%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX154^1 : 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 : n001.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 08:40:34 AM UTC 2026
% Result : Theorem 2.00s 0.80s
% Output : Refutation 2.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX154^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n001.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 16:13:58 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.34 Running higher-order theorem proving
% 0.38/0.41 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
% 1.01/0.63 % (1434135)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.01/0.63 % (1434146)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.01/0.63 % (1434146)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.01/0.63 % (1434140)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2565988911:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.01/0.63 % (1434145)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2236356147:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.01/0.63 % (1434144)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=741696227:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.01/0.63 % (1434141)lrs+10_16_si=on:nwc=1.5:random_seed=1644457025:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.01/0.63 % (1434143)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=4158122829: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)
% 1.01/0.63 % (1434146)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=1460131793:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.01/0.63 % (1434142)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3888561865:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.01/0.63 % (1434141)Instruction limit reached!
% 1.01/0.63 % (1434141)------------------------------
% 1.01/0.63 % (1434141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.63 % (1434141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.63 % (1434141)CaDiCaL version: 2.1.3
% 1.01/0.63 % (1434141)Termination reason: Instruction limit
% 1.01/0.63 % (1434141)Termination phase: shuffling
% 1.01/0.63 % (1434141)Time elapsed: 0.018 s
% 1.01/0.63 % (1434141)Peak memory usage: 10 MB
% 1.01/0.63 % (1434141)Instructions burned: 22 (million)
% 1.01/0.63 % (1434142)Instruction limit reached!
% 1.01/0.63 % (1434142)------------------------------
% 1.01/0.63 % (1434142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.63 % (1434142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.63 % (1434142)CaDiCaL version: 2.1.3
% 1.01/0.63 % (1434142)Termination reason: Instruction limit
% 1.01/0.63 % (1434142)Termination phase: shuffling
% 1.01/0.63 % (1434142)Time elapsed: 0.004 s
% 1.01/0.63 % (1434142)Peak memory usage: 9 MB
% 1.01/0.63 % (1434142)Instructions burned: 6 (million)
% 1.01/0.63 % (1434144)Instruction limit reached!
% 1.01/0.63 % (1434144)------------------------------
% 1.01/0.63 % (1434144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.63 % (1434144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.63 % (1434144)CaDiCaL version: 2.1.3
% 1.01/0.63 % (1434144)Termination reason: Instruction limit
% 1.01/0.63 % (1434144)Termination phase: Property scanning
% 1.01/0.63 % (1434144)Time elapsed: 0.021 s
% 1.01/0.63 % (1434144)Peak memory usage: 10 MB
% 1.01/0.63 % (1434144)Instructions burned: 25 (million)
% 1.01/0.63 % (1434156)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.01/0.63 % (1434154)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1678947424:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.01/0.63 % (1434156)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1206841220:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.01/0.63 % (1434154)Instruction limit reached!
% 1.01/0.63 % (1434154)------------------------------
% 1.01/0.63 % (1434154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.63 % (1434154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.69 % (1434154)CaDiCaL version: 2.1.3
% 1.77/0.69 % (1434154)Termination reason: Instruction limit
% 1.77/0.69 % (1434154)Termination phase: shuffling
% 1.77/0.69 % (1434154)Time elapsed: 0.003 s
% 1.77/0.69 % (1434154)Peak memory usage: 9 MB
% 1.77/0.69 % (1434154)Instructions burned: 2 (million)
% 1.77/0.69 % (1434155)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3704665579:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.77/0.69 % (1434156)Instruction limit reached!
% 1.77/0.69 % (1434156)------------------------------
% 1.77/0.69 % (1434156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.69 % (1434156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.69 % (1434156)CaDiCaL version: 2.1.3
% 1.77/0.69 % (1434156)Termination reason: Instruction limit
% 1.77/0.69 % (1434156)Termination phase: shuffling
% 1.77/0.69 % (1434156)Time elapsed: 0.007 s
% 1.77/0.69 % (1434156)Peak memory usage: 10 MB
% 1.77/0.69 % (1434156)Instructions burned: 8 (million)
% 1.77/0.69 % (1434145)Instruction limit reached!
% 1.77/0.69 % (1434145)------------------------------
% 1.77/0.69 % (1434145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.69 % (1434145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.69 % (1434145)CaDiCaL version: 2.1.3
% 1.77/0.69 % (1434145)Termination reason: Instruction limit
% 1.77/0.69 % (1434145)Termination phase: Preprocessing 3
% 1.77/0.69 % (1434145)Time elapsed: 0.063 s
% 1.77/0.69 % (1434145)Peak memory usage: 12 MB
% 1.77/0.69 % (1434145)Instructions burned: 76 (million)
% 1.77/0.69 % (1434155)Instruction limit reached!
% 1.77/0.69 % (1434155)------------------------------
% 1.77/0.69 % (1434155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.69 % (1434155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.69 % (1434155)CaDiCaL version: 2.1.3
% 1.77/0.69 % (1434155)Termination reason: Instruction limit
% 1.77/0.69 % (1434155)Termination phase: shuffling
% 1.77/0.69 % (1434155)Time elapsed: 0.006 s
% 1.77/0.69 % (1434155)Peak memory usage: 10 MB
% 1.77/0.69 % (1434155)Instructions burned: 12 (million)
% 1.77/0.69 % (1434140)Instruction limit reached!
% 1.77/0.69 % (1434140)------------------------------
% 1.77/0.69 % (1434140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.69 % (1434140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.69 % (1434140)CaDiCaL version: 2.1.3
% 1.77/0.69 % (1434140)Termination reason: Instruction limit
% 1.77/0.69 % (1434140)Termination phase: Preprocessing 3
% 1.77/0.69 % (1434140)Time elapsed: 0.074 s
% 1.77/0.69 % (1434140)Peak memory usage: 12 MB
% 1.77/0.69 % (1434140)Instructions burned: 88 (million)
% 1.77/0.69 % (1434163)lrs+10_1_si=on:cs=on:random_seed=794124947:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.77/0.69 % (1434159)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3127893559:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/12Mi)
% 1.77/0.69 % (1434161)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.77/0.69 % (1434161)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.77/0.69 % (1434163)Instruction limit reached!
% 1.77/0.69 % (1434163)------------------------------
% 1.77/0.69 % (1434163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.69 % (1434163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.69 % (1434163)CaDiCaL version: 2.1.3
% 1.77/0.69 % (1434163)Termination reason: Instruction limit
% 1.77/0.69 % (1434163)Termination phase: shuffling
% 1.77/0.69 % (1434163)Time elapsed: 0.004 s
% 1.77/0.69 % (1434163)Peak memory usage: 9 MB
% 1.77/0.69 % (1434163)Instructions burned: 9 (million)
% 1.77/0.69 % (1434161)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2541775363:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.77/0.69 % (1434162)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=1418122262:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.77/0.69 % (1434159)Instruction limit reached!
% 2.00/0.75 % (1434159)------------------------------
% 2.00/0.75 % (1434159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.75 % (1434159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.75 % (1434159)CaDiCaL version: 2.1.3
% 2.00/0.75 % (1434159)Termination reason: Instruction limit
% 2.00/0.75 % (1434159)Termination phase: shuffling
% 2.00/0.75 % (1434159)Time elapsed: 0.010 s
% 2.00/0.75 % (1434159)Peak memory usage: 10 MB
% 2.00/0.75 % (1434159)Instructions burned: 12 (million)
% 2.00/0.75 % (1434164)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 2.00/0.75 % (1434164)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=3837890458:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.00/0.75 % (1434167)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3296866118:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 2.00/0.75 % (1434164)Instruction limit reached!
% 2.00/0.75 % (1434164)------------------------------
% 2.00/0.75 % (1434164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.75 % (1434164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.75 % (1434164)CaDiCaL version: 2.1.3
% 2.00/0.75 % (1434164)Termination reason: Instruction limit
% 2.00/0.75 % (1434164)Termination phase: shuffling
% 2.00/0.75 % (1434164)Time elapsed: 0.003 s
% 2.00/0.75 % (1434164)Peak memory usage: 10 MB
% 2.00/0.75 % (1434164)Instructions burned: 3 (million)
% 2.00/0.75 % (1434161)Instruction limit reached!
