0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.17/0.42 % Computer : n023.cluster.edu 0.17/0.42 % Model : x86_64 x86_64 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.42 % Memory : 8046.5625MB 0.17/0.42 % OS : Linux 6.8.0-71-generic 0.17/0.42 % CPULimit : 1440 0.17/0.42 % WCLimit : 180 0.17/0.42 % DateTime : Mon Jul 27 12:58:06 UTC 2026 0.17/0.43 % CPUTime : 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.17/0.47 Running higher-order theorem proving 0.23/0.53 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 0.88/0.72 % (940431)Detected a higher-order problem, will run a greedy HOL sequence. 0.88/0.72 % (940440)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=6478870:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.88/0.72 % (940442)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.88/0.72 % (940442)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 0.88/0.72 % (940440)Instruction limit reached! 0.88/0.72 % (940440)------------------------------ 0.88/0.72 % (940440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.72 % (940440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.72 % (940440)CaDiCaL version: 2.1.3 0.88/0.72 % (940440)Termination reason: Instruction limit 0.88/0.72 % (940440)Termination phase: Property scanning 0.88/0.72 % (940440)Time elapsed: 0.009 s 0.88/0.72 % (940440)Peak memory usage: 10 MB 0.88/0.72 % (940440)Instructions burned: 26 (million) 0.88/0.72 % (940436)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3047648734:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.88/0.72 % (940437)lrs+10_16_si=on:nwc=1.5:random_seed=801977953:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.88/0.72 % (940438)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2557119876:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.88/0.72 % (940439)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=1455961818: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) 0.88/0.72 % (940442)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=507003618:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.88/0.72 % (940441)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2751150002:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.88/0.72 % (940438)Instruction limit reached! 0.88/0.72 % (940438)------------------------------ 0.88/0.72 % (940438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.72 % (940438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.72 % (940438)CaDiCaL version: 2.1.3 0.88/0.72 % (940438)Termination reason: Instruction limit 0.88/0.72 % (940438)Termination phase: shuffling 0.88/0.72 % (940438)Time elapsed: 0.003 s 0.88/0.72 % (940438)Peak memory usage: 9 MB 0.88/0.72 % (940438)Instructions burned: 4 (million) 0.88/0.72 % (940437)Instruction limit reached! 0.88/0.72 % (940437)------------------------------ 0.88/0.72 % (940437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.72 % (940437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.72 % (940437)CaDiCaL version: 2.1.3 0.88/0.72 % (940437)Termination reason: Instruction limit 0.88/0.72 % (940437)Termination phase: shuffling 0.88/0.72 % (940437)Time elapsed: 0.013 s 0.88/0.72 % (940437)Peak memory usage: 10 MB 0.88/0.72 % (940437)Instructions burned: 19 (million) 0.88/0.72 % (940444)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=212270712:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.88/0.72 % (940444)Instruction limit reached! 0.88/0.72 % (940444)------------------------------ 0.88/0.72 % (940444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.72 % (940444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.72 % (940444)CaDiCaL version: 2.1.3 0.88/0.72 % (940444)Termination reason: Instruction limit 0.88/0.72 % (940444)Termination phase: shuffling 0.88/0.72 % (940444)Time elapsed: 0.001 s 0.88/0.72 % (940444)Peak memory usage: 10 MB 0.88/0.72 % (940444)Instructions burned: 2 (million) 0.88/0.72 % (940454)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3578133166:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.88/0.72 % (940451)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=845980489:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.88/0.78 % (940451)Instruction limit reached! 0.88/0.78 % (940451)------------------------------ 0.88/0.78 % (940451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.78 % (940451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.78 % (940451)CaDiCaL version: 2.1.3 0.88/0.78 % (940451)Termination reason: Instruction limit 0.88/0.78 % (940451)Termination phase: shuffling 0.88/0.78 % (940451)Time elapsed: 0.004 s 0.88/0.78 % (940451)Peak memory usage: 9 MB 0.88/0.78 % (940451)Instructions burned: 5 (million) 0.88/0.78 % (940454)Instruction limit reached! 0.88/0.78 % (940454)------------------------------ 0.88/0.78 % (940454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.78 % (940454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.78 % (940454)CaDiCaL version: 2.1.3 0.88/0.78 % (940454)Termination reason: Instruction limit 0.88/0.78 % (940454)Termination phase: shuffling 0.88/0.78 % (940454)Time elapsed: 0.005 s 0.88/0.78 % (940454)Peak memory usage: 10 MB 0.88/0.78 % (940454)Instructions burned: 15 (million) 0.88/0.78 % (940452)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.88/0.78 % (940452)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=950701512:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.88/0.78 % (940452)Instruction limit reached! 0.88/0.78 % (940452)------------------------------ 0.88/0.78 % (940452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.78 % (940452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.78 % (940452)CaDiCaL version: 2.1.3 0.88/0.78 % (940452)Termination reason: Instruction limit 0.88/0.78 % (940452)Termination phase: shuffling 0.88/0.78 % (940452)Time elapsed: 0.006 s 0.88/0.78 % (940452)Peak memory usage: 9 MB 0.88/0.78 % (940452)Instructions burned: 8 (million) 0.88/0.78 % (940441)Instruction limit reached! 0.88/0.78 % (940441)------------------------------ 0.88/0.78 % (940441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.78 % (940441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.78 % (940441)CaDiCaL version: 2.1.3 0.88/0.78 % (940441)Termination reason: Instruction limit 0.88/0.78 % (940441)Termination phase: Preprocessing 3 0.88/0.78 % (940441)Time elapsed: 0.052 s 0.88/0.78 % (940441)Peak memory usage: 12 MB 0.88/0.78 % (940441)Instructions burned: 75 (million) 0.88/0.78 % (940458)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=2520381707:i=86:piset=equals:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/86Mi) 0.88/0.78 % (940436)Instruction limit reached! 0.88/0.78 % (940436)------------------------------ 0.88/0.78 % (940436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.88/0.78 % (940436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.88/0.78 % (940436)CaDiCaL version: 2.1.3 0.88/0.78 % (940436)Termination reason: Instruction limit 0.88/0.78 % (940436)Termination phase: Preprocessing 3 0.88/0.78 % (940436)Time elapsed: 0.061 s 0.88/0.78 % (940436)Peak memory usage: 12 MB 0.88/0.78 % (940436)Instructions burned: 88 (million) 0.88/0.78 % (940457)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 0.88/0.78 % (940457)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.88/0.78 % (940457)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3900322319:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1799 on theBenchmark for (1799ds/28Mi) 0.88/0.78 % (940461)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 0.88/0.78 % (940460)lrs+10_1_si=on:cs=on:random_seed=2630457403:i=8:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/8Mi) 1.47/0.83 % (940461)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=1006299193:i=2:add=on:rtra=on_1798 on theBenchmark for (1798ds/2Mi) 1.47/0.83 % (940461)Instruction limit reached! 1.47/0.83 % (940461)------------------------------ 1.47/0.83 % (940461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.83 % (940461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.83 % (940461)CaDiCaL version: 2.1.3 1.47/0.83 % (940461)Termination reason: Instruction limit 1.47/0.83 % (940461)Termination phase: shuffling 1.47/0.83 % (940461)Time elapsed: 0.002 s 1.47/0.83 % (940461)Peak memory usage: 9 MB 1.47/0.83 % (940461)Instructions burned: 2 (million) 1.47/0.83 % (940458)Instruction limit reached! 1.47/0.83 % (940458)------------------------------ 1.47/0.83 % (940458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.83 % (940458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.83 % (940458)CaDiCaL version: 2.1.3 1.47/0.83 % (940458)Termination reason: Instruction limit 1.47/0.83 % (940458)Termination phase: Saturation 1.47/0.83 % (940458)Time elapsed: 0.030 s 1.47/0.83 % (940458)Peak memory usage: 12 MB 1.47/0.83 % (940458)Instructions burned: 87 (million) 1.47/0.83 % (940460)Instruction limit reached! 1.47/0.83 % (940460)------------------------------ 1.47/0.83 % (940460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.83 % (940460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.83 % (940460)CaDiCaL version: 2.1.3 1.47/0.83 % (940460)Termination reason: Instruction limit 1.47/0.83 % (940460)Termination phase: shuffling 1.47/0.83 % (940460)Time elapsed: 0.007 s 1.47/0.83 % (940460)Peak memory usage: 10 MB 1.47/0.83 % (940460)Instructions burned: 9 (million) 1.47/0.83 % (940457)Instruction limit reached! 1.47/0.83 % (940457)------------------------------ 1.47/0.83 % (940457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.83 % (940457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.83 % (940457)CaDiCaL version: 2.1.3 1.47/0.83 % (940457)Termination reason: Instruction limit 1.47/0.83 % (940457)Termination phase: shuffling 1.47/0.83 % (940457)Time elapsed: 0.020 s 1.47/0.83 % (940457)Peak memory usage: 10 MB 1.47/0.83 % (940457)Instructions burned: 29 (million) 1.47/0.83 % (940463)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2902512837:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/38Mi) 1.47/0.83 % (940467)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=241645310:st=2:i=249:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/249Mi) 1.47/0.83 % (940442)Instruction limit reached! 1.47/0.83 % (940442)------------------------------ 1.47/0.83 % (940442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.83 % (940442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.83 % (940442)CaDiCaL version: 2.1.3 1.47/0.83 % (940442)Termination reason: Instruction limit 1.47/0.83 % (940442)Termination phase: Property scanning 1.47/0.83 % (940442)Time elapsed: 0.105 s 1.47/0.83 % (940442)Peak memory usage: 13 MB 1.47/0.83 % (940442)Instructions burned: 157 (million) 1.47/0.83 % (940468)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1368108969:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/25Mi) 1.47/0.83 % (940469)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1451991649:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 1.47/0.83 % (940470)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=857949209:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 1.47/0.83 % (940463)Instruction limit reached! 1.47/0.83 % (940463)------------------------------ 1.47/0.83 % (940463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.47/0.83 % (940463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.47/0.83 % (940463)CaDiCaL version: 2.1.3 1.47/0.83 % (940463)Termination reason: Instruction limit 1.47/0.83 % (940463)Termination phase: Clausification 1.47/0.83 % (940463)Time elapsed: 0.026 s 1.83/0.94 % (940463)Peak memory usage: 11 MB 1.83/0.94 % (940463)Instructions burned: 38 (million) 1.83/0.94 % (940469)Instruction limit reached! 1.83/0.94 % (940469)------------------------------ 1.83/0.94 % (940469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/0.94 % (940469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/0.94 % (940469)CaDiCaL version: 2.1.3 1.83/0.94 % (940469)Termination reason: Instruction limit 1.83/0.94 % (940469)Termination phase: shuffling 1.83/0.94 % (940469)Time elapsed: 0.010 s 1.83/0.94 % (940469)Peak memory usage: 10 MB 1.83/0.94 % (940469)Instructions burned: 15 (million) 1.83/0.94 % (940468)Instruction limit reached! 1.83/0.94 % (940468)------------------------------ 1.83/0.94 % (940468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/0.94 % (940468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/0.94 % (940468)CaDiCaL version: 2.1.3 1.83/0.94 % (940468)Termination reason: Instruction limit 1.83/0.94 % (940468)Termination phase: Property scanning 1.83/0.94 % (940468)Time elapsed: 0.017 s 1.83/0.94 % (940468)Peak memory usage: 10 MB 1.83/0.94 % (940468)Instructions burned: 26 (million) 1.83/0.94 % (940473)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3116511399:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 1.83/0.94 % (940477)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2722744055:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1798 on theBenchmark for (1798ds/2Mi) 1.83/0.94 % (940473)Instruction limit reached! 1.83/0.94 % (940473)------------------------------ 1.83/0.94 % (940473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/0.94 % (940473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/0.94 % (940473)CaDiCaL version: 2.1.3 1.83/0.94 % (940473)Termination reason: Instruction limit 1.83/0.94 % (940473)Termination phase: shuffling 1.83/0.94 % (940473)Time elapsed: 0.010 s 1.83/0.94 % (940473)Peak memory usage: 10 MB 1.83/0.94 % (940473)Instructions burned: 14 (million) 1.83/0.94 % (940477)Instruction limit reached! 1.83/0.94 % (940477)------------------------------ 1.83/0.94 % (940477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/0.94 % (940477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/0.94 % (940477)CaDiCaL version: 2.1.3 1.83/0.94 % (940477)Termination reason: Instruction limit 1.83/0.94 % (940477)Termination phase: shuffling 1.83/0.94 % (940477)Time elapsed: 0.002 s 1.83/0.94 % (940477)Peak memory usage: 9 MB 1.83/0.94 % (940477)Instructions burned: 2 (million) 1.83/0.94 % (940478)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3853246994:i=26:ep=R:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/26Mi) 1.83/0.94 % (940479)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3162630992:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1798 on theBenchmark for (1798ds/23Mi) 1.83/0.94 % (940483)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 1.83/0.94 % (940483)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 1.83/0.94 % (940478)Instruction limit reached! 1.83/0.94 % (940478)------------------------------ 1.83/0.94 % (940478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/0.94 % (940478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/0.94 % (940478)CaDiCaL version: 2.1.3 1.83/0.94 % (940478)Termination reason: Instruction limit 1.83/0.94 % (940478)Termination phase: shuffling 1.83/0.94 % (940478)Time elapsed: 0.019 s 1.83/0.94 % (940478)Peak memory usage: 10 MB 1.83/0.94 % (940478)Instructions burned: 27 (million) 1.83/0.94 % (940482)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=203355609:cond=on:i=60:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/60Mi) 1.83/0.94 % (940479)Instruction limit reached! 1.83/0.94 % (940479)------------------------------ 1.83/0.94 % (940479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/0.94 % (940479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/1.02 % (940479)CaDiCaL version: 2.1.3 1.83/1.02 % (940479)Termination reason: Instruction limit 1.83/1.02 % (940479)Termination phase: shuffling 1.83/1.02 % (940479)Time elapsed: 0.016 s 1.83/1.02 % (940479)Peak memory usage: 10 MB 1.83/1.02 % (940479)Instructions burned: 23 (million) 1.83/1.02 % (940483)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=3806086765:i=14:add=off:nm=40:rtra=on:rawr=on_1797 on theBenchmark for (1797ds/14Mi) 1.83/1.02 % (940483)Instruction limit reached! 1.83/1.02 % (940483)------------------------------ 1.83/1.02 % (940483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/1.02 % (940483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/1.02 % (940483)CaDiCaL version: 2.1.3 1.83/1.02 % (940483)Termination reason: Instruction limit 1.83/1.02 % (940483)Termination phase: shuffling 1.83/1.02 % (940483)Time elapsed: 0.010 s 1.83/1.02 % (940483)Peak memory usage: 10 MB 1.83/1.02 % (940483)Instructions burned: 14 (million) 1.83/1.02 % (940467)Instruction limit reached! 1.83/1.02 % (940467)------------------------------ 1.83/1.02 % (940467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/1.02 % (940467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/1.02 % (940467)CaDiCaL version: 2.1.3 1.83/1.02 % (940467)Termination reason: Instruction limit 1.83/1.02 % (940467)Termination phase: Saturation 1.83/1.02 % (940467)Time elapsed: 0.089 s 1.83/1.02 % (940467)Peak memory usage: 15 MB 1.83/1.02 % (940467)Instructions burned: 250 (million) 1.83/1.02 % (940486)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 1.83/1.02 % (940486)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=1564092597:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1797 on theBenchmark for (1797ds/8Mi) 1.83/1.02 % (940491)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3134133397:i=23:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/23Mi) 1.83/1.02 % (940489)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=4278564545:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1797 on theBenchmark for (1797ds/31Mi) 1.83/1.02 % (940486)Instruction limit reached! 1.83/1.02 % (940486)------------------------------ 1.83/1.02 % (940486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/1.02 % (940486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/1.02 % (940486)CaDiCaL version: 2.1.3 1.83/1.02 % (940486)Termination reason: Instruction limit 1.83/1.02 % (940486)Termination phase: shuffling 1.83/1.02 % (940486)Time elapsed: 0.006 s 1.83/1.02 % (940486)Peak memory usage: 9 MB 1.83/1.02 % (940486)Instructions burned: 8 (million) 1.83/1.02 % (940491)Instruction limit reached! 1.83/1.02 % (940491)------------------------------ 1.83/1.02 % (940491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/1.02 % (940491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/1.02 % (940491)CaDiCaL version: 2.1.3 1.83/1.02 % (940491)Termination reason: Instruction limit 1.83/1.02 % (940491)Termination phase: shuffling 1.83/1.02 % (940491)Time elapsed: 0.009 s 1.83/1.02 % (940491)Peak memory usage: 10 MB 1.83/1.02 % (940491)Instructions burned: 25 (million) 1.83/1.02 % (940490)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1370797424:i=7:hud=5:bd=preordered:rtra=on:bet=on_1797 on theBenchmark for (1797ds/7Mi) 1.83/1.02 % (940482)Instruction limit reached! 1.83/1.02 % (940482)------------------------------ 1.83/1.02 % (940482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 1.83/1.02 % (940482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 1.83/1.02 % (940482)CaDiCaL version: 2.1.3 1.83/1.02 % (940482)Termination reason: Instruction limit 1.83/1.02 % (940482)Termination phase: Preprocessing 3 1.83/1.02 % (940482)Time elapsed: 0.041 s 1.83/1.02 % (940482)Peak memory usage: 11 MB 1.83/1.02 % (940482)Instructions burned: 60 (million) 1.83/1.02 % (940490)Instruction limit reached! 1.83/1.02 % (940490)------------------------------ 3.61/1.12 % (940490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.61/1.12 % (940490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.61/1.12 % (940490)CaDiCaL version: 2.1.3 3.61/1.12 % (940490)Termination reason: Instruction limit 3.61/1.12 % (940490)Termination phase: shuffling 3.61/1.12 % (940490)Time elapsed: 0.006 s 3.61/1.12 % (940490)Peak memory usage: 10 MB 3.61/1.12 % (940490)Instructions burned: 9 (million) 3.61/1.12 % (940489)Instruction limit reached! 3.61/1.12 % (940489)------------------------------ 3.61/1.12 % (940489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.61/1.12 % (940489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.61/1.12 % (940489)CaDiCaL version: 2.1.3 3.61/1.12 % (940489)Termination reason: Instruction limit 3.61/1.12 % (940489)Termination phase: shuffling 3.61/1.12 % (940489)Time elapsed: 0.022 s 3.61/1.12 % (940489)Peak memory usage: 10 MB 3.61/1.12 % (940489)Instructions burned: 31 (million) 3.61/1.12 % (940496)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1774692787:i=1240:rtra=on:ixr=off_1797 on theBenchmark for (1797ds/1240Mi) 3.61/1.12 % (940495)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2884401426:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1797 on theBenchmark for (1797ds/20Mi) 3.61/1.12 % (940498)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1388584153:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1797 on theBenchmark for (1797ds/143Mi) 3.61/1.12 % (940499)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1797838373:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1797 on theBenchmark for (1797ds/193Mi) 3.61/1.12 % (940495)Instruction limit reached! 3.61/1.12 % (940495)------------------------------ 3.61/1.12 % (940495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.61/1.12 % (940495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.61/1.12 % (940495)CaDiCaL version: 2.1.3 3.61/1.12 % (940495)Termination reason: Instruction limit 3.61/1.12 % (940495)Termination phase: shuffling 3.61/1.12 % (940495)Time elapsed: 0.014 s 3.61/1.12 % (940495)Peak memory usage: 10 MB 3.61/1.12 % (940495)Instructions burned: 20 (million) 3.61/1.12 % (940500)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3164218362:i=42:hud=10:rtra=on_1797 on theBenchmark for (1797ds/42Mi) 3.61/1.12 % (940505)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 3.61/1.12 % (940505)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=969772974:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1796 on theBenchmark for (1796ds/7Mi) 3.61/1.12 % (940500)Instruction limit reached! 3.61/1.12 % (940500)------------------------------ 3.61/1.12 % (940500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.61/1.12 % (940500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.61/1.12 % (940500)CaDiCaL version: 2.1.3 3.61/1.12 % (940500)Termination reason: Instruction limit 3.61/1.12 % (940500)Termination phase: shuffling 3.61/1.12 % (940500)Time elapsed: 0.029 s 3.61/1.12 % (940500)Peak memory usage: 11 MB 3.61/1.12 % (940500)Instructions burned: 43 (million) 3.61/1.12 % (940505)Instruction limit reached! 3.61/1.12 % (940505)------------------------------ 3.61/1.12 % (940505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.61/1.12 % (940505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.61/1.12 % (940505)CaDiCaL version: 2.1.3 3.61/1.12 % (940505)Termination reason: Instruction limit 3.61/1.12 % (940505)Termination phase: shuffling 3.61/1.12 % (940505)Time elapsed: 0.005 s 3.61/1.12 % (940505)Peak memory usage: 9 MB 3.61/1.12 % (940505)Instructions burned: 7 (million) 3.61/1.12 % (940508)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3018340382:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1796 on theBenchmark for (1796ds/181Mi) 3.61/1.12 % (940509)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=570726133:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1796 on theBenchmark for (1796ds/169Mi) 3.61/1.12 % (940470)Instruction limit reached! 4.37/1.25 % (940470)------------------------------ 4.37/1.25 % (940470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.37/1.25 % (940470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.37/1.25 % (940470)CaDiCaL version: 2.1.3 4.37/1.25 % (940470)Termination reason: Instruction limit 4.37/1.25 % (940470)Termination phase: Saturation 4.37/1.25 % (940470)Time elapsed: 0.225 s 4.37/1.25 % (940470)Peak memory usage: 16 MB 4.37/1.25 % (940470)Instructions burned: 328 (million) 4.37/1.25 % (940498)Instruction limit reached! 4.37/1.25 % (940498)------------------------------ 4.37/1.25 % (940498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.37/1.25 % (940498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.37/1.25 % (940498)CaDiCaL version: 2.1.3 4.37/1.25 % (940498)Termination reason: Instruction limit 4.37/1.25 % (940498)Termination phase: Function definition elimination 4.37/1.25 % (940498)Time elapsed: 0.096 s 4.37/1.25 % (940498)Peak memory usage: 13 MB 4.37/1.25 % (940498)Instructions burned: 144 (million) 4.37/1.25 % (940512)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 4.37/1.25 % (940512)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1567820704:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1795 on theBenchmark for (1795ds/6Mi) 4.37/1.25 % (940513)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3152609633:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1795 on theBenchmark for (1795ds/22Mi) 4.37/1.25 % (940512)Instruction limit reached! 4.37/1.25 % (940512)------------------------------ 4.37/1.25 % (940512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.37/1.25 % (940512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.37/1.25 % (940512)CaDiCaL version: 2.1.3 4.37/1.25 % (940512)Termination reason: Instruction limit 4.37/1.25 % (940512)Termination phase: shuffling 4.37/1.25 % (940512)Time elapsed: 0.005 s 4.37/1.25 % (940512)Peak memory usage: 9 MB 4.37/1.25 % (940512)Instructions burned: 7 (million) 4.37/1.25 % (940499)Instruction limit reached! 4.37/1.25 % (940499)------------------------------ 4.37/1.25 % (940499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.37/1.25 % (940499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.37/1.25 % (940499)CaDiCaL version: 2.1.3 4.37/1.25 % (940499)Termination reason: Instruction limit 4.37/1.25 % (940499)Termination phase: Property scanning 4.37/1.25 % (940499)Time elapsed: 0.126 s 4.37/1.25 % (940499)Peak memory usage: 13 MB 4.37/1.25 % (940499)Instructions burned: 193 (million) 4.37/1.25 % (940513)Instruction limit reached! 4.37/1.25 % (940513)------------------------------ 4.37/1.25 % (940513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.37/1.25 % (940513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.37/1.25 % (940513)CaDiCaL version: 2.1.3 4.37/1.25 % (940513)Termination reason: Instruction limit 4.37/1.25 % (940513)Termination phase: shuffling 4.37/1.25 % (940513)Time elapsed: 0.015 s 4.37/1.25 % (940513)Peak memory usage: 10 MB 4.37/1.25 % (940513)Instructions burned: 22 (million) 4.37/1.25 % (940516)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3035286791:i=19:add=on:rtra=on_1795 on theBenchmark for (1795ds/19Mi) 4.37/1.25 % (940517)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3424038526:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1795 on theBenchmark for (1795ds/316Mi) 4.37/1.25 % (940518)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3673465465:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1795 on theBenchmark for (1795ds/853Mi) 4.37/1.25 % (940516)Instruction limit reached! 4.37/1.25 % (940516)------------------------------ 4.37/1.25 % (940516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.37/1.25 % (940516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.37/1.25 % (940516)CaDiCaL version: 2.1.3 4.90/1.39 % (940516)Termination reason: Instruction limit 4.90/1.39 % (940516)Termination phase: shuffling 4.90/1.39 % (940516)Time elapsed: 0.014 s 4.90/1.39 % (940516)Peak memory usage: 10 MB 4.90/1.39 % (940516)Instructions burned: 19 (million) 4.90/1.39 % (940509)Instruction limit reached! 4.90/1.39 % (940509)------------------------------ 4.90/1.39 % (940509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.90/1.39 % (940509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.90/1.39 % (940509)CaDiCaL version: 2.1.3 4.90/1.39 % (940509)Termination reason: Instruction limit 4.90/1.39 % (940509)Termination phase: Property scanning 4.90/1.39 % (940509)Time elapsed: 0.112 s 4.90/1.39 % (940509)Peak memory usage: 13 MB 4.90/1.39 % (940509)Instructions burned: 170 (million) 4.90/1.39 % (940508)Instruction limit reached! 4.90/1.39 % (940508)------------------------------ 4.90/1.39 % (940508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.90/1.39 % (940508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.90/1.39 % (940508)CaDiCaL version: 2.1.3 4.90/1.39 % (940508)Termination reason: Instruction limit 4.90/1.39 % (940508)Termination phase: Saturation 4.90/1.39 % (940508)Time elapsed: 0.121 s 4.90/1.39 % (940508)Peak memory usage: 15 MB 4.90/1.39 % (940508)Instructions burned: 181 (million) 4.90/1.39 % (940522)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2294483965:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1795 on theBenchmark for (1795ds/45Mi) 4.90/1.39 % (940523)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2794519916:i=480:rtra=on_1795 on theBenchmark for (1795ds/480Mi) 4.90/1.39 % (940524)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1421665654:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1794 on theBenchmark for (1794ds/21Mi) 4.90/1.39 % (940522)Instruction limit reached! 4.90/1.39 % (940522)------------------------------ 4.90/1.39 % (940522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.90/1.39 % (940522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.90/1.39 % (940522)CaDiCaL version: 2.1.3 4.90/1.39 % (940522)Termination reason: Instruction limit 4.90/1.39 % (940522)Termination phase: SInE selection 4.90/1.39 % (940522)Time elapsed: 0.029 s 4.90/1.39 % (940522)Peak memory usage: 10 MB 4.90/1.39 % (940522)Instructions burned: 45 (million) 4.90/1.39 % (940439)Instruction limit reached! 4.90/1.39 % (940439)------------------------------ 4.90/1.39 % (940439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.90/1.39 % (940439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.90/1.39 % (940439)CaDiCaL version: 2.1.3 4.90/1.39 % (940439)Termination reason: Instruction limit 4.90/1.39 % (940439)Termination phase: Saturation 4.90/1.39 % (940439)Time elapsed: 0.486 s 4.90/1.39 % (940439)Peak memory usage: 19 MB 4.90/1.39 % (940439)Instructions burned: 635 (million) 4.90/1.39 % (940524)Instruction limit reached! 4.90/1.39 % (940524)------------------------------ 4.90/1.39 % (940524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.90/1.39 % (940524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.90/1.39 % (940524)CaDiCaL version: 2.1.3 4.90/1.39 % (940524)Termination reason: Instruction limit 4.90/1.39 % (940524)Termination phase: shuffling 4.90/1.39 % (940524)Time elapsed: 0.015 s 4.90/1.39 % (940524)Peak memory usage: 10 MB 4.90/1.39 % (940524)Instructions burned: 22 (million) 4.90/1.39 % (940528)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 4.90/1.39 % (940528)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1992081586:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1794 on theBenchmark for (1794ds/200Mi) 4.90/1.39 % (940529)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1127127738:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1794 on theBenchmark for (1794ds/13Mi) 4.90/1.39 % (940530)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1315557337:i=66:s2at=3:nm=2:rtra=on:rawr=on_1794 on theBenchmark for (1794ds/66Mi) 6.16/1.57 % (940529)Instruction limit reached! 6.16/1.57 % (940529)------------------------------ 6.16/1.57 % (940529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.16/1.57 % (940529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.16/1.57 % (940529)CaDiCaL version: 2.1.3 6.16/1.57 % (940529)Termination reason: Instruction limit 6.16/1.57 % (940529)Termination phase: shuffling 6.16/1.57 % (940529)Time elapsed: 0.009 s 6.16/1.57 % (940529)Peak memory usage: 10 MB 6.16/1.57 % (940529)Instructions burned: 13 (million) 6.16/1.57 % (940534)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3650575373:i=51:fsr=off:rtra=on_1794 on theBenchmark for (1794ds/51Mi) 6.16/1.57 % (940530)Instruction limit reached! 6.16/1.57 % (940530)------------------------------ 6.16/1.57 % (940530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.16/1.57 % (940530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.16/1.57 % (940530)CaDiCaL version: 2.1.3 6.16/1.57 % (940530)Termination reason: Instruction limit 6.16/1.57 % (940530)Termination phase: SInE selection 6.16/1.57 % (940530)Time elapsed: 0.043 s 6.16/1.57 % (940530)Peak memory usage: 11 MB 6.16/1.57 % (940530)Instructions burned: 67 (million) 6.16/1.57 % (940534)Instruction limit reached! 6.16/1.57 % (940534)------------------------------ 6.16/1.57 % (940534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.16/1.57 % (940534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.16/1.57 % (940534)CaDiCaL version: 2.1.3 6.16/1.57 % (940534)Termination reason: Instruction limit 6.16/1.57 % (940534)Termination phase: Preprocessing 3 6.16/1.57 % (940534)Time elapsed: 0.034 s 6.16/1.57 % (940534)Peak memory usage: 11 MB 6.16/1.57 % (940534)Instructions burned: 51 (million) 6.16/1.57 % (940536)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3855396531:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1793 on theBenchmark for (1793ds/31Mi) 6.16/1.57 % (940536)Instruction limit reached! 6.16/1.57 % (940536)------------------------------ 6.16/1.57 % (940536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.16/1.57 % (940536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.16/1.57 % (940536)CaDiCaL version: 2.1.3 6.16/1.57 % (940536)Termination reason: Instruction limit 6.16/1.57 % (940536)Termination phase: Property scanning 6.16/1.57 % (940536)Time elapsed: 0.022 s 6.16/1.57 % (940536)Peak memory usage: 10 MB 6.16/1.57 % (940536)Instructions burned: 32 (million) 6.16/1.57 % (940538)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4041195491:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1793 on theBenchmark for (1793ds/137Mi) 6.16/1.57 % (940496)Instruction limit reached! 6.16/1.57 % (940496)------------------------------ 6.16/1.57 % (940496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.16/1.57 % (940496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.16/1.57 % (940496)CaDiCaL version: 2.1.3 6.16/1.57 % (940496)Termination reason: Instruction limit 6.16/1.57 % (940496)Termination phase: Saturation 6.16/1.57 % (940496)Time elapsed: 0.391 s 6.16/1.57 % (940496)Peak memory usage: 13 MB 6.16/1.57 % (940496)Instructions burned: 1241 (million) 6.16/1.57 % (940541)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3709773242:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1793 on theBenchmark for (1793ds/67Mi) 6.16/1.57 % (940539)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2271174069:cond=on:i=34:hud=10:nm=10:rtra=on_1793 on theBenchmark for (1793ds/34Mi) 6.16/1.57 % (940528)Instruction limit reached! 6.16/1.57 % (940528)------------------------------ 6.16/1.57 % (940528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.16/1.57 % (940528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.16/1.57 % (940528)CaDiCaL version: 2.1.3 6.16/1.57 % (940528)Termination reason: Instruction limit 6.16/1.57 % (940528)Termination phase: Saturation 6.16/1.57 % (940528)Time elapsed: 0.130 s 6.16/1.57 % (940528)Peak memory usage: 14 MB 6.16/1.57 % (940528)Instructions burned: 201 (million) 6.16/1.57 % (940517)Instruction limit reached! 6.16/1.57 % (940517)------------------------------ 7.04/1.73 % (940517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.04/1.73 % (940517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.04/1.73 % (940517)CaDiCaL version: 2.1.3 7.04/1.73 % (940517)Termination reason: Instruction limit 7.04/1.73 % (940517)Termination phase: Saturation 7.04/1.73 % (940517)Time elapsed: 0.236 s 7.04/1.73 % (940517)Peak memory usage: 15 MB 7.04/1.73 % (940517)Instructions burned: 317 (million) 7.04/1.73 % (940539)Instruction limit reached! 7.04/1.73 % (940539)------------------------------ 7.04/1.73 % (940539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.04/1.73 % (940539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.04/1.73 % (940539)CaDiCaL version: 2.1.3 7.04/1.73 % (940539)Termination reason: Instruction limit 7.04/1.73 % (940539)Termination phase: Property scanning 7.04/1.73 % (940539)Time elapsed: 0.024 s 7.04/1.73 % (940539)Peak memory usage: 10 MB 7.04/1.73 % (940539)Instructions burned: 35 (million) 7.04/1.73 % (940541)Instruction limit reached! 7.04/1.73 % (940541)------------------------------ 7.04/1.73 % (940541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.04/1.73 % (940541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.04/1.73 % (940541)CaDiCaL version: 2.1.3 7.04/1.73 % (940541)Termination reason: Instruction limit 7.04/1.73 % (940541)Termination phase: Preprocessing 3 7.04/1.73 % (940541)Time elapsed: 0.025 s 7.04/1.73 % (940541)Peak memory usage: 12 MB 7.04/1.73 % (940541)Instructions burned: 68 (million) 7.04/1.73 % (940544)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 7.04/1.73 % (940544)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3375198097:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1792 on theBenchmark for (1792ds/180Mi) 7.04/1.73 % (940545)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3762655781:st=2:i=246:sd=3:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/246Mi) 7.04/1.73 % (940546)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2030133941:cond=on:i=96:bd=all:rtra=on_1792 on theBenchmark for (1792ds/96Mi) 7.04/1.73 % (940547)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=917789665:i=427:sd=1:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/427Mi) 7.04/1.73 % (940538)Instruction limit reached! 7.04/1.73 % (940538)------------------------------ 7.04/1.73 % (940538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.04/1.73 % (940538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.04/1.73 % (940538)CaDiCaL version: 2.1.3 7.04/1.73 % (940538)Termination reason: Instruction limit 7.04/1.73 % (940538)Termination phase: Function definition elimination 7.04/1.73 % (940538)Time elapsed: 0.092 s 7.04/1.73 % (940538)Peak memory usage: 13 MB 7.04/1.73 % (940538)Instructions burned: 138 (million) 7.04/1.73 % (940546)Instruction limit reached! 7.04/1.73 % (940546)------------------------------ 7.04/1.73 % (940546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.04/1.73 % (940546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.04/1.73 % (940546)CaDiCaL version: 2.1.3 7.04/1.73 % (940546)Termination reason: Instruction limit 7.04/1.73 % (940546)Termination phase: Property scanning 7.04/1.73 % (940546)Time elapsed: 0.036 s 7.04/1.73 % (940546)Peak memory usage: 12 MB 7.04/1.73 % (940546)Instructions burned: 99 (million) 7.04/1.73 % (940553)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2757582197:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/515Mi) 7.04/1.73 % (940552)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1171355124:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1792 on theBenchmark for (1792ds/874Mi) 7.04/1.73 % (940544)Instruction limit reached! 7.04/1.73 % (940544)------------------------------ 7.04/1.73 % (940544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.04/1.73 % (940544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.04/1.73 % (940544)CaDiCaL version: 2.1.3 7.04/1.73 % (940544)Termination reason: Instruction limit 7.04/1.73 % (940544)Termination phase: Saturation 7.04/1.73 % (940544)Time elapsed: 0.111 s 7.04/1.73 % (940544)Peak memory usage: 12 MB 7.04/1.73 % (940544)Instructions burned: 181 (million) 7.19/1.88 % (940523)Instruction limit reached! 7.19/1.88 % (940523)------------------------------ 7.19/1.88 % (940523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.19/1.88 % (940523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.19/1.88 % (940523)CaDiCaL version: 2.1.3 7.19/1.88 % (940523)Termination reason: Instruction limit 7.19/1.88 % (940523)Termination phase: Saturation 7.19/1.88 % (940523)Time elapsed: 0.341 s 7.19/1.88 % (940523)Peak memory usage: 17 MB 7.19/1.88 % (940523)Instructions burned: 480 (million) 7.19/1.88 % (940556)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2592598126:st=1.5:i=130:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/130Mi) 7.19/1.88 % (940557)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2340858262:i=44:ep=R:rtra=on:ntd=on_1791 on theBenchmark for (1791ds/44Mi) 7.19/1.88 % (940545)Instruction limit reached! 7.19/1.88 % (940545)------------------------------ 7.19/1.88 % (940545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.19/1.88 % (940545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.19/1.88 % (940545)CaDiCaL version: 2.1.3 7.19/1.88 % (940545)Termination reason: Instruction limit 7.19/1.88 % (940545)Termination phase: Saturation 7.19/1.88 % (940545)Time elapsed: 0.164 s 7.19/1.88 % (940545)Peak memory usage: 15 MB 7.19/1.88 % (940545)Instructions burned: 246 (million) 7.19/1.88 % (940557)Instruction limit reached! 7.19/1.88 % (940557)------------------------------ 7.19/1.88 % (940557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.19/1.88 % (940557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.19/1.88 % (940557)CaDiCaL version: 2.1.3 7.19/1.88 % (940557)Termination reason: Instruction limit 7.19/1.88 % (940557)Termination phase: Property scanning 7.19/1.88 % (940557)Time elapsed: 0.030 s 7.19/1.88 % (940557)Peak memory usage: 10 MB 7.19/1.88 % (940557)Instructions burned: 44 (million) 7.19/1.88 % (940560)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2968804792:s2a=on:i=571:nm=16:rtra=on_1790 on theBenchmark for (1790ds/571Mi) 7.19/1.88 % (940556)Refutation not found, incomplete strategy 7.19/1.88 % (940556)------------------------------ 7.19/1.88 % (940556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.19/1.88 % (940556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.19/1.88 % (940556)CaDiCaL version: 2.1.3 7.19/1.88 % (940556)Termination reason: Refutation not found, incomplete strategy 7.19/1.88 % (940556)Time elapsed: 0.057 s 7.19/1.88 % (940556)Peak memory usage: 13 MB 7.19/1.88 % (940556)Instructions burned: 84 (million) 7.19/1.88 % (940556)------------------------------ 7.19/1.88 % (940556)------------------------------ 7.19/1.88 % (940561)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1476970746:i=450:rtra=on:ixr=off:ntd=on_1790 on theBenchmark for (1790ds/450Mi) 7.19/1.88 % (940563)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1471297663:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1790 on theBenchmark for (1790ds/95Mi) 7.19/1.88 % (940553)Instruction limit reached! 7.19/1.88 % (940553)------------------------------ 7.19/1.88 % (940553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.19/1.88 % (940553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.19/1.88 % (940553)CaDiCaL version: 2.1.3 7.19/1.88 % (940553)Termination reason: Instruction limit 7.19/1.88 % (940553)Termination phase: Saturation 7.19/1.88 % (940553)Time elapsed: 0.192 s 7.19/1.88 % (940553)Peak memory usage: 18 MB 7.19/1.88 % (940553)Instructions burned: 516 (million) 7.19/1.88 % (940566)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3736193313:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1790 on theBenchmark for (1790ds/65Mi) 7.19/1.88 % (940566)Instruction limit reached! 7.19/1.88 % (940566)------------------------------ 7.19/1.88 % (940566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 7.19/1.88 % (940566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 7.19/1.88 % (940566)CaDiCaL version: 2.1.3 7.19/1.88 % (940566)Termination reason: Instruction limit 8.61/2.02 % (940566)Termination phase: Property scanning 8.61/2.02 % (940566)Time elapsed: 0.022 s 8.61/2.02 % (940566)Peak memory usage: 11 MB 8.61/2.02 % (940566)Instructions burned: 66 (million) 8.61/2.02 % (940563)Instruction limit reached! 8.61/2.02 % (940563)------------------------------ 8.61/2.02 % (940563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.61/2.02 % (940563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.61/2.02 % (940563)CaDiCaL version: 2.1.3 8.61/2.02 % (940563)Termination reason: Instruction limit 8.61/2.02 % (940563)Termination phase: Property scanning 8.61/2.02 % (940563)Time elapsed: 0.066 s 8.61/2.02 % (940563)Peak memory usage: 12 MB 8.61/2.02 % (940563)Instructions burned: 96 (million) 8.61/2.02 % (940547)Instruction limit reached! 8.61/2.02 % (940547)------------------------------ 8.61/2.02 % (940547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.61/2.02 % (940547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.61/2.02 % (940547)CaDiCaL version: 2.1.3 8.61/2.02 % (940547)Termination reason: Instruction limit 8.61/2.02 % (940547)Termination phase: Saturation 8.61/2.02 % (940547)Time elapsed: 0.284 s 8.61/2.02 % (940547)Peak memory usage: 14 MB 8.61/2.02 % (940547)Instructions burned: 428 (million) 8.61/2.02 % (940568)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1946588205:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1789 on theBenchmark for (1789ds/105Mi) 8.61/2.02 % (940569)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=1062614316:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1789 on theBenchmark for (1789ds/5755Mi) 8.61/2.02 % (940570)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2834809608:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1789 on theBenchmark for (1789ds/375Mi) 8.61/2.02 % (940568)Instruction limit reached! 8.61/2.02 % (940568)------------------------------ 8.61/2.02 % (940568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.61/2.02 % (940568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.61/2.02 % (940568)CaDiCaL version: 2.1.3 8.61/2.02 % (940568)Termination reason: Instruction limit 8.61/2.02 % (940568)Termination phase: Saturation 8.61/2.02 % (940568)Time elapsed: 0.035 s 8.61/2.02 % (940568)Peak memory usage: 12 MB 8.61/2.02 % (940568)Instructions burned: 105 (million) 8.61/2.02 % (940518)Instruction limit reached! 8.61/2.02 % (940518)------------------------------ 8.61/2.02 % (940518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.61/2.02 % (940518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.61/2.02 % (940518)CaDiCaL version: 2.1.3 8.61/2.02 % (940518)Termination reason: Instruction limit 8.61/2.02 % (940518)Termination phase: Saturation 8.61/2.02 % (940518)Time elapsed: 0.619 s 8.61/2.02 % (940518)Peak memory usage: 19 MB 8.61/2.02 % (940518)Instructions burned: 854 (million) 8.61/2.02 % (940574)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=672057824:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1789 on theBenchmark for (1789ds/495Mi) 8.61/2.02 % (940576)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=180495430:cond=on:i=34:hud=10:nm=10:rtra=on_1788 on theBenchmark for (1788ds/34Mi) 8.61/2.02 % (940576)Instruction limit reached! 8.61/2.02 % (940576)------------------------------ 8.61/2.02 % (940576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.61/2.02 % (940576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.61/2.02 % (940576)CaDiCaL version: 2.1.3 8.61/2.02 % (940576)Termination reason: Instruction limit 8.61/2.02 % (940576)Termination phase: Property scanning 8.61/2.02 % (940576)Time elapsed: 0.024 s 8.61/2.02 % (940576)Peak memory usage: 10 MB 8.61/2.02 % (940576)Instructions burned: 36 (million) 8.61/2.02 % (940578)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1607044111:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1788 on theBenchmark for (1788ds/91Mi) 11.39/2.19 % (940578)Instruction limit reached! 11.39/2.19 % (940578)------------------------------ 11.39/2.19 % (940578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940578)CaDiCaL version: 2.1.3 11.39/2.19 % (940578)Termination reason: Instruction limit 11.39/2.19 % (940578)Termination phase: Preprocessing 3 11.39/2.19 % (940578)Time elapsed: 0.063 s 11.39/2.19 % (940578)Peak memory usage: 13 MB 11.39/2.19 % (940578)Instructions burned: 92 (million) 11.39/2.19 % (940561)Instruction limit reached! 11.39/2.19 % (940561)------------------------------ 11.39/2.19 % (940561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940561)CaDiCaL version: 2.1.3 11.39/2.19 % (940561)Termination reason: Instruction limit 11.39/2.19 % (940561)Termination phase: Saturation 11.39/2.19 % (940561)Time elapsed: 0.317 s 11.39/2.19 % (940561)Peak memory usage: 17 MB 11.39/2.19 % (940561)Instructions burned: 451 (million) 11.39/2.19 % (940580)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=154375770:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1787 on theBenchmark for (1787ds/66Mi) 11.39/2.19 % (940574)Instruction limit reached! 11.39/2.19 % (940574)------------------------------ 11.39/2.19 % (940574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940574)CaDiCaL version: 2.1.3 11.39/2.19 % (940574)Termination reason: Instruction limit 11.39/2.19 % (940574)Termination phase: Saturation 11.39/2.19 % (940574)Time elapsed: 0.184 s 11.39/2.19 % (940574)Peak memory usage: 16 MB 11.39/2.19 % (940574)Instructions burned: 497 (million) 11.39/2.19 % (940583)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2210350260:i=338:bd=all:ins=4:rtra=on_1787 on theBenchmark for (1787ds/338Mi) 11.39/2.19 % (940581)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1930039930:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1787 on theBenchmark for (1787ds/22Mi) 11.39/2.19 % (940581)Instruction limit reached! 11.39/2.19 % (940581)------------------------------ 11.39/2.19 % (940581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940581)CaDiCaL version: 2.1.3 11.39/2.19 % (940581)Termination reason: Instruction limit 11.39/2.19 % (940581)Termination phase: shuffling 11.39/2.19 % (940581)Time elapsed: 0.015 s 11.39/2.19 % (940581)Peak memory usage: 10 MB 11.39/2.19 % (940581)Instructions burned: 22 (million) 11.39/2.19 % (940570)Instruction limit reached! 11.39/2.19 % (940570)------------------------------ 11.39/2.19 % (940570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940570)CaDiCaL version: 2.1.3 11.39/2.19 % (940570)Termination reason: Instruction limit 11.39/2.19 % (940570)Termination phase: Saturation 11.39/2.19 % (940570)Time elapsed: 0.257 s 11.39/2.19 % (940570)Peak memory usage: 16 MB 11.39/2.19 % (940570)Instructions burned: 375 (million) 11.39/2.19 % (940580)Instruction limit reached! 11.39/2.19 % (940580)------------------------------ 11.39/2.19 % (940580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940580)CaDiCaL version: 2.1.3 11.39/2.19 % (940580)Termination reason: Instruction limit 11.39/2.19 % (940580)Termination phase: Saturation 11.39/2.19 % (940580)Time elapsed: 0.047 s 11.39/2.19 % (940580)Peak memory usage: 13 MB 11.39/2.19 % (940580)Instructions burned: 66 (million) 11.39/2.19 % (940560)Instruction limit reached! 11.39/2.19 % (940560)------------------------------ 11.39/2.19 % (940560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.39/2.19 % (940560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.39/2.19 % (940560)CaDiCaL version: 2.1.3 11.39/2.19 % (940560)Termination reason: Instruction limit 11.39/2.19 % (940560)Termination phase: Saturation 11.39/2.19 % (940560)Time elapsed: 0.399 s 12.24/2.44 % (940560)Peak memory usage: 18 MB 12.24/2.44 % (940560)Instructions burned: 571 (million) 12.24/2.44 % (940586)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2368081729:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1786 on theBenchmark for (1786ds/28Mi) 12.24/2.44 % (940587)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 12.24/2.44 % (940587)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=4125727769:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1786 on theBenchmark for (1786ds/137Mi) 12.24/2.44 % (940588)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=3244841493:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1786 on theBenchmark for (1786ds/340Mi) 12.24/2.44 % (940589)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=337690077:i=227:sd=1:bd=all:rtra=on:ss=axioms_1786 on theBenchmark for (1786ds/227Mi) 12.24/2.44 % (940586)Instruction limit reached! 12.24/2.44 % (940586)------------------------------ 12.24/2.44 % (940586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.24/2.44 % (940586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.24/2.44 % (940586)CaDiCaL version: 2.1.3 12.24/2.44 % (940586)Termination reason: Instruction limit 12.24/2.44 % (940586)Termination phase: Property scanning 12.24/2.44 % (940586)Time elapsed: 0.019 s 12.24/2.44 % (940586)Peak memory usage: 10 MB 12.24/2.44 % (940586)Instructions burned: 28 (million) 12.24/2.44 % (940594)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 12.24/2.44 % (940594)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3382245448:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1786 on theBenchmark for (1786ds/373Mi) 12.24/2.44 % (940583)Instruction limit reached! 12.24/2.44 % (940583)------------------------------ 12.24/2.44 % (940583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.24/2.44 % (940583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.24/2.44 % (940583)CaDiCaL version: 2.1.3 12.24/2.44 % (940583)Termination reason: Instruction limit 12.24/2.44 % (940583)Termination phase: Saturation 12.24/2.44 % (940583)Time elapsed: 0.114 s 12.24/2.44 % (940583)Peak memory usage: 18 MB 12.24/2.44 % (940583)Instructions burned: 338 (million) 12.24/2.44 % (940552)Instruction limit reached! 12.24/2.44 % (940552)------------------------------ 12.24/2.44 % (940552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.24/2.44 % (940552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.24/2.44 % (940552)CaDiCaL version: 2.1.3 12.24/2.44 % (940552)Termination reason: Instruction limit 12.24/2.44 % (940552)Termination phase: Saturation 12.24/2.44 % (940552)Time elapsed: 0.622 s 12.24/2.44 % (940552)Peak memory usage: 18 MB 12.24/2.44 % (940552)Instructions burned: 875 (million) 12.24/2.44 % (940596)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3204023952:i=116:ep=RSTC:rtra=on:ntd=on_1785 on theBenchmark for (1785ds/116Mi) 12.24/2.44 % (940587)Instruction limit reached! 12.24/2.44 % (940587)------------------------------ 12.24/2.44 % (940587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.24/2.44 % (940587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.24/2.44 % (940587)CaDiCaL version: 2.1.3 12.24/2.44 % (940587)Termination reason: Instruction limit 12.24/2.44 % (940587)Termination phase: Saturation 12.24/2.44 % (940587)Time elapsed: 0.086 s 12.24/2.44 % (940587)Peak memory usage: 12 MB 12.24/2.44 % (940587)Instructions burned: 138 (million) 12.24/2.44 % (940597)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=790554476:i=575:rtra=on_1785 on theBenchmark for (1785ds/575Mi) 12.24/2.44 % (940596)Instruction limit reached! 12.24/2.44 % (940596)------------------------------ 12.24/2.44 % (940596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 12.24/2.44 % (940596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 12.24/2.44 % (940596)CaDiCaL version: 2.1.3 12.24/2.44 % (940596)Termination reason: Instruction limit 12.24/2.44 % (940596)Termination phase: Property scanning 13.66/2.77 % (940596)Time elapsed: 0.042 s 13.66/2.77 % (940596)Peak memory usage: 13 MB 13.66/2.77 % (940596)Instructions burned: 117 (million) 13.66/2.77 % (940599)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=657984149:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1785 on theBenchmark for (1785ds/270Mi) 13.66/2.77 % (940589)Instruction limit reached! 13.66/2.77 % (940589)------------------------------ 13.66/2.77 % (940589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.66/2.77 % (940589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.66/2.77 % (940589)CaDiCaL version: 2.1.3 13.66/2.77 % (940589)Termination reason: Instruction limit 13.66/2.77 % (940589)Termination phase: Saturation 13.66/2.77 % (940589)Time elapsed: 0.157 s 13.66/2.77 % (940589)Peak memory usage: 13 MB 13.66/2.77 % (940589)Instructions burned: 228 (million) 13.66/2.77 % (940601)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=1743444952:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1785 on theBenchmark for (1785ds/9840Mi) 13.66/2.77 % (940603)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2056007767:i=421:rtra=on:ss=axioms_1784 on theBenchmark for (1784ds/421Mi) 13.66/2.77 % (940588)Instruction limit reached! 13.66/2.77 % (940588)------------------------------ 13.66/2.77 % (940588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.66/2.77 % (940588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.66/2.77 % (940588)CaDiCaL version: 2.1.3 13.66/2.77 % (940588)Termination reason: Instruction limit 13.66/2.77 % (940588)Termination phase: Saturation 13.66/2.77 % (940588)Time elapsed: 0.219 s 13.66/2.77 % (940588)Peak memory usage: 17 MB 13.66/2.77 % (940588)Instructions burned: 340 (million) 13.66/2.77 % (940603)Refutation not found, incomplete strategy 13.66/2.77 % (940603)------------------------------ 13.66/2.77 % (940603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.66/2.77 % (940603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.66/2.77 % (940603)CaDiCaL version: 2.1.3 13.66/2.77 % (940603)Termination reason: Refutation not found, incomplete strategy 13.66/2.77 % (940603)Time elapsed: 0.037 s 13.66/2.77 % (940603)Peak memory usage: 13 MB 13.66/2.77 % (940603)Instructions burned: 50 (million) 13.66/2.77 % (940603)------------------------------ 13.66/2.77 % (940603)------------------------------ 13.66/2.77 % (940606)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 13.66/2.77 % (940606)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=935206311:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1784 on theBenchmark for (1784ds/270Mi) 13.66/2.77 % (940607)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3912046321:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1784 on theBenchmark for (1784ds/31Mi) 13.66/2.77 % (940594)Instruction limit reached! 13.66/2.77 % (940594)------------------------------ 13.66/2.77 % (940594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.66/2.77 % (940594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.66/2.77 % (940594)CaDiCaL version: 2.1.3 13.66/2.77 % (940594)Termination reason: Instruction limit 13.66/2.77 % (940594)Termination phase: Saturation 13.66/2.77 % (940594)Time elapsed: 0.221 s 13.66/2.77 % (940594)Peak memory usage: 15 MB 13.66/2.77 % (940594)Instructions burned: 374 (million) 13.66/2.77 % (940607)Instruction limit reached! 13.66/2.77 % (940607)------------------------------ 13.66/2.77 % (940607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.66/2.77 % (940599)Instruction limit reached! 13.66/2.77 % (940599)------------------------------ 13.66/2.77 % (940599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.66/2.77 % (940599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.66/2.77 % (940599)CaDiCaL version: 2.1.3 13.66/2.77 % (940599)Termination reason: Instruction limit 14.16/3.02 % (940599)Termination phase: Saturation 14.16/3.02 % (940599)Time elapsed: 0.167 s 14.16/3.02 % (940599)Peak memory usage: 12 MB 14.16/3.02 % (940599)Instructions burned: 271 (million) 14.16/3.02 % (940607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.16/3.02 % (940607)CaDiCaL version: 2.1.3 14.16/3.02 % (940607)Termination reason: Instruction limit 14.16/3.02 % (940607)Termination phase: Property scanning 14.16/3.02 % (940607)Time elapsed: 0.024 s 14.16/3.02 % (940607)Peak memory usage: 10 MB 14.16/3.02 % (940607)Instructions burned: 33 (million) 14.16/3.02 % (940610)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 14.16/3.02 % (940610)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 14.16/3.02 % (940610)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=663687852:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1783 on theBenchmark for (1783ds/1440Mi) 14.16/3.02 % (940611)dis+10_2_sil=128000:si=on:random_seed=2555435456:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1783 on theBenchmark for (1783ds/339Mi) 14.16/3.02 % (940612)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=688952702:i=111:add=on:fgj=on:rtra=on:fdi=1024_1783 on theBenchmark for (1783ds/111Mi) 14.16/3.02 % (940612)Instruction limit reached! 14.16/3.02 % (940612)------------------------------ 14.16/3.02 % (940612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.16/3.02 % (940612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.16/3.02 % (940612)CaDiCaL version: 2.1.3 14.16/3.02 % (940612)Termination reason: Instruction limit 14.16/3.02 % (940612)Termination phase: Property scanning 14.16/3.02 % (940612)Time elapsed: 0.078 s 14.16/3.02 % (940612)Peak memory usage: 13 MB 14.16/3.02 % (940612)Instructions burned: 112 (million) 14.16/3.02 % (940616)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=130595893:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1782 on theBenchmark for (1782ds/122Mi) 14.16/3.02 % (940606)Instruction limit reached! 14.16/3.02 % (940606)------------------------------ 14.16/3.02 % (940606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.16/3.02 % (940606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.16/3.02 % (940606)CaDiCaL version: 2.1.3 14.16/3.02 % (940606)Termination reason: Instruction limit 14.16/3.02 % (940606)Termination phase: Saturation 14.16/3.02 % (940606)Time elapsed: 0.181 s 14.16/3.02 % (940606)Peak memory usage: 15 MB 14.16/3.02 % (940606)Instructions burned: 270 (million) 14.16/3.02 % (940618)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=3556161205:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1782 on theBenchmark for (1782ds/136Mi) 14.16/3.02 % (940616)Instruction limit reached! 14.16/3.02 % (940616)------------------------------ 14.16/3.02 % (940616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.16/3.02 % (940616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.16/3.02 % (940616)CaDiCaL version: 2.1.3 14.16/3.02 % (940616)Termination reason: Instruction limit 14.16/3.02 % (940616)Termination phase: Property scanning 14.16/3.02 % (940616)Time elapsed: 0.083 s 14.16/3.02 % (940616)Peak memory usage: 13 MB 14.16/3.02 % (940616)Instructions burned: 123 (million) 14.16/3.02 % (940597)Instruction limit reached! 14.16/3.02 % (940597)------------------------------ 14.16/3.02 % (940597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 14.16/3.02 % (940597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 14.16/3.02 % (940597)CaDiCaL version: 2.1.3 14.16/3.02 % (940597)Termination reason: Instruction limit 14.16/3.02 % (940597)Termination phase: Saturation 14.16/3.02 % (940597)Time elapsed: 0.417 s 14.16/3.02 % (940597)Peak memory usage: 18 MB 14.16/3.02 % (940597)Instructions burned: 576 (million) 14.16/3.02 % (940620)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3132989161:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1781 on theBenchmark for (1781ds/232Mi) 18.69/3.28 % (940621)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=1703617396:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1781 on theBenchmark for (1781ds/1254Mi) 18.69/3.28 % (940611)Instruction limit reached! 18.69/3.28 % (940611)------------------------------ 18.69/3.28 % (940611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.69/3.28 % (940611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.69/3.28 % (940611)CaDiCaL version: 2.1.3 18.69/3.28 % (940611)Termination reason: Instruction limit 18.69/3.28 % (940611)Termination phase: Saturation 18.69/3.28 % (940611)Time elapsed: 0.233 s 18.69/3.28 % (940611)Peak memory usage: 13 MB 18.69/3.28 % (940611)Instructions burned: 339 (million) 18.69/3.28 % (940618)Instruction limit reached! 18.69/3.28 % (940618)------------------------------ 18.69/3.28 % (940618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.69/3.28 % (940618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.69/3.28 % (940618)CaDiCaL version: 2.1.3 18.69/3.28 % (940618)Termination reason: Instruction limit 18.69/3.28 % (940618)Termination phase: Property scanning 18.69/3.28 % (940618)Time elapsed: 0.097 s 18.69/3.28 % (940618)Peak memory usage: 16 MB 18.69/3.28 % (940618)Instructions burned: 137 (million) 18.69/3.28 % (940624)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 18.69/3.28 % (940624)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=436771168:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1780 on theBenchmark for (1780ds/281Mi) 18.69/3.28 % (940625)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3483662511:i=619:add=on:rtra=on_1780 on theBenchmark for (1780ds/619Mi) 18.69/3.28 % (940621)Refutation not found, incomplete strategy 18.69/3.28 % (940621)------------------------------ 18.69/3.28 % (940621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.69/3.28 % (940621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.69/3.28 % (940621)CaDiCaL version: 2.1.3 18.69/3.28 % (940621)Termination reason: Refutation not found, incomplete strategy 18.69/3.28 % (940621)Time elapsed: 0.137 s 18.69/3.28 % (940621)Peak memory usage: 16 MB 18.69/3.28 % (940621)Instructions burned: 212 (million) 18.69/3.28 % (940621)------------------------------ 18.69/3.28 % (940621)------------------------------ 18.69/3.28 % (940620)Instruction limit reached! 18.69/3.28 % (940620)------------------------------ 18.69/3.28 % (940620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.69/3.28 % (940620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.69/3.28 % (940620)CaDiCaL version: 2.1.3 18.69/3.28 % (940620)Termination reason: Instruction limit 18.69/3.28 % (940620)Termination phase: Saturation 18.69/3.28 % (940620)Time elapsed: 0.154 s 18.69/3.28 % (940620)Peak memory usage: 14 MB 18.69/3.28 % (940620)Instructions burned: 232 (million) 18.69/3.28 % (940628)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3089636323:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1779 on theBenchmark for (1779ds/865Mi) 18.69/3.28 % (940629)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1196275032:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1779 on theBenchmark for (1779ds/212Mi) 18.69/3.28 % (940624)Instruction limit reached! 18.69/3.28 % (940624)------------------------------ 18.69/3.28 % (940624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.69/3.28 % (940624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.69/3.28 % (940624)CaDiCaL version: 2.1.3 18.69/3.28 % (940624)Termination reason: Instruction limit 18.69/3.28 % (940624)Termination phase: Saturation 18.69/3.28 % (940624)Time elapsed: 0.172 s 18.69/3.28 % (940624)Peak memory usage: 12 MB 18.69/3.28 % (940624)Instructions burned: 281 (million) 18.69/3.28 % (940632)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3993302713:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1778 on theBenchmark for (1778ds/130Mi) 18.69/3.28 % (940629)Instruction limit reached! 18.69/3.28 % (940629)------------------------------ 20.69/3.74 % (940629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.69/3.74 % (940629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.69/3.74 % (940629)CaDiCaL version: 2.1.3 20.69/3.74 % (940629)Termination reason: Instruction limit 20.69/3.74 % (940629)Termination phase: Saturation 20.69/3.74 % (940629)Time elapsed: 0.139 s 20.69/3.74 % (940629)Peak memory usage: 14 MB 20.69/3.74 % (940629)Instructions burned: 213 (million) 20.69/3.74 % (940632)Instruction limit reached! 20.69/3.74 % (940632)------------------------------ 20.69/3.74 % (940632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.69/3.74 % (940632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.69/3.74 % (940632)CaDiCaL version: 2.1.3 20.69/3.74 % (940632)Termination reason: Instruction limit 20.69/3.74 % (940632)Termination phase: Property scanning 20.69/3.74 % (940632)Time elapsed: 0.087 s 20.69/3.74 % (940632)Peak memory usage: 13 MB 20.69/3.74 % (940632)Instructions burned: 131 (million) 20.69/3.74 % (940634)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2678262541:st=1.5:i=346:rtra=on:ss=axioms_1777 on theBenchmark for (1777ds/346Mi) 20.69/3.74 % (940635)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=963254455:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_1777 on theBenchmark for (1777ds/152Mi) 20.69/3.74 % (940635)Instruction limit reached! 