0.00/0.01 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.03/0.31 % Computer : n024.cluster.edu 0.03/0.31 % Model : x86_64 x86_64 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.03/0.31 % Memory : 8046.5625MB 0.03/0.31 % OS : Linux 6.8.0-71-generic 0.03/0.31 % CPULimit : 1440 0.03/0.31 % WCLimit : 180 0.03/0.31 % DateTime : Mon Jul 27 07:11:30 UTC 2026 0.03/0.31 % CPUTime : 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.07/0.33 Running higher-order theorem proving 0.07/0.35 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.43/0.43 % (2977821)Detected a higher-order problem, will run a greedy HOL sequence. 0.43/0.43 % (2977832)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.43/0.43 % (2977832)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.43/0.43 % (2977826)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1043942310:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.43/0.43 % (2977832)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=4241336657:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.43/0.43 % (2977827)lrs+10_16_si=on:nwc=1.5:random_seed=3206039625:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.43/0.43 % (2977828)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=745300943:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.43/0.43 % (2977830)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2952233437:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.43/0.43 % (2977829)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=1087289865:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi) 0.43/0.43 % (2977831)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=343586211:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.43/0.43 % (2977828)Instruction limit reached! 0.43/0.43 % (2977828)------------------------------ 0.43/0.43 % (2977828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.43 % (2977828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.43 % (2977828)CaDiCaL version: 2.1.3 0.43/0.43 % (2977828)Termination reason: Instruction limit 0.43/0.43 % (2977828)Termination phase: shuffling 0.43/0.43 % (2977828)Time elapsed: 0.001 s 0.43/0.43 % (2977828)Peak memory usage: 10 MB 0.43/0.43 % (2977828)Instructions burned: 3 (million) 0.43/0.43 % (2977827)Instruction limit reached! 0.43/0.43 % (2977827)------------------------------ 0.43/0.43 % (2977827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.43 % (2977827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.43 % (2977827)CaDiCaL version: 2.1.3 0.43/0.43 % (2977827)Termination reason: Instruction limit 0.43/0.43 % (2977827)Termination phase: shuffling 0.43/0.43 % (2977827)Time elapsed: 0.005 s 0.43/0.43 % (2977827)Peak memory usage: 10 MB 0.43/0.43 % (2977827)Instructions burned: 22 (million) 0.43/0.43 % (2977830)Instruction limit reached! 0.43/0.43 % (2977830)------------------------------ 0.43/0.43 % (2977830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.43 % (2977830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.43 % (2977830)CaDiCaL version: 2.1.3 0.43/0.43 % (2977830)Termination reason: Instruction limit 0.43/0.43 % (2977830)Termination phase: Property scanning 0.43/0.43 % (2977830)Time elapsed: 0.006 s 0.43/0.43 % (2977830)Peak memory usage: 10 MB 0.43/0.43 % (2977830)Instructions burned: 27 (million) 0.43/0.43 % (2977840)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=667517654:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.43/0.43 % (2977840)Instruction limit reached! 0.43/0.43 % (2977840)------------------------------ 0.43/0.43 % (2977840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.43 % (2977840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.43 % (2977840)CaDiCaL version: 2.1.3 0.43/0.43 % (2977840)Termination reason: Instruction limit 0.43/0.43 % (2977840)Termination phase: shuffling 0.43/0.43 % (2977840)Time elapsed: 0.001 s 0.43/0.43 % (2977840)Peak memory usage: 10 MB 0.43/0.43 % (2977840)Instructions burned: 3 (million) 0.43/0.43 % (2977842)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.43/0.45 % (2977841)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3812872507:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.43/0.45 % (2977842)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1994227282:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.43/0.45 % (2977841)Instruction limit reached! 0.43/0.45 % (2977841)------------------------------ 0.43/0.45 % (2977841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.45 % (2977841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.45 % (2977841)CaDiCaL version: 2.1.3 0.43/0.45 % (2977841)Termination reason: Instruction limit 0.43/0.45 % (2977841)Termination phase: shuffling 0.43/0.45 % (2977841)Time elapsed: 0.002 s 0.43/0.45 % (2977841)Peak memory usage: 10 MB 0.43/0.45 % (2977841)Instructions burned: 8 (million) 0.43/0.45 % (2977831)Instruction limit reached! 0.43/0.45 % (2977831)------------------------------ 0.43/0.45 % (2977831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.45 % (2977831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.45 % (2977831)CaDiCaL version: 2.1.3 0.43/0.45 % (2977831)Termination reason: Instruction limit 0.43/0.45 % (2977831)Termination phase: Preprocessing 3 0.43/0.45 % (2977831)Time elapsed: 0.019 s 0.43/0.45 % (2977831)Peak memory usage: 12 MB 0.43/0.45 % (2977831)Instructions burned: 79 (million) 0.43/0.45 % (2977842)Instruction limit reached! 0.43/0.45 % (2977842)------------------------------ 0.43/0.45 % (2977842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.45 % (2977842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.45 % (2977842)CaDiCaL version: 2.1.3 0.43/0.45 % (2977842)Termination reason: Instruction limit 0.43/0.45 % (2977842)Termination phase: shuffling 0.43/0.45 % (2977842)Time elapsed: 0.002 s 0.43/0.45 % (2977842)Peak memory usage: 10 MB 0.43/0.45 % (2977842)Instructions burned: 8 (million) 0.43/0.45 % (2977826)Instruction limit reached! 0.43/0.45 % (2977826)------------------------------ 0.43/0.45 % (2977826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.45 % (2977826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.45 % (2977826)CaDiCaL version: 2.1.3 0.43/0.45 % (2977826)Termination reason: Instruction limit 0.43/0.45 % (2977826)Termination phase: Preprocessing 3 0.43/0.45 % (2977826)Time elapsed: 0.021 s 0.43/0.45 % (2977826)Peak memory usage: 13 MB 0.43/0.45 % (2977826)Instructions burned: 88 (million) 0.43/0.45 % (2977844)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1848467723:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.43/0.45 % (2977847)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.43/0.45 % (2977847)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.43/0.45 % (2977844)Instruction limit reached! 0.43/0.45 % (2977844)------------------------------ 0.43/0.45 % (2977844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.45 % (2977844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.45 % (2977844)CaDiCaL version: 2.1.3 0.43/0.45 % (2977844)Termination reason: Instruction limit 0.43/0.45 % (2977844)Termination phase: shuffling 0.43/0.45 % (2977844)Time elapsed: 0.003 s 0.43/0.45 % (2977844)Peak memory usage: 10 MB 0.43/0.45 % (2977844)Instructions burned: 13 (million) 0.43/0.45 % (2977847)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4047587698:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 0.43/0.45 % (2977850)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 0.43/0.45 % (2977849)lrs+10_1_si=on:cs=on:random_seed=448889176:i=8:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/8Mi) 0.43/0.45 % (2977848)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=1281314493:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 0.43/0.47 % (2977850)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=4043560173:i=2:add=on:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.43/0.47 % (2977850)Instruction limit reached! 0.43/0.47 % (2977850)------------------------------ 0.43/0.47 % (2977850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.47 % (2977850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.47 % (2977850)CaDiCaL version: 2.1.3 0.43/0.47 % (2977850)Termination reason: Instruction limit 0.43/0.47 % (2977850)Termination phase: shuffling 0.43/0.47 % (2977850)Time elapsed: 0.001 s 0.43/0.47 % (2977850)Peak memory usage: 10 MB 0.43/0.47 % (2977850)Instructions burned: 6 (million) 0.43/0.47 % (2977849)Instruction limit reached! 0.43/0.47 % (2977849)------------------------------ 0.43/0.47 % (2977849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.47 % (2977849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.47 % (2977849)CaDiCaL version: 2.1.3 0.43/0.47 % (2977849)Termination reason: Instruction limit 0.43/0.47 % (2977849)Termination phase: shuffling 0.43/0.47 % (2977849)Time elapsed: 0.003 s 0.43/0.47 % (2977849)Peak memory usage: 10 MB 0.43/0.47 % (2977849)Instructions burned: 14 (million) 0.43/0.47 % (2977852)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=514101517:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/38Mi) 0.43/0.47 % (2977832)Instruction limit reached! 0.43/0.47 % (2977832)------------------------------ 0.43/0.47 % (2977832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.47 % (2977832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.47 % (2977832)CaDiCaL version: 2.1.3 0.43/0.47 % (2977832)Termination reason: Instruction limit 0.43/0.47 % (2977832)Termination phase: Saturation 0.43/0.47 % (2977832)Time elapsed: 0.039 s 0.43/0.47 % (2977832)Peak memory usage: 14 MB 0.43/0.47 % (2977832)Instructions burned: 176 (million) 0.43/0.47 % (2977847)Instruction limit reached! 0.43/0.47 % (2977847)------------------------------ 0.43/0.47 % (2977847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.47 % (2977847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.47 % (2977847)CaDiCaL version: 2.1.3 0.43/0.47 % (2977847)Termination reason: Instruction limit 0.43/0.47 % (2977847)Termination phase: Property scanning 0.43/0.47 % (2977847)Time elapsed: 0.010 s 0.43/0.47 % (2977847)Peak memory usage: 10 MB 0.43/0.47 % (2977847)Instructions burned: 41 (million) 0.43/0.47 % (2977857)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1610431300:st=2:i=249:sd=1:rtra=on:ss=axioms_1799 on theBenchmark for (1799ds/249Mi) 0.43/0.47 % (2977858)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3853281532:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1799 on theBenchmark for (1799ds/25Mi) 0.43/0.47 % (2977852)Instruction limit reached! 0.43/0.47 % (2977852)------------------------------ 0.43/0.47 % (2977852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.47 % (2977852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.47 % (2977852)CaDiCaL version: 2.1.3 0.43/0.47 % (2977852)Termination reason: Instruction limit 0.43/0.47 % (2977852)Time elapsed: 0.010 s 0.43/0.47 % (2977852)Peak memory usage: 13 MB 0.43/0.47 % (2977852)Instructions burned: 40 (million) 0.43/0.47 % (2977860)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1134585850:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1799 on theBenchmark for (1799ds/14Mi) 0.43/0.47 % (2977848)Instruction limit reached! 0.43/0.47 % (2977848)------------------------------ 0.43/0.47 % (2977848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.47 % (2977848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.47 % (2977848)CaDiCaL version: 2.1.3 0.43/0.47 % (2977848)Termination reason: Instruction limit 0.43/0.47 % (2977848)Termination phase: Saturation 0.43/0.47 % (2977861)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1673721197:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1799 on theBenchmark for (1799ds/327Mi) 0.43/0.51 % (2977848)Time elapsed: 0.019 s 0.43/0.51 % (2977848)Peak memory usage: 12 MB 0.43/0.51 % (2977848)Instructions burned: 89 (million) 0.43/0.51 % (2977858)Instruction limit reached! 0.43/0.51 % (2977858)------------------------------ 0.43/0.51 % (2977858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.51 % (2977858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.51 % (2977858)CaDiCaL version: 2.1.3 0.43/0.51 % (2977858)Termination reason: Instruction limit 0.43/0.51 % (2977858)Termination phase: Property scanning 0.43/0.51 % (2977858)Time elapsed: 0.006 s 0.43/0.51 % (2977858)Peak memory usage: 11 MB 0.43/0.51 % (2977858)Instructions burned: 25 (million) 0.43/0.51 % (2977860)Instruction limit reached! 0.43/0.51 % (2977860)------------------------------ 0.43/0.51 % (2977860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.51 % (2977860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.51 % (2977860)CaDiCaL version: 2.1.3 0.43/0.51 % (2977860)Termination reason: Instruction limit 0.43/0.51 % (2977860)Termination phase: shuffling 0.43/0.51 % (2977860)Time elapsed: 0.004 s 0.43/0.51 % (2977860)Peak memory usage: 10 MB 0.43/0.51 % (2977860)Instructions burned: 18 (million) 0.43/0.51 % (2977864)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1244207132:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/14Mi) 0.43/0.51 % (2977867)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=510095383:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1799 on theBenchmark for (1799ds/2Mi) 0.43/0.51 % (2977867)Instruction limit reached! 0.43/0.51 % (2977867)------------------------------ 0.43/0.51 % (2977867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.51 % (2977867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.51 % (2977867)CaDiCaL version: 2.1.3 0.43/0.51 % (2977867)Termination reason: Instruction limit 0.43/0.51 % (2977867)Termination phase: shuffling 0.43/0.51 % (2977867)Time elapsed: 0.001 s 0.43/0.51 % (2977867)Peak memory usage: 10 MB 0.43/0.51 % (2977867)Instructions burned: 3 (million) 0.43/0.51 % (2977868)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=625779947:i=26:ep=R:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/26Mi) 0.43/0.51 % (2977864)Instruction limit reached! 0.43/0.51 % (2977864)------------------------------ 0.43/0.51 % (2977864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.51 % (2977864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.51 % (2977864)CaDiCaL version: 2.1.3 0.43/0.51 % (2977864)Termination reason: Instruction limit 0.43/0.51 % (2977864)Termination phase: shuffling 0.43/0.51 % (2977864)Time elapsed: 0.004 s 0.43/0.51 % (2977864)Peak memory usage: 10 MB 0.43/0.51 % (2977864)Instructions burned: 17 (million) 0.43/0.51 % (2977869)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=584905840:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/23Mi) 0.43/0.51 % (2977868)Instruction limit reached! 0.43/0.51 % (2977868)------------------------------ 0.43/0.51 % (2977868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.51 % (2977868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.51 % (2977868)CaDiCaL version: 2.1.3 0.43/0.51 % (2977868)Termination reason: Instruction limit 0.43/0.51 % (2977868)Termination phase: shuffling 0.43/0.51 % (2977868)Time elapsed: 0.006 s 0.43/0.51 % (2977868)Peak memory usage: 10 MB 0.43/0.51 % (2977868)Instructions burned: 27 (million) 0.43/0.51 % (2977869)Instruction limit reached! 0.43/0.51 % (2977869)------------------------------ 0.43/0.51 % (2977869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.51 % (2977869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.51 % (2977869)CaDiCaL version: 2.1.3 0.43/0.51 % (2977869)Termination reason: Instruction limit 0.43/0.51 % (2977869)Termination phase: Property scanning 0.43/0.51 % (2977869)Time elapsed: 0.006 s 0.43/0.51 % (2977869)Peak memory usage: 10 MB 0.43/0.51 % (2977869)Instructions burned: 27 (million) 0.43/0.52 % (2977874)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 0.43/0.52 % (2977874)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 0.43/0.52 % (2977872)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4275102205:cond=on:i=60:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/60Mi) 0.43/0.52 % (2977874)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=668807698:i=14:add=off:nm=40:rtra=on:rawr=on_1799 on theBenchmark for (1799ds/14Mi) 0.43/0.52 % (2977876)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 0.43/0.52 % (2977874)Instruction limit reached! 0.43/0.52 % (2977874)------------------------------ 0.43/0.52 % (2977874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977874)CaDiCaL version: 2.1.3 0.43/0.52 % (2977874)Termination reason: Instruction limit 0.43/0.52 % (2977874)Termination phase: shuffling 0.43/0.52 % (2977874)Time elapsed: 0.004 s 0.43/0.52 % (2977874)Peak memory usage: 10 MB 0.43/0.52 % (2977874)Instructions burned: 18 (million) 0.43/0.52 % (2977876)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=1035952391:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1798 on theBenchmark for (1798ds/8Mi) 0.43/0.52 % (2977877)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=4124125850:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1798 on theBenchmark for (1798ds/31Mi) 0.43/0.52 % (2977876)Instruction limit reached! 0.43/0.52 % (2977876)------------------------------ 0.43/0.52 % (2977876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977876)CaDiCaL version: 2.1.3 0.43/0.52 % (2977876)Termination reason: Instruction limit 0.43/0.52 % (2977876)Termination phase: shuffling 0.43/0.52 % (2977876)Time elapsed: 0.002 s 0.43/0.52 % (2977876)Peak memory usage: 10 MB 0.43/0.52 % (2977876)Instructions burned: 8 (million) 0.43/0.52 % (2977872)Instruction limit reached! 0.43/0.52 % (2977872)------------------------------ 0.43/0.52 % (2977872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977872)CaDiCaL version: 2.1.3 0.43/0.52 % (2977872)Termination reason: Instruction limit 0.43/0.52 % (2977872)Termination phase: Preprocessing 3 0.43/0.52 % (2977872)Time elapsed: 0.014 s 0.43/0.52 % (2977872)Peak memory usage: 12 MB 0.43/0.52 % (2977872)Instructions burned: 63 (million) 0.43/0.52 % (2977880)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=524418288:i=7:hud=5:bd=preordered:rtra=on:bet=on_1798 on theBenchmark for (1798ds/7Mi) 0.43/0.52 % (2977877)Instruction limit reached! 0.43/0.52 % (2977877)------------------------------ 0.43/0.52 % (2977877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977877)CaDiCaL version: 2.1.3 0.43/0.52 % (2977877)Termination reason: Instruction limit 0.43/0.52 % (2977877)Termination phase: Property scanning 0.43/0.52 % (2977877)Time elapsed: 0.007 s 0.43/0.52 % (2977877)Peak memory usage: 10 MB 0.43/0.52 % (2977877)Instructions burned: 31 (million) 0.43/0.52 % (2977880)Instruction limit reached! 0.43/0.52 % (2977880)------------------------------ 0.43/0.52 % (2977880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977880)CaDiCaL version: 2.1.3 0.43/0.52 % (2977880)Termination reason: Instruction limit 0.43/0.52 % (2977880)Termination phase: shuffling 0.43/0.52 % (2977880)Time elapsed: 0.002 s 0.43/0.52 % (2977880)Peak memory usage: 10 MB 0.43/0.52 % (2977880)Instructions burned: 8 (million) 0.43/0.52 % (2977883)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2756648173:i=23:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 0.43/0.52 % (2977884)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2781796878:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1798 on theBenchmark for (1798ds/20Mi) 0.43/0.52 % (2977886)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1706380483:i=1240:rtra=on:ixr=off_1798 on theBenchmark for (1798ds/1240Mi) 0.43/0.52 % (2977883)Instruction limit reached! 0.43/0.52 % (2977883)------------------------------ 0.43/0.52 % (2977883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977883)CaDiCaL version: 2.1.3 0.43/0.52 % (2977883)Termination reason: Instruction limit 0.43/0.52 % (2977883)Termination phase: shuffling 0.43/0.52 % (2977883)Time elapsed: 0.006 s 0.43/0.52 % (2977883)Peak memory usage: 10 MB 0.43/0.52 % (2977883)Instructions burned: 27 (million) 0.43/0.52 % (2977887)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2256262446:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/143Mi) 0.43/0.52 % (2977829) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2977821-2977829"... 0.43/0.52 % (2977884)Instruction limit reached! 0.43/0.52 % (2977884)------------------------------ 0.43/0.52 % (2977884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977884)CaDiCaL version: 2.1.3 0.43/0.52 % (2977884)Termination reason: Instruction limit 0.43/0.52 % (2977884)Termination phase: shuffling 0.43/0.52 % (2977884)Time elapsed: 0.005 s 0.43/0.52 % (2977884)Peak memory usage: 10 MB 0.43/0.52 % (2977884)Instructions burned: 23 (million) 0.43/0.52 % (2977857)Instruction limit reached! 0.43/0.52 % (2977857)------------------------------ 0.43/0.52 % (2977857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977857)CaDiCaL version: 2.1.3 0.43/0.52 % (2977857)Termination reason: Instruction limit 0.43/0.52 % (2977857)Termination phase: Saturation 0.43/0.52 % (2977857)Time elapsed: 0.060 s 0.43/0.52 % (2977857)Peak memory usage: 15 MB 0.43/0.52 % (2977857)Instructions burned: 250 (million) 0.43/0.52 % (2977891)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4002188695:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/193Mi) 0.43/0.52 % (2977894)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.43/0.52 % (2977893)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1183827706:i=42:hud=10:rtra=on_1798 on theBenchmark for (1798ds/42Mi) 0.43/0.52 % (2977894)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2032279211:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1798 on theBenchmark for (1798ds/7Mi) 0.43/0.52 % (2977894)Instruction limit reached! 0.43/0.52 % (2977894)------------------------------ 0.43/0.52 % (2977894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977894)CaDiCaL version: 2.1.3 0.43/0.52 % (2977894)Termination reason: Instruction limit 0.43/0.52 % (2977894)Termination phase: shuffling 0.43/0.52 % (2977894)Time elapsed: 0.002 s 0.43/0.52 % (2977894)Peak memory usage: 10 MB 0.43/0.52 % (2977894)Instructions burned: 8 (million) 0.43/0.52 % (2977861) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2977821-2977861"... 0.43/0.52 % (2977893)Instruction limit reached! 0.43/0.52 % (2977893)------------------------------ 0.43/0.52 % (2977893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977893)CaDiCaL version: 2.1.3 0.43/0.52 % (2977893)Termination reason: Instruction limit 0.43/0.52 % (2977893)Termination phase: Naming 0.43/0.52 % (2977893)Time elapsed: 0.010 s 0.43/0.52 % (2977893)Peak memory usage: 11 MB 0.43/0.52 % (2977893)Instructions burned: 45 (million) 0.43/0.52 % (2977898)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3135690460:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/181Mi) 0.43/0.52 % (2977899)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=2497970108:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/169Mi) 0.43/0.52 % (2977887)Instruction limit reached! 0.43/0.52 % (2977887)------------------------------ 0.43/0.52 % (2977887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.52 % (2977887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.52 % (2977887)CaDiCaL version: 2.1.3 0.43/0.52 % (2977887)Termination reason: Instruction limit 0.43/0.52 % (2977887)Termination phase: Property scanning 0.43/0.52 % (2977887)Time elapsed: 0.034 s 0.43/0.52 % (2977887)Peak memory usage: 13 MB 0.43/0.52 % (2977887)Instructions burned: 146 (million) 0.43/0.52 % (2977829)...printing done. 0.43/0.52 % (2977829)Refutation found. Thanks to Tanya! 0.43/0.52 % SZS status Theorem for theBenchmark 0.43/0.52 % SZS output start Proof for theBenchmark 0.43/0.52 thf(type_def_5, type, term: $tType). 0.43/0.52 thf(type_def_6, type, subst: $tType). 0.43/0.52 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType). 0.43/0.52 thf(type_def_8, type, d_term: $tType). 0.43/0.52 thf(type_def_9, type, d_subst: $tType). 0.43/0.52 thf(func_def_0, type, one: term). 0.43/0.52 thf(func_def_1, type, ap: (term > term > term)). 0.43/0.52 thf(func_def_2, type, lam: (term > term)). 0.43/0.52 thf(func_def_3, type, sub: (term > subst > term)). 0.43/0.52 thf(func_def_4, type, id: subst). 0.43/0.52 thf(func_def_5, type, sh: subst). 0.43/0.52 thf(func_def_6, type, push: (term > subst > subst)). 0.43/0.52 thf(func_def_7, type, comp: (subst > subst > subst)). 0.43/0.52 thf(func_def_8, type, var: (term > $o)). 0.43/0.52 thf(func_def_9, type, pushprop_lem1v2: $o). 0.43/0.52 thf(func_def_10, type, pushprop_lem1_gthm: $o). 0.43/0.52 thf(func_def_11, type, axmap: $o). 0.43/0.52 thf(func_def_12, type, pushprop_lem0_gthm: $o). 0.43/0.52 thf(func_def_13, type, shinj: $o). 0.43/0.52 thf(func_def_14, type, hoasinduction_lem1v2: $o). 0.43/0.52 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o). 0.43/0.52 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)). 0.43/0.52 thf(func_def_17, type, induction2lem: $o). 0.43/0.52 thf(func_def_18, type, hoasinduction_lem3v2_f: $o). 0.43/0.52 thf(func_def_19, type, axvarshift: $o). 0.43/0.52 thf(func_def_20, type, hoasapinj2: $o). 0.43/0.52 thf(func_def_21, type, hoasapnotvar_gthm: $o). 0.43/0.52 thf(func_def_22, type, hoasapinj1: $o). 0.43/0.52 thf(func_def_23, type, ulamvar1: $o). 0.43/0.52 thf(func_def_24, type, induction2lem_lthm: $o). 0.43/0.52 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o). 0.43/0.52 thf(func_def_26, type, apnotvar: $o). 0.43/0.52 thf(func_def_27, type, pushprop_lthm_orig: $o). 0.43/0.52 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o). 0.43/0.52 thf(func_def_29, type, hoasinduction_lthm: $o). 0.43/0.52 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o). 0.43/0.52 thf(func_def_31, type, hoaslaminj: $o). 0.43/0.52 thf(func_def_32, type, hoasinduction_lem3aaa: $o). 0.43/0.52 thf(func_def_33, type, induction2lem_gthm: $o). 0.43/0.52 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o). 0.43/0.52 thf(func_def_35, type, hoasinduction_lem3: $o). 0.43/0.52 thf(func_def_36, type, hoasinduction_lem2: $o). 0.43/0.52 thf(func_def_37, type, termmset_lthm: $o). 0.43/0.52 thf(func_def_38, type, hoasinduction_lem1: $o). 0.43/0.52 thf(func_def_39, type, hoaslamnotap_lthm: $o). 0.43/0.52 thf(func_def_40, type, pushprop_lem1v2_lthm: $o). 0.43/0.52 thf(func_def_41, type, hoasapnotvar: $o). 0.43/0.52 thf(func_def_42, type, hoasinduction_lem0: $o). 0.43/0.52 thf(func_def_43, type, hoasinduction: $o). 0.43/0.52 thf(func_def_44, type, hoasinduction_gthm: $o). 0.43/0.52 thf(func_def_45, type, axapp: $o). 0.43/0.52 thf(func_def_46, type, hoaslamnotvar_lthm: $o). 0.43/0.52 thf(func_def_47, type, pushprop_lem3v2_lthm: $o). 0.43/0.52 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o). 0.43/0.52 thf(func_def_49, type, ulamvarind: $o). 0.43/0.52 thf(func_def_50, type, induction: $o). 0.43/0.52 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o). 0.43/0.52 thf(func_def_52, type, termmset_gthm: $o). 0.43/0.52 thf(func_def_53, type, hoasinduction_lem3aa: $o). 0.43/0.52 thf(func_def_54, type, pushprop_lem1v2_gthm: $o). 0.43/0.52 thf(func_def_55, type, hoaslamnotap_gthm: $o). 0.43/0.52 thf(func_def_56, type, hoaslamnotvar_gthm: $o). 0.43/0.52 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o). 0.43/0.52 thf(func_def_58, type, pushprop_lem2v2: $o). 0.43/0.52 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o). 0.43/0.52 thf(func_def_60, type, axclos: $o). 0.43/0.52 thf(func_def_61, type, axassoc: $o). 0.43/0.52 thf(func_def_62, type, hoasinduction_lem2v2: $o). 0.43/0.52 thf(func_def_63, type, pushprop_lthm: $o). 0.43/0.52 thf(func_def_64, type, apinj2: $o). 0.43/0.52 thf(func_def_65, type, apinj1: $o). 0.43/0.52 thf(func_def_66, type, hoasapinj2_lthm: $o). 0.43/0.52 thf(func_def_67, type, hoasinduction_lem3v2a: $o). 0.43/0.52 thf(func_def_68, type, hoasapinj1_lthm: $o). 0.43/0.52 thf(func_def_69, type, hoaslaminj_lthm: $o). 0.43/0.52 thf(func_def_70, type, axvarcons: $o). 0.43/0.52 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)). 0.43/0.52 thf(func_def_72, type, axscons: $o). 0.43/0.52 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o). 0.43/0.52 thf(func_def_74, type, axidr: $o). 0.43/0.52 thf(func_def_75, type, pushprop_lem1: $o). 0.43/0.52 thf(func_def_76, type, laminj: $o). 0.43/0.52 thf(func_def_77, type, hoasinduction_lem3_lthm: $o). 0.43/0.52 thf(func_def_78, type, pushprop_lem0: $o). 0.43/0.52 thf(func_def_79, type, pushprop_gthm: $o). 0.43/0.52 thf(func_def_80, type, axabs: $o). 0.43/0.52 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o). 0.43/0.52 thf(func_def_82, type, hoasinduction_lem2_lthm: $o). 0.43/0.52 thf(func_def_83, type, hoasapinj2_gthm: $o). 0.43/0.52 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)). 0.43/0.52 thf(func_def_85, type, hoasinduction_lem1_lthm: $o). 0.43/0.52 thf(func_def_86, type, lamnotap: $o). 0.43/0.52 thf(func_def_87, type, hoasapinj1_gthm: $o). 0.43/0.52 thf(func_def_88, type, hoaslamnotvar: $o). 0.43/0.52 thf(func_def_89, type, axidl: $o). 0.43/0.52 thf(func_def_90, type, hoaslaminj_gthm: $o). 0.43/0.52 thf(func_def_91, type, induction2_lthm: $o). 0.43/0.52 thf(func_def_92, type, hoasinduction_lem0_lthm: $o). 0.43/0.52 thf(func_def_93, type, substmonoid_lthm: $o). 0.43/0.52 thf(func_def_94, type, pushprop: $o). 0.43/0.52 thf(func_def_95, type, hoasinduction_lem3_gthm: $o). 0.43/0.52 thf(func_def_96, type, hoasinduction_lem2_gthm: $o). 0.43/0.52 thf(func_def_97, type, hoasinduction_lem3b: $o). 0.43/0.52 thf(func_def_98, type, substmonoid: $o). 0.43/0.52 thf(func_def_99, type, lamnotvar: $o). 0.43/0.52 thf(func_def_100, type, hoasinduction_lem3a: $o). 0.43/0.52 thf(func_def_101, type, hoasinduction_lem1_gthm: $o). 0.43/0.52 thf(func_def_102, type, hoasinduction_no_psi_cond: $o). 0.43/0.52 thf(func_def_103, type, induction2_gthm: $o). 0.43/0.52 thf(func_def_104, type, pushprop_lem2v2_lthm: $o). 0.43/0.52 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_106, type, hoaslamnotap: $o). 0.43/0.52 thf(func_def_107, type, substmonoid_gthm: $o). 0.43/0.52 thf(func_def_108, type, ulamvarsh: $o). 0.43/0.52 thf(func_def_109, type, induction2: $o). 0.43/0.52 thf(func_def_110, type, pushprop_lem3v2: $o). 0.43/0.52 thf(func_def_111, type, pushprop_lem2v2_gthm: $o). 0.43/0.52 thf(func_def_112, type, pushprop_lem1_lthm: $o). 0.43/0.52 thf(func_def_113, type, hoasinduction_lem3v2: $o). 0.43/0.52 thf(func_def_114, type, axshiftcons: $o). 0.43/0.52 thf(func_def_115, type, termmset: $o). 0.43/0.52 thf(func_def_116, type, pushprop_lem0_lthm: $o). 0.43/0.52 thf(func_def_117, type, hoasapnotvar_lthm: $o). 0.43/0.52 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o). 0.43/0.52 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)). 0.43/0.52 thf(func_def_120, type, axvarid: $o). 0.43/0.52 thf(func_def_121, type, hoasinduction_lthm_3: $o). 0.43/0.52 thf(func_def_122, type, d2term: (d_term > term)). 0.43/0.52 thf(func_def_123, type, d2subst: (d_subst > subst)). 0.43/0.52 thf(func_def_124, type, d_one: d_term). 0.43/0.52 thf(func_def_125, type, d_id: d_subst). 0.43/0.52 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 0.43/0.52 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)). 0.43/0.52 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)). 0.43/0.52 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)). 0.43/0.52 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)). 0.43/0.52 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)). 0.43/0.52 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 0.43/0.52 thf(func_def_136, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 0.43/0.52 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_138, type, sP1: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_139, type, sP2: $o). 0.43/0.52 thf(func_def_140, type, sP3: $o). 0.43/0.52 thf(func_def_141, type, sP4: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_142, type, sP5: $o). 0.43/0.52 thf(func_def_143, type, sP6: $o). 0.43/0.52 thf(func_def_144, type, sP7: $o). 0.43/0.52 thf(func_def_145, type, sP8: $o). 0.43/0.52 thf(func_def_146, type, sP9: $o). 0.43/0.52 thf(func_def_147, type, sP10: $o). 0.43/0.52 thf(func_def_148, type, sP11: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_149, type, sP12: $o). 0.43/0.52 thf(func_def_150, type, sP13: $o). 0.43/0.52 thf(func_def_151, type, sP14: $o). 0.43/0.52 thf(func_def_152, type, sP15: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_153, type, sP16: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_154, type, sP17: $o). 0.43/0.52 thf(func_def_155, type, sP18: $o). 0.43/0.52 thf(func_def_156, type, sP19: $o). 0.43/0.52 thf(func_def_157, type, sP20: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_158, type, sP21: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_159, type, sP22: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_160, type, sP23: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_161, type, sP24: $o). 0.43/0.52 thf(func_def_162, type, sP25: $o). 0.43/0.52 thf(func_def_163, type, sP26: $o). 0.43/0.52 thf(func_def_164, type, sP27: ((subst > term > subst > $o) > $o)). 0.43/0.52 thf(func_def_165, type, sK28: (term > $o)). 0.43/0.52 thf(func_def_166, type, sK29: subst). 0.43/0.52 thf(func_def_167, type, sK30: term). 0.43/0.52 thf(func_def_168, type, sK31: (term > $o)). 0.43/0.52 thf(func_def_169, type, sK32: term). 0.43/0.52 thf(func_def_170, type, sK33: (subst > (term > $o) > term)). 0.43/0.52 thf(func_def_171, type, sK34: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_172, type, sK35: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_173, type, sK36: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_174, type, sK37: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_175, type, sK38: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_176, type, sK39: term). 0.43/0.52 thf(func_def_177, type, sK40: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_178, type, sK41: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_179, type, sK42: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_180, type, sK43: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_181, type, sK44: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_182, type, sK45: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_183, type, sK46: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_184, type, sK47: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_185, type, sK48: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_186, type, sK49: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_187, type, sK50: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_188, type, sK51: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_189, type, sK52: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_190, type, sK53: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_191, type, sK54: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_192, type, sK55: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_193, type, sK56: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_194, type, sK57: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_195, type, sK58: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_196, type, sK59: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_197, type, sK60: term). 0.43/0.52 thf(func_def_198, type, sK61: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_199, type, sK62: term). 0.43/0.52 thf(func_def_200, type, sK63: ((term > $o) > term)). 0.43/0.52 thf(func_def_201, type, sK64: ((term > $o) > term)). 0.43/0.52 thf(func_def_202, type, sK65: ((term > $o) > term)). 0.43/0.52 thf(func_def_203, type, sK66: ((term > $o) > term)). 0.43/0.52 thf(func_def_204, type, sK67: (term > $o)). 0.43/0.52 thf(func_def_205, type, sK68: term). 0.43/0.52 thf(func_def_206, type, sK69: (term > term)). 0.43/0.52 thf(func_def_207, type, sK70: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_208, type, sK71: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_209, type, sK72: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_210, type, sK73: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_211, type, sK74: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_212, type, sK75: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_213, type, sK76: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_214, type, sK77: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_215, type, sK78: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_216, type, sK79: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_217, type, sK80: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_218, type, sK81: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_219, type, sK82: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_220, type, sK83: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_221, type, sK84: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_222, type, sK85: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_223, type, sK86: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_224, type, sK87: (term > $o)). 0.43/0.52 thf(func_def_225, type, sK88: subst). 0.43/0.52 thf(func_def_226, type, sK89: term). 0.43/0.52 thf(func_def_227, type, sK90: (term > term)). 0.43/0.52 thf(func_def_228, type, sK91: (subst > (term > $o) > term)). 0.43/0.52 thf(func_def_229, type, sK92: ((term > $o) > term)). 0.43/0.52 thf(func_def_230, type, sK93: ((term > $o) > term)). 0.43/0.52 thf(func_def_231, type, sK94: ((term > $o) > term)). 0.43/0.52 thf(func_def_232, type, sK95: (term > $o)). 0.43/0.52 thf(func_def_233, type, sK96: term). 0.43/0.52 thf(func_def_234, type, sK97: (term > term)). 0.43/0.52 thf(func_def_235, type, sK98: ((term > $o) > term)). 0.43/0.52 thf(func_def_236, type, sK99: ((term > $o) > term)). 0.43/0.52 thf(func_def_237, type, sK100: ((term > $o) > term)). 0.43/0.52 thf(func_def_238, type, sK101: ((term > $o) > term)). 0.43/0.52 thf(func_def_239, type, sK102: term). 0.43/0.52 thf(func_def_240, type, sK103: ((term > $o) > term)). 0.43/0.52 thf(func_def_241, type, sK104: ((term > $o) > term)). 0.43/0.52 thf(func_def_242, type, sK105: ((term > $o) > term)). 0.43/0.52 thf(func_def_243, type, sK106: ((term > $o) > subst > term)). 0.43/0.52 thf(func_def_244, type, sK107: subst). 0.43/0.52 thf(func_def_245, type, sK108: term). 0.43/0.52 thf(func_def_246, type, sK109: (term > $o)). 0.43/0.52 thf(func_def_247, type, sK110: (term > term)). 0.43/0.52 thf(func_def_248, type, sK111: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_249, type, sK112: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_250, type, sK113: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_251, type, sK114: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_252, type, sK115: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_253, type, sK116: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_254, type, sK117: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_255, type, sK118: (term > $o)). 0.43/0.52 thf(func_def_256, type, sK119: term). 0.43/0.52 thf(func_def_257, type, sK120: subst). 0.43/0.52 thf(func_def_258, type, sK121: (term > term)). 0.43/0.52 thf(func_def_259, type, sK122: term). 0.43/0.52 thf(func_def_260, type, sK123: subst). 0.43/0.52 thf(func_def_261, type, sK124: subst). 0.43/0.52 thf(func_def_262, type, sK125: term). 0.43/0.52 thf(func_def_263, type, sK126: subst). 0.43/0.52 thf(func_def_264, type, sK127: (subst > (term > $o) > term)). 0.43/0.52 thf(func_def_265, type, sK128: ((term > $o) > term)). 0.43/0.52 thf(func_def_266, type, sK129: ((term > $o) > term)). 0.43/0.52 thf(func_def_267, type, sK130: ((term > $o) > term)). 0.43/0.52 thf(func_def_268, type, sK131: ((term > $o) > term)). 0.43/0.52 thf(func_def_269, type, sK132: ((term > $o) > term)). 0.43/0.52 thf(func_def_270, type, sK133: ((term > $o) > term)). 0.43/0.52 thf(func_def_271, type, sK134: ((term > $o) > term)). 0.43/0.52 thf(func_def_272, type, sK135: (term > $o)). 0.43/0.52 thf(func_def_273, type, sK136: term). 0.43/0.52 thf(func_def_274, type, sK137: term). 0.43/0.52 thf(func_def_275, type, sK138: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_276, type, sK139: ((subst > term > subst > $o) > term > term)). 0.43/0.52 thf(func_def_277, type, sK140: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_278, type, sK141: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_279, type, sK142: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_280, type, sK143: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_281, type, sK144: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_282, type, sK145: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_283, type, sK146: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_284, type, sK147: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_285, type, sK148: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_286, type, sK149: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_287, type, sK150: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_288, type, sK151: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_289, type, sK152: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_290, type, sK153: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_291, type, sK154: term). 0.43/0.52 thf(func_def_292, type, sK155: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_293, type, sK156: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_294, type, sK157: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_295, type, sK158: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_296, type, sK159: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_297, type, sK160: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_298, type, sK161: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_299, type, sK162: ((term > $o) > term)). 0.43/0.52 thf(func_def_300, type, sK163: ((term > $o) > term)). 0.43/0.52 thf(func_def_301, type, sK164: ((term > $o) > term)). 0.43/0.52 thf(func_def_302, type, sK165: ((term > $o) > term)). 0.43/0.52 thf(func_def_303, type, sK166: (term > $o)). 0.43/0.52 thf(func_def_304, type, sK167: term). 0.43/0.52 thf(func_def_305, type, sK168: (term > term)). 0.43/0.52 thf(func_def_306, type, sK169: (term > $o)). 0.43/0.52 thf(func_def_307, type, sK170: term). 0.43/0.52 thf(func_def_308, type, sK171: (term > term)). 0.43/0.52 thf(func_def_309, type, sK172: ((term > $o) > term)). 0.43/0.52 thf(func_def_310, type, sK173: ((term > $o) > term)). 0.43/0.52 thf(func_def_311, type, sK174: ((term > $o) > term)). 0.43/0.52 thf(func_def_312, type, sK175: ((term > $o) > term)). 0.43/0.52 thf(func_def_313, type, sK176: term). 0.43/0.52 thf(func_def_314, type, sK177: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_315, type, sK178: term). 0.43/0.52 thf(func_def_316, type, sK179: (term > $o)). 0.43/0.52 thf(func_def_317, type, sK180: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_318, type, sK181: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_319, type, sK182: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_320, type, sK183: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_321, type, sK184: ((term > $o) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_322, type, sK185: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_323, type, sK186: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_324, type, sK187: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_325, type, sK188: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_326, type, sK189: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_327, type, sK190: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_328, type, sK191: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_329, type, sK192: term). 0.43/0.52 thf(func_def_330, type, sK193: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_331, type, sK194: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_332, type, sK195: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_333, type, sK196: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_334, type, sK197: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_335, type, sK198: (term > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_336, type, sK199: term). 0.43/0.52 thf(func_def_337, type, sK200: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_338, type, sK201: term). 0.43/0.52 thf(func_def_339, type, sK202: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_340, type, sK203: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_341, type, sK204: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_342, type, sK205: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_343, type, sK206: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_344, type, sK207: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_345, type, sK208: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_346, type, sK209: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_347, type, sK210: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_348, type, sK211: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_349, type, sK212: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_350, type, sK213: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_351, type, sK214: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_352, type, sK215: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_353, type, sK216: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_354, type, sK217: term). 0.43/0.52 thf(func_def_355, type, sK218: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_356, type, sK219: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_357, type, sK220: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_358, type, sK221: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_359, type, sK222: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_360, type, sK223: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_361, type, sK224: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_362, type, sK225: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_363, type, sK226: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_364, type, sK227: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_365, type, sK228: ((term > $o) > term)). 0.43/0.52 thf(func_def_366, type, sK229: ((term > $o) > term)). 0.43/0.52 thf(func_def_367, type, sK230: ((term > $o) > term)). 0.43/0.52 thf(func_def_368, type, sK231: ((term > $o) > term)). 0.43/0.52 thf(func_def_369, type, sK232: (term > $o)). 0.43/0.52 thf(func_def_370, type, sK233: term). 0.43/0.52 thf(func_def_371, type, sK234: (term > term)). 0.43/0.52 thf(func_def_372, type, sK235: ((subst > term > term) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_373, type, sK236: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_374, type, sK237: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_375, type, sK238: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_376, type, sK239: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_378, type, sK241: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_379, type, sK242: (term > $o)). 0.43/0.52 thf(func_def_380, type, sK243: subst). 0.43/0.52 thf(func_def_381, type, sK244: term). 0.43/0.52 thf(func_def_382, type, sK245: (term > $o)). 0.43/0.52 thf(func_def_383, type, sK246: ((term > $o) > term > subst > (term > $o) > term)). 0.43/0.52 thf(func_def_384, type, sK247: term). 0.43/0.52 thf(func_def_385, type, sK248: term). 0.43/0.52 thf(func_def_386, type, sK249: term). 0.43/0.52 thf(func_def_387, type, sK250: term). 0.43/0.52 thf(func_def_388, type, sK251: term). 0.43/0.52 thf(func_def_389, type, sK252: term). 0.43/0.52 thf(func_def_390, type, sK253: term). 0.43/0.52 thf(func_def_391, type, sK254: term). 0.43/0.52 thf(func_def_392, type, sK255: term). 0.43/0.52 thf(func_def_393, type, sK256: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_394, type, sK257: term). 0.43/0.52 thf(func_def_395, type, sK258: (term > $o)). 0.43/0.52 thf(func_def_396, type, sK259: ((term > $o) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_398, type, sK261: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_399, type, sK262: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_400, type, sK263: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_401, type, sK264: ((term > $o) > term > term)). 0.43/0.52 thf(func_def_402, type, sK265: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_403, type, sK266: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_404, type, sK267: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_405, type, sK268: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_406, type, sK269: term). 0.43/0.52 thf(func_def_407, type, sK270: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_408, type, sK271: term). 0.43/0.52 thf(func_def_409, type, sK272: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_410, type, sK273: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_411, type, sK274: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_413, type, sK276: (term > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_414, type, sK277: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_415, type, sK278: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_416, type, sK279: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_417, type, sK280: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_418, type, sK281: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_419, type, sK282: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_420, type, sK283: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_421, type, sK284: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_422, type, sK285: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_423, type, sK286: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_424, type, sK287: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_425, type, sK288: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_426, type, sK289: ((term > $o) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_427, type, sK290: (term > (term > $o) > term)). 0.43/0.52 thf(func_def_428, type, sK291: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_429, type, sK292: (term > $o)). 0.43/0.52 thf(func_def_430, type, sK293: term). 0.43/0.52 thf(func_def_431, type, sK294: term). 0.43/0.52 thf(func_def_432, type, sK295: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_433, type, sK296: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_434, type, sK297: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_435, type, sK298: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_436, type, sK299: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_437, type, sK300: ((subst > term > subst > $o) > term > term)). 0.43/0.52 thf(func_def_438, type, sK301: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_439, type, sK302: subst). 0.43/0.52 thf(func_def_440, type, sK303: subst). 0.43/0.52 thf(func_def_441, type, sK304: subst). 0.43/0.52 thf(func_def_442, type, sK305: subst). 0.43/0.52 thf(func_def_443, type, sK306: term). 0.43/0.52 thf(func_def_444, type, sK307: term). 0.43/0.52 thf(func_def_445, type, sK308: (term > subst > term > term)). 0.43/0.52 thf(func_def_446, type, sK309: (term > subst > term > term)). 0.43/0.52 thf(func_def_447, type, sK310: term). 0.43/0.52 thf(func_def_448, type, sK311: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_449, type, sK312: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_450, type, sK313: term). 0.43/0.52 thf(func_def_451, type, sK314: term). 0.43/0.52 thf(func_def_452, type, sK315: subst). 0.43/0.52 thf(func_def_453, type, sK316: term). 0.43/0.52 thf(func_def_454, type, sK317: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_455, type, sK318: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_456, type, sK319: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_457, type, sK320: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_458, type, sK321: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_459, type, sK322: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_460, type, sK323: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_461, type, sK324: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_462, type, sK325: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_463, type, sK326: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_464, type, sK327: subst). 0.43/0.52 thf(func_def_465, type, sK328: subst). 0.43/0.52 thf(func_def_466, type, sK329: (term > $o)). 0.43/0.52 thf(func_def_467, type, sK330: term). 0.43/0.52 thf(func_def_468, type, sK331: subst). 0.43/0.52 thf(func_def_469, type, sK332: ((term > $o) > term)). 0.43/0.52 thf(func_def_470, type, sK333: (subst > term > (term > $o) > term > $o)). 0.43/0.52 thf(func_def_471, type, sK334: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_472, type, sK335: ((subst > term > subst > $o) > term > term)). 0.43/0.52 thf(func_def_473, type, sK336: term). 0.43/0.52 thf(func_def_474, type, sK337: term). 0.43/0.52 thf(func_def_475, type, sK338: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_476, type, sK339: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_477, type, sK340: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_478, type, sK341: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_479, type, sK342: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_480, type, sK343: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_481, type, sK344: ((term > $o) > term)). 0.43/0.52 thf(func_def_482, type, sK345: term). 0.43/0.52 thf(func_def_483, type, sK346: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_484, type, sK347: term). 0.43/0.52 thf(func_def_485, type, sK348: (term > $o)). 0.43/0.52 thf(func_def_486, type, sK349: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_487, type, sK350: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_488, type, sK351: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_489, type, sK352: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_490, type, sK353: ((subst > term > subst > $o) > term > $o)). 0.43/0.52 thf(func_def_491, type, sK354: ((term > $o) > term > term)). 0.43/0.52 thf(func_def_492, type, sK355: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_493, type, sK356: ((term > $o) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_494, type, sK357: term). 0.43/0.52 thf(func_def_495, type, sK358: (term > $o)). 0.43/0.52 thf(func_def_496, type, sK359: ((term > $o) > term)). 0.43/0.52 thf(func_def_497, type, sK360: ((term > $o) > term)). 0.43/0.52 thf(func_def_498, type, sK361: ((term > $o) > term)). 0.43/0.52 thf(func_def_499, type, sK362: ((term > $o) > term)). 0.43/0.52 thf(func_def_500, type, sK363: ((term > $o) > subst > term > term > $o)). 0.43/0.52 thf(func_def_501, type, sK364: term). 0.43/0.52 thf(func_def_502, type, sK365: subst). 0.43/0.52 thf(func_def_503, type, sK366: (term > $o)). 0.43/0.52 thf(func_def_504, type, sK367: ((term > $o) > term)). 0.43/0.52 thf(func_def_505, type, sK368: (term > d_term)). 0.43/0.52 thf(func_def_506, type, sK369: ((subst > term > subst > $o) > term > $o)). 0.43/0.52 thf(func_def_507, type, sK370: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_508, type, sK371: ((term > $o) > term)). 0.43/0.52 thf(func_def_509, type, sK372: term). 0.43/0.52 thf(func_def_510, type, sK373: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_511, type, sK374: term). 0.43/0.52 thf(func_def_512, type, sK375: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_513, type, sK376: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_514, type, sK377: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_515, type, sK378: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_516, type, sK379: (term > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_517, type, sK380: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_518, type, sK381: term). 0.43/0.52 thf(func_def_519, type, sK382: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_520, type, sK383: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_521, type, sK384: (term > subst > term > term)). 0.43/0.52 thf(func_def_522, type, sK385: term). 0.43/0.52 thf(func_def_523, type, sK386: term). 0.43/0.52 thf(func_def_524, type, sK387: term). 0.43/0.52 thf(func_def_525, type, sK388: term). 0.43/0.52 thf(func_def_526, type, sK389: term). 0.43/0.52 thf(func_def_527, type, sK390: term). 0.43/0.52 thf(func_def_528, type, sK391: term). 0.43/0.52 thf(func_def_529, type, sK392: term). 0.43/0.52 thf(func_def_530, type, sK393: term). 0.43/0.52 thf(func_def_531, type, sK394: term). 0.43/0.52 thf(func_def_532, type, sK395: term). 0.43/0.52 thf(func_def_533, type, sK396: term). 0.43/0.52 thf(func_def_534, type, sK397: term). 0.43/0.52 thf(func_def_535, type, sK398: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_536, type, sK399: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_537, type, sK400: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_538, type, sK401: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_539, type, sK402: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_540, type, sK403: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_541, type, sK404: term). 0.43/0.52 thf(func_def_542, type, sK405: term). 0.43/0.52 thf(func_def_543, type, sK406: subst). 0.43/0.52 thf(func_def_544, type, sK407: term). 0.43/0.52 thf(func_def_545, type, sK408: term). 0.43/0.52 thf(func_def_546, type, sK409: subst). 0.43/0.52 thf(func_def_547, type, sK410: term). 0.43/0.52 thf(func_def_548, type, sK411: subst). 0.43/0.52 thf(func_def_549, type, sK412: (subst > term > term)). 0.43/0.52 thf(func_def_550, type, sK413: (subst > term > term)). 0.43/0.52 thf(func_def_551, type, sK414: term). 0.43/0.52 thf(func_def_552, type, sK415: term). 0.43/0.52 thf(func_def_553, type, sK416: (term > $o)). 0.43/0.52 thf(func_def_554, type, sK417: (term > $o)). 0.43/0.52 thf(func_def_555, type, sK418: subst). 0.43/0.52 thf(func_def_556, type, sK419: subst). 0.43/0.52 thf(func_def_557, type, sK420: term). 0.43/0.52 thf(func_def_558, type, sK421: term). 0.43/0.52 thf(func_def_559, type, sK422: subst). 0.43/0.52 thf(func_def_560, type, sK423: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_561, type, sK424: term). 0.43/0.52 thf(func_def_562, type, sK425: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_563, type, sK426: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_564, type, sK427: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_565, type, sK428: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_566, type, sK429: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_567, type, sK430: (term > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_568, type, sK431: term). 0.43/0.52 thf(func_def_569, type, sK432: (subst > term > term)). 0.43/0.52 thf(func_def_570, type, sK433: term). 0.43/0.52 thf(func_def_571, type, sK434: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_572, type, sK435: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_573, type, sK436: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_574, type, sK437: term). 0.43/0.52 thf(func_def_575, type, sK438: term). 0.43/0.52 thf(func_def_576, type, sK439: term). 0.43/0.52 thf(func_def_577, type, sK440: term). 0.43/0.52 thf(func_def_578, type, sK441: term). 0.43/0.52 thf(func_def_579, type, sK442: term). 0.43/0.52 thf(func_def_580, type, sK443: term). 0.43/0.52 thf(func_def_581, type, sK444: term). 