% 2.00/0.75 % (1434161)------------------------------
% 2.00/0.75 % (1434161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.75 % (1434161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.75 % (1434161)CaDiCaL version: 2.1.3
% 2.00/0.75 % (1434161)Termination reason: Instruction limit
% 2.00/0.75 % (1434161)Termination phase: Property scanning
% 2.00/0.75 % (1434161)Time elapsed: 0.027 s
% 2.00/0.75 % (1434161)Peak memory usage: 10 MB
% 2.00/0.75 % (1434161)Instructions burned: 32 (million)
% 2.00/0.75 % (1434167)Refutation not found, incomplete strategy
% 2.00/0.75 % (1434167)------------------------------
% 2.00/0.75 % (1434167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.75 % (1434167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.75 % (1434167)CaDiCaL version: 2.1.3
% 2.00/0.75 % (1434167)Termination reason: Refutation not found, incomplete strategy
% 2.00/0.75 % (1434167)Time elapsed: 0.016 s
% 2.00/0.75 % (1434167)Peak memory usage: 12 MB
% 2.00/0.75 % (1434167)Instructions burned: 36 (million)
% 2.00/0.75 % (1434167)------------------------------
% 2.00/0.75 % (1434167)------------------------------
% 2.00/0.75 % (1434146)Instruction limit reached!
% 2.00/0.75 % (1434146)------------------------------
% 2.00/0.75 % (1434146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.75 % (1434146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.75 % (1434146)CaDiCaL version: 2.1.3
% 2.00/0.75 % (1434146)Termination reason: Instruction limit
% 2.00/0.75 % (1434146)Termination phase: Property scanning
% 2.00/0.75 % (1434146)Time elapsed: 0.129 s
% 2.00/0.75 % (1434146)Peak memory usage: 13 MB
% 2.00/0.75 % (1434146)Instructions burned: 158 (million)
% 2.00/0.75 % (1434170)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3205057637:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 2.00/0.75 % (1434173)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3298847815:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.00/0.75 % (1434175)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1756786688:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.00/0.75 % (1434174)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=369303689:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.00/0.75 % (1434162)Instruction limit reached!
% 2.00/0.75 % (1434162)------------------------------
% 2.00/0.75 % (1434162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434162)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434162)Termination reason: Instruction limit
% 2.00/0.80 % (1434162)Termination phase: Saturation
% 2.00/0.80 % (1434162)Time elapsed: 0.068 s
% 2.00/0.80 % (1434162)Peak memory usage: 12 MB
% 2.00/0.80 % (1434162)Instructions burned: 86 (million)
% 2.00/0.80 % (1434173)Instruction limit reached!
% 2.00/0.80 % (1434173)------------------------------
% 2.00/0.80 % (1434173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434173)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434173)Termination reason: Instruction limit
% 2.00/0.80 % (1434173)Termination phase: Property scanning
% 2.00/0.80 % (1434173)Time elapsed: 0.021 s
% 2.00/0.80 % (1434173)Peak memory usage: 10 MB
% 2.00/0.80 % (1434173)Instructions burned: 25 (million)
% 2.00/0.80 % (1434177)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=291245727:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.00/0.80 % (1434174)Instruction limit reached!
% 2.00/0.80 % (1434174)------------------------------
% 2.00/0.80 % (1434174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434174)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434174)Termination reason: Instruction limit
% 2.00/0.80 % (1434174)Termination phase: shuffling
% 2.00/0.80 % (1434174)Time elapsed: 0.013 s
% 2.00/0.80 % (1434174)Peak memory usage: 10 MB
% 2.00/0.80 % (1434174)Instructions burned: 14 (million)
% 2.00/0.80 % (1434177)Instruction limit reached!
% 2.00/0.80 % (1434177)------------------------------
% 2.00/0.80 % (1434177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434177)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434177)Termination reason: Instruction limit
% 2.00/0.80 % (1434177)Termination phase: shuffling
% 2.00/0.80 % (1434177)Time elapsed: 0.012 s
% 2.00/0.80 % (1434177)Peak memory usage: 10 MB
% 2.00/0.80 % (1434177)Instructions burned: 14 (million)
% 2.00/0.80 % (1434183)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3029666229:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.00/0.80 % (1434182)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3824749536:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.00/0.80 % (1434182)Instruction limit reached!
% 2.00/0.80 % (1434182)------------------------------
% 2.00/0.80 % (1434182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434182)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434182)Termination reason: Instruction limit
% 2.00/0.80 % (1434182)Termination phase: shuffling
% 2.00/0.80 % (1434182)Time elapsed: 0.003 s
% 2.00/0.80 % (1434182)Peak memory usage: 10 MB
% 2.00/0.80 % (1434182)Instructions burned: 3 (million)
% 2.00/0.80 % (1434184)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=746692980:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.00/0.80 % (1434185)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=328780162:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.00/0.80 % (1434183)Instruction limit reached!
% 2.00/0.80 % (1434183)------------------------------
% 2.00/0.80 % (1434183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434183)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434183)Termination reason: Instruction limit
% 2.00/0.80 % (1434183)Termination phase: shuffling
% 2.00/0.80 % (1434183)Time elapsed: 0.023 s
% 2.00/0.80 % (1434183)Peak memory usage: 10 MB
% 2.00/0.80 % (1434183)Instructions burned: 27 (million)
% 2.00/0.80 % (1434184)Instruction limit reached!
% 2.00/0.80 % (1434184)------------------------------
% 2.00/0.80 % (1434184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434184)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434184)Termination reason: Instruction limit
% 2.00/0.80 % (1434184)Termination phase: Property scanning
% 2.00/0.80 % (1434184)Time elapsed: 0.020 s
% 2.00/0.80 % (1434184)Peak memory usage: 10 MB
% 2.00/0.80 % (1434184)Instructions burned: 25 (million)
% 2.00/0.80 % (1434188)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
% 2.00/0.80 % (1434188)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.00/0.80 % (1434188)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=2368151868:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.00/0.80 % (1434188)Instruction limit reached!
% 2.00/0.80 % (1434188)------------------------------
% 2.00/0.80 % (1434188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434188)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434188)Termination reason: Instruction limit
% 2.00/0.80 % (1434188)Termination phase: shuffling
% 2.00/0.80 % (1434188)Time elapsed: 0.013 s
% 2.00/0.80 % (1434188)Peak memory usage: 10 MB
% 2.00/0.80 % (1434188)Instructions burned: 15 (million)
% 2.00/0.80 % (1434191)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.00/0.80 % (1434191)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=3461493470:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.00/0.80 % (1434192)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=2740626706:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.00/0.80 % (1434191)Instruction limit reached!
% 2.00/0.80 % (1434191)------------------------------
% 2.00/0.80 % (1434191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434191)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434191)Termination reason: Instruction limit
% 2.00/0.80 % (1434191)Termination phase: shuffling
% 2.00/0.80 % (1434191)Time elapsed: 0.007 s
% 2.00/0.80 % (1434191)Peak memory usage: 10 MB
% 2.00/0.80 % (1434191)Instructions burned: 8 (million)
% 2.00/0.80 % (1434185)Instruction limit reached!
% 2.00/0.80 % (1434185)------------------------------
% 2.00/0.80 % (1434185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434185)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434185)Termination reason: Instruction limit
% 2.00/0.80 % (1434185)Termination phase: Preprocessing 3
% 2.00/0.80 % (1434185)Time elapsed: 0.051 s
% 2.00/0.80 % (1434185)Peak memory usage: 11 MB
% 2.00/0.80 % (1434185)Instructions burned: 60 (million)
% 2.00/0.80 % (1434175) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1434135-1434175"...
% 2.00/0.80 % (1434194)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=4072815802:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.00/0.80 % (1434192)Instruction limit reached!
% 2.00/0.80 % (1434192)------------------------------
% 2.00/0.80 % (1434192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434192)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434192)Termination reason: Instruction limit
% 2.00/0.80 % (1434192)Termination phase: Property scanning
% 2.00/0.80 % (1434192)Time elapsed: 0.026 s
% 2.00/0.80 % (1434192)Peak memory usage: 10 MB
% 2.00/0.80 % (1434192)Instructions burned: 31 (million)
% 2.00/0.80 % (1434194)Instruction limit reached!
% 2.00/0.80 % (1434194)------------------------------
% 2.00/0.80 % (1434194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434194)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434194)Termination reason: Instruction limit
% 2.00/0.80 % (1434194)Termination phase: shuffling
% 2.00/0.80 % (1434194)Time elapsed: 0.006 s
% 2.00/0.80 % (1434194)Peak memory usage: 10 MB
% 2.00/0.80 % (1434194)Instructions burned: 7 (million)
% 2.00/0.80 % (1434198)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3919184575:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/20Mi)
% 2.00/0.80 % (1434197)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2565655328:i=23:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/23Mi)
% 2.00/0.80 % (1434198)Instruction limit reached!
