%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX172^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:38 AM UTC 2026
% Result : Theorem 14.62s 2.50s
% Output : Refutation 14.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX172^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n015.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:13:03 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.40 % (3715439)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.40 % (3715449)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4089426980:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.40 % (3715450)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.40 % (3715450)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
% 0.63/0.40 % (3715448)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1075612428:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.40 % (3715446)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1777914781:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.40 % (3715444)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=500983778:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.40 % (3715445)lrs+10_16_si=on:nwc=1.5:random_seed=1413884289:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.40 % (3715447)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=3355652885: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_2999 on theBenchmark for (2999ds/634Mi)
% 0.63/0.40 % (3715450)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=3819451324:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.40 % (3715446)Instruction limit reached!
% 0.63/0.40 % (3715446)------------------------------
% 0.63/0.40 % (3715446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (3715446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (3715446)CaDiCaL version: 2.1.3
% 0.63/0.40 % (3715446)Termination reason: Instruction limit
% 0.63/0.40 % (3715446)Termination phase: shuffling
% 0.63/0.40 % (3715446)Time elapsed: 0.003 s
% 0.63/0.40 % (3715446)Peak memory usage: 9 MB
% 0.63/0.40 % (3715446)Instructions burned: 5 (million)
% 0.63/0.40 % (3715445)Instruction limit reached!
% 0.63/0.40 % (3715445)------------------------------
% 0.63/0.40 % (3715445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (3715445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (3715445)CaDiCaL version: 2.1.3
% 0.63/0.40 % (3715445)Termination reason: Instruction limit
% 0.63/0.40 % (3715445)Termination phase: shuffling
% 0.63/0.40 % (3715445)Time elapsed: 0.008 s
% 0.63/0.40 % (3715445)Peak memory usage: 10 MB
% 0.63/0.40 % (3715445)Instructions burned: 18 (million)
% 0.63/0.40 % (3715449)Instruction limit reached!
% 0.63/0.40 % (3715449)------------------------------
% 0.63/0.40 % (3715449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (3715449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (3715449)CaDiCaL version: 2.1.3
% 0.63/0.40 % (3715449)Termination reason: Instruction limit
% 0.63/0.40 % (3715449)Termination phase: Preprocessing 3
% 0.63/0.40 % (3715449)Time elapsed: 0.018 s
% 0.63/0.40 % (3715449)Peak memory usage: 12 MB
% 0.63/0.40 % (3715449)Instructions burned: 78 (million)
% 0.63/0.40 % (3715448)Instruction limit reached!
% 0.63/0.40 % (3715448)------------------------------
% 0.63/0.40 % (3715448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (3715448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (3715448)CaDiCaL version: 2.1.3
% 0.63/0.40 % (3715448)Termination reason: Instruction limit
% 0.63/0.40 % (3715448)Termination phase: Property scanning
% 0.63/0.40 % (3715448)Time elapsed: 0.011 s
% 0.63/0.40 % (3715448)Peak memory usage: 10 MB
% 0.63/0.40 % (3715448)Instructions burned: 26 (million)
% 0.63/0.40 % (3715460)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.40 % (3715460)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=728060821:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.43 % (3715458)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3060944044:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.43 % (3715460)Instruction limit reached!
% 0.63/0.43 % (3715460)------------------------------
% 0.63/0.43 % (3715460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (3715460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (3715460)CaDiCaL version: 2.1.3
% 0.63/0.43 % (3715460)Termination reason: Instruction limit
% 0.63/0.43 % (3715460)Termination phase: shuffling
% 0.63/0.43 % (3715460)Time elapsed: 0.002 s
% 0.63/0.43 % (3715460)Peak memory usage: 10 MB
% 0.63/0.43 % (3715460)Instructions burned: 9 (million)
% 0.63/0.43 % (3715458)Instruction limit reached!
% 0.63/0.43 % (3715458)------------------------------
% 0.63/0.43 % (3715458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (3715458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (3715458)CaDiCaL version: 2.1.3
% 0.63/0.43 % (3715458)Termination reason: Instruction limit
% 0.63/0.43 % (3715458)Termination phase: shuffling
% 0.63/0.43 % (3715458)Time elapsed: 0.001 s
% 0.63/0.43 % (3715458)Peak memory usage: 9 MB
% 0.63/0.43 % (3715458)Instructions burned: 2 (million)
% 0.63/0.43 % (3715461)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2782897109:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.63/0.43 % (3715459)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=572651682:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.43 % (3715464)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
% 0.63/0.43 % (3715464)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.43 % (3715464)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1957897059:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.63/0.43 % (3715461)Instruction limit reached!
% 0.63/0.43 % (3715461)------------------------------
% 0.63/0.43 % (3715461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (3715461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (3715461)CaDiCaL version: 2.1.3
% 0.63/0.43 % (3715461)Termination reason: Instruction limit
% 0.63/0.43 % (3715461)Termination phase: shuffling
% 0.63/0.43 % (3715461)Time elapsed: 0.006 s
% 0.63/0.43 % (3715461)Peak memory usage: 10 MB
% 0.63/0.43 % (3715461)Instructions burned: 14 (million)
% 0.63/0.43 % (3715459)Instruction limit reached!
% 0.63/0.43 % (3715459)------------------------------
% 0.63/0.43 % (3715459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (3715459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (3715459)CaDiCaL version: 2.1.3
% 0.63/0.43 % (3715459)Termination reason: Instruction limit
% 0.63/0.43 % (3715459)Termination phase: shuffling
% 0.63/0.43 % (3715459)Time elapsed: 0.004 s
% 0.63/0.43 % (3715459)Peak memory usage: 10 MB
% 0.63/0.43 % (3715459)Instructions burned: 5 (million)
% 0.63/0.43 % (3715444)Instruction limit reached!
% 0.63/0.43 % (3715444)------------------------------
% 0.63/0.43 % (3715444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (3715444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (3715444)CaDiCaL version: 2.1.3
% 0.63/0.43 % (3715444)Termination reason: Instruction limit
% 0.63/0.43 % (3715444)Termination phase: Preprocessing 3
% 0.63/0.43 % (3715444)Time elapsed: 0.039 s
% 0.63/0.43 % (3715444)Peak memory usage: 12 MB
% 0.63/0.43 % (3715444)Instructions burned: 87 (million)
% 0.63/0.43 % (3715464)Instruction limit reached!
% 0.63/0.43 % (3715464)------------------------------
% 0.63/0.43 % (3715464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.43 % (3715464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.43 % (3715464)CaDiCaL version: 2.1.3
% 0.63/0.43 % (3715464)Termination reason: Instruction limit
% 0.63/0.46 % (3715464)Termination phase: Property scanning
% 0.63/0.46 % (3715464)Time elapsed: 0.008 s
% 0.63/0.46 % (3715464)Peak memory usage: 10 MB
% 0.63/0.46 % (3715464)Instructions burned: 33 (million)
% 0.63/0.46 % (3715472)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=659078157:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.63/0.46 % (3715469)lrs+10_1_si=on:cs=on:random_seed=1949236923:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.63/0.46 % (3715471)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3321970540:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.63/0.46 % (3715465)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=3947187717:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.63/0.46 % (3715469)Instruction limit reached!
% 0.63/0.46 % (3715469)------------------------------
% 0.63/0.46 % (3715469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.46 % (3715469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.46 % (3715469)CaDiCaL version: 2.1.3
% 0.63/0.46 % (3715469)Termination reason: Instruction limit
% 0.63/0.46 % (3715469)Termination phase: shuffling
% 0.63/0.46 % (3715469)Time elapsed: 0.005 s
% 0.63/0.46 % (3715469)Peak memory usage: 10 MB
% 0.63/0.46 % (3715469)Instructions burned: 11 (million)
% 0.63/0.46 % (3715470)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.63/0.46 % (3715470)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=1056622342:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.46 % (3715470)Instruction limit reached!
% 0.63/0.46 % (3715470)------------------------------
% 0.63/0.46 % (3715470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.46 % (3715470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.46 % (3715470)CaDiCaL version: 2.1.3
% 0.63/0.46 % (3715470)Termination reason: Instruction limit
% 0.63/0.46 % (3715470)Termination phase: shuffling
% 0.63/0.46 % (3715470)Time elapsed: 0.001 s
% 0.63/0.46 % (3715470)Peak memory usage: 9 MB
% 0.63/0.46 % (3715470)Instructions burned: 2 (million)
% 0.63/0.46 % (3715450)Instruction limit reached!
% 0.63/0.46 % (3715450)------------------------------
% 0.63/0.46 % (3715450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.46 % (3715450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.46 % (3715450)CaDiCaL version: 2.1.3
% 0.63/0.46 % (3715450)Termination reason: Instruction limit
% 0.63/0.46 % (3715450)Termination phase: Property scanning
% 0.63/0.46 % (3715450)Time elapsed: 0.069 s
% 0.63/0.46 % (3715450)Peak memory usage: 13 MB
% 0.63/0.46 % (3715450)Instructions burned: 158 (million)
% 0.63/0.46 % (3715471)Instruction limit reached!
% 0.63/0.46 % (3715471)------------------------------
% 0.63/0.46 % (3715471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.46 % (3715471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.46 % (3715471)CaDiCaL version: 2.1.3
% 0.63/0.46 % (3715471)Termination reason: Instruction limit
% 0.63/0.46 % (3715471)Termination phase: Saturation
% 0.63/0.46 % (3715471)Time elapsed: 0.017 s
% 0.63/0.46 % (3715471)Peak memory usage: 11 MB
% 0.63/0.46 % (3715471)Instructions burned: 38 (million)
% 0.63/0.46 % (3715477)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3784279468:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.63/0.46 % (3715479)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1830188413:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.63/0.46 % (3715480)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1047152946:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.63/0.46 % (3715477)Instruction limit reached!
% 0.63/0.46 % (3715477)------------------------------
% 0.63/0.46 % (3715477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.46 % (3715477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (3715477)CaDiCaL version: 2.1.3
% 1.32/0.52 % (3715477)Termination reason: Instruction limit
% 1.32/0.52 % (3715477)Termination phase: Property scanning
% 1.32/0.52 % (3715477)Time elapsed: 0.011 s
% 1.32/0.52 % (3715477)Peak memory usage: 10 MB
% 1.32/0.52 % (3715477)Instructions burned: 26 (million)
% 1.32/0.52 % (3715481)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3148821811:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.32/0.52 % (3715479)Instruction limit reached!
% 1.32/0.52 % (3715479)------------------------------
% 1.32/0.52 % (3715479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (3715479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (3715479)CaDiCaL version: 2.1.3
% 1.32/0.52 % (3715479)Termination reason: Instruction limit
% 1.32/0.52 % (3715479)Termination phase: shuffling
% 1.32/0.52 % (3715479)Time elapsed: 0.007 s
% 1.32/0.52 % (3715479)Peak memory usage: 10 MB
% 1.32/0.52 % (3715479)Instructions burned: 15 (million)
% 1.32/0.52 % (3715465)Instruction limit reached!
% 1.32/0.52 % (3715465)------------------------------
% 1.32/0.52 % (3715465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (3715465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (3715465)CaDiCaL version: 2.1.3
% 1.32/0.52 % (3715465)Termination reason: Instruction limit
% 1.32/0.52 % (3715465)Termination phase: Saturation
% 1.32/0.52 % (3715465)Time elapsed: 0.036 s
% 1.32/0.52 % (3715465)Peak memory usage: 11 MB
% 1.32/0.52 % (3715465)Instructions burned: 87 (million)
% 1.32/0.52 % (3715481)Instruction limit reached!
% 1.32/0.52 % (3715481)------------------------------
% 1.32/0.52 % (3715481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (3715481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (3715481)CaDiCaL version: 2.1.3
% 1.32/0.52 % (3715481)Termination reason: Instruction limit
% 1.32/0.52 % (3715481)Termination phase: shuffling
% 1.32/0.52 % (3715481)Time elapsed: 0.007 s
% 1.32/0.52 % (3715481)Peak memory usage: 10 MB
% 1.32/0.52 % (3715481)Instructions burned: 15 (million)
% 1.32/0.52 % (3715485)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1975009110:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.32/0.52 % (3715472)Instruction limit reached!
% 1.32/0.52 % (3715472)------------------------------
% 1.32/0.52 % (3715472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (3715472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (3715472)CaDiCaL version: 2.1.3
% 1.32/0.52 % (3715472)Termination reason: Instruction limit
% 1.32/0.52 % (3715472)Termination phase: Saturation
% 1.32/0.52 % (3715472)Time elapsed: 0.059 s
% 1.32/0.52 % (3715472)Peak memory usage: 15 MB
% 1.32/0.52 % (3715472)Instructions burned: 251 (million)
% 1.32/0.52 % (3715485)Instruction limit reached!
% 1.32/0.52 % (3715485)------------------------------
% 1.32/0.52 % (3715485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (3715485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (3715485)CaDiCaL version: 2.1.3
% 1.32/0.52 % (3715485)Termination reason: Instruction limit
% 1.32/0.52 % (3715485)Termination phase: shuffling
% 1.32/0.52 % (3715485)Time elapsed: 0.003 s
% 1.32/0.52 % (3715485)Peak memory usage: 10 MB
% 1.32/0.52 % (3715485)Instructions burned: 5 (million)
% 1.32/0.52 % (3715487)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2154153051:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.32/0.52 % (3715488)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2047612222:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.32/0.52 % (3715489)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=108128300:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.32/0.52 % (3715491)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.32/0.52 % (3715491)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.24/0.60 % (3715491)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=885093125:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.24/0.60 % (3715488)Instruction limit reached!
% 2.24/0.60 % (3715488)------------------------------
% 2.24/0.60 % (3715488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (3715488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (3715488)CaDiCaL version: 2.1.3
% 2.24/0.60 % (3715488)Termination reason: Instruction limit
% 2.24/0.60 % (3715488)Termination phase: shuffling
% 2.24/0.60 % (3715488)Time elapsed: 0.010 s
% 2.24/0.60 % (3715488)Peak memory usage: 10 MB
% 2.24/0.60 % (3715488)Instructions burned: 24 (million)
% 2.24/0.60 % (3715491)Instruction limit reached!
% 2.24/0.60 % (3715491)------------------------------
% 2.24/0.60 % (3715491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (3715491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (3715491)CaDiCaL version: 2.1.3
% 2.24/0.60 % (3715491)Termination reason: Instruction limit
% 2.24/0.60 % (3715491)Termination phase: shuffling
% 2.24/0.60 % (3715491)Time elapsed: 0.003 s
% 2.24/0.60 % (3715491)Peak memory usage: 10 MB
% 2.24/0.60 % (3715491)Instructions burned: 14 (million)
% 2.24/0.60 % (3715493)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.24/0.60 % (3715487)Instruction limit reached!
% 2.24/0.60 % (3715487)------------------------------
% 2.24/0.60 % (3715487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (3715487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (3715487)CaDiCaL version: 2.1.3
% 2.24/0.60 % (3715487)Termination reason: Instruction limit
% 2.24/0.60 % (3715487)Termination phase: shuffling
% 2.24/0.60 % (3715487)Time elapsed: 0.015 s
% 2.24/0.60 % (3715487)Peak memory usage: 10 MB
% 2.24/0.60 % (3715487)Instructions burned: 27 (million)
% 2.24/0.60 % (3715493)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=4200951235:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.24/0.60 % (3715493)Instruction limit reached!
% 2.24/0.60 % (3715493)------------------------------
% 2.24/0.60 % (3715493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (3715493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (3715493)CaDiCaL version: 2.1.3
% 2.24/0.60 % (3715493)Termination reason: Instruction limit
% 2.24/0.60 % (3715493)Termination phase: shuffling
% 2.24/0.60 % (3715493)Time elapsed: 0.004 s
% 2.24/0.60 % (3715493)Peak memory usage: 10 MB
% 2.24/0.60 % (3715493)Instructions burned: 9 (million)
% 2.24/0.60 % (3715499)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3502938351:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.24/0.60 % (3715497)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=2060331747:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.24/0.60 % (3715499)Instruction limit reached!
% 2.24/0.60 % (3715499)------------------------------
% 2.24/0.60 % (3715499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (3715499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (3715499)CaDiCaL version: 2.1.3
% 2.24/0.60 % (3715499)Termination reason: Instruction limit
% 2.24/0.60 % (3715499)Termination phase: shuffling
% 2.24/0.60 % (3715499)Time elapsed: 0.006 s
% 2.24/0.60 % (3715499)Peak memory usage: 10 MB
% 2.24/0.60 % (3715499)Instructions burned: 26 (million)
% 2.24/0.60 % (3715489)Instruction limit reached!
% 2.24/0.60 % (3715489)------------------------------
% 2.24/0.60 % (3715489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.60 % (3715489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.60 % (3715489)CaDiCaL version: 2.1.3
% 2.24/0.60 % (3715489)Termination reason: Instruction limit
% 2.24/0.60 % (3715489)Termination phase: Preprocessing 3
% 2.24/0.60 % (3715489)Time elapsed: 0.027 s
% 2.24/0.65 % (3715489)Peak memory usage: 11 MB
% 2.24/0.65 % (3715489)Instructions burned: 62 (million)
% 2.24/0.65 % (3715498)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1486432799:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.24/0.65 % (3715501)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=636429973:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.24/0.65 % (3715497)Instruction limit reached!
% 2.24/0.65 % (3715497)------------------------------
% 2.24/0.65 % (3715497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.65 % (3715497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.65 % (3715497)CaDiCaL version: 2.1.3
% 2.24/0.65 % (3715497)Termination reason: Instruction limit
% 2.24/0.65 % (3715497)Termination phase: shuffling
% 2.24/0.65 % (3715497)Time elapsed: 0.013 s
% 2.24/0.65 % (3715497)Peak memory usage: 10 MB
% 2.24/0.65 % (3715497)Instructions burned: 31 (million)
% 2.24/0.65 % (3715498)Instruction limit reached!
% 2.24/0.65 % (3715498)------------------------------
% 2.24/0.65 % (3715498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.65 % (3715498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.65 % (3715504)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=865200988:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.24/0.65 % (3715498)CaDiCaL version: 2.1.3
% 2.24/0.65 % (3715498)Termination reason: Instruction limit
% 2.24/0.65 % (3715498)Termination phase: shuffling
% 2.24/0.65 % (3715498)Time elapsed: 0.008 s
% 2.24/0.65 % (3715498)Peak memory usage: 10 MB
% 2.24/0.65 % (3715498)Instructions burned: 9 (million)
% 2.24/0.65 % (3715501)Instruction limit reached!
% 2.24/0.65 % (3715501)------------------------------
% 2.24/0.65 % (3715501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.65 % (3715501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.65 % (3715501)CaDiCaL version: 2.1.3
% 2.24/0.65 % (3715501)Termination reason: Instruction limit
% 2.24/0.65 % (3715501)Termination phase: shuffling
% 2.24/0.65 % (3715501)Time elapsed: 0.010 s
% 2.24/0.65 % (3715501)Peak memory usage: 10 MB
% 2.24/0.65 % (3715501)Instructions burned: 21 (million)
% 2.24/0.65 % (3715505)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1775888227:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.24/0.65 % (3715510)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1634843104:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.24/0.65 % (3715509)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3401925982:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.24/0.65 % (3715511)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.24/0.65 % (3715511)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4193218992:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.24/0.65 % (3715511)Instruction limit reached!
% 2.24/0.65 % (3715511)------------------------------
% 2.24/0.65 % (3715511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.65 % (3715511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.65 % (3715511)CaDiCaL version: 2.1.3
% 2.24/0.65 % (3715511)Termination reason: Instruction limit
% 2.24/0.65 % (3715511)Termination phase: shuffling
% 2.24/0.65 % (3715511)Time elapsed: 0.004 s
% 2.24/0.65 % (3715511)Peak memory usage: 10 MB
% 2.24/0.65 % (3715511)Instructions burned: 8 (million)
% 2.24/0.65 % (3715510)Instruction limit reached!
% 2.24/0.65 % (3715510)------------------------------
% 2.24/0.65 % (3715510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.65 % (3715510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.65 % (3715510)CaDiCaL version: 2.1.3
% 2.24/0.65 % (3715510)Termination reason: Instruction limit
% 2.24/0.65 % (3715510)Termination phase: shuffling
% 2.24/0.65 % (3715510)Time elapsed: 0.019 s
% 2.24/0.65 % (3715510)Peak memory usage: 11 MB
% 2.24/0.65 % (3715510)Instructions burned: 43 (million)
% 2.24/0.65 % (3715516)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3093752890:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.59/0.75 % (3715517)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=3562973340:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.59/0.75 % (3715505)Instruction limit reached!
% 2.59/0.75 % (3715505)------------------------------
% 2.59/0.75 % (3715505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (3715505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (3715505)CaDiCaL version: 2.1.3
% 2.59/0.75 % (3715505)Termination reason: Instruction limit
% 2.59/0.75 % (3715505)Termination phase: Function definition elimination
% 2.59/0.75 % (3715505)Time elapsed: 0.061 s
% 2.59/0.75 % (3715505)Peak memory usage: 13 MB
% 2.59/0.75 % (3715505)Instructions burned: 143 (million)
% 2.59/0.75 % (3715480)Instruction limit reached!
% 2.59/0.75 % (3715480)------------------------------
% 2.59/0.75 % (3715480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (3715480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (3715480)CaDiCaL version: 2.1.3
% 2.59/0.75 % (3715480)Termination reason: Instruction limit
% 2.59/0.75 % (3715480)Termination phase: Saturation
% 2.59/0.75 % (3715480)Time elapsed: 0.148 s
% 2.59/0.75 % (3715480)Peak memory usage: 16 MB
% 2.59/0.75 % (3715480)Instructions burned: 327 (million)
% 2.59/0.75 % (3715520)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.59/0.75 % (3715520)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1293185186:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.59/0.75 % (3715520)Instruction limit reached!
% 2.59/0.75 % (3715520)------------------------------
% 2.59/0.75 % (3715520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (3715520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (3715520)CaDiCaL version: 2.1.3
% 2.59/0.75 % (3715520)Termination reason: Instruction limit
% 2.59/0.75 % (3715520)Termination phase: shuffling
% 2.59/0.75 % (3715520)Time elapsed: 0.003 s
% 2.59/0.75 % (3715520)Peak memory usage: 10 MB
% 2.59/0.75 % (3715520)Instructions burned: 6 (million)
% 2.59/0.75 % (3715521)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1033693928:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.59/0.75 % (3715521)Instruction limit reached!
% 2.59/0.75 % (3715521)------------------------------
% 2.59/0.75 % (3715521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (3715521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (3715521)CaDiCaL version: 2.1.3
% 2.59/0.75 % (3715521)Termination reason: Instruction limit
% 2.59/0.75 % (3715521)Termination phase: shuffling
% 2.59/0.75 % (3715521)Time elapsed: 0.010 s
% 2.59/0.75 % (3715521)Peak memory usage: 10 MB
% 2.59/0.75 % (3715521)Instructions burned: 23 (million)
% 2.59/0.75 % (3715523)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3545654269:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.59/0.75 % (3715523)Instruction limit reached!
% 2.59/0.75 % (3715523)------------------------------
% 2.59/0.75 % (3715523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.75 % (3715523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.75 % (3715523)CaDiCaL version: 2.1.3
% 2.59/0.75 % (3715523)Termination reason: Instruction limit
% 2.59/0.75 % (3715523)Termination phase: shuffling
% 2.59/0.75 % (3715523)Time elapsed: 0.009 s
% 2.59/0.75 % (3715523)Peak memory usage: 10 MB
% 2.59/0.75 % (3715523)Instructions burned: 21 (million)
% 2.59/0.75 % (3715525)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=1086494401:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.59/0.75 % (3715517)Instruction limit reached!
% 2.59/0.75 % (3715517)------------------------------
% 2.59/0.75 % (3715517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.81 % (3715517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.81 % (3715517)CaDiCaL version: 2.1.3
% 3.43/0.81 % (3715517)Termination reason: Instruction limit
% 3.43/0.81 % (3715517)Termination phase: Property scanning
% 3.43/0.81 % (3715517)Time elapsed: 0.073 s
% 3.43/0.81 % (3715517)Peak memory usage: 13 MB
% 3.43/0.81 % (3715517)Instructions burned: 171 (million)
% 3.43/0.81 % (3715516)Instruction limit reached!
% 3.43/0.81 % (3715516)------------------------------
% 3.43/0.81 % (3715516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.81 % (3715516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.81 % (3715516)CaDiCaL version: 2.1.3
% 3.43/0.81 % (3715516)Termination reason: Instruction limit
% 3.43/0.81 % (3715516)Termination phase: Saturation
% 3.43/0.81 % (3715516)Time elapsed: 0.082 s
% 3.43/0.81 % (3715516)Peak memory usage: 15 MB
% 3.43/0.81 % (3715516)Instructions burned: 185 (million)
% 3.43/0.81 % (3715509)Instruction limit reached!
% 3.43/0.81 % (3715509)------------------------------
% 3.43/0.81 % (3715509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.81 % (3715509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.81 % (3715509)CaDiCaL version: 2.1.3
% 3.43/0.81 % (3715509)Termination reason: Instruction limit
% 3.43/0.81 % (3715509)Termination phase: Property scanning
% 3.43/0.81 % (3715509)Time elapsed: 0.117 s
% 3.43/0.81 % (3715509)Peak memory usage: 13 MB
% 3.43/0.81 % (3715509)Instructions burned: 194 (million)
% 3.43/0.81 % (3715527)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=3009899291:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.43/0.81 % (3715529)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=4186191567:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.43/0.81 % (3715530)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=708140942:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.43/0.81 % (3715531)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3369678516:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.43/0.81 % (3715531)Instruction limit reached!
% 3.43/0.81 % (3715531)------------------------------
% 3.43/0.81 % (3715531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.81 % (3715531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.81 % (3715531)CaDiCaL version: 2.1.3
% 3.43/0.81 % (3715531)Termination reason: Instruction limit
% 3.43/0.81 % (3715531)Termination phase: shuffling
% 3.43/0.81 % (3715531)Time elapsed: 0.010 s
% 3.43/0.81 % (3715531)Peak memory usage: 10 MB
% 3.43/0.81 % (3715531)Instructions burned: 23 (million)
% 3.43/0.81 % (3715447)Instruction limit reached!
% 3.43/0.81 % (3715447)------------------------------
% 3.43/0.81 % (3715447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.81 % (3715447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.81 % (3715447)CaDiCaL version: 2.1.3
% 3.43/0.81 % (3715447)Termination reason: Instruction limit
% 3.43/0.81 % (3715447)Termination phase: Saturation
% 3.43/0.81 % (3715447)Time elapsed: 0.327 s
% 3.43/0.81 % (3715447)Peak memory usage: 18 MB
% 3.43/0.81 % (3715447)Instructions burned: 634 (million)
% 3.43/0.81 % (3715529)Instruction limit reached!
% 3.43/0.81 % (3715529)------------------------------
% 3.43/0.81 % (3715529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.43/0.81 % (3715529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/0.81 % (3715529)CaDiCaL version: 2.1.3
% 3.43/0.81 % (3715529)Termination reason: Instruction limit
% 3.43/0.81 % (3715529)Termination phase: SInE selection
% 3.43/0.81 % (3715529)Time elapsed: 0.019 s
% 3.43/0.81 % (3715529)Peak memory usage: 10 MB
% 3.43/0.81 % (3715529)Instructions burned: 46 (million)
% 3.43/0.81 % (3715536)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.43/0.81 % (3715536)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=192161690:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.65/0.97 % (3715538)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=430670145:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.65/0.97 % (3715537)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1367855726:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.65/0.97 % (3715537)Instruction limit reached!
% 3.65/0.97 % (3715537)------------------------------
% 3.65/0.97 % (3715537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.65/0.97 % (3715537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/0.97 % (3715537)CaDiCaL version: 2.1.3
% 3.65/0.97 % (3715537)Termination reason: Instruction limit
% 3.65/0.97 % (3715537)Termination phase: shuffling
% 3.65/0.97 % (3715537)Time elapsed: 0.006 s
% 3.65/0.97 % (3715537)Peak memory usage: 10 MB
% 3.65/0.97 % (3715537)Instructions burned: 13 (million)
% 3.65/0.97 % (3715542)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=475940733:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.65/0.97 % (3715538)Instruction limit reached!
% 3.65/0.97 % (3715538)------------------------------
% 3.65/0.97 % (3715538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.65/0.97 % (3715538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/0.97 % (3715538)CaDiCaL version: 2.1.3
% 3.65/0.97 % (3715538)Termination reason: Instruction limit
% 3.65/0.97 % (3715538)Termination phase: Preprocessing 2
% 3.65/0.97 % (3715538)Time elapsed: 0.028 s
% 3.65/0.97 % (3715538)Peak memory usage: 11 MB
% 3.65/0.97 % (3715538)Instructions burned: 67 (million)
% 3.65/0.97 % (3715544)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1489404134:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.65/0.97 % (3715542)Instruction limit reached!
% 3.65/0.97 % (3715542)------------------------------
% 3.65/0.97 % (3715542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.65/0.97 % (3715542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/0.97 % (3715542)CaDiCaL version: 2.1.3
% 3.65/0.97 % (3715542)Termination reason: Instruction limit
% 3.65/0.97 % (3715542)Termination phase: Preprocessing 3
% 3.65/0.97 % (3715542)Time elapsed: 0.023 s
% 3.65/0.97 % (3715542)Peak memory usage: 11 MB
% 3.65/0.97 % (3715542)Instructions burned: 53 (million)
% 3.65/0.97 % (3715544)Instruction limit reached!
% 3.65/0.97 % (3715544)------------------------------
% 3.65/0.97 % (3715544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.65/0.97 % (3715544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/0.97 % (3715544)CaDiCaL version: 2.1.3
% 3.65/0.97 % (3715544)Termination reason: Instruction limit
% 3.65/0.97 % (3715544)Termination phase: Property scanning
% 3.65/0.97 % (3715544)Time elapsed: 0.014 s
% 3.65/0.97 % (3715544)Peak memory usage: 10 MB
% 3.65/0.97 % (3715544)Instructions burned: 32 (million)
% 3.65/0.97 % (3715546)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2796413934:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.65/0.97 % (3715547)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=3388964188:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.65/0.97 % (3715504)Instruction limit reached!
% 3.65/0.97 % (3715504)------------------------------
% 3.65/0.97 % (3715504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.65/0.97 % (3715504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/0.97 % (3715504)CaDiCaL version: 2.1.3
% 3.65/0.97 % (3715504)Termination reason: Instruction limit
% 3.65/0.97 % (3715504)Termination phase: Saturation
% 3.65/0.97 % (3715504)Time elapsed: 0.276 s
% 3.65/0.97 % (3715504)Peak memory usage: 14 MB
% 3.65/0.97 % (3715504)Instructions burned: 1242 (million)
% 3.65/0.97 % (3715547)Instruction limit reached!
% 3.65/0.97 % (3715547)------------------------------
% 3.65/0.97 % (3715547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.65/0.97 % (3715547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.06 % (3715547)CaDiCaL version: 2.1.3
% 5.32/1.06 % (3715547)Termination reason: Instruction limit
% 5.32/1.06 % (3715547)Termination phase: Property scanning
% 5.32/1.06 % (3715547)Time elapsed: 0.015 s
% 5.32/1.06 % (3715547)Peak memory usage: 10 MB
% 5.32/1.06 % (3715547)Instructions burned: 36 (million)
% 5.32/1.06 % (3715550)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=492054592:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.32/1.06 % (3715551)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.32/1.06 % (3715551)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3209352497:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.32/1.06 % (3715525)Instruction limit reached!
% 5.32/1.06 % (3715525)------------------------------
% 5.32/1.06 % (3715525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.06 % (3715525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.06 % (3715525)CaDiCaL version: 2.1.3
% 5.32/1.06 % (3715525)Termination reason: Instruction limit
% 5.32/1.06 % (3715525)Termination phase: Saturation
% 5.32/1.06 % (3715525)Time elapsed: 0.179 s
% 5.32/1.06 % (3715525)Peak memory usage: 15 MB
% 5.32/1.06 % (3715525)Instructions burned: 317 (million)
% 5.32/1.06 % (3715536)Instruction limit reached!
% 5.32/1.06 % (3715536)------------------------------
% 5.32/1.06 % (3715536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.06 % (3715536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.06 % (3715536)CaDiCaL version: 2.1.3
% 5.32/1.06 % (3715536)Termination reason: Instruction limit
% 5.32/1.06 % (3715536)Termination phase: Saturation
% 5.32/1.06 % (3715536)Time elapsed: 0.124 s
% 5.32/1.06 % (3715536)Peak memory usage: 13 MB
% 5.32/1.06 % (3715536)Instructions burned: 200 (million)
% 5.32/1.06 % (3715530)Refutation not found, incomplete strategy
% 5.32/1.06 % (3715530)------------------------------
% 5.32/1.06 % (3715530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.06 % (3715530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.06 % (3715530)CaDiCaL version: 2.1.3
% 5.32/1.06 % (3715530)Termination reason: Refutation not found, incomplete strategy
% 5.32/1.06 % (3715530)Time elapsed: 0.158 s
% 5.32/1.06 % (3715530)Peak memory usage: 16 MB
% 5.32/1.06 % (3715530)Instructions burned: 339 (million)
% 5.32/1.06 % (3715530)------------------------------
% 5.32/1.06 % (3715530)------------------------------
% 5.32/1.06 % (3715546)Instruction limit reached!
% 5.32/1.06 % (3715546)------------------------------
% 5.32/1.06 % (3715546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.06 % (3715546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.06 % (3715546)CaDiCaL version: 2.1.3
% 5.32/1.06 % (3715546)Termination reason: Instruction limit
% 5.32/1.06 % (3715546)Termination phase: Function definition elimination
% 5.32/1.06 % (3715546)Time elapsed: 0.060 s
% 5.32/1.06 % (3715546)Peak memory usage: 13 MB
% 5.32/1.06 % (3715546)Instructions burned: 139 (million)
% 5.32/1.06 % (3715555)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=404918161:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.32/1.06 % (3715550)Instruction limit reached!
% 5.32/1.06 % (3715550)------------------------------
% 5.32/1.06 % (3715550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.32/1.06 % (3715550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.32/1.06 % (3715550)CaDiCaL version: 2.1.3
% 5.32/1.06 % (3715550)Termination reason: Instruction limit
% 5.32/1.06 % (3715550)Termination phase: Preprocessing 3
% 5.32/1.06 % (3715550)Time elapsed: 0.030 s
% 5.32/1.06 % (3715550)Peak memory usage: 12 MB
% 5.32/1.06 % (3715550)Instructions burned: 68 (million)
% 5.32/1.06 % (3715554)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2450802182:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.32/1.06 % (3715556)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2691847741:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.32/1.06 % (3715557)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2370659249:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.76/1.19 % (3715555)Instruction limit reached!
% 5.76/1.19 % (3715555)------------------------------
% 5.76/1.19 % (3715555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.76/1.19 % (3715555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.19 % (3715555)CaDiCaL version: 2.1.3
% 5.76/1.19 % (3715555)Termination reason: Instruction limit
% 5.76/1.19 % (3715555)Termination phase: Property scanning
% 5.76/1.19 % (3715555)Time elapsed: 0.023 s
% 5.76/1.19 % (3715555)Peak memory usage: 13 MB
% 5.76/1.19 % (3715555)Instructions burned: 99 (million)
% 5.76/1.19 % (3715559)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2915021476:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.76/1.19 % (3715563)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2895274190:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.76/1.19 % (3715551)Instruction limit reached!
% 5.76/1.19 % (3715551)------------------------------
% 5.76/1.19 % (3715551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.20 % (3715551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.20 % (3715551)CaDiCaL version: 2.1.3
% 6.13/1.20 % (3715551)Termination reason: Instruction limit
% 6.13/1.20 % (3715551)Termination phase: Saturation
% 6.13/1.20 % (3715551)Time elapsed: 0.075 s
% 6.13/1.20 % (3715551)Peak memory usage: 12 MB
% 6.13/1.20 % (3715551)Instructions burned: 182 (million)
% 6.13/1.20 % (3715566)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2979595893:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 6.13/1.20 % (3715563)Refutation not found, incomplete strategy
% 6.13/1.20 % (3715563)------------------------------
% 6.13/1.20 % (3715563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.20 % (3715563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.20 % (3715563)CaDiCaL version: 2.1.3
% 6.13/1.20 % (3715563)Termination reason: Refutation not found, incomplete strategy
% 6.13/1.20 % (3715563)Time elapsed: 0.037 s
% 6.13/1.20 % (3715563)Peak memory usage: 13 MB
% 6.13/1.20 % (3715563)Instructions burned: 83 (million)
% 6.13/1.20 % (3715563)------------------------------
% 6.13/1.20 % (3715563)------------------------------
% 6.13/1.20 % (3715566)Instruction limit reached!
% 6.13/1.20 % (3715566)------------------------------
% 6.13/1.20 % (3715566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.20 % (3715566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.20 % (3715566)CaDiCaL version: 2.1.3
% 6.13/1.20 % (3715566)Termination reason: Instruction limit
% 6.13/1.20 % (3715566)Termination phase: Property scanning
% 6.13/1.20 % (3715566)Time elapsed: 0.019 s
% 6.13/1.20 % (3715566)Peak memory usage: 10 MB
% 6.13/1.20 % (3715566)Instructions burned: 46 (million)
% 6.13/1.20 % (3715568)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2364188318:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 6.13/1.20 % (3715569)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3045978012:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.13/1.20 % (3715554)Instruction limit reached!
% 6.13/1.20 % (3715554)------------------------------
% 6.13/1.20 % (3715554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.20 % (3715554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.20 % (3715554)CaDiCaL version: 2.1.3
% 6.13/1.20 % (3715554)Termination reason: Instruction limit
% 6.13/1.20 % (3715554)Termination phase: Saturation
% 6.13/1.20 % (3715554)Time elapsed: 0.107 s
% 6.13/1.20 % (3715554)Peak memory usage: 15 MB
% 6.13/1.20 % (3715554)Instructions burned: 248 (million)
% 6.13/1.20 % (3715572)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2497497260:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 6.13/1.20 % (3715572)Instruction limit reached!
% 6.13/1.20 % (3715572)------------------------------
% 6.13/1.20 % (3715572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.20 % (3715572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.20 % (3715572)CaDiCaL version: 2.1.3
% 6.13/1.29 % (3715572)Termination reason: Instruction limit
% 6.13/1.29 % (3715572)Termination phase: Property scanning
% 6.13/1.29 % (3715572)Time elapsed: 0.043 s
% 6.13/1.29 % (3715572)Peak memory usage: 12 MB
% 6.13/1.29 % (3715572)Instructions burned: 98 (million)
% 6.13/1.29 % (3715574)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=3711486691:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 6.13/1.29 % (3715556)Instruction limit reached!
% 6.13/1.29 % (3715556)------------------------------
% 6.13/1.29 % (3715556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.29 % (3715556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.29 % (3715556)CaDiCaL version: 2.1.3
% 6.13/1.29 % (3715556)Termination reason: Instruction limit
% 6.13/1.29 % (3715556)Termination phase: Saturation
% 6.13/1.29 % (3715556)Time elapsed: 0.189 s
% 6.13/1.29 % (3715556)Peak memory usage: 14 MB
% 6.13/1.29 % (3715556)Instructions burned: 428 (million)
% 6.13/1.29 % (3715568)Refutation not found, incomplete strategy
% 6.13/1.29 % (3715568)------------------------------
% 6.13/1.29 % (3715568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.29 % (3715568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.29 % (3715568)CaDiCaL version: 2.1.3
% 6.13/1.29 % (3715568)Termination reason: Refutation not found, incomplete strategy
% 6.13/1.29 % (3715568)Time elapsed: 0.103 s
% 6.13/1.29 % (3715568)Peak memory usage: 17 MB
% 6.13/1.29 % (3715568)Instructions burned: 387 (million)
% 6.13/1.29 % (3715568)------------------------------
% 6.13/1.29 % (3715568)------------------------------
% 6.13/1.29 % (3715577)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=265030403:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 6.13/1.29 % (3715576)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=3907654456: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_2992 on theBenchmark for (2992ds/105Mi)
% 6.13/1.29 % (3715574)Instruction limit reached!
% 6.13/1.29 % (3715574)------------------------------
% 6.13/1.29 % (3715574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.29 % (3715574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.29 % (3715574)CaDiCaL version: 2.1.3
% 6.13/1.29 % (3715574)Termination reason: Instruction limit
% 6.13/1.29 % (3715574)Termination phase: Property scanning
% 6.13/1.29 % (3715574)Time elapsed: 0.028 s
% 6.13/1.29 % (3715574)Peak memory usage: 11 MB
% 6.13/1.29 % (3715574)Instructions burned: 68 (million)
% 6.13/1.29 % (3715527)Instruction limit reached!
% 6.13/1.29 % (3715527)------------------------------
% 6.13/1.29 % (3715527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.29 % (3715527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.29 % (3715527)CaDiCaL version: 2.1.3
% 6.13/1.29 % (3715527)Termination reason: Instruction limit
% 6.13/1.29 % (3715527)Termination phase: Saturation
% 6.13/1.29 % (3715527)Time elapsed: 0.409 s
% 6.13/1.29 % (3715527)Peak memory usage: 19 MB
% 6.13/1.29 % (3715527)Instructions burned: 854 (million)
% 6.13/1.29 % (3715580)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=2890778995:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 6.13/1.29 % (3715581)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1812516312:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.13/1.29 % (3715576)Instruction limit reached!
% 6.13/1.29 % (3715576)------------------------------
% 6.13/1.29 % (3715576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.13/1.29 % (3715576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.13/1.29 % (3715576)CaDiCaL version: 2.1.3
% 6.13/1.29 % (3715576)Termination reason: Instruction limit
% 6.13/1.29 % (3715576)Termination phase: Saturation
% 6.13/1.29 % (3715576)Time elapsed: 0.047 s
% 6.13/1.29 % (3715576)Peak memory usage: 12 MB
% 6.13/1.29 % (3715576)Instructions burned: 107 (million)
% 7.66/1.41 % (3715584)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=1195482467:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 7.66/1.41 % (3715584)Instruction limit reached!
% 7.66/1.41 % (3715584)------------------------------
% 7.66/1.41 % (3715584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.66/1.41 % (3715584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/1.41 % (3715584)CaDiCaL version: 2.1.3
% 7.66/1.41 % (3715584)Termination reason: Instruction limit
% 7.66/1.41 % (3715584)Termination phase: Property scanning
% 7.66/1.41 % (3715584)Time elapsed: 0.015 s
% 7.66/1.41 % (3715584)Peak memory usage: 10 MB
% 7.66/1.41 % (3715584)Instructions burned: 35 (million)
% 7.66/1.41 % (3715569)Instruction limit reached!
% 7.66/1.41 % (3715569)------------------------------
% 7.66/1.41 % (3715569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.66/1.41 % (3715569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/1.41 % (3715569)CaDiCaL version: 2.1.3
% 7.66/1.41 % (3715569)Termination reason: Instruction limit
% 7.66/1.41 % (3715569)Termination phase: Saturation
% 7.66/1.41 % (3715569)Time elapsed: 0.207 s
% 7.66/1.41 % (3715569)Peak memory usage: 17 MB
% 7.66/1.41 % (3715569)Instructions burned: 451 (million)
% 7.66/1.41 % (3715586)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1472960975:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/91Mi)
% 7.66/1.41 % (3715588)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=183250629:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2991 on theBenchmark for (2991ds/66Mi)
% 7.66/1.41 % (3715586)Instruction limit reached!
% 7.66/1.41 % (3715586)------------------------------
% 7.66/1.41 % (3715586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.66/1.41 % (3715586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/1.41 % (3715586)CaDiCaL version: 2.1.3
% 7.66/1.41 % (3715586)Termination reason: Instruction limit
% 7.66/1.41 % (3715586)Termination phase: Clausification
% 7.66/1.41 % (3715586)Time elapsed: 0.041 s
% 7.66/1.41 % (3715586)Peak memory usage: 13 MB
% 7.66/1.41 % (3715586)Instructions burned: 91 (million)
% 7.66/1.41 % (3715588)Instruction limit reached!
% 7.66/1.41 % (3715588)------------------------------
% 7.66/1.41 % (3715588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.66/1.41 % (3715588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/1.41 % (3715588)CaDiCaL version: 2.1.3
% 7.66/1.41 % (3715588)Termination reason: Instruction limit
% 7.66/1.41 % (3715588)Termination phase: Saturation
% 7.66/1.41 % (3715588)Time elapsed: 0.031 s
% 7.66/1.41 % (3715588)Peak memory usage: 13 MB
% 7.66/1.41 % (3715588)Instructions burned: 67 (million)
% 7.66/1.41 % (3715590)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2283258438:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 7.66/1.41 % (3715591)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=1602346579:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 7.66/1.41 % (3715590)Instruction limit reached!
% 7.66/1.41 % (3715590)------------------------------
% 7.66/1.41 % (3715590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.66/1.41 % (3715590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/1.41 % (3715590)CaDiCaL version: 2.1.3
% 7.66/1.41 % (3715590)Termination reason: Instruction limit
% 7.66/1.41 % (3715590)Termination phase: shuffling
% 7.66/1.41 % (3715590)Time elapsed: 0.009 s
% 7.66/1.41 % (3715590)Peak memory usage: 10 MB
% 7.66/1.41 % (3715590)Instructions burned: 22 (million)
% 7.66/1.41 % (3715559)Instruction limit reached!
% 7.66/1.41 % (3715559)------------------------------
% 7.66/1.41 % (3715559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.66/1.41 % (3715559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.66/1.41 % (3715559)CaDiCaL version: 2.1.3
% 7.66/1.41 % (3715559)Termination reason: Instruction limit
% 7.66/1.41 % (3715559)Termination phase: Saturation
% 7.66/1.41 % (3715559)Time elapsed: 0.369 s
% 7.66/1.41 % (3715559)Peak memory usage: 18 MB
% 7.66/1.41 % (3715559)Instructions burned: 516 (million)
% 7.85/1.59 % (3715594)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1168228241:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/28Mi)
% 7.85/1.59 % (3715580)Instruction limit reached!
% 7.85/1.59 % (3715580)------------------------------
% 7.85/1.59 % (3715580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.85/1.59 % (3715580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.59 % (3715580)CaDiCaL version: 2.1.3
% 7.85/1.59 % (3715580)Termination reason: Instruction limit
% 7.85/1.59 % (3715580)Termination phase: Saturation
% 7.85/1.59 % (3715580)Time elapsed: 0.167 s
% 7.85/1.59 % (3715580)Peak memory usage: 16 MB
% 7.85/1.59 % (3715580)Instructions burned: 377 (million)
% 7.85/1.59 % (3715596)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 7.85/1.59 % (3715594)Instruction limit reached!
% 7.85/1.59 % (3715594)------------------------------
% 7.85/1.59 % (3715594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.85/1.59 % (3715594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.59 % (3715594)CaDiCaL version: 2.1.3
% 7.85/1.59 % (3715594)Termination reason: Instruction limit
% 7.85/1.59 % (3715594)Termination phase: Property scanning
% 7.85/1.59 % (3715594)Time elapsed: 0.013 s
% 7.85/1.59 % (3715594)Peak memory usage: 10 MB
% 7.85/1.59 % (3715594)Instructions burned: 29 (million)
% 7.85/1.59 % (3715596)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=1499999192:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2990 on theBenchmark for (2990ds/137Mi)
% 7.85/1.59 % (3715557)Instruction limit reached!
% 7.85/1.59 % (3715557)------------------------------
% 7.85/1.59 % (3715557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.85/1.59 % (3715557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.59 % (3715557)CaDiCaL version: 2.1.3
% 7.85/1.59 % (3715557)Termination reason: Instruction limit
% 7.85/1.59 % (3715557)Termination phase: Saturation
% 7.85/1.59 % (3715557)Time elapsed: 0.415 s
% 7.85/1.59 % (3715557)Peak memory usage: 18 MB
% 7.85/1.59 % (3715557)Instructions burned: 876 (million)
% 7.85/1.59 % (3715598)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=3606860436:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2990 on theBenchmark for (2990ds/340Mi)
% 7.85/1.59 % (3715599)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=3531376958:i=227:sd=1:bd=all:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/227Mi)
% 7.85/1.59 % (3715602)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 7.85/1.59 % (3715602)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2419065214:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/373Mi)
% 7.85/1.59 % (3715581)Instruction limit reached!
% 7.85/1.59 % (3715581)------------------------------
% 7.85/1.59 % (3715581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.85/1.59 % (3715581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.59 % (3715581)CaDiCaL version: 2.1.3
% 7.85/1.59 % (3715581)Termination reason: Instruction limit
% 7.85/1.59 % (3715581)Termination phase: Saturation
% 7.85/1.59 % (3715581)Time elapsed: 0.230 s
% 7.85/1.59 % (3715581)Peak memory usage: 17 MB
% 7.85/1.59 % (3715581)Instructions burned: 495 (million)
% 7.85/1.59 % (3715596)Instruction limit reached!
% 7.85/1.59 % (3715596)------------------------------
% 7.85/1.59 % (3715596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.85/1.59 % (3715596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.59 % (3715596)CaDiCaL version: 2.1.3
% 7.85/1.59 % (3715596)Termination reason: Instruction limit
% 7.85/1.59 % (3715596)Termination phase: Saturation
% 7.85/1.59 % (3715596)Time elapsed: 0.057 s
% 7.85/1.59 % (3715596)Peak memory usage: 12 MB
% 7.85/1.59 % (3715596)Instructions burned: 137 (million)
% 7.85/1.59 % (3715605)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=984118262:i=116:ep=RSTC:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/116Mi)
% 7.85/1.59 % (3715606)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1561819993:i=575:rtra=on_2989 on theBenchmark for (2989ds/575Mi)
% 9.11/1.73 % (3715599)Instruction limit reached!
% 9.11/1.73 % (3715599)------------------------------
% 9.11/1.73 % (3715599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.11/1.73 % (3715599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.11/1.73 % (3715599)CaDiCaL version: 2.1.3
% 9.11/1.73 % (3715599)Termination reason: Instruction limit
% 9.11/1.73 % (3715599)Termination phase: Saturation
% 9.11/1.73 % (3715599)Time elapsed: 0.108 s
% 9.11/1.73 % (3715599)Peak memory usage: 13 MB
% 9.11/1.73 % (3715599)Instructions burned: 228 (million)
% 9.11/1.73 % (3715591)Instruction limit reached!
% 9.11/1.73 % (3715591)------------------------------
% 9.11/1.73 % (3715591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.11/1.73 % (3715591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.11/1.73 % (3715591)CaDiCaL version: 2.1.3
% 9.11/1.73 % (3715591)Termination reason: Instruction limit
% 9.11/1.73 % (3715591)Termination phase: Saturation
% 9.11/1.73 % (3715591)Time elapsed: 0.180 s
% 9.11/1.73 % (3715591)Peak memory usage: 18 MB
% 9.11/1.73 % (3715591)Instructions burned: 339 (million)
% 9.11/1.73 % (3715609)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=823289880:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2989 on theBenchmark for (2989ds/270Mi)
% 9.11/1.73 % (3715598)Instruction limit reached!
% 9.11/1.73 % (3715598)------------------------------
% 9.11/1.73 % (3715598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.11/1.73 % (3715598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.11/1.73 % (3715598)CaDiCaL version: 2.1.3
% 9.11/1.73 % (3715598)Termination reason: Instruction limit
% 9.11/1.73 % (3715598)Termination phase: Saturation
% 9.11/1.73 % (3715598)Time elapsed: 0.154 s
% 9.11/1.73 % (3715598)Peak memory usage: 17 MB
% 9.11/1.73 % (3715598)Instructions burned: 342 (million)
% 9.11/1.73 % (3715605)Instruction limit reached!
% 9.11/1.73 % (3715605)------------------------------
% 9.11/1.73 % (3715605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.11/1.73 % (3715605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.11/1.73 % (3715605)CaDiCaL version: 2.1.3
% 9.11/1.73 % (3715605)Termination reason: Instruction limit
% 9.11/1.73 % (3715605)Termination phase: Property scanning
% 9.11/1.73 % (3715605)Time elapsed: 0.091 s
% 9.11/1.73 % (3715605)Peak memory usage: 12 MB
% 9.11/1.73 % (3715605)Instructions burned: 117 (million)
% 9.11/1.73 % (3715611)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=2067451740: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_2989 on theBenchmark for (2989ds/9840Mi)
% 9.11/1.73 % (3715602)Instruction limit reached!
% 9.11/1.73 % (3715602)------------------------------
% 9.11/1.73 % (3715602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.11/1.73 % (3715602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.11/1.73 % (3715602)CaDiCaL version: 2.1.3
% 9.11/1.73 % (3715602)Termination reason: Instruction limit
% 9.11/1.73 % (3715602)Termination phase: Saturation
% 9.11/1.73 % (3715602)Time elapsed: 0.150 s
% 9.11/1.73 % (3715602)Peak memory usage: 15 MB
% 9.11/1.73 % (3715602)Instructions burned: 374 (million)
% 9.11/1.73 % (3715612)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2938859360:i=421:rtra=on:ss=axioms_2988 on theBenchmark for (2988ds/421Mi)
% 9.11/1.73 % (3715614)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
% 9.11/1.73 % (3715614)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=400330866:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/270Mi)
% 9.11/1.73 % (3715615)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=152059256:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/31Mi)
% 9.89/1.97 % (3715615)Instruction limit reached!
% 9.89/1.97 % (3715615)------------------------------
% 9.89/1.97 % (3715615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.89/1.97 % (3715615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.89/1.97 % (3715615)CaDiCaL version: 2.1.3
% 9.89/1.97 % (3715615)Termination reason: Instruction limit
% 9.89/1.97 % (3715615)Termination phase: Property scanning
% 9.89/1.97 % (3715615)Time elapsed: 0.014 s
% 9.89/1.97 % (3715615)Peak memory usage: 10 MB
% 9.89/1.97 % (3715615)Instructions burned: 32 (million)
% 9.89/1.97 % (3715612)Refutation not found, incomplete strategy
% 9.89/1.97 % (3715612)------------------------------
% 9.89/1.97 % (3715612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.89/1.97 % (3715612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.89/1.97 % (3715612)CaDiCaL version: 2.1.3
% 9.89/1.97 % (3715612)Termination reason: Refutation not found, incomplete strategy
% 9.89/1.97 % (3715612)Time elapsed: 0.037 s
% 9.89/1.97 % (3715612)Peak memory usage: 13 MB
% 9.89/1.97 % (3715612)Instructions burned: 77 (million)
% 9.89/1.97 % (3715612)------------------------------
% 9.89/1.97 % (3715612)------------------------------
% 9.89/1.97 % (3715619)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 9.89/1.97 % (3715619)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
% 9.89/1.97 % (3715619)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=2230706546:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2988 on theBenchmark for (2988ds/1440Mi)
% 9.89/1.97 % (3715620)dis+10_2_sil=128000:si=on:random_seed=4094067838:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2988 on theBenchmark for (2988ds/339Mi)
% 9.89/1.97 % (3715614)Instruction limit reached!
% 9.89/1.97 % (3715614)------------------------------
% 9.89/1.97 % (3715614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.89/1.97 % (3715614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.89/1.97 % (3715614)CaDiCaL version: 2.1.3
% 9.89/1.97 % (3715614)Termination reason: Instruction limit
% 9.89/1.97 % (3715614)Termination phase: Saturation
% 9.89/1.97 % (3715614)Time elapsed: 0.119 s
% 9.89/1.97 % (3715614)Peak memory usage: 15 MB
% 9.89/1.97 % (3715614)Instructions burned: 272 (million)
% 9.89/1.97 % (3715609)Instruction limit reached!
% 9.89/1.97 % (3715609)------------------------------
% 9.89/1.97 % (3715609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.89/1.97 % (3715609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.89/1.97 % (3715609)CaDiCaL version: 2.1.3
% 9.89/1.97 % (3715609)Termination reason: Instruction limit
% 9.89/1.97 % (3715609)Termination phase: Saturation
% 9.89/1.97 % (3715609)Time elapsed: 0.171 s
% 9.89/1.97 % (3715609)Peak memory usage: 12 MB
% 9.89/1.97 % (3715609)Instructions burned: 270 (million)
% 9.89/1.97 % (3715623)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=2121317171:i=111:add=on:fgj=on:rtra=on:fdi=1024_2987 on theBenchmark for (2987ds/111Mi)
% 9.89/1.97 % (3715624)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=1305866737:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2987 on theBenchmark for (2987ds/122Mi)
% 9.89/1.97 % (3715606)Instruction limit reached!
% 9.89/1.97 % (3715606)------------------------------
% 9.89/1.97 % (3715606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.89/1.97 % (3715606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.89/1.97 % (3715606)CaDiCaL version: 2.1.3
% 9.89/1.97 % (3715606)Termination reason: Instruction limit
% 9.89/1.97 % (3715606)Termination phase: Saturation
% 9.89/1.97 % (3715606)Time elapsed: 0.283 s
% 9.89/1.97 % (3715606)Peak memory usage: 18 MB
% 9.89/1.97 % (3715606)Instructions burned: 576 (million)
% 9.89/1.97 % (3715623)Instruction limit reached!
% 9.89/1.97 % (3715623)------------------------------
% 9.89/1.97 % (3715623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.89/1.97 % (3715623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.16 % (3715623)CaDiCaL version: 2.1.3
% 12.57/2.16 % (3715623)Termination reason: Instruction limit
% 12.57/2.16 % (3715623)Termination phase: Property scanning
% 12.57/2.16 % (3715623)Time elapsed: 0.049 s
% 12.57/2.16 % (3715623)Peak memory usage: 13 MB
% 12.57/2.16 % (3715623)Instructions burned: 113 (million)
% 12.57/2.16 % (3715627)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=3768434939:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/136Mi)
% 12.57/2.16 % (3715624)Instruction limit reached!
% 12.57/2.16 % (3715624)------------------------------
% 12.57/2.16 % (3715624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.16 % (3715624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.16 % (3715624)CaDiCaL version: 2.1.3
% 12.57/2.16 % (3715624)Termination reason: Instruction limit
% 12.57/2.16 % (3715624)Termination phase: Property scanning
% 12.57/2.16 % (3715624)Time elapsed: 0.054 s
% 12.57/2.16 % (3715624)Peak memory usage: 13 MB
% 12.57/2.16 % (3715624)Instructions burned: 122 (million)
% 12.57/2.16 % (3715628)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4016130753:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2986 on theBenchmark for (2986ds/232Mi)
% 12.57/2.16 % (3715620)Instruction limit reached!