20.69/3.74 % (940635)------------------------------ 20.69/3.74 % (940635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.69/3.74 % (940635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.69/3.74 % (940635)CaDiCaL version: 2.1.3 20.69/3.74 % (940635)Termination reason: Instruction limit 20.69/3.74 % (940635)Termination phase: Inequality splitting 20.69/3.74 % (940635)Time elapsed: 0.103 s 20.69/3.74 % (940635)Peak memory usage: 13 MB 20.69/3.74 % (940635)Instructions burned: 152 (million) 20.69/3.74 % (940634)Refutation not found, incomplete strategy 20.69/3.74 % (940634)------------------------------ 20.69/3.74 % (940634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.69/3.74 % (940634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.69/3.74 % (940634)CaDiCaL version: 2.1.3 20.69/3.74 % (940634)Termination reason: Refutation not found, incomplete strategy 20.69/3.74 % (940634)Time elapsed: 0.122 s 20.69/3.74 % (940634)Peak memory usage: 14 MB 20.69/3.74 % (940634)Instructions burned: 165 (million) 20.69/3.74 % (940634)------------------------------ 20.69/3.74 % (940634)------------------------------ 20.69/3.74 % (940638)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3672107859:i=75:ep=R:rtra=on:ntd=on_1776 on theBenchmark for (1776ds/75Mi) 20.69/3.74 % (940625)Instruction limit reached! 20.69/3.74 % (940625)------------------------------ 20.69/3.74 % (940625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.69/3.74 % (940625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.69/3.74 % (940625)CaDiCaL version: 2.1.3 20.69/3.74 % (940625)Termination reason: Instruction limit 20.69/3.74 % (940625)Termination phase: Saturation 20.69/3.74 % (940625)Time elapsed: 0.458 s 20.69/3.74 % (940625)Peak memory usage: 18 MB 20.69/3.74 % (940625)Instructions burned: 621 (million) 20.69/3.74 % (940639)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2626168650:st=2.5:i=387:sd=2:rtra=on:ss=axioms_1776 on theBenchmark for (1776ds/387Mi) 20.69/3.74 % (940642)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=1378448644:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_1775 on theBenchmark for (1775ds/148Mi) 20.69/3.74 % (940638)Instruction limit reached! 20.69/3.74 % (940638)------------------------------ 20.69/3.74 % (940638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.69/3.74 % (940638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.69/3.74 % (940638)CaDiCaL version: 2.1.3 20.69/3.74 % (940638)Termination reason: Instruction limit 20.69/3.74 % (940638)Termination phase: Property scanning 20.69/3.74 % (940638)Time elapsed: 0.049 s 20.69/3.74 % (940638)Peak memory usage: 11 MB 20.69/3.74 % (940638)Instructions burned: 75 (million) 20.69/3.74 % (940644)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1976726179:i=161:piset=and:rtra=on:ntd=on_1775 on theBenchmark for (1775ds/161Mi) 22.24/4.03 % (940642)Instruction limit reached! 22.24/4.03 % (940642)------------------------------ 22.24/4.03 % (940642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.24/4.03 % (940642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.24/4.03 % (940642)CaDiCaL version: 2.1.3 22.24/4.03 % (940642)Termination reason: Instruction limit 22.24/4.03 % (940642)Termination phase: Saturation 22.24/4.03 % (940642)Time elapsed: 0.095 s 22.24/4.03 % (940642)Peak memory usage: 12 MB 22.24/4.03 % (940642)Instructions burned: 149 (million) 22.24/4.03 % (940646)lrs+10_1_sil=128000:si=on:random_seed=2152300706:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_1774 on theBenchmark for (1774ds/888Mi) 22.24/4.03 % (940644)Instruction limit reached! 22.24/4.03 % (940644)------------------------------ 22.24/4.03 % (940644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.24/4.03 % (940644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.24/4.03 % (940644)CaDiCaL version: 2.1.3 22.24/4.03 % (940644)Termination reason: Instruction limit 22.24/4.03 % (940644)Termination phase: Property scanning 22.24/4.03 % (940644)Time elapsed: 0.109 s 22.24/4.03 % (940644)Peak memory usage: 13 MB 22.24/4.03 % (940644)Instructions burned: 161 (million) 22.24/4.03 % (940648)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=2331392933:i=136:add=on:ins=4:rtra=on:sup=off_1774 on theBenchmark for (1774ds/136Mi) 22.24/4.03 % (940639)Instruction limit reached! 22.24/4.03 % (940639)------------------------------ 22.24/4.03 % (940639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.24/4.03 % (940639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.24/4.03 % (940639)CaDiCaL version: 2.1.3 22.24/4.03 % (940639)Termination reason: Instruction limit 22.24/4.03 % (940639)Termination phase: Saturation 22.24/4.03 % (940639)Time elapsed: 0.234 s 22.24/4.03 % (940639)Peak memory usage: 12 MB 22.24/4.03 % (940639)Instructions burned: 387 (million) 22.24/4.03 % (940650)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=835428229:i=88:s2at=3:nm=2:rtra=on:rawr=on_1773 on theBenchmark for (1773ds/88Mi) 22.24/4.03 % (940610)Instruction limit reached! 22.24/4.03 % (940610)------------------------------ 22.24/4.03 % (940610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.24/4.03 % (940610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.24/4.03 % (940610)CaDiCaL version: 2.1.3 22.24/4.03 % (940610)Termination reason: Instruction limit 22.24/4.03 % (940610)Termination phase: Saturation 22.24/4.03 % (940610)Time elapsed: 1.037 s 22.24/4.03 % (940610)Peak memory usage: 21 MB 22.24/4.03 % (940610)Instructions burned: 1441 (million) 22.24/4.03 % (940648)Instruction limit reached! 22.24/4.03 % (940648)------------------------------ 22.24/4.03 % (940648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.24/4.03 % (940648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.24/4.03 % (940648)CaDiCaL version: 2.1.3 22.24/4.03 % (940648)Termination reason: Instruction limit 22.24/4.03 % (940648)Termination phase: Function definition elimination 22.24/4.03 % (940648)Time elapsed: 0.091 s 22.24/4.03 % (940648)Peak memory usage: 12 MB 22.24/4.03 % (940648)Instructions burned: 137 (million) 22.24/4.03 % (940652)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=4171370595:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_1773 on theBenchmark for (1773ds/93Mi) 22.24/4.03 % (940628)Instruction limit reached! 22.24/4.03 % (940628)------------------------------ 22.24/4.03 % (940628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.24/4.03 % (940628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.24/4.03 % (940628)CaDiCaL version: 2.1.3 22.24/4.03 % (940628)Termination reason: Instruction limit 22.24/4.03 % (940628)Termination phase: Saturation 22.24/4.03 % (940628)Time elapsed: 0.652 s 22.24/4.03 % (940628)Peak memory usage: 19 MB 22.24/4.03 % (940628)Instructions burned: 865 (million) 22.24/4.03 % (940650)Instruction limit reached! 22.24/4.03 % (940650)------------------------------ 22.24/4.03 % (940650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940650)CaDiCaL version: 2.1.3 24.89/4.10 % (940650)Termination reason: Instruction limit 24.89/4.10 % (940650)Termination phase: Property scanning 24.89/4.10 % (940650)Time elapsed: 0.057 s 24.89/4.10 % (940650)Peak memory usage: 11 MB 24.89/4.10 % (940650)Instructions burned: 89 (million) 24.89/4.10 % (940653)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3128597619:i=2186:rtra=on:ixr=off_1772 on theBenchmark for (1772ds/2186Mi) 24.89/4.10 % (940655)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=960846315:s2a=on:i=240:rtra=on:ntd=on_1772 on theBenchmark for (1772ds/240Mi) 24.89/4.10 % (940656)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2198861755:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_1772 on theBenchmark for (1772ds/805Mi) 24.89/4.10 % (940652)Instruction limit reached! 24.89/4.10 % (940652)------------------------------ 24.89/4.10 % (940652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940652)CaDiCaL version: 2.1.3 24.89/4.10 % (940652)Termination reason: Instruction limit 24.89/4.10 % (940652)Termination phase: Saturation 24.89/4.10 % (940652)Time elapsed: 0.060 s 24.89/4.10 % (940652)Peak memory usage: 12 MB 24.89/4.10 % (940652)Instructions burned: 94 (million) 24.89/4.10 % (940660)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on 24.89/4.10 % (940660)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2082986067:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_1772 on theBenchmark for (1772ds/391Mi) 24.89/4.10 % (940655)Instruction limit reached! 24.89/4.10 % (940655)------------------------------ 24.89/4.10 % (940655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940655)CaDiCaL version: 2.1.3 24.89/4.10 % (940655)Termination reason: Instruction limit 24.89/4.10 % (940655)Termination phase: Saturation 24.89/4.10 % (940655)Time elapsed: 0.159 s 24.89/4.10 % (940655)Peak memory usage: 15 MB 24.89/4.10 % (940655)Instructions burned: 240 (million) 24.89/4.10 % (940662)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=3866945629:i=355:av=off:fsr=off:rtra=on:ixr=off_1770 on theBenchmark for (1770ds/355Mi) 24.89/4.10 % (940660)Instruction limit reached! 24.89/4.10 % (940660)------------------------------ 24.89/4.10 % (940660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940660)CaDiCaL version: 2.1.3 24.89/4.10 % (940660)Termination reason: Instruction limit 24.89/4.10 % (940660)Termination phase: Saturation 24.89/4.10 % (940660)Time elapsed: 0.239 s 24.89/4.10 % (940660)Peak memory usage: 13 MB 24.89/4.10 % (940660)Instructions burned: 394 (million) 24.89/4.10 % (940664)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=4178149908:lrd=on:i=314:sd=1:rtra=on:ss=axioms_1769 on theBenchmark for (1769ds/314Mi) 24.89/4.10 % (940664)Refutation not found, incomplete strategy 24.89/4.10 % (940664)------------------------------ 24.89/4.10 % (940664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940664)CaDiCaL version: 2.1.3 24.89/4.10 % (940664)Termination reason: Refutation not found, incomplete strategy 24.89/4.10 % (940664)Time elapsed: 0.039 s 24.89/4.10 % (940664)Peak memory usage: 13 MB 24.89/4.10 % (940664)Instructions burned: 54 (million) 24.89/4.10 % (940664)------------------------------ 24.89/4.10 % (940664)------------------------------ 24.89/4.10 % (940666)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=1387603115:s2a=on:i=251:fsr=off:rtra=on_1768 on theBenchmark for (1768ds/251Mi) 24.89/4.10 % (940662)Instruction limit reached! 24.89/4.10 % (940662)------------------------------ 24.89/4.10 % (940662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940662)CaDiCaL version: 2.1.3 24.89/4.10 % (940662)Termination reason: Instruction limit 24.89/4.10 % (940662)Termination phase: Saturation 24.89/4.10 % (940662)Time elapsed: 0.252 s 24.89/4.10 % (940662)Peak memory usage: 15 MB 24.89/4.10 % (940662)Instructions burned: 356 (million) 24.89/4.10 % (940646)Instruction limit reached! 24.89/4.10 % (940646)------------------------------ 24.89/4.10 % (940646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940646)CaDiCaL version: 2.1.3 24.89/4.10 % (940646)Termination reason: Instruction limit 24.89/4.10 % (940646)Termination phase: Saturation 24.89/4.10 % (940646)Time elapsed: 0.631 s 24.89/4.10 % (940646)Peak memory usage: 18 MB 24.89/4.10 % (940646)Instructions burned: 888 (million) 24.89/4.10 % (940668)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=43214757:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_1767 on theBenchmark for (1767ds/2470Mi) 24.89/4.10 % (940669)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=1508976103:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_1767 on theBenchmark for (1767ds/673Mi) 24.89/4.10 % (940666)Instruction limit reached! 24.89/4.10 % (940666)------------------------------ 24.89/4.10 % (940666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940666)CaDiCaL version: 2.1.3 24.89/4.10 % (940666)Termination reason: Instruction limit 24.89/4.10 % (940666)Termination phase: Saturation 24.89/4.10 % (940666)Time elapsed: 0.166 s 24.89/4.10 % (940666)Peak memory usage: 14 MB 24.89/4.10 % (940666)Instructions burned: 252 (million) 24.89/4.10 % (940672)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=4218076006:i=116:ep=RSTC:rtra=on:ntd=on_1766 on theBenchmark for (1766ds/116Mi) 24.89/4.10 % (940656)Instruction limit reached! 24.89/4.10 % (940656)------------------------------ 24.89/4.10 % (940656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940656)CaDiCaL version: 2.1.3 24.89/4.10 % (940656)Termination reason: Instruction limit 24.89/4.10 % (940656)Termination phase: Saturation 24.89/4.10 % (940656)Time elapsed: 0.590 s 24.89/4.10 % (940656)Peak memory usage: 18 MB 24.89/4.10 % (940656)Instructions burned: 805 (million) 24.89/4.10 % (940674)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1899806065:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1766 on theBenchmark for (1766ds/270Mi) 24.89/4.10 % (940672)Instruction limit reached! 24.89/4.10 % (940672)------------------------------ 24.89/4.10 % (940672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940672)CaDiCaL version: 2.1.3 24.89/4.10 % (940672)Termination reason: Instruction limit 24.89/4.10 % (940672)Termination phase: Property scanning 24.89/4.10 % (940672)Time elapsed: 0.081 s 24.89/4.10 % (940672)Peak memory usage: 12 MB 24.89/4.10 % (940672)Instructions burned: 117 (million) 24.89/4.10 % (940676)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=2441873939:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1765 on theBenchmark for (1765ds/30Mi) 24.89/4.10 % (940676)Instruction limit reached! 24.89/4.10 % (940676)------------------------------ 24.89/4.10 % (940676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940676)CaDiCaL version: 2.1.3 24.89/4.10 % (940676)Termination reason: Instruction limit 24.89/4.10 % (940676)Termination phase: shuffling 24.89/4.10 % (940676)Time elapsed: 0.021 s 24.89/4.10 % (940676)Peak memory usage: 10 MB 24.89/4.10 % (940676)Instructions burned: 31 (million) 24.89/4.10 % (940601) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-940431-940601"... 24.89/4.10 % (940678)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off 24.89/4.10 % (940678)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=1533671147:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_1765 on theBenchmark for (1765ds/39Mi) 24.89/4.10 % (940669) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-940431-940669"... 24.89/4.10 % (940678)Instruction limit reached! 24.89/4.10 % (940678)------------------------------ 24.89/4.10 % (940678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.10 % (940678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.10 % (940678)CaDiCaL version: 2.1.3 24.89/4.10 % (940678)Termination reason: Instruction limit 24.89/4.10 % (940678)Termination phase: Property scanning 24.89/4.10 % (940678)Time elapsed: 0.027 s 24.89/4.10 % (940678)Peak memory usage: 10 MB 24.89/4.10 % (940678)Instructions burned: 40 (million) 24.89/4.10 % (940601)...printing done. 24.89/4.10 % (940601)Refutation found. Thanks to Tanya! 24.89/4.10 % SZS status Theorem for theBenchmark 24.89/4.10 % SZS output start Proof for theBenchmark 24.89/4.10 thf(type_def_5, type, term: $tType). 24.89/4.10 thf(type_def_6, type, subst: $tType). 24.89/4.10 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType). 24.89/4.10 thf(type_def_8, type, d_term: $tType). 24.89/4.10 thf(type_def_9, type, d_subst: $tType). 24.89/4.10 thf(func_def_0, type, one: term). 24.89/4.10 thf(func_def_1, type, ap: (term > term > term)). 24.89/4.10 thf(func_def_2, type, lam: (term > term)). 24.89/4.10 thf(func_def_3, type, sub: (term > subst > term)). 24.89/4.10 thf(func_def_4, type, id: subst). 24.89/4.10 thf(func_def_5, type, sh: subst). 24.89/4.10 thf(func_def_6, type, push: (term > subst > subst)). 24.89/4.10 thf(func_def_7, type, comp: (subst > subst > subst)). 24.89/4.10 thf(func_def_8, type, var: (term > $o)). 24.89/4.10 thf(func_def_9, type, pushprop_lem1v2: $o). 24.89/4.10 thf(func_def_10, type, pushprop_lem1_gthm: $o). 24.89/4.10 thf(func_def_11, type, axmap: $o). 24.89/4.10 thf(func_def_12, type, pushprop_lem0_gthm: $o). 24.89/4.10 thf(func_def_13, type, shinj: $o). 24.89/4.10 thf(func_def_14, type, hoasinduction_lem1v2: $o). 24.89/4.10 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o). 24.89/4.10 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)). 24.89/4.10 thf(func_def_17, type, induction2lem: $o). 24.89/4.10 thf(func_def_18, type, hoasinduction_lem3v2_f: $o). 24.89/4.10 thf(func_def_19, type, axvarshift: $o). 24.89/4.10 thf(func_def_20, type, hoasapinj2: $o). 24.89/4.10 thf(func_def_21, type, hoasapnotvar_gthm: $o). 24.89/4.10 thf(func_def_22, type, hoasapinj1: $o). 24.89/4.10 thf(func_def_23, type, ulamvar1: $o). 24.89/4.10 thf(func_def_24, type, induction2lem_lthm: $o). 24.89/4.10 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o). 24.89/4.10 thf(func_def_26, type, apnotvar: $o). 24.89/4.10 thf(func_def_27, type, pushprop_lthm_orig: $o). 24.89/4.10 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o). 24.89/4.10 thf(func_def_29, type, hoasinduction_lthm: $o). 24.89/4.10 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o). 24.89/4.10 thf(func_def_31, type, hoaslaminj: $o). 24.89/4.10 thf(func_def_32, type, hoasinduction_lem3aaa: $o). 24.89/4.10 thf(func_def_33, type, induction2lem_gthm: $o). 24.89/4.10 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o). 24.89/4.10 thf(func_def_35, type, hoasinduction_lem3: $o). 24.89/4.10 thf(func_def_36, type, hoasinduction_lem2: $o). 24.89/4.10 thf(func_def_37, type, termmset_lthm: $o). 24.89/4.10 thf(func_def_38, type, hoasinduction_lem1: $o). 24.89/4.10 thf(func_def_39, type, hoaslamnotap_lthm: $o). 24.89/4.10 thf(func_def_40, type, pushprop_lem1v2_lthm: $o). 24.89/4.10 thf(func_def_41, type, hoasapnotvar: $o). 24.89/4.10 thf(func_def_42, type, hoasinduction_lem0: $o). 24.89/4.10 thf(func_def_43, type, hoasinduction: $o). 24.89/4.10 thf(func_def_44, type, hoasinduction_gthm: $o). 24.89/4.10 thf(func_def_45, type, axapp: $o). 24.89/4.10 thf(func_def_46, type, hoaslamnotvar_lthm: $o). 24.89/4.10 thf(func_def_47, type, pushprop_lem3v2_lthm: $o). 24.89/4.10 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o). 24.89/4.10 thf(func_def_49, type, ulamvarind: $o). 24.89/4.10 thf(func_def_50, type, induction: $o). 24.89/4.10 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o). 24.89/4.10 thf(func_def_52, type, termmset_gthm: $o). 24.89/4.10 thf(func_def_53, type, hoasinduction_lem3aa: $o). 24.89/4.10 thf(func_def_54, type, pushprop_lem1v2_gthm: $o). 24.89/4.10 thf(func_def_55, type, hoaslamnotap_gthm: $o). 24.89/4.10 thf(func_def_56, type, hoaslamnotvar_gthm: $o). 24.89/4.10 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o). 24.89/4.10 thf(func_def_58, type, pushprop_lem2v2: $o). 24.89/4.10 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o). 24.89/4.10 thf(func_def_60, type, axclos: $o). 24.89/4.10 thf(func_def_61, type, axassoc: $o). 24.89/4.10 thf(func_def_62, type, hoasinduction_lem2v2: $o). 24.89/4.10 thf(func_def_63, type, pushprop_lthm: $o). 24.89/4.10 thf(func_def_64, type, apinj2: $o). 24.89/4.10 thf(func_def_65, type, apinj1: $o). 24.89/4.10 thf(func_def_66, type, hoasapinj2_lthm: $o). 24.89/4.10 thf(func_def_67, type, hoasinduction_lem3v2a: $o). 24.89/4.10 thf(func_def_68, type, hoasapinj1_lthm: $o). 24.89/4.10 thf(func_def_69, type, hoaslaminj_lthm: $o). 24.89/4.10 thf(func_def_70, type, axvarcons: $o). 24.89/4.10 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)). 24.89/4.10 thf(func_def_72, type, axscons: $o). 24.89/4.10 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o). 24.89/4.10 thf(func_def_74, type, axidr: $o). 24.89/4.10 thf(func_def_75, type, pushprop_lem1: $o). 24.89/4.10 thf(func_def_76, type, laminj: $o). 24.89/4.10 thf(func_def_77, type, hoasinduction_lem3_lthm: $o). 24.89/4.10 thf(func_def_78, type, pushprop_lem0: $o). 24.89/4.10 thf(func_def_79, type, pushprop_gthm: $o). 24.89/4.10 thf(func_def_80, type, axabs: $o). 24.89/4.10 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o). 24.89/4.10 thf(func_def_82, type, hoasinduction_lem2_lthm: $o). 24.89/4.10 thf(func_def_83, type, hoasapinj2_gthm: $o). 24.89/4.10 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)). 24.89/4.10 thf(func_def_85, type, hoasinduction_lem1_lthm: $o). 24.89/4.10 thf(func_def_86, type, lamnotap: $o). 24.89/4.10 thf(func_def_87, type, hoasapinj1_gthm: $o). 24.89/4.10 thf(func_def_88, type, hoaslamnotvar: $o). 24.89/4.10 thf(func_def_89, type, axidl: $o). 24.89/4.10 thf(func_def_90, type, hoaslaminj_gthm: $o). 24.89/4.10 thf(func_def_91, type, induction2_lthm: $o). 24.89/4.10 thf(func_def_92, type, hoasinduction_lem0_lthm: $o). 24.89/4.10 thf(func_def_93, type, substmonoid_lthm: $o). 24.89/4.10 thf(func_def_94, type, pushprop: $o). 24.89/4.10 thf(func_def_95, type, hoasinduction_lem3_gthm: $o). 24.89/4.10 thf(func_def_96, type, hoasinduction_lem2_gthm: $o). 24.89/4.10 thf(func_def_97, type, hoasinduction_lem3b: $o). 24.89/4.10 thf(func_def_98, type, substmonoid: $o). 24.89/4.10 thf(func_def_99, type, lamnotvar: $o). 24.89/4.10 thf(func_def_100, type, hoasinduction_lem3a: $o). 24.89/4.10 thf(func_def_101, type, hoasinduction_lem1_gthm: $o). 24.89/4.10 thf(func_def_102, type, hoasinduction_no_psi_cond: $o). 24.89/4.10 thf(func_def_103, type, induction2_gthm: $o). 24.89/4.10 thf(func_def_104, type, pushprop_lem2v2_lthm: $o). 24.89/4.10 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_106, type, hoaslamnotap: $o). 24.89/4.10 thf(func_def_107, type, substmonoid_gthm: $o). 24.89/4.10 thf(func_def_108, type, ulamvarsh: $o). 24.89/4.10 thf(func_def_109, type, induction2: $o). 24.89/4.10 thf(func_def_110, type, pushprop_lem3v2: $o). 24.89/4.10 thf(func_def_111, type, pushprop_lem2v2_gthm: $o). 24.89/4.10 thf(func_def_112, type, pushprop_lem1_lthm: $o). 24.89/4.10 thf(func_def_113, type, hoasinduction_lem3v2: $o). 24.89/4.10 thf(func_def_114, type, axshiftcons: $o). 24.89/4.10 thf(func_def_115, type, termmset: $o). 24.89/4.10 thf(func_def_116, type, pushprop_lem0_lthm: $o). 24.89/4.10 thf(func_def_117, type, hoasapnotvar_lthm: $o). 24.89/4.10 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o). 24.89/4.10 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)). 24.89/4.10 thf(func_def_120, type, axvarid: $o). 24.89/4.10 thf(func_def_121, type, hoasinduction_lthm_3: $o). 24.89/4.10 thf(func_def_122, type, d2term: (d_term > term)). 24.89/4.10 thf(func_def_123, type, d2subst: (d_subst > subst)). 24.89/4.10 thf(func_def_124, type, d_one: d_term). 24.89/4.10 thf(func_def_125, type, d_id: d_subst). 24.89/4.10 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 24.89/4.10 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)). 24.89/4.10 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)). 24.89/4.10 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)). 24.89/4.10 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 24.89/4.10 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 24.89/4.10 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)). 24.89/4.10 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)). 24.89/4.10 thf(func_def_137, type, sP0: $o). 24.89/4.10 thf(func_def_138, type, sP1: $o). 24.89/4.10 thf(func_def_139, type, sP2: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_140, type, sP3: $o). 24.89/4.10 thf(func_def_141, type, sP4: $o). 24.89/4.10 thf(func_def_142, type, sP5: $o). 24.89/4.10 thf(func_def_143, type, sP6: $o). 24.89/4.10 thf(func_def_144, type, sP7: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_145, type, sP8: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_146, type, sP9: $o). 24.89/4.10 thf(func_def_147, type, sP10: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_148, type, sP11: $o). 24.89/4.10 thf(func_def_149, type, sP12: $o). 24.89/4.10 thf(func_def_150, type, sP13: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_151, type, sP14: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_152, type, sP15: $o). 24.89/4.10 thf(func_def_153, type, sP16: $o). 24.89/4.10 thf(func_def_154, type, sP17: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_155, type, sP18: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_156, type, sP19: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_157, type, sP20: $o). 24.89/4.10 thf(func_def_158, type, sP21: $o). 24.89/4.10 thf(func_def_159, type, sP22: $o). 24.89/4.10 thf(func_def_160, type, sP23: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_161, type, sP24: $o). 24.89/4.10 thf(func_def_162, type, sP25: $o). 24.89/4.10 thf(func_def_163, type, sP26: ((subst > term > subst > $o) > $o)). 24.89/4.10 thf(func_def_164, type, sP27: $o). 24.89/4.10 thf(func_def_165, type, sK28: term). 24.89/4.10 thf(func_def_166, type, sK29: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_167, type, sK30: term). 24.89/4.10 thf(func_def_168, type, sK31: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_169, type, sK32: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_170, type, sK33: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_171, type, sK34: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_172, type, sK35: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_173, type, sK36: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_174, type, sK37: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_175, type, sK38: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_176, type, sK39: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_177, type, sK40: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_178, type, sK41: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_179, type, sK42: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_180, type, sK43: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_181, type, sK44: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_182, type, sK45: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_183, type, sK46: term). 24.89/4.10 thf(func_def_184, type, sK47: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_185, type, sK48: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_186, type, sK49: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_187, type, sK50: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_188, type, sK51: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_189, type, sK52: ((subst > term > subst > $o) > term > term)). 24.89/4.10 thf(func_def_190, type, sK53: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_191, type, sK54: term). 24.89/4.10 thf(func_def_192, type, sK55: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_193, type, sK56: ((subst > term > subst > $o) > term > term)). 24.89/4.10 thf(func_def_194, type, sK57: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_195, type, sK58: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_196, type, sK59: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_197, type, sK60: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_198, type, sK61: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_199, type, sK62: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_200, type, sK63: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_201, type, sK64: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_202, type, sK65: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_203, type, sK66: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_204, type, sK67: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_205, type, sK68: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_206, type, sK69: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_207, type, sK70: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_208, type, sK71: term). 24.89/4.10 thf(func_def_209, type, sK72: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_210, type, sK73: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_211, type, sK74: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_212, type, sK75: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_213, type, sK76: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_214, type, sK77: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_215, type, sK78: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_216, type, sK79: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_217, type, sK80: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_218, type, sK81: ((term > $o) > term)). 24.89/4.10 thf(func_def_219, type, sK82: ((term > $o) > term)). 24.89/4.10 thf(func_def_220, type, sK83: ((term > $o) > term)). 24.89/4.10 thf(func_def_221, type, sK84: ((term > $o) > term)). 24.89/4.10 thf(func_def_222, type, sK85: term). 24.89/4.10 thf(func_def_223, type, sK86: (term > $o)). 24.89/4.10 thf(func_def_224, type, sK87: (term > term)). 24.89/4.10 thf(func_def_225, type, sK88: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_226, type, sK89: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_227, type, sK90: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_228, type, sK91: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_229, type, sK92: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_230, type, sK93: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_231, type, sK94: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_232, type, sK95: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_233, type, sK96: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_234, type, sK97: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_235, type, sK98: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_236, type, sK99: term). 24.89/4.10 thf(func_def_237, type, sK100: term). 24.89/4.10 thf(func_def_238, type, sK101: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_239, type, sK102: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_240, type, sK103: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_241, type, sK104: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_242, type, sK105: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_243, type, sK106: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_244, type, sK107: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_245, type, sK108: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_246, type, sK109: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_247, type, sK110: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_248, type, sK111: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_249, type, sK112: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_250, type, sK113: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_251, type, sK114: term). 24.89/4.10 thf(func_def_252, type, sK115: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_253, type, sK116: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_254, type, sK117: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_255, type, sK118: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_256, type, sK119: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_257, type, sK120: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_258, type, sK121: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_259, type, sK122: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_260, type, sK123: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_261, type, sK124: ((term > $o) > term)). 24.89/4.10 thf(func_def_262, type, sK125: ((term > $o) > term)). 24.89/4.10 thf(func_def_263, type, sK126: ((term > $o) > term)). 24.89/4.10 thf(func_def_264, type, sK127: ((term > $o) > term)). 24.89/4.10 thf(func_def_265, type, sK128: term). 24.89/4.10 thf(func_def_266, type, sK129: (term > $o)). 24.89/4.10 thf(func_def_267, type, sK130: (term > term)). 24.89/4.10 thf(func_def_268, type, sK131: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_269, type, sK132: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_270, type, sK133: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_271, type, sK134: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_272, type, sK135: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_273, type, sK136: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_274, type, sK137: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_275, type, sK138: (term > $o)). 24.89/4.10 thf(func_def_276, type, sK139: term). 24.89/4.10 thf(func_def_277, type, sK140: (term > term)). 24.89/4.10 thf(func_def_278, type, sK141: term). 24.89/4.10 thf(func_def_279, type, sK142: ((term > $o) > term)). 24.89/4.10 thf(func_def_280, type, sK143: ((term > $o) > term)). 24.89/4.10 thf(func_def_281, type, sK144: ((term > $o) > term)). 24.89/4.10 thf(func_def_282, type, sK145: ((term > $o) > term)). 24.89/4.10 thf(func_def_283, type, sK146: ((term > $o) > term)). 24.89/4.10 thf(func_def_284, type, sK147: ((term > $o) > term)). 24.89/4.10 thf(func_def_285, type, sK148: ((term > $o) > term)). 24.89/4.10 thf(func_def_286, type, sK149: ((term > $o) > subst > term)). 24.89/4.10 thf(func_def_287, type, sK150: subst). 24.89/4.10 thf(func_def_288, type, sK151: (term > $o)). 24.89/4.10 thf(func_def_289, type, sK152: term). 24.89/4.10 thf(func_def_290, type, sK153: (term > term)). 24.89/4.10 thf(func_def_291, type, sK154: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_292, type, sK155: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_293, type, sK156: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_294, type, sK157: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_295, type, sK158: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_296, type, sK159: (term > $o)). 24.89/4.10 thf(func_def_297, type, sK160: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_298, type, sK161: term). 24.89/4.10 thf(func_def_299, type, sK162: term). 24.89/4.10 thf(func_def_300, type, sK163: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_301, type, sK164: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_302, type, sK165: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_303, type, sK166: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_304, type, sK167: ((subst > term > subst > $o) > (term > $o) > term)). 24.89/4.10 thf(func_def_305, type, sK168: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_306, type, sK169: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_307, type, sK170: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_308, type, sK171: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_309, type, sK172: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_310, type, sK173: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_311, type, sK174: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_312, type, sK175: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_313, type, sK176: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_314, type, sK177: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_315, type, sK178: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_317, type, sK180: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_318, type, sK181: (term > $o)). 24.89/4.10 thf(func_def_319, type, sK182: term). 24.89/4.10 thf(func_def_320, type, sK183: (term > term)). 24.89/4.10 thf(func_def_321, type, sK184: ((term > $o) > term)). 24.89/4.10 thf(func_def_322, type, sK185: ((term > $o) > term)). 24.89/4.10 thf(func_def_323, type, sK186: ((term > $o) > term)). 24.89/4.10 thf(func_def_324, type, sK187: ((term > $o) > term)). 24.89/4.10 thf(func_def_325, type, sK188: subst). 24.89/4.10 thf(func_def_326, type, sK189: term). 24.89/4.10 thf(func_def_327, type, sK190: (term > $o)). 24.89/4.10 thf(func_def_328, type, sK191: (term > term)). 24.89/4.10 thf(func_def_329, type, sK192: ((term > $o) > term)). 24.89/4.10 thf(func_def_330, type, sK193: ((term > $o) > subst > term)). 24.89/4.10 thf(func_def_331, type, sK194: ((term > $o) > term)). 24.89/4.10 thf(func_def_332, type, sK195: ((term > $o) > term)). 24.89/4.10 thf(func_def_333, type, sK196: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_334, type, sK197: term). 24.89/4.10 thf(func_def_335, type, sK198: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_336, type, sK199: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_337, type, sK200: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_338, type, sK201: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_339, type, sK202: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_340, type, sK203: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_341, type, sK204: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_342, type, sK205: ((term > $o) > term)). 24.89/4.10 thf(func_def_343, type, sK206: ((term > $o) > term)). 24.89/4.10 thf(func_def_344, type, sK207: ((term > $o) > term)). 24.89/4.10 thf(func_def_345, type, sK208: ((term > $o) > term)). 24.89/4.10 thf(func_def_346, type, sK209: term). 24.89/4.10 thf(func_def_347, type, sK210: (term > $o)). 24.89/4.10 thf(func_def_348, type, sK211: (term > term)). 24.89/4.10 thf(func_def_349, type, sK212: ((subst > term > term) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_350, type, sK213: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_351, type, sK214: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_352, type, sK215: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_353, type, sK216: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_354, type, sK217: term). 24.89/4.10 thf(func_def_355, type, sK218: (term > $o)). 24.89/4.10 thf(func_def_356, type, sK219: subst). 24.89/4.10 thf(func_def_357, type, sK220: (term > term)). 24.89/4.10 thf(func_def_358, type, sK221: ((term > $o) > term)). 24.89/4.10 thf(func_def_359, type, sK222: ((term > $o) > term)). 24.89/4.10 thf(func_def_360, type, sK223: ((term > $o) > term)). 24.89/4.10 thf(func_def_361, type, sK224: (subst > (term > $o) > term)). 24.89/4.10 thf(func_def_362, type, sK225: subst). 24.89/4.10 thf(func_def_363, type, sK226: term). 24.89/4.10 thf(func_def_364, type, sK227: subst). 24.89/4.10 thf(func_def_365, type, sK228: term). 24.89/4.10 thf(func_def_366, type, sK229: subst). 24.89/4.10 thf(func_def_367, type, sK230: ((term > $o) > term)). 24.89/4.10 thf(func_def_368, type, sK231: ((term > $o) > term)). 24.89/4.10 thf(func_def_369, type, sK232: ((term > $o) > term)). 24.89/4.10 thf(func_def_370, type, sK233: ((term > $o) > term)). 24.89/4.10 thf(func_def_371, type, sK234: (term > $o)). 24.89/4.10 thf(func_def_372, type, sK235: term). 24.89/4.10 thf(func_def_373, type, sK236: (subst > d_subst)). 24.89/4.10 thf(func_def_374, type, sK237: term). 24.89/4.10 thf(func_def_375, type, sK238: subst). 24.89/4.10 thf(func_def_376, type, sK239: ((subst > term > subst > $o) > term > term)). 24.89/4.10 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_378, type, sK241: term). 24.89/4.10 thf(func_def_379, type, sK242: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_380, type, sK243: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_381, type, sK244: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_382, type, sK245: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_383, type, sK246: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_384, type, sK247: term). 24.89/4.10 thf(func_def_385, type, sK248: term). 24.89/4.10 thf(func_def_386, type, sK249: term). 24.89/4.10 thf(func_def_387, type, sK250: term). 24.89/4.10 thf(func_def_388, type, sK251: term). 24.89/4.10 thf(func_def_389, type, sK252: term). 24.89/4.10 thf(func_def_390, type, sK253: term). 24.89/4.10 thf(func_def_391, type, sK254: term). 24.89/4.10 thf(func_def_392, type, sK255: term). 24.89/4.10 thf(func_def_393, type, sK256: subst). 24.89/4.10 thf(func_def_394, type, sK257: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_395, type, sK258: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_396, type, sK259: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_398, type, sK261: ((term > $o) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_399, type, sK262: (term > (term > $o) > term)). 24.89/4.10 thf(func_def_400, type, sK263: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_401, type, sK264: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_402, type, sK265: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_403, type, sK266: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_404, type, sK267: term). 24.89/4.10 thf(func_def_405, type, sK268: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_406, type, sK269: (term > $o)). 24.89/4.10 thf(func_def_407, type, sK270: term). 24.89/4.10 thf(func_def_408, type, sK271: subst). 24.89/4.10 thf(func_def_409, type, sK272: term). 24.89/4.10 thf(func_def_410, type, sK273: ((term > $o) > subst > term > (term > $o) > term)). 24.89/4.10 thf(func_def_411, type, sK274: (term > $o)). 24.89/4.10 thf(func_def_412, type, sK275: term). 24.89/4.10 thf(func_def_413, type, sK276: subst). 24.89/4.10 thf(func_def_414, type, sK277: (term > $o)). 24.89/4.10 thf(func_def_415, type, sK278: term). 24.89/4.10 thf(func_def_416, type, sK279: (term > $o)). 24.89/4.10 thf(func_def_417, type, sK280: subst). 24.89/4.10 thf(func_def_418, type, sK281: (term > $o)). 24.89/4.10 thf(func_def_419, type, sK282: term). 24.89/4.10 thf(func_def_420, type, sK283: term). 24.89/4.10 thf(func_def_421, type, sK284: term). 24.89/4.10 thf(func_def_422, type, sK285: term). 24.89/4.10 thf(func_def_423, type, sK286: term). 24.89/4.10 thf(func_def_424, type, sK287: ((subst > term > subst > $o) > term > term)). 24.89/4.10 thf(func_def_425, type, sK288: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_426, type, sK289: term). 24.89/4.10 thf(func_def_427, type, sK290: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_428, type, sK291: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_429, type, sK292: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_430, type, sK293: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_431, type, sK294: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_432, type, sK295: term). 24.89/4.10 thf(func_def_433, type, sK296: term). 24.89/4.10 thf(func_def_434, type, sK297: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_435, type, sK298: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_436, type, sK299: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_437, type, sK300: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_438, type, sK301: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_439, type, sK302: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_440, type, sK303: ((subst > term > subst > $o) > term > term)). 24.89/4.10 thf(func_def_441, type, sK304: term). 24.89/4.10 thf(func_def_442, type, sK305: term). 24.89/4.10 thf(func_def_443, type, sK306: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_444, type, sK307: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_445, type, sK308: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_446, type, sK309: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_447, type, sK310: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_448, type, sK311: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_449, type, sK312: ((subst > term > subst > $o) > term > term)). 24.89/4.10 thf(func_def_450, type, sK313: (term > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_451, type, sK314: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_452, type, sK315: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_453, type, sK316: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_454, type, sK317: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_455, type, sK318: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_456, type, sK319: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_457, type, sK320: ((subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_458, type, sK321: ((subst > term > subst > $o) > subst)). 24.89/4.10 thf(func_def_459, type, sK322: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_460, type, sK323: term). 24.89/4.10 thf(func_def_461, type, sK324: term). 24.89/4.10 thf(func_def_462, type, sK325: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_463, type, sK326: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_464, type, sK327: term). 24.89/4.10 thf(func_def_465, type, sK328: ((term > $o) > (subst > term > subst > $o) > term)). 24.89/4.10 thf(func_def_466, type, sK329: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.10 thf(func_def_467, type, sK330: ((term > $o) > term > term)). 24.89/4.10 thf(func_def_468, type, sK331: (term > subst > term > term)). 24.89/4.10 thf(func_def_469, type, sK332: (subst > term > subst > $o)). 24.89/4.10 thf(func_def_470, type, sK333: term). 24.89/4.10 thf(func_def_471, type, sK334: (term > $o)). 24.89/4.10 thf(func_def_472, type, sK335: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_473, type, sK336: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_474, type, sK337: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_475, type, sK338: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_476, type, sK339: (subst > term > term)). 24.89/4.10 thf(func_def_477, type, sK340: term). 24.89/4.10 thf(func_def_478, type, sK341: (subst > term > term)). 24.89/4.10 thf(func_def_479, type, sK342: subst). 24.89/4.10 thf(func_def_480, type, sK343: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_481, type, sK344: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_482, type, sK345: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_483, type, sK346: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_484, type, sK347: ((subst > term > term) > subst)). 24.89/4.10 thf(func_def_485, type, sK348: ((subst > term > term) > term)). 24.89/4.10 thf(func_def_486, type, sK349: subst). 24.89/4.10 thf(func_def_487, type, sK350: subst). 24.89/4.10 thf(func_def_488, type, sK351: (term > subst > (term > $o) > term > $o)). 24.89/4.10 thf(func_def_489, type, sK352: (term > $o)). 24.89/4.10 thf(func_def_490, type, sK353: subst). 24.89/4.10 thf(func_def_491, type, sK354: term). 24.89/4.10 thf(func_def_492, type, sK355: ((term > $o) > term)). 24.89/4.11 thf(func_def_493, type, sK356: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_494, type, sK357: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_495, type, sK358: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_496, type, sK359: term). 24.89/4.11 thf(func_def_497, type, sK360: term). 24.89/4.11 thf(func_def_498, type, sK361: (subst > term > term)). 24.89/4.11 thf(func_def_499, type, sK362: subst). 24.89/4.11 thf(func_def_500, type, sK363: subst). 24.89/4.11 thf(func_def_501, type, sK364: subst). 24.89/4.11 thf(func_def_502, type, sK365: subst). 24.89/4.11 thf(func_def_503, type, sK366: subst). 24.89/4.11 thf(func_def_504, type, sK367: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_505, type, sK368: ((term > $o) > term)). 24.89/4.11 thf(func_def_506, type, sK369: term). 24.89/4.11 thf(func_def_507, type, sK370: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_508, type, sK371: (term > $o)). 24.89/4.11 thf(func_def_509, type, sK372: term). 24.89/4.11 thf(func_def_510, type, sK373: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_511, type, sK374: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_512, type, sK375: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_513, type, sK376: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_514, type, sK377: ((subst > term > subst > $o) > term > $o)). 24.89/4.11 thf(func_def_515, type, sK378: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_516, type, sK379: (term > (term > $o) > term)). 24.89/4.11 thf(func_def_517, type, sK380: ((term > $o) > (subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_518, type, sK381: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_519, type, sK382: ((term > $o) > term)). 24.89/4.11 thf(func_def_520, type, sK383: ((subst > term > subst > $o) > term > $o)). 24.89/4.11 thf(func_def_521, type, sK384: (term > subst > term > term)). 24.89/4.11 thf(func_def_522, type, sK385: term). 24.89/4.11 thf(func_def_523, type, sK386: term). 24.89/4.11 thf(func_def_524, type, sK387: (term > $o)). 24.89/4.11 thf(func_def_525, type, sK388: (term > $o)). 24.89/4.11 thf(func_def_526, type, sK389: subst). 24.89/4.11 thf(func_def_527, type, sK390: (subst > (term > $o) > (term > $o) > term > term)). 24.89/4.11 thf(func_def_528, type, sK391: ((subst > term > subst > $o) > term > term)). 24.89/4.11 thf(func_def_529, type, sK392: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_530, type, sK393: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_531, type, sK394: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_532, type, sK395: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_533, type, sK396: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_534, type, sK397: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_535, type, sK398: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_536, type, sK399: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_537, type, sK400: term). 24.89/4.11 thf(func_def_538, type, sK401: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_539, type, sK402: subst). 24.89/4.11 thf(func_def_540, type, sK403: (term > $o)). 24.89/4.11 thf(func_def_541, type, sK404: term). 24.89/4.11 thf(func_def_542, type, sK405: ((term > $o) > term)). 24.89/4.11 thf(func_def_543, type, sK406: ((term > $o) > term)). 24.89/4.11 thf(func_def_544, type, sK407: ((term > $o) > term)). 24.89/4.11 thf(func_def_545, type, sK408: ((term > $o) > term)). 24.89/4.11 thf(func_def_546, type, sK409: term). 24.89/4.11 thf(func_def_547, type, sK410: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_548, type, sK411: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_549, type, sK412: (term > subst > term > term)). 24.89/4.11 thf(func_def_550, type, sK413: term). 24.89/4.11 thf(func_def_551, type, sK414: subst). 24.89/4.11 thf(func_def_552, type, sK415: ((subst > term > subst > $o) > term > $o)). 24.89/4.11 thf(func_def_553, type, sK416: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_554, type, sK417: ((term > $o) > term)). 24.89/4.11 thf(func_def_555, type, sK418: term). 24.89/4.11 thf(func_def_556, type, sK419: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_557, type, sK420: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_558, type, sK421: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_559, type, sK422: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_560, type, sK423: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_561, type, sK424: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_562, type, sK425: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_563, type, sK426: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_564, type, sK427: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_565, type, sK428: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_566, type, sK429: term). 24.89/4.11 thf(func_def_567, type, sK430: term). 24.89/4.11 thf(func_def_568, type, sK431: term). 24.89/4.11 thf(func_def_569, type, sK432: term). 24.89/4.11 thf(func_def_570, type, sK433: term). 24.89/4.11 thf(func_def_571, type, sK434: (term > subst > term > term)). 24.89/4.11 thf(func_def_572, type, sK435: term). 24.89/4.11 thf(func_def_573, type, sK436: term). 24.89/4.11 thf(func_def_574, type, sK437: (subst > term > term)). 24.89/4.11 thf(func_def_575, type, sK438: term). 24.89/4.11 thf(func_def_576, type, sK439: subst). 24.89/4.11 thf(func_def_577, type, sK440: (subst > term > term)). 24.89/4.11 thf(func_def_578, type, sK441: subst). 24.89/4.11 thf(func_def_579, type, sK442: term). 24.89/4.11 thf(func_def_580, type, sK443: subst). 24.89/4.11 thf(func_def_581, type, sK444: term). 24.89/4.11 thf(func_def_582, type, sK445: term). 24.89/4.11 thf(func_def_583, type, sK446: term). 24.89/4.11 thf(func_def_584, type, sK447: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_585, type, sK448: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_586, type, sK449: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_587, type, sK450: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_588, type, sK451: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_589, type, sK452: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_590, type, sK453: term). 24.89/4.11 thf(func_def_591, type, sK454: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_592, type, sK455: (term > $o)). 24.89/4.11 thf(func_def_593, type, sK456: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_594, type, sK457: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_595, type, sK458: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_596, type, sK459: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_597, type, sK460: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_598, type, sK461: ((term > $o) > term)). 24.89/4.11 thf(func_def_599, type, sK462: term). 24.89/4.11 thf(func_def_600, type, sK463: ((term > $o) > (subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_601, type, sK464: ((term > $o) > term > term)). 24.89/4.11 thf(func_def_602, type, sK465: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_603, type, sK466: ((subst > term > subst > $o) > term > $o)). 24.89/4.11 thf(func_def_604, type, sK467: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_605, type, sK468: term). 24.89/4.11 thf(func_def_606, type, sK469: ((subst > term > term) > term > term)). 24.89/4.11 thf(func_def_607, type, sK470: ((subst > term > term) > term > subst)). 24.89/4.11 thf(func_def_608, type, sK471: ((subst > term > term) > term > subst)). 24.89/4.11 thf(func_def_609, type, sK472: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_610, type, sK473: ((subst > term > term) > term > subst)). 24.89/4.11 thf(func_def_611, type, sK474: ((subst > term > term) > term > subst)). 24.89/4.11 thf(func_def_612, type, sK475: ((subst > term > term) > term > term)). 24.89/4.11 thf(func_def_613, type, sK476: (term > (subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_614, type, sK477: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_615, type, sK478: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_616, type, sK479: term). 24.89/4.11 thf(func_def_617, type, sK480: term). 24.89/4.11 thf(func_def_618, type, sK481: term). 24.89/4.11 thf(func_def_619, type, sK482: term). 24.89/4.11 thf(func_def_620, type, sK483: (term > d_term)). 24.89/4.11 thf(func_def_621, type, sK484: (term > subst > (term > $o) > term > $o)). 24.89/4.11 thf(func_def_622, type, sK485: (term > $o)). 24.89/4.11 thf(func_def_623, type, sK486: subst). 24.89/4.11 thf(func_def_624, type, sK487: term). 24.89/4.11 thf(func_def_625, type, sK488: ((term > $o) > term)). 24.89/4.11 thf(func_def_626, type, sK489: subst). 24.89/4.11 thf(func_def_627, type, sK490: term). 24.89/4.11 thf(func_def_628, type, sK491: term). 24.89/4.11 thf(func_def_629, type, sK492: subst). 24.89/4.11 thf(func_def_630, type, sK493: term). 24.89/4.11 thf(func_def_631, type, sK494: (term > $o)). 24.89/4.11 thf(func_def_632, type, sK495: term). 24.89/4.11 thf(func_def_633, type, sK496: subst). 24.89/4.11 thf(func_def_634, type, sK497: (term > $o)). 24.89/4.11 thf(func_def_635, type, sK498: (term > (term > $o) > term)). 24.89/4.11 thf(func_def_636, type, sK499: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_637, type, sK500: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_638, type, sK501: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_639, type, sK502: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_640, type, sK503: ((subst > term > subst > $o) > (term > $o) > term)). 24.89/4.11 thf(func_def_641, type, sK504: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_642, type, sK505: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_643, type, sK506: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_644, type, sK507: ((subst > term > subst > $o) > subst)). 24.89/4.11 thf(func_def_645, type, sK508: (term > $o)). 24.89/4.11 thf(func_def_646, type, sK509: term). 24.89/4.11 thf(func_def_647, type, sK510: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_648, type, sK511: term). 24.89/4.11 thf(func_def_649, type, sK512: term). 24.89/4.11 thf(func_def_650, type, sK513: term). 24.89/4.11 thf(func_def_651, type, sK514: term). 24.89/4.11 thf(func_def_652, type, sK515: term). 24.89/4.11 thf(func_def_653, type, sK516: term). 24.89/4.11 thf(func_def_654, type, sK517: term). 24.89/4.11 thf(func_def_655, type, sK518: term). 24.89/4.11 thf(func_def_656, type, sK519: term). 24.89/4.11 thf(func_def_657, type, sK520: term). 24.89/4.11 thf(func_def_658, type, sK521: term). 24.89/4.11 thf(func_def_659, type, sK522: term). 24.89/4.11 thf(func_def_660, type, sK523: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_661, type, sK524: term). 24.89/4.11 thf(func_def_662, type, sK525: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_663, type, sK526: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_664, type, sK527: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_665, type, sK528: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_666, type, sK529: (term > (subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_667, type, sK530: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_668, type, sK531: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_669, type, sK532: (term > $o)). 24.89/4.11 thf(func_def_670, type, sK533: term). 24.89/4.11 thf(func_def_671, type, sK534: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_672, type, sK535: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_673, type, sK536: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_674, type, sK537: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_675, type, sK538: ((term > $o) > (subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_676, type, sK539: (term > (term > $o) > term)). 24.89/4.11 thf(func_def_677, type, sK540: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_678, type, sK541: term). 24.89/4.11 thf(func_def_679, type, sK542: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_680, type, sK543: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_681, type, sK544: (term > subst > term > term)). 24.89/4.11 thf(func_def_682, type, sK545: term). 24.89/4.11 thf(func_def_683, type, sK546: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_684, type, sK547: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_685, type, sK548: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_686, type, sK549: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_687, type, sK550: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_688, type, sK551: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_689, type, sK552: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_690, type, sK553: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_691, type, sK554: term). 24.89/4.11 thf(func_def_692, type, sK555: term). 24.89/4.11 thf(func_def_693, type, sK556: term). 24.89/4.11 thf(func_def_694, type, sK557: term). 24.89/4.11 thf(func_def_695, type, sK558: term). 24.89/4.11 thf(func_def_696, type, sK559: term). 24.89/4.11 thf(func_def_697, type, sK560: (subst > term > subst > $o)). 24.89/4.11 thf(func_def_698, type, sK561: term). 24.89/4.11 thf(func_def_699, type, sK562: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_700, type, sK563: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_701, type, sK564: ((subst > term > term) > subst)). 24.89/4.11 thf(func_def_702, type, sK565: ((subst > term > term) > term)). 24.89/4.11 thf(func_def_703, type, sK566: ((subst > term > subst > $o) > subst > term > term)). 24.89/4.11 thf(func_def_704, type, sK567: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_705, type, sK568: ((subst > term > subst > $o) > term)). 24.89/4.11 thf(func_def_706, type, vNOT: ($o > $o)). 24.89/4.11 thf(func_def_708, type, inv_lam_570: (term > term)). 24.89/4.11 thf(func_def_709, type, inv_lam_571: (term > term)). 24.89/4.11 thf(f1,axiom,( 24.89/4.11 ((^[X3 : subst, X4 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasapinj2 <=> ! [X8 : term,X15 : term,X14 : term,X10 : term] : ((X14 = X15) | (((ap @ (sub @ X8 @ id) @ X14)) != ((ap @ (sub @ X10 @ id) @ X15))))) & ((! [X8 : term] : (X8 = ((sub @ X8 @ id))) => ! [X8 : term] : (X8 = ((sub @ X8 @ id)))) <=> termmset_lthm) & pushprop_lem3v2 & axapp & hoaslamnotap_lthm & pushprop & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapinj1_gthm & ! [X47 : d_term,X46 : d_term] : ((((d2term @ X46)) = ((d2term @ X47))) => (X46 = X47)) & (hoasinduction_lem3b_lthm <=> ! [X10 : term] : ~ ! [X13 : (subst > term > term)] : (((X13 @ sh @ one)) != ((sub @ X10 @ (push @ one @ sh))))) & (! [X10 : term,X8 : term] : ((((lam @ X8)) != ((lam @ X10))) | (X8 = X10)) <=> laminj) & hoaslamnotvar_lthm & ((! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => (! [X9 : subst,X8 : term] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) => (! [X10 : term,X8 : term] : ((X8 = X10) | (((lam @ X8)) != ((lam @ X10)))) => ! [X34 : subst,X13 : (subst > term > term),X33 : (subst > term > term),X35 : term] : (~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (((lam @ (X13 @ sh @ one))) != ((lam @ (X33 @ sh @ one)))) | ~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X33 @ X9 @ X8) @ X18)) = ((X33 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (((X13 @ X34 @ X35)) = ((X33 @ X34 @ X35))))))) <=> hoaslaminj_lthm) & (one = ((d2term @ d_one))) & (hoasapinj2_lthm <=> (! [X15 : term,X14 : term,X10 : term,X8 : term] : ((X14 = X15) | (((ap @ X8 @ X14)) != ((ap @ X10 @ X15)))) => ! [X15 : term,X8 : term,X10 : term,X14 : term] : ((X14 = X15) | (((ap @ (sub @ X8 @ id) @ X14)) != ((ap @ (sub @ X10 @ id) @ X15)))))) & (hoasinduction_lthm_3 <=> (! [X5 : (subst > term > subst > $o)] : ~ ! [X6 : (term > $o)] : ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) => (! [X22 : term,X5 : (term > $o)] : (~ ! [X8 : term] : (~ ! [X10 : term] : ((X5 @ (sub @ X8 @ (push @ X10 @ id))) | ~(X5 @ X10)) | (X5 @ (lam @ X8))) | ~ ! [X8 : term] : (~(var @ X8) | (X5 @ X8)) | (X5 @ X22) | ~ ! [X8 : term,X10 : term] : ((X5 @ (ap @ X8 @ X10)) | ~(X5 @ X10) | ~(X5 @ X8))) => (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X5 : (subst > term > subst > $o),X26 : term,X6 : (term > $o)] : (~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X10 : term] : ((X6 @ (sub @ X26 @ (push @ X10 @ id))) | ~(X6 @ X10)) | (X6 @ (lam @ X26)) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id)))) => ! [X21 : term,X5 : (subst > term > subst > $o)] : (~ ! [X8 : term] : ((X5 @ id @ X8 @ id) | ~(var @ (sub @ X8 @ id))) | ~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | ~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18))))) | (X5 @ id @ X21 @ id) | ~ ! [X10 : term,X8 : term] : ((X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X10 @ id) | ~(X5 @ id @ X8 @ id)) | ~ ! [X8 : term,X9 : subst,X18 : subst,X19 : subst] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X19 : subst,X9 : subst,X8 : term,X18 : subst] : (~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | (X5 @ X9 @ X8 @ (comp @ X19 @ X18))))))))) & (hoasinduction_lem3v2a <=> ! [X6 : (term > $o),X5 : (subst > term > subst > $o),X26 : term] : (~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) | (X6 @ (lam @ X26)) | ~ ! [X10 : term] : (~(X6 @ X10) | (X6 @ (sub @ X26 @ (push @ X10 @ id)))) | ~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | ~ ! [X18 : subst,X9 : subst,X8 : term] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18))))))) & (pushprop_lem1_lthm <=> (! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => (! [X9 : subst,X8 : term] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) => ! [X19 : (term > $o),X10 : term,X8 : term,X9 : subst,X5 : (term > $o)] : (~(X5 @ X8) | (X19 @ (sub @ X8 @ (push @ X10 @ X9))))))) & (id = ((d2subst @ d_id))) & pushprop_lem2v2_gthm & (apinj2 <=> ! [X8 : term,X14 : term,X10 : term,X15 : term] : ((X14 = X15) | (((ap @ X8 @ X14)) != ((ap @ X10 @ X15))))) & induction2lem_gthm & hoasinduction_lem1v2_gthm & pushprop_lthm_orig & (induction2lem_lthm <=> (! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => (! [X9 : subst,X8 : term] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) => (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) => (! [X5 : (term > $o),X23 : term] : (~ ! [X8 : term,X10 : term] : (~(X5 @ X10) | ~(X5 @ X8) | (X5 @ (ap @ X8 @ X10))) | ~ ! [X8 : term] : ((X5 @ (lam @ X8)) | ~(X5 @ X8)) | (X5 @ X23) | ~ ! [X8 : term] : (~(var @ X8) | (X5 @ X8))) => ! [X5 : (term > $o),X12 : subst,X11 : term] : (~ ! [X8 : term] : (~ ! [X10 : term] : (~(X5 @ X10) | (X5 @ (sub @ X8 @ (push @ X10 @ id)))) | (X5 @ (lam @ X8))) | ~ ! [X10 : term] : ((X5 @ (sub @ X10 @ X12)) | ~(var @ X10)) | ~ ! [X10 : term,X8 : term] : ((X5 @ (ap @ X8 @ X10)) | ~(X5 @ X10) | ~(X5 @ X8)) | (X5 @ (sub @ X11 @ X12)))))))) & (! [X22 : term,X5 : (term > $o)] : (~ ! [X8 : term] : ((X5 @ (lam @ X8)) | ~ ! [X10 : term] : ((X5 @ (sub @ X8 @ (push @ X10 @ id))) | ~(X5 @ X10))) | (X5 @ X22) | ~ ! [X8 : term] : ((X5 @ X8) | ~(var @ X8)) | ~ ! [X8 : term,X10 : term] : ((X5 @ (ap @ X8 @ X10)) | ~(X5 @ X10) | ~(X5 @ X8))) <=> induction2) & (axvarid <=> ! [X8 : term] : (X8 = ((sub @ X8 @ id)))) & hoasinduction_lem1_gthm & (! [X8 : term,X14 : term,X15 : term,X10 : term] : ((X8 = X10) | (((ap @ (sub @ X8 @ id) @ X14)) != ((ap @ (sub @ X10 @ id) @ X15)))) <=> hoasapinj1) & hoasinduction_lem3_gthm & pushprop_lem2v2_lthm & hoaslaminj_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X10 : term] : ~ ! [X13 : (subst > term > term)] : ~ ! [X9 : subst,X8 : term] : (((sub @ X10 @ (push @ X8 @ X9))) = ((X13 @ X9 @ X8))) => (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => ! [X26 : term,X6 : (term > $o),X5 : (subst > term > subst > $o)] : (~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id))) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) | ~ ! [X10 : term] : (~(X6 @ X10) | (X6 @ (sub @ X26 @ (push @ X10 @ id)))) | (X6 @ (lam @ X26)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axmap & (hoasinduction_lem3v2_f <=> ! [X10 : term] : ~ ! [X13 : (subst > term > term)] : ~ ! [X9 : subst,X8 : term] : (((sub @ X10 @ (push @ X8 @ X9))) = ((X13 @ X9 @ X8)))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (axscons <=> ! [X9 : subst] : (X9 = ((push @ (sub @ one @ X9) @ (comp @ sh @ X9))))) & (sh = ((d2subst @ d_id))) & lamnotvar & (! [X34 : subst,X35 : term,X13 : (subst > term > term),X33 : (subst > term > term)] : (~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (((X13 @ X34 @ X35)) = ((X33 @ X34 @ X35))) | (((lam @ (X13 @ sh @ one))) != ((lam @ (X33 @ sh @ one)))) | ~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X33 @ X9 @ X8) @ X18)) = ((X33 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18))))) <=> hoaslaminj) & (substmonoid <=> (! [X9 : subst] : (X9 = ((comp @ id @ X9))) & ! [X9 : subst] : (X9 = ((comp @ X9 @ id))))) & ((! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X5 : (subst > term > subst > $o),X32 : term] : ((X5 @ id @ (lam @ (sub @ X32 @ (push @ one @ sh))) @ id) | ~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id))) | ~ ! [X10 : term] : (~(X5 @ id @ X10 @ id) | (X5 @ id @ (sub @ X32 @ (push @ X10 @ id)) @ id))) => ! [X5 : (subst > term > subst > $o),X20 : term] : (~ ! [X19 : subst,X9 : subst,X8 : term,X18 : subst] : ((X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | ~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | ~ ! [X18 : subst,X9 : subst,X8 : term] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | (X5 @ id @ (lam @ X20) @ id) | ~ ! [X10 : term] : (~(X5 @ id @ X10 @ id) | (X5 @ id @ (sub @ X20 @ (push @ X10 @ id)) @ id)) | ~ ! [X9 : subst,X8 : term,X18 : subst,X19 : subst] : ((X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | ~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)))))) <=> hoasinduction_lem3_lthm) & hoasinduction_gthm & ~lamnotap & (hoasinduction_lem3 <=> ! [X5 : (subst > term > subst > $o),X20 : term] : (~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | ~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X8 : term,X19 : subst,X9 : subst,X18 : subst] : ((X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | ~(X5 @ X9 @ X8 @ (comp @ X19 @ X18))) | ~ ! [X10 : term] : (~(X5 @ id @ X10 @ id) | (X5 @ id @ (sub @ X20 @ (push @ X10 @ id)) @ id)) | (X5 @ id @ (lam @ X20) @ id) | ~ ! [X19 : subst,X18 : subst,X8 : term,X9 : subst] : (~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | (X5 @ X9 @ X8 @ (comp @ X19 @ X18))))) & (! [X5 : (subst > term > subst > $o),X6 : (term > $o),X25 : term,X24 : term] : (~(X6 @ X24) | (X6 @ (ap @ X24 @ X25)) | ~(X6 @ X25) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) | ~ ! [X19 : subst,X8 : term,X18 : subst,X9 : subst] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X18 : subst,X8 : term,X19 : subst,X9 : subst] : ((X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | ~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X8 : term,X10 : term] : ((X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X10 @ id) | ~(X5 @ id @ X8 @ id))) <=> hoasinduction_lem2v2) & ((^[X8 : term, X9 : subst, X5 : (term > $o), X6 : (term > $o)] : (! [X7 : term] : (((X6 @ X7)) = ((X5 @ (sub @ X7 @ (push @ X8 @ X9))))))) = pushprop_p_and_p_prime) & (! [X12 : subst,X5 : (term > $o),X11 : term] : (~ ! [X8 : term] : ((X5 @ (lam @ X8)) | ~ ! [X10 : term] : ((X5 @ (sub @ X8 @ (push @ X10 @ id))) | ~(X5 @ X10))) | (X5 @ (sub @ X11 @ X12)) | ~ ! [X8 : term,X10 : term] : ((X5 @ (ap @ X8 @ X10)) | ~(X5 @ X10) | ~(X5 @ X8)) | ~ ! [X10 : term] : (~(var @ X10) | (X5 @ (sub @ X10 @ X12)))) <=> induction2lem) & substmonoid_gthm & induction2_gthm & pushprop_lem1v2_gthm & (induction2_lthm <=> (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X11 : term,X5 : (term > $o),X12 : subst] : ((X5 @ (sub @ X11 @ X12)) | ~ ! [X10 : term,X8 : term] : (~(X5 @ X8) | ~(X5 @ X10) | (X5 @ (ap @ X8 @ X10))) | ~ ! [X10 : term] : (~(var @ X10) | (X5 @ (sub @ X10 @ X12))) | ~ ! [X8 : term] : ((X5 @ (lam @ X8)) | ~ ! [X10 : term] : (~(X5 @ X10) | (X5 @ (sub @ X8 @ (push @ X10 @ id)))))) => ! [X22 : term,X5 : (term > $o)] : ((X5 @ X22) | ~ ! [X8 : term] : (~ ! [X10 : term] : (~(X5 @ X10) | (X5 @ (sub @ X8 @ (push @ X10 @ id)))) | (X5 @ (lam @ X8))) | ~ ! [X8 : term] : (~(var @ X8) | (X5 @ X8)) | ~ ! [X8 : term,X10 : term] : ((X5 @ (ap @ X8 @ X10)) | ~(X5 @ X8) | ~(X5 @ X10)))))) & (! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) <=> axvarcons) & (hoasinduction_p_and_p_prime = (^[X5 : (subst > term > subst > $o), X6 : (term > $o)] : (! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id)))))) & (pushprop_lem0 <=> ! [X5 : (term > $o),X9 : subst,X8 : term] : ~ ! [X6 : (term > $o)] : ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ (sub @ X7 @ (push @ X8 @ X9)))))) & (hoasinduction_lem3a_lthm <=> (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X5 : (subst > term > subst > $o),X32 : term] : (~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X18 : subst,X9 : subst,X8 : term] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id))) | (X5 @ id @ (lam @ (sub @ X32 @ (push @ one @ sh))) @ id) | ~ ! [X10 : term] : ((X5 @ id @ (sub @ X32 @ (push @ X10 @ id)) @ id) | ~(X5 @ id @ X10 @ id))) => ! [X27 : term,X5 : (subst > term > subst > $o)] : (~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | ~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X10 : term] : (~(X5 @ id @ X10 @ id) | (X5 @ id @ (sub @ X27 @ (push @ X10 @ id)) @ id)) | (X5 @ id @ (lam @ X27) @ id))))) & hoasinduction_lem1v2 & hoasinduction_lem2_lthm & ((! [X5 : (term > $o),X22 : term] : ((X5 @ X22) | ~ ! [X8 : term] : ((X5 @ X8) | ~(var @ X8)) | ~ ! [X8 : term] : ((X5 @ (lam @ X8)) | ~ ! [X10 : term] : ((X5 @ (sub @ X8 @ (push @ X10 @ id))) | ~(X5 @ X10))) | ~ ! [X8 : term,X10 : term] : (~(X5 @ X8) | (X5 @ (ap @ X8 @ X10)) | ~(X5 @ X10))) => (! [X17 : term,X16 : term,X5 : (subst > term > subst > $o)] : (~(X5 @ id @ X17 @ id) | (X5 @ id @ (ap @ X16 @ X17) @ id) | ~ ! [X18 : subst,X8 : term,X9 : subst,X19 : subst] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~(X5 @ id @ X16 @ id) | ~ ! [X18 : subst,X19 : subst,X8 : term,X9 : subst] : ((X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | ~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X8 : term,X10 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X10 @ id))) => (! [X5 : (subst > term > subst > $o),X20 : term] : (~ ! [X9 : subst,X19 : subst,X18 : subst,X8 : term] : (~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | (X5 @ X9 @ X8 @ (comp @ X19 @ X18))) | ~ ! [X10 : term] : ((X5 @ id @ (sub @ X20 @ (push @ X10 @ id)) @ id) | ~(X5 @ id @ X10 @ id)) | (X5 @ id @ (lam @ X20) @ id) | ~ ! [X19 : subst,X8 : term,X18 : subst,X9 : subst] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))))) => ! [X21 : term,X5 : (subst > term > subst > $o)] : (~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X19 : subst,X18 : subst,X8 : term,X9 : subst] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X8 : term,X10 : term] : (~(X5 @ id @ X10 @ id) | (X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X8 @ id)) | ~ ! [X8 : term] : (~(var @ (sub @ X8 @ id)) | (X5 @ id @ X8 @ id)) | ~ ! [X19 : subst,X18 : subst,X9 : subst,X8 : term] : (~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | (X5 @ X9 @ X8 @ (comp @ X19 @ X18))) | (X5 @ id @ X21 @ id))))) <=> hoasinduction_lthm) & hoasapnotvar & ((! [X8 : term] : (X8 = ((sub @ X8 @ id))) => ! [X5 : (subst > term > subst > $o),X6 : (term > $o),X28 : term] : (~ ! [X19 : subst,X8 : term,X18 : subst,X9 : subst] : ((X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | ~(X5 @ X9 @ X8 @ (comp @ X19 @ X18))) | (X6 @ (lam @ X28)) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) | ~ ! [X10 : term] : (~(X6 @ X10) | (X6 @ (sub @ X28 @ (push @ X10 @ id)))) | ~ ! [X8 : term,X9 : subst,X18 : subst,X19 : subst] : ((X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | ~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)))) <=> hoasinduction_lem3v2_lthm) & (hoasinduction_no_psi_cond <=> ! [X31 : term,X5 : (subst > term > subst > $o)] : ((X5 @ id @ X31 @ id) | ~ ! [X10 : term,X8 : term] : ((X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X8 @ id) | ~(X5 @ id @ X10 @ id)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X18 : subst,X8 : term,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)))) & (! [X5 : (subst > term > subst > $o)] : ~ ! [X6 : (term > $o)] : ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) <=> hoasinduction_lem0) & hoaslamnotvar_gthm & pushprop_lem0_gthm & (hoasinduction_no_psi_cond_lthm <=> (! [X5 : (subst > term > subst > $o)] : ~ ! [X6 : (term > $o)] : ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) => (! [X22 : term,X5 : (term > $o)] : ((X5 @ X22) | ~ ! [X8 : term] : ((X5 @ X8) | ~(var @ X8)) | ~ ! [X10 : term,X8 : term] : ((X5 @ (ap @ X8 @ X10)) | ~(X5 @ X8) | ~(X5 @ X10)) | ~ ! [X8 : term] : ((X5 @ (lam @ X8)) | ~ ! [X10 : term] : (~(X5 @ X10) | (X5 @ (sub @ X8 @ (push @ X10 @ id)))))) => (! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X6 : (term > $o),X26 : term,X5 : (subst > term > subst > $o)] : (~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) | ~ ! [X13 : (subst > term > term)] : (~ ! [X9 : subst,X18 : subst,X8 : term] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id))) | ~ ! [X10 : term] : ((X6 @ (sub @ X26 @ (push @ X10 @ id))) | ~(X6 @ X10)) | (X6 @ (lam @ X26))) => ! [X31 : term,X5 : (subst > term > subst > $o)] : (~ ! [X8 : term,X10 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X10 @ id)) | ~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | ~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18))))) | (X5 @ id @ X31 @ id))))))) & pushprop_lem3v2_lthm & apnotvar & (! [X5 : (subst > term > subst > $o),X32 : term] : (~ ! [X10 : term] : ((X5 @ id @ (sub @ X32 @ (push @ X10 @ id)) @ id) | ~(X5 @ id @ X10 @ id)) | ~ ! [X13 : (subst > term > term)] : ((X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X18 : subst,X9 : subst,X8 : term] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id))) | (X5 @ id @ (lam @ (sub @ X32 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X8 : term] : (X8 = ((sub @ X8 @ id))) => (! [X10 : term,X14 : term,X15 : term,X8 : term] : ((X8 = X10) | (((ap @ X8 @ X14)) != ((ap @ X10 @ X15)))) => ! [X14 : term,X8 : term,X10 : term,X15 : term] : ((X8 = X10) | (((ap @ (sub @ X8 @ id) @ X14)) != ((ap @ (sub @ X10 @ id) @ X15)))))) <=> hoasapinj1_lthm) & hoasapinj2_gthm & axabs & ! [X45 : subst] : ? [X44 : d_subst] : (X45 = ((d2subst @ X44))) & (termmset <=> ! [X8 : term] : (X8 = ((sub @ X8 @ id)))) & (! [X5 : (subst > term > subst > $o)] : ~ ! [X6 : (term > $o)] : ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) <=> hoasinduction_lem0_lthm) & ! [X1 : d_subst,X2 : d_subst] : ((((d2subst @ X1)) = ((d2subst @ X2))) => (X1 = X2)) & ulamvarsh & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X10 : term,X9 : subst,X5 : (term > $o),X8 : term,X19 : (term > $o)] : (~(X5 @ X8) | (X19 @ (sub @ X8 @ (push @ X10 @ X9)))) <=> pushprop_lem1) & hoaslamnotap_gthm & (! [X16 : term,X5 : (subst > term > subst > $o),X17 : term] : (~ ! [X8 : term,X9 : subst,X19 : subst,X18 : subst] : ((X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | ~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | (X5 @ id @ (ap @ X16 @ X17) @ id) | ~ ! [X8 : term,X9 : subst,X18 : subst,X19 : subst] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X8 : term,X10 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id) | ~(X5 @ id @ X10 @ id)) | ~(X5 @ id @ X17 @ id) | ~(X5 @ id @ X16 @ id)) <=> hoasinduction_lem2) & ulamvarind & hoasinduction_lem3b_gthm & ~ulamvar1 & (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) <=> axidr) & (! [X9 : subst] : (X9 = ((comp @ id @ X9))) <=> axidl) & ! [X48 : term] : ? [X0 : d_term] : (X48 = ((d2term @ X0))) & ~(var @ (d2term @ d_one)) & hoasinduction_lem3v2_gthm & hoasinduction_lem2v2_gthm & (! [X8 : term,X15 : term,X14 : term,X10 : term] : ((X8 = X10) | (((ap @ X8 @ X14)) != ((ap @ X10 @ X15)))) <=> apinj1) & (! [X23 : term,X5 : (term > $o)] : (~ ! [X8 : term] : (~(X5 @ X8) | (X5 @ (lam @ X8))) | (X5 @ X23) | ~ ! [X10 : term,X8 : term] : (~(X5 @ X10) | (X5 @ (ap @ X8 @ X10)) | ~(X5 @ X8)) | ~ ! [X8 : term] : ((X5 @ X8) | ~(var @ X8))) <=> induction) & hoasapnotvar_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoaslamnotvar & (hoasinduction_lem3aaa <=> ! [X36 : term,X5 : (subst > term > subst > $o)] : (~ ! [X13 : (subst > term > term),X37 : term] : (~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | ~ ! [X38 : subst,X39 : term,X40 : subst] : (((sub @ (X13 @ X38 @ X39) @ X40)) = ((sub @ (sub @ X37 @ (push @ X39 @ X38)) @ X40))) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X43 : subst,X42 : term,X41 : subst] : (((X13 @ (comp @ X41 @ X43) @ (sub @ X42 @ X43))) = ((sub @ X37 @ (push @ (sub @ X42 @ X43) @ (comp @ X41 @ X43)))))) | (X5 @ id @ (lam @ (sub @ X36 @ (push @ one @ sh))) @ id) | ~ ! [X10 : term] : ((X5 @ id @ (sub @ X36 @ (push @ X10 @ id)) @ id) | ~(X5 @ id @ X10 @ id)))) & ((! [X8 : term,X9 : subst] : (X8 = ((sub @ one @ (push @ X8 @ X9)))) => ! [X5 : (term > $o),X6 : (term > $o),X9 : subst,X8 : term] : ((X6 @ one) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ (sub @ X7 @ (push @ X8 @ X9))))) | ~(X5 @ X8))) <=> pushprop_lem1v2_lthm) & (! [X10 : term,X8 : term] : ((X8 = X10) | (((sub @ X8 @ sh)) != ((sub @ X10 @ sh)))) <=> shinj) & (! [X5 : (subst > term > subst > $o),X21 : term] : (~ ! [X8 : term] : (~(var @ (sub @ X8 @ id)) | (X5 @ id @ X8 @ id)) | ~ ! [X9 : subst,X19 : subst,X18 : subst,X8 : term] : (~(X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | (X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | (X5 @ id @ X21 @ id) | ~ ! [X10 : term,X8 : term] : (~(X5 @ id @ X8 @ id) | ~(X5 @ id @ X10 @ id) | (X5 @ id @ (ap @ (sub @ X8 @ id) @ X10) @ id)) | ~ ! [X8 : term,X9 : subst,X18 : subst,X19 : subst] : ((X5 @ X9 @ X8 @ (comp @ X19 @ X18)) | ~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18)) | ~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term] : (~(X5 @ id @ X8 @ id) | (X5 @ id @ (X13 @ id @ X8) @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X9 : subst,X8 : term,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))))) <=> hoasinduction) & (! [X13 : (subst > term > term),X29 : term,X30 : term] : (~ ! [X8 : term,X18 : subst,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (((lam @ (X13 @ sh @ one))) != ((ap @ (sub @ X29 @ id) @ X30)))) <=> hoaslamnotap) & hoasinduction_lem1 & (! [X10 : term] : ~ ! [X13 : (subst > term > term)] : ~ ! [X9 : subst,X8 : term] : (((sub @ X10 @ (push @ X8 @ X9))) = ((X13 @ X9 @ X8))) <=> hoasinduction_lem3v2_f_lthm) & axvarshift & hoasinduction_lem2_gthm & axassoc & (! [X5 : (term > $o),X9 : subst,X8 : term] : ~ ! [X6 : (term > $o)] : ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ (sub @ X7 @ (push @ X8 @ X9))))) <=> pushprop_lem0_lthm) & hoasapnotvar_gthm & pushprop_lem1_gthm & hoasinduction_lem1_lthm & axclos & ! [X0 : d_term] : (X0 = d_one) & pushprop_gthm & (hoasinduction_lem3aa <=> ! [X5 : (subst > term > subst > $o),X32 : term] : ((X5 @ id @ (lam @ (sub @ X32 @ (push @ one @ sh))) @ id) | ~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X9 : subst,X8 : term,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18))))) | ~ ! [X10 : term] : (~(X5 @ id @ X10 @ id) | (X5 @ id @ (sub @ X32 @ (push @ X10 @ id)) @ id)))) & ! [X44 : d_subst] : (X44 = d_id) & pushprop_lem2v2 & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_lem3a <=> ! [X27 : term,X5 : (subst > term > subst > $o)] : (~ ! [X13 : (subst > term > term)] : (~ ! [X18 : subst,X8 : term,X9 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id)) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id)) | ~ ! [X10 : term] : ((X5 @ id @ (sub @ X27 @ (push @ X10 @ id)) @ id) | ~(X5 @ id @ X10 @ id)) | (X5 @ id @ (lam @ X27) @ id))) & (hoasinduction_lem3b <=> ! [X10 : term] : ~ ! [X13 : (subst > term > term)] : (((X13 @ sh @ one)) != ((sub @ X10 @ (push @ one @ sh))))) & (hoasinduction_lem3v2 <=> ! [X28 : term,X5 : (subst > term > subst > $o),X6 : (term > $o)] : (~ ! [X10 : term] : (~(X6 @ X10) | (X6 @ (sub @ X28 @ (push @ X10 @ id)))) | ~ ! [X13 : (subst > term > term)] : (~ ! [X8 : term,X9 : subst,X18 : subst] : (((sub @ (X13 @ X9 @ X8) @ X18)) = ((X13 @ (comp @ X9 @ X18) @ (sub @ X8 @ X18)))) | (X5 @ id @ (lam @ (X13 @ sh @ one)) @ id) | ~ ! [X8 : term] : ((X5 @ id @ (X13 @ id @ X8) @ id) | ~(X5 @ id @ X8 @ id))) | ~ ! [X18 : subst,X19 : subst,X9 : subst,X8 : term] : (~(X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | (X5 @ X9 @ X8 @ (comp @ X19 @ X18))) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ id @ X7 @ id))) | ~ ! [X19 : subst,X9 : subst,X8 : term,X18 : subst] : ((X5 @ (comp @ X9 @ X19) @ (sub @ X8 @ X19) @ X18) | ~(X5 @ X9 @ X8 @ (comp @ X19 @ X18))) | (X6 @ (lam @ X28)))) & pushprop_lthm & ((! [X9 : subst] : (X9 = ((comp @ id @ X9))) => (! [X9 : subst] : (X9 = ((comp @ X9 @ id))) => (! [X9 : subst] : (X9 = ((comp @ id @ X9))) & ! [X9 : subst] : (X9 = ((comp @ X9 @ id)))))) <=> substmonoid_lthm) & hoasinduction_lem3a_gthm & termmset_gthm & (pushprop_lem1v2 <=> ! [X9 : subst,X6 : (term > $o),X8 : term,X5 : (term > $o)] : ((X6 @ one) | ~(X5 @ X8) | ~ ! [X7 : term] : (((X6 @ X7)) = ((X5 @ (sub @ X7 @ (push @ X8 @ X9))))))) & (! [X9 : subst,X8 : term] : (X9 = ((comp @ sh @ (push @ X8 @ X9)))) <=> axshiftcons)), 24.89/4.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)). 24.89/4.11 thf(f2,conjecture,( 24.89/4.11 (hoasinduction_no_psi_cond = ! [X0 : (subst > term > subst > $o)] : (! [X2 : term,X1 : term] : ((X0 @ id @ X1 @ id) => ((X0 @ id @ X2 @ id) => (X0 @ id @ (hoasap @ id @ X1 @ id @ X2) @ id))) => (! [X3 : (subst > term > term)] : (! [X5 : subst,X1 : term,X4 : subst] : (((sub @ (X3 @ X4 @ X1) @ X5)) = ((X3 @ (comp @ X4 @ X5) @ (sub @ X1 @ X5)))) => (! [X1 : term] : ((X0 @ id @ X1 @ id) => (X0 @ id @ (X3 @ id @ X1) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X4 : subst, X1 : term] : ((X3 @ X4 @ X1)))) @ id))) => ! [X1 : term] : (X0 @ id @ X1 @ id))))), 24.89/4.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_no_psi_cond)). 24.89/4.11 thf(f3,negated_conjecture,( 24.89/4.11 ~ (hoasinduction_no_psi_cond = ! [X0 : (subst > term > subst > $o)] : (! [X2 : term,X1 : term] : ((X0 @ id @ X1 @ id) => ((X0 @ id @ X2 @ id) => (X0 @ id @ (hoasap @ id @ X1 @ id @ X2) @ id))) => (! [X3 : (subst > term > term)] : (! [X5 : subst,X1 : term,X4 : subst] : (((sub @ (X3 @ X4 @ X1) @ X5)) = ((X3 @ (comp @ X4 @ X5) @ (sub @ X1 @ X5)))) => (! [X1 : term] : ((X0 @ id @ X1 @ id) => (X0 @ id @ (X3 @ id @ X1) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X4 : subst, X1 : term] : ((X3 @ X4 @ X1)))) @ id))) => ! [X1 : term] : (X0 @ id @ X1 @ id))))), 24.89/4.11 inference(negated_conjecture,[status(cth)],[f2])). 24.89/4.11 thf(f4,plain,( 24.89/4.11 ((^[X0 : subst, X1 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasapinj2 <=> ! [X2 : term,X3 : term,X4 : term,X5 : term] : ((X3 = X4) | (((ap @ (sub @ X2 @ id) @ X4)) != ((ap @ (sub @ X5 @ id) @ X3))))) & ((! [X6 : term] : (((sub @ X6 @ id)) = X6) => ! [X7 : term] : (((sub @ X7 @ id)) = X7)) <=> termmset_lthm) & pushprop_lem3v2 & axapp & hoaslamnotap_lthm & pushprop & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapinj1_gthm & ! [X8 : d_term,X9 : d_term] : ((((d2term @ X9)) = ((d2term @ X8))) => (X8 = X9)) & (hoasinduction_lem3b_lthm <=> ! [X10 : term] : ~ ! [X11 : (subst > term > term)] : (((sub @ X10 @ (push @ one @ sh))) != ((X11 @ sh @ one)))) & (! [X12 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X12))) | (X12 = X13)) <=> laminj) & hoaslamnotvar_lthm & ((! [X14 : term,X15 : subst] : (((sub @ one @ (push @ X14 @ X15))) = X14) => (! [X16 : subst,X17 : term] : (((comp @ sh @ (push @ X17 @ X16))) = X16) => (! [X18 : term,X19 : term] : ((X18 = X19) | (((lam @ X18)) != ((lam @ X19)))) => ! [X20 : subst,X21 : (subst > term > term),X22 : (subst > term > term),X23 : term] : (~ ! [X24 : term,X25 : subst,X26 : subst] : (((X21 @ (comp @ X26 @ X25) @ (sub @ X24 @ X25))) = ((sub @ (X21 @ X26 @ X24) @ X25))) | (((lam @ (X22 @ sh @ one))) != ((lam @ (X21 @ sh @ one)))) | ~ ! [X27 : term,X28 : subst,X29 : subst] : (((X22 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29))) = ((sub @ (X22 @ X28 @ X27) @ X29))) | (((X21 @ X20 @ X23)) = ((X22 @ X20 @ X23))))))) <=> hoaslaminj_lthm) & (one = ((d2term @ d_one))) & (hoasapinj2_lthm <=> (! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X31) | (((ap @ X32 @ X30)) != ((ap @ X33 @ X31)))) => ! [X34 : term,X35 : term,X36 : term,X37 : term] : ((X34 = X37) | (((ap @ (sub @ X35 @ id) @ X37)) != ((ap @ (sub @ X36 @ id) @ X34)))))) & (hoasinduction_lthm_3 <=> (! [X38 : (subst > term > subst > $o)] : ~ ! [X39 : (term > $o)] : ~ ! [X40 : term] : (((X39 @ X40)) = ((X38 @ id @ X40 @ id))) => (! [X41 : term,X42 : (term > $o)] : (~ ! [X43 : term] : (~ ! [X44 : term] : ((X42 @ (sub @ X43 @ (push @ X44 @ id))) | ~(X42 @ X44)) | (X42 @ (lam @ X43))) | ~ ! [X45 : term] : (~(var @ X45) | (X42 @ X45)) | (X42 @ X41) | ~ ! [X46 : term,X47 : term] : ((X42 @ (ap @ X46 @ X47)) | ~(X42 @ X47) | ~(X42 @ X46))) => (! [X48 : term] : (((sub @ X48 @ id)) = X48) => (! [X49 : (subst > term > subst > $o),X50 : term,X51 : (term > $o)] : (~ ! [X52 : (subst > term > term)] : (~ ! [X53 : term,X54 : subst,X55 : subst] : (((X52 @ (comp @ X54 @ X55) @ (sub @ X53 @ X55))) = ((sub @ (X52 @ X54 @ X53) @ X55))) | ~ ! [X56 : term] : ((X49 @ id @ (X52 @ id @ X56) @ id) | ~(X49 @ id @ X56 @ id)) | (X49 @ id @ (lam @ (X52 @ sh @ one)) @ id)) | ~ ! [X57 : term] : ((X51 @ (sub @ X50 @ (push @ X57 @ id))) | ~(X51 @ X57)) | (X51 @ (lam @ X50)) | ~ ! [X58 : term] : (((X49 @ id @ X58 @ id)) = ((X51 @ X58)))) => ! [X59 : term,X60 : (subst > term > subst > $o)] : (~ ! [X61 : term] : ((X60 @ id @ X61 @ id) | ~(var @ (sub @ X61 @ id))) | ~ ! [X62 : (subst > term > term)] : ((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id) | ~ ! [X63 : term] : ((X60 @ id @ (X62 @ id @ X63) @ id) | ~(X60 @ id @ X63 @ id)) | ~ ! [X64 : term,X65 : subst,X66 : subst] : (((X62 @ (comp @ X66 @ X65) @ (sub @ X64 @ X65))) = ((sub @ (X62 @ X66 @ X64) @ X65)))) | (X60 @ id @ X59 @ id) | ~ ! [X67 : term,X68 : term] : ((X60 @ id @ (ap @ (sub @ X68 @ id) @ X67) @ id) | ~(X60 @ id @ X67 @ id) | ~(X60 @ id @ X68 @ id)) | ~ ! [X69 : term,X70 : subst,X71 : subst,X72 : subst] : (~(X60 @ X70 @ X69 @ (comp @ X72 @ X71)) | (X60 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)) | ~ ! [X73 : subst,X74 : subst,X75 : term,X76 : subst] : (~(X60 @ (comp @ X74 @ X73) @ (sub @ X75 @ X73) @ X76) | (X60 @ X74 @ X75 @ (comp @ X73 @ X76))))))))) & (hoasinduction_lem3v2a <=> ! [X77 : (term > $o),X78 : (subst > term > subst > $o),X79 : term] : (~ ! [X80 : term] : (((X77 @ X80)) = ((X78 @ id @ X80 @ id))) | (X77 @ (lam @ X79)) | ~ ! [X81 : term] : (~(X77 @ X81) | (X77 @ (sub @ X79 @ (push @ X81 @ id)))) | ~ ! [X82 : (subst > term > term)] : ((X78 @ id @ (lam @ (X82 @ sh @ one)) @ id) | ~ ! [X83 : term] : ((X78 @ id @ (X82 @ id @ X83) @ id) | ~(X78 @ id @ X83 @ id)) | ~ ! [X84 : subst,X85 : subst,X86 : term] : (((X82 @ (comp @ X85 @ X84) @ (sub @ X86 @ X84))) = ((sub @ (X82 @ X85 @ X86) @ X84)))))) & (pushprop_lem1_lthm <=> (! [X87 : term,X88 : subst] : (((sub @ one @ (push @ X87 @ X88))) = X87) => (! [X89 : subst,X90 : term] : (((comp @ sh @ (push @ X90 @ X89))) = X89) => ! [X91 : (term > $o),X92 : term,X93 : term,X94 : subst,X95 : (term > $o)] : (~(X95 @ X93) | (X91 @ (sub @ X93 @ (push @ X92 @ X94))))))) & (id = ((d2subst @ d_id))) & pushprop_lem2v2_gthm & (apinj2 <=> ! [X96 : term,X97 : term,X98 : term,X99 : term] : ((X97 = X99) | (((ap @ X96 @ X97)) != ((ap @ X98 @ X99))))) & induction2lem_gthm & hoasinduction_lem1v2_gthm & pushprop_lthm_orig & (induction2lem_lthm <=> (! [X100 : term,X101 : subst] : (((sub @ one @ (push @ X100 @ X101))) = X100) => (! [X102 : subst,X103 : term] : (((comp @ sh @ (push @ X103 @ X102))) = X102) => (! [X104 : subst] : (((comp @ X104 @ id)) = X104) => (! [X105 : (term > $o),X106 : term] : (~ ! [X107 : term,X108 : term] : (~(X105 @ X108) | ~(X105 @ X107) | (X105 @ (ap @ X107 @ X108))) | ~ ! [X109 : term] : ((X105 @ (lam @ X109)) | ~(X105 @ X109)) | (X105 @ X106) | ~ ! [X110 : term] : (~(var @ X110) | (X105 @ X110))) => ! [X111 : (term > $o),X112 : subst,X113 : term] : (~ ! [X114 : term] : (~ ! [X115 : term] : (~(X111 @ X115) | (X111 @ (sub @ X114 @ (push @ X115 @ id)))) | (X111 @ (lam @ X114))) | ~ ! [X116 : term] : ((X111 @ (sub @ X116 @ X112)) | ~(var @ X116)) | ~ ! [X117 : term,X118 : term] : ((X111 @ (ap @ X118 @ X117)) | ~(X111 @ X117) | ~(X111 @ X118)) | (X111 @ (sub @ X113 @ X112)))))))) & (! [X119 : term,X120 : (term > $o)] : (~ ! [X121 : term] : ((X120 @ (lam @ X121)) | ~ ! [X122 : term] : ((X120 @ (sub @ X121 @ (push @ X122 @ id))) | ~(X120 @ X122))) | (X120 @ X119) | ~ ! [X123 : term] : ((X120 @ X123) | ~(var @ X123)) | ~ ! [X124 : term,X125 : term] : ((X120 @ (ap @ X124 @ X125)) | ~(X120 @ X125) | ~(X120 @ X124))) <=> induction2) & (axvarid <=> ! [X126 : term] : (((sub @ X126 @ id)) = X126)) & hoasinduction_lem1_gthm & (! [X127 : term,X128 : term,X129 : term,X130 : term] : ((X127 = X130) | (((ap @ (sub @ X127 @ id) @ X128)) != ((ap @ (sub @ X130 @ id) @ X129)))) <=> hoasapinj1) & hoasinduction_lem3_gthm & pushprop_lem2v2_lthm & hoaslaminj_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X131 : term] : ~ ! [X132 : (subst > term > term)] : ~ ! [X133 : subst,X134 : term] : (((sub @ X131 @ (push @ X134 @ X133))) = ((X132 @ X133 @ X134))) => (! [X135 : term] : (((sub @ X135 @ id)) = X135) => ! [X136 : term,X137 : (term > $o),X138 : (subst > term > subst > $o)] : (~ ! [X139 : (subst > term > term)] : ((X138 @ id @ (lam @ (X139 @ sh @ one)) @ id) | ~ ! [X140 : term,X141 : subst,X142 : subst] : (((sub @ (X139 @ X142 @ X140) @ X141)) = ((X139 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)))) | ~ ! [X143 : term] : ((X138 @ id @ (X139 @ id @ X143) @ id) | ~(X138 @ id @ X143 @ id))) | ~ ! [X144 : term] : (((X138 @ id @ X144 @ id)) = ((X137 @ X144))) | ~ ! [X145 : term] : (~(X137 @ X145) | (X137 @ (sub @ X136 @ (push @ X145 @ id)))) | (X137 @ (lam @ X136)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axmap & (hoasinduction_lem3v2_f <=> ! [X146 : term] : ~ ! [X147 : (subst > term > term)] : ~ ! [X148 : subst,X149 : term] : (((X147 @ X148 @ X149)) = ((sub @ X146 @ (push @ X149 @ X148))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (axscons <=> ! [X150 : subst] : (((push @ (sub @ one @ X150) @ (comp @ sh @ X150))) = X150)) & (sh = ((d2subst @ d_id))) & lamnotvar & (! [X151 : subst,X152 : term,X153 : (subst > term > term),X154 : (subst > term > term)] : (~ ! [X155 : term,X156 : subst,X157 : subst] : (((sub @ (X153 @ X156 @ X155) @ X157)) = ((X153 @ (comp @ X156 @ X157) @ (sub @ X155 @ X157)))) | (((X154 @ X151 @ X152)) = ((X153 @ X151 @ X152))) | (((lam @ (X153 @ sh @ one))) != ((lam @ (X154 @ sh @ one)))) | ~ ! [X158 : term,X159 : subst,X160 : subst] : (((sub @ (X154 @ X159 @ X158) @ X160)) = ((X154 @ (comp @ X159 @ X160) @ (sub @ X158 @ X160))))) <=> hoaslaminj) & (substmonoid <=> (! [X161 : subst] : (((comp @ id @ X161)) = X161) & ! [X162 : subst] : (((comp @ X162 @ id)) = X162))) & ((! [X163 : term] : (((sub @ X163 @ id)) = X163) => (! [X164 : (subst > term > subst > $o),X165 : term] : ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id) | ~ ! [X166 : (subst > term > term)] : ((X164 @ id @ (lam @ (X166 @ sh @ one)) @ id) | ~ ! [X167 : term,X168 : subst,X169 : subst] : (((sub @ (X166 @ X169 @ X167) @ X168)) = ((X166 @ (comp @ X169 @ X168) @ (sub @ X167 @ X168)))) | ~ ! [X170 : term] : (~(X164 @ id @ X170 @ id) | (X164 @ id @ (X166 @ id @ X170) @ id))) | ~ ! [X171 : term] : (~(X164 @ id @ X171 @ id) | (X164 @ id @ (sub @ X165 @ (push @ X171 @ id)) @ id))) => ! [X172 : (subst > term > subst > $o),X173 : term] : (~ ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : ((X172 @ X175 @ X176 @ (comp @ X174 @ X177)) | ~(X172 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)) | ~ ! [X178 : (subst > term > term)] : (~ ! [X179 : term] : (~(X172 @ id @ X179 @ id) | (X172 @ id @ (X178 @ id @ X179) @ id)) | ~ ! [X180 : subst,X181 : subst,X182 : term] : (((sub @ (X178 @ X181 @ X182) @ X180)) = ((X178 @ (comp @ X181 @ X180) @ (sub @ X182 @ X180)))) | (X172 @ id @ (lam @ (X178 @ sh @ one)) @ id)) | (X172 @ id @ (lam @ X173) @ id) | ~ ! [X183 : term] : (~(X172 @ id @ X183 @ id) | (X172 @ id @ (sub @ X173 @ (push @ X183 @ id)) @ id)) | ~ ! [X184 : subst,X185 : term,X186 : subst,X187 : subst] : ((X172 @ (comp @ X184 @ X187) @ (sub @ X185 @ X187) @ X186) | ~(X172 @ X184 @ X185 @ (comp @ X187 @ X186)))))) <=> hoasinduction_lem3_lthm) & hoasinduction_gthm & ~lamnotap & (hoasinduction_lem3 <=> ! [X188 : (subst > term > subst > $o),X189 : term] : (~ ! [X190 : (subst > term > term)] : (~ ! [X191 : term] : ((X188 @ id @ (X190 @ id @ X191) @ id) | ~(X188 @ id @ X191 @ id)) | ~ ! [X192 : term,X193 : subst,X194 : subst] : (((X190 @ (comp @ X193 @ X194) @ (sub @ X192 @ X194))) = ((sub @ (X190 @ X193 @ X192) @ X194))) | (X188 @ id @ (lam @ (X190 @ sh @ one)) @ id)) | ~ ! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : ((X188 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X198) | ~(X188 @ X197 @ X195 @ (comp @ X196 @ X198))) | ~ ! [X199 : term] : (~(X188 @ id @ X199 @ id) | (X188 @ id @ (sub @ X189 @ (push @ X199 @ id)) @ id)) | (X188 @ id @ (lam @ X189) @ id) | ~ ! [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (~(X188 @ (comp @ X203 @ X200) @ (sub @ X202 @ X200) @ X201) | (X188 @ X203 @ X202 @ (comp @ X200 @ X201))))) & (! [X204 : (subst > term > subst > $o),X205 : (term > $o),X206 : term,X207 : term] : (~(X205 @ X207) | (X205 @ (ap @ X207 @ X206)) | ~(X205 @ X206) | ~ ! [X208 : term] : (((X205 @ X208)) = ((X204 @ id @ X208 @ id))) | ~ ! [X209 : subst,X210 : term,X211 : subst,X212 : subst] : (~(X204 @ X212 @ X210 @ (comp @ X209 @ X211)) | (X204 @ (comp @ X212 @ X209) @ (sub @ X210 @ X209) @ X211)) | ~ ! [X213 : subst,X214 : term,X215 : subst,X216 : subst] : ((X204 @ X216 @ X214 @ (comp @ X215 @ X213)) | ~(X204 @ (comp @ X216 @ X215) @ (sub @ X214 @ X215) @ X213)) | ~ ! [X217 : term,X218 : term] : ((X204 @ id @ (ap @ (sub @ X217 @ id) @ X218) @ id) | ~(X204 @ id @ X218 @ id) | ~(X204 @ id @ X217 @ id))) <=> hoasinduction_lem2v2) & ((^[X219 : term, X220 : subst, X221 : (term > $o), X222 : (term > $o)] : (! [X223 : term] : (((X222 @ X223)) = ((X221 @ (sub @ X223 @ (push @ X219 @ X220))))))) = pushprop_p_and_p_prime) & (! [X224 : subst,X225 : (term > $o),X226 : term] : (~ ! [X227 : term] : ((X225 @ (lam @ X227)) | ~ ! [X228 : term] : ((X225 @ (sub @ X227 @ (push @ X228 @ id))) | ~(X225 @ X228))) | (X225 @ (sub @ X226 @ X224)) | ~ ! [X229 : term,X230 : term] : ((X225 @ (ap @ X229 @ X230)) | ~(X225 @ X230) | ~(X225 @ X229)) | ~ ! [X231 : term] : (~(var @ X231) | (X225 @ (sub @ X231 @ X224)))) <=> induction2lem) & substmonoid_gthm & induction2_gthm & pushprop_lem1v2_gthm & (induction2_lthm <=> (! [X232 : term] : (((sub @ X232 @ id)) = X232) => (! [X233 : term,X234 : (term > $o),X235 : subst] : ((X234 @ (sub @ X233 @ X235)) | ~ ! [X236 : term,X237 : term] : (~(X234 @ X237) | ~(X234 @ X236) | (X234 @ (ap @ X237 @ X236))) | ~ ! [X238 : term] : (~(var @ X238) | (X234 @ (sub @ X238 @ X235))) | ~ ! [X239 : term] : ((X234 @ (lam @ X239)) | ~ ! [X240 : term] : (~(X234 @ X240) | (X234 @ (sub @ X239 @ (push @ X240 @ id)))))) => ! [X241 : term,X242 : (term > $o)] : ((X242 @ X241) | ~ ! [X243 : term] : (~ ! [X244 : term] : (~(X242 @ X244) | (X242 @ (sub @ X243 @ (push @ X244 @ id)))) | (X242 @ (lam @ X243))) | ~ ! [X245 : term] : (~(var @ X245) | (X242 @ X245)) | ~ ! [X246 : term,X247 : term] : ((X242 @ (ap @ X246 @ X247)) | ~(X242 @ X246) | ~(X242 @ X247)))))) & (! [X248 : term,X249 : subst] : (((sub @ one @ (push @ X248 @ X249))) = X248) <=> axvarcons) & (hoasinduction_p_and_p_prime = (^[X250 : (subst > term > subst > $o), X251 : (term > $o)] : (! [X252 : term] : (((X251 @ X252)) = ((X250 @ id @ X252 @ id)))))) & (pushprop_lem0 <=> ! [X253 : (term > $o),X254 : subst,X255 : term] : ~ ! [X256 : (term > $o)] : ~ ! [X257 : term] : (((X256 @ X257)) = ((X253 @ (sub @ X257 @ (push @ X255 @ X254)))))) & (hoasinduction_lem3a_lthm <=> (! [X258 : term] : (((sub @ X258 @ id)) = X258) => (! [X259 : (subst > term > subst > $o),X260 : term] : (~ ! [X261 : (subst > term > term)] : ((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id) | ~ ! [X262 : subst,X263 : subst,X264 : term] : (((X261 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X261 @ X263 @ X264) @ X262))) | ~ ! [X265 : term] : (~(X259 @ id @ X265 @ id) | (X259 @ id @ (X261 @ id @ X265) @ id))) | (X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id) | ~ ! [X266 : term] : ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id) | ~(X259 @ id @ X266 @ id))) => ! [X267 : term,X268 : (subst > term > subst > $o)] : (~ ! [X269 : (subst > term > term)] : (~ ! [X270 : term] : (~(X268 @ id @ X270 @ id) | (X268 @ id @ (X269 @ id @ X270) @ id)) | ~ ! [X271 : term,X272 : subst,X273 : subst] : (((X269 @ (comp @ X273 @ X272) @ (sub @ X271 @ X272))) = ((sub @ (X269 @ X273 @ X271) @ X272))) | (X268 @ id @ (lam @ (X269 @ sh @ one)) @ id)) | ~ ! [X274 : term] : (~(X268 @ id @ X274 @ id) | (X268 @ id @ (sub @ X267 @ (push @ X274 @ id)) @ id)) | (X268 @ id @ (lam @ X267) @ id))))) & hoasinduction_lem1v2 & hoasinduction_lem2_lthm & ((! [X275 : (term > $o),X276 : term] : ((X275 @ X276) | ~ ! [X277 : term] : ((X275 @ X277) | ~(var @ X277)) | ~ ! [X278 : term] : ((X275 @ (lam @ X278)) | ~ ! [X279 : term] : ((X275 @ (sub @ X278 @ (push @ X279 @ id))) | ~(X275 @ X279))) | ~ ! [X280 : term,X281 : term] : (~(X275 @ X280) | (X275 @ (ap @ X280 @ X281)) | ~(X275 @ X281))) => (! [X282 : term,X283 : term,X284 : (subst > term > subst > $o)] : (~(X284 @ id @ X282 @ id) | (X284 @ id @ (ap @ X283 @ X282) @ id) | ~ ! [X285 : subst,X286 : term,X287 : subst,X288 : subst] : (~(X284 @ X287 @ X286 @ (comp @ X288 @ X285)) | (X284 @ (comp @ X287 @ X288) @ (sub @ X286 @ X288) @ X285)) | ~(X284 @ id @ X283 @ id) | ~ ! [X289 : subst,X290 : subst,X291 : term,X292 : subst] : ((X284 @ X292 @ X291 @ (comp @ X290 @ X289)) | ~(X284 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290) @ X289)) | ~ ! [X293 : term,X294 : term] : (~(X284 @ id @ X293 @ id) | (X284 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id) | ~(X284 @ id @ X294 @ id))) => (! [X295 : (subst > term > subst > $o),X296 : term] : (~ ! [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (~(X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299) | (X295 @ X297 @ X300 @ (comp @ X298 @ X299))) | ~ ! [X301 : term] : ((X295 @ id @ (sub @ X296 @ (push @ X301 @ id)) @ id) | ~(X295 @ id @ X301 @ id)) | (X295 @ id @ (lam @ X296) @ id) | ~ ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (~(X295 @ X305 @ X303 @ (comp @ X302 @ X304)) | (X295 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304)) | ~ ! [X306 : (subst > term > term)] : (~ ! [X307 : term] : (~(X295 @ id @ X307 @ id) | (X295 @ id @ (X306 @ id @ X307) @ id)) | (X295 @ id @ (lam @ (X306 @ sh @ one)) @ id) | ~ ! [X308 : term,X309 : subst,X310 : subst] : (((X306 @ (comp @ X309 @ X310) @ (sub @ X308 @ X310))) = ((sub @ (X306 @ X309 @ X308) @ X310))))) => ! [X311 : term,X312 : (subst > term > subst > $o)] : (~ ! [X313 : (subst > term > term)] : (~ ! [X314 : term,X315 : subst,X316 : subst] : (((X313 @ (comp @ X316 @ X315) @ (sub @ X314 @ X315))) = ((sub @ (X313 @ X316 @ X314) @ X315))) | ~ ! [X317 : term] : (~(X312 @ id @ X317 @ id) | (X312 @ id @ (X313 @ id @ X317) @ id)) | (X312 @ id @ (lam @ (X313 @ sh @ one)) @ id)) | ~ ! [X318 : subst,X319 : subst,X320 : term,X321 : subst] : (~(X312 @ X321 @ X320 @ (comp @ X318 @ X319)) | (X312 @ (comp @ X321 @ X318) @ (sub @ X320 @ X318) @ X319)) | ~ ! [X322 : term,X323 : term] : (~(X312 @ id @ X323 @ id) | (X312 @ id @ (ap @ (sub @ X322 @ id) @ X323) @ id) | ~(X312 @ id @ X322 @ id)) | ~ ! [X324 : term] : (~(var @ (sub @ X324 @ id)) | (X312 @ id @ X324 @ id)) | ~ ! [X325 : subst,X326 : subst,X327 : subst,X328 : term] : (~(X312 @ (comp @ X327 @ X325) @ (sub @ X328 @ X325) @ X326) | (X312 @ X327 @ X328 @ (comp @ X325 @ X326))) | (X312 @ id @ X311 @ id))))) <=> hoasinduction_lthm) & hoasapnotvar & ((! [X329 : term] : (((sub @ X329 @ id)) = X329) => ! [X330 : (subst > term > subst > $o),X331 : (term > $o),X332 : term] : (~ ! [X333 : subst,X334 : term,X335 : subst,X336 : subst] : ((X330 @ (comp @ X336 @ X333) @ (sub @ X334 @ X333) @ X335) | ~(X330 @ X336 @ X334 @ (comp @ X333 @ X335))) | (X331 @ (lam @ X332)) | ~ ! [X337 : term] : (((X331 @ X337)) = ((X330 @ id @ X337 @ id))) | ~ ! [X338 : term] : (~(X331 @ X338) | (X331 @ (sub @ X332 @ (push @ X338 @ id)))) | ~ ! [X339 : term,X340 : subst,X341 : subst,X342 : subst] : ((X330 @ X340 @ X339 @ (comp @ X342 @ X341)) | ~(X330 @ (comp @ X340 @ X342) @ (sub @ X339 @ X342) @ X341)) | ~ ! [X343 : (subst > term > term)] : (~ ! [X344 : term,X345 : subst,X346 : subst] : (((X343 @ (comp @ X345 @ X346) @ (sub @ X344 @ X346))) = ((sub @ (X343 @ X345 @ X344) @ X346))) | ~ ! [X347 : term] : ((X330 @ id @ (X343 @ id @ X347) @ id) | ~(X330 @ id @ X347 @ id)) | (X330 @ id @ (lam @ (X343 @ sh @ one)) @ id)))) <=> hoasinduction_lem3v2_lthm) & (hoasinduction_no_psi_cond <=> ! [X348 : term,X349 : (subst > term > subst > $o)] : ((X349 @ id @ X348 @ id) | ~ ! [X350 : term,X351 : term] : ((X349 @ id @ (ap @ (sub @ X351 @ id) @ X350) @ id) | ~(X349 @ id @ X351 @ id) | ~(X349 @ id @ X350 @ id)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : subst,X354 : term,X355 : subst] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) | ~ ! [X356 : term] : ((X349 @ id @ (X352 @ id @ X356) @ id) | ~(X349 @ id @ X356 @ id)) | (X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)))) & (! [X357 : (subst > term > subst > $o)] : ~ ! [X358 : (term > $o)] : ~ ! [X359 : term] : (((X358 @ X359)) = ((X357 @ id @ X359 @ id))) <=> hoasinduction_lem0) & hoaslamnotvar_gthm & pushprop_lem0_gthm & (hoasinduction_no_psi_cond_lthm <=> (! [X360 : (subst > term > subst > $o)] : ~ ! [X361 : (term > $o)] : ~ ! [X362 : term] : (((X360 @ id @ X362 @ id)) = ((X361 @ X362))) => (! [X363 : term,X364 : (term > $o)] : ((X364 @ X363) | ~ ! [X365 : term] : ((X364 @ X365) | ~(var @ X365)) | ~ ! [X366 : term,X367 : term] : ((X364 @ (ap @ X367 @ X366)) | ~(X364 @ X367) | ~(X364 @ X366)) | ~ ! [X368 : term] : ((X364 @ (lam @ X368)) | ~ ! [X369 : term] : (~(X364 @ X369) | (X364 @ (sub @ X368 @ (push @ X369 @ id)))))) => (! [X370 : term] : (((sub @ X370 @ id)) = X370) => (! [X371 : (term > $o),X372 : term,X373 : (subst > term > subst > $o)] : (~ ! [X374 : term] : (((X371 @ X374)) = ((X373 @ id @ X374 @ id))) | ~ ! [X375 : (subst > term > term)] : (~ ! [X376 : subst,X377 : subst,X378 : term] : (((sub @ (X375 @ X376 @ X378) @ X377)) = ((X375 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377)))) | (X373 @ id @ (lam @ (X375 @ sh @ one)) @ id) | ~ ! [X379 : term] : ((X373 @ id @ (X375 @ id @ X379) @ id) | ~(X373 @ id @ X379 @ id))) | ~ ! [X380 : term] : ((X371 @ (sub @ X372 @ (push @ X380 @ id))) | ~(X371 @ X380)) | (X371 @ (lam @ X372))) => ! [X381 : term,X382 : (subst > term > subst > $o)] : (~ ! [X383 : term,X384 : term] : (~(X382 @ id @ X383 @ id) | (X382 @ id @ (ap @ (sub @ X383 @ id) @ X384) @ id) | ~(X382 @ id @ X384 @ id)) | ~ ! [X385 : (subst > term > term)] : ((X382 @ id @ (lam @ (X385 @ sh @ one)) @ id) | ~ ! [X386 : term] : (~(X382 @ id @ X386 @ id) | (X382 @ id @ (X385 @ id @ X386) @ id)) | ~ ! [X387 : term,X388 : subst,X389 : subst] : (((X385 @ (comp @ X388 @ X389) @ (sub @ X387 @ X389))) = ((sub @ (X385 @ X388 @ X387) @ X389)))) | (X382 @ id @ X381 @ id))))))) & pushprop_lem3v2_lthm & apnotvar & (! [X390 : (subst > term > subst > $o),X391 : term] : (~ ! [X392 : term] : ((X390 @ id @ (sub @ X391 @ (push @ X392 @ id)) @ id) | ~(X390 @ id @ X392 @ id)) | ~ ! [X393 : (subst > term > term)] : ((X390 @ id @ (lam @ (X393 @ sh @ one)) @ id) | ~ ! [X394 : subst,X395 : subst,X396 : term] : (((sub @ (X393 @ X395 @ X396) @ X394)) = ((X393 @ (comp @ X395 @ X394) @ (sub @ X396 @ X394)))) | ~ ! [X397 : term] : (~(X390 @ id @ X397 @ id) | (X390 @ id @ (X393 @ id @ X397) @ id))) | (X390 @ id @ (lam @ (sub @ X391 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X398 : term] : (((sub @ X398 @ id)) = X398) => (! [X399 : term,X400 : term,X401 : term,X402 : term] : ((X399 = X402) | (((ap @ X399 @ X401)) != ((ap @ X402 @ X400)))) => ! [X403 : term,X404 : term,X405 : term,X406 : term] : ((X404 = X405) | (((ap @ (sub @ X404 @ id) @ X403)) != ((ap @ (sub @ X405 @ id) @ X406)))))) <=> hoasapinj1_lthm) & hoasapinj2_gthm & axabs & ! [X407 : subst] : ? [X408 : d_subst] : (((d2subst @ X408)) = X407) & (termmset <=> ! [X409 : term] : (((sub @ X409 @ id)) = X409)) & (! [X410 : (subst > term > subst > $o)] : ~ ! [X411 : (term > $o)] : ~ ! [X412 : term] : (((X411 @ X412)) = ((X410 @ id @ X412 @ id))) <=> hoasinduction_lem0_lthm) & ! [X413 : d_subst,X414 : d_subst] : ((((d2subst @ X414)) = ((d2subst @ X413))) => (X413 = X414)) & ulamvarsh & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X415 : term,X416 : subst,X417 : (term > $o),X418 : term,X419 : (term > $o)] : (~(X417 @ X418) | (X419 @ (sub @ X418 @ (push @ X415 @ X416)))) <=> pushprop_lem1) & hoaslamnotap_gthm & (! [X420 : term,X421 : (subst > term > subst > $o),X422 : term] : (~ ! [X423 : term,X424 : subst,X425 : subst,X426 : subst] : ((X421 @ X424 @ X423 @ (comp @ X425 @ X426)) | ~(X421 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)) | (X421 @ id @ (ap @ X420 @ X422) @ id) | ~ ! [X427 : term,X428 : subst,X429 : subst,X430 : subst] : (~(X421 @ X428 @ X427 @ (comp @ X430 @ X429)) | (X421 @ (comp @ X428 @ X430) @ (sub @ X427 @ X430) @ X429)) | ~ ! [X431 : term,X432 : term] : (~(X421 @ id @ X431 @ id) | (X421 @ id @ (ap @ (sub @ X431 @ id) @ X432) @ id) | ~(X421 @ id @ X432 @ id)) | ~(X421 @ id @ X422 @ id) | ~(X421 @ id @ X420 @ id)) <=> hoasinduction_lem2) & ulamvarind & hoasinduction_lem3b_gthm & ~ulamvar1 & (! [X433 : subst] : (((comp @ X433 @ id)) = X433) <=> axidr) & (! [X434 : subst] : (((comp @ id @ X434)) = X434) <=> axidl) & ! [X435 : term] : ? [X436 : d_term] : (((d2term @ X436)) = X435) & ~(var @ (d2term @ d_one)) & hoasinduction_lem3v2_gthm & hoasinduction_lem2v2_gthm & (! [X437 : term,X438 : term,X439 : term,X440 : term] : ((X437 = X440) | (((ap @ X440 @ X438)) != ((ap @ X437 @ X439)))) <=> apinj1) & (! [X441 : term,X442 : (term > $o)] : (~ ! [X443 : term] : (~(X442 @ X443) | (X442 @ (lam @ X443))) | (X442 @ X441) | ~ ! [X444 : term,X445 : term] : (~(X442 @ X444) | (X442 @ (ap @ X445 @ X444)) | ~(X442 @ X445)) | ~ ! [X446 : term] : ((X442 @ X446) | ~(var @ X446))) <=> induction) & hoasapnotvar_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoaslamnotvar & (hoasinduction_lem3aaa <=> ! [X447 : term,X448 : (subst > term > subst > $o)] : (~ ! [X449 : (subst > term > term),X450 : term] : (~ ! [X451 : term] : (~(X448 @ id @ X451 @ id) | (X448 @ id @ (X449 @ id @ X451) @ id)) | ~ ! [X452 : subst,X453 : term,X454 : subst] : (((sub @ (X449 @ X452 @ X453) @ X454)) = ((sub @ (sub @ X450 @ (push @ X453 @ X452)) @ X454))) | (X448 @ id @ (lam @ (X449 @ sh @ one)) @ id) | ~ ! [X455 : subst,X456 : term,X457 : subst] : (((X449 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455))) = ((sub @ X450 @ (push @ (sub @ X456 @ X455) @ (comp @ X457 @ X455)))))) | (X448 @ id @ (lam @ (sub @ X447 @ (push @ one @ sh))) @ id) | ~ ! [X458 : term] : ((X448 @ id @ (sub @ X447 @ (push @ X458 @ id)) @ id) | ~(X448 @ id @ X458 @ id)))) & ((! [X459 : term,X460 : subst] : (((sub @ one @ (push @ X459 @ X460))) = X459) => ! [X461 : (term > $o),X462 : (term > $o),X463 : subst,X464 : term] : ((X462 @ one) | ~ ! [X465 : term] : (((X461 @ (sub @ X465 @ (push @ X464 @ X463)))) = ((X462 @ X465))) | ~(X461 @ X464))) <=> pushprop_lem1v2_lthm) & (! [X466 : term,X467 : term] : ((X466 = X467) | (((sub @ X466 @ sh)) != ((sub @ X467 @ sh)))) <=> shinj) & (! [X468 : (subst > term > subst > $o),X469 : term] : (~ ! [X470 : term] : (~(var @ (sub @ X470 @ id)) | (X468 @ id @ X470 @ id)) | ~ ! [X471 : subst,X472 : subst,X473 : subst,X474 : term] : (~(X468 @ X471 @ X474 @ (comp @ X472 @ X473)) | (X468 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473)) | (X468 @ id @ X469 @ id) | ~ ! [X475 : term,X476 : term] : (~(X468 @ id @ X476 @ id) | ~(X468 @ id @ X475 @ id) | (X468 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) | ~ ! [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((X468 @ X478 @ X477 @ (comp @ X480 @ X479)) | ~(X468 @ (comp @ X478 @ X480) @ (sub @ X477 @ X480) @ X479)) | ~ ! [X481 : (subst > term > term)] : (~ ! [X482 : term] : (~(X468 @ id @ X482 @ id) | (X468 @ id @ (X481 @ id @ X482) @ id)) | (X468 @ id @ (lam @ (X481 @ sh @ one)) @ id) | ~ ! [X483 : subst,X484 : term,X485 : subst] : (((X481 @ (comp @ X483 @ X485) @ (sub @ X484 @ X485))) = ((sub @ (X481 @ X483 @ X484) @ X485))))) <=> hoasinduction) & (! [X486 : (subst > term > term),X487 : term,X488 : term] : (~ ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X486 @ X491 @ X489) @ X490)) = ((X486 @ (comp @ X491 @ X490) @ (sub @ X489 @ X490)))) | (((ap @ (sub @ X487 @ id) @ X488)) != ((lam @ (X486 @ sh @ one))))) <=> hoaslamnotap) & hoasinduction_lem1 & (! [X492 : term] : ~ ! [X493 : (subst > term > term)] : ~ ! [X494 : subst,X495 : term] : (((sub @ X492 @ (push @ X495 @ X494))) = ((X493 @ X494 @ X495))) <=> hoasinduction_lem3v2_f_lthm) & axvarshift & hoasinduction_lem2_gthm & axassoc & (! [X496 : (term > $o),X497 : subst,X498 : term] : ~ ! [X499 : (term > $o)] : ~ ! [X500 : term] : (((X499 @ X500)) = ((X496 @ (sub @ X500 @ (push @ X498 @ X497))))) <=> pushprop_lem0_lthm) & hoasapnotvar_gthm & pushprop_lem1_gthm & hoasinduction_lem1_lthm & axclos & ! [X501 : d_term] : (d_one = X501) & pushprop_gthm & (hoasinduction_lem3aa <=> ! [X502 : (subst > term > subst > $o),X503 : term] : ((X502 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id) | ~ ! [X504 : (subst > term > term)] : (~ ! [X505 : term] : ((X502 @ id @ (X504 @ id @ X505) @ id) | ~(X502 @ id @ X505 @ id)) | (X502 @ id @ (lam @ (X504 @ sh @ one)) @ id) | ~ ! [X506 : subst,X507 : term,X508 : subst] : (((X504 @ (comp @ X506 @ X508) @ (sub @ X507 @ X508))) = ((sub @ (X504 @ X506 @ X507) @ X508)))) | ~ ! [X509 : term] : (~(X502 @ id @ X509 @ id) | (X502 @ id @ (sub @ X503 @ (push @ X509 @ id)) @ id)))) & ! [X510 : d_subst] : (d_id = X510) & pushprop_lem2v2 & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_lem3a <=> ! [X511 : term,X512 : (subst > term > subst > $o)] : (~ ! [X513 : (subst > term > term)] : (~ ! [X514 : subst,X515 : term,X516 : subst] : (((X513 @ (comp @ X516 @ X514) @ (sub @ X515 @ X514))) = ((sub @ (X513 @ X516 @ X515) @ X514))) | ~ ! [X517 : term] : ((X512 @ id @ (X513 @ id @ X517) @ id) | ~(X512 @ id @ X517 @ id)) | (X512 @ id @ (lam @ (X513 @ sh @ one)) @ id)) | ~ ! [X518 : term] : ((X512 @ id @ (sub @ X511 @ (push @ X518 @ id)) @ id) | ~(X512 @ id @ X518 @ id)) | (X512 @ id @ (lam @ X511) @ id))) & (hoasinduction_lem3b <=> ! [X519 : term] : ~ ! [X520 : (subst > term > term)] : (((X520 @ sh @ one)) != ((sub @ X519 @ (push @ one @ sh))))) & (hoasinduction_lem3v2 <=> ! [X521 : term,X522 : (subst > term > subst > $o),X523 : (term > $o)] : (~ ! [X524 : term] : (~(X523 @ X524) | (X523 @ (sub @ X521 @ (push @ X524 @ id)))) | ~ ! [X525 : (subst > term > term)] : (~ ! [X526 : term,X527 : subst,X528 : subst] : (((sub @ (X525 @ X527 @ X526) @ X528)) = ((X525 @ (comp @ X527 @ X528) @ (sub @ X526 @ X528)))) | (X522 @ id @ (lam @ (X525 @ sh @ one)) @ id) | ~ ! [X529 : term] : ((X522 @ id @ (X525 @ id @ X529) @ id) | ~(X522 @ id @ X529 @ id))) | ~ ! [X530 : subst,X531 : subst,X532 : subst,X533 : term] : (~(X522 @ (comp @ X532 @ X531) @ (sub @ X533 @ X531) @ X530) | (X522 @ X532 @ X533 @ (comp @ X531 @ X530))) | ~ ! [X534 : term] : (((X522 @ id @ X534 @ id)) = ((X523 @ X534))) | ~ ! [X535 : subst,X536 : subst,X537 : term,X538 : subst] : ((X522 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X538) | ~(X522 @ X536 @ X537 @ (comp @ X535 @ X538))) | (X523 @ (lam @ X521)))) & pushprop_lthm & ((! [X539 : subst] : (((comp @ id @ X539)) = X539) => (! [X540 : subst] : (((comp @ X540 @ id)) = X540) => (! [X541 : subst] : (((comp @ id @ X541)) = X541) & ! [X542 : subst] : (((comp @ X542 @ id)) = X542)))) <=> substmonoid_lthm) & hoasinduction_lem3a_gthm & termmset_gthm & (pushprop_lem1v2 <=> ! [X543 : subst,X544 : (term > $o),X545 : term,X546 : (term > $o)] : ((X544 @ one) | ~(X546 @ X545) | ~ ! [X547 : term] : (((X544 @ X547)) = ((X546 @ (sub @ X547 @ (push @ X545 @ X543))))))) & (! [X548 : subst,X549 : term] : (((comp @ sh @ (push @ X549 @ X548))) = X548) <=> axshiftcons)), 24.89/4.11 inference(rectify,[],[f1])). 24.89/4.11 thf(f5,plain,( 24.89/4.11 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2 = $true) <=> ! [X2 : term,X3 : term,X4 : term,X5 : term] : ((X3 = X4) | (((ap @ (sub @ X2 @ id) @ X4)) != ((ap @ (sub @ X5 @ id) @ X3))))) & ((! [X6 : term] : (((sub @ X6 @ id)) = X6) => ! [X7 : term] : (((sub @ X7 @ id)) = X7)) <=> (termmset_lthm = $true)) & (pushprop_lem3v2 = $true) & (axapp = $true) & (hoaslamnotap_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ! [X8 : d_term,X9 : d_term] : ((((d2term @ X9)) = ((d2term @ X8))) => (X8 = X9)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X10 : term] : ~ ! [X11 : (subst > term > term)] : (((sub @ X10 @ (push @ one @ sh))) != ((X11 @ sh @ one)))) & (! [X12 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X12))) | (X12 = X13)) <=> (laminj = $true)) & (hoaslamnotvar_lthm = $true) & ((! [X14 : term,X15 : subst] : (((sub @ one @ (push @ X14 @ X15))) = X14) => (! [X16 : subst,X17 : term] : (((comp @ sh @ (push @ X17 @ X16))) = X16) => (! [X18 : term,X19 : term] : ((X18 = X19) | (((lam @ X18)) != ((lam @ X19)))) => ! [X20 : subst,X21 : (subst > term > term),X22 : (subst > term > term),X23 : term] : (~ ! [X24 : term,X25 : subst,X26 : subst] : (((X21 @ (comp @ X26 @ X25) @ (sub @ X24 @ X25))) = ((sub @ (X21 @ X26 @ X24) @ X25))) | (((lam @ (X22 @ sh @ one))) != ((lam @ (X21 @ sh @ one)))) | ~ ! [X27 : term,X28 : subst,X29 : subst] : (((X22 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29))) = ((sub @ (X22 @ X28 @ X27) @ X29))) | (((X21 @ X20 @ X23)) = ((X22 @ X20 @ X23))))))) <=> (hoaslaminj_lthm = $true)) & (one = ((d2term @ d_one))) & ((hoasapinj2_lthm = $true) <=> (! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X30 = X31) | (((ap @ X32 @ X30)) != ((ap @ X33 @ X31)))) => ! [X34 : term,X35 : term,X36 : term,X37 : term] : ((X34 = X37) | (((ap @ (sub @ X35 @ id) @ X37)) != ((ap @ (sub @ X36 @ id) @ X34)))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X38 : (subst > term > subst > $o)] : ~ ! [X39 : (term > $o)] : ~ ! [X40 : term] : (((X39 @ X40)) = ((X38 @ id @ X40 @ id))) => (! [X41 : term,X42 : (term > $o)] : (~ ! [X43 : term] : (~ ! [X44 : term] : (($true = ((X42 @ (sub @ X43 @ (push @ X44 @ id))))) | ~ ($true = ((X42 @ X44)))) | ($true = ((X42 @ (lam @ X43))))) | ~ ! [X45 : term] : (~ ($true = ((var @ X45))) | ($true = ((X42 @ X45)))) | ($true = ((X42 @ X41))) | ~ ! [X46 : term,X47 : term] : (($true = ((X42 @ (ap @ X46 @ X47)))) | ~ ($true = ((X42 @ X47))) | ~ ($true = ((X42 @ X46))))) => (! [X48 : term] : (((sub @ X48 @ id)) = X48) => (! [X49 : (subst > term > subst > $o),X50 : term,X51 : (term > $o)] : (~ ! [X52 : (subst > term > term)] : (~ ! [X53 : term,X54 : subst,X55 : subst] : (((X52 @ (comp @ X54 @ X55) @ (sub @ X53 @ X55))) = ((sub @ (X52 @ X54 @ X53) @ X55))) | ~ ! [X56 : term] : (($true = ((X49 @ id @ (X52 @ id @ X56) @ id))) | ~ ($true = ((X49 @ id @ X56 @ id)))) | ($true = ((X49 @ id @ (lam @ (X52 @ sh @ one)) @ id)))) | ~ ! [X57 : term] : (($true = ((X51 @ (sub @ X50 @ (push @ X57 @ id))))) | ~ ($true = ((X51 @ X57)))) | ($true = ((X51 @ (lam @ X50)))) | ~ ! [X58 : term] : (((X49 @ id @ X58 @ id)) = ((X51 @ X58)))) => ! [X59 : term,X60 : (subst > term > subst > $o)] : (~ ! [X61 : term] : (($true = ((X60 @ id @ X61 @ id))) | ~ ($true = ((var @ (sub @ X61 @ id))))) | ~ ! [X62 : (subst > term > term)] : ((((X60 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true) | ~ ! [X63 : term] : (($true = ((X60 @ id @ (X62 @ id @ X63) @ id))) | ~ ($true = ((X60 @ id @ X63 @ id)))) | ~ ! [X64 : term,X65 : subst,X66 : subst] : (((X62 @ (comp @ X66 @ X65) @ (sub @ X64 @ X65))) = ((sub @ (X62 @ X66 @ X64) @ X65)))) | ($true = ((X60 @ id @ X59 @ id))) | ~ ! [X67 : term,X68 : term] : (($true = ((X60 @ id @ (ap @ (sub @ X68 @ id) @ X67) @ id))) | ~ ($true = ((X60 @ id @ X67 @ id))) | ~ ($true = ((X60 @ id @ X68 @ id)))) | ~ ! [X69 : term,X70 : subst,X71 : subst,X72 : subst] : (~ ($true = ((X60 @ X70 @ X69 @ (comp @ X72 @ X71)))) | ($true = ((X60 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)))) | ~ ! [X73 : subst,X74 : subst,X75 : term,X76 : subst] : (~ ($true = ((X60 @ (comp @ X74 @ X73) @ (sub @ X75 @ X73) @ X76))) | ($true = ((X60 @ X74 @ X75 @ (comp @ X73 @ X76))))))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X77 : (term > $o),X78 : (subst > term > subst > $o),X79 : term] : (~ ! [X80 : term] : (((X77 @ X80)) = ((X78 @ id @ X80 @ id))) | ($true = ((X77 @ (lam @ X79)))) | ~ ! [X81 : term] : (~ ($true = ((X77 @ X81))) | ($true = ((X77 @ (sub @ X79 @ (push @ X81 @ id)))))) | ~ ! [X82 : (subst > term > term)] : (($true = ((X78 @ id @ (lam @ (X82 @ sh @ one)) @ id))) | ~ ! [X83 : term] : (($true = ((X78 @ id @ (X82 @ id @ X83) @ id))) | ~ ($true = ((X78 @ id @ X83 @ id)))) | ~ ! [X84 : subst,X85 : subst,X86 : term] : (((X82 @ (comp @ X85 @ X84) @ (sub @ X86 @ X84))) = ((sub @ (X82 @ X85 @ X86) @ X84)))))) & ((pushprop_lem1_lthm = $true) <=> (! [X87 : term,X88 : subst] : (((sub @ one @ (push @ X87 @ X88))) = X87) => (! [X89 : subst,X90 : term] : (((comp @ sh @ (push @ X90 @ X89))) = X89) => ! [X91 : (term > $o),X92 : term,X93 : term,X94 : subst,X95 : (term > $o)] : (~ ($true = ((X95 @ X93))) | ($true = ((X91 @ (sub @ X93 @ (push @ X92 @ X94))))))))) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2_gthm = $true) & ((apinj2 = $true) <=> ! [X96 : term,X97 : term,X98 : term,X99 : term] : ((X97 = X99) | (((ap @ X96 @ X97)) != ((ap @ X98 @ X99))))) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ((induction2lem_lthm = $true) <=> (! [X100 : term,X101 : subst] : (((sub @ one @ (push @ X100 @ X101))) = X100) => (! [X102 : subst,X103 : term] : (((comp @ sh @ (push @ X103 @ X102))) = X102) => (! [X104 : subst] : (((comp @ X104 @ id)) = X104) => (! [X105 : (term > $o),X106 : term] : (~ ! [X107 : term,X108 : term] : (~ ($true = ((X105 @ X108))) | ~ ($true = ((X105 @ X107))) | ($true = ((X105 @ (ap @ X107 @ X108))))) | ~ ! [X109 : term] : (($true = ((X105 @ (lam @ X109)))) | ~ ($true = ((X105 @ X109)))) | ($true = ((X105 @ X106))) | ~ ! [X110 : term] : (~ ($true = ((var @ X110))) | ($true = ((X105 @ X110))))) => ! [X111 : (term > $o),X112 : subst,X113 : term] : (~ ! [X114 : term] : (~ ! [X115 : term] : (~ ($true = ((X111 @ X115))) | ($true = ((X111 @ (sub @ X114 @ (push @ X115 @ id)))))) | ($true = ((X111 @ (lam @ X114))))) | ~ ! [X116 : term] : (($true = ((X111 @ (sub @ X116 @ X112)))) | ~ ($true = ((var @ X116)))) | ~ ! [X117 : term,X118 : term] : (($true = ((X111 @ (ap @ X118 @ X117)))) | ~ ($true = ((X111 @ X117))) | ~ ($true = ((X111 @ X118)))) | ($true = ((X111 @ (sub @ X113 @ X112)))))))))) & (! [X119 : term,X120 : (term > $o)] : (~ ! [X121 : term] : ((((X120 @ (lam @ X121))) = $true) | ~ ! [X122 : term] : (($true = ((X120 @ (sub @ X121 @ (push @ X122 @ id))))) | ~ ($true = ((X120 @ X122))))) | ($true = ((X120 @ X119))) | ~ ! [X123 : term] : (($true = ((X120 @ X123))) | ~ ($true = ((var @ X123)))) | ~ ! [X124 : term,X125 : term] : (($true = ((X120 @ (ap @ X124 @ X125)))) | ~ ($true = ((X120 @ X125))) | ~ ($true = ((X120 @ X124))))) <=> (induction2 = $true)) & ((axvarid = $true) <=> ! [X126 : term] : (((sub @ X126 @ id)) = X126)) & (hoasinduction_lem1_gthm = $true) & (! [X127 : term,X128 : term,X129 : term,X130 : term] : ((X127 = X130) | (((ap @ (sub @ X127 @ id) @ X128)) != ((ap @ (sub @ X130 @ id) @ X129)))) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X131 : term] : ~ ! [X132 : (subst > term > term)] : ~ ! [X133 : subst,X134 : term] : (((sub @ X131 @ (push @ X134 @ X133))) = ((X132 @ X133 @ X134))) => (! [X135 : term] : (((sub @ X135 @ id)) = X135) => ! [X136 : term,X137 : (term > $o),X138 : (subst > term > subst > $o)] : (~ ! [X139 : (subst > term > term)] : (($true = ((X138 @ id @ (lam @ (X139 @ sh @ one)) @ id))) | ~ ! [X140 : term,X141 : subst,X142 : subst] : (((sub @ (X139 @ X142 @ X140) @ X141)) = ((X139 @ (comp @ X142 @ X141) @ (sub @ X140 @ X141)))) | ~ ! [X143 : term] : (($true = ((X138 @ id @ (X139 @ id @ X143) @ id))) | ~ ($true = ((X138 @ id @ X143 @ id))))) | ~ ! [X144 : term] : (((X138 @ id @ X144 @ id)) = ((X137 @ X144))) | ~ ! [X145 : term] : (~ ($true = ((X137 @ X145))) | ($true = ((X137 @ (sub @ X136 @ (push @ X145 @ id)))))) | (((X137 @ (lam @ X136))) = $true))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axmap = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X146 : term] : ~ ! [X147 : (subst > term > term)] : ~ ! [X148 : subst,X149 : term] : (((X147 @ X148 @ X149)) = ((sub @ X146 @ (push @ X149 @ X148))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((axscons = $true) <=> ! [X150 : subst] : (((push @ (sub @ one @ X150) @ (comp @ sh @ X150))) = X150)) & (((d2subst @ d_id)) = sh) & (lamnotvar = $true) & (! [X151 : subst,X152 : term,X153 : (subst > term > term),X154 : (subst > term > term)] : (~ ! [X155 : term,X156 : subst,X157 : subst] : (((sub @ (X153 @ X156 @ X155) @ X157)) = ((X153 @ (comp @ X156 @ X157) @ (sub @ X155 @ X157)))) | (((X154 @ X151 @ X152)) = ((X153 @ X151 @ X152))) | (((lam @ (X153 @ sh @ one))) != ((lam @ (X154 @ sh @ one)))) | ~ ! [X158 : term,X159 : subst,X160 : subst] : (((sub @ (X154 @ X159 @ X158) @ X160)) = ((X154 @ (comp @ X159 @ X160) @ (sub @ X158 @ X160))))) <=> (hoaslaminj = $true)) & ((substmonoid = $true) <=> (! [X161 : subst] : (((comp @ id @ X161)) = X161) & ! [X162 : subst] : (((comp @ X162 @ id)) = X162))) & ((! [X163 : term] : (((sub @ X163 @ id)) = X163) => (! [X164 : (subst > term > subst > $o),X165 : term] : (($true = ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id))) | ~ ! [X166 : (subst > term > term)] : (($true = ((X164 @ id @ (lam @ (X166 @ sh @ one)) @ id))) | ~ ! [X167 : term,X168 : subst,X169 : subst] : (((sub @ (X166 @ X169 @ X167) @ X168)) = ((X166 @ (comp @ X169 @ X168) @ (sub @ X167 @ X168)))) | ~ ! [X170 : term] : (~ ($true = ((X164 @ id @ X170 @ id))) | ($true = ((X164 @ id @ (X166 @ id @ X170) @ id))))) | ~ ! [X171 : term] : (~ ($true = ((X164 @ id @ X171 @ id))) | ($true = ((X164 @ id @ (sub @ X165 @ (push @ X171 @ id)) @ id))))) => ! [X172 : (subst > term > subst > $o),X173 : term] : (~ ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : (($true = ((X172 @ X175 @ X176 @ (comp @ X174 @ X177)))) | ~ ($true = ((X172 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)))) | ~ ! [X178 : (subst > term > term)] : (~ ! [X179 : term] : (~ ($true = ((X172 @ id @ X179 @ id))) | ($true = ((X172 @ id @ (X178 @ id @ X179) @ id)))) | ~ ! [X180 : subst,X181 : subst,X182 : term] : (((sub @ (X178 @ X181 @ X182) @ X180)) = ((X178 @ (comp @ X181 @ X180) @ (sub @ X182 @ X180)))) | ($true = ((X172 @ id @ (lam @ (X178 @ sh @ one)) @ id)))) | ($true = ((X172 @ id @ (lam @ X173) @ id))) | ~ ! [X183 : term] : (~ ($true = ((X172 @ id @ X183 @ id))) | ($true = ((X172 @ id @ (sub @ X173 @ (push @ X183 @ id)) @ id)))) | ~ ! [X184 : subst,X185 : term,X186 : subst,X187 : subst] : (($true = ((X172 @ (comp @ X184 @ X187) @ (sub @ X185 @ X187) @ X186))) | ~ ($true = ((X172 @ X184 @ X185 @ (comp @ X187 @ X186)))))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & ((hoasinduction_lem3 = $true) <=> ! [X188 : (subst > term > subst > $o),X189 : term] : (~ ! [X190 : (subst > term > term)] : (~ ! [X191 : term] : (($true = ((X188 @ id @ (X190 @ id @ X191) @ id))) | ~ ($true = ((X188 @ id @ X191 @ id)))) | ~ ! [X192 : term,X193 : subst,X194 : subst] : (((X190 @ (comp @ X193 @ X194) @ (sub @ X192 @ X194))) = ((sub @ (X190 @ X193 @ X192) @ X194))) | ($true = ((X188 @ id @ (lam @ (X190 @ sh @ one)) @ id)))) | ~ ! [X195 : term,X196 : subst,X197 : subst,X198 : subst] : (($true = ((X188 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X198))) | ~ ($true = ((X188 @ X197 @ X195 @ (comp @ X196 @ X198))))) | ~ ! [X199 : term] : (~ ($true = ((X188 @ id @ X199 @ id))) | ($true = ((X188 @ id @ (sub @ X189 @ (push @ X199 @ id)) @ id)))) | ($true = ((X188 @ id @ (lam @ X189) @ id))) | ~ ! [X200 : subst,X201 : subst,X202 : term,X203 : subst] : (~ ($true = ((X188 @ (comp @ X203 @ X200) @ (sub @ X202 @ X200) @ X201))) | ($true = ((X188 @ X203 @ X202 @ (comp @ X200 @ X201))))))) & (! [X204 : (subst > term > subst > $o),X205 : (term > $o),X206 : term,X207 : term] : (~ (((X205 @ X207)) = $true) | ($true = ((X205 @ (ap @ X207 @ X206)))) | ~ ($true = ((X205 @ X206))) | ~ ! [X208 : term] : (((X205 @ X208)) = ((X204 @ id @ X208 @ id))) | ~ ! [X209 : subst,X210 : term,X211 : subst,X212 : subst] : (~ ($true = ((X204 @ X212 @ X210 @ (comp @ X209 @ X211)))) | ($true = ((X204 @ (comp @ X212 @ X209) @ (sub @ X210 @ X209) @ X211)))) | ~ ! [X213 : subst,X214 : term,X215 : subst,X216 : subst] : (($true = ((X204 @ X216 @ X214 @ (comp @ X215 @ X213)))) | ~ ($true = ((X204 @ (comp @ X216 @ X215) @ (sub @ X214 @ X215) @ X213)))) | ~ ! [X217 : term,X218 : term] : (($true = ((X204 @ id @ (ap @ (sub @ X217 @ id) @ X218) @ id))) | ~ ($true = ((X204 @ id @ X218 @ id))) | ~ ($true = ((X204 @ id @ X217 @ id))))) <=> (hoasinduction_lem2v2 = $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)))))))))))))) & (! [X224 : subst,X225 : (term > $o),X226 : term] : (~ ! [X227 : term] : (($true = ((X225 @ (lam @ X227)))) | ~ ! [X228 : term] : (($true = ((X225 @ (sub @ X227 @ (push @ X228 @ id))))) | ~ ($true = ((X225 @ X228))))) | ($true = ((X225 @ (sub @ X226 @ X224)))) | ~ ! [X229 : term,X230 : term] : (($true = ((X225 @ (ap @ X229 @ X230)))) | ~ ($true = ((X225 @ X230))) | ~ ($true = ((X225 @ X229)))) | ~ ! [X231 : term] : (~ ($true = ((var @ X231))) | ($true = ((X225 @ (sub @ X231 @ X224)))))) <=> (induction2lem = $true)) & (substmonoid_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2_lthm = $true) <=> (! [X232 : term] : (((sub @ X232 @ id)) = X232) => (! [X233 : term,X234 : (term > $o),X235 : subst] : (($true = ((X234 @ (sub @ X233 @ X235)))) | ~ ! [X236 : term,X237 : term] : (~ ($true = ((X234 @ X237))) | ~ ($true = ((X234 @ X236))) | ($true = ((X234 @ (ap @ X237 @ X236))))) | ~ ! [X238 : term] : (~ ($true = ((var @ X238))) | ($true = ((X234 @ (sub @ X238 @ X235))))) | ~ ! [X239 : term] : (($true = ((X234 @ (lam @ X239)))) | ~ ! [X240 : term] : (~ ($true = ((X234 @ X240))) | ($true = ((X234 @ (sub @ X239 @ (push @ X240 @ id)))))))) => ! [X241 : term,X242 : (term > $o)] : (($true = ((X242 @ X241))) | ~ ! [X243 : term] : (~ ! [X244 : term] : (~ ($true = ((X242 @ X244))) | ($true = ((X242 @ (sub @ X243 @ (push @ X244 @ id)))))) | (((X242 @ (lam @ X243))) = $true)) | ~ ! [X245 : term] : (~ ($true = ((var @ X245))) | ($true = ((X242 @ X245)))) | ~ ! [X246 : term,X247 : term] : (($true = ((X242 @ (ap @ X246 @ X247)))) | ~ ($true = ((X242 @ X246))) | ~ ($true = ((X242 @ X247)))))))) & (! [X248 : term,X249 : subst] : (((sub @ one @ (push @ X248 @ X249))) = X248) <=> (axvarcons = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((pushprop_lem0 = $true) <=> ! [X253 : (term > $o),X254 : subst,X255 : term] : ~ ! [X256 : (term > $o)] : ~ ! [X257 : term] : (((X256 @ X257)) = ((X253 @ (sub @ X257 @ (push @ X255 @ X254)))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X258 : term] : (((sub @ X258 @ id)) = X258) => (! [X259 : (subst > term > subst > $o),X260 : term] : (~ ! [X261 : (subst > term > term)] : (($true = ((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id))) | ~ ! [X262 : subst,X263 : subst,X264 : term] : (((X261 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X261 @ X263 @ X264) @ X262))) | ~ ! [X265 : term] : (~ ($true = ((X259 @ id @ X265 @ id))) | ($true = ((X259 @ id @ (X261 @ id @ X265) @ id))))) | ($true = ((X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id))) | ~ ! [X266 : term] : (($true = ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id))) | ~ ($true = ((X259 @ id @ X266 @ id))))) => ! [X267 : term,X268 : (subst > term > subst > $o)] : (~ ! [X269 : (subst > term > term)] : (~ ! [X270 : term] : (~ ($true = ((X268 @ id @ X270 @ id))) | ($true = ((X268 @ id @ (X269 @ id @ X270) @ id)))) | ~ ! [X271 : term,X272 : subst,X273 : subst] : (((X269 @ (comp @ X273 @ X272) @ (sub @ X271 @ X272))) = ((sub @ (X269 @ X273 @ X271) @ X272))) | ($true = ((X268 @ id @ (lam @ (X269 @ sh @ one)) @ id)))) | ~ ! [X274 : term] : (~ ($true = ((X268 @ id @ X274 @ id))) | ($true = ((X268 @ id @ (sub @ X267 @ (push @ X274 @ id)) @ id)))) | ($true = ((X268 @ id @ (lam @ X267) @ id))))))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((! [X275 : (term > $o),X276 : term] : (($true = ((X275 @ X276))) | ~ ! [X277 : term] : (($true = ((X275 @ X277))) | ~ ($true = ((var @ X277)))) | ~ ! [X278 : term] : (($true = ((X275 @ (lam @ X278)))) | ~ ! [X279 : term] : (($true = ((X275 @ (sub @ X278 @ (push @ X279 @ id))))) | ~ ($true = ((X275 @ X279))))) | ~ ! [X280 : term,X281 : term] : (~ ($true = ((X275 @ X280))) | ($true = ((X275 @ (ap @ X280 @ X281)))) | ~ ($true = ((X275 @ X281))))) => (! [X282 : term,X283 : term,X284 : (subst > term > subst > $o)] : (~ (((X284 @ id @ X282 @ id)) = $true) | ($true = ((X284 @ id @ (ap @ X283 @ X282) @ id))) | ~ ! [X285 : subst,X286 : term,X287 : subst,X288 : subst] : (~ ($true = ((X284 @ X287 @ X286 @ (comp @ X288 @ X285)))) | ($true = ((X284 @ (comp @ X287 @ X288) @ (sub @ X286 @ X288) @ X285)))) | ~ ($true = ((X284 @ id @ X283 @ id))) | ~ ! [X289 : subst,X290 : subst,X291 : term,X292 : subst] : (($true = ((X284 @ X292 @ X291 @ (comp @ X290 @ X289)))) | ~ (((X284 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290) @ X289)) = $true)) | ~ ! [X293 : term,X294 : term] : (~ ($true = ((X284 @ id @ X293 @ id))) | ($true = ((X284 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id))) | ~ ($true = ((X284 @ id @ X294 @ id))))) => (! [X295 : (subst > term > subst > $o),X296 : term] : (~ ! [X297 : subst,X298 : subst,X299 : subst,X300 : term] : (~ ($true = ((X295 @ (comp @ X297 @ X298) @ (sub @ X300 @ X298) @ X299))) | ($true = ((X295 @ X297 @ X300 @ (comp @ X298 @ X299))))) | ~ ! [X301 : term] : (($true = ((X295 @ id @ (sub @ X296 @ (push @ X301 @ id)) @ id))) | ~ ($true = ((X295 @ id @ X301 @ id)))) | ($true = ((X295 @ id @ (lam @ X296) @ id))) | ~ ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (~ ($true = ((X295 @ X305 @ X303 @ (comp @ X302 @ X304)))) | ($true = ((X295 @ (comp @ X305 @ X302) @ (sub @ X303 @ X302) @ X304)))) | ~ ! [X306 : (subst > term > term)] : (~ ! [X307 : term] : (~ ($true = ((X295 @ id @ X307 @ id))) | ($true = ((X295 @ id @ (X306 @ id @ X307) @ id)))) | ($true = ((X295 @ id @ (lam @ (X306 @ sh @ one)) @ id))) | ~ ! [X308 : term,X309 : subst,X310 : subst] : (((X306 @ (comp @ X309 @ X310) @ (sub @ X308 @ X310))) = ((sub @ (X306 @ X309 @ X308) @ X310))))) => ! [X311 : term,X312 : (subst > term > subst > $o)] : (~ ! [X313 : (subst > term > term)] : (~ ! [X314 : term,X315 : subst,X316 : subst] : (((X313 @ (comp @ X316 @ X315) @ (sub @ X314 @ X315))) = ((sub @ (X313 @ X316 @ X314) @ X315))) | ~ ! [X317 : term] : (~ ($true = ((X312 @ id @ X317 @ id))) | ($true = ((X312 @ id @ (X313 @ id @ X317) @ id)))) | ($true = ((X312 @ id @ (lam @ (X313 @ sh @ one)) @ id)))) | ~ ! [X318 : subst,X319 : subst,X320 : term,X321 : subst] : (~ ($true = ((X312 @ X321 @ X320 @ (comp @ X318 @ X319)))) | ($true = ((X312 @ (comp @ X321 @ X318) @ (sub @ X320 @ X318) @ X319)))) | ~ ! [X322 : term,X323 : term] : (~ ($true = ((X312 @ id @ X323 @ id))) | ($true = ((X312 @ id @ (ap @ (sub @ X322 @ id) @ X323) @ id))) | ~ ($true = ((X312 @ id @ X322 @ id)))) | ~ ! [X324 : term] : (~ ($true = ((var @ (sub @ X324 @ id)))) | ($true = ((X312 @ id @ X324 @ id)))) | ~ ! [X325 : subst,X326 : subst,X327 : subst,X328 : term] : (~ ($true = ((X312 @ (comp @ X327 @ X325) @ (sub @ X328 @ X325) @ X326))) | ($true = ((X312 @ X327 @ X328 @ (comp @ X325 @ X326))))) | ($true = ((X312 @ id @ X311 @ id))))))) <=> (hoasinduction_lthm = $true)) & (hoasapnotvar = $true) & ((! [X329 : term] : (((sub @ X329 @ id)) = X329) => ! [X330 : (subst > term > subst > $o),X331 : (term > $o),X332 : term] : (~ ! [X333 : subst,X334 : term,X335 : subst,X336 : subst] : (($true = ((X330 @ (comp @ X336 @ X333) @ (sub @ X334 @ X333) @ X335))) | ~ ($true = ((X330 @ X336 @ X334 @ (comp @ X333 @ X335))))) | ($true = ((X331 @ (lam @ X332)))) | ~ ! [X337 : term] : (((X331 @ X337)) = ((X330 @ id @ X337 @ id))) | ~ ! [X338 : term] : (~ ($true = ((X331 @ X338))) | ($true = ((X331 @ (sub @ X332 @ (push @ X338 @ id)))))) | ~ ! [X339 : term,X340 : subst,X341 : subst,X342 : subst] : (($true = ((X330 @ X340 @ X339 @ (comp @ X342 @ X341)))) | ~ ($true = ((X330 @ (comp @ X340 @ X342) @ (sub @ X339 @ X342) @ X341)))) | ~ ! [X343 : (subst > term > term)] : (~ ! [X344 : term,X345 : subst,X346 : subst] : (((X343 @ (comp @ X345 @ X346) @ (sub @ X344 @ X346))) = ((sub @ (X343 @ X345 @ X344) @ X346))) | ~ ! [X347 : term] : (($true = ((X330 @ id @ (X343 @ id @ X347) @ id))) | ~ ($true = ((X330 @ id @ X347 @ id)))) | ($true = ((X330 @ id @ (lam @ (X343 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X348 : term,X349 : (subst > term > subst > $o)] : (($true = ((X349 @ id @ X348 @ id))) | ~ ! [X350 : term,X351 : term] : (($true = ((X349 @ id @ (ap @ (sub @ X351 @ id) @ X350) @ id))) | ~ ($true = ((X349 @ id @ X351 @ id))) | ~ (((X349 @ id @ X350 @ id)) = $true)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : subst,X354 : term,X355 : subst] : (((sub @ (X352 @ X355 @ X354) @ X353)) = ((X352 @ (comp @ X355 @ X353) @ (sub @ X354 @ X353)))) | ~ ! [X356 : term] : (($true = ((X349 @ id @ (X352 @ id @ X356) @ id))) | ~ ($true = ((X349 @ id @ X356 @ id)))) | ($true = ((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)))))) & (! [X357 : (subst > term > subst > $o)] : ~ ! [X358 : (term > $o)] : ~ ! [X359 : term] : (((X358 @ X359)) = ((X357 @ id @ X359 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X360 : (subst > term > subst > $o)] : ~ ! [X361 : (term > $o)] : ~ ! [X362 : term] : (((X360 @ id @ X362 @ id)) = ((X361 @ X362))) => (! [X363 : term,X364 : (term > $o)] : (($true = ((X364 @ X363))) | ~ ! [X365 : term] : (($true = ((X364 @ X365))) | ~ ($true = ((var @ X365)))) | ~ ! [X366 : term,X367 : term] : (($true = ((X364 @ (ap @ X367 @ X366)))) | ~ ($true = ((X364 @ X367))) | ~ ($true = ((X364 @ X366)))) | ~ ! [X368 : term] : (($true = ((X364 @ (lam @ X368)))) | ~ ! [X369 : term] : (~ ($true = ((X364 @ X369))) | ($true = ((X364 @ (sub @ X368 @ (push @ X369 @ id)))))))) => (! [X370 : term] : (((sub @ X370 @ id)) = X370) => (! [X371 : (term > $o),X372 : term,X373 : (subst > term > subst > $o)] : (~ ! [X374 : term] : (((X371 @ X374)) = ((X373 @ id @ X374 @ id))) | ~ ! [X375 : (subst > term > term)] : (~ ! [X376 : subst,X377 : subst,X378 : term] : (((sub @ (X375 @ X376 @ X378) @ X377)) = ((X375 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377)))) | ($true = ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id))) | ~ ! [X379 : term] : (($true = ((X373 @ id @ (X375 @ id @ X379) @ id))) | ~ ($true = ((X373 @ id @ X379 @ id))))) | ~ ! [X380 : term] : (($true = ((X371 @ (sub @ X372 @ (push @ X380 @ id))))) | ~ ($true = ((X371 @ X380)))) | ($true = ((X371 @ (lam @ X372))))) => ! [X381 : term,X382 : (subst > term > subst > $o)] : (~ ! [X383 : term,X384 : term] : (~ ($true = ((X382 @ id @ X383 @ id))) | ($true = ((X382 @ id @ (ap @ (sub @ X383 @ id) @ X384) @ id))) | ~ ($true = ((X382 @ id @ X384 @ id)))) | ~ ! [X385 : (subst > term > term)] : (($true = ((X382 @ id @ (lam @ (X385 @ sh @ one)) @ id))) | ~ ! [X386 : term] : (~ ($true = ((X382 @ id @ X386 @ id))) | ($true = ((X382 @ id @ (X385 @ id @ X386) @ id)))) | ~ ! [X387 : term,X388 : subst,X389 : subst] : (((X385 @ (comp @ X388 @ X389) @ (sub @ X387 @ X389))) = ((sub @ (X385 @ X388 @ X387) @ X389)))) | ($true = ((X382 @ id @ X381 @ id))))))))) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & (! [X390 : (subst > term > subst > $o),X391 : term] : (~ ! [X392 : term] : (($true = ((X390 @ id @ (sub @ X391 @ (push @ X392 @ id)) @ id))) | ~ ($true = ((X390 @ id @ X392 @ id)))) | ~ ! [X393 : (subst > term > term)] : (($true = ((X390 @ id @ (lam @ (X393 @ sh @ one)) @ id))) | ~ ! [X394 : subst,X395 : subst,X396 : term] : (((sub @ (X393 @ X395 @ X396) @ X394)) = ((X393 @ (comp @ X395 @ X394) @ (sub @ X396 @ X394)))) | ~ ! [X397 : term] : (~ ($true = ((X390 @ id @ X397 @ id))) | ($true = ((X390 @ id @ (X393 @ id @ X397) @ id))))) | ($true = ((X390 @ id @ (lam @ (sub @ X391 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X398 : term] : (((sub @ X398 @ id)) = X398) => (! [X399 : term,X400 : term,X401 : term,X402 : term] : ((X399 = X402) | (((ap @ X399 @ X401)) != ((ap @ X402 @ X400)))) => ! [X403 : term,X404 : term,X405 : term,X406 : term] : ((X404 = X405) | (((ap @ (sub @ X404 @ id) @ X403)) != ((ap @ (sub @ X405 @ id) @ X406)))))) <=> (hoasapinj1_lthm = $true)) & (hoasapinj2_gthm = $true) & (axabs = $true) & ! [X407 : subst] : ? [X408 : d_subst] : (((d2subst @ X408)) = X407) & ((termmset = $true) <=> ! [X409 : term] : (((sub @ X409 @ id)) = X409)) & (! [X410 : (subst > term > subst > $o)] : ~ ! [X411 : (term > $o)] : ~ ! [X412 : term] : (((X411 @ X412)) = ((X410 @ id @ X412 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ! [X413 : d_subst,X414 : d_subst] : ((((d2subst @ X414)) = ((d2subst @ X413))) => (X413 = X414)) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X415 : term,X416 : subst,X417 : (term > $o),X418 : term,X419 : (term > $o)] : (~ ($true = ((X417 @ X418))) | ($true = ((X419 @ (sub @ X418 @ (push @ X415 @ X416)))))) <=> (pushprop_lem1 = $true)) & (hoaslamnotap_gthm = $true) & (! [X420 : term,X421 : (subst > term > subst > $o),X422 : term] : (~ ! [X423 : term,X424 : subst,X425 : subst,X426 : subst] : (($true = ((X421 @ X424 @ X423 @ (comp @ X425 @ X426)))) | ~ ($true = ((X421 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)))) | ($true = ((X421 @ id @ (ap @ X420 @ X422) @ id))) | ~ ! [X427 : term,X428 : subst,X429 : subst,X430 : subst] : (~ ($true = ((X421 @ X428 @ X427 @ (comp @ X430 @ X429)))) | ($true = ((X421 @ (comp @ X428 @ X430) @ (sub @ X427 @ X430) @ X429)))) | ~ ! [X431 : term,X432 : term] : (~ ($true = ((X421 @ id @ X431 @ id))) | ($true = ((X421 @ id @ (ap @ (sub @ X431 @ id) @ X432) @ id))) | ~ ($true = ((X421 @ id @ X432 @ id)))) | ~ ($true = ((X421 @ id @ X422 @ id))) | ~ ($true = ((X421 @ id @ X420 @ id)))) <=> (hoasinduction_lem2 = $true)) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & ~ (ulamvar1 = $true) & (! [X433 : subst] : (((comp @ X433 @ id)) = X433) <=> (axidr = $true)) & (! [X434 : subst] : (((comp @ id @ X434)) = X434) <=> (axidl = $true)) & ! [X435 : term] : ? [X436 : d_term] : (((d2term @ X436)) = X435) & ~ (((var @ (d2term @ d_one))) = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X437 : term,X438 : term,X439 : term,X440 : term] : ((X437 = X440) | (((ap @ X440 @ X438)) != ((ap @ X437 @ X439)))) <=> (apinj1 = $true)) & (! [X441 : term,X442 : (term > $o)] : (~ ! [X443 : term] : (~ ($true = ((X442 @ X443))) | ($true = ((X442 @ (lam @ X443))))) | ($true = ((X442 @ X441))) | ~ ! [X444 : term,X445 : term] : (~ ($true = ((X442 @ X444))) | ($true = ((X442 @ (ap @ X445 @ X444)))) | ~ ($true = ((X442 @ X445)))) | ~ ! [X446 : term] : (($true = ((X442 @ X446))) | ~ ($true = ((var @ X446))))) <=> (induction = $true)) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X447 : term,X448 : (subst > term > subst > $o)] : (~ ! [X449 : (subst > term > term),X450 : term] : (~ ! [X451 : term] : (~ ($true = ((X448 @ id @ X451 @ id))) | ($true = ((X448 @ id @ (X449 @ id @ X451) @ id)))) | ~ ! [X452 : subst,X453 : term,X454 : subst] : (((sub @ (X449 @ X452 @ X453) @ X454)) = ((sub @ (sub @ X450 @ (push @ X453 @ X452)) @ X454))) | ($true = ((X448 @ id @ (lam @ (X449 @ sh @ one)) @ id))) | ~ ! [X455 : subst,X456 : term,X457 : subst] : (((X449 @ (comp @ X457 @ X455) @ (sub @ X456 @ X455))) = ((sub @ X450 @ (push @ (sub @ X456 @ X455) @ (comp @ X457 @ X455)))))) | ($true = ((X448 @ id @ (lam @ (sub @ X447 @ (push @ one @ sh))) @ id))) | ~ ! [X458 : term] : (($true = ((X448 @ id @ (sub @ X447 @ (push @ X458 @ id)) @ id))) | ~ ($true = ((X448 @ id @ X458 @ id)))))) & ((! [X459 : term,X460 : subst] : (((sub @ one @ (push @ X459 @ X460))) = X459) => ! [X461 : (term > $o),X462 : (term > $o),X463 : subst,X464 : term] : (($true = ((X462 @ one))) | ~ ! [X465 : term] : (((X461 @ (sub @ X465 @ (push @ X464 @ X463)))) = ((X462 @ X465))) | ~ ($true = ((X461 @ X464))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X466 : term,X467 : term] : ((X466 = X467) | (((sub @ X466 @ sh)) != ((sub @ X467 @ sh)))) <=> (shinj = $true)) & (! [X468 : (subst > term > subst > $o),X469 : term] : (~ ! [X470 : term] : (~ ($true = ((var @ (sub @ X470 @ id)))) | ($true = ((X468 @ id @ X470 @ id)))) | ~ ! [X471 : subst,X472 : subst,X473 : subst,X474 : term] : (~ ($true = ((X468 @ X471 @ X474 @ (comp @ X472 @ X473)))) | (((X468 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473)) = $true)) | ($true = ((X468 @ id @ X469 @ id))) | ~ ! [X475 : term,X476 : term] : (~ ($true = ((X468 @ id @ X476 @ id))) | ~ ($true = ((X468 @ id @ X475 @ id))) | (((X468 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) = $true)) | ~ ! [X477 : term,X478 : subst,X479 : subst,X480 : subst] : (($true = ((X468 @ X478 @ X477 @ (comp @ X480 @ X479)))) | ~ ($true = ((X468 @ (comp @ X478 @ X480) @ (sub @ X477 @ X480) @ X479)))) | ~ ! [X481 : (subst > term > term)] : (~ ! [X482 : term] : (~ ($true = ((X468 @ id @ X482 @ id))) | ($true = ((X468 @ id @ (X481 @ id @ X482) @ id)))) | ($true = ((X468 @ id @ (lam @ (X481 @ sh @ one)) @ id))) | ~ ! [X483 : subst,X484 : term,X485 : subst] : (((X481 @ (comp @ X483 @ X485) @ (sub @ X484 @ X485))) = ((sub @ (X481 @ X483 @ X484) @ X485))))) <=> (hoasinduction = $true)) & (! [X486 : (subst > term > term),X487 : term,X488 : term] : (~ ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X486 @ X491 @ X489) @ X490)) = ((X486 @ (comp @ X491 @ X490) @ (sub @ X489 @ X490)))) | (((ap @ (sub @ X487 @ id) @ X488)) != ((lam @ (X486 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem1 = $true) & (! [X492 : term] : ~ ! [X493 : (subst > term > term)] : ~ ! [X494 : subst,X495 : term] : (((sub @ X492 @ (push @ X495 @ X494))) = ((X493 @ X494 @ X495))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (axvarshift = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (! [X496 : (term > $o),X497 : subst,X498 : term] : ~ ! [X499 : (term > $o)] : ~ ! [X500 : term] : (((X499 @ X500)) = ((X496 @ (sub @ X500 @ (push @ X498 @ X497))))) <=> (pushprop_lem0_lthm = $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ! [X501 : d_term] : (d_one = X501) & (pushprop_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X502 : (subst > term > subst > $o),X503 : term] : (($true = ((X502 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id))) | ~ ! [X504 : (subst > term > term)] : (~ ! [X505 : term] : (($true = ((X502 @ id @ (X504 @ id @ X505) @ id))) | ~ ($true = ((X502 @ id @ X505 @ id)))) | ($true = ((X502 @ id @ (lam @ (X504 @ sh @ one)) @ id))) | ~ ! [X506 : subst,X507 : term,X508 : subst] : (((X504 @ (comp @ X506 @ X508) @ (sub @ X507 @ X508))) = ((sub @ (X504 @ X506 @ X507) @ X508)))) | ~ ! [X509 : term] : (~ ($true = ((X502 @ id @ X509 @ id))) | ($true = ((X502 @ id @ (sub @ X503 @ (push @ X509 @ id)) @ id)))))) & ! [X510 : d_subst] : (d_id = X510) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3a = $true) <=> ! [X511 : term,X512 : (subst > term > subst > $o)] : (~ ! [X513 : (subst > term > term)] : (~ ! [X514 : subst,X515 : term,X516 : subst] : (((X513 @ (comp @ X516 @ X514) @ (sub @ X515 @ X514))) = ((sub @ (X513 @ X516 @ X515) @ X514))) | ~ ! [X517 : term] : (($true = ((X512 @ id @ (X513 @ id @ X517) @ id))) | ~ ($true = ((X512 @ id @ X517 @ id)))) | ($true = ((X512 @ id @ (lam @ (X513 @ sh @ one)) @ id)))) | ~ ! [X518 : term] : (($true = ((X512 @ id @ (sub @ X511 @ (push @ X518 @ id)) @ id))) | ~ ($true = ((X512 @ id @ X518 @ id)))) | ($true = ((X512 @ id @ (lam @ X511) @ id))))) & ((hoasinduction_lem3b = $true) <=> ! [X519 : term] : ~ ! [X520 : (subst > term > term)] : (((X520 @ sh @ one)) != ((sub @ X519 @ (push @ one @ sh))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X521 : term,X522 : (subst > term > subst > $o),X523 : (term > $o)] : (~ ! [X524 : term] : (~ (((X523 @ X524)) = $true) | ($true = ((X523 @ (sub @ X521 @ (push @ X524 @ id)))))) | ~ ! [X525 : (subst > term > term)] : (~ ! [X526 : term,X527 : subst,X528 : subst] : (((sub @ (X525 @ X527 @ X526) @ X528)) = ((X525 @ (comp @ X527 @ X528) @ (sub @ X526 @ X528)))) | ($true = ((X522 @ id @ (lam @ (X525 @ sh @ one)) @ id))) | ~ ! [X529 : term] : (($true = ((X522 @ id @ (X525 @ id @ X529) @ id))) | ~ ($true = ((X522 @ id @ X529 @ id))))) | ~ ! [X530 : subst,X531 : subst,X532 : subst,X533 : term] : (~ ($true = ((X522 @ (comp @ X532 @ X531) @ (sub @ X533 @ X531) @ X530))) | ($true = ((X522 @ X532 @ X533 @ (comp @ X531 @ X530))))) | ~ ! [X534 : term] : (((X522 @ id @ X534 @ id)) = ((X523 @ X534))) | ~ ! [X535 : subst,X536 : subst,X537 : term,X538 : subst] : (($true = ((X522 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X538))) | ~ ($true = ((X522 @ X536 @ X537 @ (comp @ X535 @ X538))))) | ($true = ((X523 @ (lam @ X521)))))) & (pushprop_lthm = $true) & ((! [X539 : subst] : (((comp @ id @ X539)) = X539) => (! [X540 : subst] : (((comp @ X540 @ id)) = X540) => (! [X541 : subst] : (((comp @ id @ X541)) = X541) & ! [X542 : subst] : (((comp @ X542 @ id)) = X542)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (termmset_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X543 : subst,X544 : (term > $o),X545 : term,X546 : (term > $o)] : (($true = ((X544 @ one))) | ~ ($true = ((X546 @ X545))) | ~ ! [X547 : term] : (((X544 @ X547)) = ((X546 @ (sub @ X547 @ (push @ X545 @ X543))))))) & (! [X548 : subst,X549 : term] : (((comp @ sh @ (push @ X549 @ X548))) = X548) <=> (axshiftcons = $true))), 24.89/4.11 inference(fool_elimination,[],[f4])). 24.89/4.11 thf(f6,plain,( 24.89/4.11 ~ (hoasinduction_no_psi_cond = ! [X0 : (subst > term > subst > $o)] : (! [X1 : term,X2 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X1 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))) => (! [X3 : (subst > term > term)] : (! [X4 : subst,X5 : term,X6 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))) => (! [X7 : term] : ((X0 @ id @ X7 @ id) => (X0 @ id @ (X3 @ id @ X7) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X8 : subst, X9 : term] : ((X3 @ X8 @ X9)))) @ id))) => ! [X10 : term] : (X0 @ id @ X10 @ id))))), 24.89/4.11 inference(rectify,[],[f3])). 24.89/4.11 thf(f7,plain,( 24.89/4.11 ~((hoasinduction_no_psi_cond = $true) <=> ! [X0 : (subst > term > subst > $o)] : (! [X2 : term,X1 : term] : ((((X0 @ id @ X2 @ id)) = $true) => ((((X0 @ id @ X1 @ id)) = $true) => ($true = ((X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))))) => (! [X3 : (subst > term > term)] : (! [X6 : subst,X5 : term,X4 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))) => (! [X7 : term] : (($true = ((X0 @ id @ X7 @ id))) => ($true = ((X0 @ id @ (X3 @ id @ X7) @ id)))) => ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))))) => ! [X10 : term] : (((X0 @ id @ X10 @ id)) = $true))))), 24.89/4.11 inference(fool_elimination,[],[f6])). 24.89/4.11 thf(f8,plain,( 24.89/4.11 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2 = $true) <=> ! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1))))) & ((! [X4 : term] : (((sub @ X4 @ id)) = X4) => ! [X5 : term] : (((sub @ X5 @ id)) = X5)) <=> (termmset_lthm = $true)) & (pushprop_lem3v2 = $true) & (axapp = $true) & (hoaslamnotap_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapinj1_gthm = $true) & ! [X6 : d_term,X7 : d_term] : ((((d2term @ X7)) = ((d2term @ X6))) => (X6 = X7)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X8 : term] : ~ ! [X9 : (subst > term > term)] : (((X9 @ sh @ one)) != ((sub @ X8 @ (push @ one @ sh))))) & ((laminj = $true) <=> ! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11))) & (hoaslamnotvar_lthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X12 : term,X13 : subst] : (((sub @ one @ (push @ X12 @ X13))) = X12) => (! [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) = X14) => (! [X16 : term,X17 : term] : ((X16 = X17) | (((lam @ X17)) != ((lam @ X16)))) => ! [X19 : (subst > term > term),X18 : subst,X21 : term,X20 : (subst > term > term)] : (~ ! [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) = ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ~ ! [X24 : subst,X23 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) = ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21)))))))) & (one = ((d2term @ d_one))) & ((! [X28 : term,X31 : term,X30 : term,X29 : term] : ((((ap @ X30 @ X28)) != ((ap @ X31 @ X29))) | (X28 = X29)) => ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35))))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X36 : (subst > term > subst > $o)] : ~ ! [X37 : (term > $o)] : ~ ! [X38 : term] : (((X37 @ X38)) = ((X36 @ id @ X38 @ id))) => (! [X39 : term,X40 : (term > $o)] : (~ ! [X41 : term] : (~ ! [X42 : term] : (($true = ((X40 @ (sub @ X41 @ (push @ X42 @ id))))) | ~ ($true = ((X40 @ X42)))) | ($true = ((X40 @ (lam @ X41))))) | ~ ! [X43 : term] : (~ ($true = ((var @ X43))) | ($true = ((X40 @ X43)))) | ($true = ((X40 @ X39))) | ~ ! [X44 : term,X45 : term] : (($true = ((X40 @ (ap @ X44 @ X45)))) | ~ ($true = ((X40 @ X45))) | ~ ($true = ((X40 @ X44))))) => (! [X46 : term] : (((sub @ X46 @ id)) = X46) => (! [X47 : (subst > term > subst > $o),X48 : term,X49 : (term > $o)] : (~ ! [X50 : (subst > term > term)] : (~ ! [X53 : subst,X52 : subst,X51 : term] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) = ((sub @ (X50 @ X52 @ X51) @ X53))) | ~ ! [X54 : term] : (($true = ((X47 @ id @ (X50 @ id @ X54) @ id))) | ~ ($true = ((X47 @ id @ X54 @ id)))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id)))) | ~ ! [X55 : term] : (($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id))))) | ~ ($true = ((X49 @ X55)))) | ($true = ((X49 @ (lam @ X48)))) | ~ ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id)))) => ! [X57 : term,X58 : (subst > term > subst > $o)] : (~ ! [X59 : term] : (($true = ((X58 @ id @ X59 @ id))) | ~ ($true = ((var @ (sub @ X59 @ id))))) | ~ ! [X60 : (subst > term > term)] : (($true = ((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ~ ! [X61 : term] : (($true = ((X58 @ id @ (X60 @ id @ X61) @ id))) | ~ ($true = ((X58 @ id @ X61 @ id)))) | ~ ! [X63 : subst,X64 : subst,X62 : term] : (((sub @ (X60 @ X64 @ X62) @ X63)) = ((X60 @ (comp @ X64 @ X63) @ (sub @ X62 @ X63))))) | ($true = ((X58 @ id @ X57 @ id))) | ~ ! [X65 : term,X66 : term] : (($true = ((X58 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id))) | ~ ($true = ((X58 @ id @ X65 @ id))) | ~ ($true = ((X58 @ id @ X66 @ id)))) | ~ ! [X67 : term,X68 : subst,X69 : subst,X70 : subst] : (~ ($true = ((X58 @ X68 @ X67 @ (comp @ X70 @ X69)))) | ($true = ((X58 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69)))) | ~ ! [X71 : subst,X72 : subst,X73 : term,X74 : subst] : (~ ($true = ((X58 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X74))) | ($true = ((X58 @ X72 @ X73 @ (comp @ X71 @ X74))))))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X75 : (term > $o),X76 : (subst > term > subst > $o),X77 : term] : (~ ! [X78 : term] : (((X76 @ id @ X78 @ id)) = ((X75 @ X78))) | ($true = ((X75 @ (lam @ X77)))) | ~ ! [X79 : term] : (~ ($true = ((X75 @ X79))) | ($true = ((X75 @ (sub @ X77 @ (push @ X79 @ id)))))) | ~ ! [X80 : (subst > term > term)] : (($true = ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) | ~ ! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ~ ($true = ((X76 @ id @ X81 @ id)))) | ~ ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82)))))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X88 : term,X87 : subst] : (((comp @ sh @ (push @ X88 @ X87))) = X87) => ! [X89 : (term > $o),X90 : term,X91 : term,X92 : subst,X93 : (term > $o)] : (~ ($true = ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92))))))))) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2_gthm = $true) & (! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) <=> (apinj2 = $true)) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ((induction2lem_lthm = $true) <=> (! [X99 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X99))) = X98) => (! [X101 : term,X100 : subst] : (((comp @ sh @ (push @ X101 @ X100))) = X100) => (! [X102 : subst] : (((comp @ X102 @ id)) = X102) => (! [X103 : (term > $o),X104 : term] : (~ ! [X105 : term,X106 : term] : (~ ($true = ((X103 @ X106))) | ~ ($true = ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106))))) | ~ ! [X107 : term] : (($true = ((X103 @ (lam @ X107)))) | ~ ($true = ((X103 @ X107)))) | ($true = ((X103 @ X104))) | ~ ! [X108 : term] : (~ ($true = ((var @ X108))) | ($true = ((X103 @ X108))))) => ! [X109 : (term > $o),X110 : subst,X111 : term] : (~ ! [X112 : term] : (~ ! [X113 : term] : (~ ($true = ((X109 @ X113))) | ($true = ((X109 @ (sub @ X112 @ (push @ X113 @ id)))))) | ($true = ((X109 @ (lam @ X112))))) | ~ ! [X114 : term] : ((((X109 @ (sub @ X114 @ X110))) = $true) | ~ ($true = ((var @ X114)))) | ~ ! [X115 : term,X116 : term] : (($true = ((X109 @ (ap @ X116 @ X115)))) | ~ ($true = ((X109 @ X115))) | ~ ($true = ((X109 @ X116)))) | ($true = ((X109 @ (sub @ X111 @ X110)))))))))) & (! [X117 : term,X118 : (term > $o)] : (~ ! [X119 : term] : (($true = ((X118 @ (lam @ X119)))) | ~ ! [X120 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X120 @ id))))) | ~ ($true = ((X118 @ X120))))) | ($true = ((X118 @ X117))) | ~ ! [X121 : term] : (($true = ((X118 @ X121))) | ~ (((var @ X121)) = $true)) | ~ ! [X122 : term,X123 : term] : (($true = ((X118 @ (ap @ X122 @ X123)))) | ~ ($true = ((X118 @ X123))) | ~ ($true = ((X118 @ X122))))) <=> (induction2 = $true)) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) <=> (axvarid = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X129 : term] : ~ ! [X130 : (subst > term > term)] : ~ ! [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) = ((sub @ X129 @ (push @ X132 @ X131)))) => (! [X133 : term] : (((sub @ X133 @ id)) = X133) => ! [X134 : term,X135 : (term > $o),X136 : (subst > term > subst > $o)] : (~ ! [X137 : (subst > term > term)] : (($true = ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) | ~ ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139))) | ~ ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ~ ($true = ((X136 @ id @ X141 @ id))))) | ~ ! [X142 : term] : (((X136 @ id @ X142 @ id)) = ((X135 @ X142))) | ~ ! [X143 : term] : (~ ($true = ((X135 @ X143))) | ($true = ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ($true = ((X135 @ (lam @ X134)))))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axmap = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X144 : term] : ~ ! [X145 : (subst > term > term)] : ~ ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((axscons = $true) <=> ! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148)) & (((d2subst @ d_id)) = sh) & (lamnotvar = $true) & ((hoaslaminj = $true) <=> ! [X151 : (subst > term > term),X152 : (subst > term > term),X150 : term,X149 : subst] : ((((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ~ ! [X158 : subst,X157 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) = ((sub @ (X152 @ X157 @ X156) @ X158))) | (((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | ~ ! [X153 : term,X154 : subst,X155 : subst] : (((sub @ (X151 @ X154 @ X153) @ X155)) = ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))))) & ((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) <=> (substmonoid = $true)) & ((! [X161 : term] : (((sub @ X161 @ id)) = X161) => (! [X162 : (subst > term > subst > $o),X163 : term] : (($true = ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id))) | ~ ! [X164 : (subst > term > term)] : (($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ~ ! [X165 : term,X166 : subst,X167 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) = ((sub @ (X164 @ X167 @ X165) @ X166))) | ~ ! [X168 : term] : (~ ($true = ((X162 @ id @ X168 @ id))) | ($true = ((X162 @ id @ (X164 @ id @ X168) @ id))))) | ~ ! [X169 : term] : (~ ($true = ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id))))) => ! [X170 : (subst > term > subst > $o),X171 : term] : (~ ! [X172 : subst,X173 : subst,X174 : term,X175 : subst] : (($true = ((X170 @ X173 @ X174 @ (comp @ X172 @ X175)))) | ~ ($true = ((X170 @ (comp @ X173 @ X172) @ (sub @ X174 @ X172) @ X175)))) | ~ ! [X176 : (subst > term > term)] : (~ ! [X177 : term] : (~ ($true = ((X170 @ id @ X177 @ id))) | ($true = ((X170 @ id @ (X176 @ id @ X177) @ id)))) | ~ ! [X178 : subst,X180 : term,X179 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) | ($true = ((X170 @ id @ (lam @ (X176 @ sh @ one)) @ id)))) | (((X170 @ id @ (lam @ X171) @ id)) = $true) | ~ ! [X181 : term] : (~ ($true = ((X170 @ id @ X181 @ id))) | ($true = ((X170 @ id @ (sub @ X171 @ (push @ X181 @ id)) @ id)))) | ~ ! [X182 : subst,X183 : term,X184 : subst,X185 : subst] : (($true = ((X170 @ (comp @ X182 @ X185) @ (sub @ X183 @ X185) @ X184))) | ~ ($true = ((X170 @ X182 @ X183 @ (comp @ X185 @ X184)))))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & ((hoasinduction_lem3 = $true) <=> ! [X186 : (subst > term > subst > $o),X187 : term] : (~ ! [X188 : (subst > term > term)] : (~ ! [X189 : term] : (($true = ((X186 @ id @ (X188 @ id @ X189) @ id))) | ~ ($true = ((X186 @ id @ X189 @ id)))) | ~ ! [X191 : subst,X190 : term,X192 : subst] : (((X188 @ (comp @ X191 @ X192) @ (sub @ X190 @ X192))) = ((sub @ (X188 @ X191 @ X190) @ X192))) | ($true = ((X186 @ id @ (lam @ (X188 @ sh @ one)) @ id)))) | ~ ! [X193 : term,X194 : subst,X195 : subst,X196 : subst] : (($true = ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) | ~ ($true = ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) | ~ ! [X197 : term] : (~ ($true = ((X186 @ id @ X197 @ id))) | ($true = ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ($true = ((X186 @ id @ (lam @ X187) @ id))) | ~ ! [X198 : subst,X199 : subst,X200 : term,X201 : subst] : (~ ($true = ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) | ($true = ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))))) & (! [X202 : (subst > term > subst > $o),X203 : (term > $o),X204 : term,X205 : term] : (~ ($true = ((X203 @ X205))) | ($true = ((X203 @ (ap @ X205 @ X204)))) | ~ ($true = ((X203 @ X204))) | ~ ! [X206 : term] : (((X202 @ id @ X206 @ id)) = ((X203 @ X206))) | ~ ! [X207 : subst,X208 : term,X209 : subst,X210 : subst] : (~ ($true = ((X202 @ X210 @ X208 @ (comp @ X207 @ X209)))) | ($true = ((X202 @ (comp @ X210 @ X207) @ (sub @ X208 @ X207) @ X209)))) | ~ ! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : (($true = ((X202 @ X214 @ X212 @ (comp @ X213 @ X211)))) | ~ ($true = ((X202 @ (comp @ X214 @ X213) @ (sub @ X212 @ X213) @ X211)))) | ~ ! [X215 : term,X216 : term] : (($true = ((X202 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))) | ~ ($true = ((X202 @ id @ X216 @ id))) | ~ ($true = ((X202 @ id @ X215 @ id))))) <=> (hoasinduction_lem2v2 = $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)))))))))))))) & (! [X217 : subst,X218 : (term > $o),X219 : term] : (~ ! [X220 : term] : ((((X218 @ (lam @ X220))) = $true) | ~ ! [X221 : term] : (($true = ((X218 @ (sub @ X220 @ (push @ X221 @ id))))) | ~ ($true = ((X218 @ X221))))) | ($true = ((X218 @ (sub @ X219 @ X217)))) | ~ ! [X222 : term,X223 : term] : (($true = ((X218 @ (ap @ X222 @ X223)))) | ~ ($true = ((X218 @ X223))) | ~ ($true = ((X218 @ X222)))) | ~ ! [X224 : term] : (~ ($true = ((var @ X224))) | ($true = ((X218 @ (sub @ X224 @ X217)))))) <=> (induction2lem = $true)) & (substmonoid_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((induction2_lthm = $true) <=> (! [X225 : term] : (((sub @ X225 @ id)) = X225) => (! [X226 : term,X227 : (term > $o),X228 : subst] : (($true = ((X227 @ (sub @ X226 @ X228)))) | ~ ! [X229 : term,X230 : term] : (~ ($true = ((X227 @ X230))) | ~ ($true = ((X227 @ X229))) | ($true = ((X227 @ (ap @ X230 @ X229))))) | ~ ! [X231 : term] : (~ ($true = ((var @ X231))) | ($true = ((X227 @ (sub @ X231 @ X228))))) | ~ ! [X232 : term] : (($true = ((X227 @ (lam @ X232)))) | ~ ! [X233 : term] : (~ ($true = ((X227 @ X233))) | ($true = ((X227 @ (sub @ X232 @ (push @ X233 @ id)))))))) => ! [X234 : term,X235 : (term > $o)] : (($true = ((X235 @ X234))) | ~ ! [X236 : term] : (~ ! [X237 : term] : (~ ($true = ((X235 @ X237))) | ($true = ((X235 @ (sub @ X236 @ (push @ X237 @ id)))))) | ($true = ((X235 @ (lam @ X236))))) | ~ ! [X238 : term] : (~ ($true = ((var @ X238))) | ($true = ((X235 @ X238)))) | ~ ! [X239 : term,X240 : term] : (($true = ((X235 @ (ap @ X239 @ X240)))) | ~ ($true = ((X235 @ X239))) | ~ ($true = ((X235 @ X240)))))))) & (! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) <=> (axvarcons = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((pushprop_lem0 = $true) <=> ! [X243 : (term > $o),X245 : term,X244 : subst] : ~ ! [X246 : (term > $o)] : ~ ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244)))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X248 : term] : (((sub @ X248 @ id)) = X248) => (! [X249 : (subst > term > subst > $o),X250 : term] : (~ ! [X251 : (subst > term > term)] : (($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) | ~ ! [X254 : term,X253 : subst,X252 : subst] : (((sub @ (X251 @ X253 @ X254) @ X252)) = ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))) | ~ ! [X255 : term] : (~ ($true = ((X249 @ id @ X255 @ id))) | ($true = ((X249 @ id @ (X251 @ id @ X255) @ id))))) | ($true = ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) | ~ ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ~ ($true = ((X249 @ id @ X256 @ id))))) => ! [X257 : term,X258 : (subst > term > subst > $o)] : (~ ! [X259 : (subst > term > term)] : (~ ! [X260 : term] : (~ ($true = ((X258 @ id @ X260 @ id))) | ($true = ((X258 @ id @ (X259 @ id @ X260) @ id)))) | ~ ! [X262 : subst,X261 : term,X263 : subst] : (((X259 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X263 @ X261) @ X262))) | ($true = ((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id)))) | ~ ! [X264 : term] : (~ ($true = ((X258 @ id @ X264 @ id))) | (((X258 @ id @ (sub @ X257 @ (push @ X264 @ id)) @ id)) = $true)) | (((X258 @ id @ (lam @ X257) @ id)) = $true))))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2_lthm = $true) & ((! [X265 : (term > $o),X266 : term] : (($true = ((X265 @ X266))) | ~ ! [X267 : term] : (($true = ((X265 @ X267))) | ~ ($true = ((var @ X267)))) | ~ ! [X268 : term] : (($true = ((X265 @ (lam @ X268)))) | ~ ! [X269 : term] : (($true = ((X265 @ (sub @ X268 @ (push @ X269 @ id))))) | ~ ($true = ((X265 @ X269))))) | ~ ! [X270 : term,X271 : term] : (~ ($true = ((X265 @ X270))) | ($true = ((X265 @ (ap @ X270 @ X271)))) | ~ ($true = ((X265 @ X271))))) => (! [X272 : term,X273 : term,X274 : (subst > term > subst > $o)] : (~ ($true = ((X274 @ id @ X272 @ id))) | ($true = ((X274 @ id @ (ap @ X273 @ X272) @ id))) | ~ ! [X275 : subst,X276 : term,X277 : subst,X278 : subst] : (~ ($true = ((X274 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X274 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275)))) | ~ ($true = ((X274 @ id @ X273 @ id))) | ~ ! [X279 : subst,X280 : subst,X281 : term,X282 : subst] : (($true = ((X274 @ X282 @ X281 @ (comp @ X280 @ X279)))) | ~ ($true = ((X274 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280) @ X279)))) | ~ ! [X283 : term,X284 : term] : (~ ($true = ((X274 @ id @ X283 @ id))) | ($true = ((X274 @ id @ (ap @ (sub @ X283 @ id) @ X284) @ id))) | ~ ($true = ((X274 @ id @ X284 @ id))))) => (! [X285 : (subst > term > subst > $o),X286 : term] : (~ ! [X287 : subst,X288 : subst,X289 : subst,X290 : term] : (~ ($true = ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289))) | ($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289))))) | ~ ! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ~ ($true = ((X285 @ id @ X291 @ id)))) | ($true = ((X285 @ id @ (lam @ X286) @ id))) | ~ ! [X292 : subst,X293 : term,X294 : subst,X295 : subst] : (~ ($true = ((X285 @ X295 @ X293 @ (comp @ X292 @ X294)))) | ($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294)))) | ~ ! [X296 : (subst > term > term)] : (~ ! [X297 : term] : (~ ($true = ((X285 @ id @ X297 @ id))) | ($true = ((X285 @ id @ (X296 @ id @ X297) @ id)))) | ($true = ((X285 @ id @ (lam @ (X296 @ sh @ one)) @ id))) | ~ ! [X300 : subst,X299 : subst,X298 : term] : (((X296 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ (X296 @ X299 @ X298) @ X300))))) => ! [X301 : term,X302 : (subst > term > subst > $o)] : (~ ! [X303 : (subst > term > term)] : (~ ! [X304 : term,X306 : subst,X305 : subst] : (((X303 @ (comp @ X306 @ X305) @ (sub @ X304 @ X305))) = ((sub @ (X303 @ X306 @ X304) @ X305))) | ~ ! [X307 : term] : (~ ($true = ((X302 @ id @ X307 @ id))) | ($true = ((X302 @ id @ (X303 @ id @ X307) @ id)))) | ($true = ((X302 @ id @ (lam @ (X303 @ sh @ one)) @ id)))) | ~ ! [X308 : subst,X309 : subst,X310 : term,X311 : subst] : (~ ($true = ((X302 @ X311 @ X310 @ (comp @ X308 @ X309)))) | ($true = ((X302 @ (comp @ X311 @ X308) @ (sub @ X310 @ X308) @ X309)))) | ~ ! [X312 : term,X313 : term] : (~ ($true = ((X302 @ id @ X313 @ id))) | ($true = ((X302 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id))) | ~ ($true = ((X302 @ id @ X312 @ id)))) | ~ ! [X314 : term] : (~ ($true = ((var @ (sub @ X314 @ id)))) | ($true = ((X302 @ id @ X314 @ id)))) | ~ ! [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (~ ($true = ((X302 @ (comp @ X317 @ X315) @ (sub @ X318 @ X315) @ X316))) | ($true = ((X302 @ X317 @ X318 @ (comp @ X315 @ X316))))) | ($true = ((X302 @ id @ X301 @ id))))))) <=> (hoasinduction_lthm = $true)) & (hoasapnotvar = $true) & ((! [X319 : term] : (((sub @ X319 @ id)) = X319) => ! [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (~ ! [X323 : subst,X324 : term,X325 : subst,X326 : subst] : (($true = ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) | ~ ($true = ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ($true = ((X321 @ (lam @ X322)))) | ~ ! [X327 : term] : (((X321 @ X327)) = ((X320 @ id @ X327 @ id))) | ~ ! [X328 : term] : (~ ($true = ((X321 @ X328))) | ($true = ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ~ ! [X329 : term,X330 : subst,X331 : subst,X332 : subst] : (($true = ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) | ~ ($true = ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) | ~ ! [X333 : (subst > term > term)] : (~ ! [X334 : term,X335 : subst,X336 : subst] : (((X333 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ (X333 @ X335 @ X334) @ X336))) | ~ ! [X337 : term] : (($true = ((X320 @ id @ (X333 @ id @ X337) @ id))) | ~ ($true = ((X320 @ id @ X337 @ id)))) | ($true = ((X320 @ id @ (lam @ (X333 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X338 : term,X339 : (subst > term > subst > $o)] : (($true = ((X339 @ id @ X338 @ id))) | ~ ! [X340 : term,X341 : term] : (($true = ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) | ~ ($true = ((X339 @ id @ X341 @ id))) | ~ ($true = ((X339 @ id @ X340 @ id)))) | ~ ! [X342 : (subst > term > term)] : (~ ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343))) | ~ ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ~ ($true = ((X339 @ id @ X346 @ id)))) | ($true = ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id)))))) & ((hoasinduction_lem0 = $true) <=> ! [X347 : (subst > term > subst > $o)] : ~ ! [X348 : (term > $o)] : ~ ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349)))) & (hoaslamnotvar_gthm = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X350 : (subst > term > subst > $o)] : ~ ! [X351 : (term > $o)] : ~ ! [X352 : term] : (((X350 @ id @ X352 @ id)) = ((X351 @ X352))) => (! [X353 : term,X354 : (term > $o)] : (($true = ((X354 @ X353))) | ~ ! [X355 : term] : (($true = ((X354 @ X355))) | ~ ($true = ((var @ X355)))) | ~ ! [X356 : term,X357 : term] : (($true = ((X354 @ (ap @ X357 @ X356)))) | ~ ($true = ((X354 @ X357))) | ~ ($true = ((X354 @ X356)))) | ~ ! [X358 : term] : (($true = ((X354 @ (lam @ X358)))) | ~ ! [X359 : term] : (~ ($true = ((X354 @ X359))) | ($true = ((X354 @ (sub @ X358 @ (push @ X359 @ id)))))))) => (! [X360 : term] : (((sub @ X360 @ id)) = X360) => (! [X361 : (term > $o),X362 : term,X363 : (subst > term > subst > $o)] : (~ ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) | ~ ! [X365 : (subst > term > term)] : (~ ! [X368 : term,X367 : subst,X366 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) = ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))) | ($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ~ ! [X369 : term] : (($true = ((X363 @ id @ (X365 @ id @ X369) @ id))) | ~ ($true = ((X363 @ id @ X369 @ id))))) | ~ ! [X370 : term] : (($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id))))) | ~ ($true = ((X361 @ X370)))) | ($true = ((X361 @ (lam @ X362))))) => ! [X371 : term,X372 : (subst > term > subst > $o)] : (~ ! [X373 : term,X374 : term] : (~ ($true = ((X372 @ id @ X373 @ id))) | ($true = ((X372 @ id @ (ap @ (sub @ X373 @ id) @ X374) @ id))) | ~ ($true = ((X372 @ id @ X374 @ id)))) | ~ ! [X375 : (subst > term > term)] : (($true = ((X372 @ id @ (lam @ (X375 @ sh @ one)) @ id))) | ~ ! [X376 : term] : (~ (((X372 @ id @ X376 @ id)) = $true) | ($true = ((X372 @ id @ (X375 @ id @ X376) @ id)))) | ~ ! [X379 : subst,X377 : term,X378 : subst] : (((sub @ (X375 @ X378 @ X377) @ X379)) = ((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))))) | ($true = ((X372 @ id @ X371 @ id))))))))) & (pushprop_lem3v2_lthm = $true) & (apnotvar = $true) & (! [X380 : (subst > term > subst > $o),X381 : term] : (~ ! [X382 : term] : (($true = ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id))) | ~ ($true = ((X380 @ id @ X382 @ id)))) | ~ ! [X383 : (subst > term > term)] : (($true = ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))) | ~ ! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))) | ~ ! [X387 : term] : (~ ($true = ((X380 @ id @ X387 @ id))) | ($true = ((X380 @ id @ (X383 @ id @ X387) @ id))))) | (((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X388 : term] : (((sub @ X388 @ id)) = X388) => (! [X390 : term,X391 : term,X392 : term,X389 : term] : ((((ap @ X389 @ X391)) != ((ap @ X392 @ X390))) | (X389 = X392)) => ! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)))) <=> (hoasapinj1_lthm = $true)) & (hoasapinj2_gthm = $true) & (axabs = $true) & ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & ((termmset = $true) <=> ! [X399 : term] : (((sub @ X399 @ id)) = X399)) & (! [X400 : (subst > term > subst > $o)] : ~ ! [X401 : (term > $o)] : ~ ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ! [X404 : d_subst,X403 : d_subst] : ((((d2subst @ X403)) = ((d2subst @ X404))) => (X403 = X404)) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X405 : term,X406 : subst,X407 : (term > $o),X408 : term,X409 : (term > $o)] : (~ ($true = ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406)))))) <=> (pushprop_lem1 = $true)) & (hoaslamnotap_gthm = $true) & (! [X410 : term,X411 : (subst > term > subst > $o),X412 : term] : (~ ! [X413 : term,X414 : subst,X415 : subst,X416 : subst] : (($true = ((X411 @ X414 @ X413 @ (comp @ X415 @ X416)))) | ~ ($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415) @ X416)))) | ($true = ((X411 @ id @ (ap @ X410 @ X412) @ id))) | ~ ! [X417 : term,X418 : subst,X419 : subst,X420 : subst] : (~ ($true = ((X411 @ X418 @ X417 @ (comp @ X420 @ X419)))) | ($true = ((X411 @ (comp @ X418 @ X420) @ (sub @ X417 @ X420) @ X419)))) | ~ ! [X421 : term,X422 : term] : (~ ($true = ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) | ~ ($true = ((X411 @ id @ X422 @ id)))) | ~ ($true = ((X411 @ id @ X412 @ id))) | ~ ($true = ((X411 @ id @ X410 @ id)))) <=> (hoasinduction_lem2 = $true)) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & ~ (ulamvar1 = $true) & ((axidr = $true) <=> ! [X423 : subst] : (((comp @ X423 @ id)) = X423)) & ((axidl = $true) <=> ! [X424 : subst] : (((comp @ id @ X424)) = X424)) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & ~ (((var @ (d2term @ d_one))) = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((apinj1 = $true) <=> ! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429))))) & (! [X431 : term,X432 : (term > $o)] : (~ ! [X433 : term] : (~ ($true = ((X432 @ X433))) | ($true = ((X432 @ (lam @ X433))))) | ($true = ((X432 @ X431))) | ~ ! [X434 : term,X435 : term] : (~ ($true = ((X432 @ X434))) | ($true = ((X432 @ (ap @ X435 @ X434)))) | ~ ($true = ((X432 @ X435)))) | ~ ! [X436 : term] : (($true = ((X432 @ X436))) | ~ ($true = ((var @ X436))))) <=> (induction = $true)) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X437 : term,X438 : (subst > term > subst > $o)] : (~ ! [X439 : (subst > term > term),X440 : term] : (~ ! [X441 : term] : (~ ($true = ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id)))) | ~ ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444))) | ($true = ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) | ~ ! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445)))))) | ($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ~ ! [X448 : term] : (($true = ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) | ~ ($true = ((X438 @ id @ X448 @ id)))))) & ((! [X449 : term,X450 : subst] : (((sub @ one @ (push @ X449 @ X450))) = X449) => ! [X451 : (term > $o),X452 : (term > $o),X453 : subst,X454 : term] : (($true = ((X452 @ one))) | ~ ! [X455 : term] : (((X452 @ X455)) = ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) | ~ ($true = ((X451 @ X454))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) <=> (shinj = $true)) & (! [X458 : (subst > term > subst > $o),X459 : term] : (~ ! [X460 : term] : (~ ($true = ((var @ (sub @ X460 @ id)))) | ($true = ((X458 @ id @ X460 @ id)))) | ~ ! [X461 : subst,X462 : subst,X463 : subst,X464 : term] : (~ ($true = ((X458 @ X461 @ X464 @ (comp @ X462 @ X463)))) | ($true = ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463)))) | ($true = ((X458 @ id @ X459 @ id))) | ~ ! [X465 : term,X466 : term] : (~ ($true = ((X458 @ id @ X466 @ id))) | ~ ($true = ((X458 @ id @ X465 @ id))) | ($true = ((X458 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id)))) | ~ ! [X467 : term,X468 : subst,X469 : subst,X470 : subst] : (($true = ((X458 @ X468 @ X467 @ (comp @ X470 @ X469)))) | ~ ($true = ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469)))) | ~ ! [X471 : (subst > term > term)] : (~ ! [X472 : term] : (~ ($true = ((X458 @ id @ X472 @ id))) | ($true = ((X458 @ id @ (X471 @ id @ X472) @ id)))) | ($true = ((X458 @ id @ (lam @ (X471 @ sh @ one)) @ id))) | ~ ! [X475 : subst,X473 : subst,X474 : term] : (((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475))) = ((sub @ (X471 @ X473 @ X474) @ X475))))) <=> (hoasinduction = $true)) & ((hoaslamnotap = $true) <=> ! [X476 : (subst > term > term),X478 : term,X477 : term] : (~ ! [X481 : subst,X480 : subst,X479 : term] : (((sub @ (X476 @ X481 @ X479) @ X480)) = ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one)))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X482 : term] : ~ ! [X483 : (subst > term > term)] : ~ ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484))))) & (axvarshift = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X487 : subst,X488 : term,X486 : (term > $o)] : ~ ! [X489 : (term > $o)] : ~ ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490)))) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (axclos = $true) & ! [X491 : d_term] : (d_one = X491) & (pushprop_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X492 : (subst > term > subst > $o),X493 : term] : (($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ~ ! [X494 : (subst > term > term)] : (~ ! [X495 : term] : (($true = ((X492 @ id @ (X494 @ id @ X495) @ id))) | ~ ($true = ((X492 @ id @ X495 @ id)))) | ($true = ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) | ~ ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498)))) | ~ ! [X499 : term] : (~ ($true = ((X492 @ id @ X499 @ id))) | ($true = ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & ! [X500 : d_subst] : (d_id = X500) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3a = $true) <=> ! [X501 : term,X502 : (subst > term > subst > $o)] : (~ ! [X503 : (subst > term > term)] : (~ ! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) | ~ ! [X507 : term] : (($true = ((X502 @ id @ (X503 @ id @ X507) @ id))) | ~ ($true = ((X502 @ id @ X507 @ id)))) | ($true = ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id)))) | ~ ! [X508 : term] : (($true = ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id))) | ~ ($true = ((X502 @ id @ X508 @ id)))) | ($true = ((X502 @ id @ (lam @ X501) @ id))))) & (! [X509 : term] : ~ ! [X510 : (subst > term > term)] : (((X510 @ sh @ one)) != ((sub @ X509 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X511 : term,X512 : (subst > term > subst > $o),X513 : (term > $o)] : (~ ! [X514 : term] : (~ ($true = ((X513 @ X514))) | ($true = ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) | ~ ! [X515 : (subst > term > term)] : (~ ! [X516 : term,X518 : subst,X517 : subst] : (((sub @ (X515 @ X517 @ X516) @ X518)) = ((X515 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518)))) | ($true = ((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id))) | ~ ! [X519 : term] : (($true = ((X512 @ id @ (X515 @ id @ X519) @ id))) | ~ ($true = ((X512 @ id @ X519 @ id))))) | ~ ! [X520 : subst,X521 : subst,X522 : subst,X523 : term] : (~ ($true = ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520))) | ($true = ((X512 @ X522 @ X523 @ (comp @ X521 @ X520))))) | ~ ! [X524 : term] : (((X513 @ X524)) = ((X512 @ id @ X524 @ id))) | ~ ! [X525 : subst,X526 : subst,X527 : term,X528 : subst] : ((((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) = $true) | ~ ($true = ((X512 @ X526 @ X527 @ (comp @ X525 @ X528))))) | ($true = ((X513 @ (lam @ X511)))))) & (pushprop_lthm = $true) & ((! [X529 : subst] : (((comp @ id @ X529)) = X529) => (! [X530 : subst] : (((comp @ X530 @ id)) = X530) => (! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (termmset_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X533 : subst,X534 : (term > $o),X535 : term,X536 : (term > $o)] : (($true = ((X534 @ one))) | ~ ($true = ((X536 @ X535))) | ~ ! [X537 : term] : (((X534 @ X537)) = ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))))) & ((axshiftcons = $true) <=> ! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538))), 24.89/4.11 inference(rectify,[],[f5])). 24.89/4.11 thf(f9,plain,( 24.89/4.11 (! [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X382 : term] : (($true != ((X380 @ id @ X382 @ id))) | ($true = ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) | ~ ! [X383 : (subst > term > term)] : (~ ! [X387 : term] : (($true = ((X380 @ id @ (X383 @ id @ X387) @ id))) | ($true != ((X380 @ id @ X387 @ id)))) | ($true = ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))) | ~ ! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X502 : (subst > term > subst > $o),X501 : term] : (~ ! [X503 : (subst > term > term)] : (~ ! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) | ($true = ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id))) | ~ ! [X507 : term] : (($true != ((X502 @ id @ X507 @ id))) | ($true = ((X502 @ id @ (X503 @ id @ X507) @ id))))) | ($true = ((X502 @ id @ (lam @ X501) @ id))) | ~ ! [X508 : term] : (($true = ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id))) | ($true != ((X502 @ id @ X508 @ id)))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((! [X319 : term] : (((sub @ X319 @ id)) = X319) => ! [X320 : (subst > term > subst > $o),X322 : term,X321 : (term > $o)] : (~ ! [X323 : subst,X326 : subst,X324 : term,X325 : subst] : (($true = ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) | ($true != ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ($true = ((X321 @ (lam @ X322)))) | ~ ! [X328 : term] : (($true != ((X321 @ X328))) | ($true = ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ~ ! [X333 : (subst > term > term)] : (~ ! [X334 : term,X335 : subst,X336 : subst] : (((X333 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ (X333 @ X335 @ X334) @ X336))) | ~ ! [X337 : term] : (($true = ((X320 @ id @ (X333 @ id @ X337) @ id))) | ($true != ((X320 @ id @ X337 @ id)))) | ($true = ((X320 @ id @ (lam @ (X333 @ sh @ one)) @ id)))) | ~ ! [X327 : term] : (((X321 @ X327)) = ((X320 @ id @ X327 @ id))) | ~ ! [X330 : subst,X329 : term,X331 : subst,X332 : subst] : (($true = ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) | ($true != ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapnotvar_gthm = $true) & (! [X400 : (subst > term > subst > $o)] : ~ ! [X401 : (term > $o)] : ~ ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (axassoc = $true) & (axmap = $true) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & (hoasapnotvar_lthm = $true) & ((axshiftcons = $true) <=> ! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538)) & (axapp = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X482 : term] : ~ ! [X483 : (subst > term > term)] : ~ ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484))))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((termmset = $true) <=> ! [X399 : term] : (((sub @ X399 @ id)) = X399)) & (pushprop_lem2v2_lthm = $true) & (! [X512 : (subst > term > subst > $o),X513 : (term > $o),X511 : term] : (~ ! [X522 : subst,X520 : subst,X523 : term,X521 : subst] : (($true = ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) | ($true != ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) | ~ ! [X524 : term] : (((X513 @ X524)) = ((X512 @ id @ X524 @ id))) | ~ ! [X515 : (subst > term > term)] : (($true = ((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id))) | ~ ! [X516 : term,X518 : subst,X517 : subst] : (((sub @ (X515 @ X517 @ X516) @ X518)) = ((X515 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518)))) | ~ ! [X519 : term] : (($true != ((X512 @ id @ X519 @ id))) | ($true = ((X512 @ id @ (X515 @ id @ X519) @ id))))) | ~ ! [X528 : subst,X526 : subst,X525 : subst,X527 : term] : ((((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) = $true) | ($true != ((X512 @ X526 @ X527 @ (comp @ X525 @ X528))))) | ($true = ((X513 @ (lam @ X511)))) | ~ ! [X514 : term] : (($true != ((X513 @ X514))) | ($true = ((X513 @ (sub @ X511 @ (push @ X514 @ id))))))) <=> (hoasinduction_lem3v2 = $true)) & ((induction2 = $true) <=> ! [X117 : term,X118 : (term > $o)] : (~ ! [X121 : term] : (($true = ((X118 @ X121))) | (((var @ X121)) != $true)) | ($true = ((X118 @ X117))) | ~ ! [X119 : term] : (~ ! [X120 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X120 @ id))))) | ($true != ((X118 @ X120)))) | ($true = ((X118 @ (lam @ X119))))) | ~ ! [X123 : term,X122 : term] : (($true != ((X118 @ X123))) | ($true = ((X118 @ (ap @ X122 @ X123)))) | ($true != ((X118 @ X122)))))) & (pushprop_lem3v2_lthm = $true) & ((apinj1 = $true) <=> ! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (pushprop_lem1_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axscons = $true) <=> ! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148)) & ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & ((pushprop_lem1 = $true) <=> ! [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true != ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406))))))) & (hoaslaminj_gthm = $true) & (axvarshift = $true) & ! [X491 : d_term] : (d_one = X491) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X339 : (subst > term > subst > $o),X338 : term] : (~ ! [X342 : (subst > term > term)] : (~ ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343))) | ($true = ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) | ~ ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ($true != ((X339 @ id @ X346 @ id))))) | ($true = ((X339 @ id @ X338 @ id))) | ~ ! [X340 : term,X341 : term] : (($true = ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) | ($true != ((X339 @ id @ X340 @ id))) | ($true != ((X339 @ id @ X341 @ id)))))) & (hoasinduction_lem2_lthm = $true) & ! [X404 : d_subst,X403 : d_subst] : ((((d2subst @ X403)) = ((d2subst @ X404))) => (X403 = X404)) & ((hoasinduction_lem3v2a = $true) <=> ! [X75 : (term > $o),X76 : (subst > term > subst > $o),X77 : term] : (($true = ((X75 @ (lam @ X77)))) | ~ ! [X80 : (subst > term > term)] : (~ ! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X76 @ id @ X81 @ id)))) | ($true = ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) | ~ ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82)))) | ~ ! [X78 : term] : (((X76 @ id @ X78 @ id)) = ((X75 @ X78))) | ~ ! [X79 : term] : (($true = ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) | ($true != ((X75 @ X79)))))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X129 : term] : ~ ! [X130 : (subst > term > term)] : ~ ! [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) = ((sub @ X129 @ (push @ X132 @ X131)))) => (! [X133 : term] : (((sub @ X133 @ id)) = X133) => ! [X136 : (subst > term > subst > $o),X135 : (term > $o),X134 : term] : (~ ! [X143 : term] : (($true != ((X135 @ X143))) | ($true = ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ~ ! [X137 : (subst > term > term)] : (($true = ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) | ~ ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139))) | ~ ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ($true != ((X136 @ id @ X141 @ id))))) | ~ ! [X142 : term] : (((X136 @ id @ X142 @ id)) = ((X135 @ X142))) | ($true = ((X135 @ (lam @ X134)))))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X144 : term] : ~ ! [X145 : (subst > term > term)] : ~ ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147)))) & (apnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (! [X12 : term,X13 : subst] : (((sub @ one @ (push @ X12 @ X13))) = X12) => (! [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) = X14) => (! [X16 : term,X17 : term] : ((X16 = X17) | (((lam @ X17)) != ((lam @ X16)))) => ! [X19 : (subst > term > term),X18 : subst,X21 : term,X20 : (subst > term > term)] : (~ ! [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) = ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ~ ! [X24 : subst,X23 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) = ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21)))))))) & ((hoaslaminj = $true) <=> ! [X151 : (subst > term > term),X152 : (subst > term > term),X150 : term,X149 : subst] : ((((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ~ ! [X158 : subst,X157 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) = ((sub @ (X152 @ X157 @ X156) @ X158))) | (((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | ~ ! [X153 : term,X154 : subst,X155 : subst] : (((sub @ (X151 @ X154 @ X153) @ X155)) = ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))))) & ((pushprop_lem0_lthm = $true) <=> ! [X487 : subst,X488 : term,X486 : (term > $o)] : ~ ! [X489 : (term > $o)] : ~ ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490)))) & ((axidr = $true) <=> ! [X423 : subst] : (((comp @ X423 @ id)) = X423)) & (hoasinduction_gthm = $true) & (! [X205 : term,X203 : (term > $o),X202 : (subst > term > subst > $o),X204 : term] : (($true = ((X203 @ (ap @ X205 @ X204)))) | ~ ! [X210 : subst,X209 : subst,X207 : subst,X208 : term] : (($true = ((X202 @ (comp @ X210 @ X207) @ (sub @ X208 @ X207) @ X209))) | ($true != ((X202 @ X210 @ X208 @ (comp @ X207 @ X209))))) | ~ ! [X215 : term,X216 : term] : (($true != ((X202 @ id @ X216 @ id))) | ($true = ((X202 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))) | ($true != ((X202 @ id @ X215 @ id)))) | ~ ! [X212 : term,X211 : subst,X214 : subst,X213 : subst] : (($true != ((X202 @ (comp @ X214 @ X213) @ (sub @ X212 @ X213) @ X211))) | ($true = ((X202 @ X214 @ X212 @ (comp @ X213 @ X211))))) | ($true != ((X203 @ X205))) | ~ ! [X206 : term] : (((X202 @ id @ X206 @ id)) = ((X203 @ X206))) | ($true != ((X203 @ X204)))) <=> (hoasinduction_lem2v2 = $true)) & (lamnotap != $true) & ((hoasapinj1 = $true) <=> ! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & (! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) <=> (axvarcons = $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X88 : term,X87 : subst] : (((comp @ sh @ (push @ X88 @ X87))) = X87) => ! [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true != ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92))))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X161 : term] : (((sub @ X161 @ id)) = X161) => (! [X162 : (subst > term > subst > $o),X163 : term] : (~ ! [X164 : (subst > term > term)] : (~ ! [X168 : term] : (($true != ((X162 @ id @ X168 @ id))) | ($true = ((X162 @ id @ (X164 @ id @ X168) @ id)))) | ($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ~ ! [X165 : term,X166 : subst,X167 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) = ((sub @ (X164 @ X167 @ X165) @ X166)))) | ~ ! [X169 : term] : (($true != ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) | ($true = ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id)))) => ! [X170 : (subst > term > subst > $o),X171 : term] : (~ ! [X172 : subst,X174 : term,X175 : subst,X173 : subst] : (($true = ((X170 @ X173 @ X174 @ (comp @ X172 @ X175)))) | ($true != ((X170 @ (comp @ X173 @ X172) @ (sub @ X174 @ X172) @ X175)))) | ~ ! [X181 : term] : (($true != ((X170 @ id @ X181 @ id))) | ($true = ((X170 @ id @ (sub @ X171 @ (push @ X181 @ id)) @ id)))) | (((X170 @ id @ (lam @ X171) @ id)) = $true) | ~ ! [X183 : term,X182 : subst,X184 : subst,X185 : subst] : (($true != ((X170 @ X182 @ X183 @ (comp @ X185 @ X184)))) | ($true = ((X170 @ (comp @ X182 @ X185) @ (sub @ X183 @ X185) @ X184)))) | ~ ! [X176 : (subst > term > term)] : (~ ! [X178 : subst,X180 : term,X179 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) | ($true = ((X170 @ id @ (lam @ (X176 @ sh @ one)) @ id))) | ~ ! [X177 : term] : (($true = ((X170 @ id @ (X176 @ id @ X177) @ id))) | ($true != ((X170 @ id @ X177 @ id))))))))) & ((! [X225 : term] : (((sub @ X225 @ id)) = X225) => (! [X226 : term,X227 : (term > $o),X228 : subst] : (~ ! [X230 : term,X229 : term] : (($true != ((X227 @ X230))) | ($true = ((X227 @ (ap @ X230 @ X229)))) | ($true != ((X227 @ X229)))) | ($true = ((X227 @ (sub @ X226 @ X228)))) | ~ ! [X232 : term] : (($true = ((X227 @ (lam @ X232)))) | ~ ! [X233 : term] : (($true != ((X227 @ X233))) | ($true = ((X227 @ (sub @ X232 @ (push @ X233 @ id))))))) | ~ ! [X231 : term] : (($true = ((X227 @ (sub @ X231 @ X228)))) | ($true != ((var @ X231))))) => ! [X235 : (term > $o),X234 : term] : (~ ! [X238 : term] : (($true = ((X235 @ X238))) | ($true != ((var @ X238)))) | ~ ! [X239 : term,X240 : term] : (($true != ((X235 @ X240))) | ($true = ((X235 @ (ap @ X239 @ X240)))) | ($true != ((X235 @ X239)))) | ($true = ((X235 @ X234))) | ~ ! [X236 : term] : (~ ! [X237 : term] : (($true != ((X235 @ X237))) | ($true = ((X235 @ (sub @ X236 @ (push @ X237 @ id)))))) | ($true = ((X235 @ (lam @ X236)))))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ((! [X388 : term] : (((sub @ X388 @ id)) = X388) => (! [X390 : term,X391 : term,X392 : term,X389 : term] : ((((ap @ X389 @ X391)) != ((ap @ X392 @ X390))) | (X389 = X392)) => ! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)))) <=> (hoasapinj1_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((! [X266 : term,X265 : (term > $o)] : (($true = ((X265 @ X266))) | ~ ! [X268 : term] : (~ ! [X269 : term] : (($true = ((X265 @ (sub @ X268 @ (push @ X269 @ id))))) | ($true != ((X265 @ X269)))) | ($true = ((X265 @ (lam @ X268))))) | ~ ! [X271 : term,X270 : term] : (($true != ((X265 @ X270))) | ($true != ((X265 @ X271))) | ($true = ((X265 @ (ap @ X270 @ X271))))) | ~ ! [X267 : term] : (($true = ((X265 @ X267))) | ($true != ((var @ X267))))) => (! [X274 : (subst > term > subst > $o),X273 : term,X272 : term] : (($true != ((X274 @ id @ X273 @ id))) | ($true != ((X274 @ id @ X272 @ id))) | ~ ! [X282 : subst,X279 : subst,X280 : subst,X281 : term] : (($true != ((X274 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280) @ X279))) | ($true = ((X274 @ X282 @ X281 @ (comp @ X280 @ X279))))) | ~ ! [X283 : term,X284 : term] : (($true != ((X274 @ id @ X284 @ id))) | ($true != ((X274 @ id @ X283 @ id))) | ($true = ((X274 @ id @ (ap @ (sub @ X283 @ id) @ X284) @ id)))) | ($true = ((X274 @ id @ (ap @ X273 @ X272) @ id))) | ~ ! [X277 : subst,X275 : subst,X278 : subst,X276 : term] : (($true != ((X274 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X274 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275))))) => (! [X285 : (subst > term > subst > $o),X286 : term] : (~ ! [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) | ($true != ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) | ~ ! [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) | ($true != ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) | ($true = ((X285 @ id @ (lam @ X286) @ id))) | ~ ! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ($true != ((X285 @ id @ X291 @ id)))) | ~ ! [X296 : (subst > term > term)] : (($true = ((X285 @ id @ (lam @ (X296 @ sh @ one)) @ id))) | ~ ! [X297 : term] : (($true = ((X285 @ id @ (X296 @ id @ X297) @ id))) | ($true != ((X285 @ id @ X297 @ id)))) | ~ ! [X300 : subst,X299 : subst,X298 : term] : (((X296 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) = ((sub @ (X296 @ X299 @ X298) @ X300))))) => ! [X301 : term,X302 : (subst > term > subst > $o)] : (~ ! [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true != ((X302 @ (comp @ X317 @ X315) @ (sub @ X318 @ X315) @ X316))) | ($true = ((X302 @ X317 @ X318 @ (comp @ X315 @ X316))))) | ~ ! [X314 : term] : (($true = ((X302 @ id @ X314 @ id))) | ($true != ((var @ (sub @ X314 @ id))))) | ($true = ((X302 @ id @ X301 @ id))) | ~ ! [X313 : term,X312 : term] : (($true != ((X302 @ id @ X313 @ id))) | ($true = ((X302 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id))) | ($true != ((X302 @ id @ X312 @ id)))) | ~ ! [X309 : subst,X310 : term,X311 : subst,X308 : subst] : (($true = ((X302 @ (comp @ X311 @ X308) @ (sub @ X310 @ X308) @ X309))) | ($true != ((X302 @ X311 @ X310 @ (comp @ X308 @ X309))))) | ~ ! [X303 : (subst > term > term)] : (($true = ((X302 @ id @ (lam @ (X303 @ sh @ one)) @ id))) | ~ ! [X307 : term] : (($true = ((X302 @ id @ (X303 @ id @ X307) @ id))) | ($true != ((X302 @ id @ X307 @ id)))) | ~ ! [X304 : term,X306 : subst,X305 : subst] : (((X303 @ (comp @ X306 @ X305) @ (sub @ X304 @ X305))) = ((sub @ (X303 @ X306 @ X304) @ X305)))))))) <=> (hoasinduction_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((laminj = $true) <=> ! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11))) & (ulamvarind = $true) & (! [X509 : term] : ~ ! [X510 : (subst > term > term)] : (((X510 @ sh @ one)) != ((sub @ X509 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) <=> (shinj = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((induction2lem_lthm = $true) <=> (! [X99 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X99))) = X98) => (! [X101 : term,X100 : subst] : (((comp @ sh @ (push @ X101 @ X100))) = X100) => (! [X102 : subst] : (((comp @ X102 @ id)) = X102) => (! [X104 : term,X103 : (term > $o)] : (~ ! [X107 : term] : (($true != ((X103 @ X107))) | ($true = ((X103 @ (lam @ X107))))) | ($true = ((X103 @ X104))) | ~ ! [X108 : term] : (($true != ((var @ X108))) | ($true = ((X103 @ X108)))) | ~ ! [X106 : term,X105 : term] : (($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106)))) | ($true != ((X103 @ X106))))) => ! [X110 : subst,X111 : term,X109 : (term > $o)] : (~ ! [X116 : term,X115 : term] : (($true != ((X109 @ X115))) | ($true = ((X109 @ (ap @ X116 @ X115)))) | ($true != ((X109 @ X116)))) | ~ ! [X114 : term] : ((((X109 @ (sub @ X114 @ X110))) = $true) | ($true != ((var @ X114)))) | ($true = ((X109 @ (sub @ X111 @ X110)))) | ~ ! [X112 : term] : (($true = ((X109 @ (lam @ X112)))) | ~ ! [X113 : term] : (($true != ((X109 @ X113))) | ($true = ((X109 @ (sub @ X112 @ (push @ X113 @ id))))))))))))) & ((! [X4 : term] : (((sub @ X4 @ id)) = X4) => ! [X5 : term] : (((sub @ X5 @ id)) = X5)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X187 : term,X186 : (subst > term > subst > $o)] : (~ ! [X195 : subst,X193 : term,X194 : subst,X196 : subst] : (($true != ((X186 @ X195 @ X193 @ (comp @ X194 @ X196)))) | ($true = ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196)))) | ~ ! [X197 : term] : (($true != ((X186 @ id @ X197 @ id))) | ($true = ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ~ ! [X198 : subst,X200 : term,X199 : subst,X201 : subst] : (($true != ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) | ($true = ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) | ~ ! [X188 : (subst > term > term)] : (~ ! [X189 : term] : (($true = ((X186 @ id @ (X188 @ id @ X189) @ id))) | ($true != ((X186 @ id @ X189 @ id)))) | ($true = ((X186 @ id @ (lam @ (X188 @ sh @ one)) @ id))) | ~ ! [X191 : subst,X190 : term,X192 : subst] : (((X188 @ (comp @ X191 @ X192) @ (sub @ X190 @ X192))) = ((sub @ (X188 @ X191 @ X190) @ X192)))) | ($true = ((X186 @ id @ (lam @ X187) @ id))))) & ((! [X350 : (subst > term > subst > $o)] : ~ ! [X351 : (term > $o)] : ~ ! [X352 : term] : (((X350 @ id @ X352 @ id)) = ((X351 @ X352))) => (! [X353 : term,X354 : (term > $o)] : (~ ! [X356 : term,X357 : term] : (($true != ((X354 @ X356))) | ($true != ((X354 @ X357))) | ($true = ((X354 @ (ap @ X357 @ X356))))) | ($true = ((X354 @ X353))) | ~ ! [X358 : term] : (($true = ((X354 @ (lam @ X358)))) | ~ ! [X359 : term] : (($true = ((X354 @ (sub @ X358 @ (push @ X359 @ id))))) | ($true != ((X354 @ X359))))) | ~ ! [X355 : term] : (($true != ((var @ X355))) | ($true = ((X354 @ X355))))) => (! [X360 : term] : (((sub @ X360 @ id)) = X360) => (! [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (~ ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) | ($true = ((X361 @ (lam @ X362)))) | ~ ! [X370 : term] : (($true != ((X361 @ X370))) | ($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) | ~ ! [X365 : (subst > term > term)] : (~ ! [X369 : term] : (($true = ((X363 @ id @ (X365 @ id @ X369) @ id))) | ($true != ((X363 @ id @ X369 @ id)))) | ($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ~ ! [X368 : term,X367 : subst,X366 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) = ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) => ! [X371 : term,X372 : (subst > term > subst > $o)] : (~ ! [X374 : term,X373 : term] : (($true != ((X372 @ id @ X374 @ id))) | ($true = ((X372 @ id @ (ap @ (sub @ X373 @ id) @ X374) @ id))) | ($true != ((X372 @ id @ X373 @ id)))) | ~ ! [X375 : (subst > term > term)] : (($true = ((X372 @ id @ (lam @ (X375 @ sh @ one)) @ id))) | ~ ! [X376 : term] : ((((X372 @ id @ X376 @ id)) != $true) | ($true = ((X372 @ id @ (X375 @ id @ X376) @ id)))) | ~ ! [X379 : subst,X377 : term,X378 : subst] : (((sub @ (X375 @ X378 @ X377) @ X379)) = ((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))))) | ($true = ((X372 @ id @ X371 @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X28 : term,X31 : term,X30 : term,X29 : term] : ((((ap @ X30 @ X28)) != ((ap @ X31 @ X29))) | (X28 = X29)) => ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35))))) <=> (hoasapinj2_lthm = $true)) & (! [X458 : (subst > term > subst > $o),X459 : term] : (~ ! [X461 : subst,X462 : subst,X464 : term,X463 : subst] : (($true = ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) | ($true != ((X458 @ X461 @ X464 @ (comp @ X462 @ X463))))) | ($true = ((X458 @ id @ X459 @ id))) | ~ ! [X460 : term] : (($true != ((var @ (sub @ X460 @ id)))) | ($true = ((X458 @ id @ X460 @ id)))) | ~ ! [X471 : (subst > term > term)] : (~ ! [X475 : subst,X473 : subst,X474 : term] : (((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475))) = ((sub @ (X471 @ X473 @ X474) @ X475))) | ~ ! [X472 : term] : (($true != ((X458 @ id @ X472 @ id))) | ($true = ((X458 @ id @ (X471 @ id @ X472) @ id)))) | ($true = ((X458 @ id @ (lam @ (X471 @ sh @ one)) @ id)))) | ~ ! [X468 : subst,X470 : subst,X467 : term,X469 : subst] : (($true = ((X458 @ X468 @ X467 @ (comp @ X470 @ X469)))) | ($true != ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469)))) | ~ ! [X466 : term,X465 : term] : (($true != ((X458 @ id @ X465 @ id))) | ($true = ((X458 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id))) | ($true != ((X458 @ id @ X466 @ id))))) <=> (hoasinduction = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X437 : term,X438 : (subst > term > subst > $o)] : (~ ! [X448 : term] : (($true != ((X438 @ id @ X448 @ id))) | ($true = ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id)))) | ($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ~ ! [X440 : term,X439 : (subst > term > term)] : (~ ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444))) | ($true = ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) | ~ ! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) | ~ ! [X441 : term] : (($true != ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id))))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X248 : term] : (((sub @ X248 @ id)) = X248) => (! [X250 : term,X249 : (subst > term > subst > $o)] : (~ ! [X251 : (subst > term > term)] : (~ ! [X255 : term] : (($true = ((X249 @ id @ (X251 @ id @ X255) @ id))) | ($true != ((X249 @ id @ X255 @ id)))) | ~ ! [X254 : term,X253 : subst,X252 : subst] : (((sub @ (X251 @ X253 @ X254) @ X252)) = ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))) | ($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id)))) | ($true = ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) | ~ ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ($true != ((X249 @ id @ X256 @ id))))) => ! [X258 : (subst > term > subst > $o),X257 : term] : ((((X258 @ id @ (lam @ X257) @ id)) = $true) | ~ ! [X264 : term] : (($true != ((X258 @ id @ X264 @ id))) | (((X258 @ id @ (sub @ X257 @ (push @ X264 @ id)) @ id)) = $true)) | ~ ! [X259 : (subst > term > term)] : (($true = ((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id))) | ~ ! [X260 : term] : (($true != ((X258 @ id @ X260 @ id))) | ($true = ((X258 @ id @ (X259 @ id @ X260) @ id)))) | ~ ! [X262 : subst,X261 : term,X263 : subst] : (((X259 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X263 @ X261) @ X262)))))))) & (hoaslamnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X431 : term,X432 : (term > $o)] : (($true = ((X432 @ X431))) | ~ ! [X433 : term] : (($true != ((X432 @ X433))) | ($true = ((X432 @ (lam @ X433))))) | ~ ! [X436 : term] : (($true = ((X432 @ X436))) | ($true != ((var @ X436)))) | ~ ! [X435 : term,X434 : term] : (($true = ((X432 @ (ap @ X435 @ X434)))) | ($true != ((X432 @ X435))) | ($true != ((X432 @ X434))))) <=> (induction = $true)) & ! [X6 : d_term,X7 : d_term] : ((((d2term @ X7)) = ((d2term @ X6))) => (X6 = X7)) & (hoaslamnotap_lthm = $true) & ((hoasapinj2 = $true) <=> ! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1))))) & (hoasapnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem1v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X476 : (subst > term > term),X478 : term,X477 : term] : (~ ! [X481 : subst,X480 : subst,X479 : term] : (((sub @ (X476 @ X481 @ X479) @ X480)) = ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one)))))) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) <=> (axvarid = $true)) & ((pushprop_lem0 = $true) <=> ! [X243 : (term > $o),X245 : term,X244 : subst] : ~ ! [X246 : (term > $o)] : ~ ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244)))))) & ((hoasinduction_lem0 = $true) <=> ! [X347 : (subst > term > subst > $o)] : ~ ! [X348 : (term > $o)] : ~ ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349)))) & ((pushprop_lem1v2 = $true) <=> ! [X536 : (term > $o),X534 : (term > $o),X535 : term,X533 : subst] : (~ ! [X537 : term] : (((X534 @ X537)) = ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) | ($true != ((X536 @ X535))) | ($true = ((X534 @ one))))) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & (lamnotvar = $true) & (termmset_gthm = $true) & (one = ((d2term @ d_one))) & ((hoasinduction_lem2 = $true) <=> ! [X412 : term,X411 : (subst > term > subst > $o),X410 : term] : (~ ! [X420 : subst,X419 : subst,X418 : subst,X417 : term] : (($true = ((X411 @ (comp @ X418 @ X420) @ (sub @ X417 @ X420) @ X419))) | ($true != ((X411 @ X418 @ X417 @ (comp @ X420 @ X419))))) | ($true != ((X411 @ id @ X412 @ id))) | ~ ! [X415 : subst,X416 : subst,X414 : subst,X413 : term] : (($true != ((X411 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415) @ X416))) | ($true = ((X411 @ X414 @ X413 @ (comp @ X415 @ X416))))) | ~ ! [X421 : term,X422 : term] : (($true != ((X411 @ id @ X422 @ id))) | ($true != ((X411 @ id @ X421 @ id))) | ($true = ((X411 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id)))) | ($true = ((X411 @ id @ (ap @ X410 @ X412) @ id))) | ($true != ((X411 @ id @ X410 @ id))))) & ! [X500 : d_subst] : (d_id = X500) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((induction2lem = $true) <=> ! [X218 : (term > $o),X219 : term,X217 : subst] : (~ ! [X220 : term] : (~ ! [X221 : term] : (($true != ((X218 @ X221))) | ($true = ((X218 @ (sub @ X220 @ (push @ X221 @ id)))))) | (((X218 @ (lam @ X220))) = $true)) | ~ ! [X224 : term] : (($true != ((var @ X224))) | ($true = ((X218 @ (sub @ X224 @ X217))))) | ($true = ((X218 @ (sub @ X219 @ X217)))) | ~ ! [X222 : term,X223 : term] : (($true = ((X218 @ (ap @ X222 @ X223)))) | ($true != ((X218 @ X223))) | ($true != ((X218 @ X222)))))) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (hoasapinj2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) <=> (apinj2 = $true)) & ((! [X36 : (subst > term > subst > $o)] : ~ ! [X37 : (term > $o)] : ~ ! [X38 : term] : (((X37 @ X38)) = ((X36 @ id @ X38 @ id))) => (! [X39 : term,X40 : (term > $o)] : (~ ! [X41 : term] : (($true = ((X40 @ (lam @ X41)))) | ~ ! [X42 : term] : (($true != ((X40 @ X42))) | ($true = ((X40 @ (sub @ X41 @ (push @ X42 @ id))))))) | ($true = ((X40 @ X39))) | ~ ! [X43 : term] : (($true != ((var @ X43))) | ($true = ((X40 @ X43)))) | ~ ! [X44 : term,X45 : term] : (($true != ((X40 @ X44))) | ($true = ((X40 @ (ap @ X44 @ X45)))) | ($true != ((X40 @ X45))))) => (! [X46 : term] : (((sub @ X46 @ id)) = X46) => (! [X49 : (term > $o),X47 : (subst > term > subst > $o),X48 : term] : (($true = ((X49 @ (lam @ X48)))) | ~ ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id))) | ~ ! [X55 : term] : (($true != ((X49 @ X55))) | ($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) | ~ ! [X50 : (subst > term > term)] : (~ ! [X54 : term] : (($true = ((X47 @ id @ (X50 @ id @ X54) @ id))) | ($true != ((X47 @ id @ X54 @ id)))) | ~ ! [X53 : subst,X52 : subst,X51 : term] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) = ((sub @ (X50 @ X52 @ X51) @ X53))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))))) => ! [X58 : (subst > term > subst > $o),X57 : term] : (~ ! [X60 : (subst > term > term)] : (~ ! [X63 : subst,X64 : subst,X62 : term] : (((sub @ (X60 @ X64 @ X62) @ X63)) = ((X60 @ (comp @ X64 @ X63) @ (sub @ X62 @ X63)))) | ($true = ((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ~ ! [X61 : term] : (($true = ((X58 @ id @ (X60 @ id @ X61) @ id))) | ($true != ((X58 @ id @ X61 @ id))))) | ($true = ((X58 @ id @ X57 @ id))) | ~ ! [X59 : term] : (($true != ((var @ (sub @ X59 @ id)))) | ($true = ((X58 @ id @ X59 @ id)))) | ~ ! [X70 : subst,X69 : subst,X67 : term,X68 : subst] : (($true != ((X58 @ X68 @ X67 @ (comp @ X70 @ X69)))) | ($true = ((X58 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69)))) | ~ ! [X66 : term,X65 : term] : (($true != ((X58 @ id @ X65 @ id))) | ($true != ((X58 @ id @ X66 @ id))) | ($true = ((X58 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id)))) | ~ ! [X74 : subst,X73 : term,X71 : subst,X72 : subst] : (($true = ((X58 @ X72 @ X73 @ (comp @ X71 @ X74)))) | ($true != ((X58 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X74))))))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lem2v2_gthm = $true) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = id) & (induction2_gthm = $true) & ((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) <=> (substmonoid = $true)) & ((! [X529 : subst] : (((comp @ id @ X529)) = X529) => (! [X530 : subst] : (((comp @ X530 @ id)) = X530) => (! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X492 : (subst > term > subst > $o),X493 : term] : (~ ! [X494 : (subst > term > term)] : (~ ! [X495 : term] : (($true != ((X492 @ id @ X495 @ id))) | ($true = ((X492 @ id @ (X494 @ id @ X495) @ id)))) | ~ ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498))) | ($true = ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id)))) | ($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ~ ! [X499 : term] : (($true != ((X492 @ id @ X499 @ id))) | ($true = ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & (axclos = $true) & ((! [X449 : term,X450 : subst] : (((sub @ one @ (push @ X449 @ X450))) = X449) => ! [X453 : subst,X451 : (term > $o),X454 : term,X452 : (term > $o)] : (($true != ((X451 @ X454))) | ($true = ((X452 @ one))) | ~ ! [X455 : term] : (((X452 @ X455)) = ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X8 : term] : ~ ! [X9 : (subst > term > term)] : (((X9 @ sh @ one)) != ((sub @ X8 @ (push @ one @ sh))))) & (pushprop_gthm = $true) & ((axidl = $true) <=> ! [X424 : subst] : (((comp @ id @ X424)) = X424))), 24.89/4.11 inference(flattening,[],[f8])). 24.89/4.11 thf(f10,plain,( 24.89/4.11 ~(! [X0 : (subst > term > subst > $o)] : (! [X2 : term,X1 : term] : ((((X0 @ id @ X2 @ id)) = $true) => ((((X0 @ id @ X1 @ id)) = $true) => ($true = ((X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))))) => (! [X3 : (subst > term > term)] : (! [X6 : subst,X5 : term,X4 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))) => (! [X7 : term] : (($true = ((X0 @ id @ X7 @ id))) => ($true = ((X0 @ id @ (X3 @ id @ X7) @ id)))) => ($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))))) => ! [X8 : term] : ($true = ((X0 @ id @ X8 @ id))))) <=> (hoasinduction_no_psi_cond = $true))), 24.89/4.11 inference(rectify,[],[f7])). 24.89/4.11 thf(f11,plain,( 24.89/4.11 (! [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true) | ? [X382 : term] : (($true = ((X380 @ id @ X382 @ id))) & ($true != ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) | ? [X383 : (subst > term > term)] : (! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))) & ! [X387 : term] : (($true = ((X380 @ id @ (X383 @ id @ X387) @ id))) | ($true != ((X380 @ id @ X387 @ id)))) & ($true != ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X502 : (subst > term > subst > $o),X501 : term] : (($true = ((X502 @ id @ (lam @ X501) @ id))) | ? [X508 : term] : (($true = ((X502 @ id @ X508 @ id))) & ($true != ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) | ? [X503 : (subst > term > term)] : (! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) & ! [X507 : term] : (($true != ((X502 @ id @ X507 @ id))) | ($true = ((X502 @ id @ (X503 @ id @ X507) @ id)))) & ($true != ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id)))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((! [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true = ((X321 @ (lam @ X322)))) | ? [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true != ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) & ($true = ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) | ? [X327 : term] : (((X321 @ X327)) != ((X320 @ id @ X327 @ id))) | ? [X328 : term] : (($true = ((X321 @ X328))) & ($true != ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ? [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true != ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) & ($true = ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ? [X333 : (subst > term > term)] : (($true != ((X320 @ id @ (lam @ (X333 @ sh @ one)) @ id))) & ! [X337 : term] : (($true = ((X320 @ id @ (X333 @ id @ X337) @ id))) | ($true != ((X320 @ id @ X337 @ id)))) & ! [X334 : term,X335 : subst,X336 : subst] : (((X333 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ (X333 @ X335 @ X334) @ X336))))) | ? [X319 : term] : (((sub @ X319 @ id)) != X319)) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X400 : (subst > term > subst > $o)] : ? [X401 : (term > $o)] : ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id)))) & (axassoc = $true) & (axmap = $true) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & (hoasapnotvar_lthm = $true) & ((axshiftcons = $true) <=> ! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538)) & (axapp = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X482 : term] : ? [X483 : (subst > term > term)] : ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484))))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((termmset = $true) <=> ! [X399 : term] : (((sub @ X399 @ id)) = X399)) & (pushprop_lem2v2_lthm = $true) & (! [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (? [X514 : term] : (($true = ((X513 @ X514))) & ($true != ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) | ? [X515 : (subst > term > term)] : (($true != ((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id))) & ! [X519 : term] : (($true != ((X512 @ id @ X519 @ id))) | ($true = ((X512 @ id @ (X515 @ id @ X519) @ id)))) & ! [X516 : term,X518 : subst,X517 : subst] : (((sub @ (X515 @ X517 @ X516) @ X518)) = ((X515 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))))) | ? [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true != ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) & ($true = ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) | ? [X524 : term] : (((X513 @ X524)) != ((X512 @ id @ X524 @ id))) | ($true = ((X513 @ (lam @ X511)))) | ? [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true = ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) & (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((induction2 = $true) <=> ! [X118 : (term > $o),X117 : term] : (($true = ((X118 @ X117))) | ? [X123 : term,X122 : term] : (($true = ((X118 @ X122))) & ($true != ((X118 @ (ap @ X122 @ X123)))) & ($true = ((X118 @ X123)))) | ? [X119 : term] : (($true != ((X118 @ (lam @ X119)))) & ! [X120 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X120 @ id))))) | ($true != ((X118 @ X120))))) | ? [X121 : term] : ((((var @ X121)) = $true) & ($true != ((X118 @ X121)))))) & (pushprop_lem3v2_lthm = $true) & ((apinj1 = $true) <=> ! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (pushprop_lem1_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axscons = $true) <=> ! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148)) & ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & ((pushprop_lem1 = $true) <=> ! [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true != ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406))))))) & (hoaslaminj_gthm = $true) & (axvarshift = $true) & ! [X491 : d_term] : (d_one = X491) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X342 : (subst > term > term)] : (($true != ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) & ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ($true != ((X339 @ id @ X346 @ id)))) & ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343)))) | ? [X341 : term,X340 : term] : (($true != ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) & ($true = ((X339 @ id @ X340 @ id))) & ($true = ((X339 @ id @ X341 @ id)))) | ($true = ((X339 @ id @ X338 @ id))))) & (hoasinduction_lem2_lthm = $true) & ! [X404 : d_subst,X403 : d_subst] : ((X403 = X404) | (((d2subst @ X403)) != ((d2subst @ X404)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true = ((X75 @ (lam @ X77)))) | ? [X78 : term] : (((X76 @ id @ X78 @ id)) != ((X75 @ X78))) | ? [X79 : term] : (($true != ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) & ($true = ((X75 @ X79)))) | ? [X80 : (subst > term > term)] : (! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X76 @ id @ X81 @ id)))) & ($true != ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) & ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82)))))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (? [X142 : term] : (((X136 @ id @ X142 @ id)) != ((X135 @ X142))) | ? [X137 : (subst > term > term)] : (($true != ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) & ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ($true != ((X136 @ id @ X141 @ id)))) & ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139)))) | ? [X143 : term] : (($true = ((X135 @ X143))) & ($true != ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ($true = ((X135 @ (lam @ X134))))) | ? [X133 : term] : (((sub @ X133 @ id)) != X133)) | ? [X129 : term] : ! [X130 : (subst > term > term)] : ? [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) != ((sub @ X129 @ (push @ X132 @ X131)))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X144 : term] : ? [X145 : (subst > term > term)] : ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147)))) & (apnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (? [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) != ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21))) | ? [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) != ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23))))) | ? [X17 : term,X16 : term] : ((((lam @ X17)) = ((lam @ X16))) & (X16 != X17))) | ? [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) != X14)) | ? [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) != X12))) & ((hoaslaminj = $true) <=> ! [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | (((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ? [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) != ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) | ? [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) != ((sub @ (X152 @ X157 @ X156) @ X158))))) & (! [X486 : (term > $o),X487 : subst,X488 : term] : ? [X489 : (term > $o)] : ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490))) <=> (pushprop_lem0_lthm = $true)) & ((axidr = $true) <=> ! [X423 : subst] : (((comp @ X423 @ id)) = X423)) & (hoasinduction_gthm = $true) & (! [X203 : (term > $o),X202 : (subst > term > subst > $o),X205 : term,X204 : term] : (($true = ((X203 @ (ap @ X205 @ X204)))) | ? [X207 : subst,X208 : term,X209 : subst,X210 : subst] : (($true != ((X202 @ (comp @ X210 @ X207) @ (sub @ X208 @ X207) @ X209))) & ($true = ((X202 @ X210 @ X208 @ (comp @ X207 @ X209))))) | ? [X206 : term] : (((X202 @ id @ X206 @ id)) != ((X203 @ X206))) | ? [X214 : subst,X211 : subst,X213 : subst,X212 : term] : (($true = ((X202 @ (comp @ X214 @ X213) @ (sub @ X212 @ X213) @ X211))) & ($true != ((X202 @ X214 @ X212 @ (comp @ X213 @ X211))))) | ($true != ((X203 @ X204))) | ($true != ((X203 @ X205))) | ? [X216 : term,X215 : term] : (($true = ((X202 @ id @ X216 @ id))) & ($true = ((X202 @ id @ X215 @ id))) & ($true != ((X202 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))))) <=> (hoasinduction_lem2v2 = $true)) & (lamnotap != $true) & ((hoasapinj1 = $true) <=> ! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & (! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) <=> (axvarcons = $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true != ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) | ? [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) != X87)) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X171 : term,X170 : (subst > term > subst > $o)] : (? [X181 : term] : (($true = ((X170 @ id @ X181 @ id))) & ($true != ((X170 @ id @ (sub @ X171 @ (push @ X181 @ id)) @ id)))) | ? [X176 : (subst > term > term)] : (! [X178 : subst,X180 : term,X179 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true = ((X170 @ id @ (X176 @ id @ X177) @ id))) | ($true != ((X170 @ id @ X177 @ id)))) & ($true != ((X170 @ id @ (lam @ (X176 @ sh @ one)) @ id)))) | ? [X185 : subst,X184 : subst,X182 : subst,X183 : term] : (($true != ((X170 @ (comp @ X182 @ X185) @ (sub @ X183 @ X185) @ X184))) & ($true = ((X170 @ X182 @ X183 @ (comp @ X185 @ X184))))) | (((X170 @ id @ (lam @ X171) @ id)) = $true) | ? [X175 : subst,X173 : subst,X174 : term,X172 : subst] : (($true != ((X170 @ X173 @ X174 @ (comp @ X172 @ X175)))) & ($true = ((X170 @ (comp @ X173 @ X172) @ (sub @ X174 @ X172) @ X175))))) | ? [X163 : term,X162 : (subst > term > subst > $o)] : (! [X164 : (subst > term > term)] : (? [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) != ((sub @ (X164 @ X167 @ X165) @ X166))) | ($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ? [X168 : term] : (($true != ((X162 @ id @ (X164 @ id @ X168) @ id))) & ($true = ((X162 @ id @ X168 @ id))))) & ! [X169 : term] : (($true != ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) & ($true != ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id))))) | ? [X161 : term] : (((sub @ X161 @ id)) != X161))) & (((! [X235 : (term > $o),X234 : term] : (? [X240 : term,X239 : term] : (($true != ((X235 @ (ap @ X239 @ X240)))) & ($true = ((X235 @ X240))) & ($true = ((X235 @ X239)))) | ? [X236 : term] : (! [X237 : term] : (($true != ((X235 @ X237))) | ($true = ((X235 @ (sub @ X236 @ (push @ X237 @ id)))))) & ($true != ((X235 @ (lam @ X236))))) | ($true = ((X235 @ X234))) | ? [X238 : term] : (($true != ((X235 @ X238))) & ($true = ((var @ X238))))) | ? [X228 : subst,X227 : (term > $o),X226 : term] : (! [X232 : term] : (? [X233 : term] : (($true = ((X227 @ X233))) & ($true != ((X227 @ (sub @ X232 @ (push @ X233 @ id)))))) | ($true = ((X227 @ (lam @ X232))))) & ! [X230 : term,X229 : term] : (($true != ((X227 @ X230))) | ($true = ((X227 @ (ap @ X230 @ X229)))) | ($true != ((X227 @ X229)))) & ! [X231 : term] : (($true = ((X227 @ (sub @ X231 @ X228)))) | ($true != ((var @ X231)))) & ($true != ((X227 @ (sub @ X226 @ X228)))))) | ? [X225 : term] : (((sub @ X225 @ id)) != X225)) <=> (induction2_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & (((! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)) | ? [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) = ((ap @ X392 @ X390))) & (X389 != X392))) | ? [X388 : term] : (((sub @ X388 @ id)) != X388)) <=> (hoasapinj1_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((((! [X302 : (subst > term > subst > $o),X301 : term] : (? [X314 : term] : (($true = ((var @ (sub @ X314 @ id)))) & ($true != ((X302 @ id @ X314 @ id)))) | ? [X308 : subst,X309 : subst,X311 : subst,X310 : term] : (($true = ((X302 @ X311 @ X310 @ (comp @ X308 @ X309)))) & ($true != ((X302 @ (comp @ X311 @ X308) @ (sub @ X310 @ X308) @ X309)))) | ? [X312 : term,X313 : term] : (($true != ((X302 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id))) & ($true = ((X302 @ id @ X312 @ id))) & ($true = ((X302 @ id @ X313 @ id)))) | ? [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true = ((X302 @ (comp @ X317 @ X315) @ (sub @ X318 @ X315) @ X316))) & ($true != ((X302 @ X317 @ X318 @ (comp @ X315 @ X316))))) | ? [X303 : (subst > term > term)] : (! [X304 : term,X306 : subst,X305 : subst] : (((X303 @ (comp @ X306 @ X305) @ (sub @ X304 @ X305))) = ((sub @ (X303 @ X306 @ X304) @ X305))) & ! [X307 : term] : (($true = ((X302 @ id @ (X303 @ id @ X307) @ id))) | ($true != ((X302 @ id @ X307 @ id)))) & ($true != ((X302 @ id @ (lam @ (X303 @ sh @ one)) @ id)))) | ($true = ((X302 @ id @ X301 @ id)))) | ? [X285 : (subst > term > subst > $o),X286 : term] : (! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ($true != ((X285 @ id @ X291 @ id)))) & ! [X296 : (subst > term > term)] : (? [X299 : subst,X300 : subst,X298 : term] : (((X296 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) != ((sub @ (X296 @ X299 @ X298) @ X300))) | ($true = ((X285 @ id @ (lam @ (X296 @ sh @ one)) @ id))) | ? [X297 : term] : (($true != ((X285 @ id @ (X296 @ id @ X297) @ id))) & ($true = ((X285 @ id @ X297 @ id))))) & ! [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) | ($true != ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) & ! [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) | ($true != ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) & ($true != ((X285 @ id @ (lam @ X286) @ id))))) | ? [X274 : (subst > term > subst > $o),X272 : term,X273 : term] : (($true = ((X274 @ id @ X272 @ id))) & ($true != ((X274 @ id @ (ap @ X273 @ X272) @ id))) & ! [X282 : subst,X279 : subst,X280 : subst,X281 : term] : (($true != ((X274 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280) @ X279))) | ($true = ((X274 @ X282 @ X281 @ (comp @ X280 @ X279))))) & ($true = ((X274 @ id @ X273 @ id))) & ! [X277 : subst,X275 : subst,X278 : subst,X276 : term] : (($true != ((X274 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X274 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275)))) & ! [X283 : term,X284 : term] : (($true != ((X274 @ id @ X284 @ id))) | ($true != ((X274 @ id @ X283 @ id))) | ($true = ((X274 @ id @ (ap @ (sub @ X283 @ id) @ X284) @ id)))))) | ? [X266 : term,X265 : (term > $o)] : (! [X268 : term] : (? [X269 : term] : (($true = ((X265 @ X269))) & ($true != ((X265 @ (sub @ X268 @ (push @ X269 @ id)))))) | ($true = ((X265 @ (lam @ X268))))) & ! [X271 : term,X270 : term] : (($true != ((X265 @ X270))) | ($true != ((X265 @ X271))) | ($true = ((X265 @ (ap @ X270 @ X271))))) & ! [X267 : term] : (($true = ((X265 @ X267))) | ($true != ((var @ X267)))) & ($true != ((X265 @ X266))))) <=> (hoasinduction_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((laminj = $true) <=> ! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11))) & (ulamvarind = $true) & (! [X509 : term] : ? [X510 : (subst > term > term)] : (((X510 @ sh @ one)) = ((sub @ X509 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) <=> (shinj = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((induction2lem_lthm = $true) <=> ((((! [X111 : term,X109 : (term > $o),X110 : subst] : (? [X116 : term,X115 : term] : (($true = ((X109 @ X115))) & ($true != ((X109 @ (ap @ X116 @ X115)))) & ($true = ((X109 @ X116)))) | ($true = ((X109 @ (sub @ X111 @ X110)))) | ? [X112 : term] : (($true != ((X109 @ (lam @ X112)))) & ! [X113 : term] : (($true != ((X109 @ X113))) | ($true = ((X109 @ (sub @ X112 @ (push @ X113 @ id))))))) | ? [X114 : term] : ((((X109 @ (sub @ X114 @ X110))) != $true) & ($true = ((var @ X114))))) | ? [X103 : (term > $o),X104 : term] : (($true != ((X103 @ X104))) & ! [X106 : term,X105 : term] : (($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106)))) | ($true != ((X103 @ X106)))) & ! [X107 : term] : (($true != ((X103 @ X107))) | ($true = ((X103 @ (lam @ X107))))) & ! [X108 : term] : (($true != ((var @ X108))) | ($true = ((X103 @ X108)))))) | ? [X102 : subst] : (((comp @ X102 @ id)) != X102)) | ? [X101 : term,X100 : subst] : (((comp @ sh @ (push @ X101 @ X100))) != X100)) | ? [X98 : term,X99 : subst] : (((sub @ one @ (push @ X98 @ X99))) != X98))) & ((! [X5 : term] : (((sub @ X5 @ id)) = X5) | ? [X4 : term] : (((sub @ X4 @ id)) != X4)) <=> (termmset_lthm = $true)) & (! [X187 : term,X186 : (subst > term > subst > $o)] : (? [X197 : term] : (($true = ((X186 @ id @ X197 @ id))) & ($true != ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ? [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true != ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) & ($true = ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) | ? [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true = ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) & ($true != ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) | ($true = ((X186 @ id @ (lam @ X187) @ id))) | ? [X188 : (subst > term > term)] : (! [X191 : subst,X190 : term,X192 : subst] : (((X188 @ (comp @ X191 @ X192) @ (sub @ X190 @ X192))) = ((sub @ (X188 @ X191 @ X190) @ X192))) & ($true != ((X186 @ id @ (lam @ (X188 @ sh @ one)) @ id))) & ! [X189 : term] : (($true = ((X186 @ id @ (X188 @ id @ X189) @ id))) | ($true != ((X186 @ id @ X189 @ id)))))) <=> (hoasinduction_lem3 = $true)) & (((((! [X372 : (subst > term > subst > $o),X371 : term] : (($true = ((X372 @ id @ X371 @ id))) | ? [X375 : (subst > term > term)] : (! [X376 : term] : ((((X372 @ id @ X376 @ id)) != $true) | ($true = ((X372 @ id @ (X375 @ id @ X376) @ id)))) & ($true != ((X372 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X379 : subst,X377 : term,X378 : subst] : (((sub @ (X375 @ X378 @ X377) @ X379)) = ((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))))) | ? [X374 : term,X373 : term] : (($true != ((X372 @ id @ (ap @ (sub @ X373 @ id) @ X374) @ id))) & ($true = ((X372 @ id @ X373 @ id))) & ($true = ((X372 @ id @ X374 @ id))))) | ? [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true != ((X361 @ (lam @ X362)))) & ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) & ! [X370 : term] : (($true != ((X361 @ X370))) | ($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) & ! [X365 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ? [X369 : term] : (($true != ((X363 @ id @ (X365 @ id @ X369) @ id))) & ($true = ((X363 @ id @ X369 @ id)))) | ? [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) != ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367))))))) | ? [X360 : term] : (((sub @ X360 @ id)) != X360)) | ? [X353 : term,X354 : (term > $o)] : (($true != ((X354 @ X353))) & ! [X355 : term] : (($true != ((var @ X355))) | ($true = ((X354 @ X355)))) & ! [X358 : term] : (? [X359 : term] : (($true != ((X354 @ (sub @ X358 @ (push @ X359 @ id))))) & ($true = ((X354 @ X359)))) | ($true = ((X354 @ (lam @ X358))))) & ! [X356 : term,X357 : term] : (($true != ((X354 @ X356))) | ($true != ((X354 @ X357))) | ($true = ((X354 @ (ap @ X357 @ X356))))))) | ? [X350 : (subst > term > subst > $o)] : ! [X351 : (term > $o)] : ? [X352 : term] : (((X350 @ id @ X352 @ id)) != ((X351 @ X352)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((hoasapinj2_lthm = $true) <=> (? [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 != X29) & (((ap @ X30 @ X28)) = ((ap @ X31 @ X29)))) | ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35)))))) & ((hoasinduction = $true) <=> ! [X459 : term,X458 : (subst > term > subst > $o)] : (? [X471 : (subst > term > term)] : (! [X472 : term] : (($true != ((X458 @ id @ X472 @ id))) | ($true = ((X458 @ id @ (X471 @ id @ X472) @ id)))) & ($true != ((X458 @ id @ (lam @ (X471 @ sh @ one)) @ id))) & ! [X475 : subst,X473 : subst,X474 : term] : (((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475))) = ((sub @ (X471 @ X473 @ X474) @ X475)))) | ? [X460 : term] : (($true = ((var @ (sub @ X460 @ id)))) & ($true != ((X458 @ id @ X460 @ id)))) | ? [X465 : term,X466 : term] : (($true != ((X458 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id))) & ($true = ((X458 @ id @ X465 @ id))) & ($true = ((X458 @ id @ X466 @ id)))) | ($true = ((X458 @ id @ X459 @ id))) | ? [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true = ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) & ($true != ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) | ? [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true != ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) & ($true = ((X458 @ X461 @ X464 @ (comp @ X462 @ X463))))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X438 : (subst > term > subst > $o),X437 : term] : (($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ? [X448 : term] : (($true != ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) & ($true = ((X438 @ id @ X448 @ id)))) | ? [X440 : term,X439 : (subst > term > term)] : (! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ($true != ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) & ! [X441 : term] : (($true != ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id)))) & ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444)))))) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X257 : term,X258 : (subst > term > subst > $o)] : ((((X258 @ id @ (lam @ X257) @ id)) = $true) | ? [X264 : term] : ((((X258 @ id @ (sub @ X257 @ (push @ X264 @ id)) @ id)) != $true) & ($true = ((X258 @ id @ X264 @ id)))) | ? [X259 : (subst > term > term)] : (($true != ((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id))) & ! [X260 : term] : (($true != ((X258 @ id @ X260 @ id))) | ($true = ((X258 @ id @ (X259 @ id @ X260) @ id)))) & ! [X262 : subst,X261 : term,X263 : subst] : (((X259 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X263 @ X261) @ X262))))) | ? [X250 : term,X249 : (subst > term > subst > $o)] : (($true != ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) & ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ($true != ((X249 @ id @ X256 @ id)))) & ! [X251 : (subst > term > term)] : (($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) | ? [X255 : term] : (($true = ((X249 @ id @ X255 @ id))) & ($true != ((X249 @ id @ (X251 @ id @ X255) @ id)))) | ? [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) != ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252))))))) | ? [X248 : term] : (((sub @ X248 @ id)) != X248))) & (hoaslamnotvar_gthm = $true) & (pushprop_lthm_orig = $true) & ((induction = $true) <=> ! [X432 : (term > $o),X431 : term] : (? [X436 : term] : (($true != ((X432 @ X436))) & ($true = ((var @ X436)))) | ($true = ((X432 @ X431))) | ? [X433 : term] : (($true = ((X432 @ X433))) & ($true != ((X432 @ (lam @ X433))))) | ? [X435 : term,X434 : term] : (($true = ((X432 @ X434))) & ($true != ((X432 @ (ap @ X435 @ X434)))) & ($true = ((X432 @ X435)))))) & ! [X7 : d_term,X6 : d_term] : ((X6 = X7) | (((d2term @ X7)) != ((d2term @ X6)))) & (hoaslamnotap_lthm = $true) & ((hoasapinj2 = $true) <=> ! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1))))) & (hoasapnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem1v2_gthm = $true) & (! [X477 : term,X478 : term,X476 : (subst > term > term)] : (? [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) != ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (ulamvarsh = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) <=> (axvarid = $true)) & (! [X243 : (term > $o),X244 : subst,X245 : term] : ? [X246 : (term > $o)] : ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244))))) <=> (pushprop_lem0 = $true)) & (! [X347 : (subst > term > subst > $o)] : ? [X348 : (term > $o)] : ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349))) <=> (hoasinduction_lem0 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (? [X537 : term] : (((X534 @ X537)) != ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) | ($true = ((X534 @ one))) | ($true != ((X536 @ X535))))) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & (lamnotvar = $true) & (termmset_gthm = $true) & (one = ((d2term @ d_one))) & (! [X410 : term,X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (ap @ X410 @ X412) @ id))) | ? [X420 : subst,X417 : term,X418 : subst,X419 : subst] : (($true = ((X411 @ X418 @ X417 @ (comp @ X420 @ X419)))) & ($true != ((X411 @ (comp @ X418 @ X420) @ (sub @ X417 @ X420) @ X419)))) | ($true != ((X411 @ id @ X412 @ id))) | ? [X422 : term,X421 : term] : (($true != ((X411 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) & ($true = ((X411 @ id @ X422 @ id))) & ($true = ((X411 @ id @ X421 @ id)))) | ($true != ((X411 @ id @ X410 @ id))) | ? [X416 : subst,X413 : term,X415 : subst,X414 : subst] : (($true != ((X411 @ X414 @ X413 @ (comp @ X415 @ X416)))) & ($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415) @ X416))))) <=> (hoasinduction_lem2 = $true)) & ! [X500 : d_subst] : (d_id = X500) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X217 : subst,X219 : term,X218 : (term > $o)] : (($true = ((X218 @ (sub @ X219 @ X217)))) | ? [X220 : term] : (! [X221 : term] : (($true != ((X218 @ X221))) | ($true = ((X218 @ (sub @ X220 @ (push @ X221 @ id)))))) & (((X218 @ (lam @ X220))) != $true)) | ? [X224 : term] : (($true = ((var @ X224))) & ($true != ((X218 @ (sub @ X224 @ X217))))) | ? [X223 : term,X222 : term] : (($true = ((X218 @ X223))) & ($true = ((X218 @ X222))) & ($true != ((X218 @ (ap @ X222 @ X223)))))) <=> (induction2lem = $true)) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (hoasapinj2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) <=> (apinj2 = $true)) & (((((! [X58 : (subst > term > subst > $o),X57 : term] : (($true = ((X58 @ id @ X57 @ id))) | ? [X66 : term,X65 : term] : (($true = ((X58 @ id @ X66 @ id))) & ($true = ((X58 @ id @ X65 @ id))) & ($true != ((X58 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id)))) | ? [X69 : subst,X70 : subst,X67 : term,X68 : subst] : (($true != ((X58 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69))) & ($true = ((X58 @ X68 @ X67 @ (comp @ X70 @ X69))))) | ? [X73 : term,X72 : subst,X74 : subst,X71 : subst] : (($true = ((X58 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X74))) & ($true != ((X58 @ X72 @ X73 @ (comp @ X71 @ X74))))) | ? [X59 : term] : (($true = ((var @ (sub @ X59 @ id)))) & ($true != ((X58 @ id @ X59 @ id)))) | ? [X60 : (subst > term > term)] : (! [X61 : term] : (($true = ((X58 @ id @ (X60 @ id @ X61) @ id))) | ($true != ((X58 @ id @ X61 @ id)))) & ($true != ((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id))) & ! [X63 : subst,X64 : subst,X62 : term] : (((sub @ (X60 @ X64 @ X62) @ X63)) = ((X60 @ (comp @ X64 @ X63) @ (sub @ X62 @ X63)))))) | ? [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (! [X50 : (subst > term > term)] : (? [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) != ((sub @ (X50 @ X52 @ X51) @ X53))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | ? [X54 : term] : (($true = ((X47 @ id @ X54 @ id))) & ($true != ((X47 @ id @ (X50 @ id @ X54) @ id))))) & ! [X55 : term] : (($true != ((X49 @ X55))) | ($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) & ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id))) & ($true != ((X49 @ (lam @ X48)))))) | ? [X46 : term] : (((sub @ X46 @ id)) != X46)) | ? [X39 : term,X40 : (term > $o)] : (! [X43 : term] : (($true != ((var @ X43))) | ($true = ((X40 @ X43)))) & ! [X44 : term,X45 : term] : (($true != ((X40 @ X44))) | ($true = ((X40 @ (ap @ X44 @ X45)))) | ($true != ((X40 @ X45)))) & ($true != ((X40 @ X39))) & ! [X41 : term] : (? [X42 : term] : (($true != ((X40 @ (sub @ X41 @ (push @ X42 @ id))))) & ($true = ((X40 @ X42)))) | ($true = ((X40 @ (lam @ X41))))))) | ? [X36 : (subst > term > subst > $o)] : ! [X37 : (term > $o)] : ? [X38 : term] : (((X37 @ X38)) != ((X36 @ id @ X38 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lem2v2_gthm = $true) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = id) & (induction2_gthm = $true) & ((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) <=> (substmonoid = $true)) & ((((! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531)) | ? [X530 : subst] : (((comp @ X530 @ id)) != X530)) | ? [X529 : subst] : (((comp @ id @ X529)) != X529)) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X493 : term,X492 : (subst > term > subst > $o)] : (? [X494 : (subst > term > term)] : (($true != ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498))) & ! [X495 : term] : (($true != ((X492 @ id @ X495 @ id))) | ($true = ((X492 @ id @ (X494 @ id @ X495) @ id))))) | ($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ? [X499 : term] : (($true = ((X492 @ id @ X499 @ id))) & ($true != ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & (axclos = $true) & ((? [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) != X449) | ! [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (? [X455 : term] : (((X452 @ X455)) != ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) | ($true != ((X451 @ X454))) | ($true = ((X452 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X8 : term] : ? [X9 : (subst > term > term)] : (((X9 @ sh @ one)) = ((sub @ X8 @ (push @ one @ sh))))) & (pushprop_gthm = $true) & ((axidl = $true) <=> ! [X424 : subst] : (((comp @ id @ X424)) = X424))), 24.89/4.11 inference(ennf_transformation,[],[f9])). 24.89/4.11 thf(f12,plain,( 24.89/4.11 ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & (! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) <=> (axvarcons = $true)) & (((d2subst @ d_id)) = id) & (axvarshift = $true) & (! [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true) | ? [X382 : term] : (($true = ((X380 @ id @ X382 @ id))) & ($true != ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) | ? [X383 : (subst > term > term)] : (! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))) & ! [X387 : term] : (($true = ((X380 @ id @ (X383 @ id @ X387) @ id))) | ($true != ((X380 @ id @ X387 @ id)))) & ($true != ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X410 : term,X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (ap @ X410 @ X412) @ id))) | ? [X420 : subst,X417 : term,X418 : subst,X419 : subst] : (($true = ((X411 @ X418 @ X417 @ (comp @ X420 @ X419)))) & ($true != ((X411 @ (comp @ X418 @ X420) @ (sub @ X417 @ X420) @ X419)))) | ($true != ((X411 @ id @ X412 @ id))) | ? [X422 : term,X421 : term] : (($true != ((X411 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) & ($true = ((X411 @ id @ X422 @ id))) & ($true = ((X411 @ id @ X421 @ id)))) | ($true != ((X411 @ id @ X410 @ id))) | ? [X416 : subst,X413 : term,X415 : subst,X414 : subst] : (($true != ((X411 @ X414 @ X413 @ (comp @ X415 @ X416)))) & ($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415) @ X416))))) <=> (hoasinduction_lem2 = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)) | ? [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) = ((ap @ X392 @ X390))) & (X389 != X392)) | ? [X388 : term] : (((sub @ X388 @ id)) != X388))) & (hoasapnotvar = $true) & (axabs = $true) & ! [X404 : d_subst,X403 : d_subst] : ((X403 = X404) | (((d2subst @ X403)) != ((d2subst @ X404)))) & ((axidr = $true) <=> ! [X423 : subst] : (((comp @ X423 @ id)) = X423)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true = ((X321 @ (lam @ X322)))) | ? [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true != ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) & ($true = ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) | ? [X327 : term] : (((X321 @ X327)) != ((X320 @ id @ X327 @ id))) | ? [X328 : term] : (($true = ((X321 @ X328))) & ($true != ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ? [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true != ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) & ($true = ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ? [X333 : (subst > term > term)] : (($true != ((X320 @ id @ (lam @ (X333 @ sh @ one)) @ id))) & ! [X337 : term] : (($true = ((X320 @ id @ (X333 @ id @ X337) @ id))) | ($true != ((X320 @ id @ X337 @ id)))) & ! [X334 : term,X335 : subst,X336 : subst] : (((X333 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ (X333 @ X335 @ X334) @ X336))))) | ? [X319 : term] : (((sub @ X319 @ id)) != X319)) <=> (hoasinduction_lem3v2_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((? [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) != X449) | ! [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (? [X455 : term] : (((X452 @ X455)) != ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) | ($true != ((X451 @ X454))) | ($true = ((X452 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true != ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) <=> (apinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X250 : term,X249 : (subst > term > subst > $o)] : (($true != ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) & ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ($true != ((X249 @ id @ X256 @ id)))) & ! [X251 : (subst > term > term)] : (($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) | ? [X255 : term] : (($true = ((X249 @ id @ X255 @ id))) & ($true != ((X249 @ id @ (X251 @ id @ X255) @ id)))) | ? [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) != ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))))) | ! [X257 : term,X258 : (subst > term > subst > $o)] : ((((X258 @ id @ (lam @ X257) @ id)) = $true) | ? [X264 : term] : ((((X258 @ id @ (sub @ X257 @ (push @ X264 @ id)) @ id)) != $true) & ($true = ((X258 @ id @ X264 @ id)))) | ? [X259 : (subst > term > term)] : (($true != ((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id))) & ! [X260 : term] : (($true != ((X258 @ id @ X260 @ id))) | ($true = ((X258 @ id @ (X259 @ id @ X260) @ id)))) & ! [X262 : subst,X261 : term,X263 : subst] : (((X259 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X263 @ X261) @ X262))))) | ? [X248 : term] : (((sub @ X248 @ id)) != X248))) & ((hoasinduction_lem3aa = $true) <=> ! [X493 : term,X492 : (subst > term > subst > $o)] : (? [X494 : (subst > term > term)] : (($true != ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498))) & ! [X495 : term] : (($true != ((X492 @ id @ X495 @ id))) | ($true = ((X492 @ id @ (X494 @ id @ X495) @ id))))) | ($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ? [X499 : term] : (($true = ((X492 @ id @ X499 @ id))) & ($true != ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((! [X171 : term,X170 : (subst > term > subst > $o)] : (? [X181 : term] : (($true = ((X170 @ id @ X181 @ id))) & ($true != ((X170 @ id @ (sub @ X171 @ (push @ X181 @ id)) @ id)))) | ? [X176 : (subst > term > term)] : (! [X178 : subst,X180 : term,X179 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true = ((X170 @ id @ (X176 @ id @ X177) @ id))) | ($true != ((X170 @ id @ X177 @ id)))) & ($true != ((X170 @ id @ (lam @ (X176 @ sh @ one)) @ id)))) | ? [X185 : subst,X184 : subst,X182 : subst,X183 : term] : (($true != ((X170 @ (comp @ X182 @ X185) @ (sub @ X183 @ X185) @ X184))) & ($true = ((X170 @ X182 @ X183 @ (comp @ X185 @ X184))))) | (((X170 @ id @ (lam @ X171) @ id)) = $true) | ? [X175 : subst,X173 : subst,X174 : term,X172 : subst] : (($true != ((X170 @ X173 @ X174 @ (comp @ X172 @ X175)))) & ($true = ((X170 @ (comp @ X173 @ X172) @ (sub @ X174 @ X172) @ X175))))) | ? [X161 : term] : (((sub @ X161 @ id)) != X161) | ? [X163 : term,X162 : (subst > term > subst > $o)] : (! [X164 : (subst > term > term)] : (? [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) != ((sub @ (X164 @ X167 @ X165) @ X166))) | ($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ? [X168 : term] : (($true != ((X162 @ id @ (X164 @ id @ X168) @ id))) & ($true = ((X162 @ id @ X168 @ id))))) & ! [X169 : term] : (($true != ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) & ($true != ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X302 : (subst > term > subst > $o),X301 : term] : (? [X314 : term] : (($true = ((var @ (sub @ X314 @ id)))) & ($true != ((X302 @ id @ X314 @ id)))) | ? [X308 : subst,X309 : subst,X311 : subst,X310 : term] : (($true = ((X302 @ X311 @ X310 @ (comp @ X308 @ X309)))) & ($true != ((X302 @ (comp @ X311 @ X308) @ (sub @ X310 @ X308) @ X309)))) | ? [X312 : term,X313 : term] : (($true != ((X302 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id))) & ($true = ((X302 @ id @ X312 @ id))) & ($true = ((X302 @ id @ X313 @ id)))) | ? [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true = ((X302 @ (comp @ X317 @ X315) @ (sub @ X318 @ X315) @ X316))) & ($true != ((X302 @ X317 @ X318 @ (comp @ X315 @ X316))))) | ? [X303 : (subst > term > term)] : (! [X304 : term,X306 : subst,X305 : subst] : (((X303 @ (comp @ X306 @ X305) @ (sub @ X304 @ X305))) = ((sub @ (X303 @ X306 @ X304) @ X305))) & ! [X307 : term] : (($true = ((X302 @ id @ (X303 @ id @ X307) @ id))) | ($true != ((X302 @ id @ X307 @ id)))) & ($true != ((X302 @ id @ (lam @ (X303 @ sh @ one)) @ id)))) | ($true = ((X302 @ id @ X301 @ id)))) | ? [X266 : term,X265 : (term > $o)] : (! [X268 : term] : (? [X269 : term] : (($true = ((X265 @ X269))) & ($true != ((X265 @ (sub @ X268 @ (push @ X269 @ id)))))) | ($true = ((X265 @ (lam @ X268))))) & ! [X271 : term,X270 : term] : (($true != ((X265 @ X270))) | ($true != ((X265 @ X271))) | ($true = ((X265 @ (ap @ X270 @ X271))))) & ! [X267 : term] : (($true = ((X265 @ X267))) | ($true != ((var @ X267)))) & ($true != ((X265 @ X266)))) | ? [X274 : (subst > term > subst > $o),X272 : term,X273 : term] : (($true = ((X274 @ id @ X272 @ id))) & ($true != ((X274 @ id @ (ap @ X273 @ X272) @ id))) & ! [X282 : subst,X279 : subst,X280 : subst,X281 : term] : (($true != ((X274 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280) @ X279))) | ($true = ((X274 @ X282 @ X281 @ (comp @ X280 @ X279))))) & ($true = ((X274 @ id @ X273 @ id))) & ! [X277 : subst,X275 : subst,X278 : subst,X276 : term] : (($true != ((X274 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X274 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275)))) & ! [X283 : term,X284 : term] : (($true != ((X274 @ id @ X284 @ id))) | ($true != ((X274 @ id @ X283 @ id))) | ($true = ((X274 @ id @ (ap @ (sub @ X283 @ id) @ X284) @ id))))) | ? [X285 : (subst > term > subst > $o),X286 : term] : (! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ($true != ((X285 @ id @ X291 @ id)))) & ! [X296 : (subst > term > term)] : (? [X299 : subst,X300 : subst,X298 : term] : (((X296 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) != ((sub @ (X296 @ X299 @ X298) @ X300))) | ($true = ((X285 @ id @ (lam @ (X296 @ sh @ one)) @ id))) | ? [X297 : term] : (($true != ((X285 @ id @ (X296 @ id @ X297) @ id))) & ($true = ((X285 @ id @ X297 @ id))))) & ! [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) | ($true != ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) & ! [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) | ($true != ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) & ($true != ((X285 @ id @ (lam @ X286) @ id)))))) & ((? [X129 : term] : ! [X130 : (subst > term > term)] : ? [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) != ((sub @ X129 @ (push @ X132 @ X131)))) | ? [X133 : term] : (((sub @ X133 @ id)) != X133) | ! [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (? [X142 : term] : (((X136 @ id @ X142 @ id)) != ((X135 @ X142))) | ? [X137 : (subst > term > term)] : (($true != ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) & ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ($true != ((X136 @ id @ X141 @ id)))) & ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139)))) | ? [X143 : term] : (($true = ((X135 @ X143))) & ($true != ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ($true = ((X135 @ (lam @ X134)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj = $true) <=> ! [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | (((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ? [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) != ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) | ? [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) != ((sub @ (X152 @ X157 @ X156) @ X158))))) & (hoasapinj2_gthm = $true) & ((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) <=> (substmonoid = $true)) & (axclos = $true) & (! [X243 : (term > $o),X244 : subst,X245 : term] : ? [X246 : (term > $o)] : ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X477 : term,X478 : term,X476 : (subst > term > term)] : (? [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) != ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (pushprop_lem3v2_lthm = $true) & ((? [X529 : subst] : (((comp @ id @ X529)) != X529) | ? [X530 : subst] : (((comp @ X530 @ id)) != X530) | (! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531))) <=> (substmonoid_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & ((axscons = $true) <=> ! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148)) & (hoasinduction_lem1v2_gthm = $true) & (apnotvar = $true) & ((? [X36 : (subst > term > subst > $o)] : ! [X37 : (term > $o)] : ? [X38 : term] : (((X37 @ X38)) != ((X36 @ id @ X38 @ id))) | ! [X58 : (subst > term > subst > $o),X57 : term] : (($true = ((X58 @ id @ X57 @ id))) | ? [X66 : term,X65 : term] : (($true = ((X58 @ id @ X66 @ id))) & ($true = ((X58 @ id @ X65 @ id))) & ($true != ((X58 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id)))) | ? [X69 : subst,X70 : subst,X67 : term,X68 : subst] : (($true != ((X58 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69))) & ($true = ((X58 @ X68 @ X67 @ (comp @ X70 @ X69))))) | ? [X73 : term,X72 : subst,X74 : subst,X71 : subst] : (($true = ((X58 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X74))) & ($true != ((X58 @ X72 @ X73 @ (comp @ X71 @ X74))))) | ? [X59 : term] : (($true = ((var @ (sub @ X59 @ id)))) & ($true != ((X58 @ id @ X59 @ id)))) | ? [X60 : (subst > term > term)] : (! [X61 : term] : (($true = ((X58 @ id @ (X60 @ id @ X61) @ id))) | ($true != ((X58 @ id @ X61 @ id)))) & ($true != ((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id))) & ! [X63 : subst,X64 : subst,X62 : term] : (((sub @ (X60 @ X64 @ X62) @ X63)) = ((X60 @ (comp @ X64 @ X63) @ (sub @ X62 @ X63)))))) | ? [X46 : term] : (((sub @ X46 @ id)) != X46) | ? [X39 : term,X40 : (term > $o)] : (! [X43 : term] : (($true != ((var @ X43))) | ($true = ((X40 @ X43)))) & ! [X44 : term,X45 : term] : (($true != ((X40 @ X44))) | ($true = ((X40 @ (ap @ X44 @ X45)))) | ($true != ((X40 @ X45)))) & ($true != ((X40 @ X39))) & ! [X41 : term] : (? [X42 : term] : (($true != ((X40 @ (sub @ X41 @ (push @ X42 @ id))))) & ($true = ((X40 @ X42)))) | ($true = ((X40 @ (lam @ X41)))))) | ? [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (! [X50 : (subst > term > term)] : (? [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) != ((sub @ (X50 @ X52 @ X51) @ X53))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | ? [X54 : term] : (($true = ((X47 @ id @ X54 @ id))) & ($true != ((X47 @ id @ (X50 @ id @ X54) @ id))))) & ! [X55 : term] : (($true != ((X49 @ X55))) | ($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) & ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id))) & ($true != ((X49 @ (lam @ X48)))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X400 : (subst > term > subst > $o)] : ? [X401 : (term > $o)] : ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id)))) & (! [X509 : term] : ? [X510 : (subst > term > term)] : (((X510 @ sh @ one)) = ((sub @ X509 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoaslamnotap_lthm = $true) & ((? [X228 : subst,X227 : (term > $o),X226 : term] : (! [X232 : term] : (? [X233 : term] : (($true = ((X227 @ X233))) & ($true != ((X227 @ (sub @ X232 @ (push @ X233 @ id)))))) | ($true = ((X227 @ (lam @ X232))))) & ! [X230 : term,X229 : term] : (($true != ((X227 @ X230))) | ($true = ((X227 @ (ap @ X230 @ X229)))) | ($true != ((X227 @ X229)))) & ! [X231 : term] : (($true = ((X227 @ (sub @ X231 @ X228)))) | ($true != ((var @ X231)))) & ($true != ((X227 @ (sub @ X226 @ X228))))) | ? [X225 : term] : (((sub @ X225 @ id)) != X225) | ! [X235 : (term > $o),X234 : term] : (? [X240 : term,X239 : term] : (($true != ((X235 @ (ap @ X239 @ X240)))) & ($true = ((X235 @ X240))) & ($true = ((X235 @ X239)))) | ? [X236 : term] : (! [X237 : term] : (($true != ((X235 @ X237))) | ($true = ((X235 @ (sub @ X236 @ (push @ X237 @ id)))))) & ($true != ((X235 @ (lam @ X236))))) | ($true = ((X235 @ X234))) | ? [X238 : term] : (($true != ((X235 @ X238))) & ($true = ((var @ X238)))))) <=> (induction2_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (? [X537 : term] : (((X534 @ X537)) != ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) | ($true = ((X534 @ one))) | ($true != ((X536 @ X535))))) & (! [X187 : term,X186 : (subst > term > subst > $o)] : (? [X197 : term] : (($true = ((X186 @ id @ X197 @ id))) & ($true != ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ? [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true != ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) & ($true = ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) | ? [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true = ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) & ($true != ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) | ($true = ((X186 @ id @ (lam @ X187) @ id))) | ? [X188 : (subst > term > term)] : (! [X191 : subst,X190 : term,X192 : subst] : (((X188 @ (comp @ X191 @ X192) @ (sub @ X190 @ X192))) = ((sub @ (X188 @ X191 @ X190) @ X192))) & ($true != ((X186 @ id @ (lam @ (X188 @ sh @ one)) @ id))) & ! [X189 : term] : (($true = ((X186 @ id @ (X188 @ id @ X189) @ id))) | ($true != ((X186 @ id @ X189 @ id)))))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X203 : (term > $o),X202 : (subst > term > subst > $o),X205 : term,X204 : term] : (($true = ((X203 @ (ap @ X205 @ X204)))) | ? [X207 : subst,X208 : term,X209 : subst,X210 : subst] : (($true != ((X202 @ (comp @ X210 @ X207) @ (sub @ X208 @ X207) @ X209))) & ($true = ((X202 @ X210 @ X208 @ (comp @ X207 @ X209))))) | ? [X206 : term] : (((X202 @ id @ X206 @ id)) != ((X203 @ X206))) | ? [X214 : subst,X211 : subst,X213 : subst,X212 : term] : (($true = ((X202 @ (comp @ X214 @ X213) @ (sub @ X212 @ X213) @ X211))) & ($true != ((X202 @ X214 @ X212 @ (comp @ X213 @ X211))))) | ($true != ((X203 @ X204))) | ($true != ((X203 @ X205))) | ? [X216 : term,X215 : term] : (($true = ((X202 @ id @ X216 @ id))) & ($true = ((X202 @ id @ X215 @ id))) & ($true != ((X202 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) <=> ! [X424 : subst] : (((comp @ id @ X424)) = X424)) & (lamnotap != $true) & ((induction = $true) <=> ! [X432 : (term > $o),X431 : term] : (? [X436 : term] : (($true != ((X432 @ X436))) & ($true = ((var @ X436)))) | ($true = ((X432 @ X431))) | ? [X433 : term] : (($true = ((X432 @ X433))) & ($true != ((X432 @ (lam @ X433))))) | ? [X435 : term,X434 : term] : (($true = ((X432 @ X434))) & ($true != ((X432 @ (ap @ X435 @ X434)))) & ($true = ((X432 @ X435)))))) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X482 : term] : ? [X483 : (subst > term > term)] : ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((axshiftcons = $true) <=> ! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538)) & (! [X347 : (subst > term > subst > $o)] : ? [X348 : (term > $o)] : ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349))) <=> (hoasinduction_lem0 = $true)) & (pushprop = $true) & ((hoasinduction = $true) <=> ! [X459 : term,X458 : (subst > term > subst > $o)] : (? [X471 : (subst > term > term)] : (! [X472 : term] : (($true != ((X458 @ id @ X472 @ id))) | ($true = ((X458 @ id @ (X471 @ id @ X472) @ id)))) & ($true != ((X458 @ id @ (lam @ (X471 @ sh @ one)) @ id))) & ! [X475 : subst,X473 : subst,X474 : term] : (((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475))) = ((sub @ (X471 @ X473 @ X474) @ X475)))) | ? [X460 : term] : (($true = ((var @ (sub @ X460 @ id)))) & ($true != ((X458 @ id @ X460 @ id)))) | ? [X465 : term,X466 : term] : (($true != ((X458 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id))) & ($true = ((X458 @ id @ X465 @ id))) & ($true = ((X458 @ id @ X466 @ id)))) | ($true = ((X458 @ id @ X459 @ id))) | ? [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true = ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) & ($true != ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) | ? [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true != ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) & ($true = ((X458 @ X461 @ X464 @ (comp @ X462 @ X463))))))) & (hoasinduction_lem1_lthm = $true) & ((induction2 = $true) <=> ! [X118 : (term > $o),X117 : term] : (($true = ((X118 @ X117))) | ? [X123 : term,X122 : term] : (($true = ((X118 @ X122))) & ($true != ((X118 @ (ap @ X122 @ X123)))) & ($true = ((X118 @ X123)))) | ? [X119 : term] : (($true != ((X118 @ (lam @ X119)))) & ! [X120 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X120 @ id))))) | ($true != ((X118 @ X120))))) | ? [X121 : term] : ((((var @ X121)) = $true) & ($true != ((X118 @ X121)))))) & (! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) <=> (shinj = $true)) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) <=> (axvarid = $true)) & (hoasinduction_lem1 = $true) & (axapp = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & ((termmset = $true) <=> ! [X399 : term] : (((sub @ X399 @ id)) = X399)) & ! [X491 : d_term] : (d_one = X491) & (! [X217 : subst,X219 : term,X218 : (term > $o)] : (($true = ((X218 @ (sub @ X219 @ X217)))) | ? [X220 : term] : (! [X221 : term] : (($true != ((X218 @ X221))) | ($true = ((X218 @ (sub @ X220 @ (push @ X221 @ id)))))) & (((X218 @ (lam @ X220))) != $true)) | ? [X224 : term] : (($true = ((var @ X224))) & ($true != ((X218 @ (sub @ X224 @ X217))))) | ? [X223 : term,X222 : term] : (($true = ((X218 @ X223))) & ($true = ((X218 @ X222))) & ($true != ((X218 @ (ap @ X222 @ X223)))))) <=> (induction2lem = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X8 : term] : ? [X9 : (subst > term > term)] : (((X9 @ sh @ one)) = ((sub @ X8 @ (push @ one @ sh))))) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) <=> ! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11))) & ! [X500 : d_subst] : (d_id = X500) & (ulamvarind = $true) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axmap = $true) & ((hoaslaminj_lthm = $true) <=> (? [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) != X14) | ? [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) != X12) | ? [X17 : term,X16 : term] : ((((lam @ X17)) = ((lam @ X16))) & (X16 != X17)) | ! [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (? [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) != ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21))) | ? [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) != ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23))))))) & (hoaslamnotvar_lthm = $true) & ((? [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true != ((X361 @ (lam @ X362)))) & ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) & ! [X370 : term] : (($true != ((X361 @ X370))) | ($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) & ! [X365 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ? [X369 : term] : (($true != ((X363 @ id @ (X365 @ id @ X369) @ id))) & ($true = ((X363 @ id @ X369 @ id)))) | ? [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) != ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) | ? [X353 : term,X354 : (term > $o)] : (($true != ((X354 @ X353))) & ! [X355 : term] : (($true != ((var @ X355))) | ($true = ((X354 @ X355)))) & ! [X358 : term] : (? [X359 : term] : (($true != ((X354 @ (sub @ X358 @ (push @ X359 @ id))))) & ($true = ((X354 @ X359)))) | ($true = ((X354 @ (lam @ X358))))) & ! [X356 : term,X357 : term] : (($true != ((X354 @ X356))) | ($true != ((X354 @ X357))) | ($true = ((X354 @ (ap @ X357 @ X356)))))) | ! [X372 : (subst > term > subst > $o),X371 : term] : (($true = ((X372 @ id @ X371 @ id))) | ? [X375 : (subst > term > term)] : (! [X376 : term] : ((((X372 @ id @ X376 @ id)) != $true) | ($true = ((X372 @ id @ (X375 @ id @ X376) @ id)))) & ($true != ((X372 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X379 : subst,X377 : term,X378 : subst] : (((sub @ (X375 @ X378 @ X377) @ X379)) = ((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))))) | ? [X374 : term,X373 : term] : (($true != ((X372 @ id @ (ap @ (sub @ X373 @ id) @ X374) @ id))) & ($true = ((X372 @ id @ X373 @ id))) & ($true = ((X372 @ id @ X374 @ id))))) | ? [X350 : (subst > term > subst > $o)] : ! [X351 : (term > $o)] : ? [X352 : term] : (((X350 @ id @ X352 @ id)) != ((X351 @ X352))) | ? [X360 : term] : (((sub @ X360 @ id)) != X360)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X438 : (subst > term > subst > $o),X437 : term] : (($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ? [X448 : term] : (($true != ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) & ($true = ((X438 @ id @ X448 @ id)))) | ? [X440 : term,X439 : (subst > term > term)] : (! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ($true != ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) & ! [X441 : term] : (($true != ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id)))) & ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444)))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X7 : d_term,X6 : d_term] : ((X6 = X7) | (((d2term @ X7)) != ((d2term @ X6)))) & ((hoasapinj1 = $true) <=> ! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128))) & (hoaslamnotap_gthm = $true) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & (pushprop_gthm = $true) & (hoasinduction_gthm = $true) & (! [X486 : (term > $o),X487 : subst,X488 : term] : ? [X489 : (term > $o)] : ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490))) <=> (pushprop_lem0_lthm = $true)) & ((? [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) != X87) | ! [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true != ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85)) <=> (pushprop_lem1_lthm = $true)) & (! [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (? [X514 : term] : (($true = ((X513 @ X514))) & ($true != ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) | ? [X515 : (subst > term > term)] : (($true != ((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id))) & ! [X519 : term] : (($true != ((X512 @ id @ X519 @ id))) | ($true = ((X512 @ id @ (X515 @ id @ X519) @ id)))) & ! [X516 : term,X518 : subst,X517 : subst] : (((sub @ (X515 @ X517 @ X516) @ X518)) = ((X515 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))))) | ? [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true != ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) & ($true = ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) | ? [X524 : term] : (((X513 @ X524)) != ((X512 @ id @ X524 @ id))) | ($true = ((X513 @ (lam @ X511)))) | ? [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true = ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) & (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasapinj2 = $true) <=> ! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1))))) & ((hoasapinj2_lthm = $true) <=> (? [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 != X29) & (((ap @ X30 @ X28)) = ((ap @ X31 @ X29)))) | ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35)))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X502 : (subst > term > subst > $o),X501 : term] : (($true = ((X502 @ id @ (lam @ X501) @ id))) | ? [X508 : term] : (($true = ((X502 @ id @ X508 @ id))) & ($true != ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) | ? [X503 : (subst > term > term)] : (! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) & ! [X507 : term] : (($true != ((X502 @ id @ X507 @ id))) | ($true = ((X502 @ id @ (X503 @ id @ X507) @ id)))) & ($true != ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id)))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true = ((X75 @ (lam @ X77)))) | ? [X78 : term] : (((X76 @ id @ X78 @ id)) != ((X75 @ X78))) | ? [X79 : term] : (($true != ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) & ($true = ((X75 @ X79)))) | ? [X80 : (subst > term > term)] : (! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X76 @ id @ X81 @ id)))) & ($true != ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) & ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82)))))) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X144 : term] : ? [X145 : (subst > term > term)] : ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147)))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X342 : (subst > term > term)] : (($true != ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) & ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ($true != ((X339 @ id @ X346 @ id)))) & ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343)))) | ? [X341 : term,X340 : term] : (($true != ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) & ($true = ((X339 @ id @ X340 @ id))) & ($true = ((X339 @ id @ X341 @ id)))) | ($true = ((X339 @ id @ X338 @ id))))) & (hoaslamnotvar = $true) & ((! [X5 : term] : (((sub @ X5 @ id)) = X5) | ? [X4 : term] : (((sub @ X4 @ id)) != X4)) <=> (termmset_lthm = $true)) & (lamnotvar = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((apinj1 = $true) <=> ! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429))))) & ((induction2lem_lthm = $true) <=> (! [X111 : term,X109 : (term > $o),X110 : subst] : (? [X116 : term,X115 : term] : (($true = ((X109 @ X115))) & ($true != ((X109 @ (ap @ X116 @ X115)))) & ($true = ((X109 @ X116)))) | ($true = ((X109 @ (sub @ X111 @ X110)))) | ? [X112 : term] : (($true != ((X109 @ (lam @ X112)))) & ! [X113 : term] : (($true != ((X109 @ X113))) | ($true = ((X109 @ (sub @ X112 @ (push @ X113 @ id))))))) | ? [X114 : term] : ((((X109 @ (sub @ X114 @ X110))) != $true) & ($true = ((var @ X114))))) | ? [X102 : subst] : (((comp @ X102 @ id)) != X102) | ? [X98 : term,X99 : subst] : (((sub @ one @ (push @ X98 @ X99))) != X98) | ? [X101 : term,X100 : subst] : (((comp @ sh @ (push @ X101 @ X100))) != X100) | ? [X103 : (term > $o),X104 : term] : (($true != ((X103 @ X104))) & ! [X106 : term,X105 : term] : (($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106)))) | ($true != ((X103 @ X106)))) & ! [X107 : term] : (($true != ((X103 @ X107))) | ($true = ((X103 @ (lam @ X107))))) & ! [X108 : term] : (($true != ((var @ X108))) | ($true = ((X103 @ X108)))))))), 24.89/4.11 inference(flattening,[],[f11])). 24.89/4.11 thf(f13,plain,( 24.89/4.11 ! [X0 : (subst > term > subst > $o)] : ((! [X8 : term] : ($true = ((X0 @ id @ X8 @ id))) | ? [X3 : (subst > term > term)] : ((($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))) & ! [X7 : term] : (($true != ((X0 @ id @ X7 @ id))) | ($true = ((X0 @ id @ (X3 @ id @ X7) @ id))))) & ! [X6 : subst,X5 : term,X4 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))))) | ? [X2 : term,X1 : term] : ((($true != ((X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))) & (((X0 @ id @ X1 @ id)) = $true)) & (((X0 @ id @ X2 @ id)) = $true))) <~> (hoasinduction_no_psi_cond = $true)), 24.89/4.11 inference(ennf_transformation,[],[f10])). 24.89/4.11 thf(f14,plain,( 24.89/4.11 ! [X0 : (subst > term > subst > $o)] : (! [X8 : term] : ($true = ((X0 @ id @ X8 @ id))) | ? [X3 : (subst > term > term)] : (($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))) & ! [X6 : subst,X5 : term,X4 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))) & ! [X7 : term] : (($true != ((X0 @ id @ X7 @ id))) | ($true = ((X0 @ id @ (X3 @ id @ X7) @ id))))) | ? [X1 : term,X2 : term] : ((((X0 @ id @ X1 @ id)) = $true) & ($true != ((X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))) & (((X0 @ id @ X2 @ id)) = $true))) <~> (hoasinduction_no_psi_cond = $true)), 24.89/4.11 inference(flattening,[],[f13])). 