% 2.00/0.80 % (1434198)------------------------------
% 2.00/0.80 % (1434198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434198)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434198)Termination reason: Instruction limit
% 2.00/0.80 % (1434198)Termination phase: shuffling
% 2.00/0.80 % (1434198)Time elapsed: 0.017 s
% 2.00/0.80 % (1434198)Peak memory usage: 10 MB
% 2.00/0.80 % (1434198)Instructions burned: 20 (million)
% 2.00/0.80 % (1434200)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=358500735:i=1240:rtra=on:ixr=off_2996 on theBenchmark for (2996ds/1240Mi)
% 2.00/0.80 % (1434197)Instruction limit reached!
% 2.00/0.80 % (1434197)------------------------------
% 2.00/0.80 % (1434197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.80 % (1434197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.80 % (1434197)CaDiCaL version: 2.1.3
% 2.00/0.80 % (1434197)Termination reason: Instruction limit
% 2.00/0.80 % (1434197)Termination phase: shuffling
% 2.00/0.80 % (1434197)Time elapsed: 0.020 s
% 2.00/0.80 % (1434197)Peak memory usage: 10 MB
% 2.00/0.80 % (1434197)Instructions burned: 23 (million)
% 2.00/0.80 % (1434201)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1298773100:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 2.00/0.80 % (1434175)...printing done.
% 2.00/0.80 % (1434175)Refutation found. Thanks to Tanya!
% 2.00/0.80 % SZS status Theorem for theBenchmark
% 2.00/0.80 % SZS output start Proof for theBenchmark
% 2.00/0.80 thf(type_def_5, type, term: $tType).
% 2.00/0.80 thf(type_def_6, type, subst: $tType).
% 2.00/0.80 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 2.00/0.80 thf(type_def_8, type, d_term: $tType).
% 2.00/0.80 thf(type_def_9, type, d_subst: $tType).
% 2.00/0.80 thf(func_def_0, type, one: term).
% 2.00/0.80 thf(func_def_1, type, ap: (term > term > term)).
% 2.00/0.80 thf(func_def_2, type, lam: (term > term)).
% 2.00/0.80 thf(func_def_3, type, sub: (term > subst > term)).
% 2.00/0.80 thf(func_def_4, type, id: subst).
% 2.00/0.80 thf(func_def_5, type, sh: subst).
% 2.00/0.80 thf(func_def_6, type, push: (term > subst > subst)).
% 2.00/0.80 thf(func_def_7, type, comp: (subst > subst > subst)).
% 2.00/0.80 thf(func_def_8, type, var: (term > $o)).
% 2.00/0.80 thf(func_def_9, type, pushprop_lem1v2: $o).
% 2.00/0.80 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 2.00/0.80 thf(func_def_11, type, axmap: $o).
% 2.00/0.80 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 2.00/0.80 thf(func_def_13, type, shinj: $o).
% 2.00/0.80 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 2.00/0.80 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 2.00/0.80 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 2.91/0.80 thf(func_def_17, type, induction2lem: $o).
% 2.91/0.80 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 2.91/0.80 thf(func_def_19, type, axvarshift: $o).
% 2.91/0.80 thf(func_def_20, type, hoasapinj2: $o).
% 2.91/0.80 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 2.91/0.80 thf(func_def_22, type, hoasapinj1: $o).
% 2.91/0.80 thf(func_def_23, type, ulamvar1: $o).
% 2.91/0.80 thf(func_def_24, type, induction2lem_lthm: $o).
% 2.91/0.80 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 2.91/0.80 thf(func_def_26, type, apnotvar: $o).
% 2.91/0.80 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 2.91/0.80 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 2.91/0.80 thf(func_def_29, type, hoasinduction_lthm: $o).
% 2.91/0.80 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 2.91/0.80 thf(func_def_31, type, hoaslaminj: $o).
% 2.91/0.80 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 2.91/0.80 thf(func_def_33, type, induction2lem_gthm: $o).
% 2.91/0.80 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 2.91/0.80 thf(func_def_35, type, hoasinduction_lem3: $o).
% 2.91/0.80 thf(func_def_36, type, hoasinduction_lem2: $o).
% 2.91/0.80 thf(func_def_37, type, termmset_lthm: $o).
% 2.91/0.80 thf(func_def_38, type, hoasinduction_lem1: $o).
% 2.91/0.80 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 2.91/0.80 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 2.91/0.80 thf(func_def_41, type, hoasapnotvar: $o).
% 2.91/0.80 thf(func_def_42, type, hoasinduction_lem0: $o).
% 2.91/0.80 thf(func_def_43, type, hoasinduction: $o).
% 2.91/0.80 thf(func_def_44, type, hoasinduction_gthm: $o).
% 2.91/0.80 thf(func_def_45, type, axapp: $o).
% 2.91/0.80 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 2.91/0.80 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 2.91/0.80 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 2.91/0.80 thf(func_def_49, type, ulamvarind: $o).
% 2.91/0.80 thf(func_def_50, type, induction: $o).
% 2.91/0.80 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 2.91/0.80 thf(func_def_52, type, termmset_gthm: $o).
% 2.91/0.80 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 2.91/0.80 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 2.91/0.80 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 2.91/0.80 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 2.91/0.80 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 2.91/0.80 thf(func_def_58, type, pushprop_lem2v2: $o).
% 2.91/0.80 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 2.91/0.80 thf(func_def_60, type, axclos: $o).
% 2.91/0.80 thf(func_def_61, type, axassoc: $o).
% 2.91/0.80 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 2.91/0.80 thf(func_def_63, type, pushprop_lthm: $o).
% 2.91/0.80 thf(func_def_64, type, apinj2: $o).
% 2.91/0.80 thf(func_def_65, type, apinj1: $o).
% 2.91/0.80 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 2.91/0.80 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 2.91/0.80 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 2.91/0.80 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 2.91/0.80 thf(func_def_70, type, axvarcons: $o).
% 2.91/0.80 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 2.91/0.80 thf(func_def_72, type, axscons: $o).
% 2.91/0.80 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 2.91/0.80 thf(func_def_74, type, axidr: $o).
% 2.91/0.80 thf(func_def_75, type, pushprop_lem1: $o).
% 2.91/0.80 thf(func_def_76, type, laminj: $o).
% 2.91/0.80 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 2.91/0.80 thf(func_def_78, type, pushprop_lem0: $o).
% 2.91/0.80 thf(func_def_79, type, pushprop_gthm: $o).
% 2.91/0.80 thf(func_def_80, type, axabs: $o).
% 2.91/0.80 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 2.91/0.80 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 2.91/0.80 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 2.91/0.80 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 2.91/0.80 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 2.91/0.80 thf(func_def_86, type, lamnotap: $o).
% 2.91/0.80 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 2.91/0.80 thf(func_def_88, type, hoaslamnotvar: $o).
% 2.91/0.80 thf(func_def_89, type, axidl: $o).
% 2.91/0.80 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 2.91/0.80 thf(func_def_91, type, induction2_lthm: $o).
% 2.91/0.80 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 2.91/0.80 thf(func_def_93, type, substmonoid_lthm: $o).
% 2.91/0.80 thf(func_def_94, type, pushprop: $o).
% 2.91/0.80 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 2.91/0.80 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 2.91/0.80 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 2.91/0.80 thf(func_def_98, type, substmonoid: $o).
% 2.91/0.80 thf(func_def_99, type, lamnotvar: $o).
% 2.91/0.80 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 2.91/0.80 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 2.91/0.80 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 2.91/0.80 thf(func_def_103, type, induction2_gthm: $o).
% 2.91/0.80 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 2.91/0.80 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_106, type, hoaslamnotap: $o).
% 2.91/0.80 thf(func_def_107, type, substmonoid_gthm: $o).
% 2.91/0.80 thf(func_def_108, type, ulamvarsh: $o).
% 2.91/0.80 thf(func_def_109, type, induction2: $o).
% 2.91/0.80 thf(func_def_110, type, pushprop_lem3v2: $o).
% 2.91/0.80 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 2.91/0.80 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 2.91/0.80 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 2.91/0.80 thf(func_def_114, type, axshiftcons: $o).
% 2.91/0.80 thf(func_def_115, type, termmset: $o).
% 2.91/0.80 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 2.91/0.80 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 2.91/0.80 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 2.91/0.80 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 2.91/0.80 thf(func_def_120, type, axvarid: $o).
% 2.91/0.80 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 2.91/0.80 thf(func_def_122, type, d2term: (d_term > term)).
% 2.91/0.80 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 2.91/0.80 thf(func_def_124, type, d_one: d_term).
% 2.91/0.80 thf(func_def_125, type, d_id: d_subst).