% 12.57/2.16 % (3715620)------------------------------
% 12.57/2.16 % (3715620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.16 % (3715620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.16 % (3715620)CaDiCaL version: 2.1.3
% 12.57/2.16 % (3715620)Termination reason: Instruction limit
% 12.57/2.16 % (3715620)Termination phase: Saturation
% 12.57/2.16 % (3715620)Time elapsed: 0.158 s
% 12.57/2.16 % (3715620)Peak memory usage: 13 MB
% 12.57/2.16 % (3715620)Instructions burned: 341 (million)
% 12.57/2.16 % (3715632)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 12.57/2.16 % (3715631)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=1707588722:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2986 on theBenchmark for (2986ds/1254Mi)
% 12.57/2.16 % (3715632)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=3693047118:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2986 on theBenchmark for (2986ds/281Mi)
% 12.57/2.16 % (3715627)Instruction limit reached!
% 12.57/2.16 % (3715627)------------------------------
% 12.57/2.16 % (3715627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.16 % (3715627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.16 % (3715627)CaDiCaL version: 2.1.3
% 12.57/2.16 % (3715627)Termination reason: Instruction limit
% 12.57/2.16 % (3715627)Termination phase: Property scanning
% 12.57/2.16 % (3715627)Time elapsed: 0.063 s
% 12.57/2.16 % (3715627)Peak memory usage: 16 MB
% 12.57/2.16 % (3715627)Instructions burned: 137 (million)
% 12.57/2.16 % (3715635)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2076962217:i=619:add=on:rtra=on_2986 on theBenchmark for (2986ds/619Mi)
% 12.57/2.16 % (3715628)Instruction limit reached!
% 12.57/2.16 % (3715628)------------------------------
% 12.57/2.16 % (3715628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.16 % (3715628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.16 % (3715628)CaDiCaL version: 2.1.3
% 12.57/2.16 % (3715628)Termination reason: Instruction limit
% 12.57/2.16 % (3715628)Termination phase: Saturation
% 12.57/2.16 % (3715628)Time elapsed: 0.100 s
% 12.57/2.16 % (3715628)Peak memory usage: 14 MB
% 12.57/2.16 % (3715628)Instructions burned: 233 (million)
% 12.57/2.16 % (3715631)Refutation not found, incomplete strategy
% 12.57/2.16 % (3715631)------------------------------
% 12.57/2.16 % (3715631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.57/2.16 % (3715631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.16 % (3715631)CaDiCaL version: 2.1.3
% 12.57/2.16 % (3715631)Termination reason: Refutation not found, incomplete strategy
% 12.57/2.16 % (3715631)Time elapsed: 0.098 s
% 12.57/2.16 % (3715631)Peak memory usage: 16 MB
% 12.57/2.16 % (3715631)Instructions burned: 226 (million)
% 12.57/2.16 % (3715631)------------------------------
% 13.99/2.42 % (3715631)------------------------------
% 13.99/2.42 % (3715637)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=709432336:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/865Mi)
% 13.99/2.42 % (3715632)Instruction limit reached!
% 13.99/2.42 % (3715632)------------------------------
% 13.99/2.42 % (3715632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.99/2.42 % (3715632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.99/2.42 % (3715632)CaDiCaL version: 2.1.3
% 13.99/2.42 % (3715632)Termination reason: Instruction limit
% 13.99/2.42 % (3715632)Termination phase: Saturation
% 13.99/2.42 % (3715632)Time elapsed: 0.115 s
% 13.99/2.42 % (3715632)Peak memory usage: 12 MB
% 13.99/2.42 % (3715632)Instructions burned: 282 (million)
% 13.99/2.42 % (3715638)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3423688507:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2985 on theBenchmark for (2985ds/212Mi)
% 13.99/2.42 % (3715641)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=3686648823:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/130Mi)
% 13.99/2.42 % (3715641)Instruction limit reached!
% 13.99/2.42 % (3715641)------------------------------
% 13.99/2.42 % (3715641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.99/2.42 % (3715641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.99/2.42 % (3715641)CaDiCaL version: 2.1.3
% 13.99/2.42 % (3715641)Termination reason: Instruction limit
% 13.99/2.42 % (3715641)Termination phase: Property scanning
% 13.99/2.42 % (3715641)Time elapsed: 0.057 s
% 13.99/2.42 % (3715641)Peak memory usage: 13 MB
% 13.99/2.42 % (3715641)Instructions burned: 131 (million)
% 13.99/2.42 % (3715638)Instruction limit reached!
% 13.99/2.42 % (3715638)------------------------------
% 13.99/2.42 % (3715638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.99/2.42 % (3715638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.99/2.42 % (3715638)CaDiCaL version: 2.1.3
% 13.99/2.42 % (3715638)Termination reason: Instruction limit
% 13.99/2.42 % (3715638)Termination phase: Saturation
% 13.99/2.42 % (3715638)Time elapsed: 0.090 s
% 13.99/2.42 % (3715638)Peak memory usage: 14 MB
% 13.99/2.42 % (3715638)Instructions burned: 212 (million)
% 13.99/2.42 % (3715643)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2122284786:st=1.5:i=346:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/346Mi)
% 13.99/2.42 % (3715644)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=3887010671:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2984 on theBenchmark for (2984ds/152Mi)
% 13.99/2.42 % (3715643)Refutation not found, incomplete strategy
% 13.99/2.42 % (3715643)------------------------------
% 13.99/2.42 % (3715643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.99/2.42 % (3715643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.99/2.42 % (3715643)CaDiCaL version: 2.1.3
% 13.99/2.42 % (3715643)Termination reason: Refutation not found, incomplete strategy
% 13.99/2.42 % (3715643)Time elapsed: 0.071 s
% 13.99/2.42 % (3715643)Peak memory usage: 13 MB
% 13.99/2.42 % (3715643)Instructions burned: 151 (million)
% 13.99/2.42 % (3715643)------------------------------
% 13.99/2.42 % (3715643)------------------------------
% 13.99/2.42 % (3715644)Instruction limit reached!
% 13.99/2.42 % (3715644)------------------------------
% 13.99/2.42 % (3715644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.99/2.42 % (3715644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.99/2.42 % (3715644)CaDiCaL version: 2.1.3
% 13.99/2.42 % (3715644)Termination reason: Instruction limit
% 13.99/2.42 % (3715644)Termination phase: Inequality splitting
% 13.99/2.42 % (3715644)Time elapsed: 0.067 s
% 13.99/2.42 % (3715644)Peak memory usage: 13 MB
% 13.99/2.42 % (3715644)Instructions burned: 154 (million)
% 13.99/2.42 % (3715647)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3522503053:i=75:ep=R:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/75Mi)
% 13.99/2.42 % (3715648)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2075555557:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/387Mi)
% 13.99/2.42 % (3715647)Instruction limit reached!
% 13.99/2.42 % (3715647)------------------------------
% 14.62/2.50 % (3715647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715647)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715647)Termination reason: Instruction limit
% 14.62/2.50 % (3715647)Termination phase: Property scanning
% 14.62/2.50 % (3715647)Time elapsed: 0.031 s
% 14.62/2.50 % (3715647)Peak memory usage: 11 MB
% 14.62/2.50 % (3715647)Instructions burned: 75 (million)
% 14.62/2.50 % (3715651)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=3743443050:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2982 on theBenchmark for (2982ds/148Mi)
% 14.62/2.50 % (3715651)Instruction limit reached!
% 14.62/2.50 % (3715651)------------------------------
% 14.62/2.50 % (3715651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715651)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715651)Termination reason: Instruction limit
% 14.62/2.50 % (3715651)Termination phase: Saturation
% 14.62/2.50 % (3715651)Time elapsed: 0.061 s
% 14.62/2.50 % (3715651)Peak memory usage: 12 MB
% 14.62/2.50 % (3715651)Instructions burned: 148 (million)
% 14.62/2.50 % (3715635)Instruction limit reached!
% 14.62/2.50 % (3715635)------------------------------
% 14.62/2.50 % (3715635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715635)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715635)Termination reason: Instruction limit
% 14.62/2.50 % (3715635)Termination phase: Saturation
% 14.62/2.50 % (3715635)Time elapsed: 0.383 s
% 14.62/2.50 % (3715635)Peak memory usage: 18 MB
% 14.62/2.50 % (3715635)Instructions burned: 620 (million)
% 14.62/2.50 % (3715653)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=4064491982:i=161:piset=and:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/161Mi)
% 14.62/2.50 % (3715654)lrs+10_1_sil=128000:si=on:random_seed=1242417423:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/888Mi)
% 14.62/2.50 % (3715648)Instruction limit reached!
% 14.62/2.50 % (3715648)------------------------------
% 14.62/2.50 % (3715648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715648)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715648)Termination reason: Instruction limit
% 14.62/2.50 % (3715648)Termination phase: Saturation
% 14.62/2.50 % (3715648)Time elapsed: 0.158 s
% 14.62/2.50 % (3715648)Peak memory usage: 12 MB
% 14.62/2.50 % (3715648)Instructions burned: 388 (million)
% 14.62/2.50 % (3715657)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=966647632:i=136:add=on:ins=4:rtra=on:sup=off_2981 on theBenchmark for (2981ds/136Mi)
% 14.62/2.50 % (3715619)Instruction limit reached!
% 14.62/2.50 % (3715619)------------------------------
% 14.62/2.50 % (3715619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715619)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715619)Termination reason: Instruction limit
% 14.62/2.50 % (3715619)Termination phase: Saturation
% 14.62/2.50 % (3715619)Time elapsed: 0.680 s
% 14.62/2.50 % (3715619)Peak memory usage: 21 MB
% 14.62/2.50 % (3715619)Instructions burned: 1441 (million)
% 14.62/2.50 % (3715653)Instruction limit reached!
% 14.62/2.50 % (3715653)------------------------------
% 14.62/2.50 % (3715653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715653)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715653)Termination reason: Instruction limit
% 14.62/2.50 % (3715653)Termination phase: Property scanning
% 14.62/2.50 % (3715653)Time elapsed: 0.069 s
% 14.62/2.50 % (3715653)Peak memory usage: 13 MB
% 14.62/2.50 % (3715653)Instructions burned: 162 (million)
% 14.62/2.50 % (3715659)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=519445297:i=88:s2at=3:nm=2:rtra=on:rawr=on_2981 on theBenchmark for (2981ds/88Mi)
% 14.62/2.50 % (3715660)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=1308949752:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2981 on theBenchmark for (2981ds/93Mi)
% 14.62/2.50 % (3715657)Instruction limit reached!
% 14.62/2.50 % (3715657)------------------------------
% 14.62/2.50 % (3715657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715657)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715657)Termination reason: Instruction limit
% 14.62/2.50 % (3715657)Termination phase: Function definition elimination
% 14.62/2.50 % (3715657)Time elapsed: 0.059 s
% 14.62/2.50 % (3715657)Peak memory usage: 12 MB
% 14.62/2.50 % (3715657)Instructions burned: 137 (million)
% 14.62/2.50 % (3715659)Instruction limit reached!
% 14.62/2.50 % (3715659)------------------------------
% 14.62/2.50 % (3715659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715659)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715659)Termination reason: Instruction limit
% 14.62/2.50 % (3715659)Termination phase: Property scanning
% 14.62/2.50 % (3715659)Time elapsed: 0.037 s
% 14.62/2.50 % (3715659)Peak memory usage: 11 MB
% 14.62/2.50 % (3715659)Instructions burned: 90 (million)
% 14.62/2.50 % (3715660)Instruction limit reached!
% 14.62/2.50 % (3715660)------------------------------
% 14.62/2.50 % (3715660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715660)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715660)Termination reason: Instruction limit
% 14.62/2.50 % (3715660)Termination phase: Saturation
% 14.62/2.50 % (3715660)Time elapsed: 0.039 s
% 14.62/2.50 % (3715660)Peak memory usage: 12 MB
% 14.62/2.50 % (3715660)Instructions burned: 95 (million)
% 14.62/2.50 % (3715664)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1969209975:s2a=on:i=240:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/240Mi)
% 14.62/2.50 % (3715663)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=762256625:i=2186:rtra=on:ixr=off_2980 on theBenchmark for (2980ds/2186Mi)
% 14.62/2.50 % (3715665)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=2117456004:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2980 on theBenchmark for (2980ds/805Mi)
% 14.62/2.50 % (3715637)Instruction limit reached!
% 14.62/2.50 % (3715637)------------------------------
% 14.62/2.50 % (3715637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715637)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715637)Termination reason: Instruction limit
% 14.62/2.50 % (3715637)Termination phase: Saturation
% 14.62/2.50 % (3715637)Time elapsed: 0.501 s
% 14.62/2.50 % (3715637)Peak memory usage: 19 MB
% 14.62/2.50 % (3715637)Instructions burned: 866 (million)
% 14.62/2.50 % (3715669)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 14.62/2.50 % (3715669)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=2921910289:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2980 on theBenchmark for (2980ds/391Mi)
% 14.62/2.50 % (3715664)Instruction limit reached!
% 14.62/2.50 % (3715664)------------------------------
% 14.62/2.50 % (3715664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715664)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715664)Termination reason: Instruction limit
% 14.62/2.50 % (3715664)Termination phase: Saturation
% 14.62/2.50 % (3715664)Time elapsed: 0.103 s
% 14.62/2.50 % (3715664)Peak memory usage: 15 MB
% 14.62/2.50 % (3715664)Instructions burned: 240 (million)
% 14.62/2.50 % (3715671)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=2936760023:i=355:av=off:fsr=off:rtra=on:ixr=off_2979 on theBenchmark for (2979ds/355Mi)
% 14.62/2.50 % (3715669)Instruction limit reached!
% 14.62/2.50 % (3715669)------------------------------
% 14.62/2.50 % (3715669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715669)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715669)Termination reason: Instruction limit
% 14.62/2.50 % (3715669)Termination phase: Saturation
% 14.62/2.50 % (3715669)Time elapsed: 0.160 s
% 14.62/2.50 % (3715669)Peak memory usage: 12 MB
% 14.62/2.50 % (3715669)Instructions burned: 391 (million)
% 14.62/2.50 % (3715673)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=3820304069:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2978 on theBenchmark for (2978ds/314Mi)
% 14.62/2.50 % (3715654) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3715439-3715654"...
% 14.62/2.50 % (3715673)Refutation not found, incomplete strategy
% 14.62/2.50 % (3715673)------------------------------
% 14.62/2.50 % (3715673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715673)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715673)Termination reason: Refutation not found, incomplete strategy
% 14.62/2.50 % (3715673)Time elapsed: 0.038 s
% 14.62/2.50 % (3715673)Peak memory usage: 13 MB
% 14.62/2.50 % (3715673)Instructions burned: 79 (million)
% 14.62/2.50 % (3715673)------------------------------
% 14.62/2.50 % (3715673)------------------------------
% 14.62/2.50 % (3715671)Instruction limit reached!
% 14.62/2.50 % (3715671)------------------------------
% 14.62/2.50 % (3715671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.50 % (3715671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.50 % (3715671)CaDiCaL version: 2.1.3
% 14.62/2.50 % (3715671)Termination reason: Instruction limit
% 14.62/2.50 % (3715671)Termination phase: Saturation
% 14.62/2.50 % (3715671)Time elapsed: 0.165 s
% 14.62/2.50 % (3715671)Peak memory usage: 15 MB
% 14.62/2.50 % (3715671)Instructions burned: 355 (million)
% 14.62/2.50 % (3715675)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=1966544282:s2a=on:i=251:fsr=off:rtra=on_2977 on theBenchmark for (2977ds/251Mi)
% 14.62/2.50 % (3715654)...printing done.
% 14.62/2.50 % (3715654)Refutation found. Thanks to Tanya!
% 14.62/2.50 % SZS status Theorem for theBenchmark
% 14.62/2.50 % SZS output start Proof for theBenchmark
% 14.62/2.50 thf(type_def_5, type, term: $tType).
% 14.62/2.50 thf(type_def_6, type, subst: $tType).
% 14.62/2.50 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 14.62/2.50 thf(type_def_8, type, d_term: $tType).
% 14.62/2.50 thf(type_def_9, type, d_subst: $tType).
% 14.62/2.50 thf(func_def_0, type, one: term).
% 14.62/2.50 thf(func_def_1, type, ap: (term > term > term)).
% 14.62/2.50 thf(func_def_2, type, lam: (term > term)).
% 14.62/2.50 thf(func_def_3, type, sub: (term > subst > term)).
% 14.62/2.50 thf(func_def_4, type, id: subst).
% 14.62/2.50 thf(func_def_5, type, sh: subst).
% 14.62/2.50 thf(func_def_6, type, push: (term > subst > subst)).
% 14.62/2.50 thf(func_def_7, type, comp: (subst > subst > subst)).
% 14.62/2.50 thf(func_def_8, type, var: (term > $o)).
% 14.62/2.50 thf(func_def_9, type, pushprop_lem1v2: $o).
% 14.62/2.50 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 14.62/2.50 thf(func_def_11, type, axmap: $o).
% 14.62/2.50 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 14.62/2.50 thf(func_def_13, type, shinj: $o).
% 14.62/2.50 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 14.62/2.50 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 14.62/2.50 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 14.62/2.50 thf(func_def_17, type, induction2lem: $o).
% 14.62/2.50 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 14.62/2.50 thf(func_def_19, type, axvarshift: $o).
% 14.62/2.50 thf(func_def_20, type, hoasapinj2: $o).
% 14.62/2.50 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 14.62/2.50 thf(func_def_22, type, hoasapinj1: $o).
% 14.62/2.50 thf(func_def_23, type, ulamvar1: $o).
% 14.62/2.50 thf(func_def_24, type, induction2lem_lthm: $o).
% 14.62/2.50 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 14.62/2.50 thf(func_def_26, type, apnotvar: $o).
% 14.62/2.50 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 14.62/2.50 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 14.62/2.50 thf(func_def_29, type, hoasinduction_lthm: $o).
% 14.62/2.50 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 14.62/2.50 thf(func_def_31, type, hoaslaminj: $o).
% 14.62/2.50 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 14.62/2.50 thf(func_def_33, type, induction2lem_gthm: $o).
% 14.62/2.50 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 14.62/2.50 thf(func_def_35, type, hoasinduction_lem3: $o).
% 14.62/2.50 thf(func_def_36, type, hoasinduction_lem2: $o).
% 14.62/2.50 thf(func_def_37, type, termmset_lthm: $o).
% 14.62/2.50 thf(func_def_38, type, hoasinduction_lem1: $o).
% 14.62/2.50 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 14.62/2.50 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 14.62/2.50 thf(func_def_41, type, hoasapnotvar: $o).
% 14.62/2.50 thf(func_def_42, type, hoasinduction_lem0: $o).
% 14.62/2.50 thf(func_def_43, type, hoasinduction: $o).
% 14.62/2.50 thf(func_def_44, type, hoasinduction_gthm: $o).
% 14.62/2.50 thf(func_def_45, type, axapp: $o).
% 14.62/2.50 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 14.62/2.50 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 14.62/2.50 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 14.62/2.50 thf(func_def_49, type, ulamvarind: $o).
% 14.62/2.50 thf(func_def_50, type, induction: $o).
% 14.62/2.50 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 14.62/2.50 thf(func_def_52, type, termmset_gthm: $o).
% 14.62/2.50 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 14.62/2.50 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 14.62/2.50 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 14.62/2.50 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 14.62/2.50 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 14.62/2.50 thf(func_def_58, type, pushprop_lem2v2: $o).
% 14.62/2.50 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 14.62/2.50 thf(func_def_60, type, axclos: $o).
% 14.62/2.50 thf(func_def_61, type, axassoc: $o).
% 14.62/2.50 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 14.62/2.50 thf(func_def_63, type, pushprop_lthm: $o).
% 14.62/2.50 thf(func_def_64, type, apinj2: $o).
% 14.62/2.50 thf(func_def_65, type, apinj1: $o).
% 14.62/2.50 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 14.62/2.50 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 14.62/2.50 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 14.62/2.50 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 14.62/2.50 thf(func_def_70, type, axvarcons: $o).
% 14.62/2.50 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 14.62/2.50 thf(func_def_72, type, axscons: $o).
% 14.62/2.50 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 14.62/2.50 thf(func_def_74, type, axidr: $o).
% 14.62/2.50 thf(func_def_75, type, pushprop_lem1: $o).
% 14.62/2.50 thf(func_def_76, type, laminj: $o).
% 14.62/2.50 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 14.62/2.50 thf(func_def_78, type, pushprop_lem0: $o).
% 14.62/2.50 thf(func_def_79, type, pushprop_gthm: $o).
% 14.62/2.50 thf(func_def_80, type, axabs: $o).
% 14.62/2.50 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 14.62/2.50 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 14.62/2.50 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 14.62/2.50 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 14.62/2.50 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 14.62/2.50 thf(func_def_86, type, lamnotap: $o).
% 14.62/2.50 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 14.62/2.50 thf(func_def_88, type, hoaslamnotvar: $o).
% 14.62/2.50 thf(func_def_89, type, axidl: $o).
% 14.62/2.50 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 14.62/2.50 thf(func_def_91, type, induction2_lthm: $o).
% 14.62/2.50 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 14.62/2.50 thf(func_def_93, type, substmonoid_lthm: $o).
% 14.62/2.50 thf(func_def_94, type, pushprop: $o).
% 14.62/2.50 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 14.62/2.50 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 14.62/2.50 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 14.62/2.50 thf(func_def_98, type, substmonoid: $o).
% 14.62/2.50 thf(func_def_99, type, lamnotvar: $o).
% 14.62/2.50 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 14.62/2.50 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 14.62/2.50 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 14.62/2.50 thf(func_def_103, type, induction2_gthm: $o).
% 14.62/2.50 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 14.62/2.50 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_106, type, hoaslamnotap: $o).
% 14.62/2.50 thf(func_def_107, type, substmonoid_gthm: $o).
% 14.62/2.50 thf(func_def_108, type, ulamvarsh: $o).
% 14.62/2.50 thf(func_def_109, type, induction2: $o).
% 14.62/2.50 thf(func_def_110, type, pushprop_lem3v2: $o).
% 14.62/2.50 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 14.62/2.50 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 14.62/2.50 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 14.62/2.50 thf(func_def_114, type, axshiftcons: $o).
% 14.62/2.50 thf(func_def_115, type, termmset: $o).
% 14.62/2.50 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 14.62/2.50 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 14.62/2.50 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 14.62/2.50 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 14.62/2.50 thf(func_def_120, type, axvarid: $o).
% 14.62/2.50 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 14.62/2.50 thf(func_def_122, type, d2term: (d_term > term)).
% 14.62/2.50 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 14.62/2.50 thf(func_def_124, type, d_one: d_term).
% 14.62/2.50 thf(func_def_125, type, d_id: d_subst).
% 14.62/2.50 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 14.62/2.50 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 14.62/2.50 thf(func_def_129, type, db2: !>[X0: $tType]:(X0)).
% 14.62/2.50 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)).
% 14.62/2.50 thf(func_def_131, type, db1: !>[X0: $tType]:(X0)).
% 14.62/2.50 thf(func_def_132, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 14.62/2.50 thf(func_def_133, type, db3: !>[X0: $tType]:(X0)).
% 14.62/2.50 thf(func_def_134, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 14.62/2.50 thf(func_def_137, type, db4: !>[X0: $tType]:(X0)).
% 14.62/2.50 thf(func_def_138, type, sP0: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_139, type, sP1: $o).
% 14.62/2.50 thf(func_def_140, type, sP2: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_141, type, sP3: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_142, type, sP4: $o).
% 14.62/2.50 thf(func_def_143, type, sP5: $o).
% 14.62/2.50 thf(func_def_144, type, sP6: $o).
% 14.62/2.50 thf(func_def_145, type, sP7: $o).
% 14.62/2.50 thf(func_def_146, type, sP8: $o).
% 14.62/2.50 thf(func_def_147, type, sP9: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_148, type, sP10: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_149, type, sP11: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_150, type, sP12: $o).
% 14.62/2.50 thf(func_def_151, type, sP13: $o).
% 14.62/2.50 thf(func_def_152, type, sP14: $o).
% 14.62/2.50 thf(func_def_153, type, sP15: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_154, type, sP16: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_155, type, sP17: $o).
% 14.62/2.50 thf(func_def_156, type, sP18: $o).
% 14.62/2.50 thf(func_def_157, type, sP19: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_158, type, sP20: $o).
% 14.62/2.50 thf(func_def_159, type, sP21: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_160, type, sP22: $o).
% 14.62/2.50 thf(func_def_161, type, sP23: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_162, type, sP24: $o).
% 14.62/2.50 thf(func_def_163, type, sP25: $o).
% 14.62/2.50 thf(func_def_164, type, sP26: $o).
% 14.62/2.50 thf(func_def_165, type, sP27: $o).
% 14.62/2.50 thf(func_def_166, type, sP28: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_167, type, sP29: $o).
% 14.62/2.50 thf(func_def_168, type, sP30: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_169, type, sP31: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_170, type, sP32: $o).
% 14.62/2.50 thf(func_def_171, type, sP33: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_172, type, sP34: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_173, type, sP35: $o).
% 14.62/2.50 thf(func_def_174, type, sP36: $o).
% 14.62/2.50 thf(func_def_175, type, sP37: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_176, type, sP38: $o).
% 14.62/2.50 thf(func_def_177, type, sP39: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_178, type, sP40: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_179, type, sP41: $o).
% 14.62/2.50 thf(func_def_180, type, sP42: $o).
% 14.62/2.50 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_182, type, sP44: $o).
% 14.62/2.50 thf(func_def_183, type, sP45: $o).
% 14.62/2.50 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_185, type, sP47: $o).
% 14.62/2.50 thf(func_def_186, type, sP48: ((term > $o) > $o)).
% 14.62/2.50 thf(func_def_187, type, sP49: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_188, type, sP50: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_189, type, sP51: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_190, type, sP52: ((subst > term > subst > $o) > $o)).
% 14.62/2.50 thf(func_def_191, type, sP53: $o).
% 14.62/2.50 thf(func_def_192, type, sP54: $o).
% 14.62/2.50 thf(func_def_193, type, sP55: $o).
% 14.62/2.50 thf(func_def_194, type, sP56: $o).
% 14.62/2.50 thf(func_def_195, type, sP57: $o).
% 14.62/2.50 thf(func_def_196, type, sP58: $o).
% 14.62/2.50 thf(func_def_197, type, sK59: subst).
% 14.62/2.50 thf(func_def_198, type, sK60: term).
% 14.62/2.50 thf(func_def_199, type, sK61: (subst > term > term)).
% 14.62/2.50 thf(func_def_200, type, sK62: (subst > term > term)).
% 14.62/2.50 thf(func_def_201, type, sK63: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_202, type, sK64: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_203, type, sK65: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_204, type, sK66: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_205, type, sK67: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_206, type, sK68: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_207, type, sK69: term).
% 14.62/2.50 thf(func_def_208, type, sK70: term).
% 14.62/2.50 thf(func_def_209, type, sK71: term).
% 14.62/2.50 thf(func_def_210, type, sK72: subst).
% 14.62/2.50 thf(func_def_211, type, sK73: subst).
% 14.62/2.50 thf(func_def_212, type, sK74: term).
% 14.62/2.50 thf(func_def_213, type, sK75: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_214, type, sK76: term).
% 14.62/2.50 thf(func_def_215, type, sK77: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_216, type, sK78: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_217, type, sK79: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_218, type, sK80: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_219, type, sK81: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.50 thf(func_def_220, type, sK82: (term > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_221, type, sK83: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_222, type, sK84: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_223, type, sK85: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_225, type, sK87: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_226, type, sK88: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_227, type, sK89: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_228, type, sK90: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_229, type, sK91: term).
% 14.62/2.50 thf(func_def_230, type, sK92: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_231, type, sK93: term).
% 14.62/2.50 thf(func_def_232, type, sK94: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_233, type, sK95: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_234, type, sK96: term).
% 14.62/2.50 thf(func_def_235, type, sK97: (term > $o)).
% 14.62/2.50 thf(func_def_236, type, sK98: (term > term)).
% 14.62/2.50 thf(func_def_237, type, sK99: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_238, type, sK100: term).
% 14.62/2.50 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_240, type, sK102: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_241, type, sK103: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_242, type, sK104: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_243, type, sK105: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_244, type, sK106: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_245, type, sK107: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_246, type, sK108: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_247, type, sK109: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_248, type, sK110: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_249, type, sK111: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_250, type, sK112: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_251, type, sK113: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_252, type, sK114: (term > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_253, type, sK115: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_254, type, sK116: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_255, type, sK117: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_256, type, sK118: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_257, type, sK119: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_258, type, sK120: term).
% 14.62/2.50 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.50 thf(func_def_262, type, sK124: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_263, type, sK125: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_264, type, sK126: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_265, type, sK127: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_268, type, sK130: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_269, type, sK131: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_270, type, sK132: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_271, type, sK133: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_272, type, sK134: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.50 thf(func_def_273, type, sK135: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_274, type, sK136: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_275, type, sK137: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_276, type, sK138: term).
% 14.62/2.50 thf(func_def_277, type, sK139: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_278, type, sK140: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_279, type, sK141: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_281, type, sK143: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_282, type, sK144: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_283, type, sK145: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_284, type, sK146: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_285, type, sK147: (term > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_286, type, sK148: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_287, type, sK149: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_288, type, sK150: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_289, type, sK151: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_290, type, sK152: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.50 thf(func_def_291, type, sK153: term).
% 14.62/2.50 thf(func_def_292, type, sK154: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_293, type, sK155: term).
% 14.62/2.50 thf(func_def_294, type, sK156: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_296, type, sK158: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_297, type, sK159: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_298, type, sK160: ((subst > term > subst > $o) > term > term)).
% 14.62/2.50 thf(func_def_299, type, sK161: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_300, type, sK162: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_301, type, sK163: ((subst > term > subst > $o) > subst)).
% 14.62/2.50 thf(func_def_302, type, sK164: ((subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_303, type, sK165: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.50 thf(func_def_304, type, sK166: ((subst > term > subst > $o) > term > term)).
% 14.62/2.50 thf(func_def_305, type, sK167: term).
% 14.62/2.50 thf(func_def_306, type, sK168: (subst > term > subst > $o)).
% 14.62/2.50 thf(func_def_307, type, sK169: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_308, type, sK170: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_309, type, sK171: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_310, type, sK172: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_311, type, sK173: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_312, type, sK174: ((subst > term > term) > term)).
% 14.62/2.50 thf(func_def_313, type, sK175: ((subst > term > term) > subst)).
% 14.62/2.50 thf(func_def_314, type, sK176: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.50 thf(func_def_315, type, sK177: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.50 thf(func_def_316, type, sK178: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_317, type, sK179: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_318, type, sK180: (term > $o)).
% 14.62/2.50 thf(func_def_319, type, sK181: term).
% 14.62/2.50 thf(func_def_320, type, sK182: subst).
% 14.62/2.50 thf(func_def_321, type, sK183: term).
% 14.62/2.50 thf(func_def_322, type, sK184: term).
% 14.62/2.50 thf(func_def_323, type, sK185: subst).
% 14.62/2.50 thf(func_def_324, type, sK186: subst).
% 14.62/2.50 thf(func_def_325, type, sK187: subst).
% 14.62/2.50 thf(func_def_326, type, sK188: (term > $o)).
% 14.62/2.50 thf(func_def_327, type, sK189: term).
% 14.62/2.50 thf(func_def_328, type, sK190: (term > term)).
% 14.62/2.50 thf(func_def_329, type, sK191: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_330, type, sK192: ((term > $o) > subst > term)).
% 14.62/2.50 thf(func_def_331, type, sK193: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_332, type, sK194: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_333, type, sK195: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_334, type, sK196: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_335, type, sK197: subst).
% 14.62/2.50 thf(func_def_336, type, sK198: term).
% 14.62/2.50 thf(func_def_337, type, sK199: (term > $o)).
% 14.62/2.50 thf(func_def_338, type, sK200: (term > term)).
% 14.62/2.50 thf(func_def_339, type, sK201: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_340, type, sK202: ((term > $o) > subst > term)).
% 14.62/2.50 thf(func_def_341, type, sK203: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_342, type, sK204: ((term > $o) > term)).
% 14.62/2.50 thf(func_def_343, type, sK205: (term > subst > term > term)).
% 14.62/2.50 thf(func_def_344, type, sK206: (term > $o)).
% 14.62/2.50 thf(func_def_345, type, sK207: term).
% 14.62/2.50 thf(func_def_346, type, sK208: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_347, type, sK209: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_348, type, sK210: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_349, type, sK211: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_350, type, sK212: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_351, type, sK213: term).
% 14.62/2.51 thf(func_def_352, type, sK214: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_353, type, sK215: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_354, type, sK216: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_355, type, sK217: ((subst > term > subst > $o) > (term > $o) > term)).
% 14.62/2.51 thf(func_def_356, type, sK218: (term > (term > $o) > term)).
% 14.62/2.51 thf(func_def_357, type, sK219: term).
% 14.62/2.51 thf(func_def_358, type, sK220: term).
% 14.62/2.51 thf(func_def_359, type, sK221: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_360, type, sK222: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_361, type, sK223: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_362, type, sK224: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_363, type, sK225: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_364, type, sK226: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_365, type, sK227: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_369, type, sK231: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_370, type, sK232: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_371, type, sK233: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_372, type, sK234: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_373, type, sK235: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_374, type, sK236: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_375, type, sK237: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_376, type, sK238: (term > $o)).
% 14.62/2.51 thf(func_def_377, type, sK239: term).
% 14.62/2.51 thf(func_def_378, type, sK240: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > (term > $o) > term)).
% 14.62/2.51 thf(func_def_380, type, sK242: (term > (term > $o) > term)).
% 14.62/2.51 thf(func_def_381, type, sK243: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_382, type, sK244: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_383, type, sK245: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_386, type, sK248: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_387, type, sK249: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_388, type, sK250: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_389, type, sK251: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_390, type, sK252: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_391, type, sK253: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_392, type, sK254: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_393, type, sK255: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_394, type, sK256: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_396, type, sK258: term).
% 14.62/2.51 thf(func_def_397, type, sK259: (term > $o)).
% 14.62/2.51 thf(func_def_398, type, sK260: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_399, type, sK261: term).
% 14.62/2.51 thf(func_def_400, type, sK262: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_404, type, sK266: ((term > $o) > term > term)).
% 14.62/2.51 thf(func_def_405, type, sK267: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_406, type, sK268: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_407, type, sK269: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_409, type, sK271: ((subst > term > subst > $o) > (term > $o) > term)).
% 14.62/2.51 thf(func_def_410, type, sK272: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_411, type, sK273: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_412, type, sK274: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_413, type, sK275: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_414, type, sK276: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_415, type, sK277: term).
% 14.62/2.51 thf(func_def_416, type, sK278: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_417, type, sK279: (term > (subst > term > term) > term)).
% 14.62/2.51 thf(func_def_418, type, sK280: (term > (subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_419, type, sK281: (term > (subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_420, type, sK282: (term > (subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_421, type, sK283: (term > (subst > term > term) > term)).
% 14.62/2.51 thf(func_def_422, type, sK284: (term > (subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_423, type, sK285: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_424, type, sK286: ((subst > term > subst > $o) > term > term)).
% 14.62/2.51 thf(func_def_425, type, sK287: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_426, type, sK288: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_427, type, sK289: term).
% 14.62/2.51 thf(func_def_428, type, sK290: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_429, type, sK291: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_430, type, sK292: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_431, type, sK293: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_432, type, sK294: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_433, type, sK295: term).
% 14.62/2.51 thf(func_def_434, type, sK296: ((subst > term > subst > $o) > term > term)).
% 14.62/2.51 thf(func_def_435, type, sK297: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_436, type, sK298: (term > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_437, type, sK299: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_438, type, sK300: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_439, type, sK301: term).
% 14.62/2.51 thf(func_def_440, type, sK302: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_441, type, sK303: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_442, type, sK304: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_443, type, sK305: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_444, type, sK306: term).
% 14.62/2.51 thf(func_def_445, type, sK307: (term > $o)).
% 14.62/2.51 thf(func_def_446, type, sK308: (term > term)).
% 14.62/2.51 thf(func_def_447, type, sK309: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_448, type, sK310: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_449, type, sK311: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_450, type, sK312: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_451, type, sK313: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_452, type, sK314: term).
% 14.62/2.51 thf(func_def_453, type, sK315: term).
% 14.62/2.51 thf(func_def_454, type, sK316: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_455, type, sK317: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_456, type, sK318: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_457, type, sK319: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_458, type, sK320: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_461, type, sK323: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_462, type, sK324: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_463, type, sK325: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_464, type, sK326: term).
% 14.62/2.51 thf(func_def_465, type, sK327: (term > $o)).
% 14.62/2.51 thf(func_def_466, type, sK328: term).
% 14.62/2.51 thf(func_def_467, type, sK329: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_468, type, sK330: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_469, type, sK331: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_470, type, sK332: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_471, type, sK333: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_472, type, sK334: ((subst > term > subst > $o) > (term > $o) > term)).
% 14.62/2.51 thf(func_def_473, type, sK335: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_474, type, sK336: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_475, type, sK337: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_476, type, sK338: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_477, type, sK339: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_478, type, sK340: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_479, type, sK341: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_480, type, sK342: ((term > $o) > subst > term)).
% 14.62/2.51 thf(func_def_481, type, sK343: term).
% 14.62/2.51 thf(func_def_482, type, sK344: subst).
% 14.62/2.51 thf(func_def_483, type, sK345: (term > $o)).
% 14.62/2.51 thf(func_def_484, type, sK346: (term > term)).
% 14.62/2.51 thf(func_def_485, type, sK347: term).
% 14.62/2.51 thf(func_def_486, type, sK348: (term > $o)).
% 14.62/2.51 thf(func_def_487, type, sK349: term).
% 14.62/2.51 thf(func_def_488, type, sK350: (term > term)).
% 14.62/2.51 thf(func_def_489, type, sK351: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_490, type, sK352: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_491, type, sK353: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_492, type, sK354: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_493, type, sK355: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_494, type, sK356: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_495, type, sK357: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_496, type, sK358: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_497, type, sK359: ((subst > term > subst > $o) > term > $o)).
% 14.62/2.51 thf(func_def_498, type, sK360: term).
% 14.62/2.51 thf(func_def_499, type, sK361: (term > $o)).
% 14.62/2.51 thf(func_def_500, type, sK362: term).
% 14.62/2.51 thf(func_def_501, type, sK363: (term > term)).
% 14.62/2.51 thf(func_def_502, type, sK364: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_503, type, sK365: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_504, type, sK366: ((term > $o) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_505, type, sK367: (term > (term > $o) > term)).
% 14.62/2.51 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_507, type, sK369: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_508, type, sK370: (term > $o)).
% 14.62/2.51 thf(func_def_509, type, sK371: term).
% 14.62/2.51 thf(func_def_510, type, sK372: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_511, type, sK373: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_512, type, sK374: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_513, type, sK375: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_514, type, sK376: term).
% 14.62/2.51 thf(func_def_515, type, sK377: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_516, type, sK378: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_519, type, sK381: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_520, type, sK382: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_521, type, sK383: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_522, type, sK384: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_523, type, sK385: ((subst > term > subst > $o) > subst)).
% 14.62/2.51 thf(func_def_524, type, sK386: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_525, type, sK387: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_526, type, sK388: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_527, type, sK389: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_528, type, sK390: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_529, type, sK391: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_530, type, sK392: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_532, type, sK394: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_534, type, sK396: term).
% 14.62/2.51 thf(func_def_535, type, sK397: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_536, type, sK398: (term > $o)).
% 14.62/2.51 thf(func_def_537, type, sK399: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_538, type, sK400: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_539, type, sK401: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_540, type, sK402: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_541, type, sK403: ((term > $o) > term > term)).
% 14.62/2.51 thf(func_def_542, type, sK404: ((term > $o) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_544, type, sK406: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_545, type, sK407: term).
% 14.62/2.51 thf(func_def_546, type, sK408: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_547, type, sK409: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_548, type, sK410: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_549, type, sK411: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_550, type, sK412: (term > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_552, type, sK414: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_553, type, sK415: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_554, type, sK416: ((subst > term > subst > $o) > term > $o)).
% 14.62/2.51 thf(func_def_555, type, sK417: term).
% 14.62/2.51 thf(func_def_556, type, sK418: term).
% 14.62/2.51 thf(func_def_557, type, sK419: (term > $o)).
% 14.62/2.51 thf(func_def_558, type, sK420: (term > term)).
% 14.62/2.51 thf(func_def_559, type, sK421: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_560, type, sK422: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_561, type, sK423: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_562, type, sK424: term).
% 14.62/2.51 thf(func_def_563, type, sK425: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_564, type, sK426: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_565, type, sK427: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_566, type, sK428: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_568, type, sK430: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_569, type, sK431: ((term > $o) > (subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_570, type, sK432: (term > (term > $o) > term)).
% 14.62/2.51 thf(func_def_571, type, sK433: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_572, type, sK434: (term > $o)).
% 14.62/2.51 thf(func_def_573, type, sK435: term).
% 14.62/2.51 thf(func_def_574, type, sK436: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_575, type, sK437: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_576, type, sK438: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_577, type, sK439: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_578, type, sK440: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_579, type, sK441: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_580, type, sK442: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_582, type, sK444: term).
% 14.62/2.51 thf(func_def_583, type, sK445: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_584, type, sK446: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_585, type, sK447: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_586, type, sK448: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_587, type, sK449: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_588, type, sK450: ((subst > term > subst > $o) > term > term)).
% 14.62/2.51 thf(func_def_589, type, sK451: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_590, type, sK452: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_591, type, sK453: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_592, type, sK454: subst).
% 14.62/2.51 thf(func_def_593, type, sK455: term).
% 14.62/2.51 thf(func_def_594, type, sK456: term).
% 14.62/2.51 thf(func_def_595, type, sK457: term).
% 14.62/2.51 thf(func_def_596, type, sK458: term).
% 14.62/2.51 thf(func_def_597, type, sK459: term).
% 14.62/2.51 thf(func_def_598, type, sK460: term).
% 14.62/2.51 thf(func_def_599, type, sK461: term).
% 14.62/2.51 thf(func_def_600, type, sK462: term).
% 14.62/2.51 thf(func_def_601, type, sK463: subst).
% 14.62/2.51 thf(func_def_602, type, sK464: subst).
% 14.62/2.51 thf(func_def_603, type, sK465: subst).
% 14.62/2.51 thf(func_def_604, type, sK466: subst).
% 14.62/2.51 thf(func_def_605, type, sK467: term).
% 14.62/2.51 thf(func_def_606, type, sK468: term).
% 14.62/2.51 thf(func_def_607, type, sK469: ((term > $o) > subst > term > (term > $o) > term)).
% 14.62/2.51 thf(func_def_608, type, sK470: (term > $o)).
% 14.62/2.51 thf(func_def_609, type, sK471: term).
% 14.62/2.51 thf(func_def_610, type, sK472: subst).
% 14.62/2.51 thf(func_def_611, type, sK473: (term > $o)).
% 14.62/2.51 thf(func_def_612, type, sK474: (term > $o)).
% 14.62/2.51 thf(func_def_613, type, sK475: subst).
% 14.62/2.51 thf(func_def_614, type, sK476: term).
% 14.62/2.51 thf(func_def_615, type, sK477: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_616, type, sK478: (term > subst > (term > $o) > term > $o)).
% 14.62/2.51 thf(func_def_617, type, sK479: (subst > term > term)).
% 14.62/2.51 thf(func_def_618, type, sK480: subst).
% 14.62/2.51 thf(func_def_619, type, sK481: (subst > term > term)).
% 14.62/2.51 thf(func_def_620, type, sK482: term).
% 14.62/2.51 thf(func_def_621, type, sK483: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_622, type, sK484: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_623, type, sK485: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_624, type, sK486: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_625, type, sK487: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_626, type, sK488: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_627, type, sK489: term).
% 14.62/2.51 thf(func_def_628, type, sK490: term).
% 14.62/2.51 thf(func_def_629, type, sK491: subst).
% 14.62/2.51 thf(func_def_630, type, sK492: (term > $o)).
% 14.62/2.51 thf(func_def_631, type, sK493: term).
% 14.62/2.51 thf(func_def_632, type, sK494: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_633, type, sK495: (term > (term > $o) > subst > term > $o)).
% 14.62/2.51 thf(func_def_634, type, sK496: term).
% 14.62/2.51 thf(func_def_635, type, sK497: (term > subst > term > term)).
% 14.62/2.51 thf(func_def_636, type, sK498: term).
% 14.62/2.51 thf(func_def_637, type, sK499: term).
% 14.62/2.51 thf(func_def_638, type, sK500: term).
% 14.62/2.51 thf(func_def_639, type, sK501: term).
% 14.62/2.51 thf(func_def_640, type, sK502: term).
% 14.62/2.51 thf(func_def_641, type, sK503: term).
% 14.62/2.51 thf(func_def_642, type, sK504: (term > $o)).
% 14.62/2.51 thf(func_def_643, type, sK505: subst).
% 14.62/2.51 thf(func_def_644, type, sK506: (term > $o)).
% 14.62/2.51 thf(func_def_645, type, sK507: term).
% 14.62/2.51 thf(func_def_646, type, sK508: term).
% 14.62/2.51 thf(func_def_647, type, sK509: subst).
% 14.62/2.51 thf(func_def_648, type, sK510: (term > (term > $o) > subst > (term > $o) > term)).
% 14.62/2.51 thf(func_def_649, type, sK511: term).
% 14.62/2.51 thf(func_def_650, type, sK512: (term > d_term)).
% 14.62/2.51 thf(func_def_651, type, sK513: term).
% 14.62/2.51 thf(func_def_652, type, sK514: (term > subst > term > term)).
% 14.62/2.51 thf(func_def_653, type, sK515: term).
% 14.62/2.51 thf(func_def_654, type, sK516: term).
% 14.62/2.51 thf(func_def_655, type, sK517: term).
% 14.62/2.51 thf(func_def_656, type, sK518: term).
% 14.62/2.51 thf(func_def_657, type, sK519: term).
% 14.62/2.51 thf(func_def_658, type, sK520: term).
% 14.62/2.51 thf(func_def_659, type, sK521: term).
% 14.62/2.51 thf(func_def_660, type, sK522: term).
% 14.62/2.51 thf(func_def_661, type, sK523: term).
% 14.62/2.51 thf(func_def_662, type, sK524: term).
% 14.62/2.51 thf(func_def_663, type, sK525: (term > $o)).
% 14.62/2.51 thf(func_def_664, type, sK526: term).
% 14.62/2.51 thf(func_def_665, type, sK527: (term > $o)).
% 14.62/2.51 thf(func_def_666, type, sK528: subst).
% 14.62/2.51 thf(func_def_667, type, sK529: term).
% 14.62/2.51 thf(func_def_668, type, sK530: term).
% 14.62/2.51 thf(func_def_669, type, sK531: subst).
% 14.62/2.51 thf(func_def_670, type, sK532: subst).
% 14.62/2.51 thf(func_def_671, type, sK533: term).
% 14.62/2.51 thf(func_def_672, type, sK534: (subst > d_subst)).
% 14.62/2.51 thf(func_def_673, type, sK535: term).
% 14.62/2.51 thf(func_def_674, type, sK536: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_675, type, sK537: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_676, type, sK538: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_677, type, sK539: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_678, type, sK540: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_679, type, sK541: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_680, type, sK542: term).
% 14.62/2.51 thf(func_def_681, type, sK543: term).
% 14.62/2.51 thf(func_def_682, type, sK544: term).
% 14.62/2.51 thf(func_def_683, type, sK545: term).
% 14.62/2.51 thf(func_def_684, type, sK546: term).
% 14.62/2.51 thf(func_def_685, type, sK547: term).
% 14.62/2.51 thf(func_def_686, type, sK548: term).
% 14.62/2.51 thf(func_def_687, type, sK549: term).
% 14.62/2.51 thf(func_def_688, type, sK550: term).
% 14.62/2.51 thf(func_def_689, type, sK551: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_690, type, sK552: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_691, type, sK553: (term > subst > term > term)).
% 14.62/2.51 thf(func_def_692, type, sK554: subst).
% 14.62/2.51 thf(func_def_693, type, sK555: subst).
% 14.62/2.51 thf(func_def_694, type, sK556: subst).
% 14.62/2.51 thf(func_def_695, type, sK557: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_696, type, sK558: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_697, type, sK559: ((subst > term > subst > $o) > term > $o)).
% 14.62/2.51 thf(func_def_698, type, sK560: subst).
% 14.62/2.51 thf(func_def_699, type, sK561: subst).
% 14.62/2.51 thf(func_def_700, type, sK562: term).
% 14.62/2.51 thf(func_def_701, type, sK563: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_702, type, sK564: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_703, type, sK565: ((subst > term > subst > $o) > term > $o)).
% 14.62/2.51 thf(func_def_704, type, sK566: subst).
% 14.62/2.51 thf(func_def_705, type, sK567: term).
% 14.62/2.51 thf(func_def_706, type, sK568: (term > subst > term > term)).
% 14.62/2.51 thf(func_def_707, type, sK569: term).
% 14.62/2.51 thf(func_def_708, type, sK570: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_709, type, sK571: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_710, type, sK572: term).
% 14.62/2.51 thf(func_def_711, type, sK573: (term > $o)).
% 14.62/2.51 thf(func_def_712, type, sK574: (term > $o)).
% 14.62/2.51 thf(func_def_713, type, sK575: subst).
% 14.62/2.51 thf(func_def_714, type, sK576: term).
% 14.62/2.51 thf(func_def_715, type, sK577: term).
% 14.62/2.51 thf(func_def_716, type, sK578: term).
% 14.62/2.51 thf(func_def_717, type, sK579: term).
% 14.62/2.51 thf(func_def_718, type, sK580: term).
% 14.62/2.51 thf(func_def_719, type, sK581: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_720, type, sK582: ((term > $o) > term)).
% 14.62/2.51 thf(func_def_721, type, sK583: (term > $o)).
% 14.62/2.51 thf(func_def_722, type, sK584: term).
% 14.62/2.51 thf(func_def_723, type, sK585: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_724, type, sK586: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_725, type, sK587: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_726, type, sK588: term).
% 14.62/2.51 thf(func_def_727, type, sK589: (subst > term > term)).
% 14.62/2.51 thf(func_def_728, type, sK590: term).
% 14.62/2.51 thf(func_def_729, type, vNOT: ($o > $o)).
% 14.62/2.51 thf(func_def_730, type, sK591: (subst > term > subst > $o)).
% 14.62/2.51 thf(func_def_731, type, sK592: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_732, type, sK593: ((subst > term > term) > term)).
% 14.62/2.51 thf(func_def_733, type, sK594: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_734, type, sK595: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_735, type, sK596: ((subst > term > term) > subst)).
% 14.62/2.51 thf(func_def_736, type, sK597: term).
% 14.62/2.51 thf(func_def_737, type, sK598: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_738, type, sK599: ((subst > term > subst > $o) > subst > term > term)).
% 14.62/2.51 thf(func_def_739, type, sK600: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(func_def_740, type, sK601: ((subst > term > subst > $o) > term)).
% 14.62/2.51 thf(f1,axiom,(
% 14.62/2.51 (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))))) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoaslamnotvar & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & axclos & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & hoasapinj2_gthm & hoaslamnotap_gthm & (id = ((d2subst @ d_id))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) <=> hoasapinj1_lthm) & (pushprop_lem0 <=> ! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (apinj2 <=> ! [X20 : term,X13 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X18 : (subst > term > term),X35 : term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X37 : term,X38 : subst,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X41 : subst,X40 : term,X39 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id))) & (one = ((d2term @ d_one))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X33 : term,X32 : subst,X18 : (subst > term > term),X31 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoaslaminj_lthm) & pushprop_lem2v2 & (! [X13 : term,X15 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id)) => (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id)))))))) & (induction2lem <=> ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [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 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))))) & (pushprop_lem0_lthm <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & hoasinduction_lem3_gthm & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & pushprop_lem3v2 & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & induction2lem_gthm & (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem2v2_gthm & hoasinduction_lem1v2_gthm & pushprop_lem1v2_gthm & apnotvar & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axabs & substmonoid_gthm & hoasinduction_lem1v2 & (hoasinduction_lem2v2 <=> ! [X44 : term,X11 : (term > $o),X45 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X44) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))))) <=> hoasinduction_lem3a_lthm) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))))) & ! [X1 : d_term] : (X1 = d_one) & hoasapnotvar_gthm & ((! [X20 : term,X13 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X20 : term,X13 : term,X19 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) <=> hoasapinj2_lthm) & hoasinduction_lem1 & (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X21)) <=> induction) & (pushprop_lem1v2 <=> ! [X11 : (term > $o),X13 : term,X14 : subst,X10 : (term > $o)] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13))) & hoasapnotvar & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X14 : subst,X13 : term,X10 : (term > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & hoasinduction_lem2_gthm & pushprop_gthm & pushprop_lem2v2_lthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) <=> laminj) & (! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)))))) & (sh = ((d2subst @ d_id))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & hoaslamnotvar_lthm & ulamvarind & ! [X5 : d_subst] : (X5 = d_id) & pushprop_lthm_orig & hoaslamnotap_lthm & (hoaslaminj <=> ! [X32 : subst,X31 : (subst > term > term),X33 : term,X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & pushprop_lem3v2_lthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & induction2_gthm & (induction2 <=> ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))))) & hoasinduction_lem2_lthm & axapp & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & hoasinduction_lem1_lthm & hoasinduction_lem3a_gthm & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => ! [X16 : term,X17 : subst,X10 : (term > $o)] : (~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))))))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapinj1_gthm & hoasapnotvar_lthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X14 : subst,X13 : term,X26 : (term > $o),X10 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29))))) <=> hoasinduction_lem3v2a_lthm) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X28 @ id) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))))))) <=> hoasinduction_lthm_3) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & hoaslaminj_gthm & (apinj1 <=> ! [X20 : term,X15 : term,X19 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3aa) & ulamvarsh & ~lamnotap & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop_lem0_gthm & pushprop_lem2v2_gthm & (substmonoid_lthm <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))))) & pushprop_lthm & (hoasinduction_lem2 <=> ! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : (~(X10 @ id @ X24 @ id) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)))) & hoasinduction_lem1_gthm & (! [X18 : (subst > term > term),X47 : term,X46 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoaslamnotap) & (! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48))) <=> hoasinduction_lem3v2) & hoaslamnotvar_gthm & hoasinduction_gthm & hoasinduction_lem3b_gthm & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & termmset_gthm & ~ulamvar1 & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))) & lamnotvar & axassoc & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X48 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X48)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & axvarshift & ~(var @ (d2term @ d_one)) & pushprop & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) <=> hoasinduction_lem3aa_lthm) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (! [X20 : term,X13 : term,X19 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)) <=> hoasapinj2) & (! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ X43) @ id)) <=> hoasinduction_lem3a) & (hoasinduction_lem3v2a <=> ! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (! [X15 : term,X26 : (term > $o),X14 : subst,X10 : (term > $o),X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & (hoasinduction <=> ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & ((^[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) & pushprop_lem1_gthm & axmap),
% 14.62/2.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 14.62/2.51 thf(f2,conjecture,(
% 14.62/2.51 (! [X0 : (subst > term > subst > $o)] : (! [X1 : term,X2 : term] : ((X0 @ id @ X1 @ id) => ((X0 @ id @ X2 @ id) => (X0 @ id @ (hoasap @ id @ X1 @ id @ X2) @ id))) => (! [X3 : (subst > term > term)] : (! [X5 : subst,X4 : subst,X1 : term] : (((sub @ (X3 @ X4 @ X1) @ X5)) = ((X3 @ (comp @ X4 @ X5) @ (sub @ X1 @ X5)))) => (! [X1 : term] : ((X0 @ id @ X1 @ id) => (X0 @ id @ (X3 @ id @ X1) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X4 : subst, X1 : term] : ((X3 @ X4 @ X1)))) @ id))) => ! [X1 : term] : (X0 @ id @ X1 @ id))) = hoasinduction_no_psi_cond)),
% 14.62/2.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_no_psi_cond)).
% 14.62/2.51 thf(f3,negated_conjecture,(
% 14.62/2.51 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : term,X2 : term] : ((X0 @ id @ X1 @ id) => ((X0 @ id @ X2 @ id) => (X0 @ id @ (hoasap @ id @ X1 @ id @ X2) @ id))) => (! [X3 : (subst > term > term)] : (! [X5 : subst,X4 : subst,X1 : term] : (((sub @ (X3 @ X4 @ X1) @ X5)) = ((X3 @ (comp @ X4 @ X5) @ (sub @ X1 @ X5)))) => (! [X1 : term] : ((X0 @ id @ X1 @ id) => (X0 @ id @ (X3 @ id @ X1) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X4 : subst, X1 : term] : ((X3 @ X4 @ X1)))) @ id))) => ! [X1 : term] : (X0 @ id @ X1 @ id))) = hoasinduction_no_psi_cond)),
% 14.62/2.51 inference(negated_conjecture,[status(cth)],[f2])).
% 14.62/2.51 thf(f4,plain,(
% 14.62/2.51 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : term,X2 : term] : ((X0 @ id @ X1 @ id) => ((X0 @ id @ X2 @ id) => (X0 @ id @ (hoasap @ id @ X1 @ id @ X2) @ id))) => (! [X3 : (subst > term > term)] : (! [X4 : subst,X5 : subst,X6 : term] : (((X3 @ (comp @ X5 @ X4) @ (sub @ X6 @ X4))) = ((sub @ (X3 @ X5 @ X6) @ X4))) => (! [X7 : term] : ((X0 @ id @ X7 @ id) => (X0 @ id @ (X3 @ id @ X7) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X8 : subst, X9 : term] : ((X3 @ X8 @ X9)))) @ id))) => ! [X10 : term] : (X0 @ id @ X10 @ id))) = hoasinduction_no_psi_cond)),
% 14.62/2.51 inference(rectify,[],[f3])).
% 14.62/2.51 thf(f5,plain,(
% 14.62/2.51 ~ (hoasinduction_no_psi_cond = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ 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]: (Y0 @ id @ Y1 @ id)))))))))),
% 14.62/2.51 inference(fool_elimination,[],[f4])).