0.43/0.52 thf(func_def_582, type, sK445: subst). 0.43/0.52 thf(func_def_583, type, sK446: term). 0.43/0.52 thf(func_def_584, type, sK447: ((term > $o) > term > subst > (term > $o) > term)). 0.43/0.52 thf(func_def_585, type, sK448: subst). 0.43/0.52 thf(func_def_586, type, sK449: term). 0.43/0.52 thf(func_def_587, type, sK450: (term > $o)). 0.43/0.52 thf(func_def_588, type, sK451: subst). 0.43/0.52 thf(func_def_589, type, sK452: term). 0.43/0.52 thf(func_def_590, type, sK453: (term > $o)). 0.43/0.52 thf(func_def_591, type, sK454: term). 0.43/0.52 thf(func_def_592, type, sK455: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_593, type, sK456: ((subst > term > subst > $o) > term > term)). 0.43/0.52 thf(func_def_594, type, sK457: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_595, type, sK458: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_596, type, sK459: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_597, type, sK460: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_598, type, sK461: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_599, type, sK462: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_600, type, sK463: ((subst > term > subst > $o) > subst)). 0.43/0.52 thf(func_def_601, type, sK464: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_602, type, sK465: term). 0.43/0.52 thf(func_def_603, type, sK466: term). 0.43/0.52 thf(func_def_604, type, sK467: term). 0.43/0.52 thf(func_def_605, type, sK468: term). 0.43/0.52 thf(func_def_606, type, sK469: ((subst > term > subst > $o) > term > term)). 0.43/0.52 thf(func_def_607, type, sK470: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_608, type, sK471: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_609, type, sK472: term). 0.43/0.52 thf(func_def_610, type, sK473: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_611, type, sK474: (term > (subst > term > term) > term)). 0.43/0.52 thf(func_def_612, type, sK475: (term > (subst > term > term) > subst)). 0.43/0.52 thf(func_def_613, type, sK476: (term > (subst > term > term) > subst)). 0.43/0.52 thf(func_def_614, type, sK477: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_615, type, sK478: (term > (subst > term > term) > subst)). 0.43/0.52 thf(func_def_616, type, sK479: (term > (subst > term > term) > term)). 0.43/0.52 thf(func_def_617, type, sK480: (term > (subst > term > term) > subst)). 0.43/0.52 thf(func_def_618, type, sK481: term). 0.43/0.52 thf(func_def_619, type, sK482: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_620, type, sK483: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_621, type, sK484: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_622, type, sK485: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_623, type, sK486: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_624, type, sK487: ((subst > term > subst > $o) > term > term)). 0.43/0.52 thf(func_def_625, type, sK488: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_626, type, sK489: ((term > $o) > term > term)). 0.43/0.52 thf(func_def_627, type, sK490: ((term > $o) > (subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_628, type, sK491: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_629, type, sK492: term). 0.43/0.52 thf(func_def_630, type, sK493: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_631, type, sK494: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_632, type, sK495: term). 0.43/0.52 thf(func_def_633, type, sK496: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_634, type, sK497: term). 0.43/0.52 thf(func_def_635, type, sK498: (term > $o)). 0.43/0.52 thf(func_def_636, type, sK499: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_637, type, sK500: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_638, type, sK501: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_639, type, sK502: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_640, type, sK503: (term > subst > term > term)). 0.43/0.52 thf(func_def_641, type, sK504: (term > (term > $o) > term)). 0.43/0.52 thf(func_def_642, type, sK505: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_643, type, sK506: ((subst > term > subst > $o) > (term > $o) > term)). 0.43/0.52 thf(func_def_644, type, sK507: (term > $o)). 0.43/0.52 thf(func_def_645, type, sK508: term). 0.43/0.52 thf(func_def_646, type, sK509: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_647, type, sK510: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_648, type, sK511: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_649, type, sK512: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_650, type, sK513: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_651, type, sK514: (term > $o)). 0.43/0.52 thf(func_def_652, type, sK515: term). 0.43/0.52 thf(func_def_653, type, sK516: subst). 0.43/0.52 thf(func_def_654, type, sK517: (term > $o)). 0.43/0.52 thf(func_def_655, type, sK518: term). 0.43/0.52 thf(func_def_656, type, sK519: ((subst > term > subst > $o) > (term > $o) > term)). 0.43/0.52 thf(func_def_657, type, sK520: (term > (term > $o) > term)). 0.43/0.52 thf(func_def_658, type, sK521: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_659, type, sK522: ((subst > term > subst > $o) > term > $o)). 0.43/0.52 thf(func_def_660, type, sK523: (term > $o)). 0.43/0.52 thf(func_def_661, type, sK524: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_662, type, sK525: term). 0.43/0.52 thf(func_def_663, type, sK526: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_664, type, sK527: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_665, type, sK528: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_666, type, sK529: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_667, type, sK530: term). 0.43/0.52 thf(func_def_668, type, sK531: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_669, type, sK532: ((term > $o) > term)). 0.43/0.52 thf(func_def_670, type, sK533: term). 0.43/0.52 thf(func_def_671, type, sK534: term). 0.43/0.52 thf(func_def_672, type, sK535: term). 0.43/0.52 thf(func_def_673, type, sK536: term). 0.43/0.52 thf(func_def_674, type, sK537: (subst > d_subst)). 0.43/0.52 thf(func_def_675, type, sK538: term). 0.43/0.52 thf(func_def_676, type, sK539: (term > subst > term > term)). 0.43/0.52 thf(func_def_677, type, sK540: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_678, type, sK541: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_679, type, sK542: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_680, type, sK543: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_681, type, sK544: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_682, type, sK545: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_683, type, sK546: (subst > term > term)). 0.43/0.52 thf(func_def_684, type, sK547: (subst > term > term)). 0.43/0.52 thf(func_def_685, type, sK548: subst). 0.43/0.52 thf(func_def_686, type, sK549: term). 0.43/0.52 thf(func_def_687, type, sK550: subst). 0.43/0.52 thf(func_def_688, type, sK551: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_689, type, sK552: ((subst > term > subst > $o) > term)). 0.43/0.52 thf(func_def_690, type, sK553: ((subst > term > subst > $o) > subst > term > term)). 0.43/0.52 thf(func_def_691, type, sK554: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_692, type, sK555: term). 0.43/0.52 thf(func_def_693, type, sK556: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_694, type, sK557: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_695, type, sK558: ((subst > term > term) > term)). 0.43/0.52 thf(func_def_696, type, sK559: ((subst > term > term) > subst)). 0.43/0.52 thf(func_def_697, type, sK560: ((subst > term > subst > $o) > term > $o)). 0.43/0.52 thf(func_def_698, type, sK561: (subst > term > subst > $o)). 0.43/0.52 thf(func_def_699, type, sK562: ((term > $o) > term)). 0.43/0.52 thf(func_def_700, type, sK563: subst). 0.43/0.52 thf(func_def_701, type, sK564: subst). 0.43/0.52 thf(func_def_702, type, sK565: term). 0.43/0.52 thf(func_def_703, type, vNOT: ($o > $o)). 0.43/0.52 thf(func_def_705, type, inv_lam_567: (term > term)). 0.43/0.52 thf(f1,conjecture,( 0.43/0.52 (pushprop_lem2v2 = ! [X3 : subst,X2 : term,X1 : (term > $o),X0 : (term > $o)] : ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (! [X5 : term] : ((var @ X5) => (X0 @ (sub @ X5 @ X3))) => ! [X4 : term] : ((var @ X4) => ((X1 @ X4) => (X1 @ (sub @ X4 @ sh)))))))), 0.43/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2)). 0.43/0.52 thf(f2,negated_conjecture,( 0.43/0.52 ~ (pushprop_lem2v2 = ! [X3 : subst,X2 : term,X1 : (term > $o),X0 : (term > $o)] : ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (! [X5 : term] : ((var @ X5) => (X0 @ (sub @ X5 @ X3))) => ! [X4 : term] : ((var @ X4) => ((X1 @ X4) => (X1 @ (sub @ X4 @ sh)))))))), 0.43/0.52 inference(negated_conjecture,[status(cth)],[f1])). 0.43/0.52 thf(f3,axiom,( 0.43/0.52 ! [X45 : d_term,X46 : d_term] : ((((d2term @ X45)) = ((d2term @ X46))) => (X45 = X46)) & (! [X7 : term] : (X7 = ((sub @ X7 @ id))) <=> axvarid) & hoasinduction_lem1 & (hoasinduction_lem2 <=> ! [X16 : term,X15 : term,X4 : (subst > term > subst > $o)] : (~(X4 @ id @ X16 @ id) | ~(X4 @ id @ X15 @ id) | ~ ! [X17 : subst,X7 : term,X18 : subst,X8 : subst] : ((X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | ~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | ~ ! [X7 : term,X9 : term] : (~(X4 @ id @ X9 @ id) | ~(X4 @ id @ X7 @ id) | (X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id)) | ~ ! [X7 : term,X18 : subst,X17 : subst,X8 : subst] : (~(X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | (X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | (X4 @ id @ (ap @ X15 @ X16) @ id))) & hoasapnotvar_lthm & ((! [X7 : term] : (X7 = ((sub @ X7 @ id))) => (! [X4 : (subst > term > subst > $o),X21 : term] : ((X4 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id) | ~ ! [X9 : term] : (~(X4 @ id @ X9 @ id) | (X4 @ id @ (sub @ X21 @ (push @ X9 @ id)) @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)))) => ! [X20 : term,X4 : (subst > term > subst > $o)] : (~ ! [X18 : subst,X7 : term,X17 : subst,X8 : subst] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X13 : (subst > term > term)] : (~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X18 : subst,X7 : term,X8 : subst,X17 : subst] : ((X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | ~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | (X4 @ id @ (lam @ X20) @ id) | ~ ! [X9 : term] : ((X4 @ id @ (sub @ X20 @ (push @ X9 @ id)) @ id) | ~(X4 @ id @ X9 @ id))))) <=> hoasinduction_lem3_lthm) & hoasapnotvar_gthm & pushprop_gthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2_gthm & hoaslamnotap_gthm & (! [X4 : (subst > term > subst > $o)] : ~ ! [X5 : (term > $o)] : ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) <=> hoasinduction_lem0_lthm) & ~(var @ (d2term @ d_one)) & hoaslamnotvar_lthm & pushprop_lthm_orig & hoaslamnotap_lthm & hoaslamnotvar_gthm & axvarshift & (! [X4 : (subst > term > subst > $o),X5 : (term > $o),X22 : term,X23 : term] : (~ ! [X9 : term,X7 : term] : ((X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id) | ~(X4 @ id @ X7 @ id) | ~(X4 @ id @ X9 @ id)) | ~ ! [X8 : subst,X18 : subst,X17 : subst,X7 : term] : (~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | (X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | (X5 @ (ap @ X22 @ X23)) | ~ ! [X18 : subst,X17 : subst,X8 : subst,X7 : term] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~(X5 @ X22) | ~(X5 @ X23)) <=> hoasinduction_lem2v2) & hoasinduction_lem2_gthm & (axshiftcons <=> ! [X7 : term,X8 : subst] : (X8 = ((comp @ sh @ (push @ X7 @ X8))))) & ((! [X7 : term] : (X7 = ((sub @ X7 @ id))) => (! [X11 : term,X4 : (term > $o),X12 : subst] : (~ ! [X9 : term] : ((X4 @ (sub @ X9 @ X12)) | ~(var @ X9)) | ~ ! [X7 : term,X9 : term] : ((X4 @ (ap @ X7 @ X9)) | ~(X4 @ X9) | ~(X4 @ X7)) | ~ ! [X7 : term] : (~ ! [X9 : term] : ((X4 @ (sub @ X7 @ (push @ X9 @ id))) | ~(X4 @ X9)) | (X4 @ (lam @ X7))) | (X4 @ (sub @ X11 @ X12))) => ! [X4 : (term > $o),X14 : term] : (~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~ ! [X9 : term] : ((X4 @ (sub @ X7 @ (push @ X9 @ id))) | ~(X4 @ X9))) | ~ ! [X9 : term,X7 : term] : (~(X4 @ X7) | (X4 @ (ap @ X7 @ X9)) | ~(X4 @ X9)) | (X4 @ X14) | ~ ! [X7 : term] : (~(var @ X7) | (X4 @ X7))))) <=> induction2_lthm) & hoasinduction_lem2_lthm & (hoasinduction_lem3aaa <=> ! [X4 : (subst > term > subst > $o),X35 : term] : ((X4 @ id @ (lam @ (sub @ X35 @ (push @ one @ sh))) @ id) | ~ ! [X13 : (subst > term > term),X36 : term] : (~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)) | ~ ! [X40 : subst,X42 : subst,X41 : term] : (((sub @ (X13 @ X40 @ X41) @ X42)) = ((sub @ (sub @ X36 @ (push @ X41 @ X40)) @ X42))) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X37 : subst,X38 : term,X39 : subst] : (((X13 @ (comp @ X37 @ X39) @ (sub @ X38 @ X39))) = ((sub @ X36 @ (push @ (sub @ X38 @ X39) @ (comp @ X37 @ X39)))))) | ~ ! [X9 : term] : ((X4 @ id @ (sub @ X35 @ (push @ X9 @ id)) @ id) | ~(X4 @ id @ X9 @ id)))) & pushprop_lthm & hoasinduction_gthm & (id = ((d2subst @ d_id))) & (! [X7 : term,X9 : term] : ((((sub @ X7 @ sh)) != ((sub @ X9 @ sh))) | (X7 = X9)) <=> shinj) & ((! [X7 : term] : (X7 = ((sub @ X7 @ id))) => ! [X7 : term] : (X7 = ((sub @ X7 @ id)))) <=> termmset_lthm) & ! [X0 : subst] : ? [X1 : d_subst] : (X0 = ((d2subst @ X1))) & (termmset <=> ! [X7 : term] : (X7 = ((sub @ X7 @ id)))) & (hoasapinj2 <=> ! [X25 : term,X24 : term,X7 : term,X9 : term] : ((((ap @ (sub @ X7 @ id) @ X24)) != ((ap @ (sub @ X9 @ id) @ X25))) | (X24 = X25))) & hoasapinj1_gthm & (hoaslaminj_lthm <=> (! [X7 : term,X8 : subst] : (X7 = ((sub @ one @ (push @ X7 @ X8)))) => (! [X7 : term,X8 : subst] : (X8 = ((comp @ sh @ (push @ X7 @ X8)))) => (! [X7 : term,X9 : term] : ((((lam @ X7)) != ((lam @ X9))) | (X7 = X9)) => ! [X29 : term,X27 : (subst > term > term),X13 : (subst > term > term),X28 : subst] : (~ ! [X8 : subst,X17 : subst,X7 : term] : (((sub @ (X27 @ X8 @ X7) @ X17)) = ((X27 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (((X13 @ X28 @ X29)) = ((X27 @ X28 @ X29))) | (((lam @ (X13 @ sh @ one))) != ((lam @ (X27 @ sh @ one)))) | ~ ! [X7 : term,X8 : subst,X17 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17))))))))) & ((! [X8 : subst] : (X8 = ((comp @ id @ X8))) => (! [X8 : subst] : (X8 = ((comp @ X8 @ id))) => (! [X8 : subst] : (X8 = ((comp @ X8 @ id))) & ! [X8 : subst] : (X8 = ((comp @ id @ X8)))))) <=> substmonoid_lthm) & (hoasinduction_lem3 <=> ! [X20 : term,X4 : (subst > term > subst > $o)] : (~ ! [X7 : term,X8 : subst,X18 : subst,X17 : subst] : ((X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | ~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | (X4 @ id @ (lam @ X20) @ id) | ~ ! [X9 : term] : (~(X4 @ id @ X9 @ id) | (X4 @ id @ (sub @ X20 @ (push @ X9 @ id)) @ id)) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id))) | ~ ! [X7 : term,X17 : subst,X18 : subst,X8 : subst] : (~(X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | (X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)))) & (! [X9 : term] : ~ ! [X13 : (subst > term > term)] : (((X13 @ sh @ one)) != ((sub @ X9 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & ((! [X14 : term,X4 : (term > $o)] : ((X4 @ X14) | ~ ! [X7 : term] : ((X4 @ X7) | ~(var @ X7)) | ~ ! [X9 : term,X7 : term] : (~(X4 @ X7) | ~(X4 @ X9) | (X4 @ (ap @ X7 @ X9))) | ~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~ ! [X9 : term] : (~(X4 @ X9) | (X4 @ (sub @ X7 @ (push @ X9 @ id)))))) => (! [X15 : term,X4 : (subst > term > subst > $o),X16 : term] : (~(X4 @ id @ X16 @ id) | (X4 @ id @ (ap @ X15 @ X16) @ id) | ~ ! [X18 : subst,X7 : term,X17 : subst,X8 : subst] : ((X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | ~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | ~(X4 @ id @ X15 @ id) | ~ ! [X7 : term,X8 : subst,X17 : subst,X18 : subst] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X7 : term,X9 : term] : ((X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id) | ~(X4 @ id @ X9 @ id) | ~(X4 @ id @ X7 @ id))) => (! [X4 : (subst > term > subst > $o),X20 : term] : (~ ! [X13 : (subst > term > term)] : (~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | (X4 @ id @ (lam @ X20) @ id) | ~ ! [X9 : term] : ((X4 @ id @ (sub @ X20 @ (push @ X9 @ id)) @ id) | ~(X4 @ id @ X9 @ id)) | ~ ! [X7 : term,X17 : subst,X8 : subst,X18 : subst] : (~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | (X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X17 : subst,X18 : subst,X8 : subst,X7 : term] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17)))) => ! [X19 : term,X4 : (subst > term > subst > $o)] : (~ ! [X7 : term] : (~(var @ (sub @ X7 @ id)) | (X4 @ id @ X7 @ id)) | ~ ! [X7 : term,X17 : subst,X8 : subst,X18 : subst] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X9 : term,X7 : term] : (~(X4 @ id @ X9 @ id) | (X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id) | ~(X4 @ id @ X7 @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id))) | (X4 @ id @ X19 @ id) | ~ ! [X8 : subst,X7 : term,X17 : subst,X18 : subst] : ((X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | ~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)))))) <=> hoasinduction_lthm) & axabs & (! [X4 : (subst > term > subst > $o),X30 : term] : (~ ! [X7 : term,X9 : term] : (~(X4 @ id @ X9 @ id) | ~(X4 @ id @ X7 @ id) | (X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id)) | (X4 @ id @ X30 @ id) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)))) <=> hoasinduction_no_psi_cond) & (hoaslamnotap <=> ! [X31 : term,X13 : (subst > term > term),X32 : term] : (~ ! [X7 : term,X8 : subst,X17 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (((lam @ (X13 @ sh @ one))) != ((ap @ (sub @ X31 @ id) @ X32))))) & ((! [X4 : (subst > term > subst > $o)] : ~ ! [X5 : (term > $o)] : ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) => (! [X4 : (term > $o),X14 : term] : (~ ! [X7 : term] : (~(var @ X7) | (X4 @ X7)) | (X4 @ X14) | ~ ! [X7 : term,X9 : term] : (~(X4 @ X7) | ~(X4 @ X9) | (X4 @ (ap @ X7 @ X9))) | ~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~ ! [X9 : term] : ((X4 @ (sub @ X7 @ (push @ X9 @ id))) | ~(X4 @ X9)))) => (! [X7 : term] : (X7 = ((sub @ X7 @ id))) => (! [X4 : (subst > term > subst > $o),X26 : term,X5 : (term > $o)] : (~ ! [X9 : term] : (~(X5 @ X9) | (X5 @ (sub @ X26 @ (push @ X9 @ id)))) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | (X5 @ (lam @ X26)) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)) | ~ ! [X8 : subst,X17 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))))) => ! [X19 : term,X4 : (subst > term > subst > $o)] : ((X4 @ id @ X19 @ id) | ~ ! [X7 : term,X9 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id) | ~(X4 @ id @ X9 @ id)) | ~ ! [X17 : subst,X8 : subst,X7 : term,X18 : subst] : ((X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | ~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | ~ ! [X7 : term,X17 : subst,X8 : subst,X18 : subst] : (~(X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | (X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | ~ ! [X7 : term] : (~(var @ (sub @ X7 @ id)) | (X4 @ id @ X7 @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)))))))) <=> hoasinduction_lthm_3) & (apinj2 <=> ! [X9 : term,X25 : term,X7 : term,X24 : term] : ((((ap @ X7 @ X24)) != ((ap @ X9 @ X25))) | (X24 = X25))) & (sh = ((d2subst @ d_id))) & lamnotvar & (induction2lem_lthm <=> (! [X8 : subst,X7 : term] : (X7 = ((sub @ one @ (push @ X7 @ X8)))) => (! [X7 : term,X8 : subst] : (X8 = ((comp @ sh @ (push @ X7 @ X8)))) => (! [X8 : subst] : (X8 = ((comp @ X8 @ id))) => (! [X10 : term,X4 : (term > $o)] : (~ ! [X7 : term] : (~(var @ X7) | (X4 @ X7)) | (X4 @ X10) | ~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~(X4 @ X7)) | ~ ! [X9 : term,X7 : term] : ((X4 @ (ap @ X7 @ X9)) | ~(X4 @ X7) | ~(X4 @ X9))) => ! [X4 : (term > $o),X12 : subst,X11 : term] : (~ ! [X9 : term,X7 : term] : (~(X4 @ X7) | ~(X4 @ X9) | (X4 @ (ap @ X7 @ X9))) | ~ ! [X9 : term] : ((X4 @ (sub @ X9 @ X12)) | ~(var @ X9)) | (X4 @ (sub @ X11 @ X12)) | ~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~ ! [X9 : term] : ((X4 @ (sub @ X7 @ (push @ X9 @ id))) | ~(X4 @ X9))))))))) & (! [X13 : (subst > term > term),X28 : subst,X29 : term,X27 : (subst > term > term)] : (~ ! [X8 : subst,X17 : subst,X7 : term] : (((sub @ (X27 @ X8 @ X7) @ X17)) = ((X27 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (((lam @ (X13 @ sh @ one))) != ((lam @ (X27 @ sh @ one)))) | (((X13 @ X28 @ X29)) = ((X27 @ X28 @ X29)))) <=> hoaslaminj) & ! [X43 : d_subst,X44 : d_subst] : ((((d2subst @ X43)) = ((d2subst @ X44))) => (X43 = X44)) & hoasinduction_lem1_lthm & axclos & (axvarcons <=> ! [X7 : term,X8 : subst] : (X7 = ((sub @ one @ (push @ X7 @ X8))))) & ~lamnotap & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (pushprop_lem1v2 <=> ! [X5 : (term > $o),X7 : term,X4 : (term > $o),X8 : subst] : (~(X4 @ X7) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ (sub @ X6 @ (push @ X7 @ X8))))) | (X5 @ one))) & (induction2 <=> ! [X4 : (term > $o),X14 : term] : (~ ! [X9 : term,X7 : term] : (~(X4 @ X7) | ~(X4 @ X9) | (X4 @ (ap @ X7 @ X9))) | (X4 @ X14) | ~ ! [X7 : term] : (~ ! [X9 : term] : ((X4 @ (sub @ X7 @ (push @ X9 @ id))) | ~(X4 @ X9)) | (X4 @ (lam @ X7))) | ~ ! [X7 : term] : ((X4 @ X7) | ~(var @ X7)))) & hoaslamnotvar & (substmonoid <=> (! [X8 : subst] : (X8 = ((comp @ X8 @ id))) & ! [X8 : subst] : (X8 = ((comp @ id @ X8))))) & axmap & ((! [X4 : (subst > term > subst > $o)] : ~ ! [X5 : (term > $o)] : ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) => (! [X14 : term,X4 : (term > $o)] : ((X4 @ X14) | ~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~ ! [X9 : term] : (~(X4 @ X9) | (X4 @ (sub @ X7 @ (push @ X9 @ id))))) | ~ ! [X7 : term] : (~(var @ X7) | (X4 @ X7)) | ~ ! [X7 : term,X9 : term] : (~(X4 @ X7) | ~(X4 @ X9) | (X4 @ (ap @ X7 @ X9)))) => (! [X7 : term] : (X7 = ((sub @ X7 @ id))) => (! [X26 : term,X5 : (term > $o),X4 : (subst > term > subst > $o)] : ((X5 @ (lam @ X26)) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)) | ~ ! [X17 : subst,X7 : term,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17))))) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | ~ ! [X9 : term] : (~(X5 @ X9) | (X5 @ (sub @ X26 @ (push @ X9 @ id))))) => ! [X30 : term,X4 : (subst > term > subst > $o)] : (~ ! [X7 : term,X9 : term] : ((X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id) | ~(X4 @ id @ X7 @ id) | ~(X4 @ id @ X9 @ id)) | (X4 @ id @ X30 @ id) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)))))))) <=> hoasinduction_no_psi_cond_lthm) & ! [X1 : d_subst] : (X1 = d_id) & (! [X9 : term,X8 : subst,X4 : (term > $o),X18 : (term > $o),X7 : term] : ((X18 @ (sub @ X7 @ (push @ X9 @ X8))) | ~(X4 @ X7)) <=> pushprop_lem1) & pushprop_lem1_gthm & (hoaslam = (^[X2 : subst, X3 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lem2v2 & (! [X8 : subst] : (X8 = ((comp @ id @ X8))) <=> axidl) & axapp & (pushprop_lem1v2_lthm <=> (! [X7 : term,X8 : subst] : (X7 = ((sub @ one @ (push @ X7 @ X8)))) => ! [X8 : subst,X7 : term,X4 : (term > $o),X5 : (term > $o)] : (~(X4 @ X7) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ (sub @ X6 @ (push @ X7 @ X8))))) | (X5 @ one)))) & induction2lem_gthm & ulamvarsh & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X5 : (term > $o),X26 : term,X4 : (subst > term > subst > $o)] : ((X5 @ (lam @ X26)) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | ~ ! [X13 : (subst > term > term)] : (~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id))) | ~ ! [X9 : term] : ((X5 @ (sub @ X26 @ (push @ X9 @ id))) | ~(X5 @ X9))) <=> hoasinduction_lem3v2a) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (induction <=> ! [X10 : term,X4 : (term > $o)] : (~ ! [X7 : term] : ((X4 @ (lam @ X7)) | ~(X4 @ X7)) | ~ ! [X7 : term] : (~(var @ X7) | (X4 @ X7)) | ~ ! [X9 : term,X7 : term] : (~(X4 @ X7) | ~(X4 @ X9) | (X4 @ (ap @ X7 @ X9))) | (X4 @ X10))) & (hoasinduction_lem3aa_lthm <=> ! [X4 : (subst > term > subst > $o),X21 : term] : (~ ! [X9 : term] : (~(X4 @ id @ X9 @ id) | (X4 @ id @ (sub @ X21 @ (push @ X9 @ id)) @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | (X4 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id))) & ((^[X4 : (subst > term > subst > $o), X5 : (term > $o)] : (! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))))) = hoasinduction_p_and_p_prime) & hoasinduction_lem1v2 & ! [X48 : term] : ? [X47 : d_term] : (X48 = ((d2term @ X47))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoaslaminj_gthm & (! [X4 : (subst > term > subst > $o)] : ~ ! [X5 : (term > $o)] : ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) <=> hoasinduction_lem0) & pushprop_lem3v2_lthm & ((^[X7 : term, X8 : subst, X4 : (term > $o), X5 : (term > $o)] : (! [X6 : term] : (((X5 @ X6)) = ((X4 @ (sub @ X6 @ (push @ X7 @ X8))))))) = pushprop_p_and_p_prime) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((! [X7 : term] : (X7 = ((sub @ X7 @ id))) => ! [X5 : (term > $o),X4 : (subst > term > subst > $o),X33 : term] : (~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | ~ ! [X8 : subst,X7 : term,X17 : subst,X18 : subst] : (~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | (X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X13 : (subst > term > term)] : (~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | ~ ! [X7 : term,X8 : subst,X17 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | (X5 @ (lam @ X33)) | ~ ! [X17 : subst,X8 : subst,X7 : term,X18 : subst] : (~(X4 @ X8 @ X7 @ (comp @ X18 @ X17)) | (X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17)) | ~ ! [X9 : term] : ((X5 @ (sub @ X33 @ (push @ X9 @ id))) | ~(X5 @ X9)))) <=> hoasinduction_lem3v2_lthm) & (one = ((d2term @ d_one))) & (! [X7 : term,X4 : (term > $o),X8 : subst] : ~ ! [X5 : (term > $o)] : ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ (sub @ X6 @ (push @ X7 @ X8))))) <=> pushprop_lem0) & ((! [X9 : term] : ~ ! [X13 : (subst > term > term)] : ~ ! [X7 : term,X8 : subst] : (((sub @ X9 @ (push @ X7 @ X8))) = ((X13 @ X8 @ X7))) => (! [X7 : term] : (X7 = ((sub @ X7 @ id))) => ! [X5 : (term > $o),X26 : term,X4 : (subst > term > subst > $o)] : (~ ! [X9 : term] : ((X5 @ (sub @ X26 @ (push @ X9 @ id))) | ~(X5 @ X9)) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | (X5 @ (lam @ X26)) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)))))) <=> hoasinduction_lem3v2a_lthm) & (! [X9 : term] : ~ ! [X13 : (subst > term > term)] : ~ ! [X7 : term,X8 : subst] : (((sub @ X9 @ (push @ X7 @ X8))) = ((X13 @ X8 @ X7))) <=> hoasinduction_lem3v2_f) & (laminj <=> ! [X9 : term,X7 : term] : ((((lam @ X7)) != ((lam @ X9))) | (X7 = X9))) & ((! [X25 : term,X7 : term,X9 : term,X24 : term] : ((((ap @ X7 @ X24)) != ((ap @ X9 @ X25))) | (X24 = X25)) => ! [X9 : term,X24 : term,X7 : term,X25 : term] : ((((ap @ (sub @ X7 @ id) @ X24)) != ((ap @ (sub @ X9 @ id) @ X25))) | (X24 = X25))) <=> hoasapinj2_lthm) & ((! [X7 : term] : (X7 = ((sub @ X7 @ id))) => (! [X25 : term,X24 : term,X9 : term,X7 : term] : ((((ap @ X7 @ X24)) != ((ap @ X9 @ X25))) | (X7 = X9)) => ! [X7 : term,X24 : term,X25 : term,X9 : term] : ((X7 = X9) | (((ap @ (sub @ X7 @ id) @ X24)) != ((ap @ (sub @ X9 @ id) @ X25)))))) <=> hoasapinj1_lthm) & hoasinduction_lem1v2_gthm & hoasapnotvar & ~ulamvar1 & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem3b_gthm & hoasapinj2_gthm & pushprop_lem3v2 & (! [X9 : term] : ~ ! [X13 : (subst > term > term)] : ~ ! [X8 : subst,X7 : term] : (((sub @ X9 @ (push @ X7 @ X8))) = ((X13 @ X8 @ X7))) <=> hoasinduction_lem3v2_f_lthm) & (apinj1 <=> ! [X7 : term,X25 : term,X9 : term,X24 : term] : ((((ap @ X7 @ X24)) != ((ap @ X9 @ X25))) | (X7 = X9))) & hoasinduction_lem1_gthm & (! [X19 : term,X4 : (subst > term > subst > $o)] : (~ ! [X9 : term,X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (ap @ (sub @ X7 @ id) @ X9) @ id) | ~(X4 @ id @ X9 @ id)) | ~ ! [X8 : subst,X18 : subst,X7 : term,X17 : subst] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | (X4 @ id @ X19 @ id) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | ~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17))))) | ~ ! [X7 : term] : ((X4 @ id @ X7 @ id) | ~(var @ (sub @ X7 @ id))) | ~ ! [X17 : subst,X7 : term,X8 : subst,X18 : subst] : (~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | (X4 @ X8 @ X7 @ (comp @ X18 @ X17)))) <=> hoasinduction) & hoasinduction_lem3a_gthm & hoasinduction_lem2v2_gthm & (hoasinduction_lem3a <=> ! [X34 : term,X4 : (subst > term > subst > $o)] : (~ ! [X13 : (subst > term > term)] : (~ ! [X17 : subst,X8 : subst,X7 : term] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X9 : term] : ((X4 @ id @ (sub @ X34 @ (push @ X9 @ id)) @ id) | ~(X4 @ id @ X9 @ id)) | (X4 @ id @ (lam @ X34) @ id))) & pushprop & ((! [X7 : term] : (X7 = ((sub @ X7 @ id))) => (! [X4 : (subst > term > subst > $o),X21 : term] : (~ ! [X9 : term] : (~(X4 @ id @ X9 @ id) | (X4 @ id @ (sub @ X21 @ (push @ X9 @ id)) @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : ((X4 @ id @ (X13 @ id @ X7) @ id) | ~(X4 @ id @ X7 @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | (X4 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) => ! [X4 : (subst > term > subst > $o),X34 : term] : ((X4 @ id @ (lam @ X34) @ id) | ~ ! [X9 : term] : ((X4 @ id @ (sub @ X34 @ (push @ X9 @ id)) @ id) | ~(X4 @ id @ X9 @ id)) | ~ ! [X13 : (subst > term > term)] : ((X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X17 : subst,X7 : term,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)))))) <=> hoasinduction_lem3a_lthm) & apnotvar & hoasinduction_lem3v2_gthm & substmonoid_gthm & ulamvarind & (! [X4 : (subst > term > subst > $o),X21 : term] : ((X4 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id) | ~ ! [X9 : term] : (~(X4 @ id @ X9 @ id) | (X4 @ id @ (sub @ X21 @ (push @ X9 @ id)) @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X17 : subst,X7 : term,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))))) <=> hoasinduction_lem3aa) & (hoasapinj1 <=> ! [X24 : term,X9 : term,X7 : term,X25 : term] : ((((ap @ (sub @ X7 @ id) @ X24)) != ((ap @ (sub @ X9 @ id) @ X25))) | (X7 = X9))) & ! [X47 : d_term] : (X47 = d_one) & (! [X8 : subst] : (X8 = ((comp @ X8 @ id))) <=> axidr) & (! [X8 : subst] : (X8 = ((push @ (sub @ one @ X8) @ (comp @ sh @ X8)))) <=> axscons) & (hoasinduction_lem3b <=> ! [X9 : term] : ~ ! [X13 : (subst > term > term)] : (((X13 @ sh @ one)) != ((sub @ X9 @ (push @ one @ sh))))) & pushprop_lem0_gthm & hoasinduction_lem3_gthm & termmset_gthm & induction2_gthm & (! [X8 : subst,X7 : term,X4 : (term > $o)] : ~ ! [X5 : (term > $o)] : ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ (sub @ X6 @ (push @ X7 @ X8))))) <=> pushprop_lem0_lthm) & pushprop_lem1v2_gthm & axassoc & pushprop_lem2v2_lthm & ((! [X7 : term,X8 : subst] : (X7 = ((sub @ one @ (push @ X7 @ X8)))) => (! [X7 : term,X8 : subst] : (X8 = ((comp @ sh @ (push @ X7 @ X8)))) => ! [X18 : (term > $o),X9 : term,X4 : (term > $o),X7 : term,X8 : subst] : ((X18 @ (sub @ X7 @ (push @ X9 @ X8))) | ~(X4 @ X7)))) <=> pushprop_lem1_lthm) & (hoasinduction_lem3v2 <=> ! [X33 : term,X5 : (term > $o),X4 : (subst > term > subst > $o)] : ((X5 @ (lam @ X33)) | ~ ! [X18 : subst,X7 : term,X17 : subst,X8 : subst] : ((X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | ~(X4 @ X8 @ X7 @ (comp @ X18 @ X17))) | ~ ! [X6 : term] : (((X5 @ X6)) = ((X4 @ id @ X6 @ id))) | ~ ! [X13 : (subst > term > term)] : (~ ! [X7 : term,X17 : subst,X8 : subst] : (((sub @ (X13 @ X8 @ X7) @ X17)) = ((X13 @ (comp @ X8 @ X17) @ (sub @ X7 @ X17)))) | ~ ! [X7 : term] : (~(X4 @ id @ X7 @ id) | (X4 @ id @ (X13 @ id @ X7) @ id)) | (X4 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X9 : term] : (~(X5 @ X9) | (X5 @ (sub @ X33 @ (push @ X9 @ id)))) | ~ ! [X7 : term,X17 : subst,X18 : subst,X8 : subst] : (~(X4 @ (comp @ X8 @ X18) @ (sub @ X7 @ X18) @ X17) | (X4 @ X8 @ X7 @ (comp @ X18 @ X17))))) & (! [X11 : term,X12 : subst,X4 : (term > $o)] : ((X4 @ (sub @ X11 @ X12)) | ~ ! [X9 : term,X7 : term] : (~(X4 @ X9) | (X4 @ (ap @ X7 @ X9)) | ~(X4 @ X7)) | ~ ! [X9 : term] : ((X4 @ (sub @ X9 @ X12)) | ~(var @ X9)) | ~ ! [X7 : term] : (~ ! [X9 : term] : (~(X4 @ X9) | (X4 @ (sub @ X7 @ (push @ X9 @ id)))) | (X4 @ (lam @ X7)))) <=> induction2lem)), 0.43/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)). 0.43/0.52 thf(f4,plain,( 0.43/0.52 ~ (pushprop_lem2v2 = ! [X0 : subst,X1 : term,X2 : (term > $o),X3 : (term > $o)] : ((pushprop_p_and_p_prime @ X1 @ X0 @ X3 @ X2) => (! [X4 : term] : ((var @ X4) => (X3 @ (sub @ X4 @ X0))) => ! [X5 : term] : ((var @ X5) => ((X2 @ X5) => (X2 @ (sub @ X5 @ sh)))))))), 0.43/0.52 inference(rectify,[],[f2])). 0.43/0.52 thf(f5,plain,( 0.43/0.52 ~(! [X3 : (term > $o),X0 : subst,X1 : term,X2 : (term > $o)] : ((((pushprop_p_and_p_prime @ X1 @ X0 @ X3 @ X2)) = $true) => (! [X4 : term] : ((((var @ X4)) = $true) => ($true = ((X3 @ (sub @ X4 @ X0))))) => ! [X5 : term] : ((((var @ X5)) = $true) => ((((X2 @ X5)) = $true) => ($true = ((X2 @ (sub @ X5 @ sh)))))))) <=> (pushprop_lem2v2 = $true))), 0.43/0.52 inference(fool_elimination,[],[f4])). 0.43/0.52 thf(f6,plain,( 0.43/0.52 ! [X0 : d_term,X1 : d_term] : ((((d2term @ X0)) = ((d2term @ X1))) => (X0 = X1)) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> axvarid) & hoasinduction_lem1 & (hoasinduction_lem2 <=> ! [X3 : term,X4 : term,X5 : (subst > term > subst > $o)] : (~(X5 @ id @ X3 @ id) | ~(X5 @ id @ X4 @ id) | ~ ! [X6 : subst,X7 : term,X8 : subst,X9 : subst] : ((X5 @ X9 @ X7 @ (comp @ X8 @ X6)) | ~(X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6)) | ~ ! [X10 : term,X11 : term] : (~(X5 @ id @ X11 @ id) | ~(X5 @ id @ X10 @ id) | (X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id)) | ~ ! [X12 : term,X13 : subst,X14 : subst,X15 : subst] : (~(X5 @ X15 @ X12 @ (comp @ X13 @ X14)) | (X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) | (X5 @ id @ (ap @ X4 @ X3) @ id))) & hoasapnotvar_lthm & ((! [X16 : term] : (((sub @ X16 @ id)) = X16) => (! [X17 : (subst > term > subst > $o),X18 : term] : ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id) | ~ ! [X19 : term] : (~(X17 @ id @ X19 @ id) | (X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)) | ~ ! [X20 : (subst > term > term)] : (~ ! [X21 : subst,X22 : subst,X23 : term] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) = ((sub @ (X20 @ X22 @ X23) @ X21))) | (X17 @ id @ (lam @ (X20 @ sh @ one)) @ id) | ~ ! [X24 : term] : ((X17 @ id @ (X20 @ id @ X24) @ id) | ~(X17 @ id @ X24 @ id)))) => ! [X25 : term,X26 : (subst > term > subst > $o)] : (~ ! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29) | ~(X26 @ X30 @ X28 @ (comp @ X27 @ X29))) | ~ ! [X31 : (subst > term > term)] : (~ ! [X32 : subst,X33 : subst,X34 : term] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32))) | ~ ! [X35 : term] : (~(X26 @ id @ X35 @ id) | (X26 @ id @ (X31 @ id @ X35) @ id)) | (X26 @ id @ (lam @ (X31 @ sh @ one)) @ id)) | ~ ! [X36 : subst,X37 : term,X38 : subst,X39 : subst] : ((X26 @ X38 @ X37 @ (comp @ X36 @ X39)) | ~(X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39)) | (X26 @ id @ (lam @ X25) @ id) | ~ ! [X40 : term] : ((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id) | ~(X26 @ id @ X40 @ id))))) <=> hoasinduction_lem3_lthm) & hoasapnotvar_gthm & pushprop_gthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2_gthm & hoaslamnotap_gthm & (! [X41 : (subst > term > subst > $o)] : ~ ! [X42 : (term > $o)] : ~ ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43))) <=> hoasinduction_lem0_lthm) & ~(var @ (d2term @ d_one)) & hoaslamnotvar_lthm & pushprop_lthm_orig & hoaslamnotap_lthm & hoaslamnotvar_gthm & axvarshift & (! [X44 : (subst > term > subst > $o),X45 : (term > $o),X46 : term,X47 : term] : (~ ! [X48 : term,X49 : term] : ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id) | ~(X44 @ id @ X49 @ id) | ~(X44 @ id @ X48 @ id)) | ~ ! [X50 : subst,X51 : subst,X52 : subst,X53 : term] : (~(X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52) | (X44 @ X50 @ X53 @ (comp @ X51 @ X52))) | ~ ! [X54 : term] : (((X44 @ id @ X54 @ id)) = ((X45 @ X54))) | (X45 @ (ap @ X46 @ X47)) | ~ ! [X55 : subst,X56 : subst,X57 : subst,X58 : term] : ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56) | ~(X44 @ X57 @ X58 @ (comp @ X55 @ X56))) | ~(X45 @ X46) | ~(X45 @ X47)) <=> hoasinduction_lem2v2) & hoasinduction_lem2_gthm & (axshiftcons <=> ! [X59 : term,X60 : subst] : (((comp @ sh @ (push @ X59 @ X60))) = X60)) & ((! [X61 : term] : (((sub @ X61 @ id)) = X61) => (! [X62 : term,X63 : (term > $o),X64 : subst] : (~ ! [X65 : term] : ((X63 @ (sub @ X65 @ X64)) | ~(var @ X65)) | ~ ! [X66 : term,X67 : term] : ((X63 @ (ap @ X66 @ X67)) | ~(X63 @ X67) | ~(X63 @ X66)) | ~ ! [X68 : term] : (~ ! [X69 : term] : ((X63 @ (sub @ X68 @ (push @ X69 @ id))) | ~(X63 @ X69)) | (X63 @ (lam @ X68))) | (X63 @ (sub @ X62 @ X64))) => ! [X70 : (term > $o),X71 : term] : (~ ! [X72 : term] : ((X70 @ (lam @ X72)) | ~ ! [X73 : term] : ((X70 @ (sub @ X72 @ (push @ X73 @ id))) | ~(X70 @ X73))) | ~ ! [X74 : term,X75 : term] : (~(X70 @ X75) | (X70 @ (ap @ X75 @ X74)) | ~(X70 @ X74)) | (X70 @ X71) | ~ ! [X76 : term] : (~(var @ X76) | (X70 @ X76))))) <=> induction2_lthm) & hoasinduction_lem2_lthm & (hoasinduction_lem3aaa <=> ! [X77 : (subst > term > subst > $o),X78 : term] : ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id) | ~ ! [X79 : (subst > term > term),X80 : term] : (~ ! [X81 : term] : ((X77 @ id @ (X79 @ id @ X81) @ id) | ~(X77 @ id @ X81 @ id)) | ~ ! [X82 : subst,X83 : subst,X84 : term] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))) | (X77 @ id @ (lam @ (X79 @ sh @ one)) @ id) | ~ ! [X85 : subst,X86 : term,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87))))) | ~ ! [X88 : term] : ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id) | ~(X77 @ id @ X88 @ id)))) & pushprop_lthm & hoasinduction_gthm & (id = ((d2subst @ d_id))) & (! [X89 : term,X90 : term] : ((((sub @ X90 @ sh)) != ((sub @ X89 @ sh))) | (X89 = X90)) <=> shinj) & ((! [X91 : term] : (((sub @ X91 @ id)) = X91) => ! [X92 : term] : (((sub @ X92 @ id)) = X92)) <=> termmset_lthm) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (termmset <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (hoasapinj2 <=> ! [X96 : term,X97 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97))) & hoasapinj1_gthm & (hoaslaminj_lthm <=> (! [X100 : term,X101 : subst] : (((sub @ one @ (push @ X100 @ X101))) = X100) => (! [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) = X103) => (! [X104 : term,X105 : term] : ((((lam @ X104)) != ((lam @ X105))) | (X104 = X105)) => ! [X106 : term,X107 : (subst > term > term),X108 : (subst > term > term),X109 : subst] : (~ ! [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) = ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) | (((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one)))) | ~ ! [X113 : term,X114 : subst,X115 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) = ((sub @ (X108 @ X114 @ X113) @ X115)))))))) & ((! [X116 : subst] : (((comp @ id @ X116)) = X116) => (! [X117 : subst] : (((comp @ X117 @ id)) = X117) => (! [X118 : subst] : (((comp @ X118 @ id)) = X118) & ! [X119 : subst] : (((comp @ id @ X119)) = X119)))) <=> substmonoid_lthm) & (hoasinduction_lem3 <=> ! [X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X122 : term,X123 : subst,X124 : subst,X125 : subst] : ((X121 @ X123 @ X122 @ (comp @ X124 @ X125)) | ~(X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)) | (X121 @ id @ (lam @ X120) @ id) | ~ ! [X126 : term] : (~(X121 @ id @ X126 @ id) | (X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id)) | ~ ! [X127 : (subst > term > term)] : ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id) | ~ ! [X128 : term,X129 : subst,X130 : subst] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) | ~ ! [X131 : term] : ((X121 @ id @ (X127 @ id @ X131) @ id) | ~(X121 @ id @ X131 @ id))) | ~ ! [X132 : term,X133 : subst,X134 : subst,X135 : subst] : (~(X121 @ X135 @ X132 @ (comp @ X134 @ X133)) | (X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : (((X137 @ sh @ one)) != ((sub @ X136 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & ((! [X138 : term,X139 : (term > $o)] : ((X139 @ X138) | ~ ! [X140 : term] : ((X139 @ X140) | ~(var @ X140)) | ~ ! [X141 : term,X142 : term] : (~(X139 @ X142) | ~(X139 @ X141) | (X139 @ (ap @ X142 @ X141))) | ~ ! [X143 : term] : ((X139 @ (lam @ X143)) | ~ ! [X144 : term] : (~(X139 @ X144) | (X139 @ (sub @ X143 @ (push @ X144 @ id)))))) => (! [X145 : term,X146 : (subst > term > subst > $o),X147 : term] : (~(X146 @ id @ X147 @ id) | (X146 @ id @ (ap @ X145 @ X147) @ id) | ~ ! [X148 : subst,X149 : term,X150 : subst,X151 : subst] : ((X146 @ X151 @ X149 @ (comp @ X148 @ X150)) | ~(X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150)) | ~(X146 @ id @ X145 @ id) | ~ ! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154) | ~(X146 @ X153 @ X152 @ (comp @ X155 @ X154))) | ~ ! [X156 : term,X157 : term] : ((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id) | ~(X146 @ id @ X157 @ id) | ~(X146 @ id @ X156 @ id))) => (! [X158 : (subst > term > subst > $o),X159 : term] : (~ ! [X160 : (subst > term > term)] : (~ ! [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) = ((sub @ (X160 @ X163 @ X161) @ X162))) | ~ ! [X164 : term] : (~(X158 @ id @ X164 @ id) | (X158 @ id @ (X160 @ id @ X164) @ id)) | (X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) | (X158 @ id @ (lam @ X159) @ id) | ~ ! [X165 : term] : ((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id) | ~(X158 @ id @ X165 @ id)) | ~ ! [X166 : term,X167 : subst,X168 : subst,X169 : subst] : (~(X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167) | (X158 @ X168 @ X166 @ (comp @ X169 @ X167))) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170) | ~(X158 @ X172 @ X173 @ (comp @ X171 @ X170)))) => ! [X174 : term,X175 : (subst > term > subst > $o)] : (~ ! [X176 : term] : (~(var @ (sub @ X176 @ id)) | (X175 @ id @ X176 @ id)) | ~ ! [X177 : term,X178 : subst,X179 : subst,X180 : subst] : ((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178) | ~(X175 @ X179 @ X177 @ (comp @ X180 @ X178))) | ~ ! [X181 : term,X182 : term] : (~(X175 @ id @ X181 @ id) | (X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id) | ~(X175 @ id @ X182 @ id)) | ~ ! [X183 : (subst > term > term)] : (~ ! [X184 : term,X185 : subst,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) | (X175 @ id @ (lam @ (X183 @ sh @ one)) @ id) | ~ ! [X187 : term] : (~(X175 @ id @ X187 @ id) | (X175 @ id @ (X183 @ id @ X187) @ id))) | (X175 @ id @ X174 @ id) | ~ ! [X188 : subst,X189 : term,X190 : subst,X191 : subst] : ((X175 @ X188 @ X189 @ (comp @ X191 @ X190)) | ~(X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190)))))) <=> hoasinduction_lthm) & axabs & (! [X192 : (subst > term > subst > $o),X193 : term] : (~ ! [X194 : term,X195 : term] : (~(X192 @ id @ X195 @ id) | ~(X192 @ id @ X194 @ id) | (X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) | (X192 @ id @ X193 @ id) | ~ ! [X196 : (subst > term > term)] : ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id) | ~ ! [X197 : subst,X198 : subst,X199 : term] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197))) | ~ ! [X200 : term] : ((X192 @ id @ (X196 @ id @ X200) @ id) | ~(X192 @ id @ X200 @ id)))) <=> hoasinduction_no_psi_cond) & (hoaslamnotap <=> ! [X201 : term,X202 : (subst > term > term),X203 : term] : (~ ! [X204 : term,X205 : subst,X206 : subst] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) = ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one)))))) & ((! [X207 : (subst > term > subst > $o)] : ~ ! [X208 : (term > $o)] : ~ ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))) => (! [X210 : (term > $o),X211 : term] : (~ ! [X212 : term] : (~(var @ X212) | (X210 @ X212)) | (X210 @ X211) | ~ ! [X213 : term,X214 : term] : (~(X210 @ X213) | ~(X210 @ X214) | (X210 @ (ap @ X213 @ X214))) | ~ ! [X215 : term] : ((X210 @ (lam @ X215)) | ~ ! [X216 : term] : ((X210 @ (sub @ X215 @ (push @ X216 @ id))) | ~(X210 @ X216)))) => (! [X217 : term] : (((sub @ X217 @ id)) = X217) => (! [X218 : (subst > term > subst > $o),X219 : term,X220 : (term > $o)] : (~ ! [X221 : term] : (~(X220 @ X221) | (X220 @ (sub @ X219 @ (push @ X221 @ id)))) | ~ ! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) | (X220 @ (lam @ X219)) | ~ ! [X223 : (subst > term > term)] : ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id) | ~ ! [X224 : term] : ((X218 @ id @ (X223 @ id @ X224) @ id) | ~(X218 @ id @ X224 @ id)) | ~ ! [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) = ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))))) => ! [X228 : term,X229 : (subst > term > subst > $o)] : ((X229 @ id @ X228 @ id) | ~ ! [X230 : term,X231 : term] : (~(X229 @ id @ X230 @ id) | (X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id) | ~(X229 @ id @ X231 @ id)) | ~ ! [X232 : subst,X233 : subst,X234 : term,X235 : subst] : ((X229 @ X233 @ X234 @ (comp @ X235 @ X232)) | ~(X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) | ~ ! [X236 : term,X237 : subst,X238 : subst,X239 : subst] : (~(X229 @ X238 @ X236 @ (comp @ X239 @ X237)) | (X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237)) | ~ ! [X240 : term] : (~(var @ (sub @ X240 @ id)) | (X229 @ id @ X240 @ id)) | ~ ! [X241 : (subst > term > term)] : (~ ! [X242 : subst,X243 : subst,X244 : term] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242))) | (X229 @ id @ (lam @ (X241 @ sh @ one)) @ id) | ~ ! [X245 : term] : ((X229 @ id @ (X241 @ id @ X245) @ id) | ~(X229 @ id @ X245 @ id)))))))) <=> hoasinduction_lthm_3) & (apinj2 <=> ! [X246 : term,X247 : term,X248 : term,X249 : term] : ((((ap @ X248 @ X249)) != ((ap @ X246 @ X247))) | (X247 = X249))) & (sh = ((d2subst @ d_id))) & lamnotvar & (induction2lem_lthm <=> (! [X250 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X250))) = X251) => (! [X252 : term,X253 : subst] : (((comp @ sh @ (push @ X252 @ X253))) = X253) => (! [X254 : subst] : (((comp @ X254 @ id)) = X254) => (! [X255 : term,X256 : (term > $o)] : (~ ! [X257 : term] : (~(var @ X257) | (X256 @ X257)) | (X256 @ X255) | ~ ! [X258 : term] : ((X256 @ (lam @ X258)) | ~(X256 @ X258)) | ~ ! [X259 : term,X260 : term] : ((X256 @ (ap @ X260 @ X259)) | ~(X256 @ X260) | ~(X256 @ X259))) => ! [X261 : (term > $o),X262 : subst,X263 : term] : (~ ! [X264 : term,X265 : term] : (~(X261 @ X265) | ~(X261 @ X264) | (X261 @ (ap @ X265 @ X264))) | ~ ! [X266 : term] : ((X261 @ (sub @ X266 @ X262)) | ~(var @ X266)) | (X261 @ (sub @ X263 @ X262)) | ~ ! [X267 : term] : ((X261 @ (lam @ X267)) | ~ ! [X268 : term] : ((X261 @ (sub @ X267 @ (push @ X268 @ id))) | ~(X261 @ X268))))))))) & (! [X269 : (subst > term > term),X270 : subst,X271 : term,X272 : (subst > term > term)] : (~ ! [X273 : subst,X274 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) = ((sub @ (X272 @ X273 @ X275) @ X274))) | ~ ! [X276 : subst,X277 : subst,X278 : term] : (((sub @ (X269 @ X277 @ X278) @ X276)) = ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276)))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | (((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271)))) <=> hoaslaminj) & ! [X279 : d_subst,X280 : d_subst] : ((((d2subst @ X280)) = ((d2subst @ X279))) => (X279 = X280)) & hoasinduction_lem1_lthm & axclos & (axvarcons <=> ! [X281 : term,X282 : subst] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & ~lamnotap & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (pushprop_lem1v2 <=> ! [X283 : (term > $o),X284 : term,X285 : (term > $o),X286 : subst] : (~(X285 @ X284) | ~ ! [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) = ((X283 @ X287))) | (X283 @ one))) & (induction2 <=> ! [X288 : (term > $o),X289 : term] : (~ ! [X290 : term,X291 : term] : (~(X288 @ X291) | ~(X288 @ X290) | (X288 @ (ap @ X291 @ X290))) | (X288 @ X289) | ~ ! [X292 : term] : (~ ! [X293 : term] : ((X288 @ (sub @ X292 @ (push @ X293 @ id))) | ~(X288 @ X293)) | (X288 @ (lam @ X292))) | ~ ! [X294 : term] : ((X288 @ X294) | ~(var @ X294)))) & hoaslamnotvar & (substmonoid <=> (! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296))) & axmap & ((! [X297 : (subst > term > subst > $o)] : ~ ! [X298 : (term > $o)] : ~ ! [X299 : term] : (((X298 @ X299)) = ((X297 @ id @ X299 @ id))) => (! [X300 : term,X301 : (term > $o)] : ((X301 @ X300) | ~ ! [X302 : term] : ((X301 @ (lam @ X302)) | ~ ! [X303 : term] : (~(X301 @ X303) | (X301 @ (sub @ X302 @ (push @ X303 @ id))))) | ~ ! [X304 : term] : (~(var @ X304) | (X301 @ X304)) | ~ ! [X305 : term,X306 : term] : (~(X301 @ X305) | ~(X301 @ X306) | (X301 @ (ap @ X305 @ X306)))) => (! [X307 : term] : (((sub @ X307 @ id)) = X307) => (! [X308 : term,X309 : (term > $o),X310 : (subst > term > subst > $o)] : ((X309 @ (lam @ X308)) | ~ ! [X311 : (subst > term > term)] : ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id) | ~ ! [X312 : term] : ((X310 @ id @ (X311 @ id @ X312) @ id) | ~(X310 @ id @ X312 @ id)) | ~ ! [X313 : subst,X314 : term,X315 : subst] : (((sub @ (X311 @ X315 @ X314) @ X313)) = ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) | ~ ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))) | ~ ! [X317 : term] : (~(X309 @ X317) | (X309 @ (sub @ X308 @ (push @ X317 @ id))))) => ! [X318 : term,X319 : (subst > term > subst > $o)] : (~ ! [X320 : term,X321 : term] : ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id) | ~(X319 @ id @ X320 @ id) | ~(X319 @ id @ X321 @ id)) | (X319 @ id @ X318 @ id) | ~ ! [X322 : (subst > term > term)] : ((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id) | ~ ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) | ~ ! [X326 : term] : ((X319 @ id @ (X322 @ id @ X326) @ id) | ~(X319 @ id @ X326 @ id)))))))) <=> hoasinduction_no_psi_cond_lthm) & ! [X327 : d_subst] : (d_id = X327) & (! [X328 : term,X329 : subst,X330 : (term > $o),X331 : (term > $o),X332 : term] : ((X331 @ (sub @ X332 @ (push @ X328 @ X329))) | ~(X330 @ X332)) <=> pushprop_lem1) & pushprop_lem1_gthm & (hoaslam = (^[X333 : subst, X334 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lem2v2 & (! [X335 : subst] : (((comp @ id @ X335)) = X335) <=> axidl) & axapp & (pushprop_lem1v2_lthm <=> (! [X336 : term,X337 : subst] : (((sub @ one @ (push @ X336 @ X337))) = X336) => ! [X338 : subst,X339 : term,X340 : (term > $o),X341 : (term > $o)] : (~(X340 @ X339) | ~ ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X339 @ X338)))) = ((X341 @ X342))) | (X341 @ one)))) & induction2lem_gthm & ulamvarsh & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X343 : (term > $o),X344 : term,X345 : (subst > term > subst > $o)] : ((X343 @ (lam @ X344)) | ~ ! [X346 : term] : (((X343 @ X346)) = ((X345 @ id @ X346 @ id))) | ~ ! [X347 : (subst > term > term)] : (~ ! [X348 : subst,X349 : subst,X350 : term] : (((sub @ (X347 @ X349 @ X350) @ X348)) = ((X347 @ (comp @ X349 @ X348) @ (sub @ X350 @ X348)))) | (X345 @ id @ (lam @ (X347 @ sh @ one)) @ id) | ~ ! [X351 : term] : ((X345 @ id @ (X347 @ id @ X351) @ id) | ~(X345 @ id @ X351 @ id))) | ~ ! [X352 : term] : ((X343 @ (sub @ X344 @ (push @ X352 @ id))) | ~(X343 @ X352))) <=> hoasinduction_lem3v2a) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (induction <=> ! [X353 : term,X354 : (term > $o)] : (~ ! [X355 : term] : ((X354 @ (lam @ X355)) | ~(X354 @ X355)) | ~ ! [X356 : term] : (~(var @ X356) | (X354 @ X356)) | ~ ! [X357 : term,X358 : term] : (~(X354 @ X358) | ~(X354 @ X357) | (X354 @ (ap @ X358 @ X357))) | (X354 @ X353))) & (hoasinduction_lem3aa_lthm <=> ! [X359 : (subst > term > subst > $o),X360 : term] : (~ ! [X361 : term] : (~(X359 @ id @ X361 @ id) | (X359 @ id @ (sub @ X360 @ (push @ X361 @ id)) @ id)) | ~ ! [X362 : (subst > term > term)] : (~ ! [X363 : subst,X364 : subst,X365 : term] : (((sub @ (X362 @ X364 @ X365) @ X363)) = ((X362 @ (comp @ X364 @ X363) @ (sub @ X365 @ X363)))) | ~ ! [X366 : term] : ((X359 @ id @ (X362 @ id @ X366) @ id) | ~(X359 @ id @ X366 @ id)) | (X359 @ id @ (lam @ (X362 @ sh @ one)) @ id)) | (X359 @ id @ (lam @ (sub @ X360 @ (push @ one @ sh))) @ id))) & ((^[X367 : (subst > term > subst > $o), X368 : (term > $o)] : (! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))))) = hoasinduction_p_and_p_prime) & hoasinduction_lem1v2 & ! [X370 : term] : ? [X371 : d_term] : (((d2term @ X371)) = X370) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoaslaminj_gthm & (! [X372 : (subst > term > subst > $o)] : ~ ! [X373 : (term > $o)] : ~ ! [X374 : term] : (((X372 @ id @ X374 @ id)) = ((X373 @ X374))) <=> hoasinduction_lem0) & pushprop_lem3v2_lthm & ((^[X375 : term, X376 : subst, X377 : (term > $o), X378 : (term > $o)] : (! [X379 : term] : (((X378 @ X379)) = ((X377 @ (sub @ X379 @ (push @ X375 @ X376))))))) = pushprop_p_and_p_prime) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((! [X380 : term] : (((sub @ X380 @ id)) = X380) => ! [X381 : (term > $o),X382 : (subst > term > subst > $o),X383 : term] : (~ ! [X384 : term] : (((X381 @ X384)) = ((X382 @ id @ X384 @ id))) | ~ ! [X385 : subst,X386 : term,X387 : subst,X388 : subst] : (~(X382 @ (comp @ X385 @ X388) @ (sub @ X386 @ X388) @ X387) | (X382 @ X385 @ X386 @ (comp @ X388 @ X387))) | ~ ! [X389 : (subst > term > term)] : (~ ! [X390 : term] : (~(X382 @ id @ X390 @ id) | (X382 @ id @ (X389 @ id @ X390) @ id)) | ~ ! [X391 : term,X392 : subst,X393 : subst] : (((sub @ (X389 @ X392 @ X391) @ X393)) = ((X389 @ (comp @ X392 @ X393) @ (sub @ X391 @ X393)))) | (X382 @ id @ (lam @ (X389 @ sh @ one)) @ id)) | (X381 @ (lam @ X383)) | ~ ! [X394 : subst,X395 : subst,X396 : term,X397 : subst] : (~(X382 @ X395 @ X396 @ (comp @ X397 @ X394)) | (X382 @ (comp @ X395 @ X397) @ (sub @ X396 @ X397) @ X394)) | ~ ! [X398 : term] : ((X381 @ (sub @ X383 @ (push @ X398 @ id))) | ~(X381 @ X398)))) <=> hoasinduction_lem3v2_lthm) & (one = ((d2term @ d_one))) & (! [X399 : term,X400 : (term > $o),X401 : subst] : ~ ! [X402 : (term > $o)] : ~ ! [X403 : term] : (((X402 @ X403)) = ((X400 @ (sub @ X403 @ (push @ X399 @ X401))))) <=> pushprop_lem0) & ((! [X404 : term] : ~ ! [X405 : (subst > term > term)] : ~ ! [X406 : term,X407 : subst] : (((sub @ X404 @ (push @ X406 @ X407))) = ((X405 @ X407 @ X406))) => (! [X408 : term] : (((sub @ X408 @ id)) = X408) => ! [X409 : (term > $o),X410 : term,X411 : (subst > term > subst > $o)] : (~ ! [X412 : term] : ((X409 @ (sub @ X410 @ (push @ X412 @ id))) | ~(X409 @ X412)) | ~ ! [X413 : term] : (((X409 @ X413)) = ((X411 @ id @ X413 @ id))) | (X409 @ (lam @ X410)) | ~ ! [X414 : (subst > term > term)] : ((X411 @ id @ (lam @ (X414 @ sh @ one)) @ id) | ~ ! [X415 : term,X416 : subst,X417 : subst] : (((sub @ (X414 @ X417 @ X415) @ X416)) = ((X414 @ (comp @ X417 @ X416) @ (sub @ X415 @ X416)))) | ~ ! [X418 : term] : (~(X411 @ id @ X418 @ id) | (X411 @ id @ (X414 @ id @ X418) @ id)))))) <=> hoasinduction_lem3v2a_lthm) & (! [X419 : term] : ~ ! [X420 : (subst > term > term)] : ~ ! [X421 : term,X422 : subst] : (((X420 @ X422 @ X421)) = ((sub @ X419 @ (push @ X421 @ X422)))) <=> hoasinduction_lem3v2_f) & (laminj <=> ! [X423 : term,X424 : term] : ((((lam @ X424)) != ((lam @ X423))) | (X423 = X424))) & ((! [X425 : term,X426 : term,X427 : term,X428 : term] : ((((ap @ X426 @ X428)) != ((ap @ X427 @ X425))) | (X425 = X428)) => ! [X429 : term,X430 : term,X431 : term,X432 : term] : ((((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X429 @ id) @ X432))) | (X430 = X432))) <=> hoasapinj2_lthm) & ((! [X433 : term] : (((sub @ X433 @ id)) = X433) => (! [X434 : term,X435 : term,X436 : term,X437 : term] : ((((ap @ X437 @ X435)) != ((ap @ X436 @ X434))) | (X436 = X437)) => ! [X438 : term,X439 : term,X440 : term,X441 : term] : ((X438 = X441) | (((ap @ (sub @ X438 @ id) @ X439)) != ((ap @ (sub @ X441 @ id) @ X440)))))) <=> hoasapinj1_lthm) & hoasinduction_lem1v2_gthm & hoasapnotvar & ~ulamvar1 & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem3b_gthm & hoasapinj2_gthm & pushprop_lem3v2 & (! [X442 : term] : ~ ! [X443 : (subst > term > term)] : ~ ! [X444 : subst,X445 : term] : (((X443 @ X444 @ X445)) = ((sub @ X442 @ (push @ X445 @ X444)))) <=> hoasinduction_lem3v2_f_lthm) & (apinj1 <=> ! [X446 : term,X447 : term,X448 : term,X449 : term] : ((((ap @ X448 @ X447)) != ((ap @ X446 @ X449))) | (X446 = X448))) & hoasinduction_lem1_gthm & (! [X450 : term,X451 : (subst > term > subst > $o)] : (~ ! [X452 : term,X453 : term] : (~(X451 @ id @ X453 @ id) | (X451 @ id @ (ap @ (sub @ X453 @ id) @ X452) @ id) | ~(X451 @ id @ X452 @ id)) | ~ ! [X454 : subst,X455 : subst,X456 : term,X457 : subst] : ((X451 @ (comp @ X454 @ X455) @ (sub @ X456 @ X455) @ X457) | ~(X451 @ X454 @ X456 @ (comp @ X455 @ X457))) | (X451 @ id @ X450 @ id) | ~ ! [X458 : (subst > term > term)] : ((X451 @ id @ (lam @ (X458 @ sh @ one)) @ id) | ~ ! [X459 : term] : (~(X451 @ id @ X459 @ id) | (X451 @ id @ (X458 @ id @ X459) @ id)) | ~ ! [X460 : term,X461 : subst,X462 : subst] : (((X458 @ (comp @ X462 @ X461) @ (sub @ X460 @ X461))) = ((sub @ (X458 @ X462 @ X460) @ X461)))) | ~ ! [X463 : term] : ((X451 @ id @ X463 @ id) | ~(var @ (sub @ X463 @ id))) | ~ ! [X464 : subst,X465 : term,X466 : subst,X467 : subst] : (~(X451 @ (comp @ X466 @ X467) @ (sub @ X465 @ X467) @ X464) | (X451 @ X466 @ X465 @ (comp @ X467 @ X464)))) <=> hoasinduction) & hoasinduction_lem3a_gthm & hoasinduction_lem2v2_gthm & (hoasinduction_lem3a <=> ! [X468 : term,X469 : (subst > term > subst > $o)] : (~ ! [X470 : (subst > term > term)] : (~ ! [X471 : subst,X472 : subst,X473 : term] : (((X470 @ (comp @ X472 @ X471) @ (sub @ X473 @ X471))) = ((sub @ (X470 @ X472 @ X473) @ X471))) | ~ ! [X474 : term] : (~(X469 @ id @ X474 @ id) | (X469 @ id @ (X470 @ id @ X474) @ id)) | (X469 @ id @ (lam @ (X470 @ sh @ one)) @ id)) | ~ ! [X475 : term] : ((X469 @ id @ (sub @ X468 @ (push @ X475 @ id)) @ id) | ~(X469 @ id @ X475 @ id)) | (X469 @ id @ (lam @ X468) @ id))) & pushprop & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) => (! [X477 : (subst > term > subst > $o),X478 : term] : (~ ! [X479 : term] : (~(X477 @ id @ X479 @ id) | (X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id)) | ~ ! [X480 : (subst > term > term)] : (~ ! [X481 : term,X482 : subst,X483 : subst] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X481 @ X482))) = ((sub @ (X480 @ X483 @ X481) @ X482))) | ~ ! [X484 : term] : ((X477 @ id @ (X480 @ id @ X484) @ id) | ~(X477 @ id @ X484 @ id)) | (X477 @ id @ (lam @ (X480 @ sh @ one)) @ id)) | (X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)) => ! [X485 : (subst > term > subst > $o),X486 : term] : ((X485 @ id @ (lam @ X486) @ id) | ~ ! [X487 : term] : ((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id) | ~(X485 @ id @ X487 @ id)) | ~ ! [X488 : (subst > term > term)] : ((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id) | ~ ! [X489 : subst,X490 : term,X491 : subst] : (((X488 @ (comp @ X491 @ X489) @ (sub @ X490 @ X489))) = ((sub @ (X488 @ X491 @ X490) @ X489))) | ~ ! [X492 : term] : (~(X485 @ id @ X492 @ id) | (X485 @ id @ (X488 @ id @ X492) @ id)))))) <=> hoasinduction_lem3a_lthm) & apnotvar & hoasinduction_lem3v2_gthm & substmonoid_gthm & ulamvarind & (! [X493 : (subst > term > subst > $o),X494 : term] : ((X493 @ id @ (lam @ (sub @ X494 @ (push @ one @ sh))) @ id) | ~ ! [X495 : term] : (~(X493 @ id @ X495 @ id) | (X493 @ id @ (sub @ X494 @ (push @ X495 @ id)) @ id)) | ~ ! [X496 : (subst > term > term)] : (~ ! [X497 : term] : (~(X493 @ id @ X497 @ id) | (X493 @ id @ (X496 @ id @ X497) @ id)) | (X493 @ id @ (lam @ (X496 @ sh @ one)) @ id) | ~ ! [X498 : subst,X499 : term,X500 : subst] : (((X496 @ (comp @ X500 @ X498) @ (sub @ X499 @ X498))) = ((sub @ (X496 @ X500 @ X499) @ X498))))) <=> hoasinduction_lem3aa) & (hoasapinj1 <=> ! [X501 : term,X502 : term,X503 : term,X504 : term] : ((((ap @ (sub @ X503 @ id) @ X501)) != ((ap @ (sub @ X502 @ id) @ X504))) | (X502 = X503))) & ! [X505 : d_term] : (d_one = X505) & (! [X506 : subst] : (((comp @ X506 @ id)) = X506) <=> axidr) & (! [X507 : subst] : (((push @ (sub @ one @ X507) @ (comp @ sh @ X507))) = X507) <=> axscons) & (hoasinduction_lem3b <=> ! [X508 : term] : ~ ! [X509 : (subst > term > term)] : (((sub @ X508 @ (push @ one @ sh))) != ((X509 @ sh @ one)))) & pushprop_lem0_gthm & hoasinduction_lem3_gthm & termmset_gthm & induction2_gthm & (! [X510 : subst,X511 : term,X512 : (term > $o)] : ~ ! [X513 : (term > $o)] : ~ ! [X514 : term] : (((X513 @ X514)) = ((X512 @ (sub @ X514 @ (push @ X511 @ X510))))) <=> pushprop_lem0_lthm) & pushprop_lem1v2_gthm & axassoc & pushprop_lem2v2_lthm & ((! [X515 : term,X516 : subst] : (((sub @ one @ (push @ X515 @ X516))) = X515) => (! [X517 : term,X518 : subst] : (((comp @ sh @ (push @ X517 @ X518))) = X518) => ! [X519 : (term > $o),X520 : term,X521 : (term > $o),X522 : term,X523 : subst] : ((X519 @ (sub @ X522 @ (push @ X520 @ X523))) | ~(X521 @ X522)))) <=> pushprop_lem1_lthm) & (hoasinduction_lem3v2 <=> ! [X524 : term,X525 : (term > $o),X526 : (subst > term > subst > $o)] : ((X525 @ (lam @ X524)) | ~ ! [X527 : subst,X528 : term,X529 : subst,X530 : subst] : ((X526 @ (comp @ X530 @ X527) @ (sub @ X528 @ X527) @ X529) | ~(X526 @ X530 @ X528 @ (comp @ X527 @ X529))) | ~ ! [X531 : term] : (((X525 @ X531)) = ((X526 @ id @ X531 @ id))) | ~ ! [X532 : (subst > term > term)] : (~ ! [X533 : term,X534 : subst,X535 : subst] : (((X532 @ (comp @ X535 @ X534) @ (sub @ X533 @ X534))) = ((sub @ (X532 @ X535 @ X533) @ X534))) | ~ ! [X536 : term] : (~(X526 @ id @ X536 @ id) | (X526 @ id @ (X532 @ id @ X536) @ id)) | (X526 @ id @ (lam @ (X532 @ sh @ one)) @ id)) | ~ ! [X537 : term] : (~(X525 @ X537) | (X525 @ (sub @ X524 @ (push @ X537 @ id)))) | ~ ! [X538 : term,X539 : subst,X540 : subst,X541 : subst] : (~(X526 @ (comp @ X541 @ X540) @ (sub @ X538 @ X540) @ X539) | (X526 @ X541 @ X538 @ (comp @ X540 @ X539))))) & (! [X542 : term,X543 : subst,X544 : (term > $o)] : ((X544 @ (sub @ X542 @ X543)) | ~ ! [X545 : term,X546 : term] : (~(X544 @ X545) | (X544 @ (ap @ X546 @ X545)) | ~(X544 @ X546)) | ~ ! [X547 : term] : ((X544 @ (sub @ X547 @ X543)) | ~(var @ X547)) | ~ ! [X548 : term] : (~ ! [X549 : term] : (~(X544 @ X549) | (X544 @ (sub @ X548 @ (push @ X549 @ id)))) | (X544 @ (lam @ X548)))) <=> induction2lem)), 0.43/0.52 inference(rectify,[],[f3])). 