% 2.91/0.80 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.91/0.80 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)).
% 2.91/0.80 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 2.91/0.80 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)).
% 2.91/0.80 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.91/0.80 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.91/0.80 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)).
% 2.91/0.80 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)).
% 2.91/0.80 thf(func_def_137, type, sP0: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_138, type, sP1: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_139, type, sP2: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_140, type, sP3: $o).
% 2.91/0.80 thf(func_def_141, type, sP4: $o).
% 2.91/0.80 thf(func_def_142, type, sP5: $o).
% 2.91/0.80 thf(func_def_143, type, sP6: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_144, type, sP7: $o).
% 2.91/0.80 thf(func_def_145, type, sP8: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_146, type, sP9: $o).
% 2.91/0.80 thf(func_def_147, type, sP10: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_148, type, sP11: $o).
% 2.91/0.80 thf(func_def_149, type, sP12: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_150, type, sP13: $o).
% 2.91/0.80 thf(func_def_151, type, sP14: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_152, type, sP15: $o).
% 2.91/0.80 thf(func_def_153, type, sP16: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_154, type, sP17: $o).
% 2.91/0.80 thf(func_def_155, type, sP18: $o).
% 2.91/0.80 thf(func_def_156, type, sP19: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_157, type, sP20: $o).
% 2.91/0.80 thf(func_def_158, type, sP21: $o).
% 2.91/0.80 thf(func_def_159, type, sP22: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_160, type, sP23: $o).
% 2.91/0.80 thf(func_def_161, type, sP24: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_162, type, sP25: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_163, type, sP26: $o).
% 2.91/0.80 thf(func_def_164, type, sP27: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_165, type, sP28: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_166, type, sP29: $o).
% 2.91/0.80 thf(func_def_167, type, sP30: $o).
% 2.91/0.80 thf(func_def_168, type, sP31: $o).
% 2.91/0.80 thf(func_def_169, type, sP32: $o).
% 2.91/0.80 thf(func_def_170, type, sP33: $o).
% 2.91/0.80 thf(func_def_171, type, sP34: $o).
% 2.91/0.80 thf(func_def_172, type, sP35: $o).
% 2.91/0.80 thf(func_def_173, type, sP36: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_174, type, sP37: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_175, type, sP38: $o).
% 2.91/0.80 thf(func_def_176, type, sP39: $o).
% 2.91/0.80 thf(func_def_177, type, sP40: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_178, type, sP41: $o).
% 2.91/0.80 thf(func_def_179, type, sP42: $o).
% 2.91/0.80 thf(func_def_180, type, sP43: $o).
% 2.91/0.80 thf(func_def_181, type, sP44: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_182, type, sP45: $o).
% 2.91/0.80 thf(func_def_183, type, sP46: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_184, type, sP47: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_185, type, sP48: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_186, type, sP49: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_187, type, sP50: ((subst > term > subst > $o) > $o)).
% 2.91/0.80 thf(func_def_188, type, sP51: $o).
% 2.91/0.80 thf(func_def_189, type, sP52: $o).
% 2.91/0.80 thf(func_def_190, type, sP53: $o).
% 2.91/0.80 thf(func_def_191, type, sP54: $o).
% 2.91/0.80 thf(func_def_192, type, sP55: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_193, type, sP56: ((term > $o) > $o)).
% 2.91/0.80 thf(func_def_194, type, sP57: $o).
% 2.91/0.80 thf(func_def_195, type, sP58: $o).
% 2.91/0.80 thf(func_def_196, type, sK59: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_197, type, sK60: (subst > (term > $o) > term)).
% 2.91/0.80 thf(func_def_198, type, sK61: (term > $o)).
% 2.91/0.80 thf(func_def_199, type, sK62: term).
% 2.91/0.80 thf(func_def_200, type, sK63: subst).
% 2.91/0.80 thf(func_def_201, type, sK64: (term > term)).
% 2.91/0.80 thf(func_def_202, type, sK65: term).
% 2.91/0.80 thf(func_def_203, type, sK66: (term > $o)).
% 2.91/0.80 thf(func_def_204, type, sK67: term).
% 2.91/0.80 thf(func_def_205, type, sK68: (term > term)).
% 2.91/0.80 thf(func_def_206, type, sK69: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_207, type, sK70: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_208, type, sK71: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_209, type, sK72: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_210, type, sK73: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_211, type, sK74: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_212, type, sK75: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_213, type, sK76: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_214, type, sK77: term).
% 2.91/0.80 thf(func_def_215, type, sK78: (term > $o)).
% 2.91/0.80 thf(func_def_216, type, sK79: (term > term)).
% 2.91/0.80 thf(func_def_217, type, sK80: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_218, type, sK81: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_219, type, sK82: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_220, type, sK83: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_221, type, sK84: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_222, type, sK85: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_223, type, sK86: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_224, type, sK87: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_225, type, sK88: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_226, type, sK89: term).
% 2.91/0.80 thf(func_def_227, type, sK90: term).
% 2.91/0.80 thf(func_def_228, type, sK91: term).
% 2.91/0.80 thf(func_def_229, type, sK92: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_230, type, sK93: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_231, type, sK94: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_232, type, sK95: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_233, type, sK96: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_234, type, sK97: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_235, type, sK98: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_236, type, sK99: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_237, type, sK100: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_238, type, sK101: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_239, type, sK102: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_240, type, sK103: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_241, type, sK104: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_242, type, sK105: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_243, type, sK106: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_244, type, sK107: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_245, type, sK108: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_246, type, sK109: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_247, type, sK110: ((subst > term > subst > $o) > term > term)).
% 2.91/0.80 thf(func_def_248, type, sK111: term).
% 2.91/0.80 thf(func_def_249, type, sK112: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_250, type, sK113: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_251, type, sK114: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_252, type, sK115: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_253, type, sK116: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_254, type, sK117: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_255, type, sK118: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_256, type, sK119: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_257, type, sK120: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_258, type, sK121: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_259, type, sK122: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_260, type, sK123: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_261, type, sK124: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_262, type, sK125: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_263, type, sK126: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_264, type, sK127: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_265, type, sK128: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_266, type, sK129: term).
% 2.91/0.80 thf(func_def_267, type, sK130: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_268, type, sK131: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_269, type, sK132: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_270, type, sK133: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_271, type, sK134: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_272, type, sK135: ((subst > term > subst > $o) > term > term)).
% 2.91/0.80 thf(func_def_273, type, sK136: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_274, type, sK137: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_275, type, sK138: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_276, type, sK139: (subst > term > term)).
% 2.91/0.80 thf(func_def_277, type, sK140: subst).
% 2.91/0.80 thf(func_def_278, type, sK141: (subst > term > term)).
% 2.91/0.80 thf(func_def_279, type, sK142: term).
% 2.91/0.80 thf(func_def_280, type, sK143: term).
% 2.91/0.80 thf(func_def_281, type, sK144: term).
% 2.91/0.80 thf(func_def_282, type, sK145: subst).
% 2.91/0.80 thf(func_def_283, type, sK146: term).
% 2.91/0.80 thf(func_def_284, type, sK147: subst).
% 2.91/0.80 thf(func_def_285, type, sK148: term).
% 2.91/0.80 thf(func_def_286, type, sK149: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_287, type, sK150: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_288, type, sK151: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_289, type, sK152: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_290, type, sK153: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_291, type, sK154: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_292, type, sK155: term).
% 2.91/0.80 thf(func_def_293, type, sK156: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_294, type, sK157: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_295, type, sK158: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_296, type, sK159: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_297, type, sK160: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_298, type, sK161: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_299, type, sK162: ((subst > term > subst > $o) > term > term)).
% 2.91/0.80 thf(func_def_300, type, sK163: term).
% 2.91/0.80 thf(func_def_301, type, sK164: term).
% 2.91/0.80 thf(func_def_302, type, sK165: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_303, type, sK166: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_304, type, sK167: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_305, type, sK168: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_306, type, sK169: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_307, type, sK170: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_308, type, sK171: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_309, type, sK172: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_310, type, sK173: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_311, type, sK174: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_312, type, sK175: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_313, type, sK176: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_314, type, sK177: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_315, type, sK178: subst).
% 2.91/0.80 thf(func_def_316, type, sK179: term).
% 2.91/0.80 thf(func_def_317, type, sK180: subst).
% 2.91/0.80 thf(func_def_318, type, sK181: term).
% 2.91/0.80 thf(func_def_319, type, sK182: (term > $o)).
% 2.91/0.80 thf(func_def_320, type, sK183: subst).
% 2.91/0.80 thf(func_def_321, type, sK184: term).