% 14.62/2.51 thf(f6,plain,(
% 14.62/2.51 (induction2_lthm <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => (! [X1 : (term > $o),X2 : term,X3 : subst] : (~ ! [X4 : term,X5 : term] : (~(X1 @ X5) | (X1 @ (ap @ X4 @ X5)) | ~(X1 @ X4)) | (X1 @ (sub @ X2 @ X3)) | ~ ! [X6 : term] : (~ ! [X7 : term] : ((X1 @ (sub @ X6 @ (push @ X7 @ id))) | ~(X1 @ X7)) | (X1 @ (lam @ X6))) | ~ ! [X8 : term] : ((X1 @ (sub @ X8 @ X3)) | ~(var @ X8))) => ! [X9 : term,X10 : (term > $o)] : (~ ! [X11 : term] : ((X10 @ (lam @ X11)) | ~ ! [X12 : term] : ((X10 @ (sub @ X11 @ (push @ X12 @ id))) | ~(X10 @ X12))) | ~ ! [X13 : term,X14 : term] : (~(X10 @ X14) | (X10 @ (ap @ X14 @ X13)) | ~(X10 @ X13)) | (X10 @ X9) | ~ ! [X15 : term] : ((X10 @ X15) | ~(var @ X15)))))) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & hoaslamnotvar & ! [X18 : d_term,X19 : d_term] : ((((d2term @ X18)) = ((d2term @ X19))) => (X18 = X19)) & axclos & (hoasinduction_lem3v2_f_lthm <=> ! [X20 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X22 : subst,X23 : term] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22))))) & hoasapinj2_gthm & hoaslamnotap_gthm & (id = ((d2subst @ d_id))) & ((! [X24 : term] : (((sub @ X24 @ id)) = X24) => (! [X25 : term,X26 : term,X27 : term,X28 : term] : ((((ap @ X28 @ X26)) != ((ap @ X27 @ X25))) | (X27 = X28)) => ! [X29 : term,X30 : term,X31 : term,X32 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))))) <=> hoasapinj1_lthm) & (pushprop_lem0 <=> ! [X33 : subst,X34 : (term > $o),X35 : term] : ~ ! [X36 : (term > $o)] : ~ ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37)))) & (apinj2 <=> ! [X38 : term,X39 : term,X40 : term,X41 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & (hoasinduction_lem3aaa <=> ! [X42 : (subst > term > subst > $o),X43 : term] : (~ ! [X44 : (subst > term > term),X45 : term] : ((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id) | ~ ! [X46 : term,X47 : subst,X48 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) | ~ ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49)))) | ~ ! [X52 : term] : ((X42 @ id @ (X44 @ id @ X52) @ id) | ~(X42 @ id @ X52 @ id))) | ~ ! [X53 : term] : (~(X42 @ id @ X53 @ id) | (X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) | (X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id))) & (one = ((d2term @ d_one))) & ((! [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) = X55) => (! [X56 : term,X57 : subst] : (((comp @ sh @ (push @ X56 @ X57))) = X57) => (! [X58 : term,X59 : term] : ((((lam @ X58)) != ((lam @ X59))) | (X58 = X59)) => ! [X60 : term,X61 : subst,X62 : (subst > term > term),X63 : (subst > term > term)] : (~ ! [X64 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X66 @ X65) @ X64)) = ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))) | (((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | ~ ! [X67 : subst,X68 : subst,X69 : term] : (((sub @ (X63 @ X68 @ X69) @ X67)) = ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67)))))))) <=> hoaslaminj_lthm) & pushprop_lem2v2 & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> shinj) & (axidl <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (hoasinduction_lthm <=> (! [X73 : (term > $o),X74 : term] : (~ ! [X75 : term] : (~ ! [X76 : term] : (~(X73 @ X76) | (X73 @ (sub @ X75 @ (push @ X76 @ id)))) | (X73 @ (lam @ X75))) | ~ ! [X77 : term] : ((X73 @ X77) | ~(var @ X77)) | (X73 @ X74) | ~ ! [X78 : term,X79 : term] : (~(X73 @ X79) | (X73 @ (ap @ X78 @ X79)) | ~(X73 @ X78))) => (! [X80 : term,X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X83 : subst,X84 : subst,X85 : term,X86 : subst] : (~(X82 @ X84 @ X85 @ (comp @ X83 @ X86)) | (X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) | (X82 @ id @ (ap @ X81 @ X80) @ id) | ~ ! [X87 : term,X88 : subst,X89 : subst,X90 : subst] : ((X82 @ X88 @ X87 @ (comp @ X89 @ X90)) | ~(X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) | ~ ! [X91 : term,X92 : term] : ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id) | ~(X82 @ id @ X91 @ id) | ~(X82 @ id @ X92 @ id)) | ~(X82 @ id @ X81 @ id) | ~(X82 @ id @ X80 @ id)) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X95 : subst,X96 : subst,X97 : term,X98 : subst] : ((X94 @ X95 @ X97 @ (comp @ X98 @ X96)) | ~(X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) | ~ ! [X99 : term] : ((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id) | ~(X94 @ id @ X99 @ id)) | (X94 @ id @ (lam @ X93) @ id) | ~ ! [X100 : (subst > term > term)] : ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id) | ~ ! [X101 : term,X102 : subst,X103 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) = ((sub @ (X100 @ X102 @ X101) @ X103))) | ~ ! [X104 : term] : (~(X94 @ id @ X104 @ id) | (X94 @ id @ (X100 @ id @ X104) @ id))) | ~ ! [X105 : subst,X106 : subst,X107 : term,X108 : subst] : ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106) | ~(X94 @ X105 @ X107 @ (comp @ X108 @ X106)))) => ! [X109 : (subst > term > subst > $o),X110 : term] : ((X109 @ id @ X110 @ id) | ~ ! [X111 : subst,X112 : subst,X113 : subst,X114 : term] : ((X109 @ X113 @ X114 @ (comp @ X112 @ X111)) | ~(X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) | ~ ! [X115 : (subst > term > term)] : (~ ! [X116 : term] : (~(X109 @ id @ X116 @ id) | (X109 @ id @ (X115 @ id @ X116) @ id)) | ~ ! [X117 : subst,X118 : subst,X119 : term] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) | (X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) | ~ ! [X120 : term,X121 : term] : ((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id) | ~(X109 @ id @ X121 @ id) | ~(X109 @ id @ X120 @ id)) | ~ ! [X122 : subst,X123 : subst,X124 : term,X125 : subst] : ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125) | ~(X109 @ X123 @ X124 @ (comp @ X122 @ X125))) | ~ ! [X126 : term] : ((X109 @ id @ X126 @ id) | ~(var @ (sub @ X126 @ id)))))))) & (induction2lem <=> ! [X127 : (term > $o),X128 : subst,X129 : term] : (~ ! [X130 : term] : (~ ! [X131 : term] : (~(X127 @ X131) | (X127 @ (sub @ X130 @ (push @ X131 @ id)))) | (X127 @ (lam @ X130))) | ~ ! [X132 : term] : ((X127 @ (sub @ X132 @ X128)) | ~(var @ X132)) | (X127 @ (sub @ X129 @ X128)) | ~ ! [X133 : term,X134 : term] : (~(X127 @ X133) | ~(X127 @ X134) | (X127 @ (ap @ X134 @ X133))))) & (pushprop_lem0_lthm <=> ! [X135 : (term > $o),X136 : term,X137 : subst] : ~ ! [X138 : (term > $o)] : ~ ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139)))) & hoasinduction_lem3_gthm & ! [X140 : d_subst,X141 : d_subst] : ((((d2subst @ X140)) = ((d2subst @ X141))) => (X140 = X141)) & pushprop_lem3v2 & (termmset <=> ! [X142 : term] : (((sub @ X142 @ id)) = X142)) & induction2lem_gthm & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> axshiftcons) & (! [X145 : term] : ~ ! [X146 : (subst > term > term)] : (((X146 @ sh @ one)) != ((sub @ X145 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem2v2_gthm & hoasinduction_lem1v2_gthm & pushprop_lem1v2_gthm & apnotvar & (! [X147 : (subst > term > subst > $o)] : ~ ! [X148 : (term > $o)] : ~ ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149))) <=> hoasinduction_lem0) & (! [X150 : term] : ~ ! [X151 : (subst > term > term)] : ~ ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153))) <=> hoasinduction_lem3v2_f) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axabs & substmonoid_gthm & hoasinduction_lem1v2 & (hoasinduction_lem2v2 <=> ! [X154 : term,X155 : (term > $o),X156 : term,X157 : (subst > term > subst > $o)] : (~ ! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : ((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158) | ~(X157 @ X160 @ X161 @ (comp @ X159 @ X158))) | ~ ! [X162 : term,X163 : term] : (~(X157 @ id @ X162 @ id) | ~(X157 @ id @ X163 @ id) | (X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) | ~ ! [X164 : term] : (((X155 @ X164)) = ((X157 @ id @ X164 @ id))) | ~ ! [X165 : subst,X166 : term,X167 : subst,X168 : subst] : (~(X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165) | (X157 @ X167 @ X166 @ (comp @ X168 @ X165))) | ~(X155 @ X154) | (X155 @ (ap @ X154 @ X156)) | ~(X155 @ X156))) & (termmset_lthm <=> (! [X169 : term] : (((sub @ X169 @ id)) = X169) => ! [X170 : term] : (((sub @ X170 @ id)) = X170))) & ((! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : term,X173 : (subst > term > subst > $o)] : (~ ! [X174 : (subst > term > term)] : (~ ! [X175 : subst,X176 : subst,X177 : term] : (((sub @ (X174 @ X175 @ X177) @ X176)) = ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176)))) | (X173 @ id @ (lam @ (X174 @ sh @ one)) @ id) | ~ ! [X178 : term] : ((X173 @ id @ (X174 @ id @ X178) @ id) | ~(X173 @ id @ X178 @ id))) | ~ ! [X179 : term] : ((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id) | ~(X173 @ id @ X179 @ id)) | (X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)) => ! [X180 : term,X181 : (subst > term > subst > $o)] : ((X181 @ id @ (lam @ X180) @ id) | ~ ! [X182 : (subst > term > term)] : ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id) | ~ ! [X183 : term] : (~(X181 @ id @ X183 @ id) | (X181 @ id @ (X182 @ id @ X183) @ id)) | ~ ! [X184 : subst,X185 : subst,X186 : term] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185))))) | ~ ! [X187 : term] : ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id) | ~(X181 @ id @ X187 @ id))))) <=> hoasinduction_lem3a_lthm) & (hoasinduction_no_psi_cond_lthm <=> (! [X188 : (subst > term > subst > $o)] : ~ ! [X189 : (term > $o)] : ~ ! [X190 : term] : (((X188 @ id @ X190 @ id)) = ((X189 @ X190))) => (! [X191 : (term > $o),X192 : term] : (~ ! [X193 : term] : ((X191 @ X193) | ~(var @ X193)) | (X191 @ X192) | ~ ! [X194 : term,X195 : term] : (~(X191 @ X194) | ~(X191 @ X195) | (X191 @ (ap @ X195 @ X194))) | ~ ! [X196 : term] : (~ ! [X197 : term] : (~(X191 @ X197) | (X191 @ (sub @ X196 @ (push @ X197 @ id)))) | (X191 @ (lam @ X196)))) => (! [X198 : term] : (((sub @ X198 @ id)) = X198) => (! [X199 : (term > $o),X200 : term,X201 : (subst > term > subst > $o)] : (~ ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) | ~ ! [X203 : (subst > term > term)] : (~ ! [X204 : term] : ((X201 @ id @ (X203 @ id @ X204) @ id) | ~(X201 @ id @ X204 @ id)) | (X201 @ id @ (lam @ (X203 @ sh @ one)) @ id) | ~ ! [X205 : subst,X206 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) = ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206))))) | ~ ! [X208 : term] : (~(X199 @ X208) | (X199 @ (sub @ X200 @ (push @ X208 @ id)))) | (X199 @ (lam @ X200))) => ! [X209 : term,X210 : (subst > term > subst > $o)] : (~ ! [X211 : term,X212 : term] : (~(X210 @ id @ X211 @ id) | ~(X210 @ id @ X212 @ id) | (X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id)) | (X210 @ id @ X209 @ id) | ~ ! [X213 : (subst > term > term)] : (~ ! [X214 : term] : ((X210 @ id @ (X213 @ id @ X214) @ id) | ~(X210 @ id @ X214 @ id)) | ~ ! [X215 : subst,X216 : subst,X217 : term] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) | (X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)))))))) & ! [X218 : d_term] : (d_one = X218) & hoasapnotvar_gthm & ((! [X219 : term,X220 : term,X221 : term,X222 : term] : ((((ap @ X220 @ X222)) != ((ap @ X221 @ X219))) | (X219 = X222)) => ! [X223 : term,X224 : term,X225 : term,X226 : term] : ((((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225))) | (X223 = X225))) <=> hoasapinj2_lthm) & hoasinduction_lem1 & (! [X227 : (term > $o),X228 : term] : (~ ! [X229 : term,X230 : term] : (~(X227 @ X230) | ~(X227 @ X229) | (X227 @ (ap @ X229 @ X230))) | ~ ! [X231 : term] : (~(X227 @ X231) | (X227 @ (lam @ X231))) | ~ ! [X232 : term] : ((X227 @ X232) | ~(var @ X232)) | (X227 @ X228)) <=> induction) & (pushprop_lem1v2 <=> ! [X233 : (term > $o),X234 : term,X235 : subst,X236 : (term > $o)] : ((X233 @ one) | ~ ! [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X233 @ X237))) | ~(X236 @ X234))) & hoasapnotvar & ((! [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) = X238) => ! [X240 : subst,X241 : term,X242 : (term > $o),X243 : (term > $o)] : (~ ! [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) = ((X243 @ X244))) | ~(X242 @ X241) | (X243 @ one))) <=> pushprop_lem1v2_lthm) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & hoasinduction_lem2_gthm & pushprop_gthm & pushprop_lem2v2_lthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_p_and_p_prime = (^[X247 : (subst > term > subst > $o), X248 : (term > $o)] : (! [X249 : term] : (((X247 @ id @ X249 @ id)) = ((X248 @ X249)))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X250 : term,X251 : term] : ((((lam @ X251)) != ((lam @ X250))) | (X250 = X251)) <=> laminj) & (! [X252 : term,X253 : (subst > term > subst > $o)] : (~ ! [X254 : term,X255 : term] : ((X253 @ id @ (ap @ (sub @ X254 @ id) @ X255) @ id) | ~(X253 @ id @ X254 @ id) | ~(X253 @ id @ X255 @ id)) | ~ ! [X256 : (subst > term > term)] : (~ ! [X257 : term] : ((X253 @ id @ (X256 @ id @ X257) @ id) | ~(X253 @ id @ X257 @ id)) | (X253 @ id @ (lam @ (X256 @ sh @ one)) @ id) | ~ ! [X258 : subst,X259 : term,X260 : subst] : (((sub @ (X256 @ X258 @ X259) @ X260)) = ((X256 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260))))) | (X253 @ id @ X252 @ id)) <=> hoasinduction_no_psi_cond) & (hoasinduction_lem3_lthm <=> (! [X261 : term] : (((sub @ X261 @ id)) = X261) => (! [X262 : (subst > term > subst > $o),X263 : term] : (~ ! [X264 : (subst > term > term)] : (~ ! [X265 : term,X266 : subst,X267 : subst] : (((sub @ (X264 @ X267 @ X265) @ X266)) = ((X264 @ (comp @ X267 @ X266) @ (sub @ X265 @ X266)))) | (X262 @ id @ (lam @ (X264 @ sh @ one)) @ id) | ~ ! [X268 : term] : (~(X262 @ id @ X268 @ id) | (X262 @ id @ (X264 @ id @ X268) @ id))) | ~ ! [X269 : term] : (~(X262 @ id @ X269 @ id) | (X262 @ id @ (sub @ X263 @ (push @ X269 @ id)) @ id)) | (X262 @ id @ (lam @ (sub @ X263 @ (push @ one @ sh))) @ id)) => ! [X270 : term,X271 : (subst > term > subst > $o)] : (~ ! [X272 : subst,X273 : subst,X274 : subst,X275 : term] : ((X271 @ (comp @ X273 @ X272) @ (sub @ X275 @ X272) @ X274) | ~(X271 @ X273 @ X275 @ (comp @ X272 @ X274))) | (X271 @ id @ (lam @ X270) @ id) | ~ ! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (~(X271 @ (comp @ X278 @ X276) @ (sub @ X279 @ X276) @ X277) | (X271 @ X278 @ X279 @ (comp @ X276 @ X277))) | ~ ! [X280 : (subst > term > term)] : ((X271 @ id @ (lam @ (X280 @ sh @ one)) @ id) | ~ ! [X281 : term] : ((X271 @ id @ (X280 @ id @ X281) @ id) | ~(X271 @ id @ X281 @ id)) | ~ ! [X282 : term,X283 : subst,X284 : subst] : (((sub @ (X280 @ X283 @ X282) @ X284)) = ((X280 @ (comp @ X283 @ X284) @ (sub @ X282 @ X284))))) | ~ ! [X285 : term] : (~(X271 @ id @ X285 @ id) | (X271 @ id @ (sub @ X270 @ (push @ X285 @ id)) @ id)))))) & (sh = ((d2subst @ d_id))) & (axidr <=> ! [X286 : subst] : (((comp @ X286 @ id)) = X286)) & hoaslamnotvar_lthm & ulamvarind & ! [X287 : d_subst] : (d_id = X287) & pushprop_lthm_orig & hoaslamnotap_lthm & (hoaslaminj <=> ! [X288 : subst,X289 : (subst > term > term),X290 : term,X291 : (subst > term > term)] : (~ ! [X292 : subst,X293 : subst,X294 : term] : (((sub @ (X289 @ X292 @ X294) @ X293)) = ((X289 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) | ~ ! [X295 : subst,X296 : term,X297 : subst] : (((sub @ (X291 @ X295 @ X296) @ X297)) = ((X291 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)))) | (((lam @ (X291 @ sh @ one))) != ((lam @ (X289 @ sh @ one)))) | (((X291 @ X288 @ X290)) = ((X289 @ X288 @ X290))))) & pushprop_lem3v2_lthm & (! [X298 : term] : ~ ! [X299 : (subst > term > term)] : (((sub @ X298 @ (push @ one @ sh))) != ((X299 @ sh @ one))) <=> hoasinduction_lem3b) & induction2_gthm & (induction2 <=> ! [X300 : (term > $o),X301 : term] : ((X300 @ X301) | ~ ! [X302 : term] : ((X300 @ X302) | ~(var @ X302)) | ~ ! [X303 : term,X304 : term] : (~(X300 @ X304) | (X300 @ (ap @ X303 @ X304)) | ~(X300 @ X303)) | ~ ! [X305 : term] : ((X300 @ (lam @ X305)) | ~ ! [X306 : term] : ((X300 @ (sub @ X305 @ (push @ X306 @ id))) | ~(X300 @ X306))))) & hoasinduction_lem2_lthm & axapp & (hoasinduction_lem3 <=> ! [X307 : term,X308 : (subst > term > subst > $o)] : (~ ! [X309 : term] : ((X308 @ id @ (sub @ X307 @ (push @ X309 @ id)) @ id) | ~(X308 @ id @ X309 @ id)) | ~ ! [X310 : subst,X311 : subst,X312 : term,X313 : subst] : ((X308 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313) @ X310) | ~(X308 @ X311 @ X312 @ (comp @ X313 @ X310))) | ~ ! [X314 : term,X315 : subst,X316 : subst,X317 : subst] : ((X308 @ X316 @ X314 @ (comp @ X315 @ X317)) | ~(X308 @ (comp @ X316 @ X315) @ (sub @ X314 @ X315) @ X317)) | (X308 @ id @ (lam @ X307) @ id) | ~ ! [X318 : (subst > term > term)] : (~ ! [X319 : subst,X320 : subst,X321 : term] : (((X318 @ (comp @ X319 @ X320) @ (sub @ X321 @ X320))) = ((sub @ (X318 @ X319 @ X321) @ X320))) | (X308 @ id @ (lam @ (X318 @ sh @ one)) @ id) | ~ ! [X322 : term] : (~(X308 @ id @ X322 @ id) | (X308 @ id @ (X318 @ id @ X322) @ id))))) & hoasinduction_lem1_lthm & hoasinduction_lem3a_gthm & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X323 : term,X324 : subst] : (((sub @ one @ (push @ X323 @ X324))) = X323) => (! [X325 : term,X326 : subst] : (((comp @ sh @ (push @ X325 @ X326))) = X326) => (! [X327 : subst] : (((comp @ X327 @ id)) = X327) => (! [X328 : (term > $o),X329 : term] : ((X328 @ X329) | ~ ! [X330 : term] : ((X328 @ (lam @ X330)) | ~(X328 @ X330)) | ~ ! [X331 : term,X332 : term] : (~(X328 @ X331) | (X328 @ (ap @ X332 @ X331)) | ~(X328 @ X332)) | ~ ! [X333 : term] : (~(var @ X333) | (X328 @ X333))) => ! [X334 : term,X335 : subst,X336 : (term > $o)] : (~ ! [X337 : term] : (~(var @ X337) | (X336 @ (sub @ X337 @ X335))) | (X336 @ (sub @ X334 @ X335)) | ~ ! [X338 : term,X339 : term] : (~(X336 @ X339) | ~(X336 @ X338) | (X336 @ (ap @ X339 @ X338))) | ~ ! [X340 : term] : (~ ! [X341 : term] : ((X336 @ (sub @ X340 @ (push @ X341 @ id))) | ~(X336 @ X341)) | (X336 @ (lam @ X340))))))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapinj1_gthm & hoasapnotvar_lthm & ((! [X342 : subst,X343 : term] : (((sub @ one @ (push @ X343 @ X342))) = X343) => (! [X344 : term,X345 : subst] : (((comp @ sh @ (push @ X344 @ X345))) = X345) => ! [X346 : term,X347 : subst,X348 : term,X349 : (term > $o),X350 : (term > $o)] : (~(X350 @ X348) | (X349 @ (sub @ X348 @ (push @ X346 @ X347)))))) <=> pushprop_lem1_lthm) & ((! [X351 : term] : ~ ! [X352 : (subst > term > term)] : ~ ! [X353 : term,X354 : subst] : (((X352 @ X354 @ X353)) = ((sub @ X351 @ (push @ X353 @ X354)))) => (! [X355 : term] : (((sub @ X355 @ id)) = X355) => ! [X356 : (term > $o),X357 : (subst > term > subst > $o),X358 : term] : (~ ! [X359 : (subst > term > term)] : ((X357 @ id @ (lam @ (X359 @ sh @ one)) @ id) | ~ ! [X360 : subst,X361 : subst,X362 : term] : (((X359 @ (comp @ X360 @ X361) @ (sub @ X362 @ X361))) = ((sub @ (X359 @ X360 @ X362) @ X361))) | ~ ! [X363 : term] : (~(X357 @ id @ X363 @ id) | (X357 @ id @ (X359 @ id @ X363) @ id))) | ~ ! [X364 : term] : (~(X356 @ X364) | (X356 @ (sub @ X358 @ (push @ X364 @ id)))) | ~ ! [X365 : term] : (((X356 @ X365)) = ((X357 @ id @ X365 @ id))) | (X356 @ (lam @ X358))))) <=> hoasinduction_lem3v2a_lthm) & ((! [X366 : (subst > term > subst > $o)] : ~ ! [X367 : (term > $o)] : ~ ! [X368 : term] : (((X367 @ X368)) = ((X366 @ id @ X368 @ id))) => (! [X369 : (term > $o),X370 : term] : (~ ! [X371 : term] : ((X369 @ (lam @ X371)) | ~ ! [X372 : term] : (~(X369 @ X372) | (X369 @ (sub @ X371 @ (push @ X372 @ id))))) | ~ ! [X373 : term,X374 : term] : (~(X369 @ X374) | (X369 @ (ap @ X374 @ X373)) | ~(X369 @ X373)) | (X369 @ X370) | ~ ! [X375 : term] : (~(var @ X375) | (X369 @ X375))) => (! [X376 : term] : (((sub @ X376 @ id)) = X376) => (! [X377 : term,X378 : (subst > term > subst > $o),X379 : (term > $o)] : (~ ! [X380 : term] : (~(X379 @ X380) | (X379 @ (sub @ X377 @ (push @ X380 @ id)))) | ~ ! [X381 : (subst > term > term)] : (~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X381 @ X382 @ X383) @ X384)) = ((X381 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)))) | ~ ! [X385 : term] : (~(X378 @ id @ X385 @ id) | (X378 @ id @ (X381 @ id @ X385) @ id)) | (X378 @ id @ (lam @ (X381 @ sh @ one)) @ id)) | (X379 @ (lam @ X377)) | ~ ! [X386 : term] : (((X379 @ X386)) = ((X378 @ id @ X386 @ id)))) => ! [X387 : term,X388 : (subst > term > subst > $o)] : ((X388 @ id @ X387 @ id) | ~ ! [X389 : subst,X390 : subst,X391 : subst,X392 : term] : (~(X388 @ (comp @ X391 @ X389) @ (sub @ X392 @ X389) @ X390) | (X388 @ X391 @ X392 @ (comp @ X389 @ X390))) | ~ ! [X393 : term] : ((X388 @ id @ X393 @ id) | ~(var @ (sub @ X393 @ id))) | ~ ! [X394 : (subst > term > term)] : (~ ! [X395 : term] : ((X388 @ id @ (X394 @ id @ X395) @ id) | ~(X388 @ id @ X395 @ id)) | (X388 @ id @ (lam @ (X394 @ sh @ one)) @ id) | ~ ! [X396 : subst,X397 : subst,X398 : term] : (((sub @ (X394 @ X397 @ X398) @ X396)) = ((X394 @ (comp @ X397 @ X396) @ (sub @ X398 @ X396))))) | ~ ! [X399 : subst,X400 : subst,X401 : subst,X402 : term] : ((X388 @ (comp @ X401 @ X400) @ (sub @ X402 @ X400) @ X399) | ~(X388 @ X401 @ X402 @ (comp @ X400 @ X399))) | ~ ! [X403 : term,X404 : term] : (~(X388 @ id @ X403 @ id) | ~(X388 @ id @ X404 @ id) | (X388 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id))))))) <=> hoasinduction_lthm_3) & (! [X405 : term] : (((sub @ X405 @ id)) = X405) <=> axvarid) & hoaslaminj_gthm & (apinj1 <=> ! [X406 : term,X407 : term,X408 : term,X409 : term] : ((((ap @ X409 @ X408)) != ((ap @ X407 @ X406))) | (X407 = X409))) & (! [X410 : term,X411 : (subst > term > subst > $o)] : (~ ! [X412 : term] : ((X411 @ id @ (sub @ X410 @ (push @ X412 @ id)) @ id) | ~(X411 @ id @ X412 @ id)) | (X411 @ id @ (lam @ (sub @ X410 @ (push @ one @ sh))) @ id) | ~ ! [X413 : (subst > term > term)] : (~ ! [X414 : term] : ((X411 @ id @ (X413 @ id @ X414) @ id) | ~(X411 @ id @ X414 @ id)) | (X411 @ id @ (lam @ (X413 @ sh @ one)) @ id) | ~ ! [X415 : subst,X416 : subst,X417 : term] : (((sub @ (X413 @ X416 @ X417) @ X415)) = ((X413 @ (comp @ X416 @ X415) @ (sub @ X417 @ X415)))))) <=> hoasinduction_lem3aa) & ulamvarsh & ~lamnotap & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop_lem0_gthm & pushprop_lem2v2_gthm & (substmonoid_lthm <=> (! [X418 : subst] : (((comp @ id @ X418)) = X418) => (! [X419 : subst] : (((comp @ X419 @ id)) = X419) => (! [X420 : subst] : (((comp @ id @ X420)) = X420) & ! [X421 : subst] : (((comp @ X421 @ id)) = X421))))) & pushprop_lthm & (hoasinduction_lem2 <=> ! [X422 : term,X423 : term,X424 : (subst > term > subst > $o)] : (~(X424 @ id @ X422 @ id) | ~ ! [X425 : subst,X426 : term,X427 : subst,X428 : subst] : (~(X424 @ X428 @ X426 @ (comp @ X425 @ X427)) | (X424 @ (comp @ X428 @ X425) @ (sub @ X426 @ X425) @ X427)) | ~ ! [X429 : subst,X430 : subst,X431 : term,X432 : subst] : ((X424 @ X429 @ X431 @ (comp @ X432 @ X430)) | ~(X424 @ (comp @ X429 @ X432) @ (sub @ X431 @ X432) @ X430)) | ~(X424 @ id @ X423 @ id) | (X424 @ id @ (ap @ X423 @ X422) @ id) | ~ ! [X433 : term,X434 : term] : (~(X424 @ id @ X433 @ id) | (X424 @ id @ (ap @ (sub @ X434 @ id) @ X433) @ id) | ~(X424 @ id @ X434 @ id)))) & hoasinduction_lem1_gthm & (! [X435 : (subst > term > term),X436 : term,X437 : term] : ((((ap @ (sub @ X437 @ id) @ X436)) != ((lam @ (X435 @ sh @ one)))) | ~ ! [X438 : term,X439 : subst,X440 : subst] : (((X435 @ (comp @ X439 @ X440) @ (sub @ X438 @ X440))) = ((sub @ (X435 @ X439 @ X438) @ X440)))) <=> hoaslamnotap) & (! [X441 : (subst > term > subst > $o),X442 : term,X443 : (term > $o)] : (~ ! [X444 : subst,X445 : subst,X446 : term,X447 : subst] : ((X441 @ X447 @ X446 @ (comp @ X444 @ X445)) | ~(X441 @ (comp @ X447 @ X444) @ (sub @ X446 @ X444) @ X445)) | ~ ! [X448 : subst,X449 : subst,X450 : term,X451 : subst] : (~(X441 @ X448 @ X450 @ (comp @ X451 @ X449)) | (X441 @ (comp @ X448 @ X451) @ (sub @ X450 @ X451) @ X449)) | ~ ! [X452 : term] : ((X443 @ (sub @ X442 @ (push @ X452 @ id))) | ~(X443 @ X452)) | ~ ! [X453 : (subst > term > term)] : (~ ! [X454 : term] : ((X441 @ id @ (X453 @ id @ X454) @ id) | ~(X441 @ id @ X454 @ id)) | (X441 @ id @ (lam @ (X453 @ sh @ one)) @ id) | ~ ! [X455 : term,X456 : subst,X457 : subst] : (((X453 @ (comp @ X457 @ X456) @ (sub @ X455 @ X456))) = ((sub @ (X453 @ X457 @ X455) @ X456)))) | ~ ! [X458 : term] : (((X443 @ X458)) = ((X441 @ id @ X458 @ id))) | (X443 @ (lam @ X442))) <=> hoasinduction_lem3v2) & hoaslamnotvar_gthm & hoasinduction_gthm & hoasinduction_lem3b_gthm & (axscons <=> ! [X459 : subst] : (((push @ (sub @ one @ X459) @ (comp @ sh @ X459))) = X459)) & termmset_gthm & ~ulamvar1 & (substmonoid <=> (! [X460 : subst] : (((comp @ id @ X460)) = X460) & ! [X461 : subst] : (((comp @ X461 @ id)) = X461))) & lamnotvar & axassoc & (! [X462 : (subst > term > subst > $o)] : ~ ! [X463 : (term > $o)] : ~ ! [X464 : term] : (((X462 @ id @ X464 @ id)) = ((X463 @ X464))) <=> hoasinduction_lem0_lthm) & (! [X465 : term,X466 : term,X467 : term,X468 : term] : ((X465 = X466) | (((ap @ (sub @ X466 @ id) @ X467)) != ((ap @ (sub @ X465 @ id) @ X468)))) <=> hoasapinj1) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_lthm <=> (! [X469 : term] : (((sub @ X469 @ id)) = X469) => ! [X470 : (term > $o),X471 : term,X472 : (subst > term > subst > $o)] : (~ ! [X473 : subst,X474 : term,X475 : subst,X476 : subst] : ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473) @ X476) | ~(X472 @ X475 @ X474 @ (comp @ X473 @ X476))) | ~ ! [X477 : (subst > term > term)] : ((X472 @ id @ (lam @ (X477 @ sh @ one)) @ id) | ~ ! [X478 : term,X479 : subst,X480 : subst] : (((sub @ (X477 @ X480 @ X478) @ X479)) = ((X477 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479)))) | ~ ! [X481 : term] : (~(X472 @ id @ X481 @ id) | (X472 @ id @ (X477 @ id @ X481) @ id))) | (X470 @ (lam @ X471)) | ~ ! [X482 : term,X483 : subst,X484 : subst,X485 : subst] : (~(X472 @ (comp @ X484 @ X485) @ (sub @ X482 @ X485) @ X483) | (X472 @ X484 @ X482 @ (comp @ X485 @ X483))) | ~ ! [X486 : term] : ((X470 @ (sub @ X471 @ (push @ X486 @ id))) | ~(X470 @ X486)) | ~ ! [X487 : term] : (((X472 @ id @ X487 @ id)) = ((X470 @ X487)))))) & axvarshift & ~(var @ (d2term @ d_one)) & pushprop & (hoaslam = (^[X488 : subst, X489 : (subst > term > term)] : ((d2term @ d_one)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X490 : (subst > term > subst > $o),X491 : term] : (~ ! [X492 : term] : (~(X490 @ id @ X492 @ id) | (X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id)) | (X490 @ id @ (lam @ (sub @ X491 @ (push @ one @ sh))) @ id) | ~ ! [X493 : (subst > term > term)] : ((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id) | ~ ! [X494 : term,X495 : subst,X496 : subst] : (((sub @ (X493 @ X495 @ X494) @ X496)) = ((X493 @ (comp @ X495 @ X496) @ (sub @ X494 @ X496)))) | ~ ! [X497 : term] : ((X490 @ id @ (X493 @ id @ X497) @ id) | ~(X490 @ id @ X497 @ id)))) <=> hoasinduction_lem3aa_lthm) & (axvarcons <=> ! [X498 : term,X499 : subst] : (((sub @ one @ (push @ X498 @ X499))) = X498)) & (! [X500 : term,X501 : term,X502 : term,X503 : term] : ((((ap @ (sub @ X501 @ id) @ X502)) != ((ap @ (sub @ X503 @ id) @ X500))) | (X500 = X502)) <=> hoasapinj2) & (! [X504 : (subst > term > subst > $o),X505 : term] : (~ ! [X506 : term] : (~(X504 @ id @ X506 @ id) | (X504 @ id @ (sub @ X505 @ (push @ X506 @ id)) @ id)) | ~ ! [X507 : (subst > term > term)] : ((X504 @ id @ (lam @ (X507 @ sh @ one)) @ id) | ~ ! [X508 : subst,X509 : subst,X510 : term] : (((X507 @ (comp @ X508 @ X509) @ (sub @ X510 @ X509))) = ((sub @ (X507 @ X508 @ X510) @ X509))) | ~ ! [X511 : term] : (~(X504 @ id @ X511 @ id) | (X504 @ id @ (X507 @ id @ X511) @ id))) | (X504 @ id @ (lam @ X505) @ id)) <=> hoasinduction_lem3a) & (hoasinduction_lem3v2a <=> ! [X512 : (term > $o),X513 : term,X514 : (subst > term > subst > $o)] : (~ ! [X515 : (subst > term > term)] : (~ ! [X516 : subst,X517 : subst,X518 : term] : (((sub @ (X515 @ X516 @ X518) @ X517)) = ((X515 @ (comp @ X516 @ X517) @ (sub @ X518 @ X517)))) | ~ ! [X519 : term] : ((X514 @ id @ (X515 @ id @ X519) @ id) | ~(X514 @ id @ X519 @ id)) | (X514 @ id @ (lam @ (X515 @ sh @ one)) @ id)) | (X512 @ (lam @ X513)) | ~ ! [X520 : term] : ((X512 @ (sub @ X513 @ (push @ X520 @ id))) | ~(X512 @ X520)) | ~ ! [X521 : term] : (((X514 @ id @ X521 @ id)) = ((X512 @ X521))))) & (! [X522 : term,X523 : (term > $o),X524 : subst,X525 : (term > $o),X526 : term] : (~(X525 @ X526) | (X523 @ (sub @ X526 @ (push @ X522 @ X524)))) <=> pushprop_lem1) & (hoasinduction <=> ! [X527 : term,X528 : (subst > term > subst > $o)] : (~ ! [X529 : subst,X530 : subst,X531 : term,X532 : subst] : (~(X528 @ X530 @ X531 @ (comp @ X532 @ X529)) | (X528 @ (comp @ X530 @ X532) @ (sub @ X531 @ X532) @ X529)) | ~ ! [X533 : (subst > term > term)] : (~ ! [X534 : subst,X535 : term,X536 : subst] : (((sub @ (X533 @ X534 @ X535) @ X536)) = ((X533 @ (comp @ X534 @ X536) @ (sub @ X535 @ X536)))) | (X528 @ id @ (lam @ (X533 @ sh @ one)) @ id) | ~ ! [X537 : term] : ((X528 @ id @ (X533 @ id @ X537) @ id) | ~(X528 @ id @ X537 @ id))) | ~ ! [X538 : term] : (~(var @ (sub @ X538 @ id)) | (X528 @ id @ X538 @ id)) | (X528 @ id @ X527 @ id) | ~ ! [X539 : subst,X540 : subst,X541 : subst,X542 : term] : (~(X528 @ (comp @ X541 @ X540) @ (sub @ X542 @ X540) @ X539) | (X528 @ X541 @ X542 @ (comp @ X540 @ X539))) | ~ ! [X543 : term,X544 : term] : ((X528 @ id @ (ap @ (sub @ X544 @ id) @ X543) @ id) | ~(X528 @ id @ X543 @ id) | ~(X528 @ id @ X544 @ id)))) & ((^[X545 : term, X546 : subst, X547 : (term > $o), X548 : (term > $o)] : (! [X549 : term] : (((X548 @ X549)) = ((X547 @ (sub @ X549 @ (push @ X545 @ X546))))))) = pushprop_p_and_p_prime) & pushprop_lem1_gthm & axmap),
% 14.62/2.51 inference(rectify,[],[f1])).
% 14.62/2.51 thf(f7,plain,(
% 14.62/2.51 ((induction2_lthm = $true) <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => (! [X1 : (term > $o),X2 : term,X3 : subst] : (~ ! [X4 : term,X5 : term] : (~ ($true = ((X1 @ X5))) | ($true = ((X1 @ (ap @ X4 @ X5)))) | ~ (((X1 @ X4)) = $true)) | (((X1 @ (sub @ X2 @ X3))) = $true) | ~ ! [X6 : term] : (~ ! [X7 : term] : ((((X1 @ (sub @ X6 @ (push @ X7 @ id)))) = $true) | ~ (((X1 @ X7)) = $true)) | (((X1 @ (lam @ X6))) = $true)) | ~ ! [X8 : term] : ((((X1 @ (sub @ X8 @ X3))) = $true) | ~ (((var @ X8)) = $true))) => ! [X9 : term,X10 : (term > $o)] : (~ ! [X11 : term] : ((((X10 @ (lam @ X11))) = $true) | ~ ! [X12 : term] : ((((X10 @ (sub @ X11 @ (push @ X12 @ id)))) = $true) | ~ (((X10 @ X12)) = $true))) | ~ ! [X13 : term,X14 : term] : (~ ($true = ((X10 @ X14))) | ($true = ((X10 @ (ap @ X14 @ X13)))) | ~ (((X10 @ X13)) = $true)) | (((X10 @ X9)) = $true) | ~ ! [X15 : term] : ((((X10 @ X15)) = $true) | ~ (((var @ X15)) = $true)))))) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & (hoaslamnotvar = $true) & ! [X19 : d_term,X18 : d_term] : ((((d2term @ X18)) = ((d2term @ X19))) => (X18 = X19)) & (axclos = $true) & (! [X20 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasapinj2_gthm = $true) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((! [X24 : term] : (((sub @ X24 @ id)) = X24) => (! [X26 : term,X27 : term,X28 : term,X25 : term] : ((X27 = X28) | (((ap @ X28 @ X26)) != ((ap @ X27 @ X25)))) => ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))))) <=> (hoasapinj1_lthm = $true)) & (! [X35 : term,X34 : (term > $o),X33 : subst] : ~ ! [X36 : (term > $o)] : ~ ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37))) <=> (pushprop_lem0 = $true)) & ((apinj2 = $true) <=> ! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & ((hoasinduction_lem3aaa = $true) <=> ! [X42 : (subst > term > subst > $o),X43 : term] : (~ ! [X44 : (subst > term > term),X45 : term] : ((((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id)) = $true) | ~ ! [X46 : term,X48 : subst,X47 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) | ~ ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49)))) | ~ ! [X52 : term] : ((((X42 @ id @ (X44 @ id @ X52) @ id)) = $true) | ~ (((X42 @ id @ X52 @ id)) = $true))) | ~ ! [X53 : term] : (~ (((X42 @ id @ X53 @ id)) = $true) | (((X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) = $true)) | (((X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id)) = $true))) & (one = ((d2term @ d_one))) & ((! [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) = X55) => (! [X57 : subst,X56 : term] : (((comp @ sh @ (push @ X56 @ X57))) = X57) => (! [X59 : term,X58 : term] : ((((lam @ X58)) != ((lam @ X59))) | (X58 = X59)) => ! [X63 : (subst > term > term),X61 : subst,X60 : term,X62 : (subst > term > term)] : ((((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | ~ ! [X69 : term,X67 : subst,X68 : subst] : (((sub @ (X63 @ X68 @ X69) @ X67)) = ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67)))) | ~ ! [X66 : subst,X64 : subst,X65 : term] : (((sub @ (X62 @ X66 @ X65) @ X64)) = ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))))))) <=> (hoaslaminj_lthm = $true)) & (pushprop_lem2v2 = $true) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> (shinj = $true)) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & ((hoasinduction_lthm = $true) <=> (! [X73 : (term > $o),X74 : term] : (~ ! [X75 : term] : (~ ! [X76 : term] : (~ (((X73 @ X76)) = $true) | (((X73 @ (sub @ X75 @ (push @ X76 @ id)))) = $true)) | (((X73 @ (lam @ X75))) = $true)) | ~ ! [X77 : term] : ((((X73 @ X77)) = $true) | ~ (((var @ X77)) = $true)) | ($true = ((X73 @ X74))) | ~ ! [X78 : term,X79 : term] : (~ (((X73 @ X79)) = $true) | (((X73 @ (ap @ X78 @ X79))) = $true) | ~ (((X73 @ X78)) = $true))) => (! [X80 : term,X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X83 : subst,X84 : subst,X85 : term,X86 : subst] : (~ (((X82 @ X84 @ X85 @ (comp @ X83 @ X86))) = $true) | (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) = $true)) | (((X82 @ id @ (ap @ X81 @ X80) @ id)) = $true) | ~ ! [X87 : term,X88 : subst,X89 : subst,X90 : subst] : (($true = ((X82 @ X88 @ X87 @ (comp @ X89 @ X90)))) | ~ (((X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) = $true)) | ~ ! [X91 : term,X92 : term] : (($true = ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id))) | ~ (((X82 @ id @ X91 @ id)) = $true) | ~ (((X82 @ id @ X92 @ id)) = $true)) | ~ (((X82 @ id @ X81 @ id)) = $true) | ~ ($true = ((X82 @ id @ X80 @ id)))) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X95 : subst,X96 : subst,X97 : term,X98 : subst] : ((((X94 @ X95 @ X97 @ (comp @ X98 @ X96))) = $true) | ~ (((X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) = $true)) | ~ ! [X99 : term] : ((((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id)) = $true) | ~ (((X94 @ id @ X99 @ id)) = $true)) | ($true = ((X94 @ id @ (lam @ X93) @ id))) | ~ ! [X100 : (subst > term > term)] : (($true = ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id))) | ~ ! [X101 : term,X103 : subst,X102 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) = ((sub @ (X100 @ X102 @ X101) @ X103))) | ~ ! [X104 : term] : (~ (((X94 @ id @ X104 @ id)) = $true) | (((X94 @ id @ (X100 @ id @ X104) @ id)) = $true))) | ~ ! [X105 : subst,X106 : subst,X107 : term,X108 : subst] : (($true = ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106))) | ~ (((X94 @ X105 @ X107 @ (comp @ X108 @ X106))) = $true))) => ! [X109 : (subst > term > subst > $o),X110 : term] : ((((X109 @ id @ X110 @ id)) = $true) | ~ ! [X111 : subst,X112 : subst,X113 : subst,X114 : term] : ((((X109 @ X113 @ X114 @ (comp @ X112 @ X111))) = $true) | ~ (((X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) = $true)) | ~ ! [X115 : (subst > term > term)] : (~ ! [X116 : term] : (~ (((X109 @ id @ X116 @ id)) = $true) | ($true = ((X109 @ id @ (X115 @ id @ X116) @ id)))) | ~ ! [X119 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) | (((X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true)) | ~ ! [X120 : term,X121 : term] : ((((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id)) = $true) | ~ (((X109 @ id @ X121 @ id)) = $true) | ~ (((X109 @ id @ X120 @ id)) = $true)) | ~ ! [X122 : subst,X123 : subst,X124 : term,X125 : subst] : (($true = ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125))) | ~ ($true = ((X109 @ X123 @ X124 @ (comp @ X122 @ X125))))) | ~ ! [X126 : term] : ((((X109 @ id @ X126 @ id)) = $true) | ~ ($true = ((var @ (sub @ X126 @ id)))))))))) & ((induction2lem = $true) <=> ! [X127 : (term > $o),X128 : subst,X129 : term] : (~ ! [X130 : term] : (~ ! [X131 : term] : (~ (((X127 @ X131)) = $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) | ($true = ((X127 @ (lam @ X130))))) | ~ ! [X132 : term] : ((((X127 @ (sub @ X132 @ X128))) = $true) | ~ (((var @ X132)) = $true)) | (((X127 @ (sub @ X129 @ X128))) = $true) | ~ ! [X133 : term,X134 : term] : (~ (((X127 @ X133)) = $true) | ~ ($true = ((X127 @ X134))) | (((X127 @ (ap @ X134 @ X133))) = $true)))) & (! [X136 : term,X135 : (term > $o),X137 : subst] : ~ ! [X138 : (term > $o)] : ~ ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & ! [X140 : d_subst,X141 : d_subst] : ((((d2subst @ X140)) = ((d2subst @ X141))) => (X140 = X141)) & (pushprop_lem3v2 = $true) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) <=> (termmset = $true)) & (induction2lem_gthm = $true) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> (axshiftcons = $true)) & (! [X145 : term] : ~ ! [X146 : (subst > term > term)] : (((X146 @ sh @ one)) != ((sub @ X145 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (apnotvar = $true) & (! [X147 : (subst > term > subst > $o)] : ~ ! [X148 : (term > $o)] : ~ ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149))) <=> (hoasinduction_lem0 = $true)) & (! [X150 : term] : ~ ! [X151 : (subst > term > term)] : ~ ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153))) <=> (hoasinduction_lem3v2_f = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axabs = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X154 : term,X155 : (term > $o),X156 : term,X157 : (subst > term > subst > $o)] : (~ ! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : ((((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158)) = $true) | ~ ($true = ((X157 @ X160 @ X161 @ (comp @ X159 @ X158))))) | ~ ! [X162 : term,X163 : term] : (~ (((X157 @ id @ X162 @ id)) = $true) | ~ (((X157 @ id @ X163 @ id)) = $true) | (((X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true)) | ~ ! [X164 : term] : (((X155 @ X164)) = ((X157 @ id @ X164 @ id))) | ~ ! [X165 : subst,X166 : term,X167 : subst,X168 : subst] : (~ (((X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165)) = $true) | (((X157 @ X167 @ X166 @ (comp @ X168 @ X165))) = $true)) | ~ (((X155 @ X154)) = $true) | (((X155 @ (ap @ X154 @ X156))) = $true) | ~ ($true = ((X155 @ X156))))) & ((termmset_lthm = $true) <=> (! [X169 : term] : (((sub @ X169 @ id)) = X169) => ! [X170 : term] : (((sub @ X170 @ id)) = X170))) & ((! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : term,X173 : (subst > term > subst > $o)] : (~ ! [X174 : (subst > term > term)] : (~ ! [X177 : term,X175 : subst,X176 : subst] : (((sub @ (X174 @ X175 @ X177) @ X176)) = ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176)))) | ($true = ((X173 @ id @ (lam @ (X174 @ sh @ one)) @ id))) | ~ ! [X178 : term] : ((((X173 @ id @ (X174 @ id @ X178) @ id)) = $true) | ~ (((X173 @ id @ X178 @ id)) = $true))) | ~ ! [X179 : term] : ((((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id)) = $true) | ~ ($true = ((X173 @ id @ X179 @ id)))) | ($true = ((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)))) => ! [X180 : term,X181 : (subst > term > subst > $o)] : ((((X181 @ id @ (lam @ X180) @ id)) = $true) | ~ ! [X182 : (subst > term > term)] : (($true = ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id))) | ~ ! [X183 : term] : (~ (((X181 @ id @ X183 @ id)) = $true) | (((X181 @ id @ (X182 @ id @ X183) @ id)) = $true)) | ~ ! [X185 : subst,X186 : term,X184 : subst] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185))))) | ~ ! [X187 : term] : (($true = ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id))) | ~ (((X181 @ id @ X187 @ id)) = $true))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X188 : (subst > term > subst > $o)] : ~ ! [X189 : (term > $o)] : ~ ! [X190 : term] : (((X188 @ id @ X190 @ id)) = ((X189 @ X190))) => (! [X191 : (term > $o),X192 : term] : (~ ! [X193 : term] : ((((X191 @ X193)) = $true) | ~ (((var @ X193)) = $true)) | (((X191 @ X192)) = $true) | ~ ! [X194 : term,X195 : term] : (~ ($true = ((X191 @ X194))) | ~ (((X191 @ X195)) = $true) | (((X191 @ (ap @ X195 @ X194))) = $true)) | ~ ! [X196 : term] : (~ ! [X197 : term] : (~ ($true = ((X191 @ X197))) | (((X191 @ (sub @ X196 @ (push @ X197 @ id)))) = $true)) | ($true = ((X191 @ (lam @ X196)))))) => (! [X198 : term] : (((sub @ X198 @ id)) = X198) => (! [X199 : (term > $o),X200 : term,X201 : (subst > term > subst > $o)] : (~ ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) | ~ ! [X203 : (subst > term > term)] : (~ ! [X204 : term] : ((((X201 @ id @ (X203 @ id @ X204) @ id)) = $true) | ~ ($true = ((X201 @ id @ X204 @ id)))) | (((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id)) = $true) | ~ ! [X206 : subst,X205 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) = ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206))))) | ~ ! [X208 : term] : (~ (((X199 @ X208)) = $true) | (((X199 @ (sub @ X200 @ (push @ X208 @ id)))) = $true)) | ($true = ((X199 @ (lam @ X200))))) => ! [X209 : term,X210 : (subst > term > subst > $o)] : (~ ! [X211 : term,X212 : term] : (~ (((X210 @ id @ X211 @ id)) = $true) | ~ ($true = ((X210 @ id @ X212 @ id))) | ($true = ((X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id)))) | (((X210 @ id @ X209 @ id)) = $true) | ~ ! [X213 : (subst > term > term)] : (~ ! [X214 : term] : (($true = ((X210 @ id @ (X213 @ id @ X214) @ id))) | ~ (((X210 @ id @ X214 @ id)) = $true)) | ~ ! [X216 : subst,X217 : term,X215 : subst] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) | (((X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)) = $true)))))))) & ! [X218 : d_term] : (d_one = X218) & (hoasapnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X221 : term,X219 : term,X220 : term,X222 : term] : ((X219 = X222) | (((ap @ X220 @ X222)) != ((ap @ X221 @ X219)))) => ! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))))) & (hoasinduction_lem1 = $true) & (! [X227 : (term > $o),X228 : term] : (~ ! [X229 : term,X230 : term] : (~ (((X227 @ X230)) = $true) | ~ (((X227 @ X229)) = $true) | (((X227 @ (ap @ X229 @ X230))) = $true)) | ~ ! [X231 : term] : (~ (((X227 @ X231)) = $true) | ($true = ((X227 @ (lam @ X231))))) | ~ ! [X232 : term] : ((((X227 @ X232)) = $true) | ~ ($true = ((var @ X232)))) | (((X227 @ X228)) = $true)) <=> (induction = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X233 : (term > $o),X234 : term,X235 : subst,X236 : (term > $o)] : ((((X233 @ one)) = $true) | ~ ! [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X233 @ X237))) | ~ (((X236 @ X234)) = $true))) & (hoasapnotvar = $true) & ((! [X239 : subst,X238 : term] : (((sub @ one @ (push @ X238 @ X239))) = X238) => ! [X240 : subst,X241 : term,X242 : (term > $o),X243 : (term > $o)] : (~ ! [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) = ((X243 @ X244))) | ~ (((X242 @ X241)) = $true) | ($true = ((X243 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & (hoasinduction_lem2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X250 : term,X251 : term] : ((((lam @ X251)) != ((lam @ X250))) | (X250 = X251)) <=> (laminj = $true)) & (! [X252 : term,X253 : (subst > term > subst > $o)] : (~ ! [X254 : term,X255 : term] : ((((X253 @ id @ (ap @ (sub @ X254 @ id) @ X255) @ id)) = $true) | ~ (((X253 @ id @ X254 @ id)) = $true) | ~ (((X253 @ id @ X255 @ id)) = $true)) | ~ ! [X256 : (subst > term > term)] : (~ ! [X257 : term] : ((((X253 @ id @ (X256 @ id @ X257) @ id)) = $true) | ~ ($true = ((X253 @ id @ X257 @ id)))) | (((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id)) = $true) | ~ ! [X258 : subst,X259 : term,X260 : subst] : (((sub @ (X256 @ X258 @ X259) @ X260)) = ((X256 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260))))) | (((X253 @ id @ X252 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X261 : term] : (((sub @ X261 @ id)) = X261) => (! [X262 : (subst > term > subst > $o),X263 : term] : (~ ! [X264 : (subst > term > term)] : (~ ! [X265 : term,X266 : subst,X267 : subst] : (((sub @ (X264 @ X267 @ X265) @ X266)) = ((X264 @ (comp @ X267 @ X266) @ (sub @ X265 @ X266)))) | (((X262 @ id @ (lam @ (X264 @ sh @ one)) @ id)) = $true) | ~ ! [X268 : term] : (~ ($true = ((X262 @ id @ X268 @ id))) | (((X262 @ id @ (X264 @ id @ X268) @ id)) = $true))) | ~ ! [X269 : term] : (~ (((X262 @ id @ X269 @ id)) = $true) | (((X262 @ id @ (sub @ X263 @ (push @ X269 @ id)) @ id)) = $true)) | (((X262 @ id @ (lam @ (sub @ X263 @ (push @ one @ sh))) @ id)) = $true)) => ! [X270 : term,X271 : (subst > term > subst > $o)] : (~ ! [X272 : subst,X273 : subst,X274 : subst,X275 : term] : ((((X271 @ (comp @ X273 @ X272) @ (sub @ X275 @ X272) @ X274)) = $true) | ~ ($true = ((X271 @ X273 @ X275 @ (comp @ X272 @ X274))))) | (((X271 @ id @ (lam @ X270) @ id)) = $true) | ~ ! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : (~ ($true = ((X271 @ (comp @ X278 @ X276) @ (sub @ X279 @ X276) @ X277))) | ($true = ((X271 @ X278 @ X279 @ (comp @ X276 @ X277))))) | ~ ! [X280 : (subst > term > term)] : ((((X271 @ id @ (lam @ (X280 @ sh @ one)) @ id)) = $true) | ~ ! [X281 : term] : ((((X271 @ id @ (X280 @ id @ X281) @ id)) = $true) | ~ (((X271 @ id @ X281 @ id)) = $true)) | ~ ! [X282 : term,X283 : subst,X284 : subst] : (((sub @ (X280 @ X283 @ X282) @ X284)) = ((X280 @ (comp @ X283 @ X284) @ (sub @ X282 @ X284))))) | ~ ! [X285 : term] : (~ ($true = ((X271 @ id @ X285 @ id))) | (((X271 @ id @ (sub @ X270 @ (push @ X285 @ id)) @ id)) = $true)))))) & (((d2subst @ d_id)) = sh) & ((axidr = $true) <=> ! [X286 : subst] : (((comp @ X286 @ id)) = X286)) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & ! [X287 : d_subst] : (d_id = X287) & (pushprop_lthm_orig = $true) & (hoaslamnotap_lthm = $true) & ((hoaslaminj = $true) <=> ! [X288 : subst,X289 : (subst > term > term),X290 : term,X291 : (subst > term > term)] : (~ ! [X292 : subst,X293 : subst,X294 : term] : (((sub @ (X289 @ X292 @ X294) @ X293)) = ((X289 @ (comp @ X292 @ X293) @ (sub @ X294 @ X293)))) | ~ ! [X295 : subst,X296 : term,X297 : subst] : (((sub @ (X291 @ X295 @ X296) @ X297)) = ((X291 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)))) | (((lam @ (X291 @ sh @ one))) != ((lam @ (X289 @ sh @ one)))) | (((X291 @ X288 @ X290)) = ((X289 @ X288 @ X290))))) & (pushprop_lem3v2_lthm = $true) & (! [X298 : term] : ~ ! [X299 : (subst > term > term)] : (((sub @ X298 @ (push @ one @ sh))) != ((X299 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (induction2_gthm = $true) & ((induction2 = $true) <=> ! [X300 : (term > $o),X301 : term] : (($true = ((X300 @ X301))) | ~ ! [X302 : term] : ((((X300 @ X302)) = $true) | ~ (((var @ X302)) = $true)) | ~ ! [X303 : term,X304 : term] : (~ (((X300 @ X304)) = $true) | ($true = ((X300 @ (ap @ X303 @ X304)))) | ~ (((X300 @ X303)) = $true)) | ~ ! [X305 : term] : ((((X300 @ (lam @ X305))) = $true) | ~ ! [X306 : term] : ((((X300 @ (sub @ X305 @ (push @ X306 @ id)))) = $true) | ~ (((X300 @ X306)) = $true))))) & (hoasinduction_lem2_lthm = $true) & (axapp = $true) & ((hoasinduction_lem3 = $true) <=> ! [X307 : term,X308 : (subst > term > subst > $o)] : (~ ! [X309 : term] : ((((X308 @ id @ (sub @ X307 @ (push @ X309 @ id)) @ id)) = $true) | ~ (((X308 @ id @ X309 @ id)) = $true)) | ~ ! [X310 : subst,X311 : subst,X312 : term,X313 : subst] : ((((X308 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313) @ X310)) = $true) | ~ (((X308 @ X311 @ X312 @ (comp @ X313 @ X310))) = $true)) | ~ ! [X314 : term,X315 : subst,X316 : subst,X317 : subst] : (($true = ((X308 @ X316 @ X314 @ (comp @ X315 @ X317)))) | ~ ($true = ((X308 @ (comp @ X316 @ X315) @ (sub @ X314 @ X315) @ X317)))) | (((X308 @ id @ (lam @ X307) @ id)) = $true) | ~ ! [X318 : (subst > term > term)] : (~ ! [X319 : subst,X320 : subst,X321 : term] : (((X318 @ (comp @ X319 @ X320) @ (sub @ X321 @ X320))) = ((sub @ (X318 @ X319 @ X321) @ X320))) | ($true = ((X308 @ id @ (lam @ (X318 @ sh @ one)) @ id))) | ~ ! [X322 : term] : (~ (((X308 @ id @ X322 @ id)) = $true) | (((X308 @ id @ (X318 @ id @ X322) @ id)) = $true))))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X323 : term,X324 : subst] : (((sub @ one @ (push @ X323 @ X324))) = X323) => (! [X325 : term,X326 : subst] : (((comp @ sh @ (push @ X325 @ X326))) = X326) => (! [X327 : subst] : (((comp @ X327 @ id)) = X327) => (! [X328 : (term > $o),X329 : term] : (($true = ((X328 @ X329))) | ~ ! [X330 : term] : ((((X328 @ (lam @ X330))) = $true) | ~ (((X328 @ X330)) = $true)) | ~ ! [X331 : term,X332 : term] : (~ (((X328 @ X331)) = $true) | (((X328 @ (ap @ X332 @ X331))) = $true) | ~ (((X328 @ X332)) = $true)) | ~ ! [X333 : term] : (~ (((var @ X333)) = $true) | (((X328 @ X333)) = $true))) => ! [X334 : term,X335 : subst,X336 : (term > $o)] : (~ ! [X337 : term] : (~ (((var @ X337)) = $true) | (((X336 @ (sub @ X337 @ X335))) = $true)) | (((X336 @ (sub @ X334 @ X335))) = $true) | ~ ! [X338 : term,X339 : term] : (~ ($true = ((X336 @ X339))) | ~ (((X336 @ X338)) = $true) | (((X336 @ (ap @ X339 @ X338))) = $true)) | ~ ! [X340 : term] : (~ ! [X341 : term] : ((((X336 @ (sub @ X340 @ (push @ X341 @ id)))) = $true) | ~ (((X336 @ X341)) = $true)) | (((X336 @ (lam @ X340))) = $true)))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj1_gthm = $true) & (hoasapnotvar_lthm = $true) & ((! [X342 : subst,X343 : term] : (((sub @ one @ (push @ X343 @ X342))) = X343) => (! [X344 : term,X345 : subst] : (((comp @ sh @ (push @ X344 @ X345))) = X345) => ! [X346 : term,X347 : subst,X348 : term,X349 : (term > $o),X350 : (term > $o)] : (~ ($true = ((X350 @ X348))) | (((X349 @ (sub @ X348 @ (push @ X346 @ X347)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((! [X351 : term] : ~ ! [X352 : (subst > term > term)] : ~ ! [X353 : term,X354 : subst] : (((X352 @ X354 @ X353)) = ((sub @ X351 @ (push @ X353 @ X354)))) => (! [X355 : term] : (((sub @ X355 @ id)) = X355) => ! [X356 : (term > $o),X357 : (subst > term > subst > $o),X358 : term] : (~ ! [X359 : (subst > term > term)] : ((((X357 @ id @ (lam @ (X359 @ sh @ one)) @ id)) = $true) | ~ ! [X360 : subst,X361 : subst,X362 : term] : (((X359 @ (comp @ X360 @ X361) @ (sub @ X362 @ X361))) = ((sub @ (X359 @ X360 @ X362) @ X361))) | ~ ! [X363 : term] : (~ (((X357 @ id @ X363 @ id)) = $true) | (((X357 @ id @ (X359 @ id @ X363) @ id)) = $true))) | ~ ! [X364 : term] : (~ (((X356 @ X364)) = $true) | (((X356 @ (sub @ X358 @ (push @ X364 @ id)))) = $true)) | ~ ! [X365 : term] : (((X356 @ X365)) = ((X357 @ id @ X365 @ id))) | ($true = ((X356 @ (lam @ X358))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X366 : (subst > term > subst > $o)] : ~ ! [X367 : (term > $o)] : ~ ! [X368 : term] : (((X367 @ X368)) = ((X366 @ id @ X368 @ id))) => (! [X369 : (term > $o),X370 : term] : (~ ! [X371 : term] : ((((X369 @ (lam @ X371))) = $true) | ~ ! [X372 : term] : (~ (((X369 @ X372)) = $true) | ($true = ((X369 @ (sub @ X371 @ (push @ X372 @ id))))))) | ~ ! [X373 : term,X374 : term] : (~ (((X369 @ X374)) = $true) | ($true = ((X369 @ (ap @ X374 @ X373)))) | ~ (((X369 @ X373)) = $true)) | (((X369 @ X370)) = $true) | ~ ! [X375 : term] : (~ (((var @ X375)) = $true) | (((X369 @ X375)) = $true))) => (! [X376 : term] : (((sub @ X376 @ id)) = X376) => (! [X377 : term,X378 : (subst > term > subst > $o),X379 : (term > $o)] : (~ ! [X380 : term] : (~ (((X379 @ X380)) = $true) | (((X379 @ (sub @ X377 @ (push @ X380 @ id)))) = $true)) | ~ ! [X381 : (subst > term > term)] : (~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X381 @ X382 @ X383) @ X384)) = ((X381 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)))) | ~ ! [X385 : term] : (~ ($true = ((X378 @ id @ X385 @ id))) | (((X378 @ id @ (X381 @ id @ X385) @ id)) = $true)) | (((X378 @ id @ (lam @ (X381 @ sh @ one)) @ id)) = $true)) | ($true = ((X379 @ (lam @ X377)))) | ~ ! [X386 : term] : (((X379 @ X386)) = ((X378 @ id @ X386 @ id)))) => ! [X387 : term,X388 : (subst > term > subst > $o)] : ((((X388 @ id @ X387 @ id)) = $true) | ~ ! [X389 : subst,X390 : subst,X391 : subst,X392 : term] : (~ (((X388 @ (comp @ X391 @ X389) @ (sub @ X392 @ X389) @ X390)) = $true) | (((X388 @ X391 @ X392 @ (comp @ X389 @ X390))) = $true)) | ~ ! [X393 : term] : (($true = ((X388 @ id @ X393 @ id))) | ~ (((var @ (sub @ X393 @ id))) = $true)) | ~ ! [X394 : (subst > term > term)] : (~ ! [X395 : term] : ((((X388 @ id @ (X394 @ id @ X395) @ id)) = $true) | ~ (((X388 @ id @ X395 @ id)) = $true)) | (((X388 @ id @ (lam @ (X394 @ sh @ one)) @ id)) = $true) | ~ ! [X396 : subst,X397 : subst,X398 : term] : (((sub @ (X394 @ X397 @ X398) @ X396)) = ((X394 @ (comp @ X397 @ X396) @ (sub @ X398 @ X396))))) | ~ ! [X399 : subst,X400 : subst,X401 : subst,X402 : term] : ((((X388 @ (comp @ X401 @ X400) @ (sub @ X402 @ X400) @ X399)) = $true) | ~ ($true = ((X388 @ X401 @ X402 @ (comp @ X400 @ X399))))) | ~ ! [X403 : term,X404 : term] : (~ (((X388 @ id @ X403 @ id)) = $true) | ~ (((X388 @ id @ X404 @ id)) = $true) | ($true = ((X388 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id))))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X405 : term] : (((sub @ X405 @ id)) = X405) <=> (axvarid = $true)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) <=> ! [X406 : term,X407 : term,X408 : term,X409 : term] : ((((ap @ X409 @ X408)) != ((ap @ X407 @ X406))) | (X407 = X409))) & (! [X410 : term,X411 : (subst > term > subst > $o)] : (~ ! [X412 : term] : ((((X411 @ id @ (sub @ X410 @ (push @ X412 @ id)) @ id)) = $true) | ~ ($true = ((X411 @ id @ X412 @ id)))) | ($true = ((X411 @ id @ (lam @ (sub @ X410 @ (push @ one @ sh))) @ id))) | ~ ! [X413 : (subst > term > term)] : (~ ! [X414 : term] : ((((X411 @ id @ (X413 @ id @ X414) @ id)) = $true) | ~ (((X411 @ id @ X414 @ id)) = $true)) | (((X411 @ id @ (lam @ (X413 @ sh @ one)) @ id)) = $true) | ~ ! [X415 : subst,X416 : subst,X417 : term] : (((sub @ (X413 @ X416 @ X417) @ X415)) = ((X413 @ (comp @ X416 @ X415) @ (sub @ X417 @ X415)))))) <=> (hoasinduction_lem3aa = $true)) & (ulamvarsh = $true) & ~ (lamnotap = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X418 : subst] : (((comp @ id @ X418)) = X418) => (! [X419 : subst] : (((comp @ X419 @ id)) = X419) => (! [X420 : subst] : (((comp @ id @ X420)) = X420) & ! [X421 : subst] : (((comp @ X421 @ id)) = X421))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X422 : term,X423 : term,X424 : (subst > term > subst > $o)] : (~ (((X424 @ id @ X422 @ id)) = $true) | ~ ! [X425 : subst,X426 : term,X427 : subst,X428 : subst] : (~ (((X424 @ X428 @ X426 @ (comp @ X425 @ X427))) = $true) | (((X424 @ (comp @ X428 @ X425) @ (sub @ X426 @ X425) @ X427)) = $true)) | ~ ! [X429 : subst,X430 : subst,X431 : term,X432 : subst] : (($true = ((X424 @ X429 @ X431 @ (comp @ X432 @ X430)))) | ~ (((X424 @ (comp @ X429 @ X432) @ (sub @ X431 @ X432) @ X430)) = $true)) | ~ (((X424 @ id @ X423 @ id)) = $true) | (((X424 @ id @ (ap @ X423 @ X422) @ id)) = $true) | ~ ! [X433 : term,X434 : term] : (~ (((X424 @ id @ X433 @ id)) = $true) | (((X424 @ id @ (ap @ (sub @ X434 @ id) @ X433) @ id)) = $true) | ~ (((X424 @ id @ X434 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & (! [X435 : (subst > term > term),X436 : term,X437 : term] : ((((ap @ (sub @ X437 @ id) @ X436)) != ((lam @ (X435 @ sh @ one)))) | ~ ! [X438 : term,X439 : subst,X440 : subst] : (((X435 @ (comp @ X439 @ X440) @ (sub @ X438 @ X440))) = ((sub @ (X435 @ X439 @ X438) @ X440)))) <=> (hoaslamnotap = $true)) & (! [X441 : (subst > term > subst > $o),X442 : term,X443 : (term > $o)] : (~ ! [X444 : subst,X445 : subst,X446 : term,X447 : subst] : ((((X441 @ X447 @ X446 @ (comp @ X444 @ X445))) = $true) | ~ (((X441 @ (comp @ X447 @ X444) @ (sub @ X446 @ X444) @ X445)) = $true)) | ~ ! [X448 : subst,X449 : subst,X450 : term,X451 : subst] : (~ ($true = ((X441 @ X448 @ X450 @ (comp @ X451 @ X449)))) | (((X441 @ (comp @ X448 @ X451) @ (sub @ X450 @ X451) @ X449)) = $true)) | ~ ! [X452 : term] : ((((X443 @ (sub @ X442 @ (push @ X452 @ id)))) = $true) | ~ (((X443 @ X452)) = $true)) | ~ ! [X453 : (subst > term > term)] : (~ ! [X454 : term] : (($true = ((X441 @ id @ (X453 @ id @ X454) @ id))) | ~ (((X441 @ id @ X454 @ id)) = $true)) | ($true = ((X441 @ id @ (lam @ (X453 @ sh @ one)) @ id))) | ~ ! [X455 : term,X456 : subst,X457 : subst] : (((X453 @ (comp @ X457 @ X456) @ (sub @ X455 @ X456))) = ((sub @ (X453 @ X457 @ X455) @ X456)))) | ~ ! [X458 : term] : (((X443 @ X458)) = ((X441 @ id @ X458 @ id))) | ($true = ((X443 @ (lam @ X442))))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((axscons = $true) <=> ! [X459 : subst] : (((push @ (sub @ one @ X459) @ (comp @ sh @ X459))) = X459)) & (termmset_gthm = $true) & ~ (ulamvar1 = $true) & ((substmonoid = $true) <=> (! [X460 : subst] : (((comp @ id @ X460)) = X460) & ! [X461 : subst] : (((comp @ X461 @ id)) = X461))) & (lamnotvar = $true) & (axassoc = $true) & (! [X462 : (subst > term > subst > $o)] : ~ ! [X463 : (term > $o)] : ~ ! [X464 : term] : (((X462 @ id @ X464 @ id)) = ((X463 @ X464))) <=> (hoasinduction_lem0_lthm = $true)) & (! [X465 : term,X466 : term,X467 : term,X468 : term] : ((X465 = X466) | (((ap @ (sub @ X466 @ id) @ X467)) != ((ap @ (sub @ X465 @ id) @ X468)))) <=> (hoasapinj1 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X469 : term] : (((sub @ X469 @ id)) = X469) => ! [X470 : (term > $o),X471 : term,X472 : (subst > term > subst > $o)] : (~ ! [X473 : subst,X474 : term,X475 : subst,X476 : subst] : (($true = ((X472 @ (comp @ X475 @ X473) @ (sub @ X474 @ X473) @ X476))) | ~ (((X472 @ X475 @ X474 @ (comp @ X473 @ X476))) = $true)) | ~ ! [X477 : (subst > term > term)] : ((((X472 @ id @ (lam @ (X477 @ sh @ one)) @ id)) = $true) | ~ ! [X478 : term,X479 : subst,X480 : subst] : (((sub @ (X477 @ X480 @ X478) @ X479)) = ((X477 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479)))) | ~ ! [X481 : term] : (~ (((X472 @ id @ X481 @ id)) = $true) | (((X472 @ id @ (X477 @ id @ X481) @ id)) = $true))) | (((X470 @ (lam @ X471))) = $true) | ~ ! [X482 : term,X483 : subst,X484 : subst,X485 : subst] : (~ (((X472 @ (comp @ X484 @ X485) @ (sub @ X482 @ X485) @ X483)) = $true) | (((X472 @ X484 @ X482 @ (comp @ X485 @ X483))) = $true)) | ~ ! [X486 : term] : ((((X470 @ (sub @ X471 @ (push @ X486 @ id)))) = $true) | ~ (((X470 @ X486)) = $true)) | ~ ! [X487 : term] : (((X472 @ id @ X487 @ id)) = ((X470 @ X487)))))) & (axvarshift = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X490 : (subst > term > subst > $o),X491 : term] : (~ ! [X492 : term] : (~ (((X490 @ id @ X492 @ id)) = $true) | ($true = ((X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id)))) | ($true = ((X490 @ id @ (lam @ (sub @ X491 @ (push @ one @ sh))) @ id))) | ~ ! [X493 : (subst > term > term)] : ((((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id)) = $true) | ~ ! [X494 : term,X495 : subst,X496 : subst] : (((sub @ (X493 @ X495 @ X494) @ X496)) = ((X493 @ (comp @ X495 @ X496) @ (sub @ X494 @ X496)))) | ~ ! [X497 : term] : ((((X490 @ id @ (X493 @ id @ X497) @ id)) = $true) | ~ ($true = ((X490 @ id @ X497 @ id)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axvarcons = $true) <=> ! [X498 : term,X499 : subst] : (((sub @ one @ (push @ X498 @ X499))) = X498)) & (! [X500 : term,X501 : term,X502 : term,X503 : term] : ((((ap @ (sub @ X501 @ id) @ X502)) != ((ap @ (sub @ X503 @ id) @ X500))) | (X500 = X502)) <=> (hoasapinj2 = $true)) & (! [X504 : (subst > term > subst > $o),X505 : term] : (~ ! [X506 : term] : (~ ($true = ((X504 @ id @ X506 @ id))) | ($true = ((X504 @ id @ (sub @ X505 @ (push @ X506 @ id)) @ id)))) | ~ ! [X507 : (subst > term > term)] : ((((X504 @ id @ (lam @ (X507 @ sh @ one)) @ id)) = $true) | ~ ! [X508 : subst,X509 : subst,X510 : term] : (((X507 @ (comp @ X508 @ X509) @ (sub @ X510 @ X509))) = ((sub @ (X507 @ X508 @ X510) @ X509))) | ~ ! [X511 : term] : (~ (((X504 @ id @ X511 @ id)) = $true) | (((X504 @ id @ (X507 @ id @ X511) @ id)) = $true))) | (((X504 @ id @ (lam @ X505) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X512 : (term > $o),X513 : term,X514 : (subst > term > subst > $o)] : (~ ! [X515 : (subst > term > term)] : (~ ! [X516 : subst,X517 : subst,X518 : term] : (((sub @ (X515 @ X516 @ X518) @ X517)) = ((X515 @ (comp @ X516 @ X517) @ (sub @ X518 @ X517)))) | ~ ! [X519 : term] : (($true = ((X514 @ id @ (X515 @ id @ X519) @ id))) | ~ ($true = ((X514 @ id @ X519 @ id)))) | (((X514 @ id @ (lam @ (X515 @ sh @ one)) @ id)) = $true)) | (((X512 @ (lam @ X513))) = $true) | ~ ! [X520 : term] : ((((X512 @ (sub @ X513 @ (push @ X520 @ id)))) = $true) | ~ (((X512 @ X520)) = $true)) | ~ ! [X521 : term] : (((X514 @ id @ X521 @ id)) = ((X512 @ X521))))) & (! [X522 : term,X523 : (term > $o),X524 : subst,X525 : (term > $o),X526 : term] : (~ (((X525 @ X526)) = $true) | (((X523 @ (sub @ X526 @ (push @ X522 @ X524)))) = $true)) <=> (pushprop_lem1 = $true)) & ((hoasinduction = $true) <=> ! [X527 : term,X528 : (subst > term > subst > $o)] : (~ ! [X529 : subst,X530 : subst,X531 : term,X532 : subst] : (~ (((X528 @ X530 @ X531 @ (comp @ X532 @ X529))) = $true) | (((X528 @ (comp @ X530 @ X532) @ (sub @ X531 @ X532) @ X529)) = $true)) | ~ ! [X533 : (subst > term > term)] : (~ ! [X534 : subst,X535 : term,X536 : subst] : (((sub @ (X533 @ X534 @ X535) @ X536)) = ((X533 @ (comp @ X534 @ X536) @ (sub @ X535 @ X536)))) | (((X528 @ id @ (lam @ (X533 @ sh @ one)) @ id)) = $true) | ~ ! [X537 : term] : ((((X528 @ id @ (X533 @ id @ X537) @ id)) = $true) | ~ ($true = ((X528 @ id @ X537 @ id))))) | ~ ! [X538 : term] : (~ ($true = ((var @ (sub @ X538 @ id)))) | ($true = ((X528 @ id @ X538 @ id)))) | ($true = ((X528 @ id @ X527 @ id))) | ~ ! [X539 : subst,X540 : subst,X541 : subst,X542 : term] : (~ (((X528 @ (comp @ X541 @ X540) @ (sub @ X542 @ X540) @ X539)) = $true) | ($true = ((X528 @ X541 @ X542 @ (comp @ X540 @ X539))))) | ~ ! [X543 : term,X544 : term] : ((((X528 @ id @ (ap @ (sub @ X544 @ id) @ X543) @ id)) = $true) | ~ (((X528 @ id @ X543 @ id)) = $true) | ~ (((X528 @ id @ X544 @ 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)))))))))))))) & (pushprop_lem1_gthm = $true) & (axmap = $true)),
% 14.62/2.51 inference(fool_elimination,[],[f6])).
% 14.62/2.51 thf(f8,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ 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]: (Y0 @ id @ Y1 @ id)))))))))),
% 14.62/2.51 inference(flattening,[],[f5])).
% 14.62/2.51 thf(f9,plain,(
% 14.62/2.51 ((induction2_lthm = $true) <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => (! [X1 : (term > $o),X2 : term,X3 : subst] : (~ ! [X4 : term,X5 : term] : (~ ($true = ((X1 @ X5))) | ($true = ((X1 @ (ap @ X4 @ X5)))) | ~ (((X1 @ X4)) = $true)) | (((X1 @ (sub @ X2 @ X3))) = $true) | ~ ! [X6 : term] : (~ ! [X7 : term] : ((((X1 @ (sub @ X6 @ (push @ X7 @ id)))) = $true) | ~ (((X1 @ X7)) = $true)) | (((X1 @ (lam @ X6))) = $true)) | ~ ! [X8 : term] : ((((X1 @ (sub @ X8 @ X3))) = $true) | ~ (((var @ X8)) = $true))) => ! [X9 : term,X10 : (term > $o)] : (~ ! [X11 : term] : ((((X10 @ (lam @ X11))) = $true) | ~ ! [X12 : term] : ((((X10 @ (sub @ X11 @ (push @ X12 @ id)))) = $true) | ~ (((X10 @ X12)) = $true))) | ~ ! [X13 : term,X14 : term] : (~ ($true = ((X10 @ X14))) | ($true = ((X10 @ (ap @ X14 @ X13)))) | ~ (((X10 @ X13)) = $true)) | (((X10 @ X9)) = $true) | ~ ! [X15 : term] : ((((X10 @ X15)) = $true) | ~ (((var @ X15)) = $true)))))) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & (hoaslamnotvar = $true) & ! [X19 : d_term,X18 : d_term] : ((((d2term @ X18)) = ((d2term @ X19))) => (X18 = X19)) & (axclos = $true) & (! [X20 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasapinj2_gthm = $true) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((! [X24 : term] : (((sub @ X24 @ id)) = X24) => (! [X26 : term,X27 : term,X28 : term,X25 : term] : ((X27 = X28) | (((ap @ X28 @ X26)) != ((ap @ X27 @ X25)))) => ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))))) <=> (hoasapinj1_lthm = $true)) & (! [X35 : term,X34 : (term > $o),X33 : subst] : ~ ! [X36 : (term > $o)] : ~ ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37))) <=> (pushprop_lem0 = $true)) & ((apinj2 = $true) <=> ! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & ((hoasinduction_lem3aaa = $true) <=> ! [X42 : (subst > term > subst > $o),X43 : term] : (~ ! [X44 : (subst > term > term),X45 : term] : ((((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id)) = $true) | ~ ! [X46 : term,X48 : subst,X47 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) | ~ ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49)))) | ~ ! [X52 : term] : ((((X42 @ id @ (X44 @ id @ X52) @ id)) = $true) | ~ (((X42 @ id @ X52 @ id)) = $true))) | ~ ! [X53 : term] : (~ (((X42 @ id @ X53 @ id)) = $true) | (((X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) = $true)) | (((X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id)) = $true))) & (one = ((d2term @ d_one))) & ((! [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) = X55) => (! [X57 : subst,X56 : term] : (((comp @ sh @ (push @ X56 @ X57))) = X57) => (! [X59 : term,X58 : term] : ((((lam @ X58)) != ((lam @ X59))) | (X58 = X59)) => ! [X63 : (subst > term > term),X61 : subst,X60 : term,X62 : (subst > term > term)] : ((((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | ~ ! [X69 : term,X67 : subst,X68 : subst] : (((sub @ (X63 @ X68 @ X69) @ X67)) = ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67)))) | ~ ! [X66 : subst,X64 : subst,X65 : term] : (((sub @ (X62 @ X66 @ X65) @ X64)) = ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))))))) <=> (hoaslaminj_lthm = $true)) & (pushprop_lem2v2 = $true) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> (shinj = $true)) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & ((hoasinduction_lthm = $true) <=> (! [X73 : (term > $o),X74 : term] : (~ ! [X75 : term] : (~ ! [X76 : term] : (~ (((X73 @ X76)) = $true) | (((X73 @ (sub @ X75 @ (push @ X76 @ id)))) = $true)) | (((X73 @ (lam @ X75))) = $true)) | ~ ! [X77 : term] : ((((X73 @ X77)) = $true) | ~ (((var @ X77)) = $true)) | ($true = ((X73 @ X74))) | ~ ! [X78 : term,X79 : term] : (~ (((X73 @ X79)) = $true) | (((X73 @ (ap @ X78 @ X79))) = $true) | ~ (((X73 @ X78)) = $true))) => (! [X80 : term,X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X83 : subst,X84 : subst,X85 : term,X86 : subst] : (~ (((X82 @ X84 @ X85 @ (comp @ X83 @ X86))) = $true) | (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) = $true)) | (((X82 @ id @ (ap @ X81 @ X80) @ id)) = $true) | ~ ! [X87 : term,X88 : subst,X89 : subst,X90 : subst] : (($true = ((X82 @ X88 @ X87 @ (comp @ X89 @ X90)))) | ~ (((X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) = $true)) | ~ ! [X91 : term,X92 : term] : (($true = ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id))) | ~ (((X82 @ id @ X91 @ id)) = $true) | ~ (((X82 @ id @ X92 @ id)) = $true)) | ~ (((X82 @ id @ X81 @ id)) = $true) | ~ ($true = ((X82 @ id @ X80 @ id)))) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X95 : subst,X96 : subst,X97 : term,X98 : subst] : ((((X94 @ X95 @ X97 @ (comp @ X98 @ X96))) = $true) | ~ (((X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) = $true)) | ~ ! [X99 : term] : ((((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id)) = $true) | ~ (((X94 @ id @ X99 @ id)) = $true)) | ($true = ((X94 @ id @ (lam @ X93) @ id))) | ~ ! [X100 : (subst > term > term)] : (($true = ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id))) | ~ ! [X101 : term,X103 : subst,X102 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) = ((sub @ (X100 @ X102 @ X101) @ X103))) | ~ ! [X104 : term] : (~ (((X94 @ id @ X104 @ id)) = $true) | (((X94 @ id @ (X100 @ id @ X104) @ id)) = $true))) | ~ ! [X105 : subst,X106 : subst,X107 : term,X108 : subst] : (($true = ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106))) | ~ (((X94 @ X105 @ X107 @ (comp @ X108 @ X106))) = $true))) => ! [X109 : (subst > term > subst > $o),X110 : term] : ((((X109 @ id @ X110 @ id)) = $true) | ~ ! [X111 : subst,X112 : subst,X113 : subst,X114 : term] : ((((X109 @ X113 @ X114 @ (comp @ X112 @ X111))) = $true) | ~ (((X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) = $true)) | ~ ! [X115 : (subst > term > term)] : (~ ! [X116 : term] : (~ (((X109 @ id @ X116 @ id)) = $true) | ($true = ((X109 @ id @ (X115 @ id @ X116) @ id)))) | ~ ! [X119 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) | (((X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true)) | ~ ! [X120 : term,X121 : term] : ((((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id)) = $true) | ~ (((X109 @ id @ X121 @ id)) = $true) | ~ (((X109 @ id @ X120 @ id)) = $true)) | ~ ! [X122 : subst,X123 : subst,X124 : term,X125 : subst] : (($true = ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125))) | ~ ($true = ((X109 @ X123 @ X124 @ (comp @ X122 @ X125))))) | ~ ! [X126 : term] : ((((X109 @ id @ X126 @ id)) = $true) | ~ ($true = ((var @ (sub @ X126 @ id)))))))))) & ((induction2lem = $true) <=> ! [X127 : (term > $o),X128 : subst,X129 : term] : (~ ! [X130 : term] : (~ ! [X131 : term] : (~ (((X127 @ X131)) = $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) | ($true = ((X127 @ (lam @ X130))))) | ~ ! [X132 : term] : ((((X127 @ (sub @ X132 @ X128))) = $true) | ~ (((var @ X132)) = $true)) | (((X127 @ (sub @ X129 @ X128))) = $true) | ~ ! [X133 : term,X134 : term] : (~ (((X127 @ X133)) = $true) | ~ ($true = ((X127 @ X134))) | (((X127 @ (ap @ X134 @ X133))) = $true)))) & (! [X136 : term,X135 : (term > $o),X137 : subst] : ~ ! [X138 : (term > $o)] : ~ ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & ! [X140 : d_subst,X141 : d_subst] : ((((d2subst @ X140)) = ((d2subst @ X141))) => (X140 = X141)) & (pushprop_lem3v2 = $true) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) <=> (termmset = $true)) & (induction2lem_gthm = $true) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> (axshiftcons = $true)) & (! [X145 : term] : ~ ! [X146 : (subst > term > term)] : (((X146 @ sh @ one)) != ((sub @ X145 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (apnotvar = $true) & (! [X147 : (subst > term > subst > $o)] : ~ ! [X148 : (term > $o)] : ~ ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149))) <=> (hoasinduction_lem0 = $true)) & (! [X150 : term] : ~ ! [X151 : (subst > term > term)] : ~ ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153))) <=> (hoasinduction_lem3v2_f = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axabs = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X154 : term,X155 : (term > $o),X156 : term,X157 : (subst > term > subst > $o)] : (~ ! [X158 : subst,X159 : subst,X160 : subst,X161 : term] : ((((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158)) = $true) | ~ ($true = ((X157 @ X160 @ X161 @ (comp @ X159 @ X158))))) | ~ ! [X162 : term,X163 : term] : (~ (((X157 @ id @ X162 @ id)) = $true) | ~ (((X157 @ id @ X163 @ id)) = $true) | (((X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true)) | ~ ! [X164 : term] : (((X155 @ X164)) = ((X157 @ id @ X164 @ id))) | ~ ! [X165 : subst,X166 : term,X167 : subst,X168 : subst] : (~ (((X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165)) = $true) | (((X157 @ X167 @ X166 @ (comp @ X168 @ X165))) = $true)) | ~ (((X155 @ X154)) = $true) | (((X155 @ (ap @ X154 @ X156))) = $true) | ~ ($true = ((X155 @ X156))))) & ((termmset_lthm = $true) <=> (! [X169 : term] : (((sub @ X169 @ id)) = X169) => ! [X170 : term] : (((sub @ X170 @ id)) = X170))) & ((! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X172 : term,X173 : (subst > term > subst > $o)] : (~ ! [X174 : (subst > term > term)] : (~ ! [X177 : term,X175 : subst,X176 : subst] : (((sub @ (X174 @ X175 @ X177) @ X176)) = ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176)))) | ($true = ((X173 @ id @ (lam @ (X174 @ sh @ one)) @ id))) | ~ ! [X178 : term] : ((((X173 @ id @ (X174 @ id @ X178) @ id)) = $true) | ~ (((X173 @ id @ X178 @ id)) = $true))) | ~ ! [X179 : term] : ((((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id)) = $true) | ~ ($true = ((X173 @ id @ X179 @ id)))) | ($true = ((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)))) => ! [X180 : term,X181 : (subst > term > subst > $o)] : ((((X181 @ id @ (lam @ X180) @ id)) = $true) | ~ ! [X182 : (subst > term > term)] : (($true = ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id))) | ~ ! [X183 : term] : (~ (((X181 @ id @ X183 @ id)) = $true) | (((X181 @ id @ (X182 @ id @ X183) @ id)) = $true)) | ~ ! [X185 : subst,X186 : term,X184 : subst] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185))))) | ~ ! [X187 : term] : (($true = ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id))) | ~ (((X181 @ id @ X187 @ id)) = $true))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X188 : (subst > term > subst > $o)] : ~ ! [X189 : (term > $o)] : ~ ! [X190 : term] : (((X188 @ id @ X190 @ id)) = ((X189 @ X190))) => (! [X191 : (term > $o),X192 : term] : (~ ! [X193 : term] : ((((X191 @ X193)) = $true) | ~ (((var @ X193)) = $true)) | (((X191 @ X192)) = $true) | ~ ! [X194 : term,X195 : term] : (~ ($true = ((X191 @ X194))) | ~ (((X191 @ X195)) = $true) | (((X191 @ (ap @ X195 @ X194))) = $true)) | ~ ! [X196 : term] : (~ ! [X197 : term] : (~ ($true = ((X191 @ X197))) | (((X191 @ (sub @ X196 @ (push @ X197 @ id)))) = $true)) | ($true = ((X191 @ (lam @ X196)))))) => (! [X198 : term] : (((sub @ X198 @ id)) = X198) => (! [X199 : (term > $o),X200 : term,X201 : (subst > term > subst > $o)] : (~ ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) | ~ ! [X203 : (subst > term > term)] : (~ ! [X204 : term] : ((((X201 @ id @ (X203 @ id @ X204) @ id)) = $true) | ~ ($true = ((X201 @ id @ X204 @ id)))) | (((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id)) = $true) | ~ ! [X206 : subst,X205 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) = ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206))))) | ~ ! [X208 : term] : (~ (((X199 @ X208)) = $true) | (((X199 @ (sub @ X200 @ (push @ X208 @ id)))) = $true)) | ($true = ((X199 @ (lam @ X200))))) => ! [X209 : term,X210 : (subst > term > subst > $o)] : (~ ! [X211 : term,X212 : term] : (~ (((X210 @ id @ X211 @ id)) = $true) | ~ ($true = ((X210 @ id @ X212 @ id))) | ($true = ((X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id)))) | (((X210 @ id @ X209 @ id)) = $true) | ~ ! [X213 : (subst > term > term)] : (~ ! [X214 : term] : (($true = ((X210 @ id @ (X213 @ id @ X214) @ id))) | ~ (((X210 @ id @ X214 @ id)) = $true)) | ~ ! [X216 : subst,X217 : term,X215 : subst] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) | (((X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)) = $true)))))))) & ! [X218 : d_term] : (d_one = X218) & (hoasapnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X221 : term,X219 : term,X220 : term,X222 : term] : ((X219 = X222) | (((ap @ X220 @ X222)) != ((ap @ X221 @ X219)))) => ! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))))) & (hoasinduction_lem1 = $true) & (! [X227 : (term > $o),X228 : term] : (~ ! [X229 : term,X230 : term] : (~ (((X227 @ X230)) = $true) | ~ (((X227 @ X229)) = $true) | (((X227 @ (ap @ X229 @ X230))) = $true)) | ~ ! [X231 : term] : (~ (((X227 @ X231)) = $true) | ($true = ((X227 @ (lam @ X231))))) | ~ ! [X232 : term] : ((((X227 @ X232)) = $true) | ~ ($true = ((var @ X232)))) | (((X227 @ X228)) = $true)) <=> (induction = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X233 : (term > $o),X234 : term,X235 : subst,X236 : (term > $o)] : ((((X233 @ one)) = $true) | ~ ! [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X233 @ X237))) | ~ (((X236 @ X234)) = $true))) & (hoasapnotvar = $true) & ((! [X239 : subst,X238 : term] : (((sub @ one @ (push @ X238 @ X239))) = X238) => ! [X240 : subst,X241 : term,X242 : (term > $o),X243 : (term > $o)] : (~ ! [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) = ((X243 @ X244))) | ~ (((X242 @ X241)) = $true) | ($true = ((X243 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & (hoasinduction_lem2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) <=> (laminj = $true)) & (! [X249 : term,X250 : (subst > term > subst > $o)] : (~ ! [X251 : term,X252 : term] : (($true = ((X250 @ id @ (ap @ (sub @ X251 @ id) @ X252) @ id))) | ~ ($true = ((X250 @ id @ X251 @ id))) | ~ (((X250 @ id @ X252 @ id)) = $true)) | ~ ! [X253 : (subst > term > term)] : (~ ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | ~ (((X250 @ id @ X254 @ id)) = $true)) | (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) = $true) | ~ ! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257)))) | (((X250 @ id @ X249 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X258 : term] : (((sub @ X258 @ id)) = X258) => (! [X259 : (subst > term > subst > $o),X260 : term] : (~ ! [X261 : (subst > term > term)] : (~ ! [X264 : subst,X263 : subst,X262 : term] : (((sub @ (X261 @ X264 @ X262) @ X263)) = ((X261 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263)))) | (((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id)) = $true) | ~ ! [X265 : term] : (~ (((X259 @ id @ X265 @ id)) = $true) | ($true = ((X259 @ id @ (X261 @ id @ X265) @ id))))) | ~ ! [X266 : term] : (~ (((X259 @ id @ X266 @ id)) = $true) | ($true = ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id)))) | (((X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id)) = $true)) => ! [X267 : term,X268 : (subst > term > subst > $o)] : (~ ! [X269 : subst,X270 : subst,X271 : subst,X272 : term] : ((((X268 @ (comp @ X270 @ X269) @ (sub @ X272 @ X269) @ X271)) = $true) | ~ (((X268 @ X270 @ X272 @ (comp @ X269 @ X271))) = $true)) | (((X268 @ id @ (lam @ X267) @ id)) = $true) | ~ ! [X273 : subst,X274 : subst,X275 : subst,X276 : term] : (~ (((X268 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274)) = $true) | (((X268 @ X275 @ X276 @ (comp @ X273 @ X274))) = $true)) | ~ ! [X277 : (subst > term > term)] : ((((X268 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X268 @ id @ (X277 @ id @ X278) @ id)) = $true) | ~ (((X268 @ id @ X278 @ id)) = $true)) | ~ ! [X281 : subst,X279 : term,X280 : subst] : (((sub @ (X277 @ X280 @ X279) @ X281)) = ((X277 @ (comp @ X280 @ X281) @ (sub @ X279 @ X281))))) | ~ ! [X282 : term] : (~ (((X268 @ id @ X282 @ id)) = $true) | ($true = ((X268 @ id @ (sub @ X267 @ (push @ X282 @ id)) @ id)))))))) & (((d2subst @ d_id)) = sh) & (! [X283 : subst] : (((comp @ X283 @ id)) = X283) <=> (axidr = $true)) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & ! [X284 : d_subst] : (d_id = X284) & (pushprop_lthm_orig = $true) & (hoaslamnotap_lthm = $true) & ((hoaslaminj = $true) <=> ! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (~ ! [X294 : subst,X292 : subst,X293 : term] : (((sub @ (X288 @ X292 @ X293) @ X294)) = ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | ~ ! [X291 : term,X289 : subst,X290 : subst] : (((sub @ (X286 @ X289 @ X291) @ X290)) = ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))))) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X295 : term] : ~ ! [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) != ((X296 @ sh @ one)))) & (induction2_gthm = $true) & ((induction2 = $true) <=> ! [X297 : (term > $o),X298 : term] : (($true = ((X297 @ X298))) | ~ ! [X299 : term] : ((((X297 @ X299)) = $true) | ~ (((var @ X299)) = $true)) | ~ ! [X300 : term,X301 : term] : (~ (((X297 @ X301)) = $true) | ($true = ((X297 @ (ap @ X300 @ X301)))) | ~ (((X297 @ X300)) = $true)) | ~ ! [X302 : term] : ((((X297 @ (lam @ X302))) = $true) | ~ ! [X303 : term] : (($true = ((X297 @ (sub @ X302 @ (push @ X303 @ id))))) | ~ (((X297 @ X303)) = $true))))) & (hoasinduction_lem2_lthm = $true) & (axapp = $true) & ((hoasinduction_lem3 = $true) <=> ! [X304 : term,X305 : (subst > term > subst > $o)] : (~ ! [X306 : term] : (($true = ((X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id))) | ~ (((X305 @ id @ X306 @ id)) = $true)) | ~ ! [X307 : subst,X308 : subst,X309 : term,X310 : subst] : ((((X305 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310) @ X307)) = $true) | ~ (((X305 @ X308 @ X309 @ (comp @ X310 @ X307))) = $true)) | ~ ! [X311 : term,X312 : subst,X313 : subst,X314 : subst] : ((((X305 @ X313 @ X311 @ (comp @ X312 @ X314))) = $true) | ~ ($true = ((X305 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314)))) | (((X305 @ id @ (lam @ X304) @ id)) = $true) | ~ ! [X315 : (subst > term > term)] : (~ ! [X316 : subst,X318 : term,X317 : subst] : (((sub @ (X315 @ X316 @ X318) @ X317)) = ((X315 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317)))) | (((X305 @ id @ (lam @ (X315 @ sh @ one)) @ id)) = $true) | ~ ! [X319 : term] : (~ (((X305 @ id @ X319 @ id)) = $true) | (((X305 @ id @ (X315 @ id @ X319) @ id)) = $true))))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X321 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X321))) = X320) => (! [X322 : term,X323 : subst] : (((comp @ sh @ (push @ X322 @ X323))) = X323) => (! [X324 : subst] : (((comp @ X324 @ id)) = X324) => (! [X325 : (term > $o),X326 : term] : (($true = ((X325 @ X326))) | ~ ! [X327 : term] : ((((X325 @ (lam @ X327))) = $true) | ~ (((X325 @ X327)) = $true)) | ~ ! [X328 : term,X329 : term] : (~ (((X325 @ X328)) = $true) | (((X325 @ (ap @ X329 @ X328))) = $true) | ~ (((X325 @ X329)) = $true)) | ~ ! [X330 : term] : (~ (((var @ X330)) = $true) | (((X325 @ X330)) = $true))) => ! [X331 : term,X332 : subst,X333 : (term > $o)] : (~ ! [X334 : term] : (~ (((var @ X334)) = $true) | (((X333 @ (sub @ X334 @ X332))) = $true)) | (((X333 @ (sub @ X331 @ X332))) = $true) | ~ ! [X335 : term,X336 : term] : (~ (((X333 @ X336)) = $true) | ~ (((X333 @ X335)) = $true) | (((X333 @ (ap @ X336 @ X335))) = $true)) | ~ ! [X337 : term] : (~ ! [X338 : term] : ((((X333 @ (sub @ X337 @ (push @ X338 @ id)))) = $true) | ~ (((X333 @ X338)) = $true)) | (((X333 @ (lam @ X337))) = $true)))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj1_gthm = $true) & (hoasapnotvar_lthm = $true) & ((! [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) = X340) => (! [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) = X342) => ! [X343 : term,X344 : subst,X345 : term,X346 : (term > $o),X347 : (term > $o)] : (~ (((X347 @ X345)) = $true) | (((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((! [X348 : term] : ~ ! [X349 : (subst > term > term)] : ~ ! [X351 : subst,X350 : term] : (((sub @ X348 @ (push @ X350 @ X351))) = ((X349 @ X351 @ X350))) => (! [X352 : term] : (((sub @ X352 @ id)) = X352) => ! [X353 : (term > $o),X354 : (subst > term > subst > $o),X355 : term] : (~ ! [X356 : (subst > term > term)] : (($true = ((X354 @ id @ (lam @ (X356 @ sh @ one)) @ id))) | ~ ! [X358 : subst,X359 : term,X357 : subst] : (((X356 @ (comp @ X357 @ X358) @ (sub @ X359 @ X358))) = ((sub @ (X356 @ X357 @ X359) @ X358))) | ~ ! [X360 : term] : (~ (((X354 @ id @ X360 @ id)) = $true) | ($true = ((X354 @ id @ (X356 @ id @ X360) @ id))))) | ~ ! [X361 : term] : (~ (((X353 @ X361)) = $true) | ($true = ((X353 @ (sub @ X355 @ (push @ X361 @ id)))))) | ~ ! [X362 : term] : (((X354 @ id @ X362 @ id)) = ((X353 @ X362))) | (((X353 @ (lam @ X355))) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X363 : (subst > term > subst > $o)] : ~ ! [X364 : (term > $o)] : ~ ! [X365 : term] : (((X363 @ id @ X365 @ id)) = ((X364 @ X365))) => (! [X366 : (term > $o),X367 : term] : (~ ! [X368 : term] : (($true = ((X366 @ (lam @ X368)))) | ~ ! [X369 : term] : (~ (((X366 @ X369)) = $true) | (((X366 @ (sub @ X368 @ (push @ X369 @ id)))) = $true))) | ~ ! [X370 : term,X371 : term] : (~ (((X366 @ X371)) = $true) | (((X366 @ (ap @ X371 @ X370))) = $true) | ~ (((X366 @ X370)) = $true)) | (((X366 @ X367)) = $true) | ~ ! [X372 : term] : (~ (((var @ X372)) = $true) | (((X366 @ X372)) = $true))) => (! [X373 : term] : (((sub @ X373 @ id)) = X373) => (! [X374 : term,X375 : (subst > term > subst > $o),X376 : (term > $o)] : (~ ! [X377 : term] : (~ (((X376 @ X377)) = $true) | ($true = ((X376 @ (sub @ X374 @ (push @ X377 @ id)))))) | ~ ! [X378 : (subst > term > term)] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((sub @ (X378 @ X379 @ X380) @ X381)) = ((X378 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381)))) | ~ ! [X382 : term] : (~ (((X375 @ id @ X382 @ id)) = $true) | ($true = ((X375 @ id @ (X378 @ id @ X382) @ id)))) | (((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id)) = $true)) | ($true = ((X376 @ (lam @ X374)))) | ~ ! [X383 : term] : (((X376 @ X383)) = ((X375 @ id @ X383 @ id)))) => ! [X384 : term,X385 : (subst > term > subst > $o)] : ((((X385 @ id @ X384 @ id)) = $true) | ~ ! [X386 : subst,X387 : subst,X388 : subst,X389 : term] : (~ ($true = ((X385 @ (comp @ X388 @ X386) @ (sub @ X389 @ X386) @ X387))) | (((X385 @ X388 @ X389 @ (comp @ X386 @ X387))) = $true)) | ~ ! [X390 : term] : ((((X385 @ id @ X390 @ id)) = $true) | ~ (((var @ (sub @ X390 @ id))) = $true)) | ~ ! [X391 : (subst > term > term)] : (~ ! [X392 : term] : (($true = ((X385 @ id @ (X391 @ id @ X392) @ id))) | ~ (((X385 @ id @ X392 @ id)) = $true)) | ($true = ((X385 @ id @ (lam @ (X391 @ sh @ one)) @ id))) | ~ ! [X393 : subst,X395 : term,X394 : subst] : (((sub @ (X391 @ X394 @ X395) @ X393)) = ((X391 @ (comp @ X394 @ X393) @ (sub @ X395 @ X393))))) | ~ ! [X396 : subst,X397 : subst,X398 : subst,X399 : term] : ((((X385 @ (comp @ X398 @ X397) @ (sub @ X399 @ X397) @ X396)) = $true) | ~ ($true = ((X385 @ X398 @ X399 @ (comp @ X397 @ X396))))) | ~ ! [X400 : term,X401 : term] : (~ (((X385 @ id @ X400 @ id)) = $true) | ~ ($true = ((X385 @ id @ X401 @ id))) | (((X385 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & ((axvarid = $true) <=> ! [X402 : term] : (((sub @ X402 @ id)) = X402)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) <=> ! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406))) & (! [X407 : term,X408 : (subst > term > subst > $o)] : (~ ! [X409 : term] : ((((X408 @ id @ (sub @ X407 @ (push @ X409 @ id)) @ id)) = $true) | ~ (((X408 @ id @ X409 @ id)) = $true)) | (((X408 @ id @ (lam @ (sub @ X407 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X410 : (subst > term > term)] : (~ ! [X411 : term] : ((((X408 @ id @ (X410 @ id @ X411) @ id)) = $true) | ~ (((X408 @ id @ X411 @ id)) = $true)) | (((X408 @ id @ (lam @ (X410 @ sh @ one)) @ id)) = $true) | ~ ! [X412 : subst,X413 : subst,X414 : term] : (((sub @ (X410 @ X413 @ X414) @ X412)) = ((X410 @ (comp @ X413 @ X412) @ (sub @ X414 @ X412)))))) <=> (hoasinduction_lem3aa = $true)) & (ulamvarsh = $true) & ~ (lamnotap = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((! [X415 : subst] : (((comp @ id @ X415)) = X415) => (! [X416 : subst] : (((comp @ X416 @ id)) = X416) => (! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)))) <=> (substmonoid_lthm = $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X419 : term,X420 : term,X421 : (subst > term > subst > $o)] : (~ ($true = ((X421 @ id @ X419 @ id))) | ~ ! [X422 : subst,X423 : term,X424 : subst,X425 : subst] : (~ (((X421 @ X425 @ X423 @ (comp @ X422 @ X424))) = $true) | (((X421 @ (comp @ X425 @ X422) @ (sub @ X423 @ X422) @ X424)) = $true)) | ~ ! [X426 : subst,X427 : subst,X428 : term,X429 : subst] : ((((X421 @ X426 @ X428 @ (comp @ X429 @ X427))) = $true) | ~ (((X421 @ (comp @ X426 @ X429) @ (sub @ X428 @ X429) @ X427)) = $true)) | ~ (((X421 @ id @ X420 @ id)) = $true) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | ~ ! [X430 : term,X431 : term] : (~ ($true = ((X421 @ id @ X430 @ id))) | ($true = ((X421 @ id @ (ap @ (sub @ X431 @ id) @ X430) @ id))) | ~ (((X421 @ id @ X431 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & (! [X433 : term,X434 : term,X432 : (subst > term > term)] : (~ ! [X437 : subst,X435 : term,X436 : subst] : (((sub @ (X432 @ X436 @ X435) @ X437)) = ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (! [X438 : (subst > term > subst > $o),X439 : term,X440 : (term > $o)] : (~ ! [X441 : subst,X442 : subst,X443 : term,X444 : subst] : ((((X438 @ X444 @ X443 @ (comp @ X441 @ X442))) = $true) | ~ (((X438 @ (comp @ X444 @ X441) @ (sub @ X443 @ X441) @ X442)) = $true)) | ~ ! [X445 : subst,X446 : subst,X447 : term,X448 : subst] : (~ ($true = ((X438 @ X445 @ X447 @ (comp @ X448 @ X446)))) | (((X438 @ (comp @ X445 @ X448) @ (sub @ X447 @ X448) @ X446)) = $true)) | ~ ! [X449 : term] : ((((X440 @ (sub @ X439 @ (push @ X449 @ id)))) = $true) | ~ (((X440 @ X449)) = $true)) | ~ ! [X450 : (subst > term > term)] : (~ ! [X451 : term] : ((((X438 @ id @ (X450 @ id @ X451) @ id)) = $true) | ~ (((X438 @ id @ X451 @ id)) = $true)) | (((X438 @ id @ (lam @ (X450 @ sh @ one)) @ id)) = $true) | ~ ! [X453 : subst,X454 : subst,X452 : term] : (((X450 @ (comp @ X454 @ X453) @ (sub @ X452 @ X453))) = ((sub @ (X450 @ X454 @ X452) @ X453)))) | ~ ! [X455 : term] : (((X438 @ id @ X455 @ id)) = ((X440 @ X455))) | (((X440 @ (lam @ X439))) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) <=> (axscons = $true)) & (termmset_gthm = $true) & ~ (ulamvar1 = $true) & ((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) <=> (substmonoid = $true)) & (lamnotvar = $true) & (axassoc = $true) & (! [X459 : (subst > term > subst > $o)] : ~ ! [X460 : (term > $o)] : ~ ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461))) <=> (hoasinduction_lem0_lthm = $true)) & (! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) <=> (hoasapinj1 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X466 : term] : (((sub @ X466 @ id)) = X466) => ! [X467 : (term > $o),X468 : term,X469 : (subst > term > subst > $o)] : (~ ! [X470 : subst,X471 : term,X472 : subst,X473 : subst] : ((((X469 @ (comp @ X472 @ X470) @ (sub @ X471 @ X470) @ X473)) = $true) | ~ ($true = ((X469 @ X472 @ X471 @ (comp @ X470 @ X473))))) | ~ ! [X474 : (subst > term > term)] : ((((X469 @ id @ (lam @ (X474 @ sh @ one)) @ id)) = $true) | ~ ! [X477 : subst,X476 : subst,X475 : term] : (((X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) = ((sub @ (X474 @ X477 @ X475) @ X476))) | ~ ! [X478 : term] : (~ ($true = ((X469 @ id @ X478 @ id))) | (((X469 @ id @ (X474 @ id @ X478) @ id)) = $true))) | (((X467 @ (lam @ X468))) = $true) | ~ ! [X479 : term,X480 : subst,X481 : subst,X482 : subst] : (~ (((X469 @ (comp @ X481 @ X482) @ (sub @ X479 @ X482) @ X480)) = $true) | (((X469 @ X481 @ X479 @ (comp @ X482 @ X480))) = $true)) | ~ ! [X483 : term] : ((((X467 @ (sub @ X468 @ (push @ X483 @ id)))) = $true) | ~ ($true = ((X467 @ X483)))) | ~ ! [X484 : term] : (((X467 @ X484)) = ((X469 @ id @ X484 @ id)))))) & (axvarshift = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X485 : (subst > term > subst > $o),X486 : term] : (~ ! [X487 : term] : (~ ($true = ((X485 @ id @ X487 @ id))) | (((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id)) = $true)) | (((X485 @ id @ (lam @ (sub @ X486 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X488 : (subst > term > term)] : ((((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id)) = $true) | ~ ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491)))) | ~ ! [X492 : term] : ((((X485 @ id @ (X488 @ id @ X492) @ id)) = $true) | ~ (((X485 @ id @ X492 @ id)) = $true)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axvarcons = $true) <=> ! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493)) & ((hoasapinj2 = $true) <=> ! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497))) & (! [X499 : (subst > term > subst > $o),X500 : term] : (~ ! [X501 : term] : (~ ($true = ((X499 @ id @ X501 @ id))) | (((X499 @ id @ (sub @ X500 @ (push @ X501 @ id)) @ id)) = $true)) | ~ ! [X502 : (subst > term > term)] : ((((X499 @ id @ (lam @ (X502 @ sh @ one)) @ id)) = $true) | ~ ! [X505 : term,X504 : subst,X503 : subst] : (((X502 @ (comp @ X503 @ X504) @ (sub @ X505 @ X504))) = ((sub @ (X502 @ X503 @ X505) @ X504))) | ~ ! [X506 : term] : (~ ($true = ((X499 @ id @ X506 @ id))) | (((X499 @ id @ (X502 @ id @ X506) @ id)) = $true))) | (((X499 @ id @ (lam @ X500) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X507 : (term > $o),X508 : term,X509 : (subst > term > subst > $o)] : (~ ! [X510 : (subst > term > term)] : (~ ! [X511 : subst,X513 : term,X512 : subst] : (((X510 @ (comp @ X511 @ X512) @ (sub @ X513 @ X512))) = ((sub @ (X510 @ X511 @ X513) @ X512))) | ~ ! [X514 : term] : ((((X509 @ id @ (X510 @ id @ X514) @ id)) = $true) | ~ (((X509 @ id @ X514 @ id)) = $true)) | ($true = ((X509 @ id @ (lam @ (X510 @ sh @ one)) @ id)))) | ($true = ((X507 @ (lam @ X508)))) | ~ ! [X515 : term] : (($true = ((X507 @ (sub @ X508 @ (push @ X515 @ id))))) | ~ (((X507 @ X515)) = $true)) | ~ ! [X516 : term] : (((X509 @ id @ X516 @ id)) = ((X507 @ X516))))) & (! [X517 : term,X518 : (term > $o),X519 : subst,X520 : (term > $o),X521 : term] : (~ ($true = ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) <=> (pushprop_lem1 = $true)) & ((hoasinduction = $true) <=> ! [X522 : term,X523 : (subst > term > subst > $o)] : (~ ! [X524 : subst,X525 : subst,X526 : term,X527 : subst] : (~ ($true = ((X523 @ X525 @ X526 @ (comp @ X527 @ X524)))) | ($true = ((X523 @ (comp @ X525 @ X527) @ (sub @ X526 @ X527) @ X524)))) | ~ ! [X528 : (subst > term > term)] : (~ ! [X530 : term,X531 : subst,X529 : subst] : (((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531))) = ((sub @ (X528 @ X529 @ X530) @ X531))) | (((X523 @ id @ (lam @ (X528 @ sh @ one)) @ id)) = $true) | ~ ! [X532 : term] : ((((X523 @ id @ (X528 @ id @ X532) @ id)) = $true) | ~ (((X523 @ id @ X532 @ id)) = $true))) | ~ ! [X533 : term] : (~ (((var @ (sub @ X533 @ id))) = $true) | ($true = ((X523 @ id @ X533 @ id)))) | ($true = ((X523 @ id @ X522 @ id))) | ~ ! [X534 : subst,X535 : subst,X536 : subst,X537 : term] : (~ (((X523 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X534)) = $true) | ($true = ((X523 @ X536 @ X537 @ (comp @ X535 @ X534))))) | ~ ! [X538 : term,X539 : term] : ((((X523 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) = $true) | ~ ($true = ((X523 @ id @ X538 @ id))) | ~ (((X523 @ id @ X539 @ 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)))))))))))))) & (pushprop_lem1_gthm = $true) & (axmap = $true)),
% 14.62/2.51 inference(rectify,[],[f7])).
