0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.18/0.44 % Computer : n022.cluster.edu 0.18/0.44 % Model : x86_64 x86_64 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.44 % Memory : 8046.5625MB 0.18/0.44 % OS : Linux 6.8.0-71-generic 0.18/0.44 % CPULimit : 1440 0.18/0.44 % WCLimit : 180 0.18/0.44 % DateTime : Mon Jul 27 13:24:29 UTC 2026 0.18/0.44 % CPUTime : 0.18/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.25/0.51 Running higher-order theorem proving 0.25/0.57 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 0.33/0.79 % (959179)Detected a higher-order problem, will run a greedy HOL sequence. 0.33/0.79 % (959190)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 0.33/0.79 % (959190)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 0.33/0.79 % (959190)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=3331243812:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi) 0.33/0.79 % (959188)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2864043262:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi) 0.33/0.79 % (959184)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1323464812:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi) 0.33/0.79 % (959185)lrs+10_16_si=on:nwc=1.5:random_seed=2364940934:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi) 0.33/0.79 % (959186)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2615922671:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi) 0.33/0.79 % (959187)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=4139899178: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) 0.33/0.79 % (959189)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=942226485:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi) 0.33/0.79 % (959186)Instruction limit reached! 0.33/0.79 % (959186)------------------------------ 0.33/0.79 % (959186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.79 % (959186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.79 % (959186)CaDiCaL version: 2.1.3 0.33/0.79 % (959186)Termination reason: Instruction limit 0.33/0.79 % (959186)Termination phase: shuffling 0.33/0.79 % (959186)Time elapsed: 0.003 s 0.33/0.79 % (959186)Peak memory usage: 10 MB 0.33/0.79 % (959186)Instructions burned: 3 (million) 0.33/0.79 % (959185)Instruction limit reached! 0.33/0.79 % (959185)------------------------------ 0.33/0.79 % (959185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.79 % (959185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.79 % (959185)CaDiCaL version: 2.1.3 0.33/0.79 % (959185)Termination reason: Instruction limit 0.33/0.79 % (959185)Termination phase: shuffling 0.33/0.79 % (959185)Time elapsed: 0.016 s 0.33/0.79 % (959185)Peak memory usage: 10 MB 0.33/0.79 % (959185)Instructions burned: 19 (million) 0.33/0.79 % (959188)Instruction limit reached! 0.33/0.79 % (959188)------------------------------ 0.33/0.79 % (959188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.79 % (959188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.79 % (959188)CaDiCaL version: 2.1.3 0.33/0.79 % (959188)Termination reason: Instruction limit 0.33/0.79 % (959188)Termination phase: shuffling 0.33/0.79 % (959188)Time elapsed: 0.020 s 0.33/0.79 % (959188)Peak memory usage: 10 MB 0.33/0.79 % (959188)Instructions burned: 24 (million) 0.33/0.79 % (959198)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3217949613:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi) 0.33/0.79 % (959198)Instruction limit reached! 0.33/0.79 % (959198)------------------------------ 0.33/0.79 % (959198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.79 % (959198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.79 % (959198)CaDiCaL version: 2.1.3 0.33/0.79 % (959198)Termination reason: Instruction limit 0.33/0.79 % (959198)Termination phase: shuffling 0.33/0.79 % (959198)Time elapsed: 0.003 s 0.33/0.79 % (959198)Peak memory usage: 10 MB 0.33/0.79 % (959198)Instructions burned: 3 (million) 0.33/0.79 % (959200)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 0.33/0.79 % (959199)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2341311828:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi) 0.33/0.86 % (959200)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1523389423:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi) 0.33/0.86 % (959199)Instruction limit reached! 0.33/0.86 % (959199)------------------------------ 0.33/0.86 % (959199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.86 % (959199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.86 % (959199)CaDiCaL version: 2.1.3 0.33/0.86 % (959199)Termination reason: Instruction limit 0.33/0.86 % (959199)Termination phase: shuffling 0.33/0.86 % (959199)Time elapsed: 0.005 s 0.33/0.86 % (959199)Peak memory usage: 10 MB 0.33/0.86 % (959199)Instructions burned: 5 (million) 0.33/0.86 % (959190)Instruction limit reached! 0.33/0.86 % (959190)------------------------------ 0.33/0.86 % (959190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.86 % (959190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.86 % (959190)CaDiCaL version: 2.1.3 0.33/0.86 % (959190)Termination reason: Instruction limit 0.33/0.86 % (959190)Termination phase: Property scanning 0.33/0.86 % (959190)Time elapsed: 0.069 s 0.33/0.86 % (959190)Peak memory usage: 13 MB 0.33/0.86 % (959190)Instructions burned: 158 (million) 0.33/0.86 % (959200)Instruction limit reached! 0.33/0.86 % (959200)------------------------------ 0.33/0.86 % (959200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.86 % (959200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.86 % (959200)CaDiCaL version: 2.1.3 0.33/0.86 % (959200)Termination reason: Instruction limit 0.33/0.86 % (959200)Termination phase: shuffling 0.33/0.86 % (959200)Time elapsed: 0.008 s 0.33/0.86 % (959200)Peak memory usage: 10 MB 0.33/0.86 % (959200)Instructions burned: 8 (million) 0.33/0.86 % (959189)Instruction limit reached! 0.33/0.86 % (959189)------------------------------ 0.33/0.86 % (959189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.86 % (959189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.86 % (959189)CaDiCaL version: 2.1.3 0.33/0.86 % (959189)Termination reason: Instruction limit 0.33/0.86 % (959189)Termination phase: Preprocessing 3 0.33/0.86 % (959189)Time elapsed: 0.064 s 0.33/0.86 % (959189)Peak memory usage: 12 MB 0.33/0.86 % (959189)Instructions burned: 75 (million) 0.33/0.86 % (959202)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1995472672:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_1799 on theBenchmark for (1799ds/12Mi) 0.33/0.86 % (959184)Instruction limit reached! 0.33/0.86 % (959184)------------------------------ 0.33/0.86 % (959184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.86 % (959184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.86 % (959184)CaDiCaL version: 2.1.3 0.33/0.86 % (959184)Termination reason: Instruction limit 0.33/0.86 % (959184)Termination phase: Preprocessing 3 0.33/0.86 % (959184)Time elapsed: 0.077 s 0.33/0.86 % (959184)Peak memory usage: 12 MB 0.33/0.86 % (959184)Instructions burned: 87 (million) 0.33/0.86 % (959205)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 0.33/0.86 % (959205)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on 0.33/0.86 % (959202)Instruction limit reached! 0.33/0.86 % (959202)------------------------------ 0.33/0.86 % (959202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.86 % (959202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.86 % (959202)CaDiCaL version: 2.1.3 0.33/0.86 % (959202)Termination reason: Instruction limit 0.33/0.86 % (959202)Termination phase: shuffling 0.33/0.86 % (959202)Time elapsed: 0.012 s 0.33/0.86 % (959202)Peak memory usage: 10 MB 0.33/0.86 % (959202)Instructions burned: 13 (million) 0.33/0.86 % (959205)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4203477777:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_1798 on theBenchmark for (1798ds/28Mi) 0.33/0.93 % (959206)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=3176371541:i=86:piset=equals:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/86Mi) 0.33/0.93 % (959208)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on 0.33/0.93 % (959207)lrs+10_1_si=on:cs=on:random_seed=1838628923:i=8:rtra=on:ntd=on_1798 on theBenchmark for (1798ds/8Mi) 0.33/0.93 % (959208)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=2764705127:i=2:add=on:rtra=on_1798 on theBenchmark for (1798ds/2Mi) 0.33/0.93 % (959208)Instruction limit reached! 0.33/0.93 % (959208)------------------------------ 0.33/0.93 % (959208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.93 % (959208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.93 % (959208)CaDiCaL version: 2.1.3 0.33/0.93 % (959208)Termination reason: Instruction limit 0.33/0.93 % (959208)Termination phase: shuffling 0.33/0.93 % (959208)Time elapsed: 0.002 s 0.33/0.93 % (959208)Peak memory usage: 9 MB 0.33/0.93 % (959208)Instructions burned: 2 (million) 0.33/0.93 % (959207)Instruction limit reached! 0.33/0.93 % (959207)------------------------------ 0.33/0.93 % (959207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.93 % (959207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.93 % (959207)CaDiCaL version: 2.1.3 0.33/0.93 % (959207)Termination reason: Instruction limit 0.33/0.93 % (959207)Termination phase: shuffling 0.33/0.93 % (959207)Time elapsed: 0.007 s 0.33/0.93 % (959207)Peak memory usage: 9 MB 0.33/0.93 % (959207)Instructions burned: 8 (million) 0.33/0.93 % (959210)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2956764654:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/38Mi) 0.33/0.93 % (959205)Instruction limit reached! 0.33/0.93 % (959205)------------------------------ 0.33/0.93 % (959205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.93 % (959205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.93 % (959205)CaDiCaL version: 2.1.3 0.33/0.93 % (959205)Termination reason: Instruction limit 0.33/0.93 % (959205)Termination phase: shuffling 0.33/0.93 % (959205)Time elapsed: 0.024 s 0.33/0.93 % (959205)Peak memory usage: 10 MB 0.33/0.93 % (959205)Instructions burned: 28 (million) 0.33/0.93 % (959211)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4171459683:st=2:i=249:sd=1:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/249Mi) 0.33/0.93 % (959216)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1832105772:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1798 on theBenchmark for (1798ds/25Mi) 0.33/0.93 % (959217)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=52148066:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_1798 on theBenchmark for (1798ds/14Mi) 0.33/0.93 % (959210)Instruction limit reached! 0.33/0.93 % (959210)------------------------------ 0.33/0.93 % (959210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.93 % (959210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.93 % (959210)CaDiCaL version: 2.1.3 0.33/0.93 % (959210)Termination reason: Instruction limit 0.33/0.93 % (959210)Termination phase: Preprocessing 3 0.33/0.93 % (959210)Time elapsed: 0.032 s 0.33/0.93 % (959210)Peak memory usage: 11 MB 0.33/0.93 % (959210)Instructions burned: 38 (million) 0.33/0.93 % (959219)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=268481931:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_1798 on theBenchmark for (1798ds/327Mi) 0.33/0.93 % (959217)Instruction limit reached! 0.33/0.93 % (959217)------------------------------ 0.33/0.93 % (959217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/0.93 % (959217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/0.93 % (959217)CaDiCaL version: 2.1.3 0.33/0.93 % (959217)Termination reason: Instruction limit 0.33/0.93 % (959217)Termination phase: shuffling 0.33/0.93 % (959217)Time elapsed: 0.013 s 0.33/1.07 % (959217)Peak memory usage: 10 MB 0.33/1.07 % (959217)Instructions burned: 14 (million) 0.33/1.07 % (959216)Instruction limit reached! 0.33/1.07 % (959216)------------------------------ 0.33/1.07 % (959216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/1.07 % (959216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/1.07 % (959216)CaDiCaL version: 2.1.3 0.33/1.07 % (959216)Termination reason: Instruction limit 0.33/1.07 % (959216)Termination phase: Property scanning 0.33/1.07 % (959216)Time elapsed: 0.021 s 0.33/1.07 % (959216)Peak memory usage: 10 MB 0.33/1.07 % (959216)Instructions burned: 25 (million) 0.33/1.07 % (959206)Instruction limit reached! 0.33/1.07 % (959206)------------------------------ 0.33/1.07 % (959206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/1.07 % (959206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/1.07 % (959206)CaDiCaL version: 2.1.3 0.33/1.07 % (959206)Termination reason: Instruction limit 0.33/1.07 % (959206)Termination phase: Saturation 0.33/1.07 % (959206)Time elapsed: 0.070 s 0.33/1.07 % (959206)Peak memory usage: 12 MB 0.33/1.07 % (959206)Instructions burned: 86 (million) 0.33/1.07 % (959223)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3501976647:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_1798 on theBenchmark for (1798ds/14Mi) 0.33/1.07 % (959225)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1303038090:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_1797 on theBenchmark for (1797ds/2Mi) 0.33/1.07 % (959225)Instruction limit reached! 0.33/1.07 % (959225)------------------------------ 0.33/1.07 % (959225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/1.07 % (959225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/1.07 % (959225)CaDiCaL version: 2.1.3 0.33/1.07 % (959225)Termination reason: Instruction limit 0.33/1.07 % (959225)Termination phase: shuffling 0.33/1.07 % (959225)Time elapsed: 0.002 s 0.33/1.07 % (959225)Peak memory usage: 9 MB 0.33/1.07 % (959225)Instructions burned: 2 (million) 0.33/1.07 % (959223)Instruction limit reached! 0.33/1.07 % (959223)------------------------------ 0.33/1.07 % (959223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/1.07 % (959223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/1.07 % (959223)CaDiCaL version: 2.1.3 0.33/1.07 % (959223)Termination reason: Instruction limit 0.33/1.07 % (959223)Termination phase: shuffling 0.33/1.07 % (959223)Time elapsed: 0.011 s 0.33/1.07 % (959223)Peak memory usage: 10 MB 0.33/1.07 % (959223)Instructions burned: 14 (million) 0.33/1.07 % (959226)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=522032417:i=26:ep=R:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/26Mi) 0.33/1.07 % (959227)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=340325637:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_1797 on theBenchmark for (1797ds/23Mi) 0.33/1.07 % (959226)Instruction limit reached! 0.33/1.07 % (959226)------------------------------ 0.33/1.07 % (959226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/1.07 % (959226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/1.07 % (959226)CaDiCaL version: 2.1.3 0.33/1.07 % (959226)Termination reason: Instruction limit 0.33/1.07 % (959226)Termination phase: shuffling 0.33/1.07 % (959226)Time elapsed: 0.022 s 0.33/1.07 % (959226)Peak memory usage: 10 MB 0.33/1.07 % (959226)Instructions burned: 26 (million) 0.33/1.07 % (959231)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 0.33/1.07 % (959231)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs 0.33/1.07 % (959227)Instruction limit reached! 0.33/1.07 % (959227)------------------------------ 0.33/1.07 % (959227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 0.33/1.07 % (959227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.33/1.07 % (959227)CaDiCaL version: 2.1.3 0.33/1.07 % (959227)Termination reason: Instruction limit 0.33/1.07 % (959227)Termination phase: shuffling 3.52/1.16 % (959227)Time elapsed: 0.019 s 3.52/1.16 % (959227)Peak memory usage: 10 MB 3.52/1.16 % (959227)Instructions burned: 23 (million) 3.52/1.16 % (959230)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2351770542:cond=on:i=60:rtra=on:ntd=on_1797 on theBenchmark for (1797ds/60Mi) 3.52/1.16 % (959231)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=2591888399:i=14:add=off:nm=40:rtra=on:rawr=on_1797 on theBenchmark for (1797ds/14Mi) 3.52/1.16 % (959235)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=2187034384:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_1797 on theBenchmark for (1797ds/31Mi) 3.52/1.16 % (959231)Instruction limit reached! 3.52/1.16 % (959231)------------------------------ 3.52/1.16 % (959231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.52/1.16 % (959231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.52/1.17 % (959231)CaDiCaL version: 2.1.3 3.52/1.17 % (959231)Termination reason: Instruction limit 3.52/1.17 % (959231)Termination phase: shuffling 3.52/1.17 % (959231)Time elapsed: 0.013 s 3.52/1.17 % (959231)Peak memory usage: 10 MB 3.52/1.17 % (959231)Instructions burned: 14 (million) 3.52/1.17 % (959234)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off 3.52/1.17 % (959234)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=264890899:i=8:nm=2:rtra=on:fe=abstraction:inj=on_1797 on theBenchmark for (1797ds/8Mi) 3.52/1.17 % (959235)Instruction limit reached! 3.52/1.17 % (959235)------------------------------ 3.52/1.17 % (959235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.52/1.17 % (959235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.52/1.17 % (959235)CaDiCaL version: 2.1.3 3.52/1.17 % (959235)Termination reason: Instruction limit 3.52/1.17 % (959235)Termination phase: shuffling 3.52/1.17 % (959235)Time elapsed: 0.015 s 3.52/1.17 % (959235)Peak memory usage: 10 MB 3.52/1.17 % (959235)Instructions burned: 31 (million) 3.52/1.17 % (959234)Instruction limit reached! 3.52/1.17 % (959234)------------------------------ 3.52/1.17 % (959234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.52/1.17 % (959234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.52/1.17 % (959234)CaDiCaL version: 2.1.3 3.52/1.17 % (959234)Termination reason: Instruction limit 3.52/1.17 % (959234)Termination phase: shuffling 3.52/1.17 % (959234)Time elapsed: 0.008 s 3.52/1.17 % (959234)Peak memory usage: 9 MB 3.52/1.17 % (959234)Instructions burned: 8 (million) 3.52/1.17 % (959239)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2620950366:i=7:hud=5:bd=preordered:rtra=on:bet=on_1797 on theBenchmark for (1797ds/7Mi) 3.52/1.17 % (959230)Instruction limit reached! 3.52/1.17 % (959230)------------------------------ 3.52/1.17 % (959230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.52/1.17 % (959230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.52/1.17 % (959230)CaDiCaL version: 2.1.3 3.52/1.17 % (959230)Termination reason: Instruction limit 3.52/1.17 % (959230)Termination phase: Preprocessing 3 3.52/1.17 % (959230)Time elapsed: 0.052 s 3.52/1.17 % (959230)Peak memory usage: 11 MB 3.52/1.17 % (959230)Instructions burned: 61 (million) 3.52/1.17 % (959239)Instruction limit reached! 3.52/1.17 % (959239)------------------------------ 3.52/1.17 % (959239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 3.52/1.17 % (959239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 3.52/1.17 % (959239)CaDiCaL version: 2.1.3 3.52/1.17 % (959239)Termination reason: Instruction limit 3.52/1.17 % (959239)Termination phase: shuffling 3.52/1.17 % (959239)Time elapsed: 0.007 s 3.52/1.17 % (959239)Peak memory usage: 9 MB 3.52/1.17 % (959239)Instructions burned: 8 (million) 3.52/1.17 % (959241)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3870953786:i=23:rtra=on:ntd=on_1796 on theBenchmark for (1796ds/23Mi) 3.52/1.17 % (959242)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1159114036:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_1796 on theBenchmark for (1796ds/20Mi) 4.29/1.29 % (959241)Instruction limit reached! 4.29/1.29 % (959241)------------------------------ 4.29/1.29 % (959241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.29/1.29 % (959241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.29/1.29 % (959241)CaDiCaL version: 2.1.3 4.29/1.29 % (959241)Termination reason: Instruction limit 4.29/1.29 % (959241)Termination phase: shuffling 4.29/1.29 % (959241)Time elapsed: 0.019 s 4.29/1.29 % (959241)Peak memory usage: 10 MB 4.29/1.29 % (959241)Instructions burned: 23 (million) 4.29/1.29 % (959244)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4267933330:i=1240:rtra=on:ixr=off_1796 on theBenchmark for (1796ds/1240Mi) 4.29/1.29 % (959242)Instruction limit reached! 4.29/1.29 % (959242)------------------------------ 4.29/1.29 % (959242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.29/1.29 % (959242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.29/1.29 % (959242)CaDiCaL version: 2.1.3 4.29/1.29 % (959242)Termination reason: Instruction limit 4.29/1.29 % (959242)Termination phase: shuffling 4.29/1.29 % (959242)Time elapsed: 0.018 s 4.29/1.29 % (959242)Peak memory usage: 10 MB 4.29/1.29 % (959242)Instructions burned: 20 (million) 4.29/1.29 % (959245)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3676906731:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_1796 on theBenchmark for (1796ds/143Mi) 4.29/1.29 % (959211)Instruction limit reached! 4.29/1.29 % (959211)------------------------------ 4.29/1.29 % (959211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.29/1.29 % (959211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.29/1.29 % (959211)CaDiCaL version: 2.1.3 4.29/1.29 % (959211)Termination reason: Instruction limit 4.29/1.29 % (959211)Termination phase: Saturation 4.29/1.29 % (959211)Time elapsed: 0.213 s 4.29/1.29 % (959211)Peak memory usage: 15 MB 4.29/1.29 % (959211)Instructions burned: 249 (million) 4.29/1.29 % (959248)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2373562071:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_1796 on theBenchmark for (1796ds/193Mi) 4.29/1.29 % (959250)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3226708599:i=42:hud=10:rtra=on_1796 on theBenchmark for (1796ds/42Mi) 4.29/1.29 % (959252)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on 4.29/1.29 % (959252)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3392367100:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1796 on theBenchmark for (1796ds/7Mi) 4.29/1.29 % (959252)Instruction limit reached! 4.29/1.29 % (959252)------------------------------ 4.29/1.29 % (959252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.29/1.29 % (959252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.29/1.29 % (959252)CaDiCaL version: 2.1.3 4.29/1.29 % (959252)Termination reason: Instruction limit 4.29/1.29 % (959252)Termination phase: shuffling 4.29/1.29 % (959252)Time elapsed: 0.007 s 4.29/1.29 % (959252)Peak memory usage: 10 MB 4.29/1.29 % (959252)Instructions burned: 8 (million) 4.29/1.29 % (959250)Instruction limit reached! 4.29/1.29 % (959250)------------------------------ 4.29/1.29 % (959250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 4.29/1.29 % (959250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 4.29/1.29 % (959250)CaDiCaL version: 2.1.3 4.29/1.29 % (959250)Termination reason: Instruction limit 4.29/1.29 % (959250)Termination phase: Preprocessing 1 4.29/1.29 % (959250)Time elapsed: 0.036 s 4.29/1.29 % (959250)Peak memory usage: 11 MB 4.29/1.29 % (959250)Instructions burned: 42 (million) 4.29/1.29 % (959256)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1557670250:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_1795 on theBenchmark for (1795ds/181Mi) 4.29/1.29 % (959257)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=1536763234:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1795 on theBenchmark for (1795ds/169Mi) 4.29/1.29 % (959245)Instruction limit reached! 5.08/1.43 % (959245)------------------------------ 5.08/1.43 % (959245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.08/1.43 % (959245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.08/1.43 % (959245)CaDiCaL version: 2.1.3 5.08/1.43 % (959245)Termination reason: Instruction limit 5.08/1.43 % (959245)Termination phase: Function definition elimination 5.08/1.43 % (959245)Time elapsed: 0.120 s 5.08/1.43 % (959245)Peak memory usage: 12 MB 5.08/1.43 % (959245)Instructions burned: 144 (million) 5.08/1.43 % (959219)Instruction limit reached! 5.08/1.43 % (959219)------------------------------ 5.08/1.43 % (959219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.08/1.43 % (959219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.08/1.43 % (959219)CaDiCaL version: 2.1.3 5.08/1.43 % (959219)Termination reason: Instruction limit 5.08/1.43 % (959219)Termination phase: Saturation 5.08/1.43 % (959219)Time elapsed: 0.282 s 5.08/1.43 % (959219)Peak memory usage: 16 MB 5.08/1.43 % (959219)Instructions burned: 328 (million) 5.08/1.43 % (959260)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on 5.08/1.43 % (959261)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=991038858:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1795 on theBenchmark for (1795ds/22Mi) 5.08/1.43 % (959260)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2514136384:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_1795 on theBenchmark for (1795ds/6Mi) 5.08/1.43 % (959260)Instruction limit reached! 5.08/1.43 % (959260)------------------------------ 5.08/1.43 % (959260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.08/1.43 % (959260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.08/1.43 % (959260)CaDiCaL version: 2.1.3 5.08/1.43 % (959260)Termination reason: Instruction limit 5.08/1.43 % (959260)Termination phase: shuffling 5.08/1.43 % (959260)Time elapsed: 0.007 s 5.08/1.43 % (959260)Peak memory usage: 9 MB 5.08/1.43 % (959260)Instructions burned: 7 (million) 5.08/1.43 % (959261)Instruction limit reached! 5.08/1.43 % (959261)------------------------------ 5.08/1.43 % (959261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.08/1.43 % (959261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.08/1.43 % (959261)CaDiCaL version: 2.1.3 5.08/1.43 % (959261)Termination reason: Instruction limit 5.08/1.43 % (959261)Termination phase: shuffling 5.08/1.43 % (959261)Time elapsed: 0.019 s 5.08/1.43 % (959261)Peak memory usage: 10 MB 5.08/1.43 % (959261)Instructions burned: 22 (million) 5.08/1.43 % (959248)Instruction limit reached! 5.08/1.43 % (959248)------------------------------ 5.08/1.43 % (959248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.08/1.43 % (959248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.08/1.43 % (959248)CaDiCaL version: 2.1.3 5.08/1.43 % (959248)Termination reason: Instruction limit 5.08/1.43 % (959248)Termination phase: Property scanning 5.08/1.43 % (959248)Time elapsed: 0.156 s 5.08/1.43 % (959248)Peak memory usage: 13 MB 5.08/1.43 % (959248)Instructions burned: 195 (million) 5.08/1.43 % (959264)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2419637723:i=19:add=on:rtra=on_1794 on theBenchmark for (1794ds/19Mi) 5.08/1.43 % (959265)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=556850046:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_1794 on theBenchmark for (1794ds/316Mi) 5.08/1.43 % (959264)Instruction limit reached! 5.08/1.43 % (959264)------------------------------ 5.08/1.43 % (959264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.08/1.43 % (959264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.08/1.43 % (959264)CaDiCaL version: 2.1.3 5.08/1.43 % (959264)Termination reason: Instruction limit 5.08/1.43 % (959264)Termination phase: shuffling 5.08/1.43 % (959264)Time elapsed: 0.017 s 5.08/1.43 % (959264)Peak memory usage: 10 MB 5.08/1.43 % (959264)Instructions burned: 19 (million) 5.08/1.43 % (959266)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=1525372351:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_1794 on theBenchmark for (1794ds/853Mi) 5.96/1.55 % (959257)Instruction limit reached! 5.96/1.55 % (959257)------------------------------ 5.96/1.55 % (959257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.96/1.55 % (959257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.96/1.55 % (959257)CaDiCaL version: 2.1.3 5.96/1.55 % (959257)Termination reason: Instruction limit 5.96/1.55 % (959257)Termination phase: Property scanning 5.96/1.55 % (959257)Time elapsed: 0.142 s 5.96/1.55 % (959257)Peak memory usage: 13 MB 5.96/1.55 % (959257)Instructions burned: 170 (million) 5.96/1.55 % (959269)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=1007328920:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_1794 on theBenchmark for (1794ds/45Mi) 5.96/1.55 % (959256)Instruction limit reached! 5.96/1.55 % (959256)------------------------------ 5.96/1.55 % (959256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.96/1.55 % (959256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.96/1.55 % (959256)CaDiCaL version: 2.1.3 5.96/1.55 % (959256)Termination reason: Instruction limit 5.96/1.55 % (959256)Termination phase: Saturation 5.96/1.55 % (959256)Time elapsed: 0.155 s 5.96/1.55 % (959256)Peak memory usage: 13 MB 5.96/1.55 % (959256)Instructions burned: 181 (million) 5.96/1.55 % (959187)Instruction limit reached! 5.96/1.55 % (959187)------------------------------ 5.96/1.55 % (959187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.96/1.55 % (959187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.96/1.55 % (959187)CaDiCaL version: 2.1.3 5.96/1.55 % (959187)Termination reason: Instruction limit 5.96/1.55 % (959187)Termination phase: Saturation 5.96/1.55 % (959187)Time elapsed: 0.570 s 5.96/1.55 % (959187)Peak memory usage: 18 MB 5.96/1.55 % (959187)Instructions burned: 634 (million) 5.96/1.55 % (959271)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=286802349:i=480:rtra=on_1793 on theBenchmark for (1793ds/480Mi) 5.96/1.55 % (959273)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3647539915:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_1793 on theBenchmark for (1793ds/21Mi) 5.96/1.55 % (959269)Instruction limit reached! 5.96/1.55 % (959269)------------------------------ 5.96/1.55 % (959269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.96/1.55 % (959269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.96/1.55 % (959269)CaDiCaL version: 2.1.3 5.96/1.55 % (959269)Termination reason: Instruction limit 5.96/1.55 % (959269)Termination phase: SInE selection 5.96/1.55 % (959269)Time elapsed: 0.039 s 5.96/1.55 % (959269)Peak memory usage: 10 MB 5.96/1.55 % (959269)Instructions burned: 45 (million) 5.96/1.55 % (959274)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on 5.96/1.55 % (959274)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=4289348973:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_1793 on theBenchmark for (1793ds/200Mi) 5.96/1.55 % (959273)Instruction limit reached! 5.96/1.55 % (959273)------------------------------ 5.96/1.55 % (959273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.96/1.55 % (959273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 5.96/1.55 % (959273)CaDiCaL version: 2.1.3 5.96/1.55 % (959273)Termination reason: Instruction limit 5.96/1.55 % (959273)Termination phase: shuffling 5.96/1.55 % (959273)Time elapsed: 0.020 s 5.96/1.55 % (959273)Peak memory usage: 10 MB 5.96/1.55 % (959273)Instructions burned: 22 (million) 5.96/1.55 % (959277)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3838503578:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_1793 on theBenchmark for (1793ds/13Mi) 5.96/1.55 % (959277)Instruction limit reached! 5.96/1.55 % (959277)------------------------------ 5.96/1.55 % (959277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 5.96/1.55 % (959277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.89/1.80 % (959277)CaDiCaL version: 2.1.3 6.89/1.80 % (959277)Termination reason: Instruction limit 6.89/1.80 % (959277)Termination phase: shuffling 6.89/1.80 % (959277)Time elapsed: 0.012 s 6.89/1.80 % (959277)Peak memory usage: 10 MB 6.89/1.80 % (959277)Instructions burned: 14 (million) 6.89/1.80 % (959279)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=1583285982:i=66:s2at=3:nm=2:rtra=on:rawr=on_1793 on theBenchmark for (1793ds/66Mi) 6.89/1.80 % (959265)Instruction limit reached! 6.89/1.80 % (959265)------------------------------ 6.89/1.80 % (959265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.89/1.80 % (959265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.89/1.80 % (959265)CaDiCaL version: 2.1.3 6.89/1.80 % (959265)Termination reason: Instruction limit 6.89/1.80 % (959265)Termination phase: Saturation 6.89/1.80 % (959265)Time elapsed: 0.161 s 6.89/1.80 % (959265)Peak memory usage: 15 MB 6.89/1.80 % (959265)Instructions burned: 317 (million) 6.89/1.80 % (959281)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1358521936:i=51:fsr=off:rtra=on_1792 on theBenchmark for (1792ds/51Mi) 6.89/1.80 % (959283)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=4284537103:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1792 on theBenchmark for (1792ds/31Mi) 6.89/1.80 % (959283)Instruction limit reached! 6.89/1.80 % (959283)------------------------------ 6.89/1.80 % (959283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.89/1.80 % (959283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.89/1.80 % (959283)CaDiCaL version: 2.1.3 6.89/1.80 % (959283)Termination reason: Instruction limit 6.89/1.80 % (959283)Termination phase: Property scanning 6.89/1.80 % (959283)Time elapsed: 0.014 s 6.89/1.80 % (959283)Peak memory usage: 10 MB 6.89/1.80 % (959283)Instructions burned: 33 (million) 6.89/1.80 % (959279)Instruction limit reached! 6.89/1.80 % (959279)------------------------------ 6.89/1.80 % (959279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.89/1.80 % (959279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.89/1.80 % (959279)CaDiCaL version: 2.1.3 6.89/1.80 % (959279)Termination reason: Instruction limit 6.89/1.80 % (959279)Termination phase: SInE selection 6.89/1.80 % (959279)Time elapsed: 0.062 s 6.89/1.80 % (959279)Peak memory usage: 11 MB 6.89/1.80 % (959279)Instructions burned: 66 (million) 6.89/1.80 % (959281)Instruction limit reached! 6.89/1.80 % (959281)------------------------------ 6.89/1.80 % (959281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.89/1.80 % (959281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.89/1.80 % (959281)CaDiCaL version: 2.1.3 6.89/1.80 % (959281)Termination reason: Instruction limit 6.89/1.80 % (959281)Termination phase: Preprocessing 3 6.89/1.80 % (959281)Time elapsed: 0.045 s 6.89/1.80 % (959281)Peak memory usage: 11 MB 6.89/1.80 % (959281)Instructions burned: 51 (million) 6.89/1.80 % (959286)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2978619947:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_1792 on theBenchmark for (1792ds/137Mi) 6.89/1.80 % (959287)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=131701479:cond=on:i=34:hud=10:nm=10:rtra=on_1792 on theBenchmark for (1792ds/34Mi) 6.89/1.80 % (959288)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=592728784:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_1792 on theBenchmark for (1792ds/67Mi) 6.89/1.80 % (959274)Instruction limit reached! 6.89/1.80 % (959274)------------------------------ 6.89/1.80 % (959274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 6.89/1.80 % (959274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 6.89/1.80 % (959274)CaDiCaL version: 2.1.3 6.89/1.80 % (959274)Termination reason: Instruction limit 6.89/1.80 % (959274)Termination phase: Saturation 6.89/1.80 % (959274)Time elapsed: 0.167 s 6.89/1.80 % (959274)Peak memory usage: 14 MB 6.89/1.80 % (959274)Instructions burned: 200 (million) 6.89/1.80 % (959287)Instruction limit reached! 6.89/1.80 % (959287)------------------------------ 8.55/2.03 % (959287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.55/2.03 % (959287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.55/2.03 % (959287)CaDiCaL version: 2.1.3 8.55/2.03 % (959287)Termination reason: Instruction limit 8.55/2.03 % (959287)Termination phase: Property scanning 8.55/2.03 % (959287)Time elapsed: 0.032 s 8.55/2.03 % (959287)Peak memory usage: 10 MB 8.55/2.03 % (959287)Instructions burned: 34 (million) 8.55/2.03 % (959286)Instruction limit reached! 8.55/2.03 % (959286)------------------------------ 8.55/2.03 % (959286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.55/2.03 % (959286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.55/2.03 % (959286)CaDiCaL version: 2.1.3 8.55/2.03 % (959286)Termination reason: Instruction limit 8.55/2.03 % (959286)Termination phase: Twee Goal Transformation 8.55/2.03 % (959286)Time elapsed: 0.061 s 8.55/2.03 % (959286)Peak memory usage: 13 MB 8.55/2.03 % (959286)Instructions burned: 138 (million) 8.55/2.03 % (959292)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off 8.55/2.03 % (959292)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3235178416:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_1791 on theBenchmark for (1791ds/180Mi) 8.55/2.03 % (959294)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=46320643:cond=on:i=96:bd=all:rtra=on_1791 on theBenchmark for (1791ds/96Mi) 8.55/2.03 % (959288)Instruction limit reached! 8.55/2.03 % (959288)------------------------------ 8.55/2.03 % (959288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.55/2.03 % (959288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.55/2.03 % (959288)CaDiCaL version: 2.1.3 8.55/2.03 % (959288)Termination reason: Instruction limit 8.55/2.03 % (959288)Termination phase: Preprocessing 3 8.55/2.03 % (959288)Time elapsed: 0.058 s 8.55/2.03 % (959288)Peak memory usage: 12 MB 8.55/2.03 % (959288)Instructions burned: 67 (million) 8.55/2.03 % (959293)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=193100499:st=2:i=246:sd=3:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/246Mi) 8.55/2.03 % (959271)Refutation not found, incomplete strategy 8.55/2.03 % (959271)------------------------------ 8.55/2.03 % (959271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.55/2.03 % (959271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.55/2.03 % (959271)CaDiCaL version: 2.1.3 8.55/2.03 % (959271)Termination reason: Refutation not found, incomplete strategy 8.55/2.03 % (959271)Time elapsed: 0.242 s 8.55/2.03 % (959271)Peak memory usage: 16 MB 8.55/2.03 % (959271)Instructions burned: 275 (million) 8.55/2.03 % (959271)------------------------------ 8.55/2.03 % (959271)------------------------------ 8.55/2.03 % (959297)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3982920231:i=427:sd=1:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/427Mi) 8.55/2.03 % (959294)Instruction limit reached! 8.55/2.03 % (959294)------------------------------ 8.55/2.03 % (959294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.55/2.03 % (959294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.55/2.03 % (959294)CaDiCaL version: 2.1.3 8.55/2.03 % (959294)Termination reason: Instruction limit 8.55/2.03 % (959294)Termination phase: Property scanning 8.55/2.03 % (959294)Time elapsed: 0.043 s 8.55/2.03 % (959294)Peak memory usage: 13 MB 8.55/2.03 % (959294)Instructions burned: 98 (million) 8.55/2.03 % (959299)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1950222261:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_1791 on theBenchmark for (1791ds/874Mi) 8.55/2.03 % (959301)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2800519391:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_1790 on theBenchmark for (1790ds/515Mi) 8.55/2.03 % (959297)Refutation not found, incomplete strategy 8.55/2.03 % (959297)------------------------------ 8.55/2.03 % (959297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 8.55/2.03 % (959297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 8.55/2.03 % (959297)CaDiCaL version: 2.1.3 8.55/2.03 % (959297)Termination reason: Refutation not found, incomplete strategy 8.55/2.03 % (959297)Time elapsed: 0.053 s 11.16/2.20 % (959297)Peak memory usage: 13 MB 11.16/2.20 % (959297)Instructions burned: 57 (million) 11.16/2.20 % (959297)------------------------------ 11.16/2.20 % (959297)------------------------------ 11.16/2.20 % (959304)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2622654108:st=1.5:i=130:rtra=on:ss=axioms_1790 on theBenchmark for (1790ds/130Mi) 11.16/2.20 % (959292)Instruction limit reached! 11.16/2.20 % (959292)------------------------------ 11.16/2.20 % (959292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.16/2.20 % (959292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.16/2.20 % (959292)CaDiCaL version: 2.1.3 11.16/2.20 % (959292)Termination reason: Instruction limit 11.16/2.20 % (959292)Termination phase: Saturation 11.16/2.20 % (959292)Time elapsed: 0.143 s 11.16/2.20 % (959292)Peak memory usage: 12 MB 11.16/2.20 % (959292)Instructions burned: 180 (million) 11.16/2.20 % (959306)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1421226556:i=44:ep=R:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/44Mi) 11.16/2.20 % (959306)Instruction limit reached! 11.16/2.20 % (959306)------------------------------ 11.16/2.20 % (959306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.16/2.20 % (959306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.16/2.20 % (959306)CaDiCaL version: 2.1.3 11.16/2.20 % (959306)Termination reason: Instruction limit 11.16/2.20 % (959306)Termination phase: Property scanning 11.16/2.20 % (959306)Time elapsed: 0.035 s 11.16/2.20 % (959306)Peak memory usage: 10 MB 11.16/2.20 % (959306)Instructions burned: 44 (million) 11.16/2.20 % (959304)Refutation not found, incomplete strategy 11.16/2.20 % (959304)------------------------------ 11.16/2.20 % (959304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.16/2.20 % (959304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.16/2.20 % (959304)CaDiCaL version: 2.1.3 11.16/2.20 % (959304)Termination reason: Refutation not found, incomplete strategy 11.16/2.20 % (959304)Time elapsed: 0.082 s 11.16/2.20 % (959304)Peak memory usage: 13 MB 11.16/2.20 % (959304)Instructions burned: 93 (million) 11.16/2.20 % (959304)------------------------------ 11.16/2.20 % (959304)------------------------------ 11.16/2.20 % (959293)Instruction limit reached! 11.16/2.20 % (959293)------------------------------ 11.16/2.20 % (959293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.16/2.20 % (959293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.16/2.20 % (959293)CaDiCaL version: 2.1.3 11.16/2.20 % (959293)Termination reason: Instruction limit 11.16/2.20 % (959293)Termination phase: Saturation 11.16/2.20 % (959293)Time elapsed: 0.216 s 11.16/2.20 % (959293)Peak memory usage: 15 MB 11.16/2.20 % (959293)Instructions burned: 246 (million) 11.16/2.20 % (959308)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=949649778:s2a=on:i=571:nm=16:rtra=on_1789 on theBenchmark for (1789ds/571Mi) 11.16/2.20 % (959309)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2097295687:i=450:rtra=on:ixr=off:ntd=on_1789 on theBenchmark for (1789ds/450Mi) 11.16/2.20 % (959310)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=647906855:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_1789 on theBenchmark for (1789ds/95Mi) 11.16/2.20 % (959301)Instruction limit reached! 11.16/2.20 % (959301)------------------------------ 11.16/2.20 % (959301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.16/2.20 % (959301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.16/2.20 % (959301)CaDiCaL version: 2.1.3 11.16/2.20 % (959301)Termination reason: Instruction limit 11.16/2.20 % (959301)Termination phase: Saturation 11.16/2.20 % (959301)Time elapsed: 0.244 s 11.16/2.20 % (959301)Peak memory usage: 18 MB 11.16/2.20 % (959301)Instructions burned: 515 (million) 11.16/2.20 % (959314)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=2276395866:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_1788 on theBenchmark for (1788ds/65Mi) 11.16/2.20 % (959310)Instruction limit reached! 11.16/2.20 % (959310)------------------------------ 11.16/2.20 % (959310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.68/2.38 % (959310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.68/2.38 % (959310)CaDiCaL version: 2.1.3 11.68/2.38 % (959310)Termination reason: Instruction limit 11.68/2.38 % (959310)Termination phase: Property scanning 11.68/2.38 % (959310)Time elapsed: 0.082 s 11.68/2.38 % (959310)Peak memory usage: 12 MB 11.68/2.38 % (959310)Instructions burned: 96 (million) 11.68/2.38 % (959314)Instruction limit reached! 11.68/2.38 % (959314)------------------------------ 11.68/2.38 % (959314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.68/2.38 % (959314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.68/2.38 % (959314)CaDiCaL version: 2.1.3 11.68/2.38 % (959314)Termination reason: Instruction limit 11.68/2.38 % (959314)Termination phase: Property scanning 11.68/2.38 % (959314)Time elapsed: 0.028 s 11.68/2.38 % (959314)Peak memory usage: 11 MB 11.68/2.38 % (959314)Instructions burned: 65 (million) 11.68/2.38 % (959316)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=2050029237: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_1787 on theBenchmark for (1787ds/105Mi) 11.68/2.38 % (959317)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=2141019767:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_1787 on theBenchmark for (1787ds/5755Mi) 11.68/2.38 % (959244)Instruction limit reached! 11.68/2.38 % (959244)------------------------------ 11.68/2.38 % (959244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.68/2.38 % (959244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.68/2.38 % (959244)CaDiCaL version: 2.1.3 11.68/2.38 % (959244)Termination reason: Instruction limit 11.68/2.38 % (959244)Termination phase: Saturation 11.68/2.38 % (959244)Time elapsed: 0.969 s 11.68/2.38 % (959244)Peak memory usage: 14 MB 11.68/2.38 % (959244)Instructions burned: 1241 (million) 11.68/2.38 % (959316)Instruction limit reached! 11.68/2.38 % (959316)------------------------------ 11.68/2.38 % (959316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.68/2.38 % (959316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.68/2.38 % (959316)CaDiCaL version: 2.1.3 11.68/2.38 % (959316)Termination reason: Instruction limit 11.68/2.38 % (959316)Termination phase: Saturation 11.68/2.38 % (959316)Time elapsed: 0.083 s 11.68/2.38 % (959316)Peak memory usage: 12 MB 11.68/2.38 % (959316)Instructions burned: 105 (million) 11.68/2.38 % (959266)Instruction limit reached! 11.68/2.38 % (959266)------------------------------ 11.68/2.38 % (959266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.68/2.38 % (959266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.68/2.38 % (959266)CaDiCaL version: 2.1.3 11.68/2.38 % (959266)Termination reason: Instruction limit 11.68/2.38 % (959266)Termination phase: Saturation 11.68/2.38 % (959266)Time elapsed: 0.758 s 11.68/2.38 % (959266)Peak memory usage: 19 MB 11.68/2.38 % (959266)Instructions burned: 853 (million) 11.68/2.38 % (959320)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=1681783292:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_1786 on theBenchmark for (1786ds/375Mi) 11.68/2.38 % (959321)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1905747348:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1786 on theBenchmark for (1786ds/495Mi) 11.68/2.38 % (959322)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=1212474627:cond=on:i=34:hud=10:nm=10:rtra=on_1786 on theBenchmark for (1786ds/34Mi) 11.68/2.38 % (959322)Instruction limit reached! 11.68/2.38 % (959322)------------------------------ 11.68/2.38 % (959322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 11.68/2.38 % (959322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 11.68/2.38 % (959322)CaDiCaL version: 2.1.3 11.68/2.38 % (959322)Termination reason: Instruction limit 11.68/2.38 % (959322)Termination phase: Property scanning 11.68/2.38 % (959322)Time elapsed: 0.032 s 11.68/2.38 % (959322)Peak memory usage: 10 MB 11.68/2.38 % (959322)Instructions burned: 34 (million) 11.68/2.38 % (959326)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=4011133112:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_1785 on theBenchmark for (1785ds/91Mi) 13.40/2.65 % (959308)Refutation not found, incomplete strategy 13.40/2.65 % (959308)------------------------------ 13.40/2.65 % (959308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.40/2.65 % (959308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.40/2.65 % (959308)CaDiCaL version: 2.1.3 13.40/2.65 % (959308)Termination reason: Refutation not found, incomplete strategy 13.40/2.65 % (959308)Time elapsed: 0.345 s 13.40/2.65 % (959308)Peak memory usage: 17 MB 13.40/2.65 % (959308)Instructions burned: 385 (million) 13.40/2.65 % (959308)------------------------------ 13.40/2.65 % (959308)------------------------------ 13.40/2.65 % (959328)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=70716028:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_1785 on theBenchmark for (1785ds/66Mi) 13.40/2.65 % (959309)Instruction limit reached! 13.40/2.65 % (959309)------------------------------ 13.40/2.65 % (959309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.40/2.65 % (959309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.40/2.65 % (959309)CaDiCaL version: 2.1.3 13.40/2.65 % (959309)Termination reason: Instruction limit 13.40/2.65 % (959309)Termination phase: Saturation 13.40/2.65 % (959309)Time elapsed: 0.395 s 13.40/2.65 % (959309)Peak memory usage: 17 MB 13.40/2.65 % (959309)Instructions burned: 454 (million) 13.40/2.65 % (959326)Instruction limit reached! 13.40/2.65 % (959326)------------------------------ 13.40/2.65 % (959326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.40/2.65 % (959326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.40/2.65 % (959326)CaDiCaL version: 2.1.3 13.40/2.65 % (959326)Termination reason: Instruction limit 13.40/2.65 % (959326)Termination phase: Property scanning 13.40/2.65 % (959326)Time elapsed: 0.084 s 13.40/2.65 % (959326)Peak memory usage: 13 MB 13.40/2.65 % (959326)Instructions burned: 91 (million) 13.40/2.65 % (959328)Refutation not found, incomplete strategy 13.40/2.65 % (959328)------------------------------ 13.40/2.65 % (959328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.40/2.65 % (959328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.40/2.65 % (959328)CaDiCaL version: 2.1.3 13.40/2.65 % (959328)Termination reason: Refutation not found, incomplete strategy 13.40/2.65 % (959328)Time elapsed: 0.055 s 13.40/2.65 % (959328)Peak memory usage: 13 MB 13.40/2.65 % (959328)Instructions burned: 62 (million) 13.40/2.65 % (959328)------------------------------ 13.40/2.65 % (959328)------------------------------ 13.40/2.65 % (959330)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3721250039:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_1784 on theBenchmark for (1784ds/22Mi) 13.40/2.65 % (959331)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=2837388411:i=338:bd=all:ins=4:rtra=on_1784 on theBenchmark for (1784ds/338Mi) 13.40/2.65 % (959330)Instruction limit reached! 13.40/2.65 % (959330)------------------------------ 13.40/2.65 % (959330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 13.40/2.65 % (959330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 13.40/2.65 % (959330)CaDiCaL version: 2.1.3 13.40/2.65 % (959330)Termination reason: Instruction limit 13.40/2.65 % (959330)Termination phase: shuffling 13.40/2.65 % (959330)Time elapsed: 0.018 s 13.40/2.65 % (959330)Peak memory usage: 10 MB 13.40/2.65 % (959330)Instructions burned: 23 (million) 13.40/2.65 % (959333)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1832651870:i=28:sd=1:rtra=on:ss=axioms:sgt=64_1784 on theBenchmark for (1784ds/28Mi) 13.40/2.65 % (959335)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on 13.40/2.65 % (959335)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=494153681:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_1784 on theBenchmark for (1784ds/137Mi) 13.40/2.65 % (959333)Instruction limit reached! 13.40/2.65 % (959333)------------------------------ 13.40/2.65 % (959333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.22/2.94 % (959333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.22/2.94 % (959333)CaDiCaL version: 2.1.3 15.22/2.94 % (959333)Termination reason: Instruction limit 15.22/2.94 % (959333)Termination phase: Property scanning 15.22/2.94 % (959333)Time elapsed: 0.025 s 15.22/2.94 % (959333)Peak memory usage: 10 MB 15.22/2.94 % (959333)Instructions burned: 29 (million) 15.22/2.94 % (959299)Instruction limit reached! 15.22/2.94 % (959299)------------------------------ 15.22/2.94 % (959299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.22/2.94 % (959299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.22/2.94 % (959299)CaDiCaL version: 2.1.3 15.22/2.94 % (959299)Termination reason: Instruction limit 15.22/2.94 % (959299)Termination phase: Saturation 15.22/2.94 % (959299)Time elapsed: 0.708 s 15.22/2.94 % (959299)Peak memory usage: 17 MB 15.22/2.94 % (959299)Instructions burned: 875 (million) 15.22/2.94 % (959338)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=2048839121:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_1783 on theBenchmark for (1783ds/340Mi) 15.22/2.94 % (959339)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=1614159959:i=227:sd=1:bd=all:rtra=on:ss=axioms_1783 on theBenchmark for (1783ds/227Mi) 15.22/2.94 % (959320)Instruction limit reached! 15.22/2.94 % (959320)------------------------------ 15.22/2.94 % (959320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.22/2.94 % (959320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.22/2.94 % (959320)CaDiCaL version: 2.1.3 15.22/2.94 % (959320)Termination reason: Instruction limit 15.22/2.94 % (959320)Termination phase: Saturation 15.22/2.94 % (959320)Time elapsed: 0.331 s 15.22/2.94 % (959320)Peak memory usage: 16 MB 15.22/2.94 % (959320)Instructions burned: 376 (million) 15.22/2.94 % (959339)Refutation not found, incomplete strategy 15.22/2.94 % (959339)------------------------------ 15.22/2.94 % (959339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.22/2.94 % (959339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.22/2.94 % (959339)CaDiCaL version: 2.1.3 15.22/2.94 % (959339)Termination reason: Refutation not found, incomplete strategy 15.22/2.94 % (959339)Time elapsed: 0.045 s 15.22/2.94 % (959339)Peak memory usage: 13 MB 15.22/2.94 % (959339)Instructions burned: 47 (million) 15.22/2.94 % (959339)------------------------------ 15.22/2.94 % (959339)------------------------------ 15.22/2.94 % (959335)Instruction limit reached! 15.22/2.94 % (959335)------------------------------ 15.22/2.94 % (959335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.22/2.94 % (959335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.22/2.94 % (959335)CaDiCaL version: 2.1.3 15.22/2.94 % (959335)Termination reason: Instruction limit 15.22/2.94 % (959335)Termination phase: Saturation 15.22/2.94 % (959335)Time elapsed: 0.112 s 15.22/2.94 % (959335)Peak memory usage: 12 MB 15.22/2.94 % (959335)Instructions burned: 138 (million) 15.22/2.94 % (959342)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on 15.22/2.94 % (959342)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2351504696:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_1783 on theBenchmark for (1783ds/373Mi) 15.22/2.94 % (959343)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=4283276140:i=116:ep=RSTC:rtra=on:ntd=on_1782 on theBenchmark for (1782ds/116Mi) 15.22/2.94 % (959344)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=662524533:i=575:rtra=on_1782 on theBenchmark for (1782ds/575Mi) 15.22/2.94 % (959321)Instruction limit reached! 15.22/2.94 % (959321)------------------------------ 15.22/2.94 % (959321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 15.22/2.94 % (959321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 15.22/2.94 % (959321)CaDiCaL version: 2.1.3 15.22/2.94 % (959321)Termination reason: Instruction limit 15.22/2.94 % (959321)Termination phase: Saturation 15.22/2.94 % (959321)Time elapsed: 0.432 s 15.22/2.94 % (959321)Peak memory usage: 16 MB 15.22/2.94 % (959321)Instructions burned: 496 (million) 18.42/3.23 % (959348)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1746262603:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_1781 on theBenchmark for (1781ds/270Mi) 18.42/3.23 % (959343)Instruction limit reached! 18.42/3.23 % (959343)------------------------------ 18.42/3.23 % (959343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.42/3.23 % (959343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.42/3.23 % (959343)CaDiCaL version: 2.1.3 18.42/3.23 % (959343)Termination reason: Instruction limit 18.42/3.23 % (959343)Termination phase: Property scanning 18.42/3.23 % (959343)Time elapsed: 0.100 s 18.42/3.23 % (959343)Peak memory usage: 13 MB 18.42/3.23 % (959343)Instructions burned: 116 (million) 18.42/3.23 % (959331)Instruction limit reached! 18.42/3.23 % (959331)------------------------------ 18.42/3.23 % (959331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.42/3.23 % (959331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.42/3.23 % (959331)CaDiCaL version: 2.1.3 18.42/3.23 % (959331)Termination reason: Instruction limit 18.42/3.23 % (959331)Termination phase: Saturation 18.42/3.23 % (959331)Time elapsed: 0.284 s 18.42/3.23 % (959331)Peak memory usage: 19 MB 18.42/3.23 % (959331)Instructions burned: 338 (million) 18.42/3.23 % (959350)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=1205365103: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_1781 on theBenchmark for (1781ds/9840Mi) 18.42/3.23 % (959351)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=4054395470:i=421:rtra=on:ss=axioms_1781 on theBenchmark for (1781ds/421Mi) 18.42/3.23 % (959338)Instruction limit reached! 18.42/3.23 % (959338)------------------------------ 18.42/3.23 % (959338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.42/3.23 % (959338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.42/3.23 % (959338)CaDiCaL version: 2.1.3 18.42/3.23 % (959338)Termination reason: Instruction limit 18.42/3.23 % (959338)Termination phase: Saturation 18.42/3.23 % (959338)Time elapsed: 0.268 s 18.42/3.23 % (959338)Peak memory usage: 17 MB 18.42/3.23 % (959338)Instructions burned: 340 (million) 18.42/3.23 % (959354)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on 18.42/3.23 % (959354)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=1292303820:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_1780 on theBenchmark for (1780ds/270Mi) 18.42/3.23 % (959342)Instruction limit reached! 