% 2.91/0.80 thf(func_def_322, type, sK185: (term > $o)).
% 2.91/0.80 thf(func_def_323, type, sK186: subst).
% 2.91/0.80 thf(func_def_324, type, sK187: term).
% 2.91/0.80 thf(func_def_325, type, sK188: (term > term)).
% 2.91/0.80 thf(func_def_326, type, sK189: (subst > (term > $o) > term)).
% 2.91/0.80 thf(func_def_327, type, sK190: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_328, type, sK191: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_329, type, sK192: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_330, type, sK193: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_331, type, sK194: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_332, type, sK195: (term > subst > term > term)).
% 2.91/0.80 thf(func_def_333, type, sK196: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_334, type, sK197: (term > $o)).
% 2.91/0.80 thf(func_def_335, type, sK198: term).
% 2.91/0.80 thf(func_def_336, type, sK199: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_337, type, sK200: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_338, type, sK201: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_339, type, sK202: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_340, type, sK203: term).
% 2.91/0.80 thf(func_def_341, type, sK204: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_342, type, sK205: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_343, type, sK206: term).
% 2.91/0.80 thf(func_def_344, type, sK207: (term > (term > $o) > term)).
% 2.91/0.80 thf(func_def_345, type, sK208: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_346, type, sK209: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_347, type, sK210: term).
% 2.91/0.80 thf(func_def_348, type, sK211: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_349, type, sK212: ((subst > term > term) > term > subst)).
% 2.91/0.80 thf(func_def_350, type, sK213: ((subst > term > term) > term > term)).
% 2.91/0.80 thf(func_def_351, type, sK214: ((subst > term > term) > term > subst)).
% 2.91/0.80 thf(func_def_352, type, sK215: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_353, type, sK216: ((subst > term > term) > term > term)).
% 2.91/0.80 thf(func_def_354, type, sK217: ((subst > term > term) > term > subst)).
% 2.91/0.80 thf(func_def_355, type, sK218: ((subst > term > term) > term > subst)).
% 2.91/0.80 thf(func_def_356, type, sK219: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_357, type, sK220: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_358, type, sK221: ((subst > term > subst > $o) > term > term)).
% 2.91/0.80 thf(func_def_359, type, sK222: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_360, type, sK223: term).
% 2.91/0.80 thf(func_def_361, type, sK224: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_362, type, sK225: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_363, type, sK226: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_364, type, sK227: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_365, type, sK228: term).
% 2.91/0.80 thf(func_def_366, type, sK229: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_367, type, sK230: (term > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_368, type, sK231: (term > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_369, type, sK232: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_370, type, sK233: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_371, type, sK234: term).
% 2.91/0.80 thf(func_def_372, type, sK235: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_373, type, sK236: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_374, type, sK237: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_375, type, sK238: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_376, type, sK239: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_377, type, sK240: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_378, type, sK241: ((subst > term > subst > $o) > term > $o)).
% 2.91/0.80 thf(func_def_379, type, sK242: term).
% 2.91/0.80 thf(func_def_380, type, sK243: (term > $o)).
% 2.91/0.80 thf(func_def_381, type, sK244: (term > term)).
% 2.91/0.80 thf(func_def_382, type, sK245: term).
% 2.91/0.80 thf(func_def_383, type, sK246: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_384, type, sK247: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_385, type, sK248: term).
% 2.91/0.80 thf(func_def_386, type, sK249: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_387, type, sK250: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_388, type, sK251: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_389, type, sK252: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_390, type, sK253: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_391, type, sK254: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_392, type, sK255: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_393, type, sK256: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_394, type, sK257: ((term > $o) > term > term)).
% 2.91/0.80 thf(func_def_395, type, sK258: term).
% 2.91/0.80 thf(func_def_396, type, sK259: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_397, type, sK260: (term > $o)).
% 2.91/0.80 thf(func_def_398, type, sK261: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_399, type, sK262: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_400, type, sK263: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_401, type, sK264: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_402, type, sK265: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_403, type, sK266: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_404, type, sK267: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_405, type, sK268: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_406, type, sK269: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_407, type, sK270: term).
% 2.91/0.80 thf(func_def_408, type, sK271: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_409, type, sK272: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_410, type, sK273: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_411, type, sK274: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_413, type, sK276: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_414, type, sK277: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_415, type, sK278: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_416, type, sK279: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_417, type, sK280: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_418, type, sK281: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_419, type, sK282: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_420, type, sK283: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_421, type, sK284: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_422, type, sK285: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_423, type, sK286: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_424, type, sK287: subst).
% 2.91/0.80 thf(func_def_425, type, sK288: term).
% 2.91/0.80 thf(func_def_426, type, sK289: (term > $o)).
% 2.91/0.80 thf(func_def_427, type, sK290: (term > term)).
% 2.91/0.80 thf(func_def_428, type, sK291: ((term > $o) > subst > term)).
% 2.91/0.80 thf(func_def_429, type, sK292: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_430, type, sK293: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_431, type, sK294: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_432, type, sK295: (term > $o)).
% 2.91/0.80 thf(func_def_433, type, sK296: term).
% 2.91/0.80 thf(func_def_434, type, sK297: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_435, type, sK298: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_436, type, sK299: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_437, type, sK300: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_438, type, sK301: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_439, type, sK302: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.91/0.80 thf(func_def_440, type, sK303: (term > (term > $o) > term)).
% 2.91/0.80 thf(func_def_441, type, sK304: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_442, type, sK305: term).
% 2.91/0.80 thf(func_def_443, type, sK306: term).
% 2.91/0.80 thf(func_def_444, type, sK307: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_445, type, sK308: (term > $o)).
% 2.91/0.80 thf(func_def_446, type, sK309: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_447, type, sK310: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_448, type, sK311: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_449, type, sK312: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_450, type, sK313: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_451, type, sK314: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_452, type, sK315: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_453, type, sK316: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_454, type, sK317: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_455, type, sK318: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_456, type, sK319: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_457, type, sK320: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_458, type, sK321: term).
% 2.91/0.80 thf(func_def_459, type, sK322: term).
% 2.91/0.80 thf(func_def_460, type, sK323: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_461, type, sK324: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_462, type, sK325: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_463, type, sK326: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_464, type, sK327: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_465, type, sK328: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_466, type, sK329: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_467, type, sK330: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_468, type, sK331: (term > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_469, type, sK332: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_470, type, sK333: (term > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_471, type, sK334: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_472, type, sK335: term).
% 2.91/0.80 thf(func_def_473, type, sK336: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_474, type, sK337: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_475, type, sK338: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_476, type, sK339: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_477, type, sK340: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_478, type, sK341: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_479, type, sK342: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_480, type, sK343: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_481, type, sK344: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_482, type, sK345: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_483, type, sK346: term).
% 2.91/0.80 thf(func_def_484, type, sK347: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_485, type, sK348: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_486, type, sK349: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_487, type, sK350: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_488, type, sK351: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_489, type, sK352: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_490, type, sK353: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_491, type, sK354: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_492, type, sK355: (term > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_493, type, sK356: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_494, type, sK357: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_495, type, sK358: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_496, type, sK359: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_497, type, sK360: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_498, type, sK361: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_499, type, sK362: term).
% 2.91/0.80 thf(func_def_500, type, sK363: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_501, type, sK364: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_502, type, sK365: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_503, type, sK366: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_504, type, sK367: (term > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_505, type, sK368: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_506, type, sK369: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_507, type, sK370: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_508, type, sK371: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_509, type, sK372: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_510, type, sK373: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_511, type, sK374: (term > $o)).
% 2.91/0.80 thf(func_def_512, type, sK375: term).
% 2.91/0.80 thf(func_def_513, type, sK376: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_514, type, sK377: term).
% 2.91/0.80 thf(func_def_515, type, sK378: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_516, type, sK379: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_517, type, sK380: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_518, type, sK381: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_519, type, sK382: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.91/0.80 thf(func_def_520, type, sK383: (term > (term > $o) > term)).
% 2.91/0.80 thf(func_def_521, type, sK384: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_522, type, sK385: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_523, type, sK386: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_524, type, sK387: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_525, type, sK388: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_526, type, sK389: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_527, type, sK390: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_528, type, sK391: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_529, type, sK392: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_530, type, sK393: (term > $o)).
% 2.91/0.80 thf(func_def_531, type, sK394: term).
% 2.91/0.80 thf(func_def_532, type, sK395: (term > term)).
% 2.91/0.80 thf(func_def_533, type, sK396: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_534, type, sK397: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_535, type, sK398: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_536, type, sK399: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_537, type, sK400: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_538, type, sK401: term).