% 14.62/2.51 thf(f10,plain,(
% 14.62/2.51 ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (! [X145 : term] : ~ ! [X146 : (subst > term > term)] : (((X146 @ sh @ one)) != ((sub @ X145 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> (shinj = $true)) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = sh) & ((induction2_lthm = $true) <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => (! [X1 : (term > $o),X3 : subst,X2 : term] : (~ ! [X8 : term] : ((((X1 @ (sub @ X8 @ X3))) = $true) | (((var @ X8)) != $true)) | ~ ! [X6 : term] : (~ ! [X7 : term] : ((((X1 @ (sub @ X6 @ (push @ X7 @ id)))) = $true) | (((X1 @ X7)) != $true)) | (((X1 @ (lam @ X6))) = $true)) | ~ ! [X4 : term,X5 : term] : (($true = ((X1 @ (ap @ X4 @ X5)))) | ($true != ((X1 @ X5))) | (((X1 @ X4)) != $true)) | (((X1 @ (sub @ X2 @ X3))) = $true)) => ! [X9 : term,X10 : (term > $o)] : (~ ! [X11 : term] : (~ ! [X12 : term] : ((((X10 @ X12)) != $true) | (((X10 @ (sub @ X11 @ (push @ X12 @ id)))) = $true)) | (((X10 @ (lam @ X11))) = $true)) | ~ ! [X15 : term] : ((((var @ X15)) != $true) | (((X10 @ X15)) = $true)) | ~ ! [X13 : term,X14 : term] : ((((X10 @ X13)) != $true) | ($true = ((X10 @ (ap @ X14 @ X13)))) | ($true != ((X10 @ X14)))) | (((X10 @ X9)) = $true))))) & ((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) <=> (substmonoid = $true)) & (! [X283 : subst] : (((comp @ X283 @ id)) = X283) <=> (axidr = $true)) & ((! [X258 : term] : (((sub @ X258 @ id)) = X258) => (! [X259 : (subst > term > subst > $o),X260 : term] : (~ ! [X261 : (subst > term > term)] : ((((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id)) = $true) | ~ ! [X264 : subst,X263 : subst,X262 : term] : (((sub @ (X261 @ X264 @ X262) @ X263)) = ((X261 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263)))) | ~ ! [X265 : term] : (($true = ((X259 @ id @ (X261 @ id @ X265) @ id))) | (((X259 @ id @ X265 @ id)) != $true))) | (((X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X266 : term] : (($true = ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id))) | (((X259 @ id @ X266 @ id)) != $true))) => ! [X268 : (subst > term > subst > $o),X267 : term] : (~ ! [X275 : subst,X276 : term,X273 : subst,X274 : subst] : ((((X268 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274)) != $true) | (((X268 @ X275 @ X276 @ (comp @ X273 @ X274))) = $true)) | ~ ! [X277 : (subst > term > term)] : ((((X268 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X281 : subst,X279 : term,X280 : subst] : (((sub @ (X277 @ X280 @ X279) @ X281)) = ((X277 @ (comp @ X280 @ X281) @ (sub @ X279 @ X281)))) | ~ ! [X278 : term] : ((((X268 @ id @ X278 @ id)) != $true) | (((X268 @ id @ (X277 @ id @ X278) @ id)) = $true))) | ~ ! [X270 : subst,X271 : subst,X272 : term,X269 : subst] : ((((X268 @ X270 @ X272 @ (comp @ X269 @ X271))) != $true) | (((X268 @ (comp @ X270 @ X269) @ (sub @ X272 @ X269) @ X271)) = $true)) | ~ ! [X282 : term] : ((((X268 @ id @ X282 @ id)) != $true) | ($true = ((X268 @ id @ (sub @ X267 @ (push @ X282 @ id)) @ id)))) | (((X268 @ id @ (lam @ X267) @ id)) = $true)))) <=> (hoasinduction_lem3_lthm = $true)) & ! [X284 : d_subst] : (d_id = X284) & (pushprop_lem2v2 = $true) & ((! [X321 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X321))) = X320) => (! [X322 : term,X323 : subst] : (((comp @ sh @ (push @ X322 @ X323))) = X323) => (! [X324 : subst] : (((comp @ X324 @ id)) = X324) => (! [X325 : (term > $o),X326 : term] : (($true = ((X325 @ X326))) | ~ ! [X327 : term] : ((((X325 @ (lam @ X327))) = $true) | (((X325 @ X327)) != $true)) | ~ ! [X328 : term,X329 : term] : ((((X325 @ X328)) != $true) | (((X325 @ X329)) != $true) | (((X325 @ (ap @ X329 @ X328))) = $true)) | ~ ! [X330 : term] : ((((var @ X330)) != $true) | (((X325 @ X330)) = $true))) => ! [X331 : term,X333 : (term > $o),X332 : subst] : (~ ! [X337 : term] : (~ ! [X338 : term] : ((((X333 @ X338)) != $true) | (((X333 @ (sub @ X337 @ (push @ X338 @ id)))) = $true)) | (((X333 @ (lam @ X337))) = $true)) | ~ ! [X335 : term,X336 : term] : ((((X333 @ X335)) != $true) | (((X333 @ (ap @ X336 @ X335))) = $true) | (((X333 @ X336)) != $true)) | ~ ! [X334 : term] : ((((X333 @ (sub @ X334 @ X332))) = $true) | (((var @ X334)) != $true)) | (((X333 @ (sub @ X331 @ X332))) = $true)))))) <=> (induction2lem_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X188 : (subst > term > subst > $o)] : ~ ! [X189 : (term > $o)] : ~ ! [X190 : term] : (((X188 @ id @ X190 @ id)) = ((X189 @ X190))) => (! [X192 : term,X191 : (term > $o)] : (~ ! [X196 : term] : (($true = ((X191 @ (lam @ X196)))) | ~ ! [X197 : term] : ((((X191 @ (sub @ X196 @ (push @ X197 @ id)))) = $true) | ($true != ((X191 @ X197))))) | ~ ! [X193 : term] : ((((var @ X193)) != $true) | (((X191 @ X193)) = $true)) | ~ ! [X194 : term,X195 : term] : ((((X191 @ (ap @ X195 @ X194))) = $true) | (((X191 @ X195)) != $true) | ($true != ((X191 @ X194)))) | (((X191 @ X192)) = $true)) => (! [X198 : term] : (((sub @ X198 @ id)) = X198) => (! [X200 : term,X199 : (term > $o),X201 : (subst > term > subst > $o)] : (~ ! [X208 : term] : ((((X199 @ (sub @ X200 @ (push @ X208 @ id)))) = $true) | (((X199 @ X208)) != $true)) | ~ ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) | ~ ! [X203 : (subst > term > term)] : (~ ! [X204 : term] : ((((X201 @ id @ (X203 @ id @ X204) @ id)) = $true) | ($true != ((X201 @ id @ X204 @ id)))) | ~ ! [X206 : subst,X205 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) = ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206)))) | (((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id)) = $true)) | ($true = ((X199 @ (lam @ X200))))) => ! [X209 : term,X210 : (subst > term > subst > $o)] : (~ ! [X213 : (subst > term > term)] : ((((X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)) = $true) | ~ ! [X216 : subst,X217 : term,X215 : subst] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) | ~ ! [X214 : term] : (($true = ((X210 @ id @ (X213 @ id @ X214) @ id))) | (((X210 @ id @ X214 @ id)) != $true))) | (((X210 @ id @ X209 @ id)) = $true) | ~ ! [X211 : term,X212 : term] : (($true != ((X210 @ id @ X212 @ id))) | (((X210 @ id @ X211 @ id)) != $true) | ($true = ((X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id)))))))))) & (hoasinduction_lem3a_gthm = $true) & (! [X147 : (subst > term > subst > $o)] : ~ ! [X148 : (term > $o)] : ~ ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149))) <=> (hoasinduction_lem0 = $true)) & (axabs = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X297 : (term > $o),X298 : term] : (~ ! [X302 : term] : ((((X297 @ (lam @ X302))) = $true) | ~ ! [X303 : term] : ((((X297 @ X303)) != $true) | ($true = ((X297 @ (sub @ X302 @ (push @ X303 @ id))))))) | ~ ! [X301 : term,X300 : term] : (($true = ((X297 @ (ap @ X300 @ X301)))) | (((X297 @ X301)) != $true) | (((X297 @ X300)) != $true)) | ~ ! [X299 : term] : ((((var @ X299)) != $true) | (((X297 @ X299)) = $true)) | ($true = ((X297 @ X298)))) <=> (induction2 = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((axvarcons = $true) <=> ! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493)) & (! [X136 : term,X135 : (term > $o),X137 : subst] : ~ ! [X138 : (term > $o)] : ~ ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) = X340) => (! [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) = X342) => ! [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true) | (((X347 @ X345)) != $true))))) & ((induction2lem = $true) <=> ! [X129 : term,X128 : subst,X127 : (term > $o)] : (~ ! [X132 : term] : ((((X127 @ (sub @ X132 @ X128))) = $true) | (((var @ X132)) != $true)) | ~ ! [X134 : term,X133 : term] : (($true != ((X127 @ X134))) | (((X127 @ X133)) != $true) | (((X127 @ (ap @ X134 @ X133))) = $true)) | (((X127 @ (sub @ X129 @ X128))) = $true) | ~ ! [X130 : term] : (($true = ((X127 @ (lam @ X130)))) | ~ ! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true))))) & (one = ((d2term @ d_one))) & (pushprop = $true) & (substmonoid_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X239 : subst,X238 : term] : (((sub @ one @ (push @ X238 @ X239))) = X238) => ! [X242 : (term > $o),X243 : (term > $o),X240 : subst,X241 : term] : (~ ! [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) = ((X243 @ X244))) | ($true = ((X243 @ one))) | (((X242 @ X241)) != $true)))) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (~ ! [X294 : subst,X292 : subst,X293 : term] : (((sub @ (X288 @ X292 @ X293) @ X294)) = ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | ~ ! [X291 : term,X289 : subst,X290 : subst] : (((sub @ (X286 @ X289 @ X291) @ X290)) = ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))))) & (pushprop_lem3v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X221 : term,X219 : term,X220 : term,X222 : term] : ((X219 = X222) | (((ap @ X220 @ X222)) != ((ap @ X221 @ X219)))) => ! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))))) & ((apinj2 = $true) <=> ! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & (hoasinduction_lem1v2 = $true) & (ulamvar1 != $true) & (induction2lem_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497))) & (pushprop_lthm_orig = $true) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & (axapp = $true) & ((! [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) = X55) => (! [X57 : subst,X56 : term] : (((comp @ sh @ (push @ X56 @ X57))) = X57) => (! [X59 : term,X58 : term] : ((((lam @ X58)) != ((lam @ X59))) | (X58 = X59)) => ! [X63 : (subst > term > term),X61 : subst,X60 : term,X62 : (subst > term > term)] : ((((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | ~ ! [X69 : term,X67 : subst,X68 : subst] : (((sub @ (X63 @ X68 @ X69) @ X67)) = ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67)))) | ~ ! [X66 : subst,X64 : subst,X65 : term] : (((sub @ (X62 @ X66 @ X65) @ X64)) = ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))))))) <=> (hoaslaminj_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X348 : term] : ~ ! [X349 : (subst > term > term)] : ~ ! [X351 : subst,X350 : term] : (((sub @ X348 @ (push @ X350 @ X351))) = ((X349 @ X351 @ X350))) => (! [X352 : term] : (((sub @ X352 @ id)) = X352) => ! [X354 : (subst > term > subst > $o),X355 : term,X353 : (term > $o)] : (~ ! [X361 : term] : (($true = ((X353 @ (sub @ X355 @ (push @ X361 @ id))))) | (((X353 @ X361)) != $true)) | ~ ! [X362 : term] : (((X354 @ id @ X362 @ id)) = ((X353 @ X362))) | (((X353 @ (lam @ X355))) = $true) | ~ ! [X356 : (subst > term > term)] : (($true = ((X354 @ id @ (lam @ (X356 @ sh @ one)) @ id))) | ~ ! [X360 : term] : ((((X354 @ id @ X360 @ id)) != $true) | ($true = ((X354 @ id @ (X356 @ id @ X360) @ id)))) | ~ ! [X358 : subst,X359 : term,X357 : subst] : (((X356 @ (comp @ X357 @ X358) @ (sub @ X359 @ X358))) = ((sub @ (X356 @ X357 @ X359) @ X358)))))))) & (lamnotvar = $true) & (! [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true != ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) <=> (pushprop_lem1 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X42 : (subst > term > subst > $o),X43 : term] : (~ ! [X53 : term] : ((((X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) = $true) | (((X42 @ id @ X53 @ id)) != $true)) | (((X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X44 : (subst > term > term),X45 : term] : (~ ! [X46 : term,X48 : subst,X47 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) | (((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id)) = $true) | ~ ! [X52 : term] : ((((X42 @ id @ X52 @ id)) != $true) | (((X42 @ id @ (X44 @ id @ X52) @ id)) = $true)) | ~ ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49))))))) & (! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) <=> (laminj = $true)) & ((hoasinduction_lthm = $true) <=> (! [X73 : (term > $o),X74 : term] : (~ ! [X78 : term,X79 : term] : ((((X73 @ X78)) != $true) | (((X73 @ (ap @ X78 @ X79))) = $true) | (((X73 @ X79)) != $true)) | ($true = ((X73 @ X74))) | ~ ! [X77 : term] : ((((X73 @ X77)) = $true) | (((var @ X77)) != $true)) | ~ ! [X75 : term] : (~ ! [X76 : term] : ((((X73 @ X76)) != $true) | (((X73 @ (sub @ X75 @ (push @ X76 @ id)))) = $true)) | (((X73 @ (lam @ X75))) = $true))) => (! [X80 : term,X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X86 : subst,X84 : subst,X83 : subst,X85 : term] : ((((X82 @ X84 @ X85 @ (comp @ X83 @ X86))) != $true) | (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) = $true)) | (((X82 @ id @ (ap @ X81 @ X80) @ id)) = $true) | (((X82 @ id @ X81 @ id)) != $true) | ~ ! [X92 : term,X91 : term] : ((((X82 @ id @ X91 @ id)) != $true) | (((X82 @ id @ X92 @ id)) != $true) | ($true = ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id)))) | ($true != ((X82 @ id @ X80 @ id))) | ~ ! [X89 : subst,X88 : subst,X90 : subst,X87 : term] : ((((X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) != $true) | ($true = ((X82 @ X88 @ X87 @ (comp @ X89 @ X90)))))) => (! [X93 : term,X94 : (subst > term > subst > $o)] : (~ ! [X98 : subst,X96 : subst,X97 : term,X95 : subst] : ((((X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) != $true) | (((X94 @ X95 @ X97 @ (comp @ X98 @ X96))) = $true)) | ~ ! [X107 : term,X108 : subst,X106 : subst,X105 : subst] : (($true = ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106))) | (((X94 @ X105 @ X107 @ (comp @ X108 @ X106))) != $true)) | ($true = ((X94 @ id @ (lam @ X93) @ id))) | ~ ! [X100 : (subst > term > term)] : (~ ! [X104 : term] : ((((X94 @ id @ X104 @ id)) != $true) | (((X94 @ id @ (X100 @ id @ X104) @ id)) = $true)) | ($true = ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id))) | ~ ! [X101 : term,X103 : subst,X102 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) = ((sub @ (X100 @ X102 @ X101) @ X103)))) | ~ ! [X99 : term] : ((((X94 @ id @ X99 @ id)) != $true) | (((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id)) = $true))) => ! [X110 : term,X109 : (subst > term > subst > $o)] : (~ ! [X126 : term] : ((((X109 @ id @ X126 @ id)) = $true) | ($true != ((var @ (sub @ X126 @ id))))) | ~ ! [X121 : term,X120 : term] : ((((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id)) = $true) | (((X109 @ id @ X120 @ id)) != $true) | (((X109 @ id @ X121 @ id)) != $true)) | ~ ! [X115 : (subst > term > term)] : ((((X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) = $true) | ~ ! [X119 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) | ~ ! [X116 : term] : (($true = ((X109 @ id @ (X115 @ id @ X116) @ id))) | (((X109 @ id @ X116 @ id)) != $true))) | ~ ! [X112 : subst,X114 : term,X113 : subst,X111 : subst] : ((((X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) != $true) | (((X109 @ X113 @ X114 @ (comp @ X112 @ X111))) = $true)) | (((X109 @ id @ X110 @ id)) = $true) | ~ ! [X123 : subst,X122 : subst,X124 : term,X125 : subst] : (($true = ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125))) | ($true != ((X109 @ X123 @ X124 @ (comp @ X122 @ X125)))))))))) & (! [X35 : term,X34 : (term > $o),X33 : subst] : ~ ! [X36 : (term > $o)] : ~ ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37))) <=> (pushprop_lem0 = $true)) & (! [X157 : (subst > term > subst > $o),X154 : term,X155 : (term > $o),X156 : term] : (~ ! [X162 : term,X163 : term] : ((((X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true) | (((X157 @ id @ X162 @ id)) != $true)) | (((X155 @ (ap @ X154 @ X156))) = $true) | ~ ! [X168 : subst,X167 : subst,X165 : subst,X166 : term] : ((((X157 @ X167 @ X166 @ (comp @ X168 @ X165))) = $true) | (((X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165)) != $true)) | ($true != ((X155 @ X156))) | ~ ! [X158 : subst,X160 : subst,X159 : subst,X161 : term] : ((((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158)) = $true) | ($true != ((X157 @ X160 @ X161 @ (comp @ X159 @ X158))))) | ~ ! [X164 : term] : (((X155 @ X164)) = ((X157 @ id @ X164 @ id))) | (((X155 @ X154)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X171 : term] : (((sub @ X171 @ id)) = X171) => (! [X173 : (subst > term > subst > $o),X172 : term] : (~ ! [X174 : (subst > term > term)] : (~ ! [X177 : term,X175 : subst,X176 : subst] : (((sub @ (X174 @ X175 @ X177) @ X176)) = ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176)))) | ~ ! [X178 : term] : ((((X173 @ id @ X178 @ id)) != $true) | (((X173 @ id @ (X174 @ id @ X178) @ id)) = $true)) | ($true = ((X173 @ id @ (lam @ (X174 @ sh @ one)) @ id)))) | ~ ! [X179 : term] : ((((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id)) = $true) | ($true != ((X173 @ id @ X179 @ id)))) | ($true = ((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)))) => ! [X181 : (subst > term > subst > $o),X180 : term] : (~ ! [X187 : term] : (($true = ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id))) | (((X181 @ id @ X187 @ id)) != $true)) | (((X181 @ id @ (lam @ X180) @ id)) = $true) | ~ ! [X182 : (subst > term > term)] : (~ ! [X183 : term] : ((((X181 @ id @ (X182 @ id @ X183) @ id)) = $true) | (((X181 @ id @ X183 @ id)) != $true)) | ($true = ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id))) | ~ ! [X185 : subst,X186 : term,X184 : subst] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185))))))))) & (axassoc = $true) & (hoaslamnotvar = $true) & (! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) <=> (hoasapinj1 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & ! [X218 : d_term] : (d_one = X218) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X499 : (subst > term > subst > $o),X500 : term] : (~ ! [X501 : term] : (($true != ((X499 @ id @ X501 @ id))) | (((X499 @ id @ (sub @ X500 @ (push @ X501 @ id)) @ id)) = $true)) | ~ ! [X502 : (subst > term > term)] : ((((X499 @ id @ (lam @ (X502 @ sh @ one)) @ id)) = $true) | ~ ! [X506 : term] : ((((X499 @ id @ (X502 @ id @ X506) @ id)) = $true) | ($true != ((X499 @ id @ X506 @ id)))) | ~ ! [X505 : term,X504 : subst,X503 : subst] : (((X502 @ (comp @ X503 @ X504) @ (sub @ X505 @ X504))) = ((sub @ (X502 @ X503 @ X505) @ X504)))) | (((X499 @ id @ (lam @ X500) @ id)) = $true))) & (termmset_gthm = $true) & (! [X20 : term] : ~ ! [X21 : (subst > term > term)] : ~ ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoaslamnotvar_lthm = $true) & ((! [X415 : subst] : (((comp @ id @ X415)) = X415) => (! [X416 : subst] : (((comp @ X416 @ id)) = X416) => (! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X305 : (subst > term > subst > $o),X304 : term] : (~ ! [X314 : subst,X311 : term,X312 : subst,X313 : subst] : (($true != ((X305 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314))) | (((X305 @ X313 @ X311 @ (comp @ X312 @ X314))) = $true)) | ~ ! [X306 : term] : (($true = ((X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id))) | (((X305 @ id @ X306 @ id)) != $true)) | (((X305 @ id @ (lam @ X304) @ id)) = $true) | ~ ! [X307 : subst,X308 : subst,X310 : subst,X309 : term] : ((((X305 @ X308 @ X309 @ (comp @ X310 @ X307))) != $true) | (((X305 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310) @ X307)) = $true)) | ~ ! [X315 : (subst > term > term)] : ((((X305 @ id @ (lam @ (X315 @ sh @ one)) @ id)) = $true) | ~ ! [X319 : term] : ((((X305 @ id @ X319 @ id)) != $true) | (((X305 @ id @ (X315 @ id @ X319) @ id)) = $true)) | ~ ! [X316 : subst,X318 : term,X317 : subst] : (((sub @ (X315 @ X316 @ X318) @ X317)) = ((X315 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317))))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X363 : (subst > term > subst > $o)] : ~ ! [X364 : (term > $o)] : ~ ! [X365 : term] : (((X363 @ id @ X365 @ id)) = ((X364 @ X365))) => (! [X367 : term,X366 : (term > $o)] : ((((X366 @ X367)) = $true) | ~ ! [X371 : term,X370 : term] : ((((X366 @ X370)) != $true) | (((X366 @ (ap @ X371 @ X370))) = $true) | (((X366 @ X371)) != $true)) | ~ ! [X368 : term] : (($true = ((X366 @ (lam @ X368)))) | ~ ! [X369 : term] : ((((X366 @ X369)) != $true) | (((X366 @ (sub @ X368 @ (push @ X369 @ id)))) = $true))) | ~ ! [X372 : term] : ((((X366 @ X372)) = $true) | (((var @ X372)) != $true))) => (! [X373 : term] : (((sub @ X373 @ id)) = X373) => (! [X376 : (term > $o),X374 : term,X375 : (subst > term > subst > $o)] : (~ ! [X378 : (subst > term > term)] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((sub @ (X378 @ X379 @ X380) @ X381)) = ((X378 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381)))) | (((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id)) = $true) | ~ ! [X382 : term] : (($true = ((X375 @ id @ (X378 @ id @ X382) @ id))) | (((X375 @ id @ X382 @ id)) != $true))) | ~ ! [X383 : term] : (((X376 @ X383)) = ((X375 @ id @ X383 @ id))) | ($true = ((X376 @ (lam @ X374)))) | ~ ! [X377 : term] : (($true = ((X376 @ (sub @ X374 @ (push @ X377 @ id))))) | (((X376 @ X377)) != $true))) => ! [X384 : term,X385 : (subst > term > subst > $o)] : (~ ! [X401 : term,X400 : term] : ((((X385 @ id @ X400 @ id)) != $true) | ($true != ((X385 @ id @ X401 @ id))) | (((X385 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) = $true)) | ~ ! [X391 : (subst > term > term)] : (($true = ((X385 @ id @ (lam @ (X391 @ sh @ one)) @ id))) | ~ ! [X393 : subst,X395 : term,X394 : subst] : (((sub @ (X391 @ X394 @ X395) @ X393)) = ((X391 @ (comp @ X394 @ X393) @ (sub @ X395 @ X393)))) | ~ ! [X392 : term] : (($true = ((X385 @ id @ (X391 @ id @ X392) @ id))) | (((X385 @ id @ X392 @ id)) != $true))) | ~ ! [X389 : term,X387 : subst,X388 : subst,X386 : subst] : (($true != ((X385 @ (comp @ X388 @ X386) @ (sub @ X389 @ X386) @ X387))) | (((X385 @ X388 @ X389 @ (comp @ X386 @ X387))) = $true)) | ~ ! [X399 : term,X396 : subst,X398 : subst,X397 : subst] : ((((X385 @ (comp @ X398 @ X397) @ (sub @ X399 @ X397) @ X396)) = $true) | ($true != ((X385 @ X398 @ X399 @ (comp @ X397 @ X396))))) | ~ ! [X390 : term] : ((((X385 @ id @ X390 @ id)) = $true) | (((var @ (sub @ X390 @ id))) != $true)) | (((X385 @ id @ X384 @ id)) = $true))))))) & (lamnotap != $true) & ((hoasinduction = $true) <=> ! [X522 : term,X523 : (subst > term > subst > $o)] : (~ ! [X538 : term,X539 : term] : ((((X523 @ id @ X539 @ id)) != $true) | (((X523 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) = $true) | ($true != ((X523 @ id @ X538 @ id)))) | ~ ! [X528 : (subst > term > term)] : (~ ! [X530 : term,X531 : subst,X529 : subst] : (((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531))) = ((sub @ (X528 @ X529 @ X530) @ X531))) | (((X523 @ id @ (lam @ (X528 @ sh @ one)) @ id)) = $true) | ~ ! [X532 : term] : ((((X523 @ id @ (X528 @ id @ X532) @ id)) = $true) | (((X523 @ id @ X532 @ id)) != $true))) | ~ ! [X533 : term] : ((((var @ (sub @ X533 @ id))) != $true) | ($true = ((X523 @ id @ X533 @ id)))) | ~ ! [X525 : subst,X524 : subst,X527 : subst,X526 : term] : (($true = ((X523 @ (comp @ X525 @ X527) @ (sub @ X526 @ X527) @ X524))) | ($true != ((X523 @ X525 @ X526 @ (comp @ X527 @ X524))))) | ($true = ((X523 @ id @ X522 @ id))) | ~ ! [X535 : subst,X536 : subst,X534 : subst,X537 : term] : ((((X523 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X534)) != $true) | ($true = ((X523 @ X536 @ X537 @ (comp @ X535 @ X534))))))) & (induction2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X140 : d_subst,X141 : d_subst] : ((((d2subst @ X140)) = ((d2subst @ X141))) => (X140 = X141)) & (pushprop_lem1v2_gthm = $true) & ((induction = $true) <=> ! [X228 : term,X227 : (term > $o)] : (~ ! [X230 : term,X229 : term] : ((((X227 @ X229)) != $true) | (((X227 @ (ap @ X229 @ X230))) = $true) | (((X227 @ X230)) != $true)) | (((X227 @ X228)) = $true) | ~ ! [X232 : term] : ((((X227 @ X232)) = $true) | ($true != ((var @ X232)))) | ~ ! [X231 : term] : ((((X227 @ X231)) != $true) | ($true = ((X227 @ (lam @ X231))))))) & (! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) <=> (axscons = $true)) & (! [X433 : term,X434 : term,X432 : (subst > term > term)] : (~ ! [X437 : subst,X435 : term,X436 : subst] : (((sub @ (X432 @ X436 @ X435) @ X437)) = ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (hoaslamnotap_lthm = $true) & (hoaslamnotap_gthm = $true) & ((apinj1 = $true) <=> ! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406))) & (! [X459 : (subst > term > subst > $o)] : ~ ! [X460 : (term > $o)] : ~ ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461))) <=> (hoasinduction_lem0_lthm = $true)) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & ! [X19 : d_term,X18 : d_term] : ((((d2term @ X18)) = ((d2term @ X19))) => (X18 = X19)) & ((axvarid = $true) <=> ! [X402 : term] : (((sub @ X402 @ id)) = X402)) & (! [X440 : (term > $o),X438 : (subst > term > subst > $o),X439 : term] : ((((X440 @ (lam @ X439))) = $true) | ~ ! [X446 : subst,X448 : subst,X447 : term,X445 : subst] : ((((X438 @ (comp @ X445 @ X448) @ (sub @ X447 @ X448) @ X446)) = $true) | ($true != ((X438 @ X445 @ X447 @ (comp @ X448 @ X446))))) | ~ ! [X455 : term] : (((X438 @ id @ X455 @ id)) = ((X440 @ X455))) | ~ ! [X450 : (subst > term > term)] : ((((X438 @ id @ (lam @ (X450 @ sh @ one)) @ id)) = $true) | ~ ! [X451 : term] : ((((X438 @ id @ X451 @ id)) != $true) | (((X438 @ id @ (X450 @ id @ X451) @ id)) = $true)) | ~ ! [X453 : subst,X454 : subst,X452 : term] : (((X450 @ (comp @ X454 @ X453) @ (sub @ X452 @ X453))) = ((sub @ (X450 @ X454 @ X452) @ X453)))) | ~ ! [X443 : term,X441 : subst,X444 : subst,X442 : subst] : ((((X438 @ (comp @ X444 @ X441) @ (sub @ X443 @ X441) @ X442)) != $true) | (((X438 @ X444 @ X443 @ (comp @ X441 @ X442))) = $true)) | ~ ! [X449 : term] : ((((X440 @ (sub @ X439 @ (push @ X449 @ id)))) = $true) | (((X440 @ X449)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (apnotvar = $true) & (! [X250 : (subst > term > subst > $o),X249 : term] : (~ ! [X252 : term,X251 : term] : ((((X250 @ id @ X252 @ id)) != $true) | ($true != ((X250 @ id @ X251 @ id))) | ($true = ((X250 @ id @ (ap @ (sub @ X251 @ id) @ X252) @ id)))) | (((X250 @ id @ X249 @ id)) = $true) | ~ ! [X253 : (subst > term > term)] : (~ ! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257))) | (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) = $true) | ~ ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | (((X250 @ id @ X254 @ id)) != $true)))) <=> (hoasinduction_no_psi_cond = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X236 : (term > $o),X235 : subst,X234 : term,X233 : (term > $o)] : ((((X236 @ X234)) != $true) | ~ ! [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X233 @ X237))) | (((X233 @ one)) = $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axvarshift = $true) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) <=> (termmset = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapnotvar = $true) & (axclos = $true) & (((var @ (d2term @ d_one))) != $true) & (hoaslaminj_gthm = $true) & (! [X150 : term] : ~ ! [X151 : (subst > term > term)] : ~ ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153))) <=> (hoasinduction_lem3v2_f = $true)) & ((termmset_lthm = $true) <=> (! [X169 : term] : (((sub @ X169 @ id)) = X169) => ! [X170 : term] : (((sub @ X170 @ id)) = X170))) & ((hoasinduction_lem2 = $true) <=> ! [X420 : term,X421 : (subst > term > subst > $o),X419 : term] : (~ ! [X430 : term,X431 : term] : (($true = ((X421 @ id @ (ap @ (sub @ X431 @ id) @ X430) @ id))) | (((X421 @ id @ X431 @ id)) != $true) | ($true != ((X421 @ id @ X430 @ id)))) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | (((X421 @ id @ X420 @ id)) != $true) | ($true != ((X421 @ id @ X419 @ id))) | ~ ! [X423 : term,X424 : subst,X422 : subst,X425 : subst] : ((((X421 @ (comp @ X425 @ X422) @ (sub @ X423 @ X422) @ X424)) = $true) | (((X421 @ X425 @ X423 @ (comp @ X422 @ X424))) != $true)) | ~ ! [X427 : subst,X428 : term,X429 : subst,X426 : subst] : ((((X421 @ (comp @ X426 @ X429) @ (sub @ X428 @ X429) @ X427)) != $true) | (((X421 @ X426 @ X428 @ (comp @ X429 @ X427))) = $true)))) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((! [X24 : term] : (((sub @ X24 @ id)) = X24) => (! [X26 : term,X27 : term,X28 : term,X25 : term] : ((X27 = X28) | (((ap @ X28 @ X26)) != ((ap @ X27 @ X25)))) => ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))))) <=> (hoasapinj1_lthm = $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X295 : term] : ~ ! [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) != ((X296 @ sh @ one)))) & ((hoasinduction_lem3aa = $true) <=> ! [X408 : (subst > term > subst > $o),X407 : term] : (~ ! [X409 : term] : ((((X408 @ id @ X409 @ id)) != $true) | (((X408 @ id @ (sub @ X407 @ (push @ X409 @ id)) @ id)) = $true)) | ~ ! [X410 : (subst > term > term)] : (~ ! [X412 : subst,X413 : subst,X414 : term] : (((sub @ (X410 @ X413 @ X414) @ X412)) = ((X410 @ (comp @ X413 @ X412) @ (sub @ X414 @ X412)))) | (((X408 @ id @ (lam @ (X410 @ sh @ one)) @ id)) = $true) | ~ ! [X411 : term] : ((((X408 @ id @ (X410 @ id @ X411) @ id)) = $true) | (((X408 @ id @ X411 @ id)) != $true))) | (((X408 @ id @ (lam @ (sub @ X407 @ (push @ one @ sh))) @ id)) = $true))) & (ulamvarsh = $true) & (! [X507 : (term > $o),X508 : term,X509 : (subst > term > subst > $o)] : (~ ! [X510 : (subst > term > term)] : (($true = ((X509 @ id @ (lam @ (X510 @ sh @ one)) @ id))) | ~ ! [X511 : subst,X513 : term,X512 : subst] : (((X510 @ (comp @ X511 @ X512) @ (sub @ X513 @ X512))) = ((sub @ (X510 @ X511 @ X513) @ X512))) | ~ ! [X514 : term] : ((((X509 @ id @ X514 @ id)) != $true) | (((X509 @ id @ (X510 @ id @ X514) @ id)) = $true))) | ~ ! [X516 : term] : (((X509 @ id @ X516 @ id)) = ((X507 @ X516))) | ~ ! [X515 : term] : ((((X507 @ X515)) != $true) | ($true = ((X507 @ (sub @ X508 @ (push @ X515 @ id)))))) | ($true = ((X507 @ (lam @ X508))))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X466 : term] : (((sub @ X466 @ id)) = X466) => ! [X469 : (subst > term > subst > $o),X468 : term,X467 : (term > $o)] : (~ ! [X484 : term] : (((X467 @ X484)) = ((X469 @ id @ X484 @ id))) | ~ ! [X481 : subst,X480 : subst,X482 : subst,X479 : term] : ((((X469 @ (comp @ X481 @ X482) @ (sub @ X479 @ X482) @ X480)) != $true) | (((X469 @ X481 @ X479 @ (comp @ X482 @ X480))) = $true)) | ~ ! [X470 : subst,X471 : term,X472 : subst,X473 : subst] : ((((X469 @ (comp @ X472 @ X470) @ (sub @ X471 @ X470) @ X473)) = $true) | ($true != ((X469 @ X472 @ X471 @ (comp @ X470 @ X473))))) | ~ ! [X483 : term] : ((((X467 @ (sub @ X468 @ (push @ X483 @ id)))) = $true) | ($true != ((X467 @ X483)))) | ~ ! [X474 : (subst > term > term)] : ((((X469 @ id @ (lam @ (X474 @ sh @ one)) @ id)) = $true) | ~ ! [X478 : term] : (($true != ((X469 @ id @ X478 @ id))) | (((X469 @ id @ (X474 @ id @ X478) @ id)) = $true)) | ~ ! [X477 : subst,X476 : subst,X475 : term] : (((X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) = ((sub @ (X474 @ X477 @ X475) @ X476)))) | (((X467 @ (lam @ X468))) = $true)))) & (! [X485 : (subst > term > subst > $o),X486 : term] : (~ ! [X487 : term] : (($true != ((X485 @ id @ X487 @ id))) | (((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id)) = $true)) | ~ ! [X488 : (subst > term > term)] : ((((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id)) = $true) | ~ ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491)))) | ~ ! [X492 : term] : ((((X485 @ id @ X492 @ id)) != $true) | (((X485 @ id @ (X488 @ id @ X492) @ id)) = $true))) | (((X485 @ id @ (lam @ (sub @ X486 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true))),
% 14.62/2.51 inference(flattening,[],[f9])).
% 14.62/2.51 thf(f11,plain,(
% 14.62/2.51 ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X145 : term] : ? [X146 : (subst > term > term)] : (((X146 @ sh @ one)) = ((sub @ X145 @ (push @ one @ sh))))) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> (shinj = $true)) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = sh) & ((induction2_lthm = $true) <=> ((! [X10 : (term > $o),X9 : term] : (? [X15 : term] : ((((X10 @ X15)) != $true) & (((var @ X15)) = $true)) | ? [X11 : term] : ((((X10 @ (lam @ X11))) != $true) & ! [X12 : term] : ((((X10 @ X12)) != $true) | (((X10 @ (sub @ X11 @ (push @ X12 @ id)))) = $true))) | (((X10 @ X9)) = $true) | ? [X13 : term,X14 : term] : ((((X10 @ X13)) = $true) & ($true != ((X10 @ (ap @ X14 @ X13)))) & ($true = ((X10 @ X14))))) | ? [X2 : term,X3 : subst,X1 : (term > $o)] : (! [X6 : term] : (? [X7 : term] : ((((X1 @ X7)) = $true) & (((X1 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X1 @ (lam @ X6))) = $true)) & ! [X8 : term] : ((((X1 @ (sub @ X8 @ X3))) = $true) | (((var @ X8)) != $true)) & (((X1 @ (sub @ X2 @ X3))) != $true) & ! [X4 : term,X5 : term] : (($true = ((X1 @ (ap @ X4 @ X5)))) | ($true != ((X1 @ X5))) | (((X1 @ X4)) != $true)))) | ? [X0 : term] : (((sub @ X0 @ id)) != X0))) & ((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) <=> (substmonoid = $true)) & (! [X283 : subst] : (((comp @ X283 @ id)) = X283) <=> (axidr = $true)) & (((! [X267 : term,X268 : (subst > term > subst > $o)] : ((((X268 @ id @ (lam @ X267) @ id)) = $true) | ? [X271 : subst,X270 : subst,X269 : subst,X272 : term] : ((((X268 @ (comp @ X270 @ X269) @ (sub @ X272 @ X269) @ X271)) != $true) & (((X268 @ X270 @ X272 @ (comp @ X269 @ X271))) = $true)) | ? [X282 : term] : ((((X268 @ id @ X282 @ id)) = $true) & ($true != ((X268 @ id @ (sub @ X267 @ (push @ X282 @ id)) @ id)))) | ? [X275 : subst,X273 : subst,X274 : subst,X276 : term] : ((((X268 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274)) = $true) & (((X268 @ X275 @ X276 @ (comp @ X273 @ X274))) != $true)) | ? [X277 : (subst > term > term)] : (! [X281 : subst,X279 : term,X280 : subst] : (((sub @ (X277 @ X280 @ X279) @ X281)) = ((X277 @ (comp @ X280 @ X281) @ (sub @ X279 @ X281)))) & ! [X278 : term] : ((((X268 @ id @ X278 @ id)) != $true) | (((X268 @ id @ (X277 @ id @ X278) @ id)) = $true)) & (((X268 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true))) | ? [X260 : term,X259 : (subst > term > subst > $o)] : ((((X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id)) != $true) & ! [X261 : (subst > term > term)] : (? [X264 : subst,X263 : subst,X262 : term] : (((sub @ (X261 @ X264 @ X262) @ X263)) != ((X261 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263)))) | ? [X265 : term] : (($true != ((X259 @ id @ (X261 @ id @ X265) @ id))) & (((X259 @ id @ X265 @ id)) = $true)) | (((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id)) = $true)) & ! [X266 : term] : (($true = ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id))) | (((X259 @ id @ X266 @ id)) != $true)))) | ? [X258 : term] : (((sub @ X258 @ id)) != X258)) <=> (hoasinduction_lem3_lthm = $true)) & ! [X284 : d_subst] : (d_id = X284) & (pushprop_lem2v2 = $true) & (((((! [X332 : subst,X333 : (term > $o),X331 : term] : (? [X337 : term] : (! [X338 : term] : ((((X333 @ X338)) != $true) | (((X333 @ (sub @ X337 @ (push @ X338 @ id)))) = $true)) & (((X333 @ (lam @ X337))) != $true)) | ? [X336 : term,X335 : term] : ((((X333 @ X336)) = $true) & (((X333 @ (ap @ X336 @ X335))) != $true) & (((X333 @ X335)) = $true)) | (((X333 @ (sub @ X331 @ X332))) = $true) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X333 @ (sub @ X334 @ X332))) != $true))) | ? [X325 : (term > $o),X326 : term] : (! [X330 : term] : ((((var @ X330)) != $true) | (((X325 @ X330)) = $true)) & ($true != ((X325 @ X326))) & ! [X327 : term] : ((((X325 @ (lam @ X327))) = $true) | (((X325 @ X327)) != $true)) & ! [X328 : term,X329 : term] : ((((X325 @ X328)) != $true) | (((X325 @ X329)) != $true) | (((X325 @ (ap @ X329 @ X328))) = $true)))) | ? [X324 : subst] : (((comp @ X324 @ id)) != X324)) | ? [X322 : term,X323 : subst] : (((comp @ sh @ (push @ X322 @ X323))) != X323)) | ? [X321 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X321))) != X320)) <=> (induction2lem_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X210 : (subst > term > subst > $o),X209 : term] : (? [X213 : (subst > term > term)] : (! [X214 : term] : (($true = ((X210 @ id @ (X213 @ id @ X214) @ id))) | (((X210 @ id @ X214 @ id)) != $true)) & ! [X216 : subst,X217 : term,X215 : subst] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) & (((X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)) != $true)) | (((X210 @ id @ X209 @ id)) = $true) | ? [X212 : term,X211 : term] : (($true = ((X210 @ id @ X212 @ id))) & (((X210 @ id @ X211 @ id)) = $true) & ($true != ((X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id))))) | ? [X201 : (subst > term > subst > $o),X199 : (term > $o),X200 : term] : (($true != ((X199 @ (lam @ X200)))) & ! [X203 : (subst > term > term)] : (? [X206 : subst,X205 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) != ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206)))) | (((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id)) = $true) | ? [X204 : term] : (($true = ((X201 @ id @ X204 @ id))) & (((X201 @ id @ (X203 @ id @ X204) @ id)) != $true))) & ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) & ! [X208 : term] : ((((X199 @ (sub @ X200 @ (push @ X208 @ id)))) = $true) | (((X199 @ X208)) != $true)))) | ? [X198 : term] : (((sub @ X198 @ id)) != X198)) | ? [X192 : term,X191 : (term > $o)] : (! [X196 : term] : (($true = ((X191 @ (lam @ X196)))) | ? [X197 : term] : (($true = ((X191 @ X197))) & (((X191 @ (sub @ X196 @ (push @ X197 @ id)))) != $true))) & ! [X194 : term,X195 : term] : ((((X191 @ (ap @ X195 @ X194))) = $true) | (((X191 @ X195)) != $true) | ($true != ((X191 @ X194)))) & (((X191 @ X192)) != $true) & ! [X193 : term] : ((((var @ X193)) != $true) | (((X191 @ X193)) = $true)))) | ? [X188 : (subst > term > subst > $o)] : ! [X189 : (term > $o)] : ? [X190 : term] : (((X188 @ id @ X190 @ id)) != ((X189 @ X190))))) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X147 : (subst > term > subst > $o)] : ? [X148 : (term > $o)] : ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149)))) & (axabs = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((induction2 = $true) <=> ! [X298 : term,X297 : (term > $o)] : (($true = ((X297 @ X298))) | ? [X299 : term] : ((((X297 @ X299)) != $true) & (((var @ X299)) = $true)) | ? [X302 : term] : (! [X303 : term] : ((((X297 @ X303)) != $true) | ($true = ((X297 @ (sub @ X302 @ (push @ X303 @ id)))))) & (((X297 @ (lam @ X302))) != $true)) | ? [X300 : term,X301 : term] : ((((X297 @ X301)) = $true) & (((X297 @ X300)) = $true) & ($true != ((X297 @ (ap @ X300 @ X301))))))) & (hoasinduction_lem3v2_gthm = $true) & ((axvarcons = $true) <=> ! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493)) & ((pushprop_lem0_lthm = $true) <=> ! [X135 : (term > $o),X137 : subst,X136 : term] : ? [X138 : (term > $o)] : ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139)))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true) | (((X347 @ X345)) != $true)) | ? [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) != X342)) | ? [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) != X340))) & ((induction2lem = $true) <=> ! [X128 : subst,X129 : term,X127 : (term > $o)] : (? [X130 : term] : (! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) & ($true != ((X127 @ (lam @ X130))))) | ? [X132 : term] : ((((X127 @ (sub @ X132 @ X128))) != $true) & (((var @ X132)) = $true)) | (((X127 @ (sub @ X129 @ X128))) = $true) | ? [X133 : term,X134 : term] : ((((X127 @ X133)) = $true) & (((X127 @ (ap @ X134 @ X133))) != $true) & ($true = ((X127 @ X134)))))) & (one = ((d2term @ d_one))) & (pushprop = $true) & (substmonoid_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) != X238) | ! [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) != $true) | ($true = ((X243 @ one))) | ? [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) != ((X243 @ X244)))))) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (? [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) != ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))) | ? [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) != ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))))) & (pushprop_lem3v2 = $true) & ((hoasapinj2_lthm = $true) <=> (! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))) | ? [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 != X222) & (((ap @ X220 @ X222)) = ((ap @ X221 @ X219)))))) & ((apinj2 = $true) <=> ! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & (hoasinduction_lem1v2 = $true) & (ulamvar1 != $true) & (induction2lem_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497))) & (pushprop_lthm_orig = $true) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & (axapp = $true) & ((((! [X61 : subst,X60 : term,X63 : (subst > term > term),X62 : (subst > term > term)] : ((((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))) | ? [X64 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X66 @ X65) @ X64)) != ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | ? [X69 : term,X67 : subst,X68 : subst] : (((sub @ (X63 @ X68 @ X69) @ X67)) != ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67))))) | ? [X59 : term,X58 : term] : ((X58 != X59) & (((lam @ X58)) = ((lam @ X59))))) | ? [X56 : term,X57 : subst] : (((comp @ sh @ (push @ X56 @ X57))) != X57)) | ? [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) != X55)) <=> (hoaslaminj_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X353 : (term > $o),X355 : term,X354 : (subst > term > subst > $o)] : (? [X356 : (subst > term > term)] : (! [X358 : subst,X359 : term,X357 : subst] : (((X356 @ (comp @ X357 @ X358) @ (sub @ X359 @ X358))) = ((sub @ (X356 @ X357 @ X359) @ X358))) & ! [X360 : term] : ((((X354 @ id @ X360 @ id)) != $true) | ($true = ((X354 @ id @ (X356 @ id @ X360) @ id)))) & ($true != ((X354 @ id @ (lam @ (X356 @ sh @ one)) @ id)))) | ? [X362 : term] : (((X354 @ id @ X362 @ id)) != ((X353 @ X362))) | (((X353 @ (lam @ X355))) = $true) | ? [X361 : term] : ((((X353 @ X361)) = $true) & ($true != ((X353 @ (sub @ X355 @ (push @ X361 @ id))))))) | ? [X352 : term] : (((sub @ X352 @ id)) != X352)) | ? [X348 : term] : ! [X349 : (subst > term > term)] : ? [X350 : term,X351 : subst] : (((sub @ X348 @ (push @ X350 @ X351))) != ((X349 @ X351 @ X350))))) & (lamnotvar = $true) & (! [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true != ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) <=> (pushprop_lem1 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X43 : term,X42 : (subst > term > subst > $o)] : ((((X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id)) = $true) | ? [X53 : term] : ((((X42 @ id @ X53 @ id)) = $true) & (((X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) != $true)) | ? [X44 : (subst > term > term),X45 : term] : (! [X46 : term,X48 : subst,X47 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) & ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49)))) & ! [X52 : term] : ((((X42 @ id @ X52 @ id)) != $true) | (((X42 @ id @ (X44 @ id @ X52) @ id)) = $true)) & (((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) <=> (laminj = $true)) & ((hoasinduction_lthm = $true) <=> (((! [X109 : (subst > term > subst > $o),X110 : term] : (? [X126 : term] : ((((X109 @ id @ X126 @ id)) != $true) & ($true = ((var @ (sub @ X126 @ id))))) | (((X109 @ id @ X110 @ id)) = $true) | ? [X121 : term,X120 : term] : ((((X109 @ id @ X120 @ id)) = $true) & (((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id)) != $true) & (((X109 @ id @ X121 @ id)) = $true)) | ? [X115 : (subst > term > term)] : (! [X119 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) & (((X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) != $true) & ! [X116 : term] : (($true = ((X109 @ id @ (X115 @ id @ X116) @ id))) | (((X109 @ id @ X116 @ id)) != $true))) | ? [X111 : subst,X113 : subst,X112 : subst,X114 : term] : ((((X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) = $true) & (((X109 @ X113 @ X114 @ (comp @ X112 @ X111))) != $true)) | ? [X123 : subst,X125 : subst,X124 : term,X122 : subst] : (($true = ((X109 @ X123 @ X124 @ (comp @ X122 @ X125)))) & ($true != ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125))))) | ? [X94 : (subst > term > subst > $o),X93 : term] : (! [X98 : subst,X96 : subst,X97 : term,X95 : subst] : ((((X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) != $true) | (((X94 @ X95 @ X97 @ (comp @ X98 @ X96))) = $true)) & ! [X99 : term] : ((((X94 @ id @ X99 @ id)) != $true) | (((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id)) = $true)) & ! [X107 : term,X108 : subst,X106 : subst,X105 : subst] : (($true = ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106))) | (((X94 @ X105 @ X107 @ (comp @ X108 @ X106))) != $true)) & ! [X100 : (subst > term > term)] : (($true = ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id))) | ? [X104 : term] : ((((X94 @ id @ X104 @ id)) = $true) & (((X94 @ id @ (X100 @ id @ X104) @ id)) != $true)) | ? [X103 : subst,X101 : term,X102 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) != ((sub @ (X100 @ X102 @ X101) @ X103)))) & ($true != ((X94 @ id @ (lam @ X93) @ id))))) | ? [X80 : term,X82 : (subst > term > subst > $o),X81 : term] : (! [X89 : subst,X88 : subst,X90 : subst,X87 : term] : ((((X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) != $true) | ($true = ((X82 @ X88 @ X87 @ (comp @ X89 @ X90))))) & (((X82 @ id @ (ap @ X81 @ X80) @ id)) != $true) & ($true = ((X82 @ id @ X80 @ id))) & (((X82 @ id @ X81 @ id)) = $true) & ! [X92 : term,X91 : term] : ((((X82 @ id @ X91 @ id)) != $true) | (((X82 @ id @ X92 @ id)) != $true) | ($true = ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id)))) & ! [X86 : subst,X84 : subst,X83 : subst,X85 : term] : ((((X82 @ X84 @ X85 @ (comp @ X83 @ X86))) != $true) | (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) = $true)))) | ? [X74 : term,X73 : (term > $o)] : (! [X77 : term] : ((((X73 @ X77)) = $true) | (((var @ X77)) != $true)) & ! [X78 : term,X79 : term] : ((((X73 @ X78)) != $true) | (((X73 @ (ap @ X78 @ X79))) = $true) | (((X73 @ X79)) != $true)) & ! [X75 : term] : (? [X76 : term] : ((((X73 @ (sub @ X75 @ (push @ X76 @ id)))) != $true) & (((X73 @ X76)) = $true)) | (((X73 @ (lam @ X75))) = $true)) & ($true != ((X73 @ X74)))))) & ((pushprop_lem0 = $true) <=> ! [X33 : subst,X34 : (term > $o),X35 : term] : ? [X36 : (term > $o)] : ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37)))) & (! [X156 : term,X155 : (term > $o),X154 : term,X157 : (subst > term > subst > $o)] : (? [X160 : subst,X159 : subst,X161 : term,X158 : subst] : ((((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158)) != $true) & ($true = ((X157 @ X160 @ X161 @ (comp @ X159 @ X158))))) | ($true != ((X155 @ X156))) | ? [X163 : term,X162 : term] : ((((X157 @ id @ X163 @ id)) = $true) & (((X157 @ id @ X162 @ id)) = $true) & (((X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) != $true)) | ? [X164 : term] : (((X155 @ X164)) != ((X157 @ id @ X164 @ id))) | (((X155 @ X154)) != $true) | (((X155 @ (ap @ X154 @ X156))) = $true) | ? [X167 : subst,X168 : subst,X165 : subst,X166 : term] : ((((X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165)) = $true) & (((X157 @ X167 @ X166 @ (comp @ X168 @ X165))) != $true))) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X180 : term,X181 : (subst > term > subst > $o)] : (? [X187 : term] : ((((X181 @ id @ X187 @ id)) = $true) & ($true != ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)))) | ? [X182 : (subst > term > term)] : (($true != ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id))) & ! [X185 : subst,X186 : term,X184 : subst] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185)))) & ! [X183 : term] : ((((X181 @ id @ (X182 @ id @ X183) @ id)) = $true) | (((X181 @ id @ X183 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true)) | ? [X173 : (subst > term > subst > $o),X172 : term] : (($true != ((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id))) & ! [X179 : term] : ((((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id)) = $true) | ($true != ((X173 @ id @ X179 @ id)))) & ! [X174 : (subst > term > term)] : (($true = ((X173 @ id @ (lam @ (X174 @ sh @ one)) @ id))) | ? [X178 : term] : ((((X173 @ id @ X178 @ id)) = $true) & (((X173 @ id @ (X174 @ id @ X178) @ id)) != $true)) | ? [X176 : subst,X177 : term,X175 : subst] : (((sub @ (X174 @ X175 @ X177) @ X176)) != ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176))))))) | ? [X171 : term] : (((sub @ X171 @ id)) != X171))) & (axassoc = $true) & (hoaslamnotvar = $true) & (! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) <=> (hoasapinj1 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & ! [X218 : d_term] : (d_one = X218) & (hoasapnotvar_lthm = $true) & (! [X499 : (subst > term > subst > $o),X500 : term] : (? [X501 : term] : ((((X499 @ id @ (sub @ X500 @ (push @ X501 @ id)) @ id)) != $true) & ($true = ((X499 @ id @ X501 @ id)))) | ? [X502 : (subst > term > term)] : (! [X505 : term,X504 : subst,X503 : subst] : (((X502 @ (comp @ X503 @ X504) @ (sub @ X505 @ X504))) = ((sub @ (X502 @ X503 @ X505) @ X504))) & (((X499 @ id @ (lam @ (X502 @ sh @ one)) @ id)) != $true) & ! [X506 : term] : ((((X499 @ id @ (X502 @ id @ X506) @ id)) = $true) | ($true != ((X499 @ id @ X506 @ id))))) | (((X499 @ id @ (lam @ X500) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & (termmset_gthm = $true) & (! [X20 : term] : ? [X21 : (subst > term > term)] : ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoaslamnotvar_lthm = $true) & ((((! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)) | ? [X416 : subst] : (((comp @ X416 @ id)) != X416)) | ? [X415 : subst] : (((comp @ id @ X415)) != X415)) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X305 : (subst > term > subst > $o),X304 : term] : (? [X315 : (subst > term > term)] : ((((X305 @ id @ (lam @ (X315 @ sh @ one)) @ id)) != $true) & ! [X319 : term] : ((((X305 @ id @ X319 @ id)) != $true) | (((X305 @ id @ (X315 @ id @ X319) @ id)) = $true)) & ! [X316 : subst,X318 : term,X317 : subst] : (((sub @ (X315 @ X316 @ X318) @ X317)) = ((X315 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317))))) | ? [X314 : subst,X313 : subst,X311 : term,X312 : subst] : (($true = ((X305 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314))) & (((X305 @ X313 @ X311 @ (comp @ X312 @ X314))) != $true)) | ? [X310 : subst,X309 : term,X307 : subst,X308 : subst] : ((((X305 @ X308 @ X309 @ (comp @ X310 @ X307))) = $true) & (((X305 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310) @ X307)) != $true)) | (((X305 @ id @ (lam @ X304) @ id)) = $true) | ? [X306 : term] : ((((X305 @ id @ X306 @ id)) = $true) & ($true != ((X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id)))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X384 : term,X385 : (subst > term > subst > $o)] : (? [X386 : subst,X387 : subst,X388 : subst,X389 : term] : ((((X385 @ X388 @ X389 @ (comp @ X386 @ X387))) != $true) & ($true = ((X385 @ (comp @ X388 @ X386) @ (sub @ X389 @ X386) @ X387)))) | ? [X391 : (subst > term > term)] : (($true != ((X385 @ id @ (lam @ (X391 @ sh @ one)) @ id))) & ! [X392 : term] : (($true = ((X385 @ id @ (X391 @ id @ X392) @ id))) | (((X385 @ id @ X392 @ id)) != $true)) & ! [X393 : subst,X395 : term,X394 : subst] : (((sub @ (X391 @ X394 @ X395) @ X393)) = ((X391 @ (comp @ X394 @ X393) @ (sub @ X395 @ X393))))) | (((X385 @ id @ X384 @ id)) = $true) | ? [X401 : term,X400 : term] : (($true = ((X385 @ id @ X401 @ id))) & (((X385 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X385 @ id @ X400 @ id)) = $true)) | ? [X396 : subst,X399 : term,X397 : subst,X398 : subst] : ((((X385 @ (comp @ X398 @ X397) @ (sub @ X399 @ X397) @ X396)) != $true) & ($true = ((X385 @ X398 @ X399 @ (comp @ X397 @ X396))))) | ? [X390 : term] : ((((var @ (sub @ X390 @ id))) = $true) & (((X385 @ id @ X390 @ id)) != $true))) | ? [X375 : (subst > term > subst > $o),X376 : (term > $o),X374 : term] : (! [X383 : term] : (((X376 @ X383)) = ((X375 @ id @ X383 @ id))) & ! [X377 : term] : (($true = ((X376 @ (sub @ X374 @ (push @ X377 @ id))))) | (((X376 @ X377)) != $true)) & ($true != ((X376 @ (lam @ X374)))) & ! [X378 : (subst > term > term)] : (? [X382 : term] : (($true != ((X375 @ id @ (X378 @ id @ X382) @ id))) & (((X375 @ id @ X382 @ id)) = $true)) | (((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id)) = $true) | ? [X380 : term,X381 : subst,X379 : subst] : (((sub @ (X378 @ X379 @ X380) @ X381)) != ((X378 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))))))) | ? [X373 : term] : (((sub @ X373 @ id)) != X373)) | ? [X366 : (term > $o),X367 : term] : (! [X371 : term,X370 : term] : ((((X366 @ X370)) != $true) | (((X366 @ (ap @ X371 @ X370))) = $true) | (((X366 @ X371)) != $true)) & ! [X368 : term] : (? [X369 : term] : ((((X366 @ (sub @ X368 @ (push @ X369 @ id)))) != $true) & (((X366 @ X369)) = $true)) | ($true = ((X366 @ (lam @ X368))))) & (((X366 @ X367)) != $true) & ! [X372 : term] : ((((X366 @ X372)) = $true) | (((var @ X372)) != $true)))) | ? [X363 : (subst > term > subst > $o)] : ! [X364 : (term > $o)] : ? [X365 : term] : (((X363 @ id @ X365 @ id)) != ((X364 @ X365))))) & (lamnotap != $true) & ((hoasinduction = $true) <=> ! [X522 : term,X523 : (subst > term > subst > $o)] : (? [X538 : term,X539 : term] : (($true = ((X523 @ id @ X538 @ id))) & (((X523 @ id @ X539 @ id)) = $true) & (((X523 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) != $true)) | ? [X528 : (subst > term > term)] : (! [X532 : term] : ((((X523 @ id @ (X528 @ id @ X532) @ id)) = $true) | (((X523 @ id @ X532 @ id)) != $true)) & ! [X530 : term,X531 : subst,X529 : subst] : (((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531))) = ((sub @ (X528 @ X529 @ X530) @ X531))) & (((X523 @ id @ (lam @ (X528 @ sh @ one)) @ id)) != $true)) | ($true = ((X523 @ id @ X522 @ id))) | ? [X533 : term] : (($true != ((X523 @ id @ X533 @ id))) & (((var @ (sub @ X533 @ id))) = $true)) | ? [X525 : subst,X527 : subst,X524 : subst,X526 : term] : (($true != ((X523 @ (comp @ X525 @ X527) @ (sub @ X526 @ X527) @ X524))) & ($true = ((X523 @ X525 @ X526 @ (comp @ X527 @ X524))))) | ? [X536 : subst,X537 : term,X535 : subst,X534 : subst] : (($true != ((X523 @ X536 @ X537 @ (comp @ X535 @ X534)))) & (((X523 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X534)) = $true)))) & (induction2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X141 : d_subst,X140 : d_subst] : ((((d2subst @ X140)) != ((d2subst @ X141))) | (X140 = X141)) & (pushprop_lem1v2_gthm = $true) & (! [X227 : (term > $o),X228 : term] : (? [X229 : term,X230 : term] : ((((X227 @ X230)) = $true) & (((X227 @ X229)) = $true) & (((X227 @ (ap @ X229 @ X230))) != $true)) | ? [X231 : term] : ((((X227 @ X231)) = $true) & ($true != ((X227 @ (lam @ X231))))) | ? [X232 : term] : (($true = ((var @ X232))) & (((X227 @ X232)) != $true)) | (((X227 @ X228)) = $true)) <=> (induction = $true)) & (! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) <=> (axscons = $true)) & (! [X433 : term,X432 : (subst > term > term),X434 : term] : (? [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) != ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (hoaslamnotap_lthm = $true) & (hoaslamnotap_gthm = $true) & ((apinj1 = $true) <=> ! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X459 : (subst > term > subst > $o)] : ? [X460 : (term > $o)] : ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461)))) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & ! [X18 : d_term,X19 : d_term] : ((((d2term @ X18)) != ((d2term @ X19))) | (X18 = X19)) & ((axvarid = $true) <=> ! [X402 : term] : (((sub @ X402 @ id)) = X402)) & (! [X440 : (term > $o),X439 : term,X438 : (subst > term > subst > $o)] : ((((X440 @ (lam @ X439))) = $true) | ? [X455 : term] : (((X438 @ id @ X455 @ id)) != ((X440 @ X455))) | ? [X449 : term] : ((((X440 @ X449)) = $true) & (((X440 @ (sub @ X439 @ (push @ X449 @ id)))) != $true)) | ? [X445 : subst,X448 : subst,X446 : subst,X447 : term] : ((((X438 @ (comp @ X445 @ X448) @ (sub @ X447 @ X448) @ X446)) != $true) & ($true = ((X438 @ X445 @ X447 @ (comp @ X448 @ X446))))) | ? [X450 : (subst > term > term)] : (! [X453 : subst,X454 : subst,X452 : term] : (((X450 @ (comp @ X454 @ X453) @ (sub @ X452 @ X453))) = ((sub @ (X450 @ X454 @ X452) @ X453))) & (((X438 @ id @ (lam @ (X450 @ sh @ one)) @ id)) != $true) & ! [X451 : term] : ((((X438 @ id @ X451 @ id)) != $true) | (((X438 @ id @ (X450 @ id @ X451) @ id)) = $true))) | ? [X442 : subst,X441 : subst,X443 : term,X444 : subst] : ((((X438 @ (comp @ X444 @ X441) @ (sub @ X443 @ X441) @ X442)) = $true) & (((X438 @ X444 @ X443 @ (comp @ X441 @ X442))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (apnotvar = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X249 : term,X250 : (subst > term > subst > $o)] : (? [X253 : (subst > term > term)] : (! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257))) & (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) != $true) & ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | (((X250 @ id @ X254 @ id)) != $true))) | ? [X252 : term,X251 : term] : (($true = ((X250 @ id @ X251 @ id))) & (((X250 @ id @ X252 @ id)) = $true) & ($true != ((X250 @ id @ (ap @ (sub @ X251 @ id) @ X252) @ id)))) | (((X250 @ id @ X249 @ id)) = $true))) & (! [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) != $true) | (((X233 @ one)) = $true) | ? [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) != ((X233 @ X237)))) <=> (pushprop_lem1v2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axvarshift = $true) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) <=> (termmset = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapnotvar = $true) & (axclos = $true) & (((var @ (d2term @ d_one))) != $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X150 : term] : ? [X151 : (subst > term > term)] : ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153)))) & ((! [X170 : term] : (((sub @ X170 @ id)) = X170) | ? [X169 : term] : (((sub @ X169 @ id)) != X169)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X421 : (subst > term > subst > $o),X419 : term,X420 : term] : (? [X425 : subst,X423 : term,X422 : subst,X424 : subst] : ((((X421 @ (comp @ X425 @ X422) @ (sub @ X423 @ X422) @ X424)) != $true) & (((X421 @ X425 @ X423 @ (comp @ X422 @ X424))) = $true)) | ? [X430 : term,X431 : term] : ((((X421 @ id @ X431 @ id)) = $true) & ($true = ((X421 @ id @ X430 @ id))) & ($true != ((X421 @ id @ (ap @ (sub @ X431 @ id) @ X430) @ id)))) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | (((X421 @ id @ X420 @ id)) != $true) | ? [X428 : term,X426 : subst,X429 : subst,X427 : subst] : ((((X421 @ (comp @ X426 @ X429) @ (sub @ X428 @ X429) @ X427)) = $true) & (((X421 @ X426 @ X428 @ (comp @ X429 @ X427))) != $true)) | ($true != ((X421 @ id @ X419 @ id))))) & (axmap = $true) & (pushprop_lem1_gthm = $true) & (((! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))) | ? [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 != X28) & (((ap @ X28 @ X26)) = ((ap @ X27 @ X25))))) | ? [X24 : term] : (((sub @ X24 @ id)) != X24)) <=> (hoasapinj1_lthm = $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X295 : term] : ? [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) = ((X296 @ sh @ one)))) & (! [X408 : (subst > term > subst > $o),X407 : term] : ((((X408 @ id @ (lam @ (sub @ X407 @ (push @ one @ sh))) @ id)) = $true) | ? [X410 : (subst > term > term)] : ((((X408 @ id @ (lam @ (X410 @ sh @ one)) @ id)) != $true) & ! [X411 : term] : ((((X408 @ id @ (X410 @ id @ X411) @ id)) = $true) | (((X408 @ id @ X411 @ id)) != $true)) & ! [X412 : subst,X413 : subst,X414 : term] : (((sub @ (X410 @ X413 @ X414) @ X412)) = ((X410 @ (comp @ X413 @ X412) @ (sub @ X414 @ X412))))) | ? [X409 : term] : ((((X408 @ id @ (sub @ X407 @ (push @ X409 @ id)) @ id)) != $true) & (((X408 @ id @ X409 @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (ulamvarsh = $true) & (! [X508 : term,X509 : (subst > term > subst > $o),X507 : (term > $o)] : (? [X515 : term] : ((((X507 @ X515)) = $true) & ($true != ((X507 @ (sub @ X508 @ (push @ X515 @ id)))))) | ? [X516 : term] : (((X509 @ id @ X516 @ id)) != ((X507 @ X516))) | ? [X510 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X510 @ sh @ one)) @ id))) & ! [X511 : subst,X513 : term,X512 : subst] : (((X510 @ (comp @ X511 @ X512) @ (sub @ X513 @ X512))) = ((sub @ (X510 @ X511 @ X513) @ X512))) & ! [X514 : term] : ((((X509 @ id @ X514 @ id)) != $true) | (((X509 @ id @ (X510 @ id @ X514) @ id)) = $true))) | ($true = ((X507 @ (lam @ X508))))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem0_gthm = $true) & ((? [X466 : term] : (((sub @ X466 @ id)) != X466) | ! [X468 : term,X467 : (term > $o),X469 : (subst > term > subst > $o)] : (? [X471 : term,X472 : subst,X473 : subst,X470 : subst] : (($true = ((X469 @ X472 @ X471 @ (comp @ X470 @ X473)))) & (((X469 @ (comp @ X472 @ X470) @ (sub @ X471 @ X470) @ X473)) != $true)) | ? [X483 : term] : ((((X467 @ (sub @ X468 @ (push @ X483 @ id)))) != $true) & ($true = ((X467 @ X483)))) | (((X467 @ (lam @ X468))) = $true) | ? [X474 : (subst > term > term)] : (! [X477 : subst,X476 : subst,X475 : term] : (((X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) = ((sub @ (X474 @ X477 @ X475) @ X476))) & ! [X478 : term] : (($true != ((X469 @ id @ X478 @ id))) | (((X469 @ id @ (X474 @ id @ X478) @ id)) = $true)) & (((X469 @ id @ (lam @ (X474 @ sh @ one)) @ id)) != $true)) | ? [X482 : subst,X479 : term,X480 : subst,X481 : subst] : ((((X469 @ (comp @ X481 @ X482) @ (sub @ X479 @ X482) @ X480)) = $true) & (((X469 @ X481 @ X479 @ (comp @ X482 @ X480))) != $true)) | ? [X484 : term] : (((X467 @ X484)) != ((X469 @ id @ X484 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X486 : term,X485 : (subst > term > subst > $o)] : (? [X487 : term] : (($true = ((X485 @ id @ X487 @ id))) & (((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id)) != $true)) | (((X485 @ id @ (lam @ (sub @ X486 @ (push @ one @ sh))) @ id)) = $true) | ? [X488 : (subst > term > term)] : ((((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id)) != $true) & ! [X492 : term] : ((((X485 @ id @ X492 @ id)) != $true) | (((X485 @ id @ (X488 @ id @ X492) @ id)) = $true)) & ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491)))))) <=> (hoasinduction_lem3aa_lthm = $true))),
% 14.62/2.51 inference(ennf_transformation,[],[f10])).