18.42/3.23 % (959342)------------------------------ 18.42/3.23 % (959342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.42/3.23 % (959342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.42/3.23 % (959342)CaDiCaL version: 2.1.3 18.42/3.23 % (959342)Termination reason: Instruction limit 18.42/3.23 % (959342)Termination phase: Saturation 18.42/3.23 % (959342)Time elapsed: 0.267 s 18.42/3.23 % (959342)Peak memory usage: 15 MB 18.42/3.23 % (959342)Instructions burned: 373 (million) 18.42/3.23 % (959356)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=372685905:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_1779 on theBenchmark for (1779ds/31Mi) 18.42/3.23 % (959348)Instruction limit reached! 18.42/3.23 % (959348)------------------------------ 18.42/3.23 % (959348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 18.42/3.23 % (959348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 18.42/3.23 % (959348)CaDiCaL version: 2.1.3 18.42/3.23 % (959348)Termination reason: Instruction limit 18.42/3.23 % (959348)Termination phase: Saturation 18.42/3.23 % (959348)Time elapsed: 0.210 s 18.42/3.23 % (959348)Peak memory usage: 12 MB 18.42/3.23 % (959348)Instructions burned: 270 (million) 18.42/3.23 % (959356)Instruction limit reached! 18.42/3.23 % (959356)------------------------------ 18.42/3.23 % (959356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.83/3.63 % (959356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.83/3.63 % (959356)CaDiCaL version: 2.1.3 20.83/3.63 % (959356)Termination reason: Instruction limit 20.83/3.63 % (959356)Termination phase: Property scanning 20.83/3.63 % (959356)Time elapsed: 0.027 s 20.83/3.63 % (959356)Peak memory usage: 10 MB 20.83/3.63 % (959356)Instructions burned: 31 (million) 20.83/3.63 % (959358)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on 20.83/3.63 % (959358)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 20.83/3.63 % (959358)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=1905731354:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_1779 on theBenchmark for (1779ds/1440Mi) 20.83/3.63 % (959359)dis+10_2_sil=128000:si=on:random_seed=1375229901:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_1779 on theBenchmark for (1779ds/339Mi) 20.83/3.63 % (959351)Instruction limit reached! 20.83/3.63 % (959351)------------------------------ 20.83/3.63 % (959351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.83/3.63 % (959351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.83/3.63 % (959351)CaDiCaL version: 2.1.3 20.83/3.63 % (959351)Termination reason: Instruction limit 20.83/3.63 % (959351)Termination phase: Saturation 20.83/3.63 % (959351)Time elapsed: 0.326 s 20.83/3.63 % (959351)Peak memory usage: 15 MB 20.83/3.63 % (959351)Instructions burned: 422 (million) 20.83/3.63 % (959354)Instruction limit reached! 20.83/3.63 % (959354)------------------------------ 20.83/3.63 % (959354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.83/3.63 % (959354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.83/3.63 % (959354)CaDiCaL version: 2.1.3 20.83/3.63 % (959354)Termination reason: Instruction limit 20.83/3.63 % (959354)Termination phase: Saturation 20.83/3.63 % (959354)Time elapsed: 0.252 s 20.83/3.63 % (959354)Peak memory usage: 15 MB 20.83/3.63 % (959354)Instructions burned: 270 (million) 20.83/3.63 % (959362)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2654152095:i=111:add=on:fgj=on:rtra=on:fdi=1024_1777 on theBenchmark for (1777ds/111Mi) 20.83/3.63 % (959363)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=3072231709:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_1777 on theBenchmark for (1777ds/122Mi) 20.83/3.63 % (959344)Instruction limit reached! 20.83/3.63 % (959344)------------------------------ 20.83/3.63 % (959344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.83/3.63 % (959344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.83/3.63 % (959344)CaDiCaL version: 2.1.3 20.83/3.63 % (959344)Termination reason: Instruction limit 20.83/3.63 % (959344)Termination phase: Saturation 20.83/3.63 % (959344)Time elapsed: 0.504 s 20.83/3.63 % (959344)Peak memory usage: 18 MB 20.83/3.63 % (959344)Instructions burned: 575 (million) 20.83/3.63 % (959366)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=1340261010:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_1777 on theBenchmark for (1777ds/136Mi) 20.83/3.63 % (959362)Instruction limit reached! 20.83/3.63 % (959362)------------------------------ 20.83/3.63 % (959362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.83/3.63 % (959362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.83/3.63 % (959362)CaDiCaL version: 2.1.3 20.83/3.63 % (959362)Termination reason: Instruction limit 20.83/3.63 % (959362)Termination phase: Property scanning 20.83/3.63 % (959362)Time elapsed: 0.095 s 20.83/3.63 % (959362)Peak memory usage: 13 MB 20.83/3.63 % (959362)Instructions burned: 111 (million) 20.83/3.63 % (959363)Instruction limit reached! 20.83/3.63 % (959363)------------------------------ 20.83/3.63 % (959363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 20.83/3.63 % (959363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 20.83/3.63 % (959363)CaDiCaL version: 2.1.3 20.83/3.63 % (959363)Termination reason: Instruction limit 22.16/3.96 % (959363)Termination phase: Property scanning 22.16/3.96 % (959363)Time elapsed: 0.104 s 22.16/3.96 % (959363)Peak memory usage: 13 MB 22.16/3.96 % (959363)Instructions burned: 123 (million) 22.16/3.96 % (959368)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1422256297:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_1776 on theBenchmark for (1776ds/232Mi) 22.16/3.96 % (959359)Instruction limit reached! 22.16/3.96 % (959359)------------------------------ 22.16/3.96 % (959359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.16/3.96 % (959359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.16/3.96 % (959359)CaDiCaL version: 2.1.3 22.16/3.96 % (959359)Termination reason: Instruction limit 22.16/3.96 % (959359)Termination phase: Saturation 22.16/3.96 % (959359)Time elapsed: 0.288 s 22.16/3.96 % (959359)Peak memory usage: 14 MB 22.16/3.96 % (959359)Instructions burned: 339 (million) 22.16/3.96 % (959369)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=683822722:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_1776 on theBenchmark for (1776ds/1254Mi) 22.16/3.96 % (959366)Instruction limit reached! 22.16/3.96 % (959366)------------------------------ 22.16/3.96 % (959366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.16/3.96 % (959366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.16/3.96 % (959366)CaDiCaL version: 2.1.3 22.16/3.96 % (959366)Termination reason: Instruction limit 22.16/3.96 % (959366)Termination phase: Property scanning 22.16/3.96 % (959366)Time elapsed: 0.118 s 22.16/3.96 % (959366)Peak memory usage: 16 MB 22.16/3.96 % (959366)Instructions burned: 136 (million) 22.16/3.96 % (959371)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs 22.16/3.96 % (959371)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=2727702679:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_1776 on theBenchmark for (1776ds/281Mi) 22.16/3.96 % (959373)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=4036274123:i=619:add=on:rtra=on_1775 on theBenchmark for (1775ds/619Mi) 22.16/3.96 % (959369)Refutation not found, incomplete strategy 22.16/3.96 % (959369)------------------------------ 22.16/3.96 % (959369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.16/3.96 % (959369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.16/3.96 % (959369)CaDiCaL version: 2.1.3 22.16/3.96 % (959369)Termination reason: Refutation not found, incomplete strategy 22.16/3.96 % (959369)Time elapsed: 0.178 s 22.16/3.96 % (959369)Peak memory usage: 15 MB 22.16/3.96 % (959369)Instructions burned: 218 (million) 22.16/3.96 % (959369)------------------------------ 22.16/3.96 % (959369)------------------------------ 22.16/3.96 % (959368)Instruction limit reached! 22.16/3.96 % (959368)------------------------------ 22.16/3.96 % (959368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.16/3.96 % (959368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.16/3.96 % (959368)CaDiCaL version: 2.1.3 22.16/3.96 % (959368)Termination reason: Instruction limit 22.16/3.96 % (959368)Termination phase: Saturation 22.16/3.96 % (959368)Time elapsed: 0.196 s 22.16/3.96 % (959368)Peak memory usage: 15 MB 22.16/3.96 % (959368)Instructions burned: 232 (million) 22.16/3.96 % (959376)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=2249918569:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_1774 on theBenchmark for (1774ds/865Mi) 22.16/3.96 % (959377)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1724381516:i=212:sd=1:rtra=on:ss=axioms:sgt=64_1774 on theBenchmark for (1774ds/212Mi) 22.16/3.96 % (959371)Instruction limit reached! 22.16/3.96 % (959371)------------------------------ 22.16/3.96 % (959371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 22.16/3.96 % (959371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 22.16/3.96 % (959371)CaDiCaL version: 2.1.3 22.16/3.96 % (959371)Termination reason: Instruction limit 22.16/3.96 % (959371)Termination phase: Saturation 22.16/3.96 % (959371)Time elapsed: 0.221 s 22.16/3.96 % (959371)Peak memory usage: 12 MB 27.00/4.43 % (959371)Instructions burned: 282 (million) 27.00/4.43 % (959380)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3057136674:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_1773 on theBenchmark for (1773ds/130Mi) 27.00/4.43 % (959380)Instruction limit reached! 27.00/4.43 % (959380)------------------------------ 27.00/4.43 % (959380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959380)CaDiCaL version: 2.1.3 27.00/4.43 % (959380)Termination reason: Instruction limit 27.00/4.43 % (959380)Termination phase: Property scanning 27.00/4.43 % (959380)Time elapsed: 0.110 s 27.00/4.43 % (959380)Peak memory usage: 13 MB 27.00/4.43 % (959380)Instructions burned: 130 (million) 27.00/4.43 % (959377)Instruction limit reached! 27.00/4.43 % (959377)------------------------------ 27.00/4.43 % (959377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959377)CaDiCaL version: 2.1.3 27.00/4.43 % (959377)Termination reason: Instruction limit 27.00/4.43 % (959377)Termination phase: Saturation 27.00/4.43 % (959377)Time elapsed: 0.181 s 27.00/4.43 % (959377)Peak memory usage: 14 MB 27.00/4.43 % (959377)Instructions burned: 213 (million) 27.00/4.43 % (959382)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1890585799:st=1.5:i=346:rtra=on:ss=axioms_1772 on theBenchmark for (1772ds/346Mi) 27.00/4.43 % (959383)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=193110815:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_1771 on theBenchmark for (1771ds/152Mi) 27.00/4.43 % (959382)Refutation not found, incomplete strategy 27.00/4.43 % (959382)------------------------------ 27.00/4.43 % (959382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959382)CaDiCaL version: 2.1.3 27.00/4.43 % (959382)Termination reason: Refutation not found, incomplete strategy 27.00/4.43 % (959382)Time elapsed: 0.102 s 27.00/4.43 % (959382)Peak memory usage: 13 MB 27.00/4.43 % (959382)Instructions burned: 120 (million) 27.00/4.43 % (959382)------------------------------ 27.00/4.43 % (959382)------------------------------ 27.00/4.43 % (959386)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3178579050:i=75:ep=R:rtra=on:ntd=on_1770 on theBenchmark for (1770ds/75Mi) 27.00/4.43 % (959373)Instruction limit reached! 27.00/4.43 % (959373)------------------------------ 27.00/4.43 % (959373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959373)CaDiCaL version: 2.1.3 27.00/4.43 % (959373)Termination reason: Instruction limit 27.00/4.43 % (959373)Termination phase: Saturation 27.00/4.43 % (959373)Time elapsed: 0.559 s 27.00/4.43 % (959373)Peak memory usage: 18 MB 27.00/4.43 % (959373)Instructions burned: 620 (million) 27.00/4.43 % (959383)Instruction limit reached! 27.00/4.43 % (959383)------------------------------ 27.00/4.43 % (959383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959383)CaDiCaL version: 2.1.3 27.00/4.43 % (959383)Termination reason: Instruction limit 27.00/4.43 % (959383)Termination phase: Inequality splitting 27.00/4.43 % (959383)Time elapsed: 0.140 s 27.00/4.43 % (959383)Peak memory usage: 13 MB 27.00/4.43 % (959383)Instructions burned: 152 (million) 27.00/4.43 % (959386)Instruction limit reached! 27.00/4.43 % (959386)------------------------------ 27.00/4.43 % (959386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959386)CaDiCaL version: 2.1.3 27.00/4.43 % (959386)Termination reason: Instruction limit 27.00/4.43 % (959386)Termination phase: Property scanning 27.00/4.43 % (959386)Time elapsed: 0.065 s 27.00/4.43 % (959386)Peak memory usage: 11 MB 27.00/4.43 % (959386)Instructions burned: 76 (million) 27.00/4.43 % (959388)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=108332872:st=2.5:i=387:sd=2:rtra=on:ss=axioms_1769 on theBenchmark for (1769ds/387Mi) 27.00/4.43 % (959389)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=922105117:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_1769 on theBenchmark for (1769ds/148Mi) 27.00/4.43 % (959390)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=1405406020:i=161:piset=and:rtra=on:ntd=on_1769 on theBenchmark for (1769ds/161Mi) 27.00/4.43 % (959389)Instruction limit reached! 27.00/4.43 % (959389)------------------------------ 27.00/4.43 % (959389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959389)CaDiCaL version: 2.1.3 27.00/4.43 % (959389)Termination reason: Instruction limit 27.00/4.43 % (959389)Termination phase: Saturation 27.00/4.43 % (959389)Time elapsed: 0.122 s 27.00/4.43 % (959389)Peak memory usage: 12 MB 27.00/4.43 % (959389)Instructions burned: 148 (million) 27.00/4.43 % (959394)lrs+10_1_sil=128000:si=on:random_seed=2155881927:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_1768 on theBenchmark for (1768ds/888Mi) 27.00/4.43 % (959390)Instruction limit reached! 27.00/4.43 % (959390)------------------------------ 27.00/4.43 % (959390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959390)CaDiCaL version: 2.1.3 27.00/4.43 % (959390)Termination reason: Instruction limit 27.00/4.43 % (959390)Termination phase: Property scanning 27.00/4.43 % (959390)Time elapsed: 0.138 s 27.00/4.43 % (959390)Peak memory usage: 13 MB 27.00/4.43 % (959390)Instructions burned: 161 (million) 27.00/4.43 % (959396)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=4027008263:i=136:add=on:ins=4:rtra=on:sup=off_1767 on theBenchmark for (1767ds/136Mi) 27.00/4.43 % (959358)Instruction limit reached! 27.00/4.43 % (959358)------------------------------ 27.00/4.43 % (959358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959358)CaDiCaL version: 2.1.3 27.00/4.43 % (959358)Termination reason: Instruction limit 27.00/4.43 % (959358)Termination phase: Saturation 27.00/4.43 % (959358)Time elapsed: 1.256 s 27.00/4.43 % (959358)Peak memory usage: 22 MB 27.00/4.43 % (959358)Instructions burned: 1440 (million) 27.00/4.43 % (959388)Instruction limit reached! 27.00/4.43 % (959388)------------------------------ 27.00/4.43 % (959388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959388)CaDiCaL version: 2.1.3 27.00/4.43 % (959388)Termination reason: Instruction limit 27.00/4.43 % (959388)Termination phase: Saturation 27.00/4.43 % (959388)Time elapsed: 0.298 s 27.00/4.43 % (959388)Peak memory usage: 12 MB 27.00/4.43 % (959388)Instructions burned: 388 (million) 27.00/4.43 % (959376)Instruction limit reached! 27.00/4.43 % (959376)------------------------------ 27.00/4.43 % (959376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959376)CaDiCaL version: 2.1.3 27.00/4.43 % (959376)Termination reason: Instruction limit 27.00/4.43 % (959376)Termination phase: Saturation 27.00/4.43 % (959376)Time elapsed: 0.740 s 27.00/4.43 % (959376)Peak memory usage: 18 MB 27.00/4.43 % (959376)Instructions burned: 866 (million) 27.00/4.43 % (959396)Instruction limit reached! 27.00/4.43 % (959396)------------------------------ 27.00/4.43 % (959396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959396)CaDiCaL version: 2.1.3 27.00/4.43 % (959396)Termination reason: Instruction limit 27.00/4.43 % (959396)Termination phase: Property scanning 27.00/4.43 % (959396)Time elapsed: 0.121 s 27.00/4.43 % (959396)Peak memory usage: 13 MB 27.00/4.43 % (959396)Instructions burned: 137 (million) 27.00/4.43 % (959398)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=997773397:i=88:s2at=3:nm=2:rtra=on:rawr=on_1766 on theBenchmark for (1766ds/88Mi) 27.00/4.43 % (959399)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1568010940:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_1766 on theBenchmark for (1766ds/93Mi) 27.00/4.43 % (959400)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2211760510:i=2186:rtra=on:ixr=off_1766 on theBenchmark for (1766ds/2186Mi) 27.00/4.43 % (959401)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3594093138:s2a=on:i=240:rtra=on:ntd=on_1766 on theBenchmark for (1766ds/240Mi) 27.00/4.43 % (959398)Instruction limit reached! 27.00/4.43 % (959398)------------------------------ 27.00/4.43 % (959398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959398)CaDiCaL version: 2.1.3 27.00/4.43 % (959398)Termination reason: Instruction limit 27.00/4.43 % (959398)Termination phase: Property scanning 27.00/4.43 % (959398)Time elapsed: 0.071 s 27.00/4.43 % (959398)Peak memory usage: 11 MB 27.00/4.43 % (959398)Instructions burned: 89 (million) 27.00/4.43 % (959399)Instruction limit reached! 27.00/4.43 % (959399)------------------------------ 27.00/4.43 % (959399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959399)CaDiCaL version: 2.1.3 27.00/4.43 % (959399)Termination reason: Instruction limit 27.00/4.43 % (959399)Termination phase: Saturation 27.00/4.43 % (959399)Time elapsed: 0.075 s 27.00/4.43 % (959399)Peak memory usage: 12 MB 27.00/4.43 % (959399)Instructions burned: 93 (million) 27.00/4.43 % (959407)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on 27.00/4.43 % (959406)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=3683834974:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_1765 on theBenchmark for (1765ds/805Mi) 27.00/4.43 % (959407)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=374688762:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_1765 on theBenchmark for (1765ds/391Mi) 27.00/4.43 % (959401)Instruction limit reached! 27.00/4.43 % (959401)------------------------------ 27.00/4.43 % (959401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959401)CaDiCaL version: 2.1.3 27.00/4.43 % (959401)Termination reason: Instruction limit 27.00/4.43 % (959401)Termination phase: Saturation 27.00/4.43 % (959401)Time elapsed: 0.201 s 27.00/4.43 % (959401)Peak memory usage: 14 MB 27.00/4.43 % (959401)Instructions burned: 240 (million) 27.00/4.43 % (959410)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=983332291:i=355:av=off:fsr=off:rtra=on:ixr=off_1763 on theBenchmark for (1763ds/355Mi) 27.00/4.43 % (959394) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-959179-959394"... 27.00/4.43 % (959407)Instruction limit reached! 27.00/4.43 % (959407)------------------------------ 27.00/4.43 % (959407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.43 % (959407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.43 % (959407)CaDiCaL version: 2.1.3 27.00/4.43 % (959407)Termination reason: Instruction limit 27.00/4.43 % (959407)Termination phase: Saturation 27.00/4.43 % (959407)Time elapsed: 0.301 s 27.00/4.43 % (959407)Peak memory usage: 13 MB 27.00/4.43 % (959407)Instructions burned: 391 (million) 27.00/4.43 % (959412)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=1158214053:lrd=on:i=314:sd=1:rtra=on:ss=axioms_1762 on theBenchmark for (1762ds/314Mi) 27.00/4.43 % (959394)...printing done. 27.00/4.43 % (959394)Refutation found. Thanks to Tanya! 27.00/4.43 % SZS status Theorem for theBenchmark 27.00/4.43 % SZS output start Proof for theBenchmark 27.00/4.43 thf(type_def_5, type, term: $tType). 27.00/4.43 thf(type_def_6, type, subst: $tType). 27.00/4.43 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType). 27.00/4.43 thf(type_def_8, type, d_term: $tType). 27.00/4.43 thf(type_def_9, type, d_subst: $tType). 27.00/4.43 thf(func_def_0, type, one: term). 27.00/4.43 thf(func_def_1, type, ap: (term > term > term)). 27.00/4.43 thf(func_def_2, type, lam: (term > term)). 27.00/4.43 thf(func_def_3, type, sub: (term > subst > term)). 27.00/4.43 thf(func_def_4, type, id: subst). 27.00/4.43 thf(func_def_5, type, sh: subst). 27.00/4.43 thf(func_def_6, type, push: (term > subst > subst)). 27.00/4.43 thf(func_def_7, type, comp: (subst > subst > subst)). 27.00/4.43 thf(func_def_8, type, var: (term > $o)). 27.00/4.43 thf(func_def_9, type, pushprop_lem1v2: $o). 27.00/4.43 thf(func_def_10, type, pushprop_lem1_gthm: $o). 27.00/4.43 thf(func_def_11, type, axmap: $o). 27.00/4.43 thf(func_def_12, type, pushprop_lem0_gthm: $o). 27.00/4.43 thf(func_def_13, type, shinj: $o). 27.00/4.43 thf(func_def_14, type, hoasinduction_lem1v2: $o). 27.00/4.43 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o). 27.00/4.43 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)). 27.00/4.43 thf(func_def_17, type, induction2lem: $o). 27.00/4.43 thf(func_def_18, type, hoasinduction_lem3v2_f: $o). 27.00/4.43 thf(func_def_19, type, axvarshift: $o). 27.00/4.43 thf(func_def_20, type, hoasapinj2: $o). 27.00/4.43 thf(func_def_21, type, hoasapnotvar_gthm: $o). 27.00/4.43 thf(func_def_22, type, hoasapinj1: $o). 27.00/4.43 thf(func_def_23, type, ulamvar1: $o). 27.00/4.43 thf(func_def_24, type, induction2lem_lthm: $o). 27.00/4.43 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o). 27.00/4.43 thf(func_def_26, type, apnotvar: $o). 27.00/4.43 thf(func_def_27, type, pushprop_lthm_orig: $o). 27.00/4.43 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o). 27.00/4.43 thf(func_def_29, type, hoasinduction_lthm: $o). 27.00/4.43 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o). 27.00/4.43 thf(func_def_31, type, hoaslaminj: $o). 27.00/4.43 thf(func_def_32, type, hoasinduction_lem3aaa: $o). 27.00/4.43 thf(func_def_33, type, induction2lem_gthm: $o). 27.00/4.43 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o). 27.00/4.43 thf(func_def_35, type, hoasinduction_lem3: $o). 27.00/4.43 thf(func_def_36, type, hoasinduction_lem2: $o). 27.00/4.43 thf(func_def_37, type, termmset_lthm: $o). 27.00/4.43 thf(func_def_38, type, hoasinduction_lem1: $o). 27.00/4.43 thf(func_def_39, type, hoaslamnotap_lthm: $o). 27.00/4.43 thf(func_def_40, type, pushprop_lem1v2_lthm: $o). 27.00/4.43 thf(func_def_41, type, hoasapnotvar: $o). 27.00/4.43 thf(func_def_42, type, hoasinduction_lem0: $o). 27.00/4.43 thf(func_def_43, type, hoasinduction: $o). 27.00/4.43 thf(func_def_44, type, hoasinduction_gthm: $o). 27.00/4.43 thf(func_def_45, type, axapp: $o). 27.00/4.43 thf(func_def_46, type, hoaslamnotvar_lthm: $o). 27.00/4.43 thf(func_def_47, type, pushprop_lem3v2_lthm: $o). 27.00/4.43 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o). 27.00/4.43 thf(func_def_49, type, ulamvarind: $o). 27.00/4.43 thf(func_def_50, type, induction: $o). 27.00/4.43 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o). 27.00/4.43 thf(func_def_52, type, termmset_gthm: $o). 27.00/4.43 thf(func_def_53, type, hoasinduction_lem3aa: $o). 27.00/4.43 thf(func_def_54, type, pushprop_lem1v2_gthm: $o). 27.00/4.43 thf(func_def_55, type, hoaslamnotap_gthm: $o). 27.00/4.43 thf(func_def_56, type, hoaslamnotvar_gthm: $o). 27.00/4.43 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o). 27.00/4.43 thf(func_def_58, type, pushprop_lem2v2: $o). 27.00/4.43 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o). 27.00/4.43 thf(func_def_60, type, axclos: $o). 27.00/4.43 thf(func_def_61, type, axassoc: $o). 27.00/4.43 thf(func_def_62, type, hoasinduction_lem2v2: $o). 27.00/4.43 thf(func_def_63, type, pushprop_lthm: $o). 27.00/4.43 thf(func_def_64, type, apinj2: $o). 27.00/4.43 thf(func_def_65, type, apinj1: $o). 27.00/4.43 thf(func_def_66, type, hoasapinj2_lthm: $o). 27.00/4.43 thf(func_def_67, type, hoasinduction_lem3v2a: $o). 27.00/4.43 thf(func_def_68, type, hoasapinj1_lthm: $o). 27.00/4.43 thf(func_def_69, type, hoaslaminj_lthm: $o). 27.00/4.43 thf(func_def_70, type, axvarcons: $o). 27.00/4.43 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)). 27.00/4.43 thf(func_def_72, type, axscons: $o). 27.00/4.43 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o). 27.00/4.43 thf(func_def_74, type, axidr: $o). 27.00/4.43 thf(func_def_75, type, pushprop_lem1: $o). 27.00/4.43 thf(func_def_76, type, laminj: $o). 27.00/4.43 thf(func_def_77, type, hoasinduction_lem3_lthm: $o). 27.00/4.43 thf(func_def_78, type, pushprop_lem0: $o). 27.00/4.43 thf(func_def_79, type, pushprop_gthm: $o). 27.00/4.43 thf(func_def_80, type, axabs: $o). 27.00/4.43 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o). 27.00/4.43 thf(func_def_82, type, hoasinduction_lem2_lthm: $o). 27.00/4.43 thf(func_def_83, type, hoasapinj2_gthm: $o). 27.00/4.43 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)). 27.00/4.43 thf(func_def_85, type, hoasinduction_lem1_lthm: $o). 27.00/4.43 thf(func_def_86, type, lamnotap: $o). 27.00/4.43 thf(func_def_87, type, hoasapinj1_gthm: $o). 27.00/4.43 thf(func_def_88, type, hoaslamnotvar: $o). 27.00/4.43 thf(func_def_89, type, axidl: $o). 27.00/4.43 thf(func_def_90, type, hoaslaminj_gthm: $o). 27.00/4.43 thf(func_def_91, type, induction2_lthm: $o). 27.00/4.43 thf(func_def_92, type, hoasinduction_lem0_lthm: $o). 27.00/4.43 thf(func_def_93, type, substmonoid_lthm: $o). 27.00/4.43 thf(func_def_94, type, pushprop: $o). 27.00/4.43 thf(func_def_95, type, hoasinduction_lem3_gthm: $o). 27.00/4.43 thf(func_def_96, type, hoasinduction_lem2_gthm: $o). 27.00/4.43 thf(func_def_97, type, hoasinduction_lem3b: $o). 27.00/4.43 thf(func_def_98, type, substmonoid: $o). 27.00/4.43 thf(func_def_99, type, lamnotvar: $o). 27.00/4.43 thf(func_def_100, type, hoasinduction_lem3a: $o). 27.00/4.43 thf(func_def_101, type, hoasinduction_lem1_gthm: $o). 27.00/4.43 thf(func_def_102, type, hoasinduction_no_psi_cond: $o). 27.00/4.43 thf(func_def_103, type, induction2_gthm: $o). 27.00/4.43 thf(func_def_104, type, pushprop_lem2v2_lthm: $o). 27.00/4.43 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_106, type, hoaslamnotap: $o). 27.00/4.43 thf(func_def_107, type, substmonoid_gthm: $o). 27.00/4.43 thf(func_def_108, type, ulamvarsh: $o). 27.00/4.43 thf(func_def_109, type, induction2: $o). 27.00/4.43 thf(func_def_110, type, pushprop_lem3v2: $o). 27.00/4.43 thf(func_def_111, type, pushprop_lem2v2_gthm: $o). 27.00/4.43 thf(func_def_112, type, pushprop_lem1_lthm: $o). 27.00/4.43 thf(func_def_113, type, hoasinduction_lem3v2: $o). 27.00/4.43 thf(func_def_114, type, axshiftcons: $o). 27.00/4.43 thf(func_def_115, type, termmset: $o). 27.00/4.43 thf(func_def_116, type, pushprop_lem0_lthm: $o). 27.00/4.43 thf(func_def_117, type, hoasapnotvar_lthm: $o). 27.00/4.43 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o). 27.00/4.43 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)). 27.00/4.43 thf(func_def_120, type, axvarid: $o). 27.00/4.43 thf(func_def_121, type, hoasinduction_lthm_3: $o). 27.00/4.43 thf(func_def_122, type, d2term: (d_term > term)). 27.00/4.43 thf(func_def_123, type, d2subst: (d_subst > subst)). 27.00/4.43 thf(func_def_124, type, d_one: d_term). 27.00/4.43 thf(func_def_125, type, d_id: d_subst). 27.00/4.43 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). 27.00/4.43 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)). 27.00/4.43 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)). 27.00/4.43 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)). 27.00/4.43 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)). 27.00/4.43 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)). 27.00/4.43 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))). 27.00/4.43 thf(func_def_136, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))). 27.00/4.43 thf(func_def_137, type, vIMP: ($o > $o > $o)). 27.00/4.43 thf(func_def_138, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))). 27.00/4.43 thf(func_def_139, type, vAND: ($o > $o > $o)). 27.00/4.43 thf(func_def_140, type, sP0: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_141, type, sP1: ((term > $o) > $o)). 27.00/4.43 thf(func_def_142, type, sP2: $o). 27.00/4.43 thf(func_def_143, type, sP3: $o). 27.00/4.43 thf(func_def_144, type, sP4: $o). 27.00/4.43 thf(func_def_145, type, sP5: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_146, type, sP6: $o). 27.00/4.43 thf(func_def_147, type, sP7: $o). 27.00/4.43 thf(func_def_148, type, sP8: $o). 27.00/4.43 thf(func_def_149, type, sP9: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_150, type, sP10: ((term > $o) > $o)). 27.00/4.43 thf(func_def_151, type, sP11: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_152, type, sP12: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_153, type, sP13: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_154, type, sP14: $o). 27.00/4.43 thf(func_def_155, type, sP15: $o). 27.00/4.43 thf(func_def_156, type, sP16: $o). 27.00/4.43 thf(func_def_157, type, sP17: $o). 27.00/4.43 thf(func_def_158, type, sP18: ((term > $o) > $o)). 27.00/4.43 thf(func_def_159, type, sP19: ((term > $o) > $o)). 27.00/4.43 thf(func_def_160, type, sP20: $o). 27.00/4.43 thf(func_def_161, type, sP21: $o). 27.00/4.43 thf(func_def_162, type, sP22: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_163, type, sP23: $o). 27.00/4.43 thf(func_def_164, type, sP24: ((term > $o) > $o)). 27.00/4.43 thf(func_def_165, type, sP25: $o). 27.00/4.43 thf(func_def_166, type, sP26: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_167, type, sP27: $o). 27.00/4.43 thf(func_def_168, type, sP28: $o). 27.00/4.43 thf(func_def_169, type, sP29: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_170, type, sP30: $o). 27.00/4.43 thf(func_def_171, type, sP31: ((term > $o) > $o)). 27.00/4.43 thf(func_def_172, type, sP32: $o). 27.00/4.43 thf(func_def_173, type, sP33: ((term > $o) > $o)). 27.00/4.43 thf(func_def_174, type, sP34: $o). 27.00/4.43 thf(func_def_175, type, sP35: ((term > $o) > $o)). 27.00/4.43 thf(func_def_176, type, sP36: ((term > $o) > $o)). 27.00/4.43 thf(func_def_177, type, sP37: $o). 27.00/4.43 thf(func_def_178, type, sP38: $o). 27.00/4.43 thf(func_def_179, type, sP39: $o). 27.00/4.43 thf(func_def_180, type, sP40: ((term > $o) > $o)). 27.00/4.43 thf(func_def_181, type, sP41: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_182, type, sP42: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_183, type, sP43: $o). 27.00/4.43 thf(func_def_184, type, sP44: $o). 27.00/4.43 thf(func_def_185, type, sP45: $o). 27.00/4.43 thf(func_def_186, type, sP46: $o). 27.00/4.43 thf(func_def_187, type, sP47: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_188, type, sP48: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_189, type, sP49: $o). 27.00/4.43 thf(func_def_190, type, sP50: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_191, type, sP51: $o). 27.00/4.43 thf(func_def_192, type, sP52: $o). 27.00/4.43 thf(func_def_193, type, sP53: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_194, type, sP54: $o). 27.00/4.43 thf(func_def_195, type, sP55: $o). 27.00/4.43 thf(func_def_196, type, sP56: ((subst > term > subst > $o) > $o)). 27.00/4.43 thf(func_def_197, type, sP57: $o). 27.00/4.43 thf(func_def_198, type, sP58: $o). 27.00/4.43 thf(func_def_199, type, sK59: term). 27.00/4.43 thf(func_def_200, type, sK60: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_201, type, sK61: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_202, type, sK62: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_203, type, sK63: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_204, type, sK64: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_205, type, sK65: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_206, type, sK66: ((subst > term > subst > $o) > term > term)). 27.00/4.43 thf(func_def_207, type, sK67: (term > $o)). 27.00/4.43 thf(func_def_208, type, sK68: term). 27.00/4.43 thf(func_def_209, type, sK69: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_210, type, sK70: term). 27.00/4.43 thf(func_def_211, type, sK71: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_212, type, sK72: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_213, type, sK73: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_214, type, sK74: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_215, type, sK75: ((subst > term > subst > $o) > (term > $o) > term)). 27.00/4.43 thf(func_def_216, type, sK76: (term > (term > $o) > term)). 27.00/4.43 thf(func_def_217, type, sK77: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_218, type, sK78: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_219, type, sK79: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_220, type, sK80: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_221, type, sK81: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_222, type, sK82: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_223, type, sK83: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_224, type, sK84: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_225, type, sK85: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_226, type, sK86: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_227, type, sK87: term). 27.00/4.43 thf(func_def_228, type, sK88: term). 27.00/4.43 thf(func_def_229, type, sK89: (term > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_230, type, sK90: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_231, type, sK91: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_232, type, sK92: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_233, type, sK93: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_234, type, sK94: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_235, type, sK95: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_236, type, sK96: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_237, type, sK97: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_238, type, sK98: ((subst > term > subst > $o) > term > term)). 27.00/4.43 thf(func_def_239, type, sK99: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_240, type, sK100: term). 27.00/4.43 thf(func_def_241, type, sK101: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_242, type, sK102: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_243, type, sK103: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_244, type, sK104: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_245, type, sK105: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_246, type, sK106: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_247, type, sK107: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_248, type, sK108: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_249, type, sK109: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_250, type, sK110: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_251, type, sK111: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_252, type, sK112: term). 27.00/4.43 thf(func_def_253, type, sK113: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_254, type, sK114: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_255, type, sK115: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_256, type, sK116: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_257, type, sK117: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_258, type, sK118: (term > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_259, type, sK119: term). 27.00/4.43 thf(func_def_260, type, sK120: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_261, type, sK121: (term > $o)). 27.00/4.43 thf(func_def_262, type, sK122: term). 27.00/4.43 thf(func_def_263, type, sK123: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_264, type, sK124: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_265, type, sK125: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_266, type, sK126: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_267, type, sK127: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_268, type, sK128: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_269, type, sK129: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_270, type, sK130: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_271, type, sK131: ((term > $o) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_272, type, sK132: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_273, type, sK133: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_274, type, sK134: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_275, type, sK135: term). 27.00/4.43 thf(func_def_276, type, sK136: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_277, type, sK137: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_278, type, sK138: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_279, type, sK139: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_280, type, sK140: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_281, type, sK141: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_282, type, sK142: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_283, type, sK143: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_284, type, sK144: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_285, type, sK145: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_286, type, sK146: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_287, type, sK147: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_288, type, sK148: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_289, type, sK149: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_290, type, sK150: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_291, type, sK151: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_292, type, sK152: (subst > term > term)). 27.00/4.43 thf(func_def_293, type, sK153: term). 27.00/4.43 thf(func_def_294, type, sK154: (subst > term > term)). 27.00/4.43 thf(func_def_295, type, sK155: subst). 27.00/4.43 thf(func_def_296, type, sK156: term). 27.00/4.43 thf(func_def_297, type, sK157: term). 27.00/4.43 thf(func_def_298, type, sK158: term). 27.00/4.43 thf(func_def_299, type, sK159: subst). 27.00/4.43 thf(func_def_300, type, sK160: subst). 27.00/4.43 thf(func_def_301, type, sK161: term). 27.00/4.43 thf(func_def_302, type, sK162: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_303, type, sK163: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_304, type, sK164: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_305, type, sK165: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_306, type, sK166: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_307, type, sK167: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_308, type, sK168: ((term > $o) > term)). 27.00/4.43 thf(func_def_309, type, sK169: ((term > $o) > term)). 27.00/4.43 thf(func_def_310, type, sK170: ((subst > term > subst > $o) > term > $o)). 27.00/4.43 thf(func_def_311, type, sK171: term). 27.00/4.43 thf(func_def_312, type, sK172: term). 27.00/4.43 thf(func_def_313, type, sK173: (term > $o)). 27.00/4.43 thf(func_def_314, type, sK174: (term > term)). 27.00/4.43 thf(func_def_315, type, sK175: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_316, type, sK176: ((term > $o) > term)). 27.00/4.43 thf(func_def_317, type, sK177: ((subst > term > subst > $o) > (term > $o) > term)). 27.00/4.43 thf(func_def_318, type, sK178: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_319, type, sK179: ((term > $o) > term > term)). 27.00/4.43 thf(func_def_320, type, sK180: term). 27.00/4.43 thf(func_def_321, type, sK181: (term > $o)). 27.00/4.43 thf(func_def_322, type, sK182: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_323, type, sK183: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_324, type, sK184: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_325, type, sK185: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_326, type, sK186: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_327, type, sK187: term). 27.00/4.43 thf(func_def_328, type, sK188: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_329, type, sK189: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_330, type, sK190: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_331, type, sK191: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_332, type, sK192: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_333, type, sK193: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_334, type, sK194: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_335, type, sK195: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_336, type, sK196: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_337, type, sK197: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_338, type, sK198: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_339, type, sK199: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_340, type, sK200: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_341, type, sK201: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_342, type, sK202: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_343, type, sK203: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_344, type, sK204: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_345, type, sK205: ((term > $o) > term)). 27.00/4.43 thf(func_def_346, type, sK206: ((term > $o) > term)). 27.00/4.43 thf(func_def_347, type, sK207: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_348, type, sK208: (term > $o)). 27.00/4.43 thf(func_def_349, type, sK209: term). 27.00/4.43 thf(func_def_350, type, sK210: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_351, type, sK211: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_352, type, sK212: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_353, type, sK213: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_354, type, sK214: (term > subst > term > term)). 27.00/4.43 thf(func_def_355, type, sK215: (term > (term > $o) > term)). 27.00/4.43 thf(func_def_356, type, sK216: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_357, type, sK217: ((term > $o) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_358, type, sK218: term). 27.00/4.43 thf(func_def_359, type, sK219: term). 27.00/4.43 thf(func_def_360, type, sK220: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_361, type, sK221: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_362, type, sK222: ((term > $o) > subst > term)). 27.00/4.43 thf(func_def_363, type, sK223: ((term > $o) > term)). 27.00/4.43 thf(func_def_364, type, sK224: term). 27.00/4.43 thf(func_def_365, type, sK225: subst). 27.00/4.43 thf(func_def_366, type, sK226: term). 27.00/4.43 thf(func_def_367, type, sK227: (term > $o)). 27.00/4.43 thf(func_def_368, type, sK228: (term > term)). 27.00/4.43 thf(func_def_369, type, sK229: (term > $o)). 27.00/4.43 thf(func_def_370, type, sK230: term). 27.00/4.43 thf(func_def_371, type, sK231: (term > term)). 27.00/4.43 thf(func_def_372, type, sK232: ((term > $o) > term)). 27.00/4.43 thf(func_def_373, type, sK233: ((term > $o) > term)). 27.00/4.43 thf(func_def_374, type, sK234: ((term > $o) > term)). 27.00/4.43 thf(func_def_375, type, sK235: ((term > $o) > term)). 27.00/4.43 thf(func_def_376, type, sK236: ((term > $o) > term)). 27.00/4.43 thf(func_def_377, type, sK237: ((term > $o) > term)). 27.00/4.43 thf(func_def_378, type, sK238: (term > $o)). 27.00/4.43 thf(func_def_379, type, sK239: term). 27.00/4.43 thf(func_def_380, type, sK240: (term > term)). 27.00/4.43 thf(func_def_381, type, sK241: ((term > $o) > term)). 27.00/4.43 thf(func_def_382, type, sK242: ((term > $o) > term)). 27.00/4.43 thf(func_def_383, type, sK243: ((term > $o) > term)). 27.00/4.43 thf(func_def_384, type, sK244: ((term > $o) > term)). 27.00/4.43 thf(func_def_385, type, sK245: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_386, type, sK246: (term > $o)). 27.00/4.43 thf(func_def_387, type, sK247: term). 27.00/4.43 thf(func_def_388, type, sK248: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_389, type, sK249: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_390, type, sK250: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_391, type, sK251: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_392, type, sK252: (term > (term > $o) > term)). 27.00/4.43 thf(func_def_393, type, sK253: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_394, type, sK254: ((term > $o) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_395, type, sK255: ((term > $o) > term)). 27.00/4.43 thf(func_def_396, type, sK256: ((term > $o) > term)). 27.00/4.43 thf(func_def_397, type, sK257: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_398, type, sK258: term). 27.00/4.43 thf(func_def_399, type, sK259: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_400, type, sK260: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_401, type, sK261: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_402, type, sK262: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_403, type, sK263: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_404, type, sK264: (term > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_405, type, sK265: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_406, type, sK266: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_407, type, sK267: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_408, type, sK268: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_409, type, sK269: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_410, type, sK270: term). 27.00/4.43 thf(func_def_411, type, sK271: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_412, type, sK272: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_413, type, sK273: ((subst > term > term) > term > term)). 27.00/4.43 thf(func_def_414, type, sK274: ((subst > term > term) > term > subst)). 27.00/4.43 thf(func_def_415, type, sK275: ((subst > term > term) > term > subst)). 27.00/4.43 thf(func_def_416, type, sK276: ((subst > term > term) > term > subst)). 27.00/4.43 thf(func_def_417, type, sK277: ((subst > term > term) > term > subst)). 27.00/4.43 thf(func_def_418, type, sK278: ((subst > term > term) > term > term)). 27.00/4.43 thf(func_def_419, type, sK279: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_420, type, sK280: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_421, type, sK281: ((subst > term > subst > $o) > term > term)). 27.00/4.43 thf(func_def_422, type, sK282: (term > $o)). 27.00/4.43 thf(func_def_423, type, sK283: term). 27.00/4.43 thf(func_def_424, type, sK284: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_425, type, sK285: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_426, type, sK286: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_427, type, sK287: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_428, type, sK288: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_429, type, sK289: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_430, type, sK290: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_431, type, sK291: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_432, type, sK292: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_433, type, sK293: ((subst > term > subst > $o) > (term > $o) > term)). 27.00/4.43 thf(func_def_434, type, sK294: (term > (term > $o) > term)). 27.00/4.43 thf(func_def_435, type, sK295: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_436, type, sK296: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_437, type, sK297: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_438, type, sK298: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_439, type, sK299: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_440, type, sK300: (term > $o)). 27.00/4.43 thf(func_def_441, type, sK301: subst). 27.00/4.43 thf(func_def_442, type, sK302: term). 27.00/4.43 thf(func_def_443, type, sK303: (term > term)). 27.00/4.43 thf(func_def_444, type, sK304: ((term > $o) > term)). 27.00/4.43 thf(func_def_445, type, sK305: (subst > (term > $o) > term)). 27.00/4.43 thf(func_def_446, type, sK306: ((term > $o) > term)). 27.00/4.43 thf(func_def_447, type, sK307: ((term > $o) > term)). 27.00/4.43 thf(func_def_448, type, sK308: term). 27.00/4.43 thf(func_def_449, type, sK309: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_450, type, sK310: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_451, type, sK311: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_452, type, sK312: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_453, type, sK313: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_454, type, sK314: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_455, type, sK315: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_456, type, sK316: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_457, type, sK317: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_458, type, sK318: ((subst > term > subst > $o) > term > term)). 27.00/4.43 thf(func_def_459, type, sK319: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_460, type, sK320: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_461, type, sK321: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_462, type, sK322: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_463, type, sK323: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_464, type, sK324: ((term > $o) > term)). 27.00/4.43 thf(func_def_465, type, sK325: ((term > $o) > term)). 27.00/4.43 thf(func_def_466, type, sK326: subst). 27.00/4.43 thf(func_def_467, type, sK327: term). 27.00/4.43 thf(func_def_468, type, sK328: term). 27.00/4.43 thf(func_def_469, type, sK329: subst). 27.00/4.43 thf(func_def_470, type, sK330: (term > $o)). 27.00/4.43 thf(func_def_471, type, sK331: term). 27.00/4.43 thf(func_def_472, type, sK332: subst). 27.00/4.43 thf(func_def_473, type, sK333: term). 27.00/4.43 thf(func_def_474, type, sK334: (term > $o)). 27.00/4.43 thf(func_def_475, type, sK335: subst). 27.00/4.43 thf(func_def_476, type, sK336: (term > term)). 27.00/4.43 thf(func_def_477, type, sK337: (subst > (term > $o) > term)). 27.00/4.43 thf(func_def_478, type, sK338: ((term > $o) > term)). 27.00/4.43 thf(func_def_479, type, sK339: ((term > $o) > term)). 27.00/4.43 thf(func_def_480, type, sK340: ((term > $o) > term)). 27.00/4.43 thf(func_def_481, type, sK341: ((term > $o) > term)). 27.00/4.43 thf(func_def_482, type, sK342: ((term > $o) > term)). 27.00/4.43 thf(func_def_483, type, sK343: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_484, type, sK344: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_485, type, sK345: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_486, type, sK346: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_487, type, sK347: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_488, type, sK348: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_489, type, sK349: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_490, type, sK350: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_491, type, sK351: term). 27.00/4.43 thf(func_def_492, type, sK352: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_493, type, sK353: term). 27.00/4.43 thf(func_def_494, type, sK354: ((term > $o) > term)). 27.00/4.43 thf(func_def_495, type, sK355: ((term > $o) > term)). 27.00/4.43 thf(func_def_496, type, sK356: (term > $o)). 27.00/4.43 thf(func_def_497, type, sK357: term). 27.00/4.43 thf(func_def_498, type, sK358: (term > term)). 27.00/4.43 thf(func_def_499, type, sK359: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_500, type, sK360: term). 27.00/4.43 thf(func_def_501, type, sK361: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_502, type, sK362: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_503, type, sK363: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_504, type, sK364: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_505, type, sK365: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_506, type, sK366: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_507, type, sK367: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_508, type, sK368: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_509, type, sK369: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_510, type, sK370: (term > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_511, type, sK371: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_512, type, sK372: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_513, type, sK373: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_514, type, sK374: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_515, type, sK375: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_516, type, sK376: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_517, type, sK377: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_518, type, sK378: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_519, type, sK379: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_520, type, sK380: term). 27.00/4.43 thf(func_def_521, type, sK381: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_522, type, sK382: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_523, type, sK383: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_524, type, sK384: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_525, type, sK385: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_526, type, sK386: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_527, type, sK387: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_528, type, sK388: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_529, type, sK389: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_530, type, sK390: ((term > $o) > term)). 27.00/4.43 thf(func_def_531, type, sK391: ((term > $o) > term)). 27.00/4.43 thf(func_def_532, type, sK392: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_533, type, sK393: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_534, type, sK394: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_535, type, sK395: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_536, type, sK396: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_537, type, sK397: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_538, type, sK398: term). 27.00/4.43 thf(func_def_539, type, sK399: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_540, type, sK400: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_541, type, sK401: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_542, type, sK402: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_543, type, sK403: term). 27.00/4.43 thf(func_def_544, type, sK404: (term > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_545, type, sK405: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_546, type, sK406: ((subst > term > subst > $o) > term > term)). 27.00/4.43 thf(func_def_547, type, sK407: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_548, type, sK408: term). 27.00/4.43 thf(func_def_549, type, sK409: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_550, type, sK410: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_551, type, sK411: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_552, type, sK412: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_553, type, sK413: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_554, type, sK414: term). 27.00/4.43 thf(func_def_555, type, sK415: term). 27.00/4.43 thf(func_def_556, type, sK416: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_557, type, sK417: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_558, type, sK418: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_559, type, sK419: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_560, type, sK420: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_561, type, sK421: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_562, type, sK422: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_563, type, sK423: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_564, type, sK424: ((subst > term > subst > $o) > subst)). 27.00/4.43 thf(func_def_565, type, sK425: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_566, type, sK426: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_567, type, sK427: term). 27.00/4.43 thf(func_def_568, type, sK428: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_569, type, sK429: ((subst > term > subst > $o) > term > $o)). 27.00/4.43 thf(func_def_570, type, sK430: term). 27.00/4.43 thf(func_def_571, type, sK431: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_572, type, sK432: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_573, type, sK433: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_574, type, sK434: ((term > $o) > term)). 27.00/4.43 thf(func_def_575, type, sK435: ((term > $o) > term)). 27.00/4.43 thf(func_def_576, type, sK436: ((term > $o) > term)). 27.00/4.43 thf(func_def_577, type, sK437: term). 27.00/4.43 thf(func_def_578, type, sK438: (term > $o)). 27.00/4.43 thf(func_def_579, type, sK439: (term > term)). 27.00/4.43 thf(func_def_580, type, sK440: ((subst > term > subst > $o) > (term > $o) > term)). 27.00/4.43 thf(func_def_581, type, sK441: (term > (term > $o) > term)). 27.00/4.43 thf(func_def_582, type, sK442: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_583, type, sK443: (term > $o)). 27.00/4.43 thf(func_def_584, type, sK444: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_585, type, sK445: term). 27.00/4.43 thf(func_def_586, type, sK446: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_587, type, sK447: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_588, type, sK448: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_589, type, sK449: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_590, type, sK450: ((term > $o) > term)). 27.00/4.43 thf(func_def_591, type, sK451: ((term > $o) > term)). 27.00/4.43 thf(func_def_592, type, sK452: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_593, type, sK453: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_594, type, sK454: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_595, type, sK455: ((subst > term > term) > (subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_596, type, sK456: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.43 thf(func_def_597, type, sK457: term). 