% 2.91/0.80 thf(func_def_539, type, sK402: (term > $o)).
% 2.91/0.80 thf(func_def_540, type, sK403: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_541, type, sK404: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_542, type, sK405: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_543, type, sK406: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_544, type, sK407: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_545, type, sK408: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_546, type, sK409: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_547, type, sK410: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_548, type, sK411: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_549, type, sK412: ((term > $o) > term > term)).
% 2.91/0.80 thf(func_def_550, type, sK413: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_551, type, sK414: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_552, type, sK415: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_553, type, sK416: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_554, type, sK417: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_555, type, sK418: ((subst > term > subst > $o) > term > $o)).
% 2.91/0.80 thf(func_def_556, type, sK419: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_557, type, sK420: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_558, type, sK421: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_559, type, sK422: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_560, type, sK423: term).
% 2.91/0.80 thf(func_def_561, type, sK424: (term > $o)).
% 2.91/0.80 thf(func_def_562, type, sK425: term).
% 2.91/0.80 thf(func_def_563, type, sK426: (term > term)).
% 2.91/0.80 thf(func_def_564, type, sK427: term).
% 2.91/0.80 thf(func_def_565, type, sK428: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_566, type, sK429: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_567, type, sK430: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_568, type, sK431: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_569, type, sK432: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_570, type, sK433: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_571, type, sK434: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_572, type, sK435: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_573, type, sK436: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_574, type, sK437: ((subst > term > subst > $o) > subst)).
% 2.91/0.80 thf(func_def_575, type, sK438: (term > (term > $o) > term)).
% 2.91/0.80 thf(func_def_576, type, sK439: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.91/0.80 thf(func_def_577, type, sK440: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_578, type, sK441: (term > $o)).
% 2.91/0.80 thf(func_def_579, type, sK442: term).
% 2.91/0.80 thf(func_def_580, type, sK443: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_581, type, sK444: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_582, type, sK445: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_583, type, sK446: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_584, type, sK447: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_585, type, sK448: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_586, type, sK449: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_587, type, sK450: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_588, type, sK451: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_589, type, sK452: ((subst > term > subst > $o) > subst > term > term)).
% 2.91/0.80 thf(func_def_590, type, sK453: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_591, type, sK454: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_592, type, sK455: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_593, type, sK456: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_594, type, sK457: term).
% 2.91/0.80 thf(func_def_595, type, sK458: (term > subst > term > term)).
% 2.91/0.80 thf(func_def_596, type, sK459: term).
% 2.91/0.80 thf(func_def_597, type, sK460: term).
% 2.91/0.80 thf(func_def_598, type, sK461: term).
% 2.91/0.80 thf(func_def_599, type, sK462: term).
% 2.91/0.80 thf(func_def_600, type, sK463: subst).
% 2.91/0.80 thf(func_def_601, type, sK464: term).
% 2.91/0.80 thf(func_def_602, type, sK465: (term > $o)).
% 2.91/0.80 thf(func_def_603, type, sK466: term).
% 2.91/0.80 thf(func_def_604, type, sK467: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_605, type, sK468: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_606, type, sK469: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_607, type, sK470: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_608, type, sK471: ((subst > term > subst > $o) > term > $o)).
% 2.91/0.80 thf(func_def_609, type, sK472: term).
% 2.91/0.80 thf(func_def_610, type, sK473: term).
% 2.91/0.80 thf(func_def_611, type, sK474: term).
% 2.91/0.80 thf(func_def_612, type, sK475: term).
% 2.91/0.80 thf(func_def_613, type, sK476: term).
% 2.91/0.80 thf(func_def_614, type, sK477: subst).
% 2.91/0.80 thf(func_def_615, type, sK478: term).
% 2.91/0.80 thf(func_def_616, type, sK479: subst).
% 2.91/0.80 thf(func_def_617, type, sK480: (term > $o)).
% 2.91/0.80 thf(func_def_618, type, sK481: term).
% 2.91/0.80 thf(func_def_619, type, sK482: (term > $o)).
% 2.91/0.80 thf(func_def_620, type, sK483: term).
% 2.91/0.80 thf(func_def_621, type, sK484: term).
% 2.91/0.80 thf(func_def_622, type, sK485: term).
% 2.91/0.80 thf(func_def_623, type, sK486: term).
% 2.91/0.80 thf(func_def_624, type, sK487: term).
% 2.91/0.80 thf(func_def_625, type, sK488: term).
% 2.91/0.80 thf(func_def_626, type, sK489: term).
% 2.91/0.80 thf(func_def_627, type, sK490: term).
% 2.91/0.80 thf(func_def_628, type, sK491: term).
% 2.91/0.80 thf(func_def_629, type, sK492: term).
% 2.91/0.80 thf(func_def_630, type, sK493: term).
% 2.91/0.80 thf(func_def_631, type, sK494: term).
% 2.91/0.80 thf(func_def_632, type, sK495: term).
% 2.91/0.80 thf(func_def_633, type, sK496: term).
% 2.91/0.80 thf(func_def_634, type, sK497: term).
% 2.91/0.80 thf(func_def_635, type, sK498: term).
% 2.91/0.80 thf(func_def_636, type, sK499: term).
% 2.91/0.80 thf(func_def_637, type, sK500: term).
% 2.91/0.80 thf(func_def_638, type, sK501: subst).
% 2.91/0.80 thf(func_def_639, type, sK502: subst).
% 2.91/0.80 thf(func_def_640, type, sK503: term).
% 2.91/0.80 thf(func_def_641, type, sK504: term).
% 2.91/0.80 thf(func_def_642, type, sK505: (term > $o)).
% 2.91/0.80 thf(func_def_643, type, sK506: (term > $o)).
% 2.91/0.80 thf(func_def_644, type, sK507: subst).
% 2.91/0.80 thf(func_def_645, type, sK508: term).
% 2.91/0.80 thf(func_def_646, type, sK509: subst).
% 2.91/0.80 thf(func_def_647, type, sK510: (term > subst > (term > $o) > term > $o)).
% 2.91/0.80 thf(func_def_648, type, sK511: (term > $o)).
% 2.91/0.80 thf(func_def_649, type, sK512: subst).
% 2.91/0.80 thf(func_def_650, type, sK513: term).
% 2.91/0.80 thf(func_def_651, type, sK514: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_652, type, sK515: term).
% 2.91/0.80 thf(func_def_653, type, sK516: term).
% 2.91/0.80 thf(func_def_654, type, sK517: term).
% 2.91/0.80 thf(func_def_655, type, sK518: term).
% 2.91/0.80 thf(func_def_656, type, sK519: subst).
% 2.91/0.80 thf(func_def_657, type, sK520: subst).
% 2.91/0.80 thf(func_def_658, type, sK521: subst).
% 2.91/0.80 thf(func_def_659, type, sK522: subst).
% 2.91/0.80 thf(func_def_660, type, sK523: term).
% 2.91/0.80 thf(func_def_661, type, sK524: term).
% 2.91/0.80 thf(func_def_662, type, sK525: term).
% 2.91/0.80 thf(func_def_663, type, sK526: term).
% 2.91/0.80 thf(func_def_664, type, sK527: term).
% 2.91/0.80 thf(func_def_665, type, sK528: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_666, type, sK529: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_667, type, sK530: (term > subst > term > term)).
% 2.91/0.80 thf(func_def_668, type, sK531: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_669, type, sK532: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_670, type, sK533: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_671, type, sK534: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_672, type, sK535: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_673, type, sK536: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_674, type, sK537: (subst > term > term)).
% 2.91/0.80 thf(func_def_675, type, sK538: (subst > term > term)).
% 2.91/0.80 thf(func_def_676, type, sK539: term).
% 2.91/0.80 thf(func_def_677, type, sK540: subst).
% 2.91/0.80 thf(func_def_678, type, sK541: ((subst > term > subst > $o) > term > $o)).
% 2.91/0.80 thf(func_def_679, type, sK542: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_680, type, sK543: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_681, type, sK544: term).
% 2.91/0.80 thf(func_def_682, type, sK545: term).
% 2.91/0.80 thf(func_def_683, type, sK546: subst).
% 2.91/0.80 thf(func_def_684, type, sK547: term).
% 2.91/0.80 thf(func_def_685, type, sK548: (term > subst > (term > $o) > (term > $o) > term)).
% 2.91/0.80 thf(func_def_686, type, sK549: subst).
% 2.91/0.80 thf(func_def_687, type, sK550: term).
% 2.91/0.80 thf(func_def_688, type, sK551: (term > $o)).