0.43/0.52 thf(f7,plain,( 0.43/0.52 ! [X0 : d_term,X1 : d_term] : ((((d2term @ X0)) = ((d2term @ X1))) => (X0 = X1)) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> (axvarid = $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X3 : term,X4 : term,X5 : (subst > term > subst > $o)] : (~ ($true = ((X5 @ id @ X3 @ id))) | ~ ($true = ((X5 @ id @ X4 @ id))) | ~ ! [X6 : subst,X7 : term,X8 : subst,X9 : subst] : ((((X5 @ X9 @ X7 @ (comp @ X8 @ X6))) = $true) | ~ ($true = ((X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6)))) | ~ ! [X10 : term,X11 : term] : (~ ($true = ((X5 @ id @ X11 @ id))) | ~ (((X5 @ id @ X10 @ id)) = $true) | ($true = ((X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id)))) | ~ ! [X12 : term,X13 : subst,X14 : subst,X15 : subst] : (~ (((X5 @ X15 @ X12 @ (comp @ X13 @ X14))) = $true) | (((X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) = $true)) | (((X5 @ id @ (ap @ X4 @ X3) @ id)) = $true))) & (hoasapnotvar_lthm = $true) & ((! [X16 : term] : (((sub @ X16 @ id)) = X16) => (! [X17 : (subst > term > subst > $o),X18 : term] : (($true = ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id))) | ~ ! [X19 : term] : (~ ($true = ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) | ~ ! [X20 : (subst > term > term)] : (~ ! [X21 : subst,X22 : subst,X23 : term] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) = ((sub @ (X20 @ X22 @ X23) @ X21))) | ($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ~ ! [X24 : term] : ((((X17 @ id @ (X20 @ id @ X24) @ id)) = $true) | ~ ($true = ((X17 @ id @ X24 @ id)))))) => ! [X25 : term,X26 : (subst > term > subst > $o)] : (~ ! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (($true = ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29))) | ~ (((X26 @ X30 @ X28 @ (comp @ X27 @ X29))) = $true)) | ~ ! [X31 : (subst > term > term)] : (~ ! [X32 : subst,X34 : term,X33 : subst] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32))) | ~ ! [X35 : term] : (~ ($true = ((X26 @ id @ X35 @ id))) | ($true = ((X26 @ id @ (X31 @ id @ X35) @ id)))) | ($true = ((X26 @ id @ (lam @ (X31 @ sh @ one)) @ id)))) | ~ ! [X36 : subst,X37 : term,X38 : subst,X39 : subst] : (($true = ((X26 @ X38 @ X37 @ (comp @ X36 @ X39)))) | ~ ($true = ((X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39)))) | ($true = ((X26 @ id @ (lam @ X25) @ id))) | ~ ! [X40 : term] : ((((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id)) = $true) | ~ (((X26 @ id @ X40 @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasapnotvar_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X41 : (subst > term > subst > $o)] : ~ ! [X42 : (term > $o)] : ~ ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43)))) & ~ (((var @ (d2term @ d_one))) = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_lthm_orig = $true) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (axvarshift = $true) & (! [X44 : (subst > term > subst > $o),X45 : (term > $o),X46 : term,X47 : term] : (~ ! [X48 : term,X49 : term] : (($true = ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id))) | ~ ($true = ((X44 @ id @ X49 @ id))) | ~ ($true = ((X44 @ id @ X48 @ id)))) | ~ ! [X50 : subst,X51 : subst,X52 : subst,X53 : term] : (~ ($true = ((X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52))) | (((X44 @ X50 @ X53 @ (comp @ X51 @ X52))) = $true)) | ~ ! [X54 : term] : (((X44 @ id @ X54 @ id)) = ((X45 @ X54))) | (((X45 @ (ap @ X46 @ X47))) = $true) | ~ ! [X55 : subst,X56 : subst,X57 : subst,X58 : term] : (($true = ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56))) | ~ ($true = ((X44 @ X57 @ X58 @ (comp @ X55 @ X56))))) | ~ ($true = ((X45 @ X46))) | ~ ($true = ((X45 @ X47)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) <=> (axshiftcons = $true)) & ((! [X61 : term] : (((sub @ X61 @ id)) = X61) => (! [X62 : term,X63 : (term > $o),X64 : subst] : (~ ! [X65 : term] : (($true = ((X63 @ (sub @ X65 @ X64)))) | ~ (((var @ X65)) = $true)) | ~ ! [X66 : term,X67 : term] : (($true = ((X63 @ (ap @ X66 @ X67)))) | ~ ($true = ((X63 @ X67))) | ~ ($true = ((X63 @ X66)))) | ~ ! [X68 : term] : (~ ! [X69 : term] : (($true = ((X63 @ (sub @ X68 @ (push @ X69 @ id))))) | ~ ($true = ((X63 @ X69)))) | ($true = ((X63 @ (lam @ X68))))) | (((X63 @ (sub @ X62 @ X64))) = $true)) => ! [X70 : (term > $o),X71 : term] : (~ ! [X72 : term] : ((((X70 @ (lam @ X72))) = $true) | ~ ! [X73 : term] : (($true = ((X70 @ (sub @ X72 @ (push @ X73 @ id))))) | ~ ($true = ((X70 @ X73))))) | ~ ! [X74 : term,X75 : term] : (~ ($true = ((X70 @ X75))) | (((X70 @ (ap @ X75 @ X74))) = $true) | ~ ($true = ((X70 @ X74)))) | ($true = ((X70 @ X71))) | ~ ! [X76 : term] : (~ (((var @ X76)) = $true) | ($true = ((X70 @ X76))))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X77 : (subst > term > subst > $o),X78 : term] : (($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ~ ! [X79 : (subst > term > term),X80 : term] : (~ ! [X81 : term] : ((((X77 @ id @ (X79 @ id @ X81) @ id)) = $true) | ~ ($true = ((X77 @ id @ X81 @ id)))) | ~ ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))) | ($true = ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) | ~ ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87))))) | ~ ! [X88 : term] : (($true = ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id))) | ~ (((X77 @ id @ X88 @ id)) = $true)))) & (pushprop_lthm = $true) & (hoasinduction_gthm = $true) & (id = ((d2subst @ d_id))) & ((shinj = $true) <=> ! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh))))) & ((termmset_lthm = $true) <=> (! [X91 : term] : (((sub @ X91 @ id)) = X91) => ! [X92 : term] : (((sub @ X92 @ id)) = X92))) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & ((termmset = $true) <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) <=> (hoasapinj2 = $true)) & (hoasapinj1_gthm = $true) & ((! [X100 : term,X101 : subst] : (((sub @ one @ (push @ X100 @ X101))) = X100) => (! [X103 : subst,X102 : term] : (((comp @ sh @ (push @ X102 @ X103))) = X103) => (! [X104 : term,X105 : term] : ((((lam @ X104)) != ((lam @ X105))) | (X104 = X105)) => ! [X107 : (subst > term > term),X108 : (subst > term > term),X109 : subst,X106 : term] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ~ ! [X115 : subst,X114 : subst,X113 : term] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) = ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one)))) | ~ ! [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) = ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))))))) <=> (hoaslaminj_lthm = $true)) & ((! [X116 : subst] : (((comp @ id @ X116)) = X116) => (! [X117 : subst] : (((comp @ X117 @ id)) = X117) => (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X122 : term,X123 : subst,X124 : subst,X125 : subst] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) = $true) | ~ ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id))) | ~ ! [X126 : term] : (~ ($true = ((X121 @ id @ X126 @ id))) | ($true = ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id)))) | ~ ! [X127 : (subst > term > term)] : (($true = ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id))) | ~ ! [X130 : subst,X129 : subst,X128 : term] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) | ~ ! [X131 : term] : ((((X121 @ id @ (X127 @ id @ X131) @ id)) = $true) | ~ (((X121 @ id @ X131 @ id)) = $true))) | ~ ! [X132 : term,X133 : subst,X134 : subst,X135 : subst] : (~ (((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) | (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) = $true)))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : (((X137 @ sh @ one)) != ((sub @ X136 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X138 : term,X139 : (term > $o)] : ((((X139 @ X138)) = $true) | ~ ! [X140 : term] : (($true = ((X139 @ X140))) | ~ ($true = ((var @ X140)))) | ~ ! [X141 : term,X142 : term] : (~ ($true = ((X139 @ X142))) | ~ (((X139 @ X141)) = $true) | ($true = ((X139 @ (ap @ X142 @ X141))))) | ~ ! [X143 : term] : (($true = ((X139 @ (lam @ X143)))) | ~ ! [X144 : term] : (~ ($true = ((X139 @ X144))) | (((X139 @ (sub @ X143 @ (push @ X144 @ id)))) = $true)))) => (! [X145 : term,X146 : (subst > term > subst > $o),X147 : term] : (~ ($true = ((X146 @ id @ X147 @ id))) | ($true = ((X146 @ id @ (ap @ X145 @ X147) @ id))) | ~ ! [X148 : subst,X149 : term,X150 : subst,X151 : subst] : (($true = ((X146 @ X151 @ X149 @ (comp @ X148 @ X150)))) | ~ ($true = ((X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150)))) | ~ (((X146 @ id @ X145 @ id)) = $true) | ~ ! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (($true = ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154))) | ~ (((X146 @ X153 @ X152 @ (comp @ X155 @ X154))) = $true)) | ~ ! [X156 : term,X157 : term] : ((((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id)) = $true) | ~ (((X146 @ id @ X157 @ id)) = $true) | ~ ($true = ((X146 @ id @ X156 @ id))))) => (! [X158 : (subst > term > subst > $o),X159 : term] : (~ ! [X160 : (subst > term > term)] : (~ ! [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) = ((sub @ (X160 @ X163 @ X161) @ X162))) | ~ ! [X164 : term] : (~ (((X158 @ id @ X164 @ id)) = $true) | ($true = ((X158 @ id @ (X160 @ id @ X164) @ id)))) | (((X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) = $true)) | ($true = ((X158 @ id @ (lam @ X159) @ id))) | ~ ! [X165 : term] : ((((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true) | ~ ($true = ((X158 @ id @ X165 @ id)))) | ~ ! [X166 : term,X167 : subst,X168 : subst,X169 : subst] : (~ (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) = $true) | ($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167))))) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | ~ (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) = $true))) => ! [X174 : term,X175 : (subst > term > subst > $o)] : (~ ! [X176 : term] : (~ ($true = ((var @ (sub @ X176 @ id)))) | (((X175 @ id @ X176 @ id)) = $true)) | ~ ! [X177 : term,X178 : subst,X179 : subst,X180 : subst] : ((((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178)) = $true) | ~ ($true = ((X175 @ X179 @ X177 @ (comp @ X180 @ X178))))) | ~ ! [X181 : term,X182 : term] : (~ ($true = ((X175 @ id @ X181 @ id))) | (((X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id)) = $true) | ~ ($true = ((X175 @ id @ X182 @ id)))) | ~ ! [X183 : (subst > term > term)] : (~ ! [X185 : subst,X184 : term,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) | (((X175 @ id @ (lam @ (X183 @ sh @ one)) @ id)) = $true) | ~ ! [X187 : term] : (~ ($true = ((X175 @ id @ X187 @ id))) | (((X175 @ id @ (X183 @ id @ X187) @ id)) = $true))) | ($true = ((X175 @ id @ X174 @ id))) | ~ ! [X188 : subst,X189 : term,X190 : subst,X191 : subst] : (($true = ((X175 @ X188 @ X189 @ (comp @ X191 @ X190)))) | ~ ($true = ((X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190)))))))) <=> (hoasinduction_lthm = $true)) & (axabs = $true) & (! [X192 : (subst > term > subst > $o),X193 : term] : (~ ! [X194 : term,X195 : term] : (~ ($true = ((X192 @ id @ X195 @ id))) | ~ ($true = ((X192 @ id @ X194 @ id))) | (((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) = $true)) | (((X192 @ id @ X193 @ id)) = $true) | ~ ! [X196 : (subst > term > term)] : (($true = ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ~ ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197))) | ~ ! [X200 : term] : ((((X192 @ id @ (X196 @ id @ X200) @ id)) = $true) | ~ ($true = ((X192 @ id @ X200 @ id)))))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X202 : (subst > term > term),X203 : term,X201 : term] : (~ ! [X204 : term,X205 : subst,X206 : subst] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) = ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((! [X207 : (subst > term > subst > $o)] : ~ ! [X208 : (term > $o)] : ~ ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))) => (! [X210 : (term > $o),X211 : term] : (~ ! [X212 : term] : (~ ($true = ((var @ X212))) | ($true = ((X210 @ X212)))) | ($true = ((X210 @ X211))) | ~ ! [X213 : term,X214 : term] : (~ ($true = ((X210 @ X213))) | ~ ($true = ((X210 @ X214))) | ($true = ((X210 @ (ap @ X213 @ X214))))) | ~ ! [X215 : term] : ((((X210 @ (lam @ X215))) = $true) | ~ ! [X216 : term] : ((((X210 @ (sub @ X215 @ (push @ X216 @ id)))) = $true) | ~ ($true = ((X210 @ X216)))))) => (! [X217 : term] : (((sub @ X217 @ id)) = X217) => (! [X218 : (subst > term > subst > $o),X219 : term,X220 : (term > $o)] : (~ ! [X221 : term] : (~ ($true = ((X220 @ X221))) | ($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id)))))) | ~ ! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) | (((X220 @ (lam @ X219))) = $true) | ~ ! [X223 : (subst > term > term)] : (($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id))) | ~ ! [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) = $true) | ~ ($true = ((X218 @ id @ X224 @ id)))) | ~ ! [X225 : subst,X227 : term,X226 : subst] : (((sub @ (X223 @ X225 @ X227) @ X226)) = ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))))) => ! [X228 : term,X229 : (subst > term > subst > $o)] : (($true = ((X229 @ id @ X228 @ id))) | ~ ! [X230 : term,X231 : term] : (~ (((X229 @ id @ X230 @ id)) = $true) | (((X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id)) = $true) | ~ (((X229 @ id @ X231 @ id)) = $true)) | ~ ! [X232 : subst,X233 : subst,X234 : term,X235 : subst] : ((((X229 @ X233 @ X234 @ (comp @ X235 @ X232))) = $true) | ~ (((X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) = $true)) | ~ ! [X236 : term,X237 : subst,X238 : subst,X239 : subst] : (~ ($true = ((X229 @ X238 @ X236 @ (comp @ X239 @ X237)))) | ($true = ((X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237)))) | ~ ! [X240 : term] : (~ ($true = ((var @ (sub @ X240 @ id)))) | ($true = ((X229 @ id @ X240 @ id)))) | ~ ! [X241 : (subst > term > term)] : (~ ! [X244 : term,X243 : subst,X242 : subst] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242))) | ($true = ((X229 @ id @ (lam @ (X241 @ sh @ one)) @ id))) | ~ ! [X245 : term] : (($true = ((X229 @ id @ (X241 @ id @ X245) @ id))) | ~ ($true = ((X229 @ id @ X245 @ id)))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((apinj2 = $true) <=> ! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247))))) & (sh = ((d2subst @ d_id))) & (lamnotvar = $true) & ((induction2lem_lthm = $true) <=> (! [X250 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X250))) = X251) => (! [X253 : subst,X252 : term] : (((comp @ sh @ (push @ X252 @ X253))) = X253) => (! [X254 : subst] : (((comp @ X254 @ id)) = X254) => (! [X255 : term,X256 : (term > $o)] : (~ ! [X257 : term] : (~ (((var @ X257)) = $true) | (((X256 @ X257)) = $true)) | (((X256 @ X255)) = $true) | ~ ! [X258 : term] : (($true = ((X256 @ (lam @ X258)))) | ~ ($true = ((X256 @ X258)))) | ~ ! [X259 : term,X260 : term] : (($true = ((X256 @ (ap @ X260 @ X259)))) | ~ ($true = ((X256 @ X260))) | ~ ($true = ((X256 @ X259))))) => ! [X261 : (term > $o),X262 : subst,X263 : term] : (~ ! [X264 : term,X265 : term] : (~ ($true = ((X261 @ X265))) | ~ (((X261 @ X264)) = $true) | ($true = ((X261 @ (ap @ X265 @ X264))))) | ~ ! [X266 : term] : ((((X261 @ (sub @ X266 @ X262))) = $true) | ~ (((var @ X266)) = $true)) | ($true = ((X261 @ (sub @ X263 @ X262)))) | ~ ! [X267 : term] : (($true = ((X261 @ (lam @ X267)))) | ~ ! [X268 : term] : ((((X261 @ (sub @ X267 @ (push @ X268 @ id)))) = $true) | ~ ($true = ((X261 @ X268))))))))))) & ((hoaslaminj = $true) <=> ! [X271 : term,X270 : subst,X269 : (subst > term > term),X272 : (subst > term > term)] : (~ ! [X276 : subst,X277 : subst,X278 : term] : (((sub @ (X269 @ X277 @ X278) @ X276)) = ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276)))) | (((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ~ ! [X273 : subst,X275 : term,X274 : subst] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) = ((sub @ (X272 @ X273 @ X275) @ X274))))) & ! [X279 : d_subst,X280 : d_subst] : ((((d2subst @ X280)) = ((d2subst @ X279))) => (X279 = X280)) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((axvarcons = $true) <=> ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & ~ (lamnotap = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((pushprop_lem1v2 = $true) <=> ! [X283 : (term > $o),X284 : term,X285 : (term > $o),X286 : subst] : (~ ($true = ((X285 @ X284))) | ~ ! [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) = ((X283 @ X287))) | ($true = ((X283 @ one))))) & ((induction2 = $true) <=> ! [X288 : (term > $o),X289 : term] : (~ ! [X290 : term,X291 : term] : (~ (((X288 @ X291)) = $true) | ~ ($true = ((X288 @ X290))) | ($true = ((X288 @ (ap @ X291 @ X290))))) | ($true = ((X288 @ X289))) | ~ ! [X292 : term] : (~ ! [X293 : term] : (($true = ((X288 @ (sub @ X292 @ (push @ X293 @ id))))) | ~ ($true = ((X288 @ X293)))) | ($true = ((X288 @ (lam @ X292))))) | ~ ! [X294 : term] : ((((X288 @ X294)) = $true) | ~ ($true = ((var @ X294)))))) & (hoaslamnotvar = $true) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) <=> (substmonoid = $true)) & (axmap = $true) & ((! [X297 : (subst > term > subst > $o)] : ~ ! [X298 : (term > $o)] : ~ ! [X299 : term] : (((X298 @ X299)) = ((X297 @ id @ X299 @ id))) => (! [X300 : term,X301 : (term > $o)] : ((((X301 @ X300)) = $true) | ~ ! [X302 : term] : ((((X301 @ (lam @ X302))) = $true) | ~ ! [X303 : term] : (~ ($true = ((X301 @ X303))) | ($true = ((X301 @ (sub @ X302 @ (push @ X303 @ id))))))) | ~ ! [X304 : term] : (~ (((var @ X304)) = $true) | (((X301 @ X304)) = $true)) | ~ ! [X305 : term,X306 : term] : (~ ($true = ((X301 @ X305))) | ~ ($true = ((X301 @ X306))) | ($true = ((X301 @ (ap @ X305 @ X306)))))) => (! [X307 : term] : (((sub @ X307 @ id)) = X307) => (! [X308 : term,X309 : (term > $o),X310 : (subst > term > subst > $o)] : (($true = ((X309 @ (lam @ X308)))) | ~ ! [X311 : (subst > term > term)] : (($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ~ ! [X312 : term] : (($true = ((X310 @ id @ (X311 @ id @ X312) @ id))) | ~ ($true = ((X310 @ id @ X312 @ id)))) | ~ ! [X315 : subst,X313 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) = ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) | ~ ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))) | ~ ! [X317 : term] : (~ ($true = ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true))) => ! [X318 : term,X319 : (subst > term > subst > $o)] : (~ ! [X320 : term,X321 : term] : (($true = ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id))) | ~ (((X319 @ id @ X320 @ id)) = $true) | ~ ($true = ((X319 @ id @ X321 @ id)))) | ($true = ((X319 @ id @ X318 @ id))) | ~ ! [X322 : (subst > term > term)] : ((((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id)) = $true) | ~ ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) | ~ ! [X326 : term] : ((((X319 @ id @ (X322 @ id @ X326) @ id)) = $true) | ~ ($true = ((X319 @ id @ X326 @ id)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ! [X327 : d_subst] : (d_id = X327) & (! [X328 : term,X329 : subst,X330 : (term > $o),X331 : (term > $o),X332 : term] : ((((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true) | ~ ($true = ((X330 @ X332)))) <=> (pushprop_lem1 = $true)) & (pushprop_lem1_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (! [X335 : subst] : (((comp @ id @ X335)) = X335) <=> (axidl = $true)) & (axapp = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X336 : term,X337 : subst] : (((sub @ one @ (push @ X336 @ X337))) = X336) => ! [X338 : subst,X339 : term,X340 : (term > $o),X341 : (term > $o)] : (~ ($true = ((X340 @ X339))) | ~ ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X339 @ X338)))) = ((X341 @ X342))) | (((X341 @ one)) = $true)))) & (induction2lem_gthm = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X343 : (term > $o),X344 : term,X345 : (subst > term > subst > $o)] : ((((X343 @ (lam @ X344))) = $true) | ~ ! [X346 : term] : (((X343 @ X346)) = ((X345 @ id @ X346 @ id))) | ~ ! [X347 : (subst > term > term)] : (~ ! [X348 : subst,X349 : subst,X350 : term] : (((sub @ (X347 @ X349 @ X350) @ X348)) = ((X347 @ (comp @ X349 @ X348) @ (sub @ X350 @ X348)))) | (((X345 @ id @ (lam @ (X347 @ sh @ one)) @ id)) = $true) | ~ ! [X351 : term] : (($true = ((X345 @ id @ (X347 @ id @ X351) @ id))) | ~ ($true = ((X345 @ id @ X351 @ id))))) | ~ ! [X352 : term] : (($true = ((X343 @ (sub @ X344 @ (push @ X352 @ id))))) | ~ (((X343 @ X352)) = $true))) <=> (hoasinduction_lem3v2a = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((induction = $true) <=> ! [X353 : term,X354 : (term > $o)] : (~ ! [X355 : term] : (($true = ((X354 @ (lam @ X355)))) | ~ ($true = ((X354 @ X355)))) | ~ ! [X356 : term] : (~ ($true = ((var @ X356))) | ($true = ((X354 @ X356)))) | ~ ! [X357 : term,X358 : term] : (~ ($true = ((X354 @ X358))) | ~ ($true = ((X354 @ X357))) | (((X354 @ (ap @ X358 @ X357))) = $true)) | (((X354 @ X353)) = $true))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X359 : (subst > term > subst > $o),X360 : term] : (~ ! [X361 : term] : (~ (((X359 @ id @ X361 @ id)) = $true) | ($true = ((X359 @ id @ (sub @ X360 @ (push @ X361 @ id)) @ id)))) | ~ ! [X362 : (subst > term > term)] : (~ ! [X363 : subst,X364 : subst,X365 : term] : (((sub @ (X362 @ X364 @ X365) @ X363)) = ((X362 @ (comp @ X364 @ X363) @ (sub @ X365 @ X363)))) | ~ ! [X366 : term] : ((((X359 @ id @ (X362 @ id @ X366) @ id)) = $true) | ~ ($true = ((X359 @ id @ X366 @ id)))) | ($true = ((X359 @ id @ (lam @ (X362 @ sh @ one)) @ id)))) | (((X359 @ id @ (lam @ (sub @ X360 @ (push @ one @ sh))) @ id)) = $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1v2 = $true) & ! [X370 : term] : ? [X371 : d_term] : (((d2term @ X371)) = X370) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoaslaminj_gthm = $true) & (! [X372 : (subst > term > subst > $o)] : ~ ! [X373 : (term > $o)] : ~ ! [X374 : term] : (((X372 @ id @ X374 @ id)) = ((X373 @ X374))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2_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)))))))))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X380 : term] : (((sub @ X380 @ id)) = X380) => ! [X381 : (term > $o),X382 : (subst > term > subst > $o),X383 : term] : (~ ! [X384 : term] : (((X381 @ X384)) = ((X382 @ id @ X384 @ id))) | ~ ! [X385 : subst,X386 : term,X387 : subst,X388 : subst] : (~ (((X382 @ (comp @ X385 @ X388) @ (sub @ X386 @ X388) @ X387)) = $true) | (((X382 @ X385 @ X386 @ (comp @ X388 @ X387))) = $true)) | ~ ! [X389 : (subst > term > term)] : (~ ! [X390 : term] : (~ ($true = ((X382 @ id @ X390 @ id))) | (((X382 @ id @ (X389 @ id @ X390) @ id)) = $true)) | ~ ! [X391 : term,X392 : subst,X393 : subst] : (((sub @ (X389 @ X392 @ X391) @ X393)) = ((X389 @ (comp @ X392 @ X393) @ (sub @ X391 @ X393)))) | ($true = ((X382 @ id @ (lam @ (X389 @ sh @ one)) @ id)))) | (((X381 @ (lam @ X383))) = $true) | ~ ! [X394 : subst,X395 : subst,X396 : term,X397 : subst] : (~ (((X382 @ X395 @ X396 @ (comp @ X397 @ X394))) = $true) | ($true = ((X382 @ (comp @ X395 @ X397) @ (sub @ X396 @ X397) @ X394)))) | ~ ! [X398 : term] : (($true = ((X381 @ (sub @ X383 @ (push @ X398 @ id))))) | ~ (((X381 @ X398)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (((d2term @ d_one)) = one) & (! [X399 : term,X400 : (term > $o),X401 : subst] : ~ ! [X402 : (term > $o)] : ~ ! [X403 : term] : (((X402 @ X403)) = ((X400 @ (sub @ X403 @ (push @ X399 @ X401))))) <=> (pushprop_lem0 = $true)) & ((! [X404 : term] : ~ ! [X405 : (subst > term > term)] : ~ ! [X406 : term,X407 : subst] : (((sub @ X404 @ (push @ X406 @ X407))) = ((X405 @ X407 @ X406))) => (! [X408 : term] : (((sub @ X408 @ id)) = X408) => ! [X409 : (term > $o),X410 : term,X411 : (subst > term > subst > $o)] : (~ ! [X412 : term] : (($true = ((X409 @ (sub @ X410 @ (push @ X412 @ id))))) | ~ (((X409 @ X412)) = $true)) | ~ ! [X413 : term] : (((X409 @ X413)) = ((X411 @ id @ X413 @ id))) | ($true = ((X409 @ (lam @ X410)))) | ~ ! [X414 : (subst > term > term)] : (($true = ((X411 @ id @ (lam @ (X414 @ sh @ one)) @ id))) | ~ ! [X415 : term,X416 : subst,X417 : subst] : (((sub @ (X414 @ X417 @ X415) @ X416)) = ((X414 @ (comp @ X417 @ X416) @ (sub @ X415 @ X416)))) | ~ ! [X418 : term] : (~ ($true = ((X411 @ id @ X418 @ id))) | ($true = ((X411 @ id @ (X414 @ id @ X418) @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X419 : term] : ~ ! [X420 : (subst > term > term)] : ~ ! [X421 : term,X422 : subst] : (((X420 @ X422 @ X421)) = ((sub @ X419 @ (push @ X421 @ X422)))) <=> (hoasinduction_lem3v2_f = $true)) & ((laminj = $true) <=> ! [X423 : term,X424 : term] : ((((lam @ X424)) != ((lam @ X423))) | (X423 = X424))) & ((! [X425 : term,X426 : term,X427 : term,X428 : term] : ((((ap @ X426 @ X428)) != ((ap @ X427 @ X425))) | (X425 = X428)) => ! [X429 : term,X430 : term,X431 : term,X432 : term] : ((((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X429 @ id) @ X432))) | (X430 = X432))) <=> (hoasapinj2_lthm = $true)) & ((! [X433 : term] : (((sub @ X433 @ id)) = X433) => (! [X434 : term,X435 : term,X436 : term,X437 : term] : ((((ap @ X437 @ X435)) != ((ap @ X436 @ X434))) | (X436 = X437)) => ! [X438 : term,X439 : term,X440 : term,X441 : term] : ((X438 = X441) | (((ap @ (sub @ X438 @ id) @ X439)) != ((ap @ (sub @ X441 @ id) @ X440)))))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ~ (ulamvar1 = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & (hoasapinj2_gthm = $true) & (pushprop_lem3v2 = $true) & (! [X442 : term] : ~ ! [X443 : (subst > term > term)] : ~ ! [X444 : subst,X445 : term] : (((X443 @ X444 @ X445)) = ((sub @ X442 @ (push @ X445 @ X444)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((apinj1 = $true) <=> ! [X446 : term,X447 : term,X448 : term,X449 : term] : ((((ap @ X448 @ X447)) != ((ap @ X446 @ X449))) | (X446 = X448))) & (hoasinduction_lem1_gthm = $true) & (! [X450 : term,X451 : (subst > term > subst > $o)] : (~ ! [X452 : term,X453 : term] : (~ ($true = ((X451 @ id @ X453 @ id))) | (((X451 @ id @ (ap @ (sub @ X453 @ id) @ X452) @ id)) = $true) | ~ (((X451 @ id @ X452 @ id)) = $true)) | ~ ! [X454 : subst,X455 : subst,X456 : term,X457 : subst] : ((((X451 @ (comp @ X454 @ X455) @ (sub @ X456 @ X455) @ X457)) = $true) | ~ ($true = ((X451 @ X454 @ X456 @ (comp @ X455 @ X457))))) | (((X451 @ id @ X450 @ id)) = $true) | ~ ! [X458 : (subst > term > term)] : (($true = ((X451 @ id @ (lam @ (X458 @ sh @ one)) @ id))) | ~ ! [X459 : term] : (~ ($true = ((X451 @ id @ X459 @ id))) | ($true = ((X451 @ id @ (X458 @ id @ X459) @ id)))) | ~ ! [X460 : term,X461 : subst,X462 : subst] : (((X458 @ (comp @ X462 @ X461) @ (sub @ X460 @ X461))) = ((sub @ (X458 @ X462 @ X460) @ X461)))) | ~ ! [X463 : term] : (($true = ((X451 @ id @ X463 @ id))) | ~ (((var @ (sub @ X463 @ id))) = $true)) | ~ ! [X464 : subst,X465 : term,X466 : subst,X467 : subst] : (~ ($true = ((X451 @ (comp @ X466 @ X467) @ (sub @ X465 @ X467) @ X464))) | ($true = ((X451 @ X466 @ X465 @ (comp @ X467 @ X464)))))) <=> (hoasinduction = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X468 : term,X469 : (subst > term > subst > $o)] : (~ ! [X470 : (subst > term > term)] : (~ ! [X471 : subst,X472 : subst,X473 : term] : (((X470 @ (comp @ X472 @ X471) @ (sub @ X473 @ X471))) = ((sub @ (X470 @ X472 @ X473) @ X471))) | ~ ! [X474 : term] : (~ ($true = ((X469 @ id @ X474 @ id))) | (((X469 @ id @ (X470 @ id @ X474) @ id)) = $true)) | ($true = ((X469 @ id @ (lam @ (X470 @ sh @ one)) @ id)))) | ~ ! [X475 : term] : (($true = ((X469 @ id @ (sub @ X468 @ (push @ X475 @ id)) @ id))) | ~ ($true = ((X469 @ id @ X475 @ id)))) | (((X469 @ id @ (lam @ X468) @ id)) = $true))) & (pushprop = $true) & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) => (! [X477 : (subst > term > subst > $o),X478 : term] : (~ ! [X479 : term] : (~ (((X477 @ id @ X479 @ id)) = $true) | ($true = ((X477 @ id @ (sub @ X478 @ (push @ X479 @ id)) @ id)))) | ~ ! [X480 : (subst > term > term)] : (~ ! [X481 : term,X482 : subst,X483 : subst] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X481 @ X482))) = ((sub @ (X480 @ X483 @ X481) @ X482))) | ~ ! [X484 : term] : ((((X477 @ id @ (X480 @ id @ X484) @ id)) = $true) | ~ ($true = ((X477 @ id @ X484 @ id)))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id)))) | ($true = ((X477 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)))) => ! [X485 : (subst > term > subst > $o),X486 : term] : (($true = ((X485 @ id @ (lam @ X486) @ id))) | ~ ! [X487 : term] : ((((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id)) = $true) | ~ ($true = ((X485 @ id @ X487 @ id)))) | ~ ! [X488 : (subst > term > term)] : ((((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id)) = $true) | ~ ! [X489 : subst,X490 : term,X491 : subst] : (((X488 @ (comp @ X491 @ X489) @ (sub @ X490 @ X489))) = ((sub @ (X488 @ X491 @ X490) @ X489))) | ~ ! [X492 : term] : (~ ($true = ((X485 @ id @ X492 @ id))) | (((X485 @ id @ (X488 @ id @ X492) @ id)) = $true)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X493 : (subst > term > subst > $o),X494 : term] : (($true = ((X493 @ id @ (lam @ (sub @ X494 @ (push @ one @ sh))) @ id))) | ~ ! [X495 : term] : (~ ($true = ((X493 @ id @ X495 @ id))) | ($true = ((X493 @ id @ (sub @ X494 @ (push @ X495 @ id)) @ id)))) | ~ ! [X496 : (subst > term > term)] : (~ ! [X497 : term] : (~ (((X493 @ id @ X497 @ id)) = $true) | ($true = ((X493 @ id @ (X496 @ id @ X497) @ id)))) | ($true = ((X493 @ id @ (lam @ (X496 @ sh @ one)) @ id))) | ~ ! [X498 : subst,X499 : term,X500 : subst] : (((X496 @ (comp @ X500 @ X498) @ (sub @ X499 @ X498))) = ((sub @ (X496 @ X500 @ X499) @ X498))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasapinj1 = $true) <=> ! [X501 : term,X502 : term,X503 : term,X504 : term] : ((((ap @ (sub @ X503 @ id) @ X501)) != ((ap @ (sub @ X502 @ id) @ X504))) | (X502 = X503))) & ! [X505 : d_term] : (d_one = X505) & (! [X506 : subst] : (((comp @ X506 @ id)) = X506) <=> (axidr = $true)) & (! [X507 : subst] : (((push @ (sub @ one @ X507) @ (comp @ sh @ X507))) = X507) <=> (axscons = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X508 : term] : ~ ! [X509 : (subst > term > term)] : (((sub @ X508 @ (push @ one @ sh))) != ((X509 @ sh @ one)))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (termmset_gthm = $true) & (induction2_gthm = $true) & (! [X510 : subst,X511 : term,X512 : (term > $o)] : ~ ! [X513 : (term > $o)] : ~ ! [X514 : term] : (((X513 @ X514)) = ((X512 @ (sub @ X514 @ (push @ X511 @ X510))))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (axassoc = $true) & (pushprop_lem2v2_lthm = $true) & ((! [X515 : term,X516 : subst] : (((sub @ one @ (push @ X515 @ X516))) = X515) => (! [X517 : term,X518 : subst] : (((comp @ sh @ (push @ X517 @ X518))) = X518) => ! [X519 : (term > $o),X520 : term,X521 : (term > $o),X522 : term,X523 : subst] : ((((X519 @ (sub @ X522 @ (push @ X520 @ X523)))) = $true) | ~ ($true = ((X521 @ X522)))))) <=> (pushprop_lem1_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X524 : term,X525 : (term > $o),X526 : (subst > term > subst > $o)] : ((((X525 @ (lam @ X524))) = $true) | ~ ! [X527 : subst,X528 : term,X529 : subst,X530 : subst] : ((((X526 @ (comp @ X530 @ X527) @ (sub @ X528 @ X527) @ X529)) = $true) | ~ ($true = ((X526 @ X530 @ X528 @ (comp @ X527 @ X529))))) | ~ ! [X531 : term] : (((X525 @ X531)) = ((X526 @ id @ X531 @ id))) | ~ ! [X532 : (subst > term > term)] : (~ ! [X533 : term,X534 : subst,X535 : subst] : (((X532 @ (comp @ X535 @ X534) @ (sub @ X533 @ X534))) = ((sub @ (X532 @ X535 @ X533) @ X534))) | ~ ! [X536 : term] : (~ ($true = ((X526 @ id @ X536 @ id))) | ($true = ((X526 @ id @ (X532 @ id @ X536) @ id)))) | ($true = ((X526 @ id @ (lam @ (X532 @ sh @ one)) @ id)))) | ~ ! [X537 : term] : (~ (((X525 @ X537)) = $true) | (((X525 @ (sub @ X524 @ (push @ X537 @ id)))) = $true)) | ~ ! [X538 : term,X539 : subst,X540 : subst,X541 : subst] : (~ (((X526 @ (comp @ X541 @ X540) @ (sub @ X538 @ X540) @ X539)) = $true) | ($true = ((X526 @ X541 @ X538 @ (comp @ X540 @ X539))))))) & (! [X542 : term,X543 : subst,X544 : (term > $o)] : (($true = ((X544 @ (sub @ X542 @ X543)))) | ~ ! [X545 : term,X546 : term] : (~ (((X544 @ X545)) = $true) | ($true = ((X544 @ (ap @ X546 @ X545)))) | ~ ($true = ((X544 @ X546)))) | ~ ! [X547 : term] : ((((X544 @ (sub @ X547 @ X543))) = $true) | ~ (((var @ X547)) = $true)) | ~ ! [X548 : term] : (~ ! [X549 : term] : (~ (((X544 @ X549)) = $true) | (((X544 @ (sub @ X548 @ (push @ X549 @ id)))) = $true)) | ($true = ((X544 @ (lam @ X548)))))) <=> (induction2lem = $true))), 0.43/0.52 inference(fool_elimination,[],[f6])). 0.43/0.52 thf(f8,plain,( 0.43/0.52 ! [X0 : d_term,X1 : d_term] : ((((d2term @ X0)) = ((d2term @ X1))) => (X0 = X1)) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> (axvarid = $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X3 : term,X4 : term,X5 : (subst > term > subst > $o)] : (~ ($true = ((X5 @ id @ X3 @ id))) | ~ ($true = ((X5 @ id @ X4 @ id))) | ~ ! [X6 : subst,X7 : term,X8 : subst,X9 : subst] : ((((X5 @ X9 @ X7 @ (comp @ X8 @ X6))) = $true) | ~ ($true = ((X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6)))) | ~ ! [X10 : term,X11 : term] : (~ ($true = ((X5 @ id @ X11 @ id))) | ~ (((X5 @ id @ X10 @ id)) = $true) | ($true = ((X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id)))) | ~ ! [X12 : term,X13 : subst,X14 : subst,X15 : subst] : (~ (((X5 @ X15 @ X12 @ (comp @ X13 @ X14))) = $true) | (((X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) = $true)) | (((X5 @ id @ (ap @ X4 @ X3) @ id)) = $true))) & (hoasapnotvar_lthm = $true) & ((! [X16 : term] : (((sub @ X16 @ id)) = X16) => (! [X17 : (subst > term > subst > $o),X18 : term] : (($true = ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id))) | ~ ! [X19 : term] : (~ ($true = ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) | ~ ! [X20 : (subst > term > term)] : (~ ! [X21 : subst,X22 : subst,X23 : term] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) = ((sub @ (X20 @ X22 @ X23) @ X21))) | ($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ~ ! [X24 : term] : ((((X17 @ id @ (X20 @ id @ X24) @ id)) = $true) | ~ ($true = ((X17 @ id @ X24 @ id)))))) => ! [X25 : term,X26 : (subst > term > subst > $o)] : (~ ! [X27 : subst,X28 : term,X29 : subst,X30 : subst] : (($true = ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29))) | ~ (((X26 @ X30 @ X28 @ (comp @ X27 @ X29))) = $true)) | ~ ! [X31 : (subst > term > term)] : (~ ! [X32 : subst,X34 : term,X33 : subst] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32))) | ~ ! [X35 : term] : (~ ($true = ((X26 @ id @ X35 @ id))) | ($true = ((X26 @ id @ (X31 @ id @ X35) @ id)))) | ($true = ((X26 @ id @ (lam @ (X31 @ sh @ one)) @ id)))) | ~ ! [X36 : subst,X37 : term,X38 : subst,X39 : subst] : (($true = ((X26 @ X38 @ X37 @ (comp @ X36 @ X39)))) | ~ ($true = ((X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39)))) | ($true = ((X26 @ id @ (lam @ X25) @ id))) | ~ ! [X40 : term] : ((((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id)) = $true) | ~ (((X26 @ id @ X40 @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasapnotvar_gthm = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X41 : (subst > term > subst > $o)] : ~ ! [X42 : (term > $o)] : ~ ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43)))) & ~ (((var @ (d2term @ d_one))) = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_lthm_orig = $true) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (axvarshift = $true) & (! [X44 : (subst > term > subst > $o),X45 : (term > $o),X46 : term,X47 : term] : (~ ! [X48 : term,X49 : term] : (($true = ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id))) | ~ ($true = ((X44 @ id @ X49 @ id))) | ~ ($true = ((X44 @ id @ X48 @ id)))) | ~ ! [X50 : subst,X51 : subst,X52 : subst,X53 : term] : (~ ($true = ((X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52))) | (((X44 @ X50 @ X53 @ (comp @ X51 @ X52))) = $true)) | ~ ! [X54 : term] : (((X44 @ id @ X54 @ id)) = ((X45 @ X54))) | (((X45 @ (ap @ X46 @ X47))) = $true) | ~ ! [X55 : subst,X56 : subst,X57 : subst,X58 : term] : (($true = ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56))) | ~ ($true = ((X44 @ X57 @ X58 @ (comp @ X55 @ X56))))) | ~ ($true = ((X45 @ X46))) | ~ ($true = ((X45 @ X47)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) <=> (axshiftcons = $true)) & ((! [X61 : term] : (((sub @ X61 @ id)) = X61) => (! [X62 : term,X63 : (term > $o),X64 : subst] : (~ ! [X65 : term] : (($true = ((X63 @ (sub @ X65 @ X64)))) | ~ (((var @ X65)) = $true)) | ~ ! [X66 : term,X67 : term] : (($true = ((X63 @ (ap @ X66 @ X67)))) | ~ ($true = ((X63 @ X67))) | ~ ($true = ((X63 @ X66)))) | ~ ! [X68 : term] : (~ ! [X69 : term] : (($true = ((X63 @ (sub @ X68 @ (push @ X69 @ id))))) | ~ ($true = ((X63 @ X69)))) | ($true = ((X63 @ (lam @ X68))))) | (((X63 @ (sub @ X62 @ X64))) = $true)) => ! [X70 : (term > $o),X71 : term] : (~ ! [X72 : term] : ((((X70 @ (lam @ X72))) = $true) | ~ ! [X73 : term] : (($true = ((X70 @ (sub @ X72 @ (push @ X73 @ id))))) | ~ ($true = ((X70 @ X73))))) | ~ ! [X74 : term,X75 : term] : (~ ($true = ((X70 @ X75))) | (((X70 @ (ap @ X75 @ X74))) = $true) | ~ ($true = ((X70 @ X74)))) | ($true = ((X70 @ X71))) | ~ ! [X76 : term] : (~ (((var @ X76)) = $true) | ($true = ((X70 @ X76))))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X77 : (subst > term > subst > $o),X78 : term] : (($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ~ ! [X79 : (subst > term > term),X80 : term] : (~ ! [X81 : term] : ((((X77 @ id @ (X79 @ id @ X81) @ id)) = $true) | ~ ($true = ((X77 @ id @ X81 @ id)))) | ~ ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))) | ($true = ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) | ~ ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87))))) | ~ ! [X88 : term] : (($true = ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id))) | ~ (((X77 @ id @ X88 @ id)) = $true)))) & (pushprop_lthm = $true) & (hoasinduction_gthm = $true) & (id = ((d2subst @ d_id))) & ((shinj = $true) <=> ! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh))))) & ((termmset_lthm = $true) <=> (! [X91 : term] : (((sub @ X91 @ id)) = X91) => ! [X92 : term] : (((sub @ X92 @ id)) = X92))) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & ((termmset = $true) <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) <=> (hoasapinj2 = $true)) & (hoasapinj1_gthm = $true) & ((! [X100 : term,X101 : subst] : (((sub @ one @ (push @ X100 @ X101))) = X100) => (! [X103 : subst,X102 : term] : (((comp @ sh @ (push @ X102 @ X103))) = X103) => (! [X104 : term,X105 : term] : ((((lam @ X104)) != ((lam @ X105))) | (X104 = X105)) => ! [X107 : (subst > term > term),X108 : (subst > term > term),X109 : subst,X106 : term] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ~ ! [X115 : subst,X114 : subst,X113 : term] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) = ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one)))) | ~ ! [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) = ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))))))) <=> (hoaslaminj_lthm = $true)) & ((! [X116 : subst] : (((comp @ id @ X116)) = X116) => (! [X117 : subst] : (((comp @ X117 @ id)) = X117) => (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X122 : term,X123 : subst,X124 : subst,X125 : subst] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) = $true) | ~ ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id))) | ~ ! [X126 : term] : (~ ($true = ((X121 @ id @ X126 @ id))) | ($true = ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id)))) | ~ ! [X127 : (subst > term > term)] : (($true = ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id))) | ~ ! [X130 : subst,X129 : subst,X128 : term] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) | ~ ! [X131 : term] : ((((X121 @ id @ (X127 @ id @ X131) @ id)) = $true) | ~ (((X121 @ id @ X131 @ id)) = $true))) | ~ ! [X132 : term,X133 : subst,X134 : subst,X135 : subst] : (~ (((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) | (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) = $true)))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : (((X137 @ sh @ one)) != ((sub @ X136 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X138 : term,X139 : (term > $o)] : ((((X139 @ X138)) = $true) | ~ ! [X140 : term] : (($true = ((X139 @ X140))) | ~ ($true = ((var @ X140)))) | ~ ! [X141 : term,X142 : term] : (~ ($true = ((X139 @ X142))) | ~ (((X139 @ X141)) = $true) | ($true = ((X139 @ (ap @ X142 @ X141))))) | ~ ! [X143 : term] : (($true = ((X139 @ (lam @ X143)))) | ~ ! [X144 : term] : (~ ($true = ((X139 @ X144))) | (((X139 @ (sub @ X143 @ (push @ X144 @ id)))) = $true)))) => (! [X145 : term,X146 : (subst > term > subst > $o),X147 : term] : (~ ($true = ((X146 @ id @ X147 @ id))) | ($true = ((X146 @ id @ (ap @ X145 @ X147) @ id))) | ~ ! [X148 : subst,X149 : term,X150 : subst,X151 : subst] : (($true = ((X146 @ X151 @ X149 @ (comp @ X148 @ X150)))) | ~ ($true = ((X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150)))) | ~ (((X146 @ id @ X145 @ id)) = $true) | ~ ! [X152 : term,X153 : subst,X154 : subst,X155 : subst] : (($true = ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154))) | ~ (((X146 @ X153 @ X152 @ (comp @ X155 @ X154))) = $true)) | ~ ! [X156 : term,X157 : term] : ((((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id)) = $true) | ~ (((X146 @ id @ X157 @ id)) = $true) | ~ ($true = ((X146 @ id @ X156 @ id))))) => (! [X158 : (subst > term > subst > $o),X159 : term] : (~ ! [X160 : (subst > term > term)] : (~ ! [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) = ((sub @ (X160 @ X163 @ X161) @ X162))) | ~ ! [X164 : term] : (~ (((X158 @ id @ X164 @ id)) = $true) | ($true = ((X158 @ id @ (X160 @ id @ X164) @ id)))) | (((X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) = $true)) | ($true = ((X158 @ id @ (lam @ X159) @ id))) | ~ ! [X165 : term] : ((((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true) | ~ ($true = ((X158 @ id @ X165 @ id)))) | ~ ! [X166 : term,X167 : subst,X168 : subst,X169 : subst] : (~ (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) = $true) | ($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167))))) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | ~ (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) = $true))) => ! [X174 : term,X175 : (subst > term > subst > $o)] : (~ ! [X176 : term] : (~ ($true = ((var @ (sub @ X176 @ id)))) | (((X175 @ id @ X176 @ id)) = $true)) | ~ ! [X177 : term,X178 : subst,X179 : subst,X180 : subst] : ((((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178)) = $true) | ~ ($true = ((X175 @ X179 @ X177 @ (comp @ X180 @ X178))))) | ~ ! [X181 : term,X182 : term] : (~ ($true = ((X175 @ id @ X181 @ id))) | (((X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id)) = $true) | ~ ($true = ((X175 @ id @ X182 @ id)))) | ~ ! [X183 : (subst > term > term)] : (~ ! [X185 : subst,X184 : term,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) | (((X175 @ id @ (lam @ (X183 @ sh @ one)) @ id)) = $true) | ~ ! [X187 : term] : (~ ($true = ((X175 @ id @ X187 @ id))) | (((X175 @ id @ (X183 @ id @ X187) @ id)) = $true))) | ($true = ((X175 @ id @ X174 @ id))) | ~ ! [X188 : subst,X189 : term,X190 : subst,X191 : subst] : (($true = ((X175 @ X188 @ X189 @ (comp @ X191 @ X190)))) | ~ ($true = ((X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190)))))))) <=> (hoasinduction_lthm = $true)) & (axabs = $true) & (! [X192 : (subst > term > subst > $o),X193 : term] : (~ ! [X194 : term,X195 : term] : (~ ($true = ((X192 @ id @ X195 @ id))) | ~ ($true = ((X192 @ id @ X194 @ id))) | (((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) = $true)) | (((X192 @ id @ X193 @ id)) = $true) | ~ ! [X196 : (subst > term > term)] : (($true = ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ~ ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197))) | ~ ! [X200 : term] : ((((X192 @ id @ (X196 @ id @ X200) @ id)) = $true) | ~ ($true = ((X192 @ id @ X200 @ id)))))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X202 : (subst > term > term),X203 : term,X201 : term] : (~ ! [X204 : term,X205 : subst,X206 : subst] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) = ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((! [X207 : (subst > term > subst > $o)] : ~ ! [X208 : (term > $o)] : ~ ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))) => (! [X210 : (term > $o),X211 : term] : (~ ! [X212 : term] : (~ ($true = ((var @ X212))) | ($true = ((X210 @ X212)))) | ($true = ((X210 @ X211))) | ~ ! [X213 : term,X214 : term] : (~ ($true = ((X210 @ X213))) | ~ ($true = ((X210 @ X214))) | ($true = ((X210 @ (ap @ X213 @ X214))))) | ~ ! [X215 : term] : ((((X210 @ (lam @ X215))) = $true) | ~ ! [X216 : term] : ((((X210 @ (sub @ X215 @ (push @ X216 @ id)))) = $true) | ~ ($true = ((X210 @ X216)))))) => (! [X217 : term] : (((sub @ X217 @ id)) = X217) => (! [X218 : (subst > term > subst > $o),X219 : term,X220 : (term > $o)] : (~ ! [X221 : term] : (~ ($true = ((X220 @ X221))) | ($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id)))))) | ~ ! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) | (((X220 @ (lam @ X219))) = $true) | ~ ! [X223 : (subst > term > term)] : (($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id))) | ~ ! [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) = $true) | ~ ($true = ((X218 @ id @ X224 @ id)))) | ~ ! [X225 : subst,X227 : term,X226 : subst] : (((sub @ (X223 @ X225 @ X227) @ X226)) = ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))))) => ! [X228 : term,X229 : (subst > term > subst > $o)] : (($true = ((X229 @ id @ X228 @ id))) | ~ ! [X230 : term,X231 : term] : (~ (((X229 @ id @ X230 @ id)) = $true) | (((X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id)) = $true) | ~ (((X229 @ id @ X231 @ id)) = $true)) | ~ ! [X232 : subst,X233 : subst,X234 : term,X235 : subst] : ((((X229 @ X233 @ X234 @ (comp @ X235 @ X232))) = $true) | ~ (((X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) = $true)) | ~ ! [X236 : term,X237 : subst,X238 : subst,X239 : subst] : (~ ($true = ((X229 @ X238 @ X236 @ (comp @ X239 @ X237)))) | ($true = ((X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237)))) | ~ ! [X240 : term] : (~ ($true = ((var @ (sub @ X240 @ id)))) | ($true = ((X229 @ id @ X240 @ id)))) | ~ ! [X241 : (subst > term > term)] : (~ ! [X244 : term,X243 : subst,X242 : subst] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242))) | ($true = ((X229 @ id @ (lam @ (X241 @ sh @ one)) @ id))) | ~ ! [X245 : term] : (($true = ((X229 @ id @ (X241 @ id @ X245) @ id))) | ~ ($true = ((X229 @ id @ X245 @ id)))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((apinj2 = $true) <=> ! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247))))) & (sh = ((d2subst @ d_id))) & (lamnotvar = $true) & ((induction2lem_lthm = $true) <=> (! [X250 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X250))) = X251) => (! [X253 : subst,X252 : term] : (((comp @ sh @ (push @ X252 @ X253))) = X253) => (! [X254 : subst] : (((comp @ X254 @ id)) = X254) => (! [X255 : term,X256 : (term > $o)] : (~ ! [X257 : term] : (~ (((var @ X257)) = $true) | (((X256 @ X257)) = $true)) | (((X256 @ X255)) = $true) | ~ ! [X258 : term] : (($true = ((X256 @ (lam @ X258)))) | ~ ($true = ((X256 @ X258)))) | ~ ! [X259 : term,X260 : term] : (($true = ((X256 @ (ap @ X260 @ X259)))) | ~ ($true = ((X256 @ X260))) | ~ ($true = ((X256 @ X259))))) => ! [X261 : (term > $o),X262 : subst,X263 : term] : (~ ! [X264 : term,X265 : term] : (~ ($true = ((X261 @ X265))) | ~ (((X261 @ X264)) = $true) | ($true = ((X261 @ (ap @ X265 @ X264))))) | ~ ! [X266 : term] : ((((X261 @ (sub @ X266 @ X262))) = $true) | ~ (((var @ X266)) = $true)) | ($true = ((X261 @ (sub @ X263 @ X262)))) | ~ ! [X267 : term] : (($true = ((X261 @ (lam @ X267)))) | ~ ! [X268 : term] : ((((X261 @ (sub @ X267 @ (push @ X268 @ id)))) = $true) | ~ ($true = ((X261 @ X268))))))))))) & ((hoaslaminj = $true) <=> ! [X271 : term,X270 : subst,X269 : (subst > term > term),X272 : (subst > term > term)] : (~ ! [X276 : subst,X277 : subst,X278 : term] : (((sub @ (X269 @ X277 @ X278) @ X276)) = ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276)))) | (((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ~ ! [X273 : subst,X275 : term,X274 : subst] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) = ((sub @ (X272 @ X273 @ X275) @ X274))))) & ! [X279 : d_subst,X280 : d_subst] : ((((d2subst @ X280)) = ((d2subst @ X279))) => (X279 = X280)) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((axvarcons = $true) <=> ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & ~ (lamnotap = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((pushprop_lem1v2 = $true) <=> ! [X283 : (term > $o),X284 : term,X285 : (term > $o),X286 : subst] : (~ ($true = ((X285 @ X284))) | ~ ! [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) = ((X283 @ X287))) | ($true = ((X283 @ one))))) & ((induction2 = $true) <=> ! [X288 : (term > $o),X289 : term] : (~ ! [X290 : term,X291 : term] : (~ (((X288 @ X291)) = $true) | ~ ($true = ((X288 @ X290))) | ($true = ((X288 @ (ap @ X291 @ X290))))) | ($true = ((X288 @ X289))) | ~ ! [X292 : term] : (~ ! [X293 : term] : (($true = ((X288 @ (sub @ X292 @ (push @ X293 @ id))))) | ~ ($true = ((X288 @ X293)))) | ($true = ((X288 @ (lam @ X292))))) | ~ ! [X294 : term] : ((((X288 @ X294)) = $true) | ~ ($true = ((var @ X294)))))) & (hoaslamnotvar = $true) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) <=> (substmonoid = $true)) & (axmap = $true) & ((! [X297 : (subst > term > subst > $o)] : ~ ! [X298 : (term > $o)] : ~ ! [X299 : term] : (((X298 @ X299)) = ((X297 @ id @ X299 @ id))) => (! [X300 : term,X301 : (term > $o)] : ((((X301 @ X300)) = $true) | ~ ! [X302 : term] : ((((X301 @ (lam @ X302))) = $true) | ~ ! [X303 : term] : (~ ($true = ((X301 @ X303))) | ($true = ((X301 @ (sub @ X302 @ (push @ X303 @ id))))))) | ~ ! [X304 : term] : (~ (((var @ X304)) = $true) | (((X301 @ X304)) = $true)) | ~ ! [X305 : term,X306 : term] : (~ ($true = ((X301 @ X305))) | ~ ($true = ((X301 @ X306))) | ($true = ((X301 @ (ap @ X305 @ X306)))))) => (! [X307 : term] : (((sub @ X307 @ id)) = X307) => (! [X308 : term,X309 : (term > $o),X310 : (subst > term > subst > $o)] : (($true = ((X309 @ (lam @ X308)))) | ~ ! [X311 : (subst > term > term)] : (($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ~ ! [X312 : term] : (($true = ((X310 @ id @ (X311 @ id @ X312) @ id))) | ~ ($true = ((X310 @ id @ X312 @ id)))) | ~ ! [X315 : subst,X313 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) = ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) | ~ ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))) | ~ ! [X317 : term] : (~ ($true = ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true))) => ! [X318 : term,X319 : (subst > term > subst > $o)] : (~ ! [X320 : term,X321 : term] : (($true = ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id))) | ~ (((X319 @ id @ X320 @ id)) = $true) | ~ ($true = ((X319 @ id @ X321 @ id)))) | ($true = ((X319 @ id @ X318 @ id))) | ~ ! [X322 : (subst > term > term)] : ((((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id)) = $true) | ~ ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) | ~ ! [X326 : term] : ((((X319 @ id @ (X322 @ id @ X326) @ id)) = $true) | ~ ($true = ((X319 @ id @ X326 @ id)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ! [X327 : d_subst] : (d_id = X327) & (! [X328 : term,X329 : subst,X330 : (term > $o),X331 : (term > $o),X332 : term] : ((((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true) | ~ ($true = ((X330 @ X332)))) <=> (pushprop_lem1 = $true)) & (pushprop_lem1_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2 = $true) & (! [X333 : subst] : (((comp @ id @ X333)) = X333) <=> (axidl = $true)) & (axapp = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X334 : term,X335 : subst] : (((sub @ one @ (push @ X334 @ X335))) = X334) => ! [X336 : subst,X337 : term,X338 : (term > $o),X339 : (term > $o)] : (~ (((X338 @ X337)) = $true) | ~ ! [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) = ((X339 @ X340))) | ($true = ((X339 @ one)))))) & (induction2lem_gthm = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) = $true) | ~ ! [X344 : term] : (((X343 @ id @ X344 @ id)) = ((X341 @ X344))) | ~ ! [X345 : (subst > term > term)] : (~ ! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) | ($true = ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id))) | ~ ! [X349 : term] : ((((X343 @ id @ (X345 @ id @ X349) @ id)) = $true) | ~ ($true = ((X343 @ id @ X349 @ id))))) | ~ ! [X350 : term] : (($true = ((X341 @ (sub @ X342 @ (push @ X350 @ id))))) | ~ ($true = ((X341 @ X350))))) <=> (hoasinduction_lem3v2a = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((induction = $true) <=> ! [X351 : term,X352 : (term > $o)] : (~ ! [X353 : term] : (($true = ((X352 @ (lam @ X353)))) | ~ ($true = ((X352 @ X353)))) | ~ ! [X354 : term] : (~ ($true = ((var @ X354))) | (((X352 @ X354)) = $true)) | ~ ! [X355 : term,X356 : term] : (~ ($true = ((X352 @ X356))) | ~ ($true = ((X352 @ X355))) | (((X352 @ (ap @ X356 @ X355))) = $true)) | (((X352 @ X351)) = $true))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X357 : (subst > term > subst > $o),X358 : term] : (~ ! [X359 : term] : (~ ($true = ((X357 @ id @ X359 @ id))) | ($true = ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id)))) | ~ ! [X360 : (subst > term > term)] : (~ ! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) | ~ ! [X364 : term] : (($true = ((X357 @ id @ (X360 @ id @ X364) @ id))) | ~ ($true = ((X357 @ id @ X364 @ id)))) | (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) = $true)) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1v2 = $true) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoaslaminj_gthm = $true) & (! [X367 : (subst > term > subst > $o)] : ~ ! [X368 : (term > $o)] : ~ ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2_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)))))))))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X370 : term] : (((sub @ X370 @ id)) = X370) => ! [X371 : (term > $o),X372 : (subst > term > subst > $o),X373 : term] : (~ ! [X374 : term] : (((X371 @ X374)) = ((X372 @ id @ X374 @ id))) | ~ ! [X375 : subst,X376 : term,X377 : subst,X378 : subst] : (~ (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true) | (((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) = $true)) | ~ ! [X379 : (subst > term > term)] : (~ ! [X380 : term] : (~ ($true = ((X372 @ id @ X380 @ id))) | (((X372 @ id @ (X379 @ id @ X380) @ id)) = $true)) | ~ ! [X382 : subst,X383 : subst,X381 : term] : (((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ (X379 @ X382 @ X381) @ X383))) | ($true = ((X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)))) | (((X371 @ (lam @ X373))) = $true) | ~ ! [X384 : subst,X385 : subst,X386 : term,X387 : subst] : (~ ($true = ((X372 @ X385 @ X386 @ (comp @ X387 @ X384)))) | (((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) = $true)) | ~ ! [X388 : term] : (($true = ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) | ~ ($true = ((X371 @ X388)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (((d2term @ d_one)) = one) & ((pushprop_lem0 = $true) <=> ! [X389 : term,X391 : subst,X390 : (term > $o)] : ~ ! [X392 : (term > $o)] : ~ ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393)))) & ((! [X394 : term] : ~ ! [X395 : (subst > term > term)] : ~ ! [X396 : term,X397 : subst] : (((sub @ X394 @ (push @ X396 @ X397))) = ((X395 @ X397 @ X396))) => (! [X398 : term] : (((sub @ X398 @ id)) = X398) => ! [X399 : (term > $o),X400 : term,X401 : (subst > term > subst > $o)] : (~ ! [X402 : term] : (($true = ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) | ~ ($true = ((X399 @ X402)))) | ~ ! [X403 : term] : (((X401 @ id @ X403 @ id)) = ((X399 @ X403))) | (((X399 @ (lam @ X400))) = $true) | ~ ! [X404 : (subst > term > term)] : (($true = ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))) | ~ ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) | ~ ! [X408 : term] : (~ (((X401 @ id @ X408 @ id)) = $true) | ($true = ((X401 @ id @ (X404 @ id @ X408) @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X409 : term] : ~ ! [X410 : (subst > term > term)] : ~ ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411)))) & ((laminj = $true) <=> ! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413))))) & ((! [X416 : term,X415 : term,X418 : term,X417 : term] : ((X415 = X418) | (((ap @ X416 @ X418)) != ((ap @ X417 @ X415)))) => ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422))))) <=> (hoasapinj2_lthm = $true)) & ((! [X423 : term] : (((sub @ X423 @ id)) = X423) => (! [X426 : term,X427 : term,X424 : term,X425 : term] : ((X426 = X427) | (((ap @ X426 @ X424)) != ((ap @ X427 @ X425)))) => ! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar = $true) & ~ (ulamvar1 = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & (hoasapinj2_gthm = $true) & (pushprop_lem3v2 = $true) & (! [X432 : term] : ~ ! [X433 : (subst > term > term)] : ~ ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((apinj1 = $true) <=> ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437))))) & (hoasinduction_lem1_gthm = $true) & (! [X440 : term,X441 : (subst > term > subst > $o)] : (~ ! [X442 : term,X443 : term] : (~ ($true = ((X441 @ id @ X443 @ id))) | ($true = ((X441 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id))) | ~ ($true = ((X441 @ id @ X442 @ id)))) | ~ ! [X444 : subst,X445 : subst,X446 : term,X447 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) = $true) | ~ ($true = ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))) | ($true = ((X441 @ id @ X440 @ id))) | ~ ! [X448 : (subst > term > term)] : ((((X441 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ~ ! [X449 : term] : (~ ($true = ((X441 @ id @ X449 @ id))) | ($true = ((X441 @ id @ (X448 @ id @ X449) @ id)))) | ~ ! [X450 : term,X452 : subst,X451 : subst] : (((X448 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X448 @ X452 @ X450) @ X451)))) | ~ ! [X453 : term] : ((((X441 @ id @ X453 @ id)) = $true) | ~ ($true = ((var @ (sub @ X453 @ id))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : (~ ($true = ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454))) | ($true = ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))))) <=> (hoasinduction = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X458 : term,X459 : (subst > term > subst > $o)] : (~ ! [X460 : (subst > term > term)] : (~ ! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) | ~ ! [X464 : term] : (~ (((X459 @ id @ X464 @ id)) = $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) | ($true = ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))) | ~ ! [X465 : term] : ((((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) = $true) | ~ ($true = ((X459 @ id @ X465 @ id)))) | ($true = ((X459 @ id @ (lam @ X458) @ id))))) & (pushprop = $true) & ((! [X466 : term] : (((sub @ X466 @ id)) = X466) => (! [X467 : (subst > term > subst > $o),X468 : term] : (~ ! [X469 : term] : (~ ($true = ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) | ~ ! [X470 : (subst > term > term)] : (~ ! [X472 : subst,X473 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) = ((sub @ (X470 @ X473 @ X471) @ X472))) | ~ ! [X474 : term] : (($true = ((X467 @ id @ (X470 @ id @ X474) @ id))) | ~ ($true = ((X467 @ id @ X474 @ id)))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true)) | ($true = ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id)))) => ! [X475 : (subst > term > subst > $o),X476 : term] : (($true = ((X475 @ id @ (lam @ X476) @ id))) | ~ ! [X477 : term] : (($true = ((X475 @ id @ (sub @ X476 @ (push @ X477 @ id)) @ id))) | ~ ($true = ((X475 @ id @ X477 @ id)))) | ~ ! [X478 : (subst > term > term)] : ((((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) = $true) | ~ ! [X479 : subst,X480 : term,X481 : subst] : (((sub @ (X478 @ X481 @ X480) @ X479)) = ((X478 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479)))) | ~ ! [X482 : term] : (~ ($true = ((X475 @ id @ X482 @ id))) | ($true = ((X475 @ id @ (X478 @ id @ X482) @ id)))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (substmonoid_gthm = $true) & (ulamvarind = $true) & (! [X483 : (subst > term > subst > $o),X484 : term] : (($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id))) | ~ ! [X485 : term] : (~ ($true = ((X483 @ id @ X485 @ id))) | (((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) = $true)) | ~ ! [X486 : (subst > term > term)] : (~ ! [X487 : term] : (~ (((X483 @ id @ X487 @ id)) = $true) | ($true = ((X483 @ id @ (X486 @ id @ X487) @ id)))) | (((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) = $true) | ~ ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))))) <=> (hoasinduction_lem3aa = $true)) & (! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) <=> (hoasapinj1 = $true)) & ! [X495 : d_term] : (d_one = X495) & ((axidr = $true) <=> ! [X496 : subst] : (((comp @ X496 @ id)) = X496)) & ((axscons = $true) <=> ! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497)) & (! [X498 : term] : ~ ! [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) != ((X499 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (termmset_gthm = $true) & (induction2_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X500 : subst,X502 : (term > $o),X501 : term] : ~ ! [X503 : (term > $o)] : ~ ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & (pushprop_lem1v2_gthm = $true) & (axassoc = $true) & (pushprop_lem2v2_lthm = $true) & ((! [X505 : term,X506 : subst] : (((sub @ one @ (push @ X505 @ X506))) = X505) => (! [X508 : subst,X507 : term] : (((comp @ sh @ (push @ X507 @ X508))) = X508) => ! [X509 : (term > $o),X510 : term,X511 : (term > $o),X512 : term,X513 : subst] : ((((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true) | ~ (((X511 @ X512)) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X514 : term,X515 : (term > $o),X516 : (subst > term > subst > $o)] : ((((X515 @ (lam @ X514))) = $true) | ~ ! [X517 : subst,X518 : term,X519 : subst,X520 : subst] : ((((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) = $true) | ~ (((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) = $true)) | ~ ! [X521 : term] : (((X516 @ id @ X521 @ id)) = ((X515 @ X521))) | ~ ! [X522 : (subst > term > term)] : (~ ! [X524 : subst,X523 : term,X525 : subst] : (((X522 @ (comp @ X525 @ X524) @ (sub @ X523 @ X524))) = ((sub @ (X522 @ X525 @ X523) @ X524))) | ~ ! [X526 : term] : (~ ($true = ((X516 @ id @ X526 @ id))) | ($true = ((X516 @ id @ (X522 @ id @ X526) @ id)))) | (((X516 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true)) | ~ ! [X527 : term] : (~ ($true = ((X515 @ X527))) | ($true = ((X515 @ (sub @ X514 @ (push @ X527 @ id)))))) | ~ ! [X528 : term,X529 : subst,X530 : subst,X531 : subst] : (~ ($true = ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529))) | ($true = ((X516 @ X531 @ X528 @ (comp @ X530 @ X529))))))) & (! [X532 : term,X533 : subst,X534 : (term > $o)] : (($true = ((X534 @ (sub @ X532 @ X533)))) | ~ ! [X535 : term,X536 : term] : (~ (((X534 @ X535)) = $true) | ($true = ((X534 @ (ap @ X536 @ X535)))) | ~ (((X534 @ X536)) = $true)) | ~ ! [X537 : term] : ((((X534 @ (sub @ X537 @ X533))) = $true) | ~ (((var @ X537)) = $true)) | ~ ! [X538 : term] : (~ ! [X539 : term] : (~ ($true = ((X534 @ X539))) | ($true = ((X534 @ (sub @ X538 @ (push @ X539 @ id)))))) | (((X534 @ (lam @ X538))) = $true))) <=> (induction2lem = $true))), 0.43/0.52 inference(rectify,[],[f7])). 0.43/0.52 thf(f9,plain,( 0.43/0.52 ((apinj2 = $true) <=> ! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247))))) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) <=> (axshiftcons = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((! [X100 : term,X101 : subst] : (((sub @ one @ (push @ X100 @ X101))) = X100) => (! [X103 : subst,X102 : term] : (((comp @ sh @ (push @ X102 @ X103))) = X103) => (! [X104 : term,X105 : term] : ((((lam @ X104)) != ((lam @ X105))) | (X104 = X105)) => ! [X107 : (subst > term > term),X108 : (subst > term > term),X109 : subst,X106 : term] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ~ ! [X115 : subst,X114 : subst,X113 : term] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) = ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one)))) | ~ ! [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) = ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X3 : term,X4 : term,X5 : (subst > term > subst > $o)] : ((((X5 @ id @ (ap @ X4 @ X3) @ id)) = $true) | ($true != ((X5 @ id @ X3 @ id))) | ~ ! [X6 : subst,X7 : term,X9 : subst,X8 : subst] : (($true != ((X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6))) | (((X5 @ X9 @ X7 @ (comp @ X8 @ X6))) = $true)) | ~ ! [X15 : subst,X14 : subst,X12 : term,X13 : subst] : ((((X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) = $true) | (((X5 @ X15 @ X12 @ (comp @ X13 @ X14))) != $true)) | ($true != ((X5 @ id @ X4 @ id))) | ~ ! [X10 : term,X11 : term] : (($true != ((X5 @ id @ X11 @ id))) | (((X5 @ id @ X10 @ id)) != $true) | ($true = ((X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id)))))) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((! [X116 : subst] : (((comp @ id @ X116)) = X116) => (! [X117 : subst] : (((comp @ X117 @ id)) = X117) => (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)))) <=> (substmonoid_lthm = $true)) & (! [X459 : (subst > term > subst > $o),X458 : term] : (~ ! [X460 : (subst > term > term)] : (~ ! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) | ~ ! [X464 : term] : ((((X459 @ id @ X464 @ id)) != $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) | ($true = ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))) | ~ ! [X465 : term] : ((((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) = $true) | ($true != ((X459 @ id @ X465 @ id)))) | ($true = ((X459 @ id @ (lam @ X458) @ id)))) <=> (hoasinduction_lem3a = $true)) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoaslaminj = $true) <=> ! [X271 : term,X270 : subst,X269 : (subst > term > term),X272 : (subst > term > term)] : (~ ! [X276 : subst,X277 : subst,X278 : term] : (((sub @ (X269 @ X277 @ X278) @ X276)) = ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276)))) | (((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ~ ! [X273 : subst,X275 : term,X274 : subst] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) = ((sub @ (X272 @ X273 @ X275) @ X274))))) & (pushprop_lem0_gthm = $true) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (hoaslamnotvar_gthm = $true) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) <=> (substmonoid = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X394 : term] : ~ ! [X395 : (subst > term > term)] : ~ ! [X396 : term,X397 : subst] : (((sub @ X394 @ (push @ X396 @ X397))) = ((X395 @ X397 @ X396))) => (! [X398 : term] : (((sub @ X398 @ id)) = X398) => ! [X400 : term,X399 : (term > $o),X401 : (subst > term > subst > $o)] : (~ ! [X404 : (subst > term > term)] : (~ ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) | ($true = ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))) | ~ ! [X408 : term] : (($true = ((X401 @ id @ (X404 @ id @ X408) @ id))) | (((X401 @ id @ X408 @ id)) != $true))) | ~ ! [X402 : term] : (($true = ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) | ($true != ((X399 @ X402)))) | (((X399 @ (lam @ X400))) = $true) | ~ ! [X403 : term] : (((X401 @ id @ X403 @ id)) = ((X399 @ X403))))))) & (axmap = $true) & ((axscons = $true) <=> ! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497)) & (((var @ (d2term @ d_one))) != $true) & (! [X441 : (subst > term > subst > $o),X440 : term] : (~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : (($true != ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454))) | ($true = ((X441 @ X456 @ X455 @ (comp @ X457 @ X454))))) | ~ ! [X443 : term,X442 : term] : (($true != ((X441 @ id @ X443 @ id))) | ($true = ((X441 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id))) | ($true != ((X441 @ id @ X442 @ id)))) | ~ ! [X445 : subst,X446 : term,X444 : subst,X447 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) = $true) | ($true != ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))) | ~ ! [X448 : (subst > term > term)] : (~ ! [X450 : term,X452 : subst,X451 : subst] : (((X448 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X448 @ X452 @ X450) @ X451))) | (((X441 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ~ ! [X449 : term] : (($true = ((X441 @ id @ (X448 @ id @ X449) @ id))) | ($true != ((X441 @ id @ X449 @ id))))) | ~ ! [X453 : term] : (($true != ((var @ (sub @ X453 @ id)))) | (((X441 @ id @ X453 @ id)) = $true)) | ($true = ((X441 @ id @ X440 @ id)))) <=> (hoasinduction = $true)) & ((shinj = $true) <=> ! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh))))) & ((pushprop_lem0 = $true) <=> ! [X389 : term,X391 : subst,X390 : (term > $o)] : ~ ! [X392 : (term > $o)] : ~ ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393)))) & (! [X202 : (subst > term > term),X203 : term,X201 : term] : (~ ! [X204 : term,X205 : subst,X206 : subst] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) = ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X505 : term,X506 : subst] : (((sub @ one @ (push @ X505 @ X506))) = X505) => (! [X508 : subst,X507 : term] : (((comp @ sh @ (push @ X507 @ X508))) = X508) => ! [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) != $true) | (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X409 : term] : ~ ! [X410 : (subst > term > term)] : ~ ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411)))) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & (pushprop_lem1v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> (axvarid = $true)) & ((induction2_lthm = $true) <=> (! [X61 : term] : (((sub @ X61 @ id)) = X61) => (! [X64 : subst,X62 : term,X63 : (term > $o)] : (~ ! [X65 : term] : ((((var @ X65)) != $true) | ($true = ((X63 @ (sub @ X65 @ X64))))) | ~ ! [X68 : term] : (($true = ((X63 @ (lam @ X68)))) | ~ ! [X69 : term] : (($true != ((X63 @ X69))) | ($true = ((X63 @ (sub @ X68 @ (push @ X69 @ id))))))) | (((X63 @ (sub @ X62 @ X64))) = $true) | ~ ! [X66 : term,X67 : term] : (($true != ((X63 @ X67))) | ($true = ((X63 @ (ap @ X66 @ X67)))) | ($true != ((X63 @ X66))))) => ! [X71 : term,X70 : (term > $o)] : (($true = ((X70 @ X71))) | ~ ! [X74 : term,X75 : term] : ((((X70 @ (ap @ X75 @ X74))) = $true) | ($true != ((X70 @ X75))) | ($true != ((X70 @ X74)))) | ~ ! [X72 : term] : (~ ! [X73 : term] : (($true = ((X70 @ (sub @ X72 @ (push @ X73 @ id))))) | ($true != ((X70 @ X73)))) | (((X70 @ (lam @ X72))) = $true)) | ~ ! [X76 : term] : ((((var @ X76)) != $true) | ($true = ((X70 @ X76)))))))) & (lamnotap != $true) & ((apinj1 = $true) <=> ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((d2term @ d_one)) = one) & ((induction2lem = $true) <=> ! [X532 : term,X534 : (term > $o),X533 : subst] : (~ ! [X538 : term] : ((((X534 @ (lam @ X538))) = $true) | ~ ! [X539 : term] : (($true = ((X534 @ (sub @ X538 @ (push @ X539 @ id))))) | ($true != ((X534 @ X539))))) | ~ ! [X537 : term] : ((((var @ X537)) != $true) | (((X534 @ (sub @ X537 @ X533))) = $true)) | ~ ! [X536 : term,X535 : term] : ((((X534 @ X536)) != $true) | (((X534 @ X535)) != $true) | ($true = ((X534 @ (ap @ X536 @ X535))))) | ($true = ((X534 @ (sub @ X532 @ X533)))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (pushprop_lthm_orig = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axabs = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X515 : (term > $o),X516 : (subst > term > subst > $o),X514 : term] : (~ ! [X518 : term,X519 : subst,X517 : subst,X520 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) != $true) | (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) = $true)) | ~ ! [X522 : (subst > term > term)] : ((((X516 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true) | ~ ! [X524 : subst,X523 : term,X525 : subst] : (((X522 @ (comp @ X525 @ X524) @ (sub @ X523 @ X524))) = ((sub @ (X522 @ X525 @ X523) @ X524))) | ~ ! [X526 : term] : (($true = ((X516 @ id @ (X522 @ id @ X526) @ id))) | ($true != ((X516 @ id @ X526 @ id))))) | ~ ! [X521 : term] : (((X516 @ id @ X521 @ id)) = ((X515 @ X521))) | ~ ! [X527 : term] : (($true = ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) | ($true != ((X515 @ X527)))) | (((X515 @ (lam @ X514))) = $true) | ~ ! [X528 : term,X531 : subst,X530 : subst,X529 : subst] : (($true != ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529))) | ($true = ((X516 @ X531 @ X528 @ (comp @ X530 @ X529))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem3_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X250 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X250))) = X251) => (! [X253 : subst,X252 : term] : (((comp @ sh @ (push @ X252 @ X253))) = X253) => (! [X254 : subst] : (((comp @ X254 @ id)) = X254) => (! [X256 : (term > $o),X255 : term] : ((((X256 @ X255)) = $true) | ~ ! [X257 : term] : ((((X256 @ X257)) = $true) | (((var @ X257)) != $true)) | ~ ! [X258 : term] : (($true != ((X256 @ X258))) | ($true = ((X256 @ (lam @ X258))))) | ~ ! [X259 : term,X260 : term] : (($true != ((X256 @ X260))) | ($true != ((X256 @ X259))) | ($true = ((X256 @ (ap @ X260 @ X259)))))) => ! [X262 : subst,X261 : (term > $o),X263 : term] : (~ ! [X267 : term] : (($true = ((X261 @ (lam @ X267)))) | ~ ! [X268 : term] : (($true != ((X261 @ X268))) | (((X261 @ (sub @ X267 @ (push @ X268 @ id)))) = $true))) | ($true = ((X261 @ (sub @ X263 @ X262)))) | ~ ! [X265 : term,X264 : term] : ((((X261 @ X264)) != $true) | ($true != ((X261 @ X265))) | ($true = ((X261 @ (ap @ X265 @ X264))))) | ~ ! [X266 : term] : ((((X261 @ (sub @ X266 @ X262))) = $true) | (((var @ X266)) != $true)))))))) & (hoasinduction_lem2_lthm = $true) & ((termmset = $true) <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : (((X137 @ sh @ one)) != ((sub @ X136 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & ! [X327 : d_subst] : (d_id = X327) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X370 : term] : (((sub @ X370 @ id)) = X370) => ! [X372 : (subst > term > subst > $o),X371 : (term > $o),X373 : term] : (~ ! [X388 : term] : (($true != ((X371 @ X388))) | ($true = ((X371 @ (sub @ X373 @ (push @ X388 @ id)))))) | ~ ! [X377 : subst,X378 : subst,X376 : term,X375 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) = $true) | (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) != $true)) | ~ ! [X374 : term] : (((X371 @ X374)) = ((X372 @ id @ X374 @ id))) | (((X371 @ (lam @ X373))) = $true) | ~ ! [X379 : (subst > term > term)] : (~ ! [X382 : subst,X383 : subst,X381 : term] : (((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ (X379 @ X382 @ X381) @ X383))) | ~ ! [X380 : term] : (($true != ((X372 @ id @ X380 @ id))) | (((X372 @ id @ (X379 @ id @ X380) @ id)) = $true)) | ($true = ((X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)))) | ~ ! [X386 : term,X387 : subst,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) = $true) | ($true != ((X372 @ X385 @ X386 @ (comp @ X387 @ X384)))))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X207 : (subst > term > subst > $o)] : ~ ! [X208 : (term > $o)] : ~ ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))) => (! [X211 : term,X210 : (term > $o)] : (~ ! [X214 : term,X213 : term] : (($true != ((X210 @ X213))) | ($true != ((X210 @ X214))) | ($true = ((X210 @ (ap @ X213 @ X214))))) | ($true = ((X210 @ X211))) | ~ ! [X212 : term] : (($true != ((var @ X212))) | ($true = ((X210 @ X212)))) | ~ ! [X215 : term] : ((((X210 @ (lam @ X215))) = $true) | ~ ! [X216 : term] : ((((X210 @ (sub @ X215 @ (push @ X216 @ id)))) = $true) | ($true != ((X210 @ X216)))))) => (! [X217 : term] : (((sub @ X217 @ id)) = X217) => (! [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (~ ! [X221 : term] : (($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) | ($true != ((X220 @ X221)))) | ~ ! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) | (((X220 @ (lam @ X219))) = $true) | ~ ! [X223 : (subst > term > term)] : (~ ! [X224 : term] : (($true != ((X218 @ id @ X224 @ id))) | (((X218 @ id @ (X223 @ id @ X224) @ id)) = $true)) | ~ ! [X225 : subst,X227 : term,X226 : subst] : (((sub @ (X223 @ X225 @ X227) @ X226)) = ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) | ($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id))))) => ! [X229 : (subst > term > subst > $o),X228 : term] : (~ ! [X241 : (subst > term > term)] : (~ ! [X244 : term,X243 : subst,X242 : subst] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242))) | ($true = ((X229 @ id @ (lam @ (X241 @ sh @ one)) @ id))) | ~ ! [X245 : term] : (($true != ((X229 @ id @ X245 @ id))) | ($true = ((X229 @ id @ (X241 @ id @ X245) @ id))))) | ~ ! [X236 : term,X239 : subst,X237 : subst,X238 : subst] : (($true = ((X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237))) | ($true != ((X229 @ X238 @ X236 @ (comp @ X239 @ X237))))) | ~ ! [X232 : subst,X235 : subst,X233 : subst,X234 : term] : ((((X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) != $true) | (((X229 @ X233 @ X234 @ (comp @ X235 @ X232))) = $true)) | ~ ! [X240 : term] : (($true != ((var @ (sub @ X240 @ id)))) | ($true = ((X229 @ id @ X240 @ id)))) | ~ ! [X230 : term,X231 : term] : ((((X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id)) = $true) | (((X229 @ id @ X230 @ id)) != $true) | (((X229 @ id @ X231 @ id)) != $true)) | ($true = ((X229 @ id @ X228 @ id))))))))) & ((laminj = $true) <=> ! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413))))) & (induction2_gthm = $true) & (pushprop_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X285 : (term > $o),X284 : term,X286 : subst,X283 : (term > $o)] : (($true != ((X285 @ X284))) | ~ ! [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) = ((X283 @ X287))) | ($true = ((X283 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X297 : (subst > term > subst > $o)] : ~ ! [X298 : (term > $o)] : ~ ! [X299 : term] : (((X298 @ X299)) = ((X297 @ id @ X299 @ id))) => (! [X301 : (term > $o),X300 : term] : (~ ! [X304 : term] : ((((X301 @ X304)) = $true) | (((var @ X304)) != $true)) | ~ ! [X302 : term] : ((((X301 @ (lam @ X302))) = $true) | ~ ! [X303 : term] : (($true = ((X301 @ (sub @ X302 @ (push @ X303 @ id))))) | ($true != ((X301 @ X303))))) | (((X301 @ X300)) = $true) | ~ ! [X305 : term,X306 : term] : (($true != ((X301 @ X305))) | ($true = ((X301 @ (ap @ X305 @ X306)))) | ($true != ((X301 @ X306))))) => (! [X307 : term] : (((sub @ X307 @ id)) = X307) => (! [X308 : term,X309 : (term > $o),X310 : (subst > term > subst > $o)] : (~ ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))) | ~ ! [X311 : (subst > term > term)] : (~ ! [X312 : term] : (($true = ((X310 @ id @ (X311 @ id @ X312) @ id))) | ($true != ((X310 @ id @ X312 @ id)))) | ~ ! [X315 : subst,X313 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) = ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313)))) | ($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id)))) | ($true = ((X309 @ (lam @ X308)))) | ~ ! [X317 : term] : (($true != ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true))) => ! [X319 : (subst > term > subst > $o),X318 : term] : (~ ! [X322 : (subst > term > term)] : (~ ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) | (((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id)) = $true) | ~ ! [X326 : term] : (($true != ((X319 @ id @ X326 @ id))) | (((X319 @ id @ (X322 @ id @ X326) @ id)) = $true))) | ($true = ((X319 @ id @ X318 @ id))) | ~ ! [X320 : term,X321 : term] : ((((X319 @ id @ X320 @ id)) != $true) | ($true != ((X319 @ id @ X321 @ id))) | ($true = ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id)))))))))) & (! [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true != ((X330 @ X332))) | (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true)) <=> (pushprop_lem1 = $true)) & (id = ((d2subst @ d_id))) & (ulamvarsh = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_gthm = $true) & ((! [X466 : term] : (((sub @ X466 @ id)) = X466) => (! [X467 : (subst > term > subst > $o),X468 : term] : (~ ! [X470 : (subst > term > term)] : (~ ! [X472 : subst,X473 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) = ((sub @ (X470 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true) | ~ ! [X474 : term] : (($true != ((X467 @ id @ X474 @ id))) | ($true = ((X467 @ id @ (X470 @ id @ X474) @ id))))) | ~ ! [X469 : term] : (($true != ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) | ($true = ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id)))) => ! [X475 : (subst > term > subst > $o),X476 : term] : (~ ! [X477 : term] : (($true != ((X475 @ id @ X477 @ id))) | ($true = ((X475 @ id @ (sub @ X476 @ (push @ X477 @ id)) @ id)))) | ($true = ((X475 @ id @ (lam @ X476) @ id))) | ~ ! [X478 : (subst > term > term)] : (~ ! [X482 : term] : (($true = ((X475 @ id @ (X478 @ id @ X482) @ id))) | ($true != ((X475 @ id @ X482 @ id)))) | ~ ! [X479 : subst,X480 : term,X481 : subst] : (((sub @ (X478 @ X481 @ X480) @ X479)) = ((X478 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479)))) | (((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) = $true))))) <=> (hoasinduction_lem3a_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X333 : subst] : (((comp @ id @ X333)) = X333) <=> (axidl = $true)) & (pushprop_lem3v2_lthm = $true) & ((! [X334 : term,X335 : subst] : (((sub @ one @ (push @ X334 @ X335))) = X334) => ! [X336 : subst,X337 : term,X339 : (term > $o),X338 : (term > $o)] : (($true = ((X339 @ one))) | (((X338 @ X337)) != $true) | ~ ! [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) = ((X339 @ X340))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotap_gthm = $true) & (! [X367 : (subst > term > subst > $o)] : ~ ! [X368 : (term > $o)] : ~ ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) <=> (hoasinduction_lem0 = $true)) & (sh = ((d2subst @ d_id))) & (hoasapnotvar_lthm = $true) & (axclos = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : (~ ! [X344 : term] : (((X343 @ id @ X344 @ id)) = ((X341 @ X344))) | (((X341 @ (lam @ X342))) = $true) | ~ ! [X350 : term] : (($true != ((X341 @ X350))) | ($true = ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) | ~ ! [X345 : (subst > term > term)] : (~ ! [X349 : term] : (($true != ((X343 @ id @ X349 @ id))) | (((X343 @ id @ (X345 @ id @ X349) @ id)) = $true)) | ~ ! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) | ($true = ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))))) & (! [X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X127 : (subst > term > term)] : (~ ! [X130 : subst,X129 : subst,X128 : term] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) | ~ ! [X131 : term] : ((((X121 @ id @ X131 @ id)) != $true) | (((X121 @ id @ (X127 @ id @ X131) @ id)) = $true)) | ($true = ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id)))) | ~ ! [X134 : subst,X133 : subst,X135 : subst,X132 : term] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) != $true) | (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) = $true)) | ~ ! [X126 : term] : (($true = ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) | ($true != ((X121 @ id @ X126 @ id)))) | ~ ! [X124 : subst,X122 : term,X125 : subst,X123 : subst] : (($true != ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125))) | (((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) = $true)) | ($true = ((X121 @ id @ (lam @ X120) @ id)))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem2_gthm = $true) & ((! [X416 : term,X415 : term,X418 : term,X417 : term] : ((X415 = X418) | (((ap @ X416 @ X418)) != ((ap @ X417 @ X415)))) => ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422))))) <=> (hoasapinj2_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X500 : subst,X502 : (term > $o),X501 : term] : ~ ! [X503 : (term > $o)] : ~ ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X498 : term] : ~ ! [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) != ((X499 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((termmset_lthm = $true) <=> (! [X91 : term] : (((sub @ X91 @ id)) = X91) => ! [X92 : term] : (((sub @ X92 @ id)) = X92))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & (hoaslamnotvar_lthm = $true) & (! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) <=> (hoasapinj1 = $true)) & (apnotvar = $true) & (! [X46 : term,X47 : term,X45 : (term > $o),X44 : (subst > term > subst > $o)] : (~ ! [X50 : subst,X51 : subst,X52 : subst,X53 : term] : ((((X44 @ X50 @ X53 @ (comp @ X51 @ X52))) = $true) | ($true != ((X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52)))) | ~ ! [X54 : term] : (((X44 @ id @ X54 @ id)) = ((X45 @ X54))) | ($true != ((X45 @ X47))) | (((X45 @ (ap @ X46 @ X47))) = $true) | ~ ! [X56 : subst,X58 : term,X55 : subst,X57 : subst] : (($true = ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56))) | ($true != ((X44 @ X57 @ X58 @ (comp @ X55 @ X56))))) | ($true != ((X45 @ X46))) | ~ ! [X48 : term,X49 : term] : (($true = ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id))) | ($true != ((X44 @ id @ X48 @ id))) | ($true != ((X44 @ id @ X49 @ id))))) <=> (hoasinduction_lem2v2 = $true)) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X41 : (subst > term > subst > $o)] : ~ ! [X42 : (term > $o)] : ~ ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43)))) & (hoasinduction_lem1 = $true) & ! [X279 : d_subst,X280 : d_subst] : ((((d2subst @ X280)) = ((d2subst @ X279))) => (X279 = X280)) & ((axidr = $true) <=> ! [X496 : subst] : (((comp @ X496 @ id)) = X496)) & (hoasinduction_lem1_gthm = $true) & (lamnotvar = $true) & (ulamvarind = $true) & ! [X0 : d_term,X1 : d_term] : ((((d2term @ X0)) = ((d2term @ X1))) => (X0 = X1)) & (axassoc = $true) & (axvarshift = $true) & ((induction2 = $true) <=> ! [X289 : term,X288 : (term > $o)] : (($true = ((X288 @ X289))) | ~ ! [X294 : term] : ((((X288 @ X294)) = $true) | ($true != ((var @ X294)))) | ~ ! [X290 : term,X291 : term] : ((((X288 @ X291)) != $true) | ($true != ((X288 @ X290))) | ($true = ((X288 @ (ap @ X291 @ X290))))) | ~ ! [X292 : term] : (($true = ((X288 @ (lam @ X292)))) | ~ ! [X293 : term] : (($true = ((X288 @ (sub @ X292 @ (push @ X293 @ id))))) | ($true != ((X288 @ X293))))))) & (! [X432 : term] : ~ ! [X433 : (subst > term > term)] : ~ ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((! [X139 : (term > $o),X138 : term] : (~ ! [X142 : term,X141 : term] : (($true = ((X139 @ (ap @ X142 @ X141)))) | (((X139 @ X141)) != $true) | ($true != ((X139 @ X142)))) | ~ ! [X143 : term] : (($true = ((X139 @ (lam @ X143)))) | ~ ! [X144 : term] : ((((X139 @ (sub @ X143 @ (push @ X144 @ id)))) = $true) | ($true != ((X139 @ X144))))) | (((X139 @ X138)) = $true) | ~ ! [X140 : term] : (($true != ((var @ X140))) | ($true = ((X139 @ X140))))) => (! [X147 : term,X145 : term,X146 : (subst > term > subst > $o)] : ((((X146 @ id @ X145 @ id)) != $true) | ~ ! [X153 : subst,X152 : term,X154 : subst,X155 : subst] : (($true = ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154))) | (((X146 @ X153 @ X152 @ (comp @ X155 @ X154))) != $true)) | ~ ! [X150 : subst,X149 : term,X148 : subst,X151 : subst] : (($true != ((X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150))) | ($true = ((X146 @ X151 @ X149 @ (comp @ X148 @ X150))))) | ~ ! [X156 : term,X157 : term] : ((((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id)) = $true) | (((X146 @ id @ X157 @ id)) != $true) | ($true != ((X146 @ id @ X156 @ id)))) | ($true = ((X146 @ id @ (ap @ X145 @ X147) @ id))) | ($true != ((X146 @ id @ X147 @ id)))) => (! [X159 : term,X158 : (subst > term > subst > $o)] : (~ ! [X160 : (subst > term > term)] : (~ ! [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) = ((sub @ (X160 @ X163 @ X161) @ X162))) | (((X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) = $true) | ~ ! [X164 : term] : ((((X158 @ id @ X164 @ id)) != $true) | ($true = ((X158 @ id @ (X160 @ id @ X164) @ id))))) | ~ ! [X165 : term] : (($true != ((X158 @ id @ X165 @ id))) | (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true)) | ~ ! [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) | (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) != $true)) | ($true = ((X158 @ id @ (lam @ X159) @ id))) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) != $true))) => ! [X174 : term,X175 : (subst > term > subst > $o)] : (~ ! [X190 : subst,X189 : term,X188 : subst,X191 : subst] : (($true != ((X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190))) | ($true = ((X175 @ X188 @ X189 @ (comp @ X191 @ X190))))) | ~ ! [X181 : term,X182 : term] : (($true != ((X175 @ id @ X181 @ id))) | (((X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id)) = $true) | ($true != ((X175 @ id @ X182 @ id)))) | ~ ! [X177 : term,X180 : subst,X179 : subst,X178 : subst] : (($true != ((X175 @ X179 @ X177 @ (comp @ X180 @ X178)))) | (((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178)) = $true)) | ~ ! [X176 : term] : (($true != ((var @ (sub @ X176 @ id)))) | (((X175 @ id @ X176 @ id)) = $true)) | ~ ! [X183 : (subst > term > term)] : (~ ! [X187 : term] : ((((X175 @ id @ (X183 @ id @ X187) @ id)) = $true) | ($true != ((X175 @ id @ X187 @ id)))) | ~ ! [X185 : subst,X184 : term,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) | (((X175 @ id @ (lam @ (X183 @ sh @ one)) @ id)) = $true)) | ($true = ((X175 @ id @ X174 @ id))))))) <=> (hoasinduction_lthm = $true)) & (! [X484 : term,X483 : (subst > term > subst > $o)] : (~ ! [X485 : term] : (($true != ((X483 @ id @ X485 @ id))) | (((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) = $true)) | ~ ! [X486 : (subst > term > term)] : (~ ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))) | (((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) = $true) | ~ ! [X487 : term] : (($true = ((X483 @ id @ (X486 @ id @ X487) @ id))) | (((X483 @ id @ X487 @ id)) != $true))) | ($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((! [X423 : term] : (((sub @ X423 @ id)) = X423) => (! [X426 : term,X427 : term,X424 : term,X425 : term] : ((X426 = X427) | (((ap @ X426 @ X424)) != ((ap @ X427 @ X425)))) => ! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))))) <=> (hoasapinj1_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X77 : (subst > term > subst > $o),X78 : term] : (~ ! [X88 : term] : (($true = ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id))) | (((X77 @ id @ X88 @ id)) != $true)) | ~ ! [X79 : (subst > term > term),X80 : term] : (~ ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) | ~ ! [X81 : term] : (($true != ((X77 @ id @ X81 @ id))) | (((X77 @ id @ (X79 @ id @ X81) @ id)) = $true)) | ($true = ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) | ~ ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83)))) | ($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))))) & ((! [X16 : term] : (((sub @ X16 @ id)) = X16) => (! [X18 : term,X17 : (subst > term > subst > $o)] : (($true = ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id))) | ~ ! [X19 : term] : (($true != ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) | ~ ! [X20 : (subst > term > term)] : (~ ! [X21 : subst,X22 : subst,X23 : term] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) = ((sub @ (X20 @ X22 @ X23) @ X21))) | ($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ~ ! [X24 : term] : ((((X17 @ id @ (X20 @ id @ X24) @ id)) = $true) | ($true != ((X17 @ id @ X24 @ id)))))) => ! [X26 : (subst > term > subst > $o),X25 : term] : (~ ! [X28 : term,X29 : subst,X27 : subst,X30 : subst] : ((((X26 @ X30 @ X28 @ (comp @ X27 @ X29))) != $true) | ($true = ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29)))) | ~ ! [X31 : (subst > term > term)] : (($true = ((X26 @ id @ (lam @ (X31 @ sh @ one)) @ id))) | ~ ! [X35 : term] : (($true != ((X26 @ id @ X35 @ id))) | ($true = ((X26 @ id @ (X31 @ id @ X35) @ id)))) | ~ ! [X32 : subst,X34 : term,X33 : subst] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32)))) | ($true = ((X26 @ id @ (lam @ X25) @ id))) | ~ ! [X40 : term] : ((((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id)) = $true) | (((X26 @ id @ X40 @ id)) != $true)) | ~ ! [X38 : subst,X36 : subst,X37 : term,X39 : subst] : (($true = ((X26 @ X38 @ X37 @ (comp @ X36 @ X39)))) | ($true != ((X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39))))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) <=> (hoasapinj2 = $true)) & (axapp = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (pushprop = $true) & ((axvarcons = $true) <=> ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X357 : (subst > term > subst > $o),X358 : term] : (~ ! [X360 : (subst > term > term)] : ((((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) = $true) | ~ ! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) | ~ ! [X364 : term] : (($true != ((X357 @ id @ X364 @ id))) | ($true = ((X357 @ id @ (X360 @ id @ X364) @ id))))) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) | ~ ! [X359 : term] : (($true = ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) | ($true != ((X357 @ id @ X359 @ id)))))) & (! [X351 : term,X352 : (term > $o)] : (~ ! [X353 : term] : (($true = ((X352 @ (lam @ X353)))) | ($true != ((X352 @ X353)))) | (((X352 @ X351)) = $true) | ~ ! [X354 : term] : (($true != ((var @ X354))) | (((X352 @ X354)) = $true)) | ~ ! [X356 : term,X355 : term] : (($true != ((X352 @ X355))) | (((X352 @ (ap @ X356 @ X355))) = $true) | ($true != ((X352 @ X356))))) <=> (induction = $true)) & (! [X193 : term,X192 : (subst > term > subst > $o)] : (~ ! [X196 : (subst > term > term)] : (~ ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197))) | ($true = ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ~ ! [X200 : term] : (($true != ((X192 @ id @ X200 @ id))) | (((X192 @ id @ (X196 @ id @ X200) @ id)) = $true))) | (((X192 @ id @ X193 @ id)) = $true) | ~ ! [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) = $true) | ($true != ((X192 @ id @ X194 @ id))) | ($true != ((X192 @ id @ X195 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ! [X495 : d_term] : (d_one = X495)), 0.43/0.52 inference(flattening,[],[f8])). 0.43/0.52 thf(f10,plain,( 0.43/0.52 ! [X3 : (term > $o),X0 : subst,X1 : term,X2 : (term > $o)] : ((! [X5 : term] : ((($true = ((X2 @ (sub @ X5 @ sh)))) | (((X2 @ X5)) != $true)) | (((var @ X5)) != $true)) | ? [X4 : term] : (($true != ((X3 @ (sub @ X4 @ X0)))) & (((var @ X4)) = $true))) | (((pushprop_p_and_p_prime @ X1 @ X0 @ X3 @ X2)) != $true)) <~> (pushprop_lem2v2 = $true)), 0.43/0.52 inference(ennf_transformation,[],[f5])). 0.43/0.52 thf(f11,plain,( 0.43/0.52 ! [X3 : (term > $o),X0 : subst,X1 : term,X2 : (term > $o)] : (? [X4 : term] : (($true != ((X3 @ (sub @ X4 @ X0)))) & (((var @ X4)) = $true)) | (((pushprop_p_and_p_prime @ X1 @ X0 @ X3 @ X2)) != $true) | ! [X5 : term] : (($true = ((X2 @ (sub @ X5 @ sh)))) | (((var @ X5)) != $true) | (((X2 @ X5)) != $true))) <~> (pushprop_lem2v2 = $true)), 0.43/0.52 inference(flattening,[],[f10])). 0.43/0.52 thf(f12,plain,( 0.43/0.52 ((apinj2 = $true) <=> ! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247))))) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) <=> (axshiftcons = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((((! [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ? [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) != ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) | ? [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) != ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one))))) | ? [X104 : term,X105 : term] : ((((lam @ X104)) = ((lam @ X105))) & (X104 != X105))) | ? [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) != X103)) | ? [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) != X100)) <=> (hoaslaminj_lthm = $true)) & (! [X3 : term,X5 : (subst > term > subst > $o),X4 : term] : (? [X10 : term,X11 : term] : ((((X5 @ id @ X10 @ id)) = $true) & ($true != ((X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id))) & ($true = ((X5 @ id @ X11 @ id)))) | (((X5 @ id @ (ap @ X4 @ X3) @ id)) = $true) | ? [X7 : term,X6 : subst,X9 : subst,X8 : subst] : (($true = ((X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6))) & (((X5 @ X9 @ X7 @ (comp @ X8 @ X6))) != $true)) | ($true != ((X5 @ id @ X3 @ id))) | ($true != ((X5 @ id @ X4 @ id))) | ? [X13 : subst,X14 : subst,X12 : term,X15 : subst] : ((((X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) != $true) & (((X5 @ X15 @ X12 @ (comp @ X13 @ X14))) = $true))) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((((! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | ? [X117 : subst] : (((comp @ X117 @ id)) != X117)) | ? [X116 : subst] : (((comp @ id @ X116)) != X116)) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X458 : term,X459 : (subst > term > subst > $o)] : (? [X465 : term] : (($true = ((X459 @ id @ X465 @ id))) & (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) != $true)) | ($true = ((X459 @ id @ (lam @ X458) @ id))) | ? [X460 : (subst > term > term)] : (! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) & ! [X464 : term] : ((((X459 @ id @ X464 @ id)) != $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) & ($true != ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))))) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ? [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) != ((sub @ (X272 @ X273 @ X275) @ X274))) | ? [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) != ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276))))) <=> (hoaslaminj = $true)) & (pushprop_lem0_gthm = $true) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (hoaslamnotvar_gthm = $true) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) <=> (substmonoid = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (? [X402 : term] : (($true != ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) & ($true = ((X399 @ X402)))) | ? [X403 : term] : (((X401 @ id @ X403 @ id)) != ((X399 @ X403))) | (((X399 @ (lam @ X400))) = $true) | ? [X404 : (subst > term > term)] : (! [X408 : term] : (($true = ((X401 @ id @ (X404 @ id @ X408) @ id))) | (((X401 @ id @ X408 @ id)) != $true)) & ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) & ($true != ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) | ? [X398 : term] : (((sub @ X398 @ id)) != X398)) | ? [X394 : term] : ! [X395 : (subst > term > term)] : ? [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) != ((X395 @ X397 @ X396))))) & (axmap = $true) & ((axscons = $true) <=> ! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction = $true) <=> ! [X440 : term,X441 : (subst > term > subst > $o)] : (? [X442 : term,X443 : term] : (($true = ((X441 @ id @ X443 @ id))) & ($true = ((X441 @ id @ X442 @ id))) & ($true != ((X441 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id)))) | ? [X448 : (subst > term > term)] : (! [X450 : term,X452 : subst,X451 : subst] : (((X448 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X448 @ X452 @ X450) @ X451))) & ! [X449 : term] : (($true = ((X441 @ id @ (X448 @ id @ X449) @ id))) | ($true != ((X441 @ id @ X449 @ id)))) & (((X441 @ id @ (lam @ (X448 @ sh @ one)) @ id)) != $true)) | ? [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true != ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) & ($true = ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) | ($true = ((X441 @ id @ X440 @ id))) | ? [X453 : term] : ((((X441 @ id @ X453 @ id)) != $true) & ($true = ((var @ (sub @ X453 @ id))))) | ? [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) != $true) & ($true = ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))))) & ((shinj = $true) <=> ! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh))))) & (! [X389 : term,X391 : subst,X390 : (term > $o)] : ? [X392 : (term > $o)] : ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393))) <=> (pushprop_lem0 = $true)) & ((hoaslamnotap = $true) <=> ! [X201 : term,X202 : (subst > term > term),X203 : term] : (? [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) != ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one)))))) & ((pushprop_lem1_lthm = $true) <=> ((! [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) != $true) | (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true)) | ? [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) != X508)) | ? [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) != X505))) & (induction2lem_gthm = $true) & (! [X409 : term] : ? [X410 : (subst > term > term)] : ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411))) <=> (hoasinduction_lem3v2_f = $true)) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & (pushprop_lem1v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> (axvarid = $true)) & ((induction2_lthm = $true) <=> ((! [X70 : (term > $o),X71 : term] : (? [X76 : term] : (($true != ((X70 @ X76))) & (((var @ X76)) = $true)) | ? [X72 : term] : ((((X70 @ (lam @ X72))) != $true) & ! [X73 : term] : (($true = ((X70 @ (sub @ X72 @ (push @ X73 @ id))))) | ($true != ((X70 @ X73))))) | ($true = ((X70 @ X71))) | ? [X74 : term,X75 : term] : (($true = ((X70 @ X75))) & (((X70 @ (ap @ X75 @ X74))) != $true) & ($true = ((X70 @ X74))))) | ? [X64 : subst,X62 : term,X63 : (term > $o)] : ((((X63 @ (sub @ X62 @ X64))) != $true) & ! [X66 : term,X67 : term] : (($true != ((X63 @ X67))) | ($true = ((X63 @ (ap @ X66 @ X67)))) | ($true != ((X63 @ X66)))) & ! [X68 : term] : (($true = ((X63 @ (lam @ X68)))) | ? [X69 : term] : (($true = ((X63 @ X69))) & ($true != ((X63 @ (sub @ X68 @ (push @ X69 @ id))))))) & ! [X65 : term] : ((((var @ X65)) != $true) | ($true = ((X63 @ (sub @ X65 @ X64))))))) | ? [X61 : term] : (((sub @ X61 @ id)) != X61))) & (lamnotap != $true) & ((apinj1 = $true) <=> ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((d2term @ d_one)) = one) & (! [X534 : (term > $o),X533 : subst,X532 : term] : (? [X537 : term] : ((((X534 @ (sub @ X537 @ X533))) != $true) & (((var @ X537)) = $true)) | ? [X538 : term] : ((((X534 @ (lam @ X538))) != $true) & ! [X539 : term] : (($true = ((X534 @ (sub @ X538 @ (push @ X539 @ id))))) | ($true != ((X534 @ X539))))) | ? [X536 : term,X535 : term] : ((((X534 @ X535)) = $true) & ($true != ((X534 @ (ap @ X536 @ X535)))) & (((X534 @ X536)) = $true)) | ($true = ((X534 @ (sub @ X532 @ X533))))) <=> (induction2lem = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (pushprop_lthm_orig = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axabs = $true) & (! [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (? [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) = $true) & (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) != $true)) | (((X515 @ (lam @ X514))) = $true) | ? [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true != ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) & ($true = ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) | ? [X521 : term] : (((X516 @ id @ X521 @ id)) != ((X515 @ X521))) | ? [X522 : (subst > term > term)] : ((((X516 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true) & ! [X524 : subst,X523 : term,X525 : subst] : (((X522 @ (comp @ X525 @ X524) @ (sub @ X523 @ X524))) = ((sub @ (X522 @ X525 @ X523) @ X524))) & ! [X526 : term] : (($true = ((X516 @ id @ (X522 @ id @ X526) @ id))) | ($true != ((X516 @ id @ X526 @ id))))) | ? [X527 : term] : (($true != ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) & ($true = ((X515 @ X527))))) <=> (hoasinduction_lem3v2 = $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)))))))))))))) & (hoasinduction_lem3_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X261 : (term > $o),X263 : term,X262 : subst] : (? [X266 : term] : ((((var @ X266)) = $true) & (((X261 @ (sub @ X266 @ X262))) != $true)) | ($true = ((X261 @ (sub @ X263 @ X262)))) | ? [X267 : term] : (! [X268 : term] : (($true != ((X261 @ X268))) | (((X261 @ (sub @ X267 @ (push @ X268 @ id)))) = $true)) & ($true != ((X261 @ (lam @ X267))))) | ? [X264 : term,X265 : term] : (($true != ((X261 @ (ap @ X265 @ X264)))) & ($true = ((X261 @ X265))) & (((X261 @ X264)) = $true))) | ? [X256 : (term > $o),X255 : term] : (! [X259 : term,X260 : term] : (($true != ((X256 @ X260))) | ($true != ((X256 @ X259))) | ($true = ((X256 @ (ap @ X260 @ X259))))) & ! [X258 : term] : (($true != ((X256 @ X258))) | ($true = ((X256 @ (lam @ X258))))) & ! [X257 : term] : ((((X256 @ X257)) = $true) | (((var @ X257)) != $true)) & (((X256 @ X255)) != $true))) | ? [X254 : subst] : (((comp @ X254 @ id)) != X254)) | ? [X252 : term,X253 : subst] : (((comp @ sh @ (push @ X252 @ X253))) != X253)) | ? [X251 : term,X250 : subst] : (((sub @ one @ (push @ X251 @ X250))) != X251))) & (hoasinduction_lem2_lthm = $true) & ((termmset = $true) <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X136 : term] : ? [X137 : (subst > term > term)] : (((X137 @ sh @ one)) = ((sub @ X136 @ (push @ one @ sh))))) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & ! [X327 : d_subst] : (d_id = X327) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (? [X374 : term] : (((X371 @ X374)) != ((X372 @ id @ X374 @ id))) | ? [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) != $true) & ($true = ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) | ? [X379 : (subst > term > term)] : (! [X380 : term] : (($true != ((X372 @ id @ X380 @ id))) | (((X372 @ id @ (X379 @ id @ X380) @ id)) = $true)) & ! [X382 : subst,X383 : subst,X381 : term] : (((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ (X379 @ X382 @ X381) @ X383))) & ($true != ((X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)))) | (((X371 @ (lam @ X373))) = $true) | ? [X388 : term] : (($true != ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) & ($true = ((X371 @ X388)))) | ? [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) != $true) & (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true))) | ? [X370 : term] : (((sub @ X370 @ id)) != X370))) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X228 : term,X229 : (subst > term > subst > $o)] : (? [X240 : term] : (($true = ((var @ (sub @ X240 @ id)))) & ($true != ((X229 @ id @ X240 @ id)))) | ? [X241 : (subst > term > term)] : (($true != ((X229 @ id @ (lam @ (X241 @ sh @ one)) @ id))) & ! [X245 : term] : (($true != ((X229 @ id @ X245 @ id))) | ($true = ((X229 @ id @ (X241 @ id @ X245) @ id)))) & ! [X244 : term,X243 : subst,X242 : subst] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242)))) | ? [X230 : term,X231 : term] : ((((X229 @ id @ X230 @ id)) = $true) & (((X229 @ id @ X231 @ id)) = $true) & (((X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id)) != $true)) | ($true = ((X229 @ id @ X228 @ id))) | ? [X237 : subst,X236 : term,X239 : subst,X238 : subst] : (($true != ((X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237))) & ($true = ((X229 @ X238 @ X236 @ (comp @ X239 @ X237))))) | ? [X233 : subst,X235 : subst,X232 : subst,X234 : term] : ((((X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) = $true) & (((X229 @ X233 @ X234 @ (comp @ X235 @ X232))) != $true))) | ? [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) & ! [X221 : term] : (($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) | ($true != ((X220 @ X221)))) & ! [X223 : (subst > term > term)] : (? [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) != ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) | ? [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) != $true) & ($true = ((X218 @ id @ X224 @ id)))) | ($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) & (((X220 @ (lam @ X219))) != $true))) | ? [X217 : term] : (((sub @ X217 @ id)) != X217)) | ? [X210 : (term > $o),X211 : term] : (! [X212 : term] : (($true != ((var @ X212))) | ($true = ((X210 @ X212)))) & ! [X215 : term] : (? [X216 : term] : ((((X210 @ (sub @ X215 @ (push @ X216 @ id)))) != $true) & ($true = ((X210 @ X216)))) | (((X210 @ (lam @ X215))) = $true)) & ($true != ((X210 @ X211))) & ! [X214 : term,X213 : term] : (($true != ((X210 @ X213))) | ($true != ((X210 @ X214))) | ($true = ((X210 @ (ap @ X213 @ X214))))))) | ? [X207 : (subst > term > subst > $o)] : ! [X208 : (term > $o)] : ? [X209 : term] : (((X208 @ X209)) != ((X207 @ id @ X209 @ id))))) & ((laminj = $true) <=> ! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413))))) & (induction2_gthm = $true) & (pushprop_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true = ((X283 @ one))) | ($true != ((X285 @ X284))) | ? [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) != ((X283 @ X287))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X319 : (subst > term > subst > $o),X318 : term] : (? [X322 : (subst > term > term)] : ((((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id)) != $true) & ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) & ! [X326 : term] : (($true != ((X319 @ id @ X326 @ id))) | (((X319 @ id @ (X322 @ id @ X326) @ id)) = $true))) | ? [X321 : term,X320 : term] : (($true = ((X319 @ id @ X321 @ id))) & (((X319 @ id @ X320 @ id)) = $true) & ($true != ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id)))) | ($true = ((X319 @ id @ X318 @ id)))) | ? [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (! [X317 : term] : (($true != ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true)) & ! [X311 : (subst > term > term)] : (? [X312 : term] : (($true = ((X310 @ id @ X312 @ id))) & ($true != ((X310 @ id @ (X311 @ id @ X312) @ id)))) | ($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ? [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) != ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) & ($true != ((X309 @ (lam @ X308)))) & ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))))) | ? [X307 : term] : (((sub @ X307 @ id)) != X307)) | ? [X301 : (term > $o),X300 : term] : (! [X305 : term,X306 : term] : (($true != ((X301 @ X305))) | ($true = ((X301 @ (ap @ X305 @ X306)))) | ($true != ((X301 @ X306)))) & ! [X302 : term] : (? [X303 : term] : (($true != ((X301 @ (sub @ X302 @ (push @ X303 @ id))))) & ($true = ((X301 @ X303)))) | (((X301 @ (lam @ X302))) = $true)) & (((X301 @ X300)) != $true) & ! [X304 : term] : ((((X301 @ X304)) = $true) | (((var @ X304)) != $true)))) | ? [X297 : (subst > term > subst > $o)] : ! [X298 : (term > $o)] : ? [X299 : term] : (((X298 @ X299)) != ((X297 @ id @ X299 @ id))))) & (! [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true != ((X330 @ X332))) | (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true)) <=> (pushprop_lem1 = $true)) & (id = ((d2subst @ d_id))) & (ulamvarsh = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_gthm = $true) & (((! [X475 : (subst > term > subst > $o),X476 : term] : (? [X478 : (subst > term > term)] : ((((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) != $true) & ! [X482 : term] : (($true = ((X475 @ id @ (X478 @ id @ X482) @ id))) | ($true != ((X475 @ id @ X482 @ id)))) & ! [X479 : subst,X480 : term,X481 : subst] : (((sub @ (X478 @ X481 @ X480) @ X479)) = ((X478 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479))))) | ($true = ((X475 @ id @ (lam @ X476) @ id))) | ? [X477 : term] : (($true != ((X475 @ id @ (sub @ X476 @ (push @ X477 @ id)) @ id))) & ($true = ((X475 @ id @ X477 @ id))))) | ? [X467 : (subst > term > subst > $o),X468 : term] : (! [X469 : term] : (($true != ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) & ($true != ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) & ! [X470 : (subst > term > term)] : (? [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) != ((sub @ (X470 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true) | ? [X474 : term] : (($true = ((X467 @ id @ X474 @ id))) & ($true != ((X467 @ id @ (X470 @ id @ X474) @ id))))))) | ? [X466 : term] : (((sub @ X466 @ id)) != X466)) <=> (hoasinduction_lem3a_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X333 : subst] : (((comp @ id @ X333)) = X333) <=> (axidl = $true)) & (pushprop_lem3v2_lthm = $true) & ((! [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (? [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) != ((X339 @ X340))) | (((X338 @ X337)) != $true) | ($true = ((X339 @ one)))) | ? [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) != X334)) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotap_gthm = $true) & (! [X367 : (subst > term > subst > $o)] : ? [X368 : (term > $o)] : ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) <=> (hoasinduction_lem0 = $true)) & (sh = ((d2subst @ d_id))) & (hoasapnotvar_lthm = $true) & (axclos = $true) & (! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) = $true) | ? [X350 : term] : (($true = ((X341 @ X350))) & ($true != ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) | ? [X345 : (subst > term > term)] : (! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) & ! [X349 : term] : (($true != ((X343 @ id @ X349 @ id))) | (((X343 @ id @ (X345 @ id @ X349) @ id)) = $true)) & ($true != ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) | ? [X344 : term] : (((X343 @ id @ X344 @ id)) != ((X341 @ X344)))) <=> (hoasinduction_lem3v2a = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X120 : term,X121 : (subst > term > subst > $o)] : (? [X127 : (subst > term > term)] : (! [X130 : subst,X129 : subst,X128 : term] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) & ! [X131 : term] : ((((X121 @ id @ X131 @ id)) != $true) | (((X121 @ id @ (X127 @ id @ X131) @ id)) = $true)) & ($true != ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id)))) | ? [X126 : term] : (($true != ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) & ($true = ((X121 @ id @ X126 @ id)))) | ? [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) & (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) != $true)) | ? [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) != $true) & ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id))))) & (hoasinduction_lem2_gthm = $true) & ((? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) = ((ap @ X417 @ X415))) & (X415 != X418)) | ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422))))) <=> (hoasapinj2_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X502 : (term > $o),X501 : term,X500 : subst] : ? [X503 : (term > $o)] : ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X498 : term] : ? [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) = ((X499 @ sh @ one)))) & ((termmset_lthm = $true) <=> (! [X92 : term] : (((sub @ X92 @ id)) = X92) | ? [X91 : term] : (((sub @ X91 @ id)) != X91))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & (hoaslamnotvar_lthm = $true) & (! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) <=> (hoasapinj1 = $true)) & (apnotvar = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X46 : term,X44 : (subst > term > subst > $o),X47 : term,X45 : (term > $o)] : (? [X56 : subst,X57 : subst,X58 : term,X55 : subst] : (($true != ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56))) & ($true = ((X44 @ X57 @ X58 @ (comp @ X55 @ X56))))) | ? [X54 : term] : (((X44 @ id @ X54 @ id)) != ((X45 @ X54))) | ? [X48 : term,X49 : term] : (($true = ((X44 @ id @ X49 @ id))) & ($true != ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id))) & ($true = ((X44 @ id @ X48 @ id)))) | ($true != ((X45 @ X46))) | (((X45 @ (ap @ X46 @ X47))) = $true) | ? [X53 : term,X50 : subst,X52 : subst,X51 : subst] : ((((X44 @ X50 @ X53 @ (comp @ X51 @ X52))) != $true) & ($true = ((X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52)))) | ($true != ((X45 @ X47))))) & (hoasapnotvar = $true) & (substmonoid_gthm = $true) & (! [X41 : (subst > term > subst > $o)] : ? [X42 : (term > $o)] : ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem1 = $true) & ! [X279 : d_subst,X280 : d_subst] : ((X279 = X280) | (((d2subst @ X280)) != ((d2subst @ X279)))) & ((axidr = $true) <=> ! [X496 : subst] : (((comp @ X496 @ id)) = X496)) & (hoasinduction_lem1_gthm = $true) & (lamnotvar = $true) & (ulamvarind = $true) & ! [X1 : d_term,X0 : d_term] : ((((d2term @ X0)) != ((d2term @ X1))) | (X0 = X1)) & (axassoc = $true) & (axvarshift = $true) & (! [X288 : (term > $o),X289 : term] : (? [X291 : term,X290 : term] : ((((X288 @ X291)) = $true) & ($true != ((X288 @ (ap @ X291 @ X290)))) & ($true = ((X288 @ X290)))) | ? [X294 : term] : (($true = ((var @ X294))) & (((X288 @ X294)) != $true)) | ($true = ((X288 @ X289))) | ? [X292 : term] : (! [X293 : term] : (($true = ((X288 @ (sub @ X292 @ (push @ X293 @ id))))) | ($true != ((X288 @ X293)))) & ($true != ((X288 @ (lam @ X292)))))) <=> (induction2 = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X432 : term] : ? [X433 : (subst > term > term)] : ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434))))) & ((((! [X174 : term,X175 : (subst > term > subst > $o)] : (? [X179 : subst,X177 : term,X178 : subst,X180 : subst] : ((((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178)) != $true) & ($true = ((X175 @ X179 @ X177 @ (comp @ X180 @ X178))))) | ? [X181 : term,X182 : term] : (($true = ((X175 @ id @ X181 @ id))) & ($true = ((X175 @ id @ X182 @ id))) & (((X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id)) != $true)) | ? [X188 : subst,X191 : subst,X189 : term,X190 : subst] : (($true != ((X175 @ X188 @ X189 @ (comp @ X191 @ X190)))) & ($true = ((X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190)))) | ? [X176 : term] : (($true = ((var @ (sub @ X176 @ id)))) & (((X175 @ id @ X176 @ id)) != $true)) | ? [X183 : (subst > term > term)] : (! [X187 : term] : ((((X175 @ id @ (X183 @ id @ X187) @ id)) = $true) | ($true != ((X175 @ id @ X187 @ id)))) & ! [X185 : subst,X184 : term,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) & (((X175 @ id @ (lam @ (X183 @ sh @ one)) @ id)) != $true)) | ($true = ((X175 @ id @ X174 @ id)))) | ? [X158 : (subst > term > subst > $o),X159 : term] : (! [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) | (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) != $true)) & ! [X165 : term] : (($true != ((X158 @ id @ X165 @ id))) | (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true)) & ! [X160 : (subst > term > term)] : (? [X164 : term] : (($true != ((X158 @ id @ (X160 @ id @ X164) @ id))) & (((X158 @ id @ X164 @ id)) = $true)) | (((X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) = $true) | ? [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) != ((sub @ (X160 @ X163 @ X161) @ X162)))) & ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) != $true)) & ($true != ((X158 @ id @ (lam @ X159) @ id))))) | ? [X147 : term,X146 : (subst > term > subst > $o),X145 : term] : ((((X146 @ id @ X145 @ id)) = $true) & ! [X153 : subst,X152 : term,X154 : subst,X155 : subst] : (($true = ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154))) | (((X146 @ X153 @ X152 @ (comp @ X155 @ X154))) != $true)) & ($true = ((X146 @ id @ X147 @ id))) & ! [X150 : subst,X149 : term,X148 : subst,X151 : subst] : (($true != ((X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150))) | ($true = ((X146 @ X151 @ X149 @ (comp @ X148 @ X150))))) & ($true != ((X146 @ id @ (ap @ X145 @ X147) @ id))) & ! [X156 : term,X157 : term] : ((((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id)) = $true) | (((X146 @ id @ X157 @ id)) != $true) | ($true != ((X146 @ id @ X156 @ id)))))) | ? [X139 : (term > $o),X138 : term] : ((((X139 @ X138)) != $true) & ! [X140 : term] : (($true != ((var @ X140))) | ($true = ((X139 @ X140)))) & ! [X142 : term,X141 : term] : (($true = ((X139 @ (ap @ X142 @ X141)))) | (((X139 @ X141)) != $true) | ($true != ((X139 @ X142)))) & ! [X143 : term] : (? [X144 : term] : (($true = ((X139 @ X144))) & (((X139 @ (sub @ X143 @ (push @ X144 @ id)))) != $true)) | ($true = ((X139 @ (lam @ X143))))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X483 : (subst > term > subst > $o),X484 : term] : (? [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))) & ! [X487 : term] : (($true = ((X483 @ id @ (X486 @ id @ X487) @ id))) | (((X483 @ id @ X487 @ id)) != $true))) | ? [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) != $true) & ($true = ((X483 @ id @ X485 @ id)))) | ($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id))))) & (((! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))) | ? [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) = ((ap @ X427 @ X425))) & (X426 != X427))) | ? [X423 : term] : (((sub @ X423 @ id)) != X423)) <=> (hoasapinj1_lthm = $true)) & (! [X78 : term,X77 : (subst > term > subst > $o)] : (? [X88 : term] : ((((X77 @ id @ X88 @ id)) = $true) & ($true != ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) | ($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ? [X79 : (subst > term > term),X80 : term] : (($true != ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) & ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) & ! [X81 : term] : (($true != ((X77 @ id @ X81 @ id))) | (((X77 @ id @ (X79 @ id @ X81) @ id)) = $true)) & ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))))) <=> (hoasinduction_lem3aaa = $true)) & (((! [X25 : term,X26 : (subst > term > subst > $o)] : (? [X31 : (subst > term > term)] : (! [X35 : term] : (($true != ((X26 @ id @ X35 @ id))) | ($true = ((X26 @ id @ (X31 @ id @ X35) @ id)))) & ($true != ((X26 @ id @ (lam @ (X31 @ sh @ one)) @ id))) & ! [X32 : subst,X34 : term,X33 : subst] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32)))) | ? [X40 : term] : ((((X26 @ id @ X40 @ id)) = $true) & (((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id)) != $true)) | ? [X36 : subst,X39 : subst,X37 : term,X38 : subst] : (($true = ((X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39))) & ($true != ((X26 @ X38 @ X37 @ (comp @ X36 @ X39))))) | ($true = ((X26 @ id @ (lam @ X25) @ id))) | ? [X28 : term,X29 : subst,X30 : subst,X27 : subst] : ((((X26 @ X30 @ X28 @ (comp @ X27 @ X29))) = $true) & ($true != ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29))))) | ? [X18 : term,X17 : (subst > term > subst > $o)] : (! [X20 : (subst > term > term)] : (($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ? [X24 : term] : (($true = ((X17 @ id @ X24 @ id))) & (((X17 @ id @ (X20 @ id @ X24) @ id)) != $true)) | ? [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) != ((sub @ (X20 @ X22 @ X23) @ X21)))) & ! [X19 : term] : (($true != ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) & ($true != ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id))))) | ? [X16 : term] : (((sub @ X16 @ id)) != X16)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) <=> (hoasapinj2 = $true)) & (axapp = $true) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (pushprop = $true) & ((axvarcons = $true) <=> ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X358 : term,X357 : (subst > term > subst > $o)] : (? [X359 : term] : (($true != ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) & ($true = ((X357 @ id @ X359 @ id)))) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) | ? [X360 : (subst > term > term)] : (! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) & (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true) & ! [X364 : term] : (($true != ((X357 @ id @ X364 @ id))) | ($true = ((X357 @ id @ (X360 @ id @ X364) @ id))))))) & ((induction = $true) <=> ! [X351 : term,X352 : (term > $o)] : (? [X353 : term] : (($true = ((X352 @ X353))) & ($true != ((X352 @ (lam @ X353))))) | ? [X354 : term] : ((((X352 @ X354)) != $true) & ($true = ((var @ X354)))) | (((X352 @ X351)) = $true) | ? [X355 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true = ((X352 @ X355))) & (((X352 @ (ap @ X356 @ X355))) != $true)))) & (! [X192 : (subst > term > subst > $o),X193 : term] : (? [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) != $true) & ($true = ((X192 @ id @ X194 @ id))) & ($true = ((X192 @ id @ X195 @ id)))) | ? [X196 : (subst > term > term)] : (($true != ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X200 : term] : (($true != ((X192 @ id @ X200 @ id))) | (((X192 @ id @ (X196 @ id @ X200) @ id)) = $true)) & ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197)))) | (((X192 @ id @ X193 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ! [X495 : d_term] : (d_one = X495)), 0.43/0.52 inference(ennf_transformation,[],[f9])). 0.43/0.52 thf(f13,plain,( 0.43/0.52 (axabs = $true) & (hoaslamnotvar_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true = ((X283 @ one))) | ($true != ((X285 @ X284))) | ? [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) != ((X283 @ X287))))) & ((hoasapinj1_lthm = $true) <=> (! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))) | ? [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) = ((ap @ X427 @ X425))) & (X426 != X427)) | ? [X423 : term] : (((sub @ X423 @ id)) != X423))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (? [X374 : term] : (((X371 @ X374)) != ((X372 @ id @ X374 @ id))) | ? [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) != $true) & ($true = ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) | ? [X379 : (subst > term > term)] : (! [X380 : term] : (($true != ((X372 @ id @ X380 @ id))) | (((X372 @ id @ (X379 @ id @ X380) @ id)) = $true)) & ! [X382 : subst,X383 : subst,X381 : term] : (((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ (X379 @ X382 @ X381) @ X383))) & ($true != ((X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)))) | (((X371 @ (lam @ X373))) = $true) | ? [X388 : term] : (($true != ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) & ($true = ((X371 @ X388)))) | ? [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) != $true) & (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true))) | ? [X370 : term] : (((sub @ X370 @ id)) != X370))) & ((! [X174 : term,X175 : (subst > term > subst > $o)] : (? [X179 : subst,X177 : term,X178 : subst,X180 : subst] : ((((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178)) != $true) & ($true = ((X175 @ X179 @ X177 @ (comp @ X180 @ X178))))) | ? [X181 : term,X182 : term] : (($true = ((X175 @ id @ X181 @ id))) & ($true = ((X175 @ id @ X182 @ id))) & (((X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id)) != $true)) | ? [X188 : subst,X191 : subst,X189 : term,X190 : subst] : (($true != ((X175 @ X188 @ X189 @ (comp @ X191 @ X190)))) & ($true = ((X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190)))) | ? [X176 : term] : (($true = ((var @ (sub @ X176 @ id)))) & (((X175 @ id @ X176 @ id)) != $true)) | ? [X183 : (subst > term > term)] : (! [X187 : term] : ((((X175 @ id @ (X183 @ id @ X187) @ id)) = $true) | ($true != ((X175 @ id @ X187 @ id)))) & ! [X185 : subst,X184 : term,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) & (((X175 @ id @ (lam @ (X183 @ sh @ one)) @ id)) != $true)) | ($true = ((X175 @ id @ X174 @ id)))) | ? [X158 : (subst > term > subst > $o),X159 : term] : (! [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) | (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) != $true)) & ! [X165 : term] : (($true != ((X158 @ id @ X165 @ id))) | (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true)) & ! [X160 : (subst > term > term)] : (? [X164 : term] : (($true != ((X158 @ id @ (X160 @ id @ X164) @ id))) & (((X158 @ id @ X164 @ id)) = $true)) | (((X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) = $true) | ? [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) != ((sub @ (X160 @ X163 @ X161) @ X162)))) & ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) != $true)) & ($true != ((X158 @ id @ (lam @ X159) @ id)))) | ? [X147 : term,X146 : (subst > term > subst > $o),X145 : term] : ((((X146 @ id @ X145 @ id)) = $true) & ! [X153 : subst,X152 : term,X154 : subst,X155 : subst] : (($true = ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154))) | (((X146 @ X153 @ X152 @ (comp @ X155 @ X154))) != $true)) & ($true = ((X146 @ id @ X147 @ id))) & ! [X150 : subst,X149 : term,X148 : subst,X151 : subst] : (($true != ((X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150))) | ($true = ((X146 @ X151 @ X149 @ (comp @ X148 @ X150))))) & ($true != ((X146 @ id @ (ap @ X145 @ X147) @ id))) & ! [X156 : term,X157 : term] : ((((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id)) = $true) | (((X146 @ id @ X157 @ id)) != $true) | ($true != ((X146 @ id @ X156 @ id))))) | ? [X139 : (term > $o),X138 : term] : ((((X139 @ X138)) != $true) & ! [X140 : term] : (($true != ((var @ X140))) | ($true = ((X139 @ X140)))) & ! [X142 : term,X141 : term] : (($true = ((X139 @ (ap @ X142 @ X141)))) | (((X139 @ X141)) != $true) | ($true != ((X139 @ X142)))) & ! [X143 : term] : (? [X144 : term] : (($true = ((X139 @ X144))) & (((X139 @ (sub @ X143 @ (push @ X144 @ id)))) != $true)) | ($true = ((X139 @ (lam @ X143))))))) <=> (hoasinduction_lthm = $true)) & (! [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (? [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) = $true) & (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) != $true)) | (((X515 @ (lam @ X514))) = $true) | ? [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true != ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) & ($true = ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) | ? [X521 : term] : (((X516 @ id @ X521 @ id)) != ((X515 @ X521))) | ? [X522 : (subst > term > term)] : ((((X516 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true) & ! [X524 : subst,X523 : term,X525 : subst] : (((X522 @ (comp @ X525 @ X524) @ (sub @ X523 @ X524))) = ((sub @ (X522 @ X525 @ X523) @ X524))) & ! [X526 : term] : (($true = ((X516 @ id @ (X522 @ id @ X526) @ id))) | ($true != ((X516 @ id @ X526 @ id))))) | ? [X527 : term] : (($true != ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) & ($true = ((X515 @ X527))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X358 : term,X357 : (subst > term > subst > $o)] : (? [X359 : term] : (($true != ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) & ($true = ((X357 @ id @ X359 @ id)))) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) | ? [X360 : (subst > term > term)] : (! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) & (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true) & ! [X364 : term] : (($true != ((X357 @ id @ X364 @ id))) | ($true = ((X357 @ id @ (X360 @ id @ X364) @ id))))))) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) <=> (? [X116 : subst] : (((comp @ id @ X116)) != X116) | (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | ? [X117 : subst] : (((comp @ X117 @ id)) != X117))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapnotvar = $true) & (id = ((d2subst @ d_id))) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> (axvarid = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X498 : term] : ? [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) = ((X499 @ sh @ one)))) & (! [X534 : (term > $o),X533 : subst,X532 : term] : (? [X537 : term] : ((((X534 @ (sub @ X537 @ X533))) != $true) & (((var @ X537)) = $true)) | ? [X538 : term] : ((((X534 @ (lam @ X538))) != $true) & ! [X539 : term] : (($true = ((X534 @ (sub @ X538 @ (push @ X539 @ id))))) | ($true != ((X534 @ X539))))) | ? [X536 : term,X535 : term] : ((((X534 @ X535)) = $true) & ($true != ((X534 @ (ap @ X536 @ X535)))) & (((X534 @ X536)) = $true)) | ($true = ((X534 @ (sub @ X532 @ X533))))) <=> (induction2lem = $true)) & (! [X409 : term] : ? [X410 : (subst > term > term)] : ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411))) <=> (hoasinduction_lem3v2_f = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axvarshift = $true) & ((? [X64 : subst,X62 : term,X63 : (term > $o)] : ((((X63 @ (sub @ X62 @ X64))) != $true) & ! [X66 : term,X67 : term] : (($true != ((X63 @ X67))) | ($true = ((X63 @ (ap @ X66 @ X67)))) | ($true != ((X63 @ X66)))) & ! [X68 : term] : (($true = ((X63 @ (lam @ X68)))) | ? [X69 : term] : (($true = ((X63 @ X69))) & ($true != ((X63 @ (sub @ X68 @ (push @ X69 @ id))))))) & ! [X65 : term] : ((((var @ X65)) != $true) | ($true = ((X63 @ (sub @ X65 @ X64)))))) | ! [X70 : (term > $o),X71 : term] : (? [X76 : term] : (($true != ((X70 @ X76))) & (((var @ X76)) = $true)) | ? [X72 : term] : ((((X70 @ (lam @ X72))) != $true) & ! [X73 : term] : (($true = ((X70 @ (sub @ X72 @ (push @ X73 @ id))))) | ($true != ((X70 @ X73))))) | ($true = ((X70 @ X71))) | ? [X74 : term,X75 : term] : (($true = ((X70 @ X75))) & (((X70 @ (ap @ X75 @ X74))) != $true) & ($true = ((X70 @ X74))))) | ? [X61 : term] : (((sub @ X61 @ id)) != X61)) <=> (induction2_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (induction2_gthm = $true) & (pushprop_gthm = $true) & ! [X1 : d_term,X0 : d_term] : ((((d2term @ X0)) != ((d2term @ X1))) | (X0 = X1)) & ((termmset_lthm = $true) <=> (! [X92 : term] : (((sub @ X92 @ id)) = X92) | ? [X91 : term] : (((sub @ X91 @ id)) != X91))) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & (! [X333 : subst] : (((comp @ id @ X333)) = X333) <=> (axidl = $true)) & ((hoasinduction = $true) <=> ! [X440 : term,X441 : (subst > term > subst > $o)] : (? [X442 : term,X443 : term] : (($true = ((X441 @ id @ X443 @ id))) & ($true = ((X441 @ id @ X442 @ id))) & ($true != ((X441 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id)))) | ? [X448 : (subst > term > term)] : (! [X450 : term,X452 : subst,X451 : subst] : (((X448 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X448 @ X452 @ X450) @ X451))) & ! [X449 : term] : (($true = ((X441 @ id @ (X448 @ id @ X449) @ id))) | ($true != ((X441 @ id @ X449 @ id)))) & (((X441 @ id @ (lam @ (X448 @ sh @ one)) @ id)) != $true)) | ? [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true != ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) & ($true = ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) | ($true = ((X441 @ id @ X440 @ id))) | ? [X453 : term] : ((((X441 @ id @ X453 @ id)) != $true) & ($true = ((var @ (sub @ X453 @ id))))) | ? [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) != $true) & ($true = ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))))) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) <=> (substmonoid = $true)) & ((? [X256 : (term > $o),X255 : term] : (! [X259 : term,X260 : term] : (($true != ((X256 @ X260))) | ($true != ((X256 @ X259))) | ($true = ((X256 @ (ap @ X260 @ X259))))) & ! [X258 : term] : (($true != ((X256 @ X258))) | ($true = ((X256 @ (lam @ X258))))) & ! [X257 : term] : ((((X256 @ X257)) = $true) | (((var @ X257)) != $true)) & (((X256 @ X255)) != $true)) | ? [X252 : term,X253 : subst] : (((comp @ sh @ (push @ X252 @ X253))) != X253) | ? [X254 : subst] : (((comp @ X254 @ id)) != X254) | ? [X251 : term,X250 : subst] : (((sub @ one @ (push @ X251 @ X250))) != X251) | ! [X261 : (term > $o),X263 : term,X262 : subst] : (? [X266 : term] : ((((var @ X266)) = $true) & (((X261 @ (sub @ X266 @ X262))) != $true)) | ($true = ((X261 @ (sub @ X263 @ X262)))) | ? [X267 : term] : (! [X268 : term] : (($true != ((X261 @ X268))) | (((X261 @ (sub @ X267 @ (push @ X268 @ id)))) = $true)) & ($true != ((X261 @ (lam @ X267))))) | ? [X264 : term,X265 : term] : (($true != ((X261 @ (ap @ X265 @ X264)))) & ($true = ((X261 @ X265))) & (((X261 @ X264)) = $true)))) <=> (induction2lem_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X502 : (term > $o),X501 : term,X500 : subst] : ? [X503 : (term > $o)] : ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X25 : term,X26 : (subst > term > subst > $o)] : (? [X31 : (subst > term > term)] : (! [X35 : term] : (($true != ((X26 @ id @ X35 @ id))) | ($true = ((X26 @ id @ (X31 @ id @ X35) @ id)))) & ($true != ((X26 @ id @ (lam @ (X31 @ sh @ one)) @ id))) & ! [X32 : subst,X34 : term,X33 : subst] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32)))) | ? [X40 : term] : ((((X26 @ id @ X40 @ id)) = $true) & (((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id)) != $true)) | ? [X36 : subst,X39 : subst,X37 : term,X38 : subst] : (($true = ((X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39))) & ($true != ((X26 @ X38 @ X37 @ (comp @ X36 @ X39))))) | ($true = ((X26 @ id @ (lam @ X25) @ id))) | ? [X28 : term,X29 : subst,X30 : subst,X27 : subst] : ((((X26 @ X30 @ X28 @ (comp @ X27 @ X29))) = $true) & ($true != ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29))))) | ? [X16 : term] : (((sub @ X16 @ id)) != X16) | ? [X18 : term,X17 : (subst > term > subst > $o)] : (! [X20 : (subst > term > term)] : (($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ? [X24 : term] : (($true = ((X17 @ id @ X24 @ id))) & (((X17 @ id @ (X20 @ id @ X24) @ id)) != $true)) | ? [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) != ((sub @ (X20 @ X22 @ X23) @ X21)))) & ! [X19 : term] : (($true != ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) & ($true != ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id)))))) & (pushprop_lem3v2 = $true) & ! [X327 : d_subst] : (d_id = X327) & (ulamvarsh = $true) & (lamnotvar = $true) & ((? [X301 : (term > $o),X300 : term] : (! [X305 : term,X306 : term] : (($true != ((X301 @ X305))) | ($true = ((X301 @ (ap @ X305 @ X306)))) | ($true != ((X301 @ X306)))) & ! [X302 : term] : (? [X303 : term] : (($true != ((X301 @ (sub @ X302 @ (push @ X303 @ id))))) & ($true = ((X301 @ X303)))) | (((X301 @ (lam @ X302))) = $true)) & (((X301 @ X300)) != $true) & ! [X304 : term] : ((((X301 @ X304)) = $true) | (((var @ X304)) != $true))) | ! [X319 : (subst > term > subst > $o),X318 : term] : (? [X322 : (subst > term > term)] : ((((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id)) != $true) & ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) & ! [X326 : term] : (($true != ((X319 @ id @ X326 @ id))) | (((X319 @ id @ (X322 @ id @ X326) @ id)) = $true))) | ? [X321 : term,X320 : term] : (($true = ((X319 @ id @ X321 @ id))) & (((X319 @ id @ X320 @ id)) = $true) & ($true != ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id)))) | ($true = ((X319 @ id @ X318 @ id)))) | ? [X297 : (subst > term > subst > $o)] : ! [X298 : (term > $o)] : ? [X299 : term] : (((X298 @ X299)) != ((X297 @ id @ X299 @ id))) | ? [X307 : term] : (((sub @ X307 @ id)) != X307) | ? [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (! [X317 : term] : (($true != ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true)) & ! [X311 : (subst > term > term)] : (? [X312 : term] : (($true = ((X310 @ id @ X312 @ id))) & ($true != ((X310 @ id @ (X311 @ id @ X312) @ id)))) | ($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ? [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) != ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) & ($true != ((X309 @ (lam @ X308)))) & ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X288 : (term > $o),X289 : term] : (? [X291 : term,X290 : term] : ((((X288 @ X291)) = $true) & ($true != ((X288 @ (ap @ X291 @ X290)))) & ($true = ((X288 @ X290)))) | ? [X294 : term] : (($true = ((var @ X294))) & (((X288 @ X294)) != $true)) | ($true = ((X288 @ X289))) | ? [X292 : term] : (! [X293 : term] : (($true = ((X288 @ (sub @ X292 @ (push @ X293 @ id))))) | ($true != ((X288 @ X293)))) & ($true != ((X288 @ (lam @ X292)))))) <=> (induction2 = $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X46 : term,X44 : (subst > term > subst > $o),X47 : term,X45 : (term > $o)] : (? [X56 : subst,X57 : subst,X58 : term,X55 : subst] : (($true != ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56))) & ($true = ((X44 @ X57 @ X58 @ (comp @ X55 @ X56))))) | ? [X54 : term] : (((X44 @ id @ X54 @ id)) != ((X45 @ X54))) | ? [X48 : term,X49 : term] : (($true = ((X44 @ id @ X49 @ id))) & ($true != ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id))) & ($true = ((X44 @ id @ X48 @ id)))) | ($true != ((X45 @ X46))) | (((X45 @ (ap @ X46 @ X47))) = $true) | ? [X53 : term,X50 : subst,X52 : subst,X51 : subst] : ((((X44 @ X50 @ X53 @ (comp @ X51 @ X52))) != $true) & ($true = ((X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52)))) | ($true != ((X45 @ X47))))) & (axmap = $true) & ((induction = $true) <=> ! [X351 : term,X352 : (term > $o)] : (? [X353 : term] : (($true = ((X352 @ X353))) & ($true != ((X352 @ (lam @ X353))))) | ? [X354 : term] : ((((X352 @ X354)) != $true) & ($true = ((var @ X354)))) | (((X352 @ X351)) = $true) | ? [X355 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true = ((X352 @ X355))) & (((X352 @ (ap @ X356 @ X355))) != $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)))))))))))))) & (! [X389 : term,X391 : subst,X390 : (term > $o)] : ? [X392 : (term > $o)] : ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393))) <=> (pushprop_lem0 = $true)) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X41 : (subst > term > subst > $o)] : ? [X42 : (term > $o)] : ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43))) <=> (hoasinduction_lem0_lthm = $true)) & ((? [X466 : term] : (((sub @ X466 @ id)) != X466) | ? [X467 : (subst > term > subst > $o),X468 : term] : (! [X469 : term] : (($true != ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) & ($true != ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) & ! [X470 : (subst > term > term)] : (? [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) != ((sub @ (X470 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true) | ? [X474 : term] : (($true = ((X467 @ id @ X474 @ id))) & ($true != ((X467 @ id @ (X470 @ id @ X474) @ id)))))) | ! [X475 : (subst > term > subst > $o),X476 : term] : (? [X478 : (subst > term > term)] : ((((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) != $true) & ! [X482 : term] : (($true = ((X475 @ id @ (X478 @ id @ X482) @ id))) | ($true != ((X475 @ id @ X482 @ id)))) & ! [X479 : subst,X480 : term,X481 : subst] : (((sub @ (X478 @ X481 @ X480) @ X479)) = ((X478 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479))))) | ($true = ((X475 @ id @ (lam @ X476) @ id))) | ? [X477 : term] : (($true != ((X475 @ id @ (sub @ X476 @ (push @ X477 @ id)) @ id))) & ($true = ((X475 @ id @ X477 @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (ulamvarind = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X432 : term] : ? [X433 : (subst > term > term)] : ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434))))) & ((? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) = ((ap @ X417 @ X415))) & (X415 != X418)) | ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422))))) <=> (hoasapinj2_lthm = $true)) & ((termmset = $true) <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (! [X3 : term,X5 : (subst > term > subst > $o),X4 : term] : (? [X10 : term,X11 : term] : ((((X5 @ id @ X10 @ id)) = $true) & ($true != ((X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id))) & ($true = ((X5 @ id @ X11 @ id)))) | (((X5 @ id @ (ap @ X4 @ X3) @ id)) = $true) | ? [X7 : term,X6 : subst,X9 : subst,X8 : subst] : (($true = ((X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6))) & (((X5 @ X9 @ X7 @ (comp @ X8 @ X6))) != $true)) | ($true != ((X5 @ id @ X3 @ id))) | ($true != ((X5 @ id @ X4 @ id))) | ? [X13 : subst,X14 : subst,X12 : term,X15 : subst] : ((((X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) != $true) & (((X5 @ X15 @ X12 @ (comp @ X13 @ X14))) = $true))) <=> (hoasinduction_lem2 = $true)) & ((apinj1 = $true) <=> ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437))))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & ((! [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ? [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) != ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) | ? [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) != ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one))))) | ? [X104 : term,X105 : term] : ((((lam @ X104)) = ((lam @ X105))) & (X104 != X105)) | ? [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) != X100) | ? [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) != X103)) <=> (hoaslaminj_lthm = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((pushprop_lem1_lthm = $true) <=> (? [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) != X505) | ! [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) != $true) | (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true)) | ? [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) != X508))) & (hoaslamnotap_lthm = $true) & (sh = ((d2subst @ d_id))) & ((hoasinduction_lem3aa = $true) <=> ! [X483 : (subst > term > subst > $o),X484 : term] : (? [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))) & ! [X487 : term] : (($true = ((X483 @ id @ (X486 @ id @ X487) @ id))) | (((X483 @ id @ X487 @ id)) != $true))) | ? [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) != $true) & ($true = ((X483 @ id @ X485 @ id)))) | ($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id))))) & ((hoaslamnotap = $true) <=> ! [X201 : term,X202 : (subst > term > term),X203 : term] : (? [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) != ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one)))))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop = $true) & (hoasinduction_lem2_gthm = $true) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) <=> (hoasapinj2 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) <=> (hoasapinj1 = $true)) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) <=> (axshiftcons = $true)) & (hoasinduction_lem3v2_gthm = $true) & (termmset_gthm = $true) & ((! [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (? [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) != ((X339 @ X340))) | (((X338 @ X337)) != $true) | ($true = ((X339 @ one)))) | ? [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) != X334)) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3 = $true) <=> ! [X120 : term,X121 : (subst > term > subst > $o)] : (? [X127 : (subst > term > term)] : (! [X130 : subst,X129 : subst,X128 : term] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) & ! [X131 : term] : ((((X121 @ id @ X131 @ id)) != $true) | (((X121 @ id @ (X127 @ id @ X131) @ id)) = $true)) & ($true != ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id)))) | ? [X126 : term] : (($true != ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) & ($true = ((X121 @ id @ X126 @ id)))) | ? [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) & (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) != $true)) | ? [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) != $true) & ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id))))) & ((laminj = $true) <=> ! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413))))) & (axapp = $true) & (hoasapinj1_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotvar = $true) & (apnotvar = $true) & (pushprop_lthm = $true) & ((shinj = $true) <=> ! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh))))) & (pushprop_lem1_gthm = $true) & (! [X78 : term,X77 : (subst > term > subst > $o)] : (? [X88 : term] : ((((X77 @ id @ X88 @ id)) = $true) & ($true != ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) | ($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ? [X79 : (subst > term > term),X80 : term] : (($true != ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) & ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) & ! [X81 : term] : (($true != ((X77 @ id @ X81 @ id))) | (((X77 @ id @ (X79 @ id @ X81) @ id)) = $true)) & ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X458 : term,X459 : (subst > term > subst > $o)] : (? [X465 : term] : (($true = ((X459 @ id @ X465 @ id))) & (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) != $true)) | ($true = ((X459 @ id @ (lam @ X458) @ id))) | ? [X460 : (subst > term > term)] : (! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) & ! [X464 : term] : ((((X459 @ id @ X464 @ id)) != $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) & ($true != ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))))) & ((! [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (? [X402 : term] : (($true != ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) & ($true = ((X399 @ X402)))) | ? [X403 : term] : (((X401 @ id @ X403 @ id)) != ((X399 @ X403))) | (((X399 @ (lam @ X400))) = $true) | ? [X404 : (subst > term > term)] : (! [X408 : term] : (($true = ((X401 @ id @ (X404 @ id @ X408) @ id))) | (((X401 @ id @ X408 @ id)) != $true)) & ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) & ($true != ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) | ? [X394 : term] : ! [X395 : (subst > term > term)] : ? [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) != ((X395 @ X397 @ X396))) | ? [X398 : term] : (((sub @ X398 @ id)) != X398)) <=> (hoasinduction_lem3v2a_lthm = $true)) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) = $true) | ? [X350 : term] : (($true = ((X341 @ X350))) & ($true != ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) | ? [X345 : (subst > term > term)] : (! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) & ! [X349 : term] : (($true != ((X343 @ id @ X349 @ id))) | (((X343 @ id @ (X345 @ id @ X349) @ id)) = $true)) & ($true != ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) | ? [X344 : term] : (((X343 @ id @ X344 @ id)) != ((X341 @ X344)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & (! [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true != ((X330 @ X332))) | (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true)) <=> (pushprop_lem1 = $true)) & ! [X495 : d_term] : (d_one = X495) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (? [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) & ! [X221 : term] : (($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) | ($true != ((X220 @ X221)))) & ! [X223 : (subst > term > term)] : (? [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) != ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) | ? [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) != $true) & ($true = ((X218 @ id @ X224 @ id)))) | ($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) & (((X220 @ (lam @ X219))) != $true)) | ? [X210 : (term > $o),X211 : term] : (! [X212 : term] : (($true != ((var @ X212))) | ($true = ((X210 @ X212)))) & ! [X215 : term] : (? [X216 : term] : ((((X210 @ (sub @ X215 @ (push @ X216 @ id)))) != $true) & ($true = ((X210 @ X216)))) | (((X210 @ (lam @ X215))) = $true)) & ($true != ((X210 @ X211))) & ! [X214 : term,X213 : term] : (($true != ((X210 @ X213))) | ($true != ((X210 @ X214))) | ($true = ((X210 @ (ap @ X213 @ X214)))))) | ! [X228 : term,X229 : (subst > term > subst > $o)] : (? [X240 : term] : (($true = ((var @ (sub @ X240 @ id)))) & ($true != ((X229 @ id @ X240 @ id)))) | ? [X241 : (subst > term > term)] : (($true != ((X229 @ id @ (lam @ (X241 @ sh @ one)) @ id))) & ! [X245 : term] : (($true != ((X229 @ id @ X245 @ id))) | ($true = ((X229 @ id @ (X241 @ id @ X245) @ id)))) & ! [X244 : term,X243 : subst,X242 : subst] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242)))) | ? [X230 : term,X231 : term] : ((((X229 @ id @ X230 @ id)) = $true) & (((X229 @ id @ X231 @ id)) = $true) & (((X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id)) != $true)) | ($true = ((X229 @ id @ X228 @ id))) | ? [X237 : subst,X236 : term,X239 : subst,X238 : subst] : (($true != ((X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237))) & ($true = ((X229 @ X238 @ X236 @ (comp @ X239 @ X237))))) | ? [X233 : subst,X235 : subst,X232 : subst,X234 : term] : ((((X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) = $true) & (((X229 @ X233 @ X234 @ (comp @ X235 @ X232))) != $true))) | ? [X217 : term] : (((sub @ X217 @ id)) != X217) | ? [X207 : (subst > term > subst > $o)] : ! [X208 : (term > $o)] : ? [X209 : term] : (((X208 @ X209)) != ((X207 @ id @ X209 @ id))))) & ((apinj2 = $true) <=> ! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247))))) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X136 : term] : ? [X137 : (subst > term > term)] : (((X137 @ sh @ one)) = ((sub @ X136 @ (push @ one @ sh))))) & (lamnotap != $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ? [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) != ((sub @ (X272 @ X273 @ X275) @ X274))) | ? [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) != ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276))))) <=> (hoaslaminj = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((axidr = $true) <=> ! [X496 : subst] : (((comp @ X496 @ id)) = X496)) & (hoasinduction_lem3_gthm = $true) & (! [X192 : (subst > term > subst > $o),X193 : term] : (? [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) != $true) & ($true = ((X192 @ id @ X194 @ id))) & ($true = ((X192 @ id @ X195 @ id)))) | ? [X196 : (subst > term > term)] : (($true != ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X200 : term] : (($true != ((X192 @ id @ X200 @ id))) | (((X192 @ id @ (X196 @ id @ X200) @ id)) = $true)) & ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197)))) | (((X192 @ id @ X193 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X367 : (subst > term > subst > $o)] : ? [X368 : (term > $o)] : ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) <=> (hoasinduction_lem0 = $true)) & (axassoc = $true) & ((axscons = $true) <=> ! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497)) & (hoasinduction_lem2_lthm = $true) & ((axvarcons = $true) <=> ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & ! [X279 : d_subst,X280 : d_subst] : ((X279 = X280) | (((d2subst @ X280)) != ((d2subst @ X279))))), 0.43/0.52 inference(flattening,[],[f12])). 0.43/0.52 thf(f14,definition,( 0.43/0.52 ! [X229 : (subst > term > subst > $o)] : ((((sP0 @ X229)) = $true) <=> ? [X230 : term,X231 : term] : ((((X229 @ id @ X230 @ id)) = $true) & (((X229 @ id @ X231 @ id)) = $true) & (((X229 @ id @ (ap @ (sub @ X230 @ id) @ X231) @ id)) != $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f15,definition,( 0.43/0.52 ! [X229 : (subst > term > subst > $o)] : ((((sP1 @ X229)) = $true) <=> ? [X241 : (subst > term > term)] : (($true != ((X229 @ id @ (lam @ (X241 @ sh @ one)) @ id))) & ! [X245 : term] : (($true != ((X229 @ id @ X245 @ id))) | ($true = ((X229 @ id @ (X241 @ id @ X245) @ id)))) & ! [X244 : term,X243 : subst,X242 : subst] : (((X241 @ (comp @ X243 @ X242) @ (sub @ X244 @ X242))) = ((sub @ (X241 @ X243 @ X244) @ X242)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f16,definition,( 0.43/0.52 ($true = sP2) <=> ? [X210 : (term > $o),X211 : term] : (! [X212 : term] : (($true != ((var @ X212))) | ($true = ((X210 @ X212)))) & ! [X215 : term] : (? [X216 : term] : ((((X210 @ (sub @ X215 @ (push @ X216 @ id)))) != $true) & ($true = ((X210 @ X216)))) | (((X210 @ (lam @ X215))) = $true)) & ($true != ((X210 @ X211))) & ! [X214 : term,X213 : term] : (($true != ((X210 @ X213))) | ($true != ((X210 @ X214))) | ($true = ((X210 @ (ap @ X213 @ X214))))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f17,definition,( 0.43/0.52 ($true = sP3) <=> ! [X228 : term,X229 : (subst > term > subst > $o)] : (? [X240 : term] : (($true = ((var @ (sub @ X240 @ id)))) & ($true != ((X229 @ id @ X240 @ id)))) | (((sP1 @ X229)) = $true) | (((sP0 @ X229)) = $true) | ($true = ((X229 @ id @ X228 @ id))) | ? [X237 : subst,X236 : term,X239 : subst,X238 : subst] : (($true != ((X229 @ (comp @ X238 @ X239) @ (sub @ X236 @ X239) @ X237))) & ($true = ((X229 @ X238 @ X236 @ (comp @ X239 @ X237))))) | ? [X233 : subst,X235 : subst,X232 : subst,X234 : term] : ((((X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X232)) = $true) & (((X229 @ X233 @ X234 @ (comp @ X235 @ X232))) != $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f18,definition,( 0.43/0.52 ! [X121 : (subst > term > subst > $o)] : (($true = ((sP4 @ X121))) <=> ? [X127 : (subst > term > term)] : (! [X130 : subst,X129 : subst,X128 : term] : (((X127 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X127 @ X130 @ X128) @ X129))) & ! [X131 : term] : ((((X121 @ id @ X131 @ id)) != $true) | (((X121 @ id @ (X127 @ id @ X131) @ id)) = $true)) & ($true != ((X121 @ id @ (lam @ (X127 @ sh @ one)) @ id)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f19,definition,( 0.43/0.52 ($true = sP5) <=> ! [X3 : term,X5 : (subst > term > subst > $o),X4 : term] : (? [X10 : term,X11 : term] : ((((X5 @ id @ X10 @ id)) = $true) & ($true != ((X5 @ id @ (ap @ (sub @ X10 @ id) @ X11) @ id))) & ($true = ((X5 @ id @ X11 @ id)))) | (((X5 @ id @ (ap @ X4 @ X3) @ id)) = $true) | ? [X7 : term,X6 : subst,X9 : subst,X8 : subst] : (($true = ((X5 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8) @ X6))) & (((X5 @ X9 @ X7 @ (comp @ X8 @ X6))) != $true)) | ($true != ((X5 @ id @ X3 @ id))) | ($true != ((X5 @ id @ X4 @ id))) | ? [X13 : subst,X14 : subst,X12 : term,X15 : subst] : ((((X5 @ (comp @ X15 @ X13) @ (sub @ X12 @ X13) @ X14)) != $true) & (((X5 @ X15 @ X12 @ (comp @ X13 @ X14))) = $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f20,definition,( 0.43/0.52 ($true = sP6) <=> ! [X475 : (subst > term > subst > $o),X476 : term] : (? [X478 : (subst > term > term)] : ((((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) != $true) & ! [X482 : term] : (($true = ((X475 @ id @ (X478 @ id @ X482) @ id))) | ($true != ((X475 @ id @ X482 @ id)))) & ! [X479 : subst,X480 : term,X481 : subst] : (((sub @ (X478 @ X481 @ X480) @ X479)) = ((X478 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479))))) | ($true = ((X475 @ id @ (lam @ X476) @ id))) | ? [X477 : term] : (($true != ((X475 @ id @ (sub @ X476 @ (push @ X477 @ id)) @ id))) & ($true = ((X475 @ id @ X477 @ id)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f21,definition,( 0.43/0.52 ($true = sP7) <=> ! [X46 : term,X44 : (subst > term > subst > $o),X47 : term,X45 : (term > $o)] : (? [X56 : subst,X57 : subst,X58 : term,X55 : subst] : (($true != ((X44 @ (comp @ X57 @ X55) @ (sub @ X58 @ X55) @ X56))) & ($true = ((X44 @ X57 @ X58 @ (comp @ X55 @ X56))))) | ? [X54 : term] : (((X44 @ id @ X54 @ id)) != ((X45 @ X54))) | ? [X48 : term,X49 : term] : (($true = ((X44 @ id @ X49 @ id))) & ($true != ((X44 @ id @ (ap @ (sub @ X49 @ id) @ X48) @ id))) & ($true = ((X44 @ id @ X48 @ id)))) | ($true != ((X45 @ X46))) | (((X45 @ (ap @ X46 @ X47))) = $true) | ? [X53 : term,X50 : subst,X52 : subst,X51 : subst] : ((((X44 @ X50 @ X53 @ (comp @ X51 @ X52))) != $true) & ($true = ((X44 @ (comp @ X50 @ X51) @ (sub @ X53 @ X51) @ X52)))) | ($true != ((X45 @ X47))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f22,definition,( 0.43/0.52 (sP8 = $true) <=> ! [X288 : (term > $o),X289 : term] : (? [X291 : term,X290 : term] : ((((X288 @ X291)) = $true) & ($true != ((X288 @ (ap @ X291 @ X290)))) & ($true = ((X288 @ X290)))) | ? [X294 : term] : (($true = ((var @ X294))) & (((X288 @ X294)) != $true)) | ($true = ((X288 @ X289))) | ? [X292 : term] : (! [X293 : term] : (($true = ((X288 @ (sub @ X292 @ (push @ X293 @ id))))) | ($true != ((X288 @ X293)))) & ($true != ((X288 @ (lam @ X292))))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f23,definition,( 0.43/0.52 ($true = sP9) <=> ? [X301 : (term > $o),X300 : term] : (! [X305 : term,X306 : term] : (($true != ((X301 @ X305))) | ($true = ((X301 @ (ap @ X305 @ X306)))) | ($true != ((X301 @ X306)))) & ! [X302 : term] : (? [X303 : term] : (($true != ((X301 @ (sub @ X302 @ (push @ X303 @ id))))) & ($true = ((X301 @ X303)))) | (((X301 @ (lam @ X302))) = $true)) & (((X301 @ X300)) != $true) & ! [X304 : term] : ((((X301 @ X304)) = $true) | (((var @ X304)) != $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f24,definition,( 0.43/0.52 ($true = sP10) <=> ! [X319 : (subst > term > subst > $o),X318 : term] : (? [X322 : (subst > term > term)] : ((((X319 @ id @ (lam @ (X322 @ sh @ one)) @ id)) != $true) & ! [X323 : term,X324 : subst,X325 : subst] : (((sub @ (X322 @ X325 @ X323) @ X324)) = ((X322 @ (comp @ X325 @ X324) @ (sub @ X323 @ X324)))) & ! [X326 : term] : (($true != ((X319 @ id @ X326 @ id))) | (((X319 @ id @ (X322 @ id @ X326) @ id)) = $true))) | ? [X321 : term,X320 : term] : (($true = ((X319 @ id @ X321 @ id))) & (((X319 @ id @ X320 @ id)) = $true) & ($true != ((X319 @ id @ (ap @ (sub @ X320 @ id) @ X321) @ id)))) | ($true = ((X319 @ id @ X318 @ id))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f25,definition,( 0.43/0.52 ! [X26 : (subst > term > subst > $o)] : ((((sP11 @ X26)) = $true) <=> ? [X31 : (subst > term > term)] : (! [X35 : term] : (($true != ((X26 @ id @ X35 @ id))) | ($true = ((X26 @ id @ (X31 @ id @ X35) @ id)))) & ($true != ((X26 @ id @ (lam @ (X31 @ sh @ one)) @ id))) & ! [X32 : subst,X34 : term,X33 : subst] : (((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32))) = ((sub @ (X31 @ X33 @ X34) @ X32)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f26,definition,( 0.43/0.52 ($true = sP12) <=> ! [X25 : term,X26 : (subst > term > subst > $o)] : ((((sP11 @ X26)) = $true) | ? [X40 : term] : ((((X26 @ id @ X40 @ id)) = $true) & (((X26 @ id @ (sub @ X25 @ (push @ X40 @ id)) @ id)) != $true)) | ? [X36 : subst,X39 : subst,X37 : term,X38 : subst] : (($true = ((X26 @ (comp @ X38 @ X36) @ (sub @ X37 @ X36) @ X39))) & ($true != ((X26 @ X38 @ X37 @ (comp @ X36 @ X39))))) | ($true = ((X26 @ id @ (lam @ X25) @ id))) | ? [X28 : term,X29 : subst,X30 : subst,X27 : subst] : ((((X26 @ X30 @ X28 @ (comp @ X27 @ X29))) = $true) & ($true != ((X26 @ (comp @ X30 @ X27) @ (sub @ X28 @ X27) @ X29)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f27,definition,( 0.43/0.52 ($true = sP13) <=> ? [X256 : (term > $o),X255 : term] : (! [X259 : term,X260 : term] : (($true != ((X256 @ X260))) | ($true != ((X256 @ X259))) | ($true = ((X256 @ (ap @ X260 @ X259))))) & ! [X258 : term] : (($true != ((X256 @ X258))) | ($true = ((X256 @ (lam @ X258))))) & ! [X257 : term] : ((((X256 @ X257)) = $true) | (((var @ X257)) != $true)) & (((X256 @ X255)) != $true))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f28,definition,( 0.43/0.52 ($true = sP14) <=> (($true = sP13) | ? [X252 : term,X253 : subst] : (((comp @ sh @ (push @ X252 @ X253))) != X253) | ? [X254 : subst] : (((comp @ X254 @ id)) != X254) | ? [X251 : term,X250 : subst] : (((sub @ one @ (push @ X251 @ X250))) != X251) | ! [X261 : (term > $o),X263 : term,X262 : subst] : (? [X266 : term] : ((((var @ X266)) = $true) & (((X261 @ (sub @ X266 @ X262))) != $true)) | ($true = ((X261 @ (sub @ X263 @ X262)))) | ? [X267 : term] : (! [X268 : term] : (($true != ((X261 @ X268))) | (((X261 @ (sub @ X267 @ (push @ X268 @ id)))) = $true)) & ($true != ((X261 @ (lam @ X267))))) | ? [X264 : term,X265 : term] : (($true != ((X261 @ (ap @ X265 @ X264)))) & ($true = ((X261 @ X265))) & (((X261 @ X264)) = $true))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f29,definition,( 0.43/0.52 ! [X441 : (subst > term > subst > $o)] : ((((sP15 @ X441)) = $true) <=> ? [X448 : (subst > term > term)] : (! [X450 : term,X452 : subst,X451 : subst] : (((X448 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X448 @ X452 @ X450) @ X451))) & ! [X449 : term] : (($true = ((X441 @ id @ (X448 @ id @ X449) @ id))) | ($true != ((X441 @ id @ X449 @ id)))) & (((X441 @ id @ (lam @ (X448 @ sh @ one)) @ id)) != $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f30,definition,( 0.43/0.52 ! [X441 : (subst > term > subst > $o)] : ((((sP16 @ X441)) = $true) <=> ? [X442 : term,X443 : term] : (($true = ((X441 @ id @ X443 @ id))) & ($true = ((X441 @ id @ X442 @ id))) & ($true != ((X441 @ id @ (ap @ (sub @ X443 @ id) @ X442) @ id)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f31,definition,( 0.43/0.52 ($true = sP17) <=> ? [X64 : subst,X62 : term,X63 : (term > $o)] : ((((X63 @ (sub @ X62 @ X64))) != $true) & ! [X66 : term,X67 : term] : (($true != ((X63 @ X67))) | ($true = ((X63 @ (ap @ X66 @ X67)))) | ($true != ((X63 @ X66)))) & ! [X68 : term] : (($true = ((X63 @ (lam @ X68)))) | ? [X69 : term] : (($true = ((X63 @ X69))) & ($true != ((X63 @ (sub @ X68 @ (push @ X69 @ id))))))) & ! [X65 : term] : ((((var @ X65)) != $true) | ($true = ((X63 @ (sub @ X65 @ X64))))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f32,definition,( 0.43/0.52 ($true = sP18) <=> (($true = sP17) | ! [X70 : (term > $o),X71 : term] : (? [X76 : term] : (($true != ((X70 @ X76))) & (((var @ X76)) = $true)) | ? [X72 : term] : ((((X70 @ (lam @ X72))) != $true) & ! [X73 : term] : (($true = ((X70 @ (sub @ X72 @ (push @ X73 @ id))))) | ($true != ((X70 @ X73))))) | ($true = ((X70 @ X71))) | ? [X74 : term,X75 : term] : (($true = ((X70 @ X75))) & (((X70 @ (ap @ X75 @ X74))) != $true) & ($true = ((X70 @ X74))))) | ? [X61 : term] : (((sub @ X61 @ id)) != X61))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f33,definition,( 0.43/0.52 (sP19 = $true) <=> ! [X534 : (term > $o),X533 : subst,X532 : term] : (? [X537 : term] : ((((X534 @ (sub @ X537 @ X533))) != $true) & (((var @ X537)) = $true)) | ? [X538 : term] : ((((X534 @ (lam @ X538))) != $true) & ! [X539 : term] : (($true = ((X534 @ (sub @ X538 @ (push @ X539 @ id))))) | ($true != ((X534 @ X539))))) | ? [X536 : term,X535 : term] : ((((X534 @ X535)) = $true) & ($true != ((X534 @ (ap @ X536 @ X535)))) & (((X534 @ X536)) = $true)) | ($true = ((X534 @ (sub @ X532 @ X533)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f34,definition,( 0.43/0.52 ! [X516 : (subst > term > subst > $o)] : (($true = ((sP20 @ X516))) <=> ? [X522 : (subst > term > term)] : ((((X516 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true) & ! [X524 : subst,X523 : term,X525 : subst] : (((X522 @ (comp @ X525 @ X524) @ (sub @ X523 @ X524))) = ((sub @ (X522 @ X525 @ X523) @ X524))) & ! [X526 : term] : (($true = ((X516 @ id @ (X522 @ id @ X526) @ id))) | ($true != ((X516 @ id @ X526 @ id))))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f35,definition,( 0.43/0.52 ! [X158 : (subst > term > subst > $o)] : (($true = ((sP21 @ X158))) <=> ! [X160 : (subst > term > term)] : (? [X164 : term] : (($true != ((X158 @ id @ (X160 @ id @ X164) @ id))) & (((X158 @ id @ X164 @ id)) = $true)) | (((X158 @ id @ (lam @ (X160 @ sh @ one)) @ id)) = $true) | ? [X161 : term,X162 : subst,X163 : subst] : (((X160 @ (comp @ X163 @ X162) @ (sub @ X161 @ X162))) != ((sub @ (X160 @ X163 @ X161) @ X162)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f36,definition,( 0.43/0.52 ! [X175 : (subst > term > subst > $o)] : (($true = ((sP22 @ X175))) <=> ? [X183 : (subst > term > term)] : (! [X187 : term] : ((((X175 @ id @ (X183 @ id @ X187) @ id)) = $true) | ($true != ((X175 @ id @ X187 @ id)))) & ! [X185 : subst,X184 : term,X186 : subst] : (((sub @ (X183 @ X186 @ X184) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X184 @ X185)))) & (((X175 @ id @ (lam @ (X183 @ sh @ one)) @ id)) != $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f37,definition,( 0.43/0.52 ! [X175 : (subst > term > subst > $o)] : (($true = ((sP23 @ X175))) <=> ? [X181 : term,X182 : term] : (($true = ((X175 @ id @ X181 @ id))) & ($true = ((X175 @ id @ X182 @ id))) & (((X175 @ id @ (ap @ (sub @ X182 @ id) @ X181) @ id)) != $true)))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f38,definition,( 0.43/0.52 ($true = sP24) <=> ? [X139 : (term > $o),X138 : term] : ((((X139 @ X138)) != $true) & ! [X140 : term] : (($true != ((var @ X140))) | ($true = ((X139 @ X140)))) & ! [X142 : term,X141 : term] : (($true = ((X139 @ (ap @ X142 @ X141)))) | (((X139 @ X141)) != $true) | ($true != ((X139 @ X142)))) & ! [X143 : term] : (? [X144 : term] : (($true = ((X139 @ X144))) & (((X139 @ (sub @ X143 @ (push @ X144 @ id)))) != $true)) | ($true = ((X139 @ (lam @ X143))))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f39,definition,( 0.43/0.52 ($true = sP25) <=> ? [X147 : term,X146 : (subst > term > subst > $o),X145 : term] : ((((X146 @ id @ X145 @ id)) = $true) & ! [X153 : subst,X152 : term,X154 : subst,X155 : subst] : (($true = ((X146 @ (comp @ X153 @ X155) @ (sub @ X152 @ X155) @ X154))) | (((X146 @ X153 @ X152 @ (comp @ X155 @ X154))) != $true)) & ($true = ((X146 @ id @ X147 @ id))) & ! [X150 : subst,X149 : term,X148 : subst,X151 : subst] : (($true != ((X146 @ (comp @ X151 @ X148) @ (sub @ X149 @ X148) @ X150))) | ($true = ((X146 @ X151 @ X149 @ (comp @ X148 @ X150))))) & ($true != ((X146 @ id @ (ap @ X145 @ X147) @ id))) & ! [X156 : term,X157 : term] : ((((X146 @ id @ (ap @ (sub @ X156 @ id) @ X157) @ id)) = $true) | (((X146 @ id @ X157 @ id)) != $true) | ($true != ((X146 @ id @ X156 @ id)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f40,definition,( 0.43/0.52 ($true = sP26) <=> ! [X174 : term,X175 : (subst > term > subst > $o)] : (? [X179 : subst,X177 : term,X178 : subst,X180 : subst] : ((((X175 @ (comp @ X179 @ X180) @ (sub @ X177 @ X180) @ X178)) != $true) & ($true = ((X175 @ X179 @ X177 @ (comp @ X180 @ X178))))) | ($true = ((sP23 @ X175))) | ? [X188 : subst,X191 : subst,X189 : term,X190 : subst] : (($true != ((X175 @ X188 @ X189 @ (comp @ X191 @ X190)))) & ($true = ((X175 @ (comp @ X188 @ X191) @ (sub @ X189 @ X191) @ X190)))) | ? [X176 : term] : (($true = ((var @ (sub @ X176 @ id)))) & (((X175 @ id @ X176 @ id)) != $true)) | ($true = ((sP22 @ X175))) | ($true = ((X175 @ id @ X174 @ id))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f41,definition,( 0.43/0.52 ! [X372 : (subst > term > subst > $o)] : (($true = ((sP27 @ X372))) <=> ? [X379 : (subst > term > term)] : (! [X380 : term] : (($true != ((X372 @ id @ X380 @ id))) | (((X372 @ id @ (X379 @ id @ X380) @ id)) = $true)) & ! [X382 : subst,X383 : subst,X381 : term] : (((X379 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ (X379 @ X382 @ X381) @ X383))) & ($true != ((X372 @ id @ (lam @ (X379 @ sh @ one)) @ id)))))), 0.43/0.52 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 0.43/0.52 thf(f42,plain,( 0.43/0.52 (axabs = $true) & (hoaslamnotvar_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true = ((X283 @ one))) | ($true != ((X285 @ X284))) | ? [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) != ((X283 @ X287))))) & ((hoasapinj1_lthm = $true) <=> (! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))) | ? [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) = ((ap @ X427 @ X425))) & (X426 != X427)) | ? [X423 : term] : (((sub @ X423 @ id)) != X423))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (? [X374 : term] : (((X371 @ X374)) != ((X372 @ id @ X374 @ id))) | ? [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) != $true) & ($true = ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) | ($true = ((sP27 @ X372))) | (((X371 @ (lam @ X373))) = $true) | ? [X388 : term] : (($true != ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) & ($true = ((X371 @ X388)))) | ? [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) != $true) & (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true))) | ? [X370 : term] : (((sub @ X370 @ id)) != X370))) & ((($true = sP26) | ? [X158 : (subst > term > subst > $o),X159 : term] : (! [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) | (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) != $true)) & ! [X165 : term] : (($true != ((X158 @ id @ X165 @ id))) | (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true)) & ($true = ((sP21 @ X158))) & ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) != $true)) & ($true != ((X158 @ id @ (lam @ X159) @ id)))) | ($true = sP25) | ($true = sP24)) <=> (hoasinduction_lthm = $true)) & (! [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (? [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) = $true) & (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) != $true)) | (((X515 @ (lam @ X514))) = $true) | ? [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true != ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) & ($true = ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) | ? [X521 : term] : (((X516 @ id @ X521 @ id)) != ((X515 @ X521))) | ($true = ((sP20 @ X516))) | ? [X527 : term] : (($true != ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) & ($true = ((X515 @ X527))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X358 : term,X357 : (subst > term > subst > $o)] : (? [X359 : term] : (($true != ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) & ($true = ((X357 @ id @ X359 @ id)))) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) | ? [X360 : (subst > term > term)] : (! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) & (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true) & ! [X364 : term] : (($true != ((X357 @ id @ X364 @ id))) | ($true = ((X357 @ id @ (X360 @ id @ X364) @ id))))))) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) <=> (? [X116 : subst] : (((comp @ id @ X116)) != X116) | (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | ? [X117 : subst] : (((comp @ X117 @ id)) != X117))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapnotvar = $true) & (id = ((d2subst @ d_id))) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) <=> (axvarid = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X498 : term] : ? [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) = ((X499 @ sh @ one)))) & ((sP19 = $true) <=> (induction2lem = $true)) & (! [X409 : term] : ? [X410 : (subst > term > term)] : ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411))) <=> (hoasinduction_lem3v2_f = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axvarshift = $true) & (($true = sP18) <=> (induction2_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (induction2_gthm = $true) & (pushprop_gthm = $true) & ! [X1 : d_term,X0 : d_term] : ((((d2term @ X0)) != ((d2term @ X1))) | (X0 = X1)) & ((termmset_lthm = $true) <=> (! [X92 : term] : (((sub @ X92 @ id)) = X92) | ? [X91 : term] : (((sub @ X91 @ id)) != X91))) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & (! [X333 : subst] : (((comp @ id @ X333)) = X333) <=> (axidl = $true)) & ((hoasinduction = $true) <=> ! [X440 : term,X441 : (subst > term > subst > $o)] : ((((sP16 @ X441)) = $true) | (((sP15 @ X441)) = $true) | ? [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true != ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) & ($true = ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) | ($true = ((X441 @ id @ X440 @ id))) | ? [X453 : term] : ((((X441 @ id @ X453 @ id)) != $true) & ($true = ((var @ (sub @ X453 @ id))))) | ? [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) != $true) & ($true = ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))))) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) <=> (substmonoid = $true)) & (($true = sP14) <=> (induction2lem_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X502 : (term > $o),X501 : term,X500 : subst] : ? [X503 : (term > $o)] : ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & ((hoasinduction_lem3_lthm = $true) <=> (($true = sP12) | ? [X16 : term] : (((sub @ X16 @ id)) != X16) | ? [X18 : term,X17 : (subst > term > subst > $o)] : (! [X20 : (subst > term > term)] : (($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ? [X24 : term] : (($true = ((X17 @ id @ X24 @ id))) & (((X17 @ id @ (X20 @ id @ X24) @ id)) != $true)) | ? [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) != ((sub @ (X20 @ X22 @ X23) @ X21)))) & ! [X19 : term] : (($true != ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) & ($true != ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id)))))) & (pushprop_lem3v2 = $true) & ! [X327 : d_subst] : (d_id = X327) & (ulamvarsh = $true) & (lamnotvar = $true) & ((($true = sP9) | ($true = sP10) | ? [X297 : (subst > term > subst > $o)] : ! [X298 : (term > $o)] : ? [X299 : term] : (((X298 @ X299)) != ((X297 @ id @ X299 @ id))) | ? [X307 : term] : (((sub @ X307 @ id)) != X307) | ? [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (! [X317 : term] : (($true != ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true)) & ! [X311 : (subst > term > term)] : (? [X312 : term] : (($true = ((X310 @ id @ X312 @ id))) & ($true != ((X310 @ id @ (X311 @ id @ X312) @ id)))) | ($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ? [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) != ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) & ($true != ((X309 @ (lam @ X308)))) & ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((sP8 = $true) <=> (induction2 = $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP7)) & (axmap = $true) & ((induction = $true) <=> ! [X351 : term,X352 : (term > $o)] : (? [X353 : term] : (($true = ((X352 @ X353))) & ($true != ((X352 @ (lam @ X353))))) | ? [X354 : term] : ((((X352 @ X354)) != $true) & ($true = ((var @ X354)))) | (((X352 @ X351)) = $true) | ? [X355 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true = ((X352 @ X355))) & (((X352 @ (ap @ X356 @ X355))) != $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)))))))))))))) & (! [X389 : term,X391 : subst,X390 : (term > $o)] : ? [X392 : (term > $o)] : ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393))) <=> (pushprop_lem0 = $true)) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X41 : (subst > term > subst > $o)] : ? [X42 : (term > $o)] : ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43))) <=> (hoasinduction_lem0_lthm = $true)) & ((? [X466 : term] : (((sub @ X466 @ id)) != X466) | ? [X467 : (subst > term > subst > $o),X468 : term] : (! [X469 : term] : (($true != ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) & ($true != ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) & ! [X470 : (subst > term > term)] : (? [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) != ((sub @ (X470 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true) | ? [X474 : term] : (($true = ((X467 @ id @ X474 @ id))) & ($true != ((X467 @ id @ (X470 @ id @ X474) @ id)))))) | ($true = sP6)) <=> (hoasinduction_lem3a_lthm = $true)) & (ulamvarind = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X432 : term] : ? [X433 : (subst > term > term)] : ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434))))) & ((? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) = ((ap @ X417 @ X415))) & (X415 != X418)) | ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422))))) <=> (hoasapinj2_lthm = $true)) & ((termmset = $true) <=> ! [X95 : term] : (((sub @ X95 @ id)) = X95)) & (($true = sP5) <=> (hoasinduction_lem2 = $true)) & ((apinj1 = $true) <=> ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437))))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & ((! [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ? [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) != ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) | ? [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) != ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one))))) | ? [X104 : term,X105 : term] : ((((lam @ X104)) = ((lam @ X105))) & (X104 != X105)) | ? [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) != X100) | ? [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) != X103)) <=> (hoaslaminj_lthm = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((pushprop_lem1_lthm = $true) <=> (? [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) != X505) | ! [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) != $true) | (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true)) | ? [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) != X508))) & (hoaslamnotap_lthm = $true) & (sh = ((d2subst @ d_id))) & ((hoasinduction_lem3aa = $true) <=> ! [X483 : (subst > term > subst > $o),X484 : term] : (? [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))) & ! [X487 : term] : (($true = ((X483 @ id @ (X486 @ id @ X487) @ id))) | (((X483 @ id @ X487 @ id)) != $true))) | ? [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) != $true) & ($true = ((X483 @ id @ X485 @ id)))) | ($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id))))) & ((hoaslamnotap = $true) <=> ! [X201 : term,X202 : (subst > term > term),X203 : term] : (? [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) != ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one)))))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop = $true) & (hoasinduction_lem2_gthm = $true) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) <=> (hoasapinj2 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) <=> (hoasapinj1 = $true)) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) <=> (axshiftcons = $true)) & (hoasinduction_lem3v2_gthm = $true) & (termmset_gthm = $true) & ((! [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (? [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) != ((X339 @ X340))) | (((X338 @ X337)) != $true) | ($true = ((X339 @ one)))) | ? [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) != X334)) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3 = $true) <=> ! [X120 : term,X121 : (subst > term > subst > $o)] : (($true = ((sP4 @ X121))) | ? [X126 : term] : (($true != ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) & ($true = ((X121 @ id @ X126 @ id)))) | ? [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) & (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) != $true)) | ? [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) != $true) & ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id))))) & ((laminj = $true) <=> ! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413))))) & (axapp = $true) & (hoasapinj1_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotvar = $true) & (apnotvar = $true) & (pushprop_lthm = $true) & ((shinj = $true) <=> ! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh))))) & (pushprop_lem1_gthm = $true) & (! [X78 : term,X77 : (subst > term > subst > $o)] : (? [X88 : term] : ((((X77 @ id @ X88 @ id)) = $true) & ($true != ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) | ($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ? [X79 : (subst > term > term),X80 : term] : (($true != ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) & ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) & ! [X81 : term] : (($true != ((X77 @ id @ X81 @ id))) | (((X77 @ id @ (X79 @ id @ X81) @ id)) = $true)) & ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X458 : term,X459 : (subst > term > subst > $o)] : (? [X465 : term] : (($true = ((X459 @ id @ X465 @ id))) & (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) != $true)) | ($true = ((X459 @ id @ (lam @ X458) @ id))) | ? [X460 : (subst > term > term)] : (! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) & ! [X464 : term] : ((((X459 @ id @ X464 @ id)) != $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) & ($true != ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))))) & ((! [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (? [X402 : term] : (($true != ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) & ($true = ((X399 @ X402)))) | ? [X403 : term] : (((X401 @ id @ X403 @ id)) != ((X399 @ X403))) | (((X399 @ (lam @ X400))) = $true) | ? [X404 : (subst > term > term)] : (! [X408 : term] : (($true = ((X401 @ id @ (X404 @ id @ X408) @ id))) | (((X401 @ id @ X408 @ id)) != $true)) & ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) & ($true != ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) | ? [X394 : term] : ! [X395 : (subst > term > term)] : ? [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) != ((X395 @ X397 @ X396))) | ? [X398 : term] : (((sub @ X398 @ id)) != X398)) <=> (hoasinduction_lem3v2a_lthm = $true)) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) = $true) | ? [X350 : term] : (($true = ((X341 @ X350))) & ($true != ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) | ? [X345 : (subst > term > term)] : (! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) & ! [X349 : term] : (($true != ((X343 @ id @ X349 @ id))) | (((X343 @ id @ (X345 @ id @ X349) @ id)) = $true)) & ($true != ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) | ? [X344 : term] : (((X343 @ id @ X344 @ id)) != ((X341 @ X344)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & (! [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true != ((X330 @ X332))) | (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true)) <=> (pushprop_lem1 = $true)) & ! [X495 : d_term] : (d_one = X495) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (? [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) & ! [X221 : term] : (($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) | ($true != ((X220 @ X221)))) & ! [X223 : (subst > term > term)] : (? [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) != ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) | ? [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) != $true) & ($true = ((X218 @ id @ X224 @ id)))) | ($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) & (((X220 @ (lam @ X219))) != $true)) | ($true = sP2) | ($true = sP3) | ? [X217 : term] : (((sub @ X217 @ id)) != X217) | ? [X207 : (subst > term > subst > $o)] : ! [X208 : (term > $o)] : ? [X209 : term] : (((X208 @ X209)) != ((X207 @ id @ X209 @ id))))) & ((apinj2 = $true) <=> ! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247))))) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X136 : term] : ? [X137 : (subst > term > term)] : (((X137 @ sh @ one)) = ((sub @ X136 @ (push @ one @ sh))))) & (lamnotap != $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ? [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) != ((sub @ (X272 @ X273 @ X275) @ X274))) | ? [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) != ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276))))) <=> (hoaslaminj = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((axidr = $true) <=> ! [X496 : subst] : (((comp @ X496 @ id)) = X496)) & (hoasinduction_lem3_gthm = $true) & (! [X192 : (subst > term > subst > $o),X193 : term] : (? [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) != $true) & ($true = ((X192 @ id @ X194 @ id))) & ($true = ((X192 @ id @ X195 @ id)))) | ? [X196 : (subst > term > term)] : (($true != ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X200 : term] : (($true != ((X192 @ id @ X200 @ id))) | (((X192 @ id @ (X196 @ id @ X200) @ id)) = $true)) & ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197)))) | (((X192 @ id @ X193 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X367 : (subst > term > subst > $o)] : ? [X368 : (term > $o)] : ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) <=> (hoasinduction_lem0 = $true)) & (axassoc = $true) & ((axscons = $true) <=> ! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497)) & (hoasinduction_lem2_lthm = $true) & ((axvarcons = $true) <=> ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281)) & ! [X279 : d_subst,X280 : d_subst] : ((X279 = X280) | (((d2subst @ X280)) != ((d2subst @ X279))))), 0.43/0.52 inference(definition_folding,[],[f13,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,f14])). 0.43/0.52 thf(f43,plain,( 0.43/0.52 ((pushprop_lem2v2 != $true) | ? [X3 : (term > $o),X0 : subst,X1 : term,X2 : (term > $o)] : (! [X4 : term] : (($true = ((X3 @ (sub @ X4 @ X0)))) | (((var @ X4)) != $true)) & (((pushprop_p_and_p_prime @ X1 @ X0 @ X3 @ X2)) = $true) & ? [X5 : term] : (($true != ((X2 @ (sub @ X5 @ sh)))) & (((var @ X5)) = $true) & (((X2 @ X5)) = $true)))) & ((pushprop_lem2v2 = $true) | ! [X3 : (term > $o),X0 : subst,X1 : term,X2 : (term > $o)] : (? [X4 : term] : (($true != ((X3 @ (sub @ X4 @ X0)))) & (((var @ X4)) = $true)) | (((pushprop_p_and_p_prime @ X1 @ X0 @ X3 @ X2)) != $true) | ! [X5 : term] : (($true = ((X2 @ (sub @ X5 @ sh)))) | (((var @ X5)) != $true) | (((X2 @ X5)) != $true))))), 0.43/0.52 inference(nnf_transformation,[],[f11])). 0.43/0.52 thf(f44,plain,( 0.43/0.52 ((pushprop_lem2v2 != $true) | ? [X0 : (term > $o),X1 : subst,X2 : term,X3 : (term > $o)] : (! [X4 : term] : (($true = ((X0 @ (sub @ X4 @ X1)))) | (((var @ X4)) != $true)) & (((pushprop_p_and_p_prime @ X2 @ X1 @ X0 @ X3)) = $true) & ? [X5 : term] : ((((X3 @ (sub @ X5 @ sh))) != $true) & (((var @ X5)) = $true) & (((X3 @ X5)) = $true)))) & ((pushprop_lem2v2 = $true) | ! [X6 : (term > $o),X7 : subst,X8 : term,X9 : (term > $o)] : (? [X10 : term] : (($true != ((X6 @ (sub @ X10 @ X7)))) & (((var @ X10)) = $true)) | ($true != ((pushprop_p_and_p_prime @ X8 @ X7 @ X6 @ X9))) | ! [X11 : term] : (($true = ((X9 @ (sub @ X11 @ sh)))) | (((var @ X11)) != $true) | (((X9 @ X11)) != $true))))), 0.43/0.52 inference(rectify,[],[f43])). 0.43/0.52 thf(f45,plain,( 0.43/0.52 ((pushprop_lem2v2 != $true) | (! [X4 : term] : ((((sK28 @ (sub @ X4 @ sK29))) = $true) | (((var @ X4)) != $true)) & ($true = ((pushprop_p_and_p_prime @ sK30 @ sK29 @ sK28 @ sK31))) & ((((sK31 @ (sub @ sK32 @ sh))) != $true) & (((var @ sK32)) = $true) & ($true = ((sK31 @ sK32)))))) & ((pushprop_lem2v2 = $true) | ! [X6 : (term > $o),X7 : subst,X8 : term,X9 : (term > $o)] : ((($true != ((X6 @ (sub @ (sK33 @ X7 @ X6) @ X7)))) & ($true = ((var @ (sK33 @ X7 @ X6))))) | ($true != ((pushprop_p_and_p_prime @ X8 @ X7 @ X6 @ X9))) | ! [X11 : term] : (($true = ((X9 @ (sub @ X11 @ sh)))) | (((var @ X11)) != $true) | (((X9 @ X11)) != $true))))), 0.43/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31,sK32,vAPP]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X2,sK30),skolemize(X3,sK31),skolemize(X5,sK32),skolemize(X10,sK33 @ X7 @ X6)],[f44])). 0.43/0.52 thf(f132,plain,( 0.43/0.52 (axabs = $true) & (hoaslamnotvar_gthm = $true) & (((pushprop_lem1v2 = $true) | ? [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true != ((X283 @ one))) & ($true = ((X285 @ X284))) & ! [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) = ((X283 @ X287))))) & (! [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true = ((X283 @ one))) | ($true != ((X285 @ X284))) | ? [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) != ((X283 @ X287)))) | (pushprop_lem1v2 != $true))) & (((hoasapinj1_lthm = $true) | (? [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 != X431) & (((ap @ (sub @ X431 @ id) @ X430)) = ((ap @ (sub @ X428 @ id) @ X429)))) & ! [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) != ((ap @ X427 @ X425))) | (X426 = X427)) & ! [X423 : term] : (((sub @ X423 @ id)) = X423))) & ((! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))) | ? [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) = ((ap @ X427 @ X425))) & (X426 != X427)) | ? [X423 : term] : (((sub @ X423 @ id)) != X423)) | (hoasapinj1_lthm != $true))) & (hoasapnotvar_lthm = $true) & (((hoasinduction_lem3v2_lthm = $true) | (? [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (! [X374 : term] : (((X371 @ X374)) = ((X372 @ id @ X374 @ id))) & ! [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) = $true) | ($true != ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) & ($true != ((sP27 @ X372))) & (((X371 @ (lam @ X373))) != $true) & ! [X388 : term] : (($true = ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) | ($true != ((X371 @ X388)))) & ! [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) = $true) | (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) != $true))) & ! [X370 : term] : (((sub @ X370 @ id)) = X370))) & ((! [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (? [X374 : term] : (((X371 @ X374)) != ((X372 @ id @ X374 @ id))) | ? [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) != $true) & ($true = ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) | ($true = ((sP27 @ X372))) | (((X371 @ (lam @ X373))) = $true) | ? [X388 : term] : (($true != ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) & ($true = ((X371 @ X388)))) | ? [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) != $true) & (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true))) | ? [X370 : term] : (((sub @ X370 @ id)) != X370)) | (hoasinduction_lem3v2_lthm != $true))) & (((($true = sP26) | ? [X158 : (subst > term > subst > $o),X159 : term] : (! [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) | (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) != $true)) & ! [X165 : term] : (($true != ((X158 @ id @ X165 @ id))) | (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true)) & ($true = ((sP21 @ X158))) & ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) != $true)) & ($true != ((X158 @ id @ (lam @ X159) @ id)))) | ($true = sP25) | ($true = sP24)) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP26) & ! [X158 : (subst > term > subst > $o),X159 : term] : (? [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true != ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) & (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) = $true)) | ? [X165 : term] : (($true = ((X158 @ id @ X165 @ id))) & (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) != $true)) | ($true != ((sP21 @ X158))) | ? [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) != $true) & (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) = $true)) | ($true = ((X158 @ id @ (lam @ X159) @ id)))) & ($true != sP25) & ($true != sP24)))) & ((! [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (? [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) = $true) & (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) != $true)) | (((X515 @ (lam @ X514))) = $true) | ? [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true != ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) & ($true = ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) | ? [X521 : term] : (((X516 @ id @ X521 @ id)) != ((X515 @ X521))) | ($true = ((sP20 @ X516))) | ? [X527 : term] : (($true != ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) & ($true = ((X515 @ X527))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (! [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) != $true) | (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) = $true)) & (((X515 @ (lam @ X514))) != $true) & ! [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true = ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) | ($true != ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) & ! [X521 : term] : (((X516 @ id @ X521 @ id)) = ((X515 @ X521))) & ($true != ((sP20 @ X516))) & ! [X527 : term] : (($true = ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) | ($true != ((X515 @ X527))))))) & (((hoasinduction_lem3aa_lthm = $true) | ? [X358 : term,X357 : (subst > term > subst > $o)] : (! [X359 : term] : (($true = ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) | ($true != ((X357 @ id @ X359 @ id)))) & ($true != ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) & ! [X360 : (subst > term > term)] : (? [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) != ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) | (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) = $true) | ? [X364 : term] : (($true = ((X357 @ id @ X364 @ id))) & ($true != ((X357 @ id @ (X360 @ id @ X364) @ id))))))) & (! [X358 : term,X357 : (subst > term > subst > $o)] : (? [X359 : term] : (($true != ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) & ($true = ((X357 @ id @ X359 @ id)))) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) | ? [X360 : (subst > term > term)] : (! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) & (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true) & ! [X364 : term] : (($true != ((X357 @ id @ X364 @ id))) | ($true = ((X357 @ id @ (X360 @ id @ X364) @ id)))))) | (hoasinduction_lem3aa_lthm != $true))) & (hoasinduction_lem1 = $true) & (((substmonoid_lthm = $true) | (! [X116 : subst] : (((comp @ id @ X116)) = X116) & (? [X119 : subst] : (((comp @ id @ X119)) != X119) | ? [X118 : subst] : (((comp @ X118 @ id)) != X118)) & ! [X117 : subst] : (((comp @ X117 @ id)) = X117))) & ((? [X116 : subst] : (((comp @ id @ X116)) != X116) | (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | ? [X117 : subst] : (((comp @ X117 @ id)) != X117)) | (substmonoid_lthm != $true))) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapnotvar = $true) & (id = ((d2subst @ d_id))) & ((! [X2 : term] : (((sub @ X2 @ id)) = X2) | (axvarid != $true)) & ((axvarid = $true) | ? [X2 : term] : (((sub @ X2 @ id)) != X2))) & (((hoasinduction_lem3b = $true) | ? [X498 : term] : ! [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) != ((X499 @ sh @ one)))) & (! [X498 : term] : ? [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) = ((X499 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (((sP19 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP19 != $true))) & ((! [X409 : term] : ? [X410 : (subst > term > term)] : ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X409 : term] : ! [X410 : (subst > term > term)] : ? [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) != ((X410 @ X412 @ X411))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axvarshift = $true) & ((($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18))) & (pushprop_lem3v2_lthm = $true) & (induction2_gthm = $true) & (pushprop_gthm = $true) & ! [X1 : d_term,X0 : d_term] : ((((d2term @ X0)) != ((d2term @ X1))) | (X0 = X1)) & (((termmset_lthm = $true) | (? [X92 : term] : (((sub @ X92 @ id)) != X92) & ! [X91 : term] : (((sub @ X91 @ id)) = X91))) & ((! [X92 : term] : (((sub @ X92 @ id)) = X92) | ? [X91 : term] : (((sub @ X91 @ id)) != X91)) | (termmset_lthm != $true))) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & ((! [X333 : subst] : (((comp @ id @ X333)) = X333) | (axidl != $true)) & ((axidl = $true) | ? [X333 : subst] : (((comp @ id @ X333)) != X333))) & (((hoasinduction = $true) | ? [X440 : term,X441 : (subst > term > subst > $o)] : ((((sP16 @ X441)) != $true) & (((sP15 @ X441)) != $true) & ! [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true = ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) | ($true != ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) & ($true != ((X441 @ id @ X440 @ id))) & ! [X453 : term] : ((((X441 @ id @ X453 @ id)) = $true) | ($true != ((var @ (sub @ X453 @ id))))) & ! [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) = $true) | ($true != ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))))) & (! [X440 : term,X441 : (subst > term > subst > $o)] : ((((sP16 @ X441)) = $true) | (((sP15 @ X441)) = $true) | ? [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true != ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) & ($true = ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) | ($true = ((X441 @ id @ X440 @ id))) | ? [X453 : term] : ((((X441 @ id @ X453 @ id)) != $true) & ($true = ((var @ (sub @ X453 @ id))))) | ? [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) != $true) & ($true = ((X441 @ X444 @ X446 @ (comp @ X445 @ X447)))))) | (hoasinduction != $true))) & (((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X295 : subst] : (((comp @ X295 @ id)) != X295) | ? [X296 : subst] : (((comp @ id @ X296)) != X296)))) & ((($true = sP14) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP14))) & (((pushprop_lem0_lthm = $true) | ? [X502 : (term > $o),X501 : term,X500 : subst] : ! [X503 : (term > $o)] : ? [X504 : term] : (((X503 @ X504)) != ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & (! [X502 : (term > $o),X501 : term,X500 : subst] : ? [X503 : (term > $o)] : ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500))))) | (pushprop_lem0_lthm != $true))) & (((hoasinduction_lem3_lthm = $true) | (($true != sP12) & ! [X16 : term] : (((sub @ X16 @ id)) = X16) & ! [X18 : term,X17 : (subst > term > subst > $o)] : (? [X20 : (subst > term > term)] : (($true != ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) & ! [X24 : term] : (($true != ((X17 @ id @ X24 @ id))) | (((X17 @ id @ (X20 @ id @ X24) @ id)) = $true)) & ! [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) = ((sub @ (X20 @ X22 @ X23) @ X21)))) | ? [X19 : term] : (($true = ((X17 @ id @ X19 @ id))) & ($true != ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) | ($true = ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id)))))) & ((($true = sP12) | ? [X16 : term] : (((sub @ X16 @ id)) != X16) | ? [X18 : term,X17 : (subst > term > subst > $o)] : (! [X20 : (subst > term > term)] : (($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ? [X24 : term] : (($true = ((X17 @ id @ X24 @ id))) & (((X17 @ id @ (X20 @ id @ X24) @ id)) != $true)) | ? [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) != ((sub @ (X20 @ X22 @ X23) @ X21)))) & ! [X19 : term] : (($true != ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) & ($true != ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id))))) | (hoasinduction_lem3_lthm != $true))) & (pushprop_lem3v2 = $true) & ! [X327 : d_subst] : (d_id = X327) & (ulamvarsh = $true) & (lamnotvar = $true) & (((($true = sP9) | ($true = sP10) | ? [X297 : (subst > term > subst > $o)] : ! [X298 : (term > $o)] : ? [X299 : term] : (((X298 @ X299)) != ((X297 @ id @ X299 @ id))) | ? [X307 : term] : (((sub @ X307 @ id)) != X307) | ? [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (! [X317 : term] : (($true != ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true)) & ! [X311 : (subst > term > term)] : (? [X312 : term] : (($true = ((X310 @ id @ X312 @ id))) & ($true != ((X310 @ id @ (X311 @ id @ X312) @ id)))) | ($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ? [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) != ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) & ($true != ((X309 @ (lam @ X308)))) & ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id))))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP9) & ($true != sP10) & ! [X297 : (subst > term > subst > $o)] : ? [X298 : (term > $o)] : ! [X299 : term] : (((X298 @ X299)) = ((X297 @ id @ X299 @ id))) & ! [X307 : term] : (((sub @ X307 @ id)) = X307) & ! [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (? [X317 : term] : (($true = ((X309 @ X317))) & (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) != $true)) | ? [X311 : (subst > term > term)] : (! [X312 : term] : (($true != ((X310 @ id @ X312 @ id))) | ($true = ((X310 @ id @ (X311 @ id @ X312) @ id)))) & ($true != ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) & ! [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) = ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) | ($true = ((X309 @ (lam @ X308)))) | ? [X316 : term] : (((X309 @ X316)) != ((X310 @ id @ X316 @ id))))))) & (((sP8 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP8 != $true))) & (pushprop_lem1v2_gthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP7)) & (($true = sP7) | (hoasinduction_lem2v2 != $true))) & (axmap = $true) & (((induction = $true) | ? [X351 : term,X352 : (term > $o)] : (! [X353 : term] : (($true != ((X352 @ X353))) | ($true = ((X352 @ (lam @ X353))))) & ! [X354 : term] : ((((X352 @ X354)) = $true) | ($true != ((var @ X354)))) & (((X352 @ X351)) != $true) & ! [X355 : term,X356 : term] : (($true != ((X352 @ X356))) | ($true != ((X352 @ X355))) | (((X352 @ (ap @ X356 @ X355))) = $true)))) & (! [X351 : term,X352 : (term > $o)] : (? [X353 : term] : (($true = ((X352 @ X353))) & ($true != ((X352 @ (lam @ X353))))) | ? [X354 : term] : ((((X352 @ X354)) != $true) & ($true = ((var @ X354)))) | (((X352 @ X351)) = $true) | ? [X355 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true = ((X352 @ X355))) & (((X352 @ (ap @ X356 @ X355))) != $true))) | (induction != $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)))))))))))))) & ((! [X389 : term,X391 : subst,X390 : (term > $o)] : ? [X392 : (term > $o)] : ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X389 : term,X391 : subst,X390 : (term > $o)] : ! [X392 : (term > $o)] : ? [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) != ((X392 @ X393))))) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X41 : (subst > term > subst > $o)] : ? [X42 : (term > $o)] : ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X41 : (subst > term > subst > $o)] : ! [X42 : (term > $o)] : ? [X43 : term] : (((X41 @ id @ X43 @ id)) != ((X42 @ X43))))) & (((? [X466 : term] : (((sub @ X466 @ id)) != X466) | ? [X467 : (subst > term > subst > $o),X468 : term] : (! [X469 : term] : (($true != ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) & ($true != ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) & ! [X470 : (subst > term > term)] : (? [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) != ((sub @ (X470 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true) | ? [X474 : term] : (($true = ((X467 @ id @ X474 @ id))) & ($true != ((X467 @ id @ (X470 @ id @ X474) @ id)))))) | ($true = sP6)) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X466 : term] : (((sub @ X466 @ id)) = X466) & ! [X467 : (subst > term > subst > $o),X468 : term] : (? [X469 : term] : (($true = ((X467 @ id @ X469 @ id))) & ($true != ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) | ($true = ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) | ? [X470 : (subst > term > term)] : (! [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) = ((sub @ (X470 @ X473 @ X471) @ X472))) & (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) != $true) & ! [X474 : term] : (($true != ((X467 @ id @ X474 @ id))) | ($true = ((X467 @ id @ (X470 @ id @ X474) @ id)))))) & ($true != sP6)))) & (ulamvarind = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X432 : term] : ! [X433 : (subst > term > term)] : ? [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) != ((sub @ X432 @ (push @ X435 @ X434))))) & (! [X432 : term] : ? [X433 : (subst > term > term)] : ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434)))) | (hoasinduction_lem3v2_f_lthm != $true))) & (((? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) = ((ap @ X417 @ X415))) & (X415 != X418)) | ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422))))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) != ((ap @ X417 @ X415))) | (X415 = X418)) & ? [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 != X422) & (((ap @ (sub @ X421 @ id) @ X420)) = ((ap @ (sub @ X419 @ id) @ X422))))))) & (((termmset = $true) | ? [X95 : term] : (((sub @ X95 @ id)) != X95)) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) | (termmset != $true))) & ((($true = sP5) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP5))) & (((apinj1 = $true) | ? [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 != X438) & (((ap @ X436 @ X439)) = ((ap @ X438 @ X437))))) & (! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437)))) | (apinj1 != $true))) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & (((! [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ? [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) != ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) | ? [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) != ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one))))) | ? [X104 : term,X105 : term] : ((((lam @ X104)) = ((lam @ X105))) & (X104 != X105)) | ? [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) != X100) | ? [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) != X103)) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (? [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) != ((X107 @ X109 @ X106))) & ! [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) = ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) & ! [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) = ((sub @ (X108 @ X114 @ X113) @ X115))) & (((lam @ (X107 @ sh @ one))) = ((lam @ (X108 @ sh @ one))))) & ! [X104 : term,X105 : term] : ((((lam @ X104)) != ((lam @ X105))) | (X104 = X105)) & ! [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) = X100) & ! [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) = X103)))) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & (((pushprop_lem1_lthm = $true) | (! [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) = X505) & ? [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) = $true) & (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) != $true)) & ! [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) = X508))) & ((? [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) != X505) | ! [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) != $true) | (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true)) | ? [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) != X508)) | (pushprop_lem1_lthm != $true))) & (hoaslamnotap_lthm = $true) & (sh = ((d2subst @ d_id))) & (((hoasinduction_lem3aa = $true) | ? [X483 : (subst > term > subst > $o),X484 : term] : (! [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) = $true) | ? [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) != ((sub @ (X486 @ X490 @ X489) @ X488))) | ? [X487 : term] : (($true != ((X483 @ id @ (X486 @ id @ X487) @ id))) & (((X483 @ id @ X487 @ id)) = $true))) & ! [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) = $true) | ($true != ((X483 @ id @ X485 @ id)))) & ($true != ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id))))) & (! [X483 : (subst > term > subst > $o),X484 : term] : (? [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))) & ! [X487 : term] : (($true = ((X483 @ id @ (X486 @ id @ X487) @ id))) | (((X483 @ id @ X487 @ id)) != $true))) | ? [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) != $true) & ($true = ((X483 @ id @ X485 @ id)))) | ($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3aa != $true))) & (((hoaslamnotap = $true) | ? [X201 : term,X202 : (subst > term > term),X203 : term] : (! [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) = ((sub @ (X202 @ X205 @ X204) @ X206))) & (((ap @ (sub @ X201 @ id) @ X203)) = ((lam @ (X202 @ sh @ one)))))) & (! [X201 : term,X202 : (subst > term > term),X203 : term] : (? [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) != ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one))))) | (hoaslamnotap != $true))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop = $true) & (hoasinduction_lem2_gthm = $true) & ((! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) = ((ap @ (sub @ X98 @ id) @ X97))) & (X96 != X97)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 != X493) & (((ap @ (sub @ X493 @ id) @ X491)) = ((ap @ (sub @ X492 @ id) @ X494)))))) & ((! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) != X60))) & (hoasinduction_lem3v2_gthm = $true) & (termmset_gthm = $true) & (((! [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (? [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) != ((X339 @ X340))) | (((X338 @ X337)) != $true) | ($true = ((X339 @ one)))) | ? [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) != X334)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (! [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) = ((X339 @ X340))) & (((X338 @ X337)) = $true) & ($true != ((X339 @ one)))) & ! [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) = X334)))) & (pushprop_lem2v2_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((hoasinduction_lem3 = $true) | ? [X120 : term,X121 : (subst > term > subst > $o)] : (($true != ((sP4 @ X121))) & ! [X126 : term] : (($true = ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) | ($true != ((X121 @ id @ X126 @ id)))) & ! [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) != $true) | (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) = $true)) & ! [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) = $true) | ($true != ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) & ($true != ((X121 @ id @ (lam @ X120) @ id))))) & (! [X120 : term,X121 : (subst > term > subst > $o)] : (($true = ((sP4 @ X121))) | ? [X126 : term] : (($true != ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) & ($true = ((X121 @ id @ X126 @ id)))) | ? [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) & (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) != $true)) | ? [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) != $true) & ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id)))) | (hoasinduction_lem3 != $true))) & (((laminj = $true) | ? [X414 : term,X413 : term] : ((X413 != X414) & (((lam @ X414)) = ((lam @ X413))))) & (! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413)))) | (laminj != $true))) & (axapp = $true) & (hoasapinj1_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotvar = $true) & (apnotvar = $true) & (pushprop_lthm = $true) & (((shinj = $true) | ? [X89 : term,X90 : term] : ((X89 != X90) & (((sub @ X90 @ sh)) = ((sub @ X89 @ sh))))) & (! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh)))) | (shinj != $true))) & (pushprop_lem1_gthm = $true) & ((! [X78 : term,X77 : (subst > term > subst > $o)] : (? [X88 : term] : ((((X77 @ id @ X88 @ id)) = $true) & ($true != ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) | ($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ? [X79 : (subst > term > term),X80 : term] : (($true != ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) & ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) & ! [X81 : term] : (($true != ((X77 @ id @ X81 @ id))) | (((X77 @ id @ (X79 @ id @ X81) @ id)) = $true)) & ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))))) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X78 : term,X77 : (subst > term > subst > $o)] : (! [X88 : term] : ((((X77 @ id @ X88 @ id)) != $true) | ($true = ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) & ($true != ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) & ! [X79 : (subst > term > term),X80 : term] : (($true = ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) | ? [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) != ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) | ? [X81 : term] : (($true = ((X77 @ id @ X81 @ id))) & (((X77 @ id @ (X79 @ id @ X81) @ id)) != $true)) | ? [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) != ((sub @ (X79 @ X82 @ X84) @ X83))))))) & (((hoasinduction_lem3a = $true) | ? [X458 : term,X459 : (subst > term > subst > $o)] : (! [X465 : term] : (($true != ((X459 @ id @ X465 @ id))) | (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) = $true)) & ($true != ((X459 @ id @ (lam @ X458) @ id))) & ! [X460 : (subst > term > term)] : (? [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) != ((sub @ (X460 @ X462 @ X463) @ X461))) | ? [X464 : term] : ((((X459 @ id @ X464 @ id)) = $true) & ($true != ((X459 @ id @ (X460 @ id @ X464) @ id)))) | ($true = ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))))) & (! [X458 : term,X459 : (subst > term > subst > $o)] : (? [X465 : term] : (($true = ((X459 @ id @ X465 @ id))) & (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) != $true)) | ($true = ((X459 @ id @ (lam @ X458) @ id))) | ? [X460 : (subst > term > term)] : (! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) & ! [X464 : term] : ((((X459 @ id @ X464 @ id)) != $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) & ($true != ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id))))) | (hoasinduction_lem3a != $true))) & (((! [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (? [X402 : term] : (($true != ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) & ($true = ((X399 @ X402)))) | ? [X403 : term] : (((X401 @ id @ X403 @ id)) != ((X399 @ X403))) | (((X399 @ (lam @ X400))) = $true) | ? [X404 : (subst > term > term)] : (! [X408 : term] : (($true = ((X401 @ id @ (X404 @ id @ X408) @ id))) | (((X401 @ id @ X408 @ id)) != $true)) & ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) & ($true != ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) | ? [X394 : term] : ! [X395 : (subst > term > term)] : ? [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) != ((X395 @ X397 @ X396))) | ? [X398 : term] : (((sub @ X398 @ id)) != X398)) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (? [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (! [X402 : term] : (($true = ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) | ($true != ((X399 @ X402)))) & ! [X403 : term] : (((X401 @ id @ X403 @ id)) = ((X399 @ X403))) & (((X399 @ (lam @ X400))) != $true) & ! [X404 : (subst > term > term)] : (? [X408 : term] : (($true != ((X401 @ id @ (X404 @ id @ X408) @ id))) & (((X401 @ id @ X408 @ id)) = $true)) | ? [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) != ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) | ($true = ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) & ! [X394 : term] : ? [X395 : (subst > term > term)] : ! [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) = ((X395 @ X397 @ X396))) & ! [X398 : term] : (((sub @ X398 @ id)) = X398)))) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & ((! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) = $true) | ? [X350 : term] : (($true = ((X341 @ X350))) & ($true != ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) | ? [X345 : (subst > term > term)] : (! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) & ! [X349 : term] : (($true != ((X343 @ id @ X349 @ id))) | (((X343 @ id @ (X345 @ id @ X349) @ id)) = $true)) & ($true != ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) | ? [X344 : term] : (((X343 @ id @ X344 @ id)) != ((X341 @ X344)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ? [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) != $true) & ! [X350 : term] : (($true != ((X341 @ X350))) | ($true = ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) & ! [X345 : (subst > term > term)] : (? [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) != ((sub @ (X345 @ X347 @ X348) @ X346))) | ? [X349 : term] : (($true = ((X343 @ id @ X349 @ id))) & (((X343 @ id @ (X345 @ id @ X349) @ id)) != $true)) | ($true = ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) & ! [X344 : term] : (((X343 @ id @ X344 @ id)) = ((X341 @ X344)))))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & ((! [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true != ((X330 @ X332))) | (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true = ((X330 @ X332))) & (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) != $true)))) & ! [X495 : d_term] : (d_one = X495) & (pushprop_lem0_gthm = $true) & (((hoasinduction_lthm_3 = $true) | (! [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (? [X222 : term] : (((X218 @ id @ X222 @ id)) != ((X220 @ X222))) | ? [X221 : term] : (($true != ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) & ($true = ((X220 @ X221)))) | ? [X223 : (subst > term > term)] : (! [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) = ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) & ! [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) = $true) | ($true != ((X218 @ id @ X224 @ id)))) & ($true != ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) | (((X220 @ (lam @ X219))) = $true)) & ($true != sP2) & ($true != sP3) & ! [X217 : term] : (((sub @ X217 @ id)) = X217) & ! [X207 : (subst > term > subst > $o)] : ? [X208 : (term > $o)] : ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))))) & ((? [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) & ! [X221 : term] : (($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) | ($true != ((X220 @ X221)))) & ! [X223 : (subst > term > term)] : (? [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) != ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) | ? [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) != $true) & ($true = ((X218 @ id @ X224 @ id)))) | ($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) & (((X220 @ (lam @ X219))) != $true)) | ($true = sP2) | ($true = sP3) | ? [X217 : term] : (((sub @ X217 @ id)) != X217) | ? [X207 : (subst > term > subst > $o)] : ! [X208 : (term > $o)] : ? [X209 : term] : (((X208 @ X209)) != ((X207 @ id @ X209 @ id)))) | (hoasinduction_lthm_3 != $true))) & (((apinj2 = $true) | ? [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 != X249) & (((ap @ X248 @ X249)) = ((ap @ X246 @ X247))))) & (! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247)))) | (apinj2 != $true))) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (hoasapnotvar_gthm = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X136 : term] : ! [X137 : (subst > term > term)] : (((X137 @ sh @ one)) != ((sub @ X136 @ (push @ one @ sh))))) & (! [X136 : term] : ? [X137 : (subst > term > term)] : (((X137 @ sh @ one)) = ((sub @ X136 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true))) & (lamnotap != $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ? [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) != ((sub @ (X272 @ X273 @ X275) @ X274))) | ? [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) != ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) != ((X269 @ X270 @ X271))) & (((lam @ (X269 @ sh @ one))) = ((lam @ (X272 @ sh @ one)))) & ! [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) = ((sub @ (X272 @ X273 @ X275) @ X274))) & ! [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) = ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276))))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & (((axidr = $true) | ? [X496 : subst] : (((comp @ X496 @ id)) != X496)) & (! [X496 : subst] : (((comp @ X496 @ id)) = X496) | (axidr != $true))) & (hoasinduction_lem3_gthm = $true) & ((! [X192 : (subst > term > subst > $o),X193 : term] : (? [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) != $true) & ($true = ((X192 @ id @ X194 @ id))) & ($true = ((X192 @ id @ X195 @ id)))) | ? [X196 : (subst > term > term)] : (($true != ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X200 : term] : (($true != ((X192 @ id @ X200 @ id))) | (((X192 @ id @ (X196 @ id @ X200) @ id)) = $true)) & ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197)))) | (((X192 @ id @ X193 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X192 : (subst > term > subst > $o),X193 : term] : (! [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) = $true) | ($true != ((X192 @ id @ X194 @ id))) | ($true != ((X192 @ id @ X195 @ id)))) & ! [X196 : (subst > term > term)] : (($true = ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ? [X200 : term] : (($true = ((X192 @ id @ X200 @ id))) & (((X192 @ id @ (X196 @ id @ X200) @ id)) != $true)) | ? [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) != ((sub @ (X196 @ X198 @ X199) @ X197)))) & (((X192 @ id @ X193 @ id)) != $true)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X367 : (subst > term > subst > $o)] : ? [X368 : (term > $o)] : ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X367 : (subst > term > subst > $o)] : ! [X368 : (term > $o)] : ? [X369 : term] : (((X367 @ id @ X369 @ id)) != ((X368 @ X369))))) & (axassoc = $true) & (((axscons = $true) | ? [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) != X497)) & (! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497) | (axscons != $true))) & (hoasinduction_lem2_lthm = $true) & (((axvarcons = $true) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281)) & (! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281) | (axvarcons != $true))) & ! [X279 : d_subst,X280 : d_subst] : ((X279 = X280) | (((d2subst @ X280)) != ((d2subst @ X279))))), 0.43/0.52 inference(nnf_transformation,[],[f42])). 0.43/0.52 thf(f133,plain,( 0.43/0.52 (axabs = $true) & (hoaslamnotvar_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true != ((X283 @ one))) & ($true = ((X285 @ X284))) & ! [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) = ((X283 @ X287))))) & (! [X283 : (term > $o),X286 : subst,X284 : term,X285 : (term > $o)] : (($true = ((X283 @ one))) | ($true != ((X285 @ X284))) | ? [X287 : term] : (((X285 @ (sub @ X287 @ (push @ X284 @ X286)))) != ((X283 @ X287)))) | (pushprop_lem1v2 != $true)) & ((hoasapinj1_lthm = $true) | (? [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 != X431) & (((ap @ (sub @ X431 @ id) @ X430)) = ((ap @ (sub @ X428 @ id) @ X429)))) & ! [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) != ((ap @ X427 @ X425))) | (X426 = X427)) & ! [X423 : term] : (((sub @ X423 @ id)) = X423))) & (! [X428 : term,X431 : term,X429 : term,X430 : term] : ((X428 = X431) | (((ap @ (sub @ X431 @ id) @ X430)) != ((ap @ (sub @ X428 @ id) @ X429)))) | ? [X425 : term,X426 : term,X427 : term,X424 : term] : ((((ap @ X426 @ X424)) = ((ap @ X427 @ X425))) & (X426 != X427)) | ? [X423 : term] : (((sub @ X423 @ id)) != X423) | (hoasapinj1_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | (? [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (! [X374 : term] : (((X371 @ X374)) = ((X372 @ id @ X374 @ id))) & ! [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) = $true) | ($true != ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) & ($true != ((sP27 @ X372))) & (((X371 @ (lam @ X373))) != $true) & ! [X388 : term] : (($true = ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) | ($true != ((X371 @ X388)))) & ! [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) = $true) | (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) != $true))) & ! [X370 : term] : (((sub @ X370 @ id)) = X370))) & (! [X372 : (subst > term > subst > $o),X373 : term,X371 : (term > $o)] : (? [X374 : term] : (((X371 @ X374)) != ((X372 @ id @ X374 @ id))) | ? [X387 : subst,X386 : term,X384 : subst,X385 : subst] : ((((X372 @ (comp @ X385 @ X387) @ (sub @ X386 @ X387) @ X384)) != $true) & ($true = ((X372 @ X385 @ X386 @ (comp @ X387 @ X384))))) | ($true = ((sP27 @ X372))) | (((X371 @ (lam @ X373))) = $true) | ? [X388 : term] : (($true != ((X371 @ (sub @ X373 @ (push @ X388 @ id))))) & ($true = ((X371 @ X388)))) | ? [X376 : term,X378 : subst,X375 : subst,X377 : subst] : ((((X372 @ X375 @ X376 @ (comp @ X378 @ X377))) != $true) & (((X372 @ (comp @ X375 @ X378) @ (sub @ X376 @ X378) @ X377)) = $true))) | ? [X370 : term] : (((sub @ X370 @ id)) != X370) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP26) | ? [X158 : (subst > term > subst > $o),X159 : term] : (! [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true = ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) | (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) != $true)) & ! [X165 : term] : (($true != ((X158 @ id @ X165 @ id))) | (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) = $true)) & ($true = ((sP21 @ X158))) & ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) = $true) | (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) != $true)) & ($true != ((X158 @ id @ (lam @ X159) @ id)))) | ($true = sP25) | ($true = sP24) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP26) & ! [X158 : (subst > term > subst > $o),X159 : term] : (? [X166 : term,X167 : subst,X169 : subst,X168 : subst] : (($true != ((X158 @ X168 @ X166 @ (comp @ X169 @ X167)))) & (((X158 @ (comp @ X168 @ X169) @ (sub @ X166 @ X169) @ X167)) = $true)) | ? [X165 : term] : (($true = ((X158 @ id @ X165 @ id))) & (((X158 @ id @ (sub @ X159 @ (push @ X165 @ id)) @ id)) != $true)) | ($true != ((sP21 @ X158))) | ? [X170 : subst,X171 : subst,X172 : subst,X173 : term] : ((((X158 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171) @ X170)) != $true) & (((X158 @ X172 @ X173 @ (comp @ X171 @ X170))) = $true)) | ($true = ((X158 @ id @ (lam @ X159) @ id)))) & ($true != sP25) & ($true != sP24))) & (! [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (? [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) = $true) & (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) != $true)) | (((X515 @ (lam @ X514))) = $true) | ? [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true != ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) & ($true = ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) | ? [X521 : term] : (((X516 @ id @ X521 @ id)) != ((X515 @ X521))) | ($true = ((sP20 @ X516))) | ? [X527 : term] : (($true != ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) & ($true = ((X515 @ X527))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X516 : (subst > term > subst > $o),X515 : (term > $o),X514 : term] : (! [X517 : subst,X518 : term,X520 : subst,X519 : subst] : ((((X516 @ X520 @ X518 @ (comp @ X517 @ X519))) != $true) | (((X516 @ (comp @ X520 @ X517) @ (sub @ X518 @ X517) @ X519)) = $true)) & (((X515 @ (lam @ X514))) != $true) & ! [X528 : term,X529 : subst,X531 : subst,X530 : subst] : (($true = ((X516 @ X531 @ X528 @ (comp @ X530 @ X529)))) | ($true != ((X516 @ (comp @ X531 @ X530) @ (sub @ X528 @ X530) @ X529)))) & ! [X521 : term] : (((X516 @ id @ X521 @ id)) = ((X515 @ X521))) & ($true != ((sP20 @ X516))) & ! [X527 : term] : (($true = ((X515 @ (sub @ X514 @ (push @ X527 @ id))))) | ($true != ((X515 @ X527)))))) & ((hoasinduction_lem3aa_lthm = $true) | ? [X358 : term,X357 : (subst > term > subst > $o)] : (! [X359 : term] : (($true = ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) | ($true != ((X357 @ id @ X359 @ id)))) & ($true != ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) & ! [X360 : (subst > term > term)] : (? [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) != ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) | (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) = $true) | ? [X364 : term] : (($true = ((X357 @ id @ X364 @ id))) & ($true != ((X357 @ id @ (X360 @ id @ X364) @ id))))))) & (! [X358 : term,X357 : (subst > term > subst > $o)] : (? [X359 : term] : (($true != ((X357 @ id @ (sub @ X358 @ (push @ X359 @ id)) @ id))) & ($true = ((X357 @ id @ X359 @ id)))) | ($true = ((X357 @ id @ (lam @ (sub @ X358 @ (push @ one @ sh))) @ id))) | ? [X360 : (subst > term > term)] : (! [X363 : term,X361 : subst,X362 : subst] : (((sub @ (X360 @ X362 @ X363) @ X361)) = ((X360 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361)))) & (((X357 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true) & ! [X364 : term] : (($true != ((X357 @ id @ X364 @ id))) | ($true = ((X357 @ id @ (X360 @ id @ X364) @ id)))))) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) | (! [X116 : subst] : (((comp @ id @ X116)) = X116) & (? [X119 : subst] : (((comp @ id @ X119)) != X119) | ? [X118 : subst] : (((comp @ X118 @ id)) != X118)) & ! [X117 : subst] : (((comp @ X117 @ id)) = X117))) & (? [X116 : subst] : (((comp @ id @ X116)) != X116) | (! [X119 : subst] : (((comp @ id @ X119)) = X119) & ! [X118 : subst] : (((comp @ X118 @ id)) = X118)) | ? [X117 : subst] : (((comp @ X117 @ id)) != X117) | (substmonoid_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapnotvar = $true) & (id = ((d2subst @ d_id))) & (! [X2 : term] : (((sub @ X2 @ id)) = X2) | (axvarid != $true)) & ((axvarid = $true) | ? [X2 : term] : (((sub @ X2 @ id)) != X2)) & ((hoasinduction_lem3b = $true) | ? [X498 : term] : ! [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) != ((X499 @ sh @ one)))) & (! [X498 : term] : ? [X499 : (subst > term > term)] : (((sub @ X498 @ (push @ one @ sh))) = ((X499 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((sP19 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP19 != $true)) & (! [X409 : term] : ? [X410 : (subst > term > term)] : ! [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) = ((X410 @ X412 @ X411))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X409 : term] : ! [X410 : (subst > term > term)] : ? [X411 : term,X412 : subst] : (((sub @ X409 @ (push @ X411 @ X412))) != ((X410 @ X412 @ X411)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axvarshift = $true) & (($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18)) & (pushprop_lem3v2_lthm = $true) & (induction2_gthm = $true) & (pushprop_gthm = $true) & ! [X1 : d_term,X0 : d_term] : ((((d2term @ X0)) != ((d2term @ X1))) | (X0 = X1)) & ((termmset_lthm = $true) | (? [X92 : term] : (((sub @ X92 @ id)) != X92) & ! [X91 : term] : (((sub @ X91 @ id)) = X91))) & (! [X92 : term] : (((sub @ X92 @ id)) = X92) | ? [X91 : term] : (((sub @ X91 @ id)) != X91) | (termmset_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & (! [X333 : subst] : (((comp @ id @ X333)) = X333) | (axidl != $true)) & ((axidl = $true) | ? [X333 : subst] : (((comp @ id @ X333)) != X333)) & ((hoasinduction = $true) | ? [X440 : term,X441 : (subst > term > subst > $o)] : ((((sP16 @ X441)) != $true) & (((sP15 @ X441)) != $true) & ! [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true = ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) | ($true != ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) & ($true != ((X441 @ id @ X440 @ id))) & ! [X453 : term] : ((((X441 @ id @ X453 @ id)) = $true) | ($true != ((var @ (sub @ X453 @ id))))) & ! [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) = $true) | ($true != ((X441 @ X444 @ X446 @ (comp @ X445 @ X447))))))) & (! [X440 : term,X441 : (subst > term > subst > $o)] : ((((sP16 @ X441)) = $true) | (((sP15 @ X441)) = $true) | ? [X456 : subst,X455 : term,X454 : subst,X457 : subst] : (($true != ((X441 @ X456 @ X455 @ (comp @ X457 @ X454)))) & ($true = ((X441 @ (comp @ X456 @ X457) @ (sub @ X455 @ X457) @ X454)))) | ($true = ((X441 @ id @ X440 @ id))) | ? [X453 : term] : ((((X441 @ id @ X453 @ id)) != $true) & ($true = ((var @ (sub @ X453 @ id))))) | ? [X446 : term,X445 : subst,X447 : subst,X444 : subst] : ((((X441 @ (comp @ X444 @ X445) @ (sub @ X446 @ X445) @ X447)) != $true) & ($true = ((X441 @ X444 @ X446 @ (comp @ X445 @ X447)))))) | (hoasinduction != $true)) & ((! [X295 : subst] : (((comp @ X295 @ id)) = X295) & ! [X296 : subst] : (((comp @ id @ X296)) = X296)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X295 : subst] : (((comp @ X295 @ id)) != X295) | ? [X296 : subst] : (((comp @ id @ X296)) != X296)) & (($true = sP14) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP14)) & ((pushprop_lem0_lthm = $true) | ? [X502 : (term > $o),X501 : term,X500 : subst] : ! [X503 : (term > $o)] : ? [X504 : term] : (((X503 @ X504)) != ((X502 @ (sub @ X504 @ (push @ X501 @ X500)))))) & (! [X502 : (term > $o),X501 : term,X500 : subst] : ? [X503 : (term > $o)] : ! [X504 : term] : (((X503 @ X504)) = ((X502 @ (sub @ X504 @ (push @ X501 @ X500))))) | (pushprop_lem0_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP12) & ! [X16 : term] : (((sub @ X16 @ id)) = X16) & ! [X18 : term,X17 : (subst > term > subst > $o)] : (? [X20 : (subst > term > term)] : (($true != ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) & ! [X24 : term] : (($true != ((X17 @ id @ X24 @ id))) | (((X17 @ id @ (X20 @ id @ X24) @ id)) = $true)) & ! [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) = ((sub @ (X20 @ X22 @ X23) @ X21)))) | ? [X19 : term] : (($true = ((X17 @ id @ X19 @ id))) & ($true != ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) | ($true = ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id)))))) & (($true = sP12) | ? [X16 : term] : (((sub @ X16 @ id)) != X16) | ? [X18 : term,X17 : (subst > term > subst > $o)] : (! [X20 : (subst > term > term)] : (($true = ((X17 @ id @ (lam @ (X20 @ sh @ one)) @ id))) | ? [X24 : term] : (($true = ((X17 @ id @ X24 @ id))) & (((X17 @ id @ (X20 @ id @ X24) @ id)) != $true)) | ? [X21 : subst,X23 : term,X22 : subst] : (((X20 @ (comp @ X22 @ X21) @ (sub @ X23 @ X21))) != ((sub @ (X20 @ X22 @ X23) @ X21)))) & ! [X19 : term] : (($true != ((X17 @ id @ X19 @ id))) | ($true = ((X17 @ id @ (sub @ X18 @ (push @ X19 @ id)) @ id)))) & ($true != ((X17 @ id @ (lam @ (sub @ X18 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & (pushprop_lem3v2 = $true) & ! [X327 : d_subst] : (d_id = X327) & (ulamvarsh = $true) & (lamnotvar = $true) & (($true = sP9) | ($true = sP10) | ? [X297 : (subst > term > subst > $o)] : ! [X298 : (term > $o)] : ? [X299 : term] : (((X298 @ X299)) != ((X297 @ id @ X299 @ id))) | ? [X307 : term] : (((sub @ X307 @ id)) != X307) | ? [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (! [X317 : term] : (($true != ((X309 @ X317))) | (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) = $true)) & ! [X311 : (subst > term > term)] : (? [X312 : term] : (($true = ((X310 @ id @ X312 @ id))) & ($true != ((X310 @ id @ (X311 @ id @ X312) @ id)))) | ($true = ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ? [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) != ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) & ($true != ((X309 @ (lam @ X308)))) & ! [X316 : term] : (((X309 @ X316)) = ((X310 @ id @ X316 @ id)))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP9) & ($true != sP10) & ! [X297 : (subst > term > subst > $o)] : ? [X298 : (term > $o)] : ! [X299 : term] : (((X298 @ X299)) = ((X297 @ id @ X299 @ id))) & ! [X307 : term] : (((sub @ X307 @ id)) = X307) & ! [X310 : (subst > term > subst > $o),X308 : term,X309 : (term > $o)] : (? [X317 : term] : (($true = ((X309 @ X317))) & (((X309 @ (sub @ X308 @ (push @ X317 @ id)))) != $true)) | ? [X311 : (subst > term > term)] : (! [X312 : term] : (($true != ((X310 @ id @ X312 @ id))) | ($true = ((X310 @ id @ (X311 @ id @ X312) @ id)))) & ($true != ((X310 @ id @ (lam @ (X311 @ sh @ one)) @ id))) & ! [X313 : subst,X315 : subst,X314 : term] : (((sub @ (X311 @ X315 @ X314) @ X313)) = ((X311 @ (comp @ X315 @ X313) @ (sub @ X314 @ X313))))) | ($true = ((X309 @ (lam @ X308)))) | ? [X316 : term] : (((X309 @ X316)) != ((X310 @ id @ X316 @ id)))))) & ((sP8 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP8 != $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP7)) & (($true = sP7) | (hoasinduction_lem2v2 != $true)) & (axmap = $true) & ((induction = $true) | ? [X351 : term,X352 : (term > $o)] : (! [X353 : term] : (($true != ((X352 @ X353))) | ($true = ((X352 @ (lam @ X353))))) & ! [X354 : term] : ((((X352 @ X354)) = $true) | ($true != ((var @ X354)))) & (((X352 @ X351)) != $true) & ! [X355 : term,X356 : term] : (($true != ((X352 @ X356))) | ($true != ((X352 @ X355))) | (((X352 @ (ap @ X356 @ X355))) = $true)))) & (! [X351 : term,X352 : (term > $o)] : (? [X353 : term] : (($true = ((X352 @ X353))) & ($true != ((X352 @ (lam @ X353))))) | ? [X354 : term] : ((((X352 @ X354)) != $true) & ($true = ((var @ X354)))) | (((X352 @ X351)) = $true) | ? [X355 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true = ((X352 @ X355))) & (((X352 @ (ap @ X356 @ X355))) != $true))) | (induction != $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)))))))))))))) & (! [X389 : term,X391 : subst,X390 : (term > $o)] : ? [X392 : (term > $o)] : ! [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) = ((X392 @ X393))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X389 : term,X391 : subst,X390 : (term > $o)] : ! [X392 : (term > $o)] : ? [X393 : term] : (((X390 @ (sub @ X393 @ (push @ X389 @ X391)))) != ((X392 @ X393)))) & ! [X365 : term] : ? [X366 : d_term] : (((d2term @ X366)) = X365) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X41 : (subst > term > subst > $o)] : ? [X42 : (term > $o)] : ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((X42 @ X43))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X41 : (subst > term > subst > $o)] : ! [X42 : (term > $o)] : ? [X43 : term] : (((X41 @ id @ X43 @ id)) != ((X42 @ X43)))) & (? [X466 : term] : (((sub @ X466 @ id)) != X466) | ? [X467 : (subst > term > subst > $o),X468 : term] : (! [X469 : term] : (($true != ((X467 @ id @ X469 @ id))) | ($true = ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) & ($true != ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) & ! [X470 : (subst > term > term)] : (? [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) != ((sub @ (X470 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) = $true) | ? [X474 : term] : (($true = ((X467 @ id @ X474 @ id))) & ($true != ((X467 @ id @ (X470 @ id @ X474) @ id)))))) | ($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X466 : term] : (((sub @ X466 @ id)) = X466) & ! [X467 : (subst > term > subst > $o),X468 : term] : (? [X469 : term] : (($true = ((X467 @ id @ X469 @ id))) & ($true != ((X467 @ id @ (sub @ X468 @ (push @ X469 @ id)) @ id)))) | ($true = ((X467 @ id @ (lam @ (sub @ X468 @ (push @ one @ sh))) @ id))) | ? [X470 : (subst > term > term)] : (! [X473 : subst,X472 : subst,X471 : term] : (((X470 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) = ((sub @ (X470 @ X473 @ X471) @ X472))) & (((X467 @ id @ (lam @ (X470 @ sh @ one)) @ id)) != $true) & ! [X474 : term] : (($true != ((X467 @ id @ X474 @ id))) | ($true = ((X467 @ id @ (X470 @ id @ X474) @ id)))))) & ($true != sP6))) & (ulamvarind = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X432 : term] : ! [X433 : (subst > term > term)] : ? [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) != ((sub @ X432 @ (push @ X435 @ X434))))) & (! [X432 : term] : ? [X433 : (subst > term > term)] : ! [X434 : subst,X435 : term] : (((X433 @ X434 @ X435)) = ((sub @ X432 @ (push @ X435 @ X434)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) = ((ap @ X417 @ X415))) & (X415 != X418)) | ! [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 = X422) | (((ap @ (sub @ X421 @ id) @ X420)) != ((ap @ (sub @ X419 @ id) @ X422)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ X416 @ X418)) != ((ap @ X417 @ X415))) | (X415 = X418)) & ? [X421 : term,X420 : term,X422 : term,X419 : term] : ((X420 != X422) & (((ap @ (sub @ X421 @ id) @ X420)) = ((ap @ (sub @ X419 @ id) @ X422)))))) & ((termmset = $true) | ? [X95 : term] : (((sub @ X95 @ id)) != X95)) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) | (termmset != $true)) & (($true = sP5) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP5)) & ((apinj1 = $true) | ? [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 != X438) & (((ap @ X436 @ X439)) = ((ap @ X438 @ X437))))) & (! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X436 = X438) | (((ap @ X436 @ X439)) != ((ap @ X438 @ X437)))) | (apinj1 != $true)) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & (! [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) = ((X107 @ X109 @ X106))) | ? [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) != ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) | ? [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) != ((sub @ (X108 @ X114 @ X113) @ X115))) | (((lam @ (X107 @ sh @ one))) != ((lam @ (X108 @ sh @ one))))) | ? [X104 : term,X105 : term] : ((((lam @ X104)) = ((lam @ X105))) & (X104 != X105)) | ? [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) != X100) | ? [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) != X103) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (? [X106 : term,X109 : subst,X107 : (subst > term > term),X108 : (subst > term > term)] : ((((X108 @ X109 @ X106)) != ((X107 @ X109 @ X106))) & ! [X110 : subst,X111 : subst,X112 : term] : (((sub @ (X107 @ X110 @ X112) @ X111)) = ((X107 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111)))) & ! [X113 : term,X115 : subst,X114 : subst] : (((X108 @ (comp @ X114 @ X115) @ (sub @ X113 @ X115))) = ((sub @ (X108 @ X114 @ X113) @ X115))) & (((lam @ (X107 @ sh @ one))) = ((lam @ (X108 @ sh @ one))))) & ! [X104 : term,X105 : term] : ((((lam @ X104)) != ((lam @ X105))) | (X104 = X105)) & ! [X101 : subst,X100 : term] : (((sub @ one @ (push @ X100 @ X101))) = X100) & ! [X102 : term,X103 : subst] : (((comp @ sh @ (push @ X102 @ X103))) = X103))) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((pushprop_lem1_lthm = $true) | (! [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) = X505) & ? [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) = $true) & (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) != $true)) & ! [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) = X508))) & (? [X506 : subst,X505 : term] : (((sub @ one @ (push @ X505 @ X506))) != X505) | ! [X510 : term,X512 : term,X511 : (term > $o),X509 : (term > $o),X513 : subst] : ((((X511 @ X512)) != $true) | (((X509 @ (sub @ X512 @ (push @ X510 @ X513)))) = $true)) | ? [X507 : term,X508 : subst] : (((comp @ sh @ (push @ X507 @ X508))) != X508) | (pushprop_lem1_lthm != $true)) & (hoaslamnotap_lthm = $true) & (sh = ((d2subst @ d_id))) & ((hoasinduction_lem3aa = $true) | ? [X483 : (subst > term > subst > $o),X484 : term] : (! [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) = $true) | ? [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) != ((sub @ (X486 @ X490 @ X489) @ X488))) | ? [X487 : term] : (($true != ((X483 @ id @ (X486 @ id @ X487) @ id))) & (((X483 @ id @ X487 @ id)) = $true))) & ! [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) = $true) | ($true != ((X483 @ id @ X485 @ id)))) & ($true != ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id))))) & (! [X483 : (subst > term > subst > $o),X484 : term] : (? [X486 : (subst > term > term)] : ((((X483 @ id @ (lam @ (X486 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X488 : subst,X489 : term] : (((X486 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488))) = ((sub @ (X486 @ X490 @ X489) @ X488))) & ! [X487 : term] : (($true = ((X483 @ id @ (X486 @ id @ X487) @ id))) | (((X483 @ id @ X487 @ id)) != $true))) | ? [X485 : term] : ((((X483 @ id @ (sub @ X484 @ (push @ X485 @ id)) @ id)) != $true) & ($true = ((X483 @ id @ X485 @ id)))) | ($true = ((X483 @ id @ (lam @ (sub @ X484 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3aa != $true)) & ((hoaslamnotap = $true) | ? [X201 : term,X202 : (subst > term > term),X203 : term] : (! [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) = ((sub @ (X202 @ X205 @ X204) @ X206))) & (((ap @ (sub @ X201 @ id) @ X203)) = ((lam @ (X202 @ sh @ one)))))) & (! [X201 : term,X202 : (subst > term > term),X203 : term] : (? [X205 : subst,X206 : subst,X204 : term] : (((X202 @ (comp @ X205 @ X206) @ (sub @ X204 @ X206))) != ((sub @ (X202 @ X205 @ X204) @ X206))) | (((ap @ (sub @ X201 @ id) @ X203)) != ((lam @ (X202 @ sh @ one))))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop = $true) & (hoasinduction_lem2_gthm = $true) & (! [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) != ((ap @ (sub @ X98 @ id) @ X97))) | (X96 = X97)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X97 : term,X96 : term,X98 : term,X99 : term] : ((((ap @ (sub @ X99 @ id) @ X96)) = ((ap @ (sub @ X98 @ id) @ X97))) & (X96 != X97))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 = X493) | (((ap @ (sub @ X493 @ id) @ X491)) != ((ap @ (sub @ X492 @ id) @ X494)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X491 : term,X493 : term,X492 : term,X494 : term] : ((X492 != X493) & (((ap @ (sub @ X493 @ id) @ X491)) = ((ap @ (sub @ X492 @ id) @ X494))))) & (! [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) = X60) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X60 : subst,X59 : term] : (((comp @ sh @ (push @ X59 @ X60))) != X60)) & (hoasinduction_lem3v2_gthm = $true) & (termmset_gthm = $true) & (! [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (? [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) != ((X339 @ X340))) | (((X338 @ X337)) != $true) | ($true = ((X339 @ one)))) | ? [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) != X334) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X338 : (term > $o),X336 : subst,X337 : term,X339 : (term > $o)] : (! [X340 : term] : (((X338 @ (sub @ X340 @ (push @ X337 @ X336)))) = ((X339 @ X340))) & (((X338 @ X337)) = $true) & ($true != ((X339 @ one)))) & ! [X335 : subst,X334 : term] : (((sub @ one @ (push @ X334 @ X335))) = X334))) & (pushprop_lem2v2_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3 = $true) | ? [X120 : term,X121 : (subst > term > subst > $o)] : (($true != ((sP4 @ X121))) & ! [X126 : term] : (($true = ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) | ($true != ((X121 @ id @ X126 @ id)))) & ! [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) != $true) | (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) = $true)) & ! [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) = $true) | ($true != ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) & ($true != ((X121 @ id @ (lam @ X120) @ id))))) & (! [X120 : term,X121 : (subst > term > subst > $o)] : (($true = ((sP4 @ X121))) | ? [X126 : term] : (($true != ((X121 @ id @ (sub @ X120 @ (push @ X126 @ id)) @ id))) & ($true = ((X121 @ id @ X126 @ id)))) | ? [X135 : subst,X134 : subst,X132 : term,X133 : subst] : ((((X121 @ X135 @ X132 @ (comp @ X134 @ X133))) = $true) & (((X121 @ (comp @ X135 @ X134) @ (sub @ X132 @ X134) @ X133)) != $true)) | ? [X124 : subst,X125 : subst,X123 : subst,X122 : term] : ((((X121 @ X123 @ X122 @ (comp @ X124 @ X125))) != $true) & ($true = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124) @ X125)))) | ($true = ((X121 @ id @ (lam @ X120) @ id)))) | (hoasinduction_lem3 != $true)) & ((laminj = $true) | ? [X414 : term,X413 : term] : ((X413 != X414) & (((lam @ X414)) = ((lam @ X413))))) & (! [X414 : term,X413 : term] : ((X413 = X414) | (((lam @ X414)) != ((lam @ X413)))) | (laminj != $true)) & (axapp = $true) & (hoasapinj1_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotvar = $true) & (apnotvar = $true) & (pushprop_lthm = $true) & ((shinj = $true) | ? [X89 : term,X90 : term] : ((X89 != X90) & (((sub @ X90 @ sh)) = ((sub @ X89 @ sh))))) & (! [X89 : term,X90 : term] : ((X89 = X90) | (((sub @ X90 @ sh)) != ((sub @ X89 @ sh)))) | (shinj != $true)) & (pushprop_lem1_gthm = $true) & (! [X78 : term,X77 : (subst > term > subst > $o)] : (? [X88 : term] : ((((X77 @ id @ X88 @ id)) = $true) & ($true != ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) | ($true = ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) | ? [X79 : (subst > term > term),X80 : term] : (($true != ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) & ! [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) = ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) & ! [X81 : term] : (($true != ((X77 @ id @ X81 @ id))) | (((X77 @ id @ (X79 @ id @ X81) @ id)) = $true)) & ! [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) = ((sub @ (X79 @ X82 @ X84) @ X83))))) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X78 : term,X77 : (subst > term > subst > $o)] : (! [X88 : term] : ((((X77 @ id @ X88 @ id)) != $true) | ($true = ((X77 @ id @ (sub @ X78 @ (push @ X88 @ id)) @ id)))) & ($true != ((X77 @ id @ (lam @ (sub @ X78 @ (push @ one @ sh))) @ id))) & ! [X79 : (subst > term > term),X80 : term] : (($true = ((X77 @ id @ (lam @ (X79 @ sh @ one)) @ id))) | ? [X86 : term,X85 : subst,X87 : subst] : (((sub @ X80 @ (push @ (sub @ X86 @ X87) @ (comp @ X85 @ X87)))) != ((X79 @ (comp @ X85 @ X87) @ (sub @ X86 @ X87)))) | ? [X81 : term] : (($true = ((X77 @ id @ X81 @ id))) & (((X77 @ id @ (X79 @ id @ X81) @ id)) != $true)) | ? [X82 : subst,X84 : term,X83 : subst] : (((sub @ (sub @ X80 @ (push @ X84 @ X82)) @ X83)) != ((sub @ (X79 @ X82 @ X84) @ X83)))))) & ((hoasinduction_lem3a = $true) | ? [X458 : term,X459 : (subst > term > subst > $o)] : (! [X465 : term] : (($true != ((X459 @ id @ X465 @ id))) | (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) = $true)) & ($true != ((X459 @ id @ (lam @ X458) @ id))) & ! [X460 : (subst > term > term)] : (? [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) != ((sub @ (X460 @ X462 @ X463) @ X461))) | ? [X464 : term] : ((((X459 @ id @ X464 @ id)) = $true) & ($true != ((X459 @ id @ (X460 @ id @ X464) @ id)))) | ($true = ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)))))) & (! [X458 : term,X459 : (subst > term > subst > $o)] : (? [X465 : term] : (($true = ((X459 @ id @ X465 @ id))) & (((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id)) != $true)) | ($true = ((X459 @ id @ (lam @ X458) @ id))) | ? [X460 : (subst > term > term)] : (! [X462 : subst,X461 : subst,X463 : term] : (((X460 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461))) = ((sub @ (X460 @ X462 @ X463) @ X461))) & ! [X464 : term] : ((((X459 @ id @ X464 @ id)) != $true) | ($true = ((X459 @ id @ (X460 @ id @ X464) @ id)))) & ($true != ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id))))) | (hoasinduction_lem3a != $true)) & (! [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (? [X402 : term] : (($true != ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) & ($true = ((X399 @ X402)))) | ? [X403 : term] : (((X401 @ id @ X403 @ id)) != ((X399 @ X403))) | (((X399 @ (lam @ X400))) = $true) | ? [X404 : (subst > term > term)] : (! [X408 : term] : (($true = ((X401 @ id @ (X404 @ id @ X408) @ id))) | (((X401 @ id @ X408 @ id)) != $true)) & ! [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) = ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) & ($true != ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) | ? [X394 : term] : ! [X395 : (subst > term > term)] : ? [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) != ((X395 @ X397 @ X396))) | ? [X398 : term] : (((sub @ X398 @ id)) != X398) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (? [X401 : (subst > term > subst > $o),X400 : term,X399 : (term > $o)] : (! [X402 : term] : (($true = ((X399 @ (sub @ X400 @ (push @ X402 @ id))))) | ($true != ((X399 @ X402)))) & ! [X403 : term] : (((X401 @ id @ X403 @ id)) = ((X399 @ X403))) & (((X399 @ (lam @ X400))) != $true) & ! [X404 : (subst > term > term)] : (? [X408 : term] : (($true != ((X401 @ id @ (X404 @ id @ X408) @ id))) & (((X401 @ id @ X408 @ id)) = $true)) | ? [X406 : subst,X405 : term,X407 : subst] : (((sub @ (X404 @ X407 @ X405) @ X406)) != ((X404 @ (comp @ X407 @ X406) @ (sub @ X405 @ X406)))) | ($true = ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id))))) & ! [X394 : term] : ? [X395 : (subst > term > term)] : ! [X397 : subst,X396 : term] : (((sub @ X394 @ (push @ X396 @ X397))) = ((X395 @ X397 @ X396))) & ! [X398 : term] : (((sub @ X398 @ id)) = X398))) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) = $true) | ? [X350 : term] : (($true = ((X341 @ X350))) & ($true != ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) | ? [X345 : (subst > term > term)] : (! [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) = ((sub @ (X345 @ X347 @ X348) @ X346))) & ! [X349 : term] : (($true != ((X343 @ id @ X349 @ id))) | (((X343 @ id @ (X345 @ id @ X349) @ id)) = $true)) & ($true != ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) | ? [X344 : term] : (((X343 @ id @ X344 @ id)) != ((X341 @ X344)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ? [X341 : (term > $o),X342 : term,X343 : (subst > term > subst > $o)] : ((((X341 @ (lam @ X342))) != $true) & ! [X350 : term] : (($true != ((X341 @ X350))) | ($true = ((X341 @ (sub @ X342 @ (push @ X350 @ id)))))) & ! [X345 : (subst > term > term)] : (? [X348 : term,X347 : subst,X346 : subst] : (((X345 @ (comp @ X347 @ X346) @ (sub @ X348 @ X346))) != ((sub @ (X345 @ X347 @ X348) @ X346))) | ? [X349 : term] : (($true = ((X343 @ id @ X349 @ id))) & (((X343 @ id @ (X345 @ id @ X349) @ id)) != $true)) | ($true = ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id)))) & ! [X344 : term] : (((X343 @ id @ X344 @ id)) = ((X341 @ X344))))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & (! [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true != ((X330 @ X332))) | (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X331 : (term > $o),X328 : term,X329 : subst,X330 : (term > $o),X332 : term] : (($true = ((X330 @ X332))) & (((X331 @ (sub @ X332 @ (push @ X328 @ X329)))) != $true))) & ! [X495 : d_term] : (d_one = X495) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm_3 = $true) | (! [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (? [X222 : term] : (((X218 @ id @ X222 @ id)) != ((X220 @ X222))) | ? [X221 : term] : (($true != ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) & ($true = ((X220 @ X221)))) | ? [X223 : (subst > term > term)] : (! [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) = ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) & ! [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) = $true) | ($true != ((X218 @ id @ X224 @ id)))) & ($true != ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) | (((X220 @ (lam @ X219))) = $true)) & ($true != sP2) & ($true != sP3) & ! [X217 : term] : (((sub @ X217 @ id)) = X217) & ! [X207 : (subst > term > subst > $o)] : ? [X208 : (term > $o)] : ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))))) & (? [X220 : (term > $o),X218 : (subst > term > subst > $o),X219 : term] : (! [X222 : term] : (((X218 @ id @ X222 @ id)) = ((X220 @ X222))) & ! [X221 : term] : (($true = ((X220 @ (sub @ X219 @ (push @ X221 @ id))))) | ($true != ((X220 @ X221)))) & ! [X223 : (subst > term > term)] : (? [X225 : subst,X226 : subst,X227 : term] : (((sub @ (X223 @ X225 @ X227) @ X226)) != ((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226)))) | ? [X224 : term] : ((((X218 @ id @ (X223 @ id @ X224) @ id)) != $true) & ($true = ((X218 @ id @ X224 @ id)))) | ($true = ((X218 @ id @ (lam @ (X223 @ sh @ one)) @ id)))) & (((X220 @ (lam @ X219))) != $true)) | ($true = sP2) | ($true = sP3) | ? [X217 : term] : (((sub @ X217 @ id)) != X217) | ? [X207 : (subst > term > subst > $o)] : ! [X208 : (term > $o)] : ? [X209 : term] : (((X208 @ X209)) != ((X207 @ id @ X209 @ id))) | (hoasinduction_lthm_3 != $true)) & ((apinj2 = $true) | ? [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 != X249) & (((ap @ X248 @ X249)) = ((ap @ X246 @ X247))))) & (! [X249 : term,X247 : term,X248 : term,X246 : term] : ((X247 = X249) | (((ap @ X248 @ X249)) != ((ap @ X246 @ X247)))) | (apinj2 != $true)) & ! [X93 : subst] : ? [X94 : d_subst] : (((d2subst @ X94)) = X93) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X136 : term] : ! [X137 : (subst > term > term)] : (((X137 @ sh @ one)) != ((sub @ X136 @ (push @ one @ sh))))) & (! [X136 : term] : ? [X137 : (subst > term > term)] : (((X137 @ sh @ one)) = ((sub @ X136 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (lamnotap != $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) = ((X269 @ X270 @ X271))) | (((lam @ (X269 @ sh @ one))) != ((lam @ (X272 @ sh @ one)))) | ? [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) != ((sub @ (X272 @ X273 @ X275) @ X274))) | ? [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) != ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X269 : (subst > term > term),X272 : (subst > term > term),X270 : subst,X271 : term] : ((((X272 @ X270 @ X271)) != ((X269 @ X270 @ X271))) & (((lam @ (X269 @ sh @ one))) = ((lam @ (X272 @ sh @ one)))) & ! [X274 : subst,X273 : subst,X275 : term] : (((X272 @ (comp @ X273 @ X274) @ (sub @ X275 @ X274))) = ((sub @ (X272 @ X273 @ X275) @ X274))) & ! [X276 : subst,X278 : term,X277 : subst] : (((sub @ (X269 @ X277 @ X278) @ X276)) = ((X269 @ (comp @ X277 @ X276) @ (sub @ X278 @ X276)))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((axidr = $true) | ? [X496 : subst] : (((comp @ X496 @ id)) != X496)) & (! [X496 : subst] : (((comp @ X496 @ id)) = X496) | (axidr != $true)) & (hoasinduction_lem3_gthm = $true) & (! [X192 : (subst > term > subst > $o),X193 : term] : (? [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) != $true) & ($true = ((X192 @ id @ X194 @ id))) & ($true = ((X192 @ id @ X195 @ id)))) | ? [X196 : (subst > term > term)] : (($true != ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) & ! [X200 : term] : (($true != ((X192 @ id @ X200 @ id))) | (((X192 @ id @ (X196 @ id @ X200) @ id)) = $true)) & ! [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) = ((sub @ (X196 @ X198 @ X199) @ X197)))) | (((X192 @ id @ X193 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X192 : (subst > term > subst > $o),X193 : term] : (! [X194 : term,X195 : term] : ((((X192 @ id @ (ap @ (sub @ X194 @ id) @ X195) @ id)) = $true) | ($true != ((X192 @ id @ X194 @ id))) | ($true != ((X192 @ id @ X195 @ id)))) & ! [X196 : (subst > term > term)] : (($true = ((X192 @ id @ (lam @ (X196 @ sh @ one)) @ id))) | ? [X200 : term] : (($true = ((X192 @ id @ X200 @ id))) & (((X192 @ id @ (X196 @ id @ X200) @ id)) != $true)) | ? [X197 : subst,X199 : term,X198 : subst] : (((X196 @ (comp @ X198 @ X197) @ (sub @ X199 @ X197))) != ((sub @ (X196 @ X198 @ X199) @ X197)))) & (((X192 @ id @ X193 @ id)) != $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X367 : (subst > term > subst > $o)] : ? [X368 : (term > $o)] : ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X367 : (subst > term > subst > $o)] : ! [X368 : (term > $o)] : ? [X369 : term] : (((X367 @ id @ X369 @ id)) != ((X368 @ X369)))) & (axassoc = $true) & ((axscons = $true) | ? [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) != X497)) & (! [X497 : subst] : (((push @ (sub @ one @ X497) @ (comp @ sh @ X497))) = X497) | (axscons != $true)) & (hoasinduction_lem2_lthm = $true) & ((axvarcons = $true) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281)) & (! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281) | (axvarcons != $true)) & ! [X279 : d_subst,X280 : d_subst] : ((X279 = X280) | (((d2subst @ X280)) != ((d2subst @ X279))))), 0.43/0.52 inference(flattening,[],[f132])). 0.43/0.52 thf(f134,plain,( 0.43/0.52 (axabs = $true) & (hoaslamnotvar_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X0 : (term > $o),X1 : subst,X2 : term,X3 : (term > $o)] : (($true != ((X0 @ one))) & (((X3 @ X2)) = $true) & ! [X4 : term] : (((X0 @ X4)) = ((X3 @ (sub @ X4 @ (push @ X2 @ X1))))))) & (! [X5 : (term > $o),X6 : subst,X7 : term,X8 : (term > $o)] : ((((X5 @ one)) = $true) | ($true != ((X8 @ X7))) | ? [X9 : term] : (((X5 @ X9)) != ((X8 @ (sub @ X9 @ (push @ X7 @ X6)))))) | (pushprop_lem1v2 != $true)) & ((hoasapinj1_lthm = $true) | (? [X10 : term,X11 : term,X12 : term,X13 : term] : ((X10 != X11) & (((ap @ (sub @ X11 @ id) @ X13)) = ((ap @ (sub @ X10 @ id) @ X12)))) & ! [X14 : term,X15 : term,X16 : term,X17 : term] : ((((ap @ X15 @ X17)) != ((ap @ X16 @ X14))) | (X15 = X16)) & ! [X18 : term] : (((sub @ X18 @ id)) = X18))) & (! [X19 : term,X20 : term,X21 : term,X22 : term] : ((X19 = X20) | (((ap @ (sub @ X19 @ id) @ X21)) != ((ap @ (sub @ X20 @ id) @ X22)))) | ? [X23 : term,X24 : term,X25 : term,X26 : term] : ((((ap @ X24 @ X26)) = ((ap @ X25 @ X23))) & (X24 != X25)) | ? [X27 : term] : (((sub @ X27 @ id)) != X27) | (hoasapinj1_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | (? [X28 : (subst > term > subst > $o),X29 : term,X30 : (term > $o)] : (! [X31 : term] : (((X28 @ id @ X31 @ id)) = ((X30 @ X31))) & ! [X32 : subst,X33 : term,X34 : subst,X35 : subst] : (($true = ((X28 @ (comp @ X35 @ X32) @ (sub @ X33 @ X32) @ X34))) | ($true != ((X28 @ X35 @ X33 @ (comp @ X32 @ X34))))) & ($true != ((sP27 @ X28))) & (((X30 @ (lam @ X29))) != $true) & ! [X36 : term] : (($true = ((X30 @ (sub @ X29 @ (push @ X36 @ id))))) | (((X30 @ X36)) != $true)) & ! [X37 : term,X38 : subst,X39 : subst,X40 : subst] : ((((X28 @ X39 @ X37 @ (comp @ X38 @ X40))) = $true) | (((X28 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38) @ X40)) != $true))) & ! [X41 : term] : (((sub @ X41 @ id)) = X41))) & (! [X42 : (subst > term > subst > $o),X43 : term,X44 : (term > $o)] : (? [X45 : term] : (((X42 @ id @ X45 @ id)) != ((X44 @ X45))) | ? [X46 : subst,X47 : term,X48 : subst,X49 : subst] : ((((X42 @ (comp @ X49 @ X46) @ (sub @ X47 @ X46) @ X48)) != $true) & ($true = ((X42 @ X49 @ X47 @ (comp @ X46 @ X48))))) | (((sP27 @ X42)) = $true) | (((X44 @ (lam @ X43))) = $true) | ? [X50 : term] : ((((X44 @ (sub @ X43 @ (push @ X50 @ id)))) != $true) & (((X44 @ X50)) = $true)) | ? [X51 : term,X52 : subst,X53 : subst,X54 : subst] : (($true != ((X42 @ X53 @ X51 @ (comp @ X52 @ X54)))) & ($true = ((X42 @ (comp @ X53 @ X52) @ (sub @ X51 @ X52) @ X54))))) | ? [X55 : term] : (((sub @ X55 @ id)) != X55) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP26) | ? [X56 : (subst > term > subst > $o),X57 : term] : (! [X58 : term,X59 : subst,X60 : subst,X61 : subst] : ((((X56 @ X61 @ X58 @ (comp @ X60 @ X59))) = $true) | (((X56 @ (comp @ X61 @ X60) @ (sub @ X58 @ X60) @ X59)) != $true)) & ! [X62 : term] : ((((X56 @ id @ X62 @ id)) != $true) | ($true = ((X56 @ id @ (sub @ X57 @ (push @ X62 @ id)) @ id)))) & (((sP21 @ X56)) = $true) & ! [X63 : subst,X64 : subst,X65 : subst,X66 : term] : (($true = ((X56 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63))) | ($true != ((X56 @ X65 @ X66 @ (comp @ X64 @ X63))))) & (((X56 @ id @ (lam @ X57) @ id)) != $true)) | ($true = sP25) | ($true = sP24) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP26) & ! [X67 : (subst > term > subst > $o),X68 : term] : (? [X69 : term,X70 : subst,X71 : subst,X72 : subst] : ((((X67 @ X72 @ X69 @ (comp @ X71 @ X70))) != $true) & (((X67 @ (comp @ X72 @ X71) @ (sub @ X69 @ X71) @ X70)) = $true)) | ? [X73 : term] : ((((X67 @ id @ X73 @ id)) = $true) & ($true != ((X67 @ id @ (sub @ X68 @ (push @ X73 @ id)) @ id)))) | ($true != ((sP21 @ X67))) | ? [X74 : subst,X75 : subst,X76 : subst,X77 : term] : (($true != ((X67 @ (comp @ X76 @ X75) @ (sub @ X77 @ X75) @ X74))) & ($true = ((X67 @ X76 @ X77 @ (comp @ X75 @ X74))))) | ($true = ((X67 @ id @ (lam @ X68) @ id)))) & ($true != sP25) & ($true != sP24))) & (! [X78 : (subst > term > subst > $o),X79 : (term > $o),X80 : term] : (? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X78 @ X83 @ X82 @ (comp @ X81 @ X84))) = $true) & (((X78 @ (comp @ X83 @ X81) @ (sub @ X82 @ X81) @ X84)) != $true)) | (((X79 @ (lam @ X80))) = $true) | ? [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (($true != ((X78 @ X87 @ X85 @ (comp @ X88 @ X86)))) & ($true = ((X78 @ (comp @ X87 @ X88) @ (sub @ X85 @ X88) @ X86)))) | ? [X89 : term] : (((X78 @ id @ X89 @ id)) != ((X79 @ X89))) | ($true = ((sP20 @ X78))) | ? [X90 : term] : (($true != ((X79 @ (sub @ X80 @ (push @ X90 @ id))))) & ($true = ((X79 @ X90))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X91 : (subst > term > subst > $o),X92 : (term > $o),X93 : term] : (! [X94 : subst,X95 : term,X96 : subst,X97 : subst] : (($true != ((X91 @ X96 @ X95 @ (comp @ X94 @ X97)))) | ($true = ((X91 @ (comp @ X96 @ X94) @ (sub @ X95 @ X94) @ X97)))) & ($true != ((X92 @ (lam @ X93)))) & ! [X98 : term,X99 : subst,X100 : subst,X101 : subst] : ((((X91 @ X100 @ X98 @ (comp @ X101 @ X99))) = $true) | ($true != ((X91 @ (comp @ X100 @ X101) @ (sub @ X98 @ X101) @ X99)))) & ! [X102 : term] : (((X92 @ X102)) = ((X91 @ id @ X102 @ id))) & ($true != ((sP20 @ X91))) & ! [X103 : term] : (($true = ((X92 @ (sub @ X93 @ (push @ X103 @ id))))) | (((X92 @ X103)) != $true)))) & ((hoasinduction_lem3aa_lthm = $true) | ? [X104 : term,X105 : (subst > term > subst > $o)] : (! [X106 : term] : (($true = ((X105 @ id @ (sub @ X104 @ (push @ X106 @ id)) @ id))) | (((X105 @ id @ X106 @ id)) != $true)) & (((X105 @ id @ (lam @ (sub @ X104 @ (push @ one @ sh))) @ id)) != $true) & ! [X107 : (subst > term > term)] : (? [X108 : term,X109 : subst,X110 : subst] : (((X107 @ (comp @ X110 @ X109) @ (sub @ X108 @ X109))) != ((sub @ (X107 @ X110 @ X108) @ X109))) | (((X105 @ id @ (lam @ (X107 @ sh @ one)) @ id)) = $true) | ? [X111 : term] : (($true = ((X105 @ id @ X111 @ id))) & ($true != ((X105 @ id @ (X107 @ id @ X111) @ id))))))) & (! [X112 : term,X113 : (subst > term > subst > $o)] : (? [X114 : term] : (($true != ((X113 @ id @ (sub @ X112 @ (push @ X114 @ id)) @ id))) & ($true = ((X113 @ id @ X114 @ id)))) | ($true = ((X113 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id))) | ? [X115 : (subst > term > term)] : (! [X116 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X116) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X116 @ X117)))) & (((X113 @ id @ (lam @ (X115 @ sh @ one)) @ id)) != $true) & ! [X119 : term] : ((((X113 @ id @ X119 @ id)) != $true) | (((X113 @ id @ (X115 @ id @ X119) @ id)) = $true)))) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) | (! [X120 : subst] : (((comp @ id @ X120)) = X120) & (? [X121 : subst] : (((comp @ id @ X121)) != X121) | ? [X122 : subst] : (((comp @ X122 @ id)) != X122)) & ! [X123 : subst] : (((comp @ X123 @ id)) = X123))) & (? [X124 : subst] : (((comp @ id @ X124)) != X124) | (! [X125 : subst] : (((comp @ id @ X125)) = X125) & ! [X126 : subst] : (((comp @ X126 @ id)) = X126)) | ? [X127 : subst] : (((comp @ X127 @ id)) != X127) | (substmonoid_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapnotvar = $true) & (id = ((d2subst @ d_id))) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) | (axvarid != $true)) & ((axvarid = $true) | ? [X129 : term] : (((sub @ X129 @ id)) != X129)) & ((hoasinduction_lem3b = $true) | ? [X130 : term] : ! [X131 : (subst > term > term)] : (((X131 @ sh @ one)) != ((sub @ X130 @ (push @ one @ sh))))) & (! [X132 : term] : ? [X133 : (subst > term > term)] : (((X133 @ sh @ one)) = ((sub @ X132 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((sP19 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP19 != $true)) & (! [X134 : term] : ? [X135 : (subst > term > term)] : ! [X136 : term,X137 : subst] : (((sub @ X134 @ (push @ X136 @ X137))) = ((X135 @ X137 @ X136))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X138 : term] : ! [X139 : (subst > term > term)] : ? [X140 : term,X141 : subst] : (((sub @ X138 @ (push @ X140 @ X141))) != ((X139 @ X141 @ X140)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axvarshift = $true) & (($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18)) & (pushprop_lem3v2_lthm = $true) & (induction2_gthm = $true) & (pushprop_gthm = $true) & ! [X142 : d_term,X143 : d_term] : ((((d2term @ X142)) != ((d2term @ X143))) | (X142 = X143)) & ((termmset_lthm = $true) | (? [X144 : term] : (((sub @ X144 @ id)) != X144) & ! [X145 : term] : (((sub @ X145 @ id)) = X145))) & (! [X146 : term] : (((sub @ X146 @ id)) = X146) | ? [X147 : term] : (((sub @ X147 @ id)) != X147) | (termmset_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & (! [X148 : subst] : (((comp @ id @ X148)) = X148) | (axidl != $true)) & ((axidl = $true) | ? [X149 : subst] : (((comp @ id @ X149)) != X149)) & ((hoasinduction = $true) | ? [X150 : term,X151 : (subst > term > subst > $o)] : (($true != ((sP16 @ X151))) & ($true != ((sP15 @ X151))) & ! [X152 : subst,X153 : term,X154 : subst,X155 : subst] : (($true = ((X151 @ X152 @ X153 @ (comp @ X155 @ X154)))) | (((X151 @ (comp @ X152 @ X155) @ (sub @ X153 @ X155) @ X154)) != $true)) & ($true != ((X151 @ id @ X150 @ id))) & ! [X156 : term] : ((((X151 @ id @ X156 @ id)) = $true) | ($true != ((var @ (sub @ X156 @ id))))) & ! [X157 : term,X158 : subst,X159 : subst,X160 : subst] : ((((X151 @ (comp @ X160 @ X158) @ (sub @ X157 @ X158) @ X159)) = $true) | (((X151 @ X160 @ X157 @ (comp @ X158 @ X159))) != $true)))) & (! [X161 : term,X162 : (subst > term > subst > $o)] : ((((sP16 @ X162)) = $true) | ($true = ((sP15 @ X162))) | ? [X163 : subst,X164 : term,X165 : subst,X166 : subst] : ((((X162 @ X163 @ X164 @ (comp @ X166 @ X165))) != $true) & ($true = ((X162 @ (comp @ X163 @ X166) @ (sub @ X164 @ X166) @ X165)))) | ($true = ((X162 @ id @ X161 @ id))) | ? [X167 : term] : (($true != ((X162 @ id @ X167 @ id))) & (((var @ (sub @ X167 @ id))) = $true)) | ? [X168 : term,X169 : subst,X170 : subst,X171 : subst] : (($true != ((X162 @ (comp @ X171 @ X169) @ (sub @ X168 @ X169) @ X170))) & ($true = ((X162 @ X171 @ X168 @ (comp @ X169 @ X170)))))) | (hoasinduction != $true)) & ((! [X172 : subst] : (((comp @ X172 @ id)) = X172) & ! [X173 : subst] : (((comp @ id @ X173)) = X173)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X174 : subst] : (((comp @ X174 @ id)) != X174) | ? [X175 : subst] : (((comp @ id @ X175)) != X175)) & (($true = sP14) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP14)) & ((pushprop_lem0_lthm = $true) | ? [X176 : (term > $o),X177 : term,X178 : subst] : ! [X179 : (term > $o)] : ? [X180 : term] : (((X176 @ (sub @ X180 @ (push @ X177 @ X178)))) != ((X179 @ X180)))) & (! [X181 : (term > $o),X182 : term,X183 : subst] : ? [X184 : (term > $o)] : ! [X185 : term] : (((X181 @ (sub @ X185 @ (push @ X182 @ X183)))) = ((X184 @ X185))) | (pushprop_lem0_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP12) & ! [X186 : term] : (((sub @ X186 @ id)) = X186) & ! [X187 : term,X188 : (subst > term > subst > $o)] : (? [X189 : (subst > term > term)] : ((((X188 @ id @ (lam @ (X189 @ sh @ one)) @ id)) != $true) & ! [X190 : term] : (($true != ((X188 @ id @ X190 @ id))) | (((X188 @ id @ (X189 @ id @ X190) @ id)) = $true)) & ! [X191 : subst,X192 : term,X193 : subst] : (((sub @ (X189 @ X193 @ X192) @ X191)) = ((X189 @ (comp @ X193 @ X191) @ (sub @ X192 @ X191))))) | ? [X194 : term] : ((((X188 @ id @ X194 @ id)) = $true) & ($true != ((X188 @ id @ (sub @ X187 @ (push @ X194 @ id)) @ id)))) | ($true = ((X188 @ id @ (lam @ (sub @ X187 @ (push @ one @ sh))) @ id)))))) & (($true = sP12) | ? [X195 : term] : (((sub @ X195 @ id)) != X195) | ? [X196 : term,X197 : (subst > term > subst > $o)] : (! [X198 : (subst > term > term)] : ((((X197 @ id @ (lam @ (X198 @ sh @ one)) @ id)) = $true) | ? [X199 : term] : (($true = ((X197 @ id @ X199 @ id))) & ($true != ((X197 @ id @ (X198 @ id @ X199) @ id)))) | ? [X200 : subst,X201 : term,X202 : subst] : (((sub @ (X198 @ X202 @ X201) @ X200)) != ((X198 @ (comp @ X202 @ X200) @ (sub @ X201 @ X200))))) & ! [X203 : term] : (($true != ((X197 @ id @ X203 @ id))) | (((X197 @ id @ (sub @ X196 @ (push @ X203 @ id)) @ id)) = $true)) & (((X197 @ id @ (lam @ (sub @ X196 @ (push @ one @ sh))) @ id)) != $true)) | (hoasinduction_lem3_lthm != $true)) & (pushprop_lem3v2 = $true) & ! [X204 : d_subst] : (d_id = X204) & (ulamvarsh = $true) & (lamnotvar = $true) & (($true = sP9) | ($true = sP10) | ? [X205 : (subst > term > subst > $o)] : ! [X206 : (term > $o)] : ? [X207 : term] : (((X205 @ id @ X207 @ id)) != ((X206 @ X207))) | ? [X208 : term] : (((sub @ X208 @ id)) != X208) | ? [X209 : (subst > term > subst > $o),X210 : term,X211 : (term > $o)] : (! [X212 : term] : (($true != ((X211 @ X212))) | ($true = ((X211 @ (sub @ X210 @ (push @ X212 @ id)))))) & ! [X213 : (subst > term > term)] : (? [X214 : term] : ((((X209 @ id @ X214 @ id)) = $true) & (((X209 @ id @ (X213 @ id @ X214) @ id)) != $true)) | ($true = ((X209 @ id @ (lam @ (X213 @ sh @ one)) @ id))) | ? [X215 : subst,X216 : subst,X217 : term] : (((sub @ (X213 @ X216 @ X217) @ X215)) != ((X213 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215))))) & ($true != ((X211 @ (lam @ X210)))) & ! [X218 : term] : (((X211 @ X218)) = ((X209 @ id @ X218 @ id)))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP9) & ($true != sP10) & ! [X219 : (subst > term > subst > $o)] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X220 @ X221)) = ((X219 @ id @ X221 @ id))) & ! [X222 : term] : (((sub @ X222 @ id)) = X222) & ! [X223 : (subst > term > subst > $o),X224 : term,X225 : (term > $o)] : (? [X226 : term] : (($true = ((X225 @ X226))) & ($true != ((X225 @ (sub @ X224 @ (push @ X226 @ id)))))) | ? [X227 : (subst > term > term)] : (! [X228 : term] : ((((X223 @ id @ X228 @ id)) != $true) | ($true = ((X223 @ id @ (X227 @ id @ X228) @ id)))) & ($true != ((X223 @ id @ (lam @ (X227 @ sh @ one)) @ id))) & ! [X229 : subst,X230 : subst,X231 : term] : (((sub @ (X227 @ X230 @ X231) @ X229)) = ((X227 @ (comp @ X230 @ X229) @ (sub @ X231 @ X229))))) | ($true = ((X225 @ (lam @ X224)))) | ? [X232 : term] : (((X223 @ id @ X232 @ id)) != ((X225 @ X232)))))) & ((sP8 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP8 != $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP7)) & (($true = sP7) | (hoasinduction_lem2v2 != $true)) & (axmap = $true) & ((induction = $true) | ? [X233 : term,X234 : (term > $o)] : (! [X235 : term] : ((((X234 @ X235)) != $true) | ($true = ((X234 @ (lam @ X235))))) & ! [X236 : term] : (($true = ((X234 @ X236))) | (((var @ X236)) != $true)) & ($true != ((X234 @ X233))) & ! [X237 : term,X238 : term] : (($true != ((X234 @ X238))) | (((X234 @ X237)) != $true) | ($true = ((X234 @ (ap @ X238 @ X237))))))) & (! [X239 : term,X240 : (term > $o)] : (? [X241 : term] : ((((X240 @ X241)) = $true) & (((X240 @ (lam @ X241))) != $true)) | ? [X242 : term] : (($true != ((X240 @ X242))) & (((var @ X242)) = $true)) | ($true = ((X240 @ X239))) | ? [X243 : term,X244 : term] : (($true = ((X240 @ X244))) & (((X240 @ X243)) = $true) & ($true != ((X240 @ (ap @ X244 @ X243)))))) | (induction != $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)))))))))))))) & (! [X245 : term,X246 : subst,X247 : (term > $o)] : ? [X248 : (term > $o)] : ! [X249 : term] : (((X248 @ X249)) = ((X247 @ (sub @ X249 @ (push @ X245 @ X246))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X250 : term,X251 : subst,X252 : (term > $o)] : ! [X253 : (term > $o)] : ? [X254 : term] : (((X253 @ X254)) != ((X252 @ (sub @ X254 @ (push @ X250 @ X251)))))) & ! [X255 : term] : ? [X256 : d_term] : (((d2term @ X256)) = X255) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X257 : (subst > term > subst > $o)] : ? [X258 : (term > $o)] : ! [X259 : term] : (((X258 @ X259)) = ((X257 @ id @ X259 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X260 : (subst > term > subst > $o)] : ! [X261 : (term > $o)] : ? [X262 : term] : (((X261 @ X262)) != ((X260 @ id @ X262 @ id)))) & (? [X263 : term] : (((sub @ X263 @ id)) != X263) | ? [X264 : (subst > term > subst > $o),X265 : term] : (! [X266 : term] : (($true != ((X264 @ id @ X266 @ id))) | (((X264 @ id @ (sub @ X265 @ (push @ X266 @ id)) @ id)) = $true)) & (((X264 @ id @ (lam @ (sub @ X265 @ (push @ one @ sh))) @ id)) != $true) & ! [X267 : (subst > term > term)] : (? [X268 : subst,X269 : subst,X270 : term] : (((sub @ (X267 @ X268 @ X270) @ X269)) != ((X267 @ (comp @ X268 @ X269) @ (sub @ X270 @ X269)))) | (((X264 @ id @ (lam @ (X267 @ sh @ one)) @ id)) = $true) | ? [X271 : term] : (($true = ((X264 @ id @ X271 @ id))) & (((X264 @ id @ (X267 @ id @ X271) @ id)) != $true)))) | ($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X272 : term] : (((sub @ X272 @ id)) = X272) & ! [X273 : (subst > term > subst > $o),X274 : term] : (? [X275 : term] : (($true = ((X273 @ id @ X275 @ id))) & (((X273 @ id @ (sub @ X274 @ (push @ X275 @ id)) @ id)) != $true)) | ($true = ((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id))) | ? [X276 : (subst > term > term)] : (! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (X276 @ X277 @ X279) @ X278)) = ((X276 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)))) & ($true != ((X273 @ id @ (lam @ (X276 @ sh @ one)) @ id))) & ! [X280 : term] : (($true != ((X273 @ id @ X280 @ id))) | ($true = ((X273 @ id @ (X276 @ id @ X280) @ id)))))) & ($true != sP6))) & (ulamvarind = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X281 : term] : ! [X282 : (subst > term > term)] : ? [X283 : subst,X284 : term] : (((X282 @ X283 @ X284)) != ((sub @ X281 @ (push @ X284 @ X283))))) & (! [X285 : term] : ? [X286 : (subst > term > term)] : ! [X287 : subst,X288 : term] : (((X286 @ X287 @ X288)) = ((sub @ X285 @ (push @ X288 @ X287)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (? [X289 : term,X290 : term,X291 : term,X292 : term] : ((((ap @ X291 @ X292)) = ((ap @ X290 @ X289))) & (X289 != X292)) | ! [X293 : term,X294 : term,X295 : term,X296 : term] : ((X294 = X295) | (((ap @ (sub @ X293 @ id) @ X294)) != ((ap @ (sub @ X296 @ id) @ X295)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X297 : term,X298 : term,X299 : term,X300 : term] : ((((ap @ X298 @ X297)) != ((ap @ X299 @ X300))) | (X297 = X300)) & ? [X301 : term,X302 : term,X303 : term,X304 : term] : ((X302 != X303) & (((ap @ (sub @ X301 @ id) @ X302)) = ((ap @ (sub @ X304 @ id) @ X303)))))) & ((termmset = $true) | ? [X305 : term] : (((sub @ X305 @ id)) != X305)) & (! [X306 : term] : (((sub @ X306 @ id)) = X306) | (termmset != $true)) & (($true = sP5) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP5)) & ((apinj1 = $true) | ? [X307 : term,X308 : term,X309 : term,X310 : term] : ((X307 != X309) & (((ap @ X309 @ X308)) = ((ap @ X307 @ X310))))) & (! [X311 : term,X312 : term,X313 : term,X314 : term] : ((X311 = X313) | (((ap @ X311 @ X314)) != ((ap @ X313 @ X312)))) | (apinj1 != $true)) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & (! [X315 : term,X316 : subst,X317 : (subst > term > term),X318 : (subst > term > term)] : ((((X317 @ X316 @ X315)) = ((X318 @ X316 @ X315))) | ? [X319 : subst,X320 : subst,X321 : term] : (((sub @ (X317 @ X319 @ X321) @ X320)) != ((X317 @ (comp @ X319 @ X320) @ (sub @ X321 @ X320)))) | ? [X322 : term,X323 : subst,X324 : subst] : (((sub @ (X318 @ X324 @ X322) @ X323)) != ((X318 @ (comp @ X324 @ X323) @ (sub @ X322 @ X323)))) | (((lam @ (X317 @ sh @ one))) != ((lam @ (X318 @ sh @ one))))) | ? [X325 : term,X326 : term] : ((((lam @ X326)) = ((lam @ X325))) & (X325 != X326)) | ? [X327 : subst,X328 : term] : (((sub @ one @ (push @ X328 @ X327))) != X328) | ? [X329 : term,X330 : subst] : (((comp @ sh @ (push @ X329 @ X330))) != X330) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (? [X331 : term,X332 : subst,X333 : (subst > term > term),X334 : (subst > term > term)] : ((((X334 @ X332 @ X331)) != ((X333 @ X332 @ X331))) & ! [X335 : subst,X336 : subst,X337 : term] : (((X333 @ (comp @ X335 @ X336) @ (sub @ X337 @ X336))) = ((sub @ (X333 @ X335 @ X337) @ X336))) & ! [X338 : term,X339 : subst,X340 : subst] : (((sub @ (X334 @ X340 @ X338) @ X339)) = ((X334 @ (comp @ X340 @ X339) @ (sub @ X338 @ X339)))) & (((lam @ (X333 @ sh @ one))) = ((lam @ (X334 @ sh @ one))))) & ! [X341 : term,X342 : term] : ((((lam @ X341)) != ((lam @ X342))) | (X341 = X342)) & ! [X343 : subst,X344 : term] : (((sub @ one @ (push @ X344 @ X343))) = X344) & ! [X345 : term,X346 : subst] : (((comp @ sh @ (push @ X345 @ X346))) = X346))) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((pushprop_lem1_lthm = $true) | (! [X347 : subst,X348 : term] : (((sub @ one @ (push @ X348 @ X347))) = X348) & ? [X349 : term,X350 : term,X351 : (term > $o),X352 : (term > $o),X353 : subst] : (($true = ((X351 @ X350))) & (((X352 @ (sub @ X350 @ (push @ X349 @ X353)))) != $true)) & ! [X354 : term,X355 : subst] : (((comp @ sh @ (push @ X354 @ X355))) = X355))) & (? [X356 : subst,X357 : term] : (((sub @ one @ (push @ X357 @ X356))) != X357) | ! [X358 : term,X359 : term,X360 : (term > $o),X361 : (term > $o),X362 : subst] : ((((X360 @ X359)) != $true) | (((X361 @ (sub @ X359 @ (push @ X358 @ X362)))) = $true)) | ? [X363 : term,X364 : subst] : (((comp @ sh @ (push @ X363 @ X364))) != X364) | (pushprop_lem1_lthm != $true)) & (hoaslamnotap_lthm = $true) & (sh = ((d2subst @ d_id))) & ((hoasinduction_lem3aa = $true) | ? [X365 : (subst > term > subst > $o),X366 : term] : (! [X367 : (subst > term > term)] : (($true = ((X365 @ id @ (lam @ (X367 @ sh @ one)) @ id))) | ? [X368 : subst,X369 : subst,X370 : term] : (((X367 @ (comp @ X368 @ X369) @ (sub @ X370 @ X369))) != ((sub @ (X367 @ X368 @ X370) @ X369))) | ? [X371 : term] : (($true != ((X365 @ id @ (X367 @ id @ X371) @ id))) & (((X365 @ id @ X371 @ id)) = $true))) & ! [X372 : term] : ((((X365 @ id @ (sub @ X366 @ (push @ X372 @ id)) @ id)) = $true) | (((X365 @ id @ X372 @ id)) != $true)) & ($true != ((X365 @ id @ (lam @ (sub @ X366 @ (push @ one @ sh))) @ id))))) & (! [X373 : (subst > term > subst > $o),X374 : term] : (? [X375 : (subst > term > term)] : (($true != ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X376 : subst,X377 : subst,X378 : term] : (((X375 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377))) = ((sub @ (X375 @ X376 @ X378) @ X377))) & ! [X379 : term] : (($true = ((X373 @ id @ (X375 @ id @ X379) @ id))) | ($true != ((X373 @ id @ X379 @ id))))) | ? [X380 : term] : (($true != ((X373 @ id @ (sub @ X374 @ (push @ X380 @ id)) @ id))) & ($true = ((X373 @ id @ X380 @ id)))) | ($true = ((X373 @ id @ (lam @ (sub @ X374 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3aa != $true)) & ((hoaslamnotap = $true) | ? [X381 : term,X382 : (subst > term > term),X383 : term] : (! [X384 : subst,X385 : subst,X386 : term] : (((X382 @ (comp @ X384 @ X385) @ (sub @ X386 @ X385))) = ((sub @ (X382 @ X384 @ X386) @ X385))) & (((lam @ (X382 @ sh @ one))) = ((ap @ (sub @ X381 @ id) @ X383))))) & (! [X387 : term,X388 : (subst > term > term),X389 : term] : (? [X390 : subst,X391 : subst,X392 : term] : (((sub @ (X388 @ X390 @ X392) @ X391)) != ((X388 @ (comp @ X390 @ X391) @ (sub @ X392 @ X391)))) | (((ap @ (sub @ X387 @ id) @ X389)) != ((lam @ (X388 @ sh @ one))))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop = $true) & (hoasinduction_lem2_gthm = $true) & (! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X396 @ id) @ X394)) != ((ap @ (sub @ X395 @ id) @ X393))) | (X393 = X394)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X397 : term,X398 : term,X399 : term,X400 : term] : ((((ap @ (sub @ X399 @ id) @ X397)) = ((ap @ (sub @ X400 @ id) @ X398))) & (X397 != X398))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X401 : term,X402 : term,X403 : term,X404 : term] : ((X402 = X403) | (((ap @ (sub @ X403 @ id) @ X404)) != ((ap @ (sub @ X402 @ id) @ X401)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X405 : term,X406 : term,X407 : term,X408 : term] : ((X406 != X407) & (((ap @ (sub @ X407 @ id) @ X408)) = ((ap @ (sub @ X406 @ id) @ X405))))) & (! [X409 : subst,X410 : term] : (((comp @ sh @ (push @ X410 @ X409))) = X409) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X411 : subst,X412 : term] : (((comp @ sh @ (push @ X412 @ X411))) != X411)) & (hoasinduction_lem3v2_gthm = $true) & (termmset_gthm = $true) & (! [X413 : (term > $o),X414 : subst,X415 : term,X416 : (term > $o)] : (? [X417 : term] : (((X413 @ (sub @ X417 @ (push @ X415 @ X414)))) != ((X416 @ X417))) | (((X413 @ X415)) != $true) | ($true = ((X416 @ one)))) | ? [X418 : subst,X419 : term] : (((sub @ one @ (push @ X419 @ X418))) != X419) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X420 : (term > $o),X421 : subst,X422 : term,X423 : (term > $o)] : (! [X424 : term] : (((X420 @ (sub @ X424 @ (push @ X422 @ X421)))) = ((X423 @ X424))) & ($true = ((X420 @ X422))) & ($true != ((X423 @ one)))) & ! [X425 : subst,X426 : term] : (((sub @ one @ (push @ X426 @ X425))) = X426))) & (pushprop_lem2v2_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3 = $true) | ? [X427 : term,X428 : (subst > term > subst > $o)] : (($true != ((sP4 @ X428))) & ! [X429 : term] : (($true = ((X428 @ id @ (sub @ X427 @ (push @ X429 @ id)) @ id))) | ($true != ((X428 @ id @ X429 @ id)))) & ! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (($true != ((X428 @ X430 @ X432 @ (comp @ X431 @ X433)))) | (((X428 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433)) = $true)) & ! [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true = ((X428 @ X436 @ X437 @ (comp @ X434 @ X435)))) | ($true != ((X428 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)))) & (((X428 @ id @ (lam @ X427) @ id)) != $true))) & (! [X438 : term,X439 : (subst > term > subst > $o)] : (($true = ((sP4 @ X439))) | ? [X440 : term] : ((((X439 @ id @ (sub @ X438 @ (push @ X440 @ id)) @ id)) != $true) & (((X439 @ id @ X440 @ id)) = $true)) | ? [X441 : subst,X442 : subst,X443 : term,X444 : subst] : (($true = ((X439 @ X441 @ X443 @ (comp @ X442 @ X444)))) & (((X439 @ (comp @ X441 @ X442) @ (sub @ X443 @ X442) @ X444)) != $true)) | ? [X445 : subst,X446 : subst,X447 : subst,X448 : term] : (($true != ((X439 @ X447 @ X448 @ (comp @ X445 @ X446)))) & (((X439 @ (comp @ X447 @ X445) @ (sub @ X448 @ X445) @ X446)) = $true)) | ($true = ((X439 @ id @ (lam @ X438) @ id)))) | (hoasinduction_lem3 != $true)) & ((laminj = $true) | ? [X449 : term,X450 : term] : ((X449 != X450) & (((lam @ X449)) = ((lam @ X450))))) & (! [X451 : term,X452 : term] : ((X451 = X452) | (((lam @ X452)) != ((lam @ X451)))) | (laminj != $true)) & (axapp = $true) & (hoasapinj1_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotvar = $true) & (apnotvar = $true) & (pushprop_lthm = $true) & ((shinj = $true) | ? [X453 : term,X454 : term] : ((X453 != X454) & (((sub @ X454 @ sh)) = ((sub @ X453 @ sh))))) & (! [X455 : term,X456 : term] : ((X455 = X456) | (((sub @ X456 @ sh)) != ((sub @ X455 @ sh)))) | (shinj != $true)) & (pushprop_lem1_gthm = $true) & (! [X457 : term,X458 : (subst > term > subst > $o)] : (? [X459 : term] : ((((X458 @ id @ X459 @ id)) = $true) & (((X458 @ id @ (sub @ X457 @ (push @ X459 @ id)) @ id)) != $true)) | ($true = ((X458 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id))) | ? [X460 : (subst > term > term),X461 : term] : (($true != ((X458 @ id @ (lam @ (X460 @ sh @ one)) @ id))) & ! [X462 : term,X463 : subst,X464 : subst] : (((sub @ X461 @ (push @ (sub @ X462 @ X464) @ (comp @ X463 @ X464)))) = ((X460 @ (comp @ X463 @ X464) @ (sub @ X462 @ X464)))) & ! [X465 : term] : ((((X458 @ id @ X465 @ id)) != $true) | (((X458 @ id @ (X460 @ id @ X465) @ id)) = $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (sub @ X461 @ (push @ X467 @ X466)) @ X468)) = ((sub @ (X460 @ X466 @ X467) @ X468))))) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X469 : term,X470 : (subst > term > subst > $o)] : (! [X471 : term] : (($true != ((X470 @ id @ X471 @ id))) | ($true = ((X470 @ id @ (sub @ X469 @ (push @ X471 @ id)) @ id)))) & (((X470 @ id @ (lam @ (sub @ X469 @ (push @ one @ sh))) @ id)) != $true) & ! [X472 : (subst > term > term),X473 : term] : (($true = ((X470 @ id @ (lam @ (X472 @ sh @ one)) @ id))) | ? [X474 : term,X475 : subst,X476 : subst] : (((X472 @ (comp @ X475 @ X476) @ (sub @ X474 @ X476))) != ((sub @ X473 @ (push @ (sub @ X474 @ X476) @ (comp @ X475 @ X476))))) | ? [X477 : term] : (($true = ((X470 @ id @ X477 @ id))) & ($true != ((X470 @ id @ (X472 @ id @ X477) @ id)))) | ? [X478 : subst,X479 : term,X480 : subst] : (((sub @ (X472 @ X478 @ X479) @ X480)) != ((sub @ (sub @ X473 @ (push @ X479 @ X478)) @ X480)))))) & ((hoasinduction_lem3a = $true) | ? [X481 : term,X482 : (subst > term > subst > $o)] : (! [X483 : term] : (($true != ((X482 @ id @ X483 @ id))) | (((X482 @ id @ (sub @ X481 @ (push @ X483 @ id)) @ id)) = $true)) & ($true != ((X482 @ id @ (lam @ X481) @ id))) & ! [X484 : (subst > term > term)] : (? [X485 : subst,X486 : subst,X487 : term] : (((sub @ (X484 @ X485 @ X487) @ X486)) != ((X484 @ (comp @ X485 @ X486) @ (sub @ X487 @ X486)))) | ? [X488 : term] : ((((X482 @ id @ X488 @ id)) = $true) & (((X482 @ id @ (X484 @ id @ X488) @ id)) != $true)) | (((X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true)))) & (! [X489 : term,X490 : (subst > term > subst > $o)] : (? [X491 : term] : (($true = ((X490 @ id @ X491 @ id))) & (((X490 @ id @ (sub @ X489 @ (push @ X491 @ id)) @ id)) != $true)) | ($true = ((X490 @ id @ (lam @ X489) @ id))) | ? [X492 : (subst > term > term)] : (! [X493 : subst,X494 : subst,X495 : term] : (((X492 @ (comp @ X493 @ X494) @ (sub @ X495 @ X494))) = ((sub @ (X492 @ X493 @ X495) @ X494))) & ! [X496 : term] : (($true != ((X490 @ id @ X496 @ id))) | (((X490 @ id @ (X492 @ id @ X496) @ id)) = $true)) & (((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id)) != $true))) | (hoasinduction_lem3a != $true)) & (! [X497 : (subst > term > subst > $o),X498 : term,X499 : (term > $o)] : (? [X500 : term] : (($true != ((X499 @ (sub @ X498 @ (push @ X500 @ id))))) & ($true = ((X499 @ X500)))) | ? [X501 : term] : (((X499 @ X501)) != ((X497 @ id @ X501 @ id))) | ($true = ((X499 @ (lam @ X498)))) | ? [X502 : (subst > term > term)] : (! [X503 : term] : (($true = ((X497 @ id @ (X502 @ id @ X503) @ id))) | ($true != ((X497 @ id @ X503 @ id)))) & ! [X504 : subst,X505 : term,X506 : subst] : (((sub @ (X502 @ X506 @ X505) @ X504)) = ((X502 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) & ($true != ((X497 @ id @ (lam @ (X502 @ sh @ one)) @ id))))) | ? [X507 : term] : ! [X508 : (subst > term > term)] : ? [X509 : subst,X510 : term] : (((X508 @ X509 @ X510)) != ((sub @ X507 @ (push @ X510 @ X509)))) | ? [X511 : term] : (((sub @ X511 @ id)) != X511) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (? [X512 : (subst > term > subst > $o),X513 : term,X514 : (term > $o)] : (! [X515 : term] : (($true = ((X514 @ (sub @ X513 @ (push @ X515 @ id))))) | (((X514 @ X515)) != $true)) & ! [X516 : term] : (((X512 @ id @ X516 @ id)) = ((X514 @ X516))) & (((X514 @ (lam @ X513))) != $true) & ! [X517 : (subst > term > term)] : (? [X518 : term] : (($true != ((X512 @ id @ (X517 @ id @ X518) @ id))) & (((X512 @ id @ X518 @ id)) = $true)) | ? [X519 : subst,X520 : term,X521 : subst] : (((sub @ (X517 @ X521 @ X520) @ X519)) != ((X517 @ (comp @ X521 @ X519) @ (sub @ X520 @ X519)))) | ($true = ((X512 @ id @ (lam @ (X517 @ sh @ one)) @ id))))) & ! [X522 : term] : ? [X523 : (subst > term > term)] : ! [X524 : subst,X525 : term] : (((X523 @ X524 @ X525)) = ((sub @ X522 @ (push @ X525 @ X524)))) & ! [X526 : term] : (((sub @ X526 @ id)) = X526))) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X527 : (term > $o),X528 : term,X529 : (subst > term > subst > $o)] : (($true = ((X527 @ (lam @ X528)))) | ? [X530 : term] : ((((X527 @ X530)) = $true) & (((X527 @ (sub @ X528 @ (push @ X530 @ id)))) != $true)) | ? [X531 : (subst > term > term)] : (! [X532 : term,X533 : subst,X534 : subst] : (((sub @ (X531 @ X533 @ X532) @ X534)) = ((X531 @ (comp @ X533 @ X534) @ (sub @ X532 @ X534)))) & ! [X535 : term] : ((((X529 @ id @ X535 @ id)) != $true) | ($true = ((X529 @ id @ (X531 @ id @ X535) @ id)))) & (((X529 @ id @ (lam @ (X531 @ sh @ one)) @ id)) != $true)) | ? [X536 : term] : (((X527 @ X536)) != ((X529 @ id @ X536 @ id)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ? [X537 : (term > $o),X538 : term,X539 : (subst > term > subst > $o)] : (($true != ((X537 @ (lam @ X538)))) & ! [X540 : term] : ((((X537 @ X540)) != $true) | ($true = ((X537 @ (sub @ X538 @ (push @ X540 @ id)))))) & ! [X541 : (subst > term > term)] : (? [X542 : term,X543 : subst,X544 : subst] : (((X541 @ (comp @ X543 @ X544) @ (sub @ X542 @ X544))) != ((sub @ (X541 @ X543 @ X542) @ X544))) | ? [X545 : term] : ((((X539 @ id @ X545 @ id)) = $true) & (((X539 @ id @ (X541 @ id @ X545) @ id)) != $true)) | (((X539 @ id @ (lam @ (X541 @ sh @ one)) @ id)) = $true)) & ! [X546 : term] : (((X537 @ X546)) = ((X539 @ id @ X546 @ id))))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & (! [X547 : (term > $o),X548 : term,X549 : subst,X550 : (term > $o),X551 : term] : (($true != ((X550 @ X551))) | ($true = ((X547 @ (sub @ X551 @ (push @ X548 @ X549)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X552 : (term > $o),X553 : term,X554 : subst,X555 : (term > $o),X556 : term] : (($true = ((X555 @ X556))) & ($true != ((X552 @ (sub @ X556 @ (push @ X553 @ X554))))))) & ! [X557 : d_term] : (d_one = X557) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm_3 = $true) | (! [X558 : (term > $o),X559 : (subst > term > subst > $o),X560 : term] : (? [X561 : term] : (((X558 @ X561)) != ((X559 @ id @ X561 @ id))) | ? [X562 : term] : (($true != ((X558 @ (sub @ X560 @ (push @ X562 @ id))))) & ($true = ((X558 @ X562)))) | ? [X563 : (subst > term > term)] : (! [X564 : subst,X565 : subst,X566 : term] : (((X563 @ (comp @ X564 @ X565) @ (sub @ X566 @ X565))) = ((sub @ (X563 @ X564 @ X566) @ X565))) & ! [X567 : term] : ((((X559 @ id @ (X563 @ id @ X567) @ id)) = $true) | (((X559 @ id @ X567 @ id)) != $true)) & ($true != ((X559 @ id @ (lam @ (X563 @ sh @ one)) @ id)))) | (((X558 @ (lam @ X560))) = $true)) & ($true != sP2) & ($true != sP3) & ! [X568 : term] : (((sub @ X568 @ id)) = X568) & ! [X569 : (subst > term > subst > $o)] : ? [X570 : (term > $o)] : ! [X571 : term] : (((X570 @ X571)) = ((X569 @ id @ X571 @ id))))) & (? [X572 : (term > $o),X573 : (subst > term > subst > $o),X574 : term] : (! [X575 : term] : (((X572 @ X575)) = ((X573 @ id @ X575 @ id))) & ! [X576 : term] : (($true = ((X572 @ (sub @ X574 @ (push @ X576 @ id))))) | (((X572 @ X576)) != $true)) & ! [X577 : (subst > term > term)] : (? [X578 : subst,X579 : subst,X580 : term] : (((sub @ (X577 @ X578 @ X580) @ X579)) != ((X577 @ (comp @ X578 @ X579) @ (sub @ X580 @ X579)))) | ? [X581 : term] : ((((X573 @ id @ (X577 @ id @ X581) @ id)) != $true) & ($true = ((X573 @ id @ X581 @ id)))) | ($true = ((X573 @ id @ (lam @ (X577 @ sh @ one)) @ id)))) & ($true != ((X572 @ (lam @ X574))))) | ($true = sP2) | ($true = sP3) | ? [X582 : term] : (((sub @ X582 @ id)) != X582) | ? [X583 : (subst > term > subst > $o)] : ! [X584 : (term > $o)] : ? [X585 : term] : (((X583 @ id @ X585 @ id)) != ((X584 @ X585))) | (hoasinduction_lthm_3 != $true)) & ((apinj2 = $true) | ? [X586 : term,X587 : term,X588 : term,X589 : term] : ((X586 != X587) & (((ap @ X588 @ X586)) = ((ap @ X589 @ X587))))) & (! [X590 : term,X591 : term,X592 : term,X593 : term] : ((X590 = X591) | (((ap @ X592 @ X590)) != ((ap @ X593 @ X591)))) | (apinj2 != $true)) & ! [X594 : subst] : ? [X595 : d_subst] : (((d2subst @ X595)) = X594) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X596 : term] : ! [X597 : (subst > term > term)] : (((X597 @ sh @ one)) != ((sub @ X596 @ (push @ one @ sh))))) & (! [X598 : term] : ? [X599 : (subst > term > term)] : (((X599 @ sh @ one)) = ((sub @ X598 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (lamnotap != $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X600 : (subst > term > term),X601 : (subst > term > term),X602 : subst,X603 : term] : ((((X600 @ X602 @ X603)) = ((X601 @ X602 @ X603))) | (((lam @ (X600 @ sh @ one))) != ((lam @ (X601 @ sh @ one)))) | ? [X604 : subst,X605 : subst,X606 : term] : (((X601 @ (comp @ X605 @ X604) @ (sub @ X606 @ X604))) != ((sub @ (X601 @ X605 @ X606) @ X604))) | ? [X607 : subst,X608 : term,X609 : subst] : (((sub @ (X600 @ X609 @ X608) @ X607)) != ((X600 @ (comp @ X609 @ X607) @ (sub @ X608 @ X607))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X610 : (subst > term > term),X611 : (subst > term > term),X612 : subst,X613 : term] : ((((X611 @ X612 @ X613)) != ((X610 @ X612 @ X613))) & (((lam @ (X610 @ sh @ one))) = ((lam @ (X611 @ sh @ one)))) & ! [X614 : subst,X615 : subst,X616 : term] : (((sub @ (X611 @ X615 @ X616) @ X614)) = ((X611 @ (comp @ X615 @ X614) @ (sub @ X616 @ X614)))) & ! [X617 : subst,X618 : term,X619 : subst] : (((sub @ (X610 @ X619 @ X618) @ X617)) = ((X610 @ (comp @ X619 @ X617) @ (sub @ X618 @ X617)))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((axidr = $true) | ? [X620 : subst] : (((comp @ X620 @ id)) != X620)) & (! [X621 : subst] : (((comp @ X621 @ id)) = X621) | (axidr != $true)) & (hoasinduction_lem3_gthm = $true) & (! [X622 : (subst > term > subst > $o),X623 : term] : (? [X624 : term,X625 : term] : (($true != ((X622 @ id @ (ap @ (sub @ X624 @ id) @ X625) @ id))) & ($true = ((X622 @ id @ X624 @ id))) & ($true = ((X622 @ id @ X625 @ id)))) | ? [X626 : (subst > term > term)] : ((((X622 @ id @ (lam @ (X626 @ sh @ one)) @ id)) != $true) & ! [X627 : term] : (($true != ((X622 @ id @ X627 @ id))) | ($true = ((X622 @ id @ (X626 @ id @ X627) @ id)))) & ! [X628 : subst,X629 : term,X630 : subst] : (((X626 @ (comp @ X630 @ X628) @ (sub @ X629 @ X628))) = ((sub @ (X626 @ X630 @ X629) @ X628)))) | (((X622 @ id @ X623 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X631 : (subst > term > subst > $o),X632 : term] : (! [X633 : term,X634 : term] : (($true = ((X631 @ id @ (ap @ (sub @ X633 @ id) @ X634) @ id))) | ($true != ((X631 @ id @ X633 @ id))) | ($true != ((X631 @ id @ X634 @ id)))) & ! [X635 : (subst > term > term)] : (($true = ((X631 @ id @ (lam @ (X635 @ sh @ one)) @ id))) | ? [X636 : term] : (($true = ((X631 @ id @ X636 @ id))) & ($true != ((X631 @ id @ (X635 @ id @ X636) @ id)))) | ? [X637 : subst,X638 : term,X639 : subst] : (((X635 @ (comp @ X639 @ X637) @ (sub @ X638 @ X637))) != ((sub @ (X635 @ X639 @ X638) @ X637)))) & ($true != ((X631 @ id @ X632 @ id))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X640 : (subst > term > subst > $o)] : ? [X641 : (term > $o)] : ! [X642 : term] : (((X641 @ X642)) = ((X640 @ id @ X642 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X643 : (subst > term > subst > $o)] : ! [X644 : (term > $o)] : ? [X645 : term] : (((X643 @ id @ X645 @ id)) != ((X644 @ X645)))) & (axassoc = $true) & ((axscons = $true) | ? [X646 : subst] : (((push @ (sub @ one @ X646) @ (comp @ sh @ X646))) != X646)) & (! [X647 : subst] : (((push @ (sub @ one @ X647) @ (comp @ sh @ X647))) = X647) | (axscons != $true)) & (hoasinduction_lem2_lthm = $true) & ((axvarcons = $true) | ? [X648 : subst,X649 : term] : (((sub @ one @ (push @ X649 @ X648))) != X649)) & (! [X650 : subst,X651 : term] : (((sub @ one @ (push @ X651 @ X650))) = X651) | (axvarcons != $true)) & ! [X652 : d_subst,X653 : d_subst] : ((X652 = X653) | (((d2subst @ X652)) != ((d2subst @ X653))))), 0.43/0.52 inference(rectify,[],[f133])). 