] : ((((X140 @ id @ (ap @ (sub @ X142 @ id) @ X143) @ id)) = $true) | ($true != ((X140 @ id @ X143 @ id))) | ($true != ((X140 @ id @ X142 @ id)))) & (((sP11 @ X140)) != $true) & (((X140 @ id @ X141 @ id)) != $true))) & (hoasinduction_lem3a_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((sP10 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP10 != $true)) & ((hoasinduction_lem3a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a != $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & ((hoasinduction_lem3b = $true) | ? [X144 : term] : ! [X145 : (subst > term > term)] : (((sub @ X144 @ (push @ one @ sh))) != ((X145 @ sh @ one)))) & (! [X146 : term] : ? [X147 : (subst > term > term)] : (((X147 @ sh @ one)) = ((sub @ X146 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X148 : subst,X149 : term,X150 : (term > $o),X151 : (term > $o)] : (($true = ((X150 @ X149))) & ! [X152 : term] : (((X150 @ (sub @ X152 @ (push @ X149 @ X148)))) = ((X151 @ X152))) & ($true != ((X151 @ one)))) & ! [X153 : term,X154 : subst] : (((sub @ one @ (push @ X153 @ X154))) = X153))) & (! [X155 : subst,X156 : term,X157 : (term > $o),X158 : (term > $o)] : ((((X157 @ X156)) != $true) | ? [X159 : term] : (((X158 @ X159)) != ((X157 @ (sub @ X159 @ (push @ X156 @ X155))))) | ($true = ((X158 @ one)))) | ? [X160 : term,X161 : subst] : (((sub @ one @ (push @ X160 @ X161))) != X160) | (pushprop_lem1v2_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & ((shinj = $true) | ? [X162 : term,X163 : term] : ((((sub @ X163 @ sh)) = ((sub @ X162 @ sh))) & (X162 != X163))) & (! [X164 : term,X165 : term] : ((((sub @ X164 @ sh)) != ((sub @ X165 @ sh))) | (X164 = X165)) | (shinj != $true)) & (axabs = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lthm_orig = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem2 != $true)) & (ulamvar1 != $true) & ((axvarcons = $true) | ? [X166 : subst,X167 : term] : (((sub @ one @ (push @ X167 @ X166))) != X167)) & (! [X168 : subst,X169 : term] : (((sub @ one @ (push @ X169 @ X168))) = X169) | (axvarcons != $true)) & (hoasinduction_lem2v2_gthm = $true) & (($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP6)) & ((pushprop_lem1v2 = $true) | ? [X170 : term,X171 : (term > $o),X172 : (term > $o),X173 : subst] : ((((X172 @ X170)) = $true) & (((X171 @ one)) != $true) & ! [X174 : term] : (((X172 @ (sub @ X174 @ (push @ X170 @ X173)))) = ((X171 @ X174))))) & (! [X175 : term,X176 : (term > $o),X177 : (term > $o),X178 : subst] : ((((X177 @ X175)) != $true) | (((X176 @ one)) = $true) | ? [X179 : term] : (((X177 @ (sub @ X179 @ (push @ X175 @ X178)))) != ((X176 @ X179)))) | (pushprop_lem1v2 != $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X180 : term] : ! [X181 : (subst > term > term)] : (((sub @ X180 @ (push @ one @ sh))) != ((X181 @ sh @ one)))) & (! [X182 : term] : ? [X183 : (subst > term > term)] : (((sub @ X182 @ (push @ one @ sh))) = ((X183 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X184 : term] : ! [X185 : (subst > term > term)] : ? [X186 : term,X187 : subst] : (((sub @ X184 @ (push @ X186 @ X187))) != ((X185 @ X187 @ X186)))) & (! [X188 : term] : ? [X189 : (subst > term > term)] : ! [X190 : term,X191 : subst] : (((X189 @ X191 @ X190)) = ((sub @ X188 @ (push @ X190 @ X191)))) | (hoasinduction_lem3v2_f != $true)) & ((axidl = $true) | ? [X192 : subst] : (((comp @ id @ X192)) != X192)) & (! [X193 : subst] : (((comp @ id @ X193)) = X193) | (axidl != $true)) & ((termmset = $true) | ? [X194 : term] : (((sub @ X194 @ id)) != X194)) & (! [X195 : term] : (((sub @ X195 @ id)) = X195) | (termmset != $true)) & (hoasinduction_gthm = $true) & (! [X196 : term,X197 : subst,X198 : (term > $o),X199 : term,X200 : (term > $o)] : ((((X200 @ (sub @ X199 @ (push @ X196 @ X197)))) = $true) | (((X198 @ X199)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X201 : term,X202 : subst,X203 : (term > $o),X204 : term,X205 : (term > $o)] : ((((X205 @ (sub @ X204 @ (push @ X201 @ X202)))) != $true) & (((X203 @ X204)) = $true))) & (! [X206 : subst] : (((comp @ X206 @ id)) = X206) | (axidr != $true)) & ((axidr = $true) | ? [X207 : subst] : (((comp @ X207 @ id)) != X207)) & ((hoaslamnotap = $true) | ? [X208 : (subst > term > term),X209 : term,X210 : term] : (! [X211 : term,X212 : subst,X213 : subst] : (((X208 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213))) = ((sub @ (X208 @ X212 @ X211) @ X213))) & (((ap @ (sub @ X210 @ id) @ X209)) = ((lam @ (X208 @ sh @ one)))))) & (! [X214 : (subst > term > term),X215 : term,X216 : term] : (? [X217 : term,X218 : subst,X219 : subst] : (((sub @ (X214 @ X218 @ X217) @ X219)) != ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219)))) | (((ap @ (sub @ X216 @ id) @ X215)) != ((lam @ (X214 @ sh @ one))))) | (hoaslamnotap != $true)) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) | ? [X220 : term,X221 : subst] : (((comp @ sh @ (push @ X220 @ X221))) != X221)) & (! [X222 : term,X223 : subst] : (((comp @ sh @ (push @ X222 @ X223))) = X223) | (axshiftcons != $true)) & ! [X224 : d_subst,X225 : d_subst] : ((X224 = X225) | (((d2subst @ X224)) != ((d2subst @ X225)))) & (! [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ X228 @ X227)) != ((ap @ X229 @ X226))) | (X226 = X227)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ X232 @ X231)) = ((ap @ X233 @ X230))) & (X230 != X231))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3b_gthm = $true) & ((termmset_lthm = $true) | (? [X234 : term] : (((sub @ X234 @ id)) != X234) & ! [X235 : term] : (((sub @ X235 @ id)) = X235))) & (! [X236 : term] : (((sub @ X236 @ id)) = X236) | ? [X237 : term] : (((sub @ X237 @ id)) != X237) | (termmset_lthm != $true)) & ((induction = $true) | ? [X238 : term,X239 : (term > $o)] : (! [X240 : term] : ((((X239 @ X240)) != $true) | (((X239 @ (lam @ X240))) = $true)) & ! [X241 : term] : ((((var @ X241)) != $true) | ($true = ((X239 @ X241)))) & (((sP4 @ X239)) != $true) & (((X239 @ X238)) != $true))) & (! [X242 : term,X243 : (term > $o)] : (? [X244 : term] : ((((X243 @ X244)) = $true) & (((X243 @ (lam @ X244))) != $true)) | ? [X245 : term] : (($true = ((var @ X245))) & (((X243 @ X245)) != $true)) | (((sP4 @ X243)) = $true) | (((X243 @ X242)) = $true)) | (induction != $true)) & (hoaslamnotap_lthm = $true) & ((induction2_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2_lthm != $true)) & (pushprop_lthm = $true) & (! [X246 : term] : ? [X247 : (subst > term > term)] : ! [X248 : term,X249 : subst] : (((X247 @ X249 @ X248)) = ((sub @ X246 @ (push @ X248 @ X249)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X250 : term] : ! [X251 : (subst > term > term)] : ? [X252 : term,X253 : subst] : (((X251 @ X253 @ X252)) != ((sub @ X250 @ (push @ X252 @ X253))))) & ((substmonoid_lthm = $true) | ((? [X254 : subst] : (((comp @ X254 @ id)) != X254) | ? [X255 : subst] : (((comp @ id @ X255)) != X255)) & ! [X256 : subst] : (((comp @ id @ X256)) = X256) & ! [X257 : subst] : (((comp @ X257 @ id)) = X257))) & ((! [X258 : subst] : (((comp @ X258 @ id)) = X258) & ! [X259 : subst] : (((comp @ id @ X259)) = X259)) | ? [X260 : subst] : (((comp @ id @ X260)) != X260) | ? [X261 : subst] : (((comp @ X261 @ id)) != X261) | (substmonoid_lthm != $true)) & ((axscons = $true) | ? [X262 : subst] : (((push @ (sub @ one @ X262) @ (comp @ sh @ X262))) != X262)) & (! [X263 : subst] : (((push @ (sub @ one @ X263) @ (comp @ sh @ X263))) = X263) | (axscons != $true)) & (ulamvarind = $true) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem0 = $true) | ? [X264 : (term > $o),X265 : term,X266 : subst] : ! [X267 : (term > $o)] : ? [X268 : term] : (((X267 @ X268)) != ((X264 @ (sub @ X268 @ (push @ X265 @ X266)))))) & (! [X269 : (term > $o),X270 : term,X271 : subst] : ? [X272 : (term > $o)] : ! [X273 : term] : (((X272 @ X273)) = ((X269 @ (sub @ X273 @ (push @ X270 @ X271))))) | (pushprop_lem0 != $true))), 50.81/8.71 inference(rectify,[],[f267])). 50.81/8.71 thf(f269,plain,( 50.81/8.71 ((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axclos = $true) & (axapp = $true) & (termmset_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2 = $true) & (($true = sP55) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP55)) & (pushprop_lem0_gthm = $true) & ((hoaslaminj_lthm = $true) | (sP54 != $true)) & ((sP54 = $true) | (hoaslaminj_lthm != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP53 != $true)) & (! [X0 : term,X1 : term,X2 : term,X3 : term] : ((((ap @ (sub @ X2 @ id) @ X3)) != ((ap @ (sub @ X0 @ id) @ X1))) | (X0 = X2)) | (sK460 != ((sub @ sK460 @ id))) | ((((ap @ sK464 @ sK461)) = ((ap @ sK463 @ sK462))) & (sK463 != sK464)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (((((ap @ (sub @ sK465 @ id) @ sK466)) = ((ap @ (sub @ sK467 @ id) @ sK468))) & (sK467 != sK465)) & ! [X13 : term] : (((sub @ X13 @ id)) = X13) & ! [X14 : term,X15 : term,X16 : term,X17 : term] : ((((ap @ X16 @ X15)) != ((ap @ X17 @ X14))) | (X16 = X17)))) & (lamnotvar = $true) & (hoasinduction_lem3_gthm = $true) & ((sP51 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP51 != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (! [X18 : term,X19 : (term > $o),X20 : (term > $o),X21 : subst,X22 : term] : ((((X19 @ X18)) != $true) | ($true = ((X20 @ (sub @ X18 @ (push @ X22 @ X21)))))) | (((sub @ one @ (push @ sK469 @ sK470))) != sK469) | (sK471 != ((comp @ sh @ (push @ sK472 @ sK471)))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | ((($true = ((sK474 @ sK473))) & (((sK475 @ (sub @ sK473 @ (push @ sK477 @ sK476)))) != $true)) & ! [X32 : term,X33 : subst] : (((sub @ one @ (push @ X32 @ X33))) = X32) & ! [X34 : subst,X35 : term] : (((comp @ sh @ (push @ X35 @ X34))) = X34))) & ((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true)) & (hoasinduction_lem1_gthm = $true) & (! [X36 : term,X37 : term,X38 : term,X39 : term] : ((X38 = X39) | (((ap @ X39 @ X37)) != ((ap @ X38 @ X36)))) | (apinj1 != $true)) & ((apinj1 = $true) | ((sK480 != sK481) & (((ap @ sK480 @ sK478)) = ((ap @ sK481 @ sK479))))) & (! [X44 : (subst > term > subst > $o)] : ! [X46 : term] : (((sK482 @ X44 @ X46)) = ((X44 @ id @ X46 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X48 : (term > $o)] : (((X48 @ (sK484 @ X48))) != ((sK483 @ id @ (sK484 @ X48) @ id)))) & (pushprop_lem3v2_lthm = $true) & ((hoasapinj2_lthm = $true) | (((sK487 != sK488) & (((ap @ (sub @ sK486 @ id) @ sK488)) = ((ap @ (sub @ sK485 @ id) @ sK487)))) & ! [X54 : term,X55 : term,X56 : term,X57 : term] : ((((ap @ X56 @ X57)) != ((ap @ X55 @ X54))) | (X54 = X57)))) & (! [X58 : term,X59 : term,X60 : term,X61 : term] : ((X60 = X61) | (((ap @ (sub @ X58 @ id) @ X60)) != ((ap @ (sub @ X59 @ id) @ X61)))) | ((((ap @ sK491 @ sK492)) = ((ap @ sK490 @ sK489))) & (sK492 != sK489)) | (hoasapinj2_lthm != $true)) & (axassoc = $true) & (ulamvarsh = $true) & ((hoasapinj2 = $true) | ((sK494 != sK493) & (((ap @ (sub @ sK495 @ id) @ sK494)) = ((ap @ (sub @ sK496 @ id) @ sK493))))) & (! [X70 : term,X71 : term,X72 : term,X73 : term] : ((X70 = X71) | (((ap @ (sub @ X73 @ id) @ X70)) != ((ap @ (sub @ X72 @ id) @ X71)))) | (hoasapinj2 != $true)) & (hoasinduction_lem1 = $true) & ! [X74 : term] : (((d2term @ (sK497 @ X74))) = X74) & ! [X76 : d_term,X77 : d_term] : ((X76 = X77) | (((d2term @ X76)) != ((d2term @ X77)))) & (hoasinduction_lem2_lthm = $true) & ((induction2lem_lthm = $true) | (sP44 != $true)) & ((sP44 = $true) | (induction2lem_lthm != $true)) & ((sP40 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP40 != $true)) & (! [X78 : subst,X79 : term,X80 : (term > $o)] : ! [X82 : term] : (((sK498 @ X80 @ X79 @ X78 @ X82)) = ((X80 @ (sub @ X82 @ (push @ X79 @ X78))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X86 : (term > $o)] : (((X86 @ (sK502 @ X86))) != ((sK501 @ (sub @ (sK502 @ X86) @ (push @ sK500 @ sK499)))))) & (hoaslamnotvar_gthm = $true) & ! [X88 : d_subst] : (d_id = X88) & (hoasinduction_lem1v2 = $true) & (pushprop_lem1v2_gthm = $true) & (lamnotap != $true) & (induction2_gthm = $true) & (apnotvar = $true) & (axmap = $true) & (! [X89 : (subst > term > term),X90 : (subst > term > term),X91 : term,X92 : subst] : ((((X90 @ X92 @ X91)) = ((X89 @ X92 @ X91))) | (((X90 @ (comp @ (sK503 @ X90) @ (sK505 @ X90)) @ (sub @ (sK504 @ X90) @ (sK505 @ X90)))) != ((sub @ (X90 @ (sK503 @ X90) @ (sK504 @ X90)) @ (sK505 @ X90)))) | (((X89 @ (comp @ (sK507 @ X89) @ (sK508 @ X89)) @ (sub @ (sK506 @ X89) @ (sK508 @ X89)))) != ((sub @ (X89 @ (sK507 @ X89) @ (sK506 @ X89)) @ (sK508 @ X89)))) | (((lam @ (X90 @ sh @ one))) != ((lam @ (X89 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((sK509 @ sK512 @ sK511)) != ((sK510 @ sK512 @ sK511))) & ! [X103 : subst,X104 : term,X105 : subst] : (((sub @ (sK510 @ X103 @ X104) @ X105)) = ((sK510 @ (comp @ X103 @ X105) @ (sub @ X104 @ X105)))) & ! [X106 : term,X107 : subst,X108 : subst] : (((sK509 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (sK509 @ X107 @ X106) @ X108))) & (((lam @ (sK509 @ sh @ one))) = ((lam @ (sK510 @ sh @ one)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = id) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X109 : term,X110 : term] : ((X109 = X110) | (((lam @ X109)) != ((lam @ X110)))) | (laminj != $true)) & ((laminj = $true) | ((sK513 != sK514) & (((lam @ sK514)) = ((lam @ sK513))))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP33 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP33 != $true)) & ((sP31 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP31 != $true)) & ((sP29 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP29 != $true)) & (induction2lem_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ((substmonoid = $true) | (((comp @ sK515 @ id)) != sK515) | (((comp @ id @ sK516)) != sK516)) & ((! [X115 : subst] : (((comp @ X115 @ id)) = X115) & ! [X116 : subst] : (((comp @ id @ X116)) = X116)) | (substmonoid != $true)) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & (($true = sP28) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP28)) & (($true = sP19) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP19)) & ! [X117 : d_term] : (d_one = X117) & ((induction2 = $true) | ($true != sP18)) & (($true = sP18) | (induction2 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP16) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP16)) & ! [X118 : subst] : (((d2subst @ (sK517 @ X118))) = X118) & ((hoasinduction_lem0_lthm = $true) | ! [X121 : (term > $o)] : (((X121 @ (sK519 @ X121))) != ((sK518 @ id @ (sK519 @ X121) @ id)))) & (! [X123 : (subst > term > subst > $o)] : ! [X125 : term] : (((X123 @ id @ X125 @ id)) = ((sK520 @ X123 @ X125))) | (hoasinduction_lem0_lthm != $true)) & ((sP14 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP14 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) | ((sK523 != sK522) & (((ap @ (sub @ sK523 @ id) @ sK524)) = ((ap @ (sub @ sK522 @ id) @ sK521))))) & (! [X130 : term,X131 : term,X132 : term,X133 : term] : ((X131 = X132) | (((ap @ (sub @ X132 @ id) @ X133)) != ((ap @ (sub @ X131 @ id) @ X130)))) | (hoasapinj1 != $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)))))))))))))) & (hoaslamnotvar_lthm = $true) & ((axvarid = $true) | (((sub @ sK525 @ id)) != sK525)) & (! [X135 : term] : (((sub @ X135 @ id)) = X135) | (axvarid != $true)) & (! [X136 : (subst > term > subst > $o),X137 : term] : (((((X136 @ id @ (ap @ (sub @ (sK526 @ X136) @ id) @ (sK527 @ X136)) @ id)) != $true) & (((X136 @ id @ (sK527 @ X136) @ id)) = $true) & (((X136 @ id @ (sK526 @ X136) @ id)) = $true)) | (((sP11 @ X136)) = $true) | (((X136 @ id @ X137 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X142 : term,X143 : term] : ((((sK528 @ id @ (ap @ (sub @ X142 @ id) @ X143) @ id)) = $true) | (((sK528 @ id @ X143 @ id)) != $true) | (((sK528 @ id @ X142 @ id)) != $true)) & ($true != ((sP11 @ sK528))) & (((sK528 @ id @ sK529 @ id)) != $true))) & (hoasinduction_lem3a_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar = $true) & (hoaslamnotvar = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((sP10 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP10 != $true)) & ((hoasinduction_lem3a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a != $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & ((hoasinduction_lem3b = $true) | ! [X145 : (subst > term > term)] : (((X145 @ sh @ one)) != ((sub @ sK530 @ (push @ one @ sh))))) & (! [X146 : term] : (((sK531 @ X146 @ sh @ one)) = ((sub @ X146 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((pushprop_lem1v2_lthm = $true) | (((((sK534 @ sK533)) = $true) & ! [X152 : term] : (((sK535 @ X152)) = ((sK534 @ (sub @ X152 @ (push @ sK533 @ sK532))))) & ($true != ((sK535 @ one)))) & ! [X153 : term,X154 : subst] : (((sub @ one @ (push @ X153 @ X154))) = X153))) & (! [X155 : subst,X156 : term,X157 : (term > $o),X158 : (term > $o)] : ((((X157 @ X156)) != $true) | (((X158 @ (sK536 @ X158 @ X157 @ X156 @ X155))) != ((X157 @ (sub @ (sK536 @ X158 @ X157 @ X156 @ X155) @ (push @ X156 @ X155))))) | ($true = ((X158 @ one)))) | (((sub @ one @ (push @ sK537 @ sK538))) != sK537) | (pushprop_lem1v2_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & ((shinj = $true) | ((((sub @ sK540 @ sh)) = ((sub @ sK539 @ sh))) & (sK540 != sK539))) & (! [X164 : term,X165 : term] : ((((sub @ X164 @ sh)) != ((sub @ X165 @ sh))) | (X164 = X165)) | (shinj != $true)) & (axabs = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lthm_orig = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem2 != $true)) & (ulamvar1 != $true) & ((axvarcons = $true) | (sK542 != ((sub @ one @ (push @ sK542 @ sK541))))) & (! [X168 : subst,X169 : term] : (((sub @ one @ (push @ X169 @ X168))) = X169) | (axvarcons != $true)) & (hoasinduction_lem2v2_gthm = $true) & (($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP6)) & ((pushprop_lem1v2 = $true) | ((((sK545 @ sK543)) = $true) & (((sK544 @ one)) != $true) & ! [X174 : term] : (((sK544 @ X174)) = ((sK545 @ (sub @ X174 @ (push @ sK543 @ sK546))))))) & (! [X175 : term,X176 : (term > $o),X177 : (term > $o),X178 : subst] : ((((X177 @ X175)) != $true) | (((X176 @ one)) = $true) | (((X177 @ (sub @ (sK547 @ X178 @ X177 @ X176 @ X175) @ (push @ X175 @ X178)))) != ((X176 @ (sK547 @ X178 @ X177 @ X176 @ X175))))) | (pushprop_lem1v2 != $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X181 : (subst > term > term)] : (((sub @ sK548 @ (push @ one @ sh))) != ((X181 @ sh @ one)))) & (! [X182 : term] : (((sub @ X182 @ (push @ one @ sh))) = ((sK549 @ X182 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X185 : (subst > term > term)] : (((sub @ sK550 @ (push @ (sK551 @ X185) @ (sK552 @ X185)))) != ((X185 @ (sK552 @ X185) @ (sK551 @ X185))))) & (! [X188 : term] : ! [X190 : term,X191 : subst] : (((sK553 @ X188 @ X191 @ X190)) = ((sub @ X188 @ (push @ X190 @ X191)))) | (hoasinduction_lem3v2_f != $true)) & ((axidl = $true) | (((comp @ id @ sK554)) != sK554)) & (! [X193 : subst] : (((comp @ id @ X193)) = X193) | (axidl != $true)) & ((termmset = $true) | (sK555 != ((sub @ sK555 @ id)))) & (! [X195 : term] : (((sub @ X195 @ id)) = X195) | (termmset != $true)) & (hoasinduction_gthm = $true) & (! [X196 : term,X197 : subst,X198 : (term > $o),X199 : term,X200 : (term > $o)] : ((((X200 @ (sub @ X199 @ (push @ X196 @ X197)))) = $true) | (((X198 @ X199)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK560 @ (sub @ sK559 @ (push @ sK556 @ sK557)))) != $true) & ($true = ((sK558 @ sK559))))) & (! [X206 : subst] : (((comp @ X206 @ id)) = X206) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK561 @ id)) != sK561)) & ((hoaslamnotap = $true) | (! [X211 : term,X212 : subst,X213 : subst] : (((sub @ (sK562 @ X212 @ X211) @ X213)) = ((sK562 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213)))) & (((ap @ (sub @ sK564 @ id) @ sK563)) = ((lam @ (sK562 @ sh @ one)))))) & (! [X214 : (subst > term > term),X215 : term,X216 : term] : ((((sub @ (X214 @ (sK566 @ X214) @ (sK565 @ X214)) @ (sK567 @ X214))) != ((X214 @ (comp @ (sK566 @ X214) @ (sK567 @ X214)) @ (sub @ (sK565 @ X214) @ (sK567 @ X214))))) | (((ap @ (sub @ X216 @ id) @ X215)) != ((lam @ (X214 @ sh @ one))))) | (hoaslamnotap != $true)) & (hoasapinj2_gthm = $true) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK568 @ sK569))) != sK569)) & (! [X222 : term,X223 : subst] : (((comp @ sh @ (push @ X222 @ X223))) = X223) | (axshiftcons != $true)) & ! [X224 : d_subst,X225 : d_subst] : ((X224 = X225) | (((d2subst @ X224)) != ((d2subst @ X225)))) & (! [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ X228 @ X227)) != ((ap @ X229 @ X226))) | (X226 = X227)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK572 @ sK571)) = ((ap @ sK573 @ sK570))) & (sK571 != sK570))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3b_gthm = $true) & ((termmset_lthm = $true) | ((sK574 != ((sub @ sK574 @ id))) & ! [X235 : term] : (((sub @ X235 @ id)) = X235))) & (! [X236 : term] : (((sub @ X236 @ id)) = X236) | (((sub @ sK575 @ id)) != sK575) | (termmset_lthm != $true)) & ((induction = $true) | (! [X240 : term] : ((((sK577 @ X240)) != $true) | (((sK577 @ (lam @ X240))) = $true)) & ! [X241 : term] : ((((var @ X241)) != $true) | (((sK577 @ X241)) = $true)) & (((sP4 @ sK577)) != $true) & ($true != ((sK577 @ sK576))))) & (! [X242 : term,X243 : (term > $o)] : ((($true = ((X243 @ (sK578 @ X243)))) & ($true != ((X243 @ (lam @ (sK578 @ X243)))))) | (($true = ((var @ (sK579 @ X243)))) & (((X243 @ (sK579 @ X243))) != $true)) | (((sP4 @ X243)) = $true) | (((X243 @ X242)) = $true)) | (induction != $true)) & (hoaslamnotap_lthm = $true) & ((induction2_lthm = $true) | (sP3 != $true)) & ((sP3 = $true) | (induction2_lthm != $true)) & (pushprop_lthm = $true) & (! [X246 : term] : ! [X248 : term,X249 : subst] : (((sK580 @ X246 @ X249 @ X248)) = ((sub @ X246 @ (push @ X248 @ X249)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X251 : (subst > term > term)] : (((sub @ sK581 @ (push @ (sK582 @ X251) @ (sK583 @ X251)))) != ((X251 @ (sK583 @ X251) @ (sK582 @ X251))))) & ((substmonoid_lthm = $true) | (((((comp @ sK584 @ id)) != sK584) | (((comp @ id @ sK585)) != sK585)) & ! [X256 : subst] : (((comp @ id @ X256)) = X256) & ! [X257 : subst] : (((comp @ X257 @ id)) = X257))) & ((! [X258 : subst] : (((comp @ X258 @ id)) = X258) & ! [X259 : subst] : (((comp @ id @ X259)) = X259)) | (sK586 != ((comp @ id @ sK586))) | (((comp @ sK587 @ id)) != sK587) | (substmonoid_lthm != $true)) & ((axscons = $true) | (sK588 != ((push @ (sub @ one @ sK588) @ (comp @ sh @ sK588))))) & (! [X263 : subst] : (((push @ (sub @ one @ X263) @ (comp @ sh @ X263))) = X263) | (axscons != $true)) & (ulamvarind = $true) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem0 = $true) | ! [X267 : (term > $o)] : (((sK589 @ (sub @ (sK592 @ X267) @ (push @ sK590 @ sK591)))) != ((X267 @ (sK592 @ X267))))) & (! [X269 : (term > $o),X270 : term,X271 : subst] : ! [X273 : term] : (((sK593 @ X271 @ X270 @ X269 @ X273)) = ((X269 @ (sub @ X273 @ (push @ X270 @ X271))))) | (pushprop_lem0 != $true))), 50.81/8.