27.00/4.43 thf(func_def_598, type, sK458: term). 27.00/4.43 thf(func_def_599, type, sK459: (subst > d_subst)). 27.00/4.43 thf(func_def_600, type, sK460: subst). 27.00/4.43 thf(func_def_601, type, sK461: subst). 27.00/4.43 thf(func_def_602, type, sK462: subst). 27.00/4.43 thf(func_def_603, type, sK463: subst). 27.00/4.43 thf(func_def_604, type, sK464: subst). 27.00/4.43 thf(func_def_605, type, sK465: subst). 27.00/4.43 thf(func_def_606, type, sK466: subst). 27.00/4.43 thf(func_def_607, type, sK467: subst). 27.00/4.43 thf(func_def_608, type, sK468: (subst > (term > $o) > (term > $o) > term > term)). 27.00/4.43 thf(func_def_609, type, sK469: term). 27.00/4.43 thf(func_def_610, type, sK470: (term > $o)). 27.00/4.43 thf(func_def_611, type, sK471: (term > $o)). 27.00/4.43 thf(func_def_612, type, sK472: subst). 27.00/4.43 thf(func_def_613, type, sK473: (term > subst > term > term)). 27.00/4.43 thf(func_def_614, type, sK474: term). 27.00/4.43 thf(func_def_615, type, sK475: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_616, type, sK476: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_617, type, sK477: subst). 27.00/4.43 thf(func_def_618, type, sK478: (term > $o)). 27.00/4.43 thf(func_def_619, type, sK479: term). 27.00/4.43 thf(func_def_620, type, sK480: ((term > $o) > term)). 27.00/4.43 thf(func_def_621, type, sK481: (term > (term > $o) > subst > term > $o)). 27.00/4.43 thf(func_def_622, type, sK482: subst). 27.00/4.43 thf(func_def_623, type, sK483: term). 27.00/4.43 thf(func_def_624, type, sK484: (term > $o)). 27.00/4.43 thf(func_def_625, type, sK485: (term > $o)). 27.00/4.43 thf(func_def_626, type, sK486: ((term > $o) > (term > $o) > term > subst > term)). 27.00/4.43 thf(func_def_627, type, sK487: term). 27.00/4.43 thf(func_def_628, type, sK488: subst). 27.00/4.43 thf(func_def_629, type, sK489: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_630, type, sK490: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_631, type, sK491: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_632, type, sK492: (subst > term > term)). 27.00/4.43 thf(func_def_633, type, sK493: term). 27.00/4.43 thf(func_def_634, type, sK494: term). 27.00/4.43 thf(func_def_635, type, sK495: subst). 27.00/4.43 thf(func_def_636, type, sK496: term). 27.00/4.43 thf(func_def_637, type, sK497: (term > $o)). 27.00/4.43 thf(func_def_638, type, sK498: ((term > $o) > term)). 27.00/4.43 thf(func_def_639, type, sK499: ((term > $o) > term > subst > term > $o)). 27.00/4.43 thf(func_def_640, type, sK500: term). 27.00/4.43 thf(func_def_641, type, sK501: term). 27.00/4.43 thf(func_def_642, type, sK502: term). 27.00/4.43 thf(func_def_643, type, sK503: term). 27.00/4.43 thf(func_def_644, type, sK504: (term > $o)). 27.00/4.43 thf(func_def_645, type, sK505: term). 27.00/4.43 thf(func_def_646, type, sK506: ((term > $o) > term)). 27.00/4.43 thf(func_def_647, type, sK507: ((term > $o) > term)). 27.00/4.43 thf(func_def_648, type, sK508: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_649, type, sK509: ((term > $o) > term)). 27.00/4.43 thf(func_def_650, type, sK510: ((subst > term > subst > $o) > term > $o)). 27.00/4.43 thf(func_def_651, type, sK511: term). 27.00/4.43 thf(func_def_652, type, sK512: (term > subst > term > term)). 27.00/4.43 thf(func_def_653, type, sK513: term). 27.00/4.43 thf(func_def_654, type, sK514: subst). 27.00/4.43 thf(func_def_655, type, sK515: term). 27.00/4.43 thf(func_def_656, type, sK516: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_657, type, sK517: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_658, type, sK518: (term > subst > term > term)). 27.00/4.43 thf(func_def_659, type, sK519: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_660, type, sK520: ((subst > term > subst > $o) > term)). 27.00/4.43 thf(func_def_661, type, sK521: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_662, type, sK522: term). 27.00/4.43 thf(func_def_663, type, sK523: term). 27.00/4.43 thf(func_def_664, type, sK524: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_665, type, sK525: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_666, type, sK526: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_667, type, sK527: ((subst > term > term) > term)). 27.00/4.43 thf(func_def_668, type, sK528: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_669, type, sK529: ((subst > term > term) > subst)). 27.00/4.43 thf(func_def_670, type, sK530: (subst > term > term)). 27.00/4.43 thf(func_def_671, type, sK531: term). 27.00/4.43 thf(func_def_672, type, sK532: subst). 27.00/4.43 thf(func_def_673, type, sK533: (subst > term > term)). 27.00/4.43 thf(func_def_674, type, sK534: (term > subst > term > term)). 27.00/4.43 thf(func_def_675, type, sK535: term). 27.00/4.43 thf(func_def_676, type, sK536: term). 27.00/4.43 thf(func_def_677, type, sK537: term). 27.00/4.43 thf(func_def_678, type, sK538: term). 27.00/4.43 thf(func_def_679, type, sK539: term). 27.00/4.43 thf(func_def_680, type, sK540: term). 27.00/4.43 thf(func_def_681, type, sK541: term). 27.00/4.43 thf(func_def_682, type, sK542: term). 27.00/4.43 thf(func_def_683, type, sK543: term). 27.00/4.43 thf(func_def_684, type, sK544: term). 27.00/4.43 thf(func_def_685, type, sK545: term). 27.00/4.43 thf(func_def_686, type, sK546: (subst > term > subst > $o)). 27.00/4.43 thf(func_def_687, type, sK547: ((term > $o) > term)). 27.00/4.43 thf(func_def_688, type, sK548: ((subst > term > subst > $o) > term > $o)). 27.00/4.43 thf(func_def_689, type, sK549: subst). 27.00/4.43 thf(func_def_690, type, sK550: term). 27.00/4.43 thf(func_def_691, type, sK551: term). 27.00/4.43 thf(func_def_692, type, sK552: term). 27.00/4.43 thf(func_def_693, type, sK553: term). 27.00/4.43 thf(func_def_694, type, sK554: term). 27.00/4.43 thf(func_def_695, type, sK555: term). 27.00/4.43 thf(func_def_696, type, sK556: term). 27.00/4.43 thf(func_def_697, type, sK557: term). 27.00/4.43 thf(func_def_698, type, sK558: term). 27.00/4.43 thf(func_def_699, type, sK559: term). 27.00/4.43 thf(func_def_700, type, sK560: subst). 27.00/4.44 thf(func_def_701, type, sK561: term). 27.00/4.44 thf(func_def_702, type, sK562: subst). 27.00/4.44 thf(func_def_703, type, sK563: subst). 27.00/4.44 thf(func_def_704, type, sK564: (term > $o)). 27.00/4.44 thf(func_def_705, type, sK565: term). 27.00/4.44 thf(func_def_706, type, sK566: term). 27.00/4.44 thf(func_def_707, type, sK567: (term > $o)). 27.00/4.44 thf(func_def_708, type, sK568: (term > d_term)). 27.00/4.44 thf(func_def_709, type, sK569: term). 27.00/4.44 thf(func_def_710, type, sK570: (term > $o)). 27.00/4.44 thf(func_def_711, type, sK571: subst). 27.00/4.44 thf(func_def_712, type, sK572: (term > $o)). 27.00/4.44 thf(func_def_713, type, sK573: term). 27.00/4.44 thf(func_def_714, type, sK574: term). 27.00/4.44 thf(func_def_715, type, sK575: term). 27.00/4.44 thf(func_def_716, type, sK576: term). 27.00/4.44 thf(func_def_717, type, sK577: term). 27.00/4.44 thf(func_def_718, type, sK578: term). 27.00/4.44 thf(func_def_719, type, sK579: term). 27.00/4.44 thf(func_def_720, type, sK580: term). 27.00/4.44 thf(func_def_721, type, sK581: term). 27.00/4.44 thf(func_def_722, type, sK582: term). 27.00/4.44 thf(func_def_723, type, sK583: term). 27.00/4.44 thf(func_def_724, type, sK584: subst). 27.00/4.44 thf(func_def_725, type, sK585: term). 27.00/4.44 thf(func_def_726, type, sK586: term). 27.00/4.44 thf(func_def_727, type, sK587: term). 27.00/4.44 thf(func_def_728, type, sK588: term). 27.00/4.44 thf(func_def_729, type, sK589: term). 27.00/4.44 thf(func_def_730, type, sK590: term). 27.00/4.44 thf(func_def_731, type, vNOT: ($o > $o)). 27.00/4.44 thf(func_def_732, type, sK591: (subst > term > subst > $o)). 27.00/4.44 thf(func_def_733, type, sK592: ((subst > term > term) > term)). 27.00/4.44 thf(func_def_734, type, sK593: ((subst > term > term) > term > subst)). 27.00/4.44 thf(func_def_735, type, sK594: ((subst > term > term) > term > subst)). 27.00/4.44 thf(func_def_736, type, sK595: ((subst > term > term) > term > term)). 27.00/4.44 thf(func_def_737, type, sK596: ((subst > term > term) > term > subst)). 27.00/4.44 thf(func_def_738, type, sK597: ((subst > term > term) > term > term)). 27.00/4.44 thf(func_def_739, type, sK598: term). 27.00/4.44 thf(func_def_740, type, sK599: ((subst > term > subst > $o) > subst > term > term)). 27.00/4.44 thf(func_def_741, type, sK600: ((subst > term > subst > $o) > term)). 27.00/4.44 thf(func_def_742, type, sK601: ((subst > term > subst > $o) > term > term)). 27.00/4.44 thf(func_def_743, type, sK602: ((subst > term > subst > $o) > term > term)). 27.00/4.44 thf(f1,axiom,( 27.00/4.44 axmap & hoasinduction_lem2_lthm & hoasapinj1_gthm & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X13 : term,X32 : (term > $o),X15 : term,X14 : subst,X10 : (term > $o)] : ((X32 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem1_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & induction2lem_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X19 : term,X15 : term,X13 : term,X18 : term] : ((X18 = X19) | (((ap @ (sub @ X13 @ id) @ X18)) != ((ap @ (sub @ X15 @ id) @ X19)))) <=> hoasapinj2) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & hoasinduction_lem3_gthm & (sh = ((d2subst @ d_id))) & (pushprop_lem1 <=> ! [X32 : (term > $o),X10 : (term > $o),X15 : term,X14 : subst,X13 : term] : (~(X10 @ X13) | (X32 @ (sub @ X13 @ (push @ X15 @ X14))))) & hoasapinj2_gthm & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & pushprop_lem3v2 & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X29 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X24 : subst,X14 : subst,X13 : term] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))))) => ! [X10 : (subst > term > subst > $o),X35 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X35 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X24 : subst,X13 : term] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X35) @ id))))) & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & pushprop_lthm_orig & pushprop_lem2v2 & ((! [X18 : term,X19 : term,X15 : term,X13 : term] : ((((ap @ X13 @ X18)) != ((ap @ X15 @ X19))) | (X18 = X19)) => ! [X13 : term,X18 : term,X15 : term,X19 : term] : ((((ap @ (sub @ X13 @ id) @ X18)) != ((ap @ (sub @ X15 @ id) @ X19))) | (X18 = X19))) <=> hoasapinj2_lthm) & (! [X38 : term,X10 : (subst > term > subst > $o)] : (~ ! [X32 : subst,X14 : subst,X13 : term,X24 : subst] : (~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | (X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X13 : term,X24 : subst,X14 : subst,X32 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | (X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X24 : subst,X14 : subst,X13 : term] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X38 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id))) <=> hoasinduction) & termmset_gthm & (induction <=> ! [X20 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X20) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoaslamnotvar & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X23 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : ((X11 @ (lam @ X23)) | ~ ! [X15 : term] : ((X11 @ (sub @ X23 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id))) => ! [X10 : (subst > term > subst > $o),X38 : term] : (~ ! [X14 : subst,X24 : subst,X32 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | ~(X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id))) | (X10 @ id @ X38 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X24 : subst,X32 : subst] : ((X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | ~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24))))))) <=> hoasinduction_lthm_3) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & hoasapnotvar_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ~lamnotap & (! [X15 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X21 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & (laminj <=> ! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X16 : term,X17 : subst,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) => ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)))))) & pushprop_lem3v2_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X15 : term,X19 : term,X13 : term,X18 : term] : ((((ap @ X13 @ X18)) != ((ap @ X15 @ X19))) | (X13 = X15)) => ! [X13 : term,X18 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X18)) != ((ap @ (sub @ X15 @ id) @ X19))))))) & substmonoid_gthm & induction2_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X10 : (term > $o),X14 : subst,X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & hoasinduction_lem3v2_gthm & (hoasinduction_lem3a <=> ! [X35 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X35 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X35) @ id) | ~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24))))))) & hoaslaminj_gthm & (pushprop_lem0_lthm <=> ! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (! [X18 : term,X15 : term,X19 : term,X13 : term] : ((X13 = X15) | (((ap @ X13 @ X18)) != ((ap @ X15 @ X19)))) <=> apinj1) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X39 : term] : (~ ! [X13 : term,X14 : subst,X24 : subst,X32 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | (X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~ ! [X21 : (subst > term > term)] : (~ ! [X24 : subst,X14 : subst,X13 : term] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X39 @ (push @ X15 @ id)))) | (X11 @ (lam @ X39)) | ~ ! [X13 : term,X24 : subst,X14 : subst,X32 : subst] : (~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | (X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) <=> hoasinduction_lem3v2_lthm) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & hoasinduction_lem3b_gthm & hoasinduction_lem1v2_gthm & ~(var @ (d2term @ d_one)) & axassoc & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & (hoaslamnotap <=> ! [X21 : (subst > term > term),X37 : term,X36 : term] : ((((lam @ (X21 @ sh @ one))) != ((ap @ (sub @ X36 @ id) @ X37))) | ~ ! [X14 : subst,X13 : term,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))))) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (! [X28 : term,X27 : subst,X26 : (subst > term > term),X21 : (subst > term > term)] : (~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term,X14 : subst,X24 : subst] : (((sub @ (X26 @ X14 @ X13) @ X24)) = ((X26 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (((lam @ (X21 @ sh @ one))) != ((lam @ (X26 @ sh @ one)))) | (((X21 @ X27 @ X28)) = ((X26 @ X27 @ X28)))) <=> hoaslaminj) & (hoasinduction_lem3aaa <=> ! [X41 : term,X10 : (subst > term > subst > $o)] : (~ ! [X21 : (subst > term > term),X42 : term] : (~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X46 : subst,X48 : subst,X47 : term] : (((X21 @ (comp @ X46 @ X48) @ (sub @ X47 @ X48))) = ((sub @ X42 @ (push @ (sub @ X47 @ X48) @ (comp @ X46 @ X48))))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X44 : term,X45 : subst,X43 : subst] : (((sub @ (X21 @ X43 @ X44) @ X45)) = ((sub @ (sub @ X42 @ (push @ X44 @ X43)) @ X45)))) | (X10 @ id @ (lam @ (sub @ X41 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X41 @ (push @ X15 @ id)) @ id)))) & ! [X5 : d_subst] : (X5 = d_id) & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X31 : term,X30 : term,X10 : (subst > term > subst > $o)] : (~(X10 @ id @ X31 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X32 : subst,X24 : subst] : ((X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | ~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~(X10 @ id @ X30 @ id) | (X10 @ id @ (ap @ X30 @ X31) @ id) | ~ ! [X24 : subst,X14 : subst,X13 : term,X32 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | (X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24))) => (! [X40 : term,X10 : (subst > term > subst > $o)] : (~ ! [X32 : subst,X24 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | ~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~ ! [X32 : subst,X13 : term,X24 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | ~(X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X40 @ (push @ X15 @ id)) @ id)) | ~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id)) | ~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24))))) | (X10 @ id @ (lam @ X40) @ id)) => ! [X38 : term,X10 : (subst > term > subst > $o)] : (~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X24 : subst,X13 : term,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24))))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X32 : subst,X14 : subst,X24 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | (X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | (X10 @ id @ X38 @ id) | ~ ! [X24 : subst,X13 : term,X14 : subst,X32 : subst] : ((X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | ~(X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))))))) & hoasinduction_lem1v2 & (hoasinduction_lem3aa_lthm <=> ! [X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X29 @ (push @ X15 @ id)) @ id)) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24))))) | (X10 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id))) & (! [X13 : term,X15 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & pushprop_lthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X24 : subst,X13 : term,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X29 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id)) => ! [X40 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X40 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X40) @ id) | ~ ! [X24 : subst,X13 : term,X32 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | ~(X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24))))) | ~ ! [X24 : subst,X14 : subst,X32 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | ~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24))))) <=> hoasinduction_lem3_lthm) & pushprop_lem2v2_gthm & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X21 : (subst > term > term)] : (((X21 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & hoaslamnotap_gthm & ! [X1 : d_term] : (X1 = d_one) & ulamvarsh & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X13 : term,X10 : (term > $o),X14 : subst] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one) | ~(X10 @ X13)))) & hoasinduction_lem1_lthm & (! [X15 : term] : ~ ! [X21 : (subst > term > term)] : (((X21 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoaslamnotvar_lthm & (! [X19 : term,X18 : term,X13 : term,X15 : term] : ((X18 = X19) | (((ap @ X13 @ X18)) != ((ap @ X15 @ X19)))) <=> apinj2) & (hoasapinj1 <=> ! [X15 : term,X18 : term,X19 : term,X13 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X18)) != ((ap @ (sub @ X15 @ id) @ X19))))) & pushprop & hoaslamnotap_lthm & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X20 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X20) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15))) => ! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17))))))) <=> induction2lem_lthm) & (hoasinduction_lem3v2 <=> ! [X39 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X39)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X39 @ (push @ X15 @ id)))) | ~ ! [X24 : subst,X32 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | (X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~ ! [X24 : subst,X13 : term,X32 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | ~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~ ! [X21 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))) & lamnotvar & ~ulamvar1 & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X23 : term] : (~ ! [X21 : (subst > term > term)] : (~ ! [X24 : subst,X14 : subst,X13 : term] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id)) | (X11 @ (lam @ X23)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X23 @ (push @ X15 @ id))) | ~(X11 @ X15))) => ! [X10 : (subst > term > subst > $o),X25 : term] : ((X10 @ id @ X25 @ id) | ~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (! [X10 : (subst > term > subst > $o),X25 : term] : ((X10 @ id @ X25 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X24 : subst,X13 : term,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id)))) <=> hoasinduction_no_psi_cond) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X21 @ X14 @ X13)))) & axapp & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) <=> substmonoid) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X33 : term,X34 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X24 : subst,X13 : term,X14 : subst,X32 : subst] : ((X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | ~(X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~(X11 @ X33) | ~ ! [X13 : term,X14 : subst,X32 : subst,X24 : subst] : (~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | (X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | (X11 @ (ap @ X33 @ X34)) | ~(X11 @ X34) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem2v2) & pushprop_lem2v2_lthm & hoaslamnotvar_gthm & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X26 : (subst > term > term),X21 : (subst > term > term),X28 : term,X27 : subst] : (~ ! [X24 : subst,X13 : term,X14 : subst] : (((sub @ (X26 @ X14 @ X13) @ X24)) = ((X26 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (((X21 @ X27 @ X28)) = ((X26 @ X27 @ X28))) | ~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (((lam @ (X21 @ sh @ one))) != ((lam @ (X26 @ sh @ one)))))))) <=> hoaslaminj_lthm) & hoasapnotvar & (one = ((d2term @ d_one))) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & (! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) <=> induction2lem) & (! [X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X21 : (subst > term > term)] : (~ ! [X14 : subst,X24 : subst,X13 : term] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ (sub @ X29 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X29 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aa) & hoasinduction_gthm & axabs & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & (! [X11 : (term > $o),X23 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X23 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X23)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X21 : (subst > term > term)] : ((X10 @ id @ (lam @ (X21 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))))) <=> hoasinduction_lem3v2a) & ((^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) = pushprop_p_and_p_prime) & hoasinduction_lem2_gthm & (pushprop_lem1v2 <=> ! [X13 : term,X14 : subst,X10 : (term > $o),X11 : (term > $o)] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13))) & pushprop_lem0_gthm & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & pushprop_lem1v2_gthm & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & ((! [X15 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X21 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X23 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X21 : (subst > term > term)] : (~ ! [X13 : term,X24 : subst,X14 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term] : ((X10 @ id @ (X21 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X23 @ (push @ X15 @ id)))) | (X11 @ (lam @ X23))))) <=> hoasinduction_lem3v2a_lthm) & pushprop_lem1_gthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (! [X40 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X24 : subst,X32 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X32 @ X24)) | (X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24)) | ~ ! [X13 : term,X14 : subst,X24 : subst,X32 : subst] : (~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | (X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X21 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X24 : subst] : (((sub @ (X21 @ X14 @ X13) @ X24)) = ((X21 @ (comp @ X14 @ X24) @ (sub @ X13 @ X24)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X21 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X21 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X40 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X40) @ id)) <=> hoasinduction_lem3) & hoasinduction_lem2v2_gthm & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & axclos & hoasinduction_lem3a_gthm & (induction2 <=> ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22))) & (hoasinduction_lem2 <=> ! [X30 : term,X10 : (subst > term > subst > $o),X31 : term] : (~ ! [X24 : subst,X32 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | (X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~ ! [X14 : subst,X24 : subst,X32 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X32) @ (sub @ X13 @ X32) @ X24) | ~(X10 @ X14 @ X13 @ (comp @ X32 @ X24))) | ~(X10 @ id @ X31 @ id) | ~(X10 @ id @ X30 @ id) | (X10 @ id @ (ap @ X30 @ X31) @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)))) & hoasapnotvar_lthm & hoasinduction_lem1 & ulamvarind & pushprop_gthm & (id = ((d2subst @ d_id))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & apnotvar & axvarshift), 27.00/4.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)). 27.00/4.44 thf(f2,conjecture,( 27.00/4.44 (! [X0 : (subst > term > subst > $o)] : (! [X3 : (subst > term > term)] : (? [X4 : term] : ! [X1 : term,X6 : subst,X5 : subst] : ((((sub @ (X3 @ X5 @ X1) @ X6)) = ((sub @ (sub @ X4 @ (push @ X1 @ X5)) @ X6))) & (((sub @ X4 @ (push @ (sub @ X1 @ X6) @ (comp @ X5 @ X6)))) = ((X3 @ (comp @ X5 @ X6) @ (sub @ X1 @ X6))))) => (! [X1 : term] : ((X0 @ id @ X1 @ id) => (X0 @ id @ (X3 @ id @ X1) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X5 : subst, X1 : term] : ((X3 @ X5 @ X1)))) @ id))) => ! [X1 : term] : (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)), 27.00/4.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aaa)). 27.00/4.44 thf(f3,negated_conjecture,( 27.00/4.44 ~ (! [X0 : (subst > term > subst > $o)] : (! [X3 : (subst > term > term)] : (? [X4 : term] : ! [X1 : term,X6 : subst,X5 : subst] : ((((sub @ (X3 @ X5 @ X1) @ X6)) = ((sub @ (sub @ X4 @ (push @ X1 @ X5)) @ X6))) & (((sub @ X4 @ (push @ (sub @ X1 @ X6) @ (comp @ X5 @ X6)))) = ((X3 @ (comp @ X5 @ X6) @ (sub @ X1 @ X6))))) => (! [X1 : term] : ((X0 @ id @ X1 @ id) => (X0 @ id @ (X3 @ id @ X1) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X5 : subst, X1 : term] : ((X3 @ X5 @ X1)))) @ id))) => ! [X1 : term] : (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)), 27.00/4.44 inference(negated_conjecture,[status(cth)],[f2])). 27.00/4.44 thf(f4,plain,( 27.00/4.44 axmap & hoasinduction_lem2_lthm & hoasapinj1_gthm & (pushprop_lem1_lthm <=> (! [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) = X1) => (! [X2 : subst,X3 : term] : (((comp @ sh @ (push @ X3 @ X2))) = X2) => ! [X4 : term,X5 : (term > $o),X6 : term,X7 : subst,X8 : (term > $o)] : ((X5 @ (sub @ X4 @ (push @ X6 @ X7))) | ~(X8 @ X4))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem1_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & induction2lem_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X9 : term,X10 : term,X11 : term,X12 : term] : ((X9 = X12) | (((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9)))) <=> hoasapinj2) & ((! [X13 : subst] : (((comp @ id @ X13)) = X13) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X15 : subst] : (((comp @ id @ X15)) = X15) & ! [X16 : subst] : (((comp @ X16 @ id)) = X16)))) <=> substmonoid_lthm) & hoasinduction_lem3_gthm & (sh = ((d2subst @ d_id))) & (pushprop_lem1 <=> ! [X17 : (term > $o),X18 : (term > $o),X19 : term,X20 : subst,X21 : term] : (~(X18 @ X21) | (X17 @ (sub @ X21 @ (push @ X19 @ X20))))) & hoasapinj2_gthm & ((^[X22 : subst, X23 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & pushprop_lem3v2 & (hoasinduction_lem3a_lthm <=> (! [X24 : term] : (((sub @ X24 @ id)) = X24) => (! [X25 : term,X26 : (subst > term > subst > $o)] : (~ ! [X27 : term] : (~(X26 @ id @ X27 @ id) | (X26 @ id @ (sub @ X25 @ (push @ X27 @ id)) @ id)) | (X26 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id) | ~ ! [X28 : (subst > term > term)] : (~ ! [X29 : term] : (~(X26 @ id @ X29 @ id) | (X26 @ id @ (X28 @ id @ X29) @ id)) | (X26 @ id @ (lam @ (X28 @ sh @ one)) @ id) | ~ ! [X30 : subst,X31 : subst,X32 : term] : (((sub @ (X28 @ X31 @ X32) @ X30)) = ((X28 @ (comp @ X31 @ X30) @ (sub @ X32 @ X30)))))) => ! [X33 : (subst > term > subst > $o),X34 : term] : (~ ! [X35 : term] : ((X33 @ id @ (sub @ X34 @ (push @ X35 @ id)) @ id) | ~(X33 @ id @ X35 @ id)) | ~ ! [X36 : (subst > term > term)] : (~ ! [X37 : term] : ((X33 @ id @ (X36 @ id @ X37) @ id) | ~(X33 @ id @ X37 @ id)) | ~ ! [X38 : subst,X39 : subst,X40 : term] : (((sub @ (X36 @ X38 @ X40) @ X39)) = ((X36 @ (comp @ X38 @ X39) @ (sub @ X40 @ X39)))) | (X33 @ id @ (lam @ (X36 @ sh @ one)) @ id)) | (X33 @ id @ (lam @ X34) @ id))))) & (! [X41 : subst] : (((comp @ X41 @ id)) = X41) <=> axidr) & pushprop_lthm_orig & pushprop_lem2v2 & ((! [X42 : term,X43 : term,X44 : term,X45 : term] : ((((ap @ X45 @ X42)) != ((ap @ X44 @ X43))) | (X42 = X43)) => ! [X46 : term,X47 : term,X48 : term,X49 : term] : ((((ap @ (sub @ X46 @ id) @ X47)) != ((ap @ (sub @ X48 @ id) @ X49))) | (X47 = X49))) <=> hoasapinj2_lthm) & (! [X50 : term,X51 : (subst > term > subst > $o)] : (~ ! [X52 : subst,X53 : subst,X54 : term,X55 : subst] : (~(X51 @ (comp @ X53 @ X52) @ (sub @ X54 @ X52) @ X55) | (X51 @ X53 @ X54 @ (comp @ X52 @ X55))) | ~ ! [X56 : term,X57 : subst,X58 : subst,X59 : subst] : (~(X51 @ X58 @ X56 @ (comp @ X59 @ X57)) | (X51 @ (comp @ X58 @ X59) @ (sub @ X56 @ X59) @ X57)) | ~ ! [X60 : (subst > term > term)] : ((X51 @ id @ (lam @ (X60 @ sh @ one)) @ id) | ~ ! [X61 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X61)) = ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | ~ ! [X64 : term] : (~(X51 @ id @ X64 @ id) | (X51 @ id @ (X60 @ id @ X64) @ id))) | ~ ! [X65 : term,X66 : term] : (~(X51 @ id @ X66 @ id) | (X51 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id) | ~(X51 @ id @ X65 @ id)) | (X51 @ id @ X50 @ id) | ~ ! [X67 : term] : (~(var @ (sub @ X67 @ id)) | (X51 @ id @ X67 @ id))) <=> hoasinduction) & termmset_gthm & (induction <=> ! [X68 : term,X69 : (term > $o)] : (~ ! [X70 : term] : ((X69 @ X70) | ~(var @ X70)) | (X69 @ X68) | ~ ! [X71 : term] : (~(X69 @ X71) | (X69 @ (lam @ X71))) | ~ ! [X72 : term,X73 : term] : ((X69 @ (ap @ X72 @ X73)) | ~(X69 @ X72) | ~(X69 @ X73)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoaslamnotvar & ((! [X74 : (subst > term > subst > $o)] : ~ ! [X75 : (term > $o)] : ~ ! [X76 : term] : (((X75 @ X76)) = ((X74 @ id @ X76 @ id))) => (! [X77 : (term > $o),X78 : term] : (~ ! [X79 : term] : (~(var @ X79) | (X77 @ X79)) | ~ ! [X80 : term] : (~ ! [X81 : term] : (~(X77 @ X81) | (X77 @ (sub @ X80 @ (push @ X81 @ id)))) | (X77 @ (lam @ X80))) | (X77 @ X78) | ~ ! [X82 : term,X83 : term] : ((X77 @ (ap @ X82 @ X83)) | ~(X77 @ X83) | ~(X77 @ X82))) => (! [X84 : term] : (((sub @ X84 @ id)) = X84) => (! [X85 : term,X86 : (subst > term > subst > $o),X87 : (term > $o)] : ((X87 @ (lam @ X85)) | ~ ! [X88 : term] : ((X87 @ (sub @ X85 @ (push @ X88 @ id))) | ~(X87 @ X88)) | ~ ! [X89 : term] : (((X87 @ X89)) = ((X86 @ id @ X89 @ id))) | ~ ! [X90 : (subst > term > term)] : (~ ! [X91 : term] : ((X86 @ id @ (X90 @ id @ X91) @ id) | ~(X86 @ id @ X91 @ id)) | ~ ! [X92 : term,X93 : subst,X94 : subst] : (((X90 @ (comp @ X93 @ X94) @ (sub @ X92 @ X94))) = ((sub @ (X90 @ X93 @ X92) @ X94))) | (X86 @ id @ (lam @ (X90 @ sh @ one)) @ id))) => ! [X95 : (subst > term > subst > $o),X96 : term] : (~ ! [X97 : subst,X98 : subst,X99 : subst,X100 : term] : ((X95 @ (comp @ X97 @ X99) @ (sub @ X100 @ X99) @ X98) | ~(X95 @ X97 @ X100 @ (comp @ X99 @ X98))) | ~ ! [X101 : term,X102 : term] : (~(X95 @ id @ X102 @ id) | (X95 @ id @ (ap @ (sub @ X102 @ id) @ X101) @ id) | ~(X95 @ id @ X101 @ id)) | ~ ! [X103 : (subst > term > term)] : (~ ! [X104 : term,X105 : subst,X106 : subst] : (((sub @ (X103 @ X105 @ X104) @ X106)) = ((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106)))) | (X95 @ id @ (lam @ (X103 @ sh @ one)) @ id) | ~ ! [X107 : term] : (~(X95 @ id @ X107 @ id) | (X95 @ id @ (X103 @ id @ X107) @ id))) | (X95 @ id @ X96 @ id) | ~ ! [X108 : term] : (~(var @ (sub @ X108 @ id)) | (X95 @ id @ X108 @ id)) | ~ ! [X109 : subst,X110 : term,X111 : subst,X112 : subst] : ((X95 @ X109 @ X110 @ (comp @ X112 @ X111)) | ~(X95 @ (comp @ X109 @ X112) @ (sub @ X110 @ X112) @ X111))))))) <=> hoasinduction_lthm_3) & (axscons <=> ! [X113 : subst] : (((push @ (sub @ one @ X113) @ (comp @ sh @ X113))) = X113)) & hoasapnotvar_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ~lamnotap & (! [X114 : term] : ~ ! [X115 : (subst > term > term)] : ~ ! [X116 : term,X117 : subst] : (((X115 @ X117 @ X116)) = ((sub @ X114 @ (push @ X116 @ X117)))) <=> hoasinduction_lem3v2_f) & (laminj <=> ! [X118 : term,X119 : term] : ((((lam @ X118)) != ((lam @ X119))) | (X118 = X119))) & (induction2_lthm <=> (! [X120 : term] : (((sub @ X120 @ id)) = X120) => (! [X121 : term,X122 : subst,X123 : (term > $o)] : (~ ! [X124 : term] : (~ ! [X125 : term] : (~(X123 @ X125) | (X123 @ (sub @ X124 @ (push @ X125 @ id)))) | (X123 @ (lam @ X124))) | ~ ! [X126 : term] : ((X123 @ (sub @ X126 @ X122)) | ~(var @ X126)) | (X123 @ (sub @ X121 @ X122)) | ~ ! [X127 : term,X128 : term] : (~(X123 @ X128) | ~(X123 @ X127) | (X123 @ (ap @ X128 @ X127)))) => ! [X129 : (term > $o),X130 : term] : (~ ! [X131 : term] : ((X129 @ X131) | ~(var @ X131)) | (X129 @ X130) | ~ ! [X132 : term] : (~ ! [X133 : term] : (~(X129 @ X133) | (X129 @ (sub @ X132 @ (push @ X133 @ id)))) | (X129 @ (lam @ X132))) | ~ ! [X134 : term,X135 : term] : (~(X129 @ X134) | (X129 @ (ap @ X135 @ X134)) | ~(X129 @ X135)))))) & pushprop_lem3v2_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (hoasapinj1_lthm <=> (! [X136 : term] : (((sub @ X136 @ id)) = X136) => (! [X137 : term,X138 : term,X139 : term,X140 : term] : ((((ap @ X139 @ X140)) != ((ap @ X137 @ X138))) | (X137 = X139)) => ! [X141 : term,X142 : term,X143 : term,X144 : term] : ((X141 = X143) | (((ap @ (sub @ X143 @ id) @ X144)) != ((ap @ (sub @ X141 @ id) @ X142))))))) & substmonoid_gthm & induction2_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X145 : (term > $o),X146 : subst,X147 : term] : ~ ! [X148 : (term > $o)] : ~ ! [X149 : term] : (((X148 @ X149)) = ((X145 @ (sub @ X149 @ (push @ X147 @ X146))))) <=> pushprop_lem0) & hoasinduction_lem3v2_gthm & (hoasinduction_lem3a <=> ! [X150 : term,X151 : (subst > term > subst > $o)] : (~ ! [X152 : term] : ((X151 @ id @ (sub @ X150 @ (push @ X152 @ id)) @ id) | ~(X151 @ id @ X152 @ id)) | (X151 @ id @ (lam @ X150) @ id) | ~ ! [X153 : (subst > term > term)] : ((X151 @ id @ (lam @ (X153 @ sh @ one)) @ id) | ~ ! [X154 : term] : ((X151 @ id @ (X153 @ id @ X154) @ id) | ~(X151 @ id @ X154 @ id)) | ~ ! [X155 : term,X156 : subst,X157 : subst] : (((sub @ (X153 @ X157 @ X155) @ X156)) = ((X153 @ (comp @ X157 @ X156) @ (sub @ X155 @ X156))))))) & hoaslaminj_gthm & (pushprop_lem0_lthm <=> ! [X158 : subst,X159 : (term > $o),X160 : term] : ~ ! [X161 : (term > $o)] : ~ ! [X162 : term] : (((X159 @ (sub @ X162 @ (push @ X160 @ X158)))) = ((X161 @ X162)))) & (! [X163 : term,X164 : term,X165 : term,X166 : term] : ((X164 = X166) | (((ap @ X164 @ X165)) != ((ap @ X166 @ X163)))) <=> apinj1) & ((! [X167 : term] : (((sub @ X167 @ id)) = X167) => ! [X168 : (subst > term > subst > $o),X169 : (term > $o),X170 : term] : (~ ! [X171 : term,X172 : subst,X173 : subst,X174 : subst] : (~(X168 @ X172 @ X171 @ (comp @ X174 @ X173)) | (X168 @ (comp @ X172 @ X174) @ (sub @ X171 @ X174) @ X173)) | ~ ! [X175 : (subst > term > term)] : (~ ! [X176 : subst,X177 : subst,X178 : term] : (((sub @ (X175 @ X177 @ X178) @ X176)) = ((X175 @ (comp @ X177 @ X176) @ (sub @ X178 @ X176)))) | (X168 @ id @ (lam @ (X175 @ sh @ one)) @ id) | ~ ! [X179 : term] : ((X168 @ id @ (X175 @ id @ X179) @ id) | ~(X168 @ id @ X179 @ id))) | ~ ! [X180 : term] : (~(X169 @ X180) | (X169 @ (sub @ X170 @ (push @ X180 @ id)))) | (X169 @ (lam @ X170)) | ~ ! [X181 : term,X182 : subst,X183 : subst,X184 : subst] : (~(X168 @ (comp @ X183 @ X184) @ (sub @ X181 @ X184) @ X182) | (X168 @ X183 @ X181 @ (comp @ X184 @ X182))) | ~ ! [X185 : term] : (((X169 @ X185)) = ((X168 @ id @ X185 @ id))))) <=> hoasinduction_lem3v2_lthm) & (! [X186 : (subst > term > subst > $o)] : ~ ! [X187 : (term > $o)] : ~ ! [X188 : term] : (((X186 @ id @ X188 @ id)) = ((X187 @ X188))) <=> hoasinduction_lem0) & hoasinduction_lem3b_gthm & hoasinduction_lem1v2_gthm & ~(var @ (d2term @ d_one)) & axassoc & ((! [X189 : term] : (((sub @ X189 @ id)) = X189) => ! [X190 : term] : (((sub @ X190 @ id)) = X190)) <=> termmset_lthm) & (hoaslamnotap <=> ! [X191 : (subst > term > term),X192 : term,X193 : term] : ((((ap @ (sub @ X193 @ id) @ X192)) != ((lam @ (X191 @ sh @ one)))) | ~ ! [X194 : subst,X195 : term,X196 : subst] : (((X191 @ (comp @ X194 @ X196) @ (sub @ X195 @ X196))) = ((sub @ (X191 @ X194 @ X195) @ X196))))) & (hoasinduction_lem0_lthm <=> ! [X197 : (subst > term > subst > $o)] : ~ ! [X198 : (term > $o)] : ~ ! [X199 : term] : (((X198 @ X199)) = ((X197 @ id @ X199 @ id)))) & (! [X200 : term,X201 : subst,X202 : (subst > term > term),X203 : (subst > term > term)] : (~ ! [X204 : term,X205 : subst,X206 : subst] : (((sub @ (X203 @ X206 @ X204) @ X205)) = ((X203 @ (comp @ X206 @ X205) @ (sub @ X204 @ X205)))) | ~ ! [X207 : term,X208 : subst,X209 : subst] : (((X202 @ (comp @ X208 @ X209) @ (sub @ X207 @ X209))) = ((sub @ (X202 @ X208 @ X207) @ X209))) | (((lam @ (X202 @ sh @ one))) != ((lam @ (X203 @ sh @ one)))) | (((X203 @ X201 @ X200)) = ((X202 @ X201 @ X200)))) <=> hoaslaminj) & (hoasinduction_lem3aaa <=> ! [X210 : term,X211 : (subst > term > subst > $o)] : (~ ! [X212 : (subst > term > term),X213 : term] : (~ ! [X214 : term] : ((X211 @ id @ (X212 @ id @ X214) @ id) | ~(X211 @ id @ X214 @ id)) | ~ ! [X215 : subst,X216 : subst,X217 : term] : (((sub @ X213 @ (push @ (sub @ X217 @ X216) @ (comp @ X215 @ X216)))) = ((X212 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216)))) | (X211 @ id @ (lam @ (X212 @ sh @ one)) @ id) | ~ ! [X218 : term,X219 : subst,X220 : subst] : (((sub @ (X212 @ X220 @ X218) @ X219)) = ((sub @ (sub @ X213 @ (push @ X218 @ X220)) @ X219)))) | (X211 @ id @ (lam @ (sub @ X210 @ (push @ one @ sh))) @ id) | ~ ! [X221 : term] : (~(X211 @ id @ X221 @ id) | (X211 @ id @ (sub @ X210 @ (push @ X221 @ id)) @ id)))) & ! [X222 : d_subst] : (d_id = X222) & (hoasinduction_lthm <=> (! [X223 : (term > $o),X224 : term] : ((X223 @ X224) | ~ ! [X225 : term] : (~ ! [X226 : term] : ((X223 @ (sub @ X225 @ (push @ X226 @ id))) | ~(X223 @ X226)) | (X223 @ (lam @ X225))) | ~ ! [X227 : term,X228 : term] : (~(X223 @ X227) | ~(X223 @ X228) | (X223 @ (ap @ X227 @ X228))) | ~ ! [X229 : term] : (~(var @ X229) | (X223 @ X229))) => (! [X230 : term,X231 : term,X232 : (subst > term > subst > $o)] : (~(X232 @ id @ X230 @ id) | ~ ! [X233 : term,X234 : term] : (~(X232 @ id @ X233 @ id) | (X232 @ id @ (ap @ (sub @ X234 @ id) @ X233) @ id) | ~(X232 @ id @ X234 @ id)) | ~ ! [X235 : subst,X236 : term,X237 : subst,X238 : subst] : ((X232 @ X235 @ X236 @ (comp @ X237 @ X238)) | ~(X232 @ (comp @ X235 @ X237) @ (sub @ X236 @ X237) @ X238)) | ~(X232 @ id @ X231 @ id) | (X232 @ id @ (ap @ X231 @ X230) @ id) | ~ ! [X239 : subst,X240 : subst,X241 : term,X242 : subst] : (~(X232 @ X240 @ X241 @ (comp @ X242 @ X239)) | (X232 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X239))) => (! [X243 : term,X244 : (subst > term > subst > $o)] : (~ ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : ((X244 @ X248 @ X247 @ (comp @ X245 @ X246)) | ~(X244 @ (comp @ X248 @ X245) @ (sub @ X247 @ X245) @ X246)) | ~ ! [X249 : subst,X250 : term,X251 : subst,X252 : subst] : ((X244 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251) | ~(X244 @ X252 @ X250 @ (comp @ X249 @ X251))) | ~ ! [X253 : term] : (~(X244 @ id @ X253 @ id) | (X244 @ id @ (sub @ X243 @ (push @ X253 @ id)) @ id)) | ~ ! [X254 : (subst > term > term)] : ((X244 @ id @ (lam @ (X254 @ sh @ one)) @ id) | ~ ! [X255 : term] : (~(X244 @ id @ X255 @ id) | (X244 @ id @ (X254 @ id @ X255) @ id)) | ~ ! [X256 : term,X257 : subst,X258 : subst] : (((X254 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X254 @ X258 @ X256) @ X257)))) | (X244 @ id @ (lam @ X243) @ id)) => ! [X259 : term,X260 : (subst > term > subst > $o)] : (~ ! [X261 : (subst > term > term)] : ((X260 @ id @ (lam @ (X261 @ sh @ one)) @ id) | ~ ! [X262 : term] : ((X260 @ id @ (X261 @ id @ X262) @ id) | ~(X260 @ id @ X262 @ id)) | ~ ! [X263 : subst,X264 : term,X265 : subst] : (((sub @ (X261 @ X265 @ X264) @ X263)) = ((X261 @ (comp @ X265 @ X263) @ (sub @ X264 @ X263))))) | ~ ! [X266 : term] : ((X260 @ id @ X266 @ id) | ~(var @ (sub @ X266 @ id))) | ~ ! [X267 : subst,X268 : subst,X269 : subst,X270 : term] : (~(X260 @ (comp @ X268 @ X267) @ (sub @ X270 @ X267) @ X269) | (X260 @ X268 @ X270 @ (comp @ X267 @ X269))) | (X260 @ id @ X259 @ id) | ~ ! [X271 : subst,X272 : term,X273 : subst,X274 : subst] : ((X260 @ (comp @ X273 @ X274) @ (sub @ X272 @ X274) @ X271) | ~(X260 @ X273 @ X272 @ (comp @ X274 @ X271))) | ~ ! [X275 : term,X276 : term] : (~(X260 @ id @ X276 @ id) | (X260 @ id @ (ap @ (sub @ X276 @ id) @ X275) @ id) | ~(X260 @ id @ X275 @ id))))))) & hoasinduction_lem1v2 & (hoasinduction_lem3aa_lthm <=> ! [X277 : term,X278 : (subst > term > subst > $o)] : (~ ! [X279 : term] : (~(X278 @ id @ X279 @ id) | (X278 @ id @ (sub @ X277 @ (push @ X279 @ id)) @ id)) | ~ ! [X280 : (subst > term > term)] : (~ ! [X281 : term] : ((X278 @ id @ (X280 @ id @ X281) @ id) | ~(X278 @ id @ X281 @ id)) | (X278 @ id @ (lam @ (X280 @ sh @ one)) @ id) | ~ ! [X282 : term,X283 : subst,X284 : subst] : (((X280 @ (comp @ X284 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (X280 @ X284 @ X282) @ X283)))) | (X278 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id))) & (! [X285 : term,X286 : term] : ((((sub @ X285 @ sh)) != ((sub @ X286 @ sh))) | (X285 = X286)) <=> shinj) & pushprop_lthm & ((! [X287 : term] : (((sub @ X287 @ id)) = X287) => (! [X288 : (subst > term > subst > $o),X289 : term] : (~ ! [X290 : (subst > term > term)] : (~ ! [X291 : term] : (~(X288 @ id @ X291 @ id) | (X288 @ id @ (X290 @ id @ X291) @ id)) | (X288 @ id @ (lam @ (X290 @ sh @ one)) @ id) | ~ ! [X292 : subst,X293 : term,X294 : subst] : (((X290 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292))) = ((sub @ (X290 @ X294 @ X293) @ X292)))) | ~ ! [X295 : term] : ((X288 @ id @ (sub @ X289 @ (push @ X295 @ id)) @ id) | ~(X288 @ id @ X295 @ id)) | (X288 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) => ! [X296 : term,X297 : (subst > term > subst > $o)] : (~ ! [X298 : term] : ((X297 @ id @ (sub @ X296 @ (push @ X298 @ id)) @ id) | ~(X297 @ id @ X298 @ id)) | (X297 @ id @ (lam @ X296) @ id) | ~ ! [X299 : subst,X300 : term,X301 : subst,X302 : subst] : ((X297 @ (comp @ X302 @ X301) @ (sub @ X300 @ X301) @ X299) | ~(X297 @ X302 @ X300 @ (comp @ X301 @ X299))) | ~ ! [X303 : (subst > term > term)] : (~ ! [X304 : term] : ((X297 @ id @ (X303 @ id @ X304) @ id) | ~(X297 @ id @ X304 @ id)) | (X297 @ id @ (lam @ (X303 @ sh @ one)) @ id) | ~ ! [X305 : subst,X306 : term,X307 : subst] : (((sub @ (X303 @ X305 @ X306) @ X307)) = ((X303 @ (comp @ X305 @ X307) @ (sub @ X306 @ X307))))) | ~ ! [X308 : subst,X309 : subst,X310 : subst,X311 : term] : ((X297 @ X309 @ X311 @ (comp @ X310 @ X308)) | ~(X297 @ (comp @ X309 @ X310) @ (sub @ X311 @ X310) @ X308))))) <=> hoasinduction_lem3_lthm) & pushprop_lem2v2_gthm & (hoasinduction_lem3b_lthm <=> ! [X312 : term] : ~ ! [X313 : (subst > term > term)] : (((X313 @ sh @ one)) != ((sub @ X312 @ (push @ one @ sh))))) & (axvarid <=> ! [X314 : term] : (((sub @ X314 @ id)) = X314)) & hoaslamnotap_gthm & ! [X315 : d_term] : (d_one = X315) & ulamvarsh & (pushprop_lem1v2_lthm <=> (! [X316 : term,X317 : subst] : (((sub @ one @ (push @ X316 @ X317))) = X316) => ! [X318 : (term > $o),X319 : term,X320 : (term > $o),X321 : subst] : (~ ! [X322 : term] : (((X318 @ X322)) = ((X320 @ (sub @ X322 @ (push @ X319 @ X321))))) | (X318 @ one) | ~(X320 @ X319)))) & hoasinduction_lem1_lthm & (! [X323 : term] : ~ ! [X324 : (subst > term > term)] : (((X324 @ sh @ one)) != ((sub @ X323 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoaslamnotvar_lthm & (! [X325 : term,X326 : term,X327 : term,X328 : term] : ((X325 = X326) | (((ap @ X328 @ X325)) != ((ap @ X327 @ X326)))) <=> apinj2) & (hoasapinj1 <=> ! [X329 : term,X330 : term,X331 : term,X332 : term] : ((X329 = X332) | (((ap @ (sub @ X332 @ id) @ X330)) != ((ap @ (sub @ X329 @ id) @ X331))))) & pushprop & hoaslamnotap_lthm & ((! [X333 : term,X334 : subst] : (((sub @ one @ (push @ X333 @ X334))) = X333) => (! [X335 : subst,X336 : term] : (((comp @ sh @ (push @ X336 @ X335))) = X335) => (! [X337 : subst] : (((comp @ X337 @ id)) = X337) => (! [X338 : term,X339 : (term > $o)] : (~ ! [X340 : term] : (~(X339 @ X340) | (X339 @ (lam @ X340))) | (X339 @ X338) | ~ ! [X341 : term] : (~(var @ X341) | (X339 @ X341)) | ~ ! [X342 : term,X343 : term] : (~(X339 @ X342) | (X339 @ (ap @ X342 @ X343)) | ~(X339 @ X343))) => ! [X344 : term,X345 : (term > $o),X346 : subst] : (~ ! [X347 : term] : (~(var @ X347) | (X345 @ (sub @ X347 @ X346))) | ~ ! [X348 : term] : ((X345 @ (lam @ X348)) | ~ ! [X349 : term] : ((X345 @ (sub @ X348 @ (push @ X349 @ id))) | ~(X345 @ X349))) | ~ ! [X350 : term,X351 : term] : (~(X345 @ X351) | ~(X345 @ X350) | (X345 @ (ap @ X351 @ X350))) | (X345 @ (sub @ X344 @ X346))))))) <=> induction2lem_lthm) & (hoasinduction_lem3v2 <=> ! [X352 : term,X353 : (term > $o),X354 : (subst > term > subst > $o)] : ((X353 @ (lam @ X352)) | ~ ! [X355 : term] : (((X354 @ id @ X355 @ id)) = ((X353 @ X355))) | ~ ! [X356 : term] : (~(X353 @ X356) | (X353 @ (sub @ X352 @ (push @ X356 @ id)))) | ~ ! [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (~(X354 @ X360 @ X359 @ (comp @ X358 @ X357)) | (X354 @ (comp @ X360 @ X358) @ (sub @ X359 @ X358) @ X357)) | ~ ! [X361 : subst,X362 : term,X363 : subst,X364 : subst] : ((X354 @ X364 @ X362 @ (comp @ X363 @ X361)) | ~(X354 @ (comp @ X364 @ X363) @ (sub @ X362 @ X363) @ X361)) | ~ ! [X365 : (subst > term > term)] : (~ ! [X366 : subst,X367 : term,X368 : subst] : (((sub @ (X365 @ X366 @ X367) @ X368)) = ((X365 @ (comp @ X366 @ X368) @ (sub @ X367 @ X368)))) | (X354 @ id @ (lam @ (X365 @ sh @ one)) @ id) | ~ ! [X369 : term] : ((X354 @ id @ (X365 @ id @ X369) @ id) | ~(X354 @ id @ X369 @ id))))) & lamnotvar & ~ulamvar1 & ((! [X370 : (subst > term > subst > $o)] : ~ ! [X371 : (term > $o)] : ~ ! [X372 : term] : (((X371 @ X372)) = ((X370 @ id @ X372 @ id))) => (! [X373 : term,X374 : (term > $o)] : ((X374 @ X373) | ~ ! [X375 : term,X376 : term] : ((X374 @ (ap @ X376 @ X375)) | ~(X374 @ X376) | ~(X374 @ X375)) | ~ ! [X377 : term] : (~(var @ X377) | (X374 @ X377)) | ~ ! [X378 : term] : ((X374 @ (lam @ X378)) | ~ ! [X379 : term] : (~(X374 @ X379) | (X374 @ (sub @ X378 @ (push @ X379 @ id)))))) => (! [X380 : term] : (((sub @ X380 @ id)) = X380) => (! [X381 : (subst > term > subst > $o),X382 : (term > $o),X383 : term] : (~ ! [X384 : (subst > term > term)] : (~ ! [X385 : subst,X386 : subst,X387 : term] : (((X384 @ (comp @ X386 @ X385) @ (sub @ X387 @ X385))) = ((sub @ (X384 @ X386 @ X387) @ X385))) | ~ ! [X388 : term] : ((X381 @ id @ (X384 @ id @ X388) @ id) | ~(X381 @ id @ X388 @ id)) | (X381 @ id @ (lam @ (X384 @ sh @ one)) @ id)) | (X382 @ (lam @ X383)) | ~ ! [X389 : term] : (((X381 @ id @ X389 @ id)) = ((X382 @ X389))) | ~ ! [X390 : term] : ((X382 @ (sub @ X383 @ (push @ X390 @ id))) | ~(X382 @ X390))) => ! [X391 : (subst > term > subst > $o),X392 : term] : ((X391 @ id @ X392 @ id) | ~ ! [X393 : (subst > term > term)] : ((X391 @ id @ (lam @ (X393 @ sh @ one)) @ id) | ~ ! [X394 : subst,X395 : term,X396 : subst] : (((X393 @ (comp @ X394 @ X396) @ (sub @ X395 @ X396))) = ((sub @ (X393 @ X394 @ X395) @ X396))) | ~ ! [X397 : term] : (~(X391 @ id @ X397 @ id) | (X391 @ id @ (X393 @ id @ X397) @ id))) | ~ ! [X398 : term,X399 : term] : (~(X391 @ id @ X399 @ id) | (X391 @ id @ (ap @ (sub @ X398 @ id) @ X399) @ id) | ~(X391 @ id @ X398 @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (! [X400 : (subst > term > subst > $o),X401 : term] : ((X400 @ id @ X401 @ id) | ~ ! [X402 : term,X403 : term] : (~(X400 @ id @ X403 @ id) | ~(X400 @ id @ X402 @ id) | (X400 @ id @ (ap @ (sub @ X402 @ id) @ X403) @ id)) | ~ ! [X404 : (subst > term > term)] : ((X400 @ id @ (lam @ (X404 @ sh @ one)) @ id) | ~ ! [X405 : subst,X406 : term,X407 : subst] : (((X404 @ (comp @ X407 @ X405) @ (sub @ X406 @ X405))) = ((sub @ (X404 @ X407 @ X406) @ X405))) | ~ ! [X408 : term] : (~(X400 @ id @ X408 @ id) | (X400 @ id @ (X404 @ id @ X408) @ id)))) <=> hoasinduction_no_psi_cond) & (hoasinduction_lem3v2_f_lthm <=> ! [X409 : term] : ~ ! [X410 : (subst > term > term)] : ~ ! [X411 : term,X412 : subst] : (((X410 @ X412 @ X411)) = ((sub @ X409 @ (push @ X411 @ X412))))) & axapp & ((! [X413 : subst] : (((comp @ id @ X413)) = X413) & ! [X414 : subst] : (((comp @ X414 @ id)) = X414)) <=> substmonoid) & (hoasinduction_p_and_p_prime = (^[X415 : (subst > term > subst > $o), X416 : (term > $o)] : (! [X417 : term] : (((X415 @ id @ X417 @ id)) = ((X416 @ X417)))))) & (! [X418 : (subst > term > subst > $o),X419 : (term > $o),X420 : term,X421 : term] : (~ ! [X422 : term,X423 : term] : (~(X418 @ id @ X422 @ id) | ~(X418 @ id @ X423 @ id) | (X418 @ id @ (ap @ (sub @ X423 @ id) @ X422) @ id)) | ~ ! [X424 : subst,X425 : term,X426 : subst,X427 : subst] : ((X418 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427) @ X424) | ~(X418 @ X426 @ X425 @ (comp @ X427 @ X424))) | ~(X419 @ X420) | ~ ! [X428 : term,X429 : subst,X430 : subst,X431 : subst] : (~(X418 @ (comp @ X429 @ X430) @ (sub @ X428 @ X430) @ X431) | (X418 @ X429 @ X428 @ (comp @ X430 @ X431))) | (X419 @ (ap @ X420 @ X421)) | ~(X419 @ X421) | ~ ! [X432 : term] : (((X418 @ id @ X432 @ id)) = ((X419 @ X432)))) <=> hoasinduction_lem2v2) & pushprop_lem2v2_lthm & hoaslamnotvar_gthm & ((! [X433 : term,X434 : subst] : (((sub @ one @ (push @ X433 @ X434))) = X433) => (! [X435 : term,X436 : subst] : (((comp @ sh @ (push @ X435 @ X436))) = X436) => (! [X437 : term,X438 : term] : ((X437 = X438) | (((lam @ X438)) != ((lam @ X437)))) => ! [X439 : (subst > term > term),X440 : (subst > term > term),X441 : term,X442 : subst] : (~ ! [X443 : subst,X444 : term,X445 : subst] : (((X439 @ (comp @ X445 @ X443) @ (sub @ X444 @ X443))) = ((sub @ (X439 @ X445 @ X444) @ X443))) | (((X440 @ X442 @ X441)) = ((X439 @ X442 @ X441))) | ~ ! [X446 : term,X447 : subst,X448 : subst] : (((X440 @ (comp @ X448 @ X447) @ (sub @ X446 @ X447))) = ((sub @ (X440 @ X448 @ X446) @ X447))) | (((lam @ (X440 @ sh @ one))) != ((lam @ (X439 @ sh @ one)))))))) <=> hoaslaminj_lthm) & hoasapnotvar & (one = ((d2term @ d_one))) & (! [X449 : term] : (((sub @ X449 @ id)) = X449) <=> termmset) & (! [X450 : term,X451 : (term > $o),X452 : subst] : (~ ! [X453 : term] : (~(var @ X453) | (X451 @ (sub @ X453 @ X452))) | (X451 @ (sub @ X450 @ X452)) | ~ ! [X454 : term,X455 : term] : ((X451 @ (ap @ X454 @ X455)) | ~(X451 @ X454) | ~(X451 @ X455)) | ~ ! [X456 : term] : (~ ! [X457 : term] : (~(X451 @ X457) | (X451 @ (sub @ X456 @ (push @ X457 @ id)))) | (X451 @ (lam @ X456)))) <=> induction2lem) & (! [X458 : (subst > term > subst > $o),X459 : term] : (~ ! [X460 : (subst > term > term)] : (~ ! [X461 : subst,X462 : subst,X463 : term] : (((X460 @ (comp @ X461 @ X462) @ (sub @ X463 @ X462))) = ((sub @ (X460 @ X461 @ X463) @ X462))) | (X458 @ id @ (lam @ (X460 @ sh @ one)) @ id) | ~ ! [X464 : term] : ((X458 @ id @ (X460 @ id @ X464) @ id) | ~(X458 @ id @ X464 @ id))) | (X458 @ id @ (lam @ (sub @ X459 @ (push @ one @ sh))) @ id) | ~ ! [X465 : term] : ((X458 @ id @ (sub @ X459 @ (push @ X465 @ id)) @ id) | ~(X458 @ id @ X465 @ id))) <=> hoasinduction_lem3aa) & hoasinduction_gthm & axabs & (axshiftcons <=> ! [X466 : term,X467 : subst] : (((comp @ sh @ (push @ X466 @ X467))) = X467)) & (axidl <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & (! [X469 : (term > $o),X470 : term,X471 : (subst > term > subst > $o)] : (~ ! [X472 : term] : ((X469 @ (sub @ X470 @ (push @ X472 @ id))) | ~(X469 @ X472)) | (X469 @ (lam @ X470)) | ~ ! [X473 : term] : (((X471 @ id @ X473 @ id)) = ((X469 @ X473))) | ~ ! [X474 : (subst > term > term)] : ((X471 @ id @ (lam @ (X474 @ sh @ one)) @ id) | ~ ! [X475 : term] : ((X471 @ id @ (X474 @ id @ X475) @ id) | ~(X471 @ id @ X475 @ id)) | ~ ! [X476 : term,X477 : subst,X478 : subst] : (((X474 @ (comp @ X478 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X474 @ X478 @ X476) @ X477))))) <=> hoasinduction_lem3v2a) & ((^[X479 : term, X480 : subst, X481 : (term > $o), X482 : (term > $o)] : (! [X483 : term] : (((X482 @ X483)) = ((X481 @ (sub @ X483 @ (push @ X479 @ X480))))))) = pushprop_p_and_p_prime) & hoasinduction_lem2_gthm & (pushprop_lem1v2 <=> ! [X484 : term,X485 : subst,X486 : (term > $o),X487 : (term > $o)] : ((X487 @ one) | ~ ! [X488 : term] : (((X486 @ (sub @ X488 @ (push @ X484 @ X485)))) = ((X487 @ X488))) | ~(X486 @ X484))) & pushprop_lem0_gthm & ! [X489 : d_subst,X490 : d_subst] : ((((d2subst @ X490)) = ((d2subst @ X489))) => (X489 = X490)) & pushprop_lem1v2_gthm & ! [X491 : d_term,X492 : d_term] : ((((d2term @ X491)) = ((d2term @ X492))) => (X491 = X492)) & ((! [X493 : term] : ~ ! [X494 : (subst > term > term)] : ~ ! [X495 : subst,X496 : term] : (((sub @ X493 @ (push @ X496 @ X495))) = ((X494 @ X495 @ X496))) => (! [X497 : term] : (((sub @ X497 @ id)) = X497) => ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (~ ! [X501 : term] : (((X500 @ id @ X501 @ id)) = ((X499 @ X501))) | ~ ! [X502 : (subst > term > term)] : (~ ! [X503 : term,X504 : subst,X505 : subst] : (((X502 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504))) = ((sub @ (X502 @ X505 @ X503) @ X504))) | ~ ! [X506 : term] : ((X500 @ id @ (X502 @ id @ X506) @ id) | ~(X500 @ id @ X506 @ id)) | (X500 @ id @ (lam @ (X502 @ sh @ one)) @ id)) | ~ ! [X507 : term] : (~(X499 @ X507) | (X499 @ (sub @ X498 @ (push @ X507 @ id)))) | (X499 @ (lam @ X498))))) <=> hoasinduction_lem3v2a_lthm) & pushprop_lem1_gthm & ! [X508 : subst] : ? [X509 : d_subst] : (((d2subst @ X509)) = X508) & (! [X510 : term,X511 : (subst > term > subst > $o)] : (~ ! [X512 : subst,X513 : subst,X514 : subst,X515 : term] : (~(X511 @ X512 @ X515 @ (comp @ X514 @ X513)) | (X511 @ (comp @ X512 @ X514) @ (sub @ X515 @ X514) @ X513)) | ~ ! [X516 : term,X517 : subst,X518 : subst,X519 : subst] : (~(X511 @ (comp @ X517 @ X519) @ (sub @ X516 @ X519) @ X518) | (X511 @ X517 @ X516 @ (comp @ X519 @ X518))) | ~ ! [X520 : (subst > term > term)] : (~ ! [X521 : subst,X522 : term,X523 : subst] : (((X520 @ (comp @ X521 @ X523) @ (sub @ X522 @ X523))) = ((sub @ (X520 @ X521 @ X522) @ X523))) | ~ ! [X524 : term] : (~(X511 @ id @ X524 @ id) | (X511 @ id @ (X520 @ id @ X524) @ id)) | (X511 @ id @ (lam @ (X520 @ sh @ one)) @ id)) | ~ ! [X525 : term] : ((X511 @ id @ (sub @ X510 @ (push @ X525 @ id)) @ id) | ~(X511 @ id @ X525 @ id)) | (X511 @ id @ (lam @ X510) @ id)) <=> hoasinduction_lem3) & hoasinduction_lem2v2_gthm & (axvarcons <=> ! [X526 : term,X527 : subst] : (((sub @ one @ (push @ X526 @ X527))) = X526)) & axclos & hoasinduction_lem3a_gthm & (induction2 <=> ! [X528 : (term > $o),X529 : term] : (~ ! [X530 : term] : ((X528 @ (lam @ X530)) | ~ ! [X531 : term] : (~(X528 @ X531) | (X528 @ (sub @ X530 @ (push @ X531 @ id))))) | ~ ! [X532 : term] : ((X528 @ X532) | ~(var @ X532)) | ~ ! [X533 : term,X534 : term] : (~(X528 @ X533) | (X528 @ (ap @ X533 @ X534)) | ~(X528 @ X534)) | (X528 @ X529))) & (hoasinduction_lem2 <=> ! [X535 : term,X536 : (subst > term > subst > $o),X537 : term] : (~ ! [X538 : subst,X539 : subst,X540 : subst,X541 : term] : (~(X536 @ (comp @ X540 @ X539) @ (sub @ X541 @ X539) @ X538) | (X536 @ X540 @ X541 @ (comp @ X539 @ X538))) | ~ ! [X542 : subst,X543 : subst,X544 : subst,X545 : term] : ((X536 @ (comp @ X542 @ X544) @ (sub @ X545 @ X544) @ X543) | ~(X536 @ X542 @ X545 @ (comp @ X544 @ X543))) | ~(X536 @ id @ X537 @ id) | ~(X536 @ id @ X535 @ id) | (X536 @ id @ (ap @ X535 @ X537) @ id) | ~ ! [X546 : term,X547 : term] : (~(X536 @ id @ X546 @ id) | (X536 @ id @ (ap @ (sub @ X547 @ id) @ X546) @ id) | ~(X536 @ id @ X547 @ id)))) & hoasapnotvar_lthm & hoasinduction_lem1 & ulamvarind & pushprop_gthm & (id = ((d2subst @ d_id))) & ! [X548 : term] : ? [X549 : d_term] : (((d2term @ X549)) = X548) & apnotvar & axvarshift), 27.00/4.44 inference(rectify,[],[f1])). 27.00/4.44 thf(f5,plain,( 27.00/4.44 (axmap = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) = X1) => (! [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) = X2) => ! [X4 : term,X5 : (term > $o),X6 : term,X7 : subst,X8 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | ~ (((X8 @ X4)) = $true))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) <=> (hoasapinj2 = $true)) & ((substmonoid_lthm = $true) <=> (! [X13 : subst] : (((comp @ id @ X13)) = X13) => (! [X14 : subst] : (((comp @ X14 @ id)) = X14) => (! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15))))) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1 = $true) <=> ! [X17 : (term > $o),X18 : (term > $o),X19 : term,X20 : subst,X21 : term] : (~ (((X18 @ X21)) = $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true))) & (hoasapinj2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X24 : term] : (((sub @ X24 @ id)) = X24) => (! [X25 : term,X26 : (subst > term > subst > $o)] : (~ ! [X27 : term] : (~ (((X26 @ id @ X27 @ id)) = $true) | (((X26 @ id @ (sub @ X25 @ (push @ X27 @ id)) @ id)) = $true)) | (((X26 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X28 : (subst > term > term)] : (~ ! [X29 : term] : (~ (((X26 @ id @ X29 @ id)) = $true) | ($true = ((X26 @ id @ (X28 @ id @ X29) @ id)))) | (((X26 @ id @ (lam @ (X28 @ sh @ one)) @ id)) = $true) | ~ ! [X30 : subst,X31 : subst,X32 : term] : (((sub @ (X28 @ X31 @ X32) @ X30)) = ((X28 @ (comp @ X31 @ X30) @ (sub @ X32 @ X30)))))) => ! [X33 : (subst > term > subst > $o),X34 : term] : (~ ! [X35 : term] : ((((X33 @ id @ (sub @ X34 @ (push @ X35 @ id)) @ id)) = $true) | ~ (((X33 @ id @ X35 @ id)) = $true)) | ~ ! [X36 : (subst > term > term)] : (~ ! [X37 : term] : ((((X33 @ id @ (X36 @ id @ X37) @ id)) = $true) | ~ (((X33 @ id @ X37 @ id)) = $true)) | ~ ! [X38 : subst,X39 : subst,X40 : term] : (((sub @ (X36 @ X38 @ X40) @ X39)) = ((X36 @ (comp @ X38 @ X39) @ (sub @ X40 @ X39)))) | (((X33 @ id @ (lam @ (X36 @ sh @ one)) @ id)) = $true)) | (((X33 @ id @ (lam @ X34) @ id)) = $true))))) & (! [X41 : subst] : (((comp @ X41 @ id)) = X41) <=> (axidr = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & ((! [X42 : term,X43 : term,X44 : term,X45 : term] : ((((ap @ X45 @ X42)) != ((ap @ X44 @ X43))) | (X42 = X43)) => ! [X46 : term,X47 : term,X48 : term,X49 : term] : ((((ap @ (sub @ X46 @ id) @ X47)) != ((ap @ (sub @ X48 @ id) @ X49))) | (X47 = X49))) <=> (hoasapinj2_lthm = $true)) & (! [X50 : term,X51 : (subst > term > subst > $o)] : (~ ! [X52 : subst,X53 : subst,X54 : term,X55 : subst] : (~ (((X51 @ (comp @ X53 @ X52) @ (sub @ X54 @ X52) @ X55)) = $true) | (((X51 @ X53 @ X54 @ (comp @ X52 @ X55))) = $true)) | ~ ! [X56 : term,X57 : subst,X58 : subst,X59 : subst] : (~ (((X51 @ X58 @ X56 @ (comp @ X59 @ X57))) = $true) | (((X51 @ (comp @ X58 @ X59) @ (sub @ X56 @ X59) @ X57)) = $true)) | ~ ! [X60 : (subst > term > term)] : ((((X51 @ id @ (lam @ (X60 @ sh @ one)) @ id)) = $true) | ~ ! [X61 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X61)) = ((X60 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61)))) | ~ ! [X64 : term] : (~ (((X51 @ id @ X64 @ id)) = $true) | (((X51 @ id @ (X60 @ id @ X64) @ id)) = $true))) | ~ ! [X65 : term,X66 : term] : (~ (((X51 @ id @ X66 @ id)) = $true) | (((X51 @ id @ (ap @ (sub @ X66 @ id) @ X65) @ id)) = $true) | ~ (((X51 @ id @ X65 @ id)) = $true)) | (((X51 @ id @ X50 @ id)) = $true) | ~ ! [X67 : term] : (~ (((var @ (sub @ X67 @ id))) = $true) | (((X51 @ id @ X67 @ id)) = $true))) <=> (hoasinduction = $true)) & (termmset_gthm = $true) & ((induction = $true) <=> ! [X68 : term,X69 : (term > $o)] : (~ ! [X70 : term] : ((((X69 @ X70)) = $true) | ~ (((var @ X70)) = $true)) | (((X69 @ X68)) = $true) | ~ ! [X71 : term] : (~ ($true = ((X69 @ X71))) | ($true = ((X69 @ (lam @ X71))))) | ~ ! [X72 : term,X73 : term] : ((((X69 @ (ap @ X72 @ X73))) = $true) | ~ (((X69 @ X72)) = $true) | ~ ($true = ((X69 @ X73)))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar = $true) & ((! [X74 : (subst > term > subst > $o)] : ~ ! [X75 : (term > $o)] : ~ ! [X76 : term] : (((X75 @ X76)) = ((X74 @ id @ X76 @ id))) => (! [X77 : (term > $o),X78 : term] : (~ ! [X79 : term] : (~ (((var @ X79)) = $true) | (((X77 @ X79)) = $true)) | ~ ! [X80 : term] : (~ ! [X81 : term] : (~ ($true = ((X77 @ X81))) | ($true = ((X77 @ (sub @ X80 @ (push @ X81 @ id)))))) | (((X77 @ (lam @ X80))) = $true)) | (((X77 @ X78)) = $true) | ~ ! [X82 : term,X83 : term] : ((((X77 @ (ap @ X82 @ X83))) = $true) | ~ (((X77 @ X83)) = $true) | ~ (((X77 @ X82)) = $true))) => (! [X84 : term] : (((sub @ X84 @ id)) = X84) => (! [X85 : term,X86 : (subst > term > subst > $o),X87 : (term > $o)] : ((((X87 @ (lam @ X85))) = $true) | ~ ! [X88 : term] : ((((X87 @ (sub @ X85 @ (push @ X88 @ id)))) = $true) | ~ (((X87 @ X88)) = $true)) | ~ ! [X89 : term] : (((X87 @ X89)) = ((X86 @ id @ X89 @ id))) | ~ ! [X90 : (subst > term > term)] : (~ ! [X91 : term] : ((((X86 @ id @ (X90 @ id @ X91) @ id)) = $true) | ~ ($true = ((X86 @ id @ X91 @ id)))) | ~ ! [X92 : term,X93 : subst,X94 : subst] : (((X90 @ (comp @ X93 @ X94) @ (sub @ X92 @ X94))) = ((sub @ (X90 @ X93 @ X92) @ X94))) | (((X86 @ id @ (lam @ (X90 @ sh @ one)) @ id)) = $true))) => ! [X95 : (subst > term > subst > $o),X96 : term] : (~ ! [X97 : subst,X98 : subst,X99 : subst,X100 : term] : ((((X95 @ (comp @ X97 @ X99) @ (sub @ X100 @ X99) @ X98)) = $true) | ~ (((X95 @ X97 @ X100 @ (comp @ X99 @ X98))) = $true)) | ~ ! [X101 : term,X102 : term] : (~ (((X95 @ id @ X102 @ id)) = $true) | (((X95 @ id @ (ap @ (sub @ X102 @ id) @ X101) @ id)) = $true) | ~ (((X95 @ id @ X101 @ id)) = $true)) | ~ ! [X103 : (subst > term > term)] : (~ ! [X104 : term,X105 : subst,X106 : subst] : (((sub @ (X103 @ X105 @ X104) @ X106)) = ((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106)))) | (((X95 @ id @ (lam @ (X103 @ sh @ one)) @ id)) = $true) | ~ ! [X107 : term] : (~ (((X95 @ id @ X107 @ id)) = $true) | (((X95 @ id @ (X103 @ id @ X107) @ id)) = $true))) | (((X95 @ id @ X96 @ id)) = $true) | ~ ! [X108 : term] : (~ (((var @ (sub @ X108 @ id))) = $true) | (((X95 @ id @ X108 @ id)) = $true)) | ~ ! [X109 : subst,X110 : term,X111 : subst,X112 : subst] : ((((X95 @ X109 @ X110 @ (comp @ X112 @ X111))) = $true) | ~ ($true = ((X95 @ (comp @ X109 @ X112) @ (sub @ X110 @ X112) @ X111))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((axscons = $true) <=> ! [X113 : subst] : (((push @ (sub @ one @ X113) @ (comp @ sh @ X113))) = X113)) & (hoasapnotvar_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ~ (lamnotap = $true) & (! [X114 : term] : ~ ! [X115 : (subst > term > term)] : ~ ! [X116 : term,X117 : subst] : (((X115 @ X117 @ X116)) = ((sub @ X114 @ (push @ X116 @ X117)))) <=> (hoasinduction_lem3v2_f = $true)) & ((laminj = $true) <=> ! [X118 : term,X119 : term] : ((((lam @ X118)) != ((lam @ X119))) | (X118 = X119))) & ((induction2_lthm = $true) <=> (! [X120 : term] : (((sub @ X120 @ id)) = X120) => (! [X121 : term,X122 : subst,X123 : (term > $o)] : (~ ! [X124 : term] : (~ ! [X125 : term] : (~ (((X123 @ X125)) = $true) | (((X123 @ (sub @ X124 @ (push @ X125 @ id)))) = $true)) | ($true = ((X123 @ (lam @ X124))))) | ~ ! [X126 : term] : ((((X123 @ (sub @ X126 @ X122))) = $true) | ~ (((var @ X126)) = $true)) | (((X123 @ (sub @ X121 @ X122))) = $true) | ~ ! [X127 : term,X128 : term] : (~ (((X123 @ X128)) = $true) | ~ (((X123 @ X127)) = $true) | (((X123 @ (ap @ X128 @ X127))) = $true))) => ! [X129 : (term > $o),X130 : term] : (~ ! [X131 : term] : (($true = ((X129 @ X131))) | ~ (((var @ X131)) = $true)) | (((X129 @ X130)) = $true) | ~ ! [X132 : term] : (~ ! [X133 : term] : (~ (((X129 @ X133)) = $true) | (((X129 @ (sub @ X132 @ (push @ X133 @ id)))) = $true)) | (((X129 @ (lam @ X132))) = $true)) | ~ ! [X134 : term,X135 : term] : (~ (((X129 @ X134)) = $true) | (((X129 @ (ap @ X135 @ X134))) = $true) | ~ (((X129 @ X135)) = $true)))))) & (pushprop_lem3v2_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1_lthm = $true) <=> (! [X136 : term] : (((sub @ X136 @ id)) = X136) => (! [X137 : term,X138 : term,X139 : term,X140 : term] : ((((ap @ X139 @ X140)) != ((ap @ X137 @ X138))) | (X137 = X139)) => ! [X141 : term,X142 : term,X143 : term,X144 : term] : ((X141 = X143) | (((ap @ (sub @ X143 @ id) @ X144)) != ((ap @ (sub @ X141 @ id) @ X142))))))) & (substmonoid_gthm = $true) & (induction2_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (! [X145 : (term > $o),X146 : subst,X147 : term] : ~ ! [X148 : (term > $o)] : ~ ! [X149 : term] : (((X148 @ X149)) = ((X145 @ (sub @ X149 @ (push @ X147 @ X146))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X150 : term,X151 : (subst > term > subst > $o)] : (~ ! [X152 : term] : ((((X151 @ id @ (sub @ X150 @ (push @ X152 @ id)) @ id)) = $true) | ~ (((X151 @ id @ X152 @ id)) = $true)) | (((X151 @ id @ (lam @ X150) @ id)) = $true) | ~ ! [X153 : (subst > term > term)] : ((((X151 @ id @ (lam @ (X153 @ sh @ one)) @ id)) = $true) | ~ ! [X154 : term] : ((((X151 @ id @ (X153 @ id @ X154) @ id)) = $true) | ~ (((X151 @ id @ X154 @ id)) = $true)) | ~ ! [X155 : term,X156 : subst,X157 : subst] : (((sub @ (X153 @ X157 @ X155) @ X156)) = ((X153 @ (comp @ X157 @ X156) @ (sub @ X155 @ X156))))))) & (hoaslaminj_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X158 : subst,X159 : (term > $o),X160 : term] : ~ ! [X161 : (term > $o)] : ~ ! [X162 : term] : (((X159 @ (sub @ X162 @ (push @ X160 @ X158)))) = ((X161 @ X162)))) & (! [X163 : term,X164 : term,X165 : term,X166 : term] : ((X164 = X166) | (((ap @ X164 @ X165)) != ((ap @ X166 @ X163)))) <=> (apinj1 = $true)) & ((! [X167 : term] : (((sub @ X167 @ id)) = X167) => ! [X168 : (subst > term > subst > $o),X169 : (term > $o),X170 : term] : (~ ! [X171 : term,X172 : subst,X173 : subst,X174 : subst] : (~ (((X168 @ X172 @ X171 @ (comp @ X174 @ X173))) = $true) | (((X168 @ (comp @ X172 @ X174) @ (sub @ X171 @ X174) @ X173)) = $true)) | ~ ! [X175 : (subst > term > term)] : (~ ! [X176 : subst,X177 : subst,X178 : term] : (((sub @ (X175 @ X177 @ X178) @ X176)) = ((X175 @ (comp @ X177 @ X176) @ (sub @ X178 @ X176)))) | ($true = ((X168 @ id @ (lam @ (X175 @ sh @ one)) @ id))) | ~ ! [X179 : term] : ((((X168 @ id @ (X175 @ id @ X179) @ id)) = $true) | ~ (((X168 @ id @ X179 @ id)) = $true))) | ~ ! [X180 : term] : (~ (((X169 @ X180)) = $true) | ($true = ((X169 @ (sub @ X170 @ (push @ X180 @ id)))))) | (((X169 @ (lam @ X170))) = $true) | ~ ! [X181 : term,X182 : subst,X183 : subst,X184 : subst] : (~ (((X168 @ (comp @ X183 @ X184) @ (sub @ X181 @ X184) @ X182)) = $true) | (((X168 @ X183 @ X181 @ (comp @ X184 @ X182))) = $true)) | ~ ! [X185 : term] : (((X169 @ X185)) = ((X168 @ id @ X185 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X186 : (subst > term > subst > $o)] : ~ ! [X187 : (term > $o)] : ~ ! [X188 : term] : (((X186 @ id @ X188 @ id)) = ((X187 @ X188))) <=> (hoasinduction_lem0 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (axassoc = $true) & ((! [X189 : term] : (((sub @ X189 @ id)) = X189) => ! [X190 : term] : (((sub @ X190 @ id)) = X190)) <=> (termmset_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X191 : (subst > term > term),X192 : term,X193 : term] : ((((ap @ (sub @ X193 @ id) @ X192)) != ((lam @ (X191 @ sh @ one)))) | ~ ! [X194 : subst,X195 : term,X196 : subst] : (((X191 @ (comp @ X194 @ X196) @ (sub @ X195 @ X196))) = ((sub @ (X191 @ X194 @ X195) @ X196))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X197 : (subst > term > subst > $o)] : ~ ! [X198 : (term > $o)] : ~ ! [X199 : term] : (((X198 @ X199)) = ((X197 @ id @ X199 @ id)))) & (! [X200 : term,X201 : subst,X202 : (subst > term > term),X203 : (subst > term > term)] : (~ ! [X204 : term,X205 : subst,X206 : subst] : (((sub @ (X203 @ X206 @ X204) @ X205)) = ((X203 @ (comp @ X206 @ X205) @ (sub @ X204 @ X205)))) | ~ ! [X207 : term,X208 : subst,X209 : subst] : (((X202 @ (comp @ X208 @ X209) @ (sub @ X207 @ X209))) = ((sub @ (X202 @ X208 @ X207) @ X209))) | (((lam @ (X202 @ sh @ one))) != ((lam @ (X203 @ sh @ one)))) | (((X203 @ X201 @ X200)) = ((X202 @ X201 @ X200)))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X210 : term,X211 : (subst > term > subst > $o)] : (~ ! [X212 : (subst > term > term),X213 : term] : (~ ! [X214 : term] : ((((X211 @ id @ (X212 @ id @ X214) @ id)) = $true) | ~ ($true = ((X211 @ id @ X214 @ id)))) | ~ ! [X215 : subst,X216 : subst,X217 : term] : (((sub @ X213 @ (push @ (sub @ X217 @ X216) @ (comp @ X215 @ X216)))) = ((X212 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216)))) | (((X211 @ id @ (lam @ (X212 @ sh @ one)) @ id)) = $true) | ~ ! [X218 : term,X219 : subst,X220 : subst] : (((sub @ (X212 @ X220 @ X218) @ X219)) = ((sub @ (sub @ X213 @ (push @ X218 @ X220)) @ X219)))) | (((X211 @ id @ (lam @ (sub @ X210 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X221 : term] : (~ (((X211 @ id @ X221 @ id)) = $true) | (((X211 @ id @ (sub @ X210 @ (push @ X221 @ id)) @ id)) = $true)))) & ! [X222 : d_subst] : (d_id = X222) & ((hoasinduction_lthm = $true) <=> (! [X223 : (term > $o),X224 : term] : ((((X223 @ X224)) = $true) | ~ ! [X225 : term] : (~ ! [X226 : term] : ((((X223 @ (sub @ X225 @ (push @ X226 @ id)))) = $true) | ~ (((X223 @ X226)) = $true)) | (((X223 @ (lam @ X225))) = $true)) | ~ ! [X227 : term,X228 : term] : (~ (((X223 @ X227)) = $true) | ~ (((X223 @ X228)) = $true) | (((X223 @ (ap @ X227 @ X228))) = $true)) | ~ ! [X229 : term] : (~ (((var @ X229)) = $true) | (((X223 @ X229)) = $true))) => (! [X230 : term,X231 : term,X232 : (subst > term > subst > $o)] : (~ (((X232 @ id @ X230 @ id)) = $true) | ~ ! [X233 : term,X234 : term] : (~ (((X232 @ id @ X233 @ id)) = $true) | (((X232 @ id @ (ap @ (sub @ X234 @ id) @ X233) @ id)) = $true) | ~ (((X232 @ id @ X234 @ id)) = $true)) | ~ ! [X235 : subst,X236 : term,X237 : subst,X238 : subst] : ((((X232 @ X235 @ X236 @ (comp @ X237 @ X238))) = $true) | ~ (((X232 @ (comp @ X235 @ X237) @ (sub @ X236 @ X237) @ X238)) = $true)) | ~ (((X232 @ id @ X231 @ id)) = $true) | (((X232 @ id @ (ap @ X231 @ X230) @ id)) = $true) | ~ ! [X239 : subst,X240 : subst,X241 : term,X242 : subst] : (~ (((X232 @ X240 @ X241 @ (comp @ X242 @ X239))) = $true) | (((X232 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242) @ X239)) = $true))) => (! [X243 : term,X244 : (subst > term > subst > $o)] : (~ ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (($true = ((X244 @ X248 @ X247 @ (comp @ X245 @ X246)))) | ~ (((X244 @ (comp @ X248 @ X245) @ (sub @ X247 @ X245) @ X246)) = $true)) | ~ ! [X249 : subst,X250 : term,X251 : subst,X252 : subst] : ((((X244 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)) = $true) | ~ (((X244 @ X252 @ X250 @ (comp @ X249 @ X251))) = $true)) | ~ ! [X253 : term] : (~ (((X244 @ id @ X253 @ id)) = $true) | (((X244 @ id @ (sub @ X243 @ (push @ X253 @ id)) @ id)) = $true)) | ~ ! [X254 : (subst > term > term)] : ((((X244 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true) | ~ ! [X255 : term] : (~ ($true = ((X244 @ id @ X255 @ id))) | (((X244 @ id @ (X254 @ id @ X255) @ id)) = $true)) | ~ ! [X256 : term,X257 : subst,X258 : subst] : (((X254 @ (comp @ X258 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X254 @ X258 @ X256) @ X257)))) | (((X244 @ id @ (lam @ X243) @ id)) = $true)) => ! [X259 : term,X260 : (subst > term > subst > $o)] : (~ ! [X261 : (subst > term > term)] : ((((X260 @ id @ (lam @ (X261 @ sh @ one)) @ id)) = $true) | ~ ! [X262 : term] : ((((X260 @ id @ (X261 @ id @ X262) @ id)) = $true) | ~ (((X260 @ id @ X262 @ id)) = $true)) | ~ ! [X263 : subst,X264 : term,X265 : subst] : (((sub @ (X261 @ X265 @ X264) @ X263)) = ((X261 @ (comp @ X265 @ X263) @ (sub @ X264 @ X263))))) | ~ ! [X266 : term] : ((((X260 @ id @ X266 @ id)) = $true) | ~ (((var @ (sub @ X266 @ id))) = $true)) | ~ ! [X267 : subst,X268 : subst,X269 : subst,X270 : term] : (~ (((X260 @ (comp @ X268 @ X267) @ (sub @ X270 @ X267) @ X269)) = $true) | (((X260 @ X268 @ X270 @ (comp @ X267 @ X269))) = $true)) | (((X260 @ id @ X259 @ id)) = $true) | ~ ! [X271 : subst,X272 : term,X273 : subst,X274 : subst] : ((((X260 @ (comp @ X273 @ X274) @ (sub @ X272 @ X274) @ X271)) = $true) | ~ (((X260 @ X273 @ X272 @ (comp @ X274 @ X271))) = $true)) | ~ ! [X275 : term,X276 : term] : (~ (((X260 @ id @ X276 @ id)) = $true) | (((X260 @ id @ (ap @ (sub @ X276 @ id) @ X275) @ id)) = $true) | ~ (((X260 @ id @ X275 @ id)) = $true))))))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X277 : term,X278 : (subst > term > subst > $o)] : (~ ! [X279 : term] : (~ (((X278 @ id @ X279 @ id)) = $true) | (((X278 @ id @ (sub @ X277 @ (push @ X279 @ id)) @ id)) = $true)) | ~ ! [X280 : (subst > term > term)] : (~ ! [X281 : term] : ((((X278 @ id @ (X280 @ id @ X281) @ id)) = $true) | ~ (((X278 @ id @ X281 @ id)) = $true)) | (((X278 @ id @ (lam @ (X280 @ sh @ one)) @ id)) = $true) | ~ ! [X282 : term,X283 : subst,X284 : subst] : (((X280 @ (comp @ X284 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (X280 @ X284 @ X282) @ X283)))) | ($true = ((X278 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id))))) & (! [X285 : term,X286 : term] : ((((sub @ X285 @ sh)) != ((sub @ X286 @ sh))) | (X285 = X286)) <=> (shinj = $true)) & (pushprop_lthm = $true) & ((! [X287 : term] : (((sub @ X287 @ id)) = X287) => (! [X288 : (subst > term > subst > $o),X289 : term] : (~ ! [X290 : (subst > term > term)] : (~ ! [X291 : term] : (~ (((X288 @ id @ X291 @ id)) = $true) | (((X288 @ id @ (X290 @ id @ X291) @ id)) = $true)) | (((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id)) = $true) | ~ ! [X292 : subst,X293 : term,X294 : subst] : (((X290 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292))) = ((sub @ (X290 @ X294 @ X293) @ X292)))) | ~ ! [X295 : term] : ((((X288 @ id @ (sub @ X289 @ (push @ X295 @ id)) @ id)) = $true) | ~ (((X288 @ id @ X295 @ id)) = $true)) | (((X288 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) = $true)) => ! [X296 : term,X297 : (subst > term > subst > $o)] : (~ ! [X298 : term] : ((((X297 @ id @ (sub @ X296 @ (push @ X298 @ id)) @ id)) = $true) | ~ (((X297 @ id @ X298 @ id)) = $true)) | (((X297 @ id @ (lam @ X296) @ id)) = $true) | ~ ! [X299 : subst,X300 : term,X301 : subst,X302 : subst] : ((((X297 @ (comp @ X302 @ X301) @ (sub @ X300 @ X301) @ X299)) = $true) | ~ ($true = ((X297 @ X302 @ X300 @ (comp @ X301 @ X299))))) | ~ ! [X303 : (subst > term > term)] : (~ ! [X304 : term] : ((((X297 @ id @ (X303 @ id @ X304) @ id)) = $true) | ~ (((X297 @ id @ X304 @ id)) = $true)) | (((X297 @ id @ (lam @ (X303 @ sh @ one)) @ id)) = $true) | ~ ! [X305 : subst,X306 : term,X307 : subst] : (((sub @ (X303 @ X305 @ X306) @ X307)) = ((X303 @ (comp @ X305 @ X307) @ (sub @ X306 @ X307))))) | ~ ! [X308 : subst,X309 : subst,X310 : subst,X311 : term] : ((((X297 @ X309 @ X311 @ (comp @ X310 @ X308))) = $true) | ~ ($true = ((X297 @ (comp @ X309 @ X310) @ (sub @ X311 @ X310) @ X308))))))) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X312 : term] : ~ ! [X313 : (subst > term > term)] : (((X313 @ sh @ one)) != ((sub @ X312 @ (push @ one @ sh))))) & ((axvarid = $true) <=> ! [X314 : term] : (((sub @ X314 @ id)) = X314)) & (hoaslamnotap_gthm = $true) & ! [X315 : d_term] : (d_one = X315) & (ulamvarsh = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X316 : term,X317 : subst] : (((sub @ one @ (push @ X316 @ X317))) = X316) => ! [X318 : (term > $o),X319 : term,X320 : (term > $o),X321 : subst] : (~ ! [X322 : term] : (((X318 @ X322)) = ((X320 @ (sub @ X322 @ (push @ X319 @ X321))))) | (((X318 @ one)) = $true) | ~ (((X320 @ X319)) = $true)))) & (hoasinduction_lem1_lthm = $true) & (! [X323 : term] : ~ ! [X324 : (subst > term > term)] : (((X324 @ sh @ one)) != ((sub @ X323 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoaslamnotvar_lthm = $true) & (! [X325 : term,X326 : term,X327 : term,X328 : term] : ((X325 = X326) | (((ap @ X328 @ X325)) != ((ap @ X327 @ X326)))) <=> (apinj2 = $true)) & ((hoasapinj1 = $true) <=> ! [X329 : term,X330 : term,X331 : term,X332 : term] : ((X329 = X332) | (((ap @ (sub @ X332 @ id) @ X330)) != ((ap @ (sub @ X329 @ id) @ X331))))) & (pushprop = $true) & (hoaslamnotap_lthm = $true) & ((! [X333 : term,X334 : subst] : (((sub @ one @ (push @ X333 @ X334))) = X333) => (! [X335 : subst,X336 : term] : (((comp @ sh @ (push @ X336 @ X335))) = X335) => (! [X337 : subst] : (((comp @ X337 @ id)) = X337) => (! [X338 : term,X339 : (term > $o)] : (~ ! [X340 : term] : (~ (((X339 @ X340)) = $true) | (((X339 @ (lam @ X340))) = $true)) | ($true = ((X339 @ X338))) | ~ ! [X341 : term] : (~ (((var @ X341)) = $true) | (((X339 @ X341)) = $true)) | ~ ! [X342 : term,X343 : term] : (~ (((X339 @ X342)) = $true) | (((X339 @ (ap @ X342 @ X343))) = $true) | ~ (((X339 @ X343)) = $true))) => ! [X344 : term,X345 : (term > $o),X346 : subst] : (~ ! [X347 : term] : (~ ($true = ((var @ X347))) | (((X345 @ (sub @ X347 @ X346))) = $true)) | ~ ! [X348 : term] : ((((X345 @ (lam @ X348))) = $true) | ~ ! [X349 : term] : ((((X345 @ (sub @ X348 @ (push @ X349 @ id)))) = $true) | ~ (((X345 @ X349)) = $true))) | ~ ! [X350 : term,X351 : term] : (~ (((X345 @ X351)) = $true) | ~ (((X345 @ X350)) = $true) | ($true = ((X345 @ (ap @ X351 @ X350))))) | (((X345 @ (sub @ X344 @ X346))) = $true)))))) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X352 : term,X353 : (term > $o),X354 : (subst > term > subst > $o)] : ((((X353 @ (lam @ X352))) = $true) | ~ ! [X355 : term] : (((X354 @ id @ X355 @ id)) = ((X353 @ X355))) | ~ ! [X356 : term] : (~ (((X353 @ X356)) = $true) | (((X353 @ (sub @ X352 @ (push @ X356 @ id)))) = $true)) | ~ ! [X357 : subst,X358 : subst,X359 : term,X360 : subst] : (~ (((X354 @ X360 @ X359 @ (comp @ X358 @ X357))) = $true) | (((X354 @ (comp @ X360 @ X358) @ (sub @ X359 @ X358) @ X357)) = $true)) | ~ ! [X361 : subst,X362 : term,X363 : subst,X364 : subst] : (($true = ((X354 @ X364 @ X362 @ (comp @ X363 @ X361)))) | ~ ($true = ((X354 @ (comp @ X364 @ X363) @ (sub @ X362 @ X363) @ X361)))) | ~ ! [X365 : (subst > term > term)] : (~ ! [X366 : subst,X367 : term,X368 : subst] : (((sub @ (X365 @ X366 @ X367) @ X368)) = ((X365 @ (comp @ X366 @ X368) @ (sub @ X367 @ X368)))) | (((X354 @ id @ (lam @ (X365 @ sh @ one)) @ id)) = $true) | ~ ! [X369 : term] : ((((X354 @ id @ (X365 @ id @ X369) @ id)) = $true) | ~ (((X354 @ id @ X369 @ id)) = $true))))) & (lamnotvar = $true) & ~ (ulamvar1 = $true) & ((! [X370 : (subst > term > subst > $o)] : ~ ! [X371 : (term > $o)] : ~ ! [X372 : term] : (((X371 @ X372)) = ((X370 @ id @ X372 @ id))) => (! [X373 : term,X374 : (term > $o)] : ((((X374 @ X373)) = $true) | ~ ! [X375 : term,X376 : term] : ((((X374 @ (ap @ X376 @ X375))) = $true) | ~ (((X374 @ X376)) = $true) | ~ (((X374 @ X375)) = $true)) | ~ ! [X377 : term] : (~ (((var @ X377)) = $true) | (((X374 @ X377)) = $true)) | ~ ! [X378 : term] : ((((X374 @ (lam @ X378))) = $true) | ~ ! [X379 : term] : (~ ($true = ((X374 @ X379))) | (((X374 @ (sub @ X378 @ (push @ X379 @ id)))) = $true)))) => (! [X380 : term] : (((sub @ X380 @ id)) = X380) => (! [X381 : (subst > term > subst > $o),X382 : (term > $o),X383 : term] : (~ ! [X384 : (subst > term > term)] : (~ ! [X385 : subst,X386 : subst,X387 : term] : (((X384 @ (comp @ X386 @ X385) @ (sub @ X387 @ X385))) = ((sub @ (X384 @ X386 @ X387) @ X385))) | ~ ! [X388 : term] : ((((X381 @ id @ (X384 @ id @ X388) @ id)) = $true) | ~ (((X381 @ id @ X388 @ id)) = $true)) | ($true = ((X381 @ id @ (lam @ (X384 @ sh @ one)) @ id)))) | (((X382 @ (lam @ X383))) = $true) | ~ ! [X389 : term] : (((X381 @ id @ X389 @ id)) = ((X382 @ X389))) | ~ ! [X390 : term] : ((((X382 @ (sub @ X383 @ (push @ X390 @ id)))) = $true) | ~ (((X382 @ X390)) = $true))) => ! [X391 : (subst > term > subst > $o),X392 : term] : ((((X391 @ id @ X392 @ id)) = $true) | ~ ! [X393 : (subst > term > term)] : ((((X391 @ id @ (lam @ (X393 @ sh @ one)) @ id)) = $true) | ~ ! [X394 : subst,X395 : term,X396 : subst] : (((X393 @ (comp @ X394 @ X396) @ (sub @ X395 @ X396))) = ((sub @ (X393 @ X394 @ X395) @ X396))) | ~ ! [X397 : term] : (~ (((X391 @ id @ X397 @ id)) = $true) | (((X391 @ id @ (X393 @ id @ X397) @ id)) = $true))) | ~ ! [X398 : term,X399 : term] : (~ (((X391 @ id @ X399 @ id)) = $true) | (((X391 @ id @ (ap @ (sub @ X398 @ id) @ X399) @ id)) = $true) | ~ (((X391 @ id @ X398 @ id)) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X400 : (subst > term > subst > $o),X401 : term] : ((((X400 @ id @ X401 @ id)) = $true) | ~ ! [X402 : term,X403 : term] : (~ (((X400 @ id @ X403 @ id)) = $true) | ~ (((X400 @ id @ X402 @ id)) = $true) | (((X400 @ id @ (ap @ (sub @ X402 @ id) @ X403) @ id)) = $true)) | ~ ! [X404 : (subst > term > term)] : ((((X400 @ id @ (lam @ (X404 @ sh @ one)) @ id)) = $true) | ~ ! [X405 : subst,X406 : term,X407 : subst] : (((X404 @ (comp @ X407 @ X405) @ (sub @ X406 @ X405))) = ((sub @ (X404 @ X407 @ X406) @ X405))) | ~ ! [X408 : term] : (~ (((X400 @ id @ X408 @ id)) = $true) | (((X400 @ id @ (X404 @ id @ X408) @ id)) = $true)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X409 : term] : ~ ! [X410 : (subst > term > term)] : ~ ! [X411 : term,X412 : subst] : (((X410 @ X412 @ X411)) = ((sub @ X409 @ (push @ X411 @ X412))))) & (axapp = $true) & ((! [X413 : subst] : (((comp @ id @ X413)) = X413) & ! [X414 : subst] : (((comp @ X414 @ id)) = X414)) <=> (substmonoid = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X418 : (subst > term > subst > $o),X419 : (term > $o),X420 : term,X421 : term] : (~ ! [X422 : term,X423 : term] : (~ (((X418 @ id @ X422 @ id)) = $true) | ~ ($true = ((X418 @ id @ X423 @ id))) | (((X418 @ id @ (ap @ (sub @ X423 @ id) @ X422) @ id)) = $true)) | ~ ! [X424 : subst,X425 : term,X426 : subst,X427 : subst] : ((((X418 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427) @ X424)) = $true) | ~ (((X418 @ X426 @ X425 @ (comp @ X427 @ X424))) = $true)) | ~ (((X419 @ X420)) = $true) | ~ ! [X428 : term,X429 : subst,X430 : subst,X431 : subst] : (~ (((X418 @ (comp @ X429 @ X430) @ (sub @ X428 @ X430) @ X431)) = $true) | (((X418 @ X429 @ X428 @ (comp @ X430 @ X431))) = $true)) | (((X419 @ (ap @ X420 @ X421))) = $true) | ~ (((X419 @ X421)) = $true) | ~ ! [X432 : term] : (((X418 @ id @ X432 @ id)) = ((X419 @ X432)))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & ((! [X433 : term,X434 : subst] : (((sub @ one @ (push @ X433 @ X434))) = X433) => (! [X435 : term,X436 : subst] : (((comp @ sh @ (push @ X435 @ X436))) = X436) => (! [X437 : term,X438 : term] : ((X437 = X438) | (((lam @ X438)) != ((lam @ X437)))) => ! [X439 : (subst > term > term),X440 : (subst > term > term),X441 : term,X442 : subst] : (~ ! [X443 : subst,X444 : term,X445 : subst] : (((X439 @ (comp @ X445 @ X443) @ (sub @ X444 @ X443))) = ((sub @ (X439 @ X445 @ X444) @ X443))) | (((X440 @ X442 @ X441)) = ((X439 @ X442 @ X441))) | ~ ! [X446 : term,X447 : subst,X448 : subst] : (((X440 @ (comp @ X448 @ X447) @ (sub @ X446 @ X447))) = ((sub @ (X440 @ X448 @ X446) @ X447))) | (((lam @ (X440 @ sh @ one))) != ((lam @ (X439 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (hoasapnotvar = $true) & (one = ((d2term @ d_one))) & (! [X449 : term] : (((sub @ X449 @ id)) = X449) <=> (termmset = $true)) & (! [X450 : term,X451 : (term > $o),X452 : subst] : (~ ! [X453 : term] : (~ (((var @ X453)) = $true) | (((X451 @ (sub @ X453 @ X452))) = $true)) | ($true = ((X451 @ (sub @ X450 @ X452)))) | ~ ! [X454 : term,X455 : term] : ((((X451 @ (ap @ X454 @ X455))) = $true) | ~ (((X451 @ X454)) = $true) | ~ (((X451 @ X455)) = $true)) | ~ ! [X456 : term] : (~ ! [X457 : term] : (~ (((X451 @ X457)) = $true) | (((X451 @ (sub @ X456 @ (push @ X457 @ id)))) = $true)) | (((X451 @ (lam @ X456))) = $true))) <=> (induction2lem = $true)) & (! [X458 : (subst > term > subst > $o),X459 : term] : (~ ! [X460 : (subst > term > term)] : (~ ! [X461 : subst,X462 : subst,X463 : term] : (((X460 @ (comp @ X461 @ X462) @ (sub @ X463 @ X462))) = ((sub @ (X460 @ X461 @ X463) @ X462))) | (((X458 @ id @ (lam @ (X460 @ sh @ one)) @ id)) = $true) | ~ ! [X464 : term] : ((((X458 @ id @ (X460 @ id @ X464) @ id)) = $true) | ~ (((X458 @ id @ X464 @ id)) = $true))) | (((X458 @ id @ (lam @ (sub @ X459 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X465 : term] : ((((X458 @ id @ (sub @ X459 @ (push @ X465 @ id)) @ id)) = $true) | ~ (((X458 @ id @ X465 @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_gthm = $true) & (axabs = $true) & ((axshiftcons = $true) <=> ! [X466 : term,X467 : subst] : (((comp @ sh @ (push @ X466 @ X467))) = X467)) & ((axidl = $true) <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & (! [X469 : (term > $o),X470 : term,X471 : (subst > term > subst > $o)] : (~ ! [X472 : term] : ((((X469 @ (sub @ X470 @ (push @ X472 @ id)))) = $true) | ~ (((X469 @ X472)) = $true)) | (((X469 @ (lam @ X470))) = $true) | ~ ! [X473 : term] : (((X471 @ id @ X473 @ id)) = ((X469 @ X473))) | ~ ! [X474 : (subst > term > term)] : ((((X471 @ id @ (lam @ (X474 @ sh @ one)) @ id)) = $true) | ~ ! [X475 : term] : ((((X471 @ id @ (X474 @ id @ X475) @ id)) = $true) | ~ (((X471 @ id @ X475 @ id)) = $true)) | ~ ! [X476 : term,X477 : subst,X478 : subst] : (((X474 @ (comp @ X478 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X474 @ X478 @ X476) @ X477))))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X484 : term,X485 : subst,X486 : (term > $o),X487 : (term > $o)] : ((((X487 @ one)) = $true) | ~ ! [X488 : term] : (((X486 @ (sub @ X488 @ (push @ X484 @ X485)))) = ((X487 @ X488))) | ~ (((X486 @ X484)) = $true))) & (pushprop_lem0_gthm = $true) & ! [X489 : d_subst,X490 : d_subst] : ((((d2subst @ X490)) = ((d2subst @ X489))) => (X489 = X490)) & (pushprop_lem1v2_gthm = $true) & ! [X491 : d_term,X492 : d_term] : ((((d2term @ X491)) = ((d2term @ X492))) => (X491 = X492)) & ((! [X493 : term] : ~ ! [X494 : (subst > term > term)] : ~ ! [X495 : subst,X496 : term] : (((sub @ X493 @ (push @ X496 @ X495))) = ((X494 @ X495 @ X496))) => (! [X497 : term] : (((sub @ X497 @ id)) = X497) => ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (~ ! [X501 : term] : (((X500 @ id @ X501 @ id)) = ((X499 @ X501))) | ~ ! [X502 : (subst > term > term)] : (~ ! [X503 : term,X504 : subst,X505 : subst] : (((X502 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504))) = ((sub @ (X502 @ X505 @ X503) @ X504))) | ~ ! [X506 : term] : ((((X500 @ id @ (X502 @ id @ X506) @ id)) = $true) | ~ (((X500 @ id @ X506 @ id)) = $true)) | (((X500 @ id @ (lam @ (X502 @ sh @ one)) @ id)) = $true)) | ~ ! [X507 : term] : (~ (((X499 @ X507)) = $true) | (((X499 @ (sub @ X498 @ (push @ X507 @ id)))) = $true)) | (((X499 @ (lam @ X498))) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem1_gthm = $true) & ! [X508 : subst] : ? [X509 : d_subst] : (((d2subst @ X509)) = X508) & (! [X510 : term,X511 : (subst > term > subst > $o)] : (~ ! [X512 : subst,X513 : subst,X514 : subst,X515 : term] : (~ (((X511 @ X512 @ X515 @ (comp @ X514 @ X513))) = $true) | (((X511 @ (comp @ X512 @ X514) @ (sub @ X515 @ X514) @ X513)) = $true)) | ~ ! [X516 : term,X517 : subst,X518 : subst,X519 : subst] : (~ (((X511 @ (comp @ X517 @ X519) @ (sub @ X516 @ X519) @ X518)) = $true) | (((X511 @ X517 @ X516 @ (comp @ X519 @ X518))) = $true)) | ~ ! [X520 : (subst > term > term)] : (~ ! [X521 : subst,X522 : term,X523 : subst] : (((X520 @ (comp @ X521 @ X523) @ (sub @ X522 @ X523))) = ((sub @ (X520 @ X521 @ X522) @ X523))) | ~ ! [X524 : term] : (~ (((X511 @ id @ X524 @ id)) = $true) | (((X511 @ id @ (X520 @ id @ X524) @ id)) = $true)) | (((X511 @ id @ (lam @ (X520 @ sh @ one)) @ id)) = $true)) | ~ ! [X525 : term] : ((((X511 @ id @ (sub @ X510 @ (push @ X525 @ id)) @ id)) = $true) | ~ (((X511 @ id @ X525 @ id)) = $true)) | (((X511 @ id @ (lam @ X510) @ id)) = $true)) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) <=> ! [X526 : term,X527 : subst] : (((sub @ one @ (push @ X526 @ X527))) = X526)) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) <=> ! [X528 : (term > $o),X529 : term] : (~ ! [X530 : term] : ((((X528 @ (lam @ X530))) = $true) | ~ ! [X531 : term] : (~ (((X528 @ X531)) = $true) | (((X528 @ (sub @ X530 @ (push @ X531 @ id)))) = $true))) | ~ ! [X532 : term] : ((((X528 @ X532)) = $true) | ~ (((var @ X532)) = $true)) | ~ ! [X533 : term,X534 : term] : (~ (((X528 @ X533)) = $true) | (((X528 @ (ap @ X533 @ X534))) = $true) | ~ (((X528 @ X534)) = $true)) | (((X528 @ X529)) = $true))) & ((hoasinduction_lem2 = $true) <=> ! [X535 : term,X536 : (subst > term > subst > $o),X537 : term] : (~ ! [X538 : subst,X539 : subst,X540 : subst,X541 : term] : (~ (((X536 @ (comp @ X540 @ X539) @ (sub @ X541 @ X539) @ X538)) = $true) | (((X536 @ X540 @ X541 @ (comp @ X539 @ X538))) = $true)) | ~ ! [X542 : subst,X543 : subst,X544 : subst,X545 : term] : ((((X536 @ (comp @ X542 @ X544) @ (sub @ X545 @ X544) @ X543)) = $true) | ~ (((X536 @ X542 @ X545 @ (comp @ X544 @ X543))) = $true)) | ~ (((X536 @ id @ X537 @ id)) = $true) | ~ (((X536 @ id @ X535 @ id)) = $true) | (((X536 @ id @ (ap @ X535 @ X537) @ id)) = $true) | ~ ! [X546 : term,X547 : term] : (~ (((X536 @ id @ X546 @ id)) = $true) | (((X536 @ id @ (ap @ (sub @ X547 @ id) @ X546) @ id)) = $true) | ~ (((X536 @ id @ X547 @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1 = $true) & (ulamvarind = $true) & (pushprop_gthm = $true) & (((d2subst @ d_id)) = id) & ! [X548 : term] : ? [X549 : d_term] : (((d2term @ X549)) = X548) & (apnotvar = $true) & (axvarshift = $true)), 27.00/4.44 inference(fool_elimination,[],[f4])). 27.00/4.44 thf(f6,plain,( 27.00/4.44 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (? [X2 : term] : ! [X3 : term,X4 : subst,X5 : subst] : ((((sub @ (X1 @ X5 @ X3) @ X4)) = ((sub @ (sub @ X2 @ (push @ X3 @ X5)) @ X4))) & (((sub @ X2 @ (push @ (sub @ X3 @ X4) @ (comp @ X5 @ X4)))) = ((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4))))) => (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (X1 @ id @ X6) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X7 : subst, X8 : term] : ((X1 @ X7 @ X8)))) @ id))) => ! [X9 : term] : (! [X10 : term] : ((X0 @ id @ X10 @ id) => (X0 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)), 27.00/4.44 inference(rectify,[],[f3])). 27.00/4.44 thf(f7,plain,( 27.00/4.44 ~ (hoasinduction_lem3aaa = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ Y2 @ (push @ (sub @ Y5 @ Y4) @ (comp @ Y3 @ Y4))) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y5 @ Y4))) & ((sub @ (Y1 @ Y3 @ Y5) @ Y4) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y3)) @ Y4))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))), 27.00/4.44 inference(fool_elimination,[],[f6])). 27.00/4.44 thf(f8,plain,( 27.00/4.44 (hoasinduction_lem3aaa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ Y2 @ (push @ (sub @ Y5 @ Y4) @ (comp @ Y3 @ Y4))) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y5 @ Y4))) & ((sub @ (Y1 @ Y3 @ Y5) @ Y4) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y3)) @ Y4))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))), 27.00/4.44 inference(flattening,[],[f7])). 27.00/4.44 thf(f9,plain,( 27.00/4.44 (axmap = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) = X1) => (! [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) = X2) => ! [X4 : term,X5 : (term > $o),X6 : term,X7 : subst,X8 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | ~ (((X8 @ X4)) = $true))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) <=> (hoasapinj2 = $true)) & ((substmonoid_lthm = $true) <=> (! [X13 : subst] : (((comp @ id @ X13)) = X13) => (! [X14 : subst] : (((comp @ X14 @ id)) = X14) => (! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15))))) & (hoasinduction_lem3_gthm = $true) & (((d2subst @ d_id)) = sh) & ((pushprop_lem1 = $true) <=> ! [X17 : (term > $o),X18 : (term > $o),X19 : term,X20 : subst,X21 : term] : (~ (((X18 @ X21)) = $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true))) & (hoasapinj2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X22 : term] : (((sub @ X22 @ id)) = X22) => (! [X23 : term,X24 : (subst > term > subst > $o)] : (~ ! [X25 : term] : (~ (((X24 @ id @ X25 @ id)) = $true) | (((X24 @ id @ (sub @ X23 @ (push @ X25 @ id)) @ id)) = $true)) | (((X24 @ id @ (lam @ (sub @ X23 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X26 : (subst > term > term)] : (~ ! [X27 : term] : (~ (((X24 @ id @ X27 @ id)) = $true) | (((X24 @ id @ (X26 @ id @ X27) @ id)) = $true)) | (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true) | ~ ! [X29 : subst,X30 : term,X28 : subst] : (((X26 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28))) = ((sub @ (X26 @ X29 @ X30) @ X28))))) => ! [X31 : (subst > term > subst > $o),X32 : term] : (~ ! [X33 : term] : ((((X31 @ id @ (sub @ X32 @ (push @ X33 @ id)) @ id)) = $true) | ~ (((X31 @ id @ X33 @ id)) = $true)) | ~ ! [X34 : (subst > term > term)] : (~ ! [X35 : term] : ((((X31 @ id @ (X34 @ id @ X35) @ id)) = $true) | ~ (((X31 @ id @ X35 @ id)) = $true)) | ~ ! [X36 : subst,X37 : subst,X38 : term] : (((sub @ (X34 @ X36 @ X38) @ X37)) = ((X34 @ (comp @ X36 @ X37) @ (sub @ X38 @ X37)))) | ($true = ((X31 @ id @ (lam @ (X34 @ sh @ one)) @ id)))) | (((X31 @ id @ (lam @ X32) @ id)) = $true))))) & ((axidr = $true) <=> ! [X39 : subst] : (((comp @ X39 @ id)) = X39)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X41 : term,X43 : term,X42 : term,X40 : term] : ((((ap @ X42 @ X41)) != ((ap @ X43 @ X40))) | (X40 = X41)) => ! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))))) & (! [X48 : term,X49 : (subst > term > subst > $o)] : (~ ! [X50 : subst,X51 : subst,X52 : term,X53 : subst] : (~ (((X49 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50) @ X53)) = $true) | (((X49 @ X51 @ X52 @ (comp @ X50 @ X53))) = $true)) | ~ ! [X54 : term,X55 : subst,X56 : subst,X57 : subst] : (~ (((X49 @ X56 @ X54 @ (comp @ X57 @ X55))) = $true) | (((X49 @ (comp @ X56 @ X57) @ (sub @ X54 @ X57) @ X55)) = $true)) | ~ ! [X58 : (subst > term > term)] : ((((X49 @ id @ (lam @ (X58 @ sh @ one)) @ id)) = $true) | ~ ! [X60 : subst,X61 : term,X59 : subst] : (((X58 @ (comp @ X60 @ X59) @ (sub @ X61 @ X59))) = ((sub @ (X58 @ X60 @ X61) @ X59))) | ~ ! [X62 : term] : (~ (((X49 @ id @ X62 @ id)) = $true) | (((X49 @ id @ (X58 @ id @ X62) @ id)) = $true))) | ~ ! [X63 : term,X64 : term] : (~ (((X49 @ id @ X64 @ id)) = $true) | (((X49 @ id @ (ap @ (sub @ X64 @ id) @ X63) @ id)) = $true) | ~ (((X49 @ id @ X63 @ id)) = $true)) | (((X49 @ id @ X48 @ id)) = $true) | ~ ! [X65 : term] : (~ (((var @ (sub @ X65 @ id))) = $true) | (((X49 @ id @ X65 @ id)) = $true))) <=> (hoasinduction = $true)) & (termmset_gthm = $true) & ((induction = $true) <=> ! [X66 : term,X67 : (term > $o)] : (~ ! [X68 : term] : ((((X67 @ X68)) = $true) | ~ (((var @ X68)) = $true)) | (((X67 @ X66)) = $true) | ~ ! [X69 : term] : (~ (((X67 @ X69)) = $true) | (((X67 @ (lam @ X69))) = $true)) | ~ ! [X70 : term,X71 : term] : ((((X67 @ (ap @ X70 @ X71))) = $true) | ~ (((X67 @ X70)) = $true) | ~ (((X67 @ X71)) = $true)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar = $true) & ((! [X72 : (subst > term > subst > $o)] : ~ ! [X73 : (term > $o)] : ~ ! [X74 : term] : (((X73 @ X74)) = ((X72 @ id @ X74 @ id))) => (! [X75 : (term > $o),X76 : term] : (~ ! [X77 : term] : (~ (((var @ X77)) = $true) | (((X75 @ X77)) = $true)) | ~ ! [X78 : term] : (~ ! [X79 : term] : (~ (((X75 @ X79)) = $true) | (((X75 @ (sub @ X78 @ (push @ X79 @ id)))) = $true)) | (((X75 @ (lam @ X78))) = $true)) | (((X75 @ X76)) = $true) | ~ ! [X80 : term,X81 : term] : ((((X75 @ (ap @ X80 @ X81))) = $true) | ~ (((X75 @ X81)) = $true) | ~ (((X75 @ X80)) = $true))) => (! [X82 : term] : (((sub @ X82 @ id)) = X82) => (! [X83 : term,X84 : (subst > term > subst > $o),X85 : (term > $o)] : ((((X85 @ (lam @ X83))) = $true) | ~ ! [X86 : term] : ((((X85 @ (sub @ X83 @ (push @ X86 @ id)))) = $true) | ~ (((X85 @ X86)) = $true)) | ~ ! [X87 : term] : (((X84 @ id @ X87 @ id)) = ((X85 @ X87))) | ~ ! [X88 : (subst > term > term)] : (~ ! [X89 : term] : ((((X84 @ id @ (X88 @ id @ X89) @ id)) = $true) | ~ ($true = ((X84 @ id @ X89 @ id)))) | ~ ! [X91 : subst,X90 : term,X92 : subst] : (((X88 @ (comp @ X91 @ X92) @ (sub @ X90 @ X92))) = ((sub @ (X88 @ X91 @ X90) @ X92))) | (((X84 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true))) => ! [X93 : (subst > term > subst > $o),X94 : term] : (~ ! [X95 : subst,X96 : subst,X97 : subst,X98 : term] : ((((X93 @ (comp @ X95 @ X97) @ (sub @ X98 @ X97) @ X96)) = $true) | ~ (((X93 @ X95 @ X98 @ (comp @ X97 @ X96))) = $true)) | ~ ! [X99 : term,X100 : term] : (~ (((X93 @ id @ X100 @ id)) = $true) | ($true = ((X93 @ id @ (ap @ (sub @ X100 @ id) @ X99) @ id))) | ~ (((X93 @ id @ X99 @ id)) = $true)) | ~ ! [X101 : (subst > term > term)] : (~ ! [X102 : term,X104 : subst,X103 : subst] : (((sub @ (X101 @ X103 @ X102) @ X104)) = ((X101 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104)))) | (((X93 @ id @ (lam @ (X101 @ sh @ one)) @ id)) = $true) | ~ ! [X105 : term] : (~ (((X93 @ id @ X105 @ id)) = $true) | (((X93 @ id @ (X101 @ id @ X105) @ id)) = $true))) | (((X93 @ id @ X94 @ id)) = $true) | ~ ! [X106 : term] : (~ (((var @ (sub @ X106 @ id))) = $true) | (((X93 @ id @ X106 @ id)) = $true)) | ~ ! [X107 : subst,X108 : term,X109 : subst,X110 : subst] : ((((X93 @ X107 @ X108 @ (comp @ X110 @ X109))) = $true) | ~ ($true = ((X93 @ (comp @ X107 @ X110) @ (sub @ X108 @ X110) @ X109))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((axscons = $true) <=> ! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111)) & (hoasapnotvar_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ~ (lamnotap = $true) & (! [X112 : term] : ~ ! [X113 : (subst > term > term)] : ~ ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) <=> (laminj = $true)) & ((induction2_lthm = $true) <=> (! [X118 : term] : (((sub @ X118 @ id)) = X118) => (! [X119 : term,X120 : subst,X121 : (term > $o)] : (~ ! [X122 : term] : (~ ! [X123 : term] : (~ (((X121 @ X123)) = $true) | (((X121 @ (sub @ X122 @ (push @ X123 @ id)))) = $true)) | (((X121 @ (lam @ X122))) = $true)) | ~ ! [X124 : term] : ((((X121 @ (sub @ X124 @ X120))) = $true) | ~ (((var @ X124)) = $true)) | (((X121 @ (sub @ X119 @ X120))) = $true) | ~ ! [X125 : term,X126 : term] : (~ (((X121 @ X126)) = $true) | ~ (((X121 @ X125)) = $true) | (((X121 @ (ap @ X126 @ X125))) = $true))) => ! [X127 : (term > $o),X128 : term] : (~ ! [X129 : term] : ((((X127 @ X129)) = $true) | ~ ($true = ((var @ X129)))) | (((X127 @ X128)) = $true) | ~ ! [X130 : term] : (~ ! [X131 : term] : (~ (((X127 @ X131)) = $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) | (((X127 @ (lam @ X130))) = $true)) | ~ ! [X132 : term,X133 : term] : (~ (((X127 @ X132)) = $true) | (((X127 @ (ap @ X133 @ X132))) = $true) | ~ (((X127 @ X133)) = $true)))))) & (pushprop_lem3v2_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X134 : term] : (((sub @ X134 @ id)) = X134) => (! [X135 : term,X138 : term,X137 : term,X136 : term] : ((X135 = X137) | (((ap @ X137 @ X138)) != ((ap @ X135 @ X136)))) => ! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))))) <=> (hoasapinj1_lthm = $true)) & (substmonoid_gthm = $true) & (induction2_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (! [X145 : term,X143 : (term > $o),X144 : subst] : ~ ! [X146 : (term > $o)] : ~ ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X148 : term,X149 : (subst > term > subst > $o)] : (~ ! [X150 : term] : ((((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true) | ~ (((X149 @ id @ X150 @ id)) = $true)) | (((X149 @ id @ (lam @ X148) @ id)) = $true) | ~ ! [X151 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X151 @ sh @ one)) @ id)) = $true) | ~ ! [X152 : term] : ((((X149 @ id @ (X151 @ id @ X152) @ id)) = $true) | ~ (((X149 @ id @ X152 @ id)) = $true)) | ~ ! [X155 : subst,X153 : term,X154 : subst] : (((sub @ (X151 @ X155 @ X153) @ X154)) = ((X151 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154))))))) & (hoaslaminj_gthm = $true) & (! [X157 : (term > $o),X158 : term,X156 : subst] : ~ ! [X159 : (term > $o)] : ~ ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160))) <=> (pushprop_lem0_lthm = $true)) & ((apinj1 = $true) <=> ! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164))) & ((! [X165 : term] : (((sub @ X165 @ id)) = X165) => ! [X166 : (subst > term > subst > $o),X167 : (term > $o),X168 : term] : (~ ! [X169 : term,X170 : subst,X171 : subst,X172 : subst] : (~ (((X166 @ X170 @ X169 @ (comp @ X172 @ X171))) = $true) | (((X166 @ (comp @ X170 @ X172) @ (sub @ X169 @ X172) @ X171)) = $true)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X176 : term,X175 : subst,X174 : subst] : (((X173 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174))) = ((sub @ (X173 @ X175 @ X176) @ X174))) | (((X166 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X166 @ id @ (X173 @ id @ X177) @ id)) = $true) | ~ (((X166 @ id @ X177 @ id)) = $true))) | ~ ! [X178 : term] : (~ (((X167 @ X178)) = $true) | (((X167 @ (sub @ X168 @ (push @ X178 @ id)))) = $true)) | (((X167 @ (lam @ X168))) = $true) | ~ ! [X179 : term,X180 : subst,X181 : subst,X182 : subst] : (~ ($true = ((X166 @ (comp @ X181 @ X182) @ (sub @ X179 @ X182) @ X180))) | (((X166 @ X181 @ X179 @ (comp @ X182 @ X180))) = $true)) | ~ ! [X183 : term] : (((X167 @ X183)) = ((X166 @ id @ X183 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X184 : (subst > term > subst > $o)] : ~ ! [X185 : (term > $o)] : ~ ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186))) <=> (hoasinduction_lem0 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (axassoc = $true) & ((termmset_lthm = $true) <=> (! [X187 : term] : (((sub @ X187 @ id)) = X187) => ! [X188 : term] : (((sub @ X188 @ id)) = X188))) & (! [X190 : term,X191 : term,X189 : (subst > term > term)] : ((((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one)))) | ~ ! [X193 : term,X194 : subst,X192 : subst] : (((sub @ (X189 @ X192 @ X193) @ X194)) = ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194))))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X195 : (subst > term > subst > $o)] : ~ ! [X196 : (term > $o)] : ~ ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197)))) & ((hoaslaminj = $true) <=> ! [X199 : subst,X198 : term,X200 : (subst > term > term),X201 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | ~ ! [X206 : subst,X207 : subst,X205 : term] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X200 @ X206 @ X205) @ X207))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ~ ! [X202 : term,X204 : subst,X203 : subst] : (((sub @ (X201 @ X204 @ X202) @ X203)) = ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X208 : term,X209 : (subst > term > subst > $o)] : (~ ! [X210 : (subst > term > term),X211 : term] : (~ ! [X212 : term] : ((((X209 @ id @ (X210 @ id @ X212) @ id)) = $true) | ~ (((X209 @ id @ X212 @ id)) = $true)) | ~ ! [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) = ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) | (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) = $true) | ~ ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) = ((sub @ (X210 @ X218 @ X216) @ X217)))) | (((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X219 : term] : (~ (((X209 @ id @ X219 @ id)) = $true) | (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) = $true)))) & ! [X220 : d_subst] : (d_id = X220) & ((hoasinduction_lthm = $true) <=> (! [X221 : (term > $o),X222 : term] : ((((X221 @ X222)) = $true) | ~ ! [X223 : term] : (~ ! [X224 : term] : ((((X221 @ (sub @ X223 @ (push @ X224 @ id)))) = $true) | ~ (((X221 @ X224)) = $true)) | (((X221 @ (lam @ X223))) = $true)) | ~ ! [X225 : term,X226 : term] : (~ (((X221 @ X225)) = $true) | ~ (((X221 @ X226)) = $true) | (((X221 @ (ap @ X225 @ X226))) = $true)) | ~ ! [X227 : term] : (~ (((var @ X227)) = $true) | (((X221 @ X227)) = $true))) => (! [X228 : term,X229 : term,X230 : (subst > term > subst > $o)] : (~ (((X230 @ id @ X228 @ id)) = $true) | ~ ! [X231 : term,X232 : term] : (~ (((X230 @ id @ X231 @ id)) = $true) | (((X230 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)) = $true) | ~ (((X230 @ id @ X232 @ id)) = $true)) | ~ ! [X233 : subst,X234 : term,X235 : subst,X236 : subst] : ((((X230 @ X233 @ X234 @ (comp @ X235 @ X236))) = $true) | ~ (((X230 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X236)) = $true)) | ~ (((X230 @ id @ X229 @ id)) = $true) | (((X230 @ id @ (ap @ X229 @ X228) @ id)) = $true) | ~ ! [X237 : subst,X238 : subst,X239 : term,X240 : subst] : (~ (((X230 @ X238 @ X239 @ (comp @ X240 @ X237))) = $true) | (((X230 @ (comp @ X238 @ X240) @ (sub @ X239 @ X240) @ X237)) = $true))) => (! [X241 : term,X242 : (subst > term > subst > $o)] : (~ ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : ((((X242 @ X246 @ X245 @ (comp @ X243 @ X244))) = $true) | ~ (((X242 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) = $true)) | ~ ! [X247 : subst,X248 : term,X249 : subst,X250 : subst] : ((((X242 @ (comp @ X250 @ X247) @ (sub @ X248 @ X247) @ X249)) = $true) | ~ (((X242 @ X250 @ X248 @ (comp @ X247 @ X249))) = $true)) | ~ ! [X251 : term] : (~ (((X242 @ id @ X251 @ id)) = $true) | (((X242 @ id @ (sub @ X241 @ (push @ X251 @ id)) @ id)) = $true)) | ~ ! [X252 : (subst > term > term)] : ((((X242 @ id @ (lam @ (X252 @ sh @ one)) @ id)) = $true) | ~ ! [X253 : term] : (~ (((X242 @ id @ X253 @ id)) = $true) | ($true = ((X242 @ id @ (X252 @ id @ X253) @ id)))) | ~ ! [X255 : subst,X254 : term,X256 : subst] : (((sub @ (X252 @ X256 @ X254) @ X255)) = ((X252 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255))))) | (((X242 @ id @ (lam @ X241) @ id)) = $true)) => ! [X257 : term,X258 : (subst > term > subst > $o)] : (~ ! [X259 : (subst > term > term)] : ((((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id)) = $true) | ~ ! [X260 : term] : ((((X258 @ id @ (X259 @ id @ X260) @ id)) = $true) | ~ (((X258 @ id @ X260 @ id)) = $true)) | ~ ! [X263 : subst,X261 : subst,X262 : term] : (((X259 @ (comp @ X263 @ X261) @ (sub @ X262 @ X261))) = ((sub @ (X259 @ X263 @ X262) @ X261)))) | ~ ! [X264 : term] : ((((X258 @ id @ X264 @ id)) = $true) | ~ (((var @ (sub @ X264 @ id))) = $true)) | ~ ! [X265 : subst,X266 : subst,X267 : subst,X268 : term] : (~ (((X258 @ (comp @ X266 @ X265) @ (sub @ X268 @ X265) @ X267)) = $true) | ($true = ((X258 @ X266 @ X268 @ (comp @ X265 @ X267))))) | ($true = ((X258 @ id @ X257 @ id))) | ~ ! [X269 : subst,X270 : term,X271 : subst,X272 : subst] : ((((X258 @ (comp @ X271 @ X272) @ (sub @ X270 @ X272) @ X269)) = $true) | ~ (((X258 @ X271 @ X270 @ (comp @ X272 @ X269))) = $true)) | ~ ! [X273 : term,X274 : term] : (~ (((X258 @ id @ X274 @ id)) = $true) | (((X258 @ id @ (ap @ (sub @ X274 @ id) @ X273) @ id)) = $true) | ~ (((X258 @ id @ X273 @ id)) = $true))))))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X275 : term,X276 : (subst > term > subst > $o)] : (~ ! [X277 : term] : (~ (((X276 @ id @ X277 @ id)) = $true) | (((X276 @ id @ (sub @ X275 @ (push @ X277 @ id)) @ id)) = $true)) | ~ ! [X278 : (subst > term > term)] : (~ ! [X279 : term] : ((((X276 @ id @ (X278 @ id @ X279) @ id)) = $true) | ~ (((X276 @ id @ X279 @ id)) = $true)) | (((X276 @ id @ (lam @ (X278 @ sh @ one)) @ id)) = $true) | ~ ! [X282 : subst,X280 : term,X281 : subst] : (((sub @ (X278 @ X282 @ X280) @ X281)) = ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281))))) | (((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true))) & (! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) <=> (shinj = $true)) & (pushprop_lthm = $true) & ((! [X285 : term] : (((sub @ X285 @ id)) = X285) => (! [X286 : (subst > term > subst > $o),X287 : term] : (~ ! [X288 : (subst > term > term)] : (~ ! [X289 : term] : (~ (((X286 @ id @ X289 @ id)) = $true) | (((X286 @ id @ (X288 @ id @ X289) @ id)) = $true)) | (((X286 @ id @ (lam @ (X288 @ sh @ one)) @ id)) = $true) | ~ ! [X292 : subst,X291 : term,X290 : subst] : (((X288 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290))) = ((sub @ (X288 @ X292 @ X291) @ X290)))) | ~ ! [X293 : term] : ((((X286 @ id @ (sub @ X287 @ (push @ X293 @ id)) @ id)) = $true) | ~ (((X286 @ id @ X293 @ id)) = $true)) | (((X286 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id)) = $true)) => ! [X294 : term,X295 : (subst > term > subst > $o)] : (~ ! [X296 : term] : ((((X295 @ id @ (sub @ X294 @ (push @ X296 @ id)) @ id)) = $true) | ~ (((X295 @ id @ X296 @ id)) = $true)) | (((X295 @ id @ (lam @ X294) @ id)) = $true) | ~ ! [X297 : subst,X298 : term,X299 : subst,X300 : subst] : ((((X295 @ (comp @ X300 @ X299) @ (sub @ X298 @ X299) @ X297)) = $true) | ~ (((X295 @ X300 @ X298 @ (comp @ X299 @ X297))) = $true)) | ~ ! [X301 : (subst > term > term)] : (~ ! [X302 : term] : ((((X295 @ id @ (X301 @ id @ X302) @ id)) = $true) | ~ (((X295 @ id @ X302 @ id)) = $true)) | ($true = ((X295 @ id @ (lam @ (X301 @ sh @ one)) @ id))) | ~ ! [X303 : subst,X305 : subst,X304 : term] : (((sub @ (X301 @ X303 @ X304) @ X305)) = ((X301 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305))))) | ~ ! [X306 : subst,X307 : subst,X308 : subst,X309 : term] : ((((X295 @ X307 @ X309 @ (comp @ X308 @ X306))) = $true) | ~ (((X295 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X310 : term] : ~ ! [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) != ((X311 @ sh @ one)))) & ((axvarid = $true) <=> ! [X312 : term] : (((sub @ X312 @ id)) = X312)) & (hoaslamnotap_gthm = $true) & ! [X313 : d_term] : (d_one = X313) & (ulamvarsh = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X315 : subst,X314 : term] : (((sub @ one @ (push @ X314 @ X315))) = X314) => ! [X316 : (term > $o),X317 : term,X318 : (term > $o),X319 : subst] : (~ ! [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) = ((X316 @ X320))) | (((X316 @ one)) = $true) | ~ (((X318 @ X317)) = $true)))) & (hoasinduction_lem1_lthm = $true) & (! [X321 : term] : ~ ! [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) != ((X322 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (hoaslamnotvar_lthm = $true) & ((apinj2 = $true) <=> ! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324))) & ((hoasapinj1 = $true) <=> ! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330))) & (pushprop = $true) & (hoaslamnotap_lthm = $true) & ((! [X331 : term,X332 : subst] : (((sub @ one @ (push @ X331 @ X332))) = X331) => (! [X334 : term,X333 : subst] : (((comp @ sh @ (push @ X334 @ X333))) = X333) => (! [X335 : subst] : (((comp @ X335 @ id)) = X335) => (! [X336 : term,X337 : (term > $o)] : (~ ! [X338 : term] : (~ (((X337 @ X338)) = $true) | (((X337 @ (lam @ X338))) = $true)) | (((X337 @ X336)) = $true) | ~ ! [X339 : term] : (~ ($true = ((var @ X339))) | (((X337 @ X339)) = $true)) | ~ ! [X340 : term,X341 : term] : (~ (((X337 @ X340)) = $true) | (((X337 @ (ap @ X340 @ X341))) = $true) | ~ (((X337 @ X341)) = $true))) => ! [X342 : term,X343 : (term > $o),X344 : subst] : (~ ! [X345 : term] : (~ (((var @ X345)) = $true) | (((X343 @ (sub @ X345 @ X344))) = $true)) | ~ ! [X346 : term] : (($true = ((X343 @ (lam @ X346)))) | ~ ! [X347 : term] : (($true = ((X343 @ (sub @ X346 @ (push @ X347 @ id))))) | ~ (((X343 @ X347)) = $true))) | ~ ! [X348 : term,X349 : term] : (~ (((X343 @ X349)) = $true) | ~ (((X343 @ X348)) = $true) | (((X343 @ (ap @ X349 @ X348))) = $true)) | (((X343 @ (sub @ X342 @ X344))) = $true)))))) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X350 : term,X351 : (term > $o),X352 : (subst > term > subst > $o)] : ((((X351 @ (lam @ X350))) = $true) | ~ ! [X353 : term] : (((X352 @ id @ X353 @ id)) = ((X351 @ X353))) | ~ ! [X354 : term] : (~ (((X351 @ X354)) = $true) | (((X351 @ (sub @ X350 @ (push @ X354 @ id)))) = $true)) | ~ ! [X355 : subst,X356 : subst,X357 : term,X358 : subst] : (~ (((X352 @ X358 @ X357 @ (comp @ X356 @ X355))) = $true) | ($true = ((X352 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356) @ X355)))) | ~ ! [X359 : subst,X360 : term,X361 : subst,X362 : subst] : (($true = ((X352 @ X362 @ X360 @ (comp @ X361 @ X359)))) | ~ (((X352 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359)) = $true)) | ~ ! [X363 : (subst > term > term)] : (~ ! [X365 : term,X364 : subst,X366 : subst] : (((sub @ (X363 @ X364 @ X365) @ X366)) = ((X363 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366)))) | (((X352 @ id @ (lam @ (X363 @ sh @ one)) @ id)) = $true) | ~ ! [X367 : term] : ((((X352 @ id @ (X363 @ id @ X367) @ id)) = $true) | ~ (((X352 @ id @ X367 @ id)) = $true))))) & (lamnotvar = $true) & ~ (ulamvar1 = $true) & ((! [X368 : (subst > term > subst > $o)] : ~ ! [X369 : (term > $o)] : ~ ! [X370 : term] : (((X368 @ id @ X370 @ id)) = ((X369 @ X370))) => (! [X371 : term,X372 : (term > $o)] : ((((X372 @ X371)) = $true) | ~ ! [X373 : term,X374 : term] : ((((X372 @ (ap @ X374 @ X373))) = $true) | ~ (((X372 @ X374)) = $true) | ~ (((X372 @ X373)) = $true)) | ~ ! [X375 : term] : (~ (((var @ X375)) = $true) | (((X372 @ X375)) = $true)) | ~ ! [X376 : term] : ((((X372 @ (lam @ X376))) = $true) | ~ ! [X377 : term] : (~ (((X372 @ X377)) = $true) | (((X372 @ (sub @ X376 @ (push @ X377 @ id)))) = $true)))) => (! [X378 : term] : (((sub @ X378 @ id)) = X378) => (! [X379 : (subst > term > subst > $o),X380 : (term > $o),X381 : term] : (~ ! [X382 : (subst > term > term)] : (~ ! [X384 : subst,X383 : subst,X385 : term] : (((X382 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383))) = ((sub @ (X382 @ X384 @ X385) @ X383))) | ~ ! [X386 : term] : ((((X379 @ id @ (X382 @ id @ X386) @ id)) = $true) | ~ (((X379 @ id @ X386 @ id)) = $true)) | (((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true)) | (((X380 @ (lam @ X381))) = $true) | ~ ! [X387 : term] : (((X380 @ X387)) = ((X379 @ id @ X387 @ id))) | ~ ! [X388 : term] : (($true = ((X380 @ (sub @ X381 @ (push @ X388 @ id))))) | ~ (((X380 @ X388)) = $true))) => ! [X389 : (subst > term > subst > $o),X390 : term] : ((((X389 @ id @ X390 @ id)) = $true) | ~ ! [X391 : (subst > term > term)] : ((((X389 @ id @ (lam @ (X391 @ sh @ one)) @ id)) = $true) | ~ ! [X392 : subst,X393 : term,X394 : subst] : (((X391 @ (comp @ X392 @ X394) @ (sub @ X393 @ X394))) = ((sub @ (X391 @ X392 @ X393) @ X394))) | ~ ! [X395 : term] : (~ ($true = ((X389 @ id @ X395 @ id))) | (((X389 @ id @ (X391 @ id @ X395) @ id)) = $true))) | ~ ! [X396 : term,X397 : term] : (~ (((X389 @ id @ X397 @ id)) = $true) | (((X389 @ id @ (ap @ (sub @ X396 @ id) @ X397) @ id)) = $true) | ~ (((X389 @ id @ X396 @ id)) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X398 : (subst > term > subst > $o),X399 : term] : ((((X398 @ id @ X399 @ id)) = $true) | ~ ! [X400 : term,X401 : term] : (~ (((X398 @ id @ X401 @ id)) = $true) | ~ (((X398 @ id @ X400 @ id)) = $true) | (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) = $true)) | ~ ! [X402 : (subst > term > term)] : ((((X398 @ id @ (lam @ (X402 @ sh @ one)) @ id)) = $true) | ~ ! [X405 : subst,X403 : subst,X404 : term] : (((sub @ (X402 @ X405 @ X404) @ X403)) = ((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403)))) | ~ ! [X406 : term] : (~ ($true = ((X398 @ id @ X406 @ id))) | (((X398 @ id @ (X402 @ id @ X406) @ id)) = $true)))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X407 : term] : ~ ! [X408 : (subst > term > term)] : ~ ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (axapp = $true) & ((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) <=> (substmonoid = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X413 : (subst > term > subst > $o),X414 : (term > $o),X415 : term,X416 : term] : (~ ! [X417 : term,X418 : term] : (~ (((X413 @ id @ X417 @ id)) = $true) | ~ (((X413 @ id @ X418 @ id)) = $true) | (((X413 @ id @ (ap @ (sub @ X418 @ id) @ X417) @ id)) = $true)) | ~ ! [X419 : subst,X420 : term,X421 : subst,X422 : subst] : ((((X413 @ (comp @ X421 @ X422) @ (sub @ X420 @ X422) @ X419)) = $true) | ~ (((X413 @ X421 @ X420 @ (comp @ X422 @ X419))) = $true)) | ~ (((X414 @ X415)) = $true) | ~ ! [X423 : term,X424 : subst,X425 : subst,X426 : subst] : (~ (((X413 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)) = $true) | (((X413 @ X424 @ X423 @ (comp @ X425 @ X426))) = $true)) | (((X414 @ (ap @ X415 @ X416))) = $true) | ~ (((X414 @ X416)) = $true) | ~ ! [X427 : term] : (((X413 @ id @ X427 @ id)) = ((X414 @ X427)))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X428 : term,X429 : subst] : (((sub @ one @ (push @ X428 @ X429))) = X428) => (! [X430 : term,X431 : subst] : (((comp @ sh @ (push @ X430 @ X431))) = X431) => (! [X432 : term,X433 : term] : ((X432 = X433) | (((lam @ X433)) != ((lam @ X432)))) => ! [X437 : subst,X436 : term,X434 : (subst > term > term),X435 : (subst > term > term)] : ((((lam @ (X435 @ sh @ one))) != ((lam @ (X434 @ sh @ one)))) | ~ ! [X442 : subst,X441 : term,X443 : subst] : (((X435 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))) = ((sub @ (X435 @ X443 @ X441) @ X442))) | ~ ! [X439 : term,X440 : subst,X438 : subst] : (((sub @ (X434 @ X440 @ X439) @ X438)) = ((X434 @ (comp @ X440 @ X438) @ (sub @ X439 @ X438)))) | (((X434 @ X437 @ X436)) = ((X435 @ X437 @ X436)))))))) & (hoasapnotvar = $true) & (one = ((d2term @ d_one))) & ((termmset = $true) <=> ! [X444 : term] : (((sub @ X444 @ id)) = X444)) & (! [X445 : term,X446 : (term > $o),X447 : subst] : (~ ! [X448 : term] : (~ (((var @ X448)) = $true) | (((X446 @ (sub @ X448 @ X447))) = $true)) | ($true = ((X446 @ (sub @ X445 @ X447)))) | ~ ! [X449 : term,X450 : term] : (($true = ((X446 @ (ap @ X449 @ X450)))) | ~ (((X446 @ X449)) = $true) | ~ (((X446 @ X450)) = $true)) | ~ ! [X451 : term] : (~ ! [X452 : term] : (~ (((X446 @ X452)) = $true) | (((X446 @ (sub @ X451 @ (push @ X452 @ id)))) = $true)) | (((X446 @ (lam @ X451))) = $true))) <=> (induction2lem = $true)) & (! [X453 : (subst > term > subst > $o),X454 : term] : (~ ! [X455 : (subst > term > term)] : (~ ! [X456 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X456 @ X458) @ X457)) = ((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457)))) | (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true) | ~ ! [X459 : term] : ((((X453 @ id @ (X455 @ id @ X459) @ id)) = $true) | ~ (((X453 @ id @ X459 @ id)) = $true))) | (((X453 @ id @ (lam @ (sub @ X454 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X460 : term] : ((((X453 @ id @ (sub @ X454 @ (push @ X460 @ id)) @ id)) = $true) | ~ (((X453 @ id @ X460 @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_gthm = $true) & (axabs = $true) & ((axshiftcons = $true) <=> ! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462)) & (! [X463 : subst] : (((comp @ id @ X463)) = X463) <=> (axidl = $true)) & (! [X464 : (term > $o),X465 : term,X466 : (subst > term > subst > $o)] : (~ ! [X467 : term] : ((((X464 @ (sub @ X465 @ (push @ X467 @ id)))) = $true) | ~ ($true = ((X464 @ X467)))) | (((X464 @ (lam @ X465))) = $true) | ~ ! [X468 : term] : (((X466 @ id @ X468 @ id)) = ((X464 @ X468))) | ~ ! [X469 : (subst > term > term)] : ((((X466 @ id @ (lam @ (X469 @ sh @ one)) @ id)) = $true) | ~ ! [X470 : term] : (($true = ((X466 @ id @ (X469 @ id @ X470) @ id))) | ~ (((X466 @ id @ X470 @ id)) = $true)) | ~ ! [X473 : subst,X471 : term,X472 : subst] : (((sub @ (X469 @ X473 @ X471) @ X472)) = ((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472)))))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X474 : term,X475 : subst,X476 : (term > $o),X477 : (term > $o)] : ((((X477 @ one)) = $true) | ~ ! [X478 : term] : (((X477 @ X478)) = ((X476 @ (sub @ X478 @ (push @ X474 @ X475))))) | ~ (((X476 @ X474)) = $true))) & (pushprop_lem0_gthm = $true) & ! [X480 : d_subst,X479 : d_subst] : ((((d2subst @ X480)) = ((d2subst @ X479))) => (X479 = X480)) & (pushprop_lem1v2_gthm = $true) & ! [X481 : d_term,X482 : d_term] : ((((d2term @ X482)) = ((d2term @ X481))) => (X481 = X482)) & ((! [X483 : term] : ~ ! [X484 : (subst > term > term)] : ~ ! [X485 : subst,X486 : term] : (((X484 @ X485 @ X486)) = ((sub @ X483 @ (push @ X486 @ X485)))) => (! [X487 : term] : (((sub @ X487 @ id)) = X487) => ! [X488 : term,X489 : (term > $o),X490 : (subst > term > subst > $o)] : (~ ! [X491 : term] : (((X490 @ id @ X491 @ id)) = ((X489 @ X491))) | ~ ! [X492 : (subst > term > term)] : (~ ! [X495 : subst,X493 : term,X494 : subst] : (((sub @ (X492 @ X495 @ X493) @ X494)) = ((X492 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494)))) | ~ ! [X496 : term] : ((((X490 @ id @ (X492 @ id @ X496) @ id)) = $true) | ~ ($true = ((X490 @ id @ X496 @ id)))) | (((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id)) = $true)) | ~ ! [X497 : term] : (~ (((X489 @ X497)) = $true) | ($true = ((X489 @ (sub @ X488 @ (push @ X497 @ id)))))) | (((X489 @ (lam @ X488))) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem1_gthm = $true) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & (! [X500 : term,X501 : (subst > term > subst > $o)] : (~ ! [X502 : subst,X503 : subst,X504 : subst,X505 : term] : (~ (((X501 @ X502 @ X505 @ (comp @ X504 @ X503))) = $true) | (((X501 @ (comp @ X502 @ X504) @ (sub @ X505 @ X504) @ X503)) = $true)) | ~ ! [X506 : term,X507 : subst,X508 : subst,X509 : subst] : (~ (((X501 @ (comp @ X507 @ X509) @ (sub @ X506 @ X509) @ X508)) = $true) | ($true = ((X501 @ X507 @ X506 @ (comp @ X509 @ X508))))) | ~ ! [X510 : (subst > term > term)] : (~ ! [X513 : subst,X511 : subst,X512 : term] : (((X510 @ (comp @ X511 @ X513) @ (sub @ X512 @ X513))) = ((sub @ (X510 @ X511 @ X512) @ X513))) | ~ ! [X514 : term] : (~ (((X501 @ id @ X514 @ id)) = $true) | (((X501 @ id @ (X510 @ id @ X514) @ id)) = $true)) | (((X501 @ id @ (lam @ (X510 @ sh @ one)) @ id)) = $true)) | ~ ! [X515 : term] : (($true = ((X501 @ id @ (sub @ X500 @ (push @ X515 @ id)) @ id))) | ~ (((X501 @ id @ X515 @ id)) = $true)) | (((X501 @ id @ (lam @ X500) @ id)) = $true)) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) <=> ! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516)) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) <=> ! [X518 : (term > $o),X519 : term] : (~ ! [X520 : term] : ((((X518 @ (lam @ X520))) = $true) | ~ ! [X521 : term] : (~ (((X518 @ X521)) = $true) | (((X518 @ (sub @ X520 @ (push @ X521 @ id)))) = $true))) | ~ ! [X522 : term] : ((((X518 @ X522)) = $true) | ~ (((var @ X522)) = $true)) | ~ ! [X523 : term,X524 : term] : (~ (((X518 @ X523)) = $true) | (((X518 @ (ap @ X523 @ X524))) = $true) | ~ (((X518 @ X524)) = $true)) | (((X518 @ X519)) = $true))) & ((hoasinduction_lem2 = $true) <=> ! [X525 : term,X526 : (subst > term > subst > $o),X527 : term] : (~ ! [X528 : subst,X529 : subst,X530 : subst,X531 : term] : (~ (((X526 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529) @ X528)) = $true) | (((X526 @ X530 @ X531 @ (comp @ X529 @ X528))) = $true)) | ~ ! [X532 : subst,X533 : subst,X534 : subst,X535 : term] : ((((X526 @ (comp @ X532 @ X534) @ (sub @ X535 @ X534) @ X533)) = $true) | ~ (((X526 @ X532 @ X535 @ (comp @ X534 @ X533))) = $true)) | ~ (((X526 @ id @ X527 @ id)) = $true) | ~ (((X526 @ id @ X525 @ id)) = $true) | (((X526 @ id @ (ap @ X525 @ X527) @ id)) = $true) | ~ ! [X536 : term,X537 : term] : (~ (((X526 @ id @ X536 @ id)) = $true) | (((X526 @ id @ (ap @ (sub @ X537 @ id) @ X536) @ id)) = $true) | ~ (((X526 @ id @ X537 @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem1 = $true) & (ulamvarind = $true) & (pushprop_gthm = $true) & (((d2subst @ d_id)) = id) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & (apnotvar = $true) & (axvarshift = $true)), 27.00/4.44 inference(rectify,[],[f5])). 27.00/4.44 thf(f10,plain,( 27.00/4.44 (hoasapinj2_gthm = $true) & (! [X463 : subst] : (((comp @ id @ X463)) = X463) <=> (axidl = $true)) & (one = ((d2term @ d_one))) & (hoasinduction_lem2_lthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (ulamvarind = $true) & ((! [X22 : term] : (((sub @ X22 @ id)) = X22) => (! [X23 : term,X24 : (subst > term > subst > $o)] : (~ ! [X25 : term] : ((((X24 @ id @ (sub @ X23 @ (push @ X25 @ id)) @ id)) = $true) | (((X24 @ id @ X25 @ id)) != $true)) | ~ ! [X26 : (subst > term > term)] : (~ ! [X27 : term] : ((((X24 @ id @ (X26 @ id @ X27) @ id)) = $true) | (((X24 @ id @ X27 @ id)) != $true)) | (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true) | ~ ! [X29 : subst,X30 : term,X28 : subst] : (((X26 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28))) = ((sub @ (X26 @ X29 @ X30) @ X28)))) | (((X24 @ id @ (lam @ (sub @ X23 @ (push @ one @ sh))) @ id)) = $true)) => ! [X31 : (subst > term > subst > $o),X32 : term] : (~ ! [X33 : term] : ((((X31 @ id @ X33 @ id)) != $true) | (((X31 @ id @ (sub @ X32 @ (push @ X33 @ id)) @ id)) = $true)) | ~ ! [X34 : (subst > term > term)] : (~ ! [X35 : term] : ((((X31 @ id @ X35 @ id)) != $true) | (((X31 @ id @ (X34 @ id @ X35) @ id)) = $true)) | ~ ! [X36 : subst,X37 : subst,X38 : term] : (((sub @ (X34 @ X36 @ X38) @ X37)) = ((X34 @ (comp @ X36 @ X37) @ (sub @ X38 @ X37)))) | ($true = ((X31 @ id @ (lam @ (X34 @ sh @ one)) @ id)))) | (((X31 @ id @ (lam @ X32) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X275 : term,X276 : (subst > term > subst > $o)] : ((((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X277 : term] : ((((X276 @ id @ X277 @ id)) != $true) | (((X276 @ id @ (sub @ X275 @ (push @ X277 @ id)) @ id)) = $true)) | ~ ! [X278 : (subst > term > term)] : ((((X276 @ id @ (lam @ (X278 @ sh @ one)) @ id)) = $true) | ~ ! [X282 : subst,X280 : term,X281 : subst] : (((sub @ (X278 @ X282 @ X280) @ X281)) = ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281)))) | ~ ! [X279 : term] : ((((X276 @ id @ (X278 @ id @ X279) @ id)) = $true) | (((X276 @ id @ X279 @ id)) != $true))))) & (((d2subst @ d_id)) = sh) & (! [X407 : term] : ~ ! [X408 : (subst > term > term)] : ~ ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & ((axvarid = $true) <=> ! [X312 : term] : (((sub @ X312 @ id)) = X312)) & (! [X190 : term,X191 : term,X189 : (subst > term > term)] : ((((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one)))) | ~ ! [X193 : term,X194 : subst,X192 : subst] : (((sub @ (X189 @ X192 @ X193) @ X194)) = ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194))))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem2_gthm = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X72 : (subst > term > subst > $o)] : ~ ! [X73 : (term > $o)] : ~ ! [X74 : term] : (((X73 @ X74)) = ((X72 @ id @ X74 @ id))) => (! [X75 : (term > $o),X76 : term] : (~ ! [X78 : term] : ((((X75 @ (lam @ X78))) = $true) | ~ ! [X79 : term] : ((((X75 @ (sub @ X78 @ (push @ X79 @ id)))) = $true) | (((X75 @ X79)) != $true))) | ~ ! [X80 : term,X81 : term] : ((((X75 @ X80)) != $true) | (((X75 @ (ap @ X80 @ X81))) = $true) | (((X75 @ X81)) != $true)) | (((X75 @ X76)) = $true) | ~ ! [X77 : term] : ((((var @ X77)) != $true) | (((X75 @ X77)) = $true))) => (! [X82 : term] : (((sub @ X82 @ id)) = X82) => (! [X84 : (subst > term > subst > $o),X85 : (term > $o),X83 : term] : ((((X85 @ (lam @ X83))) = $true) | ~ ! [X88 : (subst > term > term)] : (~ ! [X89 : term] : ((((X84 @ id @ (X88 @ id @ X89) @ id)) = $true) | ($true != ((X84 @ id @ X89 @ id)))) | ~ ! [X91 : subst,X90 : term,X92 : subst] : (((X88 @ (comp @ X91 @ X92) @ (sub @ X90 @ X92))) = ((sub @ (X88 @ X91 @ X90) @ X92))) | (((X84 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true)) | ~ ! [X87 : term] : (((X84 @ id @ X87 @ id)) = ((X85 @ X87))) | ~ ! [X86 : term] : ((((X85 @ X86)) != $true) | (((X85 @ (sub @ X83 @ (push @ X86 @ id)))) = $true))) => ! [X93 : (subst > term > subst > $o),X94 : term] : (~ ! [X109 : subst,X108 : term,X110 : subst,X107 : subst] : (($true != ((X93 @ (comp @ X107 @ X110) @ (sub @ X108 @ X110) @ X109))) | (((X93 @ X107 @ X108 @ (comp @ X110 @ X109))) = $true)) | (((X93 @ id @ X94 @ id)) = $true) | ~ ! [X98 : term,X97 : subst,X96 : subst,X95 : subst] : ((((X93 @ (comp @ X95 @ X97) @ (sub @ X98 @ X97) @ X96)) = $true) | (((X93 @ X95 @ X98 @ (comp @ X97 @ X96))) != $true)) | ~ ! [X99 : term,X100 : term] : (($true = ((X93 @ id @ (ap @ (sub @ X100 @ id) @ X99) @ id))) | (((X93 @ id @ X99 @ id)) != $true) | (((X93 @ id @ X100 @ id)) != $true)) | ~ ! [X106 : term] : ((((var @ (sub @ X106 @ id))) != $true) | (((X93 @ id @ X106 @ id)) = $true)) | ~ ! [X101 : (subst > term > term)] : ((((X93 @ id @ (lam @ (X101 @ sh @ one)) @ id)) = $true) | ~ ! [X102 : term,X104 : subst,X103 : subst] : (((sub @ (X101 @ X103 @ X102) @ X104)) = ((X101 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104)))) | ~ ! [X105 : term] : ((((X93 @ id @ X105 @ id)) != $true) | (((X93 @ id @ (X101 @ id @ X105) @ id)) = $true))))))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((hoasinduction_lem3aa = $true) <=> ! [X453 : (subst > term > subst > $o),X454 : term] : (~ ! [X455 : (subst > term > term)] : (~ ! [X456 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X456 @ X458) @ X457)) = ((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457)))) | (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true) | ~ ! [X459 : term] : ((((X453 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X453 @ id @ X459 @ id)) != $true))) | (((X453 @ id @ (lam @ (sub @ X454 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X460 : term] : ((((X453 @ id @ (sub @ X454 @ (push @ X460 @ id)) @ id)) = $true) | (((X453 @ id @ X460 @ id)) != $true)))) & (pushprop_lem3v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X41 : term,X43 : term,X42 : term,X40 : term] : ((((ap @ X42 @ X41)) != ((ap @ X43 @ X40))) | (X40 = X41)) => ! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))))) & (pushprop_lem3v2_lthm = $true) & (! [X413 : (subst > term > subst > $o),X415 : term,X414 : (term > $o),X416 : term] : ((((X414 @ X415)) != $true) | (((X414 @ (ap @ X415 @ X416))) = $true) | ~ ! [X420 : term,X422 : subst,X421 : subst,X419 : subst] : ((((X413 @ (comp @ X421 @ X422) @ (sub @ X420 @ X422) @ X419)) = $true) | (((X413 @ X421 @ X420 @ (comp @ X422 @ X419))) != $true)) | ~ ! [X427 : term] : (((X413 @ id @ X427 @ id)) = ((X414 @ X427))) | ~ ! [X418 : term,X417 : term] : ((((X413 @ id @ X417 @ id)) != $true) | (((X413 @ id @ (ap @ (sub @ X418 @ id) @ X417) @ id)) = $true) | (((X413 @ id @ X418 @ id)) != $true)) | (((X414 @ X416)) != $true) | ~ ! [X425 : subst,X423 : term,X426 : subst,X424 : subst] : ((((X413 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)) != $true) | (((X413 @ X424 @ X423 @ (comp @ X425 @ X426))) = $true))) <=> (hoasinduction_lem2v2 = $true)) & ! [X480 : d_subst,X479 : d_subst] : ((((d2subst @ X480)) = ((d2subst @ X479))) => (X479 = X480)) & ((! [X134 : term] : (((sub @ X134 @ id)) = X134) => (! [X135 : term,X138 : term,X137 : term,X136 : term] : ((X135 = X137) | (((ap @ X137 @ X138)) != ((ap @ X135 @ X136)))) => ! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))))) <=> (hoasapinj1_lthm = $true)) & ((! [X483 : term] : ~ ! [X484 : (subst > term > term)] : ~ ! [X485 : subst,X486 : term] : (((X484 @ X485 @ X486)) = ((sub @ X483 @ (push @ X486 @ X485)))) => (! [X487 : term] : (((sub @ X487 @ id)) = X487) => ! [X488 : term,X490 : (subst > term > subst > $o),X489 : (term > $o)] : (~ ! [X491 : term] : (((X490 @ id @ X491 @ id)) = ((X489 @ X491))) | ~ ! [X492 : (subst > term > term)] : (~ ! [X496 : term] : ((((X490 @ id @ (X492 @ id @ X496) @ id)) = $true) | ($true != ((X490 @ id @ X496 @ id)))) | ~ ! [X495 : subst,X493 : term,X494 : subst] : (((sub @ (X492 @ X495 @ X493) @ X494)) = ((X492 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494)))) | (((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id)) = $true)) | ~ ! [X497 : term] : ((((X489 @ X497)) != $true) | ($true = ((X489 @ (sub @ X488 @ (push @ X497 @ id)))))) | (((X489 @ (lam @ X488))) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (axapp = $true) & ((hoasinduction_lem3 = $true) <=> ! [X501 : (subst > term > subst > $o),X500 : term] : (~ ! [X505 : term,X504 : subst,X503 : subst,X502 : subst] : ((((X501 @ X502 @ X505 @ (comp @ X504 @ X503))) != $true) | (((X501 @ (comp @ X502 @ X504) @ (sub @ X505 @ X504) @ X503)) = $true)) | ~ ! [X508 : subst,X507 : subst,X509 : subst,X506 : term] : ((((X501 @ (comp @ X507 @ X509) @ (sub @ X506 @ X509) @ X508)) != $true) | ($true = ((X501 @ X507 @ X506 @ (comp @ X509 @ X508))))) | ~ ! [X510 : (subst > term > term)] : ((((X501 @ id @ (lam @ (X510 @ sh @ one)) @ id)) = $true) | ~ ! [X513 : subst,X511 : subst,X512 : term] : (((X510 @ (comp @ X511 @ X513) @ (sub @ X512 @ X513))) = ((sub @ (X510 @ X511 @ X512) @ X513))) | ~ ! [X514 : term] : ((((X501 @ id @ (X510 @ id @ X514) @ id)) = $true) | (((X501 @ id @ X514 @ id)) != $true))) | ~ ! [X515 : term] : (($true = ((X501 @ id @ (sub @ X500 @ (push @ X515 @ id)) @ id))) | (((X501 @ id @ X515 @ id)) != $true)) | (((X501 @ id @ (lam @ X500) @ id)) = $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X195 : (subst > term > subst > $o)] : ~ ! [X196 : (term > $o)] : ~ ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197)))) & ((hoasinduction_lem3v2 = $true) <=> ! [X352 : (subst > term > subst > $o),X351 : (term > $o),X350 : term] : (~ ! [X353 : term] : (((X352 @ id @ X353 @ id)) = ((X351 @ X353))) | ~ ! [X359 : subst,X360 : term,X362 : subst,X361 : subst] : ((((X352 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359)) != $true) | ($true = ((X352 @ X362 @ X360 @ (comp @ X361 @ X359))))) | ~ ! [X356 : subst,X355 : subst,X358 : subst,X357 : term] : ((((X352 @ X358 @ X357 @ (comp @ X356 @ X355))) != $true) | ($true = ((X352 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356) @ X355)))) | (((X351 @ (lam @ X350))) = $true) | ~ ! [X363 : (subst > term > term)] : ((((X352 @ id @ (lam @ (X363 @ sh @ one)) @ id)) = $true) | ~ ! [X367 : term] : ((((X352 @ id @ (X363 @ id @ X367) @ id)) = $true) | (((X352 @ id @ X367 @ id)) != $true)) | ~ ! [X365 : term,X364 : subst,X366 : subst] : (((sub @ (X363 @ X364 @ X365) @ X366)) = ((X363 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366))))) | ~ ! [X354 : term] : ((((X351 @ (sub @ X350 @ (push @ X354 @ id)))) = $true) | (((X351 @ X354)) != $true)))) & ((termmset = $true) <=> ! [X444 : term] : (((sub @ X444 @ id)) = X444)) & (hoasinduction_lem3a_gthm = $true) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) <=> (hoasapinj2 = $true)) & (axclos = $true) & ((apinj1 = $true) <=> ! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164))) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X145 : term,X143 : (term > $o),X144 : subst] : ~ ! [X146 : (term > $o)] : ~ ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X399 : term,X398 : (subst > term > subst > $o)] : (~ ! [X402 : (subst > term > term)] : (~ ! [X405 : subst,X403 : subst,X404 : term] : (((sub @ (X402 @ X405 @ X404) @ X403)) = ((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403)))) | ~ ! [X406 : term] : (($true != ((X398 @ id @ X406 @ id))) | (((X398 @ id @ (X402 @ id @ X406) @ id)) = $true)) | (((X398 @ id @ (lam @ (X402 @ sh @ one)) @ id)) = $true)) | (((X398 @ id @ X399 @ id)) = $true) | ~ ! [X400 : term,X401 : term] : ((((X398 @ id @ X401 @ id)) != $true) | (((X398 @ id @ X400 @ id)) != $true) | (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) = $true)))) & (pushprop_lem2v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((axscons = $true) <=> ! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111)) & ((axidr = $true) <=> ! [X39 : subst] : (((comp @ X39 @ id)) = X39)) & (apnotvar = $true) & (substmonoid_gthm = $true) & (axabs = $true) & (axassoc = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X13 : subst] : (((comp @ id @ X13)) = X13) => (! [X14 : subst] : (((comp @ X14 @ id)) = X14) => (! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15))))) & (hoaslamnotvar = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X285 : term] : (((sub @ X285 @ id)) = X285) => (! [X287 : term,X286 : (subst > term > subst > $o)] : (~ ! [X293 : term] : ((((X286 @ id @ X293 @ id)) != $true) | (((X286 @ id @ (sub @ X287 @ (push @ X293 @ id)) @ id)) = $true)) | ~ ! [X288 : (subst > term > term)] : (~ ! [X289 : term] : ((((X286 @ id @ (X288 @ id @ X289) @ id)) = $true) | (((X286 @ id @ X289 @ id)) != $true)) | (((X286 @ id @ (lam @ (X288 @ sh @ one)) @ id)) = $true) | ~ ! [X292 : subst,X291 : term,X290 : subst] : (((X288 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290))) = ((sub @ (X288 @ X292 @ X291) @ X290)))) | (((X286 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id)) = $true)) => ! [X295 : (subst > term > subst > $o),X294 : term] : (~ ! [X296 : term] : ((((X295 @ id @ X296 @ id)) != $true) | (((X295 @ id @ (sub @ X294 @ (push @ X296 @ id)) @ id)) = $true)) | ~ ! [X301 : (subst > term > term)] : (~ ! [X302 : term] : ((((X295 @ id @ X302 @ id)) != $true) | (((X295 @ id @ (X301 @ id @ X302) @ id)) = $true)) | ~ ! [X303 : subst,X305 : subst,X304 : term] : (((sub @ (X301 @ X303 @ X304) @ X305)) = ((X301 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))) | ($true = ((X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)))) | ~ ! [X300 : subst,X297 : subst,X299 : subst,X298 : term] : ((((X295 @ X300 @ X298 @ (comp @ X299 @ X297))) != $true) | (((X295 @ (comp @ X300 @ X299) @ (sub @ X298 @ X299) @ X297)) = $true)) | ~ ! [X309 : term,X307 : subst,X306 : subst,X308 : subst] : ((((X295 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)) != $true) | (((X295 @ X307 @ X309 @ (comp @ X308 @ X306))) = $true)) | (((X295 @ id @ (lam @ X294) @ id)) = $true))))) & (pushprop_lem2v2_lthm = $true) & (! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) <=> (laminj = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X465 : term,X466 : (subst > term > subst > $o),X464 : (term > $o)] : (~ ! [X467 : term] : ((((X464 @ (sub @ X465 @ (push @ X467 @ id)))) = $true) | ($true != ((X464 @ X467)))) | ~ ! [X469 : (subst > term > term)] : (~ ! [X473 : subst,X471 : term,X472 : subst] : (((sub @ (X469 @ X473 @ X471) @ X472)) = ((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472)))) | ~ ! [X470 : term] : (($true = ((X466 @ id @ (X469 @ id @ X470) @ id))) | (((X466 @ id @ X470 @ id)) != $true)) | (((X466 @ id @ (lam @ (X469 @ sh @ one)) @ id)) = $true)) | ~ ! [X468 : term] : (((X466 @ id @ X468 @ id)) = ((X464 @ X468))) | (((X464 @ (lam @ X465))) = $true))) & ((apinj2 = $true) <=> ! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324))) & (lamnotap != $true) & (! [X184 : (subst > term > subst > $o)] : ~ ! [X185 : (term > $o)] : ~ ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186))) <=> (hoasinduction_lem0 = $true)) & ((induction2 = $true) <=> ! [X518 : (term > $o),X519 : term] : (~ ! [X522 : term] : ((((var @ X522)) != $true) | (((X518 @ X522)) = $true)) | ~ ! [X520 : term] : (~ ! [X521 : term] : ((((X518 @ X521)) != $true) | (((X518 @ (sub @ X520 @ (push @ X521 @ id)))) = $true)) | (((X518 @ (lam @ X520))) = $true)) | ~ ! [X524 : term,X523 : term] : ((((X518 @ X524)) != $true) | (((X518 @ (ap @ X523 @ X524))) = $true) | (((X518 @ X523)) != $true)) | (((X518 @ X519)) = $true))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & ((pushprop_lem1v2 = $true) <=> ! [X475 : subst,X477 : (term > $o),X476 : (term > $o),X474 : term] : ((((X476 @ X474)) != $true) | (((X477 @ one)) = $true) | ~ ! [X478 : term] : (((X477 @ X478)) = ((X476 @ (sub @ X478 @ (push @ X474 @ X475))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X527 : term,X525 : term,X526 : (subst > term > subst > $o)] : (~ ! [X536 : term,X537 : term] : ((((X526 @ id @ X537 @ id)) != $true) | (((X526 @ id @ X536 @ id)) != $true) | (((X526 @ id @ (ap @ (sub @ X537 @ id) @ X536) @ id)) = $true)) | (((X526 @ id @ X525 @ id)) != $true) | ~ ! [X534 : subst,X532 : subst,X535 : term,X533 : subst] : ((((X526 @ X532 @ X535 @ (comp @ X534 @ X533))) != $true) | (((X526 @ (comp @ X532 @ X534) @ (sub @ X535 @ X534) @ X533)) = $true)) | (((X526 @ id @ X527 @ id)) != $true) | (((X526 @ id @ (ap @ X525 @ X527) @ id)) = $true) | ~ ! [X530 : subst,X528 : subst,X531 : term,X529 : subst] : ((((X526 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529) @ X528)) != $true) | (((X526 @ X530 @ X531 @ (comp @ X529 @ X528))) = $true))) <=> (hoasinduction_lem2 = $true)) & (! [X157 : (term > $o),X158 : term,X156 : subst] : ~ ! [X159 : (term > $o)] : ~ ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160))) <=> (pushprop_lem0_lthm = $true)) & (hoasapnotvar_lthm = $true) & (hoaslamnotap_gthm = $true) & ((! [X368 : (subst > term > subst > $o)] : ~ ! [X369 : (term > $o)] : ~ ! [X370 : term] : (((X368 @ id @ X370 @ id)) = ((X369 @ X370))) => (! [X371 : term,X372 : (term > $o)] : ((((X372 @ X371)) = $true) | ~ ! [X374 : term,X373 : term] : ((((X372 @ X373)) != $true) | (((X372 @ X374)) != $true) | (((X372 @ (ap @ X374 @ X373))) = $true)) | ~ ! [X375 : term] : ((((X372 @ X375)) = $true) | (((var @ X375)) != $true)) | ~ ! [X376 : term] : ((((X372 @ (lam @ X376))) = $true) | ~ ! [X377 : term] : ((((X372 @ X377)) != $true) | (((X372 @ (sub @ X376 @ (push @ X377 @ id)))) = $true)))) => (! [X378 : term] : (((sub @ X378 @ id)) = X378) => (! [X381 : term,X380 : (term > $o),X379 : (subst > term > subst > $o)] : ((((X380 @ (lam @ X381))) = $true) | ~ ! [X387 : term] : (((X380 @ X387)) = ((X379 @ id @ X387 @ id))) | ~ ! [X382 : (subst > term > term)] : (~ ! [X386 : term] : ((((X379 @ id @ (X382 @ id @ X386) @ id)) = $true) | (((X379 @ id @ X386 @ id)) != $true)) | (((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ~ ! [X384 : subst,X383 : subst,X385 : term] : (((X382 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383))) = ((sub @ (X382 @ X384 @ X385) @ X383)))) | ~ ! [X388 : term] : (($true = ((X380 @ (sub @ X381 @ (push @ X388 @ id))))) | (((X380 @ X388)) != $true))) => ! [X390 : term,X389 : (subst > term > subst > $o)] : ((((X389 @ id @ X390 @ id)) = $true) | ~ ! [X396 : term,X397 : term] : ((((X389 @ id @ (ap @ (sub @ X396 @ id) @ X397) @ id)) = $true) | (((X389 @ id @ X396 @ id)) != $true) | (((X389 @ id @ X397 @ id)) != $true)) | ~ ! [X391 : (subst > term > term)] : ((((X389 @ id @ (lam @ (X391 @ sh @ one)) @ id)) = $true) | ~ ! [X395 : term] : (($true != ((X389 @ id @ X395 @ id))) | (((X389 @ id @ (X391 @ id @ X395) @ id)) = $true)) | ~ ! [X392 : subst,X393 : term,X394 : subst] : (((X391 @ (comp @ X392 @ X394) @ (sub @ X393 @ X394))) = ((sub @ (X391 @ X392 @ X393) @ X394))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X315 : subst,X314 : term] : (((sub @ one @ (push @ X314 @ X315))) = X314) => ! [X318 : (term > $o),X316 : (term > $o),X317 : term,X319 : subst] : ((((X318 @ X317)) != $true) | (((X316 @ one)) = $true) | ~ ! [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) = ((X316 @ X320))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (ulamvar1 != $true) & ((! [X165 : term] : (((sub @ X165 @ id)) = X165) => ! [X166 : (subst > term > subst > $o),X167 : (term > $o),X168 : term] : (~ ! [X183 : term] : (((X167 @ X183)) = ((X166 @ id @ X183 @ id))) | ~ ! [X173 : (subst > term > term)] : (~ ! [X176 : term,X175 : subst,X174 : subst] : (((X173 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174))) = ((sub @ (X173 @ X175 @ X176) @ X174))) | (((X166 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X166 @ id @ (X173 @ id @ X177) @ id)) = $true) | (((X166 @ id @ X177 @ id)) != $true))) | (((X167 @ (lam @ X168))) = $true) | ~ ! [X178 : term] : ((((X167 @ (sub @ X168 @ (push @ X178 @ id)))) = $true) | (((X167 @ X178)) != $true)) | ~ ! [X182 : subst,X180 : subst,X181 : subst,X179 : term] : (($true != ((X166 @ (comp @ X181 @ X182) @ (sub @ X179 @ X182) @ X180))) | (((X166 @ X181 @ X179 @ (comp @ X182 @ X180))) = $true)) | ~ ! [X169 : term,X172 : subst,X171 : subst,X170 : subst] : ((((X166 @ X170 @ X169 @ (comp @ X172 @ X171))) != $true) | (((X166 @ (comp @ X170 @ X172) @ (sub @ X169 @ X172) @ X171)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((! [X331 : term,X332 : subst] : (((sub @ one @ (push @ X331 @ X332))) = X331) => (! [X334 : term,X333 : subst] : (((comp @ sh @ (push @ X334 @ X333))) = X333) => (! [X335 : subst] : (((comp @ X335 @ id)) = X335) => (! [X337 : (term > $o),X336 : term] : (~ ! [X340 : term,X341 : term] : ((((X337 @ (ap @ X340 @ X341))) = $true) | (((X337 @ X340)) != $true) | (((X337 @ X341)) != $true)) | ~ ! [X339 : term] : ((((X337 @ X339)) = $true) | ($true != ((var @ X339)))) | ~ ! [X338 : term] : ((((X337 @ X338)) != $true) | (((X337 @ (lam @ X338))) = $true)) | (((X337 @ X336)) = $true)) => ! [X342 : term,X343 : (term > $o),X344 : subst] : (~ ! [X346 : term] : (($true = ((X343 @ (lam @ X346)))) | ~ ! [X347 : term] : (($true = ((X343 @ (sub @ X346 @ (push @ X347 @ id))))) | (((X343 @ X347)) != $true))) | ~ ! [X345 : term] : ((((X343 @ (sub @ X345 @ X344))) = $true) | (((var @ X345)) != $true)) | (((X343 @ (sub @ X342 @ X344))) = $true) | ~ ! [X349 : term,X348 : term] : ((((X343 @ X349)) != $true) | (((X343 @ (ap @ X349 @ X348))) = $true) | (((X343 @ X348)) != $true))))))) <=> (induction2lem_lthm = $true)) & (induction2_gthm = $true) & ! [X220 : d_subst] : (d_id = X220) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & (! [X67 : (term > $o),X66 : term] : (~ ! [X69 : term] : ((((X67 @ X69)) != $true) | (((X67 @ (lam @ X69))) = $true)) | ~ ! [X68 : term] : ((((var @ X68)) != $true) | (((X67 @ X68)) = $true)) | ~ ! [X71 : term,X70 : term] : ((((X67 @ X71)) != $true) | (((X67 @ X70)) != $true) | (((X67 @ (ap @ X70 @ X71))) = $true)) | (((X67 @ X66)) = $true)) <=> (induction = $true)) & ((hoasinduction = $true) <=> ! [X48 : term,X49 : (subst > term > subst > $o)] : (~ ! [X58 : (subst > term > term)] : ((((X49 @ id @ (lam @ (X58 @ sh @ one)) @ id)) = $true) | ~ ! [X60 : subst,X61 : term,X59 : subst] : (((X58 @ (comp @ X60 @ X59) @ (sub @ X61 @ X59))) = ((sub @ (X58 @ X60 @ X61) @ X59))) | ~ ! [X62 : term] : ((((X49 @ id @ X62 @ id)) != $true) | (((X49 @ id @ (X58 @ id @ X62) @ id)) = $true))) | (((X49 @ id @ X48 @ id)) = $true) | ~ ! [X63 : term,X64 : term] : ((((X49 @ id @ X63 @ id)) != $true) | (((X49 @ id @ (ap @ (sub @ X64 @ id) @ X63) @ id)) = $true) | (((X49 @ id @ X64 @ id)) != $true)) | ~ ! [X65 : term] : ((((X49 @ id @ X65 @ id)) = $true) | (((var @ (sub @ X65 @ id))) != $true)) | ~ ! [X57 : subst,X55 : subst,X56 : subst,X54 : term] : ((((X49 @ (comp @ X56 @ X57) @ (sub @ X54 @ X57) @ X55)) = $true) | (((X49 @ X56 @ X54 @ (comp @ X57 @ X55))) != $true)) | ~ ! [X52 : term,X51 : subst,X53 : subst,X50 : subst] : ((((X49 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50) @ X53)) != $true) | (((X49 @ X51 @ X52 @ (comp @ X50 @ X53))) = $true)))) & ((induction2lem = $true) <=> ! [X446 : (term > $o),X445 : term,X447 : subst] : (($true = ((X446 @ (sub @ X445 @ X447)))) | ~ ! [X451 : term] : ((((X446 @ (lam @ X451))) = $true) | ~ ! [X452 : term] : ((((X446 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X446 @ X452)) != $true))) | ~ ! [X449 : term,X450 : term] : ((((X446 @ X449)) != $true) | ($true = ((X446 @ (ap @ X449 @ X450)))) | (((X446 @ X450)) != $true)) | ~ ! [X448 : term] : ((((X446 @ (sub @ X448 @ X447))) = $true) | (((var @ X448)) != $true)))) & (hoasinduction_gthm = $true) & (hoasinduction_lem1 = $true) & (axvarshift = $true) & ((hoasapinj1 = $true) <=> ! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330))) & ! [X313 : d_term] : (d_one = X313) & (hoasinduction_lem1v2 = $true) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lthm = $true) <=> (! [X221 : (term > $o),X222 : term] : (~ ! [X225 : term,X226 : term] : ((((X221 @ X226)) != $true) | (((X221 @ (ap @ X225 @ X226))) = $true) | (((X221 @ X225)) != $true)) | (((X221 @ X222)) = $true) | ~ ! [X223 : term] : (~ ! [X224 : term] : ((((X221 @ X224)) != $true) | (((X221 @ (sub @ X223 @ (push @ X224 @ id)))) = $true)) | (((X221 @ (lam @ X223))) = $true)) | ~ ! [X227 : term] : ((((X221 @ X227)) = $true) | (((var @ X227)) != $true))) => (! [X228 : term,X230 : (subst > term > subst > $o),X229 : term] : (~ ! [X234 : term,X233 : subst,X236 : subst,X235 : subst] : ((((X230 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X236)) != $true) | (((X230 @ X233 @ X234 @ (comp @ X235 @ X236))) = $true)) | (((X230 @ id @ (ap @ X229 @ X228) @ id)) = $true) | ~ ! [X239 : term,X237 : subst,X238 : subst,X240 : subst] : ((((X230 @ X238 @ X239 @ (comp @ X240 @ X237))) != $true) | (((X230 @ (comp @ X238 @ X240) @ (sub @ X239 @ X240) @ X237)) = $true)) | ~ ! [X232 : term,X231 : term] : ((((X230 @ id @ X232 @ id)) != $true) | (((X230 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)) = $true) | (((X230 @ id @ X231 @ id)) != $true)) | (((X230 @ id @ X229 @ id)) != $true) | (((X230 @ id @ X228 @ id)) != $true)) => (! [X241 : term,X242 : (subst > term > subst > $o)] : (~ ! [X252 : (subst > term > term)] : (~ ! [X255 : subst,X254 : term,X256 : subst] : (((sub @ (X252 @ X256 @ X254) @ X255)) = ((X252 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | ~ ! [X253 : term] : ((((X242 @ id @ X253 @ id)) != $true) | ($true = ((X242 @ id @ (X252 @ id @ X253) @ id)))) | (((X242 @ id @ (lam @ (X252 @ sh @ one)) @ id)) = $true)) | ~ ! [X243 : subst,X245 : term,X246 : subst,X244 : subst] : ((((X242 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) != $true) | (((X242 @ X246 @ X245 @ (comp @ X243 @ X244))) = $true)) | (((X242 @ id @ (lam @ X241) @ id)) = $true) | ~ ! [X251 : term] : ((((X242 @ id @ (sub @ X241 @ (push @ X251 @ id)) @ id)) = $true) | (((X242 @ id @ X251 @ id)) != $true)) | ~ ! [X249 : subst,X250 : subst,X248 : term,X247 : subst] : ((((X242 @ X250 @ X248 @ (comp @ X247 @ X249))) != $true) | (((X242 @ (comp @ X250 @ X247) @ (sub @ X248 @ X247) @ X249)) = $true))) => ! [X258 : (subst > term > subst > $o),X257 : term] : (($true = ((X258 @ id @ X257 @ id))) | ~ ! [X271 : subst,X269 : subst,X270 : term,X272 : subst] : ((((X258 @ (comp @ X271 @ X272) @ (sub @ X270 @ X272) @ X269)) = $true) | (((X258 @ X271 @ X270 @ (comp @ X272 @ X269))) != $true)) | ~ ! [X259 : (subst > term > term)] : (~ ! [X260 : term] : ((((X258 @ id @ X260 @ id)) != $true) | (((X258 @ id @ (X259 @ id @ X260) @ id)) = $true)) | (((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id)) = $true) | ~ ! [X263 : subst,X261 : subst,X262 : term] : (((X259 @ (comp @ X263 @ X261) @ (sub @ X262 @ X261))) = ((sub @ (X259 @ X263 @ X262) @ X261)))) | ~ ! [X264 : term] : ((((X258 @ id @ X264 @ id)) = $true) | (((var @ (sub @ X264 @ id))) != $true)) | ~ ! [X273 : term,X274 : term] : ((((X258 @ id @ X273 @ id)) != $true) | (((X258 @ id @ (ap @ (sub @ X274 @ id) @ X273) @ id)) = $true) | (((X258 @ id @ X274 @ id)) != $true)) | ~ ! [X265 : subst,X267 : subst,X268 : term,X266 : subst] : ((((X258 @ (comp @ X266 @ X265) @ (sub @ X268 @ X265) @ X267)) != $true) | ($true = ((X258 @ X266 @ X268 @ (comp @ X265 @ X267)))))))))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) <=> (substmonoid = $true)) & (termmset_gthm = $true) & (! [X321 : term] : ~ ! [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) != ((X322 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (pushprop_lthm = $true) & (lamnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X310 : term] : ~ ! [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) != ((X311 @ sh @ one)))) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3a = $true) <=> ! [X149 : (subst > term > subst > $o),X148 : term] : ((((X149 @ id @ (lam @ X148) @ id)) = $true) | ~ ! [X151 : (subst > term > term)] : (~ ! [X152 : term] : ((((X149 @ id @ (X151 @ id @ X152) @ id)) = $true) | (((X149 @ id @ X152 @ id)) != $true)) | (((X149 @ id @ (lam @ (X151 @ sh @ one)) @ id)) = $true) | ~ ! [X155 : subst,X153 : term,X154 : subst] : (((sub @ (X151 @ X155 @ X153) @ X154)) = ((X151 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154))))) | ~ ! [X150 : term] : ((((X149 @ id @ X150 @ id)) != $true) | (((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) = $true)))) & ((axshiftcons = $true) <=> ! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462)) & ((pushprop_lem1_lthm = $true) <=> (! [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) = X1) => (! [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) = X2) => ! [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | (((X8 @ X4)) != $true))))) & ((hoaslaminj_lthm = $true) <=> (! [X428 : term,X429 : subst] : (((sub @ one @ (push @ X428 @ X429))) = X428) => (! [X430 : term,X431 : subst] : (((comp @ sh @ (push @ X430 @ X431))) = X431) => (! [X432 : term,X433 : term] : ((X432 = X433) | (((lam @ X433)) != ((lam @ X432)))) => ! [X437 : subst,X436 : term,X434 : (subst > term > term),X435 : (subst > term > term)] : ((((lam @ (X435 @ sh @ one))) != ((lam @ (X434 @ sh @ one)))) | ~ ! [X442 : subst,X441 : term,X443 : subst] : (((X435 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))) = ((sub @ (X435 @ X443 @ X441) @ X442))) | ~ ! [X439 : term,X440 : subst,X438 : subst] : (((sub @ (X434 @ X440 @ X439) @ X438)) = ((X434 @ (comp @ X440 @ X438) @ (sub @ X439 @ X438)))) | (((X434 @ X437 @ X436)) = ((X435 @ X437 @ X436)))))))) & ((axvarcons = $true) <=> ! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516)) & (pushprop_lem1_gthm = $true) & ((! [X118 : term] : (((sub @ X118 @ id)) = X118) => (! [X120 : subst,X119 : term,X121 : (term > $o)] : ((((X121 @ (sub @ X119 @ X120))) = $true) | ~ ! [X122 : term] : (~ ! [X123 : term] : ((((X121 @ X123)) != $true) | (((X121 @ (sub @ X122 @ (push @ X123 @ id)))) = $true)) | (((X121 @ (lam @ X122))) = $true)) | ~ ! [X124 : term] : ((((X121 @ (sub @ X124 @ X120))) = $true) | (((var @ X124)) != $true)) | ~ ! [X125 : term,X126 : term] : ((((X121 @ X125)) != $true) | (((X121 @ (ap @ X126 @ X125))) = $true) | (((X121 @ X126)) != $true))) => ! [X127 : (term > $o),X128 : term] : (~ ! [X129 : term] : (($true != ((var @ X129))) | (((X127 @ X129)) = $true)) | ~ ! [X130 : term] : (~ ! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) | (((X127 @ (lam @ X130))) = $true)) | ~ ! [X132 : term,X133 : term] : ((((X127 @ X132)) != $true) | (((X127 @ (ap @ X133 @ X132))) = $true) | (((X127 @ X133)) != $true)) | (((X127 @ X128)) = $true)))) <=> (induction2_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (! [X209 : (subst > term > subst > $o),X208 : term] : ((((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X219 : term] : ((((X209 @ id @ X219 @ id)) != $true) | (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) = $true)) | ~ ! [X211 : term,X210 : (subst > term > term)] : (~ ! [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) = ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) | ~ ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) = ((sub @ (X210 @ X218 @ X216) @ X217))) | (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) = $true) | ~ ! [X212 : term] : ((((X209 @ id @ X212 @ id)) != $true) | (((X209 @ id @ (X210 @ id @ X212) @ id)) = $true)))) <=> (hoasinduction_lem3aaa = $true)) & (! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) <=> (shinj = $true)) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((termmset_lthm = $true) <=> (! [X187 : term] : (((sub @ X187 @ id)) = X187) => ! [X188 : term] : (((sub @ X188 @ id)) = X188))) & ((hoaslaminj = $true) <=> ! [X199 : subst,X198 : term,X200 : (subst > term > term),X201 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | ~ ! [X206 : subst,X207 : subst,X205 : term] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X200 @ X206 @ X205) @ X207))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ~ ! [X202 : term,X204 : subst,X203 : subst] : (((sub @ (X201 @ X204 @ X202) @ X203)) = ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))))) & ! [X481 : d_term,X482 : d_term] : ((((d2term @ X482)) = ((d2term @ X481))) => (X481 = X482)) & (! [X112 : term] : ~ ! [X113 : (subst > term > term)] : ~ ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) != $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true)) <=> (pushprop_lem1 = $true)) & (((var @ (d2term @ d_one))) != $true)), 27.00/4.44 inference(flattening,[],[f9])). 27.00/4.44 thf(f11,plain,( 27.00/4.44 (hoasapinj2_gthm = $true) & (! [X463 : subst] : (((comp @ id @ X463)) = X463) <=> (axidl = $true)) & (one = ((d2term @ d_one))) & (hoasinduction_lem2_lthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (ulamvarind = $true) & (((! [X31 : (subst > term > subst > $o),X32 : term] : ((((X31 @ id @ (lam @ X32) @ id)) = $true) | ? [X33 : term] : ((((X31 @ id @ X33 @ id)) = $true) & (((X31 @ id @ (sub @ X32 @ (push @ X33 @ id)) @ id)) != $true)) | ? [X34 : (subst > term > term)] : (! [X35 : term] : ((((X31 @ id @ X35 @ id)) != $true) | (((X31 @ id @ (X34 @ id @ X35) @ id)) = $true)) & ! [X36 : subst,X37 : subst,X38 : term] : (((sub @ (X34 @ X36 @ X38) @ X37)) = ((X34 @ (comp @ X36 @ X37) @ (sub @ X38 @ X37)))) & ($true != ((X31 @ id @ (lam @ (X34 @ sh @ one)) @ id))))) | ? [X23 : term,X24 : (subst > term > subst > $o)] : ((((X24 @ id @ (lam @ (sub @ X23 @ (push @ one @ sh))) @ id)) != $true) & ! [X25 : term] : ((((X24 @ id @ (sub @ X23 @ (push @ X25 @ id)) @ id)) = $true) | (((X24 @ id @ X25 @ id)) != $true)) & ! [X26 : (subst > term > term)] : ((((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true) | ? [X29 : subst,X30 : term,X28 : subst] : (((X26 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28))) != ((sub @ (X26 @ X29 @ X30) @ X28))) | ? [X27 : term] : ((((X24 @ id @ (X26 @ id @ X27) @ id)) != $true) & (((X24 @ id @ X27 @ id)) = $true))))) | ? [X22 : term] : (((sub @ X22 @ id)) != X22)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X276 : (subst > term > subst > $o),X275 : term] : (? [X278 : (subst > term > term)] : ((((X276 @ id @ (lam @ (X278 @ sh @ one)) @ id)) != $true) & ! [X279 : term] : ((((X276 @ id @ (X278 @ id @ X279) @ id)) = $true) | (((X276 @ id @ X279 @ id)) != $true)) & ! [X282 : subst,X280 : term,X281 : subst] : (((sub @ (X278 @ X282 @ X280) @ X281)) = ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281))))) | ? [X277 : term] : ((((X276 @ id @ (sub @ X275 @ (push @ X277 @ id)) @ id)) != $true) & (((X276 @ id @ X277 @ id)) = $true)) | (((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true))) & (((d2subst @ d_id)) = sh) & (! [X407 : term] : ? [X408 : (subst > term > term)] : ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & ((axvarid = $true) <=> ! [X312 : term] : (((sub @ X312 @ id)) = X312)) & (! [X189 : (subst > term > term),X191 : term,X190 : term] : (? [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) != ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) | (((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem2_gthm = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X94 : term,X93 : (subst > term > subst > $o)] : ((((X93 @ id @ X94 @ id)) = $true) | ? [X106 : term] : ((((X93 @ id @ X106 @ id)) != $true) & (((var @ (sub @ X106 @ id))) = $true)) | ? [X98 : term,X97 : subst,X96 : subst,X95 : subst] : ((((X93 @ X95 @ X98 @ (comp @ X97 @ X96))) = $true) & (((X93 @ (comp @ X95 @ X97) @ (sub @ X98 @ X97) @ X96)) != $true)) | ? [X101 : (subst > term > term)] : (! [X105 : term] : ((((X93 @ id @ X105 @ id)) != $true) | (((X93 @ id @ (X101 @ id @ X105) @ id)) = $true)) & ! [X102 : term,X104 : subst,X103 : subst] : (((sub @ (X101 @ X103 @ X102) @ X104)) = ((X101 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104)))) & (((X93 @ id @ (lam @ (X101 @ sh @ one)) @ id)) != $true)) | ? [X108 : term,X107 : subst,X110 : subst,X109 : subst] : (($true = ((X93 @ (comp @ X107 @ X110) @ (sub @ X108 @ X110) @ X109))) & (((X93 @ X107 @ X108 @ (comp @ X110 @ X109))) != $true)) | ? [X99 : term,X100 : term] : ((((X93 @ id @ X100 @ id)) = $true) & (((X93 @ id @ X99 @ id)) = $true) & ($true != ((X93 @ id @ (ap @ (sub @ X100 @ id) @ X99) @ id))))) | ? [X83 : term,X85 : (term > $o),X84 : (subst > term > subst > $o)] : (! [X87 : term] : (((X84 @ id @ X87 @ id)) = ((X85 @ X87))) & (((X85 @ (lam @ X83))) != $true) & ! [X88 : (subst > term > term)] : (? [X89 : term] : (($true = ((X84 @ id @ X89 @ id))) & (((X84 @ id @ (X88 @ id @ X89) @ id)) != $true)) | (((X84 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true) | ? [X91 : subst,X92 : subst,X90 : term] : (((X88 @ (comp @ X91 @ X92) @ (sub @ X90 @ X92))) != ((sub @ (X88 @ X91 @ X90) @ X92)))) & ! [X86 : term] : ((((X85 @ X86)) != $true) | (((X85 @ (sub @ X83 @ (push @ X86 @ id)))) = $true)))) | ? [X82 : term] : (((sub @ X82 @ id)) != X82)) | ? [X76 : term,X75 : (term > $o)] : (! [X77 : term] : ((((var @ X77)) != $true) | (((X75 @ X77)) = $true)) & ! [X78 : term] : ((((X75 @ (lam @ X78))) = $true) | ? [X79 : term] : ((((X75 @ X79)) = $true) & (((X75 @ (sub @ X78 @ (push @ X79 @ id)))) != $true))) & (((X75 @ X76)) != $true) & ! [X80 : term,X81 : term] : ((((X75 @ X80)) != $true) | (((X75 @ (ap @ X80 @ X81))) = $true) | (((X75 @ X81)) != $true)))) | ? [X72 : (subst > term > subst > $o)] : ! [X73 : (term > $o)] : ? [X74 : term] : (((X73 @ X74)) != ((X72 @ id @ X74 @ 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)))))))))))))) & ((hoasinduction_lem3aa = $true) <=> ! [X454 : term,X453 : (subst > term > subst > $o)] : ((((X453 @ id @ (lam @ (sub @ X454 @ (push @ one @ sh))) @ id)) = $true) | ? [X455 : (subst > term > term)] : (! [X459 : term] : ((((X453 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X453 @ id @ X459 @ id)) != $true)) & (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true) & ! [X456 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X456 @ X458) @ X457)) = ((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))))) | ? [X460 : term] : ((((X453 @ id @ (sub @ X454 @ (push @ X460 @ id)) @ id)) != $true) & (((X453 @ id @ X460 @ id)) = $true)))) & (pushprop_lem3v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))) | ? [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) = ((ap @ X43 @ X40))) & (X40 != X41)))) & (pushprop_lem3v2_lthm = $true) & (! [X415 : term,X413 : (subst > term > subst > $o),X414 : (term > $o),X416 : term] : (? [X423 : term,X424 : subst,X426 : subst,X425 : subst] : ((((X413 @ X424 @ X423 @ (comp @ X425 @ X426))) != $true) & (((X413 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)) = $true)) | ? [X418 : term,X417 : term] : ((((X413 @ id @ X418 @ id)) = $true) & (((X413 @ id @ X417 @ id)) = $true) & (((X413 @ id @ (ap @ (sub @ X418 @ id) @ X417) @ id)) != $true)) | ? [X419 : subst,X421 : subst,X420 : term,X422 : subst] : ((((X413 @ X421 @ X420 @ (comp @ X422 @ X419))) = $true) & (((X413 @ (comp @ X421 @ X422) @ (sub @ X420 @ X422) @ X419)) != $true)) | (((X414 @ (ap @ X415 @ X416))) = $true) | (((X414 @ X416)) != $true) | (((X414 @ X415)) != $true) | ? [X427 : term] : (((X413 @ id @ X427 @ id)) != ((X414 @ X427)))) <=> (hoasinduction_lem2v2 = $true)) & ! [X479 : d_subst,X480 : d_subst] : ((X479 = X480) | (((d2subst @ X480)) != ((d2subst @ X479)))) & (((! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))) | ? [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) = ((ap @ X135 @ X136))) & (X135 != X137))) | ? [X134 : term] : (((sub @ X134 @ id)) != X134)) <=> (hoasapinj1_lthm = $true)) & (((! [X490 : (subst > term > subst > $o),X489 : (term > $o),X488 : term] : (? [X497 : term] : ((((X489 @ X497)) = $true) & ($true != ((X489 @ (sub @ X488 @ (push @ X497 @ id)))))) | ? [X492 : (subst > term > term)] : ((((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id)) != $true) & ! [X496 : term] : ((((X490 @ id @ (X492 @ id @ X496) @ id)) = $true) | ($true != ((X490 @ id @ X496 @ id)))) & ! [X495 : subst,X493 : term,X494 : subst] : (((sub @ (X492 @ X495 @ X493) @ X494)) = ((X492 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494))))) | ? [X491 : term] : (((X490 @ id @ X491 @ id)) != ((X489 @ X491))) | (((X489 @ (lam @ X488))) = $true)) | ? [X487 : term] : (((sub @ X487 @ id)) != X487)) | ? [X483 : term] : ! [X484 : (subst > term > term)] : ? [X485 : subst,X486 : term] : (((X484 @ X485 @ X486)) != ((sub @ X483 @ (push @ X486 @ X485))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (axapp = $true) & ((hoasinduction_lem3 = $true) <=> ! [X500 : term,X501 : (subst > term > subst > $o)] : (? [X503 : subst,X502 : subst,X504 : subst,X505 : term] : ((((X501 @ (comp @ X502 @ X504) @ (sub @ X505 @ X504) @ X503)) != $true) & (((X501 @ X502 @ X505 @ (comp @ X504 @ X503))) = $true)) | ? [X506 : term,X507 : subst,X509 : subst,X508 : subst] : (($true != ((X501 @ X507 @ X506 @ (comp @ X509 @ X508)))) & (((X501 @ (comp @ X507 @ X509) @ (sub @ X506 @ X509) @ X508)) = $true)) | ? [X510 : (subst > term > term)] : (! [X513 : subst,X511 : subst,X512 : term] : (((X510 @ (comp @ X511 @ X513) @ (sub @ X512 @ X513))) = ((sub @ (X510 @ X511 @ X512) @ X513))) & (((X501 @ id @ (lam @ (X510 @ sh @ one)) @ id)) != $true) & ! [X514 : term] : ((((X501 @ id @ (X510 @ id @ X514) @ id)) = $true) | (((X501 @ id @ X514 @ id)) != $true))) | ? [X515 : term] : ((((X501 @ id @ X515 @ id)) = $true) & ($true != ((X501 @ id @ (sub @ X500 @ (push @ X515 @ id)) @ id)))) | (((X501 @ id @ (lam @ X500) @ id)) = $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X195 : (subst > term > subst > $o)] : ? [X196 : (term > $o)] : ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197)))) & (! [X351 : (term > $o),X350 : term,X352 : (subst > term > subst > $o)] : (? [X363 : (subst > term > term)] : (! [X365 : term,X364 : subst,X366 : subst] : (((sub @ (X363 @ X364 @ X365) @ X366)) = ((X363 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366)))) & ! [X367 : term] : ((((X352 @ id @ (X363 @ id @ X367) @ id)) = $true) | (((X352 @ id @ X367 @ id)) != $true)) & (((X352 @ id @ (lam @ (X363 @ sh @ one)) @ id)) != $true)) | ? [X356 : subst,X358 : subst,X357 : term,X355 : subst] : ((((X352 @ X358 @ X357 @ (comp @ X356 @ X355))) = $true) & ($true != ((X352 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356) @ X355)))) | ? [X362 : subst,X360 : term,X361 : subst,X359 : subst] : (($true != ((X352 @ X362 @ X360 @ (comp @ X361 @ X359)))) & (((X352 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359)) = $true)) | (((X351 @ (lam @ X350))) = $true) | ? [X353 : term] : (((X352 @ id @ X353 @ id)) != ((X351 @ X353))) | ? [X354 : term] : ((((X351 @ X354)) = $true) & (((X351 @ (sub @ X350 @ (push @ X354 @ id)))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((termmset = $true) <=> ! [X444 : term] : (((sub @ X444 @ id)) = X444)) & (hoasinduction_lem3a_gthm = $true) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) <=> (hoasapinj2 = $true)) & (axclos = $true) & ((apinj1 = $true) <=> ! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164))) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X144 : subst,X143 : (term > $o),X145 : term] : ? [X146 : (term > $o)] : ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147)))) & (! [X398 : (subst > term > subst > $o),X399 : term] : (? [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) = $true) & (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X398 @ id @ X400 @ id)) = $true)) | (((X398 @ id @ X399 @ id)) = $true) | ? [X402 : (subst > term > term)] : (! [X405 : subst,X403 : subst,X404 : term] : (((sub @ (X402 @ X405 @ X404) @ X403)) = ((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403)))) & ! [X406 : term] : (($true != ((X398 @ id @ X406 @ id))) | (((X398 @ id @ (X402 @ id @ X406) @ id)) = $true)) & (((X398 @ id @ (lam @ (X402 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((axscons = $true) <=> ! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111)) & ((axidr = $true) <=> ! [X39 : subst] : (((comp @ X39 @ id)) = X39)) & (apnotvar = $true) & (substmonoid_gthm = $true) & (axabs = $true) & (axassoc = $true) & (pushprop = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((substmonoid_lthm = $true) <=> (((! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15)) | ? [X14 : subst] : (((comp @ X14 @ id)) != X14)) | ? [X13 : subst] : (((comp @ id @ X13)) != X13))) & (hoaslamnotvar = $true) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X295 : (subst > term > subst > $o),X294 : term] : (? [X296 : term] : ((((X295 @ id @ X296 @ id)) = $true) & (((X295 @ id @ (sub @ X294 @ (push @ X296 @ id)) @ id)) != $true)) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X305 : subst,X304 : term] : (((sub @ (X301 @ X303 @ X304) @ X305)) = ((X301 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))) & ! [X302 : term] : ((((X295 @ id @ X302 @ id)) != $true) | (((X295 @ id @ (X301 @ id @ X302) @ id)) = $true)) & ($true != ((X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)))) | ? [X300 : subst,X298 : term,X297 : subst,X299 : subst] : ((((X295 @ (comp @ X300 @ X299) @ (sub @ X298 @ X299) @ X297)) != $true) & (((X295 @ X300 @ X298 @ (comp @ X299 @ X297))) = $true)) | (((X295 @ id @ (lam @ X294) @ id)) = $true) | ? [X307 : subst,X306 : subst,X309 : term,X308 : subst] : ((((X295 @ X307 @ X309 @ (comp @ X308 @ X306))) != $true) & (((X295 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)) = $true))) | ? [X287 : term,X286 : (subst > term > subst > $o)] : (! [X293 : term] : ((((X286 @ id @ X293 @ id)) != $true) | (((X286 @ id @ (sub @ X287 @ (push @ X293 @ id)) @ id)) = $true)) & (((X286 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id)) != $true) & ! [X288 : (subst > term > term)] : ((((X286 @ id @ (lam @ (X288 @ sh @ one)) @ id)) = $true) | ? [X291 : term,X290 : subst,X292 : subst] : (((X288 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290))) != ((sub @ (X288 @ X292 @ X291) @ X290))) | ? [X289 : term] : ((((X286 @ id @ (X288 @ id @ X289) @ id)) != $true) & (((X286 @ id @ X289 @ id)) = $true))))) | ? [X285 : term] : (((sub @ X285 @ id)) != X285))) & (pushprop_lem2v2_lthm = $true) & (! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) <=> (laminj = $true)) & (! [X466 : (subst > term > subst > $o),X464 : (term > $o),X465 : term] : (? [X467 : term] : (($true = ((X464 @ X467))) & (((X464 @ (sub @ X465 @ (push @ X467 @ id)))) != $true)) | ? [X469 : (subst > term > term)] : (! [X470 : term] : (($true = ((X466 @ id @ (X469 @ id @ X470) @ id))) | (((X466 @ id @ X470 @ id)) != $true)) & ! [X473 : subst,X471 : term,X472 : subst] : (((sub @ (X469 @ X473 @ X471) @ X472)) = ((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472)))) & (((X466 @ id @ (lam @ (X469 @ sh @ one)) @ id)) != $true)) | ? [X468 : term] : (((X466 @ id @ X468 @ id)) != ((X464 @ X468))) | (((X464 @ (lam @ X465))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & ((apinj2 = $true) <=> ! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324))) & (lamnotap != $true) & ((hoasinduction_lem0 = $true) <=> ! [X184 : (subst > term > subst > $o)] : ? [X185 : (term > $o)] : ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186)))) & ((induction2 = $true) <=> ! [X518 : (term > $o),X519 : term] : (? [X522 : term] : ((((X518 @ X522)) != $true) & (((var @ X522)) = $true)) | ? [X520 : term] : (! [X521 : term] : ((((X518 @ X521)) != $true) | (((X518 @ (sub @ X520 @ (push @ X521 @ id)))) = $true)) & (((X518 @ (lam @ X520))) != $true)) | (((X518 @ X519)) = $true) | ? [X524 : term,X523 : term] : ((((X518 @ X524)) = $true) & (((X518 @ (ap @ X523 @ X524))) != $true) & (((X518 @ X523)) = $true)))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (! [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) = $true) | (((X476 @ X474)) != $true) | ? [X478 : term] : (((X477 @ X478)) != ((X476 @ (sub @ X478 @ (push @ X474 @ X475)))))) <=> (pushprop_lem1v2 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem2 = $true) <=> ! [X525 : term,X527 : term,X526 : (subst > term > subst > $o)] : (? [X529 : subst,X528 : subst,X531 : term,X530 : subst] : ((((X526 @ X530 @ X531 @ (comp @ X529 @ X528))) != $true) & (((X526 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529) @ X528)) = $true)) | (((X526 @ id @ X525 @ id)) != $true) | (((X526 @ id @ X527 @ id)) != $true) | (((X526 @ id @ (ap @ X525 @ X527) @ id)) = $true) | ? [X537 : term,X536 : term] : ((((X526 @ id @ X537 @ id)) = $true) & (((X526 @ id @ X536 @ id)) = $true) & (((X526 @ id @ (ap @ (sub @ X537 @ id) @ X536) @ id)) != $true)) | ? [X535 : term,X534 : subst,X532 : subst,X533 : subst] : ((((X526 @ X532 @ X535 @ (comp @ X534 @ X533))) = $true) & (((X526 @ (comp @ X532 @ X534) @ (sub @ X535 @ X534) @ X533)) != $true)))) & ((pushprop_lem0_lthm = $true) <=> ! [X156 : subst,X158 : term,X157 : (term > $o)] : ? [X159 : (term > $o)] : ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160)))) & (hoasapnotvar_lthm = $true) & (hoaslamnotap_gthm = $true) & (((((! [X390 : term,X389 : (subst > term > subst > $o)] : ((((X389 @ id @ X390 @ id)) = $true) | ? [X396 : term,X397 : term] : ((((X389 @ id @ X396 @ id)) = $true) & (((X389 @ id @ X397 @ id)) = $true) & (((X389 @ id @ (ap @ (sub @ X396 @ id) @ X397) @ id)) != $true)) | ? [X391 : (subst > term > term)] : (! [X392 : subst,X393 : term,X394 : subst] : (((X391 @ (comp @ X392 @ X394) @ (sub @ X393 @ X394))) = ((sub @ (X391 @ X392 @ X393) @ X394))) & ! [X395 : term] : (($true != ((X389 @ id @ X395 @ id))) | (((X389 @ id @ (X391 @ id @ X395) @ id)) = $true)) & (((X389 @ id @ (lam @ (X391 @ sh @ one)) @ id)) != $true))) | ? [X380 : (term > $o),X379 : (subst > term > subst > $o),X381 : term] : (! [X387 : term] : (((X380 @ X387)) = ((X379 @ id @ X387 @ id))) & ! [X388 : term] : (($true = ((X380 @ (sub @ X381 @ (push @ X388 @ id))))) | (((X380 @ X388)) != $true)) & (((X380 @ (lam @ X381))) != $true) & ! [X382 : (subst > term > term)] : ((((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ? [X383 : subst,X385 : term,X384 : subst] : (((X382 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383))) != ((sub @ (X382 @ X384 @ X385) @ X383))) | ? [X386 : term] : ((((X379 @ id @ (X382 @ id @ X386) @ id)) != $true) & (((X379 @ id @ X386 @ id)) = $true))))) | ? [X378 : term] : (((sub @ X378 @ id)) != X378)) | ? [X371 : term,X372 : (term > $o)] : (! [X374 : term,X373 : term] : ((((X372 @ X373)) != $true) | (((X372 @ X374)) != $true) | (((X372 @ (ap @ X374 @ X373))) = $true)) & ! [X376 : term] : (? [X377 : term] : ((((X372 @ (sub @ X376 @ (push @ X377 @ id)))) != $true) & (((X372 @ X377)) = $true)) | (((X372 @ (lam @ X376))) = $true)) & ! [X375 : term] : ((((X372 @ X375)) = $true) | (((var @ X375)) != $true)) & (((X372 @ X371)) != $true))) | ? [X368 : (subst > term > subst > $o)] : ! [X369 : (term > $o)] : ? [X370 : term] : (((X368 @ id @ X370 @ id)) != ((X369 @ X370)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) = $true) | ? [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) != ((X316 @ X320))) | (((X318 @ X317)) != $true)) | ? [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) != X314))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (ulamvar1 != $true) & ((? [X165 : term] : (((sub @ X165 @ id)) != X165) | ! [X167 : (term > $o),X168 : term,X166 : (subst > term > subst > $o)] : (? [X173 : (subst > term > term)] : (! [X176 : term,X175 : subst,X174 : subst] : (((X173 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174))) = ((sub @ (X173 @ X175 @ X176) @ X174))) & ! [X177 : term] : ((((X166 @ id @ (X173 @ id @ X177) @ id)) = $true) | (((X166 @ id @ X177 @ id)) != $true)) & (((X166 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true)) | ? [X172 : subst,X169 : term,X170 : subst,X171 : subst] : ((((X166 @ (comp @ X170 @ X172) @ (sub @ X169 @ X172) @ X171)) != $true) & (((X166 @ X170 @ X169 @ (comp @ X172 @ X171))) = $true)) | ? [X183 : term] : (((X167 @ X183)) != ((X166 @ id @ X183 @ id))) | ? [X178 : term] : ((((X167 @ (sub @ X168 @ (push @ X178 @ id)))) != $true) & (((X167 @ X178)) = $true)) | (((X167 @ (lam @ X168))) = $true) | ? [X179 : term,X182 : subst,X180 : subst,X181 : subst] : ((((X166 @ X181 @ X179 @ (comp @ X182 @ X180))) != $true) & ($true = ((X166 @ (comp @ X181 @ X182) @ (sub @ X179 @ X182) @ X180)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (((((! [X342 : term,X343 : (term > $o),X344 : subst] : ((((X343 @ (sub @ X342 @ X344))) = $true) | ? [X345 : term] : ((((X343 @ (sub @ X345 @ X344))) != $true) & (((var @ X345)) = $true)) | ? [X346 : term] : (! [X347 : term] : (($true = ((X343 @ (sub @ X346 @ (push @ X347 @ id))))) | (((X343 @ X347)) != $true)) & ($true != ((X343 @ (lam @ X346))))) | ? [X349 : term,X348 : term] : ((((X343 @ (ap @ X349 @ X348))) != $true) & (((X343 @ X348)) = $true) & (((X343 @ X349)) = $true))) | ? [X337 : (term > $o),X336 : term] : (! [X338 : term] : ((((X337 @ X338)) != $true) | (((X337 @ (lam @ X338))) = $true)) & ! [X339 : term] : ((((X337 @ X339)) = $true) | ($true != ((var @ X339)))) & ! [X340 : term,X341 : term] : ((((X337 @ (ap @ X340 @ X341))) = $true) | (((X337 @ X340)) != $true) | (((X337 @ X341)) != $true)) & (((X337 @ X336)) != $true))) | ? [X335 : subst] : (((comp @ X335 @ id)) != X335)) | ? [X333 : subst,X334 : term] : (((comp @ sh @ (push @ X334 @ X333))) != X333)) | ? [X331 : term,X332 : subst] : (((sub @ one @ (push @ X331 @ X332))) != X331)) <=> (induction2lem_lthm = $true)) & (induction2_gthm = $true) & ! [X220 : d_subst] : (d_id = X220) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & ((induction = $true) <=> ! [X67 : (term > $o),X66 : term] : (? [X68 : term] : ((((var @ X68)) = $true) & (((X67 @ X68)) != $true)) | ? [X69 : term] : ((((X67 @ X69)) = $true) & (((X67 @ (lam @ X69))) != $true)) | ? [X71 : term,X70 : term] : ((((X67 @ X70)) = $true) & (((X67 @ X71)) = $true) & (((X67 @ (ap @ X70 @ X71))) != $true)) | (((X67 @ X66)) = $true))) & ((hoasinduction = $true) <=> ! [X49 : (subst > term > subst > $o),X48 : term] : (? [X50 : subst,X52 : term,X53 : subst,X51 : subst] : ((((X49 @ X51 @ X52 @ (comp @ X50 @ X53))) != $true) & (((X49 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50) @ X53)) = $true)) | (((X49 @ id @ X48 @ id)) = $true) | ? [X63 : term,X64 : term] : ((((X49 @ id @ X63 @ id)) = $true) & (((X49 @ id @ (ap @ (sub @ X64 @ id) @ X63) @ id)) != $true) & (((X49 @ id @ X64 @ id)) = $true)) | ? [X56 : subst,X55 : subst,X57 : subst,X54 : term] : ((((X49 @ (comp @ X56 @ X57) @ (sub @ X54 @ X57) @ X55)) != $true) & (((X49 @ X56 @ X54 @ (comp @ X57 @ X55))) = $true)) | ? [X65 : term] : ((((var @ (sub @ X65 @ id))) = $true) & (((X49 @ id @ X65 @ id)) != $true)) | ? [X58 : (subst > term > term)] : (! [X60 : subst,X61 : term,X59 : subst] : (((X58 @ (comp @ X60 @ X59) @ (sub @ X61 @ X59))) = ((sub @ (X58 @ X60 @ X61) @ X59))) & (((X49 @ id @ (lam @ (X58 @ sh @ one)) @ id)) != $true) & ! [X62 : term] : ((((X49 @ id @ X62 @ id)) != $true) | (((X49 @ id @ (X58 @ id @ X62) @ id)) = $true))))) & (! [X446 : (term > $o),X447 : subst,X445 : term] : (($true = ((X446 @ (sub @ X445 @ X447)))) | ? [X451 : term] : (! [X452 : term] : ((((X446 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X446 @ X452)) != $true)) & (((X446 @ (lam @ X451))) != $true)) | ? [X450 : term,X449 : term] : ((((X446 @ X449)) = $true) & ($true != ((X446 @ (ap @ X449 @ X450)))) & (((X446 @ X450)) = $true)) | ? [X448 : term] : ((((X446 @ (sub @ X448 @ X447))) != $true) & (((var @ X448)) = $true))) <=> (induction2lem = $true)) & (hoasinduction_gthm = $true) & (hoasinduction_lem1 = $true) & (axvarshift = $true) & ((hoasapinj1 = $true) <=> ! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330))) & ! [X313 : d_term] : (d_one = X313) & (hoasinduction_lem1v2 = $true) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lthm = $true) <=> (((! [X258 : (subst > term > subst > $o),X257 : term] : (($true = ((X258 @ id @ X257 @ id))) | ? [X264 : term] : ((((var @ (sub @ X264 @ id))) = $true) & (((X258 @ id @ X264 @ id)) != $true)) | ? [X268 : term,X266 : subst,X267 : subst,X265 : subst] : ((((X258 @ (comp @ X266 @ X265) @ (sub @ X268 @ X265) @ X267)) = $true) & ($true != ((X258 @ X266 @ X268 @ (comp @ X265 @ X267))))) | ? [X274 : term,X273 : term] : ((((X258 @ id @ X274 @ id)) = $true) & (((X258 @ id @ (ap @ (sub @ X274 @ id) @ X273) @ id)) != $true) & (((X258 @ id @ X273 @ id)) = $true)) | ? [X272 : subst,X269 : subst,X270 : term,X271 : subst] : ((((X258 @ X271 @ X270 @ (comp @ X272 @ X269))) = $true) & (((X258 @ (comp @ X271 @ X272) @ (sub @ X270 @ X272) @ X269)) != $true)) | ? [X259 : (subst > term > term)] : (! [X263 : subst,X261 : subst,X262 : term] : (((X259 @ (comp @ X263 @ X261) @ (sub @ X262 @ X261))) = ((sub @ (X259 @ X263 @ X262) @ X261))) & ! [X260 : term] : ((((X258 @ id @ X260 @ id)) != $true) | (((X258 @ id @ (X259 @ id @ X260) @ id)) = $true)) & (((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id)) != $true))) | ? [X242 : (subst > term > subst > $o),X241 : term] : (! [X251 : term] : ((((X242 @ id @ (sub @ X241 @ (push @ X251 @ id)) @ id)) = $true) | (((X242 @ id @ X251 @ id)) != $true)) & ! [X249 : subst,X250 : subst,X248 : term,X247 : subst] : ((((X242 @ X250 @ X248 @ (comp @ X247 @ X249))) != $true) | (((X242 @ (comp @ X250 @ X247) @ (sub @ X248 @ X247) @ X249)) = $true)) & ! [X243 : subst,X245 : term,X246 : subst,X244 : subst] : ((((X242 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) != $true) | (((X242 @ X246 @ X245 @ (comp @ X243 @ X244))) = $true)) & ! [X252 : (subst > term > term)] : (? [X256 : subst,X254 : term,X255 : subst] : (((sub @ (X252 @ X256 @ X254) @ X255)) != ((X252 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | ? [X253 : term] : ((((X242 @ id @ X253 @ id)) = $true) & ($true != ((X242 @ id @ (X252 @ id @ X253) @ id)))) | (((X242 @ id @ (lam @ (X252 @ sh @ one)) @ id)) = $true)) & (((X242 @ id @ (lam @ X241) @ id)) != $true))) | ? [X228 : term,X230 : (subst > term > subst > $o),X229 : term] : ((((X230 @ id @ X229 @ id)) = $true) & ! [X232 : term,X231 : term] : ((((X230 @ id @ X232 @ id)) != $true) | (((X230 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)) = $true) | (((X230 @ id @ X231 @ id)) != $true)) & (((X230 @ id @ X228 @ id)) = $true) & ! [X234 : term,X233 : subst,X236 : subst,X235 : subst] : ((((X230 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X236)) != $true) | (((X230 @ X233 @ X234 @ (comp @ X235 @ X236))) = $true)) & ! [X239 : term,X237 : subst,X238 : subst,X240 : subst] : ((((X230 @ X238 @ X239 @ (comp @ X240 @ X237))) != $true) | (((X230 @ (comp @ X238 @ X240) @ (sub @ X239 @ X240) @ X237)) = $true)) & (((X230 @ id @ (ap @ X229 @ X228) @ id)) != $true))) | ? [X221 : (term > $o),X222 : term] : (! [X223 : term] : ((((X221 @ (lam @ X223))) = $true) | ? [X224 : term] : ((((X221 @ X224)) = $true) & (((X221 @ (sub @ X223 @ (push @ X224 @ id)))) != $true))) & (((X221 @ X222)) != $true) & ! [X227 : term] : ((((X221 @ X227)) = $true) | (((var @ X227)) != $true)) & ! [X225 : term,X226 : term] : ((((X221 @ X226)) != $true) | (((X221 @ (ap @ X225 @ X226))) = $true) | (((X221 @ X225)) != $true))))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) <=> (substmonoid = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X321 : term] : ? [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) = ((X322 @ sh @ one)))) & (pushprop_lthm = $true) & (lamnotvar = $true) & (! [X310 : term] : ? [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) = ((X311 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X149 : (subst > term > subst > $o),X148 : term] : (? [X151 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X151 @ sh @ one)) @ id)) != $true) & ! [X152 : term] : ((((X149 @ id @ (X151 @ id @ X152) @ id)) = $true) | (((X149 @ id @ X152 @ id)) != $true)) & ! [X155 : subst,X153 : term,X154 : subst] : (((sub @ (X151 @ X155 @ X153) @ X154)) = ((X151 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154))))) | (((X149 @ id @ (lam @ X148) @ id)) = $true) | ? [X150 : term] : ((((X149 @ id @ X150 @ id)) = $true) & (((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & ((axshiftcons = $true) <=> ! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462)) & ((pushprop_lem1_lthm = $true) <=> ((! [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | (((X8 @ X4)) != $true)) | ? [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) != X2)) | ? [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) != X1))) & ((hoaslaminj_lthm = $true) <=> (((! [X435 : (subst > term > term),X436 : term,X434 : (subst > term > term),X437 : subst] : (? [X441 : term,X442 : subst,X443 : subst] : (((X435 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))) != ((sub @ (X435 @ X443 @ X441) @ X442))) | (((X434 @ X437 @ X436)) = ((X435 @ X437 @ X436))) | (((lam @ (X435 @ sh @ one))) != ((lam @ (X434 @ sh @ one)))) | ? [X439 : term,X438 : subst,X440 : subst] : (((sub @ (X434 @ X440 @ X439) @ X438)) != ((X434 @ (comp @ X440 @ X438) @ (sub @ X439 @ X438))))) | ? [X433 : term,X432 : term] : ((((lam @ X433)) = ((lam @ X432))) & (X432 != X433))) | ? [X431 : subst,X430 : term] : (((comp @ sh @ (push @ X430 @ X431))) != X431)) | ? [X428 : term,X429 : subst] : (((sub @ one @ (push @ X428 @ X429))) != X428))) & ((axvarcons = $true) <=> ! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516)) & (pushprop_lem1_gthm = $true) & (((! [X127 : (term > $o),X128 : term] : (? [X133 : term,X132 : term] : ((((X127 @ X133)) = $true) & (((X127 @ (ap @ X133 @ X132))) != $true) & (((X127 @ X132)) = $true)) | ? [X130 : term] : ((((X127 @ (lam @ X130))) != $true) & ! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true))) | (((X127 @ X128)) = $true) | ? [X129 : term] : (($true = ((var @ X129))) & (((X127 @ X129)) != $true))) | ? [X120 : subst,X119 : term,X121 : (term > $o)] : (! [X124 : term] : ((((X121 @ (sub @ X124 @ X120))) = $true) | (((var @ X124)) != $true)) & (((X121 @ (sub @ X119 @ X120))) != $true) & ! [X122 : term] : ((((X121 @ (lam @ X122))) = $true) | ? [X123 : term] : ((((X121 @ X123)) = $true) & (((X121 @ (sub @ X122 @ (push @ X123 @ id)))) != $true))) & ! [X125 : term,X126 : term] : ((((X121 @ X125)) != $true) | (((X121 @ (ap @ X126 @ X125))) = $true) | (((X121 @ X126)) != $true)))) | ? [X118 : term] : (((sub @ X118 @ id)) != X118)) <=> (induction2_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (! [X208 : term,X209 : (subst > term > subst > $o)] : (? [X211 : term,X210 : (subst > term > term)] : (! [X212 : term] : ((((X209 @ id @ X212 @ id)) != $true) | (((X209 @ id @ (X210 @ id @ X212) @ id)) = $true)) & ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) = ((sub @ (X210 @ X218 @ X216) @ X217))) & ! [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) = ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) & (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) != $true)) | (((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) = $true) | ? [X219 : term] : ((((X209 @ id @ X219 @ id)) = $true) & (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) <=> (shinj = $true)) & (induction2lem_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((termmset_lthm = $true) <=> (! [X188 : term] : (((sub @ X188 @ id)) = X188) | ? [X187 : term] : (((sub @ X187 @ id)) != X187))) & (! [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) != ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | ? [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X200 @ X206 @ X205) @ X207)))) <=> (hoaslaminj = $true)) & ! [X481 : d_term,X482 : d_term] : ((X481 = X482) | (((d2term @ X482)) != ((d2term @ X481)))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X112 : term] : ? [X113 : (subst > term > term)] : ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114)))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) != $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true)) <=> (pushprop_lem1 = $true)) & (((var @ (d2term @ d_one))) != $true)), 27.00/4.44 inference(ennf_transformation,[],[f10])). 27.00/4.44 thf(f12,plain,( 27.00/4.44 (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X454 : term,X453 : (subst > term > subst > $o)] : ((((X453 @ id @ (lam @ (sub @ X454 @ (push @ one @ sh))) @ id)) = $true) | ? [X455 : (subst > term > term)] : (! [X459 : term] : ((((X453 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X453 @ id @ X459 @ id)) != $true)) & (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true) & ! [X456 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X456 @ X458) @ X457)) = ((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))))) | ? [X460 : term] : ((((X453 @ id @ (sub @ X454 @ (push @ X460 @ id)) @ id)) != $true) & (((X453 @ id @ X460 @ id)) = $true)))) & ((? [X165 : term] : (((sub @ X165 @ id)) != X165) | ! [X167 : (term > $o),X168 : term,X166 : (subst > term > subst > $o)] : (? [X173 : (subst > term > term)] : (! [X176 : term,X175 : subst,X174 : subst] : (((X173 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174))) = ((sub @ (X173 @ X175 @ X176) @ X174))) & ! [X177 : term] : ((((X166 @ id @ (X173 @ id @ X177) @ id)) = $true) | (((X166 @ id @ X177 @ id)) != $true)) & (((X166 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true)) | ? [X172 : subst,X169 : term,X170 : subst,X171 : subst] : ((((X166 @ (comp @ X170 @ X172) @ (sub @ X169 @ X172) @ X171)) != $true) & (((X166 @ X170 @ X169 @ (comp @ X172 @ X171))) = $true)) | ? [X183 : term] : (((X167 @ X183)) != ((X166 @ id @ X183 @ id))) | ? [X178 : term] : ((((X167 @ (sub @ X168 @ (push @ X178 @ id)))) != $true) & (((X167 @ X178)) = $true)) | (((X167 @ (lam @ X168))) = $true) | ? [X179 : term,X182 : subst,X180 : subst,X181 : subst] : ((((X166 @ X181 @ X179 @ (comp @ X182 @ X180))) != $true) & ($true = ((X166 @ (comp @ X181 @ X182) @ (sub @ X179 @ X182) @ X180)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) <=> (laminj = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & ((? [X285 : term] : (((sub @ X285 @ id)) != X285) | ! [X295 : (subst > term > subst > $o),X294 : term] : (? [X296 : term] : ((((X295 @ id @ X296 @ id)) = $true) & (((X295 @ id @ (sub @ X294 @ (push @ X296 @ id)) @ id)) != $true)) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X305 : subst,X304 : term] : (((sub @ (X301 @ X303 @ X304) @ X305)) = ((X301 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))) & ! [X302 : term] : ((((X295 @ id @ X302 @ id)) != $true) | (((X295 @ id @ (X301 @ id @ X302) @ id)) = $true)) & ($true != ((X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)))) | ? [X300 : subst,X298 : term,X297 : subst,X299 : subst] : ((((X295 @ (comp @ X300 @ X299) @ (sub @ X298 @ X299) @ X297)) != $true) & (((X295 @ X300 @ X298 @ (comp @ X299 @ X297))) = $true)) | (((X295 @ id @ (lam @ X294) @ id)) = $true) | ? [X307 : subst,X306 : subst,X309 : term,X308 : subst] : ((((X295 @ X307 @ X309 @ (comp @ X308 @ X306))) != $true) & (((X295 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)) = $true))) | ? [X287 : term,X286 : (subst > term > subst > $o)] : (! [X293 : term] : ((((X286 @ id @ X293 @ id)) != $true) | (((X286 @ id @ (sub @ X287 @ (push @ X293 @ id)) @ id)) = $true)) & (((X286 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id)) != $true) & ! [X288 : (subst > term > term)] : ((((X286 @ id @ (lam @ (X288 @ sh @ one)) @ id)) = $true) | ? [X291 : term,X290 : subst,X292 : subst] : (((X288 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290))) != ((sub @ (X288 @ X292 @ X291) @ X290))) | ? [X289 : term] : ((((X286 @ id @ (X288 @ id @ X289) @ id)) != $true) & (((X286 @ id @ X289 @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X463 : subst] : (((comp @ id @ X463)) = X463) <=> (axidl = $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) <=> (substmonoid = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X481 : d_term,X482 : d_term] : ((X481 = X482) | (((d2term @ X482)) != ((d2term @ X481)))) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) <=> ((! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15)) | ? [X14 : subst] : (((comp @ X14 @ id)) != X14) | ? [X13 : subst] : (((comp @ id @ X13)) != X13))) & ((axidr = $true) <=> ! [X39 : subst] : (((comp @ X39 @ id)) = X39)) & (! [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) = $true) | (((X476 @ X474)) != $true) | ? [X478 : term] : (((X477 @ X478)) != ((X476 @ (sub @ X478 @ (push @ X474 @ X475)))))) <=> (pushprop_lem1v2 = $true)) & (! [X149 : (subst > term > subst > $o),X148 : term] : (? [X151 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X151 @ sh @ one)) @ id)) != $true) & ! [X152 : term] : ((((X149 @ id @ (X151 @ id @ X152) @ id)) = $true) | (((X149 @ id @ X152 @ id)) != $true)) & ! [X155 : subst,X153 : term,X154 : subst] : (((sub @ (X151 @ X155 @ X153) @ X154)) = ((X151 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154))))) | (((X149 @ id @ (lam @ X148) @ id)) = $true) | ? [X150 : term] : ((((X149 @ id @ X150 @ id)) = $true) & (((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & (apnotvar = $true) & (! [X407 : term] : ? [X408 : (subst > term > term)] : ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X415 : term,X413 : (subst > term > subst > $o),X414 : (term > $o),X416 : term] : (? [X423 : term,X424 : subst,X426 : subst,X425 : subst] : ((((X413 @ X424 @ X423 @ (comp @ X425 @ X426))) != $true) & (((X413 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)) = $true)) | ? [X418 : term,X417 : term] : ((((X413 @ id @ X418 @ id)) = $true) & (((X413 @ id @ X417 @ id)) = $true) & (((X413 @ id @ (ap @ (sub @ X418 @ id) @ X417) @ id)) != $true)) | ? [X419 : subst,X421 : subst,X420 : term,X422 : subst] : ((((X413 @ X421 @ X420 @ (comp @ X422 @ X419))) = $true) & (((X413 @ (comp @ X421 @ X422) @ (sub @ X420 @ X422) @ X419)) != $true)) | (((X414 @ (ap @ X415 @ X416))) = $true) | (((X414 @ X416)) != $true) | (((X414 @ X415)) != $true) | ? [X427 : term] : (((X413 @ id @ X427 @ id)) != ((X414 @ X427)))) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction = $true) <=> ! [X49 : (subst > term > subst > $o),X48 : term] : (? [X50 : subst,X52 : term,X53 : subst,X51 : subst] : ((((X49 @ X51 @ X52 @ (comp @ X50 @ X53))) != $true) & (((X49 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50) @ X53)) = $true)) | (((X49 @ id @ X48 @ id)) = $true) | ? [X63 : term,X64 : term] : ((((X49 @ id @ X63 @ id)) = $true) & (((X49 @ id @ (ap @ (sub @ X64 @ id) @ X63) @ id)) != $true) & (((X49 @ id @ X64 @ id)) = $true)) | ? [X56 : subst,X55 : subst,X57 : subst,X54 : term] : ((((X49 @ (comp @ X56 @ X57) @ (sub @ X54 @ X57) @ X55)) != $true) & (((X49 @ X56 @ X54 @ (comp @ X57 @ X55))) = $true)) | ? [X65 : term] : ((((var @ (sub @ X65 @ id))) = $true) & (((X49 @ id @ X65 @ id)) != $true)) | ? [X58 : (subst > term > term)] : (! [X60 : subst,X61 : term,X59 : subst] : (((X58 @ (comp @ X60 @ X59) @ (sub @ X61 @ X59))) = ((sub @ (X58 @ X60 @ X61) @ X59))) & (((X49 @ id @ (lam @ (X58 @ sh @ one)) @ id)) != $true) & ! [X62 : term] : ((((X49 @ id @ X62 @ id)) != $true) | (((X49 @ id @ (X58 @ id @ X62) @ id)) = $true))))) & (ulamvarind = $true) & ((? [X433 : term,X432 : term] : ((((lam @ X433)) = ((lam @ X432))) & (X432 != X433)) | ? [X428 : term,X429 : subst] : (((sub @ one @ (push @ X428 @ X429))) != X428) | ? [X431 : subst,X430 : term] : (((comp @ sh @ (push @ X430 @ X431))) != X431) | ! [X435 : (subst > term > term),X436 : term,X434 : (subst > term > term),X437 : subst] : (? [X441 : term,X442 : subst,X443 : subst] : (((X435 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))) != ((sub @ (X435 @ X443 @ X441) @ X442))) | (((X434 @ X437 @ X436)) = ((X435 @ X437 @ X436))) | (((lam @ (X435 @ sh @ one))) != ((lam @ (X434 @ sh @ one)))) | ? [X439 : term,X438 : subst,X440 : subst] : (((sub @ (X434 @ X440 @ X439) @ X438)) != ((X434 @ (comp @ X440 @ X438) @ (sub @ X439 @ X438)))))) <=> (hoaslaminj_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lthm_3 = $true) <=> (? [X83 : term,X85 : (term > $o),X84 : (subst > term > subst > $o)] : (! [X87 : term] : (((X84 @ id @ X87 @ id)) = ((X85 @ X87))) & (((X85 @ (lam @ X83))) != $true) & ! [X88 : (subst > term > term)] : (? [X89 : term] : (($true = ((X84 @ id @ X89 @ id))) & (((X84 @ id @ (X88 @ id @ X89) @ id)) != $true)) | (((X84 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true) | ? [X91 : subst,X92 : subst,X90 : term] : (((X88 @ (comp @ X91 @ X92) @ (sub @ X90 @ X92))) != ((sub @ (X88 @ X91 @ X90) @ X92)))) & ! [X86 : term] : ((((X85 @ X86)) != $true) | (((X85 @ (sub @ X83 @ (push @ X86 @ id)))) = $true))) | ! [X94 : term,X93 : (subst > term > subst > $o)] : ((((X93 @ id @ X94 @ id)) = $true) | ? [X106 : term] : ((((X93 @ id @ X106 @ id)) != $true) & (((var @ (sub @ X106 @ id))) = $true)) | ? [X98 : term,X97 : subst,X96 : subst,X95 : subst] : ((((X93 @ X95 @ X98 @ (comp @ X97 @ X96))) = $true) & (((X93 @ (comp @ X95 @ X97) @ (sub @ X98 @ X97) @ X96)) != $true)) | ? [X101 : (subst > term > term)] : (! [X105 : term] : ((((X93 @ id @ X105 @ id)) != $true) | (((X93 @ id @ (X101 @ id @ X105) @ id)) = $true)) & ! [X102 : term,X104 : subst,X103 : subst] : (((sub @ (X101 @ X103 @ X102) @ X104)) = ((X101 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104)))) & (((X93 @ id @ (lam @ (X101 @ sh @ one)) @ id)) != $true)) | ? [X108 : term,X107 : subst,X110 : subst,X109 : subst] : (($true = ((X93 @ (comp @ X107 @ X110) @ (sub @ X108 @ X110) @ X109))) & (((X93 @ X107 @ X108 @ (comp @ X110 @ X109))) != $true)) | ? [X99 : term,X100 : term] : ((((X93 @ id @ X100 @ id)) = $true) & (((X93 @ id @ X99 @ id)) = $true) & ($true != ((X93 @ id @ (ap @ (sub @ X100 @ id) @ X99) @ id))))) | ? [X82 : term] : (((sub @ X82 @ id)) != X82) | ? [X76 : term,X75 : (term > $o)] : (! [X77 : term] : ((((var @ X77)) != $true) | (((X75 @ X77)) = $true)) & ! [X78 : term] : ((((X75 @ (lam @ X78))) = $true) | ? [X79 : term] : ((((X75 @ X79)) = $true) & (((X75 @ (sub @ X78 @ (push @ X79 @ id)))) != $true))) & (((X75 @ X76)) != $true) & ! [X80 : term,X81 : term] : ((((X75 @ X80)) != $true) | (((X75 @ (ap @ X80 @ X81))) = $true) | (((X75 @ X81)) != $true))) | ? [X72 : (subst > term > subst > $o)] : ! [X73 : (term > $o)] : ? [X74 : term] : (((X73 @ X74)) != ((X72 @ id @ X74 @ id))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((pushprop_lem0 = $true) <=> ! [X144 : subst,X143 : (term > $o),X145 : term] : ? [X146 : (term > $o)] : ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147)))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) = $true) | ? [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) != ((X316 @ X320))) | (((X318 @ X317)) != $true)) | ? [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) != X314))) & (axapp = $true) & ((! [X490 : (subst > term > subst > $o),X489 : (term > $o),X488 : term] : (? [X497 : term] : ((((X489 @ X497)) = $true) & ($true != ((X489 @ (sub @ X488 @ (push @ X497 @ id)))))) | ? [X492 : (subst > term > term)] : ((((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id)) != $true) & ! [X496 : term] : ((((X490 @ id @ (X492 @ id @ X496) @ id)) = $true) | ($true != ((X490 @ id @ X496 @ id)))) & ! [X495 : subst,X493 : term,X494 : subst] : (((sub @ (X492 @ X495 @ X493) @ X494)) = ((X492 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494))))) | ? [X491 : term] : (((X490 @ id @ X491 @ id)) != ((X489 @ X491))) | (((X489 @ (lam @ X488))) = $true)) | ? [X487 : term] : (((sub @ X487 @ id)) != X487) | ? [X483 : term] : ! [X484 : (subst > term > term)] : ? [X485 : subst,X486 : term] : (((X484 @ X485 @ X486)) != ((sub @ X483 @ (push @ X486 @ X485))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X189 : (subst > term > term),X191 : term,X190 : term] : (? [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) != ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) | (((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((induction2_lthm = $true) <=> (? [X118 : term] : (((sub @ X118 @ id)) != X118) | ? [X120 : subst,X119 : term,X121 : (term > $o)] : (! [X124 : term] : ((((X121 @ (sub @ X124 @ X120))) = $true) | (((var @ X124)) != $true)) & (((X121 @ (sub @ X119 @ X120))) != $true) & ! [X122 : term] : ((((X121 @ (lam @ X122))) = $true) | ? [X123 : term] : ((((X121 @ X123)) = $true) & (((X121 @ (sub @ X122 @ (push @ X123 @ id)))) != $true))) & ! [X125 : term,X126 : term] : ((((X121 @ X125)) != $true) | (((X121 @ (ap @ X126 @ X125))) = $true) | (((X121 @ X126)) != $true))) | ! [X127 : (term > $o),X128 : term] : (? [X133 : term,X132 : term] : ((((X127 @ X133)) = $true) & (((X127 @ (ap @ X133 @ X132))) != $true) & (((X127 @ X132)) = $true)) | ? [X130 : term] : ((((X127 @ (lam @ X130))) != $true) & ! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true))) | (((X127 @ X128)) = $true) | ? [X129 : term] : (($true = ((var @ X129))) & (((X127 @ X129)) != $true))))) & ! [X313 : d_term] : (d_one = X313) & ! [X479 : d_subst,X480 : d_subst] : ((X479 = X480) | (((d2subst @ X480)) != ((d2subst @ X479)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2 = $true) <=> ! [X518 : (term > $o),X519 : term] : (? [X522 : term] : ((((X518 @ X522)) != $true) & (((var @ X522)) = $true)) | ? [X520 : term] : (! [X521 : term] : ((((X518 @ X521)) != $true) | (((X518 @ (sub @ X520 @ (push @ X521 @ id)))) = $true)) & (((X518 @ (lam @ X520))) != $true)) | (((X518 @ X519)) = $true) | ? [X524 : term,X523 : term] : ((((X518 @ X524)) = $true) & (((X518 @ (ap @ X523 @ X524))) != $true) & (((X518 @ X523)) = $true)))) & (pushprop_lthm = $true) & (pushprop_lem0_gthm = $true) & (! [X466 : (subst > term > subst > $o),X464 : (term > $o),X465 : term] : (? [X467 : term] : (($true = ((X464 @ X467))) & (((X464 @ (sub @ X465 @ (push @ X467 @ id)))) != $true)) | ? [X469 : (subst > term > term)] : (! [X470 : term] : (($true = ((X466 @ id @ (X469 @ id @ X470) @ id))) | (((X466 @ id @ X470 @ id)) != $true)) & ! [X473 : subst,X471 : term,X472 : subst] : (((sub @ (X469 @ X473 @ X471) @ X472)) = ((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472)))) & (((X466 @ id @ (lam @ (X469 @ sh @ one)) @ id)) != $true)) | ? [X468 : term] : (((X466 @ id @ X468 @ id)) != ((X464 @ X468))) | (((X464 @ (lam @ X465))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X156 : subst,X158 : term,X157 : (term > $o)] : ? [X159 : (term > $o)] : ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160)))) & ((hoasapinj1 = $true) <=> ! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330))) & ((induction = $true) <=> ! [X67 : (term > $o),X66 : term] : (? [X68 : term] : ((((var @ X68)) = $true) & (((X67 @ X68)) != $true)) | ? [X69 : term] : ((((X67 @ X69)) = $true) & (((X67 @ (lam @ X69))) != $true)) | ? [X71 : term,X70 : term] : ((((X67 @ X70)) = $true) & (((X67 @ X71)) = $true) & (((X67 @ (ap @ X70 @ X71))) != $true)) | (((X67 @ X66)) = $true))) & ((hoasinduction_lem0 = $true) <=> ! [X184 : (subst > term > subst > $o)] : ? [X185 : (term > $o)] : ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186)))) & ((hoasinduction_lem3b = $true) <=> ! [X321 : term] : ? [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) = ((X322 @ sh @ one)))) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = sh) & (lamnotap != $true) & ((axshiftcons = $true) <=> ! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X276 : (subst > term > subst > $o),X275 : term] : (? [X278 : (subst > term > term)] : ((((X276 @ id @ (lam @ (X278 @ sh @ one)) @ id)) != $true) & ! [X279 : term] : ((((X276 @ id @ (X278 @ id @ X279) @ id)) = $true) | (((X276 @ id @ X279 @ id)) != $true)) & ! [X282 : subst,X280 : term,X281 : subst] : (((sub @ (X278 @ X282 @ X280) @ X281)) = ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281))))) | ? [X277 : term] : ((((X276 @ id @ (sub @ X275 @ (push @ X277 @ id)) @ id)) != $true) & (((X276 @ id @ X277 @ id)) = $true)) | (((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X112 : term] : ? [X113 : (subst > term > term)] : ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114)))) & (pushprop = $true) & (! [X398 : (subst > term > subst > $o),X399 : term] : (? [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) = $true) & (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X398 @ id @ X400 @ id)) = $true)) | (((X398 @ id @ X399 @ id)) = $true) | ? [X402 : (subst > term > term)] : (! [X405 : subst,X403 : subst,X404 : term] : (((sub @ (X402 @ X405 @ X404) @ X403)) = ((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403)))) & ! [X406 : term] : (($true != ((X398 @ id @ X406 @ id))) | (((X398 @ id @ (X402 @ id @ X406) @ id)) = $true)) & (((X398 @ id @ (lam @ (X402 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (axmap = $true) & ((axvarid = $true) <=> ! [X312 : term] : (((sub @ X312 @ id)) = X312)) & (! [X208 : term,X209 : (subst > term > subst > $o)] : (? [X211 : term,X210 : (subst > term > term)] : (! [X212 : term] : ((((X209 @ id @ X212 @ id)) != $true) | (((X209 @ id @ (X210 @ id @ X212) @ id)) = $true)) & ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) = ((sub @ (X210 @ X218 @ X216) @ X217))) & ! [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) = ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) & (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) != $true)) | (((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) = $true) | ? [X219 : term] : ((((X209 @ id @ X219 @ id)) = $true) & (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (! [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) != ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | ? [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X200 @ X206 @ X205) @ X207)))) <=> (hoaslaminj = $true)) & (! [X351 : (term > $o),X350 : term,X352 : (subst > term > subst > $o)] : (? [X363 : (subst > term > term)] : (! [X365 : term,X364 : subst,X366 : subst] : (((sub @ (X363 @ X364 @ X365) @ X366)) = ((X363 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366)))) & ! [X367 : term] : ((((X352 @ id @ (X363 @ id @ X367) @ id)) = $true) | (((X352 @ id @ X367 @ id)) != $true)) & (((X352 @ id @ (lam @ (X363 @ sh @ one)) @ id)) != $true)) | ? [X356 : subst,X358 : subst,X357 : term,X355 : subst] : ((((X352 @ X358 @ X357 @ (comp @ X356 @ X355))) = $true) & ($true != ((X352 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356) @ X355)))) | ? [X362 : subst,X360 : term,X361 : subst,X359 : subst] : (($true != ((X352 @ X362 @ X360 @ (comp @ X361 @ X359)))) & (((X352 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359)) = $true)) | (((X351 @ (lam @ X350))) = $true) | ? [X353 : term] : (((X352 @ id @ X353 @ id)) != ((X351 @ X353))) | ? [X354 : term] : ((((X351 @ X354)) = $true) & (((X351 @ (sub @ X350 @ (push @ X354 @ id)))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X310 : term] : ? [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) = ((X311 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem1 = $true) & (hoaslamnotap_lthm = $true) & (! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) <=> (shinj = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2_lthm = $true) <=> (! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))) | ? [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) = ((ap @ X43 @ X40))) & (X40 != X41)))) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X195 : (subst > term > subst > $o)] : ? [X196 : (term > $o)] : ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197)))) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((axscons = $true) <=> ! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((termmset = $true) <=> ! [X444 : term] : (((sub @ X444 @ id)) = X444)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X446 : (term > $o),X447 : subst,X445 : term] : (($true = ((X446 @ (sub @ X445 @ X447)))) | ? [X451 : term] : (! [X452 : term] : ((((X446 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X446 @ X452)) != $true)) & (((X446 @ (lam @ X451))) != $true)) | ? [X450 : term,X449 : term] : ((((X446 @ X449)) = $true) & ($true != ((X446 @ (ap @ X449 @ X450)))) & (((X446 @ X450)) = $true)) | ? [X448 : term] : ((((X446 @ (sub @ X448 @ X447))) != $true) & (((var @ X448)) = $true))) <=> (induction2lem = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X500 : term,X501 : (subst > term > subst > $o)] : (? [X503 : subst,X502 : subst,X504 : subst,X505 : term] : ((((X501 @ (comp @ X502 @ X504) @ (sub @ X505 @ X504) @ X503)) != $true) & (((X501 @ X502 @ X505 @ (comp @ X504 @ X503))) = $true)) | ? [X506 : term,X507 : subst,X509 : subst,X508 : subst] : (($true != ((X501 @ X507 @ X506 @ (comp @ X509 @ X508)))) & (((X501 @ (comp @ X507 @ X509) @ (sub @ X506 @ X509) @ X508)) = $true)) | ? [X510 : (subst > term > term)] : (! [X513 : subst,X511 : subst,X512 : term] : (((X510 @ (comp @ X511 @ X513) @ (sub @ X512 @ X513))) = ((sub @ (X510 @ X511 @ X512) @ X513))) & (((X501 @ id @ (lam @ (X510 @ sh @ one)) @ id)) != $true) & ! [X514 : term] : ((((X501 @ id @ (X510 @ id @ X514) @ id)) = $true) | (((X501 @ id @ X514 @ id)) != $true))) | ? [X515 : term] : ((((X501 @ id @ X515 @ id)) = $true) & ($true != ((X501 @ id @ (sub @ X500 @ (push @ X515 @ id)) @ id)))) | (((X501 @ id @ (lam @ X500) @ id)) = $true))) & ((induction2lem_lthm = $true) <=> (? [X333 : subst,X334 : term] : (((comp @ sh @ (push @ X334 @ X333))) != X333) | ! [X342 : term,X343 : (term > $o),X344 : subst] : ((((X343 @ (sub @ X342 @ X344))) = $true) | ? [X345 : term] : ((((X343 @ (sub @ X345 @ X344))) != $true) & (((var @ X345)) = $true)) | ? [X346 : term] : (! [X347 : term] : (($true = ((X343 @ (sub @ X346 @ (push @ X347 @ id))))) | (((X343 @ X347)) != $true)) & ($true != ((X343 @ (lam @ X346))))) | ? [X349 : term,X348 : term] : ((((X343 @ (ap @ X349 @ X348))) != $true) & (((X343 @ X348)) = $true) & (((X343 @ X349)) = $true))) | ? [X331 : term,X332 : subst] : (((sub @ one @ (push @ X331 @ X332))) != X331) | ? [X337 : (term > $o),X336 : term] : (! [X338 : term] : ((((X337 @ X338)) != $true) | (((X337 @ (lam @ X338))) = $true)) & ! [X339 : term] : ((((X337 @ X339)) = $true) | ($true != ((var @ X339)))) & ! [X340 : term,X341 : term] : ((((X337 @ (ap @ X340 @ X341))) = $true) | (((X337 @ X340)) != $true) | (((X337 @ X341)) != $true)) & (((X337 @ X336)) != $true)) | ? [X335 : subst] : (((comp @ X335 @ id)) != X335))) & (hoasapnotvar = $true) & (axabs = $true) & ((apinj2 = $true) <=> ! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324))) & ((apinj1 = $true) <=> ! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((? [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) != X2) | ? [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) != X1) | ! [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | (((X8 @ X4)) != $true))) <=> (pushprop_lem1_lthm = $true)) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & (! [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) != $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true)) <=> (pushprop_lem1 = $true)) & (substmonoid_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (? [X134 : term] : (((sub @ X134 @ id)) != X134) | ! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))) | ? [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) = ((ap @ X135 @ X136))) & (X135 != X137)))) & ! [X220 : d_subst] : (d_id = X220) & ((? [X228 : term,X230 : (subst > term > subst > $o),X229 : term] : ((((X230 @ id @ X229 @ id)) = $true) & ! [X232 : term,X231 : term] : ((((X230 @ id @ X232 @ id)) != $true) | (((X230 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)) = $true) | (((X230 @ id @ X231 @ id)) != $true)) & (((X230 @ id @ X228 @ id)) = $true) & ! [X234 : term,X233 : subst,X236 : subst,X235 : subst] : ((((X230 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X236)) != $true) | (((X230 @ X233 @ X234 @ (comp @ X235 @ X236))) = $true)) & ! [X239 : term,X237 : subst,X238 : subst,X240 : subst] : ((((X230 @ X238 @ X239 @ (comp @ X240 @ X237))) != $true) | (((X230 @ (comp @ X238 @ X240) @ (sub @ X239 @ X240) @ X237)) = $true)) & (((X230 @ id @ (ap @ X229 @ X228) @ id)) != $true)) | ! [X258 : (subst > term > subst > $o),X257 : term] : (($true = ((X258 @ id @ X257 @ id))) | ? [X264 : term] : ((((var @ (sub @ X264 @ id))) = $true) & (((X258 @ id @ X264 @ id)) != $true)) | ? [X268 : term,X266 : subst,X267 : subst,X265 : subst] : ((((X258 @ (comp @ X266 @ X265) @ (sub @ X268 @ X265) @ X267)) = $true) & ($true != ((X258 @ X266 @ X268 @ (comp @ X265 @ X267))))) | ? [X274 : term,X273 : term] : ((((X258 @ id @ X274 @ id)) = $true) & (((X258 @ id @ (ap @ (sub @ X274 @ id) @ X273) @ id)) != $true) & (((X258 @ id @ X273 @ id)) = $true)) | ? [X272 : subst,X269 : subst,X270 : term,X271 : subst] : ((((X258 @ X271 @ X270 @ (comp @ X272 @ X269))) = $true) & (((X258 @ (comp @ X271 @ X272) @ (sub @ X270 @ X272) @ X269)) != $true)) | ? [X259 : (subst > term > term)] : (! [X263 : subst,X261 : subst,X262 : term] : (((X259 @ (comp @ X263 @ X261) @ (sub @ X262 @ X261))) = ((sub @ (X259 @ X263 @ X262) @ X261))) & ! [X260 : term] : ((((X258 @ id @ X260 @ id)) != $true) | (((X258 @ id @ (X259 @ id @ X260) @ id)) = $true)) & (((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id)) != $true))) | ? [X221 : (term > $o),X222 : term] : (! [X223 : term] : ((((X221 @ (lam @ X223))) = $true) | ? [X224 : term] : ((((X221 @ X224)) = $true) & (((X221 @ (sub @ X223 @ (push @ X224 @ id)))) != $true))) & (((X221 @ X222)) != $true) & ! [X227 : term] : ((((X221 @ X227)) = $true) | (((var @ X227)) != $true)) & ! [X225 : term,X226 : term] : ((((X221 @ X226)) != $true) | (((X221 @ (ap @ X225 @ X226))) = $true) | (((X221 @ X225)) != $true))) | ? [X242 : (subst > term > subst > $o),X241 : term] : (! [X251 : term] : ((((X242 @ id @ (sub @ X241 @ (push @ X251 @ id)) @ id)) = $true) | (((X242 @ id @ X251 @ id)) != $true)) & ! [X249 : subst,X250 : subst,X248 : term,X247 : subst] : ((((X242 @ X250 @ X248 @ (comp @ X247 @ X249))) != $true) | (((X242 @ (comp @ X250 @ X247) @ (sub @ X248 @ X247) @ X249)) = $true)) & ! [X243 : subst,X245 : term,X246 : subst,X244 : subst] : ((((X242 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) != $true) | (((X242 @ X246 @ X245 @ (comp @ X243 @ X244))) = $true)) & ! [X252 : (subst > term > term)] : (? [X256 : subst,X254 : term,X255 : subst] : (((sub @ (X252 @ X256 @ X254) @ X255)) != ((X252 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | ? [X253 : term] : ((((X242 @ id @ X253 @ id)) = $true) & ($true != ((X242 @ id @ (X252 @ id @ X253) @ id)))) | (((X242 @ id @ (lam @ (X252 @ sh @ one)) @ id)) = $true)) & (((X242 @ id @ (lam @ X241) @ id)) != $true))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X22 : term] : (((sub @ X22 @ id)) != X22) | ! [X31 : (subst > term > subst > $o),X32 : term] : ((((X31 @ id @ (lam @ X32) @ id)) = $true) | ? [X33 : term] : ((((X31 @ id @ X33 @ id)) = $true) & (((X31 @ id @ (sub @ X32 @ (push @ X33 @ id)) @ id)) != $true)) | ? [X34 : (subst > term > term)] : (! [X35 : term] : ((((X31 @ id @ X35 @ id)) != $true) | (((X31 @ id @ (X34 @ id @ X35) @ id)) = $true)) & ! [X36 : subst,X37 : subst,X38 : term] : (((sub @ (X34 @ X36 @ X38) @ X37)) = ((X34 @ (comp @ X36 @ X37) @ (sub @ X38 @ X37)))) & ($true != ((X31 @ id @ (lam @ (X34 @ sh @ one)) @ id))))) | ? [X23 : term,X24 : (subst > term > subst > $o)] : ((((X24 @ id @ (lam @ (sub @ X23 @ (push @ one @ sh))) @ id)) != $true) & ! [X25 : term] : ((((X24 @ id @ (sub @ X23 @ (push @ X25 @ id)) @ id)) = $true) | (((X24 @ id @ X25 @ id)) != $true)) & ! [X26 : (subst > term > term)] : ((((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true) | ? [X29 : subst,X30 : term,X28 : subst] : (((X26 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28))) != ((sub @ (X26 @ X29 @ X30) @ X28))) | ? [X27 : term] : ((((X24 @ id @ (X26 @ id @ X27) @ id)) != $true) & (((X24 @ id @ X27 @ id)) = $true)))))) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (axclos = $true) & ((hoasinduction_lem2 = $true) <=> ! [X525 : term,X527 : term,X526 : (subst > term > subst > $o)] : (? [X529 : subst,X528 : subst,X531 : term,X530 : subst] : ((((X526 @ X530 @ X531 @ (comp @ X529 @ X528))) != $true) & (((X526 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529) @ X528)) = $true)) | (((X526 @ id @ X525 @ id)) != $true) | (((X526 @ id @ X527 @ id)) != $true) | (((X526 @ id @ (ap @ X525 @ X527) @ id)) = $true) | ? [X537 : term,X536 : term] : ((((X526 @ id @ X537 @ id)) = $true) & (((X526 @ id @ X536 @ id)) = $true) & (((X526 @ id @ (ap @ (sub @ X537 @ id) @ X536) @ id)) != $true)) | ? [X535 : term,X534 : subst,X532 : subst,X533 : subst] : ((((X526 @ X532 @ X535 @ (comp @ X534 @ X533))) = $true) & (((X526 @ (comp @ X532 @ X534) @ (sub @ X535 @ X534) @ X533)) != $true)))) & ((axvarcons = $true) <=> ! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516)) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) <=> (hoasapinj2 = $true)) & (one = ((d2term @ d_one))) & (pushprop_gthm = $true) & ((? [X380 : (term > $o),X379 : (subst > term > subst > $o),X381 : term] : (! [X387 : term] : (((X380 @ X387)) = ((X379 @ id @ X387 @ id))) & ! [X388 : term] : (($true = ((X380 @ (sub @ X381 @ (push @ X388 @ id))))) | (((X380 @ X388)) != $true)) & (((X380 @ (lam @ X381))) != $true) & ! [X382 : (subst > term > term)] : ((((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ? [X383 : subst,X385 : term,X384 : subst] : (((X382 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383))) != ((sub @ (X382 @ X384 @ X385) @ X383))) | ? [X386 : term] : ((((X379 @ id @ (X382 @ id @ X386) @ id)) != $true) & (((X379 @ id @ X386 @ id)) = $true)))) | ? [X378 : term] : (((sub @ X378 @ id)) != X378) | ? [X371 : term,X372 : (term > $o)] : (! [X374 : term,X373 : term] : ((((X372 @ X373)) != $true) | (((X372 @ X374)) != $true) | (((X372 @ (ap @ X374 @ X373))) = $true)) & ! [X376 : term] : (? [X377 : term] : ((((X372 @ (sub @ X376 @ (push @ X377 @ id)))) != $true) & (((X372 @ X377)) = $true)) | (((X372 @ (lam @ X376))) = $true)) & ! [X375 : term] : ((((X372 @ X375)) = $true) | (((var @ X375)) != $true)) & (((X372 @ X371)) != $true)) | ! [X390 : term,X389 : (subst > term > subst > $o)] : ((((X389 @ id @ X390 @ id)) = $true) | ? [X396 : term,X397 : term] : ((((X389 @ id @ X396 @ id)) = $true) & (((X389 @ id @ X397 @ id)) = $true) & (((X389 @ id @ (ap @ (sub @ X396 @ id) @ X397) @ id)) != $true)) | ? [X391 : (subst > term > term)] : (! [X392 : subst,X393 : term,X394 : subst] : (((X391 @ (comp @ X392 @ X394) @ (sub @ X393 @ X394))) = ((sub @ (X391 @ X392 @ X393) @ X394))) & ! [X395 : term] : (($true != ((X389 @ id @ X395 @ id))) | (((X389 @ id @ (X391 @ id @ X395) @ id)) = $true)) & (((X389 @ id @ (lam @ (X391 @ sh @ one)) @ id)) != $true))) | ? [X368 : (subst > term > subst > $o)] : ! [X369 : (term > $o)] : ? [X370 : term] : (((X368 @ id @ X370 @ id)) != ((X369 @ X370)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X188 : term] : (((sub @ X188 @ id)) = X188) | ? [X187 : term] : (((sub @ X187 @ id)) != X187)))), 27.00/4.44 inference(flattening,[],[f11])). 27.00/4.44 thf(f13,definition,( 27.00/4.44 ! [X389 : (subst > term > subst > $o)] : ((((sP0 @ X389)) = $true) <=> ? [X391 : (subst > term > term)] : (! [X392 : subst,X393 : term,X394 : subst] : (((X391 @ (comp @ X392 @ X394) @ (sub @ X393 @ X394))) = ((sub @ (X391 @ X392 @ X393) @ X394))) & ! [X395 : term] : (($true != ((X389 @ id @ X395 @ id))) | (((X389 @ id @ (X391 @ id @ X395) @ id)) = $true)) & (((X389 @ id @ (lam @ (X391 @ sh @ one)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f14,definition,( 27.00/4.44 ! [X372 : (term > $o)] : ((((sP1 @ X372)) = $true) <=> ! [X374 : term,X373 : term] : ((((X372 @ X373)) != $true) | (((X372 @ X374)) != $true) | (((X372 @ (ap @ X374 @ X373))) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f15,definition,( 27.00/4.44 (sP2 = $true) <=> ? [X380 : (term > $o),X379 : (subst > term > subst > $o),X381 : term] : (! [X387 : term] : (((X380 @ X387)) = ((X379 @ id @ X387 @ id))) & ! [X388 : term] : (($true = ((X380 @ (sub @ X381 @ (push @ X388 @ id))))) | (((X380 @ X388)) != $true)) & (((X380 @ (lam @ X381))) != $true) & ! [X382 : (subst > term > term)] : ((((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ? [X383 : subst,X385 : term,X384 : subst] : (((X382 @ (comp @ X384 @ X383) @ (sub @ X385 @ X383))) != ((sub @ (X382 @ X384 @ X385) @ X383))) | ? [X386 : term] : ((((X379 @ id @ (X382 @ id @ X386) @ id)) != $true) & (((X379 @ id @ X386 @ id)) = $true))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f16,definition,( 27.00/4.44 (sP3 = $true) <=> ? [X371 : term,X372 : (term > $o)] : ((((sP1 @ X372)) = $true) & ! [X376 : term] : (? [X377 : term] : ((((X372 @ (sub @ X376 @ (push @ X377 @ id)))) != $true) & (((X372 @ X377)) = $true)) | (((X372 @ (lam @ X376))) = $true)) & ! [X375 : term] : ((((X372 @ X375)) = $true) | (((var @ X375)) != $true)) & (((X372 @ X371)) != $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f17,definition,( 27.00/4.44 (sP4 = $true) <=> ((sP2 = $true) | ? [X378 : term] : (((sub @ X378 @ id)) != X378) | (sP3 = $true) | ! [X390 : term,X389 : (subst > term > subst > $o)] : ((((X389 @ id @ X390 @ id)) = $true) | ? [X396 : term,X397 : term] : ((((X389 @ id @ X396 @ id)) = $true) & (((X389 @ id @ X397 @ id)) = $true) & (((X389 @ id @ (ap @ (sub @ X396 @ id) @ X397) @ id)) != $true)) | (((sP0 @ X389)) = $true)) | ? [X368 : (subst > term > subst > $o)] : ! [X369 : (term > $o)] : ? [X370 : term] : (((X368 @ id @ X370 @ id)) != ((X369 @ X370))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f18,definition,( 27.00/4.44 ! [X526 : (subst > term > subst > $o)] : ((((sP5 @ X526)) = $true) <=> ? [X537 : term,X536 : term] : ((((X526 @ id @ X537 @ id)) = $true) & (((X526 @ id @ X536 @ id)) = $true) & (((X526 @ id @ (ap @ (sub @ X537 @ id) @ X536) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f19,definition,( 27.00/4.44 (sP6 = $true) <=> ! [X525 : term,X527 : term,X526 : (subst > term > subst > $o)] : (? [X529 : subst,X528 : subst,X531 : term,X530 : subst] : ((((X526 @ X530 @ X531 @ (comp @ X529 @ X528))) != $true) & (((X526 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529) @ X528)) = $true)) | (((X526 @ id @ X525 @ id)) != $true) | (((X526 @ id @ X527 @ id)) != $true) | (((X526 @ id @ (ap @ X525 @ X527) @ id)) = $true) | (((sP5 @ X526)) = $true) | ? [X535 : term,X534 : subst,X532 : subst,X533 : subst] : ((((X526 @ X532 @ X535 @ (comp @ X534 @ X533))) = $true) & (((X526 @ (comp @ X532 @ X534) @ (sub @ X535 @ X534) @ X533)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f20,definition,( 27.00/4.44 (sP7 = $true) <=> ? [X23 : term,X24 : (subst > term > subst > $o)] : ((((X24 @ id @ (lam @ (sub @ X23 @ (push @ one @ sh))) @ id)) != $true) & ! [X25 : term] : ((((X24 @ id @ (sub @ X23 @ (push @ X25 @ id)) @ id)) = $true) | (((X24 @ id @ X25 @ id)) != $true)) & ! [X26 : (subst > term > term)] : ((((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true) | ? [X29 : subst,X30 : term,X28 : subst] : (((X26 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28))) != ((sub @ (X26 @ X29 @ X30) @ X28))) | ? [X27 : term] : ((((X24 @ id @ (X26 @ id @ X27) @ id)) != $true) & (((X24 @ id @ X27 @ id)) = $true))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f21,definition,( 27.00/4.44 (sP8 = $true) <=> (? [X22 : term] : (((sub @ X22 @ id)) != X22) | ! [X31 : (subst > term > subst > $o),X32 : term] : ((((X31 @ id @ (lam @ X32) @ id)) = $true) | ? [X33 : term] : ((((X31 @ id @ X33 @ id)) = $true) & (((X31 @ id @ (sub @ X32 @ (push @ X33 @ id)) @ id)) != $true)) | ? [X34 : (subst > term > term)] : (! [X35 : term] : ((((X31 @ id @ X35 @ id)) != $true) | (((X31 @ id @ (X34 @ id @ X35) @ id)) = $true)) & ! [X36 : subst,X37 : subst,X38 : term] : (((sub @ (X34 @ X36 @ X38) @ X37)) = ((X34 @ (comp @ X36 @ X37) @ (sub @ X38 @ X37)))) & ($true != ((X31 @ id @ (lam @ (X34 @ sh @ one)) @ id))))) | (sP7 = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f22,definition,( 27.00/4.44 ! [X242 : (subst > term > subst > $o)] : ((((sP9 @ X242)) = $true) <=> ! [X252 : (subst > term > term)] : (? [X256 : subst,X254 : term,X255 : subst] : (((sub @ (X252 @ X256 @ X254) @ X255)) != ((X252 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | ? [X253 : term] : ((((X242 @ id @ X253 @ id)) = $true) & ($true != ((X242 @ id @ (X252 @ id @ X253) @ id)))) | (((X242 @ id @ (lam @ (X252 @ sh @ one)) @ id)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f23,definition,( 27.00/4.44 ! [X221 : (term > $o)] : ((((sP10 @ X221)) = $true) <=> ! [X225 : term,X226 : term] : ((((X221 @ X226)) != $true) | (((X221 @ (ap @ X225 @ X226))) = $true) | (((X221 @ X225)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f24,definition,( 27.00/4.44 ! [X258 : (subst > term > subst > $o)] : ((((sP11 @ X258)) = $true) <=> ? [X259 : (subst > term > term)] : (! [X263 : subst,X261 : subst,X262 : term] : (((X259 @ (comp @ X263 @ X261) @ (sub @ X262 @ X261))) = ((sub @ (X259 @ X263 @ X262) @ X261))) & ! [X260 : term] : ((((X258 @ id @ X260 @ id)) != $true) | (((X258 @ id @ (X259 @ id @ X260) @ id)) = $true)) & (((X258 @ id @ (lam @ (X259 @ sh @ one)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f25,definition,( 27.00/4.44 ! [X258 : (subst > term > subst > $o)] : ((((sP12 @ X258)) = $true) <=> ? [X274 : term,X273 : term] : ((((X258 @ id @ X274 @ id)) = $true) & (((X258 @ id @ (ap @ (sub @ X274 @ id) @ X273) @ id)) != $true) & (((X258 @ id @ X273 @ id)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f26,definition,( 27.00/4.44 ! [X230 : (subst > term > subst > $o)] : ((((sP13 @ X230)) = $true) <=> ! [X232 : term,X231 : term] : ((((X230 @ id @ X232 @ id)) != $true) | (((X230 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)) = $true) | (((X230 @ id @ X231 @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f27,definition,( 27.00/4.44 (sP14 = $true) <=> ? [X242 : (subst > term > subst > $o),X241 : term] : (! [X251 : term] : ((((X242 @ id @ (sub @ X241 @ (push @ X251 @ id)) @ id)) = $true) | (((X242 @ id @ X251 @ id)) != $true)) & ! [X249 : subst,X250 : subst,X248 : term,X247 : subst] : ((((X242 @ X250 @ X248 @ (comp @ X247 @ X249))) != $true) | (((X242 @ (comp @ X250 @ X247) @ (sub @ X248 @ X247) @ X249)) = $true)) & ! [X243 : subst,X245 : term,X246 : subst,X244 : subst] : ((((X242 @ (comp @ X246 @ X243) @ (sub @ X245 @ X243) @ X244)) != $true) | (((X242 @ X246 @ X245 @ (comp @ X243 @ X244))) = $true)) & (((sP9 @ X242)) = $true) & (((X242 @ id @ (lam @ X241) @ id)) != $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f28,definition,( 27.00/4.44 (sP15 = $true) <=> ! [X258 : (subst > term > subst > $o),X257 : term] : (($true = ((X258 @ id @ X257 @ id))) | ? [X264 : term] : ((((var @ (sub @ X264 @ id))) = $true) & (((X258 @ id @ X264 @ id)) != $true)) | ? [X268 : term,X266 : subst,X267 : subst,X265 : subst] : ((((X258 @ (comp @ X266 @ X265) @ (sub @ X268 @ X265) @ X267)) = $true) & ($true != ((X258 @ X266 @ X268 @ (comp @ X265 @ X267))))) | (((sP12 @ X258)) = $true) | ? [X272 : subst,X269 : subst,X270 : term,X271 : subst] : ((((X258 @ X271 @ X270 @ (comp @ X272 @ X269))) = $true) & (((X258 @ (comp @ X271 @ X272) @ (sub @ X270 @ X272) @ X269)) != $true)) | (((sP11 @ X258)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f29,definition,( 27.00/4.44 (sP16 = $true) <=> ? [X221 : (term > $o),X222 : term] : (! [X223 : term] : ((((X221 @ (lam @ X223))) = $true) | ? [X224 : term] : ((((X221 @ X224)) = $true) & (((X221 @ (sub @ X223 @ (push @ X224 @ id)))) != $true))) & (((X221 @ X222)) != $true) & ! [X227 : term] : ((((X221 @ X227)) = $true) | (((var @ X227)) != $true)) & (((sP10 @ X221)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f30,definition,( 27.00/4.44 (sP17 = $true) <=> (? [X228 : term,X230 : (subst > term > subst > $o),X229 : term] : ((((X230 @ id @ X229 @ id)) = $true) & (((sP13 @ X230)) = $true) & (((X230 @ id @ X228 @ id)) = $true) & ! [X234 : term,X233 : subst,X236 : subst,X235 : subst] : ((((X230 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235) @ X236)) != $true) | (((X230 @ X233 @ X234 @ (comp @ X235 @ X236))) = $true)) & ! [X239 : term,X237 : subst,X238 : subst,X240 : subst] : ((((X230 @ X238 @ X239 @ (comp @ X240 @ X237))) != $true) | (((X230 @ (comp @ X238 @ X240) @ (sub @ X239 @ X240) @ X237)) = $true)) & (((X230 @ id @ (ap @ X229 @ X228) @ id)) != $true)) | (sP15 = $true) | (sP16 = $true) | (sP14 = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f31,definition,( 27.00/4.44 ! [X337 : (term > $o)] : ((((sP18 @ X337)) = $true) <=> ! [X340 : term,X341 : term] : ((((X337 @ (ap @ X340 @ X341))) = $true) | (((X337 @ X340)) != $true) | (((X337 @ X341)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f32,definition,( 27.00/4.44 ! [X343 : (term > $o)] : ((((sP19 @ X343)) = $true) <=> ? [X349 : term,X348 : term] : ((((X343 @ (ap @ X349 @ X348))) != $true) & (((X343 @ X348)) = $true) & (((X343 @ X349)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f33,definition,( 27.00/4.44 (sP20 = $true) <=> ! [X342 : term,X343 : (term > $o),X344 : subst] : ((((X343 @ (sub @ X342 @ X344))) = $true) | ? [X345 : term] : ((((X343 @ (sub @ X345 @ X344))) != $true) & (((var @ X345)) = $true)) | ? [X346 : term] : (! [X347 : term] : (($true = ((X343 @ (sub @ X346 @ (push @ X347 @ id))))) | (((X343 @ X347)) != $true)) & ($true != ((X343 @ (lam @ X346))))) | (((sP19 @ X343)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f34,definition,( 27.00/4.44 (sP21 = $true) <=> (? [X333 : subst,X334 : term] : (((comp @ sh @ (push @ X334 @ X333))) != X333) | (sP20 = $true) | ? [X331 : term,X332 : subst] : (((sub @ one @ (push @ X331 @ X332))) != X331) | ? [X337 : (term > $o),X336 : term] : (! [X338 : term] : ((((X337 @ X338)) != $true) | (((X337 @ (lam @ X338))) = $true)) & ! [X339 : term] : ((((X337 @ X339)) = $true) | ($true != ((var @ X339)))) & (((sP18 @ X337)) = $true) & (((X337 @ X336)) != $true)) | ? [X335 : subst] : (((comp @ X335 @ id)) != X335))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f35,definition,( 27.00/4.44 ! [X501 : (subst > term > subst > $o)] : ((((sP22 @ X501)) = $true) <=> ? [X510 : (subst > term > term)] : (! [X513 : subst,X511 : subst,X512 : term] : (((X510 @ (comp @ X511 @ X513) @ (sub @ X512 @ X513))) = ((sub @ (X510 @ X511 @ X512) @ X513))) & (((X501 @ id @ (lam @ (X510 @ sh @ one)) @ id)) != $true) & ! [X514 : term] : ((((X501 @ id @ (X510 @ id @ X514) @ id)) = $true) | (((X501 @ id @ X514 @ id)) != $true))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f36,definition,( 27.00/4.44 (sP23 = $true) <=> ! [X500 : term,X501 : (subst > term > subst > $o)] : (? [X503 : subst,X502 : subst,X504 : subst,X505 : term] : ((((X501 @ (comp @ X502 @ X504) @ (sub @ X505 @ X504) @ X503)) != $true) & (((X501 @ X502 @ X505 @ (comp @ X504 @ X503))) = $true)) | ? [X506 : term,X507 : subst,X509 : subst,X508 : subst] : (($true != ((X501 @ X507 @ X506 @ (comp @ X509 @ X508)))) & (((X501 @ (comp @ X507 @ X509) @ (sub @ X506 @ X509) @ X508)) = $true)) | (((sP22 @ X501)) = $true) | ? [X515 : term] : ((((X501 @ id @ X515 @ id)) = $true) & ($true != ((X501 @ id @ (sub @ X500 @ (push @ X515 @ id)) @ id)))) | (((X501 @ id @ (lam @ X500) @ id)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f37,definition,( 27.00/4.44 ! [X446 : (term > $o)] : ((((sP24 @ X446)) = $true) <=> ? [X450 : term,X449 : term] : ((((X446 @ X449)) = $true) & ($true != ((X446 @ (ap @ X449 @ X450)))) & (((X446 @ X450)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f38,definition,( 27.00/4.44 (sP25 = $true) <=> ! [X446 : (term > $o),X447 : subst,X445 : term] : (($true = ((X446 @ (sub @ X445 @ X447)))) | ? [X451 : term] : (! [X452 : term] : ((((X446 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X446 @ X452)) != $true)) & (((X446 @ (lam @ X451))) != $true)) | (((sP24 @ X446)) = $true) | ? [X448 : term] : ((((X446 @ (sub @ X448 @ X447))) != $true) & (((var @ X448)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f39,definition,( 27.00/4.44 ! [X352 : (subst > term > subst > $o)] : ((((sP26 @ X352)) = $true) <=> ? [X363 : (subst > term > term)] : (! [X365 : term,X364 : subst,X366 : subst] : (((sub @ (X363 @ X364 @ X365) @ X366)) = ((X363 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366)))) & ! [X367 : term] : ((((X352 @ id @ (X363 @ id @ X367) @ id)) = $true) | (((X352 @ id @ X367 @ id)) != $true)) & (((X352 @ id @ (lam @ (X363 @ sh @ one)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f40,definition,( 27.00/4.44 (sP27 = $true) <=> ! [X351 : (term > $o),X350 : term,X352 : (subst > term > subst > $o)] : ((((sP26 @ X352)) = $true) | ? [X356 : subst,X358 : subst,X357 : term,X355 : subst] : ((((X352 @ X358 @ X357 @ (comp @ X356 @ X355))) = $true) & ($true != ((X352 @ (comp @ X358 @ X356) @ (sub @ X357 @ X356) @ X355)))) | ? [X362 : subst,X360 : term,X361 : subst,X359 : subst] : (($true != ((X352 @ X362 @ X360 @ (comp @ X361 @ X359)))) & (((X352 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359)) = $true)) | (((X351 @ (lam @ X350))) = $true) | ? [X353 : term] : (((X352 @ id @ X353 @ id)) != ((X351 @ X353))) | ? [X354 : term] : ((((X351 @ X354)) = $true) & (((X351 @ (sub @ X350 @ (push @ X354 @ id)))) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f41,definition,( 27.00/4.44 ($true = sP28) <=> ! [X208 : term,X209 : (subst > term > subst > $o)] : (? [X211 : term,X210 : (subst > term > term)] : (! [X212 : term] : ((((X209 @ id @ X212 @ id)) != $true) | (((X209 @ id @ (X210 @ id @ X212) @ id)) = $true)) & ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) = ((sub @ (X210 @ X218 @ X216) @ X217))) & ! [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) = ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) & (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) != $true)) | (((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) = $true) | ? [X219 : term] : ((((X209 @ id @ X219 @ id)) = $true) & (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f42,definition,( 27.00/4.44 ! [X398 : (subst > term > subst > $o)] : ((((sP29 @ X398)) = $true) <=> ? [X402 : (subst > term > term)] : (! [X405 : subst,X403 : subst,X404 : term] : (((sub @ (X402 @ X405 @ X404) @ X403)) = ((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403)))) & ! [X406 : term] : (($true != ((X398 @ id @ X406 @ id))) | (((X398 @ id @ (X402 @ id @ X406) @ id)) = $true)) & (((X398 @ id @ (lam @ (X402 @ sh @ one)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f43,definition,( 27.00/4.44 (sP30 = $true) <=> ! [X276 : (subst > term > subst > $o),X275 : term] : (? [X278 : (subst > term > term)] : ((((X276 @ id @ (lam @ (X278 @ sh @ one)) @ id)) != $true) & ! [X279 : term] : ((((X276 @ id @ (X278 @ id @ X279) @ id)) = $true) | (((X276 @ id @ X279 @ id)) != $true)) & ! [X282 : subst,X280 : term,X281 : subst] : (((sub @ (X278 @ X282 @ X280) @ X281)) = ((X278 @ (comp @ X282 @ X281) @ (sub @ X280 @ X281))))) | ? [X277 : term] : ((((X276 @ id @ (sub @ X275 @ (push @ X277 @ id)) @ id)) != $true) & (((X276 @ id @ X277 @ id)) = $true)) | (((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f44,definition,( 27.00/4.44 ! [X67 : (term > $o)] : ((((sP31 @ X67)) = $true) <=> ? [X71 : term,X70 : term] : ((((X67 @ X70)) = $true) & (((X67 @ X71)) = $true) & (((X67 @ (ap @ X70 @ X71))) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f45,definition,( 27.00/4.44 (sP32 = $true) <=> ! [X466 : (subst > term > subst > $o),X464 : (term > $o),X465 : term] : (? [X467 : term] : (($true = ((X464 @ X467))) & (((X464 @ (sub @ X465 @ (push @ X467 @ id)))) != $true)) | ? [X469 : (subst > term > term)] : (! [X470 : term] : (($true = ((X466 @ id @ (X469 @ id @ X470) @ id))) | (((X466 @ id @ X470 @ id)) != $true)) & ! [X473 : subst,X471 : term,X472 : subst] : (((sub @ (X469 @ X473 @ X471) @ X472)) = ((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472)))) & (((X466 @ id @ (lam @ (X469 @ sh @ one)) @ id)) != $true)) | ? [X468 : term] : (((X466 @ id @ X468 @ id)) != ((X464 @ X468))) | (((X464 @ (lam @ X465))) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f46,definition,( 27.00/4.44 ! [X518 : (term > $o)] : ((((sP33 @ X518)) = $true) <=> ? [X524 : term,X523 : term] : ((((X518 @ X524)) = $true) & (((X518 @ (ap @ X523 @ X524))) != $true) & (((X518 @ X523)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f47,definition,( 27.00/4.44 (sP34 = $true) <=> ! [X518 : (term > $o),X519 : term] : (? [X522 : term] : ((((X518 @ X522)) != $true) & (((var @ X522)) = $true)) | ? [X520 : term] : (! [X521 : term] : ((((X518 @ X521)) != $true) | (((X518 @ (sub @ X520 @ (push @ X521 @ id)))) = $true)) & (((X518 @ (lam @ X520))) != $true)) | (((X518 @ X519)) = $true) | (((sP33 @ X518)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f48,definition,( 27.00/4.44 ! [X127 : (term > $o)] : (($true = ((sP35 @ X127))) <=> ? [X133 : term,X132 : term] : ((((X127 @ X133)) = $true) & (((X127 @ (ap @ X133 @ X132))) != $true) & (((X127 @ X132)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f49,definition,( 27.00/4.44 ! [X121 : (term > $o)] : ((((sP36 @ X121)) = $true) <=> ! [X125 : term,X126 : term] : ((((X121 @ X125)) != $true) | (((X121 @ (ap @ X126 @ X125))) = $true) | (((X121 @ X126)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f50,definition,( 27.00/4.44 (sP37 = $true) <=> ! [X127 : (term > $o),X128 : term] : (($true = ((sP35 @ X127))) | ? [X130 : term] : ((((X127 @ (lam @ X130))) != $true) & ! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true))) | (((X127 @ X128)) = $true) | ? [X129 : term] : (($true = ((var @ X129))) & (((X127 @ X129)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f51,definition,( 27.00/4.44 (sP38 = $true) <=> (? [X118 : term] : (((sub @ X118 @ id)) != X118) | ? [X120 : subst,X119 : term,X121 : (term > $o)] : (! [X124 : term] : ((((X121 @ (sub @ X124 @ X120))) = $true) | (((var @ X124)) != $true)) & (((X121 @ (sub @ X119 @ X120))) != $true) & ! [X122 : term] : ((((X121 @ (lam @ X122))) = $true) | ? [X123 : term] : ((((X121 @ X123)) = $true) & (((X121 @ (sub @ X122 @ (push @ X123 @ id)))) != $true))) & (((sP36 @ X121)) = $true)) | (sP37 = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f52,definition,( 27.00/4.44 (sP39 = $true) <=> (! [X490 : (subst > term > subst > $o),X489 : (term > $o),X488 : term] : (? [X497 : term] : ((((X489 @ X497)) = $true) & ($true != ((X489 @ (sub @ X488 @ (push @ X497 @ id)))))) | ? [X492 : (subst > term > term)] : ((((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id)) != $true) & ! [X496 : term] : ((((X490 @ id @ (X492 @ id @ X496) @ id)) = $true) | ($true != ((X490 @ id @ X496 @ id)))) & ! [X495 : subst,X493 : term,X494 : subst] : (((sub @ (X492 @ X495 @ X493) @ X494)) = ((X492 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494))))) | ? [X491 : term] : (((X490 @ id @ X491 @ id)) != ((X489 @ X491))) | (((X489 @ (lam @ X488))) = $true)) | ? [X487 : term] : (((sub @ X487 @ id)) != X487) | ? [X483 : term] : ! [X484 : (subst > term > term)] : ? [X485 : subst,X486 : term] : (((X484 @ X485 @ X486)) != ((sub @ X483 @ (push @ X486 @ X485)))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f53,definition,( 27.00/4.44 ! [X75 : (term > $o)] : ((((sP40 @ X75)) = $true) <=> ! [X80 : term,X81 : term] : ((((X75 @ X80)) != $true) | (((X75 @ (ap @ X80 @ X81))) = $true) | (((X75 @ X81)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f54,definition,( 27.00/4.44 ! [X93 : (subst > term > subst > $o)] : ((((sP41 @ X93)) = $true) <=> ? [X99 : term,X100 : term] : ((((X93 @ id @ X100 @ id)) = $true) & (((X93 @ id @ X99 @ id)) = $true) & ($true != ((X93 @ id @ (ap @ (sub @ X100 @ id) @ X99) @ id)))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f55,definition,( 27.00/4.44 ! [X93 : (subst > term > subst > $o)] : ((((sP42 @ X93)) = $true) <=> ? [X101 : (subst > term > term)] : (! [X105 : term] : ((((X93 @ id @ X105 @ id)) != $true) | (((X93 @ id @ (X101 @ id @ X105) @ id)) = $true)) & ! [X102 : term,X104 : subst,X103 : subst] : (((sub @ (X101 @ X103 @ X102) @ X104)) = ((X101 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104)))) & (((X93 @ id @ (lam @ (X101 @ sh @ one)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f56,definition,( 27.00/4.44 (sP43 = $true) <=> ! [X94 : term,X93 : (subst > term > subst > $o)] : ((((X93 @ id @ X94 @ id)) = $true) | ? [X106 : term] : ((((X93 @ id @ X106 @ id)) != $true) & (((var @ (sub @ X106 @ id))) = $true)) | ? [X98 : term,X97 : subst,X96 : subst,X95 : subst] : ((((X93 @ X95 @ X98 @ (comp @ X97 @ X96))) = $true) & (((X93 @ (comp @ X95 @ X97) @ (sub @ X98 @ X97) @ X96)) != $true)) | (((sP42 @ X93)) = $true) | ? [X108 : term,X107 : subst,X110 : subst,X109 : subst] : (($true = ((X93 @ (comp @ X107 @ X110) @ (sub @ X108 @ X110) @ X109))) & (((X93 @ X107 @ X108 @ (comp @ X110 @ X109))) != $true)) | (((sP41 @ X93)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f57,definition,( 27.00/4.44 (sP44 = $true) <=> ? [X83 : term,X85 : (term > $o),X84 : (subst > term > subst > $o)] : (! [X87 : term] : (((X84 @ id @ X87 @ id)) = ((X85 @ X87))) & (((X85 @ (lam @ X83))) != $true) & ! [X88 : (subst > term > term)] : (? [X89 : term] : (($true = ((X84 @ id @ X89 @ id))) & (((X84 @ id @ (X88 @ id @ X89) @ id)) != $true)) | (((X84 @ id @ (lam @ (X88 @ sh @ one)) @ id)) = $true) | ? [X91 : subst,X92 : subst,X90 : term] : (((X88 @ (comp @ X91 @ X92) @ (sub @ X90 @ X92))) != ((sub @ (X88 @ X91 @ X90) @ X92)))) & ! [X86 : term] : ((((X85 @ X86)) != $true) | (((X85 @ (sub @ X83 @ (push @ X86 @ id)))) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f58,definition,( 27.00/4.44 (sP45 = $true) <=> ((sP44 = $true) | (sP43 = $true) | ? [X82 : term] : (((sub @ X82 @ id)) != X82) | ? [X76 : term,X75 : (term > $o)] : (! [X77 : term] : ((((var @ X77)) != $true) | (((X75 @ X77)) = $true)) & ! [X78 : term] : ((((X75 @ (lam @ X78))) = $true) | ? [X79 : term] : ((((X75 @ X79)) = $true) & (((X75 @ (sub @ X78 @ (push @ X79 @ id)))) != $true))) & (((X75 @ X76)) != $true) & (((sP40 @ X75)) = $true)) | ? [X72 : (subst > term > subst > $o)] : ! [X73 : (term > $o)] : ? [X74 : term] : (((X73 @ X74)) != ((X72 @ id @ X74 @ id))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f59,definition,( 27.00/4.44 (sP46 = $true) <=> (? [X433 : term,X432 : term] : ((((lam @ X433)) = ((lam @ X432))) & (X432 != X433)) | ? [X428 : term,X429 : subst] : (((sub @ one @ (push @ X428 @ X429))) != X428) | ? [X431 : subst,X430 : term] : (((comp @ sh @ (push @ X430 @ X431))) != X431) | ! [X435 : (subst > term > term),X436 : term,X434 : (subst > term > term),X437 : subst] : (? [X441 : term,X442 : subst,X443 : subst] : (((X435 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))) != ((sub @ (X435 @ X443 @ X441) @ X442))) | (((X434 @ X437 @ X436)) = ((X435 @ X437 @ X436))) | (((lam @ (X435 @ sh @ one))) != ((lam @ (X434 @ sh @ one)))) | ? [X439 : term,X438 : subst,X440 : subst] : (((sub @ (X434 @ X440 @ X439) @ X438)) != ((X434 @ (comp @ X440 @ X438) @ (sub @ X439 @ X438))))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f60,definition,( 27.00/4.44 ! [X49 : (subst > term > subst > $o)] : ((((sP47 @ X49)) = $true) <=> ? [X58 : (subst > term > term)] : (! [X60 : subst,X61 : term,X59 : subst] : (((X58 @ (comp @ X60 @ X59) @ (sub @ X61 @ X59))) = ((sub @ (X58 @ X60 @ X61) @ X59))) & (((X49 @ id @ (lam @ (X58 @ sh @ one)) @ id)) != $true) & ! [X62 : term] : ((((X49 @ id @ X62 @ id)) != $true) | (((X49 @ id @ (X58 @ id @ X62) @ id)) = $true))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f61,definition,( 27.00/4.44 ! [X49 : (subst > term > subst > $o)] : ((((sP48 @ X49)) = $true) <=> ? [X63 : term,X64 : term] : ((((X49 @ id @ X63 @ id)) = $true) & (((X49 @ id @ (ap @ (sub @ X64 @ id) @ X63) @ id)) != $true) & (((X49 @ id @ X64 @ id)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f62,definition,( 27.00/4.44 (sP49 = $true) <=> ! [X49 : (subst > term > subst > $o),X48 : term] : (? [X50 : subst,X52 : term,X53 : subst,X51 : subst] : ((((X49 @ X51 @ X52 @ (comp @ X50 @ X53))) != $true) & (((X49 @ (comp @ X51 @ X50) @ (sub @ X52 @ X50) @ X53)) = $true)) | (((X49 @ id @ X48 @ id)) = $true) | (((sP48 @ X49)) = $true) | ? [X56 : subst,X55 : subst,X57 : subst,X54 : term] : ((((X49 @ (comp @ X56 @ X57) @ (sub @ X54 @ X57) @ X55)) != $true) & (((X49 @ X56 @ X54 @ (comp @ X57 @ X55))) = $true)) | ? [X65 : term] : ((((var @ (sub @ X65 @ id))) = $true) & (((X49 @ id @ X65 @ id)) != $true)) | (((sP47 @ X49)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f63,definition,( 27.00/4.44 ! [X413 : (subst > term > subst > $o)] : ((((sP50 @ X413)) = $true) <=> ? [X418 : term,X417 : term] : ((((X413 @ id @ X418 @ id)) = $true) & (((X413 @ id @ X417 @ id)) = $true) & (((X413 @ id @ (ap @ (sub @ X418 @ id) @ X417) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f64,definition,( 27.00/4.44 (sP51 = $true) <=> ! [X415 : term,X413 : (subst > term > subst > $o),X414 : (term > $o),X416 : term] : (? [X423 : term,X424 : subst,X426 : subst,X425 : subst] : ((((X413 @ X424 @ X423 @ (comp @ X425 @ X426))) != $true) & (((X413 @ (comp @ X424 @ X425) @ (sub @ X423 @ X425) @ X426)) = $true)) | (((sP50 @ X413)) = $true) | ? [X419 : subst,X421 : subst,X420 : term,X422 : subst] : ((((X413 @ X421 @ X420 @ (comp @ X422 @ X419))) = $true) & (((X413 @ (comp @ X421 @ X422) @ (sub @ X420 @ X422) @ X419)) != $true)) | (((X414 @ (ap @ X415 @ X416))) = $true) | (((X414 @ X416)) != $true) | (((X414 @ X415)) != $true) | ? [X427 : term] : (((X413 @ id @ X427 @ id)) != ((X414 @ X427))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f65,definition,( 27.00/4.44 (sP52 = $true) <=> ! [X149 : (subst > term > subst > $o),X148 : term] : (? [X151 : (subst > term > term)] : ((((X149 @ id @ (lam @ (X151 @ sh @ one)) @ id)) != $true) & ! [X152 : term] : ((((X149 @ id @ (X151 @ id @ X152) @ id)) = $true) | (((X149 @ id @ X152 @ id)) != $true)) & ! [X155 : subst,X153 : term,X154 : subst] : (((sub @ (X151 @ X155 @ X153) @ X154)) = ((X151 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154))))) | (((X149 @ id @ (lam @ X148) @ id)) = $true) | ? [X150 : term] : ((((X149 @ id @ X150 @ id)) = $true) & (((X149 @ id @ (sub @ X148 @ (push @ X150 @ id)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f66,definition,( 27.00/4.44 ! [X295 : (subst > term > subst > $o)] : ((((sP53 @ X295)) = $true) <=> ? [X301 : (subst > term > term)] : (! [X303 : subst,X305 : subst,X304 : term] : (((sub @ (X301 @ X303 @ X304) @ X305)) = ((X301 @ (comp @ X303 @ X305) @ (sub @ X304 @ X305)))) & ! [X302 : term] : ((((X295 @ id @ X302 @ id)) != $true) | (((X295 @ id @ (X301 @ id @ X302) @ id)) = $true)) & ($true != ((X295 @ id @ (lam @ (X301 @ sh @ one)) @ id)))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f67,definition,( 27.00/4.44 (sP54 = $true) <=> ? [X287 : term,X286 : (subst > term > subst > $o)] : (! [X293 : term] : ((((X286 @ id @ X293 @ id)) != $true) | (((X286 @ id @ (sub @ X287 @ (push @ X293 @ id)) @ id)) = $true)) & (((X286 @ id @ (lam @ (sub @ X287 @ (push @ one @ sh))) @ id)) != $true) & ! [X288 : (subst > term > term)] : ((((X286 @ id @ (lam @ (X288 @ sh @ one)) @ id)) = $true) | ? [X291 : term,X290 : subst,X292 : subst] : (((X288 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290))) != ((sub @ (X288 @ X292 @ X291) @ X290))) | ? [X289 : term] : ((((X286 @ id @ (X288 @ id @ X289) @ id)) != $true) & (((X286 @ id @ X289 @ id)) = $true))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f68,definition,( 27.00/4.44 (sP55 = $true) <=> (? [X285 : term] : (((sub @ X285 @ id)) != X285) | ! [X295 : (subst > term > subst > $o),X294 : term] : (? [X296 : term] : ((((X295 @ id @ X296 @ id)) = $true) & (((X295 @ id @ (sub @ X294 @ (push @ X296 @ id)) @ id)) != $true)) | (((sP53 @ X295)) = $true) | ? [X300 : subst,X298 : term,X297 : subst,X299 : subst] : ((((X295 @ (comp @ X300 @ X299) @ (sub @ X298 @ X299) @ X297)) != $true) & (((X295 @ X300 @ X298 @ (comp @ X299 @ X297))) = $true)) | (((X295 @ id @ (lam @ X294) @ id)) = $true) | ? [X307 : subst,X306 : subst,X309 : term,X308 : subst] : ((((X295 @ X307 @ X309 @ (comp @ X308 @ X306))) != $true) & (((X295 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)) = $true))) | (sP54 = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f69,definition,( 27.00/4.44 ! [X166 : (subst > term > subst > $o)] : ((((sP56 @ X166)) = $true) <=> ? [X173 : (subst > term > term)] : (! [X176 : term,X175 : subst,X174 : subst] : (((X173 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174))) = ((sub @ (X173 @ X175 @ X176) @ X174))) & ! [X177 : term] : ((((X166 @ id @ (X173 @ id @ X177) @ id)) = $true) | (((X166 @ id @ X177 @ id)) != $true)) & (((X166 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f70,definition,( 27.00/4.44 (sP57 = $true) <=> (? [X165 : term] : (((sub @ X165 @ id)) != X165) | ! [X167 : (term > $o),X168 : term,X166 : (subst > term > subst > $o)] : ((((sP56 @ X166)) = $true) | ? [X172 : subst,X169 : term,X170 : subst,X171 : subst] : ((((X166 @ (comp @ X170 @ X172) @ (sub @ X169 @ X172) @ X171)) != $true) & (((X166 @ X170 @ X169 @ (comp @ X172 @ X171))) = $true)) | ? [X183 : term] : (((X167 @ X183)) != ((X166 @ id @ X183 @ id))) | ? [X178 : term] : ((((X167 @ (sub @ X168 @ (push @ X178 @ id)))) != $true) & (((X167 @ X178)) = $true)) | (((X167 @ (lam @ X168))) = $true) | ? [X179 : term,X182 : subst,X180 : subst,X181 : subst] : ((((X166 @ X181 @ X179 @ (comp @ X182 @ X180))) != $true) & ($true = ((X166 @ (comp @ X181 @ X182) @ (sub @ X179 @ X182) @ X180))))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f71,definition,( 27.00/4.44 (sP58 = $true) <=> ! [X454 : term,X453 : (subst > term > subst > $o)] : ((((X453 @ id @ (lam @ (sub @ X454 @ (push @ one @ sh))) @ id)) = $true) | ? [X455 : (subst > term > term)] : (! [X459 : term] : ((((X453 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X453 @ id @ X459 @ id)) != $true)) & (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true) & ! [X456 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X456 @ X458) @ X457)) = ((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))))) | ? [X460 : term] : ((((X453 @ id @ (sub @ X454 @ (push @ X460 @ id)) @ id)) != $true) & (((X453 @ id @ X460 @ id)) = $true)))), 27.00/4.44 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])). 27.00/4.44 thf(f72,plain,( 27.00/4.44 (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> (sP58 = $true)) & ((sP57 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) <=> (laminj = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & ((sP55 = $true) <=> (hoasinduction_lem3_lthm = $true)) & (! [X463 : subst] : (((comp @ id @ X463)) = X463) <=> (axidl = $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) <=> (substmonoid = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X481 : d_term,X482 : d_term] : ((X481 = X482) | (((d2term @ X482)) != ((d2term @ X481)))) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) <=> ((! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15)) | ? [X14 : subst] : (((comp @ X14 @ id)) != X14) | ? [X13 : subst] : (((comp @ id @ X13)) != X13))) & ((axidr = $true) <=> ! [X39 : subst] : (((comp @ X39 @ id)) = X39)) & (! [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) = $true) | (((X476 @ X474)) != $true) | ? [X478 : term] : (((X477 @ X478)) != ((X476 @ (sub @ X478 @ (push @ X474 @ X475)))))) <=> (pushprop_lem1v2 = $true)) & ((sP52 = $true) <=> (hoasinduction_lem3a = $true)) & (apnotvar = $true) & (! [X407 : term] : ? [X408 : (subst > term > term)] : ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((sP51 = $true) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction = $true) <=> (sP49 = $true)) & (ulamvarind = $true) & ((sP46 = $true) <=> (hoaslaminj_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lthm_3 = $true) <=> (sP45 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((pushprop_lem0 = $true) <=> ! [X144 : subst,X143 : (term > $o),X145 : term] : ? [X146 : (term > $o)] : ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147)))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) = $true) | ? [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) != ((X316 @ X320))) | (((X318 @ X317)) != $true)) | ? [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) != X314))) & (axapp = $true) & ((sP39 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X189 : (subst > term > term),X191 : term,X190 : term] : (? [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) != ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) | (((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((induction2_lthm = $true) <=> (sP38 = $true)) & ! [X313 : d_term] : (d_one = X313) & ! [X479 : d_subst,X480 : d_subst] : ((X479 = X480) | (((d2subst @ X480)) != ((d2subst @ X479)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2 = $true) <=> (sP34 = $true)) & (pushprop_lthm = $true) & (pushprop_lem0_gthm = $true) & ((sP32 = $true) <=> (hoasinduction_lem3v2a = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X156 : subst,X158 : term,X157 : (term > $o)] : ? [X159 : (term > $o)] : ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160)))) & ((hoasapinj1 = $true) <=> ! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330))) & ((induction = $true) <=> ! [X67 : (term > $o),X66 : term] : (? [X68 : term] : ((((var @ X68)) = $true) & (((X67 @ X68)) != $true)) | ? [X69 : term] : ((((X67 @ X69)) = $true) & (((X67 @ (lam @ X69))) != $true)) | (((sP31 @ X67)) = $true) | (((X67 @ X66)) = $true))) & ((hoasinduction_lem0 = $true) <=> ! [X184 : (subst > term > subst > $o)] : ? [X185 : (term > $o)] : ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186)))) & ((hoasinduction_lem3b = $true) <=> ! [X321 : term] : ? [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) = ((X322 @ sh @ one)))) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = sh) & (lamnotap != $true) & ((axshiftcons = $true) <=> ! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP30 = $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X112 : term] : ? [X113 : (subst > term > term)] : ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114)))) & (pushprop = $true) & (! [X398 : (subst > term > subst > $o),X399 : term] : (? [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) = $true) & (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X398 @ id @ X400 @ id)) = $true)) | (((X398 @ id @ X399 @ id)) = $true) | (((sP29 @ X398)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (axmap = $true) & ((axvarid = $true) <=> ! [X312 : term] : (((sub @ X312 @ id)) = X312)) & (($true = sP28) <=> (hoasinduction_lem3aaa = $true)) & (! [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) != ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | ? [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X200 @ X206 @ X205) @ X207)))) <=> (hoaslaminj = $true)) & ((sP27 = $true) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X310 : term] : ? [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) = ((X311 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem1 = $true) & (hoaslamnotap_lthm = $true) & (! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) <=> (shinj = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2_lthm = $true) <=> (! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))) | ? [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) = ((ap @ X43 @ X40))) & (X40 != X41)))) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X195 : (subst > term > subst > $o)] : ? [X196 : (term > $o)] : ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197)))) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((axscons = $true) <=> ! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((termmset = $true) <=> ! [X444 : term] : (((sub @ X444 @ id)) = X444)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP25 = $true) <=> (induction2lem = $true)) & ((hoasinduction_lem3 = $true) <=> (sP23 = $true)) & ((induction2lem_lthm = $true) <=> (sP21 = $true)) & (hoasapnotvar = $true) & (axabs = $true) & ((apinj2 = $true) <=> ! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324))) & ((apinj1 = $true) <=> ! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((? [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) != X2) | ? [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) != X1) | ! [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | (((X8 @ X4)) != $true))) <=> (pushprop_lem1_lthm = $true)) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & (! [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) != $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true)) <=> (pushprop_lem1 = $true)) & (substmonoid_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (? [X134 : term] : (((sub @ X134 @ id)) != X134) | ! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))) | ? [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) = ((ap @ X135 @ X136))) & (X135 != X137)))) & ! [X220 : d_subst] : (d_id = X220) & ((sP17 = $true) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (sP8 = $true)) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (axclos = $true) & ((hoasinduction_lem2 = $true) <=> (sP6 = $true)) & ((axvarcons = $true) <=> ! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516)) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) <=> (hoasapinj2 = $true)) & (one = ((d2term @ d_one))) & (pushprop_gthm = $true) & ((sP4 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X188 : term] : (((sub @ X188 @ id)) = X188) | ? [X187 : term] : (((sub @ X187 @ id)) != X187)))), 27.00/4.44 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])). 27.00/4.44 thf(f169,plain,( 27.00/4.44 (($true = sP28) | ? [X208 : term,X209 : (subst > term > subst > $o)] : (! [X211 : term,X210 : (subst > term > term)] : (? [X212 : term] : ((((X209 @ id @ X212 @ id)) = $true) & (((X209 @ id @ (X210 @ id @ X212) @ id)) != $true)) | ? [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) != ((sub @ (X210 @ X218 @ X216) @ X217))) | ? [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) != ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) | (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) = $true)) & (((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) != $true) & ! [X219 : term] : ((((X209 @ id @ X219 @ id)) != $true) | (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) = $true)))) & (! [X208 : term,X209 : (subst > term > subst > $o)] : (? [X211 : term,X210 : (subst > term > term)] : (! [X212 : term] : ((((X209 @ id @ X212 @ id)) != $true) | (((X209 @ id @ (X210 @ id @ X212) @ id)) = $true)) & ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (sub @ X211 @ (push @ X216 @ X218)) @ X217)) = ((sub @ (X210 @ X218 @ X216) @ X217))) & ! [X214 : subst,X213 : subst,X215 : term] : (((sub @ X211 @ (push @ (sub @ X215 @ X214) @ (comp @ X213 @ X214)))) = ((X210 @ (comp @ X213 @ X214) @ (sub @ X215 @ X214)))) & (((X209 @ id @ (lam @ (X210 @ sh @ one)) @ id)) != $true)) | (((X209 @ id @ (lam @ (sub @ X208 @ (push @ one @ sh))) @ id)) = $true) | ? [X219 : term] : ((((X209 @ id @ X219 @ id)) = $true) & (((X209 @ id @ (sub @ X208 @ (push @ X219 @ id)) @ id)) != $true))) | ($true != sP28))), 27.00/4.44 inference(nnf_transformation,[],[f41])). 27.00/4.44 thf(f170,plain,( 27.00/4.44 (($true = sP28) | ? [X0 : term,X1 : (subst > term > subst > $o)] : (! [X2 : term,X3 : (subst > term > term)] : (? [X4 : term] : ((((X1 @ id @ X4 @ id)) = $true) & (((X1 @ id @ (X3 @ id @ X4) @ id)) != $true)) | ? [X5 : term,X6 : subst,X7 : subst] : (((sub @ (X3 @ X7 @ X5) @ X6)) != ((sub @ (sub @ X2 @ (push @ X5 @ X7)) @ X6))) | ? [X8 : subst,X9 : subst,X10 : term] : (((X3 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) != ((sub @ X2 @ (push @ (sub @ X10 @ X8) @ (comp @ X9 @ X8))))) | (((X1 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) & (((X1 @ id @ (lam @ (sub @ X0 @ (push @ one @ sh))) @ id)) != $true) & ! [X11 : term] : ((((X1 @ id @ X11 @ id)) != $true) | (((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) = $true)))) & (! [X12 : term,X13 : (subst > term > subst > $o)] : (? [X14 : term,X15 : (subst > term > term)] : (! [X16 : term] : ((((X13 @ id @ X16 @ id)) != $true) | (((X13 @ id @ (X15 @ id @ X16) @ id)) = $true)) & ! [X17 : term,X18 : subst,X19 : subst] : (((sub @ (X15 @ X19 @ X17) @ X18)) = ((sub @ (sub @ X14 @ (push @ X17 @ X19)) @ X18))) & ! [X20 : subst,X21 : subst,X22 : term] : (((sub @ X14 @ (push @ (sub @ X22 @ X20) @ (comp @ X21 @ X20)))) = ((X15 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20)))) & (((X13 @ id @ (lam @ (X15 @ sh @ one)) @ id)) != $true)) | (((X13 @ id @ (lam @ (sub @ X12 @ (push @ one @ sh))) @ id)) = $true) | ? [X23 : term] : ((((X13 @ id @ X23 @ id)) = $true) & (((X13 @ id @ (sub @ X12 @ (push @ X23 @ id)) @ id)) != $true))) | ($true != sP28))), 27.00/4.44 inference(rectify,[],[f169])). 27.00/4.44 thf(f171,plain,( 27.00/4.44 (($true = sP28) | (! [X2 : term,X3 : (subst > term > term)] : (((((sK271 @ id @ (sK272 @ X3) @ id)) = $true) & (((sK271 @ id @ (X3 @ id @ (sK272 @ X3)) @ id)) != $true)) | (((sub @ (sub @ X2 @ (push @ (sK273 @ X3 @ X2) @ (sK275 @ X3 @ X2))) @ (sK274 @ X3 @ X2))) != ((sub @ (X3 @ (sK275 @ X3 @ X2) @ (sK273 @ X3 @ X2)) @ (sK274 @ X3 @ X2)))) | (((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) | (((sK271 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) & (((sK271 @ id @ (lam @ (sub @ sK270 @ (push @ one @ sh))) @ id)) != $true) & ! [X11 : term] : ((((sK271 @ id @ X11 @ id)) != $true) | (((sK271 @ id @ (sub @ sK270 @ (push @ X11 @ id)) @ id)) = $true)))) & (! [X12 : term,X13 : (subst > term > subst > $o)] : ((! [X16 : term] : ((((X13 @ id @ X16 @ id)) != $true) | (((X13 @ id @ (sK280 @ X13 @ id @ X16) @ id)) = $true)) & ! [X17 : term,X18 : subst,X19 : subst] : (((sub @ (sub @ (sK279 @ X13) @ (push @ X17 @ X19)) @ X18)) = ((sub @ (sK280 @ X13 @ X19 @ X17) @ X18))) & ! [X20 : subst,X21 : subst,X22 : term] : (((sK280 @ X13 @ (comp @ X21 @ X20) @ (sub @ X22 @ X20))) = ((sub @ (sK279 @ X13) @ (push @ (sub @ X22 @ X20) @ (comp @ X21 @ X20))))) & ($true != ((X13 @ id @ (lam @ (sK280 @ X13 @ sh @ one)) @ id)))) | (((X13 @ id @ (lam @ (sub @ X12 @ (push @ one @ sh))) @ id)) = $true) | ((((X13 @ id @ (sK281 @ X13 @ X12) @ id)) = $true) & (((X13 @ id @ (sub @ X12 @ (push @ (sK281 @ X13 @ X12) @ id)) @ id)) != $true))) | ($true != sP28))), 27.00/4.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK270,sK271,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK270),skolemize(X1,sK271),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8)],[f170])). 27.00/4.44 thf(f260,plain,( 27.00/4.44 (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (((hoasinduction_lem3aa = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa != $true))) & (((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true))) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & ((! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) | (laminj != $true)) & ((laminj = $true) | ? [X116 : term,X117 : term] : ((((lam @ X116)) = ((lam @ X117))) & (X116 != X117)))) & (hoasinduction_lem3a_gthm = $true) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & (((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true))) & ((! [X463 : subst] : (((comp @ id @ X463)) = X463) | (axidl != $true)) & ((axidl = $true) | ? [X463 : subst] : (((comp @ id @ X463)) != X463))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & (((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X411 : subst] : (((comp @ id @ X411)) != X411) | ? [X412 : subst] : (((comp @ X412 @ id)) != X412)))) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X481 : d_term,X482 : d_term] : ((X481 = X482) | (((d2term @ X482)) != ((d2term @ X481)))) & (((d2subst @ d_id)) = id) & (((substmonoid_lthm = $true) | ((? [X16 : subst] : (((comp @ X16 @ id)) != X16) | ? [X15 : subst] : (((comp @ id @ X15)) != X15)) & ! [X14 : subst] : (((comp @ X14 @ id)) = X14) & ! [X13 : subst] : (((comp @ id @ X13)) = X13))) & (((! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15)) | ? [X14 : subst] : (((comp @ X14 @ id)) != X14) | ? [X13 : subst] : (((comp @ id @ X13)) != X13)) | (substmonoid_lthm != $true))) & (((axidr = $true) | ? [X39 : subst] : (((comp @ X39 @ id)) != X39)) & (! [X39 : subst] : (((comp @ X39 @ id)) = X39) | (axidr != $true))) & ((! [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) = $true) | (((X476 @ X474)) != $true) | ? [X478 : term] : (((X477 @ X478)) != ((X476 @ (sub @ X478 @ (push @ X474 @ X475)))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) != $true) & (((X476 @ X474)) = $true) & ! [X478 : term] : (((X477 @ X478)) = ((X476 @ (sub @ X478 @ (push @ X474 @ X475)))))))) & (((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP52 != $true))) & (apnotvar = $true) & ((! [X407 : term] : ? [X408 : (subst > term > term)] : ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X407 : term] : ! [X408 : (subst > term > term)] : ? [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) != ((sub @ X407 @ (push @ X409 @ X410)))))) & (((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true))) & (((hoasinduction = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction != $true))) & (ulamvarind = $true) & (((sP46 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP46 != $true))) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & (((hoasinduction_lthm_3 = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lthm_3 != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((pushprop_lem0 = $true) | ? [X144 : subst,X143 : (term > $o),X145 : term] : ! [X146 : (term > $o)] : ? [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) != ((X146 @ X147)))) & (! [X144 : subst,X143 : (term > $o),X145 : term] : ? [X146 : (term > $o)] : ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147))) | (pushprop_lem0 != $true))) & (((var @ (d2term @ d_one))) != $true) & (((pushprop_lem1v2_lthm = $true) | (? [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) != $true) & ! [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) = ((X316 @ X320))) & (((X318 @ X317)) = $true)) & ! [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) = X314))) & ((! [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) = $true) | ? [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) != ((X316 @ X320))) | (((X318 @ X317)) != $true)) | ? [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) != X314)) | (pushprop_lem1v2_lthm != $true))) & (axapp = $true) & (((sP39 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP39 != $true))) & ((! [X189 : (subst > term > term),X191 : term,X190 : term] : (? [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) != ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) | (((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X189 : (subst > term > term),X191 : term,X190 : term] : (! [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) = ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) & (((ap @ (sub @ X191 @ id) @ X190)) = ((lam @ (X189 @ sh @ one))))))) & (((induction2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2_lthm != $true))) & ! [X313 : d_term] : (d_one = X313) & ! [X479 : d_subst,X480 : d_subst] : ((X479 = X480) | (((d2subst @ X480)) != ((d2subst @ X479)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & (((induction2 = $true) | (sP34 != $true)) & ((sP34 = $true) | (induction2 != $true))) & (pushprop_lthm = $true) & (pushprop_lem0_gthm = $true) & (((sP32 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP32 != $true))) & (((pushprop_lem0_lthm = $true) | ? [X156 : subst,X158 : term,X157 : (term > $o)] : ! [X159 : (term > $o)] : ? [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) != ((X159 @ X160)))) & (! [X156 : subst,X158 : term,X157 : (term > $o)] : ? [X159 : (term > $o)] : ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160))) | (pushprop_lem0_lthm != $true))) & (((hoasapinj1 = $true) | ? [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) = ((ap @ (sub @ X327 @ id) @ X329))) & (X327 != X330))) & (! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330)) | (hoasapinj1 != $true))) & (((induction = $true) | ? [X67 : (term > $o),X66 : term] : (! [X68 : term] : ((((var @ X68)) != $true) | (((X67 @ X68)) = $true)) & ! [X69 : term] : ((((X67 @ X69)) != $true) | (((X67 @ (lam @ X69))) = $true)) & (((sP31 @ X67)) != $true) & (((X67 @ X66)) != $true))) & (! [X67 : (term > $o),X66 : term] : (? [X68 : term] : ((((var @ X68)) = $true) & (((X67 @ X68)) != $true)) | ? [X69 : term] : ((((X67 @ X69)) = $true) & (((X67 @ (lam @ X69))) != $true)) | (((sP31 @ X67)) = $true) | (((X67 @ X66)) = $true)) | (induction != $true))) & (((hoasinduction_lem0 = $true) | ? [X184 : (subst > term > subst > $o)] : ! [X185 : (term > $o)] : ? [X186 : term] : (((X184 @ id @ X186 @ id)) != ((X185 @ X186)))) & (! [X184 : (subst > term > subst > $o)] : ? [X185 : (term > $o)] : ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186))) | (hoasinduction_lem0 != $true))) & (((hoasinduction_lem3b = $true) | ? [X321 : term] : ! [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) != ((X322 @ sh @ one)))) & (! [X321 : term] : ? [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) = ((X322 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = sh) & (lamnotap != $true) & (((axshiftcons = $true) | ? [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) != X462)) & (! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462) | (axshiftcons != $true))) & (hoaslamnotap_gthm = $true) & (((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (pushprop_lem3v2 = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X112 : term] : ! [X113 : (subst > term > term)] : ? [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) != ((X113 @ X115 @ X114)))) & (! [X112 : term] : ? [X113 : (subst > term > term)] : ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114))) | (hoasinduction_lem3v2_f != $true))) & (pushprop = $true) & ((! [X398 : (subst > term > subst > $o),X399 : term] : (? [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) = $true) & (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X398 @ id @ X400 @ id)) = $true)) | (((X398 @ id @ X399 @ id)) = $true) | (((sP29 @ X398)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X398 : (subst > term > subst > $o),X399 : term] : (! [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) != $true) | (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) = $true) | (((X398 @ id @ X400 @ id)) != $true)) & (((X398 @ id @ X399 @ id)) != $true) & (((sP29 @ X398)) != $true)))) & (axmap = $true) & (((axvarid = $true) | ? [X312 : term] : (((sub @ X312 @ id)) != X312)) & (! [X312 : term] : (((sub @ X312 @ id)) = X312) | (axvarid != $true))) & ((($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28))) & ((! [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) != ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | ? [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X200 @ X206 @ X205) @ X207)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) = ((lam @ (X200 @ sh @ one)))) & (((X201 @ X199 @ X198)) != ((X200 @ X199 @ X198))) & ! [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) = ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) & ! [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X200 @ X206 @ X205) @ X207)))))) & (((sP27 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP27 != $true))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & ((! [X310 : term] : ? [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) = ((X311 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X310 : term] : ! [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) != ((X311 @ sh @ one))))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_lthm = $true) & ((! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X284 : term,X283 : term] : ((X283 != X284) & (((sub @ X284 @ sh)) = ((sub @ X283 @ sh)))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((hoasapinj2_lthm = $true) | (? [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 != X47) & (((ap @ (sub @ X44 @ id) @ X45)) = ((ap @ (sub @ X46 @ id) @ X47)))) & ! [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) != ((ap @ X43 @ X40))) | (X40 = X41)))) & ((! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))) | ? [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) = ((ap @ X43 @ X40))) & (X40 != X41))) | (hoasapinj2_lthm != $true))) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X195 : (subst > term > subst > $o)] : ! [X196 : (term > $o)] : ? [X197 : term] : (((X195 @ id @ X197 @ id)) != ((X196 @ X197)))) & (! [X195 : (subst > term > subst > $o)] : ? [X196 : (term > $o)] : ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197))) | (hoasinduction_lem0_lthm != $true))) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (((axscons = $true) | ? [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) != X111)) & (! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111) | (axscons != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((termmset = $true) | ? [X444 : term] : (((sub @ X444 @ id)) != X444)) & (! [X444 : term] : (((sub @ X444 @ id)) = X444) | (termmset != $true))) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((sP25 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP25 != $true))) & (((hoasinduction_lem3 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem3 != $true))) & (((induction2lem_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2lem_lthm != $true))) & (hoasapnotvar = $true) & (axabs = $true) & (((apinj2 = $true) | ? [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) = ((ap @ X326 @ X323))) & (X323 != X324))) & (! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324)) | (apinj2 != $true))) & (((apinj1 = $true) | ? [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) = ((ap @ X164 @ X161))) & (X162 != X164))) & (! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164)) | (apinj1 != $true))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((? [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) != X2) | ? [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) != X1) | ! [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | (((X8 @ X4)) != $true))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) = X2) & ! [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) = X1) & ? [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) != $true) & (((X8 @ X4)) = $true))))) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & ((! [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) != $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) = $true) & (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) != $true)))) & (substmonoid_gthm = $true) & (((hoasapinj1_lthm = $true) | (! [X134 : term] : (((sub @ X134 @ id)) = X134) & ? [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 != X141) & (((ap @ (sub @ X139 @ id) @ X140)) = ((ap @ (sub @ X141 @ id) @ X142)))) & ! [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) != ((ap @ X135 @ X136))) | (X135 = X137)))) & ((? [X134 : term] : (((sub @ X134 @ id)) != X134) | ! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))) | ? [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) = ((ap @ X135 @ X136))) & (X135 != X137))) | (hoasapinj1_lthm != $true))) & ! [X220 : d_subst] : (d_id = X220) & (((sP17 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP17 != $true))) & (((hoasinduction_lem3a_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem3a_lthm != $true))) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (axclos = $true) & (((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem2 != $true))) & (((axvarcons = $true) | ? [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) != X516)) & (! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516) | (axvarcons != $true))) & ((! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) = ((ap @ (sub @ X10 @ id) @ X9))) & (X9 != X12)))) & (one = ((d2term @ d_one))) & (pushprop_gthm = $true) & (((sP4 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP4 != $true))) & (((termmset_lthm = $true) | (? [X188 : term] : (((sub @ X188 @ id)) != X188) & ! [X187 : term] : (((sub @ X187 @ id)) = X187))) & ((! [X188 : term] : (((sub @ X188 @ id)) = X188) | ? [X187 : term] : (((sub @ X187 @ id)) != X187)) | (termmset_lthm != $true)))), 27.00/4.44 inference(nnf_transformation,[],[f72])). 27.00/4.44 thf(f261,plain,( 27.00/4.44 (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3aa = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa != $true)) & ((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true)) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X116 : term,X117 : term] : ((((lam @ X116)) != ((lam @ X117))) | (X116 = X117)) | (laminj != $true)) & ((laminj = $true) | ? [X116 : term,X117 : term] : ((((lam @ X116)) = ((lam @ X117))) & (X116 != X117))) & (hoasinduction_lem3a_gthm = $true) & ! [X498 : subst] : ? [X499 : d_subst] : (((d2subst @ X499)) = X498) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & (! [X463 : subst] : (((comp @ id @ X463)) = X463) | (axidl != $true)) & ((axidl = $true) | ? [X463 : subst] : (((comp @ id @ X463)) != X463)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((! [X411 : subst] : (((comp @ id @ X411)) = X411) & ! [X412 : subst] : (((comp @ X412 @ id)) = X412)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X411 : subst] : (((comp @ id @ X411)) != X411) | ? [X412 : subst] : (((comp @ X412 @ id)) != X412)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X481 : d_term,X482 : d_term] : ((X481 = X482) | (((d2term @ X482)) != ((d2term @ X481)))) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) | ((? [X16 : subst] : (((comp @ X16 @ id)) != X16) | ? [X15 : subst] : (((comp @ id @ X15)) != X15)) & ! [X14 : subst] : (((comp @ X14 @ id)) = X14) & ! [X13 : subst] : (((comp @ id @ X13)) = X13))) & ((! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X15 : subst] : (((comp @ id @ X15)) = X15)) | ? [X14 : subst] : (((comp @ X14 @ id)) != X14) | ? [X13 : subst] : (((comp @ id @ X13)) != X13) | (substmonoid_lthm != $true)) & ((axidr = $true) | ? [X39 : subst] : (((comp @ X39 @ id)) != X39)) & (! [X39 : subst] : (((comp @ X39 @ id)) = X39) | (axidr != $true)) & (! [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) = $true) | (((X476 @ X474)) != $true) | ? [X478 : term] : (((X477 @ X478)) != ((X476 @ (sub @ X478 @ (push @ X474 @ X475)))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X474 : term,X477 : (term > $o),X476 : (term > $o),X475 : subst] : ((((X477 @ one)) != $true) & (((X476 @ X474)) = $true) & ! [X478 : term] : (((X477 @ X478)) = ((X476 @ (sub @ X478 @ (push @ X474 @ X475))))))) & ((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP52 != $true)) & (apnotvar = $true) & (! [X407 : term] : ? [X408 : (subst > term > term)] : ! [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) = ((sub @ X407 @ (push @ X409 @ X410)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X407 : term] : ! [X408 : (subst > term > term)] : ? [X410 : subst,X409 : term] : (((X408 @ X410 @ X409)) != ((sub @ X407 @ (push @ X409 @ X410))))) & ((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true)) & ((hoasinduction = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction != $true)) & (ulamvarind = $true) & ((sP46 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP46 != $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lthm_3 = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lthm_3 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((pushprop_lem0 = $true) | ? [X144 : subst,X143 : (term > $o),X145 : term] : ! [X146 : (term > $o)] : ? [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) != ((X146 @ X147)))) & (! [X144 : subst,X143 : (term > $o),X145 : term] : ? [X146 : (term > $o)] : ! [X147 : term] : (((X143 @ (sub @ X147 @ (push @ X145 @ X144)))) = ((X146 @ X147))) | (pushprop_lem0 != $true)) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1v2_lthm = $true) | (? [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) != $true) & ! [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) = ((X316 @ X320))) & (((X318 @ X317)) = $true)) & ! [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) = X314))) & (! [X319 : subst,X317 : term,X318 : (term > $o),X316 : (term > $o)] : ((((X316 @ one)) = $true) | ? [X320 : term] : (((X318 @ (sub @ X320 @ (push @ X317 @ X319)))) != ((X316 @ X320))) | (((X318 @ X317)) != $true)) | ? [X314 : term,X315 : subst] : (((sub @ one @ (push @ X314 @ X315))) != X314) | (pushprop_lem1v2_lthm != $true)) & (axapp = $true) & ((sP39 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP39 != $true)) & (! [X189 : (subst > term > term),X191 : term,X190 : term] : (? [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) != ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) | (((ap @ (sub @ X191 @ id) @ X190)) != ((lam @ (X189 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X189 : (subst > term > term),X191 : term,X190 : term] : (! [X194 : subst,X192 : subst,X193 : term] : (((sub @ (X189 @ X192 @ X193) @ X194)) = ((X189 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194)))) & (((ap @ (sub @ X191 @ id) @ X190)) = ((lam @ (X189 @ sh @ one)))))) & ((induction2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2_lthm != $true)) & ! [X313 : d_term] : (d_one = X313) & ! [X479 : d_subst,X480 : d_subst] : ((X479 = X480) | (((d2subst @ X480)) != ((d2subst @ X479)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2 = $true) | (sP34 != $true)) & ((sP34 = $true) | (induction2 != $true)) & (pushprop_lthm = $true) & (pushprop_lem0_gthm = $true) & ((sP32 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP32 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X156 : subst,X158 : term,X157 : (term > $o)] : ! [X159 : (term > $o)] : ? [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) != ((X159 @ X160)))) & (! [X156 : subst,X158 : term,X157 : (term > $o)] : ? [X159 : (term > $o)] : ! [X160 : term] : (((X157 @ (sub @ X160 @ (push @ X158 @ X156)))) = ((X159 @ X160))) | (pushprop_lem0_lthm != $true)) & ((hoasapinj1 = $true) | ? [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) = ((ap @ (sub @ X327 @ id) @ X329))) & (X327 != X330))) & (! [X328 : term,X329 : term,X330 : term,X327 : term] : ((((ap @ (sub @ X330 @ id) @ X328)) != ((ap @ (sub @ X327 @ id) @ X329))) | (X327 = X330)) | (hoasapinj1 != $true)) & ((induction = $true) | ? [X67 : (term > $o),X66 : term] : (! [X68 : term] : ((((var @ X68)) != $true) | (((X67 @ X68)) = $true)) & ! [X69 : term] : ((((X67 @ X69)) != $true) | (((X67 @ (lam @ X69))) = $true)) & (((sP31 @ X67)) != $true) & (((X67 @ X66)) != $true))) & (! [X67 : (term > $o),X66 : term] : (? [X68 : term] : ((((var @ X68)) = $true) & (((X67 @ X68)) != $true)) | ? [X69 : term] : ((((X67 @ X69)) = $true) & (((X67 @ (lam @ X69))) != $true)) | (((sP31 @ X67)) = $true) | (((X67 @ X66)) = $true)) | (induction != $true)) & ((hoasinduction_lem0 = $true) | ? [X184 : (subst > term > subst > $o)] : ! [X185 : (term > $o)] : ? [X186 : term] : (((X184 @ id @ X186 @ id)) != ((X185 @ X186)))) & (! [X184 : (subst > term > subst > $o)] : ? [X185 : (term > $o)] : ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem3b = $true) | ? [X321 : term] : ! [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) != ((X322 @ sh @ one)))) & (! [X321 : term] : ? [X322 : (subst > term > term)] : (((sub @ X321 @ (push @ one @ sh))) = ((X322 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = sh) & (lamnotap != $true) & ((axshiftcons = $true) | ? [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) != X462)) & (! [X461 : term,X462 : subst] : (((comp @ sh @ (push @ X461 @ X462))) = X462) | (axshiftcons != $true)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X112 : term] : ! [X113 : (subst > term > term)] : ? [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) != ((X113 @ X115 @ X114)))) & (! [X112 : term] : ? [X113 : (subst > term > term)] : ! [X115 : subst,X114 : term] : (((sub @ X112 @ (push @ X114 @ X115))) = ((X113 @ X115 @ X114))) | (hoasinduction_lem3v2_f != $true)) & (pushprop = $true) & (! [X398 : (subst > term > subst > $o),X399 : term] : (? [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) = $true) & (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X398 @ id @ X400 @ id)) = $true)) | (((X398 @ id @ X399 @ id)) = $true) | (((sP29 @ X398)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X398 : (subst > term > subst > $o),X399 : term] : (! [X401 : term,X400 : term] : ((((X398 @ id @ X401 @ id)) != $true) | (((X398 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) = $true) | (((X398 @ id @ X400 @ id)) != $true)) & (((X398 @ id @ X399 @ id)) != $true) & (((sP29 @ X398)) != $true))) & (axmap = $true) & ((axvarid = $true) | ? [X312 : term] : (((sub @ X312 @ id)) != X312)) & (! [X312 : term] : (((sub @ X312 @ id)) = X312) | (axvarid != $true)) & (($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28)) & (! [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | (((X201 @ X199 @ X198)) = ((X200 @ X199 @ X198))) | ? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) != ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | ? [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) != ((sub @ (X200 @ X206 @ X205) @ X207)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X201 : (subst > term > term),X198 : term,X199 : subst,X200 : (subst > term > term)] : ((((lam @ (X201 @ sh @ one))) = ((lam @ (X200 @ sh @ one)))) & (((X201 @ X199 @ X198)) != ((X200 @ X199 @ X198))) & ! [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X201 @ X204 @ X202) @ X203)) = ((X201 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) & ! [X205 : term,X207 : subst,X206 : subst] : (((X200 @ (comp @ X206 @ X207) @ (sub @ X205 @ X207))) = ((sub @ (X200 @ X206 @ X205) @ X207))))) & ((sP27 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP27 != $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X310 : term] : ? [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) = ((X311 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X310 : term] : ! [X311 : (subst > term > term)] : (((sub @ X310 @ (push @ one @ sh))) != ((X311 @ sh @ one)))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_lthm = $true) & (! [X284 : term,X283 : term] : ((X283 = X284) | (((sub @ X284 @ sh)) != ((sub @ X283 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X284 : term,X283 : term] : ((X283 != X284) & (((sub @ X284 @ sh)) = ((sub @ X283 @ sh))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2_lthm = $true) | (? [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 != X47) & (((ap @ (sub @ X44 @ id) @ X45)) = ((ap @ (sub @ X46 @ id) @ X47)))) & ! [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) != ((ap @ X43 @ X40))) | (X40 = X41)))) & (! [X46 : term,X47 : term,X44 : term,X45 : term] : ((X45 = X47) | (((ap @ (sub @ X44 @ id) @ X45)) != ((ap @ (sub @ X46 @ id) @ X47)))) | ? [X42 : term,X43 : term,X41 : term,X40 : term] : ((((ap @ X42 @ X41)) = ((ap @ X43 @ X40))) & (X40 != X41)) | (hoasapinj2_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X195 : (subst > term > subst > $o)] : ! [X196 : (term > $o)] : ? [X197 : term] : (((X195 @ id @ X197 @ id)) != ((X196 @ X197)))) & (! [X195 : (subst > term > subst > $o)] : ? [X196 : (term > $o)] : ! [X197 : term] : (((X195 @ id @ X197 @ id)) = ((X196 @ X197))) | (hoasinduction_lem0_lthm != $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((axscons = $true) | ? [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) != X111)) & (! [X111 : subst] : (((push @ (sub @ one @ X111) @ (comp @ sh @ X111))) = X111) | (axscons != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((termmset = $true) | ? [X444 : term] : (((sub @ X444 @ id)) != X444)) & (! [X444 : term] : (((sub @ X444 @ id)) = X444) | (termmset != $true)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP25 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP25 != $true)) & ((hoasinduction_lem3 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem3 != $true)) & ((induction2lem_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2lem_lthm != $true)) & (hoasapnotvar = $true) & (axabs = $true) & ((apinj2 = $true) | ? [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) = ((ap @ X326 @ X323))) & (X323 != X324))) & (! [X326 : term,X325 : term,X324 : term,X323 : term] : ((((ap @ X325 @ X324)) != ((ap @ X326 @ X323))) | (X323 = X324)) | (apinj2 != $true)) & ((apinj1 = $true) | ? [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) = ((ap @ X164 @ X161))) & (X162 != X164))) & (! [X161 : term,X162 : term,X164 : term,X163 : term] : ((((ap @ X162 @ X163)) != ((ap @ X164 @ X161))) | (X162 = X164)) | (apinj1 != $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (? [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) != X2) | ? [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) != X1) | ! [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) = $true) | (((X8 @ X4)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X3 : term,X2 : subst] : (((comp @ sh @ (push @ X3 @ X2))) = X2) & ! [X1 : term,X0 : subst] : (((sub @ one @ (push @ X1 @ X0))) = X1) & ? [X7 : subst,X8 : (term > $o),X6 : term,X4 : term,X5 : (term > $o)] : ((((X5 @ (sub @ X4 @ (push @ X6 @ X7)))) != $true) & (((X8 @ X4)) = $true)))) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538) & (! [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) != $true) | (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X21 : term,X18 : (term > $o),X20 : subst,X17 : (term > $o),X19 : term] : ((((X18 @ X21)) = $true) & (((X17 @ (sub @ X21 @ (push @ X19 @ X20)))) != $true))) & (substmonoid_gthm = $true) & ((hoasapinj1_lthm = $true) | (! [X134 : term] : (((sub @ X134 @ id)) = X134) & ? [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 != X141) & (((ap @ (sub @ X139 @ id) @ X140)) = ((ap @ (sub @ X141 @ id) @ X142)))) & ! [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) != ((ap @ X135 @ X136))) | (X135 = X137)))) & (? [X134 : term] : (((sub @ X134 @ id)) != X134) | ! [X140 : term,X141 : term,X142 : term,X139 : term] : ((X139 = X141) | (((ap @ (sub @ X139 @ id) @ X140)) != ((ap @ (sub @ X141 @ id) @ X142)))) | ? [X136 : term,X137 : term,X138 : term,X135 : term] : ((((ap @ X137 @ X138)) = ((ap @ X135 @ X136))) & (X135 != X137)) | (hoasapinj1_lthm != $true)) & ! [X220 : d_subst] : (d_id = X220) & ((sP17 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP17 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem3a_lthm != $true)) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (axclos = $true) & ((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((axvarcons = $true) | ? [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) != X516)) & (! [X516 : term,X517 : subst] : (((sub @ one @ (push @ X516 @ X517))) = X516) | (axvarcons != $true)) & (! [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) != ((ap @ (sub @ X10 @ id) @ X9))) | (X9 = X12)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X10 : term,X9 : term,X11 : term,X12 : term] : ((((ap @ (sub @ X11 @ id) @ X12)) = ((ap @ (sub @ X10 @ id) @ X9))) & (X9 != X12))) & (one = ((d2term @ d_one))) & (pushprop_gthm = $true) & ((sP4 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP4 != $true)) & ((termmset_lthm = $true) | (? [X188 : term] : (((sub @ X188 @ id)) != X188) & ! [X187 : term] : (((sub @ X187 @ id)) = X187))) & (! [X188 : term] : (((sub @ X188 @ id)) = X188) | ? [X187 : term] : (((sub @ X187 @ id)) != X187) | (termmset_lthm != $true))), 27.00/4.44 inference(flattening,[],[f260])). 27.00/4.44 thf(f262,plain,( 27.00/4.44 (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3aa = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa != $true)) & ((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true)) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X0 : term,X1 : term] : ((((lam @ X0)) != ((lam @ X1))) | (X0 = X1)) | (laminj != $true)) & ((laminj = $true) | ? [X2 : term,X3 : term] : ((((lam @ X2)) = ((lam @ X3))) & (X2 != X3))) & (hoasinduction_lem3a_gthm = $true) & ! [X4 : subst] : ? [X5 : d_subst] : (((d2subst @ X5)) = X4) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & (! [X6 : subst] : (((comp @ id @ X6)) = X6) | (axidl != $true)) & ((axidl = $true) | ? [X7 : subst] : (((comp @ id @ X7)) != X7)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((! [X8 : subst] : (((comp @ id @ X8)) = X8) & ! [X9 : subst] : (((comp @ X9 @ id)) = X9)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X10 : subst] : (((comp @ id @ X10)) != X10) | ? [X11 : subst] : (((comp @ X11 @ id)) != X11)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X12 : d_term,X13 : d_term] : ((X12 = X13) | (((d2term @ X13)) != ((d2term @ X12)))) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) | ((? [X14 : subst] : (((comp @ X14 @ id)) != X14) | ? [X15 : subst] : (((comp @ id @ X15)) != X15)) & ! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X17 : subst] : (((comp @ id @ X17)) = X17))) & ((! [X18 : subst] : (((comp @ X18 @ id)) = X18) & ! [X19 : subst] : (((comp @ id @ X19)) = X19)) | ? [X20 : subst] : (((comp @ X20 @ id)) != X20) | ? [X21 : subst] : (((comp @ id @ X21)) != X21) | (substmonoid_lthm != $true)) & ((axidr = $true) | ? [X22 : subst] : (((comp @ X22 @ id)) != X22)) & (! [X23 : subst] : (((comp @ X23 @ id)) = X23) | (axidr != $true)) & (! [X24 : term,X25 : (term > $o),X26 : (term > $o),X27 : subst] : ((((X25 @ one)) = $true) | (((X26 @ X24)) != $true) | ? [X28 : term] : (((X25 @ X28)) != ((X26 @ (sub @ X28 @ (push @ X24 @ X27)))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X29 : term,X30 : (term > $o),X31 : (term > $o),X32 : subst] : ((((X30 @ one)) != $true) & (((X31 @ X29)) = $true) & ! [X33 : term] : (((X30 @ X33)) = ((X31 @ (sub @ X33 @ (push @ X29 @ X32))))))) & ((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP52 != $true)) & (apnotvar = $true) & (! [X34 : term] : ? [X35 : (subst > term > term)] : ! [X36 : subst,X37 : term] : (((X35 @ X36 @ X37)) = ((sub @ X34 @ (push @ X37 @ X36)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X38 : term] : ! [X39 : (subst > term > term)] : ? [X40 : subst,X41 : term] : (((sub @ X38 @ (push @ X41 @ X40))) != ((X39 @ X40 @ X41)))) & ((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true)) & ((hoasinduction = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction != $true)) & (ulamvarind = $true) & ((sP46 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP46 != $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lthm_3 = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lthm_3 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((pushprop_lem0 = $true) | ? [X42 : subst,X43 : (term > $o),X44 : term] : ! [X45 : (term > $o)] : ? [X46 : term] : (((X45 @ X46)) != ((X43 @ (sub @ X46 @ (push @ X44 @ X42)))))) & (! [X47 : subst,X48 : (term > $o),X49 : term] : ? [X50 : (term > $o)] : ! [X51 : term] : (((X48 @ (sub @ X51 @ (push @ X49 @ X47)))) = ((X50 @ X51))) | (pushprop_lem0 != $true)) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1v2_lthm = $true) | (? [X52 : subst,X53 : term,X54 : (term > $o),X55 : (term > $o)] : ((((X55 @ one)) != $true) & ! [X56 : term] : (((X54 @ (sub @ X56 @ (push @ X53 @ X52)))) = ((X55 @ X56))) & (((X54 @ X53)) = $true)) & ! [X57 : term,X58 : subst] : (((sub @ one @ (push @ X57 @ X58))) = X57))) & (! [X59 : subst,X60 : term,X61 : (term > $o),X62 : (term > $o)] : ((((X62 @ one)) = $true) | ? [X63 : term] : (((X62 @ X63)) != ((X61 @ (sub @ X63 @ (push @ X60 @ X59))))) | (((X61 @ X60)) != $true)) | ? [X64 : term,X65 : subst] : (((sub @ one @ (push @ X64 @ X65))) != X64) | (pushprop_lem1v2_lthm != $true)) & (axapp = $true) & ((sP39 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP39 != $true)) & (! [X66 : (subst > term > term),X67 : term,X68 : term] : (? [X69 : subst,X70 : subst,X71 : term] : (((sub @ (X66 @ X70 @ X71) @ X69)) != ((X66 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69)))) | (((lam @ (X66 @ sh @ one))) != ((ap @ (sub @ X67 @ id) @ X68)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X72 : (subst > term > term),X73 : term,X74 : term] : (! [X75 : subst,X76 : subst,X77 : term] : (((sub @ (X72 @ X76 @ X77) @ X75)) = ((X72 @ (comp @ X76 @ X75) @ (sub @ X77 @ X75)))) & (((ap @ (sub @ X73 @ id) @ X74)) = ((lam @ (X72 @ sh @ one)))))) & ((induction2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2_lthm != $true)) & ! [X78 : d_term] : (d_one = X78) & ! [X79 : d_subst,X80 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2 = $true) | (sP34 != $true)) & ((sP34 = $true) | (induction2 != $true)) & (pushprop_lthm = $true) & (pushprop_lem0_gthm = $true) & ((sP32 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP32 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X81 : subst,X82 : term,X83 : (term > $o)] : ! [X84 : (term > $o)] : ? [X85 : term] : (((X83 @ (sub @ X85 @ (push @ X82 @ X81)))) != ((X84 @ X85)))) & (! [X86 : subst,X87 : term,X88 : (term > $o)] : ? [X89 : (term > $o)] : ! [X90 : term] : (((X88 @ (sub @ X90 @ (push @ X87 @ X86)))) = ((X89 @ X90))) | (pushprop_lem0_lthm != $true)) & ((hoasapinj1 = $true) | ? [X91 : term,X92 : term,X93 : term,X94 : term] : ((((ap @ (sub @ X93 @ id) @ X91)) = ((ap @ (sub @ X94 @ id) @ X92))) & (X93 != X94))) & (! [X95 : term,X96 : term,X97 : term,X98 : term] : ((((ap @ (sub @ X98 @ id) @ X96)) != ((ap @ (sub @ X97 @ id) @ X95))) | (X97 = X98)) | (hoasapinj1 != $true)) & ((induction = $true) | ? [X99 : (term > $o),X100 : term] : (! [X101 : term] : ((((var @ X101)) != $true) | (((X99 @ X101)) = $true)) & ! [X102 : term] : ((((X99 @ X102)) != $true) | (((X99 @ (lam @ X102))) = $true)) & (((sP31 @ X99)) != $true) & (((X99 @ X100)) != $true))) & (! [X103 : (term > $o),X104 : term] : (? [X105 : term] : ((((var @ X105)) = $true) & (((X103 @ X105)) != $true)) | ? [X106 : term] : ((((X103 @ X106)) = $true) & (((X103 @ (lam @ X106))) != $true)) | (((sP31 @ X103)) = $true) | (((X103 @ X104)) = $true)) | (induction != $true)) & ((hoasinduction_lem0 = $true) | ? [X107 : (subst > term > subst > $o)] : ! [X108 : (term > $o)] : ? [X109 : term] : (((X107 @ id @ X109 @ id)) != ((X108 @ X109)))) & (! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X110 @ id @ X112 @ id)) = ((X111 @ X112))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem3b = $true) | ? [X113 : term] : ! [X114 : (subst > term > term)] : (((sub @ X113 @ (push @ one @ sh))) != ((X114 @ sh @ one)))) & (! [X115 : term] : ? [X116 : (subst > term > term)] : (((sub @ X115 @ (push @ one @ sh))) = ((X116 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = sh) & (lamnotap != $true) & ((axshiftcons = $true) | ? [X117 : term,X118 : subst] : (((comp @ sh @ (push @ X117 @ X118))) != X118)) & (! [X119 : term,X120 : subst] : (((comp @ sh @ (push @ X119 @ X120))) = X120) | (axshiftcons != $true)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X121 : term] : ! [X122 : (subst > term > term)] : ? [X123 : subst,X124 : term] : (((sub @ X121 @ (push @ X124 @ X123))) != ((X122 @ X123 @ X124)))) & (! [X125 : term] : ? [X126 : (subst > term > term)] : ! [X127 : subst,X128 : term] : (((sub @ X125 @ (push @ X128 @ X127))) = ((X126 @ X127 @ X128))) | (hoasinduction_lem3v2_f != $true)) & (pushprop = $true) & (! [X129 : (subst > term > subst > $o),X130 : term] : (? [X131 : term,X132 : term] : ((((X129 @ id @ X131 @ id)) = $true) & (((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) != $true) & (((X129 @ id @ X132 @ id)) = $true)) | (((X129 @ id @ X130 @ id)) = $true) | ($true = ((sP29 @ X129)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X133 : (subst > term > subst > $o),X134 : term] : (! [X135 : term,X136 : term] : ((((X133 @ id @ X135 @ id)) != $true) | (((X133 @ id @ (ap @ (sub @ X136 @ id) @ X135) @ id)) = $true) | (((X133 @ id @ X136 @ id)) != $true)) & (((X133 @ id @ X134 @ id)) != $true) & (((sP29 @ X133)) != $true))) & (axmap = $true) & ((axvarid = $true) | ? [X137 : term] : (((sub @ X137 @ id)) != X137)) & (! [X138 : term] : (((sub @ X138 @ id)) = X138) | (axvarid != $true)) & (($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28)) & (! [X139 : (subst > term > term),X140 : term,X141 : subst,X142 : (subst > term > term)] : ((((lam @ (X139 @ sh @ one))) != ((lam @ (X142 @ sh @ one)))) | (((X139 @ X141 @ X140)) = ((X142 @ X141 @ X140))) | ? [X143 : subst,X144 : subst,X145 : term] : (((sub @ (X139 @ X143 @ X145) @ X144)) != ((X139 @ (comp @ X143 @ X144) @ (sub @ X145 @ X144)))) | ? [X146 : term,X147 : subst,X148 : subst] : (((X142 @ (comp @ X148 @ X147) @ (sub @ X146 @ X147))) != ((sub @ (X142 @ X148 @ X146) @ X147)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X149 : (subst > term > term),X150 : term,X151 : subst,X152 : (subst > term > term)] : ((((lam @ (X152 @ sh @ one))) = ((lam @ (X149 @ sh @ one)))) & (((X149 @ X151 @ X150)) != ((X152 @ X151 @ X150))) & ! [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X153 @ X155) @ X154)) = ((X149 @ (comp @ X153 @ X154) @ (sub @ X155 @ X154)))) & ! [X156 : term,X157 : subst,X158 : subst] : (((sub @ (X152 @ X158 @ X156) @ X157)) = ((X152 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157)))))) & ((sP27 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP27 != $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X159 : term] : ? [X160 : (subst > term > term)] : (((X160 @ sh @ one)) = ((sub @ X159 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X161 : term] : ! [X162 : (subst > term > term)] : (((X162 @ sh @ one)) != ((sub @ X161 @ (push @ one @ sh))))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_lthm = $true) & (! [X163 : term,X164 : term] : ((X163 = X164) | (((sub @ X163 @ sh)) != ((sub @ X164 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X165 : term,X166 : term] : ((X165 != X166) & (((sub @ X166 @ sh)) = ((sub @ X165 @ sh))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2_lthm = $true) | (? [X167 : term,X168 : term,X169 : term,X170 : term] : ((X168 != X170) & (((ap @ (sub @ X167 @ id) @ X168)) = ((ap @ (sub @ X169 @ id) @ X170)))) & ! [X171 : term,X172 : term,X173 : term,X174 : term] : ((((ap @ X171 @ X173)) != ((ap @ X172 @ X174))) | (X173 = X174)))) & (! [X175 : term,X176 : term,X177 : term,X178 : term] : ((X176 = X178) | (((ap @ (sub @ X177 @ id) @ X178)) != ((ap @ (sub @ X175 @ id) @ X176)))) | ? [X179 : term,X180 : term,X181 : term,X182 : term] : ((((ap @ X180 @ X182)) = ((ap @ X179 @ X181))) & (X181 != X182)) | (hoasapinj2_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X183 : (subst > term > subst > $o)] : ! [X184 : (term > $o)] : ? [X185 : term] : (((X183 @ id @ X185 @ id)) != ((X184 @ X185)))) & (! [X186 : (subst > term > subst > $o)] : ? [X187 : (term > $o)] : ! [X188 : term] : (((X186 @ id @ X188 @ id)) = ((X187 @ X188))) | (hoasinduction_lem0_lthm != $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((axscons = $true) | ? [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) != X189)) & (! [X190 : subst] : (((push @ (sub @ one @ X190) @ (comp @ sh @ X190))) = X190) | (axscons != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((termmset = $true) | ? [X191 : term] : (((sub @ X191 @ id)) != X191)) & (! [X192 : term] : (((sub @ X192 @ id)) = X192) | (termmset != $true)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP25 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP25 != $true)) & ((hoasinduction_lem3 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem3 != $true)) & ((induction2lem_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2lem_lthm != $true)) & (hoasapnotvar = $true) & (axabs = $true) & ((apinj2 = $true) | ? [X193 : term,X194 : term,X195 : term,X196 : term] : ((((ap @ X193 @ X196)) = ((ap @ X194 @ X195))) & (X195 != X196))) & (! [X197 : term,X198 : term,X199 : term,X200 : term] : ((((ap @ X198 @ X199)) != ((ap @ X197 @ X200))) | (X199 = X200)) | (apinj2 != $true)) & ((apinj1 = $true) | ? [X201 : term,X202 : term,X203 : term,X204 : term] : ((((ap @ X202 @ X204)) = ((ap @ X203 @ X201))) & (X202 != X203))) & (! [X205 : term,X206 : term,X207 : term,X208 : term] : ((((ap @ X206 @ X208)) != ((ap @ X207 @ X205))) | (X206 = X207)) | (apinj1 != $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (? [X209 : term,X210 : subst] : (((comp @ sh @ (push @ X209 @ X210))) != X210) | ? [X211 : term,X212 : subst] : (((sub @ one @ (push @ X211 @ X212))) != X211) | ! [X213 : subst,X214 : (term > $o),X215 : term,X216 : term,X217 : (term > $o)] : ((((X217 @ (sub @ X216 @ (push @ X215 @ X213)))) = $true) | (((X214 @ X216)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X218 : term,X219 : subst] : (((comp @ sh @ (push @ X218 @ X219))) = X219) & ! [X220 : term,X221 : subst] : (((sub @ one @ (push @ X220 @ X221))) = X220) & ? [X222 : subst,X223 : (term > $o),X224 : term,X225 : term,X226 : (term > $o)] : ((((X226 @ (sub @ X225 @ (push @ X224 @ X222)))) != $true) & (((X223 @ X225)) = $true)))) & ! [X227 : term] : ? [X228 : d_term] : (((d2term @ X228)) = X227) & (! [X229 : term,X230 : (term > $o),X231 : subst,X232 : (term > $o),X233 : term] : ((((X230 @ X229)) != $true) | (((X232 @ (sub @ X229 @ (push @ X233 @ X231)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X234 : term,X235 : (term > $o),X236 : subst,X237 : (term > $o),X238 : term] : ((((X235 @ X234)) = $true) & (((X237 @ (sub @ X234 @ (push @ X238 @ X236)))) != $true))) & (substmonoid_gthm = $true) & ((hoasapinj1_lthm = $true) | (! [X239 : term] : (((sub @ X239 @ id)) = X239) & ? [X240 : term,X241 : term,X242 : term,X243 : term] : ((X241 != X243) & (((ap @ (sub @ X243 @ id) @ X240)) = ((ap @ (sub @ X241 @ id) @ X242)))) & ! [X244 : term,X245 : term,X246 : term,X247 : term] : ((((ap @ X247 @ X244)) != ((ap @ X245 @ X246))) | (X245 = X247)))) & (? [X248 : term] : (((sub @ X248 @ id)) != X248) | ! [X249 : term,X250 : term,X251 : term,X252 : term] : ((X250 = X252) | (((ap @ (sub @ X250 @ id) @ X251)) != ((ap @ (sub @ X252 @ id) @ X249)))) | ? [X253 : term,X254 : term,X255 : term,X256 : term] : ((((ap @ X254 @ X255)) = ((ap @ X256 @ X253))) & (X254 != X256)) | (hoasapinj1_lthm != $true)) & ! [X257 : d_subst] : (d_id = X257) & ((sP17 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP17 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem3a_lthm != $true)) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (axclos = $true) & ((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((axvarcons = $true) | ? [X258 : term,X259 : subst] : (((sub @ one @ (push @ X258 @ X259))) != X258)) & (! [X260 : term,X261 : subst] : (((sub @ one @ (push @ X260 @ X261))) = X260) | (axvarcons != $true)) & (! [X262 : term,X263 : term,X264 : term,X265 : term] : ((((ap @ (sub @ X264 @ id) @ X265)) != ((ap @ (sub @ X262 @ id) @ X263))) | (X263 = X265)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X266 : term,X267 : term,X268 : term,X269 : term] : ((((ap @ (sub @ X266 @ id) @ X267)) = ((ap @ (sub @ X268 @ id) @ X269))) & (X267 != X269))) & (one = ((d2term @ d_one))) & (pushprop_gthm = $true) & ((sP4 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP4 != $true)) & ((termmset_lthm = $true) | (? [X270 : term] : (((sub @ X270 @ id)) != X270) & ! [X271 : term] : (((sub @ X271 @ id)) = X271))) & (! [X272 : term] : (((sub @ X272 @ id)) = X272) | ? [X273 : term] : (((sub @ X273 @ id)) != X273) | (termmset_lthm != $true))), 27.00/4.44 inference(rectify,[],[f261])). 27.00/4.44 thf(f263,plain,( 27.00/4.44 (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3aa = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3aa != $true)) & ((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true)) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X0 : term,X1 : term] : ((((lam @ X0)) != ((lam @ X1))) | (X0 = X1)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK457)) = ((lam @ sK458))) & (sK458 != sK457))) & (hoasinduction_lem3a_gthm = $true) & ! [X4 : subst] : (((d2subst @ (sK459 @ X4))) = X4) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & (! [X6 : subst] : (((comp @ id @ X6)) = X6) | (axidl != $true)) & ((axidl = $true) | (((comp @ id @ sK460)) != sK460)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem1_gthm = $true) & ((! [X8 : subst] : (((comp @ id @ X8)) = X8) & ! [X9 : subst] : (((comp @ X9 @ id)) = X9)) | (substmonoid != $true)) & ((substmonoid = $true) | (sK461 != ((comp @ id @ sK461))) | (((comp @ sK462 @ id)) != sK462)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ! [X12 : d_term,X13 : d_term] : ((X12 = X13) | (((d2term @ X13)) != ((d2term @ X12)))) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) | (((sK463 != ((comp @ sK463 @ id))) | (sK464 != ((comp @ id @ sK464)))) & ! [X16 : subst] : (((comp @ X16 @ id)) = X16) & ! [X17 : subst] : (((comp @ id @ X17)) = X17))) & ((! [X18 : subst] : (((comp @ X18 @ id)) = X18) & ! [X19 : subst] : (((comp @ id @ X19)) = X19)) | (((comp @ sK465 @ id)) != sK465) | (((comp @ id @ sK466)) != sK466) | (substmonoid_lthm != $true)) & ((axidr = $true) | (((comp @ sK467 @ id)) != sK467)) & (! [X23 : subst] : (((comp @ X23 @ id)) = X23) | (axidr != $true)) & (! [X24 : term,X25 : (term > $o),X26 : (term > $o),X27 : subst] : ((((X25 @ one)) = $true) | (((X26 @ X24)) != $true) | (((X26 @ (sub @ (sK468 @ X27 @ X26 @ X25 @ X24) @ (push @ X24 @ X27)))) != ((X25 @ (sK468 @ X27 @ X26 @ X25 @ X24))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ((((sK470 @ one)) != $true) & (((sK471 @ sK469)) = $true) & ! [X33 : term] : (((sK471 @ (sub @ X33 @ (push @ sK469 @ sK472)))) = ((sK470 @ X33))))) & ((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP52 != $true)) & (apnotvar = $true) & (! [X34 : term] : ! [X36 : subst,X37 : term] : (((sK473 @ X34 @ X36 @ X37)) = ((sub @ X34 @ (push @ X37 @ X36)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X39 : (subst > term > term)] : (((X39 @ (sK475 @ X39) @ (sK476 @ X39))) != ((sub @ sK474 @ (push @ (sK476 @ X39) @ (sK475 @ X39)))))) & ((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true)) & ((hoasinduction = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction != $true)) & (ulamvarind = $true) & ((sP46 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP46 != $true)) & (hoaslamnotvar_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lthm_3 = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lthm_3 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((pushprop_lem0 = $true) | ! [X45 : (term > $o)] : (((sK478 @ (sub @ (sK480 @ X45) @ (push @ sK479 @ sK477)))) != ((X45 @ (sK480 @ X45))))) & (! [X47 : subst,X48 : (term > $o),X49 : term] : ! [X51 : term] : (((X48 @ (sub @ X51 @ (push @ X49 @ X47)))) = ((sK481 @ X49 @ X48 @ X47 @ X51))) | (pushprop_lem0 != $true)) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1v2_lthm = $true) | (((((sK485 @ one)) != $true) & ! [X56 : term] : (((sK484 @ (sub @ X56 @ (push @ sK483 @ sK482)))) = ((sK485 @ X56))) & (((sK484 @ sK483)) = $true)) & ! [X57 : term,X58 : subst] : (((sub @ one @ (push @ X57 @ X58))) = X57))) & (! [X59 : subst,X60 : term,X61 : (term > $o),X62 : (term > $o)] : ((((X62 @ one)) = $true) | (((X61 @ (sub @ (sK486 @ X62 @ X61 @ X60 @ X59) @ (push @ X60 @ X59)))) != ((X62 @ (sK486 @ X62 @ X61 @ X60 @ X59)))) | (((X61 @ X60)) != $true)) | (sK487 != ((sub @ one @ (push @ sK487 @ sK488)))) | (pushprop_lem1v2_lthm != $true)) & (axapp = $true) & ((sP39 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP39 != $true)) & (! [X66 : (subst > term > term),X67 : term,X68 : term] : ((((sub @ (X66 @ (sK490 @ X66) @ (sK491 @ X66)) @ (sK489 @ X66))) != ((X66 @ (comp @ (sK490 @ X66) @ (sK489 @ X66)) @ (sub @ (sK491 @ X66) @ (sK489 @ X66))))) | (((lam @ (X66 @ sh @ one))) != ((ap @ (sub @ X67 @ id) @ X68)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X75 : subst,X76 : subst,X77 : term] : (((sK492 @ (comp @ X76 @ X75) @ (sub @ X77 @ X75))) = ((sub @ (sK492 @ X76 @ X77) @ X75))) & (((ap @ (sub @ sK493 @ id) @ sK494)) = ((lam @ (sK492 @ sh @ one)))))) & ((induction2_lthm = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2_lthm != $true)) & ! [X78 : d_term] : (d_one = X78) & ! [X79 : d_subst,X80 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((induction2 = $true) | (sP34 != $true)) & ((sP34 = $true) | (induction2 != $true)) & (pushprop_lthm = $true) & (pushprop_lem0_gthm = $true) & ((sP32 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP32 != $true)) & ((pushprop_lem0_lthm = $true) | ! [X84 : (term > $o)] : (((X84 @ (sK498 @ X84))) != ((sK497 @ (sub @ (sK498 @ X84) @ (push @ sK496 @ sK495)))))) & (! [X86 : subst,X87 : term,X88 : (term > $o)] : ! [X90 : term] : (((sK499 @ X88 @ X87 @ X86 @ X90)) = ((X88 @ (sub @ X90 @ (push @ X87 @ X86))))) | (pushprop_lem0_lthm != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK503 @ id) @ sK501)) = ((ap @ (sub @ sK502 @ id) @ sK500))) & (sK502 != sK503))) & (! [X95 : term,X96 : term,X97 : term,X98 : term] : ((((ap @ (sub @ X98 @ id) @ X96)) != ((ap @ (sub @ X97 @ id) @ X95))) | (X97 = X98)) | (hoasapinj1 != $true)) & ((induction = $true) | (! [X101 : term] : ((((var @ X101)) != $true) | (((sK504 @ X101)) = $true)) & ! [X102 : term] : (($true != ((sK504 @ X102))) | (((sK504 @ (lam @ X102))) = $true)) & (((sP31 @ sK504)) != $true) & (((sK504 @ sK505)) != $true))) & (! [X103 : (term > $o),X104 : term] : (((((var @ (sK506 @ X103))) = $true) & ($true != ((X103 @ (sK506 @ X103))))) | ((((X103 @ (sK507 @ X103))) = $true) & (((X103 @ (lam @ (sK507 @ X103)))) != $true)) | (((sP31 @ X103)) = $true) | (((X103 @ X104)) = $true)) | (induction != $true)) & ((hoasinduction_lem0 = $true) | ! [X108 : (term > $o)] : (((sK508 @ id @ (sK509 @ X108) @ id)) != ((X108 @ (sK509 @ X108))))) & (! [X110 : (subst > term > subst > $o)] : ! [X112 : term] : (((X110 @ id @ X112 @ id)) = ((sK510 @ X110 @ X112))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem3b = $true) | ! [X114 : (subst > term > term)] : (((sub @ sK511 @ (push @ one @ sh))) != ((X114 @ sh @ one)))) & (! [X115 : term] : (((sub @ X115 @ (push @ one @ sh))) = ((sK512 @ X115 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = sh) & (lamnotap != $true) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK513 @ sK514))) != sK514)) & (! [X119 : term,X120 : subst] : (((comp @ sh @ (push @ X119 @ X120))) = X120) | (axshiftcons != $true)) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X122 : (subst > term > term)] : (((sub @ sK515 @ (push @ (sK517 @ X122) @ (sK516 @ X122)))) != ((X122 @ (sK516 @ X122) @ (sK517 @ X122))))) & (! [X125 : term] : ! [X127 : subst,X128 : term] : (((sK518 @ X125 @ X127 @ X128)) = ((sub @ X125 @ (push @ X128 @ X127)))) | (hoasinduction_lem3v2_f != $true)) & (pushprop = $true) & (! [X129 : (subst > term > subst > $o),X130 : term] : (((((X129 @ id @ (sK519 @ X129) @ id)) = $true) & (((X129 @ id @ (ap @ (sub @ (sK520 @ X129) @ id) @ (sK519 @ X129)) @ id)) != $true) & (((X129 @ id @ (sK520 @ X129) @ id)) = $true)) | (((X129 @ id @ X130 @ id)) = $true) | ($true = ((sP29 @ X129)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X135 : term,X136 : term] : (($true != ((sK521 @ id @ X135 @ id))) | ($true = ((sK521 @ id @ (ap @ (sub @ X136 @ id) @ X135) @ id))) | ($true != ((sK521 @ id @ X136 @ id)))) & (((sK521 @ id @ sK522 @ id)) != $true) & (((sP29 @ sK521)) != $true))) & (axmap = $true) & ((axvarid = $true) | (((sub @ sK523 @ id)) != sK523)) & (! [X138 : term] : (((sub @ X138 @ id)) = X138) | (axvarid != $true)) & (($true = sP28) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP28)) & (! [X139 : (subst > term > term),X140 : term,X141 : subst,X142 : (subst > term > term)] : ((((lam @ (X139 @ sh @ one))) != ((lam @ (X142 @ sh @ one)))) | (((X139 @ X141 @ X140)) = ((X142 @ X141 @ X140))) | (((X139 @ (comp @ (sK524 @ X139) @ (sK525 @ X139)) @ (sub @ (sK526 @ X139) @ (sK525 @ X139)))) != ((sub @ (X139 @ (sK524 @ X139) @ (sK526 @ X139)) @ (sK525 @ X139)))) | (((X142 @ (comp @ (sK529 @ X142) @ (sK528 @ X142)) @ (sub @ (sK527 @ X142) @ (sK528 @ X142)))) != ((sub @ (X142 @ (sK529 @ X142) @ (sK527 @ X142)) @ (sK528 @ X142))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((lam @ (sK533 @ sh @ one))) = ((lam @ (sK530 @ sh @ one)))) & (((sK533 @ sK532 @ sK531)) != ((sK530 @ sK532 @ sK531))) & ! [X153 : subst,X154 : subst,X155 : term] : (((sub @ (sK530 @ X153 @ X155) @ X154)) = ((sK530 @ (comp @ X153 @ X154) @ (sub @ X155 @ X154)))) & ! [X156 : term,X157 : subst,X158 : subst] : (((sub @ (sK533 @ X158 @ X156) @ X157)) = ((sK533 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157)))))) & ((sP27 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP27 != $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X159 : term] : (((sK534 @ X159 @ sh @ one)) = ((sub @ X159 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X162 : (subst > term > term)] : (((X162 @ sh @ one)) != ((sub @ sK535 @ (push @ one @ sh))))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_lthm = $true) & (! [X163 : term,X164 : term] : ((X163 = X164) | (((sub @ X163 @ sh)) != ((sub @ X164 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ((sK537 != sK536) & (((sub @ sK537 @ sh)) = ((sub @ sK536 @ sh))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2_lthm = $true) | (((sK541 != sK539) & (((ap @ (sub @ sK540 @ id) @ sK541)) = ((ap @ (sub @ sK538 @ id) @ sK539)))) & ! [X171 : term,X172 : term,X173 : term,X174 : term] : ((((ap @ X171 @ X173)) != ((ap @ X172 @ X174))) | (X173 = X174)))) & (! [X175 : term,X176 : term,X177 : term,X178 : term] : ((X176 = X178) | (((ap @ (sub @ X177 @ id) @ X178)) != ((ap @ (sub @ X175 @ id) @ X176)))) | ((((ap @ sK542 @ sK544)) = ((ap @ sK543 @ sK545))) & (sK544 != sK545)) | (hoasapinj2_lthm != $true)) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X184 : (term > $o)] : (((sK546 @ id @ (sK547 @ X184) @ id)) != ((X184 @ (sK547 @ X184))))) & (! [X186 : (subst > term > subst > $o)] : ! [X188 : term] : (((sK548 @ X186 @ X188)) = ((X186 @ id @ X188 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((axscons = $true) | (sK549 != ((push @ (sub @ one @ sK549) @ (comp @ sh @ sK549))))) & (! [X190 : subst] : (((push @ (sub @ one @ X190) @ (comp @ sh @ X190))) = X190) | (axscons != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((termmset = $true) | (((sub @ sK550 @ id)) != sK550)) & (! [X192 : term] : (((sub @ X192 @ id)) = X192) | (termmset != $true)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP25 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP25 != $true)) & ((hoasinduction_lem3 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem3 != $true)) & ((induction2lem_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2lem_lthm != $true)) & (hoasapnotvar = $true) & (axabs = $true) & ((apinj2 = $true) | ((((ap @ sK551 @ sK554)) = ((ap @ sK552 @ sK553))) & (sK553 != sK554))) & (! [X197 : term,X198 : term,X199 : term,X200 : term] : ((((ap @ X198 @ X199)) != ((ap @ X197 @ X200))) | (X199 = X200)) | (apinj2 != $true)) & ((apinj1 = $true) | ((((ap @ sK557 @ sK555)) = ((ap @ sK556 @ sK558))) & (sK557 != sK556))) & (! [X205 : term,X206 : term,X207 : term,X208 : term] : ((((ap @ X206 @ X208)) != ((ap @ X207 @ X205))) | (X206 = X207)) | (apinj1 != $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((((comp @ sh @ (push @ sK559 @ sK560))) != sK560) | (sK561 != ((sub @ one @ (push @ sK561 @ sK562)))) | ! [X213 : subst,X214 : (term > $o),X215 : term,X216 : term,X217 : (term > $o)] : ((((X217 @ (sub @ X216 @ (push @ X215 @ X213)))) = $true) | (((X214 @ X216)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X218 : term,X219 : subst] : (((comp @ sh @ (push @ X218 @ X219))) = X219) & ! [X220 : term,X221 : subst] : (((sub @ one @ (push @ X220 @ X221))) = X220) & ((((sK567 @ (sub @ sK566 @ (push @ sK565 @ sK563)))) != $true) & (((sK564 @ sK566)) = $true)))) & ! [X227 : term] : (((d2term @ (sK568 @ X227))) = X227) & (! [X229 : term,X230 : (term > $o),X231 : subst,X232 : (term > $o),X233 : term] : ((((X230 @ X229)) != $true) | (((X232 @ (sub @ X229 @ (push @ X233 @ X231)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK570 @ sK569)) = $true) & (((sK572 @ (sub @ sK569 @ (push @ sK573 @ sK571)))) != $true))) & (substmonoid_gthm = $true) & ((hoasapinj1_lthm = $true) | (! [X239 : term] : (((sub @ X239 @ id)) = X239) & ((sK577 != sK575) & (((ap @ (sub @ sK575 @ id) @ sK576)) = ((ap @ (sub @ sK577 @ id) @ sK574)))) & ! [X244 : term,X245 : term,X246 : term,X247 : term] : ((((ap @ X247 @ X244)) != ((ap @ X245 @ X246))) | (X245 = X247)))) & ((sK578 != ((sub @ sK578 @ id))) | ! [X249 : term,X250 : term,X251 : term,X252 : term] : ((X250 = X252) | (((ap @ (sub @ X250 @ id) @ X251)) != ((ap @ (sub @ X252 @ id) @ X249)))) | ((((ap @ sK580 @ sK581)) = ((ap @ sK582 @ sK579))) & (sK582 != sK580)) | (hoasapinj1_lthm != $true)) & ! [X257 : d_subst] : (d_id = X257) & ((sP17 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP17 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (hoasinduction_lem3a_lthm != $true)) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (axclos = $true) & ((hoasinduction_lem2 = $true) | (sP6 != $true)) & ((sP6 = $true) | (hoasinduction_lem2 != $true)) & ((axvarcons = $true) | (sK583 != ((sub @ one @ (push @ sK583 @ sK584))))) & (! [X260 : term,X261 : subst] : (((sub @ one @ (push @ X260 @ X261))) = X260) | (axvarcons != $true)) & (! [X262 : term,X263 : term,X264 : term,X265 : term] : ((((ap @ (sub @ X264 @ id) @ X265)) != ((ap @ (sub @ X262 @ id) @ X263))) | (X263 = X265)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK585 @ id) @ sK586)) = ((ap @ (sub @ sK587 @ id) @ sK588))) & (sK588 != sK586))) & (one = ((d2term @ d_one))) & (pushprop_gthm = $true) & ((sP4 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP4 != $true)) & ((termmset_lthm = $true) | ((((sub @ sK589 @ id)) != sK589) & ! [X271 : term] : (((sub @ X271 @ id)) = X271))) & (! [X272 : term] : (((sub @ X272 @ id)) = X272) | (((sub @ sK590 @ id)) != sK590) | (termmset_lthm != $true))), 27.00/4.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,vAPP,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,vAPP,sK469,sK470,sK471,sK472,vAPP,sK474,vAPP,vAPP,sK477,sK478,sK479,vAPP,vAPP,sK482,sK483,sK484,sK485,vAPP,sK487,sK488,vAPP,vAPP,vAPP,sK492,sK493,sK494,sK495,sK496,sK497,vAPP,vAPP,sK500,sK501,sK502,sK503,sK504,sK505,vAPP,vAPP,sK508,vAPP,vAPP,sK511,vAPP,sK513,sK514,sK515,vAPP,vAPP,vAPP,vAPP,vAPP,sK521,sK522,sK523,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK530,sK531,sK532,sK533,vAPP,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,vAPP,vAPP,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,vAPP,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590]),skolemize(X2,sK457),skolemize(X3,sK458),skolemize(X15,sK66 @ X9 @ X8),skolemize(X7,sK460),skolemize(X10,sK461),skolemize(X11,sK462),skolemize(X14,sK463),skolemize(X15,sK464),skolemize(X20,sK465),skolemize(X21,sK466),skolemize(X22,sK467),skolemize(X15,sK66 @ X9 @ X8),skolemize(X29,sK469),skolemize(X30,sK470),skolemize(X31,sK471),skolemize(X32,sK472),skolemize(X15,sK66 @ X9 @ X8),skolemize(X38,sK474),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X42,sK477),skolemize(X43,sK478),skolemize(X44,sK479),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X52,sK482),skolemize(X53,sK483),skolemize(X54,sK484),skolemize(X55,sK485),skolemize(X15,sK66 @ X9 @ X8),skolemize(X64,sK487),skolemize(X65,sK488),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X72,sK492),skolemize(X73,sK493),skolemize(X74,sK494),skolemize(X81,sK495),skolemize(X82,sK496),skolemize(X83,sK497),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X91,sK500),skolemize(X92,sK501),skolemize(X93,sK502),skolemize(X94,sK503),skolemize(X99,sK504),skolemize(X100,sK505),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X107,sK508),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X113,sK511),skolemize(X15,sK66 @ X9 @ X8),skolemize(X117,sK513),skolemize(X118,sK514),skolemize(X121,sK515),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X133,sK521),skolemize(X134,sK522),skolemize(X137,sK523),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X149,sK530),skolemize(X150,sK531),skolemize(X151,sK532),skolemize(X152,sK533),skolemize(X15,sK66 @ X9 @ X8),skolemize(X161,sK535),skolemize(X165,sK536),skolemize(X166,sK537),skolemize(X167,sK538),skolemize(X168,sK539),skolemize(X169,sK540),skolemize(X170,sK541),skolemize(X179,sK542),skolemize(X180,sK543),skolemize(X181,sK544),skolemize(X182,sK545),skolemize(X183,sK546),skolemize(X15,sK66 @ X9 @ X8),skolemize(X15,sK66 @ X9 @ X8),skolemize(X189,sK549),skolemize(X191,sK550),skolemize(X193,sK551),skolemize(X194,sK552),skolemize(X195,sK553),skolemize(X196,sK554),skolemize(X201,sK555),skolemize(X202,sK556),skolemize(X203,sK557),skolemize(X204,sK558),skolemize(X209,sK559),skolemize(X210,sK560),skolemize(X211,sK561),skolemize(X212,sK562),skolemize(X222,sK563),skolemize(X223,sK564),skolemize(X224,sK565),skolemize(X225,sK566),skolemize(X226,sK567),skolemize(X15,sK66 @ X9 @ X8),skolemize(X234,sK569),skolemize(X235,sK570),skolemize(X236,sK571),skolemize(X237,sK572),skolemize(X238,sK573),skolemize(X240,sK574),skolemize(X241,sK575),skolemize(X242,sK576),skolemize(X243,sK577),skolemize(X248,sK578),skolemize(X253,sK579),skolemize(X254,sK580),skolemize(X255,sK581),skolemize(X256,sK582),skolemize(X258,sK583),skolemize(X259,sK584),skolemize(X266,sK585),skolemize(X267,sK586),skolemize(X268,sK587),skolemize(X269,sK588),skolemize(X270,sK589),skolemize(X273,sK590)],[f262])). 27.00/4.44 thf(f264,plain,( 27.00/4.44 (hoasinduction_lem3aaa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ Y2 @ (push @ (sub @ Y5 @ Y4) @ (comp @ Y3 @ Y4))) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y5 @ Y4))) & ((sub @ (Y1 @ Y3 @ Y5) @ Y4) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y3)) @ Y4))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))), 27.00/4.44 inference(cnf_transformation,[],[f8])). 27.00/4.44 thf(f525,plain,( 27.00/4.44 ( ! [X11 : term] : (($true = sP28) | (((sK271 @ id @ X11 @ id)) != $true) | (((sK271 @ id @ (sub @ sK270 @ (push @ X11 @ id)) @ id)) = $true)) )), 27.00/4.44 inference(cnf_transformation,[],[f171])). 27.00/4.44 thf(f526,plain,( 27.00/4.44 ($true = sP28) | (((sK271 @ id @ (lam @ (sub @ sK270 @ (push @ one @ sh))) @ id)) != $true)), 27.00/4.44 inference(cnf_transformation,[],[f171])). 27.00/4.44 thf(f528,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((sK271 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | ($true = sP28) | (((sub @ (sub @ X2 @ (push @ (sK273 @ X3 @ X2) @ (sK275 @ X3 @ X2))) @ (sK274 @ X3 @ X2))) != ((sub @ (X3 @ (sK275 @ X3 @ X2) @ (sK273 @ X3 @ X2)) @ (sK274 @ X3 @ X2)))) | (((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) | (((sK271 @ id @ (sK272 @ X3) @ id)) = $true)) )), 27.00/4.44 inference(cnf_transformation,[],[f171])). 27.00/4.44 thf(f760,plain,( 27.00/4.44 (one = ((d2term @ d_one)))), 27.00/4.44 inference(cnf_transformation,[],[f263])). 27.00/4.44 thf(f786,plain,( 27.00/4.44 ( ! [X227 : term] : ((((d2term @ (sK568 @ X227))) = X227)) )), 27.00/4.44 inference(cnf_transformation,[],[f263])). 27.00/4.44 thf(f831,plain,( 27.00/4.44 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))), 27.00/4.44 inference(cnf_transformation,[],[f263])). 27.00/4.44 thf(f849,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $true) | ($true != sP28)), 27.00/4.44 inference(cnf_transformation,[],[f263])). 27.00/4.44 thf(f900,plain,( 27.00/4.44 ( ! [X78 : d_term] : ((d_one = X78)) )), 27.00/4.44 inference(cnf_transformation,[],[f263])). 27.00/4.44 thf(f981,plain,( 27.00/4.44 (hoasinduction_lem3aaa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ Y2 @ (push @ (sub @ Y5 @ Y4) @ (comp @ Y3 @ Y4))) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y5 @ Y4))) & ((sub @ (Y1 @ Y3 @ Y5) @ Y4) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y3)) @ Y4))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))), 27.00/4.44 inference(definition_unfolding,[],[f264,f831])). 27.00/4.44 thf(f1049,plain,( 27.00/4.44 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ Y2 @ (push @ (sub @ Y5 @ Y4) @ (comp @ Y3 @ Y4))) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y5 @ Y4))) & ((sub @ (Y1 @ Y3 @ Y5) @ Y4) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y3)) @ Y4))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))) = $false) | (hoasinduction_lem3aaa = $false)), 27.00/4.44 inference(xor_proxy_clausification,[],[f981])). 27.00/4.44 thf(f1050,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | ((((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ Y2 @ (push @ (sub @ Y5 @ Y4) @ (comp @ Y3 @ Y4))) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y5 @ Y4))) & ((sub @ (Y1 @ Y3 @ Y5) @ Y4) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y3)) @ Y4))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))) @ sK591)) = $false)), 27.00/4.44 inference(sigma_proxy_clausification,[],[f1049])). 27.00/4.44 thf(f1051,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((?? @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (((sub @ Y1 @ (push @ (sub @ Y4 @ Y3) @ (comp @ Y2 @ Y3))) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))) & ((sub @ (Y0 @ Y2 @ Y4) @ Y3) = (sub @ (sub @ Y1 @ (push @ Y4 @ Y2)) @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))))) = $false)), 27.00/4.44 inference(beta-eta_normalization,[],[f1050])). 27.00/4.44 thf(f1052,plain,( 27.00/4.44 ($false = ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))))) | (hoasinduction_lem3aaa = $false)), 27.00/4.44 inference(imp_proxy_clausification,[],[f1051])). 27.00/4.44 thf(f1053,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((?? @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (((sub @ Y1 @ (push @ (sub @ Y4 @ Y3) @ (comp @ Y2 @ Y3))) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))) & ((sub @ (Y0 @ Y2 @ Y4) @ Y3) = (sub @ (sub @ Y1 @ (push @ Y4 @ Y2)) @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))))) = $true)), 27.00/4.44 inference(imp_proxy_clausification,[],[f1051])). 27.00/4.44 thf(f1054,plain,( 27.00/4.44 ( ! [X1 : (subst > term > term)] : (((((^[Y0 : subst > term > term]: ((?? @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (((sub @ Y1 @ (push @ (sub @ Y4 @ Y3) @ (comp @ Y2 @ Y3))) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3))) & ((sub @ (Y0 @ Y2 @ Y4) @ Y3) = (sub @ (sub @ Y1 @ (push @ Y4 @ Y2)) @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) @ X1)) = $true) | (hoasinduction_lem3aaa = $false)) )), 27.00/4.44 inference(pi_proxy_clausification,[],[f1053])). 27.00/4.44 thf(f1055,plain,( 27.00/4.44 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | ((((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ Y0 @ (push @ (sub @ Y3 @ Y2) @ (comp @ Y1 @ Y2))) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))) & ((sub @ (X1 @ Y1 @ Y3) @ Y2) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y1)) @ Y2))))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) = $true)) )), 27.00/4.44 inference(beta-eta_normalization,[],[f1054])). 27.00/4.44 thf(f1056,plain,( 27.00/4.44 ( ! [X1 : (subst > term > term)] : (((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))) = $true) | (hoasinduction_lem3aaa = $false) | ($false = ((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ Y0 @ (push @ (sub @ Y3 @ Y2) @ (comp @ Y1 @ Y2))) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))) & ((sub @ (X1 @ Y1 @ Y3) @ Y2) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y1)) @ Y2)))))))))))))) )), 27.00/4.44 inference(imp_proxy_clausification,[],[f1055])). 27.00/4.44 thf(f1057,plain,( 27.00/4.44 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ($false = ((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ Y0 @ (push @ (sub @ Y3 @ Y2) @ (comp @ Y1 @ Y2))) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))) & ((sub @ (X1 @ Y1 @ Y3) @ Y2) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y1)) @ Y2))))))))))))) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))))))) )), 27.00/4.44 inference(imp_proxy_clausification,[],[f1056])). 27.00/4.44 thf(f1058,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))))) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ Y0 @ (push @ (sub @ Y3 @ Y2) @ (comp @ Y1 @ Y2))) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))) & ((sub @ (X1 @ Y1 @ Y3) @ Y2) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y1)) @ Y2)))))))))) @ X2)))) )), 27.00/4.44 inference(pi_proxy_clausification,[],[f1057])). 27.00/4.44 thf(f1059,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ Y0 @ (push @ (sub @ Y3 @ Y2) @ (comp @ Y1 @ Y2))) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2))) & ((sub @ (X1 @ Y1 @ Y3) @ Y2) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y1)) @ Y2)))))))))) @ X2))) | ($false = (((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK592 @ X1)))) | (hoasinduction_lem3aaa = $false)) )), 27.00/4.44 inference(sigma_proxy_clausification,[],[f1058])). 27.00/4.44 thf(f1060,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (((sub @ X2 @ (push @ (sub @ Y2 @ Y1) @ (comp @ Y0 @ Y1))) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1))) & ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (sub @ (sub @ X2 @ (push @ Y2 @ Y0)) @ Y1)))))))))) = $false) | (hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ((((sK591 @ id @ (sK592 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK592 @ X1)) @ id))) = $false)) )), 27.00/4.44 inference(beta-eta_normalization,[],[f1059])). 27.00/4.44 thf(f1061,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : (((((sK591 @ id @ (sK592 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK592 @ X1)) @ id))) = $false) | (hoasinduction_lem3aaa = $false) | ($false = (((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (((sub @ X2 @ (push @ (sub @ Y2 @ Y1) @ (comp @ Y0 @ Y1))) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1))) & ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (sub @ (sub @ X2 @ (push @ Y2 @ Y0)) @ Y1)))))))) @ (sK593 @ X1 @ X2)))) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) )), 27.00/4.44 inference(sigma_proxy_clausification,[],[f1060])). 27.00/4.44 thf(f1063,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (hoasinduction_lem3aaa = $false) | ($false = (((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (((sub @ X2 @ (push @ (sub @ Y2 @ Y1) @ (comp @ Y0 @ Y1))) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1))) & ((sub @ (X1 @ Y0 @ Y2) @ Y1) = (sub @ (sub @ X2 @ (push @ Y2 @ Y0)) @ Y1)))))))) @ (sK593 @ X1 @ X2))))) )), 27.00/4.44 inference(imp_proxy_clausification,[],[f1061])). 27.00/4.44 thf(f1064,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (((sub @ X2 @ (push @ (sub @ Y1 @ Y0) @ (comp @ (sK593 @ X1 @ X2) @ Y0))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ Y0) @ (sub @ Y1 @ Y0))) & ((sub @ (X1 @ (sK593 @ X1 @ X2) @ Y1) @ Y0) = (sub @ (sub @ X2 @ (push @ Y1 @ (sK593 @ X1 @ X2))) @ Y0)))))))) = $false) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (hoasinduction_lem3aaa = $false)) )), 27.00/4.44 inference(beta-eta_normalization,[],[f1063])). 27.00/4.44 thf(f1065,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : (((((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (((sub @ X2 @ (push @ (sub @ Y1 @ Y0) @ (comp @ (sK593 @ X1 @ X2) @ Y0))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ Y0) @ (sub @ Y1 @ Y0))) & ((sub @ (X1 @ (sK593 @ X1 @ X2) @ Y1) @ Y0) = (sub @ (sub @ X2 @ (push @ Y1 @ (sK593 @ X1 @ X2))) @ Y0)))))) @ (sK594 @ X1 @ X2))) = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (hoasinduction_lem3aaa = $false)) )), 27.00/4.44 inference(sigma_proxy_clausification,[],[f1064])). 27.00/4.44 thf(f1066,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (((!! @ term @ (^[Y0 : term]: (((sub @ X2 @ (push @ (sub @ Y0 @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ Y0 @ (sK594 @ X1 @ X2)))) & ((sub @ (X1 @ (sK593 @ X1 @ X2) @ Y0) @ (sK594 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ Y0 @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))))))) = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (hoasinduction_lem3aaa = $false)) )), 27.00/4.44 inference(beta-eta_normalization,[],[f1065])). 27.00/4.44 thf(f1067,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ((((^[Y0 : term]: (((sub @ X2 @ (push @ (sub @ Y0 @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ Y0 @ (sK594 @ X1 @ X2)))) & ((sub @ (X1 @ (sK593 @ X1 @ X2) @ Y0) @ (sK594 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ Y0 @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))))) @ (sK595 @ X1 @ X2))) = $false) | (hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true)) )), 27.00/4.44 inference(sigma_proxy_clausification,[],[f1066])). 27.00/4.44 thf(f1068,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) & ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))))) = $false)) )), 27.00/4.44 inference(beta-eta_normalization,[],[f1067])). 27.00/4.44 thf(f1069,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : (($false = (((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))))) | ($false = (((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) | (hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) )), 27.00/4.44 inference(and_proxy_clausification,[],[f1068])). 27.00/4.44 thf(f1070,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)))) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (hoasinduction_lem3aaa = $false) | ($false = (((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) = (X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true)) )), 27.00/4.44 inference(equality_proxy_clausification,[],[f1069])). 27.00/4.44 thf(f1071,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | (((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)))) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) )), 27.00/4.44 inference(equality_proxy_clausification,[],[f1070])). 27.00/4.44 thf(f1080,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | ($false = (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))) @ sK598)))), 27.00/4.44 inference(sigma_proxy_clausification,[],[f1052])). 27.00/4.44 thf(f1081,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (sub @ sK598 @ (push @ Y0 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ sK598 @ (push @ one @ sh))) @ id))) = $false)), 27.00/4.44 inference(beta-eta_normalization,[],[f1080])). 27.00/4.44 thf(f1082,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | (((sK591 @ id @ (lam @ (sub @ sK598 @ (push @ one @ sh))) @ id)) = $false)), 27.00/4.44 inference(imp_proxy_clausification,[],[f1081])). 27.00/4.44 thf(f1215,definition,( 27.00/4.44 spl603_1 <=> ($true = sP28)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_1])],[avatar_definition])). 27.00/4.44 thf(f1908,plain,( 27.00/4.44 ( ! [X227 : term] : ((((d2term @ d_one)) = X227)) )), 27.00/4.44 inference(forward_demodulation,[],[f786,f900])). 27.00/4.44 thf(f2672,definition,( 27.00/4.44 spl603_343 <=> (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_343])],[avatar_definition])). 27.00/4.44 thf(f2674,plain,( 27.00/4.44 (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ~spl603_343), 27.00/4.44 inference(avatar_component_clause,[],[f2672])). 27.00/4.44 thf(f2676,definition,( 27.00/4.44 spl603_344 <=> ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)))) | (((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_344])],[avatar_definition])). 27.00/4.44 thf(f2677,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (sK592 @ X1) @ id)) = $true) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) | (((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2))))) ) | ~spl603_344), 27.00/4.44 inference(avatar_component_clause,[],[f2676])). 27.00/4.44 thf(f2679,definition,( 27.00/4.44 spl603_345 <=> (hoasinduction_lem3aaa = $false)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_345])],[avatar_definition])). 27.00/4.44 thf(f2681,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $false) | ~spl603_345), 27.00/4.44 inference(avatar_component_clause,[],[f2679])). 27.00/4.44 thf(f2682,plain,( 27.00/4.44 spl603_343 | spl603_344 | spl603_345), 27.00/4.44 inference(avatar_split_clause,[],[f1071,f2679,f2676,f2672])). 27.00/4.44 thf(f2692,definition,( 27.00/4.44 spl603_348 <=> (((sK591 @ id @ (lam @ (sub @ sK598 @ (push @ one @ sh))) @ id)) = $false)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_348])],[avatar_definition])). 27.00/4.44 thf(f2694,plain,( 27.00/4.44 (((sK591 @ id @ (lam @ (sub @ sK598 @ (push @ one @ sh))) @ id)) = $false) | ~spl603_348), 27.00/4.44 inference(avatar_component_clause,[],[f2692])). 27.00/4.44 thf(f2695,plain,( 27.00/4.44 spl603_348 | spl603_345), 27.00/4.44 inference(avatar_split_clause,[],[f1082,f2679,f2692])). 27.00/4.44 thf(f2700,definition,( 27.00/4.44 spl603_350 <=> (hoasinduction_lem3aaa = $true)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_350])],[avatar_definition])). 27.00/4.44 thf(f2702,plain,( 27.00/4.44 (hoasinduction_lem3aaa = $true) | ~spl603_350), 27.00/4.44 inference(avatar_component_clause,[],[f2700])). 27.00/4.44 thf(f3197,definition,( 27.00/4.44 spl603_465 <=> ! [X2 : term,X3 : (subst > term > term)] : ((((sK271 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK271 @ id @ (sK272 @ X3) @ id)) = $true) | (((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) | (((sub @ (sub @ X2 @ (push @ (sK273 @ X3 @ X2) @ (sK275 @ X3 @ X2))) @ (sK274 @ X3 @ X2))) != ((sub @ (X3 @ (sK275 @ X3 @ X2) @ (sK273 @ X3 @ X2)) @ (sK274 @ X3 @ X2)))))), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_465])],[avatar_definition])). 27.00/4.44 thf(f3198,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((sub @ (sub @ X2 @ (push @ (sK273 @ X3 @ X2) @ (sK275 @ X3 @ X2))) @ (sK274 @ X3 @ X2))) != ((sub @ (X3 @ (sK275 @ X3 @ X2) @ (sK273 @ X3 @ X2)) @ (sK274 @ X3 @ X2)))) | (((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) | (((sK271 @ id @ (sK272 @ X3) @ id)) = $true) | (((sK271 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) ) | ~spl603_465), 27.00/4.44 inference(avatar_component_clause,[],[f3197])). 27.00/4.44 thf(f3199,plain,( 27.00/4.44 spl603_465 | spl603_1), 27.00/4.44 inference(avatar_split_clause,[],[f528,f1215,f3197])). 27.00/4.44 thf(f3262,definition,( 27.00/4.44 spl603_480 <=> ! [X11 : term] : ((((sK271 @ id @ X11 @ id)) != $true) | (((sK271 @ id @ (sub @ sK270 @ (push @ X11 @ id)) @ id)) = $true))), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_480])],[avatar_definition])). 27.00/4.44 thf(f3263,plain,( 27.00/4.44 ( ! [X11 : term] : ((((sK271 @ id @ (sub @ sK270 @ (push @ X11 @ id)) @ id)) = $true) | (((sK271 @ id @ X11 @ id)) != $true)) ) | ~spl603_480), 27.00/4.44 inference(avatar_component_clause,[],[f3262])). 27.00/4.44 thf(f3264,plain,( 27.00/4.44 spl603_480 | spl603_1), 27.00/4.44 inference(avatar_split_clause,[],[f525,f1215,f3262])). 27.00/4.44 thf(f3328,plain,( 27.00/4.44 spl603_350 | ~spl603_1), 27.00/4.44 inference(avatar_split_clause,[],[f849,f1215,f2700])). 27.00/4.44 thf(f3437,definition,( 27.00/4.44 spl603_519 <=> (((sK271 @ id @ (lam @ (sub @ sK270 @ (push @ one @ sh))) @ id)) = $true)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_519])],[avatar_definition])). 27.00/4.44 thf(f3439,plain,( 27.00/4.44 (((sK271 @ id @ (lam @ (sub @ sK270 @ (push @ one @ sh))) @ id)) != $true) | spl603_519), 27.00/4.44 inference(avatar_component_clause,[],[f3437])). 27.00/4.44 thf(f3440,plain,( 27.00/4.44 ~spl603_519 | spl603_1), 27.00/4.44 inference(avatar_split_clause,[],[f526,f1215,f3437])). 27.00/4.44 thf(f4141,plain,( 27.00/4.44 ( ! [X11 : term] : ((((sK271 @ id @ X11 @ id)) != $true) | (((sK271 @ id @ (d2term @ d_one) @ id)) = $true)) ) | ~spl603_480), 27.00/4.44 inference(forward_demodulation,[],[f3263,f1908])). 27.00/4.44 thf(f4179,plain,( 27.00/4.44 (((sK271 @ id @ (d2term @ d_one) @ id)) != $true) | spl603_519), 27.00/4.44 inference(forward_demodulation,[],[f3439,f1908])). 27.00/4.44 thf(f4237,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((sK271 @ id @ (sK272 @ X3) @ id)) = $true) | (((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) | (((d2term @ d_one)) != ((sub @ (sub @ X2 @ (push @ (sK273 @ X3 @ X2) @ (sK275 @ X3 @ X2))) @ (sK274 @ X3 @ X2)))) | (((sK271 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) ) | ~spl603_465), 27.00/4.44 inference(forward_demodulation,[],[f3198,f1908])). 27.00/4.44 thf(f4289,plain,( 27.00/4.44 ( ! [X11 : term] : ((((sK271 @ id @ one @ id)) = $true) | (((sK271 @ id @ X11 @ id)) != $true)) ) | ~spl603_480), 27.00/4.44 inference(forward_demodulation,[],[f4141,f760])). 27.00/4.44 thf(f4330,plain,( 27.00/4.44 (((sK271 @ id @ one @ id)) != $true) | spl603_519), 27.00/4.44 inference(forward_demodulation,[],[f4179,f760])). 27.00/4.44 thf(f4396,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) | (((sK271 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK271 @ id @ (sK272 @ X3) @ id)) = $true)) ) | ~spl603_465), 27.00/4.44 inference(forward_subsumption_resolution,[],[f4237,f1908])). 27.00/4.44 thf(f4471,definition,( 27.00/4.44 spl603_644 <=> (((sK271 @ id @ one @ id)) = $true)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_644])],[avatar_definition])). 27.00/4.44 thf(f4475,definition,( 27.00/4.44 spl603_645 <=> ! [X11 : term] : (((sK271 @ id @ X11 @ id)) != $true)), 27.00/4.44 introduced(definition,[new_symbols(definition,[spl603_645])],[avatar_definition])). 27.00/4.44 thf(f4476,plain,( 27.00/4.44 ( ! [X11 : term] : ((((sK271 @ id @ X11 @ id)) != $true)) ) | ~spl603_645), 27.00/4.44 inference(avatar_component_clause,[],[f4475])). 27.00/4.44 thf(f4477,plain,( 27.00/4.44 spl603_644 | spl603_645 | ~spl603_480), 27.00/4.44 inference(avatar_split_clause,[],[f4289,f3262,f4475,f4471])). 27.00/4.44 thf(f4534,plain,( 27.00/4.44 ~spl603_644 | spl603_519), 27.00/4.44 inference(avatar_split_clause,[],[f4330,f3437,f4471])). 27.00/4.44 thf(f5656,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((sK271 @ id @ (sK272 @ X3) @ id)) = $true) | (((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)))))) ) | (~spl603_465 | ~spl603_645)), 27.00/4.44 inference(forward_subsumption_resolution,[],[f4396,f4476])). 27.00/4.44 thf(f5845,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))) != ((X3 @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)))))) ) | (~spl603_465 | ~spl603_645)), 27.00/4.44 inference(forward_subsumption_resolution,[],[f5656,f4476])). 27.00/4.44 thf(f5936,plain,( 27.00/4.44 ( ! [X2 : term,X3 : (subst > term > term)] : ((((d2term @ d_one)) != ((sub @ X2 @ (push @ (sub @ (sK278 @ X3 @ X2) @ (sK276 @ X3 @ X2)) @ (comp @ (sK277 @ X3 @ X2) @ (sK276 @ X3 @ X2))))))) ) | (~spl603_465 | ~spl603_645)), 27.00/4.44 inference(forward_demodulation,[],[f5845,f1908])). 27.00/4.44 thf(f5966,plain,( 27.00/4.44 $false | (~spl603_465 | ~spl603_645)), 27.00/4.44 inference(forward_subsumption_resolution,[],[f5936,f1908])). 27.00/4.44 thf(f5967,plain,( 27.00/4.44 ~spl603_465 | ~spl603_645), 27.00/4.44 inference(avatar_contradiction_clause,[],[f5966])). 27.00/4.44 thf(f6043,plain,( 27.00/4.44 ($false = $true) | (~spl603_345 | ~spl603_350)), 27.00/4.44 inference(forward_demodulation,[],[f2702,f2681])). 27.00/4.44 thf(f6044,plain,( 27.00/4.44 $false | (~spl603_345 | ~spl603_350)), 27.00/4.44 inference(trivial_inequality_removal,[],[f6043])). 27.00/4.44 thf(f6045,plain,( 27.00/4.44 ~spl603_345 | ~spl603_350), 27.00/4.44 inference(avatar_contradiction_clause,[],[f6044])). 27.00/4.44 thf(f6098,plain,( 27.00/4.44 (((sK591 @ id @ (d2term @ d_one) @ id)) = $false) | ~spl603_348), 27.00/4.44 inference(forward_demodulation,[],[f2694,f1908])). 27.00/4.44 thf(f6100,plain,( 27.00/4.44 (((sK591 @ id @ one @ id)) = $true) | ~spl603_343), 27.00/4.44 inference(forward_demodulation,[],[f2674,f760])). 27.00/4.44 thf(f6117,plain,( 27.00/4.44 (((sK591 @ id @ one @ id)) = $false) | ~spl603_348), 27.00/4.44 inference(forward_demodulation,[],[f6098,f760])). 27.00/4.44 thf(f6127,plain,( 27.00/4.44 ($false = $true) | (~spl603_343 | ~spl603_348)), 27.00/4.44 inference(backward_demodulation,[],[f6100,f6117])). 27.00/4.44 thf(f6128,plain,( 27.00/4.44 $false | (~spl603_343 | ~spl603_348)), 27.00/4.44 inference(trivial_inequality_removal,[],[f6127])). 27.00/4.44 thf(f6129,plain,( 27.00/4.44 ~spl603_343 | ~spl603_348), 27.00/4.44 inference(avatar_contradiction_clause,[],[f6128])). 27.00/4.44 thf(f6173,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) | (((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2))))) ) | ~spl603_344), 27.00/4.44 inference(forward_demodulation,[],[f2677,f1908])). 27.00/4.44 thf(f6203,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sK591 @ id @ one @ id)) = $true) | (((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)))) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2))))))) ) | ~spl603_344), 27.00/4.44 inference(forward_demodulation,[],[f6173,f760])). 27.00/4.44 thf(f6221,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : (($false = $true) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) | (((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2))))) ) | (~spl603_344 | ~spl603_348)), 27.00/4.44 inference(forward_demodulation,[],[f6203,f6117])). 27.00/4.44 thf(f6222,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2))) != ((sub @ (X1 @ (sK593 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK594 @ X1 @ X2)))) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2))))))) ) | (~spl603_344 | ~spl603_348)), 27.00/4.44 inference(trivial_inequality_removal,[],[f6221])). 27.00/4.44 thf(f6235,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((d2term @ d_one)) != ((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) @ (sK594 @ X1 @ X2)))) | (((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2))))))) ) | (~spl603_344 | ~spl603_348)), 27.00/4.44 inference(forward_demodulation,[],[f6222,f1908])). 27.00/4.44 thf(f6247,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2))))))) ) | (~spl603_344 | ~spl603_348)), 27.00/4.44 inference(forward_subsumption_resolution,[],[f6235,f1908])). 27.00/4.44 thf(f6253,plain,( 27.00/4.44 ( ! [X2 : term,X1 : (subst > term > term)] : ((((d2term @ d_one)) != ((X1 @ (comp @ (sK593 @ X1 @ X2) @ (sK594 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2)))))) ) | (~spl603_344 | ~spl603_348)), 27.00/4.44 inference(forward_demodulation,[],[f6247,f1908])). 27.00/4.44 thf(f6255,plain,( 27.00/4.44 $false | (~spl603_344 | ~spl603_348)), 27.00/4.44 inference(forward_subsumption_resolution,[],[f6253,f1908])). 27.00/4.44 thf(f6256,plain,( 27.00/4.44 ~spl603_344 | ~spl603_348), 27.00/4.44 inference(avatar_contradiction_clause,[],[f6255])). 27.00/4.44 cnf(s280, plain, spl603_343 | spl603_344 | spl603_345, inference(sat_conversion,[],[f2682])). 27.00/4.44 cnf(s283, plain, spl603_345 | spl603_348, inference(sat_conversion,[],[f2695])). 27.00/4.44 cnf(s403, plain, spl603_1 | spl603_465, inference(sat_conversion,[],[f3199])). 27.00/4.44 cnf(s420, plain, spl603_1 | spl603_480, inference(sat_conversion,[],[f3264])). 27.00/4.44 cnf(s439, plain, ~spl603_1 | spl603_350, inference(sat_conversion,[],[f3328])). 27.00/4.44 cnf(s471, plain, spl603_1 | ~spl603_519, inference(sat_conversion,[],[f3440])). 27.00/4.44 cnf(s636, plain, ~spl603_480 | spl603_644 | spl603_645, inference(sat_conversion,[],[f4477])). 27.00/4.44 cnf(s642, plain, spl603_519 | ~spl603_644, inference(sat_conversion,[],[f4534])). 27.00/4.44 cnf(s720, plain, ~spl603_465 | ~spl603_645, inference(sat_conversion,[],[f5967])). 27.00/4.44 cnf(s728, plain, ~spl603_345 | ~spl603_350, inference(sat_conversion,[],[f6045])). 27.00/4.44 cnf(s732, plain, ~spl603_343 | ~spl603_348, inference(sat_conversion,[],[f6129])). 27.00/4.44 cnf(s746, plain, ~spl603_344 | ~spl603_348, inference(sat_conversion,[],[f6256])). 27.00/4.44 cnf(s836, plain, spl603_1, inference(rat,[],[s636,s720,s642,s403,s420,s471])). 27.00/4.44 cnf(s838, plain, spl603_350, inference(rat,[],[s439,s836])). 27.00/4.44 cnf(s846, plain, ~spl603_345, inference(rat,[],[s728,s838])). 27.00/4.44 cnf(s847, plain, spl603_348, inference(rat,[],[s283,s846])). 27.00/4.44 cnf(s849, plain, ~spl603_344, inference(rat,[],[s746,s847])). 27.00/4.44 cnf(s850, plain, ~spl603_343, inference(rat,[],[s732,s847])). 27.00/4.44 cnf(s851, plain, $false, inference(rat,[],[s280,s846,s849,s850])). 27.00/4.44 thf(f6261,plain,( 27.00/4.44 $false), 27.00/4.44 inference(avatar_sat_refutation,[],[s851])). 27.00/4.44 % SZS output end Proof for theBenchmark 27.00/4.44 % (959394)------------------------------ 27.00/4.44 % (959394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200) 27.00/4.44 % (959394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 27.00/4.45 % (959394)CaDiCaL version: 2.1.3 27.00/4.45 % (959394)Termination reason: Refutation 27.00/4.45 % (959394)Time elapsed: 0.634 s 27.00/4.45 % (959394)Peak memory usage: 18 MB 27.00/4.45 % (959394)Instructions burned: 731 (million) 27.00/4.45 % (959179)Success in time 3.846 s 27.00/4.45 % Vampire exiting 27.00/4.45 EOF