% 2.91/0.80 thf(func_def_689, type, sK552: (term > $o)).
% 2.91/0.80 thf(func_def_690, type, sK553: subst).
% 2.91/0.80 thf(func_def_691, type, sK554: term).
% 2.91/0.80 thf(func_def_692, type, sK555: (term > d_term)).
% 2.91/0.80 thf(func_def_693, type, sK556: (term > $o)).
% 2.91/0.80 thf(func_def_694, type, sK557: subst).
% 2.91/0.80 thf(func_def_695, type, sK558: term).
% 2.91/0.80 thf(func_def_696, type, sK559: (term > $o)).
% 2.91/0.80 thf(func_def_697, type, sK560: ((term > $o) > term > subst > (term > $o) > term)).
% 2.91/0.80 thf(func_def_698, type, sK561: term).
% 2.91/0.80 thf(func_def_699, type, sK562: (term > subst > term > term)).
% 2.91/0.80 thf(func_def_700, type, sK563: subst).
% 2.91/0.80 thf(func_def_701, type, sK564: subst).
% 2.91/0.80 thf(func_def_702, type, sK565: (subst > term > subst > $o)).
% 2.91/0.80 thf(func_def_703, type, sK566: term).
% 2.91/0.80 thf(func_def_704, type, sK567: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_705, type, sK568: ((subst > term > subst > $o) > term)).
% 2.91/0.80 thf(func_def_706, type, sK569: term).
% 2.91/0.80 thf(func_def_707, type, sK570: term).
% 2.91/0.80 thf(func_def_708, type, sK571: term).
% 2.91/0.80 thf(func_def_709, type, sK572: term).
% 2.91/0.80 thf(func_def_710, type, sK573: (subst > d_subst)).
% 2.91/0.80 thf(func_def_711, type, sK574: term).
% 2.91/0.80 thf(func_def_712, type, sK575: (term > subst > term > term)).
% 2.91/0.80 thf(func_def_713, type, sK576: term).
% 2.91/0.80 thf(func_def_714, type, sK577: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_715, type, sK578: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_716, type, sK579: term).
% 2.91/0.80 thf(func_def_717, type, sK580: (subst > term > term)).
% 2.91/0.80 thf(func_def_718, type, sK581: term).
% 2.91/0.80 thf(func_def_719, type, sK582: ((subst > term > term) > term)).
% 2.91/0.80 thf(func_def_720, type, sK583: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_721, type, sK584: ((subst > term > term) > subst)).
% 2.91/0.80 thf(func_def_722, type, sK585: subst).
% 2.91/0.80 thf(func_def_723, type, sK586: ((term > $o) > subst > term > term > $o)).
% 2.91/0.80 thf(func_def_724, type, sK587: term).
% 2.91/0.80 thf(func_def_725, type, sK588: subst).
% 2.91/0.80 thf(func_def_726, type, sK589: (term > $o)).
% 2.91/0.80 thf(func_def_727, type, sK590: ((term > $o) > term)).
% 2.91/0.80 thf(func_def_728, type, vNOT: ($o > $o)).
% 2.91/0.80 thf(func_def_729, type, sK591: subst).
% 2.91/0.80 thf(func_def_730, type, sK592: term).
% 2.91/0.80 thf(func_def_731, type, sK593: subst).
% 2.91/0.80 thf(f1,axiom,(
% 2.91/0.80 ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : ((X11 @ (lam @ X29)) | ~ ! [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) | ~ ! [X25 : subst,X14 : 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))))) => ! [X28 : 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)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [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)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) <=> hoasinduction_lthm_3) & ~ulamvar1 & hoasapnotvar & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X13 : term,X14 : subst,X10 : (term > $o),X26 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : 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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & termmset_gthm & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) => ! [X17 : subst,X16 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))))))))) & (! [X13 : term,X15 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & hoasinduction_gthm & hoasapinj1_gthm & hoasapnotvar_lthm & pushprop & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X13 : term,X14 : subst,X10 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & ! [X5 : d_subst] : (X5 = d_id) & (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ 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,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & axapp & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axassoc & hoaslamnotap_lthm & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & pushprop_lem2v2 & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X19 : term,X20 : term,X15 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X20 : term,X15 : term,X19 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & (hoasinduction_no_psi_cond <=> ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [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))))) | (X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : 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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48))) <=> hoasinduction_lem3v2) & ((^[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_lem3v2 & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapinj2_gthm & substmonoid_gthm & hoaslamnotap_gthm & ~lamnotap & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22))) & pushprop_lem0_gthm & hoasinduction_lem1_gthm & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : ((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)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X30 @ id)))))) <=> hoasinduction_no_psi_cond_lthm) & hoasinduction_lem3v2_gthm & pushprop_lem2v2_lthm & axabs & pushprop_gthm & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & hoaslamnotvar_lthm & (! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj2) & hoasinduction_lem1v2 & ulamvarsh & (pushprop_lem1v2 <=> ! [X14 : subst,X13 : term,X10 : (term > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one) | ~(X10 @ X13))) & pushprop_lem3v2_lthm & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & hoasinduction_lem3_gthm & lamnotvar & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [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)] : (~ ! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,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 @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) & ulamvarind & (one = ((d2term @ d_one))) & (! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & (hoasinduction_lem2v2 <=> ! [X44 : term,X45 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X11 @ X44) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45))) & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasapinj2_lthm <=> (! [X15 : term,X20 : term,X13 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X13 : term,X20 : term,X19 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)))) & axvarshift & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & hoasinduction_lem2v2_gthm & induction2_gthm & pushprop_lem2v2_gthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (laminj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & ! [X1 : d_term] : (X1 = d_one) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & (! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [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)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id)) <=> hoasinduction_lem3a) & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & (sh = ((d2subst @ d_id))) & (hoaslaminj <=> ! [X32 : subst,X31 : (subst > term > term),X33 : term,X18 : (subst > term > term)] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & axclos & (! [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) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) <=> hoasinduction_lem3v2a) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X47 : term,X46 : term,X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47)))) <=> hoaslamnotap) & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id))) & hoasinduction_lem1_lthm & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)))) & (! [X19 : term,X15 : term,X20 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [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)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : 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)))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [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,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & pushprop_lthm & apnotvar & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ 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))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29))))) <=> hoasinduction_lem3v2a_lthm) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) => ! [X10 : (term > $o),X22 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))))))) & hoaslamnotvar & hoasinduction_lem3a_gthm & (pushprop_lem1 <=> ! [X14 : subst,X13 : term,X10 : (term > $o),X26 : (term > $o),X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X32 : subst,X31 : (subst > term > term),X33 : term,X18 : (subst > term > term)] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & hoaslamnotvar_gthm & (! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop_lthm_orig & (! [X15 : term,X19 : term,X13 : term,X20 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)) <=> hoasapinj1) & hoasinduction_lem3b_gthm & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | (X10 @ X22)) => (! [X10 : (subst > term > subst > $o),X24 : term,X23 : term] : (~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id))) => (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : 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))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((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)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))))))) & (hoasapinj2 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & induction2lem_gthm & axmap & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & ~(var @ (d2term @ d_one)) & hoaslaminj_gthm & hoasinduction_lem1v2_gthm & hoasapnotvar_gthm & pushprop_lem1_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & (id = ((d2subst @ d_id))) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & hoasinduction_lem2_lthm & hoasinduction_lem2_gthm & hoasinduction_lem1 & pushprop_lem1v2_gthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (! [X10 : (subst > term > subst > $o),X24 : term,X23 : term] : (~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) <=> hoasinduction_lem2) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : ((X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ 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)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)))) <=> hoasinduction_lem3v2_lthm) & (! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X39 : subst,X40 : term,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X37 : term,X36 : subst,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)))) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aaa) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) <=> induction) & (induction2lem <=> ! [X17 : subst,X16 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))))),
% 2.91/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 2.91/0.81 thf(f2,conjecture,(
% 2.91/0.81 (axclos = ! [X1 : subst,X0 : term,X2 : subst] : (((sub @ (sub @ X0 @ X1) @ X2)) = ((sub @ X0 @ (comp @ X1 @ X2)))))),
% 2.91/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axclos)).
% 2.91/0.81 thf(f3,negated_conjecture,(
% 2.91/0.81 ~ (axclos = ! [X1 : subst,X0 : term,X2 : subst] : (((sub @ (sub @ X0 @ X1) @ X2)) = ((sub @ X0 @ (comp @ X1 @ X2)))))),
% 2.91/0.81 inference(negated_conjecture,[status(cth)],[f2])).