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,vAPP,sK483,vAPP,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,vAPP,vAPP,sK499,sK500,sK501,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,vAPP,sK518,vAPP,vAPP,sK521,sK522,sK523,sK524,sK525,vAPP,vAPP,sK528,sK529,sK530,vAPP,sK532,sK533,sK534,sK535,vAPP,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,vAPP,sK548,vAPP,sK550,vAPP,vAPP,vAPP,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,vAPP,vAPP,vAPP,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,vAPP,vAPP,vAPP,sK581,vAPP,vAPP,sK584,sK585,sK586,sK587,sK588,sK589,sK590,sK591,vAPP,vAPP]),skolemize(X4,sK460),skolemize(X5,sK461),skolemize(X6,sK462),skolemize(X7,sK463),skolemize(X8,sK464),skolemize(X9,sK465),skolemize(X10,sK466),skolemize(X11,sK467),skolemize(X12,sK468),skolemize(X23,sK469),skolemize(X24,sK470),skolemize(X25,sK471),skolemize(X26,sK472),skolemize(X27,sK473),skolemize(X28,sK474),skolemize(X29,sK475),skolemize(X30,sK476),skolemize(X31,sK477),skolemize(X40,sK478),skolemize(X41,sK479),skolemize(X42,sK480),skolemize(X43,sK481),skolemize(X21,sK72 @ X12),skolemize(X47,sK483),skolemize(X21,sK72 @ X12),skolemize(X50,sK485),skolemize(X51,sK486),skolemize(X52,sK487),skolemize(X53,sK488),skolemize(X62,sK489),skolemize(X63,sK490),skolemize(X64,sK491),skolemize(X65,sK492),skolemize(X66,sK493),skolemize(X67,sK494),skolemize(X68,sK495),skolemize(X69,sK496),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X83,sK499),skolemize(X84,sK500),skolemize(X85,sK501),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X99,sK509),skolemize(X100,sK510),skolemize(X101,sK511),skolemize(X102,sK512),skolemize(X111,sK513),skolemize(X112,sK514),skolemize(X113,sK515),skolemize(X114,sK516),skolemize(X21,sK72 @ X12),skolemize(X120,sK518),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X126,sK521),skolemize(X127,sK522),skolemize(X128,sK523),skolemize(X129,sK524),skolemize(X134,sK525),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X140,sK528),skolemize(X141,sK529),skolemize(X144,sK530),skolemize(X21,sK72 @ X12),skolemize(X148,sK532),skolemize(X149,sK533),skolemize(X150,sK534),skolemize(X151,sK535),skolemize(X21,sK72 @ X12),skolemize(X160,sK537),skolemize(X161,sK538),skolemize(X162,sK539),skolemize(X163,sK540),skolemize(X166,sK541),skolemize(X167,sK542),skolemize(X170,sK543),skolemize(X171,sK544),skolemize(X172,sK545),skolemize(X173,sK546),skolemize(X21,sK72 @ X12),skolemize(X180,sK548),skolemize(X21,sK72 @ X12),skolemize(X184,sK550),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X192,sK554),skolemize(X194,sK555),skolemize(X201,sK556),skolemize(X202,sK557),skolemize(X203,sK558),skolemize(X204,sK559),skolemize(X205,sK560),skolemize(X207,sK561),skolemize(X208,sK562),skolemize(X209,sK563),skolemize(X210,sK564),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X220,sK568),skolemize(X221,sK569),skolemize(X230,sK570),skolemize(X231,sK571),skolemize(X232,sK572),skolemize(X233,sK573),skolemize(X234,sK574),skolemize(X237,sK575),skolemize(X238,sK576),skolemize(X239,sK577),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X250,sK581),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X254,sK584),skolemize(X255,sK585),skolemize(X260,sK586),skolemize(X261,sK587),skolemize(X262,sK588),skolemize(X264,sK589),skolemize(X265,sK590),skolemize(X266,sK591),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12)],[f268])). 50.81/8.72 thf(f270,plain,( 50.81/8.72 ((sP61 = $true) | ? [X0 : (subst > term > subst > $o)] : (! [X7 : subst,X8 : term,X6 : subst,X5 : subst] : ((((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) = $true) | ($true != ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6)))) & ! [X9 : term] : (($true = ((X0 @ id @ X9 @ id))) | (((hoasvar @ id @ X9 @ id)) != $true)) & ! [X3 : term,X1 : subst,X2 : subst,X4 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) != $true) | (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) = $true)) & (((sP60 @ X0)) != $true) & ? [X17 : term] : (((X0 @ id @ X17 @ id)) != $true) & ($true != ((sP59 @ X0))))) & (! [X0 : (subst > term > subst > $o)] : (? [X7 : subst,X8 : term,X6 : subst,X5 : subst] : ((((X0 @ X5 @ X8 @ (comp @ X7 @ X6))) != $true) & ($true = ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6)))) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true)) | ? [X3 : term,X1 : subst,X2 : subst,X4 : subst] : ((((X0 @ X4 @ X3 @ (comp @ X2 @ X1))) = $true) & (((X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2) @ X1)) != $true)) | (((sP60 @ X0)) = $true) | ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | ($true = ((sP59 @ X0)))) | (sP61 != $true))), 50.81/8.72 inference(nnf_transformation,[],[f77])). 50.81/8.72 thf(f271,plain,( 50.81/8.72 ((sP61 = $true) | ? [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : term,X3 : subst,X4 : subst] : ((((X0 @ X4 @ X2 @ (comp @ X1 @ X3))) = $true) | (((X0 @ (comp @ X4 @ X1) @ (sub @ X2 @ X1) @ X3)) != $true)) & ! [X5 : term] : ((((X0 @ id @ X5 @ id)) = $true) | (((hoasvar @ id @ X5 @ id)) != $true)) & ! [X6 : term,X7 : subst,X8 : subst,X9 : subst] : (($true != ((X0 @ X9 @ X6 @ (comp @ X8 @ X7)))) | (((X0 @ (comp @ X9 @ X8) @ (sub @ X6 @ X8) @ X7)) = $true)) & (((sP60 @ X0)) != $true) & ? [X10 : term] : (((X0 @ id @ X10 @ id)) != $true) & ($true != ((sP59 @ X0))))) & (! [X11 : (subst > term > subst > $o)] : (? [X12 : subst,X13 : term,X14 : subst,X15 : subst] : (($true != ((X11 @ X15 @ X13 @ (comp @ X12 @ X14)))) & (((X11 @ (comp @ X15 @ X12) @ (sub @ X13 @ X12) @ X14)) = $true)) | ? [X16 : term] : ((((X11 @ id @ X16 @ id)) != $true) & (((hoasvar @ id @ X16 @ id)) = $true)) | ? [X17 : term,X18 : subst,X19 : subst,X20 : subst] : ((((X11 @ X20 @ X17 @ (comp @ X19 @ X18))) = $true) & (((X11 @ (comp @ X20 @ X19) @ (sub @ X17 @ X19) @ X18)) != $true)) | ($true = ((sP60 @ X11))) | ! [X21 : term] : (((X11 @ id @ X21 @ id)) = $true) | (((sP59 @ X11)) = $true)) | (sP61 != $true))), 50.81/8.72 inference(rectify,[],[f270])). 