% 14.62/2.51 thf(f12,plain,(
% 14.62/2.51 (hoasinduction_lem1v2 = $true) & (! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) <=> (axscons = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X141 : d_subst,X140 : d_subst] : ((((d2subst @ X140)) != ((d2subst @ X141))) | (X140 = X141)) & ((hoasapinj2_lthm = $true) <=> (! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))) | ? [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 != X222) & (((ap @ X220 @ X222)) = ((ap @ X221 @ X219)))))) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) <=> (? [X416 : subst] : (((comp @ X416 @ id)) != X416) | (! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)) | ? [X415 : subst] : (((comp @ id @ X415)) != X415))) & (! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) <=> (laminj = $true)) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) != $true) | (((X233 @ one)) = $true) | ? [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) != ((X233 @ X237)))) <=> (pushprop_lem1v2 = $true)) & ((! [X61 : subst,X60 : term,X63 : (subst > term > term),X62 : (subst > term > term)] : ((((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))) | ? [X64 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X66 @ X65) @ X64)) != ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | ? [X69 : term,X67 : subst,X68 : subst] : (((sub @ (X63 @ X68 @ X69) @ X67)) != ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67))))) | ? [X59 : term,X58 : term] : ((X58 != X59) & (((lam @ X58)) = ((lam @ X59)))) | ? [X56 : term,X57 : subst] : (((comp @ sh @ (push @ X56 @ X57))) != X57) | ? [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) != X55)) <=> (hoaslaminj_lthm = $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & (! [X408 : (subst > term > subst > $o),X407 : term] : ((((X408 @ id @ (lam @ (sub @ X407 @ (push @ one @ sh))) @ id)) = $true) | ? [X410 : (subst > term > term)] : ((((X408 @ id @ (lam @ (X410 @ sh @ one)) @ id)) != $true) & ! [X411 : term] : ((((X408 @ id @ (X410 @ id @ X411) @ id)) = $true) | (((X408 @ id @ X411 @ id)) != $true)) & ! [X412 : subst,X413 : subst,X414 : term] : (((sub @ (X410 @ X413 @ X414) @ X412)) = ((X410 @ (comp @ X413 @ X412) @ (sub @ X414 @ X412))))) | ? [X409 : term] : ((((X408 @ id @ (sub @ X407 @ (push @ X409 @ id)) @ id)) != $true) & (((X408 @ id @ X409 @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X135 : (term > $o),X137 : subst,X136 : term] : ? [X138 : (term > $o)] : ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139)))) & ((hoaslaminj = $true) <=> ! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (? [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) != ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))) | ? [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) != ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))))) & (axassoc = $true) & ((! [X170 : term] : (((sub @ X170 @ id)) = X170) | ? [X169 : term] : (((sub @ X169 @ id)) != X169)) <=> (termmset_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X33 : subst,X34 : (term > $o),X35 : term] : ? [X36 : (term > $o)] : ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37)))) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((? [X80 : term,X82 : (subst > term > subst > $o),X81 : term] : (! [X89 : subst,X88 : subst,X90 : subst,X87 : term] : ((((X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) != $true) | ($true = ((X82 @ X88 @ X87 @ (comp @ X89 @ X90))))) & (((X82 @ id @ (ap @ X81 @ X80) @ id)) != $true) & ($true = ((X82 @ id @ X80 @ id))) & (((X82 @ id @ X81 @ id)) = $true) & ! [X92 : term,X91 : term] : ((((X82 @ id @ X91 @ id)) != $true) | (((X82 @ id @ X92 @ id)) != $true) | ($true = ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id)))) & ! [X86 : subst,X84 : subst,X83 : subst,X85 : term] : ((((X82 @ X84 @ X85 @ (comp @ X83 @ X86))) != $true) | (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) = $true))) | ? [X94 : (subst > term > subst > $o),X93 : term] : (! [X98 : subst,X96 : subst,X97 : term,X95 : subst] : ((((X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) != $true) | (((X94 @ X95 @ X97 @ (comp @ X98 @ X96))) = $true)) & ! [X99 : term] : ((((X94 @ id @ X99 @ id)) != $true) | (((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id)) = $true)) & ! [X107 : term,X108 : subst,X106 : subst,X105 : subst] : (($true = ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106))) | (((X94 @ X105 @ X107 @ (comp @ X108 @ X106))) != $true)) & ! [X100 : (subst > term > term)] : (($true = ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id))) | ? [X104 : term] : ((((X94 @ id @ X104 @ id)) = $true) & (((X94 @ id @ (X100 @ id @ X104) @ id)) != $true)) | ? [X103 : subst,X101 : term,X102 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) != ((sub @ (X100 @ X102 @ X101) @ X103)))) & ($true != ((X94 @ id @ (lam @ X93) @ id)))) | ! [X109 : (subst > term > subst > $o),X110 : term] : (? [X126 : term] : ((((X109 @ id @ X126 @ id)) != $true) & ($true = ((var @ (sub @ X126 @ id))))) | (((X109 @ id @ X110 @ id)) = $true) | ? [X121 : term,X120 : term] : ((((X109 @ id @ X120 @ id)) = $true) & (((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id)) != $true) & (((X109 @ id @ X121 @ id)) = $true)) | ? [X115 : (subst > term > term)] : (! [X119 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) & (((X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) != $true) & ! [X116 : term] : (($true = ((X109 @ id @ (X115 @ id @ X116) @ id))) | (((X109 @ id @ X116 @ id)) != $true))) | ? [X111 : subst,X113 : subst,X112 : subst,X114 : term] : ((((X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) = $true) & (((X109 @ X113 @ X114 @ (comp @ X112 @ X111))) != $true)) | ? [X123 : subst,X125 : subst,X124 : term,X122 : subst] : (($true = ((X109 @ X123 @ X124 @ (comp @ X122 @ X125)))) & ($true != ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125))))) | ? [X74 : term,X73 : (term > $o)] : (! [X77 : term] : ((((X73 @ X77)) = $true) | (((var @ X77)) != $true)) & ! [X78 : term,X79 : term] : ((((X73 @ X78)) != $true) | (((X73 @ (ap @ X78 @ X79))) = $true) | (((X73 @ X79)) != $true)) & ! [X75 : term] : (? [X76 : term] : ((((X73 @ (sub @ X75 @ (push @ X76 @ id)))) != $true) & (((X73 @ X76)) = $true)) | (((X73 @ (lam @ X75))) = $true)) & ($true != ((X73 @ X74))))) <=> (hoasinduction_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3 = $true) <=> ! [X305 : (subst > term > subst > $o),X304 : term] : (? [X315 : (subst > term > term)] : ((((X305 @ id @ (lam @ (X315 @ sh @ one)) @ id)) != $true) & ! [X319 : term] : ((((X305 @ id @ X319 @ id)) != $true) | (((X305 @ id @ (X315 @ id @ X319) @ id)) = $true)) & ! [X316 : subst,X318 : term,X317 : subst] : (((sub @ (X315 @ X316 @ X318) @ X317)) = ((X315 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317))))) | ? [X314 : subst,X313 : subst,X311 : term,X312 : subst] : (($true = ((X305 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314))) & (((X305 @ X313 @ X311 @ (comp @ X312 @ X314))) != $true)) | ? [X310 : subst,X309 : term,X307 : subst,X308 : subst] : ((((X305 @ X308 @ X309 @ (comp @ X310 @ X307))) = $true) & (((X305 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310) @ X307)) != $true)) | (((X305 @ id @ (lam @ X304) @ id)) = $true) | ? [X306 : term] : ((((X305 @ id @ X306 @ id)) = $true) & ($true != ((X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id)))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X145 : term] : ? [X146 : (subst > term > term)] : (((X146 @ sh @ one)) = ((sub @ X145 @ (push @ one @ sh))))) & ((hoasapinj2 = $true) <=> ! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497))) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> (shinj = $true)) & (hoasapinj2_gthm = $true) & ((? [X258 : term] : (((sub @ X258 @ id)) != X258) | ! [X267 : term,X268 : (subst > term > subst > $o)] : ((((X268 @ id @ (lam @ X267) @ id)) = $true) | ? [X271 : subst,X270 : subst,X269 : subst,X272 : term] : ((((X268 @ (comp @ X270 @ X269) @ (sub @ X272 @ X269) @ X271)) != $true) & (((X268 @ X270 @ X272 @ (comp @ X269 @ X271))) = $true)) | ? [X282 : term] : ((((X268 @ id @ X282 @ id)) = $true) & ($true != ((X268 @ id @ (sub @ X267 @ (push @ X282 @ id)) @ id)))) | ? [X275 : subst,X273 : subst,X274 : subst,X276 : term] : ((((X268 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274)) = $true) & (((X268 @ X275 @ X276 @ (comp @ X273 @ X274))) != $true)) | ? [X277 : (subst > term > term)] : (! [X281 : subst,X279 : term,X280 : subst] : (((sub @ (X277 @ X280 @ X279) @ X281)) = ((X277 @ (comp @ X280 @ X281) @ (sub @ X279 @ X281)))) & ! [X278 : term] : ((((X268 @ id @ X278 @ id)) != $true) | (((X268 @ id @ (X277 @ id @ X278) @ id)) = $true)) & (((X268 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true))) | ? [X260 : term,X259 : (subst > term > subst > $o)] : ((((X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id)) != $true) & ! [X261 : (subst > term > term)] : (? [X264 : subst,X263 : subst,X262 : term] : (((sub @ (X261 @ X264 @ X262) @ X263)) != ((X261 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263)))) | ? [X265 : term] : (($true != ((X259 @ id @ (X261 @ id @ X265) @ id))) & (((X259 @ id @ X265 @ id)) = $true)) | (((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id)) = $true)) & ! [X266 : term] : (($true = ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id))) | (((X259 @ id @ X266 @ id)) != $true)))) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) != X238) | ! [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) != $true) | ($true = ((X243 @ one))) | ? [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) != ((X243 @ X244)))))) & ((? [X325 : (term > $o),X326 : term] : (! [X330 : term] : ((((var @ X330)) != $true) | (((X325 @ X330)) = $true)) & ($true != ((X325 @ X326))) & ! [X327 : term] : ((((X325 @ (lam @ X327))) = $true) | (((X325 @ X327)) != $true)) & ! [X328 : term,X329 : term] : ((((X325 @ X328)) != $true) | (((X325 @ X329)) != $true) | (((X325 @ (ap @ X329 @ X328))) = $true))) | ! [X332 : subst,X333 : (term > $o),X331 : term] : (? [X337 : term] : (! [X338 : term] : ((((X333 @ X338)) != $true) | (((X333 @ (sub @ X337 @ (push @ X338 @ id)))) = $true)) & (((X333 @ (lam @ X337))) != $true)) | ? [X336 : term,X335 : term] : ((((X333 @ X336)) = $true) & (((X333 @ (ap @ X336 @ X335))) != $true) & (((X333 @ X335)) = $true)) | (((X333 @ (sub @ X331 @ X332))) = $true) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X333 @ (sub @ X334 @ X332))) != $true))) | ? [X321 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X321))) != X320) | ? [X322 : term,X323 : subst] : (((comp @ sh @ (push @ X322 @ X323))) != X323) | ? [X324 : subst] : (((comp @ X324 @ id)) != X324)) <=> (induction2lem_lthm = $true)) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) <=> (termmset = $true)) & ((induction2lem = $true) <=> ! [X128 : subst,X129 : term,X127 : (term > $o)] : (? [X130 : term] : (! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) & ($true != ((X127 @ (lam @ X130))))) | ? [X132 : term] : ((((X127 @ (sub @ X132 @ X128))) != $true) & (((var @ X132)) = $true)) | (((X127 @ (sub @ X129 @ X128))) = $true) | ? [X133 : term,X134 : term] : ((((X127 @ X133)) = $true) & (((X127 @ (ap @ X134 @ X133))) != $true) & ($true = ((X127 @ X134)))))) & (pushprop_lem3v2_lthm = $true) & (axvarshift = $true) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & (hoasinduction_lem3b_gthm = $true) & ! [X218 : d_term] : (d_one = X218) & (axapp = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b = $true) <=> ! [X295 : term] : ? [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) = ((X296 @ sh @ one)))) & (induction2lem_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (lamnotap != $true) & ((axvarid = $true) <=> ! [X402 : term] : (((sub @ X402 @ id)) = X402)) & ! [X284 : d_subst] : (d_id = X284) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X348 : term] : ! [X349 : (subst > term > term)] : ? [X350 : term,X351 : subst] : (((sub @ X348 @ (push @ X350 @ X351))) != ((X349 @ X351 @ X350))) | ! [X353 : (term > $o),X355 : term,X354 : (subst > term > subst > $o)] : (? [X356 : (subst > term > term)] : (! [X358 : subst,X359 : term,X357 : subst] : (((X356 @ (comp @ X357 @ X358) @ (sub @ X359 @ X358))) = ((sub @ (X356 @ X357 @ X359) @ X358))) & ! [X360 : term] : ((((X354 @ id @ X360 @ id)) != $true) | ($true = ((X354 @ id @ (X356 @ id @ X360) @ id)))) & ($true != ((X354 @ id @ (lam @ (X356 @ sh @ one)) @ id)))) | ? [X362 : term] : (((X354 @ id @ X362 @ id)) != ((X353 @ X362))) | (((X353 @ (lam @ X355))) = $true) | ? [X361 : term] : ((((X353 @ X361)) = $true) & ($true != ((X353 @ (sub @ X355 @ (push @ X361 @ id))))))) | ? [X352 : term] : (((sub @ X352 @ id)) != X352))) & (pushprop_lem2v2 = $true) & ((hoasapinj1_lthm = $true) <=> (? [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 != X28) & (((ap @ X28 @ X26)) = ((ap @ X27 @ X25)))) | ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))) | ? [X24 : term] : (((sub @ X24 @ id)) != X24))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem1_lthm = $true) <=> (! [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true) | (((X347 @ X345)) != $true)) | ? [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) != X342) | ? [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) != X340))) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & ((hoasinduction = $true) <=> ! [X522 : term,X523 : (subst > term > subst > $o)] : (? [X538 : term,X539 : term] : (($true = ((X523 @ id @ X538 @ id))) & (((X523 @ id @ X539 @ id)) = $true) & (((X523 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) != $true)) | ? [X528 : (subst > term > term)] : (! [X532 : term] : ((((X523 @ id @ (X528 @ id @ X532) @ id)) = $true) | (((X523 @ id @ X532 @ id)) != $true)) & ! [X530 : term,X531 : subst,X529 : subst] : (((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531))) = ((sub @ (X528 @ X529 @ X530) @ X531))) & (((X523 @ id @ (lam @ (X528 @ sh @ one)) @ id)) != $true)) | ($true = ((X523 @ id @ X522 @ id))) | ? [X533 : term] : (($true != ((X523 @ id @ X533 @ id))) & (((var @ (sub @ X533 @ id))) = $true)) | ? [X525 : subst,X527 : subst,X524 : subst,X526 : term] : (($true != ((X523 @ (comp @ X525 @ X527) @ (sub @ X526 @ X527) @ X524))) & ($true = ((X523 @ X525 @ X526 @ (comp @ X527 @ X524))))) | ? [X536 : subst,X537 : term,X535 : subst,X534 : subst] : (($true != ((X523 @ X536 @ X537 @ (comp @ X535 @ X534)))) & (((X523 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X534)) = $true)))) & (! [X440 : (term > $o),X439 : term,X438 : (subst > term > subst > $o)] : ((((X440 @ (lam @ X439))) = $true) | ? [X455 : term] : (((X438 @ id @ X455 @ id)) != ((X440 @ X455))) | ? [X449 : term] : ((((X440 @ X449)) = $true) & (((X440 @ (sub @ X439 @ (push @ X449 @ id)))) != $true)) | ? [X445 : subst,X448 : subst,X446 : subst,X447 : term] : ((((X438 @ (comp @ X445 @ X448) @ (sub @ X447 @ X448) @ X446)) != $true) & ($true = ((X438 @ X445 @ X447 @ (comp @ X448 @ X446))))) | ? [X450 : (subst > term > term)] : (! [X453 : subst,X454 : subst,X452 : term] : (((X450 @ (comp @ X454 @ X453) @ (sub @ X452 @ X453))) = ((sub @ (X450 @ X454 @ X452) @ X453))) & (((X438 @ id @ (lam @ (X450 @ sh @ one)) @ id)) != $true) & ! [X451 : term] : ((((X438 @ id @ X451 @ id)) != $true) | (((X438 @ id @ (X450 @ id @ X451) @ id)) = $true))) | ? [X442 : subst,X441 : subst,X443 : term,X444 : subst] : ((((X438 @ (comp @ X444 @ X441) @ (sub @ X443 @ X441) @ X442)) = $true) & (((X438 @ X444 @ X443 @ (comp @ X441 @ X442))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X249 : term,X250 : (subst > term > subst > $o)] : (? [X253 : (subst > term > term)] : (! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257))) & (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) != $true) & ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | (((X250 @ id @ X254 @ id)) != $true))) | ? [X252 : term,X251 : term] : (($true = ((X250 @ id @ X251 @ id))) & (((X250 @ id @ X252 @ id)) = $true) & ($true != ((X250 @ id @ (ap @ (sub @ X251 @ id) @ X252) @ id)))) | (((X250 @ id @ X249 @ id)) = $true))) & (substmonoid_gthm = $true) & ((? [X466 : term] : (((sub @ X466 @ id)) != X466) | ! [X468 : term,X467 : (term > $o),X469 : (subst > term > subst > $o)] : (? [X471 : term,X472 : subst,X473 : subst,X470 : subst] : (($true = ((X469 @ X472 @ X471 @ (comp @ X470 @ X473)))) & (((X469 @ (comp @ X472 @ X470) @ (sub @ X471 @ X470) @ X473)) != $true)) | ? [X483 : term] : ((((X467 @ (sub @ X468 @ (push @ X483 @ id)))) != $true) & ($true = ((X467 @ X483)))) | (((X467 @ (lam @ X468))) = $true) | ? [X474 : (subst > term > term)] : (! [X477 : subst,X476 : subst,X475 : term] : (((X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) = ((sub @ (X474 @ X477 @ X475) @ X476))) & ! [X478 : term] : (($true != ((X469 @ id @ X478 @ id))) | (((X469 @ id @ (X474 @ id @ X478) @ id)) = $true)) & (((X469 @ id @ (lam @ (X474 @ sh @ one)) @ id)) != $true)) | ? [X482 : subst,X479 : term,X480 : subst,X481 : subst] : ((((X469 @ (comp @ X481 @ X482) @ (sub @ X479 @ X482) @ X480)) = $true) & (((X469 @ X481 @ X479 @ (comp @ X482 @ X480))) != $true)) | ? [X484 : term] : (((X467 @ X484)) != ((X469 @ id @ X484 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X43 : term,X42 : (subst > term > subst > $o)] : ((((X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id)) = $true) | ? [X53 : term] : ((((X42 @ id @ X53 @ id)) = $true) & (((X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) != $true)) | ? [X44 : (subst > term > term),X45 : term] : (! [X46 : term,X48 : subst,X47 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) & ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49)))) & ! [X52 : term] : ((((X42 @ id @ X52 @ id)) != $true) | (((X42 @ id @ (X44 @ id @ X52) @ id)) = $true)) & (((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3a_gthm = $true) & (axabs = $true) & ((apinj2 = $true) <=> ! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X171 : term] : (((sub @ X171 @ id)) != X171) | ? [X173 : (subst > term > subst > $o),X172 : term] : (($true != ((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id))) & ! [X179 : term] : ((((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id)) = $true) | ($true != ((X173 @ id @ X179 @ id)))) & ! [X174 : (subst > term > term)] : (($true = ((X173 @ id @ (lam @ (X174 @ sh @ one)) @ id))) | ? [X178 : term] : ((((X173 @ id @ X178 @ id)) = $true) & (((X173 @ id @ (X174 @ id @ X178) @ id)) != $true)) | ? [X176 : subst,X177 : term,X175 : subst] : (((sub @ (X174 @ X175 @ X177) @ X176)) != ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176)))))) | ! [X180 : term,X181 : (subst > term > subst > $o)] : (? [X187 : term] : ((((X181 @ id @ X187 @ id)) = $true) & ($true != ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)))) | ? [X182 : (subst > term > term)] : (($true != ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id))) & ! [X185 : subst,X186 : term,X184 : subst] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185)))) & ! [X183 : term] : ((((X181 @ id @ (X182 @ id @ X183) @ id)) = $true) | (((X181 @ id @ X183 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true)))) & ((induction2 = $true) <=> ! [X298 : term,X297 : (term > $o)] : (($true = ((X297 @ X298))) | ? [X299 : term] : ((((X297 @ X299)) != $true) & (((var @ X299)) = $true)) | ? [X302 : term] : (! [X303 : term] : ((((X297 @ X303)) != $true) | ($true = ((X297 @ (sub @ X302 @ (push @ X303 @ id)))))) & (((X297 @ (lam @ X302))) != $true)) | ? [X300 : term,X301 : term] : ((((X297 @ X301)) = $true) & (((X297 @ X300)) = $true) & ($true != ((X297 @ (ap @ X300 @ X301))))))) & (ulamvarind = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X421 : (subst > term > subst > $o),X419 : term,X420 : term] : (? [X425 : subst,X423 : term,X422 : subst,X424 : subst] : ((((X421 @ (comp @ X425 @ X422) @ (sub @ X423 @ X422) @ X424)) != $true) & (((X421 @ X425 @ X423 @ (comp @ X422 @ X424))) = $true)) | ? [X430 : term,X431 : term] : ((((X421 @ id @ X431 @ id)) = $true) & ($true = ((X421 @ id @ X430 @ id))) & ($true != ((X421 @ id @ (ap @ (sub @ X431 @ id) @ X430) @ id)))) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | (((X421 @ id @ X420 @ id)) != $true) | ? [X428 : term,X426 : subst,X429 : subst,X427 : subst] : ((((X421 @ (comp @ X426 @ X429) @ (sub @ X428 @ X429) @ X427)) = $true) & (((X421 @ X426 @ X428 @ (comp @ X429 @ X427))) != $true)) | ($true != ((X421 @ id @ X419 @ id))))) & (! [X156 : term,X155 : (term > $o),X154 : term,X157 : (subst > term > subst > $o)] : (? [X160 : subst,X159 : subst,X161 : term,X158 : subst] : ((((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158)) != $true) & ($true = ((X157 @ X160 @ X161 @ (comp @ X159 @ X158))))) | ($true != ((X155 @ X156))) | ? [X163 : term,X162 : term] : ((((X157 @ id @ X163 @ id)) = $true) & (((X157 @ id @ X162 @ id)) = $true) & (((X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) != $true)) | ? [X164 : term] : (((X155 @ X164)) != ((X157 @ id @ X164 @ id))) | (((X155 @ X154)) != $true) | (((X155 @ (ap @ X154 @ X156))) = $true) | ? [X167 : subst,X168 : subst,X165 : subst,X166 : term] : ((((X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165)) = $true) & (((X157 @ X167 @ X166 @ (comp @ X168 @ X165))) != $true))) <=> (hoasinduction_lem2v2 = $true)) & ((? [X2 : term,X3 : subst,X1 : (term > $o)] : (! [X6 : term] : (? [X7 : term] : ((((X1 @ X7)) = $true) & (((X1 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X1 @ (lam @ X6))) = $true)) & ! [X8 : term] : ((((X1 @ (sub @ X8 @ X3))) = $true) | (((var @ X8)) != $true)) & (((X1 @ (sub @ X2 @ X3))) != $true) & ! [X4 : term,X5 : term] : (($true = ((X1 @ (ap @ X4 @ X5)))) | ($true != ((X1 @ X5))) | (((X1 @ X4)) != $true))) | ! [X10 : (term > $o),X9 : term] : (? [X15 : term] : ((((X10 @ X15)) != $true) & (((var @ X15)) = $true)) | ? [X11 : term] : ((((X10 @ (lam @ X11))) != $true) & ! [X12 : term] : ((((X10 @ X12)) != $true) | (((X10 @ (sub @ X11 @ (push @ X12 @ id)))) = $true))) | (((X10 @ X9)) = $true) | ? [X13 : term,X14 : term] : ((((X10 @ X13)) = $true) & ($true != ((X10 @ (ap @ X14 @ X13)))) & ($true = ((X10 @ X14))))) | ? [X0 : term] : (((sub @ X0 @ id)) != X0)) <=> (induction2_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((? [X373 : term] : (((sub @ X373 @ id)) != X373) | ? [X375 : (subst > term > subst > $o),X376 : (term > $o),X374 : term] : (! [X383 : term] : (((X376 @ X383)) = ((X375 @ id @ X383 @ id))) & ! [X377 : term] : (($true = ((X376 @ (sub @ X374 @ (push @ X377 @ id))))) | (((X376 @ X377)) != $true)) & ($true != ((X376 @ (lam @ X374)))) & ! [X378 : (subst > term > term)] : (? [X382 : term] : (($true != ((X375 @ id @ (X378 @ id @ X382) @ id))) & (((X375 @ id @ X382 @ id)) = $true)) | (((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id)) = $true) | ? [X380 : term,X381 : subst,X379 : subst] : (((sub @ (X378 @ X379 @ X380) @ X381)) != ((X378 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381)))))) | ? [X366 : (term > $o),X367 : term] : (! [X371 : term,X370 : term] : ((((X366 @ X370)) != $true) | (((X366 @ (ap @ X371 @ X370))) = $true) | (((X366 @ X371)) != $true)) & ! [X368 : term] : (? [X369 : term] : ((((X366 @ (sub @ X368 @ (push @ X369 @ id)))) != $true) & (((X366 @ X369)) = $true)) | ($true = ((X366 @ (lam @ X368))))) & (((X366 @ X367)) != $true) & ! [X372 : term] : ((((X366 @ X372)) = $true) | (((var @ X372)) != $true))) | ? [X363 : (subst > term > subst > $o)] : ! [X364 : (term > $o)] : ? [X365 : term] : (((X363 @ id @ X365 @ id)) != ((X364 @ X365))) | ! [X384 : term,X385 : (subst > term > subst > $o)] : (? [X386 : subst,X387 : subst,X388 : subst,X389 : term] : ((((X385 @ X388 @ X389 @ (comp @ X386 @ X387))) != $true) & ($true = ((X385 @ (comp @ X388 @ X386) @ (sub @ X389 @ X386) @ X387)))) | ? [X391 : (subst > term > term)] : (($true != ((X385 @ id @ (lam @ (X391 @ sh @ one)) @ id))) & ! [X392 : term] : (($true = ((X385 @ id @ (X391 @ id @ X392) @ id))) | (((X385 @ id @ X392 @ id)) != $true)) & ! [X393 : subst,X395 : term,X394 : subst] : (((sub @ (X391 @ X394 @ X395) @ X393)) = ((X391 @ (comp @ X394 @ X393) @ (sub @ X395 @ X393))))) | (((X385 @ id @ X384 @ id)) = $true) | ? [X401 : term,X400 : term] : (($true = ((X385 @ id @ X401 @ id))) & (((X385 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X385 @ id @ X400 @ id)) = $true)) | ? [X396 : subst,X399 : term,X397 : subst,X398 : subst] : ((((X385 @ (comp @ X398 @ X397) @ (sub @ X399 @ X397) @ X396)) != $true) & ($true = ((X385 @ X398 @ X399 @ (comp @ X397 @ X396))))) | ? [X390 : term] : ((((var @ (sub @ X390 @ id))) = $true) & (((X385 @ id @ X390 @ id)) != $true)))) <=> (hoasinduction_lthm_3 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = id) & (! [X508 : term,X509 : (subst > term > subst > $o),X507 : (term > $o)] : (? [X515 : term] : ((((X507 @ X515)) = $true) & ($true != ((X507 @ (sub @ X508 @ (push @ X515 @ id)))))) | ? [X516 : term] : (((X509 @ id @ X516 @ id)) != ((X507 @ X516))) | ? [X510 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X510 @ sh @ one)) @ id))) & ! [X511 : subst,X513 : term,X512 : subst] : (((X510 @ (comp @ X511 @ X512) @ (sub @ X513 @ X512))) = ((sub @ (X510 @ X511 @ X513) @ X512))) & ! [X514 : term] : ((((X509 @ id @ X514 @ id)) != $true) | (((X509 @ id @ (X510 @ id @ X514) @ id)) = $true))) | ($true = ((X507 @ (lam @ X508))))) <=> (hoasinduction_lem3v2a = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X150 : term] : ? [X151 : (subst > term > term)] : ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153)))) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (axmap = $true) & (ulamvar1 != $true) & (pushprop = $true) & (apnotvar = $true) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & ((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) <=> (substmonoid = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X147 : (subst > term > subst > $o)] : ? [X148 : (term > $o)] : ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149)))) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X283 : subst] : (((comp @ X283 @ id)) = X283) <=> (axidr = $true)) & (! [X499 : (subst > term > subst > $o),X500 : term] : (? [X501 : term] : ((((X499 @ id @ (sub @ X500 @ (push @ X501 @ id)) @ id)) != $true) & ($true = ((X499 @ id @ X501 @ id)))) | ? [X502 : (subst > term > term)] : (! [X505 : term,X504 : subst,X503 : subst] : (((X502 @ (comp @ X503 @ X504) @ (sub @ X505 @ X504))) = ((sub @ (X502 @ X503 @ X505) @ X504))) & (((X499 @ id @ (lam @ (X502 @ sh @ one)) @ id)) != $true) & ! [X506 : term] : ((((X499 @ id @ (X502 @ id @ X506) @ id)) = $true) | ($true != ((X499 @ id @ X506 @ id))))) | (((X499 @ id @ (lam @ X500) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> (axshiftcons = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X459 : (subst > term > subst > $o)] : ? [X460 : (term > $o)] : ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461)))) & (hoasinduction_lem1 = $true) & ((? [X198 : term] : (((sub @ X198 @ id)) != X198) | ? [X192 : term,X191 : (term > $o)] : (! [X196 : term] : (($true = ((X191 @ (lam @ X196)))) | ? [X197 : term] : (($true = ((X191 @ X197))) & (((X191 @ (sub @ X196 @ (push @ X197 @ id)))) != $true))) & ! [X194 : term,X195 : term] : ((((X191 @ (ap @ X195 @ X194))) = $true) | (((X191 @ X195)) != $true) | ($true != ((X191 @ X194)))) & (((X191 @ X192)) != $true) & ! [X193 : term] : ((((var @ X193)) != $true) | (((X191 @ X193)) = $true))) | ? [X188 : (subst > term > subst > $o)] : ! [X189 : (term > $o)] : ? [X190 : term] : (((X188 @ id @ X190 @ id)) != ((X189 @ X190))) | ! [X210 : (subst > term > subst > $o),X209 : term] : (? [X213 : (subst > term > term)] : (! [X214 : term] : (($true = ((X210 @ id @ (X213 @ id @ X214) @ id))) | (((X210 @ id @ X214 @ id)) != $true)) & ! [X216 : subst,X217 : term,X215 : subst] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) & (((X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)) != $true)) | (((X210 @ id @ X209 @ id)) = $true) | ? [X212 : term,X211 : term] : (($true = ((X210 @ id @ X212 @ id))) & (((X210 @ id @ X211 @ id)) = $true) & ($true != ((X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id))))) | ? [X201 : (subst > term > subst > $o),X199 : (term > $o),X200 : term] : (($true != ((X199 @ (lam @ X200)))) & ! [X203 : (subst > term > term)] : (? [X206 : subst,X205 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) != ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206)))) | (((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id)) = $true) | ? [X204 : term] : (($true = ((X201 @ id @ X204 @ id))) & (((X201 @ id @ (X203 @ id @ X204) @ id)) != $true))) & ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) & ! [X208 : term] : ((((X199 @ (sub @ X200 @ (push @ X208 @ id)))) = $true) | (((X199 @ X208)) != $true)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axvarcons = $true) <=> ! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493)) & (! [X486 : term,X485 : (subst > term > subst > $o)] : (? [X487 : term] : (($true = ((X485 @ id @ X487 @ id))) & (((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id)) != $true)) | (((X485 @ id @ (lam @ (sub @ X486 @ (push @ one @ sh))) @ id)) = $true) | ? [X488 : (subst > term > term)] : ((((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id)) != $true) & ! [X492 : term] : ((((X485 @ id @ X492 @ id)) != $true) | (((X485 @ id @ (X488 @ id @ X492) @ id)) = $true)) & ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491)))))) <=> (hoasinduction_lem3aa_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)))))))))))))) & (lamnotvar = $true) & (! [X20 : term] : ? [X21 : (subst > term > term)] : ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true != ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ! [X18 : d_term,X19 : d_term] : ((((d2term @ X18)) != ((d2term @ X19))) | (X18 = X19)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) <=> ! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406))) & (! [X227 : (term > $o),X228 : term] : (? [X229 : term,X230 : term] : ((((X227 @ X230)) = $true) & (((X227 @ X229)) = $true) & (((X227 @ (ap @ X229 @ X230))) != $true)) | ? [X231 : term] : ((((X227 @ X231)) = $true) & ($true != ((X227 @ (lam @ X231))))) | ? [X232 : term] : (($true = ((var @ X232))) & (((X227 @ X232)) != $true)) | (((X227 @ X228)) = $true)) <=> (induction = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem1_gthm = $true) & (! [X433 : term,X432 : (subst > term > term),X434 : term] : (? [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) != ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (termmset_gthm = $true)),
% 14.62/2.51 inference(flattening,[],[f11])).