24.89/4.11 thf(f15,definition,( 24.89/4.11 ($true = sP0) <=> ? [X103 : (term > $o),X104 : term] : (($true != ((X103 @ X104))) & ! [X106 : term,X105 : term] : (($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106)))) | ($true != ((X103 @ X106)))) & ! [X107 : term] : (($true != ((X103 @ X107))) | ($true = ((X103 @ (lam @ X107))))) & ! [X108 : term] : (($true != ((var @ X108))) | ($true = ((X103 @ X108)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f16,definition,( 24.89/4.11 ($true = sP1) <=> (! [X111 : term,X109 : (term > $o),X110 : subst] : (? [X116 : term,X115 : term] : (($true = ((X109 @ X115))) & ($true != ((X109 @ (ap @ X116 @ X115)))) & ($true = ((X109 @ X116)))) | ($true = ((X109 @ (sub @ X111 @ X110)))) | ? [X112 : term] : (($true != ((X109 @ (lam @ X112)))) & ! [X113 : term] : (($true != ((X109 @ X113))) | ($true = ((X109 @ (sub @ X112 @ (push @ X113 @ id))))))) | ? [X114 : term] : ((((X109 @ (sub @ X114 @ X110))) != $true) & ($true = ((var @ X114))))) | ? [X102 : subst] : (((comp @ X102 @ id)) != X102) | ? [X98 : term,X99 : subst] : (((sub @ one @ (push @ X98 @ X99))) != X98) | ? [X101 : term,X100 : subst] : (((comp @ sh @ (push @ X101 @ X100))) != X100) | ($true = sP0))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f17,definition,( 24.89/4.11 ! [X512 : (subst > term > subst > $o)] : (($true = ((sP2 @ X512))) <=> ? [X515 : (subst > term > term)] : (($true != ((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id))) & ! [X519 : term] : (($true != ((X512 @ id @ X519 @ id))) | ($true = ((X512 @ id @ (X515 @ id @ X519) @ id)))) & ! [X516 : term,X518 : subst,X517 : subst] : (((sub @ (X515 @ X517 @ X516) @ X518)) = ((X515 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f18,definition,( 24.89/4.11 ($true = sP3) <=> ? [X353 : term,X354 : (term > $o)] : (($true != ((X354 @ X353))) & ! [X355 : term] : (($true != ((var @ X355))) | ($true = ((X354 @ X355)))) & ! [X358 : term] : (? [X359 : term] : (($true != ((X354 @ (sub @ X358 @ (push @ X359 @ id))))) & ($true = ((X354 @ X359)))) | ($true = ((X354 @ (lam @ X358))))) & ! [X356 : term,X357 : term] : (($true != ((X354 @ X356))) | ($true != ((X354 @ X357))) | ($true = ((X354 @ (ap @ X357 @ X356))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f19,definition,( 24.89/4.11 ($true = sP4) <=> ! [X372 : (subst > term > subst > $o),X371 : term] : (($true = ((X372 @ id @ X371 @ id))) | ? [X375 : (subst > term > term)] : (! [X376 : term] : ((((X372 @ id @ X376 @ id)) != $true) | ($true = ((X372 @ id @ (X375 @ id @ X376) @ id)))) & ($true != ((X372 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X379 : subst,X377 : term,X378 : subst] : (((sub @ (X375 @ X378 @ X377) @ X379)) = ((X375 @ (comp @ X378 @ X379) @ (sub @ X377 @ X379))))) | ? [X374 : term,X373 : term] : (($true != ((X372 @ id @ (ap @ (sub @ X373 @ id) @ X374) @ id))) & ($true = ((X372 @ id @ X373 @ id))) & ($true = ((X372 @ id @ X374 @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f20,definition,( 24.89/4.11 ($true = sP5) <=> ! [X217 : subst,X219 : term,X218 : (term > $o)] : (($true = ((X218 @ (sub @ X219 @ X217)))) | ? [X220 : term] : (! [X221 : term] : (($true != ((X218 @ X221))) | ($true = ((X218 @ (sub @ X220 @ (push @ X221 @ id)))))) & (((X218 @ (lam @ X220))) != $true)) | ? [X224 : term] : (($true = ((var @ X224))) & ($true != ((X218 @ (sub @ X224 @ X217))))) | ? [X223 : term,X222 : term] : (($true = ((X218 @ X223))) & ($true = ((X218 @ X222))) & ($true != ((X218 @ (ap @ X222 @ X223))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f21,definition,( 24.89/4.11 ($true = sP6) <=> ! [X118 : (term > $o),X117 : term] : (($true = ((X118 @ X117))) | ? [X123 : term,X122 : term] : (($true = ((X118 @ X122))) & ($true != ((X118 @ (ap @ X122 @ X123)))) & ($true = ((X118 @ X123)))) | ? [X119 : term] : (($true != ((X118 @ (lam @ X119)))) & ! [X120 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X120 @ id))))) | ($true != ((X118 @ X120))))) | ? [X121 : term] : ((((var @ X121)) = $true) & ($true != ((X118 @ X121)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f22,definition,( 24.89/4.11 ! [X458 : (subst > term > subst > $o)] : (($true = ((sP7 @ X458))) <=> ? [X465 : term,X466 : term] : (($true != ((X458 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id))) & ($true = ((X458 @ id @ X465 @ id))) & ($true = ((X458 @ id @ X466 @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f23,definition,( 24.89/4.11 ! [X458 : (subst > term > subst > $o)] : (($true = ((sP8 @ X458))) <=> ? [X471 : (subst > term > term)] : (! [X472 : term] : (($true != ((X458 @ id @ X472 @ id))) | ($true = ((X458 @ id @ (X471 @ id @ X472) @ id)))) & ($true != ((X458 @ id @ (lam @ (X471 @ sh @ one)) @ id))) & ! [X475 : subst,X473 : subst,X474 : term] : (((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475))) = ((sub @ (X471 @ X473 @ X474) @ X475)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f24,definition,( 24.89/4.11 ($true = sP9) <=> ! [X203 : (term > $o),X202 : (subst > term > subst > $o),X205 : term,X204 : term] : (($true = ((X203 @ (ap @ X205 @ X204)))) | ? [X207 : subst,X208 : term,X209 : subst,X210 : subst] : (($true != ((X202 @ (comp @ X210 @ X207) @ (sub @ X208 @ X207) @ X209))) & ($true = ((X202 @ X210 @ X208 @ (comp @ X207 @ X209))))) | ? [X206 : term] : (((X202 @ id @ X206 @ id)) != ((X203 @ X206))) | ? [X214 : subst,X211 : subst,X213 : subst,X212 : term] : (($true = ((X202 @ (comp @ X214 @ X213) @ (sub @ X212 @ X213) @ X211))) & ($true != ((X202 @ X214 @ X212 @ (comp @ X213 @ X211))))) | ($true != ((X203 @ X204))) | ($true != ((X203 @ X205))) | ? [X216 : term,X215 : term] : (($true = ((X202 @ id @ X216 @ id))) & ($true = ((X202 @ id @ X215 @ id))) & ($true != ((X202 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f25,definition,( 24.89/4.11 ! [X186 : (subst > term > subst > $o)] : (($true = ((sP10 @ X186))) <=> ? [X188 : (subst > term > term)] : (! [X191 : subst,X190 : term,X192 : subst] : (((X188 @ (comp @ X191 @ X192) @ (sub @ X190 @ X192))) = ((sub @ (X188 @ X191 @ X190) @ X192))) & ($true != ((X186 @ id @ (lam @ (X188 @ sh @ one)) @ id))) & ! [X189 : term] : (($true = ((X186 @ id @ (X188 @ id @ X189) @ id))) | ($true != ((X186 @ id @ X189 @ id))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f26,definition,( 24.89/4.11 ($true = sP11) <=> ? [X228 : subst,X227 : (term > $o),X226 : term] : (! [X232 : term] : (? [X233 : term] : (($true = ((X227 @ X233))) & ($true != ((X227 @ (sub @ X232 @ (push @ X233 @ id)))))) | ($true = ((X227 @ (lam @ X232))))) & ! [X230 : term,X229 : term] : (($true != ((X227 @ X230))) | ($true = ((X227 @ (ap @ X230 @ X229)))) | ($true != ((X227 @ X229)))) & ! [X231 : term] : (($true = ((X227 @ (sub @ X231 @ X228)))) | ($true != ((var @ X231)))) & ($true != ((X227 @ (sub @ X226 @ X228)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f27,definition,( 24.89/4.11 ($true = sP12) <=> (($true = sP11) | ? [X225 : term] : (((sub @ X225 @ id)) != X225) | ! [X235 : (term > $o),X234 : term] : (? [X240 : term,X239 : term] : (($true != ((X235 @ (ap @ X239 @ X240)))) & ($true = ((X235 @ X240))) & ($true = ((X235 @ X239)))) | ? [X236 : term] : (! [X237 : term] : (($true != ((X235 @ X237))) | ($true = ((X235 @ (sub @ X236 @ (push @ X237 @ id)))))) & ($true != ((X235 @ (lam @ X236))))) | ($true = ((X235 @ X234))) | ? [X238 : term] : (($true != ((X235 @ X238))) & ($true = ((var @ X238))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f28,definition,( 24.89/4.11 ! [X58 : (subst > term > subst > $o)] : (($true = ((sP13 @ X58))) <=> ? [X60 : (subst > term > term)] : (! [X61 : term] : (($true = ((X58 @ id @ (X60 @ id @ X61) @ id))) | ($true != ((X58 @ id @ X61 @ id)))) & ($true != ((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id))) & ! [X63 : subst,X64 : subst,X62 : term] : (((sub @ (X60 @ X64 @ X62) @ X63)) = ((X60 @ (comp @ X64 @ X63) @ (sub @ X62 @ X63))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f29,definition,( 24.89/4.11 ! [X58 : (subst > term > subst > $o)] : (($true = ((sP14 @ X58))) <=> ? [X66 : term,X65 : term] : (($true = ((X58 @ id @ X66 @ id))) & ($true = ((X58 @ id @ X65 @ id))) & ($true != ((X58 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f30,definition,( 24.89/4.11 ($true = sP15) <=> ? [X39 : term,X40 : (term > $o)] : (! [X43 : term] : (($true != ((var @ X43))) | ($true = ((X40 @ X43)))) & ! [X44 : term,X45 : term] : (($true != ((X40 @ X44))) | ($true = ((X40 @ (ap @ X44 @ X45)))) | ($true != ((X40 @ X45)))) & ($true != ((X40 @ X39))) & ! [X41 : term] : (? [X42 : term] : (($true != ((X40 @ (sub @ X41 @ (push @ X42 @ id))))) & ($true = ((X40 @ X42)))) | ($true = ((X40 @ (lam @ X41))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f31,definition,( 24.89/4.11 ($true = sP16) <=> ! [X58 : (subst > term > subst > $o),X57 : term] : (($true = ((X58 @ id @ X57 @ id))) | ($true = ((sP14 @ X58))) | ? [X69 : subst,X70 : subst,X67 : term,X68 : subst] : (($true != ((X58 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69))) & ($true = ((X58 @ X68 @ X67 @ (comp @ X70 @ X69))))) | ? [X73 : term,X72 : subst,X74 : subst,X71 : subst] : (($true = ((X58 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71) @ X74))) & ($true != ((X58 @ X72 @ X73 @ (comp @ X71 @ X74))))) | ? [X59 : term] : (($true = ((var @ (sub @ X59 @ id)))) & ($true != ((X58 @ id @ X59 @ id)))) | ($true = ((sP13 @ X58))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f32,definition,( 24.89/4.11 ! [X285 : (subst > term > subst > $o)] : (($true = ((sP17 @ X285))) <=> ! [X296 : (subst > term > term)] : (? [X299 : subst,X300 : subst,X298 : term] : (((X296 @ (comp @ X299 @ X300) @ (sub @ X298 @ X300))) != ((sub @ (X296 @ X299 @ X298) @ X300))) | ($true = ((X285 @ id @ (lam @ (X296 @ sh @ one)) @ id))) | ? [X297 : term] : (($true != ((X285 @ id @ (X296 @ id @ X297) @ id))) & ($true = ((X285 @ id @ X297 @ id))))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f33,definition,( 24.89/4.11 ! [X302 : (subst > term > subst > $o)] : (($true = ((sP18 @ X302))) <=> ? [X303 : (subst > term > term)] : (! [X304 : term,X306 : subst,X305 : subst] : (((X303 @ (comp @ X306 @ X305) @ (sub @ X304 @ X305))) = ((sub @ (X303 @ X306 @ X304) @ X305))) & ! [X307 : term] : (($true = ((X302 @ id @ (X303 @ id @ X307) @ id))) | ($true != ((X302 @ id @ X307 @ id)))) & ($true != ((X302 @ id @ (lam @ (X303 @ sh @ one)) @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f34,definition,( 24.89/4.11 ! [X302 : (subst > term > subst > $o)] : (($true = ((sP19 @ X302))) <=> ? [X312 : term,X313 : term] : (($true != ((X302 @ id @ (ap @ (sub @ X312 @ id) @ X313) @ id))) & ($true = ((X302 @ id @ X312 @ id))) & ($true = ((X302 @ id @ X313 @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f35,definition,( 24.89/4.11 ($true = sP20) <=> ? [X274 : (subst > term > subst > $o),X272 : term,X273 : term] : (($true = ((X274 @ id @ X272 @ id))) & ($true != ((X274 @ id @ (ap @ X273 @ X272) @ id))) & ! [X282 : subst,X279 : subst,X280 : subst,X281 : term] : (($true != ((X274 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280) @ X279))) | ($true = ((X274 @ X282 @ X281 @ (comp @ X280 @ X279))))) & ($true = ((X274 @ id @ X273 @ id))) & ! [X277 : subst,X275 : subst,X278 : subst,X276 : term] : (($true != ((X274 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X274 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275)))) & ! [X283 : term,X284 : term] : (($true != ((X274 @ id @ X284 @ id))) | ($true != ((X274 @ id @ X283 @ id))) | ($true = ((X274 @ id @ (ap @ (sub @ X283 @ id) @ X284) @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f36,definition,( 24.89/4.11 ($true = sP21) <=> ? [X266 : term,X265 : (term > $o)] : (! [X268 : term] : (? [X269 : term] : (($true = ((X265 @ X269))) & ($true != ((X265 @ (sub @ X268 @ (push @ X269 @ id)))))) | ($true = ((X265 @ (lam @ X268))))) & ! [X271 : term,X270 : term] : (($true != ((X265 @ X270))) | ($true != ((X265 @ X271))) | ($true = ((X265 @ (ap @ X270 @ X271))))) & ! [X267 : term] : (($true = ((X265 @ X267))) | ($true != ((var @ X267)))) & ($true != ((X265 @ X266))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f37,definition,( 24.89/4.11 ($true = sP22) <=> ! [X302 : (subst > term > subst > $o),X301 : term] : (? [X314 : term] : (($true = ((var @ (sub @ X314 @ id)))) & ($true != ((X302 @ id @ X314 @ id)))) | ? [X308 : subst,X309 : subst,X311 : subst,X310 : term] : (($true = ((X302 @ X311 @ X310 @ (comp @ X308 @ X309)))) & ($true != ((X302 @ (comp @ X311 @ X308) @ (sub @ X310 @ X308) @ X309)))) | ($true = ((sP19 @ X302))) | ? [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true = ((X302 @ (comp @ X317 @ X315) @ (sub @ X318 @ X315) @ X316))) & ($true != ((X302 @ X317 @ X318 @ (comp @ X315 @ X316))))) | ($true = ((sP18 @ X302))) | ($true = ((X302 @ id @ X301 @ id))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f38,definition,( 24.89/4.11 ! [X170 : (subst > term > subst > $o)] : (($true = ((sP23 @ X170))) <=> ? [X176 : (subst > term > term)] : (! [X178 : subst,X180 : term,X179 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true = ((X170 @ id @ (X176 @ id @ X177) @ id))) | ($true != ((X170 @ id @ X177 @ id)))) & ($true != ((X170 @ id @ (lam @ (X176 @ sh @ one)) @ id)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f39,definition,( 24.89/4.11 ($true = sP24) <=> ! [X171 : term,X170 : (subst > term > subst > $o)] : (? [X181 : term] : (($true = ((X170 @ id @ X181 @ id))) & ($true != ((X170 @ id @ (sub @ X171 @ (push @ X181 @ id)) @ id)))) | ($true = ((sP23 @ X170))) | ? [X185 : subst,X184 : subst,X182 : subst,X183 : term] : (($true != ((X170 @ (comp @ X182 @ X185) @ (sub @ X183 @ X185) @ X184))) & ($true = ((X170 @ X182 @ X183 @ (comp @ X185 @ X184))))) | (((X170 @ id @ (lam @ X171) @ id)) = $true) | ? [X175 : subst,X173 : subst,X174 : term,X172 : subst] : (($true != ((X170 @ X173 @ X174 @ (comp @ X172 @ X175)))) & ($true = ((X170 @ (comp @ X173 @ X172) @ (sub @ X174 @ X172) @ X175)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f40,definition,( 24.89/4.11 ($true = sP25) <=> ! [X257 : term,X258 : (subst > term > subst > $o)] : ((((X258 @ id @ (lam @ X257) @ id)) = $true) | ? [X264 : term] : ((((X258 @ id @ (sub @ X257 @ (push @ X264 @ id)) @ id)) != $true) & ($true = ((X258 @ id @ X264 @ id)))) | ? [X259 : (subst > term > term)] : (($true != ((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id))) & ! [X260 : term] : (($true != ((X258 @ id @ X260 @ id))) | ($true = ((X258 @ id @ (X259 @ id @ X260) @ id)))) & ! [X262 : subst,X261 : term,X263 : subst] : (((X259 @ (comp @ X263 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X263 @ X261) @ X262)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f41,definition,( 24.89/4.11 ! [X320 : (subst > term > subst > $o)] : (($true = ((sP26 @ X320))) <=> ? [X333 : (subst > term > term)] : (($true != ((X320 @ id @ (lam @ (X333 @ sh @ one)) @ id))) & ! [X337 : term] : (($true = ((X320 @ id @ (X333 @ id @ X337) @ id))) | ($true != ((X320 @ id @ X337 @ id)))) & ! [X334 : term,X335 : subst,X336 : subst] : (((X333 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ (X333 @ X335 @ X334) @ X336)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f42,definition,( 24.89/4.11 ($true = sP27) <=> ! [X410 : term,X411 : (subst > term > subst > $o),X412 : term] : (($true = ((X411 @ id @ (ap @ X410 @ X412) @ id))) | ? [X420 : subst,X417 : term,X418 : subst,X419 : subst] : (($true = ((X411 @ X418 @ X417 @ (comp @ X420 @ X419)))) & ($true != ((X411 @ (comp @ X418 @ X420) @ (sub @ X417 @ X420) @ X419)))) | ($true != ((X411 @ id @ X412 @ id))) | ? [X422 : term,X421 : term] : (($true != ((X411 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) & ($true = ((X411 @ id @ X422 @ id))) & ($true = ((X411 @ id @ X421 @ id)))) | ($true != ((X411 @ id @ X410 @ id))) | ? [X416 : subst,X413 : term,X415 : subst,X414 : subst] : (($true != ((X411 @ X414 @ X413 @ (comp @ X415 @ X416)))) & ($true = ((X411 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415) @ X416)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 24.89/4.11 thf(f43,plain,( 24.89/4.11 ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & (! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) <=> (axvarcons = $true)) & (((d2subst @ d_id)) = id) & (axvarshift = $true) & (! [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true) | ? [X382 : term] : (($true = ((X380 @ id @ X382 @ id))) & ($true != ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) | ? [X383 : (subst > term > term)] : (! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))) & ! [X387 : term] : (($true = ((X380 @ id @ (X383 @ id @ X387) @ id))) | ($true != ((X380 @ id @ X387 @ id)))) & ($true != ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP27) <=> (hoasinduction_lem2 = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)) | ? [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) = ((ap @ X392 @ X390))) & (X389 != X392)) | ? [X388 : term] : (((sub @ X388 @ id)) != X388))) & (hoasapnotvar = $true) & (axabs = $true) & ! [X404 : d_subst,X403 : d_subst] : ((X403 = X404) | (((d2subst @ X403)) != ((d2subst @ X404)))) & ((axidr = $true) <=> ! [X423 : subst] : (((comp @ X423 @ id)) = X423)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true = ((X321 @ (lam @ X322)))) | ? [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true != ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) & ($true = ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) | ? [X327 : term] : (((X321 @ X327)) != ((X320 @ id @ X327 @ id))) | ? [X328 : term] : (($true = ((X321 @ X328))) & ($true != ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ? [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true != ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) & ($true = ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ($true = ((sP26 @ X320)))) | ? [X319 : term] : (((sub @ X319 @ id)) != X319)) <=> (hoasinduction_lem3v2_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((? [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) != X449) | ! [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (? [X455 : term] : (((X452 @ X455)) != ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) | ($true != ((X451 @ X454))) | ($true = ((X452 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true != ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) <=> (apinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X250 : term,X249 : (subst > term > subst > $o)] : (($true != ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) & ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ($true != ((X249 @ id @ X256 @ id)))) & ! [X251 : (subst > term > term)] : (($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) | ? [X255 : term] : (($true = ((X249 @ id @ X255 @ id))) & ($true != ((X249 @ id @ (X251 @ id @ X255) @ id)))) | ? [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) != ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))))) | ($true = sP25) | ? [X248 : term] : (((sub @ X248 @ id)) != X248))) & ((hoasinduction_lem3aa = $true) <=> ! [X493 : term,X492 : (subst > term > subst > $o)] : (? [X494 : (subst > term > term)] : (($true != ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498))) & ! [X495 : term] : (($true != ((X492 @ id @ X495 @ id))) | ($true = ((X492 @ id @ (X494 @ id @ X495) @ id))))) | ($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ? [X499 : term] : (($true = ((X492 @ id @ X499 @ id))) & ($true != ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((($true = sP24) | ? [X161 : term] : (((sub @ X161 @ id)) != X161) | ? [X163 : term,X162 : (subst > term > subst > $o)] : (! [X164 : (subst > term > term)] : (? [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) != ((sub @ (X164 @ X167 @ X165) @ X166))) | ($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ? [X168 : term] : (($true != ((X162 @ id @ (X164 @ id @ X168) @ id))) & ($true = ((X162 @ id @ X168 @ id))))) & ! [X169 : term] : (($true != ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) & ($true != ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm = $true) <=> (($true = sP22) | ($true = sP21) | ($true = sP20) | ? [X285 : (subst > term > subst > $o),X286 : term] : (! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ($true != ((X285 @ id @ X291 @ id)))) & ($true = ((sP17 @ X285))) & ! [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) | ($true != ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) & ! [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) | ($true != ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) & ($true != ((X285 @ id @ (lam @ X286) @ id)))))) & ((? [X129 : term] : ! [X130 : (subst > term > term)] : ? [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) != ((sub @ X129 @ (push @ X132 @ X131)))) | ? [X133 : term] : (((sub @ X133 @ id)) != X133) | ! [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (? [X142 : term] : (((X136 @ id @ X142 @ id)) != ((X135 @ X142))) | ? [X137 : (subst > term > term)] : (($true != ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) & ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ($true != ((X136 @ id @ X141 @ id)))) & ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139)))) | ? [X143 : term] : (($true = ((X135 @ X143))) & ($true != ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ($true = ((X135 @ (lam @ X134)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj = $true) <=> ! [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | (((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ? [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) != ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) | ? [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) != ((sub @ (X152 @ X157 @ X156) @ X158))))) & (hoasapinj2_gthm = $true) & ((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) <=> (substmonoid = $true)) & (axclos = $true) & (! [X243 : (term > $o),X244 : subst,X245 : term] : ? [X246 : (term > $o)] : ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X477 : term,X478 : term,X476 : (subst > term > term)] : (? [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) != ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (pushprop_lem3v2_lthm = $true) & ((? [X529 : subst] : (((comp @ id @ X529)) != X529) | ? [X530 : subst] : (((comp @ X530 @ id)) != X530) | (! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531))) <=> (substmonoid_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & ((axscons = $true) <=> ! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148)) & (hoasinduction_lem1v2_gthm = $true) & (apnotvar = $true) & ((? [X36 : (subst > term > subst > $o)] : ! [X37 : (term > $o)] : ? [X38 : term] : (((X37 @ X38)) != ((X36 @ id @ X38 @ id))) | ($true = sP16) | ? [X46 : term] : (((sub @ X46 @ id)) != X46) | ($true = sP15) | ? [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (! [X50 : (subst > term > term)] : (? [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) != ((sub @ (X50 @ X52 @ X51) @ X53))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | ? [X54 : term] : (($true = ((X47 @ id @ X54 @ id))) & ($true != ((X47 @ id @ (X50 @ id @ X54) @ id))))) & ! [X55 : term] : (($true != ((X49 @ X55))) | ($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) & ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id))) & ($true != ((X49 @ (lam @ X48)))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X400 : (subst > term > subst > $o)] : ? [X401 : (term > $o)] : ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id)))) & (! [X509 : term] : ? [X510 : (subst > term > term)] : (((X510 @ sh @ one)) = ((sub @ X509 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoaslamnotap_lthm = $true) & (($true = sP12) <=> (induction2_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (? [X537 : term] : (((X534 @ X537)) != ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) | ($true = ((X534 @ one))) | ($true != ((X536 @ X535))))) & (! [X187 : term,X186 : (subst > term > subst > $o)] : (? [X197 : term] : (($true = ((X186 @ id @ X197 @ id))) & ($true != ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ? [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true != ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) & ($true = ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) | ? [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true = ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) & ($true != ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) | ($true = ((X186 @ id @ (lam @ X187) @ id))) | ($true = ((sP10 @ X186)))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem3v2_gthm = $true) & (($true = sP9) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) <=> ! [X424 : subst] : (((comp @ id @ X424)) = X424)) & (lamnotap != $true) & ((induction = $true) <=> ! [X432 : (term > $o),X431 : term] : (? [X436 : term] : (($true != ((X432 @ X436))) & ($true = ((var @ X436)))) | ($true = ((X432 @ X431))) | ? [X433 : term] : (($true = ((X432 @ X433))) & ($true != ((X432 @ (lam @ X433))))) | ? [X435 : term,X434 : term] : (($true = ((X432 @ X434))) & ($true != ((X432 @ (ap @ X435 @ X434)))) & ($true = ((X432 @ X435)))))) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X482 : term] : ? [X483 : (subst > term > term)] : ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((axshiftcons = $true) <=> ! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538)) & (! [X347 : (subst > term > subst > $o)] : ? [X348 : (term > $o)] : ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349))) <=> (hoasinduction_lem0 = $true)) & (pushprop = $true) & ((hoasinduction = $true) <=> ! [X459 : term,X458 : (subst > term > subst > $o)] : (($true = ((sP8 @ X458))) | ? [X460 : term] : (($true = ((var @ (sub @ X460 @ id)))) & ($true != ((X458 @ id @ X460 @ id)))) | ($true = ((sP7 @ X458))) | ($true = ((X458 @ id @ X459 @ id))) | ? [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true = ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) & ($true != ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) | ? [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true != ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) & ($true = ((X458 @ X461 @ X464 @ (comp @ X462 @ X463))))))) & (hoasinduction_lem1_lthm = $true) & ((induction2 = $true) <=> ($true = sP6)) & (! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) <=> (shinj = $true)) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) <=> (axvarid = $true)) & (hoasinduction_lem1 = $true) & (axapp = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & ((termmset = $true) <=> ! [X399 : term] : (((sub @ X399 @ id)) = X399)) & ! [X491 : d_term] : (d_one = X491) & (($true = sP5) <=> (induction2lem = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X8 : term] : ? [X9 : (subst > term > term)] : (((X9 @ sh @ one)) = ((sub @ X8 @ (push @ one @ sh))))) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) <=> ! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11))) & ! [X500 : d_subst] : (d_id = X500) & (ulamvarind = $true) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axmap = $true) & ((hoaslaminj_lthm = $true) <=> (? [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) != X14) | ? [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) != X12) | ? [X17 : term,X16 : term] : ((((lam @ X17)) = ((lam @ X16))) & (X16 != X17)) | ! [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (? [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) != ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21))) | ? [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) != ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23))))))) & (hoaslamnotvar_lthm = $true) & ((? [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true != ((X361 @ (lam @ X362)))) & ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) & ! [X370 : term] : (($true != ((X361 @ X370))) | ($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) & ! [X365 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ? [X369 : term] : (($true != ((X363 @ id @ (X365 @ id @ X369) @ id))) & ($true = ((X363 @ id @ X369 @ id)))) | ? [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) != ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) | ($true = sP3) | ($true = sP4) | ? [X350 : (subst > term > subst > $o)] : ! [X351 : (term > $o)] : ? [X352 : term] : (((X350 @ id @ X352 @ id)) != ((X351 @ X352))) | ? [X360 : term] : (((sub @ X360 @ id)) != X360)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X438 : (subst > term > subst > $o),X437 : term] : (($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ? [X448 : term] : (($true != ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) & ($true = ((X438 @ id @ X448 @ id)))) | ? [X440 : term,X439 : (subst > term > term)] : (! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ($true != ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) & ! [X441 : term] : (($true != ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id)))) & ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444)))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X7 : d_term,X6 : d_term] : ((X6 = X7) | (((d2term @ X7)) != ((d2term @ X6)))) & ((hoasapinj1 = $true) <=> ! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128))) & (hoaslamnotap_gthm = $true) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & (pushprop_gthm = $true) & (hoasinduction_gthm = $true) & (! [X486 : (term > $o),X487 : subst,X488 : term] : ? [X489 : (term > $o)] : ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490))) <=> (pushprop_lem0_lthm = $true)) & ((? [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) != X87) | ! [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true != ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85)) <=> (pushprop_lem1_lthm = $true)) & (! [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (? [X514 : term] : (($true = ((X513 @ X514))) & ($true != ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) | ($true = ((sP2 @ X512))) | ? [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true != ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) & ($true = ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) | ? [X524 : term] : (((X513 @ X524)) != ((X512 @ id @ X524 @ id))) | ($true = ((X513 @ (lam @ X511)))) | ? [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true = ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) & (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasapinj2 = $true) <=> ! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1))))) & ((hoasapinj2_lthm = $true) <=> (? [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 != X29) & (((ap @ X30 @ X28)) = ((ap @ X31 @ X29)))) | ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35)))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X502 : (subst > term > subst > $o),X501 : term] : (($true = ((X502 @ id @ (lam @ X501) @ id))) | ? [X508 : term] : (($true = ((X502 @ id @ X508 @ id))) & ($true != ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) | ? [X503 : (subst > term > term)] : (! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) & ! [X507 : term] : (($true != ((X502 @ id @ X507 @ id))) | ($true = ((X502 @ id @ (X503 @ id @ X507) @ id)))) & ($true != ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id)))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true = ((X75 @ (lam @ X77)))) | ? [X78 : term] : (((X76 @ id @ X78 @ id)) != ((X75 @ X78))) | ? [X79 : term] : (($true != ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) & ($true = ((X75 @ X79)))) | ? [X80 : (subst > term > term)] : (! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X76 @ id @ X81 @ id)))) & ($true != ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) & ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82)))))) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X144 : term] : ? [X145 : (subst > term > term)] : ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147)))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X342 : (subst > term > term)] : (($true != ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) & ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ($true != ((X339 @ id @ X346 @ id)))) & ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343)))) | ? [X341 : term,X340 : term] : (($true != ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) & ($true = ((X339 @ id @ X340 @ id))) & ($true = ((X339 @ id @ X341 @ id)))) | ($true = ((X339 @ id @ X338 @ id))))) & (hoaslamnotvar = $true) & ((! [X5 : term] : (((sub @ X5 @ id)) = X5) | ? [X4 : term] : (((sub @ X4 @ id)) != X4)) <=> (termmset_lthm = $true)) & (lamnotvar = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((apinj1 = $true) <=> ! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429))))) & ((induction2lem_lthm = $true) <=> ($true = sP1))), 24.89/4.11 inference(definition_folding,[],[f12,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15])). 24.89/4.11 thf(f130,plain,( 24.89/4.11 ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & ((! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) != X241))) & (((d2subst @ d_id)) = id) & (axvarshift = $true) & ((! [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true) | ? [X382 : term] : (($true = ((X380 @ id @ X382 @ id))) & ($true != ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) | ? [X383 : (subst > term > term)] : (! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))) & ! [X387 : term] : (($true = ((X380 @ id @ (X383 @ id @ X387) @ id))) | ($true != ((X380 @ id @ X387 @ id)))) & ($true != ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) != $true) & ! [X382 : term] : (($true != ((X380 @ id @ X382 @ id))) | ($true = ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) & ! [X383 : (subst > term > term)] : (? [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) != ((sub @ (X383 @ X385 @ X386) @ X384))) | ? [X387 : term] : (($true != ((X380 @ id @ (X383 @ id @ X387) @ id))) & ($true = ((X380 @ id @ X387 @ id)))) | ($true = ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))))))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((($true = sP27) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP27))) & (((hoasapinj1_lthm = $true) | (? [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) = ((ap @ (sub @ X395 @ id) @ X396))) & (X394 != X395)) & ! [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) != ((ap @ X392 @ X390))) | (X389 = X392)) & ! [X388 : term] : (((sub @ X388 @ id)) = X388))) & ((! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)) | ? [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) = ((ap @ X392 @ X390))) & (X389 != X392)) | ? [X388 : term] : (((sub @ X388 @ id)) != X388)) | (hoasapinj1_lthm != $true))) & (hoasapnotvar = $true) & (axabs = $true) & ! [X404 : d_subst,X403 : d_subst] : ((X403 = X404) | (((d2subst @ X403)) != ((d2subst @ X404)))) & (((axidr = $true) | ? [X423 : subst] : (((comp @ X423 @ id)) != X423)) & (! [X423 : subst] : (((comp @ X423 @ id)) = X423) | (axidr != $true))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((! [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true = ((X321 @ (lam @ X322)))) | ? [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true != ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) & ($true = ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) | ? [X327 : term] : (((X321 @ X327)) != ((X320 @ id @ X327 @ id))) | ? [X328 : term] : (($true = ((X321 @ X328))) & ($true != ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ? [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true != ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) & ($true = ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ($true = ((sP26 @ X320)))) | ? [X319 : term] : (((sub @ X319 @ id)) != X319)) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (? [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true != ((X321 @ (lam @ X322)))) & ! [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true = ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) | ($true != ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) & ! [X327 : term] : (((X321 @ X327)) = ((X320 @ id @ X327 @ id))) & ! [X328 : term] : (($true != ((X321 @ X328))) | ($true = ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) & ! [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true = ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) | ($true != ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) & ($true != ((sP26 @ X320)))) & ! [X319 : term] : (((sub @ X319 @ id)) = X319)))) & (pushprop_lem2v2_gthm = $true) & (((? [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) != X449) | ! [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (? [X455 : term] : (((X452 @ X455)) != ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) | ($true != ((X451 @ X454))) | ($true = ((X452 @ one))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) = X449) & ? [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (! [X455 : term] : (((X452 @ X455)) = ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) & ($true = ((X451 @ X454))) & ($true != ((X452 @ one))))))) & (((pushprop_lem1 = $true) | ? [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true = ((X407 @ X408))) & ($true != ((X409 @ (sub @ X408 @ (push @ X405 @ X406))))))) & (! [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true != ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406)))))) | (pushprop_lem1 != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 != X97) & (((ap @ X96 @ X97)) = ((ap @ X94 @ X95)))))) & (((hoasinduction_lem3a_lthm = $true) | (! [X250 : term,X249 : (subst > term > subst > $o)] : (($true = ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) | ? [X256 : term] : (($true != ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) & ($true = ((X249 @ id @ X256 @ id)))) | ? [X251 : (subst > term > term)] : (($true != ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) & ! [X255 : term] : (($true != ((X249 @ id @ X255 @ id))) | ($true = ((X249 @ id @ (X251 @ id @ X255) @ id)))) & ! [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) = ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))))) & ($true != sP25) & ! [X248 : term] : (((sub @ X248 @ id)) = X248))) & ((? [X250 : term,X249 : (subst > term > subst > $o)] : (($true != ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) & ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ($true != ((X249 @ id @ X256 @ id)))) & ! [X251 : (subst > term > term)] : (($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) | ? [X255 : term] : (($true = ((X249 @ id @ X255 @ id))) & ($true != ((X249 @ id @ (X251 @ id @ X255) @ id)))) | ? [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) != ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))))) | ($true = sP25) | ? [X248 : term] : (((sub @ X248 @ id)) != X248)) | (hoasinduction_lem3a_lthm != $true))) & (((hoasinduction_lem3aa = $true) | ? [X493 : term,X492 : (subst > term > subst > $o)] : (! [X494 : (subst > term > term)] : (($true = ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) | ? [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) != ((sub @ (X494 @ X496 @ X497) @ X498))) | ? [X495 : term] : (($true = ((X492 @ id @ X495 @ id))) & ($true != ((X492 @ id @ (X494 @ id @ X495) @ id))))) & ($true != ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) & ! [X499 : term] : (($true != ((X492 @ id @ X499 @ id))) | ($true = ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & (! [X493 : term,X492 : (subst > term > subst > $o)] : (? [X494 : (subst > term > term)] : (($true != ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498))) & ! [X495 : term] : (($true != ((X492 @ id @ X495 @ id))) | ($true = ((X492 @ id @ (X494 @ id @ X495) @ id))))) | ($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ? [X499 : term] : (($true = ((X492 @ id @ X499 @ id))) & ($true != ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id))))) | (hoasinduction_lem3aa != $true))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((($true = sP24) | ? [X161 : term] : (((sub @ X161 @ id)) != X161) | ? [X163 : term,X162 : (subst > term > subst > $o)] : (! [X164 : (subst > term > term)] : (? [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) != ((sub @ (X164 @ X167 @ X165) @ X166))) | ($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ? [X168 : term] : (($true != ((X162 @ id @ (X164 @ id @ X168) @ id))) & ($true = ((X162 @ id @ X168 @ id))))) & ! [X169 : term] : (($true != ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) & ($true != ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id))))) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP24) & ! [X161 : term] : (((sub @ X161 @ id)) = X161) & ! [X163 : term,X162 : (subst > term > subst > $o)] : (? [X164 : (subst > term > term)] : (! [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) = ((sub @ (X164 @ X167 @ X165) @ X166))) & ($true != ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) & ! [X168 : term] : (($true = ((X162 @ id @ (X164 @ id @ X168) @ id))) | ($true != ((X162 @ id @ X168 @ id))))) | ? [X169 : term] : (($true = ((X162 @ id @ X169 @ id))) & ($true != ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) | ($true = ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id))))))) & (hoaslamnotvar_gthm = $true) & (((hoasinduction_lthm = $true) | (($true != sP22) & ($true != sP21) & ($true != sP20) & ! [X285 : (subst > term > subst > $o),X286 : term] : (? [X291 : term] : (($true != ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) & ($true = ((X285 @ id @ X291 @ id)))) | ($true != ((sP17 @ X285))) | ? [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true != ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) & ($true = ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) | ? [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true != ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) & ($true = ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) | ($true = ((X285 @ id @ (lam @ X286) @ id)))))) & ((($true = sP22) | ($true = sP21) | ($true = sP20) | ? [X285 : (subst > term > subst > $o),X286 : term] : (! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ($true != ((X285 @ id @ X291 @ id)))) & ($true = ((sP17 @ X285))) & ! [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) | ($true != ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) & ! [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) | ($true != ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) & ($true != ((X285 @ id @ (lam @ X286) @ id))))) | (hoasinduction_lthm != $true))) & (((? [X129 : term] : ! [X130 : (subst > term > term)] : ? [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) != ((sub @ X129 @ (push @ X132 @ X131)))) | ? [X133 : term] : (((sub @ X133 @ id)) != X133) | ! [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (? [X142 : term] : (((X136 @ id @ X142 @ id)) != ((X135 @ X142))) | ? [X137 : (subst > term > term)] : (($true != ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) & ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ($true != ((X136 @ id @ X141 @ id)))) & ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139)))) | ? [X143 : term] : (($true = ((X135 @ X143))) & ($true != ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ($true = ((X135 @ (lam @ X134)))))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X129 : term] : ? [X130 : (subst > term > term)] : ! [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) = ((sub @ X129 @ (push @ X132 @ X131)))) & ! [X133 : term] : (((sub @ X133 @ id)) = X133) & ? [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (! [X142 : term] : (((X136 @ id @ X142 @ id)) = ((X135 @ X142))) & ! [X137 : (subst > term > term)] : (($true = ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) | ? [X141 : term] : (($true != ((X136 @ id @ (X137 @ id @ X141) @ id))) & ($true = ((X136 @ id @ X141 @ id)))) | ? [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) != ((sub @ (X137 @ X140 @ X138) @ X139)))) & ! [X143 : term] : (($true != ((X135 @ X143))) | ($true = ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) & ($true != ((X135 @ (lam @ X134)))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoaslaminj = $true) | ? [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) != ((X151 @ X149 @ X150))) & (((lam @ (X151 @ sh @ one))) = ((lam @ (X152 @ sh @ one)))) & ! [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) = ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) & ! [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) = ((sub @ (X152 @ X157 @ X156) @ X158))))) & (! [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | (((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ? [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) != ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) | ? [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) != ((sub @ (X152 @ X157 @ X156) @ X158)))) | (hoaslaminj != $true))) & (hoasapinj2_gthm = $true) & (((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X159 : subst] : (((comp @ id @ X159)) != X159) | ? [X160 : subst] : (((comp @ X160 @ id)) != X160)))) & (axclos = $true) & ((! [X243 : (term > $o),X244 : subst,X245 : term] : ? [X246 : (term > $o)] : ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X243 : (term > $o),X244 : subst,X245 : term] : ! [X246 : (term > $o)] : ? [X247 : term] : (((X246 @ X247)) != ((X243 @ (sub @ X247 @ (push @ X245 @ X244))))))) & (hoasinduction_lem2_lthm = $true) & ((! [X477 : term,X478 : term,X476 : (subst > term > term)] : (? [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) != ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X477 : term,X478 : term,X476 : (subst > term > term)] : (! [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) = ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) & (((ap @ (sub @ X477 @ id) @ X478)) = ((lam @ (X476 @ sh @ one))))))) & (pushprop_lem3v2_lthm = $true) & (((? [X529 : subst] : (((comp @ id @ X529)) != X529) | ? [X530 : subst] : (((comp @ X530 @ id)) != X530) | (! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X529 : subst] : (((comp @ id @ X529)) = X529) & ! [X530 : subst] : (((comp @ X530 @ id)) = X530) & (? [X532 : subst] : (((comp @ X532 @ id)) != X532) | ? [X531 : subst] : (((comp @ id @ X531)) != X531))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & (((axscons = $true) | ? [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) != X148)) & (! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148) | (axscons != $true))) & (hoasinduction_lem1v2_gthm = $true) & (apnotvar = $true) & (((? [X36 : (subst > term > subst > $o)] : ! [X37 : (term > $o)] : ? [X38 : term] : (((X37 @ X38)) != ((X36 @ id @ X38 @ id))) | ($true = sP16) | ? [X46 : term] : (((sub @ X46 @ id)) != X46) | ($true = sP15) | ? [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (! [X50 : (subst > term > term)] : (? [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) != ((sub @ (X50 @ X52 @ X51) @ X53))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | ? [X54 : term] : (($true = ((X47 @ id @ X54 @ id))) & ($true != ((X47 @ id @ (X50 @ id @ X54) @ id))))) & ! [X55 : term] : (($true != ((X49 @ X55))) | ($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) & ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id))) & ($true != ((X49 @ (lam @ X48)))))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X36 : (subst > term > subst > $o)] : ? [X37 : (term > $o)] : ! [X38 : term] : (((X37 @ X38)) = ((X36 @ id @ X38 @ id))) & ($true != sP16) & ! [X46 : term] : (((sub @ X46 @ id)) = X46) & ($true != sP15) & ! [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (? [X50 : (subst > term > term)] : (! [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) = ((sub @ (X50 @ X52 @ X51) @ X53))) & ($true != ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) & ! [X54 : term] : (($true != ((X47 @ id @ X54 @ id))) | ($true = ((X47 @ id @ (X50 @ id @ X54) @ id))))) | ? [X55 : term] : (($true = ((X49 @ X55))) & ($true != ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) | ? [X56 : term] : (((X49 @ X56)) != ((X47 @ id @ X56 @ id))) | ($true = ((X49 @ (lam @ X48)))))))) & (((hoasinduction_lem0_lthm = $true) | ? [X400 : (subst > term > subst > $o)] : ! [X401 : (term > $o)] : ? [X402 : term] : (((X401 @ X402)) != ((X400 @ id @ X402 @ id)))) & (! [X400 : (subst > term > subst > $o)] : ? [X401 : (term > $o)] : ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id))) | (hoasinduction_lem0_lthm != $true))) & ((! [X509 : term] : ? [X510 : (subst > term > term)] : (((X510 @ sh @ one)) = ((sub @ X509 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X509 : term] : ! [X510 : (subst > term > term)] : (((X510 @ sh @ one)) != ((sub @ X509 @ (push @ one @ sh)))))) & (hoaslamnotap_lthm = $true) & ((($true = sP12) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP12))) & (((pushprop_lem1v2 = $true) | ? [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (! [X537 : term] : (((X534 @ X537)) = ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) & ($true != ((X534 @ one))) & ($true = ((X536 @ X535))))) & (! [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (? [X537 : term] : (((X534 @ X537)) != ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) | ($true = ((X534 @ one))) | ($true != ((X536 @ X535)))) | (pushprop_lem1v2 != $true))) & ((! [X187 : term,X186 : (subst > term > subst > $o)] : (? [X197 : term] : (($true = ((X186 @ id @ X197 @ id))) & ($true != ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ? [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true != ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) & ($true = ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) | ? [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true = ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) & ($true != ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) | ($true = ((X186 @ id @ (lam @ X187) @ id))) | ($true = ((sP10 @ X186)))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ? [X187 : term,X186 : (subst > term > subst > $o)] : (! [X197 : term] : (($true != ((X186 @ id @ X197 @ id))) | ($true = ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) & ! [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true = ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) | ($true != ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) & ! [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true != ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) | ($true = ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) & ($true != ((X186 @ id @ (lam @ X187) @ id))) & ($true != ((sP10 @ X186)))))) & (hoasinduction_lem3v2_gthm = $true) & ((($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9))) & (hoasinduction_lem3b_gthm = $true) & (((axidl = $true) | ? [X424 : subst] : (((comp @ id @ X424)) != X424)) & (! [X424 : subst] : (((comp @ id @ X424)) = X424) | (axidl != $true))) & (lamnotap != $true) & (((induction = $true) | ? [X432 : (term > $o),X431 : term] : (! [X436 : term] : (($true = ((X432 @ X436))) | ($true != ((var @ X436)))) & ($true != ((X432 @ X431))) & ! [X433 : term] : (($true != ((X432 @ X433))) | ($true = ((X432 @ (lam @ X433))))) & ! [X435 : term,X434 : term] : (($true != ((X432 @ X434))) | ($true = ((X432 @ (ap @ X435 @ X434)))) | ($true != ((X432 @ X435)))))) & (! [X432 : (term > $o),X431 : term] : (? [X436 : term] : (($true != ((X432 @ X436))) & ($true = ((var @ X436)))) | ($true = ((X432 @ X431))) | ? [X433 : term] : (($true = ((X432 @ X433))) & ($true != ((X432 @ (lam @ X433))))) | ? [X435 : term,X434 : term] : (($true = ((X432 @ X434))) & ($true != ((X432 @ (ap @ X435 @ X434)))) & ($true = ((X432 @ X435))))) | (induction != $true))) & (hoasapnotvar_gthm = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X482 : term] : ! [X483 : (subst > term > term)] : ? [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) != ((sub @ X482 @ (push @ X485 @ X484))))) & (! [X482 : term] : ? [X483 : (subst > term > term)] : ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484)))) | (hoasinduction_lem3v2_f_lthm != $true))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (((axshiftcons = $true) | ? [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) != X538)) & (! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538) | (axshiftcons != $true))) & ((! [X347 : (subst > term > subst > $o)] : ? [X348 : (term > $o)] : ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X347 : (subst > term > subst > $o)] : ! [X348 : (term > $o)] : ? [X349 : term] : (((X347 @ id @ X349 @ id)) != ((X348 @ X349))))) & (pushprop = $true) & (((hoasinduction = $true) | ? [X459 : term,X458 : (subst > term > subst > $o)] : (($true != ((sP8 @ X458))) & ! [X460 : term] : (($true != ((var @ (sub @ X460 @ id)))) | ($true = ((X458 @ id @ X460 @ id)))) & ($true != ((sP7 @ X458))) & ($true != ((X458 @ id @ X459 @ id))) & ! [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true != ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) | ($true = ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) & ! [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true = ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) | ($true != ((X458 @ X461 @ X464 @ (comp @ X462 @ X463))))))) & (! [X459 : term,X458 : (subst > term > subst > $o)] : (($true = ((sP8 @ X458))) | ? [X460 : term] : (($true = ((var @ (sub @ X460 @ id)))) & ($true != ((X458 @ id @ X460 @ id)))) | ($true = ((sP7 @ X458))) | ($true = ((X458 @ id @ X459 @ id))) | ? [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true = ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) & ($true != ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) | ? [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true != ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) & ($true = ((X458 @ X461 @ X464 @ (comp @ X462 @ X463)))))) | (hoasinduction != $true))) & (hoasinduction_lem1_lthm = $true) & (((induction2 = $true) | ($true != sP6)) & (($true = sP6) | (induction2 != $true))) & ((! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X456 : term,X457 : term] : ((X456 != X457) & (((sub @ X456 @ sh)) = ((sub @ X457 @ sh)))))) & ((! [X124 : term] : (((sub @ X124 @ id)) = X124) | (axvarid != $true)) & ((axvarid = $true) | ? [X124 : term] : (((sub @ X124 @ id)) != X124))) & (hoasinduction_lem1 = $true) & (axapp = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (((termmset = $true) | ? [X399 : term] : (((sub @ X399 @ id)) != X399)) & (! [X399 : term] : (((sub @ X399 @ id)) = X399) | (termmset != $true))) & ! [X491 : d_term] : (d_one = X491) & ((($true = sP5) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP5))) & (((hoasinduction_lem3b_lthm = $true) | ? [X8 : term] : ! [X9 : (subst > term > term)] : (((X9 @ sh @ one)) != ((sub @ X8 @ (push @ one @ sh))))) & (! [X8 : term] : ? [X9 : (subst > term > term)] : (((X9 @ sh @ one)) = ((sub @ X8 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true))) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & (((laminj = $true) | ? [X11 : term,X10 : term] : ((((lam @ X10)) = ((lam @ X11))) & (X10 != X11))) & (! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11)) | (laminj != $true))) & ! [X500 : d_subst] : (d_id = X500) & (ulamvarind = $true) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axmap = $true) & (((hoaslaminj_lthm = $true) | (! [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) = X14) & ! [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) = X12) & ! [X17 : term,X16 : term] : ((((lam @ X17)) != ((lam @ X16))) | (X16 = X17)) & ? [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (! [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) = ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) & (((lam @ (X19 @ sh @ one))) = ((lam @ (X20 @ sh @ one)))) & (((X20 @ X18 @ X21)) != ((X19 @ X18 @ X21))) & ! [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) = ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23))))))) & ((? [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) != X14) | ? [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) != X12) | ? [X17 : term,X16 : term] : ((((lam @ X17)) = ((lam @ X16))) & (X16 != X17)) | ! [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (? [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) != ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21))) | ? [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) != ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23)))))) | (hoaslaminj_lthm != $true))) & (hoaslamnotvar_lthm = $true) & (((? [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true != ((X361 @ (lam @ X362)))) & ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) & ! [X370 : term] : (($true != ((X361 @ X370))) | ($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) & ! [X365 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ? [X369 : term] : (($true != ((X363 @ id @ (X365 @ id @ X369) @ id))) & ($true = ((X363 @ id @ X369 @ id)))) | ? [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) != ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) | ($true = sP3) | ($true = sP4) | ? [X350 : (subst > term > subst > $o)] : ! [X351 : (term > $o)] : ? [X352 : term] : (((X350 @ id @ X352 @ id)) != ((X351 @ X352))) | ? [X360 : term] : (((sub @ X360 @ id)) != X360)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true = ((X361 @ (lam @ X362)))) | ? [X364 : term] : (((X363 @ id @ X364 @ id)) != ((X361 @ X364))) | ? [X370 : term] : (($true = ((X361 @ X370))) & ($true != ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) | ? [X365 : (subst > term > term)] : (($true != ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) & ! [X369 : term] : (($true = ((X363 @ id @ (X365 @ id @ X369) @ id))) | ($true != ((X363 @ id @ X369 @ id)))) & ! [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) = ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) & ($true != sP3) & ($true != sP4) & ! [X350 : (subst > term > subst > $o)] : ? [X351 : (term > $o)] : ! [X352 : term] : (((X350 @ id @ X352 @ id)) = ((X351 @ X352))) & ! [X360 : term] : (((sub @ X360 @ id)) = X360)))) & (((hoasinduction_lem3aaa = $true) | ? [X438 : (subst > term > subst > $o),X437 : term] : (($true != ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) & ! [X448 : term] : (($true = ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) | ($true != ((X438 @ id @ X448 @ id)))) & ! [X440 : term,X439 : (subst > term > term)] : (? [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) != ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) | ($true = ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) | ? [X441 : term] : (($true = ((X438 @ id @ X441 @ id))) & ($true != ((X438 @ id @ (X439 @ id @ X441) @ id)))) | ? [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) != ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444)))))) & (! [X438 : (subst > term > subst > $o),X437 : term] : (($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ? [X448 : term] : (($true != ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) & ($true = ((X438 @ id @ X448 @ id)))) | ? [X440 : term,X439 : (subst > term > term)] : (! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ($true != ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) & ! [X441 : term] : (($true != ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id)))) & ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444))))) | (hoasinduction_lem3aaa != $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X7 : d_term,X6 : d_term] : ((X6 = X7) | (((d2term @ X7)) != ((d2term @ X6)))) & (((hoasapinj1 = $true) | ? [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) = ((ap @ (sub @ X128 @ id) @ X127))) & (X125 != X128))) & (! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128)) | (hoasapinj1 != $true))) & (hoaslamnotap_gthm = $true) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & (pushprop_gthm = $true) & (hoasinduction_gthm = $true) & ((! [X486 : (term > $o),X487 : subst,X488 : term] : ? [X489 : (term > $o)] : ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X486 : (term > $o),X487 : subst,X488 : term] : ! [X489 : (term > $o)] : ? [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) != ((X489 @ X490))))) & (((? [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) != X87) | ! [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true != ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) = X87) & ? [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true = ((X93 @ X91))) & ($true != ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) & ! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85)))) & ((! [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (? [X514 : term] : (($true = ((X513 @ X514))) & ($true != ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) | ($true = ((sP2 @ X512))) | ? [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true != ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) & ($true = ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) | ? [X524 : term] : (((X513 @ X524)) != ((X512 @ id @ X524 @ id))) | ($true = ((X513 @ (lam @ X511)))) | ? [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true = ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) & (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) != $true))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (! [X514 : term] : (($true != ((X513 @ X514))) | ($true = ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) & ($true != ((sP2 @ X512))) & ! [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true = ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) | ($true != ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) & ! [X524 : term] : (((X513 @ X524)) = ((X512 @ id @ X524 @ id))) & ($true != ((X513 @ (lam @ X511)))) & ! [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true != ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) | (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) = $true))))) & (((hoasapinj2 = $true) | ? [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 != X2) & (((ap @ (sub @ X0 @ id) @ X2)) = ((ap @ (sub @ X3 @ id) @ X1))))) & (! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1)))) | (hoasapinj2 != $true))) & (((hoasapinj2_lthm = $true) | (! [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 = X29) | (((ap @ X30 @ X28)) != ((ap @ X31 @ X29)))) & ? [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 != X35) & (((ap @ (sub @ X34 @ id) @ X32)) = ((ap @ (sub @ X33 @ id) @ X35)))))) & ((? [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 != X29) & (((ap @ X30 @ X28)) = ((ap @ X31 @ X29)))) | ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35))))) | (hoasapinj2_lthm != $true))) & (pushprop_lem2v2_lthm = $true) & (((hoasinduction_lem3a = $true) | ? [X502 : (subst > term > subst > $o),X501 : term] : (($true != ((X502 @ id @ (lam @ X501) @ id))) & ! [X508 : term] : (($true != ((X502 @ id @ X508 @ id))) | ($true = ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) & ! [X503 : (subst > term > term)] : (? [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) != ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) | ? [X507 : term] : (($true = ((X502 @ id @ X507 @ id))) & ($true != ((X502 @ id @ (X503 @ id @ X507) @ id)))) | ($true = ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id)))))) & (! [X502 : (subst > term > subst > $o),X501 : term] : (($true = ((X502 @ id @ (lam @ X501) @ id))) | ? [X508 : term] : (($true = ((X502 @ id @ X508 @ id))) & ($true != ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) | ? [X503 : (subst > term > term)] : (! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) & ! [X507 : term] : (($true != ((X502 @ id @ X507 @ id))) | ($true = ((X502 @ id @ (X503 @ id @ X507) @ id)))) & ($true != ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id))))) | (hoasinduction_lem3a != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasinduction_lem3v2a = $true) | ? [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true != ((X75 @ (lam @ X77)))) & ! [X78 : term] : (((X76 @ id @ X78 @ id)) = ((X75 @ X78))) & ! [X79 : term] : (($true = ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) | ($true != ((X75 @ X79)))) & ! [X80 : (subst > term > term)] : (? [X81 : term] : (($true != ((X76 @ id @ (X80 @ id @ X81) @ id))) & ($true = ((X76 @ id @ X81 @ id)))) | ($true = ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) | ? [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) != ((sub @ (X80 @ X83 @ X84) @ X82)))))) & (! [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true = ((X75 @ (lam @ X77)))) | ? [X78 : term] : (((X76 @ id @ X78 @ id)) != ((X75 @ X78))) | ? [X79 : term] : (($true != ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) & ($true = ((X75 @ X79)))) | ? [X80 : (subst > term > term)] : (! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X76 @ id @ X81 @ id)))) & ($true != ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) & ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82))))) | (hoasinduction_lem3v2a != $true))) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X144 : term] : ! [X145 : (subst > term > term)] : ? [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) != ((X145 @ X146 @ X147)))) & (! [X144 : term] : ? [X145 : (subst > term > term)] : ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147))) | (hoasinduction_lem3v2_f != $true))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X338 : term,X339 : (subst > term > subst > $o)] : (! [X342 : (subst > term > term)] : (($true = ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) | ? [X346 : term] : (($true != ((X339 @ id @ (X342 @ id @ X346) @ id))) & ($true = ((X339 @ id @ X346 @ id)))) | ? [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) != ((sub @ (X342 @ X345 @ X344) @ X343)))) & ! [X341 : term,X340 : term] : (($true = ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) | ($true != ((X339 @ id @ X340 @ id))) | ($true != ((X339 @ id @ X341 @ id)))) & ($true != ((X339 @ id @ X338 @ id))))) & (! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X342 : (subst > term > term)] : (($true != ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) & ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ($true != ((X339 @ id @ X346 @ id)))) & ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343)))) | ? [X341 : term,X340 : term] : (($true != ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) & ($true = ((X339 @ id @ X340 @ id))) & ($true = ((X339 @ id @ X341 @ id)))) | ($true = ((X339 @ id @ X338 @ id)))) | (hoasinduction_no_psi_cond != $true))) & (hoaslamnotvar = $true) & (((! [X5 : term] : (((sub @ X5 @ id)) = X5) | ? [X4 : term] : (((sub @ X4 @ id)) != X4)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X5 : term] : (((sub @ X5 @ id)) != X5) & ! [X4 : term] : (((sub @ X4 @ id)) = X4)))) & (lamnotvar = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & (((apinj1 = $true) | ? [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 != X430) & (((ap @ X430 @ X428)) = ((ap @ X427 @ X429))))) & (! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429)))) | (apinj1 != $true))) & (((induction2lem_lthm = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem_lthm != $true)))), 24.89/4.11 inference(nnf_transformation,[],[f43])). 