50.81/8.72 thf(f272,plain,( 50.81/8.72 ((sP61 = $true) | (! [X1 : subst,X2 : term,X3 : subst,X4 : subst] : (($true = ((sK594 @ X4 @ X2 @ (comp @ X1 @ X3)))) | (((sK594 @ (comp @ X4 @ X1) @ (sub @ X2 @ X1) @ X3)) != $true)) & ! [X5 : term] : ((((sK594 @ id @ X5 @ id)) = $true) | (((hoasvar @ id @ X5 @ id)) != $true)) & ! [X6 : term,X7 : subst,X8 : subst,X9 : subst] : ((((sK594 @ X9 @ X6 @ (comp @ X8 @ X7))) != $true) | ($true = ((sK594 @ (comp @ X9 @ X8) @ (sub @ X6 @ X8) @ X7)))) & ($true != ((sP60 @ sK594))) & ($true != ((sK594 @ id @ sK595 @ id))) & (((sP59 @ sK594)) != $true))) & (! [X11 : (subst > term > subst > $o)] : (((((X11 @ (sK599 @ X11) @ (sK597 @ X11) @ (comp @ (sK596 @ X11) @ (sK598 @ X11)))) != $true) & (((X11 @ (comp @ (sK599 @ X11) @ (sK596 @ X11)) @ (sub @ (sK597 @ X11) @ (sK596 @ X11)) @ (sK598 @ X11))) = $true)) | ((((X11 @ id @ (sK600 @ X11) @ id)) != $true) & (((hoasvar @ id @ (sK600 @ X11) @ id)) = $true)) | ((((X11 @ (sK604 @ X11) @ (sK601 @ X11) @ (comp @ (sK603 @ X11) @ (sK602 @ X11)))) = $true) & (((X11 @ (comp @ (sK604 @ X11) @ (sK603 @ X11)) @ (sub @ (sK601 @ X11) @ (sK603 @ X11)) @ (sK602 @ X11))) != $true)) | ($true = ((sP60 @ X11))) | ! [X21 : term] : (((X11 @ id @ X21 @ id)) = $true) | (((sP59 @ X11)) = $true)) | (sP61 != $true))), 50.81/8.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK594,sK595,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK594),skolemize(X10,sK595),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12)],[f271])). 50.81/8.72 thf(f276,plain,( 50.81/8.72 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP59 @ X0))) | ! [X12 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) = $true) | ? [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) != ((sub @ (X12 @ X15 @ X14) @ X13))) | ? [X16 : term] : ((((X0 @ id @ (X12 @ id @ X16) @ id)) != $true) & (((X0 @ id @ X16 @ id)) = $true)))) & (? [X12 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true) & ! [X13 : subst,X14 : term,X15 : subst] : (((X12 @ (comp @ X15 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X12 @ X15 @ X14) @ X13))) & ! [X16 : term] : ((((X0 @ id @ (X12 @ id @ X16) @ id)) = $true) | (((X0 @ id @ X16 @ id)) != $true))) | ($true != ((sP59 @ X0)))))), 50.81/8.72 inference(nnf_transformation,[],[f75])). 50.81/8.72 thf(f277,plain,( 50.81/8.72 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP59 @ X0))) | ! [X1 : (subst > term > term)] : (($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | ? [X2 : subst,X3 : term,X4 : subst] : (((sub @ (X1 @ X4 @ X3) @ X2)) != ((X1 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2)))) | ? [X5 : term] : (($true != ((X0 @ id @ (X1 @ id @ X5) @ id))) & (((X0 @ id @ X5 @ id)) = $true)))) & (? [X6 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X6 @ Y0 @ Y1))))) @ id)) != $true) & ! [X7 : subst,X8 : term,X9 : subst] : (((X6 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7))) = ((sub @ (X6 @ X9 @ X8) @ X7))) & ! [X10 : term] : ((((X0 @ id @ (X6 @ id @ X10) @ id)) = $true) | (((X0 @ id @ X10 @ id)) != $true))) | ($true != ((sP59 @ X0)))))), 50.81/8.72 inference(rectify,[],[f276])). 50.81/8.72 thf(f278,plain,( 50.81/8.72 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP59 @ X0))) | ! [X1 : (subst > term > term)] : (($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | (((X1 @ (comp @ (sK609 @ X1) @ (sK607 @ X1)) @ (sub @ (sK608 @ X1) @ (sK607 @ X1)))) != ((sub @ (X1 @ (sK609 @ X1) @ (sK608 @ X1)) @ (sK607 @ X1)))) | (($true != ((X0 @ id @ (X1 @ id @ (sK610 @ X1 @ X0)) @ id))) & ($true = ((X0 @ id @ (sK610 @ X1 @ X0) @ id)))))) & ((($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK611 @ X0 @ Y0 @ Y1))))) @ id))) & ! [X7 : subst,X8 : term,X9 : subst] : (((sub @ (sK611 @ X0 @ X9 @ X8) @ X7)) = ((sK611 @ X0 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)))) & ! [X10 : term] : ((((X0 @ id @ (sK611 @ X0 @ id @ X10) @ id)) = $true) | (((X0 @ id @ X10 @ id)) != $true))) | ($true != ((sP59 @ X0)))))), 50.81/8.72 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12),skolemize(X21,sK72 @ X12)],[f277])). 50.81/8.72 thf(f279,plain,( 50.81/8.72 ((sP61 != $true) | (hoasinduction != $true)) & ((sP61 = $true) | (hoasinduction = $true))), 50.81/8.72 inference(nnf_transformation,[],[f78])). 50.81/8.72 thf(f288,plain,( 50.81/8.72 (sP58 = $true) | (((sP56 @ sK63)) != $true)), 50.81/8.72 inference(cnf_transformation,[],[f81])). 50.81/8.72 thf(f289,plain,( 50.81/8.72 (((sK63 @ id @ sK62 @ id)) != $true) | (sP58 = $true)), 50.81/8.72 inference(cnf_transformation,[],[f81])). 50.81/8.72 thf(f302,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((X1 @ (comp @ (sK76 @ X1) @ (sK77 @ X1)) @ (sub @ (sK78 @ X1) @ (sK77 @ X1)))) != ((sub @ (X1 @ (sK76 @ X1) @ (sK78 @ X1)) @ (sK77 @ X1)))) | ($true = ((X0 @ id @ (sK75 @ X1 @ X0) @ id))) | ($true = ((sP56 @ X0)))) )), 50.81/8.72 inference(cnf_transformation,[],[f87])). 50.81/8.72 thf(f595,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X6 : (subst > term > term)] : ((((X0 @ id @ (X6 @ id @ (sK328 @ X6 @ X0)) @ id)) != $true) | ($true != ((sP22 @ X0))) | (((sub @ (X6 @ (sK327 @ X6) @ (sK325 @ X6)) @ (sK326 @ X6))) != ((X6 @ (comp @ (sK327 @ X6) @ (sK326 @ X6)) @ (sub @ (sK325 @ X6) @ (sK326 @ X6))))) | (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true)) )), 50.81/8.72 inference(cnf_transformation,[],[f196])). 50.81/8.72 thf(f598,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (lam @ (sK324 @ X0 @ sh @ one)) @ id)) != $true) | ($true = ((sP22 @ X0)))) )), 50.81/8.72 inference(cnf_transformation,[],[f196])). 50.81/8.72 thf(f881,plain,( 50.81/8.72 ( ! [X118 : subst] : ((((d2subst @ (sK517 @ X118))) = X118)) )), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f886,plain,( 50.81/8.72 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f889,plain,( 50.81/8.72 ( ! [X117 : d_term] : ((d_one = X117)) )), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f916,plain,( 50.81/8.72 (((d2subst @ d_id)) = id)), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f917,plain,( 50.81/8.72 (((d2term @ d_one)) = one)), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f930,plain,( 50.81/8.72 ( ! [X88 : d_subst] : ((d_id = X88)) )), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f940,plain,( 50.81/8.72 ( ! [X74 : term] : ((((d2term @ (sK497 @ X74))) = X74)) )), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f993,plain,( 50.81/8.72 (hoasinduction = $true) | (sP58 != $true)), 50.81/8.72 inference(cnf_transformation,[],[f269])). 