% 14.62/2.51 thf(f13,definition,(
% 14.62/2.51 ! [X227 : (term > $o)] : ((((sP0 @ X227)) = $true) <=> ? [X229 : term,X230 : term] : ((((X227 @ X230)) = $true) & (((X227 @ X229)) = $true) & (((X227 @ (ap @ X229 @ X230))) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f14,definition,(
% 14.62/2.51 ($true = sP1) <=> ! [X486 : term,X485 : (subst > term > subst > $o)] : (? [X487 : term] : (($true = ((X485 @ id @ X487 @ id))) & (((X485 @ id @ (sub @ X486 @ (push @ X487 @ id)) @ id)) != $true)) | (((X485 @ id @ (lam @ (sub @ X486 @ (push @ one @ sh))) @ id)) = $true) | ? [X488 : (subst > term > term)] : ((((X485 @ id @ (lam @ (X488 @ sh @ one)) @ id)) != $true) & ! [X492 : term] : ((((X485 @ id @ X492 @ id)) != $true) | (((X485 @ id @ (X488 @ id @ X492) @ id)) = $true)) & ! [X489 : term,X490 : subst,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491))))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f15,definition,(
% 14.62/2.51 ! [X210 : (subst > term > subst > $o)] : (($true = ((sP2 @ X210))) <=> ? [X212 : term,X211 : term] : (($true = ((X210 @ id @ X212 @ id))) & (((X210 @ id @ X211 @ id)) = $true) & ($true != ((X210 @ id @ (ap @ (sub @ X212 @ id) @ X211) @ id)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f16,definition,(
% 14.62/2.51 ! [X191 : (term > $o)] : ((((sP3 @ X191)) = $true) <=> ! [X194 : term,X195 : term] : ((((X191 @ (ap @ X195 @ X194))) = $true) | (((X191 @ X195)) != $true) | ($true != ((X191 @ X194)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f17,definition,(
% 14.62/2.51 (sP4 = $true) <=> ? [X201 : (subst > term > subst > $o),X199 : (term > $o),X200 : term] : (($true != ((X199 @ (lam @ X200)))) & ! [X203 : (subst > term > term)] : (? [X206 : subst,X205 : subst,X207 : term] : (((sub @ (X203 @ X205 @ X207) @ X206)) != ((X203 @ (comp @ X205 @ X206) @ (sub @ X207 @ X206)))) | (((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id)) = $true) | ? [X204 : term] : (($true = ((X201 @ id @ X204 @ id))) & (((X201 @ id @ (X203 @ id @ X204) @ id)) != $true))) & ! [X202 : term] : (((X201 @ id @ X202 @ id)) = ((X199 @ X202))) & ! [X208 : term] : ((((X199 @ (sub @ X200 @ (push @ X208 @ id)))) = $true) | (((X199 @ X208)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f18,definition,(
% 14.62/2.51 ($true = sP5) <=> ! [X210 : (subst > term > subst > $o),X209 : term] : (? [X213 : (subst > term > term)] : (! [X214 : term] : (($true = ((X210 @ id @ (X213 @ id @ X214) @ id))) | (((X210 @ id @ X214 @ id)) != $true)) & ! [X216 : subst,X217 : term,X215 : subst] : (((X213 @ (comp @ X215 @ X216) @ (sub @ X217 @ X216))) = ((sub @ (X213 @ X215 @ X217) @ X216))) & (((X210 @ id @ (lam @ (X213 @ sh @ one)) @ id)) != $true)) | (((X210 @ id @ X209 @ id)) = $true) | ($true = ((sP2 @ X210))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f19,definition,(
% 14.62/2.51 (sP6 = $true) <=> (? [X198 : term] : (((sub @ X198 @ id)) != X198) | ? [X192 : term,X191 : (term > $o)] : (! [X196 : term] : (($true = ((X191 @ (lam @ X196)))) | ? [X197 : term] : (($true = ((X191 @ X197))) & (((X191 @ (sub @ X196 @ (push @ X197 @ id)))) != $true))) & (((sP3 @ X191)) = $true) & (((X191 @ X192)) != $true) & ! [X193 : term] : ((((var @ X193)) != $true) | (((X191 @ X193)) = $true))) | ? [X188 : (subst > term > subst > $o)] : ! [X189 : (term > $o)] : ? [X190 : term] : (((X188 @ id @ X190 @ id)) != ((X189 @ X190))) | ($true = sP5) | (sP4 = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f20,definition,(
% 14.62/2.51 (sP7 = $true) <=> ! [X499 : (subst > term > subst > $o),X500 : term] : (? [X501 : term] : ((((X499 @ id @ (sub @ X500 @ (push @ X501 @ id)) @ id)) != $true) & ($true = ((X499 @ id @ X501 @ id)))) | ? [X502 : (subst > term > term)] : (! [X505 : term,X504 : subst,X503 : subst] : (((X502 @ (comp @ X503 @ X504) @ (sub @ X505 @ X504))) = ((sub @ (X502 @ X503 @ X505) @ X504))) & (((X499 @ id @ (lam @ (X502 @ sh @ one)) @ id)) != $true) & ! [X506 : term] : ((((X499 @ id @ (X502 @ id @ X506) @ id)) = $true) | ($true != ((X499 @ id @ X506 @ id))))) | (((X499 @ id @ (lam @ X500) @ id)) = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f21,definition,(
% 14.62/2.51 (sP8 = $true) <=> ! [X508 : term,X509 : (subst > term > subst > $o),X507 : (term > $o)] : (? [X515 : term] : ((((X507 @ X515)) = $true) & ($true != ((X507 @ (sub @ X508 @ (push @ X515 @ id)))))) | ? [X516 : term] : (((X509 @ id @ X516 @ id)) != ((X507 @ X516))) | ? [X510 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X510 @ sh @ one)) @ id))) & ! [X511 : subst,X513 : term,X512 : subst] : (((X510 @ (comp @ X511 @ X512) @ (sub @ X513 @ X512))) = ((sub @ (X510 @ X511 @ X513) @ X512))) & ! [X514 : term] : ((((X509 @ id @ X514 @ id)) != $true) | (((X509 @ id @ (X510 @ id @ X514) @ id)) = $true))) | ($true = ((X507 @ (lam @ X508)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f22,definition,(
% 14.62/2.51 ! [X385 : (subst > term > subst > $o)] : ((((sP9 @ X385)) = $true) <=> ? [X401 : term,X400 : term] : (($true = ((X385 @ id @ X401 @ id))) & (((X385 @ id @ (ap @ (sub @ X400 @ id) @ X401) @ id)) != $true) & (((X385 @ id @ X400 @ id)) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f23,definition,(
% 14.62/2.51 ! [X385 : (subst > term > subst > $o)] : ((((sP10 @ X385)) = $true) <=> ? [X391 : (subst > term > term)] : (($true != ((X385 @ id @ (lam @ (X391 @ sh @ one)) @ id))) & ! [X392 : term] : (($true = ((X385 @ id @ (X391 @ id @ X392) @ id))) | (((X385 @ id @ X392 @ id)) != $true)) & ! [X393 : subst,X395 : term,X394 : subst] : (((sub @ (X391 @ X394 @ X395) @ X393)) = ((X391 @ (comp @ X394 @ X393) @ (sub @ X395 @ X393))))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f24,definition,(
% 14.62/2.51 ! [X366 : (term > $o)] : ((((sP11 @ X366)) = $true) <=> ! [X371 : term,X370 : term] : ((((X366 @ X370)) != $true) | (((X366 @ (ap @ X371 @ X370))) = $true) | (((X366 @ X371)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f25,definition,(
% 14.62/2.51 (sP12 = $true) <=> ! [X384 : term,X385 : (subst > term > subst > $o)] : (? [X386 : subst,X387 : subst,X388 : subst,X389 : term] : ((((X385 @ X388 @ X389 @ (comp @ X386 @ X387))) != $true) & ($true = ((X385 @ (comp @ X388 @ X386) @ (sub @ X389 @ X386) @ X387)))) | (((sP10 @ X385)) = $true) | (((X385 @ id @ X384 @ id)) = $true) | (((sP9 @ X385)) = $true) | ? [X396 : subst,X399 : term,X397 : subst,X398 : subst] : ((((X385 @ (comp @ X398 @ X397) @ (sub @ X399 @ X397) @ X396)) != $true) & ($true = ((X385 @ X398 @ X399 @ (comp @ X397 @ X396))))) | ? [X390 : term] : ((((var @ (sub @ X390 @ id))) = $true) & (((X385 @ id @ X390 @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f26,definition,(
% 14.62/2.51 (sP13 = $true) <=> ? [X375 : (subst > term > subst > $o),X376 : (term > $o),X374 : term] : (! [X383 : term] : (((X376 @ X383)) = ((X375 @ id @ X383 @ id))) & ! [X377 : term] : (($true = ((X376 @ (sub @ X374 @ (push @ X377 @ id))))) | (((X376 @ X377)) != $true)) & ($true != ((X376 @ (lam @ X374)))) & ! [X378 : (subst > term > term)] : (? [X382 : term] : (($true != ((X375 @ id @ (X378 @ id @ X382) @ id))) & (((X375 @ id @ X382 @ id)) = $true)) | (((X375 @ id @ (lam @ (X378 @ sh @ one)) @ id)) = $true) | ? [X380 : term,X381 : subst,X379 : subst] : (((sub @ (X378 @ X379 @ X380) @ X381)) != ((X378 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f27,definition,(
% 14.62/2.51 (sP14 = $true) <=> (? [X373 : term] : (((sub @ X373 @ id)) != X373) | (sP13 = $true) | ? [X366 : (term > $o),X367 : term] : ((((sP11 @ X366)) = $true) & ! [X368 : term] : (? [X369 : term] : ((((X366 @ (sub @ X368 @ (push @ X369 @ id)))) != $true) & (((X366 @ X369)) = $true)) | ($true = ((X366 @ (lam @ X368))))) & (((X366 @ X367)) != $true) & ! [X372 : term] : ((((X366 @ X372)) = $true) | (((var @ X372)) != $true))) | ? [X363 : (subst > term > subst > $o)] : ! [X364 : (term > $o)] : ? [X365 : term] : (((X363 @ id @ X365 @ id)) != ((X364 @ X365))) | (sP12 = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f28,definition,(
% 14.62/2.51 ! [X10 : (term > $o)] : ((((sP15 @ X10)) = $true) <=> ? [X13 : term,X14 : term] : ((((X10 @ X13)) = $true) & ($true != ((X10 @ (ap @ X14 @ X13)))) & ($true = ((X10 @ X14)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f29,definition,(
% 14.62/2.51 ! [X1 : (term > $o)] : (($true = ((sP16 @ X1))) <=> ! [X4 : term,X5 : term] : (($true = ((X1 @ (ap @ X4 @ X5)))) | ($true != ((X1 @ X5))) | (((X1 @ X4)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f30,definition,(
% 14.62/2.51 ($true = sP17) <=> ! [X10 : (term > $o),X9 : term] : (? [X15 : term] : ((((X10 @ X15)) != $true) & (((var @ X15)) = $true)) | ? [X11 : term] : ((((X10 @ (lam @ X11))) != $true) & ! [X12 : term] : ((((X10 @ X12)) != $true) | (((X10 @ (sub @ X11 @ (push @ X12 @ id)))) = $true))) | (((X10 @ X9)) = $true) | (((sP15 @ X10)) = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f31,definition,(
% 14.62/2.51 (sP18 = $true) <=> (? [X2 : term,X3 : subst,X1 : (term > $o)] : (! [X6 : term] : (? [X7 : term] : ((((X1 @ X7)) = $true) & (((X1 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X1 @ (lam @ X6))) = $true)) & ! [X8 : term] : ((((X1 @ (sub @ X8 @ X3))) = $true) | (((var @ X8)) != $true)) & (((X1 @ (sub @ X2 @ X3))) != $true) & ($true = ((sP16 @ X1)))) | ($true = sP17) | ? [X0 : term] : (((sub @ X0 @ id)) != X0))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f32,definition,(
% 14.62/2.51 ! [X157 : (subst > term > subst > $o)] : ((((sP19 @ X157)) = $true) <=> ? [X163 : term,X162 : term] : ((((X157 @ id @ X163 @ id)) = $true) & (((X157 @ id @ X162 @ id)) = $true) & (((X157 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f33,definition,(
% 14.62/2.51 (sP20 = $true) <=> ! [X156 : term,X155 : (term > $o),X154 : term,X157 : (subst > term > subst > $o)] : (? [X160 : subst,X159 : subst,X161 : term,X158 : subst] : ((((X157 @ (comp @ X160 @ X159) @ (sub @ X161 @ X159) @ X158)) != $true) & ($true = ((X157 @ X160 @ X161 @ (comp @ X159 @ X158))))) | ($true != ((X155 @ X156))) | (((sP19 @ X157)) = $true) | ? [X164 : term] : (((X155 @ X164)) != ((X157 @ id @ X164 @ id))) | (((X155 @ X154)) != $true) | (((X155 @ (ap @ X154 @ X156))) = $true) | ? [X167 : subst,X168 : subst,X165 : subst,X166 : term] : ((((X157 @ (comp @ X167 @ X168) @ (sub @ X166 @ X168) @ X165)) = $true) & (((X157 @ X167 @ X166 @ (comp @ X168 @ X165))) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f34,definition,(
% 14.62/2.51 ! [X421 : (subst > term > subst > $o)] : ((((sP21 @ X421)) = $true) <=> ? [X430 : term,X431 : term] : ((((X421 @ id @ X431 @ id)) = $true) & ($true = ((X421 @ id @ X430 @ id))) & ($true != ((X421 @ id @ (ap @ (sub @ X431 @ id) @ X430) @ id)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f35,definition,(
% 14.62/2.51 (sP22 = $true) <=> ! [X421 : (subst > term > subst > $o),X419 : term,X420 : term] : (? [X425 : subst,X423 : term,X422 : subst,X424 : subst] : ((((X421 @ (comp @ X425 @ X422) @ (sub @ X423 @ X422) @ X424)) != $true) & (((X421 @ X425 @ X423 @ (comp @ X422 @ X424))) = $true)) | (((sP21 @ X421)) = $true) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | (((X421 @ id @ X420 @ id)) != $true) | ? [X428 : term,X426 : subst,X429 : subst,X427 : subst] : ((((X421 @ (comp @ X426 @ X429) @ (sub @ X428 @ X429) @ X427)) = $true) & (((X421 @ X426 @ X428 @ (comp @ X429 @ X427))) != $true)) | ($true != ((X421 @ id @ X419 @ id))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f36,definition,(
% 14.62/2.51 ! [X297 : (term > $o)] : ((((sP23 @ X297)) = $true) <=> ? [X300 : term,X301 : term] : ((((X297 @ X301)) = $true) & (((X297 @ X300)) = $true) & ($true != ((X297 @ (ap @ X300 @ X301))))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f37,definition,(
% 14.62/2.51 (sP24 = $true) <=> ! [X298 : term,X297 : (term > $o)] : (($true = ((X297 @ X298))) | ? [X299 : term] : ((((X297 @ X299)) != $true) & (((var @ X299)) = $true)) | ? [X302 : term] : (! [X303 : term] : ((((X297 @ X303)) != $true) | ($true = ((X297 @ (sub @ X302 @ (push @ X303 @ id)))))) & (((X297 @ (lam @ X302))) != $true)) | (((sP23 @ X297)) = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f38,definition,(
% 14.62/2.51 (sP25 = $true) <=> ? [X173 : (subst > term > subst > $o),X172 : term] : (($true != ((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id))) & ! [X179 : term] : ((((X173 @ id @ (sub @ X172 @ (push @ X179 @ id)) @ id)) = $true) | ($true != ((X173 @ id @ X179 @ id)))) & ! [X174 : (subst > term > term)] : (($true = ((X173 @ id @ (lam @ (X174 @ sh @ one)) @ id))) | ? [X178 : term] : ((((X173 @ id @ X178 @ id)) = $true) & (((X173 @ id @ (X174 @ id @ X178) @ id)) != $true)) | ? [X176 : subst,X177 : term,X175 : subst] : (((sub @ (X174 @ X175 @ X177) @ X176)) != ((X174 @ (comp @ X175 @ X176) @ (sub @ X177 @ X176))))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f39,definition,(
% 14.62/2.51 (sP26 = $true) <=> (? [X171 : term] : (((sub @ X171 @ id)) != X171) | (sP25 = $true) | ! [X180 : term,X181 : (subst > term > subst > $o)] : (? [X187 : term] : ((((X181 @ id @ X187 @ id)) = $true) & ($true != ((X181 @ id @ (sub @ X180 @ (push @ X187 @ id)) @ id)))) | ? [X182 : (subst > term > term)] : (($true != ((X181 @ id @ (lam @ (X182 @ sh @ one)) @ id))) & ! [X185 : subst,X186 : term,X184 : subst] : (((sub @ (X182 @ X184 @ X186) @ X185)) = ((X182 @ (comp @ X184 @ X185) @ (sub @ X186 @ X185)))) & ! [X183 : term] : ((((X181 @ id @ (X182 @ id @ X183) @ id)) = $true) | (((X181 @ id @ X183 @ id)) != $true))) | (((X181 @ id @ (lam @ X180) @ id)) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f40,definition,(
% 14.62/2.51 (sP27 = $true) <=> ! [X43 : term,X42 : (subst > term > subst > $o)] : ((((X42 @ id @ (lam @ (sub @ X43 @ (push @ one @ sh))) @ id)) = $true) | ? [X53 : term] : ((((X42 @ id @ X53 @ id)) = $true) & (((X42 @ id @ (sub @ X43 @ (push @ X53 @ id)) @ id)) != $true)) | ? [X44 : (subst > term > term),X45 : term] : (! [X46 : term,X48 : subst,X47 : subst] : (((sub @ (X44 @ X48 @ X46) @ X47)) = ((sub @ (sub @ X45 @ (push @ X46 @ X48)) @ X47))) & ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ X45 @ (push @ (sub @ X50 @ X49) @ (comp @ X51 @ X49)))) = ((X44 @ (comp @ X51 @ X49) @ (sub @ X50 @ X49)))) & ! [X52 : term] : ((((X42 @ id @ X52 @ id)) != $true) | (((X42 @ id @ (X44 @ id @ X52) @ id)) = $true)) & (((X42 @ id @ (lam @ (X44 @ sh @ one)) @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f41,definition,(
% 14.62/2.51 ! [X469 : (subst > term > subst > $o)] : (($true = ((sP28 @ X469))) <=> ? [X474 : (subst > term > term)] : (! [X477 : subst,X476 : subst,X475 : term] : (((X474 @ (comp @ X477 @ X476) @ (sub @ X475 @ X476))) = ((sub @ (X474 @ X477 @ X475) @ X476))) & ! [X478 : term] : (($true != ((X469 @ id @ X478 @ id))) | (((X469 @ id @ (X474 @ id @ X478) @ id)) = $true)) & (((X469 @ id @ (lam @ (X474 @ sh @ one)) @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f42,definition,(
% 14.62/2.51 (sP29 = $true) <=> (? [X466 : term] : (((sub @ X466 @ id)) != X466) | ! [X468 : term,X467 : (term > $o),X469 : (subst > term > subst > $o)] : (? [X471 : term,X472 : subst,X473 : subst,X470 : subst] : (($true = ((X469 @ X472 @ X471 @ (comp @ X470 @ X473)))) & (((X469 @ (comp @ X472 @ X470) @ (sub @ X471 @ X470) @ X473)) != $true)) | ? [X483 : term] : ((((X467 @ (sub @ X468 @ (push @ X483 @ id)))) != $true) & ($true = ((X467 @ X483)))) | (((X467 @ (lam @ X468))) = $true) | ($true = ((sP28 @ X469))) | ? [X482 : subst,X479 : term,X480 : subst,X481 : subst] : ((((X469 @ (comp @ X481 @ X482) @ (sub @ X479 @ X482) @ X480)) = $true) & (((X469 @ X481 @ X479 @ (comp @ X482 @ X480))) != $true)) | ? [X484 : term] : (((X467 @ X484)) != ((X469 @ id @ X484 @ id)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f43,definition,(
% 14.62/2.51 ! [X250 : (subst > term > subst > $o)] : ((((sP30 @ X250)) = $true) <=> ? [X252 : term,X251 : term] : (($true = ((X250 @ id @ X251 @ id))) & (((X250 @ id @ X252 @ id)) = $true) & ($true != ((X250 @ id @ (ap @ (sub @ X251 @ id) @ X252) @ id)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f44,definition,(
% 14.62/2.51 ! [X438 : (subst > term > subst > $o)] : ((((sP31 @ X438)) = $true) <=> ? [X450 : (subst > term > term)] : (! [X453 : subst,X454 : subst,X452 : term] : (((X450 @ (comp @ X454 @ X453) @ (sub @ X452 @ X453))) = ((sub @ (X450 @ X454 @ X452) @ X453))) & (((X438 @ id @ (lam @ (X450 @ sh @ one)) @ id)) != $true) & ! [X451 : term] : ((((X438 @ id @ X451 @ id)) != $true) | (((X438 @ id @ (X450 @ id @ X451) @ id)) = $true))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f45,definition,(
% 14.62/2.51 (sP32 = $true) <=> ! [X440 : (term > $o),X439 : term,X438 : (subst > term > subst > $o)] : ((((X440 @ (lam @ X439))) = $true) | ? [X455 : term] : (((X438 @ id @ X455 @ id)) != ((X440 @ X455))) | ? [X449 : term] : ((((X440 @ X449)) = $true) & (((X440 @ (sub @ X439 @ (push @ X449 @ id)))) != $true)) | ? [X445 : subst,X448 : subst,X446 : subst,X447 : term] : ((((X438 @ (comp @ X445 @ X448) @ (sub @ X447 @ X448) @ X446)) != $true) & ($true = ((X438 @ X445 @ X447 @ (comp @ X448 @ X446))))) | (((sP31 @ X438)) = $true) | ? [X442 : subst,X441 : subst,X443 : term,X444 : subst] : ((((X438 @ (comp @ X444 @ X441) @ (sub @ X443 @ X441) @ X442)) = $true) & (((X438 @ X444 @ X443 @ (comp @ X441 @ X442))) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f46,definition,(
% 14.62/2.51 ! [X523 : (subst > term > subst > $o)] : ((((sP33 @ X523)) = $true) <=> ? [X528 : (subst > term > term)] : (! [X532 : term] : ((((X523 @ id @ (X528 @ id @ X532) @ id)) = $true) | (((X523 @ id @ X532 @ id)) != $true)) & ! [X530 : term,X531 : subst,X529 : subst] : (((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531))) = ((sub @ (X528 @ X529 @ X530) @ X531))) & (((X523 @ id @ (lam @ (X528 @ sh @ one)) @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f47,definition,(
% 14.62/2.51 ! [X523 : (subst > term > subst > $o)] : ((((sP34 @ X523)) = $true) <=> ? [X538 : term,X539 : term] : (($true = ((X523 @ id @ X538 @ id))) & (((X523 @ id @ X539 @ id)) = $true) & (((X523 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f48,definition,(
% 14.62/2.51 (sP35 = $true) <=> ! [X522 : term,X523 : (subst > term > subst > $o)] : ((((sP34 @ X523)) = $true) | (((sP33 @ X523)) = $true) | ($true = ((X523 @ id @ X522 @ id))) | ? [X533 : term] : (($true != ((X523 @ id @ X533 @ id))) & (((var @ (sub @ X533 @ id))) = $true)) | ? [X525 : subst,X527 : subst,X524 : subst,X526 : term] : (($true != ((X523 @ (comp @ X525 @ X527) @ (sub @ X526 @ X527) @ X524))) & ($true = ((X523 @ X525 @ X526 @ (comp @ X527 @ X524))))) | ? [X536 : subst,X537 : term,X535 : subst,X534 : subst] : (($true != ((X523 @ X536 @ X537 @ (comp @ X535 @ X534)))) & (((X523 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535) @ X534)) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f49,definition,(
% 14.62/2.51 ($true = sP36) <=> (? [X348 : term] : ! [X349 : (subst > term > term)] : ? [X350 : term,X351 : subst] : (((sub @ X348 @ (push @ X350 @ X351))) != ((X349 @ X351 @ X350))) | ! [X353 : (term > $o),X355 : term,X354 : (subst > term > subst > $o)] : (? [X356 : (subst > term > term)] : (! [X358 : subst,X359 : term,X357 : subst] : (((X356 @ (comp @ X357 @ X358) @ (sub @ X359 @ X358))) = ((sub @ (X356 @ X357 @ X359) @ X358))) & ! [X360 : term] : ((((X354 @ id @ X360 @ id)) != $true) | ($true = ((X354 @ id @ (X356 @ id @ X360) @ id)))) & ($true != ((X354 @ id @ (lam @ (X356 @ sh @ one)) @ id)))) | ? [X362 : term] : (((X354 @ id @ X362 @ id)) != ((X353 @ X362))) | (((X353 @ (lam @ X355))) = $true) | ? [X361 : term] : ((((X353 @ X361)) = $true) & ($true != ((X353 @ (sub @ X355 @ (push @ X361 @ id))))))) | ? [X352 : term] : (((sub @ X352 @ id)) != X352))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f50,definition,(
% 14.62/2.51 ! [X127 : (term > $o)] : ((((sP37 @ X127)) = $true) <=> ? [X133 : term,X134 : term] : ((((X127 @ X133)) = $true) & (((X127 @ (ap @ X134 @ X133))) != $true) & ($true = ((X127 @ X134)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f51,definition,(
% 14.62/2.51 (sP38 = $true) <=> ! [X128 : subst,X129 : term,X127 : (term > $o)] : (? [X130 : term] : (! [X131 : term] : ((((X127 @ X131)) != $true) | (((X127 @ (sub @ X130 @ (push @ X131 @ id)))) = $true)) & ($true != ((X127 @ (lam @ X130))))) | ? [X132 : term] : ((((X127 @ (sub @ X132 @ X128))) != $true) & (((var @ X132)) = $true)) | (((X127 @ (sub @ X129 @ X128))) = $true) | (((sP37 @ X127)) = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f52,definition,(
% 14.62/2.51 ! [X333 : (term > $o)] : (($true = ((sP39 @ X333))) <=> ? [X336 : term,X335 : term] : ((((X333 @ X336)) = $true) & (((X333 @ (ap @ X336 @ X335))) != $true) & (((X333 @ X335)) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f53,definition,(
% 14.62/2.51 ! [X325 : (term > $o)] : ((((sP40 @ X325)) = $true) <=> ! [X328 : term,X329 : term] : ((((X325 @ X328)) != $true) | (((X325 @ X329)) != $true) | (((X325 @ (ap @ X329 @ X328))) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f54,definition,(
% 14.62/2.51 (sP41 = $true) <=> ! [X332 : subst,X333 : (term > $o),X331 : term] : (? [X337 : term] : (! [X338 : term] : ((((X333 @ X338)) != $true) | (((X333 @ (sub @ X337 @ (push @ X338 @ id)))) = $true)) & (((X333 @ (lam @ X337))) != $true)) | ($true = ((sP39 @ X333))) | (((X333 @ (sub @ X331 @ X332))) = $true) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X333 @ (sub @ X334 @ X332))) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f55,definition,(
% 14.62/2.51 (sP42 = $true) <=> (? [X325 : (term > $o),X326 : term] : (! [X330 : term] : ((((var @ X330)) != $true) | (((X325 @ X330)) = $true)) & ($true != ((X325 @ X326))) & ! [X327 : term] : ((((X325 @ (lam @ X327))) = $true) | (((X325 @ X327)) != $true)) & (((sP40 @ X325)) = $true)) | (sP41 = $true) | ? [X321 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X321))) != X320) | ? [X322 : term,X323 : subst] : (((comp @ sh @ (push @ X322 @ X323))) != X323) | ? [X324 : subst] : (((comp @ X324 @ id)) != X324))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f56,definition,(
% 14.62/2.51 ! [X268 : (subst > term > subst > $o)] : ((((sP43 @ X268)) = $true) <=> ? [X277 : (subst > term > term)] : (! [X281 : subst,X279 : term,X280 : subst] : (((sub @ (X277 @ X280 @ X279) @ X281)) = ((X277 @ (comp @ X280 @ X281) @ (sub @ X279 @ X281)))) & ! [X278 : term] : ((((X268 @ id @ X278 @ id)) != $true) | (((X268 @ id @ (X277 @ id @ X278) @ id)) = $true)) & (((X268 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f57,definition,(
% 14.62/2.51 ($true = sP44) <=> ? [X260 : term,X259 : (subst > term > subst > $o)] : ((((X259 @ id @ (lam @ (sub @ X260 @ (push @ one @ sh))) @ id)) != $true) & ! [X261 : (subst > term > term)] : (? [X264 : subst,X263 : subst,X262 : term] : (((sub @ (X261 @ X264 @ X262) @ X263)) != ((X261 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263)))) | ? [X265 : term] : (($true != ((X259 @ id @ (X261 @ id @ X265) @ id))) & (((X259 @ id @ X265 @ id)) = $true)) | (((X259 @ id @ (lam @ (X261 @ sh @ one)) @ id)) = $true)) & ! [X266 : term] : (($true = ((X259 @ id @ (sub @ X260 @ (push @ X266 @ id)) @ id))) | (((X259 @ id @ X266 @ id)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f58,definition,(
% 14.62/2.51 (sP45 = $true) <=> (? [X258 : term] : (((sub @ X258 @ id)) != X258) | ! [X267 : term,X268 : (subst > term > subst > $o)] : ((((X268 @ id @ (lam @ X267) @ id)) = $true) | ? [X271 : subst,X270 : subst,X269 : subst,X272 : term] : ((((X268 @ (comp @ X270 @ X269) @ (sub @ X272 @ X269) @ X271)) != $true) & (((X268 @ X270 @ X272 @ (comp @ X269 @ X271))) = $true)) | ? [X282 : term] : ((((X268 @ id @ X282 @ id)) = $true) & ($true != ((X268 @ id @ (sub @ X267 @ (push @ X282 @ id)) @ id)))) | ? [X275 : subst,X273 : subst,X274 : subst,X276 : term] : ((((X268 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274)) = $true) & (((X268 @ X275 @ X276 @ (comp @ X273 @ X274))) != $true)) | (((sP43 @ X268)) = $true)) | ($true = sP44))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f59,definition,(
% 14.62/2.51 ! [X305 : (subst > term > subst > $o)] : ((((sP46 @ X305)) = $true) <=> ? [X315 : (subst > term > term)] : ((((X305 @ id @ (lam @ (X315 @ sh @ one)) @ id)) != $true) & ! [X319 : term] : ((((X305 @ id @ X319 @ id)) != $true) | (((X305 @ id @ (X315 @ id @ X319) @ id)) = $true)) & ! [X316 : subst,X318 : term,X317 : subst] : (((sub @ (X315 @ X316 @ X318) @ X317)) = ((X315 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317))))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f60,definition,(
% 14.62/2.51 (sP47 = $true) <=> ! [X305 : (subst > term > subst > $o),X304 : term] : ((((sP46 @ X305)) = $true) | ? [X314 : subst,X313 : subst,X311 : term,X312 : subst] : (($true = ((X305 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314))) & (((X305 @ X313 @ X311 @ (comp @ X312 @ X314))) != $true)) | ? [X310 : subst,X309 : term,X307 : subst,X308 : subst] : ((((X305 @ X308 @ X309 @ (comp @ X310 @ X307))) = $true) & (((X305 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310) @ X307)) != $true)) | (((X305 @ id @ (lam @ X304) @ id)) = $true) | ? [X306 : term] : ((((X305 @ id @ X306 @ id)) = $true) & ($true != ((X305 @ id @ (sub @ X304 @ (push @ X306 @ id)) @ id)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f61,definition,(
% 14.62/2.51 ! [X73 : (term > $o)] : (($true = ((sP48 @ X73))) <=> ! [X78 : term,X79 : term] : ((((X73 @ X78)) != $true) | (((X73 @ (ap @ X78 @ X79))) = $true) | (((X73 @ X79)) != $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f62,definition,(
% 14.62/2.51 ! [X109 : (subst > term > subst > $o)] : ((((sP49 @ X109)) = $true) <=> ? [X115 : (subst > term > term)] : (! [X119 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X118 @ X119) @ X117)) = ((X115 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117)))) & (((X109 @ id @ (lam @ (X115 @ sh @ one)) @ id)) != $true) & ! [X116 : term] : (($true = ((X109 @ id @ (X115 @ id @ X116) @ id))) | (((X109 @ id @ X116 @ id)) != $true))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f63,definition,(
% 14.62/2.51 ! [X109 : (subst > term > subst > $o)] : (($true = ((sP50 @ X109))) <=> ? [X121 : term,X120 : term] : ((((X109 @ id @ X120 @ id)) = $true) & (((X109 @ id @ (ap @ (sub @ X120 @ id) @ X121) @ id)) != $true) & (((X109 @ id @ X121 @ id)) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f64,definition,(
% 14.62/2.51 ! [X94 : (subst > term > subst > $o)] : ((((sP51 @ X94)) = $true) <=> ! [X100 : (subst > term > term)] : (($true = ((X94 @ id @ (lam @ (X100 @ sh @ one)) @ id))) | ? [X104 : term] : ((((X94 @ id @ X104 @ id)) = $true) & (((X94 @ id @ (X100 @ id @ X104) @ id)) != $true)) | ? [X103 : subst,X101 : term,X102 : subst] : (((X100 @ (comp @ X102 @ X103) @ (sub @ X101 @ X103))) != ((sub @ (X100 @ X102 @ X101) @ X103)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f65,definition,(
% 14.62/2.51 ! [X82 : (subst > term > subst > $o)] : ((((sP52 @ X82)) = $true) <=> ! [X92 : term,X91 : term] : ((((X82 @ id @ X91 @ id)) != $true) | (((X82 @ id @ X92 @ id)) != $true) | ($true = ((X82 @ id @ (ap @ (sub @ X91 @ id) @ X92) @ id)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f66,definition,(
% 14.62/2.51 (sP53 = $true) <=> ? [X94 : (subst > term > subst > $o),X93 : term] : (! [X98 : subst,X96 : subst,X97 : term,X95 : subst] : ((((X94 @ (comp @ X95 @ X98) @ (sub @ X97 @ X98) @ X96)) != $true) | (((X94 @ X95 @ X97 @ (comp @ X98 @ X96))) = $true)) & ! [X99 : term] : ((((X94 @ id @ X99 @ id)) != $true) | (((X94 @ id @ (sub @ X93 @ (push @ X99 @ id)) @ id)) = $true)) & ! [X107 : term,X108 : subst,X106 : subst,X105 : subst] : (($true = ((X94 @ (comp @ X105 @ X108) @ (sub @ X107 @ X108) @ X106))) | (((X94 @ X105 @ X107 @ (comp @ X108 @ X106))) != $true)) & (((sP51 @ X94)) = $true) & ($true != ((X94 @ id @ (lam @ X93) @ id))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f67,definition,(
% 14.62/2.51 (sP54 = $true) <=> ! [X109 : (subst > term > subst > $o),X110 : term] : (? [X126 : term] : ((((X109 @ id @ X126 @ id)) != $true) & ($true = ((var @ (sub @ X126 @ id))))) | (((X109 @ id @ X110 @ id)) = $true) | ($true = ((sP50 @ X109))) | (((sP49 @ X109)) = $true) | ? [X111 : subst,X113 : subst,X112 : subst,X114 : term] : ((((X109 @ (comp @ X113 @ X112) @ (sub @ X114 @ X112) @ X111)) = $true) & (((X109 @ X113 @ X114 @ (comp @ X112 @ X111))) != $true)) | ? [X123 : subst,X125 : subst,X124 : term,X122 : subst] : (($true = ((X109 @ X123 @ X124 @ (comp @ X122 @ X125)))) & ($true != ((X109 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122) @ X125)))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f68,definition,(
% 14.62/2.51 (sP55 = $true) <=> ? [X74 : term,X73 : (term > $o)] : (! [X77 : term] : ((((X73 @ X77)) = $true) | (((var @ X77)) != $true)) & ($true = ((sP48 @ X73))) & ! [X75 : term] : (? [X76 : term] : ((((X73 @ (sub @ X75 @ (push @ X76 @ id)))) != $true) & (((X73 @ X76)) = $true)) | (((X73 @ (lam @ X75))) = $true)) & ($true != ((X73 @ X74))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f69,definition,(
% 14.62/2.51 (sP56 = $true) <=> (? [X80 : term,X82 : (subst > term > subst > $o),X81 : term] : (! [X89 : subst,X88 : subst,X90 : subst,X87 : term] : ((((X82 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89) @ X90)) != $true) | ($true = ((X82 @ X88 @ X87 @ (comp @ X89 @ X90))))) & (((X82 @ id @ (ap @ X81 @ X80) @ id)) != $true) & ($true = ((X82 @ id @ X80 @ id))) & (((X82 @ id @ X81 @ id)) = $true) & (((sP52 @ X82)) = $true) & ! [X86 : subst,X84 : subst,X83 : subst,X85 : term] : ((((X82 @ X84 @ X85 @ (comp @ X83 @ X86))) != $true) | (((X82 @ (comp @ X84 @ X83) @ (sub @ X85 @ X83) @ X86)) = $true))) | (sP53 = $true) | (sP54 = $true) | (sP55 = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f70,definition,(
% 14.62/2.51 (sP57 = $true) <=> ! [X408 : (subst > term > subst > $o),X407 : term] : ((((X408 @ id @ (lam @ (sub @ X407 @ (push @ one @ sh))) @ id)) = $true) | ? [X410 : (subst > term > term)] : ((((X408 @ id @ (lam @ (X410 @ sh @ one)) @ id)) != $true) & ! [X411 : term] : ((((X408 @ id @ (X410 @ id @ X411) @ id)) = $true) | (((X408 @ id @ X411 @ id)) != $true)) & ! [X412 : subst,X413 : subst,X414 : term] : (((sub @ (X410 @ X413 @ X414) @ X412)) = ((X410 @ (comp @ X413 @ X412) @ (sub @ X414 @ X412))))) | ? [X409 : term] : ((((X408 @ id @ (sub @ X407 @ (push @ X409 @ id)) @ id)) != $true) & (((X408 @ id @ X409 @ id)) = $true)))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f71,definition,(
% 14.62/2.51 ($true = sP58) <=> (! [X61 : subst,X60 : term,X63 : (subst > term > term),X62 : (subst > term > term)] : ((((lam @ (X63 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | (((X63 @ X61 @ X60)) = ((X62 @ X61 @ X60))) | ? [X64 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X66 @ X65) @ X64)) != ((X62 @ (comp @ X66 @ X64) @ (sub @ X65 @ X64)))) | ? [X69 : term,X67 : subst,X68 : subst] : (((sub @ (X63 @ X68 @ X69) @ X67)) != ((X63 @ (comp @ X68 @ X67) @ (sub @ X69 @ X67))))) | ? [X59 : term,X58 : term] : ((X58 != X59) & (((lam @ X58)) = ((lam @ X59)))) | ? [X56 : term,X57 : subst] : (((comp @ sh @ (push @ X56 @ X57))) != X57) | ? [X54 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X54))) != X55))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 14.62/2.51 thf(f72,plain,(
% 14.62/2.51 (hoasinduction_lem1v2 = $true) & (! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) <=> (axscons = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X141 : d_subst,X140 : d_subst] : ((((d2subst @ X140)) != ((d2subst @ X141))) | (X140 = X141)) & ((hoasapinj2_lthm = $true) <=> (! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))) | ? [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 != X222) & (((ap @ X220 @ X222)) = ((ap @ X221 @ X219)))))) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) <=> (? [X416 : subst] : (((comp @ X416 @ id)) != X416) | (! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)) | ? [X415 : subst] : (((comp @ id @ X415)) != X415))) & (! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) <=> (laminj = $true)) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) != $true) | (((X233 @ one)) = $true) | ? [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) != ((X233 @ X237)))) <=> (pushprop_lem1v2 = $true)) & (($true = sP58) <=> (hoaslaminj_lthm = $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & ((sP57 = $true) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X135 : (term > $o),X137 : subst,X136 : term] : ? [X138 : (term > $o)] : ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139)))) & ((hoaslaminj = $true) <=> ! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (? [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) != ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))) | ? [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) != ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one)))))) & (axassoc = $true) & ((! [X170 : term] : (((sub @ X170 @ id)) = X170) | ? [X169 : term] : (((sub @ X169 @ id)) != X169)) <=> (termmset_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X33 : subst,X34 : (term > $o),X35 : term] : ? [X36 : (term > $o)] : ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37)))) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((sP56 = $true) <=> (hoasinduction_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3 = $true) <=> (sP47 = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X145 : term] : ? [X146 : (subst > term > term)] : (((X146 @ sh @ one)) = ((sub @ X145 @ (push @ one @ sh))))) & ((hoasapinj2 = $true) <=> ! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497))) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) <=> (shinj = $true)) & (hoasapinj2_gthm = $true) & ((sP45 = $true) <=> (hoasinduction_lem3_lthm = $true)) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) != X238) | ! [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) != $true) | ($true = ((X243 @ one))) | ? [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) != ((X243 @ X244)))))) & ((sP42 = $true) <=> (induction2lem_lthm = $true)) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) <=> (termmset = $true)) & ((induction2lem = $true) <=> (sP38 = $true)) & (pushprop_lem3v2_lthm = $true) & (axvarshift = $true) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & (hoasinduction_lem3b_gthm = $true) & ! [X218 : d_term] : (d_one = X218) & (axapp = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b = $true) <=> ! [X295 : term] : ? [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) = ((X296 @ sh @ one)))) & (induction2lem_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (lamnotap != $true) & ((axvarid = $true) <=> ! [X402 : term] : (((sub @ X402 @ id)) = X402)) & ! [X284 : d_subst] : (d_id = X284) & ((hoasinduction_lem3v2a_lthm = $true) <=> ($true = sP36)) & (pushprop_lem2v2 = $true) & ((hoasapinj1_lthm = $true) <=> (? [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 != X28) & (((ap @ X28 @ X26)) = ((ap @ X27 @ X25)))) | ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))) | ? [X24 : term] : (((sub @ X24 @ id)) != X24))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem1_lthm = $true) <=> (! [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true) | (((X347 @ X345)) != $true)) | ? [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) != X342) | ? [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) != X340))) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & ((hoasinduction = $true) <=> (sP35 = $true)) & ((sP32 = $true) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X249 : term,X250 : (subst > term > subst > $o)] : (? [X253 : (subst > term > term)] : (! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257))) & (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) != $true) & ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | (((X250 @ id @ X254 @ id)) != $true))) | (((sP30 @ X250)) = $true) | (((X250 @ id @ X249 @ id)) = $true))) & (substmonoid_gthm = $true) & ((sP29 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & ((sP27 = $true) <=> (hoasinduction_lem3aaa = $true)) & (! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3a_gthm = $true) & (axabs = $true) & ((apinj2 = $true) <=> ! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (sP26 = $true)) & ((induction2 = $true) <=> (sP24 = $true)) & (ulamvarind = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) <=> (sP22 = $true)) & ((sP20 = $true) <=> (hoasinduction_lem2v2 = $true)) & ((sP18 = $true) <=> (induction2_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP14 = $true) <=> (hoasinduction_lthm_3 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = id) & ((sP8 = $true) <=> (hoasinduction_lem3v2a = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X150 : term] : ? [X151 : (subst > term > term)] : ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153)))) & ((axidl = $true) <=> ! [X72 : subst] : (((comp @ id @ X72)) = X72)) & (axmap = $true) & (ulamvar1 != $true) & (pushprop = $true) & (apnotvar = $true) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & ((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) <=> (substmonoid = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X147 : (subst > term > subst > $o)] : ? [X148 : (term > $o)] : ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149)))) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X283 : subst] : (((comp @ X283 @ id)) = X283) <=> (axidr = $true)) & ((sP7 = $true) <=> (hoasinduction_lem3a = $true)) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) <=> (axshiftcons = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X459 : (subst > term > subst > $o)] : ? [X460 : (term > $o)] : ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461)))) & (hoasinduction_lem1 = $true) & ((sP6 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axvarcons = $true) <=> ! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493)) & (($true = sP1) <=> (hoasinduction_lem3aa_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)))))))))))))) & (lamnotvar = $true) & (! [X20 : term] : ? [X21 : (subst > term > term)] : ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true != ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ! [X18 : d_term,X19 : d_term] : ((((d2term @ X18)) != ((d2term @ X19))) | (X18 = X19)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) <=> ! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406))) & (! [X227 : (term > $o),X228 : term] : ((((sP0 @ X227)) = $true) | ? [X231 : term] : ((((X227 @ X231)) = $true) & ($true != ((X227 @ (lam @ X231))))) | ? [X232 : term] : (($true = ((var @ X232))) & (((X227 @ X232)) != $true)) | (((X227 @ X228)) = $true)) <=> (induction = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem1_gthm = $true) & (! [X433 : term,X432 : (subst > term > term),X434 : term] : (? [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) != ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (termmset_gthm = $true)),
% 14.62/2.51 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])).
% 14.62/2.51 thf(f260,plain,(
% 14.62/2.51 (hoasinduction_lem1v2 = $true) & ((! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) | (axscons != $true)) & ((axscons = $true) | ? [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) != X456))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X141 : d_subst,X140 : d_subst] : ((((d2subst @ X140)) != ((d2subst @ X141))) | (X140 = X141)) & (((hoasapinj2_lthm = $true) | (? [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 != X225) & (((ap @ (sub @ X226 @ id) @ X223)) = ((ap @ (sub @ X224 @ id) @ X225)))) & ! [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 = X222) | (((ap @ X220 @ X222)) != ((ap @ X221 @ X219)))))) & ((! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))) | ? [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 != X222) & (((ap @ X220 @ X222)) = ((ap @ X221 @ X219))))) | (hoasapinj2_lthm != $true))) & (induction2_gthm = $true) & (((substmonoid_lthm = $true) | (! [X416 : subst] : (((comp @ X416 @ id)) = X416) & (? [X418 : subst] : (((comp @ X418 @ id)) != X418) | ? [X417 : subst] : (((comp @ id @ X417)) != X417)) & ! [X415 : subst] : (((comp @ id @ X415)) = X415))) & ((? [X416 : subst] : (((comp @ X416 @ id)) != X416) | (! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)) | ? [X415 : subst] : (((comp @ id @ X415)) != X415)) | (substmonoid_lthm != $true))) & ((! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) | (laminj != $true)) & ((laminj = $true) | ? [X247 : term,X248 : term] : ((((lam @ X247)) = ((lam @ X248))) & (X247 != X248)))) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar = $true) & ((! [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) != $true) | (((X233 @ one)) = $true) | ? [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) != ((X233 @ X237)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) = $true) & (((X233 @ one)) != $true) & ! [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X233 @ X237)))))) & ((($true = sP58) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP58))) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & (((sP57 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP57 != $true))) & (((pushprop_lem0_lthm = $true) | ? [X135 : (term > $o),X137 : subst,X136 : term] : ! [X138 : (term > $o)] : ? [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) != ((X138 @ X139)))) & (! [X135 : (term > $o),X137 : subst,X136 : term] : ? [X138 : (term > $o)] : ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139))) | (pushprop_lem0_lthm != $true))) & (((hoaslaminj = $true) | ? [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (! [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) = ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) & (((X286 @ X285 @ X287)) != ((X288 @ X285 @ X287))) & ! [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) = ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) & (((lam @ (X288 @ sh @ one))) = ((lam @ (X286 @ sh @ one)))))) & (! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (? [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) != ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))) | ? [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) != ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one))))) | (hoaslaminj != $true))) & (axassoc = $true) & (((! [X170 : term] : (((sub @ X170 @ id)) = X170) | ? [X169 : term] : (((sub @ X169 @ id)) != X169)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X170 : term] : (((sub @ X170 @ id)) != X170) & ! [X169 : term] : (((sub @ X169 @ id)) = X169)))) & (hoasinduction_lem1_lthm = $true) & (((pushprop_lem0 = $true) | ? [X33 : subst,X34 : (term > $o),X35 : term] : ! [X36 : (term > $o)] : ? [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) != ((X36 @ X37)))) & (! [X33 : subst,X34 : (term > $o),X35 : term] : ? [X36 : (term > $o)] : ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37))) | (pushprop_lem0 != $true))) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & (((sP56 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP56 != $true))) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((hoasinduction_lem3 = $true) | (sP47 != $true)) & ((sP47 = $true) | (hoasinduction_lem3 != $true))) & (((hoasinduction_lem3b_lthm = $true) | ? [X145 : term] : ! [X146 : (subst > term > term)] : (((X146 @ sh @ one)) != ((sub @ X145 @ (push @ one @ sh))))) & (! [X145 : term] : ? [X146 : (subst > term > term)] : (((X146 @ sh @ one)) = ((sub @ X145 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true))) & (((hoasapinj2 = $true) | ? [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) = ((ap @ (sub @ X496 @ id) @ X497))) & (X495 != X497))) & (! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497)) | (hoasapinj2 != $true))) & ((! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) | (shinj != $true)) & ((shinj = $true) | ? [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) = ((sub @ X70 @ sh))) & (X70 != X71)))) & (hoasapinj2_gthm = $true) & (((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true))) & (pushprop_gthm = $true) & (((pushprop_lem1v2_lthm = $true) | (! [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) = X238) & ? [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) = $true) & ($true != ((X243 @ one))) & ! [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) = ((X243 @ X244)))))) & ((? [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) != X238) | ! [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) != $true) | ($true = ((X243 @ one))) | ? [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) != ((X243 @ X244))))) | (pushprop_lem1v2_lthm != $true))) & (((sP42 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP42 != $true))) & ((! [X142 : term] : (((sub @ X142 @ id)) = X142) | (termmset != $true)) & ((termmset = $true) | ? [X142 : term] : (((sub @ X142 @ id)) != X142))) & (((induction2lem = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2lem != $true))) & (pushprop_lem3v2_lthm = $true) & (axvarshift = $true) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & (hoasinduction_lem3b_gthm = $true) & ! [X218 : d_term] : (d_one = X218) & (axapp = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((hoasinduction_lem3b = $true) | ? [X295 : term] : ! [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) != ((X296 @ sh @ one)))) & (! [X295 : term] : ? [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) = ((X296 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (induction2lem_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (lamnotap != $true) & (((axvarid = $true) | ? [X402 : term] : (((sub @ X402 @ id)) != X402)) & (! [X402 : term] : (((sub @ X402 @ id)) = X402) | (axvarid != $true))) & ! [X284 : d_subst] : (d_id = X284) & (((hoasinduction_lem3v2a_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3v2a_lthm != $true))) & (pushprop_lem2v2 = $true) & (((hoasapinj1_lthm = $true) | (! [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 = X28) | (((ap @ X28 @ X26)) != ((ap @ X27 @ X25)))) & ? [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 != X30) & (((ap @ (sub @ X29 @ id) @ X31)) = ((ap @ (sub @ X30 @ id) @ X32)))) & ! [X24 : term] : (((sub @ X24 @ id)) = X24))) & ((? [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 != X28) & (((ap @ X28 @ X26)) = ((ap @ X27 @ X25)))) | ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))) | ? [X24 : term] : (((sub @ X24 @ id)) != X24)) | (hoasapinj1_lthm != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((pushprop_lem1_lthm = $true) | (? [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) != $true) & (((X347 @ X345)) = $true)) & ! [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) = X342) & ! [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) = X340))) & ((! [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true) | (((X347 @ X345)) != $true)) | ? [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) != X342) | ? [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) != X340)) | (pushprop_lem1_lthm != $true))) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & (((hoasinduction = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction != $true))) & (((sP32 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP32 != $true))) & (((hoasinduction_no_psi_cond = $true) | ? [X249 : term,X250 : (subst > term > subst > $o)] : (! [X253 : (subst > term > term)] : (? [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) != ((sub @ (X253 @ X255 @ X256) @ X257))) | (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) = $true) | ? [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) != $true) & (((X250 @ id @ X254 @ id)) = $true))) & (((sP30 @ X250)) != $true) & (((X250 @ id @ X249 @ id)) != $true))) & (! [X249 : term,X250 : (subst > term > subst > $o)] : (? [X253 : (subst > term > term)] : (! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257))) & (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) != $true) & ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | (((X250 @ id @ X254 @ id)) != $true))) | (((sP30 @ X250)) = $true) | (((X250 @ id @ X249 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true))) & (substmonoid_gthm = $true) & (((sP29 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP29 != $true))) & (((sP27 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP27 != $true))) & ((! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) = ((ap @ (sub @ X462 @ id) @ X465))) & (X462 != X463)))) & (hoasinduction_lem3a_gthm = $true) & (axabs = $true) & (((apinj2 = $true) | ? [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) = ((ap @ X40 @ X38))) & (X38 != X41))) & (! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41)) | (apinj2 != $true))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (((hoasinduction_lem3a_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a_lthm != $true))) & (((induction2 = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2 != $true))) & (ulamvarind = $true) & (pushprop_lthm = $true) & (((hoasinduction_lem2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2 != $true))) & (((sP20 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP20 != $true))) & (((sP18 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP18 != $true))) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((sP14 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP14 != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = id) & (((sP8 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP8 != $true))) & (((hoasinduction_lem3v2_f = $true) | ? [X150 : term] : ! [X151 : (subst > term > term)] : ? [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) != ((X151 @ X152 @ X153)))) & (! [X150 : term] : ? [X151 : (subst > term > term)] : ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153))) | (hoasinduction_lem3v2_f != $true))) & (((axidl = $true) | ? [X72 : subst] : (((comp @ id @ X72)) != X72)) & (! [X72 : subst] : (((comp @ id @ X72)) = X72) | (axidl != $true))) & (axmap = $true) & (ulamvar1 != $true) & (pushprop = $true) & (apnotvar = $true) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & (((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X458 : subst] : (((comp @ X458 @ id)) != X458) | ? [X457 : subst] : (((comp @ id @ X457)) != X457)))) & (((hoasinduction_lem0 = $true) | ? [X147 : (subst > term > subst > $o)] : ! [X148 : (term > $o)] : ? [X149 : term] : (((X147 @ id @ X149 @ id)) != ((X148 @ X149)))) & (! [X147 : (subst > term > subst > $o)] : ? [X148 : (term > $o)] : ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149))) | (hoasinduction_lem0 != $true))) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapinj1_gthm = $true) & ((! [X283 : subst] : (((comp @ X283 @ id)) = X283) | (axidr != $true)) & ((axidr = $true) | ? [X283 : subst] : (((comp @ X283 @ id)) != X283))) & (((sP7 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP7 != $true))) & ((! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) != X143))) & (((hoasinduction_lem0_lthm = $true) | ? [X459 : (subst > term > subst > $o)] : ! [X460 : (term > $o)] : ? [X461 : term] : (((X459 @ id @ X461 @ id)) != ((X460 @ X461)))) & (! [X459 : (subst > term > subst > $o)] : ? [X460 : (term > $o)] : ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461))) | (hoasinduction_lem0_lthm != $true))) & (hoasinduction_lem1 = $true) & (((sP6 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP6 != $true))) & (((axvarcons = $true) | ? [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) != X493)) & (! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493) | (axvarcons != $true))) & ((($true = sP1) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP1))) & (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)))))))))))))) & (lamnotvar = $true) & ((! [X20 : term] : ? [X21 : (subst > term > term)] : ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X20 : term] : ! [X21 : (subst > term > term)] : ? [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) != ((sub @ X20 @ (push @ X23 @ X22)))))) & ((! [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true != ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true = ((X520 @ X521))) & (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) != $true)))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ! [X18 : d_term,X19 : d_term] : ((((d2term @ X18)) != ((d2term @ X19))) | (X18 = X19)) & (hoaslaminj_gthm = $true) & (((apinj1 = $true) | ? [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) = ((ap @ X406 @ X405))) & (X404 != X406))) & (! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406)) | (apinj1 != $true))) & ((! [X227 : (term > $o),X228 : term] : ((((sP0 @ X227)) = $true) | ? [X231 : term] : ((((X227 @ X231)) = $true) & ($true != ((X227 @ (lam @ X231))))) | ? [X232 : term] : (($true = ((var @ X232))) & (((X227 @ X232)) != $true)) | (((X227 @ X228)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X227 : (term > $o),X228 : term] : ((((sP0 @ X227)) != $true) & ! [X231 : term] : ((((X227 @ X231)) != $true) | ($true = ((X227 @ (lam @ X231))))) & ! [X232 : term] : (($true != ((var @ X232))) | (((X227 @ X232)) = $true)) & (((X227 @ X228)) != $true)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem1_gthm = $true) & ((! [X433 : term,X432 : (subst > term > term),X434 : term] : (? [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) != ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X433 : term,X432 : (subst > term > term),X434 : term] : (! [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) = ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) & (((ap @ (sub @ X434 @ id) @ X433)) = ((lam @ (X432 @ sh @ one))))))) & (termmset_gthm = $true)),
% 14.62/2.51 inference(nnf_transformation,[],[f72])).
% 14.62/2.51 thf(f261,plain,(
% 14.62/2.51 (hoasinduction_lem1v2 = $true) & (! [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) = X456) | (axscons != $true)) & ((axscons = $true) | ? [X456 : subst] : (((push @ (sub @ one @ X456) @ (comp @ sh @ X456))) != X456)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X141 : d_subst,X140 : d_subst] : ((((d2subst @ X140)) != ((d2subst @ X141))) | (X140 = X141)) & ((hoasapinj2_lthm = $true) | (? [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 != X225) & (((ap @ (sub @ X226 @ id) @ X223)) = ((ap @ (sub @ X224 @ id) @ X225)))) & ! [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 = X222) | (((ap @ X220 @ X222)) != ((ap @ X221 @ X219)))))) & (! [X225 : term,X223 : term,X226 : term,X224 : term] : ((X223 = X225) | (((ap @ (sub @ X226 @ id) @ X223)) != ((ap @ (sub @ X224 @ id) @ X225)))) | ? [X222 : term,X221 : term,X219 : term,X220 : term] : ((X219 != X222) & (((ap @ X220 @ X222)) = ((ap @ X221 @ X219)))) | (hoasapinj2_lthm != $true)) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) | (! [X416 : subst] : (((comp @ X416 @ id)) = X416) & (? [X418 : subst] : (((comp @ X418 @ id)) != X418) | ? [X417 : subst] : (((comp @ id @ X417)) != X417)) & ! [X415 : subst] : (((comp @ id @ X415)) = X415))) & (? [X416 : subst] : (((comp @ X416 @ id)) != X416) | (! [X418 : subst] : (((comp @ X418 @ id)) = X418) & ! [X417 : subst] : (((comp @ id @ X417)) = X417)) | ? [X415 : subst] : (((comp @ id @ X415)) != X415) | (substmonoid_lthm != $true)) & (! [X247 : term,X248 : term] : ((((lam @ X247)) != ((lam @ X248))) | (X247 = X248)) | (laminj != $true)) & ((laminj = $true) | ? [X247 : term,X248 : term] : ((((lam @ X247)) = ((lam @ X248))) & (X247 != X248))) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) != $true) | (((X233 @ one)) = $true) | ? [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) != ((X233 @ X237)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X236 : (term > $o),X234 : term,X235 : subst,X233 : (term > $o)] : ((((X236 @ X234)) = $true) & (((X233 @ one)) != $true) & ! [X237 : term] : (((X236 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X233 @ X237))))) & (($true = sP58) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP58)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & ((sP57 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP57 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X135 : (term > $o),X137 : subst,X136 : term] : ! [X138 : (term > $o)] : ? [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) != ((X138 @ X139)))) & (! [X135 : (term > $o),X137 : subst,X136 : term] : ? [X138 : (term > $o)] : ! [X139 : term] : (((X135 @ (sub @ X139 @ (push @ X136 @ X137)))) = ((X138 @ X139))) | (pushprop_lem0_lthm != $true)) & ((hoaslaminj = $true) | ? [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (! [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) = ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) & (((X286 @ X285 @ X287)) != ((X288 @ X285 @ X287))) & ! [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) = ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) & (((lam @ (X288 @ sh @ one))) = ((lam @ (X286 @ sh @ one)))))) & (! [X286 : (subst > term > term),X285 : subst,X288 : (subst > term > term),X287 : term] : (? [X289 : subst,X290 : subst,X291 : term] : (((sub @ (X286 @ X289 @ X291) @ X290)) != ((X286 @ (comp @ X289 @ X290) @ (sub @ X291 @ X290)))) | (((X286 @ X285 @ X287)) = ((X288 @ X285 @ X287))) | ? [X292 : subst,X293 : term,X294 : subst] : (((sub @ (X288 @ X292 @ X293) @ X294)) != ((X288 @ (comp @ X292 @ X294) @ (sub @ X293 @ X294)))) | (((lam @ (X288 @ sh @ one))) != ((lam @ (X286 @ sh @ one))))) | (hoaslaminj != $true)) & (axassoc = $true) & (! [X170 : term] : (((sub @ X170 @ id)) = X170) | ? [X169 : term] : (((sub @ X169 @ id)) != X169) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X170 : term] : (((sub @ X170 @ id)) != X170) & ! [X169 : term] : (((sub @ X169 @ id)) = X169))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) | ? [X33 : subst,X34 : (term > $o),X35 : term] : ! [X36 : (term > $o)] : ? [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) != ((X36 @ X37)))) & (! [X33 : subst,X34 : (term > $o),X35 : term] : ? [X36 : (term > $o)] : ! [X37 : term] : (((X34 @ (sub @ X37 @ (push @ X35 @ X33)))) = ((X36 @ X37))) | (pushprop_lem0 != $true)) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((sP56 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP56 != $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3 = $true) | (sP47 != $true)) & ((sP47 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X145 : term] : ! [X146 : (subst > term > term)] : (((X146 @ sh @ one)) != ((sub @ X145 @ (push @ one @ sh))))) & (! [X145 : term] : ? [X146 : (subst > term > term)] : (((X146 @ sh @ one)) = ((sub @ X145 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasapinj2 = $true) | ? [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) = ((ap @ (sub @ X496 @ id) @ X497))) & (X495 != X497))) & (! [X498 : term,X496 : term,X495 : term,X497 : term] : ((((ap @ (sub @ X498 @ id) @ X495)) != ((ap @ (sub @ X496 @ id) @ X497))) | (X495 = X497)) | (hoasapinj2 != $true)) & (! [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) != ((sub @ X70 @ sh))) | (X70 = X71)) | (shinj != $true)) & ((shinj = $true) | ? [X70 : term,X71 : term] : ((((sub @ X71 @ sh)) = ((sub @ X70 @ sh))) & (X70 != X71))) & (hoasapinj2_gthm = $true) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) = X238) & ? [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) = $true) & ($true != ((X243 @ one))) & ! [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) = ((X243 @ X244)))))) & (? [X238 : term,X239 : subst] : (((sub @ one @ (push @ X238 @ X239))) != X238) | ! [X242 : (term > $o),X240 : subst,X243 : (term > $o),X241 : term] : ((((X242 @ X241)) != $true) | ($true = ((X243 @ one))) | ? [X244 : term] : (((X242 @ (sub @ X244 @ (push @ X241 @ X240)))) != ((X243 @ X244)))) | (pushprop_lem1v2_lthm != $true)) & ((sP42 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP42 != $true)) & (! [X142 : term] : (((sub @ X142 @ id)) = X142) | (termmset != $true)) & ((termmset = $true) | ? [X142 : term] : (((sub @ X142 @ id)) != X142)) & ((induction2lem = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2lem != $true)) & (pushprop_lem3v2_lthm = $true) & (axvarshift = $true) & ! [X245 : term] : ? [X246 : d_term] : (((d2term @ X246)) = X245) & (hoasinduction_lem3b_gthm = $true) & ! [X218 : d_term] : (d_one = X218) & (axapp = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b = $true) | ? [X295 : term] : ! [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) != ((X296 @ sh @ one)))) & (! [X295 : term] : ? [X296 : (subst > term > term)] : (((sub @ X295 @ (push @ one @ sh))) = ((X296 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (induction2lem_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (lamnotap != $true) & ((axvarid = $true) | ? [X402 : term] : (((sub @ X402 @ id)) != X402)) & (! [X402 : term] : (((sub @ X402 @ id)) = X402) | (axvarid != $true)) & ! [X284 : d_subst] : (d_id = X284) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3v2a_lthm != $true)) & (pushprop_lem2v2 = $true) & ((hoasapinj1_lthm = $true) | (! [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 = X28) | (((ap @ X28 @ X26)) != ((ap @ X27 @ X25)))) & ? [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 != X30) & (((ap @ (sub @ X29 @ id) @ X31)) = ((ap @ (sub @ X30 @ id) @ X32)))) & ! [X24 : term] : (((sub @ X24 @ id)) = X24))) & (? [X27 : term,X26 : term,X25 : term,X28 : term] : ((X27 != X28) & (((ap @ X28 @ X26)) = ((ap @ X27 @ X25)))) | ! [X30 : term,X31 : term,X32 : term,X29 : term] : ((X29 = X30) | (((ap @ (sub @ X29 @ id) @ X31)) != ((ap @ (sub @ X30 @ id) @ X32)))) | ? [X24 : term] : (((sub @ X24 @ id)) != X24) | (hoasapinj1_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem1_lthm = $true) | (? [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) != $true) & (((X347 @ X345)) = $true)) & ! [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) = X342) & ! [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) = X340))) & (! [X347 : (term > $o),X343 : term,X346 : (term > $o),X344 : subst,X345 : term] : ((((X346 @ (sub @ X345 @ (push @ X343 @ X344)))) = $true) | (((X347 @ X345)) != $true)) | ? [X341 : term,X342 : subst] : (((comp @ sh @ (push @ X341 @ X342))) != X342) | ? [X339 : subst,X340 : term] : (((sub @ one @ (push @ X340 @ X339))) != X340) | (pushprop_lem1_lthm != $true)) & ! [X16 : subst] : ? [X17 : d_subst] : (((d2subst @ X17)) = X16) & ((hoasinduction = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction != $true)) & ((sP32 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP32 != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X249 : term,X250 : (subst > term > subst > $o)] : (! [X253 : (subst > term > term)] : (? [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) != ((sub @ (X253 @ X255 @ X256) @ X257))) | (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) = $true) | ? [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) != $true) & (((X250 @ id @ X254 @ id)) = $true))) & (((sP30 @ X250)) != $true) & (((X250 @ id @ X249 @ id)) != $true))) & (! [X249 : term,X250 : (subst > term > subst > $o)] : (? [X253 : (subst > term > term)] : (! [X257 : subst,X256 : term,X255 : subst] : (((X253 @ (comp @ X255 @ X257) @ (sub @ X256 @ X257))) = ((sub @ (X253 @ X255 @ X256) @ X257))) & (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) != $true) & ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | (((X250 @ id @ X254 @ id)) != $true))) | (((sP30 @ X250)) = $true) | (((X250 @ id @ X249 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (substmonoid_gthm = $true) & ((sP29 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP29 != $true)) & ((sP27 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP27 != $true)) & (! [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) != ((ap @ (sub @ X462 @ id) @ X465))) | (X462 = X463)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X464 : term,X463 : term,X462 : term,X465 : term] : ((((ap @ (sub @ X463 @ id) @ X464)) = ((ap @ (sub @ X462 @ id) @ X465))) & (X462 != X463))) & (hoasinduction_lem3a_gthm = $true) & (axabs = $true) & ((apinj2 = $true) | ? [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) = ((ap @ X40 @ X38))) & (X38 != X41))) & (! [X40 : term,X41 : term,X38 : term,X39 : term] : ((((ap @ X39 @ X41)) != ((ap @ X40 @ X38))) | (X38 = X41)) | (apinj2 != $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((induction2 = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2 != $true)) & (ulamvarind = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2 != $true)) & ((sP20 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP20 != $true)) & ((sP18 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP18 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP14 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP14 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = id) & ((sP8 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP8 != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X150 : term] : ! [X151 : (subst > term > term)] : ? [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) != ((X151 @ X152 @ X153)))) & (! [X150 : term] : ? [X151 : (subst > term > term)] : ! [X152 : subst,X153 : term] : (((sub @ X150 @ (push @ X153 @ X152))) = ((X151 @ X152 @ X153))) | (hoasinduction_lem3v2_f != $true)) & ((axidl = $true) | ? [X72 : subst] : (((comp @ id @ X72)) != X72)) & (! [X72 : subst] : (((comp @ id @ X72)) = X72) | (axidl != $true)) & (axmap = $true) & (ulamvar1 != $true) & (pushprop = $true) & (apnotvar = $true) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & ((! [X458 : subst] : (((comp @ X458 @ id)) = X458) & ! [X457 : subst] : (((comp @ id @ X457)) = X457)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X458 : subst] : (((comp @ X458 @ id)) != X458) | ? [X457 : subst] : (((comp @ id @ X457)) != X457)) & ((hoasinduction_lem0 = $true) | ? [X147 : (subst > term > subst > $o)] : ! [X148 : (term > $o)] : ? [X149 : term] : (((X147 @ id @ X149 @ id)) != ((X148 @ X149)))) & (! [X147 : (subst > term > subst > $o)] : ? [X148 : (term > $o)] : ! [X149 : term] : (((X147 @ id @ X149 @ id)) = ((X148 @ X149))) | (hoasinduction_lem0 != $true)) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X283 : subst] : (((comp @ X283 @ id)) = X283) | (axidr != $true)) & ((axidr = $true) | ? [X283 : subst] : (((comp @ X283 @ id)) != X283)) & ((sP7 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP7 != $true)) & (! [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) = X143) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X143 : subst,X144 : term] : (((comp @ sh @ (push @ X144 @ X143))) != X143)) & ((hoasinduction_lem0_lthm = $true) | ? [X459 : (subst > term > subst > $o)] : ! [X460 : (term > $o)] : ? [X461 : term] : (((X459 @ id @ X461 @ id)) != ((X460 @ X461)))) & (! [X459 : (subst > term > subst > $o)] : ? [X460 : (term > $o)] : ! [X461 : term] : (((X459 @ id @ X461 @ id)) = ((X460 @ X461))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1 = $true) & ((sP6 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP6 != $true)) & ((axvarcons = $true) | ? [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) != X493)) & (! [X494 : subst,X493 : term] : (((sub @ one @ (push @ X493 @ X494))) = X493) | (axvarcons != $true)) & (($true = sP1) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP1)) & (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)))))))))))))) & (lamnotvar = $true) & (! [X20 : term] : ? [X21 : (subst > term > term)] : ! [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) = ((sub @ X20 @ (push @ X23 @ X22)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X20 : term] : ! [X21 : (subst > term > term)] : ? [X23 : term,X22 : subst] : (((X21 @ X22 @ X23)) != ((sub @ X20 @ (push @ X23 @ X22))))) & (! [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true != ((X520 @ X521))) | (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X517 : term,X520 : (term > $o),X518 : (term > $o),X519 : subst,X521 : term] : (($true = ((X520 @ X521))) & (((X518 @ (sub @ X521 @ (push @ X517 @ X519)))) != $true))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ! [X18 : d_term,X19 : d_term] : ((((d2term @ X18)) != ((d2term @ X19))) | (X18 = X19)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) | ? [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) = ((ap @ X406 @ X405))) & (X404 != X406))) & (! [X406 : term,X405 : term,X403 : term,X404 : term] : ((((ap @ X404 @ X403)) != ((ap @ X406 @ X405))) | (X404 = X406)) | (apinj1 != $true)) & (! [X227 : (term > $o),X228 : term] : ((((sP0 @ X227)) = $true) | ? [X231 : term] : ((((X227 @ X231)) = $true) & ($true != ((X227 @ (lam @ X231))))) | ? [X232 : term] : (($true = ((var @ X232))) & (((X227 @ X232)) != $true)) | (((X227 @ X228)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X227 : (term > $o),X228 : term] : ((((sP0 @ X227)) != $true) & ! [X231 : term] : ((((X227 @ X231)) != $true) | ($true = ((X227 @ (lam @ X231))))) & ! [X232 : term] : (($true != ((var @ X232))) | (((X227 @ X232)) = $true)) & (((X227 @ X228)) != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem1_gthm = $true) & (! [X433 : term,X432 : (subst > term > term),X434 : term] : (? [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) != ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | (((ap @ (sub @ X434 @ id) @ X433)) != ((lam @ (X432 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X433 : term,X432 : (subst > term > term),X434 : term] : (! [X436 : subst,X437 : subst,X435 : term] : (((sub @ (X432 @ X436 @ X435) @ X437)) = ((X432 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) & (((ap @ (sub @ X434 @ id) @ X433)) = ((lam @ (X432 @ sh @ one)))))) & (termmset_gthm = $true)),
% 14.62/2.51 inference(flattening,[],[f260])).