0.43/0.52 thf(f135,plain,( 0.43/0.52 (axabs = $true) & (hoaslamnotvar_gthm = $true) & ((pushprop_lem1v2 = $true) | (($true != ((sK242 @ one))) & ($true = ((sK245 @ sK244))) & ! [X4 : term] : (((sK245 @ (sub @ X4 @ (push @ sK244 @ sK243)))) = ((sK242 @ X4))))) & (! [X5 : (term > $o),X6 : subst,X7 : term,X8 : (term > $o)] : ((((X5 @ one)) = $true) | ($true != ((X8 @ X7))) | (((X8 @ (sub @ (sK246 @ X8 @ X7 @ X6 @ X5) @ (push @ X7 @ X6)))) != ((X5 @ (sK246 @ X8 @ X7 @ X6 @ X5))))) | (pushprop_lem1v2 != $true)) & ((hoasapinj1_lthm = $true) | (((sK247 != sK248) & (((ap @ (sub @ sK248 @ id) @ sK250)) = ((ap @ (sub @ sK247 @ id) @ sK249)))) & ! [X14 : term,X15 : term,X16 : term,X17 : term] : ((((ap @ X15 @ X17)) != ((ap @ X16 @ X14))) | (X15 = X16)) & ! [X18 : term] : (((sub @ X18 @ id)) = X18))) & (! [X19 : term,X20 : term,X21 : term,X22 : term] : ((X19 = X20) | (((ap @ (sub @ X19 @ id) @ X21)) != ((ap @ (sub @ X20 @ id) @ X22)))) | ((((ap @ sK253 @ sK251)) = ((ap @ sK252 @ sK254))) & (sK252 != sK253)) | (((sub @ sK255 @ id)) != sK255) | (hoasapinj1_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ((! [X31 : term] : (((sK258 @ X31)) = ((sK256 @ id @ X31 @ id))) & ! [X32 : subst,X33 : term,X34 : subst,X35 : subst] : (($true = ((sK256 @ (comp @ X35 @ X32) @ (sub @ X33 @ X32) @ X34))) | ($true != ((sK256 @ X35 @ X33 @ (comp @ X32 @ X34))))) & (((sP27 @ sK256)) != $true) & (((sK258 @ (lam @ sK257))) != $true) & ! [X36 : term] : ((((sK258 @ (sub @ sK257 @ (push @ X36 @ id)))) = $true) | ($true != ((sK258 @ X36)))) & ! [X37 : term,X38 : subst,X39 : subst,X40 : subst] : (($true = ((sK256 @ X39 @ X37 @ (comp @ X38 @ X40)))) | (((sK256 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38) @ X40)) != $true))) & ! [X41 : term] : (((sub @ X41 @ id)) = X41))) & (! [X42 : (subst > term > subst > $o),X43 : term,X44 : (term > $o)] : ((((X42 @ id @ (sK259 @ X44 @ X42) @ id)) != ((X44 @ (sK259 @ X44 @ X42)))) | (($true != ((X42 @ (comp @ (sK263 @ X42) @ (sK260 @ X42)) @ (sub @ (sK261 @ X42) @ (sK260 @ X42)) @ (sK262 @ X42)))) & (((X42 @ (sK263 @ X42) @ (sK261 @ X42) @ (comp @ (sK260 @ X42) @ (sK262 @ X42)))) = $true)) | (((sP27 @ X42)) = $true) | (((X44 @ (lam @ X43))) = $true) | (($true != ((X44 @ (sub @ X43 @ (push @ (sK264 @ X44 @ X43) @ id))))) & (((X44 @ (sK264 @ X44 @ X43))) = $true)) | ((((X42 @ (sK267 @ X42) @ (sK265 @ X42) @ (comp @ (sK266 @ X42) @ (sK268 @ X42)))) != $true) & (((X42 @ (comp @ (sK267 @ X42) @ (sK266 @ X42)) @ (sub @ (sK265 @ X42) @ (sK266 @ X42)) @ (sK268 @ X42))) = $true))) | (sK269 != ((sub @ sK269 @ id))) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP26) | (! [X58 : term,X59 : subst,X60 : subst,X61 : subst] : (($true = ((sK270 @ X61 @ X58 @ (comp @ X60 @ X59)))) | ($true != ((sK270 @ (comp @ X61 @ X60) @ (sub @ X58 @ X60) @ X59)))) & ! [X62 : term] : (($true != ((sK270 @ id @ X62 @ id))) | ($true = ((sK270 @ id @ (sub @ sK271 @ (push @ X62 @ id)) @ id)))) & (((sP21 @ sK270)) = $true) & ! [X63 : subst,X64 : subst,X65 : subst,X66 : term] : (($true = ((sK270 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63))) | ($true != ((sK270 @ X65 @ X66 @ (comp @ X64 @ X63))))) & (((sK270 @ id @ (lam @ sK271) @ id)) != $true)) | ($true = sP25) | ($true = sP24) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP26) & ! [X67 : (subst > term > subst > $o),X68 : term] : ((($true != ((X67 @ (sK275 @ X67) @ (sK272 @ X67) @ (comp @ (sK274 @ X67) @ (sK273 @ X67))))) & ($true = ((X67 @ (comp @ (sK275 @ X67) @ (sK274 @ X67)) @ (sub @ (sK272 @ X67) @ (sK274 @ X67)) @ (sK273 @ X67))))) | (($true = ((X67 @ id @ (sK276 @ X68 @ X67) @ id))) & ($true != ((X67 @ id @ (sub @ X68 @ (push @ (sK276 @ X68 @ X67) @ id)) @ id)))) | ($true != ((sP21 @ X67))) | ((((X67 @ (comp @ (sK279 @ X67) @ (sK278 @ X67)) @ (sub @ (sK280 @ X67) @ (sK278 @ X67)) @ (sK277 @ X67))) != $true) & ($true = ((X67 @ (sK279 @ X67) @ (sK280 @ X67) @ (comp @ (sK278 @ X67) @ (sK277 @ X67)))))) | ($true = ((X67 @ id @ (lam @ X68) @ id)))) & ($true != sP25) & ($true != sP24))) & (! [X78 : (subst > term > subst > $o),X79 : (term > $o),X80 : term] : (((((X78 @ (sK283 @ X78) @ (sK282 @ X78) @ (comp @ (sK281 @ X78) @ (sK284 @ X78)))) = $true) & (((X78 @ (comp @ (sK283 @ X78) @ (sK281 @ X78)) @ (sub @ (sK282 @ X78) @ (sK281 @ X78)) @ (sK284 @ X78))) != $true)) | (((X79 @ (lam @ X80))) = $true) | ((((X78 @ (sK287 @ X78) @ (sK285 @ X78) @ (comp @ (sK288 @ X78) @ (sK286 @ X78)))) != $true) & (((X78 @ (comp @ (sK287 @ X78) @ (sK288 @ X78)) @ (sub @ (sK285 @ X78) @ (sK288 @ X78)) @ (sK286 @ X78))) = $true)) | (((X78 @ id @ (sK289 @ X79 @ X78) @ id)) != ((X79 @ (sK289 @ X79 @ X78)))) | ($true = ((sP20 @ X78))) | (($true != ((X79 @ (sub @ X80 @ (push @ (sK290 @ X80 @ X79) @ id))))) & (((X79 @ (sK290 @ X80 @ X79))) = $true))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (! [X94 : subst,X95 : term,X96 : subst,X97 : subst] : ((((sK291 @ X96 @ X95 @ (comp @ X94 @ X97))) != $true) | (((sK291 @ (comp @ X96 @ X94) @ (sub @ X95 @ X94) @ X97)) = $true)) & ($true != ((sK292 @ (lam @ sK293)))) & ! [X98 : term,X99 : subst,X100 : subst,X101 : subst] : (($true = ((sK291 @ X100 @ X98 @ (comp @ X101 @ X99)))) | ($true != ((sK291 @ (comp @ X100 @ X101) @ (sub @ X98 @ X101) @ X99)))) & ! [X102 : term] : (((sK291 @ id @ X102 @ id)) = ((sK292 @ X102))) & ($true != ((sP20 @ sK291))) & ! [X103 : term] : (($true = ((sK292 @ (sub @ sK293 @ (push @ X103 @ id))))) | ($true != ((sK292 @ X103)))))) & ((hoasinduction_lem3aa_lthm = $true) | (! [X106 : term] : (($true = ((sK295 @ id @ (sub @ sK294 @ (push @ X106 @ id)) @ id))) | ($true != ((sK295 @ id @ X106 @ id)))) & ($true != ((sK295 @ id @ (lam @ (sub @ sK294 @ (push @ one @ sh))) @ id))) & ! [X107 : (subst > term > term)] : ((((X107 @ (comp @ (sK298 @ X107) @ (sK297 @ X107)) @ (sub @ (sK296 @ X107) @ (sK297 @ X107)))) != ((sub @ (X107 @ (sK298 @ X107) @ (sK296 @ X107)) @ (sK297 @ X107)))) | ($true = ((sK295 @ id @ (lam @ (X107 @ sh @ one)) @ id))) | (($true = ((sK295 @ id @ (sK299 @ X107) @ id))) & ($true != ((sK295 @ id @ (X107 @ id @ (sK299 @ X107)) @ id))))))) & (! [X112 : term,X113 : (subst > term > subst > $o)] : (((((X113 @ id @ (sub @ X112 @ (push @ (sK300 @ X113 @ X112) @ id)) @ id)) != $true) & (((X113 @ id @ (sK300 @ X113 @ X112) @ id)) = $true)) | ($true = ((X113 @ id @ (lam @ (sub @ X112 @ (push @ one @ sh))) @ id))) | (! [X116 : term,X117 : subst,X118 : subst] : (((sK301 @ X113 @ (comp @ X118 @ X117) @ (sub @ X116 @ X117))) = ((sub @ (sK301 @ X113 @ X118 @ X116) @ X117))) & ($true != ((X113 @ id @ (lam @ (sK301 @ X113 @ sh @ one)) @ id))) & ! [X119 : term] : ((((X113 @ id @ X119 @ id)) != $true) | ($true = ((X113 @ id @ (sK301 @ X113 @ id @ X119) @ id)))))) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem1 = $true) & ((substmonoid_lthm = $true) | (! [X120 : subst] : (((comp @ id @ X120)) = X120) & ((sK302 != ((comp @ id @ sK302))) | (sK303 != ((comp @ sK303 @ id)))) & ! [X123 : subst] : (((comp @ X123 @ id)) = X123))) & ((sK304 != ((comp @ id @ sK304))) | (! [X125 : subst] : (((comp @ id @ X125)) = X125) & ! [X126 : subst] : (((comp @ X126 @ id)) = X126)) | (((comp @ sK305 @ id)) != sK305) | (substmonoid_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapnotvar = $true) & (id = ((d2subst @ d_id))) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) | (axvarid != $true)) & ((axvarid = $true) | (sK306 != ((sub @ sK306 @ id)))) & ((hoasinduction_lem3b = $true) | ! [X131 : (subst > term > term)] : (((X131 @ sh @ one)) != ((sub @ sK307 @ (push @ one @ sh))))) & (! [X132 : term] : (((sK308 @ X132 @ sh @ one)) = ((sub @ X132 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((sP19 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP19 != $true)) & (! [X134 : term] : ! [X136 : term,X137 : subst] : (((sub @ X134 @ (push @ X136 @ X137))) = ((sK309 @ X134 @ X137 @ X136))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X139 : (subst > term > term)] : (((sub @ sK310 @ (push @ (sK311 @ X139) @ (sK312 @ X139)))) != ((X139 @ (sK312 @ X139) @ (sK311 @ X139))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axvarshift = $true) & (($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18)) & (pushprop_lem3v2_lthm = $true) & (induction2_gthm = $true) & (pushprop_gthm = $true) & ! [X142 : d_term,X143 : d_term] : ((((d2term @ X142)) != ((d2term @ X143))) | (X142 = X143)) & ((termmset_lthm = $true) | ((((sub @ sK313 @ id)) != sK313) & ! [X145 : term] : (((sub @ X145 @ id)) = X145))) & (! [X146 : term] : (((sub @ X146 @ id)) = X146) | (((sub @ sK314 @ id)) != sK314) | (termmset_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & (! [X148 : subst] : (((comp @ id @ X148)) = X148) | (axidl != $true)) & ((axidl = $true) | (sK315 != ((comp @ id @ sK315)))) & ((hoasinduction = $true) | ((((sP16 @ sK317)) != $true) & (((sP15 @ sK317)) != $true) & ! [X152 : subst,X153 : term,X154 : subst,X155 : subst] : ((((sK317 @ X152 @ X153 @ (comp @ X155 @ X154))) = $true) | ($true != ((sK317 @ (comp @ X152 @ X155) @ (sub @ X153 @ X155) @ X154)))) & ($true != ((sK317 @ id @ sK316 @ id))) & ! [X156 : term] : ((((sK317 @ id @ X156 @ id)) = $true) | ($true != ((var @ (sub @ X156 @ id))))) & ! [X157 : term,X158 : subst,X159 : subst,X160 : subst] : (($true = ((sK317 @ (comp @ X160 @ X158) @ (sub @ X157 @ X158) @ X159))) | ($true != ((sK317 @ X160 @ X157 @ (comp @ X158 @ X159))))))) & (! [X161 : term,X162 : (subst > term > subst > $o)] : ((((sP16 @ X162)) = $true) | ($true = ((sP15 @ X162))) | (($true != ((X162 @ (sK318 @ X162) @ (sK319 @ X162) @ (comp @ (sK321 @ X162) @ (sK320 @ X162))))) & (((X162 @ (comp @ (sK318 @ X162) @ (sK321 @ X162)) @ (sub @ (sK319 @ X162) @ (sK321 @ X162)) @ (sK320 @ X162))) = $true)) | ($true = ((X162 @ id @ X161 @ id))) | (($true != ((X162 @ id @ (sK322 @ X162) @ id))) & ($true = ((var @ (sub @ (sK322 @ X162) @ id))))) | (($true != ((X162 @ (comp @ (sK326 @ X162) @ (sK324 @ X162)) @ (sub @ (sK323 @ X162) @ (sK324 @ X162)) @ (sK325 @ X162)))) & ($true = ((X162 @ (sK326 @ X162) @ (sK323 @ X162) @ (comp @ (sK324 @ X162) @ (sK325 @ X162))))))) | (hoasinduction != $true)) & ((! [X172 : subst] : (((comp @ X172 @ id)) = X172) & ! [X173 : subst] : (((comp @ id @ X173)) = X173)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ sK327 @ id)) != sK327) | (((comp @ id @ sK328)) != sK328)) & (($true = sP14) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP14)) & ((pushprop_lem0_lthm = $true) | ! [X179 : (term > $o)] : (((sK329 @ (sub @ (sK332 @ X179) @ (push @ sK330 @ sK331)))) != ((X179 @ (sK332 @ X179))))) & (! [X181 : (term > $o),X182 : term,X183 : subst] : ! [X185 : term] : (((X181 @ (sub @ X185 @ (push @ X182 @ X183)))) = ((sK333 @ X183 @ X182 @ X181 @ X185))) | (pushprop_lem0_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP12) & ! [X186 : term] : (((sub @ X186 @ id)) = X186) & ! [X187 : term,X188 : (subst > term > subst > $o)] : (((((X188 @ id @ (lam @ (sK334 @ X188 @ sh @ one)) @ id)) != $true) & ! [X190 : term] : (($true != ((X188 @ id @ X190 @ id))) | (((X188 @ id @ (sK334 @ X188 @ id @ X190) @ id)) = $true)) & ! [X191 : subst,X192 : term,X193 : subst] : (((sK334 @ X188 @ (comp @ X193 @ X191) @ (sub @ X192 @ X191))) = ((sub @ (sK334 @ X188 @ X193 @ X192) @ X191)))) | (($true = ((X188 @ id @ (sK335 @ X188 @ X187) @ id))) & (((X188 @ id @ (sub @ X187 @ (push @ (sK335 @ X188 @ X187) @ id)) @ id)) != $true)) | ($true = ((X188 @ id @ (lam @ (sub @ X187 @ (push @ one @ sh))) @ id)))))) & (($true = sP12) | (sK336 != ((sub @ sK336 @ id))) | (! [X198 : (subst > term > term)] : ((((sK338 @ id @ (lam @ (X198 @ sh @ one)) @ id)) = $true) | (($true = ((sK338 @ id @ (sK339 @ X198) @ id))) & ($true != ((sK338 @ id @ (X198 @ id @ (sK339 @ X198)) @ id)))) | (((X198 @ (comp @ (sK342 @ X198) @ (sK340 @ X198)) @ (sub @ (sK341 @ X198) @ (sK340 @ X198)))) != ((sub @ (X198 @ (sK342 @ X198) @ (sK341 @ X198)) @ (sK340 @ X198))))) & ! [X203 : term] : (($true != ((sK338 @ id @ X203 @ id))) | (((sK338 @ id @ (sub @ sK337 @ (push @ X203 @ id)) @ id)) = $true)) & ($true != ((sK338 @ id @ (lam @ (sub @ sK337 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & (pushprop_lem3v2 = $true) & ! [X204 : d_subst] : (d_id = X204) & (ulamvarsh = $true) & (lamnotvar = $true) & (($true = sP9) | ($true = sP10) | ! [X206 : (term > $o)] : (((X206 @ (sK344 @ X206))) != ((sK343 @ id @ (sK344 @ X206) @ id))) | (sK345 != ((sub @ sK345 @ id))) | (! [X212 : term] : (($true != ((sK348 @ X212))) | (((sK348 @ (sub @ sK347 @ (push @ X212 @ id)))) = $true)) & ! [X213 : (subst > term > term)] : (((((sK346 @ id @ (sK349 @ X213) @ id)) = $true) & ($true != ((sK346 @ id @ (X213 @ id @ (sK349 @ X213)) @ id)))) | ($true = ((sK346 @ id @ (lam @ (X213 @ sh @ one)) @ id))) | (((X213 @ (comp @ (sK351 @ X213) @ (sK350 @ X213)) @ (sub @ (sK352 @ X213) @ (sK350 @ X213)))) != ((sub @ (X213 @ (sK351 @ X213) @ (sK352 @ X213)) @ (sK350 @ X213))))) & (((sK348 @ (lam @ sK347))) != $true) & ! [X218 : term] : (((sK348 @ X218)) = ((sK346 @ id @ X218 @ id)))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP9) & ($true != sP10) & ! [X219 : (subst > term > subst > $o)] : ! [X221 : term] : (((sK353 @ X219 @ X221)) = ((X219 @ id @ X221 @ id))) & ! [X222 : term] : (((sub @ X222 @ id)) = X222) & ! [X223 : (subst > term > subst > $o),X224 : term,X225 : (term > $o)] : (((((X225 @ (sK354 @ X225 @ X224))) = $true) & (((X225 @ (sub @ X224 @ (push @ (sK354 @ X225 @ X224) @ id)))) != $true)) | (! [X228 : term] : ((((X223 @ id @ X228 @ id)) != $true) | (((X223 @ id @ (sK355 @ X223 @ id @ X228) @ id)) = $true)) & ($true != ((X223 @ id @ (lam @ (sK355 @ X223 @ sh @ one)) @ id))) & ! [X229 : subst,X230 : subst,X231 : term] : (((sK355 @ X223 @ (comp @ X230 @ X229) @ (sub @ X231 @ X229))) = ((sub @ (sK355 @ X223 @ X230 @ X231) @ X229)))) | ($true = ((X225 @ (lam @ X224)))) | (((X223 @ id @ (sK356 @ X225 @ X223) @ id)) != ((X225 @ (sK356 @ X225 @ X223))))))) & ((sP8 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP8 != $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP7)) & (($true = sP7) | (hoasinduction_lem2v2 != $true)) & (axmap = $true) & ((induction = $true) | (! [X235 : term] : ((((sK358 @ X235)) != $true) | ($true = ((sK358 @ (lam @ X235))))) & ! [X236 : term] : ((((sK358 @ X236)) = $true) | (((var @ X236)) != $true)) & (((sK358 @ sK357)) != $true) & ! [X237 : term,X238 : term] : ((((sK358 @ X238)) != $true) | ($true != ((sK358 @ X237))) | ($true = ((sK358 @ (ap @ X238 @ X237))))))) & (! [X239 : term,X240 : (term > $o)] : ((($true = ((X240 @ (sK359 @ X240)))) & (((X240 @ (lam @ (sK359 @ X240)))) != $true)) | ((((X240 @ (sK360 @ X240))) != $true) & (((var @ (sK360 @ X240))) = $true)) | ($true = ((X240 @ X239))) | (($true = ((X240 @ (sK362 @ X240)))) & ($true = ((X240 @ (sK361 @ X240)))) & ($true != ((X240 @ (ap @ (sK362 @ X240) @ (sK361 @ X240))))))) | (induction != $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)))))))))))))) & (! [X245 : term,X246 : subst,X247 : (term > $o)] : ! [X249 : term] : (((sK363 @ X247 @ X246 @ X245 @ X249)) = ((X247 @ (sub @ X249 @ (push @ X245 @ X246))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X253 : (term > $o)] : (((sK366 @ (sub @ (sK367 @ X253) @ (push @ sK364 @ sK365)))) != ((X253 @ (sK367 @ X253))))) & ! [X255 : term] : (((d2term @ (sK368 @ X255))) = X255) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X257 : (subst > term > subst > $o)] : ! [X259 : term] : (((sK369 @ X257 @ X259)) = ((X257 @ id @ X259 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X261 : (term > $o)] : (((X261 @ (sK371 @ X261))) != ((sK370 @ id @ (sK371 @ X261) @ id)))) & ((((sub @ sK372 @ id)) != sK372) | (! [X266 : term] : ((((sK373 @ id @ X266 @ id)) != $true) | ($true = ((sK373 @ id @ (sub @ sK374 @ (push @ X266 @ id)) @ id)))) & ($true != ((sK373 @ id @ (lam @ (sub @ sK374 @ (push @ one @ sh))) @ id))) & ! [X267 : (subst > term > term)] : ((((sub @ (X267 @ (sK375 @ X267) @ (sK377 @ X267)) @ (sK376 @ X267))) != ((X267 @ (comp @ (sK375 @ X267) @ (sK376 @ X267)) @ (sub @ (sK377 @ X267) @ (sK376 @ X267))))) | ($true = ((sK373 @ id @ (lam @ (X267 @ sh @ one)) @ id))) | (($true = ((sK373 @ id @ (sK378 @ X267) @ id))) & ($true != ((sK373 @ id @ (X267 @ id @ (sK378 @ X267)) @ id)))))) | ($true = sP6) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X272 : term] : (((sub @ X272 @ id)) = X272) & ! [X273 : (subst > term > subst > $o),X274 : term] : ((($true = ((X273 @ id @ (sK379 @ X274 @ X273) @ id))) & ($true != ((X273 @ id @ (sub @ X274 @ (push @ (sK379 @ X274 @ X273) @ id)) @ id)))) | ($true = ((X273 @ id @ (lam @ (sub @ X274 @ (push @ one @ sh))) @ id))) | (! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sK380 @ X273 @ X277 @ X279) @ X278)) = ((sK380 @ X273 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)))) & (((X273 @ id @ (lam @ (sK380 @ X273 @ sh @ one)) @ id)) != $true) & ! [X280 : term] : (($true != ((X273 @ id @ X280 @ id))) | ($true = ((X273 @ id @ (sK380 @ X273 @ id @ X280) @ id)))))) & ($true != sP6))) & (ulamvarind = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X282 : (subst > term > term)] : (((sub @ sK381 @ (push @ (sK383 @ X282) @ (sK382 @ X282)))) != ((X282 @ (sK382 @ X282) @ (sK383 @ X282))))) & (! [X285 : term] : ! [X287 : subst,X288 : term] : (((sK384 @ X285 @ X287 @ X288)) = ((sub @ X285 @ (push @ X288 @ X287)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (((((ap @ sK386 @ sK385)) = ((ap @ sK387 @ sK388))) & (sK388 != sK385)) | ! [X293 : term,X294 : term,X295 : term,X296 : term] : ((X294 = X295) | (((ap @ (sub @ X293 @ id) @ X294)) != ((ap @ (sub @ X296 @ id) @ X295)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X297 : term,X298 : term,X299 : term,X300 : term] : ((((ap @ X298 @ X297)) != ((ap @ X299 @ X300))) | (X297 = X300)) & ((sK390 != sK391) & (((ap @ (sub @ sK392 @ id) @ sK391)) = ((ap @ (sub @ sK389 @ id) @ sK390)))))) & ((termmset = $true) | (sK393 != ((sub @ sK393 @ id)))) & (! [X306 : term] : (((sub @ X306 @ id)) = X306) | (termmset != $true)) & (($true = sP5) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP5)) & ((apinj1 = $true) | ((sK396 != sK394) & (((ap @ sK396 @ sK395)) = ((ap @ sK394 @ sK397))))) & (! [X311 : term,X312 : term,X313 : term,X314 : term] : ((X311 = X313) | (((ap @ X311 @ X314)) != ((ap @ X313 @ X312)))) | (apinj1 != $true)) & (((d2term @ d_one)) = one) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((var @ (d2term @ d_one))) != $true) & (! [X315 : term,X316 : subst,X317 : (subst > term > term),X318 : (subst > term > term)] : ((((X317 @ X316 @ X315)) = ((X318 @ X316 @ X315))) | (((sub @ (X317 @ (sK398 @ X317) @ (sK400 @ X317)) @ (sK399 @ X317))) != ((X317 @ (comp @ (sK398 @ X317) @ (sK399 @ X317)) @ (sub @ (sK400 @ X317) @ (sK399 @ X317))))) | (((sub @ (X318 @ (sK403 @ X318) @ (sK401 @ X318)) @ (sK402 @ X318))) != ((X318 @ (comp @ (sK403 @ X318) @ (sK402 @ X318)) @ (sub @ (sK401 @ X318) @ (sK402 @ X318))))) | (((lam @ (X317 @ sh @ one))) != ((lam @ (X318 @ sh @ one))))) | ((((lam @ sK404)) = ((lam @ sK405))) & (sK405 != sK404)) | (((sub @ one @ (push @ sK407 @ sK406))) != sK407) | (((comp @ sh @ (push @ sK408 @ sK409))) != sK409) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (((((sK412 @ sK411 @ sK410)) != ((sK413 @ sK411 @ sK410))) & ! [X335 : subst,X336 : subst,X337 : term] : (((sK412 @ (comp @ X335 @ X336) @ (sub @ X337 @ X336))) = ((sub @ (sK412 @ X335 @ X337) @ X336))) & ! [X338 : term,X339 : subst,X340 : subst] : (((sub @ (sK413 @ X340 @ X338) @ X339)) = ((sK413 @ (comp @ X340 @ X339) @ (sub @ X338 @ X339)))) & (((lam @ (sK412 @ sh @ one))) = ((lam @ (sK413 @ sh @ one))))) & ! [X341 : term,X342 : term] : ((((lam @ X341)) != ((lam @ X342))) | (X341 = X342)) & ! [X343 : subst,X344 : term] : (((sub @ one @ (push @ X344 @ X343))) = X344) & ! [X345 : term,X346 : subst] : (((comp @ sh @ (push @ X345 @ X346))) = X346))) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ((pushprop_lem1_lthm = $true) | (! [X347 : subst,X348 : term] : (((sub @ one @ (push @ X348 @ X347))) = X348) & (($true = ((sK416 @ sK415))) & ($true != ((sK417 @ (sub @ sK415 @ (push @ sK414 @ sK418)))))) & ! [X354 : term,X355 : subst] : (((comp @ sh @ (push @ X354 @ X355))) = X355))) & ((((sub @ one @ (push @ sK420 @ sK419))) != sK420) | ! [X358 : term,X359 : term,X360 : (term > $o),X361 : (term > $o),X362 : subst] : ((((X360 @ X359)) != $true) | (((X361 @ (sub @ X359 @ (push @ X358 @ X362)))) = $true)) | (sK422 != ((comp @ sh @ (push @ sK421 @ sK422)))) | (pushprop_lem1_lthm != $true)) & (hoaslamnotap_lthm = $true) & (sh = ((d2subst @ d_id))) & ((hoasinduction_lem3aa = $true) | (! [X367 : (subst > term > term)] : ((((sK423 @ id @ (lam @ (X367 @ sh @ one)) @ id)) = $true) | (((sub @ (X367 @ (sK425 @ X367) @ (sK427 @ X367)) @ (sK426 @ X367))) != ((X367 @ (comp @ (sK425 @ X367) @ (sK426 @ X367)) @ (sub @ (sK427 @ X367) @ (sK426 @ X367))))) | ((((sK423 @ id @ (X367 @ id @ (sK428 @ X367)) @ id)) != $true) & ($true = ((sK423 @ id @ (sK428 @ X367) @ id))))) & ! [X372 : term] : ((((sK423 @ id @ (sub @ sK424 @ (push @ X372 @ id)) @ id)) = $true) | (((sK423 @ id @ X372 @ id)) != $true)) & ($true != ((sK423 @ id @ (lam @ (sub @ sK424 @ (push @ one @ sh))) @ id))))) & (! [X373 : (subst > term > subst > $o),X374 : term] : ((($true != ((X373 @ id @ (lam @ (sK429 @ X373 @ sh @ one)) @ id))) & ! [X376 : subst,X377 : subst,X378 : term] : (((sub @ (sK429 @ X373 @ X376 @ X378) @ X377)) = ((sK429 @ X373 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377)))) & ! [X379 : term] : (($true = ((X373 @ id @ (sK429 @ X373 @ id @ X379) @ id))) | ($true != ((X373 @ id @ X379 @ id))))) | (($true != ((X373 @ id @ (sub @ X374 @ (push @ (sK430 @ X374 @ X373) @ id)) @ id))) & ($true = ((X373 @ id @ (sK430 @ X374 @ X373) @ id)))) | ($true = ((X373 @ id @ (lam @ (sub @ X374 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3aa != $true)) & ((hoaslamnotap = $true) | (! [X384 : subst,X385 : subst,X386 : term] : (((sub @ (sK432 @ X384 @ X386) @ X385)) = ((sK432 @ (comp @ X384 @ X385) @ (sub @ X386 @ X385)))) & (((ap @ (sub @ sK431 @ id) @ sK433)) = ((lam @ (sK432 @ sh @ one)))))) & (! [X387 : term,X388 : (subst > term > term),X389 : term] : ((((sub @ (X388 @ (sK434 @ X388) @ (sK436 @ X388)) @ (sK435 @ X388))) != ((X388 @ (comp @ (sK434 @ X388) @ (sK435 @ X388)) @ (sub @ (sK436 @ X388) @ (sK435 @ X388))))) | (((ap @ (sub @ X387 @ id) @ X389)) != ((lam @ (X388 @ sh @ one))))) | (hoaslamnotap != $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop = $true) & (hoasinduction_lem2_gthm = $true) & (! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X396 @ id) @ X394)) != ((ap @ (sub @ X395 @ id) @ X393))) | (X393 = X394)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK440 @ id) @ sK438)) = ((ap @ (sub @ sK439 @ id) @ sK437))) & (sK438 != sK437))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X401 : term,X402 : term,X403 : term,X404 : term] : ((X402 = X403) | (((ap @ (sub @ X403 @ id) @ X404)) != ((ap @ (sub @ X402 @ id) @ X401)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((sK442 != sK443) & (((ap @ (sub @ sK443 @ id) @ sK444)) = ((ap @ (sub @ sK442 @ id) @ sK441))))) & (! [X409 : subst,X410 : term] : (((comp @ sh @ (push @ X410 @ X409))) = X409) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK445 != ((comp @ sh @ (push @ sK446 @ sK445))))) & (hoasinduction_lem3v2_gthm = $true) & (termmset_gthm = $true) & (! [X413 : (term > $o),X414 : subst,X415 : term,X416 : (term > $o)] : ((((X413 @ (sub @ (sK447 @ X416 @ X415 @ X414 @ X413) @ (push @ X415 @ X414)))) != ((X416 @ (sK447 @ X416 @ X415 @ X414 @ X413)))) | (((X413 @ X415)) != $true) | ($true = ((X416 @ one)))) | (sK449 != ((sub @ one @ (push @ sK449 @ sK448)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((! [X424 : term] : (((sK450 @ (sub @ X424 @ (push @ sK452 @ sK451)))) = ((sK453 @ X424))) & ($true = ((sK450 @ sK452))) & ($true != ((sK453 @ one)))) & ! [X425 : subst,X426 : term] : (((sub @ one @ (push @ X426 @ X425))) = X426))) & (pushprop_lem2v2_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3 = $true) | (($true != ((sP4 @ sK455))) & ! [X429 : term] : (($true = ((sK455 @ id @ (sub @ sK454 @ (push @ X429 @ id)) @ id))) | ($true != ((sK455 @ id @ X429 @ id)))) & ! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : ((((sK455 @ X430 @ X432 @ (comp @ X431 @ X433))) != $true) | (((sK455 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X433)) = $true)) & ! [X434 : subst,X435 : subst,X436 : subst,X437 : term] : (($true = ((sK455 @ X436 @ X437 @ (comp @ X434 @ X435)))) | ($true != ((sK455 @ (comp @ X436 @ X434) @ (sub @ X437 @ X434) @ X435)))) & ($true != ((sK455 @ id @ (lam @ sK454) @ id))))) & (! [X438 : term,X439 : (subst > term > subst > $o)] : (($true = ((sP4 @ X439))) | (($true != ((X439 @ id @ (sub @ X438 @ (push @ (sK456 @ X439 @ X438) @ id)) @ id))) & (((X439 @ id @ (sK456 @ X439 @ X438) @ id)) = $true)) | ((((X439 @ (sK457 @ X439) @ (sK459 @ X439) @ (comp @ (sK458 @ X439) @ (sK460 @ X439)))) = $true) & ($true != ((X439 @ (comp @ (sK457 @ X439) @ (sK458 @ X439)) @ (sub @ (sK459 @ X439) @ (sK458 @ X439)) @ (sK460 @ X439))))) | ((((X439 @ (sK463 @ X439) @ (sK464 @ X439) @ (comp @ (sK461 @ X439) @ (sK462 @ X439)))) != $true) & ($true = ((X439 @ (comp @ (sK463 @ X439) @ (sK461 @ X439)) @ (sub @ (sK464 @ X439) @ (sK461 @ X439)) @ (sK462 @ X439))))) | ($true = ((X439 @ id @ (lam @ X438) @ id)))) | (hoasinduction_lem3 != $true)) & ((laminj = $true) | ((sK466 != sK465) & (((lam @ sK466)) = ((lam @ sK465))))) & (! [X451 : term,X452 : term] : ((X451 = X452) | (((lam @ X452)) != ((lam @ X451)))) | (laminj != $true)) & (axapp = $true) & (hoasapinj1_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasapinj2_gthm = $true) & (hoaslamnotvar = $true) & (apnotvar = $true) & (pushprop_lthm = $true) & ((shinj = $true) | ((sK468 != sK467) & (((sub @ sK467 @ sh)) = ((sub @ sK468 @ sh))))) & (! [X455 : term,X456 : term] : ((X455 = X456) | (((sub @ X456 @ sh)) != ((sub @ X455 @ sh)))) | (shinj != $true)) & (pushprop_lem1_gthm = $true) & (! [X457 : term,X458 : (subst > term > subst > $o)] : ((($true = ((X458 @ id @ (sK469 @ X458 @ X457) @ id))) & ($true != ((X458 @ id @ (sub @ X457 @ (push @ (sK469 @ X458 @ X457) @ id)) @ id)))) | ($true = ((X458 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id))) | (($true != ((X458 @ id @ (lam @ (sK470 @ X458 @ sh @ one)) @ id))) & ! [X462 : term,X463 : subst,X464 : subst] : (((sK470 @ X458 @ (comp @ X463 @ X464) @ (sub @ X462 @ X464))) = ((sub @ (sK471 @ X458) @ (push @ (sub @ X462 @ X464) @ (comp @ X463 @ X464))))) & ! [X465 : term] : ((((X458 @ id @ X465 @ id)) != $true) | (((X458 @ id @ (sK470 @ X458 @ id @ X465) @ id)) = $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (sK470 @ X458 @ X466 @ X467) @ X468)) = ((sub @ (sub @ (sK471 @ X458) @ (push @ X467 @ X466)) @ X468))))) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (! [X471 : term] : (($true != ((sK473 @ id @ X471 @ id))) | (((sK473 @ id @ (sub @ sK472 @ (push @ X471 @ id)) @ id)) = $true)) & (((sK473 @ id @ (lam @ (sub @ sK472 @ (push @ one @ sh))) @ id)) != $true) & ! [X472 : (subst > term > term),X473 : term] : (($true = ((sK473 @ id @ (lam @ (X472 @ sh @ one)) @ id))) | (((X472 @ (comp @ (sK475 @ X473 @ X472) @ (sK476 @ X473 @ X472)) @ (sub @ (sK474 @ X473 @ X472) @ (sK476 @ X473 @ X472)))) != ((sub @ X473 @ (push @ (sub @ (sK474 @ X473 @ X472) @ (sK476 @ X473 @ X472)) @ (comp @ (sK475 @ X473 @ X472) @ (sK476 @ X473 @ X472)))))) | ((((sK473 @ id @ (sK477 @ X472) @ id)) = $true) & ($true != ((sK473 @ id @ (X472 @ id @ (sK477 @ X472)) @ id)))) | (((sub @ (X472 @ (sK478 @ X473 @ X472) @ (sK479 @ X473 @ X472)) @ (sK480 @ X473 @ X472))) != ((sub @ (sub @ X473 @ (push @ (sK479 @ X473 @ X472) @ (sK478 @ X473 @ X472))) @ (sK480 @ X473 @ X472))))))) & ((hoasinduction_lem3a = $true) | (! [X483 : term] : ((((sK482 @ id @ X483 @ id)) != $true) | ($true = ((sK482 @ id @ (sub @ sK481 @ (push @ X483 @ id)) @ id)))) & (((sK482 @ id @ (lam @ sK481) @ id)) != $true) & ! [X484 : (subst > term > term)] : ((((X484 @ (comp @ (sK483 @ X484) @ (sK484 @ X484)) @ (sub @ (sK485 @ X484) @ (sK484 @ X484)))) != ((sub @ (X484 @ (sK483 @ X484) @ (sK485 @ X484)) @ (sK484 @ X484)))) | ((((sK482 @ id @ (sK486 @ X484) @ id)) = $true) & ($true != ((sK482 @ id @ (X484 @ id @ (sK486 @ X484)) @ id)))) | (((sK482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true)))) & (! [X489 : term,X490 : (subst > term > subst > $o)] : (((((X490 @ id @ (sK487 @ X490 @ X489) @ id)) = $true) & (((X490 @ id @ (sub @ X489 @ (push @ (sK487 @ X490 @ X489) @ id)) @ id)) != $true)) | ($true = ((X490 @ id @ (lam @ X489) @ id))) | (! [X493 : subst,X494 : subst,X495 : term] : (((sub @ (sK488 @ X490 @ X493 @ X495) @ X494)) = ((sK488 @ X490 @ (comp @ X493 @ X494) @ (sub @ X495 @ X494)))) & ! [X496 : term] : (($true != ((X490 @ id @ X496 @ id))) | ($true = ((X490 @ id @ (sK488 @ X490 @ id @ X496) @ id)))) & (((X490 @ id @ (lam @ (sK488 @ X490 @ sh @ one)) @ id)) != $true))) | (hoasinduction_lem3a != $true)) & (! [X497 : (subst > term > subst > $o),X498 : term,X499 : (term > $o)] : ((($true != ((X499 @ (sub @ X498 @ (push @ (sK489 @ X499 @ X498) @ id))))) & (((X499 @ (sK489 @ X499 @ X498))) = $true)) | (((X497 @ id @ (sK490 @ X499 @ X497) @ id)) != ((X499 @ (sK490 @ X499 @ X497)))) | ($true = ((X499 @ (lam @ X498)))) | (! [X503 : term] : ((((X497 @ id @ (sK491 @ X497 @ id @ X503) @ id)) = $true) | ($true != ((X497 @ id @ X503 @ id)))) & ! [X504 : subst,X505 : term,X506 : subst] : (((sK491 @ X497 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504))) = ((sub @ (sK491 @ X497 @ X506 @ X505) @ X504))) & (((X497 @ id @ (lam @ (sK491 @ X497 @ sh @ one)) @ id)) != $true))) | ! [X508 : (subst > term > term)] : (((X508 @ (sK493 @ X508) @ (sK494 @ X508))) != ((sub @ sK492 @ (push @ (sK494 @ X508) @ (sK493 @ X508))))) | (((sub @ sK495 @ id)) != sK495) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ((! [X515 : term] : (($true = ((sK498 @ (sub @ sK497 @ (push @ X515 @ id))))) | (((sK498 @ X515)) != $true)) & ! [X516 : term] : (((sK498 @ X516)) = ((sK496 @ id @ X516 @ id))) & ($true != ((sK498 @ (lam @ sK497)))) & ! [X517 : (subst > term > term)] : ((($true != ((sK496 @ id @ (X517 @ id @ (sK499 @ X517)) @ id))) & ($true = ((sK496 @ id @ (sK499 @ X517) @ id)))) | (((sub @ (X517 @ (sK502 @ X517) @ (sK501 @ X517)) @ (sK500 @ X517))) != ((X517 @ (comp @ (sK502 @ X517) @ (sK500 @ X517)) @ (sub @ (sK501 @ X517) @ (sK500 @ X517))))) | ($true = ((sK496 @ id @ (lam @ (X517 @ sh @ one)) @ id))))) & ! [X522 : term] : ! [X524 : subst,X525 : term] : (((sub @ X522 @ (push @ X525 @ X524))) = ((sK503 @ X522 @ X524 @ X525))) & ! [X526 : term] : (((sub @ X526 @ id)) = X526))) & (ulamvar1 != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X527 : (term > $o),X528 : term,X529 : (subst > term > subst > $o)] : (($true = ((X527 @ (lam @ X528)))) | ((((X527 @ (sK504 @ X528 @ X527))) = $true) & ($true != ((X527 @ (sub @ X528 @ (push @ (sK504 @ X528 @ X527) @ id)))))) | (! [X532 : term,X533 : subst,X534 : subst] : (((sK505 @ X529 @ (comp @ X533 @ X534) @ (sub @ X532 @ X534))) = ((sub @ (sK505 @ X529 @ X533 @ X532) @ X534))) & ! [X535 : term] : ((((X529 @ id @ X535 @ id)) != $true) | (((X529 @ id @ (sK505 @ X529 @ id @ X535) @ id)) = $true)) & ($true != ((X529 @ id @ (lam @ (sK505 @ X529 @ sh @ one)) @ id)))) | (((X527 @ (sK506 @ X529 @ X527))) != ((X529 @ id @ (sK506 @ X529 @ X527) @ id)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ((((sK507 @ (lam @ sK508))) != $true) & ! [X540 : term] : (($true != ((sK507 @ X540))) | ($true = ((sK507 @ (sub @ sK508 @ (push @ X540 @ id)))))) & ! [X541 : (subst > term > term)] : ((((X541 @ (comp @ (sK511 @ X541) @ (sK512 @ X541)) @ (sub @ (sK510 @ X541) @ (sK512 @ X541)))) != ((sub @ (X541 @ (sK511 @ X541) @ (sK510 @ X541)) @ (sK512 @ X541)))) | (($true = ((sK509 @ id @ (sK513 @ X541) @ id))) & (((sK509 @ id @ (X541 @ id @ (sK513 @ X541)) @ id)) != $true)) | ($true = ((sK509 @ id @ (lam @ (X541 @ sh @ one)) @ id)))) & ! [X546 : term] : (((sK507 @ X546)) = ((sK509 @ id @ X546 @ id))))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_gthm = $true) & (! [X547 : (term > $o),X548 : term,X549 : subst,X550 : (term > $o),X551 : term] : (($true != ((X550 @ X551))) | ($true = ((X547 @ (sub @ X551 @ (push @ X548 @ X549)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true = ((sK517 @ sK518))) & (((sK514 @ (sub @ sK518 @ (push @ sK515 @ sK516)))) != $true))) & ! [X557 : d_term] : (d_one = X557) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm_3 = $true) | (! [X558 : (term > $o),X559 : (subst > term > subst > $o),X560 : term] : ((((X559 @ id @ (sK519 @ X559 @ X558) @ id)) != ((X558 @ (sK519 @ X559 @ X558)))) | (($true != ((X558 @ (sub @ X560 @ (push @ (sK520 @ X560 @ X558) @ id))))) & (((X558 @ (sK520 @ X560 @ X558))) = $true)) | (! [X564 : subst,X565 : subst,X566 : term] : (((sK521 @ X559 @ (comp @ X564 @ X565) @ (sub @ X566 @ X565))) = ((sub @ (sK521 @ X559 @ X564 @ X566) @ X565))) & ! [X567 : term] : ((((X559 @ id @ (sK521 @ X559 @ id @ X567) @ id)) = $true) | (((X559 @ id @ X567 @ id)) != $true)) & ($true != ((X559 @ id @ (lam @ (sK521 @ X559 @ sh @ one)) @ id)))) | (((X558 @ (lam @ X560))) = $true)) & ($true != sP2) & ($true != sP3) & ! [X568 : term] : (((sub @ X568 @ id)) = X568) & ! [X569 : (subst > term > subst > $o)] : ! [X571 : term] : (((sK522 @ X569 @ X571)) = ((X569 @ id @ X571 @ id))))) & ((! [X575 : term] : (((sK523 @ X575)) = ((sK524 @ id @ X575 @ id))) & ! [X576 : term] : (($true = ((sK523 @ (sub @ sK525 @ (push @ X576 @ id))))) | ($true != ((sK523 @ X576)))) & ! [X577 : (subst > term > term)] : ((((X577 @ (comp @ (sK526 @ X577) @ (sK527 @ X577)) @ (sub @ (sK528 @ X577) @ (sK527 @ X577)))) != ((sub @ (X577 @ (sK526 @ X577) @ (sK528 @ X577)) @ (sK527 @ X577)))) | ((((sK524 @ id @ (X577 @ id @ (sK529 @ X577)) @ id)) != $true) & (((sK524 @ id @ (sK529 @ X577) @ id)) = $true)) | ($true = ((sK524 @ id @ (lam @ (X577 @ sh @ one)) @ id)))) & ($true != ((sK523 @ (lam @ sK525))))) | ($true = sP2) | ($true = sP3) | (((sub @ sK530 @ id)) != sK530) | ! [X584 : (term > $o)] : (((X584 @ (sK532 @ X584))) != ((sK531 @ id @ (sK532 @ X584) @ id))) | (hoasinduction_lthm_3 != $true)) & ((apinj2 = $true) | ((sK533 != sK534) & (((ap @ sK535 @ sK533)) = ((ap @ sK536 @ sK534))))) & (! [X590 : term,X591 : term,X592 : term,X593 : term] : ((X590 = X591) | (((ap @ X592 @ X590)) != ((ap @ X593 @ X591)))) | (apinj2 != $true)) & ! [X594 : subst] : (((d2subst @ (sK537 @ X594))) = X594) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X597 : (subst > term > term)] : (((sub @ sK538 @ (push @ one @ sh))) != ((X597 @ sh @ one)))) & (! [X598 : term] : (((sK539 @ X598 @ sh @ one)) = ((sub @ X598 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (lamnotap != $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X600 : (subst > term > term),X601 : (subst > term > term),X602 : subst,X603 : term] : ((((X600 @ X602 @ X603)) = ((X601 @ X602 @ X603))) | (((lam @ (X600 @ sh @ one))) != ((lam @ (X601 @ sh @ one)))) | (((sub @ (X601 @ (sK541 @ X601) @ (sK542 @ X601)) @ (sK540 @ X601))) != ((X601 @ (comp @ (sK541 @ X601) @ (sK540 @ X601)) @ (sub @ (sK542 @ X601) @ (sK540 @ X601))))) | (((sub @ (X600 @ (sK545 @ X600) @ (sK544 @ X600)) @ (sK543 @ X600))) != ((X600 @ (comp @ (sK545 @ X600) @ (sK543 @ X600)) @ (sub @ (sK544 @ X600) @ (sK543 @ X600)))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((sK547 @ sK548 @ sK549)) != ((sK546 @ sK548 @ sK549))) & (((lam @ (sK546 @ sh @ one))) = ((lam @ (sK547 @ sh @ one)))) & ! [X614 : subst,X615 : subst,X616 : term] : (((sub @ (sK547 @ X615 @ X616) @ X614)) = ((sK547 @ (comp @ X615 @ X614) @ (sub @ X616 @ X614)))) & ! [X617 : subst,X618 : term,X619 : subst] : (((sK546 @ (comp @ X619 @ X617) @ (sub @ X618 @ X617))) = ((sub @ (sK546 @ X619 @ X618) @ X617))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((axidr = $true) | (((comp @ sK550 @ id)) != sK550)) & (! [X621 : subst] : (((comp @ X621 @ id)) = X621) | (axidr != $true)) & (hoasinduction_lem3_gthm = $true) & (! [X622 : (subst > term > subst > $o),X623 : term] : (((((X622 @ id @ (ap @ (sub @ (sK551 @ X622) @ id) @ (sK552 @ X622)) @ id)) != $true) & ($true = ((X622 @ id @ (sK551 @ X622) @ id))) & ($true = ((X622 @ id @ (sK552 @ X622) @ id)))) | (($true != ((X622 @ id @ (lam @ (sK553 @ X622 @ sh @ one)) @ id))) & ! [X627 : term] : (($true != ((X622 @ id @ X627 @ id))) | ($true = ((X622 @ id @ (sK553 @ X622 @ id @ X627) @ id)))) & ! [X628 : subst,X629 : term,X630 : subst] : (((sub @ (sK553 @ X622 @ X630 @ X629) @ X628)) = ((sK553 @ X622 @ (comp @ X630 @ X628) @ (sub @ X629 @ X628))))) | (((X622 @ id @ X623 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X633 : term,X634 : term] : ((((sK554 @ id @ (ap @ (sub @ X633 @ id) @ X634) @ id)) = $true) | (((sK554 @ id @ X633 @ id)) != $true) | ($true != ((sK554 @ id @ X634 @ id)))) & ! [X635 : (subst > term > term)] : ((((sK554 @ id @ (lam @ (X635 @ sh @ one)) @ id)) = $true) | (($true = ((sK554 @ id @ (sK556 @ X635) @ id))) & ($true != ((sK554 @ id @ (X635 @ id @ (sK556 @ X635)) @ id)))) | (((X635 @ (comp @ (sK559 @ X635) @ (sK557 @ X635)) @ (sub @ (sK558 @ X635) @ (sK557 @ X635)))) != ((sub @ (X635 @ (sK559 @ X635) @ (sK558 @ X635)) @ (sK557 @ X635))))) & ($true != ((sK554 @ id @ sK555 @ id))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X640 : (subst > term > subst > $o)] : ! [X642 : term] : (((sK560 @ X640 @ X642)) = ((X640 @ id @ X642 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X644 : (term > $o)] : (((sK561 @ id @ (sK562 @ X644) @ id)) != ((X644 @ (sK562 @ X644))))) & (axassoc = $true) & ((axscons = $true) | (sK563 != ((push @ (sub @ one @ sK563) @ (comp @ sh @ sK563))))) & (! [X647 : subst] : (((push @ (sub @ one @ X647) @ (comp @ sh @ X647))) = X647) | (axscons != $true)) & (hoasinduction_lem2_lthm = $true) & ((axvarcons = $true) | (((sub @ one @ (push @ sK565 @ sK564))) != sK565)) & (! [X650 : subst,X651 : term] : (((sub @ one @ (push @ X651 @ X650))) = X651) | (axvarcons != $true)) & ! [X652 : d_subst,X653 : d_subst] : ((X652 = X653) | (((d2subst @ X652)) != ((d2subst @ X653))))), 0.43/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK242,sK243,sK244,sK245,vAPP,sK247,sK248,sK249,sK250,sK251,sK252,sK253,sK254,sK255,sK256,sK257,sK258,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK269,sK270,sK271,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK291,sK292,sK293,sK294,sK295,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK302,sK303,sK304,sK305,sK306,sK307,vAPP,vAPP,sK310,vAPP,vAPP,sK313,sK314,sK315,sK316,sK317,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK327,sK328,sK329,sK330,sK331,vAPP,vAPP,vAPP,vAPP,sK336,sK337,sK338,vAPP,vAPP,vAPP,vAPP,sK343,vAPP,sK345,sK346,sK347,sK348,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK357,sK358,vAPP,vAPP,vAPP,vAPP,vAPP,sK364,sK365,sK366,vAPP,vAPP,vAPP,sK370,vAPP,sK372,sK373,sK374,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK381,vAPP,vAPP,vAPP,sK385,sK386,sK387,sK388,sK389,sK390,sK391,sK392,sK393,sK394,sK395,sK396,sK397,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK404,sK405,sK406,sK407,sK408,sK409,sK410,sK411,sK412,sK413,sK414,sK415,sK416,sK417,sK418,sK419,sK420,sK421,sK422,sK423,sK424,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK431,sK432,sK433,vAPP,vAPP,vAPP,sK437,sK438,sK439,sK440,sK441,sK442,sK443,sK444,sK445,sK446,vAPP,sK448,sK449,sK450,sK451,sK452,sK453,sK454,sK455,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK465,sK466,sK467,sK468,vAPP,vAPP,vAPP,sK472,sK473,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK481,sK482,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK492,vAPP,vAPP,sK495,sK496,sK497,sK498,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK507,sK508,sK509,vAPP,vAPP,vAPP,vAPP,sK514,sK515,sK516,sK517,sK518,vAPP,vAPP,vAPP,vAPP,sK523,sK524,sK525,vAPP,vAPP,vAPP,vAPP,sK530,sK531,vAPP,sK533,sK534,sK535,sK536,vAPP,sK538,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK546,sK547,sK548,sK549,sK550,vAPP,vAPP,vAPP,sK554,sK555,vAPP,vAPP,vAPP,vAPP,vAPP,sK561,vAPP,sK563,sK564,sK565]),skolemize(X0,sK242),skolemize(X1,sK243),skolemize(X2,sK244),skolemize(X3,sK245),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK247),skolemize(X11,sK248),skolemize(X12,sK249),skolemize(X13,sK250),skolemize(X23,sK251),skolemize(X24,sK252),skolemize(X25,sK253),skolemize(X26,sK254),skolemize(X27,sK255),skolemize(X28,sK256),skolemize(X29,sK257),skolemize(X30,sK258),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X55,sK269),skolemize(X56,sK270),skolemize(X57,sK271),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X91,sK291),skolemize(X92,sK292),skolemize(X93,sK293),skolemize(X104,sK294),skolemize(X105,sK295),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X121,sK302),skolemize(X122,sK303),skolemize(X124,sK304),skolemize(X127,sK305),skolemize(X129,sK306),skolemize(X130,sK307),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X138,sK310),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X144,sK313),skolemize(X147,sK314),skolemize(X149,sK315),skolemize(X150,sK316),skolemize(X151,sK317),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X174,sK327),skolemize(X175,sK328),skolemize(X176,sK329),skolemize(X177,sK330),skolemize(X178,sK331),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X195,sK336),skolemize(X196,sK337),skolemize(X197,sK338),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X205,sK343),skolemize(X10,sK33 @ X7 @ X6),skolemize(X208,sK345),skolemize(X209,sK346),skolemize(X210,sK347),skolemize(X211,sK348),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X233,sK357),skolemize(X234,sK358),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X250,sK364),skolemize(X251,sK365),skolemize(X252,sK366),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X260,sK370),skolemize(X10,sK33 @ X7 @ X6),skolemize(X263,sK372),skolemize(X264,sK373),skolemize(X265,sK374),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X281,sK381),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X289,sK385),skolemize(X290,sK386),skolemize(X291,sK387),skolemize(X292,sK388),skolemize(X301,sK389),skolemize(X302,sK390),skolemize(X303,sK391),skolemize(X304,sK392),skolemize(X305,sK393),skolemize(X307,sK394),skolemize(X308,sK395),skolemize(X309,sK396),skolemize(X310,sK397),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X325,sK404),skolemize(X326,sK405),skolemize(X327,sK406),skolemize(X328,sK407),skolemize(X329,sK408),skolemize(X330,sK409),skolemize(X331,sK410),skolemize(X332,sK411),skolemize(X333,sK412),skolemize(X334,sK413),skolemize(X349,sK414),skolemize(X350,sK415),skolemize(X351,sK416),skolemize(X352,sK417),skolemize(X353,sK418),skolemize(X356,sK419),skolemize(X357,sK420),skolemize(X363,sK421),skolemize(X364,sK422),skolemize(X365,sK423),skolemize(X366,sK424),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X381,sK431),skolemize(X382,sK432),skolemize(X383,sK433),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X397,sK437),skolemize(X398,sK438),skolemize(X399,sK439),skolemize(X400,sK440),skolemize(X405,sK441),skolemize(X406,sK442),skolemize(X407,sK443),skolemize(X408,sK444),skolemize(X411,sK445),skolemize(X412,sK446),skolemize(X10,sK33 @ X7 @ X6),skolemize(X418,sK448),skolemize(X419,sK449),skolemize(X420,sK450),skolemize(X421,sK451),skolemize(X422,sK452),skolemize(X423,sK453),skolemize(X427,sK454),skolemize(X428,sK455),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X449,sK465),skolemize(X450,sK466),skolemize(X453,sK467),skolemize(X454,sK468),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X469,sK472),skolemize(X470,sK473),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X481,sK481),skolemize(X482,sK482),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X507,sK492),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X511,sK495),skolemize(X512,sK496),skolemize(X513,sK497),skolemize(X514,sK498),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X537,sK507),skolemize(X538,sK508),skolemize(X539,sK509),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X552,sK514),skolemize(X553,sK515),skolemize(X554,sK516),skolemize(X555,sK517),skolemize(X556,sK518),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X572,sK523),skolemize(X573,sK524),skolemize(X574,sK525),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X582,sK530),skolemize(X583,sK531),skolemize(X10,sK33 @ X7 @ X6),skolemize(X586,sK533),skolemize(X587,sK534),skolemize(X588,sK535),skolemize(X589,sK536),skolemize(X10,sK33 @ X7 @ X6),skolemize(X596,sK538),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X610,sK546),skolemize(X611,sK547),skolemize(X612,sK548),skolemize(X613,sK549),skolemize(X620,sK550),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X631,sK554),skolemize(X632,sK555),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X10,sK33 @ X7 @ X6),skolemize(X643,sK561),skolemize(X10,sK33 @ X7 @ X6),skolemize(X646,sK563),skolemize(X648,sK564),skolemize(X649,sK565)],[f134])). 0.43/0.53 thf(f138,plain,( 0.43/0.53 ($true = ((sK31 @ sK32))) | (pushprop_lem2v2 != $true)), 0.43/0.53 inference(cnf_transformation,[],[f45])). 0.43/0.53 thf(f140,plain,( 0.43/0.53 (((sK31 @ (sub @ sK32 @ sh))) != $true) | (pushprop_lem2v2 != $true)), 0.43/0.53 inference(cnf_transformation,[],[f45])). 0.43/0.53 thf(f482,plain,( 0.43/0.53 (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id))))), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f531,plain,( 0.43/0.53 ( ! [X557 : d_term] : ((d_one = X557)) )), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f648,plain,( 0.43/0.53 (sh = ((d2subst @ d_id)))), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f657,plain,( 0.43/0.53 (pushprop_lem2v2 = $true)), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f670,plain,( 0.43/0.53 (((d2term @ d_one)) = one)), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f701,plain,( 0.43/0.53 ( ! [X255 : term] : ((((d2term @ (sK368 @ X255))) = X255)) )), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f803,plain,( 0.43/0.53 (id = ((d2subst @ d_id)))), 0.43/0.53 inference(cnf_transformation,[],[f135])). 0.43/0.53 thf(f1595,definition,( 0.43/0.53 spl566_132 <=> ! [X128 : term] : (((sub @ X128 @ id)) = X128)), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_132])],[avatar_definition])). 0.43/0.53 thf(f1596,plain,( 0.43/0.53 ( ! [X128 : term] : ((((sub @ X128 @ id)) = X128)) ) | ~spl566_132), 0.43/0.53 inference(avatar_component_clause,[],[f1595])). 0.43/0.53 thf(f2119,definition,( 0.43/0.53 spl566_257 <=> (pushprop_lem2v2 = $true)), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_257])],[avatar_definition])). 0.43/0.53 thf(f2123,definition,( 0.43/0.53 spl566_258 <=> ($true = ((sK31 @ sK32)))), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_258])],[avatar_definition])). 0.43/0.53 thf(f2125,plain,( 0.43/0.53 ($true = ((sK31 @ sK32))) | ~spl566_258), 0.43/0.53 inference(avatar_component_clause,[],[f2123])). 0.43/0.53 thf(f2126,plain,( 0.43/0.53 ~spl566_257 | spl566_258), 0.43/0.53 inference(avatar_split_clause,[],[f138,f2123,f2119])). 0.43/0.53 thf(f2422,definition,( 0.43/0.53 spl566_328 <=> (sh = ((d2subst @ d_id)))), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_328])],[avatar_definition])). 0.43/0.53 thf(f2424,plain,( 0.43/0.53 (sh = ((d2subst @ d_id))) | ~spl566_328), 0.43/0.53 inference(avatar_component_clause,[],[f2422])). 0.43/0.53 thf(f2425,plain,( 0.43/0.53 spl566_328), 0.43/0.53 inference(avatar_split_clause,[],[f648,f2422])). 0.43/0.53 thf(f3383,definition,( 0.43/0.53 spl566_551 <=> (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id))))), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_551])],[avatar_definition])). 0.43/0.53 thf(f3385,plain,( 0.43/0.53 (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) | ~spl566_551), 0.43/0.53 inference(avatar_component_clause,[],[f3383])). 0.43/0.53 thf(f3386,plain,( 0.43/0.53 spl566_551), 0.43/0.53 inference(avatar_split_clause,[],[f482,f3383])). 0.43/0.53 thf(f3565,definition,( 0.43/0.53 spl566_593 <=> (((sK31 @ (sub @ sK32 @ sh))) = $true)), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_593])],[avatar_definition])). 0.43/0.53 thf(f3567,plain,( 0.43/0.53 (((sK31 @ (sub @ sK32 @ sh))) != $true) | spl566_593), 0.43/0.53 inference(avatar_component_clause,[],[f3565])). 0.43/0.53 thf(f3568,plain,( 0.43/0.53 ~spl566_593 | ~spl566_257), 0.43/0.53 inference(avatar_split_clause,[],[f140,f2119,f3565])). 0.43/0.53 thf(f3899,plain,( 0.43/0.53 spl566_257), 0.43/0.53 inference(avatar_split_clause,[],[f657,f2119])). 0.43/0.53 thf(f4122,definition,( 0.43/0.53 spl566_722 <=> (((d2term @ d_one)) = one)), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_722])],[avatar_definition])). 0.43/0.53 thf(f4124,plain,( 0.43/0.53 (((d2term @ d_one)) = one) | ~spl566_722), 0.43/0.53 inference(avatar_component_clause,[],[f4122])). 0.43/0.53 thf(f4125,plain,( 0.43/0.53 spl566_722), 0.43/0.53 inference(avatar_split_clause,[],[f670,f4122])). 0.43/0.53 thf(f4400,definition,( 0.43/0.53 spl566_784 <=> (id = ((d2subst @ d_id)))), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_784])],[avatar_definition])). 0.43/0.53 thf(f4402,plain,( 0.43/0.53 (id = ((d2subst @ d_id))) | ~spl566_784), 0.43/0.53 inference(avatar_component_clause,[],[f4400])). 0.43/0.53 thf(f4403,plain,( 0.43/0.53 spl566_784), 0.43/0.53 inference(avatar_split_clause,[],[f803,f4400])). 0.43/0.53 thf(f4747,plain,( 0.43/0.53 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) ) | ~spl566_722), 0.43/0.53 inference(superposition,[],[f4124,f531])). 0.43/0.53 thf(f4750,plain,( 0.43/0.53 (sh = id) | (~spl566_328 | ~spl566_784)), 0.43/0.53 inference(superposition,[],[f4402,f2424])). 0.43/0.53 thf(f4753,definition,( 0.43/0.53 spl566_829 <=> (sh = id)), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_829])],[avatar_definition])). 0.43/0.53 thf(f4755,plain,( 0.43/0.53 (sh = id) | ~spl566_829), 0.43/0.53 inference(avatar_component_clause,[],[f4753])). 0.43/0.53 thf(f4756,plain,( 0.43/0.53 spl566_829 | ~spl566_328 | ~spl566_784), 0.43/0.53 inference(avatar_split_clause,[],[f4750,f4400,f2422,f4753])). 0.43/0.53 thf(f4784,plain,( 0.43/0.53 (one = ((sub @ one @ (d2subst @ d_id)))) | (~spl566_551 | ~spl566_722)), 0.43/0.53 inference(forward_demodulation,[],[f3385,f4124])). 0.43/0.53 thf(f4785,plain,( 0.43/0.53 (one = ((sub @ one @ sh))) | (~spl566_328 | ~spl566_551 | ~spl566_722)), 0.43/0.53 inference(forward_demodulation,[],[f4784,f2424])). 0.43/0.53 thf(f4787,definition,( 0.43/0.53 spl566_833 <=> (one = ((sub @ one @ sh)))), 0.43/0.53 introduced(definition,[new_symbols(definition,[spl566_833])],[avatar_definition])). 0.43/0.53 thf(f4789,plain,( 0.43/0.53 (one = ((sub @ one @ sh))) | ~spl566_833), 0.43/0.53 inference(avatar_component_clause,[],[f4787])). 0.43/0.53 thf(f4790,plain,( 0.43/0.53 spl566_833 | ~spl566_328 | ~spl566_551 | ~spl566_722), 0.43/0.53 inference(avatar_split_clause,[],[f4785,f4122,f3383,f2422,f4787])). 0.43/0.53 thf(f5140,plain,( 0.43/0.53 (((sK31 @ (sub @ sK32 @ id))) != $true) | (spl566_593 | ~spl566_829)), 0.43/0.53 inference(superposition,[],[f3567,f4755])). 0.43/0.53 thf(f5151,plain,( 0.43/0.53 ($true != ((sK31 @ sK32))) | (~spl566_132 | spl566_593 | ~spl566_829)), 0.43/0.53 inference(forward_demodulation,[],[f5140,f1596])). 0.43/0.53 thf(f5164,plain,( 0.43/0.53 $false | (~spl566_132 | ~spl566_258 | spl566_593 | ~spl566_829)), 0.43/0.53 inference(forward_subsumption_resolution,[],[f5151,f2125])). 0.43/0.53 thf(f5165,plain,( 0.43/0.53 ~spl566_132 | ~spl566_258 | spl566_593 | ~spl566_829), 0.43/0.53 inference(avatar_contradiction_clause,[],[f5164])). 0.43/0.53 thf(f5217,plain,( 0.43/0.53 ( ! [X0 : term] : ((one = X0)) ) | ~spl566_722), 0.43/0.53 inference(superposition,[],[f4747,f701])). 0.43/0.53 thf(f5268,plain,( 0.43/0.53 ( ! [X0 : term] : ((((sub @ X0 @ sh)) = X0)) ) | (~spl566_722 | ~spl566_833)), 0.43/0.53 inference(superposition,[],[f4789,f5217])). 0.43/0.53 thf(f5276,plain,( 0.43/0.53 ( ! [X0 : term] : ((((sub @ X0 @ id)) = X0)) ) | (~spl566_722 | ~spl566_829 | ~spl566_833)), 0.43/0.53 inference(forward_demodulation,[],[f5268,f4755])). 0.43/0.53 thf(f5279,plain,( 0.43/0.53 spl566_132 | ~spl566_722 | ~spl566_829 | ~spl566_833), 0.43/0.53 inference(avatar_split_clause,[],[f5276,f4787,f4753,f4122,f1595])). 0.43/0.53 cnf(s193, plain, ~spl566_257 | spl566_258, inference(sat_conversion,[],[f2126])). 0.43/0.53 cnf(s264, plain, spl566_328, inference(sat_conversion,[],[f2425])). 0.43/0.53 cnf(s491, plain, spl566_551, inference(sat_conversion,[],[f3386])). 0.43/0.53 cnf(s534, plain, ~spl566_257 | ~spl566_593, inference(sat_conversion,[],[f3568])). 0.43/0.53 cnf(s617, plain, spl566_257, inference(sat_conversion,[],[f3899])). 0.43/0.53 cnf(s675, plain, spl566_722, inference(sat_conversion,[],[f4125])). 0.43/0.53 cnf(s745, plain, spl566_784, inference(sat_conversion,[],[f4403])). 0.43/0.53 cnf(s793, plain, ~spl566_328 | ~spl566_784 | spl566_829, inference(sat_conversion,[],[f4756])). 0.43/0.53 cnf(s798, plain, ~spl566_328 | ~spl566_551 | ~spl566_722 | spl566_833, inference(sat_conversion,[],[f4790])). 0.43/0.53 cnf(s832, plain, ~spl566_132 | ~spl566_258 | spl566_593 | ~spl566_829, inference(sat_conversion,[],[f5165])). 0.43/0.53 cnf(s845, plain, spl566_132 | ~spl566_722 | ~spl566_829 | ~spl566_833, inference(sat_conversion,[],[f5279])). 0.43/0.53 cnf(s848, plain, ~spl566_593, inference(rat,[],[s534,s617])). 0.43/0.53 cnf(s857, plain, spl566_833, inference(rat,[],[s798,s491,s675,s264])). 0.43/0.53 cnf(s858, plain, spl566_829, inference(rat,[],[s793,s745,s264])). 0.43/0.53 cnf(s863, plain, spl566_132, inference(rat,[],[s845,s857,s675,s858])). 0.43/0.53 cnf(s864, plain, ~spl566_258, inference(rat,[],[s832,s858,s848,s863])). 0.43/0.53 cnf(s872, plain, $false, inference(rat,[],[s193,s864,s617])). 0.43/0.53 thf(f5280,plain,( 0.43/0.53 $false), 0.43/0.53 inference(avatar_sat_refutation,[],[s872])). 0.43/0.53 % SZS output end Proof for theBenchmark 0.43/0.53 % (2977829)------------------------------ 0.43/0.53 % (2977829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.43/0.53 % (2977829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.43/0.53 % (2977829)CaDiCaL version: 2.1.3 0.43/0.53 % (2977829)Termination reason: Refutation 0.43/0.53 % (2977829)Time elapsed: 0.135 s 0.43/0.53 % (2977829)Peak memory usage: 18 MB 0.43/0.53 % (2977829)Instructions burned: 522 (million) 0.43/0.53 % (2977821)Success in time 0.173 s 0.43/0.53 % Vampire exiting 0.43/0.53 EOF