50.81/8.72 thf(f1002,plain,( 50.81/8.72 (((sP59 @ sK594)) != $true) | (sP61 = $true)), 50.81/8.72 inference(cnf_transformation,[],[f272])). 50.81/8.72 thf(f1003,plain,( 50.81/8.72 ($true != ((sK594 @ id @ sK595 @ id))) | (sP61 = $true)), 50.81/8.72 inference(cnf_transformation,[],[f272])). 50.81/8.72 thf(f1015,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : (($true = ((sP59 @ X0))) | ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id))) | (((X1 @ (comp @ (sK609 @ X1) @ (sK607 @ X1)) @ (sub @ (sK608 @ X1) @ (sK607 @ X1)))) != ((sub @ (X1 @ (sK609 @ X1) @ (sK608 @ X1)) @ (sK607 @ X1)))) | ($true = ((X0 @ id @ (sK610 @ X1 @ X0) @ id)))) )), 50.81/8.72 inference(cnf_transformation,[],[f278])). 50.81/8.72 thf(f1018,plain,( 50.81/8.72 (sP61 != $true) | (hoasinduction != $true)), 50.81/8.72 inference(cnf_transformation,[],[f279])). 50.81/8.72 thf(f1022,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ ((^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true) | ($true = ((X0 @ id @ (sK610 @ X1 @ X0) @ id))) | (((X1 @ (comp @ (sK609 @ X1) @ (sK607 @ X1)) @ (sub @ (sK608 @ X1) @ (sK607 @ X1)))) != ((sub @ (X1 @ (sK609 @ X1) @ (sK608 @ X1)) @ (sK607 @ X1)))) | ($true = ((sP59 @ X0)))) )), 50.81/8.72 inference(definition_unfolding,[],[f1015,f886])). 50.81/8.72 thf(f1111,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X1 @ (comp @ (sK609 @ X1) @ (sK607 @ X1)) @ (sub @ (sK608 @ X1) @ (sK607 @ X1)))) != ((sub @ (X1 @ (sK609 @ X1) @ (sK608 @ X1)) @ (sK607 @ X1)))) | (((X0 @ id @ (d2term @ d_one) @ id)) = $true) | ($true = ((X0 @ id @ (sK610 @ X1 @ X0) @ id))) | ($true = ((sP59 @ X0)))) )), 50.81/8.72 inference(beta-eta_normalization,[],[f1022])). 50.81/8.72 thf(f1284,definition,( 50.81/8.72 spl612_32 <=> (sP61 = $true)), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_32])],[avatar_definition])). 50.81/8.72 thf(f1287,definition,( 50.81/8.72 spl612_33 <=> (hoasinduction = $true)), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_33])],[avatar_definition])). 50.81/8.72 thf(f1594,definition,( 50.81/8.72 spl612_115 <=> (sP58 = $true)), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_115])],[avatar_definition])). 50.81/8.72 thf(f2613,definition,( 50.81/8.72 spl612_364 <=> (((sP59 @ sK594)) = $true)), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_364])],[avatar_definition])). 50.81/8.72 thf(f2614,plain,( 50.81/8.72 (((sP59 @ sK594)) != $true) | spl612_364), 50.81/8.72 inference(avatar_component_clause,[],[f2613])). 50.81/8.72 thf(f2615,plain,( 50.81/8.72 ~spl612_364 | spl612_32), 50.81/8.72 inference(avatar_split_clause,[],[f1002,f1284,f2613])). 50.81/8.72 thf(f2894,plain,( 50.81/8.72 ~spl612_32 | ~spl612_33), 50.81/8.72 inference(avatar_split_clause,[],[f1018,f1287,f1284])). 50.81/8.72 thf(f3134,plain,( 50.81/8.72 spl612_33 | ~spl612_115), 50.81/8.72 inference(avatar_split_clause,[],[f993,f1594,f1287])). 50.81/8.72 thf(f3257,definition,( 50.81/8.72 spl612_517 <=> ($true = ((sK594 @ id @ sK595 @ id)))), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_517])],[avatar_definition])). 50.81/8.72 thf(f3258,plain,( 50.81/8.72 ($true != ((sK594 @ id @ sK595 @ id))) | spl612_517), 50.81/8.72 inference(avatar_component_clause,[],[f3257])). 50.81/8.72 thf(f3259,plain,( 50.81/8.72 ~spl612_517 | spl612_32), 50.81/8.72 inference(avatar_split_clause,[],[f1003,f1284,f3257])). 50.81/8.72 thf(f3596,definition,( 50.81/8.72 spl612_594 <=> (((sP56 @ sK63)) = $true)), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_594])],[avatar_definition])). 50.81/8.72 thf(f3597,plain,( 50.81/8.72 (((sP56 @ sK63)) != $true) | spl612_594), 50.81/8.72 inference(avatar_component_clause,[],[f3596])). 50.81/8.72 thf(f3598,plain,( 50.81/8.72 spl612_115 | ~spl612_594), 50.81/8.72 inference(avatar_split_clause,[],[f288,f3596,f1594])). 50.81/8.72 thf(f3671,definition,( 50.81/8.72 spl612_611 <=> (((sK63 @ id @ sK62 @ id)) = $true)), 50.81/8.72 introduced(definition,[new_symbols(definition,[spl612_611])],[avatar_definition])). 50.81/8.72 thf(f3672,plain,( 50.81/8.72 (((sK63 @ id @ sK62 @ id)) != $true) | spl612_611), 50.81/8.72 inference(avatar_component_clause,[],[f3671])). 50.81/8.72 thf(f3673,plain,( 50.81/8.72 spl612_115 | ~spl612_611), 50.81/8.72 inference(avatar_split_clause,[],[f289,f3671,f1594])). 50.81/8.72 thf(f3825,plain,( 50.81/8.72 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )), 50.81/8.72 inference(constrained_superposition,[],[f916,f930])). 50.81/8.72 thf(f3830,plain,( 50.81/8.72 ( ! [X0 : d_term] : ((((d2term @ X0)) = one)) )), 50.81/8.72 inference(constrained_superposition,[],[f917,f889])). 50.81/8.72 thf(f3847,plain,( 50.81/8.72 ( ! [X0 : subst] : ((id = X0)) )), 50.81/8.72 inference(constrained_superposition,[],[f881,f3825])). 50.81/8.72 thf(f3889,plain,( 50.81/8.72 ( ! [X0 : term] : ((one = X0)) )), 50.81/8.72 inference(constrained_superposition,[],[f940,f3830])). 50.81/8.72 thf(f3891,plain,( 50.81/8.72 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )), 50.81/8.72 inference(constrained_superposition,[],[f3889,f3889])). 50.81/8.72 thf(f4049,plain,( 50.81/8.72 ( ! [X0 : term] : ((((sK594 @ id @ X0 @ id)) != $true)) ) | spl612_517), 50.81/8.72 inference(constrained_superposition,[],[f3258,f3891])). 50.81/8.72 thf(f4052,plain,( 50.81/8.72 ( ! [X0 : subst] : (($true != ((sK594 @ X0 @ sK595 @ X0)))) ) | spl612_517), 50.81/8.72 inference(constrained_superposition,[],[f3258,f3847])). 50.81/8.72 thf(f4061,plain,( 50.81/8.72 ( ! [X0 : term,X1 : subst] : ((((sK594 @ X1 @ X0 @ X1)) != $true)) ) | spl612_517), 50.81/8.72 inference(constrained_superposition,[],[f4052,f3891])). 