% 14.62/2.51 thf(f262,plain,(
% 14.62/2.51 (hoasinduction_lem1v2 = $true) & (! [X0 : subst] : (((push @ (sub @ one @ X0) @ (comp @ sh @ X0))) = X0) | (axscons != $true)) & ((axscons = $true) | ? [X1 : subst] : (((push @ (sub @ one @ X1) @ (comp @ sh @ X1))) != X1)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X2 : d_subst,X3 : d_subst] : ((((d2subst @ X3)) != ((d2subst @ X2))) | (X2 = X3)) & ((hoasapinj2_lthm = $true) | (? [X4 : term,X5 : term,X6 : term,X7 : term] : ((X4 != X5) & (((ap @ (sub @ X7 @ id) @ X4)) = ((ap @ (sub @ X6 @ id) @ X5)))) & ! [X8 : term,X9 : term,X10 : term,X11 : term] : ((X8 = X10) | (((ap @ X11 @ X8)) != ((ap @ X9 @ X10)))))) & (! [X12 : term,X13 : term,X14 : term,X15 : term] : ((X12 = X13) | (((ap @ (sub @ X14 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X12)))) | ? [X16 : term,X17 : term,X18 : term,X19 : term] : ((X16 != X18) & (((ap @ X19 @ X16)) = ((ap @ X17 @ X18)))) | (hoasapinj2_lthm != $true)) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) | (! [X20 : subst] : (((comp @ X20 @ id)) = X20) & (? [X21 : subst] : (((comp @ X21 @ id)) != X21) | ? [X22 : subst] : (((comp @ id @ X22)) != X22)) & ! [X23 : subst] : (((comp @ id @ X23)) = X23))) & (? [X24 : subst] : (((comp @ X24 @ id)) != X24) | (! [X25 : subst] : (((comp @ X25 @ id)) = X25) & ! [X26 : subst] : (((comp @ id @ X26)) = X26)) | ? [X27 : subst] : (((comp @ id @ X27)) != X27) | (substmonoid_lthm != $true)) & (! [X28 : term,X29 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) | (laminj != $true)) & ((laminj = $true) | ? [X30 : term,X31 : term] : ((((lam @ X31)) = ((lam @ X30))) & (X30 != X31))) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X32 : (term > $o),X33 : term,X34 : subst,X35 : (term > $o)] : ((((X32 @ X33)) != $true) | (((X35 @ one)) = $true) | ? [X36 : term] : (((X32 @ (sub @ X36 @ (push @ X33 @ X34)))) != ((X35 @ X36)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X37 : (term > $o),X38 : term,X39 : subst,X40 : (term > $o)] : (($true = ((X37 @ X38))) & ($true != ((X40 @ one))) & ! [X41 : term] : (((X37 @ (sub @ X41 @ (push @ X38 @ X39)))) = ((X40 @ X41))))) & (($true = sP58) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP58)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & ((sP57 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP57 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X42 : (term > $o),X43 : subst,X44 : term] : ! [X45 : (term > $o)] : ? [X46 : term] : (((X45 @ X46)) != ((X42 @ (sub @ X46 @ (push @ X44 @ X43)))))) & (! [X47 : (term > $o),X48 : subst,X49 : term] : ? [X50 : (term > $o)] : ! [X51 : term] : (((X50 @ X51)) = ((X47 @ (sub @ X51 @ (push @ X49 @ X48))))) | (pushprop_lem0_lthm != $true)) & ((hoaslaminj = $true) | ? [X52 : (subst > term > term),X53 : subst,X54 : (subst > term > term),X55 : term] : (! [X56 : subst,X57 : subst,X58 : term] : (((X52 @ (comp @ X56 @ X57) @ (sub @ X58 @ X57))) = ((sub @ (X52 @ X56 @ X58) @ X57))) & (((X54 @ X53 @ X55)) != ((X52 @ X53 @ X55))) & ! [X59 : subst,X60 : term,X61 : subst] : (((sub @ (X54 @ X59 @ X60) @ X61)) = ((X54 @ (comp @ X59 @ X61) @ (sub @ X60 @ X61)))) & (((lam @ (X52 @ sh @ one))) = ((lam @ (X54 @ sh @ one)))))) & (! [X62 : (subst > term > term),X63 : subst,X64 : (subst > term > term),X65 : term] : (? [X66 : subst,X67 : subst,X68 : term] : (((X62 @ (comp @ X66 @ X67) @ (sub @ X68 @ X67))) != ((sub @ (X62 @ X66 @ X68) @ X67))) | (((X64 @ X63 @ X65)) = ((X62 @ X63 @ X65))) | ? [X69 : subst,X70 : term,X71 : subst] : (((sub @ (X64 @ X69 @ X70) @ X71)) != ((X64 @ (comp @ X69 @ X71) @ (sub @ X70 @ X71)))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one))))) | (hoaslaminj != $true)) & (axassoc = $true) & (! [X72 : term] : (((sub @ X72 @ id)) = X72) | ? [X73 : term] : (((sub @ X73 @ id)) != X73) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X74 : term] : (((sub @ X74 @ id)) != X74) & ! [X75 : term] : (((sub @ X75 @ id)) = X75))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) | ? [X76 : subst,X77 : (term > $o),X78 : term] : ! [X79 : (term > $o)] : ? [X80 : term] : (((X79 @ X80)) != ((X77 @ (sub @ X80 @ (push @ X78 @ X76)))))) & (! [X81 : subst,X82 : (term > $o),X83 : term] : ? [X84 : (term > $o)] : ! [X85 : term] : (((X82 @ (sub @ X85 @ (push @ X83 @ X81)))) = ((X84 @ X85))) | (pushprop_lem0 != $true)) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((sP56 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP56 != $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3 = $true) | (sP47 != $true)) & ((sP47 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X86 : term] : ! [X87 : (subst > term > term)] : (((X87 @ sh @ one)) != ((sub @ X86 @ (push @ one @ sh))))) & (! [X88 : term] : ? [X89 : (subst > term > term)] : (((sub @ X88 @ (push @ one @ sh))) = ((X89 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasapinj2 = $true) | ? [X90 : term,X91 : term,X92 : term,X93 : term] : ((((ap @ (sub @ X91 @ id) @ X93)) = ((ap @ (sub @ X90 @ id) @ X92))) & (X92 != X93))) & (! [X94 : term,X95 : term,X96 : term,X97 : term] : ((((ap @ (sub @ X95 @ id) @ X97)) != ((ap @ (sub @ X94 @ id) @ X96))) | (X96 = X97)) | (hoasapinj2 != $true)) & (! [X98 : term,X99 : term] : ((((sub @ X98 @ sh)) != ((sub @ X99 @ sh))) | (X98 = X99)) | (shinj != $true)) & ((shinj = $true) | ? [X100 : term,X101 : term] : ((((sub @ X100 @ sh)) = ((sub @ X101 @ sh))) & (X100 != X101))) & (hoasapinj2_gthm = $true) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X102 : term,X103 : subst] : (((sub @ one @ (push @ X102 @ X103))) = X102) & ? [X104 : (term > $o),X105 : subst,X106 : (term > $o),X107 : term] : ((((X104 @ X107)) = $true) & ($true != ((X106 @ one))) & ! [X108 : term] : (((X104 @ (sub @ X108 @ (push @ X107 @ X105)))) = ((X106 @ X108)))))) & (? [X109 : term,X110 : subst] : (((sub @ one @ (push @ X109 @ X110))) != X109) | ! [X111 : (term > $o),X112 : subst,X113 : (term > $o),X114 : term] : ((((X111 @ X114)) != $true) | (((X113 @ one)) = $true) | ? [X115 : term] : (((X111 @ (sub @ X115 @ (push @ X114 @ X112)))) != ((X113 @ X115)))) | (pushprop_lem1v2_lthm != $true)) & ((sP42 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP42 != $true)) & (! [X116 : term] : (((sub @ X116 @ id)) = X116) | (termmset != $true)) & ((termmset = $true) | ? [X117 : term] : (((sub @ X117 @ id)) != X117)) & ((induction2lem = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2lem != $true)) & (pushprop_lem3v2_lthm = $true) & (axvarshift = $true) & ! [X118 : term] : ? [X119 : d_term] : (((d2term @ X119)) = X118) & (hoasinduction_lem3b_gthm = $true) & ! [X120 : d_term] : (d_one = X120) & (axapp = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b = $true) | ? [X121 : term] : ! [X122 : (subst > term > term)] : (((sub @ X121 @ (push @ one @ sh))) != ((X122 @ sh @ one)))) & (! [X123 : term] : ? [X124 : (subst > term > term)] : (((sub @ X123 @ (push @ one @ sh))) = ((X124 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (induction2lem_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (lamnotap != $true) & ((axvarid = $true) | ? [X125 : term] : (((sub @ X125 @ id)) != X125)) & (! [X126 : term] : (((sub @ X126 @ id)) = X126) | (axvarid != $true)) & ! [X127 : d_subst] : (d_id = X127) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3v2a_lthm != $true)) & (pushprop_lem2v2 = $true) & ((hoasapinj1_lthm = $true) | (! [X128 : term,X129 : term,X130 : term,X131 : term] : ((X128 = X131) | (((ap @ X128 @ X130)) != ((ap @ X131 @ X129)))) & ? [X132 : term,X133 : term,X134 : term,X135 : term] : ((X132 != X135) & (((ap @ (sub @ X135 @ id) @ X133)) = ((ap @ (sub @ X132 @ id) @ X134)))) & ! [X136 : term] : (((sub @ X136 @ id)) = X136))) & (? [X137 : term,X138 : term,X139 : term,X140 : term] : ((X137 != X140) & (((ap @ X140 @ X138)) = ((ap @ X137 @ X139)))) | ! [X141 : term,X142 : term,X143 : term,X144 : term] : ((X141 = X144) | (((ap @ (sub @ X141 @ id) @ X143)) != ((ap @ (sub @ X144 @ id) @ X142)))) | ? [X145 : term] : (((sub @ X145 @ id)) != X145) | (hoasapinj1_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem1_lthm = $true) | (? [X146 : (term > $o),X147 : term,X148 : (term > $o),X149 : subst,X150 : term] : (($true != ((X148 @ (sub @ X150 @ (push @ X147 @ X149))))) & ($true = ((X146 @ X150)))) & ! [X151 : term,X152 : subst] : (((comp @ sh @ (push @ X151 @ X152))) = X152) & ! [X153 : subst,X154 : term] : (((sub @ one @ (push @ X154 @ X153))) = X154))) & (! [X155 : (term > $o),X156 : term,X157 : (term > $o),X158 : subst,X159 : term] : (($true = ((X157 @ (sub @ X159 @ (push @ X156 @ X158))))) | (((X155 @ X159)) != $true)) | ? [X160 : term,X161 : subst] : (((comp @ sh @ (push @ X160 @ X161))) != X161) | ? [X162 : subst,X163 : term] : (((sub @ one @ (push @ X163 @ X162))) != X163) | (pushprop_lem1_lthm != $true)) & ! [X164 : subst] : ? [X165 : d_subst] : (((d2subst @ X165)) = X164) & ((hoasinduction = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction != $true)) & ((sP32 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP32 != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X166 : term,X167 : (subst > term > subst > $o)] : (! [X168 : (subst > term > term)] : (? [X169 : subst,X170 : term,X171 : subst] : (((X168 @ (comp @ X171 @ X169) @ (sub @ X170 @ X169))) != ((sub @ (X168 @ X171 @ X170) @ X169))) | (((X167 @ id @ (lam @ (X168 @ sh @ one)) @ id)) = $true) | ? [X172 : term] : (($true != ((X167 @ id @ (X168 @ id @ X172) @ id))) & (((X167 @ id @ X172 @ id)) = $true))) & ($true != ((sP30 @ X167))) & (((X167 @ id @ X166 @ id)) != $true))) & (! [X173 : term,X174 : (subst > term > subst > $o)] : (? [X175 : (subst > term > term)] : (! [X176 : subst,X177 : term,X178 : subst] : (((sub @ (X175 @ X178 @ X177) @ X176)) = ((X175 @ (comp @ X178 @ X176) @ (sub @ X177 @ X176)))) & (((X174 @ id @ (lam @ (X175 @ sh @ one)) @ id)) != $true) & ! [X179 : term] : ((((X174 @ id @ (X175 @ id @ X179) @ id)) = $true) | (((X174 @ id @ X179 @ id)) != $true))) | ($true = ((sP30 @ X174))) | ($true = ((X174 @ id @ X173 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (substmonoid_gthm = $true) & ((sP29 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP29 != $true)) & ((sP27 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP27 != $true)) & (! [X180 : term,X181 : term,X182 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X180)) != ((ap @ (sub @ X182 @ id) @ X183))) | (X181 = X182)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X184 : term,X185 : term,X186 : term,X187 : term] : ((((ap @ (sub @ X186 @ id) @ X187)) = ((ap @ (sub @ X185 @ id) @ X184))) & (X185 != X186))) & (hoasinduction_lem3a_gthm = $true) & (axabs = $true) & ((apinj2 = $true) | ? [X188 : term,X189 : term,X190 : term,X191 : term] : ((((ap @ X191 @ X189)) = ((ap @ X188 @ X190))) & (X189 != X190))) & (! [X192 : term,X193 : term,X194 : term,X195 : term] : ((((ap @ X195 @ X193)) != ((ap @ X192 @ X194))) | (X193 = X194)) | (apinj2 != $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((induction2 = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2 != $true)) & (ulamvarind = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2 != $true)) & ((sP20 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP20 != $true)) & ((sP18 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP18 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP14 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP14 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = id) & ((sP8 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP8 != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X196 : term] : ! [X197 : (subst > term > term)] : ? [X198 : subst,X199 : term] : (((sub @ X196 @ (push @ X199 @ X198))) != ((X197 @ X198 @ X199)))) & (! [X200 : term] : ? [X201 : (subst > term > term)] : ! [X202 : subst,X203 : term] : (((sub @ X200 @ (push @ X203 @ X202))) = ((X201 @ X202 @ X203))) | (hoasinduction_lem3v2_f != $true)) & ((axidl = $true) | ? [X204 : subst] : (((comp @ id @ X204)) != X204)) & (! [X205 : subst] : (((comp @ id @ X205)) = X205) | (axidl != $true)) & (axmap = $true) & (ulamvar1 != $true) & (pushprop = $true) & (apnotvar = $true) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & ((! [X206 : subst] : (((comp @ X206 @ id)) = X206) & ! [X207 : subst] : (((comp @ id @ X207)) = X207)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X208 : subst] : (((comp @ X208 @ id)) != X208) | ? [X209 : subst] : (((comp @ id @ X209)) != X209)) & ((hoasinduction_lem0 = $true) | ? [X210 : (subst > term > subst > $o)] : ! [X211 : (term > $o)] : ? [X212 : term] : (((X211 @ X212)) != ((X210 @ id @ X212 @ id)))) & (! [X213 : (subst > term > subst > $o)] : ? [X214 : (term > $o)] : ! [X215 : term] : (((X214 @ X215)) = ((X213 @ id @ X215 @ id))) | (hoasinduction_lem0 != $true)) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X216 : subst] : (((comp @ X216 @ id)) = X216) | (axidr != $true)) & ((axidr = $true) | ? [X217 : subst] : (((comp @ X217 @ id)) != X217)) & ((sP7 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP7 != $true)) & (! [X218 : subst,X219 : term] : (((comp @ sh @ (push @ X219 @ X218))) = X218) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X220 : subst,X221 : term] : (((comp @ sh @ (push @ X221 @ X220))) != X220)) & ((hoasinduction_lem0_lthm = $true) | ? [X222 : (subst > term > subst > $o)] : ! [X223 : (term > $o)] : ? [X224 : term] : (((X222 @ id @ X224 @ id)) != ((X223 @ X224)))) & (! [X225 : (subst > term > subst > $o)] : ? [X226 : (term > $o)] : ! [X227 : term] : (((X225 @ id @ X227 @ id)) = ((X226 @ X227))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1 = $true) & ((sP6 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP6 != $true)) & ((axvarcons = $true) | ? [X228 : subst,X229 : term] : (((sub @ one @ (push @ X229 @ X228))) != X229)) & (! [X230 : subst,X231 : term] : (((sub @ one @ (push @ X231 @ X230))) = X231) | (axvarcons != $true)) & (($true = sP1) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP1)) & (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)))))))))))))) & (lamnotvar = $true) & (! [X232 : term] : ? [X233 : (subst > term > term)] : ! [X234 : term,X235 : subst] : (((X233 @ X235 @ X234)) = ((sub @ X232 @ (push @ X234 @ X235)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X236 : term] : ! [X237 : (subst > term > term)] : ? [X238 : term,X239 : subst] : (((sub @ X236 @ (push @ X238 @ X239))) != ((X237 @ X239 @ X238)))) & (! [X240 : term,X241 : (term > $o),X242 : (term > $o),X243 : subst,X244 : term] : ((((X241 @ X244)) != $true) | (((X242 @ (sub @ X244 @ (push @ X240 @ X243)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X245 : term,X246 : (term > $o),X247 : (term > $o),X248 : subst,X249 : term] : ((((X246 @ X249)) = $true) & ($true != ((X247 @ (sub @ X249 @ (push @ X245 @ X248))))))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ! [X250 : d_term,X251 : d_term] : ((((d2term @ X250)) != ((d2term @ X251))) | (X250 = X251)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) | ? [X252 : term,X253 : term,X254 : term,X255 : term] : ((((ap @ X255 @ X254)) = ((ap @ X252 @ X253))) & (X252 != X255))) & (! [X256 : term,X257 : term,X258 : term,X259 : term] : ((((ap @ X256 @ X257)) != ((ap @ X259 @ X258))) | (X256 = X259)) | (apinj1 != $true)) & (! [X260 : (term > $o),X261 : term] : ((((sP0 @ X260)) = $true) | ? [X262 : term] : ((((X260 @ X262)) = $true) & (((X260 @ (lam @ X262))) != $true)) | ? [X263 : term] : (($true = ((var @ X263))) & (((X260 @ X263)) != $true)) | (((X260 @ X261)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X264 : (term > $o),X265 : term] : (($true != ((sP0 @ X264))) & ! [X266 : term] : (($true != ((X264 @ X266))) | (((X264 @ (lam @ X266))) = $true)) & ! [X267 : term] : ((((var @ X267)) != $true) | (((X264 @ X267)) = $true)) & (((X264 @ X265)) != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem1_gthm = $true) & (! [X268 : term,X269 : (subst > term > term),X270 : term] : (? [X271 : subst,X272 : subst,X273 : term] : (((X269 @ (comp @ X271 @ X272) @ (sub @ X273 @ X272))) != ((sub @ (X269 @ X271 @ X273) @ X272))) | (((lam @ (X269 @ sh @ one))) != ((ap @ (sub @ X270 @ id) @ X268)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X274 : term,X275 : (subst > term > term),X276 : term] : (! [X277 : subst,X278 : subst,X279 : term] : (((X275 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278))) = ((sub @ (X275 @ X277 @ X279) @ X278))) & (((ap @ (sub @ X276 @ id) @ X274)) = ((lam @ (X275 @ sh @ one)))))) & (termmset_gthm = $true)),
% 14.62/2.51 inference(rectify,[],[f261])).
% 14.62/2.51 thf(f263,plain,(
% 14.62/2.51 (hoasinduction_lem1v2 = $true) & (! [X0 : subst] : (((push @ (sub @ one @ X0) @ (comp @ sh @ X0))) = X0) | (axscons != $true)) & ((axscons = $true) | (sK454 != ((push @ (sub @ one @ sK454) @ (comp @ sh @ sK454))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X2 : d_subst,X3 : d_subst] : ((((d2subst @ X3)) != ((d2subst @ X2))) | (X2 = X3)) & ((hoasapinj2_lthm = $true) | (((sK456 != sK455) & (((ap @ (sub @ sK457 @ id) @ sK456)) = ((ap @ (sub @ sK458 @ id) @ sK455)))) & ! [X8 : term,X9 : term,X10 : term,X11 : term] : ((X8 = X10) | (((ap @ X11 @ X8)) != ((ap @ X9 @ X10)))))) & (! [X12 : term,X13 : term,X14 : term,X15 : term] : ((X12 = X13) | (((ap @ (sub @ X14 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X12)))) | ((sK459 != sK461) & (((ap @ sK462 @ sK459)) = ((ap @ sK460 @ sK461)))) | (hoasapinj2_lthm != $true)) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) | (! [X20 : subst] : (((comp @ X20 @ id)) = X20) & ((((comp @ sK463 @ id)) != sK463) | (sK464 != ((comp @ id @ sK464)))) & ! [X23 : subst] : (((comp @ id @ X23)) = X23))) & ((((comp @ sK465 @ id)) != sK465) | (! [X25 : subst] : (((comp @ X25 @ id)) = X25) & ! [X26 : subst] : (((comp @ id @ X26)) = X26)) | (((comp @ id @ sK466)) != sK466) | (substmonoid_lthm != $true)) & (! [X28 : term,X29 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK467)) = ((lam @ sK468))) & (sK467 != sK468))) & (pushprop_lem0_gthm = $true) & (axclos = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X32 : (term > $o),X33 : term,X34 : subst,X35 : (term > $o)] : ((((X32 @ X33)) != $true) | (((X35 @ one)) = $true) | (((X32 @ (sub @ (sK469 @ X35 @ X34 @ X33 @ X32) @ (push @ X33 @ X34)))) != ((X35 @ (sK469 @ X35 @ X34 @ X33 @ X32))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ((((sK470 @ sK471)) = $true) & (((sK473 @ one)) != $true) & ! [X41 : term] : (((sK473 @ X41)) = ((sK470 @ (sub @ X41 @ (push @ sK471 @ sK472))))))) & (($true = sP58) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP58)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & ((sP57 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP57 != $true)) & ((pushprop_lem0_lthm = $true) | ! [X45 : (term > $o)] : (((sK474 @ (sub @ (sK477 @ X45) @ (push @ sK476 @ sK475)))) != ((X45 @ (sK477 @ X45))))) & (! [X47 : (term > $o),X48 : subst,X49 : term] : ! [X51 : term] : (((sK478 @ X49 @ X48 @ X47 @ X51)) = ((X47 @ (sub @ X51 @ (push @ X49 @ X48))))) | (pushprop_lem0_lthm != $true)) & ((hoaslaminj = $true) | (! [X56 : subst,X57 : subst,X58 : term] : (((sub @ (sK479 @ X56 @ X58) @ X57)) = ((sK479 @ (comp @ X56 @ X57) @ (sub @ X58 @ X57)))) & (((sK479 @ sK480 @ sK482)) != ((sK481 @ sK480 @ sK482))) & ! [X59 : subst,X60 : term,X61 : subst] : (((sub @ (sK481 @ X59 @ X60) @ X61)) = ((sK481 @ (comp @ X59 @ X61) @ (sub @ X60 @ X61)))) & (((lam @ (sK481 @ sh @ one))) = ((lam @ (sK479 @ sh @ one)))))) & (! [X62 : (subst > term > term),X63 : subst,X64 : (subst > term > term),X65 : term] : ((((X62 @ (comp @ (sK483 @ X62) @ (sK484 @ X62)) @ (sub @ (sK485 @ X62) @ (sK484 @ X62)))) != ((sub @ (X62 @ (sK483 @ X62) @ (sK485 @ X62)) @ (sK484 @ X62)))) | (((X64 @ X63 @ X65)) = ((X62 @ X63 @ X65))) | (((X64 @ (comp @ (sK486 @ X64) @ (sK488 @ X64)) @ (sub @ (sK487 @ X64) @ (sK488 @ X64)))) != ((sub @ (X64 @ (sK486 @ X64) @ (sK487 @ X64)) @ (sK488 @ X64)))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one))))) | (hoaslaminj != $true)) & (axassoc = $true) & (! [X72 : term] : (((sub @ X72 @ id)) = X72) | (((sub @ sK489 @ id)) != sK489) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK490 @ id)) != sK490) & ! [X75 : term] : (((sub @ X75 @ id)) = X75))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) | ! [X79 : (term > $o)] : (((sK492 @ (sub @ (sK494 @ X79) @ (push @ sK493 @ sK491)))) != ((X79 @ (sK494 @ X79))))) & (! [X81 : subst,X82 : (term > $o),X83 : term] : ! [X85 : term] : (((X82 @ (sub @ X85 @ (push @ X83 @ X81)))) = ((sK495 @ X83 @ X82 @ X81 @ X85))) | (pushprop_lem0 != $true)) & (hoaslamnotap_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((sP56 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP56 != $true)) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3 = $true) | (sP47 != $true)) & ((sP47 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X87 : (subst > term > term)] : (((X87 @ sh @ one)) != ((sub @ sK496 @ (push @ one @ sh))))) & (! [X88 : term] : (((sK497 @ X88 @ sh @ one)) = ((sub @ X88 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK498 @ id) @ sK500)) = ((ap @ (sub @ sK499 @ id) @ sK501))) & (sK501 != sK500))) & (! [X94 : term,X95 : term,X96 : term,X97 : term] : ((((ap @ (sub @ X95 @ id) @ X97)) != ((ap @ (sub @ X94 @ id) @ X96))) | (X96 = X97)) | (hoasapinj2 != $true)) & (! [X98 : term,X99 : term] : ((((sub @ X98 @ sh)) != ((sub @ X99 @ sh))) | (X98 = X99)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK503 @ sh)) = ((sub @ sK502 @ sh))) & (sK502 != sK503))) & (hoasapinj2_gthm = $true) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & (pushprop_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X102 : term,X103 : subst] : (((sub @ one @ (push @ X102 @ X103))) = X102) & ((((sK504 @ sK507)) = $true) & ($true != ((sK506 @ one))) & ! [X108 : term] : (((sK504 @ (sub @ X108 @ (push @ sK507 @ sK505)))) = ((sK506 @ X108)))))) & ((sK508 != ((sub @ one @ (push @ sK508 @ sK509)))) | ! [X111 : (term > $o),X112 : subst,X113 : (term > $o),X114 : term] : ((((X111 @ X114)) != $true) | (((X113 @ one)) = $true) | (((X113 @ (sK510 @ X114 @ X113 @ X112 @ X111))) != ((X111 @ (sub @ (sK510 @ X114 @ X113 @ X112 @ X111) @ (push @ X114 @ X112)))))) | (pushprop_lem1v2_lthm != $true)) & ((sP42 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP42 != $true)) & (! [X116 : term] : (((sub @ X116 @ id)) = X116) | (termmset != $true)) & ((termmset = $true) | (((sub @ sK511 @ id)) != sK511)) & ((induction2lem = $true) | (sP38 != $true)) & ((sP38 = $true) | (induction2lem != $true)) & (pushprop_lem3v2_lthm = $true) & (axvarshift = $true) & ! [X118 : term] : (((d2term @ (sK512 @ X118))) = X118) & (hoasinduction_lem3b_gthm = $true) & ! [X120 : d_term] : (d_one = X120) & (axapp = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b = $true) | ! [X122 : (subst > term > term)] : (((sub @ sK513 @ (push @ one @ sh))) != ((X122 @ sh @ one)))) & (! [X123 : term] : (((sub @ X123 @ (push @ one @ sh))) = ((sK514 @ X123 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (induction2lem_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (lamnotap != $true) & ((axvarid = $true) | (((sub @ sK515 @ id)) != sK515)) & (! [X126 : term] : (((sub @ X126 @ id)) = X126) | (axvarid != $true)) & ! [X127 : d_subst] : (d_id = X127) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3v2a_lthm != $true)) & (pushprop_lem2v2 = $true) & ((hoasapinj1_lthm = $true) | (! [X128 : term,X129 : term,X130 : term,X131 : term] : ((X128 = X131) | (((ap @ X128 @ X130)) != ((ap @ X131 @ X129)))) & ((sK516 != sK519) & (((ap @ (sub @ sK519 @ id) @ sK517)) = ((ap @ (sub @ sK516 @ id) @ sK518)))) & ! [X136 : term] : (((sub @ X136 @ id)) = X136))) & (((sK520 != sK523) & (((ap @ sK520 @ sK522)) = ((ap @ sK523 @ sK521)))) | ! [X141 : term,X142 : term,X143 : term,X144 : term] : ((X141 = X144) | (((ap @ (sub @ X141 @ id) @ X143)) != ((ap @ (sub @ X144 @ id) @ X142)))) | (sK524 != ((sub @ sK524 @ id))) | (hoasapinj1_lthm != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem1_lthm = $true) | (((((sK527 @ (sub @ sK529 @ (push @ sK526 @ sK528)))) != $true) & (((sK525 @ sK529)) = $true)) & ! [X151 : term,X152 : subst] : (((comp @ sh @ (push @ X151 @ X152))) = X152) & ! [X153 : subst,X154 : term] : (((sub @ one @ (push @ X154 @ X153))) = X154))) & (! [X155 : (term > $o),X156 : term,X157 : (term > $o),X158 : subst,X159 : term] : (($true = ((X157 @ (sub @ X159 @ (push @ X156 @ X158))))) | (((X155 @ X159)) != $true)) | (sK531 != ((comp @ sh @ (push @ sK530 @ sK531)))) | (((sub @ one @ (push @ sK533 @ sK532))) != sK533) | (pushprop_lem1_lthm != $true)) & ! [X164 : subst] : (((d2subst @ (sK534 @ X164))) = X164) & ((hoasinduction = $true) | (sP35 != $true)) & ((sP35 = $true) | (hoasinduction != $true)) & ((sP32 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP32 != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X168 : (subst > term > term)] : ((((X168 @ (comp @ (sK539 @ X168) @ (sK537 @ X168)) @ (sub @ (sK538 @ X168) @ (sK537 @ X168)))) != ((sub @ (X168 @ (sK539 @ X168) @ (sK538 @ X168)) @ (sK537 @ X168)))) | ($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id))) | ((((sK536 @ id @ (X168 @ id @ (sK540 @ X168)) @ id)) != $true) & ($true = ((sK536 @ id @ (sK540 @ X168) @ id))))) & (((sP30 @ sK536)) != $true) & (((sK536 @ id @ sK535 @ id)) != $true))) & (! [X173 : term,X174 : (subst > term > subst > $o)] : ((! [X176 : subst,X177 : term,X178 : subst] : (((sK541 @ X174 @ (comp @ X178 @ X176) @ (sub @ X177 @ X176))) = ((sub @ (sK541 @ X174 @ X178 @ X177) @ X176))) & (((X174 @ id @ (lam @ (sK541 @ X174 @ sh @ one)) @ id)) != $true) & ! [X179 : term] : (($true = ((X174 @ id @ (sK541 @ X174 @ id @ X179) @ id))) | (((X174 @ id @ X179 @ id)) != $true))) | ($true = ((sP30 @ X174))) | ($true = ((X174 @ id @ X173 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (substmonoid_gthm = $true) & ((sP29 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP29 != $true)) & ((sP27 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP27 != $true)) & (! [X180 : term,X181 : term,X182 : term,X183 : term] : ((((ap @ (sub @ X181 @ id) @ X180)) != ((ap @ (sub @ X182 @ id) @ X183))) | (X181 = X182)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK543 @ id) @ sK542)) = ((ap @ (sub @ sK544 @ id) @ sK545))) & (sK544 != sK543))) & (hoasinduction_lem3a_gthm = $true) & (axabs = $true) & ((apinj2 = $true) | ((((ap @ sK549 @ sK547)) = ((ap @ sK546 @ sK548))) & (sK547 != sK548))) & (! [X192 : term,X193 : term,X194 : term,X195 : term] : ((((ap @ X195 @ X193)) != ((ap @ X192 @ X194))) | (X193 = X194)) | (apinj2 != $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((induction2 = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2 != $true)) & (ulamvarind = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem2 = $true) | (sP22 != $true)) & ((sP22 = $true) | (hoasinduction_lem2 != $true)) & ((sP20 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP20 != $true)) & ((sP18 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP18 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((sP14 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP14 != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = id) & ((sP8 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP8 != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X197 : (subst > term > term)] : (((sub @ sK550 @ (push @ (sK552 @ X197) @ (sK551 @ X197)))) != ((X197 @ (sK551 @ X197) @ (sK552 @ X197))))) & (! [X200 : term] : ! [X202 : subst,X203 : term] : (((sub @ X200 @ (push @ X203 @ X202))) = ((sK553 @ X200 @ X202 @ X203))) | (hoasinduction_lem3v2_f != $true)) & ((axidl = $true) | (sK554 != ((comp @ id @ sK554)))) & (! [X205 : subst] : (((comp @ id @ X205)) = X205) | (axidl != $true)) & (axmap = $true) & (ulamvar1 != $true) & (pushprop = $true) & (apnotvar = $true) & (ulamvarsh = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & ((! [X206 : subst] : (((comp @ X206 @ id)) = X206) & ! [X207 : subst] : (((comp @ id @ X207)) = X207)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ sK555 @ id)) != sK555) | (sK556 != ((comp @ id @ sK556)))) & ((hoasinduction_lem0 = $true) | ! [X211 : (term > $o)] : (((sK557 @ id @ (sK558 @ X211) @ id)) != ((X211 @ (sK558 @ X211))))) & (! [X213 : (subst > term > subst > $o)] : ! [X215 : term] : (((sK559 @ X213 @ X215)) = ((X213 @ id @ X215 @ id))) | (hoasinduction_lem0 != $true)) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapinj1_gthm = $true) & (! [X216 : subst] : (((comp @ X216 @ id)) = X216) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK560 @ id)) != sK560)) & ((sP7 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (sP7 != $true)) & (! [X218 : subst,X219 : term] : (((comp @ sh @ (push @ X219 @ X218))) = X218) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK561 != ((comp @ sh @ (push @ sK562 @ sK561))))) & ((hoasinduction_lem0_lthm = $true) | ! [X223 : (term > $o)] : (((sK563 @ id @ (sK564 @ X223) @ id)) != ((X223 @ (sK564 @ X223))))) & (! [X225 : (subst > term > subst > $o)] : ! [X227 : term] : (((X225 @ id @ X227 @ id)) = ((sK565 @ X225 @ X227))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1 = $true) & ((sP6 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP6 != $true)) & ((axvarcons = $true) | (sK567 != ((sub @ one @ (push @ sK567 @ sK566))))) & (! [X230 : subst,X231 : term] : (((sub @ one @ (push @ X231 @ X230))) = X231) | (axvarcons != $true)) & (($true = sP1) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP1)) & (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)))))))))))))) & (lamnotvar = $true) & (! [X232 : term] : ! [X234 : term,X235 : subst] : (((sK568 @ X232 @ X235 @ X234)) = ((sub @ X232 @ (push @ X234 @ X235)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X237 : (subst > term > term)] : (((X237 @ (sK571 @ X237) @ (sK570 @ X237))) != ((sub @ sK569 @ (push @ (sK570 @ X237) @ (sK571 @ X237)))))) & (! [X240 : term,X241 : (term > $o),X242 : (term > $o),X243 : subst,X244 : term] : ((((X241 @ X244)) != $true) | (((X242 @ (sub @ X244 @ (push @ X240 @ X243)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true = ((sK573 @ sK576))) & (((sK574 @ (sub @ sK576 @ (push @ sK572 @ sK575)))) != $true))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lthm_orig = $true) & ! [X250 : d_term,X251 : d_term] : ((((d2term @ X250)) != ((d2term @ X251))) | (X250 = X251)) & (hoaslaminj_gthm = $true) & ((apinj1 = $true) | ((((ap @ sK580 @ sK579)) = ((ap @ sK577 @ sK578))) & (sK577 != sK580))) & (! [X256 : term,X257 : term,X258 : term,X259 : term] : ((((ap @ X256 @ X257)) != ((ap @ X259 @ X258))) | (X256 = X259)) | (apinj1 != $true)) & (! [X260 : (term > $o),X261 : term] : ((((sP0 @ X260)) = $true) | ((((X260 @ (sK581 @ X260))) = $true) & (((X260 @ (lam @ (sK581 @ X260)))) != $true)) | ((((var @ (sK582 @ X260))) = $true) & (((X260 @ (sK582 @ X260))) != $true)) | (((X260 @ X261)) = $true)) | (induction != $true)) & ((induction = $true) | ((((sP0 @ sK583)) != $true) & ! [X266 : term] : ((((sK583 @ X266)) != $true) | (((sK583 @ (lam @ X266))) = $true)) & ! [X267 : term] : ((((var @ X267)) != $true) | (((sK583 @ X267)) = $true)) & ($true != ((sK583 @ sK584))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem3v2 = $true) & (pushprop_lem2v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem1_gthm = $true) & (! [X268 : term,X269 : (subst > term > term),X270 : term] : ((((X269 @ (comp @ (sK585 @ X269) @ (sK586 @ X269)) @ (sub @ (sK587 @ X269) @ (sK586 @ X269)))) != ((sub @ (X269 @ (sK585 @ X269) @ (sK587 @ X269)) @ (sK586 @ X269)))) | (((lam @ (X269 @ sh @ one))) != ((ap @ (sub @ X270 @ id) @ X268)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X277 : subst,X278 : subst,X279 : term] : (((sub @ (sK589 @ X277 @ X279) @ X278)) = ((sK589 @ (comp @ X277 @ X278) @ (sub @ X279 @ X278)))) & (((ap @ (sub @ sK590 @ id) @ sK588)) = ((lam @ (sK589 @ sh @ one)))))) & (termmset_gthm = $true)),
% 14.62/2.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,vAPP,sK470,sK471,sK472,sK473,sK474,sK475,sK476,vAPP,vAPP,sK479,sK480,sK481,sK482,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK489,sK490,sK491,sK492,sK493,vAPP,vAPP,sK496,vAPP,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,vAPP,sK511,vAPP,sK513,vAPP,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,vAPP,sK535,sK536,vAPP,vAPP,vAPP,vAPP,vAPP,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,vAPP,vAPP,vAPP,sK554,sK555,sK556,sK557,vAPP,vAPP,sK560,sK561,sK562,sK563,vAPP,vAPP,sK566,sK567,vAPP,sK569,vAPP,vAPP,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,vAPP,vAPP,sK583,sK584,vAPP,vAPP,vAPP,sK588,sK589,sK590]),skolemize(X1,sK454),skolemize(X4,sK455),skolemize(X5,sK456),skolemize(X6,sK457),skolemize(X7,sK458),skolemize(X16,sK459),skolemize(X17,sK460),skolemize(X18,sK461),skolemize(X19,sK462),skolemize(X21,sK463),skolemize(X22,sK464),skolemize(X24,sK465),skolemize(X27,sK466),skolemize(X30,sK467),skolemize(X31,sK468),skolemize(X25,sK68 @ X18),skolemize(X37,sK470),skolemize(X38,sK471),skolemize(X39,sK472),skolemize(X40,sK473),skolemize(X42,sK474),skolemize(X43,sK475),skolemize(X44,sK476),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X52,sK479),skolemize(X53,sK480),skolemize(X54,sK481),skolemize(X55,sK482),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X73,sK489),skolemize(X74,sK490),skolemize(X76,sK491),skolemize(X77,sK492),skolemize(X78,sK493),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X86,sK496),skolemize(X25,sK68 @ X18),skolemize(X90,sK498),skolemize(X91,sK499),skolemize(X92,sK500),skolemize(X93,sK501),skolemize(X100,sK502),skolemize(X101,sK503),skolemize(X104,sK504),skolemize(X105,sK505),skolemize(X106,sK506),skolemize(X107,sK507),skolemize(X109,sK508),skolemize(X110,sK509),skolemize(X25,sK68 @ X18),skolemize(X117,sK511),skolemize(X25,sK68 @ X18),skolemize(X121,sK513),skolemize(X25,sK68 @ X18),skolemize(X125,sK515),skolemize(X132,sK516),skolemize(X133,sK517),skolemize(X134,sK518),skolemize(X135,sK519),skolemize(X137,sK520),skolemize(X138,sK521),skolemize(X139,sK522),skolemize(X140,sK523),skolemize(X145,sK524),skolemize(X146,sK525),skolemize(X147,sK526),skolemize(X148,sK527),skolemize(X149,sK528),skolemize(X150,sK529),skolemize(X160,sK530),skolemize(X161,sK531),skolemize(X162,sK532),skolemize(X163,sK533),skolemize(X25,sK68 @ X18),skolemize(X166,sK535),skolemize(X167,sK536),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X184,sK542),skolemize(X185,sK543),skolemize(X186,sK544),skolemize(X187,sK545),skolemize(X188,sK546),skolemize(X189,sK547),skolemize(X190,sK548),skolemize(X191,sK549),skolemize(X196,sK550),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X204,sK554),skolemize(X208,sK555),skolemize(X209,sK556),skolemize(X210,sK557),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X217,sK560),skolemize(X220,sK561),skolemize(X221,sK562),skolemize(X222,sK563),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X228,sK566),skolemize(X229,sK567),skolemize(X25,sK68 @ X18),skolemize(X236,sK569),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X245,sK572),skolemize(X246,sK573),skolemize(X247,sK574),skolemize(X248,sK575),skolemize(X249,sK576),skolemize(X252,sK577),skolemize(X253,sK578),skolemize(X254,sK579),skolemize(X255,sK580),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X264,sK583),skolemize(X265,sK584),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X274,sK588),skolemize(X275,sK589),skolemize(X276,sK590)],[f262])).
% 14.62/2.51 thf(f821,plain,(
% 14.62/2.51 (((d2subst @ d_id)) = id)),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f857,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond = $true) | (((sK536 @ id @ sK535 @ id)) != $true)),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f859,plain,(
% 14.62/2.51 ( ! [X168 : (subst > term > term)] : (($true = ((sK536 @ id @ (sK540 @ X168) @ id))) | ($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id))) | (((X168 @ (comp @ (sK539 @ X168) @ (sK537 @ X168)) @ (sub @ (sK538 @ X168) @ (sK537 @ X168)))) != ((sub @ (X168 @ (sK539 @ X168) @ (sK538 @ X168)) @ (sK537 @ X168)))) | (hoasinduction_no_psi_cond = $true)) )),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f865,plain,(
% 14.62/2.51 ( ! [X164 : subst] : ((((d2subst @ (sK534 @ X164))) = X164)) )),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f881,plain,(
% 14.62/2.51 ( ! [X127 : d_subst] : ((d_id = X127)) )),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f885,plain,(
% 14.62/2.51 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f892,plain,(
% 14.62/2.51 ( ! [X120 : d_term] : ((d_one = X120)) )),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f894,plain,(
% 14.62/2.51 ( ! [X118 : term] : ((((d2term @ (sK512 @ X118))) = X118)) )),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f946,plain,(
% 14.62/2.51 (one = ((d2term @ d_one)))),
% 14.62/2.51 inference(cnf_transformation,[],[f263])).
% 14.62/2.51 thf(f978,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ 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]: (Y0 @ id @ Y1 @ id)))))))))),
% 14.62/2.51 inference(cnf_transformation,[],[f8])).
% 14.62/2.51 thf(f981,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ 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]: (Y0 @ id @ Y1 @ id)))))))))),
% 14.62/2.51 inference(definition_unfolding,[],[f978,f885])).
% 14.62/2.51 thf(f1069,plain,(
% 14.62/2.51 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ 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]: (Y0 @ id @ Y1 @ id)))))))) = $false) | (hoasinduction_no_psi_cond = $false)),
% 14.62/2.51 inference(xor_proxy_clausification,[],[f981])).
% 14.62/2.51 thf(f1070,plain,(
% 14.62/2.51 ((((^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4)) = (sub @ (Y1 @ Y3 @ Y2) @ 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]: (Y0 @ id @ Y1 @ id)))))) @ sK591)) = $false) | (hoasinduction_no_psi_cond = $false)),
% 14.62/2.51 inference(sigma_proxy_clausification,[],[f1069])).
% 14.62/2.51 thf(f1071,plain,(
% 14.62/2.51 ($false = (((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id))))))) | (hoasinduction_no_psi_cond = $false)),
% 14.62/2.51 inference(beta-eta_normalization,[],[f1070])).
% 14.62/2.51 thf(f1072,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond = $false) | ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id))))) = $false)),
% 14.62/2.51 inference(imp_proxy_clausification,[],[f1071])).
% 14.62/2.51 thf(f1080,plain,(
% 14.62/2.51 (((!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id)))) = $false) | (hoasinduction_no_psi_cond = $false)),
% 14.62/2.51 inference(imp_proxy_clausification,[],[f1072])).
% 14.62/2.51 thf(f1081,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond = $false) | ($true = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))))))),
% 14.62/2.51 inference(imp_proxy_clausification,[],[f1072])).
% 14.62/2.51 thf(f1082,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : (((((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3)) = (sub @ (Y0 @ Y2 @ Y1) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) @ X1)) = $true) | (hoasinduction_no_psi_cond = $false)) )),
% 14.62/2.51 inference(pi_proxy_clausification,[],[f1081])).
% 14.62/2.51 thf(f1083,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((hoasinduction_no_psi_cond = $false) | ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2)))))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) = $true)) )),
% 14.62/2.51 inference(beta-eta_normalization,[],[f1082])).
% 14.62/2.51 thf(f1084,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) | (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))))) = $false) | (hoasinduction_no_psi_cond = $false)) )),
% 14.62/2.51 inference(imp_proxy_clausification,[],[f1083])).
% 14.62/2.51 thf(f1085,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))))) = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))))) = $false) | (hoasinduction_no_psi_cond = $false)) )),
% 14.62/2.51 inference(imp_proxy_clausification,[],[f1084])).
% 14.62/2.51 thf(f1086,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))))) = $false) | (hoasinduction_no_psi_cond = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))) @ (sK592 @ X1))) = $false)) )),
% 14.62/2.51 inference(sigma_proxy_clausification,[],[f1085])).
% 14.62/2.51 thf(f1087,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ((((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK593 @ X1))) = $false) | (hoasinduction_no_psi_cond = $false) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)) = (sub @ (X1 @ Y1 @ Y0) @ Y2))))))) @ (sK592 @ X1))) = $false)) )),
% 14.62/2.51 inference(sigma_proxy_clausification,[],[f1086])).
% 14.62/2.51 thf(f1088,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK592 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK592 @ X1)) @ Y1))))))) = $false) | (hoasinduction_no_psi_cond = $false) | ($false = (((sK591 @ id @ (sK593 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK593 @ X1)) @ id)))) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) )),
% 14.62/2.51 inference(beta-eta_normalization,[],[f1087])).
% 14.62/2.51 thf(f1089,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : (($false = (((sK591 @ id @ (sK593 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK593 @ X1)) @ id)))) | ((((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK592 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK592 @ X1)) @ Y1))))) @ (sK594 @ X1))) = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (hoasinduction_no_psi_cond = $false)) )),
% 14.62/2.51 inference(sigma_proxy_clausification,[],[f1088])).
% 14.62/2.51 thf(f1091,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((hoasinduction_no_psi_cond = $false) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | ((((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK592 @ X1) @ Y1)) = (sub @ (X1 @ Y0 @ (sK592 @ X1)) @ Y1))))) @ (sK594 @ X1))) = $false)) )),
% 14.62/2.51 inference(imp_proxy_clausification,[],[f1089])).
% 14.62/2.51 thf(f1092,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (hoasinduction_no_psi_cond = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | (((!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK592 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ Y0))))) = $false)) )),
% 14.62/2.51 inference(beta-eta_normalization,[],[f1091])).
% 14.62/2.51 thf(f1093,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | ((((^[Y0 : subst]: ((X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK592 @ X1) @ Y0)) = (sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ Y0))) @ (sK595 @ X1))) = $false) | (hoasinduction_no_psi_cond = $false)) )),
% 14.62/2.51 inference(sigma_proxy_clausification,[],[f1092])).
% 14.62/2.51 thf(f1094,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((hoasinduction_no_psi_cond = $false) | ((((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1))) = (sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1)))) = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) )),
% 14.62/2.51 inference(beta-eta_normalization,[],[f1093])).
% 14.62/2.51 thf(f1095,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1)))) != ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1)))) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | (hoasinduction_no_psi_cond = $false)) )),
% 14.62/2.51 inference(equality_proxy_clausification,[],[f1094])).
% 14.62/2.51 thf(f1100,plain,(
% 14.62/2.51 ((((^[Y0 : term]: (sK591 @ id @ Y0 @ id)) @ sK597)) = $false) | (hoasinduction_no_psi_cond = $false)),
% 14.62/2.51 inference(sigma_proxy_clausification,[],[f1080])).
% 14.62/2.51 thf(f1101,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond = $false) | (((sK591 @ id @ sK597 @ id)) = $false)),
% 14.62/2.51 inference(beta-eta_normalization,[],[f1100])).
% 14.62/2.51 thf(f1559,definition,(
% 14.62/2.51 spl602_83 <=> (hoasinduction_no_psi_cond = $true)),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_83])],[avatar_definition])).
% 14.62/2.51 thf(f1561,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond = $true) | ~spl602_83),
% 14.62/2.51 inference(avatar_component_clause,[],[f1559])).
% 14.62/2.51 thf(f2079,definition,(
% 14.62/2.51 spl602_208 <=> ! [X168 : (subst > term > term)] : (($true = ((sK536 @ id @ (sK540 @ X168) @ id))) | (((X168 @ (comp @ (sK539 @ X168) @ (sK537 @ X168)) @ (sub @ (sK538 @ X168) @ (sK537 @ X168)))) != ((sub @ (X168 @ (sK539 @ X168) @ (sK538 @ X168)) @ (sK537 @ X168)))) | ($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id))))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_208])],[avatar_definition])).
% 14.62/2.51 thf(f2080,plain,(
% 14.62/2.51 ( ! [X168 : (subst > term > term)] : ((((X168 @ (comp @ (sK539 @ X168) @ (sK537 @ X168)) @ (sub @ (sK538 @ X168) @ (sK537 @ X168)))) != ((sub @ (X168 @ (sK539 @ X168) @ (sK538 @ X168)) @ (sK537 @ X168)))) | ($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id))) | ($true = ((sK536 @ id @ (sK540 @ X168) @ id)))) ) | ~spl602_208),
% 14.62/2.51 inference(avatar_component_clause,[],[f2079])).
% 14.62/2.51 thf(f2081,plain,(
% 14.62/2.51 spl602_208 | spl602_83),
% 14.62/2.51 inference(avatar_split_clause,[],[f859,f1559,f2079])).
% 14.62/2.51 thf(f2686,definition,(
% 14.62/2.51 spl602_349 <=> (hoasinduction_no_psi_cond = $false)),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_349])],[avatar_definition])).
% 14.62/2.51 thf(f2688,plain,(
% 14.62/2.51 (hoasinduction_no_psi_cond = $false) | ~spl602_349),
% 14.62/2.51 inference(avatar_component_clause,[],[f2686])).
% 14.62/2.51 thf(f2694,definition,(
% 14.62/2.51 spl602_351 <=> ! [X1 : (subst > term > term)] : ((((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1)))) != ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1)))) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true))),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_351])],[avatar_definition])).
% 14.62/2.51 thf(f2695,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | (((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1)))) != ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1))))) ) | ~spl602_351),
% 14.62/2.51 inference(avatar_component_clause,[],[f2694])).
% 14.62/2.51 thf(f2697,definition,(
% 14.62/2.51 spl602_352 <=> (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_352])],[avatar_definition])).
% 14.62/2.51 thf(f2699,plain,(
% 14.62/2.51 (((sK591 @ id @ (d2term @ d_one) @ id)) = $true) | ~spl602_352),
% 14.62/2.51 inference(avatar_component_clause,[],[f2697])).
% 14.62/2.51 thf(f2700,plain,(
% 14.62/2.51 spl602_351 | spl602_352 | spl602_349),
% 14.62/2.51 inference(avatar_split_clause,[],[f1095,f2686,f2697,f2694])).
% 14.62/2.51 thf(f2706,definition,(
% 14.62/2.51 spl602_354 <=> (((sK591 @ id @ sK597 @ id)) = $false)),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_354])],[avatar_definition])).
% 14.62/2.51 thf(f2708,plain,(
% 14.62/2.51 (((sK591 @ id @ sK597 @ id)) = $false) | ~spl602_354),
% 14.62/2.51 inference(avatar_component_clause,[],[f2706])).
% 14.62/2.51 thf(f2709,plain,(
% 14.62/2.51 spl602_354 | spl602_349),
% 14.62/2.51 inference(avatar_split_clause,[],[f1101,f2686,f2706])).
% 14.62/2.51 thf(f3610,definition,(
% 14.62/2.51 spl602_559 <=> (((sK536 @ id @ sK535 @ id)) = $true)),
% 14.62/2.51 introduced(definition,[new_symbols(definition,[spl602_559])],[avatar_definition])).
% 14.62/2.51 thf(f3612,plain,(
% 14.62/2.51 (((sK536 @ id @ sK535 @ id)) != $true) | spl602_559),
% 14.62/2.51 inference(avatar_component_clause,[],[f3610])).
% 14.62/2.51 thf(f3613,plain,(
% 14.62/2.51 ~spl602_559 | spl602_83),
% 14.62/2.51 inference(avatar_split_clause,[],[f857,f1559,f3610])).
% 14.62/2.51 thf(f3935,plain,(
% 14.62/2.51 ( ! [X164 : subst] : ((((d2subst @ d_id)) = X164)) )),
% 14.62/2.51 inference(forward_demodulation,[],[f865,f881])).
% 14.62/2.51 thf(f4186,plain,(
% 14.62/2.51 ($true = $false) | (~spl602_83 | ~spl602_349)),
% 14.62/2.51 inference(forward_demodulation,[],[f1561,f2688])).
% 14.62/2.51 thf(f4187,plain,(
% 14.62/2.51 $false | (~spl602_83 | ~spl602_349)),
% 14.62/2.51 inference(trivial_inequality_removal,[],[f4186])).
% 14.62/2.51 thf(f4188,plain,(
% 14.62/2.51 ~spl602_83 | ~spl602_349),
% 14.62/2.51 inference(avatar_contradiction_clause,[],[f4187])).
% 14.62/2.51 thf(f5203,plain,(
% 14.62/2.51 (((sK591 @ id @ one @ id)) = $true) | ~spl602_352),
% 14.62/2.51 inference(forward_demodulation,[],[f2699,f946])).
% 14.62/2.51 thf(f5800,plain,(
% 14.62/2.51 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )),
% 14.62/2.51 inference(constrained_superposition,[],[f821,f881])).
% 14.62/2.51 thf(f5801,plain,(
% 14.62/2.51 ( ! [X164 : subst] : ((id = X164)) )),
% 14.62/2.51 inference(backward_demodulation,[],[f3935,f5800])).
% 14.62/2.51 thf(f5804,plain,(
% 14.62/2.51 ( ! [X0 : subst] : ((((sK591 @ X0 @ one @ X0)) = $true)) ) | ~spl602_352),
% 14.62/2.51 inference(constrained_superposition,[],[f5203,f5801])).
% 14.62/2.51 thf(f5805,plain,(
% 14.62/2.51 ( ! [X0 : subst] : ((((sK591 @ X0 @ sK597 @ X0)) = $false)) ) | ~spl602_354),
% 14.62/2.51 inference(constrained_superposition,[],[f2708,f5801])).
% 14.62/2.51 thf(f5806,plain,(
% 14.62/2.51 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 14.62/2.51 inference(constrained_superposition,[],[f946,f892])).
% 14.62/2.51 thf(f5807,plain,(
% 14.62/2.51 ( ! [X118 : term] : ((one = X118)) )),
% 14.62/2.51 inference(backward_demodulation,[],[f894,f5806])).
% 14.62/2.51 thf(f5811,plain,(
% 14.62/2.51 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 14.62/2.51 inference(constrained_superposition,[],[f5807,f5807])).
% 14.62/2.51 thf(f5816,plain,(
% 14.62/2.51 ( ! [X0 : subst] : ((((sK591 @ X0 @ one @ X0)) = $false)) ) | ~spl602_354),
% 14.62/2.51 inference(constrained_superposition,[],[f5805,f5807])).
% 14.62/2.51 thf(f5823,plain,(
% 14.62/2.51 ($true = $false) | (~spl602_352 | ~spl602_354)),
% 14.62/2.51 inference(backward_demodulation,[],[f5804,f5816])).
% 14.62/2.51 thf(f5824,plain,(
% 14.62/2.51 $false | (~spl602_352 | ~spl602_354)),
% 14.62/2.51 inference(trivial_inequality_removal,[],[f5823])).
% 14.62/2.51 thf(f5825,plain,(
% 14.62/2.51 ~spl602_352 | ~spl602_354),
% 14.62/2.51 inference(avatar_contradiction_clause,[],[f5824])).
% 14.62/2.51 thf(f5829,plain,(
% 14.62/2.51 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (sK593 @ X1) @ id)) = $true)) ) | ~spl602_351),
% 14.62/2.51 inference(forward_subsumption_resolution,[],[f2695,f5811])).
% 14.62/2.51 thf(f5834,plain,(
% 14.62/2.51 (((sK591 @ id @ one @ id)) = $true) | ~spl602_351),
% 14.62/2.51 inference(forward_demodulation,[],[f5829,f5807])).
% 14.62/2.51 thf(f5836,plain,(
% 14.62/2.51 ($true = $false) | (~spl602_351 | ~spl602_354)),
% 14.62/2.51 inference(forward_demodulation,[],[f5834,f5816])).
% 14.62/2.51 thf(f5837,plain,(
% 14.62/2.51 $false | (~spl602_351 | ~spl602_354)),
% 14.62/2.51 inference(trivial_inequality_removal,[],[f5836])).
% 14.62/2.51 thf(f5838,plain,(
% 14.62/2.51 ~spl602_351 | ~spl602_354),
% 14.62/2.51 inference(avatar_contradiction_clause,[],[f5837])).
% 14.62/2.51 thf(f5839,plain,(
% 14.62/2.51 ( ! [X168 : (subst > term > term)] : (($true = ((sK536 @ id @ (sK540 @ X168) @ id))) | ($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id)))) ) | ~spl602_208),
% 14.62/2.51 inference(forward_subsumption_resolution,[],[f2080,f5811])).
% 14.62/2.51 thf(f5852,plain,(
% 14.62/2.51 (((sK536 @ id @ one @ id)) != $true) | spl602_559),
% 14.62/2.51 inference(forward_demodulation,[],[f3612,f5807])).
% 14.62/2.51 thf(f5853,plain,(
% 14.62/2.51 ( ! [X168 : (subst > term > term)] : ((((sK536 @ id @ one @ id)) = $true) | ($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id)))) ) | ~spl602_208),
% 14.62/2.51 inference(forward_demodulation,[],[f5839,f5807])).
% 14.62/2.51 thf(f5869,plain,(
% 14.62/2.51 ( ! [X168 : (subst > term > term)] : (($true = ((sK536 @ id @ (lam @ (X168 @ sh @ one)) @ id)))) ) | (~spl602_208 | spl602_559)),
% 14.62/2.51 inference(forward_subsumption_resolution,[],[f5853,f5852])).
% 14.62/2.51 thf(f5873,plain,(
% 14.62/2.51 (((sK536 @ id @ one @ id)) = $true) | (~spl602_208 | spl602_559)),
% 14.62/2.51 inference(forward_demodulation,[],[f5869,f5807])).
% 14.62/2.51 thf(f5876,plain,(
% 14.62/2.51 $false | (~spl602_208 | spl602_559)),
% 14.62/2.51 inference(forward_subsumption_resolution,[],[f5873,f5852])).
% 14.62/2.51 thf(f5877,plain,(
% 14.62/2.51 ~spl602_208 | spl602_559),
% 14.62/2.51 inference(avatar_contradiction_clause,[],[f5876])).
% 14.62/2.51 cnf(s147, plain, spl602_83 | spl602_208, inference(sat_conversion,[],[f2081])).
% 14.62/2.51 cnf(s282, plain, spl602_349 | spl602_351 | spl602_352, inference(sat_conversion,[],[f2700])).
% 14.62/2.51 cnf(s284, plain, spl602_349 | spl602_354, inference(sat_conversion,[],[f2709])).
% 14.62/2.51 cnf(s511, plain, spl602_83 | ~spl602_559, inference(sat_conversion,[],[f3613])).
% 14.62/2.51 cnf(s619, plain, ~spl602_83 | ~spl602_349, inference(sat_conversion,[],[f4188])).
% 14.62/2.51 cnf(s654, plain, ~spl602_352 | ~spl602_354, inference(sat_conversion,[],[f5825])).
% 14.62/2.51 cnf(s657, plain, ~spl602_351 | ~spl602_354, inference(sat_conversion,[],[f5838])).
% 14.62/2.51 cnf(s658, plain, ~spl602_208 | spl602_559, inference(sat_conversion,[],[f5877])).
% 14.62/2.51 cnf(s680, plain, spl602_83, inference(rat,[],[s658,s147,s511])).
% 14.62/2.51 cnf(s681, plain, ~spl602_349, inference(rat,[],[s619,s680])).
% 14.62/2.51 cnf(s685, plain, spl602_354, inference(rat,[],[s284,s681])).
% 14.62/2.51 cnf(s687, plain, ~spl602_351, inference(rat,[],[s657,s685])).
% 14.62/2.51 cnf(s688, plain, ~spl602_352, inference(rat,[],[s654,s685])).
% 14.62/2.51 cnf(s689, plain, $false, inference(rat,[],[s282,s681,s688,s687])).
% 14.62/2.51 thf(f5878,plain,(
% 14.62/2.51 $false),
% 14.62/2.51 inference(avatar_sat_refutation,[],[s689])).
% 14.62/2.51 % SZS output end Proof for theBenchmark
% 14.62/2.51 % (3715654)------------------------------
% 14.62/2.51 % (3715654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.62/2.51 % (3715654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.62/2.51 % (3715654)CaDiCaL version: 2.1.3
% 14.62/2.51 % (3715654)Termination reason: Refutation
% 14.62/2.51 % (3715654)Time elapsed: 0.412 s
% 14.62/2.51 % (3715654)Peak memory usage: 19 MB
% 14.62/2.51 % (3715654)Instructions burned: 889 (million)
% 14.62/2.51 % (3715439)Success in time 2.239 s
% 14.62/2.51 % Vampire exiting
%------------------------------------------------------------------------------