24.89/4.11 thf(f131,plain,( 24.89/4.11 ! [X397 : subst] : ? [X398 : d_subst] : (((d2subst @ X398)) = X397) & (! [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) = X241) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X241 : term,X242 : subst] : (((sub @ one @ (push @ X241 @ X242))) != X241)) & (((d2subst @ d_id)) = id) & (axvarshift = $true) & (! [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) = $true) | ? [X382 : term] : (($true = ((X380 @ id @ X382 @ id))) & ($true != ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) | ? [X383 : (subst > term > term)] : (! [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) = ((sub @ (X383 @ X385 @ X386) @ X384))) & ! [X387 : term] : (($true = ((X380 @ id @ (X383 @ id @ X387) @ id))) | ($true != ((X380 @ id @ X387 @ id)))) & ($true != ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X381 : term,X380 : (subst > term > subst > $o)] : ((((X380 @ id @ (lam @ (sub @ X381 @ (push @ one @ sh))) @ id)) != $true) & ! [X382 : term] : (($true != ((X380 @ id @ X382 @ id))) | ($true = ((X380 @ id @ (sub @ X381 @ (push @ X382 @ id)) @ id)))) & ! [X383 : (subst > term > term)] : (? [X386 : term,X385 : subst,X384 : subst] : (((X383 @ (comp @ X385 @ X384) @ (sub @ X386 @ X384))) != ((sub @ (X383 @ X385 @ X386) @ X384))) | ? [X387 : term] : (($true != ((X380 @ id @ (X383 @ id @ X387) @ id))) & ($true = ((X380 @ id @ X387 @ id)))) | ($true = ((X380 @ id @ (lam @ (X383 @ sh @ one)) @ id)))))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP27) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP27)) & ((hoasapinj1_lthm = $true) | (? [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) = ((ap @ (sub @ X395 @ id) @ X396))) & (X394 != X395)) & ! [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) != ((ap @ X392 @ X390))) | (X389 = X392)) & ! [X388 : term] : (((sub @ X388 @ id)) = X388))) & (! [X393 : term,X394 : term,X395 : term,X396 : term] : ((((ap @ (sub @ X394 @ id) @ X393)) != ((ap @ (sub @ X395 @ id) @ X396))) | (X394 = X395)) | ? [X391 : term,X389 : term,X392 : term,X390 : term] : ((((ap @ X389 @ X391)) = ((ap @ X392 @ X390))) & (X389 != X392)) | ? [X388 : term] : (((sub @ X388 @ id)) != X388) | (hoasapinj1_lthm != $true)) & (hoasapnotvar = $true) & (axabs = $true) & ! [X404 : d_subst,X403 : d_subst] : ((X403 = X404) | (((d2subst @ X403)) != ((d2subst @ X404)))) & ((axidr = $true) | ? [X423 : subst] : (((comp @ X423 @ id)) != X423)) & (! [X423 : subst] : (((comp @ X423 @ id)) = X423) | (axidr != $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true = ((X321 @ (lam @ X322)))) | ? [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true != ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) & ($true = ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) | ? [X327 : term] : (((X321 @ X327)) != ((X320 @ id @ X327 @ id))) | ? [X328 : term] : (($true = ((X321 @ X328))) & ($true != ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) | ? [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true != ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) & ($true = ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) | ($true = ((sP26 @ X320)))) | ? [X319 : term] : (((sub @ X319 @ id)) != X319) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (? [X320 : (subst > term > subst > $o),X321 : (term > $o),X322 : term] : (($true != ((X321 @ (lam @ X322)))) & ! [X332 : subst,X329 : term,X331 : subst,X330 : subst] : (($true = ((X320 @ X330 @ X329 @ (comp @ X332 @ X331)))) | ($true != ((X320 @ (comp @ X330 @ X332) @ (sub @ X329 @ X332) @ X331)))) & ! [X327 : term] : (((X321 @ X327)) = ((X320 @ id @ X327 @ id))) & ! [X328 : term] : (($true != ((X321 @ X328))) | ($true = ((X321 @ (sub @ X322 @ (push @ X328 @ id)))))) & ! [X324 : term,X326 : subst,X325 : subst,X323 : subst] : (($true = ((X320 @ (comp @ X326 @ X323) @ (sub @ X324 @ X323) @ X325))) | ($true != ((X320 @ X326 @ X324 @ (comp @ X323 @ X325))))) & ($true != ((sP26 @ X320)))) & ! [X319 : term] : (((sub @ X319 @ id)) = X319))) & (pushprop_lem2v2_gthm = $true) & (? [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) != X449) | ! [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (? [X455 : term] : (((X452 @ X455)) != ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) | ($true != ((X451 @ X454))) | ($true = ((X452 @ one)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X450 : subst,X449 : term] : (((sub @ one @ (push @ X449 @ X450))) = X449) & ? [X452 : (term > $o),X454 : term,X453 : subst,X451 : (term > $o)] : (! [X455 : term] : (((X452 @ X455)) = ((X451 @ (sub @ X455 @ (push @ X454 @ X453))))) & ($true = ((X451 @ X454))) & ($true != ((X452 @ one)))))) & ((pushprop_lem1 = $true) | ? [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true = ((X407 @ X408))) & ($true != ((X409 @ (sub @ X408 @ (push @ X405 @ X406))))))) & (! [X408 : term,X407 : (term > $o),X406 : subst,X409 : (term > $o),X405 : term] : (($true != ((X407 @ X408))) | ($true = ((X409 @ (sub @ X408 @ (push @ X405 @ X406)))))) | (pushprop_lem1 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 = X97) | (((ap @ X96 @ X97)) != ((ap @ X94 @ X95)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X95 : term,X94 : term,X96 : term,X97 : term] : ((X95 != X97) & (((ap @ X96 @ X97)) = ((ap @ X94 @ X95))))) & ((hoasinduction_lem3a_lthm = $true) | (! [X250 : term,X249 : (subst > term > subst > $o)] : (($true = ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) | ? [X256 : term] : (($true != ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) & ($true = ((X249 @ id @ X256 @ id)))) | ? [X251 : (subst > term > term)] : (($true != ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) & ! [X255 : term] : (($true != ((X249 @ id @ X255 @ id))) | ($true = ((X249 @ id @ (X251 @ id @ X255) @ id)))) & ! [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) = ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))))) & ($true != sP25) & ! [X248 : term] : (((sub @ X248 @ id)) = X248))) & (? [X250 : term,X249 : (subst > term > subst > $o)] : (($true != ((X249 @ id @ (lam @ (sub @ X250 @ (push @ one @ sh))) @ id))) & ! [X256 : term] : (($true = ((X249 @ id @ (sub @ X250 @ (push @ X256 @ id)) @ id))) | ($true != ((X249 @ id @ X256 @ id)))) & ! [X251 : (subst > term > term)] : (($true = ((X249 @ id @ (lam @ (X251 @ sh @ one)) @ id))) | ? [X255 : term] : (($true = ((X249 @ id @ X255 @ id))) & ($true != ((X249 @ id @ (X251 @ id @ X255) @ id)))) | ? [X253 : subst,X252 : subst,X254 : term] : (((sub @ (X251 @ X253 @ X254) @ X252)) != ((X251 @ (comp @ X253 @ X252) @ (sub @ X254 @ X252)))))) | ($true = sP25) | ? [X248 : term] : (((sub @ X248 @ id)) != X248) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3aa = $true) | ? [X493 : term,X492 : (subst > term > subst > $o)] : (! [X494 : (subst > term > term)] : (($true = ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) | ? [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) != ((sub @ (X494 @ X496 @ X497) @ X498))) | ? [X495 : term] : (($true = ((X492 @ id @ X495 @ id))) & ($true != ((X492 @ id @ (X494 @ id @ X495) @ id))))) & ($true != ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) & ! [X499 : term] : (($true != ((X492 @ id @ X499 @ id))) | ($true = ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id)))))) & (! [X493 : term,X492 : (subst > term > subst > $o)] : (? [X494 : (subst > term > term)] : (($true != ((X492 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X497 : term,X496 : subst,X498 : subst] : (((X494 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498))) = ((sub @ (X494 @ X496 @ X497) @ X498))) & ! [X495 : term] : (($true != ((X492 @ id @ X495 @ id))) | ($true = ((X492 @ id @ (X494 @ id @ X495) @ id))))) | ($true = ((X492 @ id @ (lam @ (sub @ X493 @ (push @ one @ sh))) @ id))) | ? [X499 : term] : (($true = ((X492 @ id @ X499 @ id))) & ($true != ((X492 @ id @ (sub @ X493 @ (push @ X499 @ id)) @ id))))) | (hoasinduction_lem3aa != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (($true = sP24) | ? [X161 : term] : (((sub @ X161 @ id)) != X161) | ? [X163 : term,X162 : (subst > term > subst > $o)] : (! [X164 : (subst > term > term)] : (? [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) != ((sub @ (X164 @ X167 @ X165) @ X166))) | ($true = ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) | ? [X168 : term] : (($true != ((X162 @ id @ (X164 @ id @ X168) @ id))) & ($true = ((X162 @ id @ X168 @ id))))) & ! [X169 : term] : (($true != ((X162 @ id @ X169 @ id))) | ($true = ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) & ($true != ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP24) & ! [X161 : term] : (((sub @ X161 @ id)) = X161) & ! [X163 : term,X162 : (subst > term > subst > $o)] : (? [X164 : (subst > term > term)] : (! [X165 : term,X167 : subst,X166 : subst] : (((X164 @ (comp @ X167 @ X166) @ (sub @ X165 @ X166))) = ((sub @ (X164 @ X167 @ X165) @ X166))) & ($true != ((X162 @ id @ (lam @ (X164 @ sh @ one)) @ id))) & ! [X168 : term] : (($true = ((X162 @ id @ (X164 @ id @ X168) @ id))) | ($true != ((X162 @ id @ X168 @ id))))) | ? [X169 : term] : (($true = ((X162 @ id @ X169 @ id))) & ($true != ((X162 @ id @ (sub @ X163 @ (push @ X169 @ id)) @ id)))) | ($true = ((X162 @ id @ (lam @ (sub @ X163 @ (push @ one @ sh))) @ id)))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm = $true) | (($true != sP22) & ($true != sP21) & ($true != sP20) & ! [X285 : (subst > term > subst > $o),X286 : term] : (? [X291 : term] : (($true != ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) & ($true = ((X285 @ id @ X291 @ id)))) | ($true != ((sP17 @ X285))) | ? [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true != ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) & ($true = ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) | ? [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true != ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) & ($true = ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) | ($true = ((X285 @ id @ (lam @ X286) @ id)))))) & (($true = sP22) | ($true = sP21) | ($true = sP20) | ? [X285 : (subst > term > subst > $o),X286 : term] : (! [X291 : term] : (($true = ((X285 @ id @ (sub @ X286 @ (push @ X291 @ id)) @ id))) | ($true != ((X285 @ id @ X291 @ id)))) & ($true = ((sP17 @ X285))) & ! [X292 : subst,X295 : subst,X293 : term,X294 : subst] : (($true = ((X285 @ (comp @ X295 @ X292) @ (sub @ X293 @ X292) @ X294))) | ($true != ((X285 @ X295 @ X293 @ (comp @ X292 @ X294))))) & ! [X289 : subst,X288 : subst,X290 : term,X287 : subst] : (($true = ((X285 @ X287 @ X290 @ (comp @ X288 @ X289)))) | ($true != ((X285 @ (comp @ X287 @ X288) @ (sub @ X290 @ X288) @ X289)))) & ($true != ((X285 @ id @ (lam @ X286) @ id)))) | (hoasinduction_lthm != $true)) & (? [X129 : term] : ! [X130 : (subst > term > term)] : ? [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) != ((sub @ X129 @ (push @ X132 @ X131)))) | ? [X133 : term] : (((sub @ X133 @ id)) != X133) | ! [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (? [X142 : term] : (((X136 @ id @ X142 @ id)) != ((X135 @ X142))) | ? [X137 : (subst > term > term)] : (($true != ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) & ! [X141 : term] : (($true = ((X136 @ id @ (X137 @ id @ X141) @ id))) | ($true != ((X136 @ id @ X141 @ id)))) & ! [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) = ((sub @ (X137 @ X140 @ X138) @ X139)))) | ? [X143 : term] : (($true = ((X135 @ X143))) & ($true != ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) | ($true = ((X135 @ (lam @ X134))))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X129 : term] : ? [X130 : (subst > term > term)] : ! [X132 : term,X131 : subst] : (((X130 @ X131 @ X132)) = ((sub @ X129 @ (push @ X132 @ X131)))) & ! [X133 : term] : (((sub @ X133 @ id)) = X133) & ? [X136 : (subst > term > subst > $o),X134 : term,X135 : (term > $o)] : (! [X142 : term] : (((X136 @ id @ X142 @ id)) = ((X135 @ X142))) & ! [X137 : (subst > term > term)] : (($true = ((X136 @ id @ (lam @ (X137 @ sh @ one)) @ id))) | ? [X141 : term] : (($true != ((X136 @ id @ (X137 @ id @ X141) @ id))) & ($true = ((X136 @ id @ X141 @ id)))) | ? [X139 : subst,X138 : term,X140 : subst] : (((X137 @ (comp @ X140 @ X139) @ (sub @ X138 @ X139))) != ((sub @ (X137 @ X140 @ X138) @ X139)))) & ! [X143 : term] : (($true != ((X135 @ X143))) | ($true = ((X135 @ (sub @ X134 @ (push @ X143 @ id)))))) & ($true != ((X135 @ (lam @ X134))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj = $true) | ? [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) != ((X151 @ X149 @ X150))) & (((lam @ (X151 @ sh @ one))) = ((lam @ (X152 @ sh @ one)))) & ! [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) = ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) & ! [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) = ((sub @ (X152 @ X157 @ X156) @ X158))))) & (! [X152 : (subst > term > term),X150 : term,X151 : (subst > term > term),X149 : subst] : ((((X152 @ X149 @ X150)) = ((X151 @ X149 @ X150))) | (((lam @ (X151 @ sh @ one))) != ((lam @ (X152 @ sh @ one)))) | ? [X154 : subst,X155 : subst,X153 : term] : (((sub @ (X151 @ X154 @ X153) @ X155)) != ((X151 @ (comp @ X154 @ X155) @ (sub @ X153 @ X155)))) | ? [X157 : subst,X158 : subst,X156 : term] : (((X152 @ (comp @ X157 @ X158) @ (sub @ X156 @ X158))) != ((sub @ (X152 @ X157 @ X156) @ X158)))) | (hoaslaminj != $true)) & (hoasapinj2_gthm = $true) & ((! [X159 : subst] : (((comp @ id @ X159)) = X159) & ! [X160 : subst] : (((comp @ X160 @ id)) = X160)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X159 : subst] : (((comp @ id @ X159)) != X159) | ? [X160 : subst] : (((comp @ X160 @ id)) != X160)) & (axclos = $true) & (! [X243 : (term > $o),X244 : subst,X245 : term] : ? [X246 : (term > $o)] : ! [X247 : term] : (((X246 @ X247)) = ((X243 @ (sub @ X247 @ (push @ X245 @ X244))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X243 : (term > $o),X244 : subst,X245 : term] : ! [X246 : (term > $o)] : ? [X247 : term] : (((X246 @ X247)) != ((X243 @ (sub @ X247 @ (push @ X245 @ X244)))))) & (hoasinduction_lem2_lthm = $true) & (! [X477 : term,X478 : term,X476 : (subst > term > term)] : (? [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) != ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) | (((ap @ (sub @ X477 @ id) @ X478)) != ((lam @ (X476 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X477 : term,X478 : term,X476 : (subst > term > term)] : (! [X481 : subst,X479 : term,X480 : subst] : (((sub @ (X476 @ X481 @ X479) @ X480)) = ((X476 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480)))) & (((ap @ (sub @ X477 @ id) @ X478)) = ((lam @ (X476 @ sh @ one)))))) & (pushprop_lem3v2_lthm = $true) & (? [X529 : subst] : (((comp @ id @ X529)) != X529) | ? [X530 : subst] : (((comp @ X530 @ id)) != X530) | (! [X532 : subst] : (((comp @ X532 @ id)) = X532) & ! [X531 : subst] : (((comp @ id @ X531)) = X531)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X529 : subst] : (((comp @ id @ X529)) = X529) & ! [X530 : subst] : (((comp @ X530 @ id)) = X530) & (? [X532 : subst] : (((comp @ X532 @ id)) != X532) | ? [X531 : subst] : (((comp @ id @ X531)) != X531)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & ((axscons = $true) | ? [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) != X148)) & (! [X148 : subst] : (((push @ (sub @ one @ X148) @ (comp @ sh @ X148))) = X148) | (axscons != $true)) & (hoasinduction_lem1v2_gthm = $true) & (apnotvar = $true) & (? [X36 : (subst > term > subst > $o)] : ! [X37 : (term > $o)] : ? [X38 : term] : (((X37 @ X38)) != ((X36 @ id @ X38 @ id))) | ($true = sP16) | ? [X46 : term] : (((sub @ X46 @ id)) != X46) | ($true = sP15) | ? [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (! [X50 : (subst > term > term)] : (? [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) != ((sub @ (X50 @ X52 @ X51) @ X53))) | ($true = ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | ? [X54 : term] : (($true = ((X47 @ id @ X54 @ id))) & ($true != ((X47 @ id @ (X50 @ id @ X54) @ id))))) & ! [X55 : term] : (($true != ((X49 @ X55))) | ($true = ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) & ! [X56 : term] : (((X49 @ X56)) = ((X47 @ id @ X56 @ id))) & ($true != ((X49 @ (lam @ X48))))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X36 : (subst > term > subst > $o)] : ? [X37 : (term > $o)] : ! [X38 : term] : (((X37 @ X38)) = ((X36 @ id @ X38 @ id))) & ($true != sP16) & ! [X46 : term] : (((sub @ X46 @ id)) = X46) & ($true != sP15) & ! [X47 : (subst > term > subst > $o),X49 : (term > $o),X48 : term] : (? [X50 : (subst > term > term)] : (! [X51 : term,X53 : subst,X52 : subst] : (((X50 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53))) = ((sub @ (X50 @ X52 @ X51) @ X53))) & ($true != ((X47 @ id @ (lam @ (X50 @ sh @ one)) @ id))) & ! [X54 : term] : (($true != ((X47 @ id @ X54 @ id))) | ($true = ((X47 @ id @ (X50 @ id @ X54) @ id))))) | ? [X55 : term] : (($true = ((X49 @ X55))) & ($true != ((X49 @ (sub @ X48 @ (push @ X55 @ id)))))) | ? [X56 : term] : (((X49 @ X56)) != ((X47 @ id @ X56 @ id))) | ($true = ((X49 @ (lam @ X48))))))) & ((hoasinduction_lem0_lthm = $true) | ? [X400 : (subst > term > subst > $o)] : ! [X401 : (term > $o)] : ? [X402 : term] : (((X401 @ X402)) != ((X400 @ id @ X402 @ id)))) & (! [X400 : (subst > term > subst > $o)] : ? [X401 : (term > $o)] : ! [X402 : term] : (((X401 @ X402)) = ((X400 @ id @ X402 @ id))) | (hoasinduction_lem0_lthm != $true)) & (! [X509 : term] : ? [X510 : (subst > term > term)] : (((X510 @ sh @ one)) = ((sub @ X509 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X509 : term] : ! [X510 : (subst > term > term)] : (((X510 @ sh @ one)) != ((sub @ X509 @ (push @ one @ sh))))) & (hoaslamnotap_lthm = $true) & (($true = sP12) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP12)) & ((pushprop_lem1v2 = $true) | ? [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (! [X537 : term] : (((X534 @ X537)) = ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) & ($true != ((X534 @ one))) & ($true = ((X536 @ X535))))) & (! [X535 : term,X534 : (term > $o),X536 : (term > $o),X533 : subst] : (? [X537 : term] : (((X534 @ X537)) != ((X536 @ (sub @ X537 @ (push @ X535 @ X533))))) | ($true = ((X534 @ one))) | ($true != ((X536 @ X535)))) | (pushprop_lem1v2 != $true)) & (! [X187 : term,X186 : (subst > term > subst > $o)] : (? [X197 : term] : (($true = ((X186 @ id @ X197 @ id))) & ($true != ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) | ? [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true != ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) & ($true = ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) | ? [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true = ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) & ($true != ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) | ($true = ((X186 @ id @ (lam @ X187) @ id))) | ($true = ((sP10 @ X186)))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ? [X187 : term,X186 : (subst > term > subst > $o)] : (! [X197 : term] : (($true != ((X186 @ id @ X197 @ id))) | ($true = ((X186 @ id @ (sub @ X187 @ (push @ X197 @ id)) @ id)))) & ! [X196 : subst,X195 : subst,X193 : term,X194 : subst] : (($true = ((X186 @ (comp @ X195 @ X194) @ (sub @ X193 @ X194) @ X196))) | ($true != ((X186 @ X195 @ X193 @ (comp @ X194 @ X196))))) & ! [X201 : subst,X198 : subst,X199 : subst,X200 : term] : (($true != ((X186 @ (comp @ X201 @ X198) @ (sub @ X200 @ X198) @ X199))) | ($true = ((X186 @ X201 @ X200 @ (comp @ X198 @ X199))))) & ($true != ((X186 @ id @ (lam @ X187) @ id))) & ($true != ((sP10 @ X186))))) & (hoasinduction_lem3v2_gthm = $true) & (($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) | ? [X424 : subst] : (((comp @ id @ X424)) != X424)) & (! [X424 : subst] : (((comp @ id @ X424)) = X424) | (axidl != $true)) & (lamnotap != $true) & ((induction = $true) | ? [X432 : (term > $o),X431 : term] : (! [X436 : term] : (($true = ((X432 @ X436))) | ($true != ((var @ X436)))) & ($true != ((X432 @ X431))) & ! [X433 : term] : (($true != ((X432 @ X433))) | ($true = ((X432 @ (lam @ X433))))) & ! [X435 : term,X434 : term] : (($true != ((X432 @ X434))) | ($true = ((X432 @ (ap @ X435 @ X434)))) | ($true != ((X432 @ X435)))))) & (! [X432 : (term > $o),X431 : term] : (? [X436 : term] : (($true != ((X432 @ X436))) & ($true = ((var @ X436)))) | ($true = ((X432 @ X431))) | ? [X433 : term] : (($true = ((X432 @ X433))) & ($true != ((X432 @ (lam @ X433))))) | ? [X435 : term,X434 : term] : (($true = ((X432 @ X434))) & ($true != ((X432 @ (ap @ X435 @ X434)))) & ($true = ((X432 @ X435))))) | (induction != $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X482 : term] : ! [X483 : (subst > term > term)] : ? [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) != ((sub @ X482 @ (push @ X485 @ X484))))) & (! [X482 : term] : ? [X483 : (subst > term > term)] : ! [X485 : term,X484 : subst] : (((X483 @ X484 @ X485)) = ((sub @ X482 @ (push @ X485 @ X484)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((axshiftcons = $true) | ? [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) != X538)) & (! [X539 : term,X538 : subst] : (((comp @ sh @ (push @ X539 @ X538))) = X538) | (axshiftcons != $true)) & (! [X347 : (subst > term > subst > $o)] : ? [X348 : (term > $o)] : ! [X349 : term] : (((X347 @ id @ X349 @ id)) = ((X348 @ X349))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X347 : (subst > term > subst > $o)] : ! [X348 : (term > $o)] : ? [X349 : term] : (((X347 @ id @ X349 @ id)) != ((X348 @ X349)))) & (pushprop = $true) & ((hoasinduction = $true) | ? [X459 : term,X458 : (subst > term > subst > $o)] : (($true != ((sP8 @ X458))) & ! [X460 : term] : (($true != ((var @ (sub @ X460 @ id)))) | ($true = ((X458 @ id @ X460 @ id)))) & ($true != ((sP7 @ X458))) & ($true != ((X458 @ id @ X459 @ id))) & ! [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true != ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) | ($true = ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) & ! [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true = ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) | ($true != ((X458 @ X461 @ X464 @ (comp @ X462 @ X463))))))) & (! [X459 : term,X458 : (subst > term > subst > $o)] : (($true = ((sP8 @ X458))) | ? [X460 : term] : (($true = ((var @ (sub @ X460 @ id)))) & ($true != ((X458 @ id @ X460 @ id)))) | ($true = ((sP7 @ X458))) | ($true = ((X458 @ id @ X459 @ id))) | ? [X467 : term,X468 : subst,X470 : subst,X469 : subst] : (($true = ((X458 @ (comp @ X468 @ X470) @ (sub @ X467 @ X470) @ X469))) & ($true != ((X458 @ X468 @ X467 @ (comp @ X470 @ X469))))) | ? [X464 : term,X462 : subst,X463 : subst,X461 : subst] : (($true != ((X458 @ (comp @ X461 @ X462) @ (sub @ X464 @ X462) @ X463))) & ($true = ((X458 @ X461 @ X464 @ (comp @ X462 @ X463)))))) | (hoasinduction != $true)) & (hoasinduction_lem1_lthm = $true) & ((induction2 = $true) | ($true != sP6)) & (($true = sP6) | (induction2 != $true)) & (! [X456 : term,X457 : term] : ((X456 = X457) | (((sub @ X456 @ sh)) != ((sub @ X457 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X456 : term,X457 : term] : ((X456 != X457) & (((sub @ X456 @ sh)) = ((sub @ X457 @ sh))))) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) | (axvarid != $true)) & ((axvarid = $true) | ? [X124 : term] : (((sub @ X124 @ id)) != X124)) & (hoasinduction_lem1 = $true) & (axapp = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & ((termmset = $true) | ? [X399 : term] : (((sub @ X399 @ id)) != X399)) & (! [X399 : term] : (((sub @ X399 @ id)) = X399) | (termmset != $true)) & ! [X491 : d_term] : (d_one = X491) & (($true = sP5) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP5)) & ((hoasinduction_lem3b_lthm = $true) | ? [X8 : term] : ! [X9 : (subst > term > term)] : (((X9 @ sh @ one)) != ((sub @ X8 @ (push @ one @ sh))))) & (! [X8 : term] : ? [X9 : (subst > term > term)] : (((X9 @ sh @ one)) = ((sub @ X8 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) | ? [X11 : term,X10 : term] : ((((lam @ X10)) = ((lam @ X11))) & (X10 != X11))) & (! [X11 : term,X10 : term] : ((((lam @ X10)) != ((lam @ X11))) | (X10 = X11)) | (laminj != $true)) & ! [X500 : d_subst] : (d_id = X500) & (ulamvarind = $true) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axmap = $true) & ((hoaslaminj_lthm = $true) | (! [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) = X14) & ! [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) = X12) & ! [X17 : term,X16 : term] : ((((lam @ X17)) != ((lam @ X16))) | (X16 = X17)) & ? [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (! [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) = ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) & (((lam @ (X19 @ sh @ one))) = ((lam @ (X20 @ sh @ one)))) & (((X20 @ X18 @ X21)) != ((X19 @ X18 @ X21))) & ! [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) = ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23))))))) & (? [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) != X14) | ? [X13 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X13))) != X12) | ? [X17 : term,X16 : term] : ((((lam @ X17)) = ((lam @ X16))) & (X16 != X17)) | ! [X20 : (subst > term > term),X21 : term,X18 : subst,X19 : (subst > term > term)] : (? [X26 : subst,X25 : term,X27 : subst] : (((sub @ (X20 @ X26 @ X25) @ X27)) != ((X20 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | (((lam @ (X19 @ sh @ one))) != ((lam @ (X20 @ sh @ one)))) | (((X20 @ X18 @ X21)) = ((X19 @ X18 @ X21))) | ? [X23 : subst,X24 : subst,X22 : term] : (((sub @ (X19 @ X24 @ X22) @ X23)) != ((X19 @ (comp @ X24 @ X23) @ (sub @ X22 @ X23))))) | (hoaslaminj_lthm != $true)) & (hoaslamnotvar_lthm = $true) & (? [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true != ((X361 @ (lam @ X362)))) & ! [X364 : term] : (((X363 @ id @ X364 @ id)) = ((X361 @ X364))) & ! [X370 : term] : (($true != ((X361 @ X370))) | ($true = ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) & ! [X365 : (subst > term > term)] : (($true = ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) | ? [X369 : term] : (($true != ((X363 @ id @ (X365 @ id @ X369) @ id))) & ($true = ((X363 @ id @ X369 @ id)))) | ? [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) != ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) | ($true = sP3) | ($true = sP4) | ? [X350 : (subst > term > subst > $o)] : ! [X351 : (term > $o)] : ? [X352 : term] : (((X350 @ id @ X352 @ id)) != ((X351 @ X352))) | ? [X360 : term] : (((sub @ X360 @ id)) != X360) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X362 : term,X363 : (subst > term > subst > $o),X361 : (term > $o)] : (($true = ((X361 @ (lam @ X362)))) | ? [X364 : term] : (((X363 @ id @ X364 @ id)) != ((X361 @ X364))) | ? [X370 : term] : (($true = ((X361 @ X370))) & ($true != ((X361 @ (sub @ X362 @ (push @ X370 @ id)))))) | ? [X365 : (subst > term > term)] : (($true != ((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id))) & ! [X369 : term] : (($true = ((X363 @ id @ (X365 @ id @ X369) @ id))) | ($true != ((X363 @ id @ X369 @ id)))) & ! [X366 : subst,X368 : term,X367 : subst] : (((sub @ (X365 @ X366 @ X368) @ X367)) = ((X365 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))))) & ($true != sP3) & ($true != sP4) & ! [X350 : (subst > term > subst > $o)] : ? [X351 : (term > $o)] : ! [X352 : term] : (((X350 @ id @ X352 @ id)) = ((X351 @ X352))) & ! [X360 : term] : (((sub @ X360 @ id)) = X360))) & ((hoasinduction_lem3aaa = $true) | ? [X438 : (subst > term > subst > $o),X437 : term] : (($true != ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) & ! [X448 : term] : (($true = ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) | ($true != ((X438 @ id @ X448 @ id)))) & ! [X440 : term,X439 : (subst > term > term)] : (? [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) != ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) | ($true = ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) | ? [X441 : term] : (($true = ((X438 @ id @ X441 @ id))) & ($true != ((X438 @ id @ (X439 @ id @ X441) @ id)))) | ? [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) != ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444)))))) & (! [X438 : (subst > term > subst > $o),X437 : term] : (($true = ((X438 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id))) | ? [X448 : term] : (($true != ((X438 @ id @ (sub @ X437 @ (push @ X448 @ id)) @ id))) & ($true = ((X438 @ id @ X448 @ id)))) | ? [X440 : term,X439 : (subst > term > term)] : (! [X446 : term,X447 : subst,X445 : subst] : (((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X440 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ($true != ((X438 @ id @ (lam @ (X439 @ sh @ one)) @ id))) & ! [X441 : term] : (($true != ((X438 @ id @ X441 @ id))) | ($true = ((X438 @ id @ (X439 @ id @ X441) @ id)))) & ! [X442 : subst,X444 : subst,X443 : term] : (((sub @ (X439 @ X442 @ X443) @ X444)) = ((sub @ (sub @ X440 @ (push @ X443 @ X442)) @ X444))))) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X7 : d_term,X6 : d_term] : ((X6 = X7) | (((d2term @ X7)) != ((d2term @ X6)))) & ((hoasapinj1 = $true) | ? [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) = ((ap @ (sub @ X128 @ id) @ X127))) & (X125 != X128))) & (! [X125 : term,X128 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X125 @ id) @ X126)) != ((ap @ (sub @ X128 @ id) @ X127))) | (X125 = X128)) | (hoasapinj1 != $true)) & (hoaslamnotap_gthm = $true) & ! [X425 : term] : ? [X426 : d_term] : (((d2term @ X426)) = X425) & (pushprop_gthm = $true) & (hoasinduction_gthm = $true) & (! [X486 : (term > $o),X487 : subst,X488 : term] : ? [X489 : (term > $o)] : ! [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) = ((X489 @ X490))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X486 : (term > $o),X487 : subst,X488 : term] : ! [X489 : (term > $o)] : ? [X490 : term] : (((X486 @ (sub @ X490 @ (push @ X488 @ X487)))) != ((X489 @ X490)))) & (? [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) != X87) | ! [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true != ((X93 @ X91))) | ($true = ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X87 : subst,X88 : term] : (((comp @ sh @ (push @ X88 @ X87))) = X87) & ? [X90 : term,X93 : (term > $o),X91 : term,X92 : subst,X89 : (term > $o)] : (($true = ((X93 @ X91))) & ($true != ((X89 @ (sub @ X91 @ (push @ X90 @ X92)))))) & ! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85))) & (! [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (? [X514 : term] : (($true = ((X513 @ X514))) & ($true != ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) | ($true = ((sP2 @ X512))) | ? [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true != ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) & ($true = ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) | ? [X524 : term] : (((X513 @ X524)) != ((X512 @ id @ X524 @ id))) | ($true = ((X513 @ (lam @ X511)))) | ? [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true = ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) & (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) != $true))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X513 : (term > $o),X511 : term,X512 : (subst > term > subst > $o)] : (! [X514 : term] : (($true != ((X513 @ X514))) | ($true = ((X513 @ (sub @ X511 @ (push @ X514 @ id)))))) & ($true != ((sP2 @ X512))) & ! [X523 : term,X520 : subst,X522 : subst,X521 : subst] : (($true = ((X512 @ X522 @ X523 @ (comp @ X521 @ X520)))) | ($true != ((X512 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521) @ X520)))) & ! [X524 : term] : (((X513 @ X524)) = ((X512 @ id @ X524 @ id))) & ($true != ((X513 @ (lam @ X511)))) & ! [X526 : subst,X527 : term,X528 : subst,X525 : subst] : (($true != ((X512 @ X526 @ X527 @ (comp @ X525 @ X528)))) | (((X512 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525) @ X528)) = $true)))) & ((hoasapinj2 = $true) | ? [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 != X2) & (((ap @ (sub @ X0 @ id) @ X2)) = ((ap @ (sub @ X3 @ id) @ X1))))) & (! [X3 : term,X2 : term,X1 : term,X0 : term] : ((X1 = X2) | (((ap @ (sub @ X0 @ id) @ X2)) != ((ap @ (sub @ X3 @ id) @ X1)))) | (hoasapinj2 != $true)) & ((hoasapinj2_lthm = $true) | (! [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 = X29) | (((ap @ X30 @ X28)) != ((ap @ X31 @ X29)))) & ? [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 != X35) & (((ap @ (sub @ X34 @ id) @ X32)) = ((ap @ (sub @ X33 @ id) @ X35)))))) & (? [X29 : term,X31 : term,X30 : term,X28 : term] : ((X28 != X29) & (((ap @ X30 @ X28)) = ((ap @ X31 @ X29)))) | ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X32)) != ((ap @ (sub @ X33 @ id) @ X35)))) | (hoasapinj2_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) | ? [X502 : (subst > term > subst > $o),X501 : term] : (($true != ((X502 @ id @ (lam @ X501) @ id))) & ! [X508 : term] : (($true != ((X502 @ id @ X508 @ id))) | ($true = ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) & ! [X503 : (subst > term > term)] : (? [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) != ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) | ? [X507 : term] : (($true = ((X502 @ id @ X507 @ id))) & ($true != ((X502 @ id @ (X503 @ id @ X507) @ id)))) | ($true = ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id)))))) & (! [X502 : (subst > term > subst > $o),X501 : term] : (($true = ((X502 @ id @ (lam @ X501) @ id))) | ? [X508 : term] : (($true = ((X502 @ id @ X508 @ id))) & ($true != ((X502 @ id @ (sub @ X501 @ (push @ X508 @ id)) @ id)))) | ? [X503 : (subst > term > term)] : (! [X505 : term,X506 : subst,X504 : subst] : (((sub @ (X503 @ X506 @ X505) @ X504)) = ((X503 @ (comp @ X506 @ X504) @ (sub @ X505 @ X504)))) & ! [X507 : term] : (($true != ((X502 @ id @ X507 @ id))) | ($true = ((X502 @ id @ (X503 @ id @ X507) @ id)))) & ($true != ((X502 @ id @ (lam @ (X503 @ sh @ one)) @ id))))) | (hoasinduction_lem3a != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) | ? [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true != ((X75 @ (lam @ X77)))) & ! [X78 : term] : (((X76 @ id @ X78 @ id)) = ((X75 @ X78))) & ! [X79 : term] : (($true = ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) | ($true != ((X75 @ X79)))) & ! [X80 : (subst > term > term)] : (? [X81 : term] : (($true != ((X76 @ id @ (X80 @ id @ X81) @ id))) & ($true = ((X76 @ id @ X81 @ id)))) | ($true = ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) | ? [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) != ((sub @ (X80 @ X83 @ X84) @ X82)))))) & (! [X76 : (subst > term > subst > $o),X75 : (term > $o),X77 : term] : (($true = ((X75 @ (lam @ X77)))) | ? [X78 : term] : (((X76 @ id @ X78 @ id)) != ((X75 @ X78))) | ? [X79 : term] : (($true != ((X75 @ (sub @ X77 @ (push @ X79 @ id))))) & ($true = ((X75 @ X79)))) | ? [X80 : (subst > term > term)] : (! [X81 : term] : (($true = ((X76 @ id @ (X80 @ id @ X81) @ id))) | ($true != ((X76 @ id @ X81 @ id)))) & ($true != ((X76 @ id @ (lam @ (X80 @ sh @ one)) @ id))) & ! [X84 : term,X82 : subst,X83 : subst] : (((X80 @ (comp @ X83 @ X82) @ (sub @ X84 @ X82))) = ((sub @ (X80 @ X83 @ X84) @ X82))))) | (hoasinduction_lem3v2a != $true)) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X144 : term] : ! [X145 : (subst > term > term)] : ? [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) != ((X145 @ X146 @ X147)))) & (! [X144 : term] : ? [X145 : (subst > term > term)] : ! [X147 : term,X146 : subst] : (((sub @ X144 @ (push @ X147 @ X146))) = ((X145 @ X146 @ X147))) | (hoasinduction_lem3v2_f != $true)) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X338 : term,X339 : (subst > term > subst > $o)] : (! [X342 : (subst > term > term)] : (($true = ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) | ? [X346 : term] : (($true != ((X339 @ id @ (X342 @ id @ X346) @ id))) & ($true = ((X339 @ id @ X346 @ id)))) | ? [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) != ((sub @ (X342 @ X345 @ X344) @ X343)))) & ! [X341 : term,X340 : term] : (($true = ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) | ($true != ((X339 @ id @ X340 @ id))) | ($true != ((X339 @ id @ X341 @ id)))) & ($true != ((X339 @ id @ X338 @ id))))) & (! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X342 : (subst > term > term)] : (($true != ((X339 @ id @ (lam @ (X342 @ sh @ one)) @ id))) & ! [X346 : term] : (($true = ((X339 @ id @ (X342 @ id @ X346) @ id))) | ($true != ((X339 @ id @ X346 @ id)))) & ! [X344 : term,X343 : subst,X345 : subst] : (((X342 @ (comp @ X345 @ X343) @ (sub @ X344 @ X343))) = ((sub @ (X342 @ X345 @ X344) @ X343)))) | ? [X341 : term,X340 : term] : (($true != ((X339 @ id @ (ap @ (sub @ X341 @ id) @ X340) @ id))) & ($true = ((X339 @ id @ X340 @ id))) & ($true = ((X339 @ id @ X341 @ id)))) | ($true = ((X339 @ id @ X338 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (hoaslamnotvar = $true) & (! [X5 : term] : (((sub @ X5 @ id)) = X5) | ? [X4 : term] : (((sub @ X4 @ id)) != X4) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X5 : term] : (((sub @ X5 @ id)) != X5) & ! [X4 : term] : (((sub @ X4 @ id)) = X4))) & (lamnotvar = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((apinj1 = $true) | ? [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 != X430) & (((ap @ X430 @ X428)) = ((ap @ X427 @ X429))))) & (! [X430 : term,X427 : term,X429 : term,X428 : term] : ((X427 = X430) | (((ap @ X430 @ X428)) != ((ap @ X427 @ X429)))) | (apinj1 != $true)) & ((induction2lem_lthm = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem_lthm != $true))), 24.89/4.11 inference(flattening,[],[f130])). 24.89/4.11 thf(f132,plain,( 24.89/4.11 ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & (! [X2 : term,X3 : subst] : (((sub @ one @ (push @ X2 @ X3))) = X2) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X4 : term,X5 : subst] : (((sub @ one @ (push @ X4 @ X5))) != X4)) & (((d2subst @ d_id)) = id) & (axvarshift = $true) & (! [X6 : term,X7 : (subst > term > subst > $o)] : (($true = ((X7 @ id @ (lam @ (sub @ X6 @ (push @ one @ sh))) @ id))) | ? [X8 : term] : (($true = ((X7 @ id @ X8 @ id))) & ($true != ((X7 @ id @ (sub @ X6 @ (push @ X8 @ id)) @ id)))) | ? [X9 : (subst > term > term)] : (! [X10 : term,X11 : subst,X12 : subst] : (((sub @ (X9 @ X11 @ X10) @ X12)) = ((X9 @ (comp @ X11 @ X12) @ (sub @ X10 @ X12)))) & ! [X13 : term] : (($true = ((X7 @ id @ (X9 @ id @ X13) @ id))) | ($true != ((X7 @ id @ X13 @ id)))) & ($true != ((X7 @ id @ (lam @ (X9 @ sh @ one)) @ id))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X14 : term,X15 : (subst > term > subst > $o)] : (($true != ((X15 @ id @ (lam @ (sub @ X14 @ (push @ one @ sh))) @ id))) & ! [X16 : term] : (($true != ((X15 @ id @ X16 @ id))) | ($true = ((X15 @ id @ (sub @ X14 @ (push @ X16 @ id)) @ id)))) & ! [X17 : (subst > term > term)] : (? [X18 : term,X19 : subst,X20 : subst] : (((sub @ (X17 @ X19 @ X18) @ X20)) != ((X17 @ (comp @ X19 @ X20) @ (sub @ X18 @ X20)))) | ? [X21 : term] : (($true != ((X15 @ id @ (X17 @ id @ X21) @ id))) & ($true = ((X15 @ id @ X21 @ id)))) | ($true = ((X15 @ id @ (lam @ (X17 @ sh @ one)) @ id)))))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP27) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP27)) & ((hoasapinj1_lthm = $true) | (? [X22 : term,X23 : term,X24 : term,X25 : term] : ((((ap @ (sub @ X24 @ id) @ X25)) = ((ap @ (sub @ X23 @ id) @ X22))) & (X23 != X24)) & ! [X26 : term,X27 : term,X28 : term,X29 : term] : ((((ap @ X28 @ X29)) != ((ap @ X27 @ X26))) | (X27 = X28)) & ! [X30 : term] : (((sub @ X30 @ id)) = X30))) & (! [X31 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X33 @ id) @ X34)) != ((ap @ (sub @ X32 @ id) @ X31))) | (X32 = X33)) | ? [X35 : term,X36 : term,X37 : term,X38 : term] : ((((ap @ X36 @ X35)) = ((ap @ X37 @ X38))) & (X36 != X37)) | ? [X39 : term] : (((sub @ X39 @ id)) != X39) | (hoasapinj1_lthm != $true)) & (hoasapnotvar = $true) & (axabs = $true) & ! [X40 : d_subst,X41 : d_subst] : ((X40 = X41) | (((d2subst @ X40)) != ((d2subst @ X41)))) & ((axidr = $true) | ? [X42 : subst] : (((comp @ X42 @ id)) != X42)) & (! [X43 : subst] : (((comp @ X43 @ id)) = X43) | (axidr != $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X44 : (subst > term > subst > $o),X45 : (term > $o),X46 : term] : (($true = ((X45 @ (lam @ X46)))) | ? [X47 : subst,X48 : term,X49 : subst,X50 : subst] : (($true != ((X44 @ X50 @ X48 @ (comp @ X47 @ X49)))) & ($true = ((X44 @ (comp @ X50 @ X47) @ (sub @ X48 @ X47) @ X49)))) | ? [X51 : term] : (((X44 @ id @ X51 @ id)) != ((X45 @ X51))) | ? [X52 : term] : (($true = ((X45 @ X52))) & ($true != ((X45 @ (sub @ X46 @ (push @ X52 @ id)))))) | ? [X53 : term,X54 : subst,X55 : subst,X56 : subst] : (($true != ((X44 @ (comp @ X54 @ X56) @ (sub @ X53 @ X56) @ X55))) & ($true = ((X44 @ X54 @ X53 @ (comp @ X56 @ X55))))) | ($true = ((sP26 @ X44)))) | ? [X57 : term] : (((sub @ X57 @ id)) != X57) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (? [X58 : (subst > term > subst > $o),X59 : (term > $o),X60 : term] : (($true != ((X59 @ (lam @ X60)))) & ! [X61 : subst,X62 : term,X63 : subst,X64 : subst] : (($true = ((X58 @ X64 @ X62 @ (comp @ X61 @ X63)))) | ($true != ((X58 @ (comp @ X64 @ X61) @ (sub @ X62 @ X61) @ X63)))) & ! [X65 : term] : (((X59 @ X65)) = ((X58 @ id @ X65 @ id))) & ! [X66 : term] : (($true != ((X59 @ X66))) | ($true = ((X59 @ (sub @ X60 @ (push @ X66 @ id)))))) & ! [X67 : term,X68 : subst,X69 : subst,X70 : subst] : (($true = ((X58 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69))) | ($true != ((X58 @ X68 @ X67 @ (comp @ X70 @ X69))))) & ($true != ((sP26 @ X58)))) & ! [X71 : term] : (((sub @ X71 @ id)) = X71))) & (pushprop_lem2v2_gthm = $true) & (? [X72 : subst,X73 : term] : (((sub @ one @ (push @ X73 @ X72))) != X73) | ! [X74 : (term > $o),X75 : term,X76 : subst,X77 : (term > $o)] : (? [X78 : term] : (((X74 @ X78)) != ((X77 @ (sub @ X78 @ (push @ X75 @ X76))))) | ($true != ((X77 @ X75))) | ($true = ((X74 @ one)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X79 : subst,X80 : term] : (((sub @ one @ (push @ X80 @ X79))) = X80) & ? [X81 : (term > $o),X82 : term,X83 : subst,X84 : (term > $o)] : (! [X85 : term] : (((X81 @ X85)) = ((X84 @ (sub @ X85 @ (push @ X82 @ X83))))) & ($true = ((X84 @ X82))) & ($true != ((X81 @ one)))))) & ((pushprop_lem1 = $true) | ? [X86 : term,X87 : (term > $o),X88 : subst,X89 : (term > $o),X90 : term] : (($true = ((X87 @ X86))) & ($true != ((X89 @ (sub @ X86 @ (push @ X90 @ X88))))))) & (! [X91 : term,X92 : (term > $o),X93 : subst,X94 : (term > $o),X95 : term] : (($true != ((X92 @ X91))) | ($true = ((X94 @ (sub @ X91 @ (push @ X95 @ X93)))))) | (pushprop_lem1 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X96 : term,X97 : term,X98 : term,X99 : term] : ((X96 = X99) | (((ap @ X98 @ X99)) != ((ap @ X97 @ X96)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X100 : term,X101 : term,X102 : term,X103 : term] : ((X100 != X103) & (((ap @ X101 @ X100)) = ((ap @ X102 @ X103))))) & ((hoasinduction_lem3a_lthm = $true) | (! [X104 : term,X105 : (subst > term > subst > $o)] : (($true = ((X105 @ id @ (lam @ (sub @ X104 @ (push @ one @ sh))) @ id))) | ? [X106 : term] : (($true != ((X105 @ id @ (sub @ X104 @ (push @ X106 @ id)) @ id))) & ($true = ((X105 @ id @ X106 @ id)))) | ? [X107 : (subst > term > term)] : (($true != ((X105 @ id @ (lam @ (X107 @ sh @ one)) @ id))) & ! [X108 : term] : (($true != ((X105 @ id @ X108 @ id))) | ($true = ((X105 @ id @ (X107 @ id @ X108) @ id)))) & ! [X109 : subst,X110 : subst,X111 : term] : (((sub @ (X107 @ X109 @ X111) @ X110)) = ((X107 @ (comp @ X109 @ X110) @ (sub @ X111 @ X110)))))) & ($true != sP25) & ! [X112 : term] : (((sub @ X112 @ id)) = X112))) & (? [X113 : term,X114 : (subst > term > subst > $o)] : (($true != ((X114 @ id @ (lam @ (sub @ X113 @ (push @ one @ sh))) @ id))) & ! [X115 : term] : (($true = ((X114 @ id @ (sub @ X113 @ (push @ X115 @ id)) @ id))) | ($true != ((X114 @ id @ X115 @ id)))) & ! [X116 : (subst > term > term)] : ((((X114 @ id @ (lam @ (X116 @ sh @ one)) @ id)) = $true) | ? [X117 : term] : (($true = ((X114 @ id @ X117 @ id))) & ($true != ((X114 @ id @ (X116 @ id @ X117) @ id)))) | ? [X118 : subst,X119 : subst,X120 : term] : (((X116 @ (comp @ X118 @ X119) @ (sub @ X120 @ X119))) != ((sub @ (X116 @ X118 @ X120) @ X119))))) | ($true = sP25) | ? [X121 : term] : (((sub @ X121 @ id)) != X121) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3aa = $true) | ? [X122 : term,X123 : (subst > term > subst > $o)] : (! [X124 : (subst > term > term)] : (($true = ((X123 @ id @ (lam @ (X124 @ sh @ one)) @ id))) | ? [X125 : term,X126 : subst,X127 : subst] : (((X124 @ (comp @ X126 @ X127) @ (sub @ X125 @ X127))) != ((sub @ (X124 @ X126 @ X125) @ X127))) | ? [X128 : term] : (($true = ((X123 @ id @ X128 @ id))) & ($true != ((X123 @ id @ (X124 @ id @ X128) @ id))))) & ($true != ((X123 @ id @ (lam @ (sub @ X122 @ (push @ one @ sh))) @ id))) & ! [X129 : term] : (($true != ((X123 @ id @ X129 @ id))) | ($true = ((X123 @ id @ (sub @ X122 @ (push @ X129 @ id)) @ id)))))) & (! [X130 : term,X131 : (subst > term > subst > $o)] : (? [X132 : (subst > term > term)] : (($true != ((X131 @ id @ (lam @ (X132 @ sh @ one)) @ id))) & ! [X133 : term,X134 : subst,X135 : subst] : (((X132 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135))) = ((sub @ (X132 @ X134 @ X133) @ X135))) & ! [X136 : term] : (($true != ((X131 @ id @ X136 @ id))) | ($true = ((X131 @ id @ (X132 @ id @ X136) @ id))))) | ($true = ((X131 @ id @ (lam @ (sub @ X130 @ (push @ one @ sh))) @ id))) | ? [X137 : term] : (($true = ((X131 @ id @ X137 @ id))) & ($true != ((X131 @ id @ (sub @ X130 @ (push @ X137 @ id)) @ id))))) | (hoasinduction_lem3aa != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (($true = sP24) | ? [X138 : term] : (((sub @ X138 @ id)) != X138) | ? [X139 : term,X140 : (subst > term > subst > $o)] : (! [X141 : (subst > term > term)] : (? [X142 : term,X143 : subst,X144 : subst] : (((sub @ (X141 @ X143 @ X142) @ X144)) != ((X141 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144)))) | ($true = ((X140 @ id @ (lam @ (X141 @ sh @ one)) @ id))) | ? [X145 : term] : (($true != ((X140 @ id @ (X141 @ id @ X145) @ id))) & ($true = ((X140 @ id @ X145 @ id))))) & ! [X146 : term] : (($true != ((X140 @ id @ X146 @ id))) | ($true = ((X140 @ id @ (sub @ X139 @ (push @ X146 @ id)) @ id)))) & ($true != ((X140 @ id @ (lam @ (sub @ X139 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP24) & ! [X147 : term] : (((sub @ X147 @ id)) = X147) & ! [X148 : term,X149 : (subst > term > subst > $o)] : (? [X150 : (subst > term > term)] : (! [X151 : term,X152 : subst,X153 : subst] : (((sub @ (X150 @ X152 @ X151) @ X153)) = ((X150 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153)))) & ($true != ((X149 @ id @ (lam @ (X150 @ sh @ one)) @ id))) & ! [X154 : term] : (($true = ((X149 @ id @ (X150 @ id @ X154) @ id))) | ($true != ((X149 @ id @ X154 @ id))))) | ? [X155 : term] : (($true = ((X149 @ id @ X155 @ id))) & ($true != ((X149 @ id @ (sub @ X148 @ (push @ X155 @ id)) @ id)))) | ($true = ((X149 @ id @ (lam @ (sub @ X148 @ (push @ one @ sh))) @ id)))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm = $true) | (($true != sP22) & ($true != sP21) & ($true != sP20) & ! [X156 : (subst > term > subst > $o),X157 : term] : (? [X158 : term] : (($true != ((X156 @ id @ (sub @ X157 @ (push @ X158 @ id)) @ id))) & ($true = ((X156 @ id @ X158 @ id)))) | ($true != ((sP17 @ X156))) | ? [X159 : subst,X160 : subst,X161 : term,X162 : subst] : (($true != ((X156 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X162))) & ($true = ((X156 @ X160 @ X161 @ (comp @ X159 @ X162))))) | ? [X163 : subst,X164 : subst,X165 : term,X166 : subst] : (($true != ((X156 @ X166 @ X165 @ (comp @ X164 @ X163)))) & ($true = ((X156 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164) @ X163)))) | ($true = ((X156 @ id @ (lam @ X157) @ id)))))) & (($true = sP22) | ($true = sP21) | ($true = sP20) | ? [X167 : (subst > term > subst > $o),X168 : term] : (! [X169 : term] : (($true = ((X167 @ id @ (sub @ X168 @ (push @ X169 @ id)) @ id))) | ($true != ((X167 @ id @ X169 @ id)))) & ($true = ((sP17 @ X167))) & ! [X170 : subst,X171 : subst,X172 : term,X173 : subst] : (($true = ((X167 @ (comp @ X171 @ X170) @ (sub @ X172 @ X170) @ X173))) | ($true != ((X167 @ X171 @ X172 @ (comp @ X170 @ X173))))) & ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : (($true = ((X167 @ X177 @ X176 @ (comp @ X175 @ X174)))) | ($true != ((X167 @ (comp @ X177 @ X175) @ (sub @ X176 @ X175) @ X174)))) & ($true != ((X167 @ id @ (lam @ X168) @ id)))) | (hoasinduction_lthm != $true)) & (? [X178 : term] : ! [X179 : (subst > term > term)] : ? [X180 : term,X181 : subst] : (((sub @ X178 @ (push @ X180 @ X181))) != ((X179 @ X181 @ X180))) | ? [X182 : term] : (((sub @ X182 @ id)) != X182) | ! [X183 : (subst > term > subst > $o),X184 : term,X185 : (term > $o)] : (? [X186 : term] : (((X185 @ X186)) != ((X183 @ id @ X186 @ id))) | ? [X187 : (subst > term > term)] : (($true != ((X183 @ id @ (lam @ (X187 @ sh @ one)) @ id))) & ! [X188 : term] : (($true = ((X183 @ id @ (X187 @ id @ X188) @ id))) | ($true != ((X183 @ id @ X188 @ id)))) & ! [X189 : subst,X190 : term,X191 : subst] : (((sub @ (X187 @ X191 @ X190) @ X189)) = ((X187 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189))))) | ? [X192 : term] : (($true = ((X185 @ X192))) & ($true != ((X185 @ (sub @ X184 @ (push @ X192 @ id)))))) | ($true = ((X185 @ (lam @ X184))))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X193 : term] : ? [X194 : (subst > term > term)] : ! [X195 : term,X196 : subst] : (((X194 @ X196 @ X195)) = ((sub @ X193 @ (push @ X195 @ X196)))) & ! [X197 : term] : (((sub @ X197 @ id)) = X197) & ? [X198 : (subst > term > subst > $o),X199 : term,X200 : (term > $o)] : (! [X201 : term] : (((X198 @ id @ X201 @ id)) = ((X200 @ X201))) & ! [X202 : (subst > term > term)] : (($true = ((X198 @ id @ (lam @ (X202 @ sh @ one)) @ id))) | ? [X203 : term] : (($true != ((X198 @ id @ (X202 @ id @ X203) @ id))) & ($true = ((X198 @ id @ X203 @ id)))) | ? [X204 : subst,X205 : term,X206 : subst] : (((sub @ (X202 @ X206 @ X205) @ X204)) != ((X202 @ (comp @ X206 @ X204) @ (sub @ X205 @ X204))))) & ! [X207 : term] : (($true != ((X200 @ X207))) | ($true = ((X200 @ (sub @ X199 @ (push @ X207 @ id)))))) & ($true != ((X200 @ (lam @ X199))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj = $true) | ? [X208 : (subst > term > term),X209 : term,X210 : (subst > term > term),X211 : subst] : ((((X208 @ X211 @ X209)) != ((X210 @ X211 @ X209))) & (((lam @ (X208 @ sh @ one))) = ((lam @ (X210 @ sh @ one)))) & ! [X212 : subst,X213 : subst,X214 : term] : (((X210 @ (comp @ X212 @ X213) @ (sub @ X214 @ X213))) = ((sub @ (X210 @ X212 @ X214) @ X213))) & ! [X215 : subst,X216 : subst,X217 : term] : (((sub @ (X208 @ X215 @ X217) @ X216)) = ((X208 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216)))))) & (! [X218 : (subst > term > term),X219 : term,X220 : (subst > term > term),X221 : subst] : ((((X220 @ X221 @ X219)) = ((X218 @ X221 @ X219))) | (((lam @ (X218 @ sh @ one))) != ((lam @ (X220 @ sh @ one)))) | ? [X222 : subst,X223 : subst,X224 : term] : (((sub @ (X220 @ X222 @ X224) @ X223)) != ((X220 @ (comp @ X222 @ X223) @ (sub @ X224 @ X223)))) | ? [X225 : subst,X226 : subst,X227 : term] : (((X218 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226))) != ((sub @ (X218 @ X225 @ X227) @ X226)))) | (hoaslaminj != $true)) & (hoasapinj2_gthm = $true) & ((! [X228 : subst] : (((comp @ id @ X228)) = X228) & ! [X229 : subst] : (((comp @ X229 @ id)) = X229)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X230 : subst] : (((comp @ id @ X230)) != X230) | ? [X231 : subst] : (((comp @ X231 @ id)) != X231)) & (axclos = $true) & (! [X232 : (term > $o),X233 : subst,X234 : term] : ? [X235 : (term > $o)] : ! [X236 : term] : (((X232 @ (sub @ X236 @ (push @ X234 @ X233)))) = ((X235 @ X236))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X237 : (term > $o),X238 : subst,X239 : term] : ! [X240 : (term > $o)] : ? [X241 : term] : (((X237 @ (sub @ X241 @ (push @ X239 @ X238)))) != ((X240 @ X241)))) & (hoasinduction_lem2_lthm = $true) & (! [X242 : term,X243 : term,X244 : (subst > term > term)] : (? [X245 : subst,X246 : term,X247 : subst] : (((X244 @ (comp @ X245 @ X247) @ (sub @ X246 @ X247))) != ((sub @ (X244 @ X245 @ X246) @ X247))) | (((ap @ (sub @ X242 @ id) @ X243)) != ((lam @ (X244 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X248 : term,X249 : term,X250 : (subst > term > term)] : (! [X251 : subst,X252 : term,X253 : subst] : (((X250 @ (comp @ X251 @ X253) @ (sub @ X252 @ X253))) = ((sub @ (X250 @ X251 @ X252) @ X253))) & (((lam @ (X250 @ sh @ one))) = ((ap @ (sub @ X248 @ id) @ X249))))) & (pushprop_lem3v2_lthm = $true) & (? [X254 : subst] : (((comp @ id @ X254)) != X254) | ? [X255 : subst] : (((comp @ X255 @ id)) != X255) | (! [X256 : subst] : (((comp @ X256 @ id)) = X256) & ! [X257 : subst] : (((comp @ id @ X257)) = X257)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X258 : subst] : (((comp @ id @ X258)) = X258) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259) & (? [X260 : subst] : (((comp @ X260 @ id)) != X260) | ? [X261 : subst] : (((comp @ id @ X261)) != X261)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & ((axscons = $true) | ? [X262 : subst] : (((push @ (sub @ one @ X262) @ (comp @ sh @ X262))) != X262)) & (! [X263 : subst] : (((push @ (sub @ one @ X263) @ (comp @ sh @ X263))) = X263) | (axscons != $true)) & (hoasinduction_lem1v2_gthm = $true) & (apnotvar = $true) & (? [X264 : (subst > term > subst > $o)] : ! [X265 : (term > $o)] : ? [X266 : term] : (((X264 @ id @ X266 @ id)) != ((X265 @ X266))) | ($true = sP16) | ? [X267 : term] : (((sub @ X267 @ id)) != X267) | ($true = sP15) | ? [X268 : (subst > term > subst > $o),X269 : (term > $o),X270 : term] : (! [X271 : (subst > term > term)] : (? [X272 : term,X273 : subst,X274 : subst] : (((sub @ (X271 @ X274 @ X272) @ X273)) != ((X271 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273)))) | ($true = ((X268 @ id @ (lam @ (X271 @ sh @ one)) @ id))) | ? [X275 : term] : (($true = ((X268 @ id @ X275 @ id))) & ($true != ((X268 @ id @ (X271 @ id @ X275) @ id))))) & ! [X276 : term] : (($true != ((X269 @ X276))) | ($true = ((X269 @ (sub @ X270 @ (push @ X276 @ id)))))) & ! [X277 : term] : (((X269 @ X277)) = ((X268 @ id @ X277 @ id))) & ($true != ((X269 @ (lam @ X270))))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X278 : (subst > term > subst > $o)] : ? [X279 : (term > $o)] : ! [X280 : term] : (((X279 @ X280)) = ((X278 @ id @ X280 @ id))) & ($true != sP16) & ! [X281 : term] : (((sub @ X281 @ id)) = X281) & ($true != sP15) & ! [X282 : (subst > term > subst > $o),X283 : (term > $o),X284 : term] : (? [X285 : (subst > term > term)] : (! [X286 : term,X287 : subst,X288 : subst] : (((sub @ (X285 @ X288 @ X286) @ X287)) = ((X285 @ (comp @ X288 @ X287) @ (sub @ X286 @ X287)))) & ($true != ((X282 @ id @ (lam @ (X285 @ sh @ one)) @ id))) & ! [X289 : term] : (($true != ((X282 @ id @ X289 @ id))) | ($true = ((X282 @ id @ (X285 @ id @ X289) @ id))))) | ? [X290 : term] : (($true = ((X283 @ X290))) & ($true != ((X283 @ (sub @ X284 @ (push @ X290 @ id)))))) | ? [X291 : term] : (((X282 @ id @ X291 @ id)) != ((X283 @ X291))) | ($true = ((X283 @ (lam @ X284))))))) & ((hoasinduction_lem0_lthm = $true) | ? [X292 : (subst > term > subst > $o)] : ! [X293 : (term > $o)] : ? [X294 : term] : (((X292 @ id @ X294 @ id)) != ((X293 @ X294)))) & (! [X295 : (subst > term > subst > $o)] : ? [X296 : (term > $o)] : ! [X297 : term] : (((X296 @ X297)) = ((X295 @ id @ X297 @ id))) | (hoasinduction_lem0_lthm != $true)) & (! [X298 : term] : ? [X299 : (subst > term > term)] : (((sub @ X298 @ (push @ one @ sh))) = ((X299 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X300 : term] : ! [X301 : (subst > term > term)] : (((sub @ X300 @ (push @ one @ sh))) != ((X301 @ sh @ one)))) & (hoaslamnotap_lthm = $true) & (($true = sP12) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP12)) & ((pushprop_lem1v2 = $true) | ? [X302 : term,X303 : (term > $o),X304 : (term > $o),X305 : subst] : (! [X306 : term] : (((X304 @ (sub @ X306 @ (push @ X302 @ X305)))) = ((X303 @ X306))) & (((X303 @ one)) != $true) & ($true = ((X304 @ X302))))) & (! [X307 : term,X308 : (term > $o),X309 : (term > $o),X310 : subst] : (? [X311 : term] : (((X308 @ X311)) != ((X309 @ (sub @ X311 @ (push @ X307 @ X310))))) | ($true = ((X308 @ one))) | ($true != ((X309 @ X307)))) | (pushprop_lem1v2 != $true)) & (! [X312 : term,X313 : (subst > term > subst > $o)] : (? [X314 : term] : (($true = ((X313 @ id @ X314 @ id))) & ($true != ((X313 @ id @ (sub @ X312 @ (push @ X314 @ id)) @ id)))) | ? [X315 : subst,X316 : subst,X317 : term,X318 : subst] : (($true != ((X313 @ (comp @ X316 @ X318) @ (sub @ X317 @ X318) @ X315))) & (((X313 @ X316 @ X317 @ (comp @ X318 @ X315))) = $true)) | ? [X319 : subst,X320 : subst,X321 : subst,X322 : term] : (($true = ((X313 @ (comp @ X319 @ X320) @ (sub @ X322 @ X320) @ X321))) & ($true != ((X313 @ X319 @ X322 @ (comp @ X320 @ X321))))) | ($true = ((X313 @ id @ (lam @ X312) @ id))) | ($true = ((sP10 @ X313)))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ? [X323 : term,X324 : (subst > term > subst > $o)] : (! [X325 : term] : (($true != ((X324 @ id @ X325 @ id))) | ($true = ((X324 @ id @ (sub @ X323 @ (push @ X325 @ id)) @ id)))) & ! [X326 : subst,X327 : subst,X328 : term,X329 : subst] : (($true = ((X324 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329) @ X326))) | ($true != ((X324 @ X327 @ X328 @ (comp @ X329 @ X326))))) & ! [X330 : subst,X331 : subst,X332 : subst,X333 : term] : (($true != ((X324 @ (comp @ X330 @ X331) @ (sub @ X333 @ X331) @ X332))) | ($true = ((X324 @ X330 @ X333 @ (comp @ X331 @ X332))))) & ($true != ((X324 @ id @ (lam @ X323) @ id))) & ($true != ((sP10 @ X324))))) & (hoasinduction_lem3v2_gthm = $true) & (($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) | ? [X334 : subst] : (((comp @ id @ X334)) != X334)) & (! [X335 : subst] : (((comp @ id @ X335)) = X335) | (axidl != $true)) & (lamnotap != $true) & ((induction = $true) | ? [X336 : (term > $o),X337 : term] : (! [X338 : term] : (($true = ((X336 @ X338))) | ($true != ((var @ X338)))) & ($true != ((X336 @ X337))) & ! [X339 : term] : (($true != ((X336 @ X339))) | ($true = ((X336 @ (lam @ X339))))) & ! [X340 : term,X341 : term] : (($true != ((X336 @ X341))) | ($true = ((X336 @ (ap @ X340 @ X341)))) | ($true != ((X336 @ X340)))))) & (! [X342 : (term > $o),X343 : term] : (? [X344 : term] : (($true != ((X342 @ X344))) & ($true = ((var @ X344)))) | ($true = ((X342 @ X343))) | ? [X345 : term] : (($true = ((X342 @ X345))) & ($true != ((X342 @ (lam @ X345))))) | ? [X346 : term,X347 : term] : (($true = ((X342 @ X347))) & ($true != ((X342 @ (ap @ X346 @ X347)))) & ($true = ((X342 @ X346))))) | (induction != $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X348 : term] : ! [X349 : (subst > term > term)] : ? [X350 : term,X351 : subst] : (((sub @ X348 @ (push @ X350 @ X351))) != ((X349 @ X351 @ X350)))) & (! [X352 : term] : ? [X353 : (subst > term > term)] : ! [X354 : term,X355 : subst] : (((sub @ X352 @ (push @ X354 @ X355))) = ((X353 @ X355 @ X354))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((axshiftcons = $true) | ? [X356 : term,X357 : subst] : (((comp @ sh @ (push @ X356 @ X357))) != X357)) & (! [X358 : term,X359 : subst] : (((comp @ sh @ (push @ X358 @ X359))) = X359) | (axshiftcons != $true)) & (! [X360 : (subst > term > subst > $o)] : ? [X361 : (term > $o)] : ! [X362 : term] : (((X360 @ id @ X362 @ id)) = ((X361 @ X362))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X363 : (subst > term > subst > $o)] : ! [X364 : (term > $o)] : ? [X365 : term] : (((X364 @ X365)) != ((X363 @ id @ X365 @ id)))) & (pushprop = $true) & ((hoasinduction = $true) | ? [X366 : term,X367 : (subst > term > subst > $o)] : (($true != ((sP8 @ X367))) & ! [X368 : term] : (($true != ((var @ (sub @ X368 @ id)))) | ($true = ((X367 @ id @ X368 @ id)))) & ($true != ((sP7 @ X367))) & ($true != ((X367 @ id @ X366 @ id))) & ! [X369 : term,X370 : subst,X371 : subst,X372 : subst] : (($true != ((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371) @ X372))) | ($true = ((X367 @ X370 @ X369 @ (comp @ X371 @ X372))))) & ! [X373 : term,X374 : subst,X375 : subst,X376 : subst] : (($true = ((X367 @ (comp @ X376 @ X374) @ (sub @ X373 @ X374) @ X375))) | ($true != ((X367 @ X376 @ X373 @ (comp @ X374 @ X375))))))) & (! [X377 : term,X378 : (subst > term > subst > $o)] : (($true = ((sP8 @ X378))) | ? [X379 : term] : (($true = ((var @ (sub @ X379 @ id)))) & ($true != ((X378 @ id @ X379 @ id)))) | ($true = ((sP7 @ X378))) | ($true = ((X378 @ id @ X377 @ id))) | ? [X380 : term,X381 : subst,X382 : subst,X383 : subst] : (($true = ((X378 @ (comp @ X381 @ X382) @ (sub @ X380 @ X382) @ X383))) & ($true != ((X378 @ X381 @ X380 @ (comp @ X382 @ X383))))) | ? [X384 : term,X385 : subst,X386 : subst,X387 : subst] : (($true != ((X378 @ (comp @ X387 @ X385) @ (sub @ X384 @ X385) @ X386))) & ($true = ((X378 @ X387 @ X384 @ (comp @ X385 @ X386)))))) | (hoasinduction != $true)) & (hoasinduction_lem1_lthm = $true) & ((induction2 = $true) | ($true != sP6)) & (($true = sP6) | (induction2 != $true)) & (! [X388 : term,X389 : term] : ((X388 = X389) | (((sub @ X389 @ sh)) != ((sub @ X388 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X390 : term,X391 : term] : ((X390 != X391) & (((sub @ X390 @ sh)) = ((sub @ X391 @ sh))))) & (! [X392 : term] : (((sub @ X392 @ id)) = X392) | (axvarid != $true)) & ((axvarid = $true) | ? [X393 : term] : (((sub @ X393 @ id)) != X393)) & (hoasinduction_lem1 = $true) & (axapp = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & ((termmset = $true) | ? [X394 : term] : (((sub @ X394 @ id)) != X394)) & (! [X395 : term] : (((sub @ X395 @ id)) = X395) | (termmset != $true)) & ! [X396 : d_term] : (d_one = X396) & (($true = sP5) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP5)) & ((hoasinduction_lem3b_lthm = $true) | ? [X397 : term] : ! [X398 : (subst > term > term)] : (((sub @ X397 @ (push @ one @ sh))) != ((X398 @ sh @ one)))) & (! [X399 : term] : ? [X400 : (subst > term > term)] : (((sub @ X399 @ (push @ one @ sh))) = ((X400 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) | ? [X401 : term,X402 : term] : ((((lam @ X401)) = ((lam @ X402))) & (X401 != X402))) & (! [X403 : term,X404 : term] : ((((lam @ X403)) != ((lam @ X404))) | (X403 = X404)) | (laminj != $true)) & ! [X405 : d_subst] : (d_id = X405) & (ulamvarind = $true) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axmap = $true) & ((hoaslaminj_lthm = $true) | (! [X406 : subst,X407 : term] : (((comp @ sh @ (push @ X407 @ X406))) = X406) & ! [X408 : subst,X409 : term] : (((sub @ one @ (push @ X409 @ X408))) = X409) & ! [X410 : term,X411 : term] : ((((lam @ X410)) != ((lam @ X411))) | (X410 = X411)) & ? [X412 : (subst > term > term),X413 : term,X414 : subst,X415 : (subst > term > term)] : (! [X416 : subst,X417 : term,X418 : subst] : (((sub @ (X412 @ X416 @ X417) @ X418)) = ((X412 @ (comp @ X416 @ X418) @ (sub @ X417 @ X418)))) & (((lam @ (X412 @ sh @ one))) = ((lam @ (X415 @ sh @ one)))) & (((X415 @ X414 @ X413)) != ((X412 @ X414 @ X413))) & ! [X419 : subst,X420 : subst,X421 : term] : (((sub @ (X415 @ X420 @ X421) @ X419)) = ((X415 @ (comp @ X420 @ X419) @ (sub @ X421 @ X419))))))) & (? [X422 : subst,X423 : term] : (((comp @ sh @ (push @ X423 @ X422))) != X422) | ? [X424 : subst,X425 : term] : (((sub @ one @ (push @ X425 @ X424))) != X425) | ? [X426 : term,X427 : term] : ((((lam @ X426)) = ((lam @ X427))) & (X426 != X427)) | ! [X428 : (subst > term > term),X429 : term,X430 : subst,X431 : (subst > term > term)] : (? [X432 : subst,X433 : term,X434 : subst] : (((sub @ (X428 @ X432 @ X433) @ X434)) != ((X428 @ (comp @ X432 @ X434) @ (sub @ X433 @ X434)))) | (((lam @ (X428 @ sh @ one))) != ((lam @ (X431 @ sh @ one)))) | (((X431 @ X430 @ X429)) = ((X428 @ X430 @ X429))) | ? [X435 : subst,X436 : subst,X437 : term] : (((X431 @ (comp @ X436 @ X435) @ (sub @ X437 @ X435))) != ((sub @ (X431 @ X436 @ X437) @ X435)))) | (hoaslaminj_lthm != $true)) & (hoaslamnotvar_lthm = $true) & (? [X438 : term,X439 : (subst > term > subst > $o),X440 : (term > $o)] : (($true != ((X440 @ (lam @ X438)))) & ! [X441 : term] : (((X439 @ id @ X441 @ id)) = ((X440 @ X441))) & ! [X442 : term] : (($true != ((X440 @ X442))) | ($true = ((X440 @ (sub @ X438 @ (push @ X442 @ id)))))) & ! [X443 : (subst > term > term)] : (($true = ((X439 @ id @ (lam @ (X443 @ sh @ one)) @ id))) | ? [X444 : term] : (($true != ((X439 @ id @ (X443 @ id @ X444) @ id))) & ($true = ((X439 @ id @ X444 @ id)))) | ? [X445 : subst,X446 : term,X447 : subst] : (((sub @ (X443 @ X445 @ X446) @ X447)) != ((X443 @ (comp @ X445 @ X447) @ (sub @ X446 @ X447)))))) | ($true = sP3) | ($true = sP4) | ? [X448 : (subst > term > subst > $o)] : ! [X449 : (term > $o)] : ? [X450 : term] : (((X448 @ id @ X450 @ id)) != ((X449 @ X450))) | ? [X451 : term] : (((sub @ X451 @ id)) != X451) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X452 : term,X453 : (subst > term > subst > $o),X454 : (term > $o)] : (($true = ((X454 @ (lam @ X452)))) | ? [X455 : term] : (((X453 @ id @ X455 @ id)) != ((X454 @ X455))) | ? [X456 : term] : (($true = ((X454 @ X456))) & ($true != ((X454 @ (sub @ X452 @ (push @ X456 @ id)))))) | ? [X457 : (subst > term > term)] : (($true != ((X453 @ id @ (lam @ (X457 @ sh @ one)) @ id))) & ! [X458 : term] : (($true = ((X453 @ id @ (X457 @ id @ X458) @ id))) | ($true != ((X453 @ id @ X458 @ id)))) & ! [X459 : subst,X460 : term,X461 : subst] : (((sub @ (X457 @ X459 @ X460) @ X461)) = ((X457 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461)))))) & ($true != sP3) & ($true != sP4) & ! [X462 : (subst > term > subst > $o)] : ? [X463 : (term > $o)] : ! [X464 : term] : (((X463 @ X464)) = ((X462 @ id @ X464 @ id))) & ! [X465 : term] : (((sub @ X465 @ id)) = X465))) & ((hoasinduction_lem3aaa = $true) | ? [X466 : (subst > term > subst > $o),X467 : term] : (($true != ((X466 @ id @ (lam @ (sub @ X467 @ (push @ one @ sh))) @ id))) & ! [X468 : term] : (($true = ((X466 @ id @ (sub @ X467 @ (push @ X468 @ id)) @ id))) | ($true != ((X466 @ id @ X468 @ id)))) & ! [X469 : term,X470 : (subst > term > term)] : (? [X471 : term,X472 : subst,X473 : subst] : (((X470 @ (comp @ X472 @ X473) @ (sub @ X471 @ X473))) != ((sub @ X469 @ (push @ (sub @ X471 @ X473) @ (comp @ X472 @ X473))))) | ($true = ((X466 @ id @ (lam @ (X470 @ sh @ one)) @ id))) | ? [X474 : term] : (($true = ((X466 @ id @ X474 @ id))) & ($true != ((X466 @ id @ (X470 @ id @ X474) @ id)))) | ? [X475 : subst,X476 : subst,X477 : term] : (((sub @ (sub @ X469 @ (push @ X477 @ X475)) @ X476)) != ((sub @ (X470 @ X475 @ X477) @ X476)))))) & (! [X478 : (subst > term > subst > $o),X479 : term] : (($true = ((X478 @ id @ (lam @ (sub @ X479 @ (push @ one @ sh))) @ id))) | ? [X480 : term] : (($true != ((X478 @ id @ (sub @ X479 @ (push @ X480 @ id)) @ id))) & ($true = ((X478 @ id @ X480 @ id)))) | ? [X481 : term,X482 : (subst > term > term)] : (! [X483 : term,X484 : subst,X485 : subst] : (((sub @ X481 @ (push @ (sub @ X483 @ X485) @ (comp @ X484 @ X485)))) = ((X482 @ (comp @ X484 @ X485) @ (sub @ X483 @ X485)))) & ($true != ((X478 @ id @ (lam @ (X482 @ sh @ one)) @ id))) & ! [X486 : term] : (($true != ((X478 @ id @ X486 @ id))) | ($true = ((X478 @ id @ (X482 @ id @ X486) @ id)))) & ! [X487 : subst,X488 : subst,X489 : term] : (((sub @ (X482 @ X487 @ X489) @ X488)) = ((sub @ (sub @ X481 @ (push @ X489 @ X487)) @ X488))))) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X490 : d_term,X491 : d_term] : ((X490 = X491) | (((d2term @ X490)) != ((d2term @ X491)))) & ((hoasapinj1 = $true) | ? [X492 : term,X493 : term,X494 : term,X495 : term] : ((((ap @ (sub @ X493 @ id) @ X495)) = ((ap @ (sub @ X492 @ id) @ X494))) & (X492 != X493))) & (! [X496 : term,X497 : term,X498 : term,X499 : term] : ((((ap @ (sub @ X496 @ id) @ X498)) != ((ap @ (sub @ X497 @ id) @ X499))) | (X496 = X497)) | (hoasapinj1 != $true)) & (hoaslamnotap_gthm = $true) & ! [X500 : term] : ? [X501 : d_term] : (((d2term @ X501)) = X500) & (pushprop_gthm = $true) & (hoasinduction_gthm = $true) & (! [X502 : (term > $o),X503 : subst,X504 : term] : ? [X505 : (term > $o)] : ! [X506 : term] : (((X505 @ X506)) = ((X502 @ (sub @ X506 @ (push @ X504 @ X503))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X507 : (term > $o),X508 : subst,X509 : term] : ! [X510 : (term > $o)] : ? [X511 : term] : (((X510 @ X511)) != ((X507 @ (sub @ X511 @ (push @ X509 @ X508)))))) & (? [X512 : subst,X513 : term] : (((comp @ sh @ (push @ X513 @ X512))) != X512) | ! [X514 : term,X515 : (term > $o),X516 : term,X517 : subst,X518 : (term > $o)] : (($true != ((X515 @ X516))) | ($true = ((X518 @ (sub @ X516 @ (push @ X514 @ X517)))))) | ? [X519 : term,X520 : subst] : (((sub @ one @ (push @ X519 @ X520))) != X519) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X521 : subst,X522 : term] : (((comp @ sh @ (push @ X522 @ X521))) = X521) & ? [X523 : term,X524 : (term > $o),X525 : term,X526 : subst,X527 : (term > $o)] : (($true = ((X524 @ X525))) & ($true != ((X527 @ (sub @ X525 @ (push @ X523 @ X526)))))) & ! [X528 : term,X529 : subst] : (((sub @ one @ (push @ X528 @ X529))) = X528))) & (! [X530 : (term > $o),X531 : term,X532 : (subst > term > subst > $o)] : (? [X533 : term] : (($true = ((X530 @ X533))) & ($true != ((X530 @ (sub @ X531 @ (push @ X533 @ id)))))) | ($true = ((sP2 @ X532))) | ? [X534 : term,X535 : subst,X536 : subst,X537 : subst] : (($true != ((X532 @ X536 @ X534 @ (comp @ X537 @ X535)))) & ($true = ((X532 @ (comp @ X536 @ X537) @ (sub @ X534 @ X537) @ X535)))) | ? [X538 : term] : (((X532 @ id @ X538 @ id)) != ((X530 @ X538))) | ($true = ((X530 @ (lam @ X531)))) | ? [X539 : subst,X540 : term,X541 : subst,X542 : subst] : (($true = ((X532 @ X539 @ X540 @ (comp @ X542 @ X541)))) & ($true != ((X532 @ (comp @ X539 @ X542) @ (sub @ X540 @ X542) @ X541))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X543 : (term > $o),X544 : term,X545 : (subst > term > subst > $o)] : (! [X546 : term] : (($true != ((X543 @ X546))) | ($true = ((X543 @ (sub @ X544 @ (push @ X546 @ id)))))) & ($true != ((sP2 @ X545))) & ! [X547 : term,X548 : subst,X549 : subst,X550 : subst] : (($true = ((X545 @ X549 @ X547 @ (comp @ X550 @ X548)))) | ($true != ((X545 @ (comp @ X549 @ X550) @ (sub @ X547 @ X550) @ X548)))) & ! [X551 : term] : (((X543 @ X551)) = ((X545 @ id @ X551 @ id))) & ($true != ((X543 @ (lam @ X544)))) & ! [X552 : subst,X553 : term,X554 : subst,X555 : subst] : (($true != ((X545 @ X552 @ X553 @ (comp @ X555 @ X554)))) | ($true = ((X545 @ (comp @ X552 @ X555) @ (sub @ X553 @ X555) @ X554)))))) & ((hoasapinj2 = $true) | ? [X556 : term,X557 : term,X558 : term,X559 : term] : ((X557 != X558) & (((ap @ (sub @ X559 @ id) @ X557)) = ((ap @ (sub @ X556 @ id) @ X558))))) & (! [X560 : term,X561 : term,X562 : term,X563 : term] : ((X561 = X562) | (((ap @ (sub @ X563 @ id) @ X561)) != ((ap @ (sub @ X560 @ id) @ X562)))) | (hoasapinj2 != $true)) & ((hoasapinj2_lthm = $true) | (! [X564 : term,X565 : term,X566 : term,X567 : term] : ((X564 = X567) | (((ap @ X566 @ X567)) != ((ap @ X565 @ X564)))) & ? [X568 : term,X569 : term,X570 : term,X571 : term] : ((X568 != X569) & (((ap @ (sub @ X570 @ id) @ X568)) = ((ap @ (sub @ X571 @ id) @ X569)))))) & (? [X572 : term,X573 : term,X574 : term,X575 : term] : ((X572 != X575) & (((ap @ X574 @ X575)) = ((ap @ X573 @ X572)))) | ! [X576 : term,X577 : term,X578 : term,X579 : term] : ((X576 = X577) | (((ap @ (sub @ X579 @ id) @ X577)) != ((ap @ (sub @ X578 @ id) @ X576)))) | (hoasapinj2_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) | ? [X580 : (subst > term > subst > $o),X581 : term] : (($true != ((X580 @ id @ (lam @ X581) @ id))) & ! [X582 : term] : (($true != ((X580 @ id @ X582 @ id))) | ($true = ((X580 @ id @ (sub @ X581 @ (push @ X582 @ id)) @ id)))) & ! [X583 : (subst > term > term)] : (? [X584 : term,X585 : subst,X586 : subst] : (((sub @ (X583 @ X585 @ X584) @ X586)) != ((X583 @ (comp @ X585 @ X586) @ (sub @ X584 @ X586)))) | ? [X587 : term] : (($true = ((X580 @ id @ X587 @ id))) & ($true != ((X580 @ id @ (X583 @ id @ X587) @ id)))) | ($true = ((X580 @ id @ (lam @ (X583 @ sh @ one)) @ id)))))) & (! [X588 : (subst > term > subst > $o),X589 : term] : (($true = ((X588 @ id @ (lam @ X589) @ id))) | ? [X590 : term] : (($true = ((X588 @ id @ X590 @ id))) & ($true != ((X588 @ id @ (sub @ X589 @ (push @ X590 @ id)) @ id)))) | ? [X591 : (subst > term > term)] : (! [X592 : term,X593 : subst,X594 : subst] : (((X591 @ (comp @ X593 @ X594) @ (sub @ X592 @ X594))) = ((sub @ (X591 @ X593 @ X592) @ X594))) & ! [X595 : term] : (($true != ((X588 @ id @ X595 @ id))) | (((X588 @ id @ (X591 @ id @ X595) @ id)) = $true)) & (((X588 @ id @ (lam @ (X591 @ sh @ one)) @ id)) != $true))) | (hoasinduction_lem3a != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) | ? [X596 : (subst > term > subst > $o),X597 : (term > $o),X598 : term] : (($true != ((X597 @ (lam @ X598)))) & ! [X599 : term] : (((X597 @ X599)) = ((X596 @ id @ X599 @ id))) & ! [X600 : term] : (($true = ((X597 @ (sub @ X598 @ (push @ X600 @ id))))) | ($true != ((X597 @ X600)))) & ! [X601 : (subst > term > term)] : (? [X602 : term] : (($true != ((X596 @ id @ (X601 @ id @ X602) @ id))) & ($true = ((X596 @ id @ X602 @ id)))) | ($true = ((X596 @ id @ (lam @ (X601 @ sh @ one)) @ id))) | ? [X603 : term,X604 : subst,X605 : subst] : (((X601 @ (comp @ X605 @ X604) @ (sub @ X603 @ X604))) != ((sub @ (X601 @ X605 @ X603) @ X604)))))) & (! [X606 : (subst > term > subst > $o),X607 : (term > $o),X608 : term] : (($true = ((X607 @ (lam @ X608)))) | ? [X609 : term] : (((X606 @ id @ X609 @ id)) != ((X607 @ X609))) | ? [X610 : term] : (($true != ((X607 @ (sub @ X608 @ (push @ X610 @ id))))) & ($true = ((X607 @ X610)))) | ? [X611 : (subst > term > term)] : (! [X612 : term] : (($true = ((X606 @ id @ (X611 @ id @ X612) @ id))) | ($true != ((X606 @ id @ X612 @ id)))) & ($true != ((X606 @ id @ (lam @ (X611 @ sh @ one)) @ id))) & ! [X613 : term,X614 : subst,X615 : subst] : (((sub @ (X611 @ X615 @ X613) @ X614)) = ((X611 @ (comp @ X615 @ X614) @ (sub @ X613 @ X614)))))) | (hoasinduction_lem3v2a != $true)) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X616 : term] : ! [X617 : (subst > term > term)] : ? [X618 : term,X619 : subst] : (((sub @ X616 @ (push @ X618 @ X619))) != ((X617 @ X619 @ X618)))) & (! [X620 : term] : ? [X621 : (subst > term > term)] : ! [X622 : term,X623 : subst] : (((sub @ X620 @ (push @ X622 @ X623))) = ((X621 @ X623 @ X622))) | (hoasinduction_lem3v2_f != $true)) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X624 : term,X625 : (subst > term > subst > $o)] : (! [X626 : (subst > term > term)] : (($true = ((X625 @ id @ (lam @ (X626 @ sh @ one)) @ id))) | ? [X627 : term] : (($true != ((X625 @ id @ (X626 @ id @ X627) @ id))) & ($true = ((X625 @ id @ X627 @ id)))) | ? [X628 : term,X629 : subst,X630 : subst] : (((X626 @ (comp @ X630 @ X629) @ (sub @ X628 @ X629))) != ((sub @ (X626 @ X630 @ X628) @ X629)))) & ! [X631 : term,X632 : term] : (($true = ((X625 @ id @ (ap @ (sub @ X631 @ id) @ X632) @ id))) | ($true != ((X625 @ id @ X632 @ id))) | ($true != ((X625 @ id @ X631 @ id)))) & ($true != ((X625 @ id @ X624 @ id))))) & (! [X633 : term,X634 : (subst > term > subst > $o)] : (? [X635 : (subst > term > term)] : (($true != ((X634 @ id @ (lam @ (X635 @ sh @ one)) @ id))) & ! [X636 : term] : (($true = ((X634 @ id @ (X635 @ id @ X636) @ id))) | (((X634 @ id @ X636 @ id)) != $true)) & ! [X637 : term,X638 : subst,X639 : subst] : (((sub @ (X635 @ X639 @ X637) @ X638)) = ((X635 @ (comp @ X639 @ X638) @ (sub @ X637 @ X638))))) | ? [X640 : term,X641 : term] : (($true != ((X634 @ id @ (ap @ (sub @ X640 @ id) @ X641) @ id))) & ($true = ((X634 @ id @ X641 @ id))) & ($true = ((X634 @ id @ X640 @ id)))) | ($true = ((X634 @ id @ X633 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (hoaslamnotvar = $true) & (! [X642 : term] : (((sub @ X642 @ id)) = X642) | ? [X643 : term] : (((sub @ X643 @ id)) != X643) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X644 : term] : (((sub @ X644 @ id)) != X644) & ! [X645 : term] : (((sub @ X645 @ id)) = X645))) & (lamnotvar = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((apinj1 = $true) | ? [X646 : term,X647 : term,X648 : term,X649 : term] : ((X646 != X647) & (((ap @ X647 @ X648)) = ((ap @ X646 @ X649))))) & (! [X650 : term,X651 : term,X652 : term,X653 : term] : ((X650 = X651) | (((ap @ X651 @ X652)) != ((ap @ X650 @ X653)))) | (apinj1 != $true)) & ((induction2lem_lthm = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem_lthm != $true))), 24.89/4.11 inference(rectify,[],[f131])). 24.89/4.11 thf(f133,plain,( 24.89/4.11 ! [X0 : subst] : (((d2subst @ (sK236 @ X0))) = X0) & (! [X2 : term,X3 : subst] : (((sub @ one @ (push @ X2 @ X3))) = X2) | (axvarcons != $true)) & ((axvarcons = $true) | (sK237 != ((sub @ one @ (push @ sK237 @ sK238))))) & (((d2subst @ d_id)) = id) & (axvarshift = $true) & (! [X6 : term,X7 : (subst > term > subst > $o)] : (($true = ((X7 @ id @ (lam @ (sub @ X6 @ (push @ one @ sh))) @ id))) | (($true = ((X7 @ id @ (sK239 @ X7 @ X6) @ id))) & ($true != ((X7 @ id @ (sub @ X6 @ (push @ (sK239 @ X7 @ X6) @ id)) @ id)))) | (! [X10 : term,X11 : subst,X12 : subst] : (((sub @ (sK240 @ X7 @ X11 @ X10) @ X12)) = ((sK240 @ X7 @ (comp @ X11 @ X12) @ (sub @ X10 @ X12)))) & ! [X13 : term] : (($true = ((X7 @ id @ (sK240 @ X7 @ id @ X13) @ id))) | ($true != ((X7 @ id @ X13 @ id)))) & ($true != ((X7 @ id @ (lam @ (sK240 @ X7 @ sh @ one)) @ id))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (($true != ((sK242 @ id @ (lam @ (sub @ sK241 @ (push @ one @ sh))) @ id))) & ! [X16 : term] : (($true != ((sK242 @ id @ X16 @ id))) | ($true = ((sK242 @ id @ (sub @ sK241 @ (push @ X16 @ id)) @ id)))) & ! [X17 : (subst > term > term)] : ((((sub @ (X17 @ (sK244 @ X17) @ (sK243 @ X17)) @ (sK245 @ X17))) != ((X17 @ (comp @ (sK244 @ X17) @ (sK245 @ X17)) @ (sub @ (sK243 @ X17) @ (sK245 @ X17))))) | (($true != ((sK242 @ id @ (X17 @ id @ (sK246 @ X17)) @ id))) & ($true = ((sK242 @ id @ (sK246 @ X17) @ id)))) | ($true = ((sK242 @ id @ (lam @ (X17 @ sh @ one)) @ id)))))) & (pushprop_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP27) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP27)) & ((hoasapinj1_lthm = $true) | (((((ap @ (sub @ sK248 @ id) @ sK247)) = ((ap @ (sub @ sK249 @ id) @ sK250))) & (sK248 != sK249)) & ! [X26 : term,X27 : term,X28 : term,X29 : term] : ((((ap @ X28 @ X29)) != ((ap @ X27 @ X26))) | (X27 = X28)) & ! [X30 : term] : (((sub @ X30 @ id)) = X30))) & (! [X31 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X33 @ id) @ X34)) != ((ap @ (sub @ X32 @ id) @ X31))) | (X32 = X33)) | ((((ap @ sK252 @ sK251)) = ((ap @ sK253 @ sK254))) & (sK253 != sK252)) | (((sub @ sK255 @ id)) != sK255) | (hoasapinj1_lthm != $true)) & (hoasapnotvar = $true) & (axabs = $true) & ! [X40 : d_subst,X41 : d_subst] : ((X40 = X41) | (((d2subst @ X40)) != ((d2subst @ X41)))) & ((axidr = $true) | (sK256 != ((comp @ sK256 @ id)))) & (! [X43 : subst] : (((comp @ X43 @ id)) = X43) | (axidr != $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X44 : (subst > term > subst > $o),X45 : (term > $o),X46 : term] : (($true = ((X45 @ (lam @ X46)))) | (($true != ((X44 @ (sK260 @ X44) @ (sK258 @ X44) @ (comp @ (sK257 @ X44) @ (sK259 @ X44))))) & ($true = ((X44 @ (comp @ (sK260 @ X44) @ (sK257 @ X44)) @ (sub @ (sK258 @ X44) @ (sK257 @ X44)) @ (sK259 @ X44))))) | (((X44 @ id @ (sK261 @ X45 @ X44) @ id)) != ((X45 @ (sK261 @ X45 @ X44)))) | (($true = ((X45 @ (sK262 @ X46 @ X45)))) & ($true != ((X45 @ (sub @ X46 @ (push @ (sK262 @ X46 @ X45) @ id)))))) | (($true != ((X44 @ (comp @ (sK264 @ X44) @ (sK266 @ X44)) @ (sub @ (sK263 @ X44) @ (sK266 @ X44)) @ (sK265 @ X44)))) & ($true = ((X44 @ (sK264 @ X44) @ (sK263 @ X44) @ (comp @ (sK266 @ X44) @ (sK265 @ X44)))))) | ($true = ((sP26 @ X44)))) | (((sub @ sK267 @ id)) != sK267) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ((($true != ((sK269 @ (lam @ sK270)))) & ! [X61 : subst,X62 : term,X63 : subst,X64 : subst] : (($true = ((sK268 @ X64 @ X62 @ (comp @ X61 @ X63)))) | ($true != ((sK268 @ (comp @ X64 @ X61) @ (sub @ X62 @ X61) @ X63)))) & ! [X65 : term] : (((sK268 @ id @ X65 @ id)) = ((sK269 @ X65))) & ! [X66 : term] : (($true != ((sK269 @ X66))) | ($true = ((sK269 @ (sub @ sK270 @ (push @ X66 @ id)))))) & ! [X67 : term,X68 : subst,X69 : subst,X70 : subst] : (($true = ((sK268 @ (comp @ X68 @ X70) @ (sub @ X67 @ X70) @ X69))) | ($true != ((sK268 @ X68 @ X67 @ (comp @ X70 @ X69))))) & ($true != ((sP26 @ sK268)))) & ! [X71 : term] : (((sub @ X71 @ id)) = X71))) & (pushprop_lem2v2_gthm = $true) & ((((sub @ one @ (push @ sK272 @ sK271))) != sK272) | ! [X74 : (term > $o),X75 : term,X76 : subst,X77 : (term > $o)] : ((((X74 @ (sK273 @ X77 @ X76 @ X75 @ X74))) != ((X77 @ (sub @ (sK273 @ X77 @ X76 @ X75 @ X74) @ (push @ X75 @ X76))))) | ($true != ((X77 @ X75))) | ($true = ((X74 @ one)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X79 : subst,X80 : term] : (((sub @ one @ (push @ X80 @ X79))) = X80) & (! [X85 : term] : (((sK274 @ X85)) = ((sK277 @ (sub @ X85 @ (push @ sK275 @ sK276))))) & ($true = ((sK277 @ sK275))) & ($true != ((sK274 @ one)))))) & ((pushprop_lem1 = $true) | (($true = ((sK279 @ sK278))) & (((sK281 @ (sub @ sK278 @ (push @ sK282 @ sK280)))) != $true))) & (! [X91 : term,X92 : (term > $o),X93 : subst,X94 : (term > $o),X95 : term] : (($true != ((X92 @ X91))) | ($true = ((X94 @ (sub @ X91 @ (push @ X95 @ X93)))))) | (pushprop_lem1 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X96 : term,X97 : term,X98 : term,X99 : term] : ((X96 = X99) | (((ap @ X98 @ X99)) != ((ap @ X97 @ X96)))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK286 != sK283) & (((ap @ sK284 @ sK283)) = ((ap @ sK285 @ sK286))))) & ((hoasinduction_lem3a_lthm = $true) | (! [X104 : term,X105 : (subst > term > subst > $o)] : (($true = ((X105 @ id @ (lam @ (sub @ X104 @ (push @ one @ sh))) @ id))) | (($true != ((X105 @ id @ (sub @ X104 @ (push @ (sK287 @ X105 @ X104) @ id)) @ id))) & ($true = ((X105 @ id @ (sK287 @ X105 @ X104) @ id)))) | (($true != ((X105 @ id @ (lam @ (sK288 @ X105 @ sh @ one)) @ id))) & ! [X108 : term] : (($true != ((X105 @ id @ X108 @ id))) | ($true = ((X105 @ id @ (sK288 @ X105 @ id @ X108) @ id)))) & ! [X109 : subst,X110 : subst,X111 : term] : (((sub @ (sK288 @ X105 @ X109 @ X111) @ X110)) = ((sK288 @ X105 @ (comp @ X109 @ X110) @ (sub @ X111 @ X110)))))) & ($true != sP25) & ! [X112 : term] : (((sub @ X112 @ id)) = X112))) & ((($true != ((sK290 @ id @ (lam @ (sub @ sK289 @ (push @ one @ sh))) @ id))) & ! [X115 : term] : (($true = ((sK290 @ id @ (sub @ sK289 @ (push @ X115 @ id)) @ id))) | ($true != ((sK290 @ id @ X115 @ id)))) & ! [X116 : (subst > term > term)] : (($true = ((sK290 @ id @ (lam @ (X116 @ sh @ one)) @ id))) | (($true = ((sK290 @ id @ (sK291 @ X116) @ id))) & ($true != ((sK290 @ id @ (X116 @ id @ (sK291 @ X116)) @ id)))) | (((sub @ (X116 @ (sK292 @ X116) @ (sK294 @ X116)) @ (sK293 @ X116))) != ((X116 @ (comp @ (sK292 @ X116) @ (sK293 @ X116)) @ (sub @ (sK294 @ X116) @ (sK293 @ X116))))))) | ($true = sP25) | (((sub @ sK295 @ id)) != sK295) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3aa = $true) | (! [X124 : (subst > term > term)] : (($true = ((sK297 @ id @ (lam @ (X124 @ sh @ one)) @ id))) | (((sub @ (X124 @ (sK299 @ X124) @ (sK298 @ X124)) @ (sK300 @ X124))) != ((X124 @ (comp @ (sK299 @ X124) @ (sK300 @ X124)) @ (sub @ (sK298 @ X124) @ (sK300 @ X124))))) | (($true = ((sK297 @ id @ (sK301 @ X124) @ id))) & ($true != ((sK297 @ id @ (X124 @ id @ (sK301 @ X124)) @ id))))) & ($true != ((sK297 @ id @ (lam @ (sub @ sK296 @ (push @ one @ sh))) @ id))) & ! [X129 : term] : (($true != ((sK297 @ id @ X129 @ id))) | ($true = ((sK297 @ id @ (sub @ sK296 @ (push @ X129 @ id)) @ id)))))) & (! [X130 : term,X131 : (subst > term > subst > $o)] : ((($true != ((X131 @ id @ (lam @ (sK302 @ X131 @ sh @ one)) @ id))) & ! [X133 : term,X134 : subst,X135 : subst] : (((sub @ (sK302 @ X131 @ X134 @ X133) @ X135)) = ((sK302 @ X131 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135)))) & ! [X136 : term] : (($true != ((X131 @ id @ X136 @ id))) | ($true = ((X131 @ id @ (sK302 @ X131 @ id @ X136) @ id))))) | ($true = ((X131 @ id @ (lam @ (sub @ X130 @ (push @ one @ sh))) @ id))) | (($true = ((X131 @ id @ (sK303 @ X131 @ X130) @ id))) & ($true != ((X131 @ id @ (sub @ X130 @ (push @ (sK303 @ X131 @ X130) @ id)) @ id))))) | (hoasinduction_lem3aa != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (($true = sP24) | (sK304 != ((sub @ sK304 @ id))) | (! [X141 : (subst > term > term)] : ((((sub @ (X141 @ (sK308 @ X141) @ (sK307 @ X141)) @ (sK309 @ X141))) != ((X141 @ (comp @ (sK308 @ X141) @ (sK309 @ X141)) @ (sub @ (sK307 @ X141) @ (sK309 @ X141))))) | ($true = ((sK306 @ id @ (lam @ (X141 @ sh @ one)) @ id))) | (($true != ((sK306 @ id @ (X141 @ id @ (sK310 @ X141)) @ id))) & ($true = ((sK306 @ id @ (sK310 @ X141) @ id))))) & ! [X146 : term] : (($true != ((sK306 @ id @ X146 @ id))) | ($true = ((sK306 @ id @ (sub @ sK305 @ (push @ X146 @ id)) @ id)))) & ($true != ((sK306 @ id @ (lam @ (sub @ sK305 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP24) & ! [X147 : term] : (((sub @ X147 @ id)) = X147) & ! [X148 : term,X149 : (subst > term > subst > $o)] : ((! [X151 : term,X152 : subst,X153 : subst] : (((sub @ (sK311 @ X149 @ X152 @ X151) @ X153)) = ((sK311 @ X149 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153)))) & ($true != ((X149 @ id @ (lam @ (sK311 @ X149 @ sh @ one)) @ id))) & ! [X154 : term] : (($true = ((X149 @ id @ (sK311 @ X149 @ id @ X154) @ id))) | ($true != ((X149 @ id @ X154 @ id))))) | (($true = ((X149 @ id @ (sK312 @ X149 @ X148) @ id))) & ($true != ((X149 @ id @ (sub @ X148 @ (push @ (sK312 @ X149 @ X148) @ id)) @ id)))) | ($true = ((X149 @ id @ (lam @ (sub @ X148 @ (push @ one @ sh))) @ id)))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm = $true) | (($true != sP22) & ($true != sP21) & ($true != sP20) & ! [X156 : (subst > term > subst > $o),X157 : term] : ((($true != ((X156 @ id @ (sub @ X157 @ (push @ (sK313 @ X157 @ X156) @ id)) @ id))) & ($true = ((X156 @ id @ (sK313 @ X157 @ X156) @ id)))) | ($true != ((sP17 @ X156))) | (($true != ((X156 @ (comp @ (sK315 @ X156) @ (sK314 @ X156)) @ (sub @ (sK316 @ X156) @ (sK314 @ X156)) @ (sK317 @ X156)))) & ($true = ((X156 @ (sK315 @ X156) @ (sK316 @ X156) @ (comp @ (sK314 @ X156) @ (sK317 @ X156)))))) | ((((X156 @ (sK321 @ X156) @ (sK320 @ X156) @ (comp @ (sK319 @ X156) @ (sK318 @ X156)))) != $true) & ($true = ((X156 @ (comp @ (sK321 @ X156) @ (sK319 @ X156)) @ (sub @ (sK320 @ X156) @ (sK319 @ X156)) @ (sK318 @ X156))))) | ($true = ((X156 @ id @ (lam @ X157) @ id)))))) & (($true = sP22) | ($true = sP21) | ($true = sP20) | (! [X169 : term] : (($true = ((sK322 @ id @ (sub @ sK323 @ (push @ X169 @ id)) @ id))) | ($true != ((sK322 @ id @ X169 @ id)))) & ($true = ((sP17 @ sK322))) & ! [X170 : subst,X171 : subst,X172 : term,X173 : subst] : (($true = ((sK322 @ (comp @ X171 @ X170) @ (sub @ X172 @ X170) @ X173))) | ($true != ((sK322 @ X171 @ X172 @ (comp @ X170 @ X173))))) & ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : (($true = ((sK322 @ X177 @ X176 @ (comp @ X175 @ X174)))) | ($true != ((sK322 @ (comp @ X177 @ X175) @ (sub @ X176 @ X175) @ X174)))) & ($true != ((sK322 @ id @ (lam @ sK323) @ id)))) | (hoasinduction_lthm != $true)) & (! [X179 : (subst > term > term)] : (((X179 @ (sK326 @ X179) @ (sK325 @ X179))) != ((sub @ sK324 @ (push @ (sK325 @ X179) @ (sK326 @ X179))))) | (((sub @ sK327 @ id)) != sK327) | ! [X183 : (subst > term > subst > $o),X184 : term,X185 : (term > $o)] : ((((X185 @ (sK328 @ X185 @ X183))) != ((X183 @ id @ (sK328 @ X185 @ X183) @ id))) | (($true != ((X183 @ id @ (lam @ (sK329 @ X183 @ sh @ one)) @ id))) & ! [X188 : term] : (($true = ((X183 @ id @ (sK329 @ X183 @ id @ X188) @ id))) | ($true != ((X183 @ id @ X188 @ id)))) & ! [X189 : subst,X190 : term,X191 : subst] : (((sub @ (sK329 @ X183 @ X191 @ X190) @ X189)) = ((sK329 @ X183 @ (comp @ X191 @ X189) @ (sub @ X190 @ X189))))) | (($true = ((X185 @ (sK330 @ X185 @ X184)))) & ($true != ((X185 @ (sub @ X184 @ (push @ (sK330 @ X185 @ X184) @ id)))))) | ($true = ((X185 @ (lam @ X184))))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X193 : term] : ! [X195 : term,X196 : subst] : (((sK331 @ X193 @ X196 @ X195)) = ((sub @ X193 @ (push @ X195 @ X196)))) & ! [X197 : term] : (((sub @ X197 @ id)) = X197) & (! [X201 : term] : (((sK332 @ id @ X201 @ id)) = ((sK334 @ X201))) & ! [X202 : (subst > term > term)] : (($true = ((sK332 @ id @ (lam @ (X202 @ sh @ one)) @ id))) | (($true != ((sK332 @ id @ (X202 @ id @ (sK335 @ X202)) @ id))) & ($true = ((sK332 @ id @ (sK335 @ X202) @ id)))) | (((sub @ (X202 @ (sK338 @ X202) @ (sK337 @ X202)) @ (sK336 @ X202))) != ((X202 @ (comp @ (sK338 @ X202) @ (sK336 @ X202)) @ (sub @ (sK337 @ X202) @ (sK336 @ X202)))))) & ! [X207 : term] : (($true != ((sK334 @ X207))) | ($true = ((sK334 @ (sub @ sK333 @ (push @ X207 @ id)))))) & ($true != ((sK334 @ (lam @ sK333))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj = $true) | ((((sK339 @ sK342 @ sK340)) != ((sK341 @ sK342 @ sK340))) & (((lam @ (sK339 @ sh @ one))) = ((lam @ (sK341 @ sh @ one)))) & ! [X212 : subst,X213 : subst,X214 : term] : (((sK341 @ (comp @ X212 @ X213) @ (sub @ X214 @ X213))) = ((sub @ (sK341 @ X212 @ X214) @ X213))) & ! [X215 : subst,X216 : subst,X217 : term] : (((sub @ (sK339 @ X215 @ X217) @ X216)) = ((sK339 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216)))))) & (! [X218 : (subst > term > term),X219 : term,X220 : (subst > term > term),X221 : subst] : ((((X220 @ X221 @ X219)) = ((X218 @ X221 @ X219))) | (((lam @ (X218 @ sh @ one))) != ((lam @ (X220 @ sh @ one)))) | (((sub @ (X220 @ (sK343 @ X220) @ (sK345 @ X220)) @ (sK344 @ X220))) != ((X220 @ (comp @ (sK343 @ X220) @ (sK344 @ X220)) @ (sub @ (sK345 @ X220) @ (sK344 @ X220))))) | (((X218 @ (comp @ (sK346 @ X218) @ (sK347 @ X218)) @ (sub @ (sK348 @ X218) @ (sK347 @ X218)))) != ((sub @ (X218 @ (sK346 @ X218) @ (sK348 @ X218)) @ (sK347 @ X218))))) | (hoaslaminj != $true)) & (hoasapinj2_gthm = $true) & ((! [X228 : subst] : (((comp @ id @ X228)) = X228) & ! [X229 : subst] : (((comp @ X229 @ id)) = X229)) | (substmonoid != $true)) & ((substmonoid = $true) | (sK349 != ((comp @ id @ sK349))) | (sK350 != ((comp @ sK350 @ id)))) & (axclos = $true) & (! [X232 : (term > $o),X233 : subst,X234 : term] : ! [X236 : term] : (((sK351 @ X234 @ X233 @ X232 @ X236)) = ((X232 @ (sub @ X236 @ (push @ X234 @ X233))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X240 : (term > $o)] : (((X240 @ (sK355 @ X240))) != ((sK352 @ (sub @ (sK355 @ X240) @ (push @ sK354 @ sK353)))))) & (hoasinduction_lem2_lthm = $true) & (! [X242 : term,X243 : term,X244 : (subst > term > term)] : ((((sub @ (X244 @ (sK356 @ X244) @ (sK357 @ X244)) @ (sK358 @ X244))) != ((X244 @ (comp @ (sK356 @ X244) @ (sK358 @ X244)) @ (sub @ (sK357 @ X244) @ (sK358 @ X244))))) | (((ap @ (sub @ X242 @ id) @ X243)) != ((lam @ (X244 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X251 : subst,X252 : term,X253 : subst] : (((sub @ (sK361 @ X251 @ X252) @ X253)) = ((sK361 @ (comp @ X251 @ X253) @ (sub @ X252 @ X253)))) & (((ap @ (sub @ sK359 @ id) @ sK360)) = ((lam @ (sK361 @ sh @ one)))))) & (pushprop_lem3v2_lthm = $true) & ((((comp @ id @ sK362)) != sK362) | (((comp @ sK363 @ id)) != sK363) | (! [X256 : subst] : (((comp @ X256 @ id)) = X256) & ! [X257 : subst] : (((comp @ id @ X257)) = X257)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X258 : subst] : (((comp @ id @ X258)) = X258) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259) & ((sK364 != ((comp @ sK364 @ id))) | (((comp @ id @ sK365)) != sK365)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & ((axscons = $true) | (sK366 != ((push @ (sub @ one @ sK366) @ (comp @ sh @ sK366))))) & (! [X263 : subst] : (((push @ (sub @ one @ X263) @ (comp @ sh @ X263))) = X263) | (axscons != $true)) & (hoasinduction_lem1v2_gthm = $true) & (apnotvar = $true) & (! [X265 : (term > $o)] : (((sK367 @ id @ (sK368 @ X265) @ id)) != ((X265 @ (sK368 @ X265)))) | ($true = sP16) | (sK369 != ((sub @ sK369 @ id))) | ($true = sP15) | (! [X271 : (subst > term > term)] : ((((X271 @ (comp @ (sK375 @ X271) @ (sK374 @ X271)) @ (sub @ (sK373 @ X271) @ (sK374 @ X271)))) != ((sub @ (X271 @ (sK375 @ X271) @ (sK373 @ X271)) @ (sK374 @ X271)))) | ($true = ((sK370 @ id @ (lam @ (X271 @ sh @ one)) @ id))) | ((((sK370 @ id @ (sK376 @ X271) @ id)) = $true) & ($true != ((sK370 @ id @ (X271 @ id @ (sK376 @ X271)) @ id))))) & ! [X276 : term] : (($true != ((sK371 @ X276))) | ($true = ((sK371 @ (sub @ sK372 @ (push @ X276 @ id)))))) & ! [X277 : term] : (((sK371 @ X277)) = ((sK370 @ id @ X277 @ id))) & ($true != ((sK371 @ (lam @ sK372))))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X278 : (subst > term > subst > $o)] : ! [X280 : term] : (((sK377 @ X278 @ X280)) = ((X278 @ id @ X280 @ id))) & ($true != sP16) & ! [X281 : term] : (((sub @ X281 @ id)) = X281) & ($true != sP15) & ! [X282 : (subst > term > subst > $o),X283 : (term > $o),X284 : term] : ((! [X286 : term,X287 : subst,X288 : subst] : (((sub @ (sK378 @ X282 @ X288 @ X286) @ X287)) = ((sK378 @ X282 @ (comp @ X288 @ X287) @ (sub @ X286 @ X287)))) & ($true != ((X282 @ id @ (lam @ (sK378 @ X282 @ sh @ one)) @ id))) & ! [X289 : term] : (($true != ((X282 @ id @ X289 @ id))) | ($true = ((X282 @ id @ (sK378 @ X282 @ id @ X289) @ id))))) | (($true = ((X283 @ (sK379 @ X284 @ X283)))) & ($true != ((X283 @ (sub @ X284 @ (push @ (sK379 @ X284 @ X283) @ id)))))) | (((X282 @ id @ (sK380 @ X283 @ X282) @ id)) != ((X283 @ (sK380 @ X283 @ X282)))) | ($true = ((X283 @ (lam @ X284))))))) & ((hoasinduction_lem0_lthm = $true) | ! [X293 : (term > $o)] : (((sK381 @ id @ (sK382 @ X293) @ id)) != ((X293 @ (sK382 @ X293))))) & (! [X295 : (subst > term > subst > $o)] : ! [X297 : term] : (((sK383 @ X295 @ X297)) = ((X295 @ id @ X297 @ id))) | (hoasinduction_lem0_lthm != $true)) & (! [X298 : term] : (((sK384 @ X298 @ sh @ one)) = ((sub @ X298 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X301 : (subst > term > term)] : (((sub @ sK385 @ (push @ one @ sh))) != ((X301 @ sh @ one)))) & (hoaslamnotap_lthm = $true) & (($true = sP12) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP12)) & ((pushprop_lem1v2 = $true) | (! [X306 : term] : (((sK387 @ X306)) = ((sK388 @ (sub @ X306 @ (push @ sK386 @ sK389))))) & ($true != ((sK387 @ one))) & ($true = ((sK388 @ sK386))))) & (! [X307 : term,X308 : (term > $o),X309 : (term > $o),X310 : subst] : ((((X308 @ (sK390 @ X310 @ X309 @ X308 @ X307))) != ((X309 @ (sub @ (sK390 @ X310 @ X309 @ X308 @ X307) @ (push @ X307 @ X310))))) | ($true = ((X308 @ one))) | ($true != ((X309 @ X307)))) | (pushprop_lem1v2 != $true)) & (! [X312 : term,X313 : (subst > term > subst > $o)] : ((($true = ((X313 @ id @ (sK391 @ X313 @ X312) @ id))) & ($true != ((X313 @ id @ (sub @ X312 @ (push @ (sK391 @ X313 @ X312) @ id)) @ id)))) | (($true != ((X313 @ (comp @ (sK393 @ X313) @ (sK395 @ X313)) @ (sub @ (sK394 @ X313) @ (sK395 @ X313)) @ (sK392 @ X313)))) & ($true = ((X313 @ (sK393 @ X313) @ (sK394 @ X313) @ (comp @ (sK395 @ X313) @ (sK392 @ X313)))))) | (($true = ((X313 @ (comp @ (sK396 @ X313) @ (sK397 @ X313)) @ (sub @ (sK399 @ X313) @ (sK397 @ X313)) @ (sK398 @ X313)))) & ($true != ((X313 @ (sK396 @ X313) @ (sK399 @ X313) @ (comp @ (sK397 @ X313) @ (sK398 @ X313)))))) | ($true = ((X313 @ id @ (lam @ X312) @ id))) | ($true = ((sP10 @ X313)))) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (! [X325 : term] : (($true != ((sK401 @ id @ X325 @ id))) | ($true = ((sK401 @ id @ (sub @ sK400 @ (push @ X325 @ id)) @ id)))) & ! [X326 : subst,X327 : subst,X328 : term,X329 : subst] : (($true = ((sK401 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329) @ X326))) | ($true != ((sK401 @ X327 @ X328 @ (comp @ X329 @ X326))))) & ! [X330 : subst,X331 : subst,X332 : subst,X333 : term] : (($true != ((sK401 @ (comp @ X330 @ X331) @ (sub @ X333 @ X331) @ X332))) | ($true = ((sK401 @ X330 @ X333 @ (comp @ X331 @ X332))))) & ($true != ((sK401 @ id @ (lam @ sK400) @ id))) & ($true != ((sP10 @ sK401))))) & (hoasinduction_lem3v2_gthm = $true) & (($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9)) & (hoasinduction_lem3b_gthm = $true) & ((axidl = $true) | (((comp @ id @ sK402)) != sK402)) & (! [X335 : subst] : (((comp @ id @ X335)) = X335) | (axidl != $true)) & (lamnotap != $true) & ((induction = $true) | (! [X338 : term] : (($true = ((sK403 @ X338))) | ($true != ((var @ X338)))) & ($true != ((sK403 @ sK404))) & ! [X339 : term] : (($true != ((sK403 @ X339))) | ($true = ((sK403 @ (lam @ X339))))) & ! [X340 : term,X341 : term] : (($true != ((sK403 @ X341))) | ($true = ((sK403 @ (ap @ X340 @ X341)))) | ($true != ((sK403 @ X340)))))) & (! [X342 : (term > $o),X343 : term] : ((($true != ((X342 @ (sK405 @ X342)))) & (((var @ (sK405 @ X342))) = $true)) | ($true = ((X342 @ X343))) | (($true = ((X342 @ (sK406 @ X342)))) & ($true != ((X342 @ (lam @ (sK406 @ X342)))))) | (($true = ((X342 @ (sK408 @ X342)))) & ($true != ((X342 @ (ap @ (sK407 @ X342) @ (sK408 @ X342))))) & ($true = ((X342 @ (sK407 @ X342)))))) | (induction != $true)) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X349 : (subst > term > term)] : (((X349 @ (sK411 @ X349) @ (sK410 @ X349))) != ((sub @ sK409 @ (push @ (sK410 @ X349) @ (sK411 @ X349)))))) & (! [X352 : term] : ! [X354 : term,X355 : subst] : (((sK412 @ X352 @ X355 @ X354)) = ((sub @ X352 @ (push @ X354 @ X355)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((axshiftcons = $true) | (sK414 != ((comp @ sh @ (push @ sK413 @ sK414))))) & (! [X358 : term,X359 : subst] : (((comp @ sh @ (push @ X358 @ X359))) = X359) | (axshiftcons != $true)) & (! [X360 : (subst > term > subst > $o)] : ! [X362 : term] : (((X360 @ id @ X362 @ id)) = ((sK415 @ X360 @ X362))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X364 : (term > $o)] : (((sK416 @ id @ (sK417 @ X364) @ id)) != ((X364 @ (sK417 @ X364))))) & (pushprop = $true) & ((hoasinduction = $true) | (($true != ((sP8 @ sK419))) & ! [X368 : term] : (($true != ((var @ (sub @ X368 @ id)))) | ($true = ((sK419 @ id @ X368 @ id)))) & ($true != ((sP7 @ sK419))) & ($true != ((sK419 @ id @ sK418 @ id))) & ! [X369 : term,X370 : subst,X371 : subst,X372 : subst] : (($true != ((sK419 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371) @ X372))) | ($true = ((sK419 @ X370 @ X369 @ (comp @ X371 @ X372))))) & ! [X373 : term,X374 : subst,X375 : subst,X376 : subst] : (($true = ((sK419 @ (comp @ X376 @ X374) @ (sub @ X373 @ X374) @ X375))) | ($true != ((sK419 @ X376 @ X373 @ (comp @ X374 @ X375))))))) & (! [X377 : term,X378 : (subst > term > subst > $o)] : (($true = ((sP8 @ X378))) | (($true = ((var @ (sub @ (sK420 @ X378) @ id)))) & ($true != ((X378 @ id @ (sK420 @ X378) @ id)))) | ($true = ((sP7 @ X378))) | ($true = ((X378 @ id @ X377 @ id))) | (($true = ((X378 @ (comp @ (sK422 @ X378) @ (sK423 @ X378)) @ (sub @ (sK421 @ X378) @ (sK423 @ X378)) @ (sK424 @ X378)))) & ($true != ((X378 @ (sK422 @ X378) @ (sK421 @ X378) @ (comp @ (sK423 @ X378) @ (sK424 @ X378)))))) | (($true != ((X378 @ (comp @ (sK428 @ X378) @ (sK426 @ X378)) @ (sub @ (sK425 @ X378) @ (sK426 @ X378)) @ (sK427 @ X378)))) & ($true = ((X378 @ (sK428 @ X378) @ (sK425 @ X378) @ (comp @ (sK426 @ X378) @ (sK427 @ X378))))))) | (hoasinduction != $true)) & (hoasinduction_lem1_lthm = $true) & ((induction2 = $true) | ($true != sP6)) & (($true = sP6) | (induction2 != $true)) & (! [X388 : term,X389 : term] : ((X388 = X389) | (((sub @ X389 @ sh)) != ((sub @ X388 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ((sK430 != sK429) & (((sub @ sK429 @ sh)) = ((sub @ sK430 @ sh))))) & (! [X392 : term] : (((sub @ X392 @ id)) = X392) | (axvarid != $true)) & ((axvarid = $true) | (sK431 != ((sub @ sK431 @ id)))) & (hoasinduction_lem1 = $true) & (axapp = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & ((termmset = $true) | (((sub @ sK432 @ id)) != sK432)) & (! [X395 : term] : (((sub @ X395 @ id)) = X395) | (termmset != $true)) & ! [X396 : d_term] : (d_one = X396) & (($true = sP5) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP5)) & ((hoasinduction_lem3b_lthm = $true) | ! [X398 : (subst > term > term)] : (((sub @ sK433 @ (push @ one @ sh))) != ((X398 @ sh @ one)))) & (! [X399 : term] : (((sK434 @ X399 @ sh @ one)) = ((sub @ X399 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (induction2_gthm = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & ((laminj = $true) | ((((lam @ sK435)) = ((lam @ sK436))) & (sK435 != sK436))) & (! [X403 : term,X404 : term] : ((((lam @ X403)) != ((lam @ X404))) | (X403 = X404)) | (laminj != $true)) & ! [X405 : d_subst] : (d_id = X405) & (ulamvarind = $true) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axmap = $true) & ((hoaslaminj_lthm = $true) | (! [X406 : subst,X407 : term] : (((comp @ sh @ (push @ X407 @ X406))) = X406) & ! [X408 : subst,X409 : term] : (((sub @ one @ (push @ X409 @ X408))) = X409) & ! [X410 : term,X411 : term] : ((((lam @ X410)) != ((lam @ X411))) | (X410 = X411)) & (! [X416 : subst,X417 : term,X418 : subst] : (((sub @ (sK437 @ X416 @ X417) @ X418)) = ((sK437 @ (comp @ X416 @ X418) @ (sub @ X417 @ X418)))) & (((lam @ (sK440 @ sh @ one))) = ((lam @ (sK437 @ sh @ one)))) & (((sK440 @ sK439 @ sK438)) != ((sK437 @ sK439 @ sK438))) & ! [X419 : subst,X420 : subst,X421 : term] : (((sK440 @ (comp @ X420 @ X419) @ (sub @ X421 @ X419))) = ((sub @ (sK440 @ X420 @ X421) @ X419)))))) & ((sK441 != ((comp @ sh @ (push @ sK442 @ sK441)))) | (sK444 != ((sub @ one @ (push @ sK444 @ sK443)))) | ((((lam @ sK446)) = ((lam @ sK445))) & (sK446 != sK445)) | ! [X428 : (subst > term > term),X429 : term,X430 : subst,X431 : (subst > term > term)] : ((((sub @ (X428 @ (sK447 @ X428) @ (sK448 @ X428)) @ (sK449 @ X428))) != ((X428 @ (comp @ (sK447 @ X428) @ (sK449 @ X428)) @ (sub @ (sK448 @ X428) @ (sK449 @ X428))))) | (((lam @ (X428 @ sh @ one))) != ((lam @ (X431 @ sh @ one)))) | (((X431 @ X430 @ X429)) = ((X428 @ X430 @ X429))) | (((sub @ (X431 @ (sK451 @ X431) @ (sK452 @ X431)) @ (sK450 @ X431))) != ((X431 @ (comp @ (sK451 @ X431) @ (sK450 @ X431)) @ (sub @ (sK452 @ X431) @ (sK450 @ X431)))))) | (hoaslaminj_lthm != $true)) & (hoaslamnotvar_lthm = $true) & ((($true != ((sK455 @ (lam @ sK453)))) & ! [X441 : term] : (((sK454 @ id @ X441 @ id)) = ((sK455 @ X441))) & ! [X442 : term] : (($true != ((sK455 @ X442))) | ($true = ((sK455 @ (sub @ sK453 @ (push @ X442 @ id)))))) & ! [X443 : (subst > term > term)] : (($true = ((sK454 @ id @ (lam @ (X443 @ sh @ one)) @ id))) | (($true != ((sK454 @ id @ (X443 @ id @ (sK456 @ X443)) @ id))) & ($true = ((sK454 @ id @ (sK456 @ X443) @ id)))) | (((X443 @ (comp @ (sK457 @ X443) @ (sK459 @ X443)) @ (sub @ (sK458 @ X443) @ (sK459 @ X443)))) != ((sub @ (X443 @ (sK457 @ X443) @ (sK458 @ X443)) @ (sK459 @ X443)))))) | ($true = sP3) | ($true = sP4) | ! [X449 : (term > $o)] : (((sK460 @ id @ (sK461 @ X449) @ id)) != ((X449 @ (sK461 @ X449)))) | (((sub @ sK462 @ id)) != sK462) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X452 : term,X453 : (subst > term > subst > $o),X454 : (term > $o)] : (($true = ((X454 @ (lam @ X452)))) | (((X454 @ (sK463 @ X454 @ X453))) != ((X453 @ id @ (sK463 @ X454 @ X453) @ id))) | (($true = ((X454 @ (sK464 @ X454 @ X452)))) & ($true != ((X454 @ (sub @ X452 @ (push @ (sK464 @ X454 @ X452) @ id)))))) | (($true != ((X453 @ id @ (lam @ (sK465 @ X453 @ sh @ one)) @ id))) & ! [X458 : term] : (($true = ((X453 @ id @ (sK465 @ X453 @ id @ X458) @ id))) | ($true != ((X453 @ id @ X458 @ id)))) & ! [X459 : subst,X460 : term,X461 : subst] : (((sK465 @ X453 @ (comp @ X459 @ X461) @ (sub @ X460 @ X461))) = ((sub @ (sK465 @ X453 @ X459 @ X460) @ X461))))) & ($true != sP3) & ($true != sP4) & ! [X462 : (subst > term > subst > $o)] : ! [X464 : term] : (((sK466 @ X462 @ X464)) = ((X462 @ id @ X464 @ id))) & ! [X465 : term] : (((sub @ X465 @ id)) = X465))) & ((hoasinduction_lem3aaa = $true) | (($true != ((sK467 @ id @ (lam @ (sub @ sK468 @ (push @ one @ sh))) @ id))) & ! [X468 : term] : (($true = ((sK467 @ id @ (sub @ sK468 @ (push @ X468 @ id)) @ id))) | ($true != ((sK467 @ id @ X468 @ id)))) & ! [X469 : term,X470 : (subst > term > term)] : ((((X470 @ (comp @ (sK470 @ X470 @ X469) @ (sK471 @ X470 @ X469)) @ (sub @ (sK469 @ X470 @ X469) @ (sK471 @ X470 @ X469)))) != ((sub @ X469 @ (push @ (sub @ (sK469 @ X470 @ X469) @ (sK471 @ X470 @ X469)) @ (comp @ (sK470 @ X470 @ X469) @ (sK471 @ X470 @ X469)))))) | ($true = ((sK467 @ id @ (lam @ (X470 @ sh @ one)) @ id))) | (($true = ((sK467 @ id @ (sK472 @ X470) @ id))) & ($true != ((sK467 @ id @ (X470 @ id @ (sK472 @ X470)) @ id)))) | (((sub @ (sub @ X469 @ (push @ (sK475 @ X470 @ X469) @ (sK473 @ X470 @ X469))) @ (sK474 @ X470 @ X469))) != ((sub @ (X470 @ (sK473 @ X470 @ X469) @ (sK475 @ X470 @ X469)) @ (sK474 @ X470 @ X469))))))) & (! [X478 : (subst > term > subst > $o),X479 : term] : (($true = ((X478 @ id @ (lam @ (sub @ X479 @ (push @ one @ sh))) @ id))) | (($true != ((X478 @ id @ (sub @ X479 @ (push @ (sK476 @ X479 @ X478) @ id)) @ id))) & ($true = ((X478 @ id @ (sK476 @ X479 @ X478) @ id)))) | (! [X483 : term,X484 : subst,X485 : subst] : (((sK478 @ X478 @ (comp @ X484 @ X485) @ (sub @ X483 @ X485))) = ((sub @ (sK477 @ X478) @ (push @ (sub @ X483 @ X485) @ (comp @ X484 @ X485))))) & ($true != ((X478 @ id @ (lam @ (sK478 @ X478 @ sh @ one)) @ id))) & ! [X486 : term] : (($true != ((X478 @ id @ X486 @ id))) | ($true = ((X478 @ id @ (sK478 @ X478 @ id @ X486) @ id)))) & ! [X487 : subst,X488 : subst,X489 : term] : (((sub @ (sub @ (sK477 @ X478) @ (push @ X489 @ X487)) @ X488)) = ((sub @ (sK478 @ X478 @ X487 @ X489) @ X488))))) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X490 : d_term,X491 : d_term] : ((X490 = X491) | (((d2term @ X490)) != ((d2term @ X491)))) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK479 @ id) @ sK481)) = ((ap @ (sub @ sK480 @ id) @ sK482))) & (sK480 != sK479))) & (! [X496 : term,X497 : term,X498 : term,X499 : term] : ((((ap @ (sub @ X496 @ id) @ X498)) != ((ap @ (sub @ X497 @ id) @ X499))) | (X496 = X497)) | (hoasapinj1 != $true)) & (hoaslamnotap_gthm = $true) & ! [X500 : term] : (((d2term @ (sK483 @ X500))) = X500) & (pushprop_gthm = $true) & (hoasinduction_gthm = $true) & (! [X502 : (term > $o),X503 : subst,X504 : term] : ! [X506 : term] : (((sK484 @ X504 @ X503 @ X502 @ X506)) = ((X502 @ (sub @ X506 @ (push @ X504 @ X503))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X510 : (term > $o)] : (((sK485 @ (sub @ (sK488 @ X510) @ (push @ sK487 @ sK486)))) != ((X510 @ (sK488 @ X510))))) & ((((comp @ sh @ (push @ sK490 @ sK489))) != sK489) | ! [X514 : term,X515 : (term > $o),X516 : term,X517 : subst,X518 : (term > $o)] : (($true != ((X515 @ X516))) | ($true = ((X518 @ (sub @ X516 @ (push @ X514 @ X517)))))) | (sK491 != ((sub @ one @ (push @ sK491 @ sK492)))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X521 : subst,X522 : term] : (((comp @ sh @ (push @ X522 @ X521))) = X521) & (($true = ((sK494 @ sK495))) & ($true != ((sK497 @ (sub @ sK495 @ (push @ sK493 @ sK496)))))) & ! [X528 : term,X529 : subst] : (((sub @ one @ (push @ X528 @ X529))) = X528))) & (! [X530 : (term > $o),X531 : term,X532 : (subst > term > subst > $o)] : ((($true = ((X530 @ (sK498 @ X531 @ X530)))) & ($true != ((X530 @ (sub @ X531 @ (push @ (sK498 @ X531 @ X530) @ id)))))) | ($true = ((sP2 @ X532))) | (($true != ((X532 @ (sK501 @ X532) @ (sK499 @ X532) @ (comp @ (sK502 @ X532) @ (sK500 @ X532))))) & ($true = ((X532 @ (comp @ (sK501 @ X532) @ (sK502 @ X532)) @ (sub @ (sK499 @ X532) @ (sK502 @ X532)) @ (sK500 @ X532))))) | (((X532 @ id @ (sK503 @ X532 @ X530) @ id)) != ((X530 @ (sK503 @ X532 @ X530)))) | ($true = ((X530 @ (lam @ X531)))) | (($true = ((X532 @ (sK504 @ X532) @ (sK505 @ X532) @ (comp @ (sK507 @ X532) @ (sK506 @ X532))))) & ($true != ((X532 @ (comp @ (sK504 @ X532) @ (sK507 @ X532)) @ (sub @ (sK505 @ X532) @ (sK507 @ X532)) @ (sK506 @ X532)))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (! [X546 : term] : ((((sK508 @ X546)) != $true) | ($true = ((sK508 @ (sub @ sK509 @ (push @ X546 @ id)))))) & ($true != ((sP2 @ sK510))) & ! [X547 : term,X548 : subst,X549 : subst,X550 : subst] : (($true = ((sK510 @ X549 @ X547 @ (comp @ X550 @ X548)))) | ($true != ((sK510 @ (comp @ X549 @ X550) @ (sub @ X547 @ X550) @ X548)))) & ! [X551 : term] : (((sK510 @ id @ X551 @ id)) = ((sK508 @ X551))) & ($true != ((sK508 @ (lam @ sK509)))) & ! [X552 : subst,X553 : term,X554 : subst,X555 : subst] : ((((sK510 @ X552 @ X553 @ (comp @ X555 @ X554))) != $true) | ($true = ((sK510 @ (comp @ X552 @ X555) @ (sub @ X553 @ X555) @ X554)))))) & ((hoasapinj2 = $true) | ((sK512 != sK513) & (((ap @ (sub @ sK514 @ id) @ sK512)) = ((ap @ (sub @ sK511 @ id) @ sK513))))) & (! [X560 : term,X561 : term,X562 : term,X563 : term] : ((X561 = X562) | (((ap @ (sub @ X563 @ id) @ X561)) != ((ap @ (sub @ X560 @ id) @ X562)))) | (hoasapinj2 != $true)) & ((hoasapinj2_lthm = $true) | (! [X564 : term,X565 : term,X566 : term,X567 : term] : ((X564 = X567) | (((ap @ X566 @ X567)) != ((ap @ X565 @ X564)))) & ((sK516 != sK515) & (((ap @ (sub @ sK518 @ id) @ sK516)) = ((ap @ (sub @ sK517 @ id) @ sK515)))))) & (((sK519 != sK522) & (((ap @ sK520 @ sK519)) = ((ap @ sK521 @ sK522)))) | ! [X576 : term,X577 : term,X578 : term,X579 : term] : ((X576 = X577) | (((ap @ (sub @ X579 @ id) @ X577)) != ((ap @ (sub @ X578 @ id) @ X576)))) | (hoasapinj2_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3a = $true) | ((((sK523 @ id @ (lam @ sK524) @ id)) != $true) & ! [X582 : term] : (($true != ((sK523 @ id @ X582 @ id))) | ($true = ((sK523 @ id @ (sub @ sK524 @ (push @ X582 @ id)) @ id)))) & ! [X583 : (subst > term > term)] : ((((sub @ (X583 @ (sK526 @ X583) @ (sK525 @ X583)) @ (sK527 @ X583))) != ((X583 @ (comp @ (sK526 @ X583) @ (sK527 @ X583)) @ (sub @ (sK525 @ X583) @ (sK527 @ X583))))) | (($true = ((sK523 @ id @ (sK528 @ X583) @ id))) & ($true != ((sK523 @ id @ (X583 @ id @ (sK528 @ X583)) @ id)))) | ($true = ((sK523 @ id @ (lam @ (X583 @ sh @ one)) @ id)))))) & (! [X588 : (subst > term > subst > $o),X589 : term] : (($true = ((X588 @ id @ (lam @ X589) @ id))) | (($true = ((X588 @ id @ (sK529 @ X589 @ X588) @ id))) & ($true != ((X588 @ id @ (sub @ X589 @ (push @ (sK529 @ X589 @ X588) @ id)) @ id)))) | (! [X592 : term,X593 : subst,X594 : subst] : (((sK530 @ X588 @ (comp @ X593 @ X594) @ (sub @ X592 @ X594))) = ((sub @ (sK530 @ X588 @ X593 @ X592) @ X594))) & ! [X595 : term] : (($true != ((X588 @ id @ X595 @ id))) | ($true = ((X588 @ id @ (sK530 @ X588 @ id @ X595) @ id)))) & ($true != ((X588 @ id @ (lam @ (sK530 @ X588 @ sh @ one)) @ id))))) | (hoasinduction_lem3a != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) | (($true != ((sK532 @ (lam @ sK533)))) & ! [X599 : term] : (((sK531 @ id @ X599 @ id)) = ((sK532 @ X599))) & ! [X600 : term] : (($true = ((sK532 @ (sub @ sK533 @ (push @ X600 @ id))))) | ($true != ((sK532 @ X600)))) & ! [X601 : (subst > term > term)] : ((($true != ((sK531 @ id @ (X601 @ id @ (sK534 @ X601)) @ id))) & ($true = ((sK531 @ id @ (sK534 @ X601) @ id)))) | ($true = ((sK531 @ id @ (lam @ (X601 @ sh @ one)) @ id))) | (((sub @ (X601 @ (sK537 @ X601) @ (sK535 @ X601)) @ (sK536 @ X601))) != ((X601 @ (comp @ (sK537 @ X601) @ (sK536 @ X601)) @ (sub @ (sK535 @ X601) @ (sK536 @ X601)))))))) & (! [X606 : (subst > term > subst > $o),X607 : (term > $o),X608 : term] : (($true = ((X607 @ (lam @ X608)))) | (((X607 @ (sK538 @ X607 @ X606))) != ((X606 @ id @ (sK538 @ X607 @ X606) @ id))) | (($true != ((X607 @ (sub @ X608 @ (push @ (sK539 @ X608 @ X607) @ id))))) & ($true = ((X607 @ (sK539 @ X608 @ X607))))) | (! [X612 : term] : (($true = ((X606 @ id @ (sK540 @ X606 @ id @ X612) @ id))) | ($true != ((X606 @ id @ X612 @ id)))) & ($true != ((X606 @ id @ (lam @ (sK540 @ X606 @ sh @ one)) @ id))) & ! [X613 : term,X614 : subst,X615 : subst] : (((sub @ (sK540 @ X606 @ X615 @ X613) @ X614)) = ((sK540 @ X606 @ (comp @ X615 @ X614) @ (sub @ X613 @ X614)))))) | (hoasinduction_lem3v2a != $true)) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X617 : (subst > term > term)] : (((sub @ sK541 @ (push @ (sK542 @ X617) @ (sK543 @ X617)))) != ((X617 @ (sK543 @ X617) @ (sK542 @ X617))))) & (! [X620 : term] : ! [X622 : term,X623 : subst] : (((sK544 @ X620 @ X623 @ X622)) = ((sub @ X620 @ (push @ X622 @ X623)))) | (hoasinduction_lem3v2_f != $true)) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | (! [X626 : (subst > term > term)] : (($true = ((sK546 @ id @ (lam @ (X626 @ sh @ one)) @ id))) | (($true != ((sK546 @ id @ (X626 @ id @ (sK547 @ X626)) @ id))) & ($true = ((sK546 @ id @ (sK547 @ X626) @ id)))) | (((X626 @ (comp @ (sK550 @ X626) @ (sK549 @ X626)) @ (sub @ (sK548 @ X626) @ (sK549 @ X626)))) != ((sub @ (X626 @ (sK550 @ X626) @ (sK548 @ X626)) @ (sK549 @ X626))))) & ! [X631 : term,X632 : term] : (($true = ((sK546 @ id @ (ap @ (sub @ X631 @ id) @ X632) @ id))) | ($true != ((sK546 @ id @ X632 @ id))) | ($true != ((sK546 @ id @ X631 @ id)))) & ($true != ((sK546 @ id @ sK545 @ id))))) & (! [X633 : term,X634 : (subst > term > subst > $o)] : ((($true != ((X634 @ id @ (lam @ (sK551 @ X634 @ sh @ one)) @ id))) & ! [X636 : term] : (($true = ((X634 @ id @ (sK551 @ X634 @ id @ X636) @ id))) | (((X634 @ id @ X636 @ id)) != $true)) & ! [X637 : term,X638 : subst,X639 : subst] : (((sK551 @ X634 @ (comp @ X639 @ X638) @ (sub @ X637 @ X638))) = ((sub @ (sK551 @ X634 @ X639 @ X637) @ X638)))) | (($true != ((X634 @ id @ (ap @ (sub @ (sK552 @ X634) @ id) @ (sK553 @ X634)) @ id))) & ($true = ((X634 @ id @ (sK553 @ X634) @ id))) & ($true = ((X634 @ id @ (sK552 @ X634) @ id)))) | ($true = ((X634 @ id @ X633 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (hoaslamnotvar = $true) & (! [X642 : term] : (((sub @ X642 @ id)) = X642) | (sK554 != ((sub @ sK554 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK555 @ id)) != sK555) & ! [X645 : term] : (((sub @ X645 @ id)) = X645))) & (lamnotvar = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((apinj1 = $true) | ((sK557 != sK556) & (((ap @ sK556 @ sK559)) = ((ap @ sK557 @ sK558))))) & (! [X650 : term,X651 : term,X652 : term,X653 : term] : ((X650 = X651) | (((ap @ X651 @ X652)) != ((ap @ X650 @ X653)))) | (apinj1 != $true)) & ((induction2lem_lthm = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem_lthm != $true))), 24.89/4.11 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK237,sK238,vAPP,vAPP,sK241,sK242,vAPP,vAPP,vAPP,vAPP,sK247,sK248,sK249,sK250,sK251,sK252,sK253,sK254,sK255,sK256,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK267,sK268,sK269,sK270,sK271,sK272,vAPP,sK274,sK275,sK276,sK277,sK278,sK279,sK280,sK281,sK282,sK283,sK284,sK285,sK286,vAPP,vAPP,sK289,sK290,vAPP,vAPP,vAPP,vAPP,sK295,sK296,sK297,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK304,sK305,sK306,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK322,sK323,sK324,vAPP,vAPP,sK327,vAPP,vAPP,vAPP,vAPP,sK332,sK333,sK334,vAPP,vAPP,vAPP,vAPP,sK339,sK340,sK341,sK342,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK349,sK350,vAPP,sK352,sK353,sK354,vAPP,vAPP,vAPP,vAPP,sK359,sK360,sK361,sK362,sK363,sK364,sK365,sK366,sK367,vAPP,sK369,sK370,sK371,sK372,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK381,vAPP,vAPP,vAPP,sK385,sK386,sK387,sK388,sK389,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK400,sK401,sK402,sK403,sK404,vAPP,vAPP,vAPP,vAPP,sK409,vAPP,vAPP,vAPP,sK413,sK414,vAPP,sK416,vAPP,sK418,sK419,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK429,sK430,sK431,sK432,sK433,vAPP,sK435,sK436,sK437,sK438,sK439,sK440,sK441,sK442,sK443,sK444,sK445,sK446,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK453,sK454,sK455,vAPP,vAPP,vAPP,vAPP,sK460,vAPP,sK462,vAPP,vAPP,vAPP,vAPP,sK467,sK468,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK479,sK480,sK481,sK482,vAPP,vAPP,sK485,sK486,sK487,vAPP,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK531,sK532,sK533,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK541,vAPP,vAPP,vAPP,sK545,sK546,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK554,sK555,sK556,sK557,sK558,sK559]),skolemize(X25,sK40 @ X14),skolemize(X4,sK237),skolemize(X5,sK238),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X14,sK241),skolemize(X15,sK242),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X22,sK247),skolemize(X23,sK248),skolemize(X24,sK249),skolemize(X25,sK250),skolemize(X35,sK251),skolemize(X36,sK252),skolemize(X37,sK253),skolemize(X38,sK254),skolemize(X39,sK255),skolemize(X42,sK256),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X57,sK267),skolemize(X58,sK268),skolemize(X59,sK269),skolemize(X60,sK270),skolemize(X72,sK271),skolemize(X73,sK272),skolemize(X25,sK40 @ X14),skolemize(X81,sK274),skolemize(X82,sK275),skolemize(X83,sK276),skolemize(X84,sK277),skolemize(X86,sK278),skolemize(X87,sK279),skolemize(X88,sK280),skolemize(X89,sK281),skolemize(X90,sK282),skolemize(X100,sK283),skolemize(X101,sK284),skolemize(X102,sK285),skolemize(X103,sK286),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X113,sK289),skolemize(X114,sK290),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X121,sK295),skolemize(X122,sK296),skolemize(X123,sK297),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X138,sK304),skolemize(X139,sK305),skolemize(X140,sK306),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X167,sK322),skolemize(X168,sK323),skolemize(X178,sK324),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X182,sK327),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X198,sK332),skolemize(X199,sK333),skolemize(X200,sK334),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X208,sK339),skolemize(X209,sK340),skolemize(X210,sK341),skolemize(X211,sK342),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X230,sK349),skolemize(X231,sK350),skolemize(X25,sK40 @ X14),skolemize(X237,sK352),skolemize(X238,sK353),skolemize(X239,sK354),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X248,sK359),skolemize(X249,sK360),skolemize(X250,sK361),skolemize(X254,sK362),skolemize(X255,sK363),skolemize(X260,sK364),skolemize(X261,sK365),skolemize(X262,sK366),skolemize(X264,sK367),skolemize(X25,sK40 @ X14),skolemize(X267,sK369),skolemize(X268,sK370),skolemize(X269,sK371),skolemize(X270,sK372),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X292,sK381),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X300,sK385),skolemize(X302,sK386),skolemize(X303,sK387),skolemize(X304,sK388),skolemize(X305,sK389),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X323,sK400),skolemize(X324,sK401),skolemize(X334,sK402),skolemize(X336,sK403),skolemize(X337,sK404),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X348,sK409),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X356,sK413),skolemize(X357,sK414),skolemize(X25,sK40 @ X14),skolemize(X363,sK416),skolemize(X25,sK40 @ X14),skolemize(X366,sK418),skolemize(X367,sK419),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X390,sK429),skolemize(X391,sK430),skolemize(X393,sK431),skolemize(X394,sK432),skolemize(X397,sK433),skolemize(X25,sK40 @ X14),skolemize(X401,sK435),skolemize(X402,sK436),skolemize(X412,sK437),skolemize(X413,sK438),skolemize(X414,sK439),skolemize(X415,sK440),skolemize(X422,sK441),skolemize(X423,sK442),skolemize(X424,sK443),skolemize(X425,sK444),skolemize(X426,sK445),skolemize(X427,sK446),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X438,sK453),skolemize(X439,sK454),skolemize(X440,sK455),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X448,sK460),skolemize(X25,sK40 @ X14),skolemize(X451,sK462),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X466,sK467),skolemize(X467,sK468),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X492,sK479),skolemize(X493,sK480),skolemize(X494,sK481),skolemize(X495,sK482),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X507,sK485),skolemize(X508,sK486),skolemize(X509,sK487),skolemize(X25,sK40 @ X14),skolemize(X512,sK489),skolemize(X513,sK490),skolemize(X519,sK491),skolemize(X520,sK492),skolemize(X523,sK493),skolemize(X524,sK494),skolemize(X525,sK495),skolemize(X526,sK496),skolemize(X527,sK497),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X543,sK508),skolemize(X544,sK509),skolemize(X545,sK510),skolemize(X556,sK511),skolemize(X557,sK512),skolemize(X558,sK513),skolemize(X559,sK514),skolemize(X568,sK515),skolemize(X569,sK516),skolemize(X570,sK517),skolemize(X571,sK518),skolemize(X572,sK519),skolemize(X573,sK520),skolemize(X574,sK521),skolemize(X575,sK522),skolemize(X580,sK523),skolemize(X581,sK524),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X596,sK531),skolemize(X597,sK532),skolemize(X598,sK533),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X616,sK541),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X624,sK545),skolemize(X625,sK546),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X643,sK554),skolemize(X644,sK555),skolemize(X646,sK556),skolemize(X647,sK557),skolemize(X648,sK558),skolemize(X649,sK559)],[f132])). 24.89/4.11 thf(f134,plain,( 24.89/4.11 ((hoasinduction_no_psi_cond != $true) | ? [X0 : (subst > term > subst > $o)] : (? [X8 : term] : ($true != ((X0 @ id @ X8 @ id))) & ! [X3 : (subst > term > term)] : (($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))) | ? [X6 : subst,X5 : term,X4 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) != ((sub @ (X3 @ X6 @ X5) @ X4))) | ? [X7 : term] : (($true = ((X0 @ id @ X7 @ id))) & ($true != ((X0 @ id @ (X3 @ id @ X7) @ id))))) & ! [X1 : term,X2 : term] : ((((X0 @ id @ X1 @ id)) != $true) | ($true = ((X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))) | (((X0 @ id @ X2 @ id)) != $true)))) & ((hoasinduction_no_psi_cond = $true) | ! [X0 : (subst > term > subst > $o)] : (! [X8 : term] : ($true = ((X0 @ id @ X8 @ id))) | ? [X3 : (subst > term > term)] : (($true != ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))) & ! [X6 : subst,X5 : term,X4 : subst] : (((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (X3 @ X6 @ X5) @ X4))) & ! [X7 : term] : (($true != ((X0 @ id @ X7 @ id))) | ($true = ((X0 @ id @ (X3 @ id @ X7) @ id))))) | ? [X1 : term,X2 : term] : ((((X0 @ id @ X1 @ id)) = $true) & ($true != ((X0 @ id @ (hoasap @ id @ X2 @ id @ X1) @ id))) & (((X0 @ id @ X2 @ id)) = $true))))), 24.89/4.11 inference(nnf_transformation,[],[f14])). 24.89/4.11 thf(f135,plain,( 24.89/4.11 ((hoasinduction_no_psi_cond != $true) | ? [X0 : (subst > term > subst > $o)] : (? [X1 : term] : (((X0 @ id @ X1 @ id)) != $true) & ! [X2 : (subst > term > term)] : (($true = ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X2 @ Y0 @ Y1))))) @ id))) | ? [X3 : subst,X4 : term,X5 : subst] : (((sub @ (X2 @ X3 @ X4) @ X5)) != ((X2 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) | ? [X6 : term] : (($true = ((X0 @ id @ X6 @ id))) & ($true != ((X0 @ id @ (X2 @ id @ X6) @ id))))) & ! [X7 : term,X8 : term] : (($true != ((X0 @ id @ X7 @ id))) | ($true = ((X0 @ id @ (hoasap @ id @ X8 @ id @ X7) @ id))) | ($true != ((X0 @ id @ X8 @ id)))))) & ((hoasinduction_no_psi_cond = $true) | ! [X9 : (subst > term > subst > $o)] : (! [X10 : term] : ($true = ((X9 @ id @ X10 @ id))) | ? [X11 : (subst > term > term)] : (($true != ((X9 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X11 @ Y0 @ Y1))))) @ id))) & ! [X12 : subst,X13 : term,X14 : subst] : (((X11 @ (comp @ X12 @ X14) @ (sub @ X13 @ X14))) = ((sub @ (X11 @ X12 @ X13) @ X14))) & ! [X15 : term] : ((((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true))) | ? [X16 : term,X17 : term] : (($true = ((X9 @ id @ X16 @ id))) & ($true != ((X9 @ id @ (hoasap @ id @ X17 @ id @ X16) @ id))) & ($true = ((X9 @ id @ X17 @ id))))))), 24.89/4.11 inference(rectify,[],[f134])). 24.89/4.11 thf(f136,plain,( 24.89/4.11 ((hoasinduction_no_psi_cond != $true) | (($true != ((sK560 @ id @ sK561 @ id))) & ! [X2 : (subst > term > term)] : (($true = ((sK560 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X2 @ Y0 @ Y1))))) @ id))) | (((sub @ (X2 @ (sK562 @ X2) @ (sK563 @ X2)) @ (sK564 @ X2))) != ((X2 @ (comp @ (sK562 @ X2) @ (sK564 @ X2)) @ (sub @ (sK563 @ X2) @ (sK564 @ X2))))) | (($true = ((sK560 @ id @ (sK565 @ X2) @ id))) & ($true != ((sK560 @ id @ (X2 @ id @ (sK565 @ X2)) @ id))))) & ! [X7 : term,X8 : term] : (($true != ((sK560 @ id @ X7 @ id))) | ($true = ((sK560 @ id @ (hoasap @ id @ X8 @ id @ X7) @ id))) | ($true != ((sK560 @ id @ X8 @ id)))))) & ((hoasinduction_no_psi_cond = $true) | ! [X9 : (subst > term > subst > $o)] : (! [X10 : term] : ($true = ((X9 @ id @ X10 @ id))) | (($true != ((X9 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK566 @ X9 @ Y0 @ Y1))))) @ id))) & ! [X12 : subst,X13 : term,X14 : subst] : (((sK566 @ X9 @ (comp @ X12 @ X14) @ (sub @ X13 @ X14))) = ((sub @ (sK566 @ X9 @ X12 @ X13) @ X14))) & ! [X15 : term] : ((((X9 @ id @ X15 @ id)) != $true) | ($true = ((X9 @ id @ (sK566 @ X9 @ id @ X15) @ id))))) | (($true = ((X9 @ id @ (sK567 @ X9) @ id))) & ($true != ((X9 @ id @ (hoasap @ id @ (sK568 @ X9) @ id @ (sK567 @ X9)) @ id))) & ($true = ((X9 @ id @ (sK568 @ X9) @ id))))))), 24.89/4.11 inference(skolemize,[status(esa),new_symbols(skolem,[sK560,sK561,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK560),skolemize(X1,sK561),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14),skolemize(X25,sK40 @ X14)],[f135])). 24.89/4.11 thf(f487,plain,( 24.89/4.11 (hoasinduction_no_psi_cond = $true) | ($true != ((sK546 @ id @ sK545 @ id)))), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f489,plain,( 24.89/4.11 ( ! [X626 : (subst > term > term)] : (($true = ((sK546 @ id @ (lam @ (X626 @ sh @ one)) @ id))) | (((X626 @ (comp @ (sK550 @ X626) @ (sK549 @ X626)) @ (sub @ (sK548 @ X626) @ (sK549 @ X626)))) != ((sub @ (X626 @ (sK550 @ X626) @ (sK548 @ X626)) @ (sK549 @ X626)))) | (hoasinduction_no_psi_cond = $true) | ($true = ((sK546 @ id @ (sK547 @ X626) @ id)))) )), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f553,plain,( 24.89/4.11 ( ! [X500 : term] : ((((d2term @ (sK483 @ X500))) = X500)) )), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f602,plain,( 24.89/4.11 ( ! [X405 : d_subst] : ((d_id = X405)) )), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f613,plain,( 24.89/4.11 ( ! [X396 : d_term] : ((d_one = X396)) )), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f647,plain,( 24.89/4.11 (one = ((d2term @ d_one)))), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f871,plain,( 24.89/4.11 (((d2subst @ d_id)) = id)), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f874,plain,( 24.89/4.11 ( ! [X0 : subst] : ((((d2subst @ (sK236 @ X0))) = X0)) )), 24.89/4.11 inference(cnf_transformation,[],[f133])). 24.89/4.11 thf(f886,plain,( 24.89/4.11 ( ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK562 @ X2) @ (sK563 @ X2)) @ (sK564 @ X2))) != ((X2 @ (comp @ (sK562 @ X2) @ (sK564 @ X2)) @ (sub @ (sK563 @ X2) @ (sK564 @ X2))))) | ($true = ((sK560 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X2 @ Y0 @ Y1))))) @ id))) | ($true = ((sK560 @ id @ (sK565 @ X2) @ id))) | (hoasinduction_no_psi_cond != $true)) )), 24.89/4.11 inference(cnf_transformation,[],[f136])). 24.89/4.11 thf(f887,plain,( 24.89/4.11 (hoasinduction_no_psi_cond != $true) | ($true != ((sK560 @ id @ sK561 @ id)))), 24.89/4.11 inference(cnf_transformation,[],[f136])). 24.89/4.11 thf(f929,plain,( 24.89/4.11 ( ! [X2 : (subst > term > term)] : (($true = ((sK560 @ id @ (sK565 @ X2) @ id))) | ($true = ((sK560 @ id @ (hoaslam @ id @ X2) @ id))) | (((sub @ (X2 @ (sK562 @ X2) @ (sK563 @ X2)) @ (sK564 @ X2))) != ((X2 @ (comp @ (sK562 @ X2) @ (sK564 @ X2)) @ (sub @ (sK563 @ X2) @ (sK564 @ X2))))) | (hoasinduction_no_psi_cond != $true)) )), 24.89/4.11 inference(beta-eta_normalization,[],[f886])). 24.89/4.11 thf(f1084,definition,( 24.89/4.11 spl569_6 <=> (hoasinduction_no_psi_cond = $true)), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_6])],[avatar_definition])). 24.89/4.11 thf(f2207,definition,( 24.89/4.11 spl569_272 <=> (one = ((d2term @ d_one)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_272])],[avatar_definition])). 24.89/4.11 thf(f2209,plain,( 24.89/4.11 (one = ((d2term @ d_one))) | ~spl569_272), 24.89/4.11 inference(avatar_component_clause,[],[f2207])). 24.89/4.11 thf(f2210,plain,( 24.89/4.11 spl569_272), 24.89/4.11 inference(avatar_split_clause,[],[f647,f2207])). 24.89/4.11 thf(f2260,definition,( 24.89/4.11 spl569_285 <=> ! [X2 : (subst > term > term)] : (($true = ((sK560 @ id @ (sK565 @ X2) @ id))) | (((sub @ (X2 @ (sK562 @ X2) @ (sK563 @ X2)) @ (sK564 @ X2))) != ((X2 @ (comp @ (sK562 @ X2) @ (sK564 @ X2)) @ (sub @ (sK563 @ X2) @ (sK564 @ X2))))) | ($true = ((sK560 @ id @ (hoaslam @ id @ X2) @ id))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_285])],[avatar_definition])). 24.89/4.11 thf(f2261,plain,( 24.89/4.11 ( ! [X2 : (subst > term > term)] : (($true = ((sK560 @ id @ (hoaslam @ id @ X2) @ id))) | (((sub @ (X2 @ (sK562 @ X2) @ (sK563 @ X2)) @ (sK564 @ X2))) != ((X2 @ (comp @ (sK562 @ X2) @ (sK564 @ X2)) @ (sub @ (sK563 @ X2) @ (sK564 @ X2))))) | ($true = ((sK560 @ id @ (sK565 @ X2) @ id)))) ) | ~spl569_285), 24.89/4.11 inference(avatar_component_clause,[],[f2260])). 24.89/4.11 thf(f2262,plain,( 24.89/4.11 spl569_285 | ~spl569_6), 24.89/4.11 inference(avatar_split_clause,[],[f929,f1084,f2260])). 24.89/4.11 thf(f2863,definition,( 24.89/4.11 spl569_426 <=> (((d2subst @ d_id)) = id)), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_426])],[avatar_definition])). 24.89/4.11 thf(f2865,plain,( 24.89/4.11 (((d2subst @ d_id)) = id) | ~spl569_426), 24.89/4.11 inference(avatar_component_clause,[],[f2863])). 24.89/4.11 thf(f2866,plain,( 24.89/4.11 spl569_426), 24.89/4.11 inference(avatar_split_clause,[],[f871,f2863])). 24.89/4.11 thf(f4118,definition,( 24.89/4.11 spl569_716 <=> ! [X626 : (subst > term > term)] : (($true = ((sK546 @ id @ (lam @ (X626 @ sh @ one)) @ id))) | ($true = ((sK546 @ id @ (sK547 @ X626) @ id))) | (((X626 @ (comp @ (sK550 @ X626) @ (sK549 @ X626)) @ (sub @ (sK548 @ X626) @ (sK549 @ X626)))) != ((sub @ (X626 @ (sK550 @ X626) @ (sK548 @ X626)) @ (sK549 @ X626)))))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_716])],[avatar_definition])). 24.89/4.11 thf(f4119,plain,( 24.89/4.11 ( ! [X626 : (subst > term > term)] : (($true = ((sK546 @ id @ (lam @ (X626 @ sh @ one)) @ id))) | ($true = ((sK546 @ id @ (sK547 @ X626) @ id))) | (((X626 @ (comp @ (sK550 @ X626) @ (sK549 @ X626)) @ (sub @ (sK548 @ X626) @ (sK549 @ X626)))) != ((sub @ (X626 @ (sK550 @ X626) @ (sK548 @ X626)) @ (sK549 @ X626))))) ) | ~spl569_716), 24.89/4.11 inference(avatar_component_clause,[],[f4118])). 24.89/4.11 thf(f4120,plain,( 24.89/4.11 spl569_716 | spl569_6), 24.89/4.11 inference(avatar_split_clause,[],[f489,f1084,f4118])). 24.89/4.11 thf(f4288,definition,( 24.89/4.11 spl569_756 <=> ($true = ((sK546 @ id @ sK545 @ id)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_756])],[avatar_definition])). 24.89/4.11 thf(f4290,plain,( 24.89/4.11 ($true != ((sK546 @ id @ sK545 @ id))) | spl569_756), 24.89/4.11 inference(avatar_component_clause,[],[f4288])). 24.89/4.11 thf(f4291,plain,( 24.89/4.11 ~spl569_756 | spl569_6), 24.89/4.11 inference(avatar_split_clause,[],[f487,f1084,f4288])). 24.89/4.11 thf(f4502,definition,( 24.89/4.11 spl569_806 <=> ($true = ((sK560 @ id @ sK561 @ id)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_806])],[avatar_definition])). 24.89/4.11 thf(f4504,plain,( 24.89/4.11 ($true != ((sK560 @ id @ sK561 @ id))) | spl569_806), 24.89/4.11 inference(avatar_component_clause,[],[f4502])). 24.89/4.11 thf(f4505,plain,( 24.89/4.11 ~spl569_806 | ~spl569_6), 24.89/4.11 inference(avatar_split_clause,[],[f887,f1084,f4502])). 24.89/4.11 thf(f4858,plain,( 24.89/4.11 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) ) | ~spl569_272), 24.89/4.11 inference(superposition,[],[f2209,f613])). 24.89/4.11 thf(f4859,plain,( 24.89/4.11 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) ) | ~spl569_426), 24.89/4.11 inference(superposition,[],[f2865,f602])). 24.89/4.11 thf(f5488,plain,( 24.89/4.11 ( ! [X0 : term] : ((one = X0)) ) | ~spl569_272), 24.89/4.11 inference(superposition,[],[f4858,f553])). 24.89/4.11 thf(f5490,plain,( 24.89/4.11 ( ! [X0 : subst] : ((id = X0)) ) | ~spl569_426), 24.89/4.11 inference(superposition,[],[f4859,f874])). 24.89/4.11 thf(f5583,plain,( 24.89/4.11 ( ! [X0 : term,X1 : term] : ((X0 = X1)) ) | ~spl569_272), 24.89/4.11 inference(superposition,[],[f5488,f5488])). 24.89/4.11 thf(f5843,plain,( 24.89/4.11 ( ! [X0 : subst] : (($true != ((sK546 @ X0 @ sK545 @ X0)))) ) | (~spl569_426 | spl569_756)), 24.89/4.11 inference(superposition,[],[f4290,f5490])). 24.89/4.11 thf(f8025,plain,( 24.89/4.11 ( ! [X2 : (subst > term > term)] : (($true = ((sK560 @ id @ (hoaslam @ id @ X2) @ id))) | ($true = ((sK560 @ id @ (sK565 @ X2) @ id)))) ) | (~spl569_272 | ~spl569_285)), 24.89/4.11 inference(forward_subsumption_resolution,[],[f2261,f5583])). 24.89/4.11 thf(f8045,definition,( 24.89/4.11 spl569_919 <=> ! [X0 : term] : ($true = ((sK560 @ id @ X0 @ id)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_919])],[avatar_definition])). 24.89/4.11 thf(f8046,plain,( 24.89/4.11 ( ! [X0 : term] : (($true = ((sK560 @ id @ X0 @ id)))) ) | ~spl569_919), 24.89/4.11 inference(avatar_component_clause,[],[f8045])). 24.89/4.11 thf(f21174,definition,( 24.89/4.11 spl569_998 <=> ! [X0 : term] : ($true = ((sK546 @ id @ X0 @ id)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_998])],[avatar_definition])). 24.89/4.11 thf(f21175,plain,( 24.89/4.11 ( ! [X0 : term] : (($true = ((sK546 @ id @ X0 @ id)))) ) | ~spl569_998), 24.89/4.11 inference(avatar_component_clause,[],[f21174])). 24.89/4.11 thf(f21600,plain,( 24.89/4.11 ($true != $true) | (~spl569_426 | spl569_756 | ~spl569_998)), 24.89/4.11 inference(superposition,[],[f5843,f21175])). 24.89/4.11 thf(f21619,plain,( 24.89/4.11 $false | (~spl569_426 | spl569_756 | ~spl569_998)), 24.89/4.11 inference(trivial_inequality_removal,[],[f21600])). 24.89/4.11 thf(f21620,plain,( 24.89/4.11 ~spl569_426 | spl569_756 | ~spl569_998), 24.89/4.11 inference(avatar_contradiction_clause,[],[f21619])). 24.89/4.11 thf(f22590,definition,( 24.89/4.11 spl569_1035 <=> ($true = ((sK546 @ id @ one @ id)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_1035])],[avatar_definition])). 24.89/4.11 thf(f22591,plain,( 24.89/4.11 ($true != ((sK546 @ id @ one @ id))) | spl569_1035), 24.89/4.11 inference(avatar_component_clause,[],[f22590])). 24.89/4.11 thf(f22592,plain,( 24.89/4.11 ($true = ((sK546 @ id @ one @ id))) | ~spl569_1035), 24.89/4.11 inference(avatar_component_clause,[],[f22590])). 24.89/4.11 thf(f37847,definition,( 24.89/4.11 spl569_1237 <=> ($true = ((sK560 @ id @ one @ id)))), 24.89/4.11 introduced(definition,[new_symbols(definition,[spl569_1237])],[avatar_definition])). 24.89/4.11 thf(f37848,plain,( 24.89/4.11 ($true = ((sK560 @ id @ one @ id))) | ~spl569_1237), 24.89/4.11 inference(avatar_component_clause,[],[f37847])). 24.89/4.11 thf(f37849,plain,( 24.89/4.11 ($true != ((sK560 @ id @ one @ id))) | spl569_1237), 24.89/4.11 inference(avatar_component_clause,[],[f37847])). 24.89/4.11 thf(f37851,plain,( 24.89/4.11 ( ! [X0 : term] : (($true != ((sK560 @ id @ X0 @ id)))) ) | (~spl569_272 | spl569_1237)), 24.89/4.11 inference(superposition,[],[f37849,f5488])). 24.89/4.11 thf(f37878,plain,( 24.89/4.11 ( ! [X0 : (subst > term > term)] : (($true != $true) | ($true = ((sK560 @ id @ (sK565 @ X0) @ id)))) ) | (~spl569_272 | ~spl569_285 | spl569_1237)), 24.89/4.11 inference(superposition,[],[f37851,f8025])). 24.89/4.11 thf(f37889,plain,( 24.89/4.11 ( ! [X0 : (subst > term > term)] : (($true = ((sK560 @ id @ (sK565 @ X0) @ id)))) ) | (~spl569_272 | ~spl569_285 | spl569_1237)), 24.89/4.11 inference(trivial_inequality_removal,[],[f37878])). 24.89/4.11 thf(f37895,plain,( 24.89/4.11 $false | (~spl569_272 | ~spl569_285 | spl569_1237)), 24.89/4.11 inference(forward_subsumption_resolution,[],[f37889,f37851])). 24.89/4.11 thf(f37896,plain,( 24.89/4.11 ~spl569_272 | ~spl569_285 | spl569_1237), 24.89/4.11 inference(avatar_contradiction_clause,[],[f37895])). 24.89/4.11 thf(f37936,plain,( 24.89/4.11 ( ! [X0 : term] : (($true != ((sK546 @ id @ X0 @ id)))) ) | (~spl569_272 | spl569_1035)), 24.89/4.11 inference(superposition,[],[f22591,f5488])). 24.89/4.11 thf(f37964,plain,( 24.89/4.11 ( ! [X0 : term] : (($true = ((sK560 @ id @ X0 @ id)))) ) | (~spl569_272 | ~spl569_1237)), 24.89/4.11 inference(superposition,[],[f37848,f5488])). 24.89/4.11 thf(f37970,plain,( 24.89/4.11 spl569_919 | ~spl569_272 | ~spl569_1237), 24.89/4.11 inference(avatar_split_clause,[],[f37964,f37847,f2207,f8045])). 24.89/4.11 thf(f37997,plain,( 24.89/4.11 ( ! [X626 : (subst > term > term)] : (($true = ((sK546 @ id @ (lam @ (X626 @ sh @ one)) @ id))) | (((X626 @ (comp @ (sK550 @ X626) @ (sK549 @ X626)) @ (sub @ (sK548 @ X626) @ (sK549 @ X626)))) != ((sub @ (X626 @ (sK550 @ X626) @ (sK548 @ X626)) @ (sK549 @ X626))))) ) | (~spl569_272 | ~spl569_716 | spl569_1035)), 24.89/4.11 inference(forward_subsumption_resolution,[],[f4119,f37936])). 24.89/4.11 thf(f38044,plain,( 24.89/4.11 ( ! [X626 : (subst > term > term)] : ((((X626 @ (comp @ (sK550 @ X626) @ (sK549 @ X626)) @ (sub @ (sK548 @ X626) @ (sK549 @ X626)))) != ((sub @ (X626 @ (sK550 @ X626) @ (sK548 @ X626)) @ (sK549 @ X626))))) ) | (~spl569_272 | ~spl569_716 | spl569_1035)), 24.89/4.11 inference(forward_subsumption_resolution,[],[f37997,f37936])). 24.89/4.11 thf(f38070,plain,( 24.89/4.11 $false | (~spl569_272 | ~spl569_716 | spl569_1035)), 24.89/4.11 inference(forward_subsumption_resolution,[],[f38044,f5583])). 24.89/4.11 thf(f38071,plain,( 24.89/4.11 ~spl569_272 | ~spl569_716 | spl569_1035), 24.89/4.11 inference(avatar_contradiction_clause,[],[f38070])). 24.89/4.11 thf(f38301,plain,( 24.89/4.11 ( ! [X0 : term] : (($true = ((sK546 @ id @ X0 @ id)))) ) | (~spl569_272 | ~spl569_1035)), 24.89/4.11 inference(superposition,[],[f22592,f5488])). 24.89/4.11 thf(f38308,plain,( 24.89/4.11 spl569_998 | ~spl569_272 | ~spl569_1035), 24.89/4.11 inference(avatar_split_clause,[],[f38301,f22590,f2207,f21174])). 24.89/4.11 thf(f38404,plain,( 24.89/4.11 ($true != $true) | (spl569_806 | ~spl569_919)), 24.89/4.11 inference(superposition,[],[f4504,f8046])). 24.89/4.11 thf(f38424,plain,( 24.89/4.11 $false | (spl569_806 | ~spl569_919)), 24.89/4.11 inference(trivial_inequality_removal,[],[f38404])). 24.89/4.11 thf(f38425,plain,( 24.89/4.11 spl569_806 | ~spl569_919), 24.89/4.11 inference(avatar_contradiction_clause,[],[f38424])). 24.89/4.11 cnf(s215, plain, spl569_272, inference(sat_conversion,[],[f2210])). 24.89/4.11 cnf(s227, plain, ~spl569_6 | spl569_285, inference(sat_conversion,[],[f2262])). 24.89/4.11 cnf(s366, plain, spl569_426, inference(sat_conversion,[],[f2866])). 24.89/4.11 cnf(s677, plain, spl569_6 | spl569_716, inference(sat_conversion,[],[f4120])). 24.89/4.11 cnf(s717, plain, spl569_6 | ~spl569_756, inference(sat_conversion,[],[f4291])). 24.89/4.11 cnf(s769, plain, ~spl569_6 | ~spl569_806, inference(sat_conversion,[],[f4505])). 24.89/4.11 cnf(s1073, plain, ~spl569_426 | spl569_756 | ~spl569_998, inference(sat_conversion,[],[f21620])). 24.89/4.11 cnf(s1491, plain, ~spl569_272 | ~spl569_285 | spl569_1237, inference(sat_conversion,[],[f37896])). 24.89/4.11 cnf(s1496, plain, ~spl569_272 | spl569_919 | ~spl569_1237, inference(sat_conversion,[],[f37970])). 24.89/4.11 cnf(s1503, plain, ~spl569_272 | ~spl569_716 | spl569_1035, inference(sat_conversion,[],[f38071])). 24.89/4.11 cnf(s1516, plain, ~spl569_272 | spl569_998 | ~spl569_1035, inference(sat_conversion,[],[f38308])). 24.89/4.11 cnf(s1521, plain, spl569_806 | ~spl569_919, inference(sat_conversion,[],[f38425])). 24.89/4.11 cnf(s1658, plain, spl569_6, inference(rat,[],[s1516,s1503,s1073,s677,s717,s215,s366])). 24.89/4.11 cnf(s1660, plain, ~spl569_806, inference(rat,[],[s769,s1658])). 24.89/4.11 cnf(s1669, plain, spl569_285, inference(rat,[],[s227,s1658])). 24.89/4.11 cnf(s1673, plain, ~spl569_919, inference(rat,[],[s1521,s1660])). 24.89/4.11 cnf(s1674, plain, spl569_1237, inference(rat,[],[s1491,s215,s1669])). 24.89/4.11 cnf(s1675, plain, $false, inference(rat,[],[s1496,s215,s1674,s1673])). 24.89/4.11 thf(f38566,plain,( 24.89/4.11 $false), 24.89/4.11 inference(avatar_sat_refutation,[],[s1675])). 24.89/4.11 % SZS output end Proof for theBenchmark 24.89/4.11 % (940601)------------------------------ 24.89/4.11 % (940601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 24.89/4.11 % (940601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 24.89/4.11 % (940601)CaDiCaL version: 2.1.3 24.89/4.11 % (940601)Termination reason: Refutation 24.89/4.11 % (940601)Time elapsed: 2.014 s 24.89/4.11 % (940601)Peak memory usage: 38 MB 24.89/4.11 % (940601)Instructions burned: 4912 (million) 24.89/4.11 % (940431)Success in time 3.566 s 24.89/4.11 % Vampire exiting 24.89/4.12 EOF