50.81/8.72 thf(f5676,plain,( 50.81/8.72 ( ! [X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ X0 @ id)) != $true) | (((sP22 @ X1)) = $true)) )), 50.81/8.72 inference(constrained_superposition,[],[f598,f3891])). 50.81/8.72 thf(f46653,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : (($true = ((X0 @ id @ (sK610 @ X1 @ X0) @ id))) | (((X0 @ id @ (d2term @ d_one) @ id)) = $true) | ($true = ((sP59 @ X0)))) )), 50.81/8.72 inference(forward_subsumption_resolution,[],[f1111,f3891])). 50.81/8.72 thf(f47080,plain,( 50.81/8.72 ($true != $true) | ($true = ((sK594 @ id @ (d2term @ d_one) @ id))) | (((sP59 @ sK594)) = $true) | spl612_517), 50.81/8.72 inference(constrained_superposition,[],[f4061,f46653])). 50.81/8.72 thf(f47173,plain,( 50.81/8.72 ($true = ((sK594 @ id @ (d2term @ d_one) @ id))) | (((sP59 @ sK594)) = $true) | spl612_517), 50.81/8.72 inference(trivial_inequality_removal,[],[f47080])). 50.81/8.72 thf(f47324,plain,( 50.81/8.72 (((sP59 @ sK594)) = $true) | spl612_517), 50.81/8.72 inference(forward_subsumption_resolution,[],[f47173,f4049])). 50.81/8.72 thf(f47396,plain,( 50.81/8.72 $false | (spl612_364 | spl612_517)), 50.81/8.72 inference(forward_subsumption_resolution,[],[f47324,f2614])). 50.81/8.72 thf(f47397,plain,( 50.81/8.72 spl612_364 | spl612_517), 50.81/8.72 inference(avatar_contradiction_clause,[],[f47396])). 50.81/8.72 thf(f47559,plain,( 50.81/8.72 ( ! [X0 : subst] : (($true != ((sK63 @ X0 @ sK62 @ X0)))) ) | spl612_611), 50.81/8.72 inference(constrained_superposition,[],[f3672,f3847])). 50.81/8.72 thf(f47940,plain,( 50.81/8.72 ( ! [X0 : term,X1 : subst] : ((((sK63 @ X1 @ X0 @ X1)) != $true)) ) | spl612_611), 50.81/8.72 inference(constrained_superposition,[],[f47559,f3891])). 50.81/8.72 thf(f49474,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X6 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true) | (((X0 @ id @ (X6 @ id @ (sK328 @ X6 @ X0)) @ id)) != $true) | (((sub @ (X6 @ (sK327 @ X6) @ (sK325 @ X6)) @ (sK326 @ X6))) != ((X6 @ (comp @ (sK327 @ X6) @ (sK326 @ X6)) @ (sub @ (sK325 @ X6) @ (sK326 @ X6)))))) )), 50.81/8.72 inference(forward_subsumption_resolution,[],[f595,f5676])). 50.81/8.72 thf(f49476,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X6 : (subst > term > term)] : ((((X0 @ id @ (X6 @ id @ (sK328 @ X6 @ X0)) @ id)) != $true) | (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true)) )), 50.81/8.72 inference(forward_subsumption_resolution,[],[f49474,f3891])). 50.81/8.72 thf(f53256,plain,( 50.81/8.72 ( ! [X2 : (subst > term > term),X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ X0 @ id)) != $true) | ($true = ((X1 @ id @ (lam @ (X2 @ sh @ one)) @ id)))) )), 50.81/8.72 inference(constrained_superposition,[],[f49476,f3891])). 50.81/8.72 thf(f96493,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : (($true = ((sP56 @ X0))) | (((X1 @ (comp @ (sK76 @ X1) @ (sK77 @ X1)) @ (sub @ (sK78 @ X1) @ (sK77 @ X1)))) != ((sub @ (X1 @ (sK76 @ X1) @ (sK78 @ X1)) @ (sK77 @ X1)))) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true)) )), 50.81/8.72 inference(forward_subsumption_resolution,[],[f302,f53256])). 50.81/8.72 thf(f96522,plain,( 50.81/8.72 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ($true = ((sP56 @ X0)))) )), 50.81/8.72 inference(forward_subsumption_resolution,[],[f96493,f3891])). 50.81/8.72 thf(f109335,plain,( 50.81/8.72 ($true != $true) | (((sP56 @ sK63)) = $true) | spl612_611), 50.81/8.72 inference(constrained_superposition,[],[f47940,f96522])). 50.81/8.72 thf(f109460,plain,( 50.81/8.72 (((sP56 @ sK63)) = $true) | spl612_611), 50.81/8.72 inference(trivial_inequality_removal,[],[f109335])). 50.81/8.72 thf(f109549,plain,( 50.81/8.72 $false | (spl612_594 | spl612_611)), 50.81/8.72 inference(forward_subsumption_resolution,[],[f109460,f3597])). 50.81/8.72 thf(f109550,plain,( 50.81/8.72 spl612_594 | spl612_611), 50.81/8.72 inference(avatar_contradiction_clause,[],[f109549])). 50.81/8.72 cnf(s301, plain, spl612_32 | ~spl612_364, inference(sat_conversion,[],[f2615])). 50.81/8.72 cnf(s370, plain, ~spl612_32 | ~spl612_33, inference(sat_conversion,[],[f2894])). 50.81/8.72 cnf(s431, plain, spl612_33 | ~spl612_115, inference(sat_conversion,[],[f3134])). 50.81/8.72 cnf(s465, plain, spl612_32 | ~spl612_517, inference(sat_conversion,[],[f3259])). 50.81/8.72 cnf(s562, plain, spl612_115 | ~spl612_594, inference(sat_conversion,[],[f3598])). 50.81/8.72 cnf(s582, plain, spl612_115 | ~spl612_611, inference(sat_conversion,[],[f3673])). 50.81/8.72 cnf(s1402, plain, spl612_364 | spl612_517, inference(sat_conversion,[],[f47397])). 50.81/8.72 cnf(s2383, plain, spl612_594 | spl612_611, inference(sat_conversion,[],[f109550])). 50.81/8.72 cnf(s2609, plain, spl612_32, inference(rat,[],[s1402,s301,s465])). 50.81/8.72 cnf(s2612, plain, ~spl612_33, inference(rat,[],[s370,s2609])). 50.81/8.72 cnf(s2619, plain, ~spl612_115, inference(rat,[],[s431,s2612])). 50.81/8.72 cnf(s2620, plain, ~spl612_611, inference(rat,[],[s582,s2619])). 50.81/8.72 cnf(s2621, plain, ~spl612_594, inference(rat,[],[s562,s2619])). 50.81/8.72 cnf(s2626, plain, $false, inference(rat,[],[s2383,s2620,s2621])). 50.81/8.72 thf(f109566,plain,( 50.81/8.72 $false), 50.81/8.72 inference(avatar_sat_refutation,[],[s2626])). 50.81/8.72 % SZS output end Proof for theBenchmark 50.81/8.72 % (2898513)------------------------------ 50.81/8.72 % (2898513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 50.81/8.72 % (2898513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 50.81/8.72 % (2898513)CaDiCaL version: 2.1.3 50.81/8.72 % (2898513)Termination reason: Refutation 50.81/8.72 % (2898513)Time elapsed: 2.377 s 50.81/8.72 % (2898513)Peak memory usage: 35 MB 50.81/8.72 % (2898513)Instructions burned: 4689 (million) 50.81/8.72 % (2898188)Success in time 8.209 s 50.81/8.72 % Vampire exiting 50.81/8.72 EOF