% 2.91/0.81 thf(f4,plain,(
% 2.91/0.81 ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : ((X4 @ X5) | ~(var @ X5)) | ~ ! [X6 : term,X7 : term] : ((X4 @ (ap @ X7 @ X6)) | ~(X4 @ X6) | ~(X4 @ X7)) | (X4 @ X3) | ~ ! [X8 : term] : ((X4 @ (lam @ X8)) | ~ ! [X9 : term] : (~(X4 @ X9) | (X4 @ (sub @ X8 @ (push @ X9 @ id)))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (subst > term > subst > $o),X13 : (term > $o)] : ((X13 @ (lam @ X11)) | ~ ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : ((X12 @ id @ (X15 @ id @ X16) @ id) | ~(X12 @ id @ X16 @ id)) | (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id) | ~ ! [X17 : subst,X18 : subst,X19 : term] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) = ((sub @ (X15 @ X18 @ X19) @ X17)))) | ~ ! [X20 : term] : (~(X13 @ X20) | (X13 @ (sub @ X11 @ (push @ X20 @ id))))) => ! [X21 : term,X22 : (subst > term > subst > $o)] : (~ ! [X23 : term,X24 : term] : ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id) | ~(X22 @ id @ X23 @ id) | ~(X22 @ id @ X24 @ id)) | ~ ! [X25 : subst,X26 : subst,X27 : subst,X28 : term] : (~(X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25) | (X22 @ X26 @ X28 @ (comp @ X27 @ X25))) | ~ ! [X29 : term] : (~(var @ (sub @ X29 @ id)) | (X22 @ id @ X29 @ id)) | ~ ! [X30 : (subst > term > term)] : (~ ! [X31 : subst,X32 : subst,X33 : term] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32)))) | ~ ! [X34 : term] : ((X22 @ id @ (X30 @ id @ X34) @ id) | ~(X22 @ id @ X34 @ id)) | (X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) | (X22 @ id @ X21 @ id) | ~ ! [X35 : term,X36 : subst,X37 : subst,X38 : subst] : (~(X22 @ X36 @ X35 @ (comp @ X38 @ X37)) | (X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37))))))) <=> hoasinduction_lthm_3) & ~ulamvar1 & hoasapnotvar & (hoasinduction_lem3v2_f <=> ! [X39 : term] : ~ ! [X40 : (subst > term > term)] : ~ ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42))))) & (! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44) <=> axvarcons) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> axscons) & (pushprop_lem1_lthm <=> (! [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) = X49) => (! [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) = X51) => ! [X52 : term,X53 : term,X54 : subst,X55 : (term > $o),X56 : (term > $o)] : (~(X55 @ X53) | (X56 @ (sub @ X53 @ (push @ X52 @ X54))))))) & (! [X57 : term,X58 : (subst > term > subst > $o)] : (~ ! [X59 : (subst > term > term)] : (~ ! [X60 : subst,X61 : term,X62 : subst] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) | ~ ! [X63 : term] : ((X58 @ id @ (X59 @ id @ X63) @ id) | ~(X58 @ id @ X63 @ id)) | (X58 @ id @ (lam @ (X59 @ sh @ one)) @ id)) | ~ ! [X64 : term] : (~(X58 @ id @ X64 @ id) | (X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id)) | (X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & termmset_gthm & (induction2lem_lthm <=> (! [X65 : subst,X66 : term] : (((sub @ one @ (push @ X66 @ X65))) = X66) => (! [X67 : term,X68 : subst] : (((comp @ sh @ (push @ X67 @ X68))) = X68) => (! [X69 : subst] : (((comp @ X69 @ id)) = X69) => (! [X70 : term,X71 : (term > $o)] : (~ ! [X72 : term] : (~(var @ X72) | (X71 @ X72)) | ~ ! [X73 : term,X74 : term] : (~(X71 @ X74) | (X71 @ (ap @ X74 @ X73)) | ~(X71 @ X73)) | (X71 @ X70) | ~ ! [X75 : term] : ((X71 @ (lam @ X75)) | ~(X71 @ X75))) => ! [X76 : subst,X77 : term,X78 : (term > $o)] : (~ ! [X79 : term,X80 : term] : (~(X78 @ X79) | (X78 @ (ap @ X80 @ X79)) | ~(X78 @ X80)) | ~ ! [X81 : term] : (~(var @ X81) | (X78 @ (sub @ X81 @ X76))) | (X78 @ (sub @ X77 @ X76)) | ~ ! [X82 : term] : (~ ! [X83 : term] : ((X78 @ (sub @ X82 @ (push @ X83 @ id))) | ~(X78 @ X83)) | (X78 @ (lam @ X82))))))))) & (! [X84 : term,X85 : term] : ((X84 = X85) | (((sub @ X84 @ sh)) != ((sub @ X85 @ sh)))) <=> shinj) & hoasinduction_gthm & hoasapinj1_gthm & hoasapnotvar_lthm & pushprop & (pushprop_lem1v2_lthm <=> (! [X86 : term,X87 : subst] : (((sub @ one @ (push @ X86 @ X87))) = X86) => ! [X88 : (term > $o),X89 : term,X90 : subst,X91 : (term > $o)] : ((X88 @ one) | ~(X91 @ X89) | ~ ! [X92 : term] : (((X88 @ X92)) = ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))))) & ! [X93 : d_subst] : (d_id = X93) & (! [X94 : term,X95 : (subst > term > subst > $o)] : (~ ! [X96 : term] : (~(X95 @ id @ X96 @ id) | (X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id)) | (X95 @ id @ (lam @ X94) @ id) | ~ ! [X97 : (subst > term > term)] : (~ ! [X98 : subst,X99 : term,X100 : subst] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98))) | ~ ! [X101 : term] : (~(X95 @ id @ X101 @ id) | (X95 @ id @ (X97 @ id @ X101) @ id)) | (X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) | ~ ! [X102 : subst,X103 : subst,X104 : term,X105 : subst] : ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105) | ~(X95 @ X103 @ X104 @ (comp @ X102 @ X105))) | ~ ! [X106 : term,X107 : subst,X108 : subst,X109 : subst] : ((X95 @ X109 @ X106 @ (comp @ X107 @ X108)) | ~(X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108))) <=> hoasinduction_lem3) & axapp & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axassoc & hoaslamnotap_lthm & (hoasinduction_lem0_lthm <=> ! [X110 : (subst > term > subst > $o)] : ~ ! [X111 : (term > $o)] : ~ ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id)))) & pushprop_lem2v2 & (! [X113 : (subst > term > subst > $o)] : ~ ! [X114 : (term > $o)] : ~ ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id))) <=> hoasinduction_lem0) & (hoasapinj1_lthm <=> (! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X117 : term,X118 : term,X119 : term,X120 : term] : ((X117 = X120) | (((ap @ X117 @ X118)) != ((ap @ X120 @ X119)))) => ! [X121 : term,X122 : term,X123 : term,X124 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124))))) & (! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125) <=> axshiftcons) & (hoasinduction_no_psi_cond <=> ! [X127 : term,X128 : (subst > term > subst > $o)] : (~ ! [X129 : (subst > term > term)] : ((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id) | ~ ! [X130 : term] : ((X128 @ id @ (X129 @ id @ X130) @ id) | ~(X128 @ id @ X130 @ id)) | ~ ! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133))))) | (X128 @ id @ X127 @ id) | ~ ! [X134 : term,X135 : term] : (~(X128 @ id @ X135 @ id) | (X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id) | ~(X128 @ id @ X134 @ id)))) & (axidr <=> ! [X136 : subst] : (((comp @ X136 @ id)) = X136)) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X137 : (subst > term > subst > $o),X138 : (term > $o),X139 : term] : (~ ! [X140 : (subst > term > term)] : (~ ! [X141 : term,X142 : subst,X143 : subst] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) | ~ ! [X144 : term] : ((X137 @ id @ (X140 @ id @ X144) @ id) | ~(X137 @ id @ X144 @ id)) | (X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) | ~ ! [X145 : term] : (((X138 @ X145)) = ((X137 @ id @ X145 @ id))) | ~ ! [X146 : subst,X147 : term,X148 : subst,X149 : subst] : ((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148) | ~(X137 @ X149 @ X147 @ (comp @ X146 @ X148))) | ~ ! [X150 : term] : (~(X138 @ X150) | (X138 @ (sub @ X139 @ (push @ X150 @ id)))) | ~ ! [X151 : term,X152 : subst,X153 : subst,X154 : subst] : ((X137 @ X152 @ X151 @ (comp @ X153 @ X154)) | ~(X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154)) | (X138 @ (lam @ X139))) <=> hoasinduction_lem3v2) & ((^[X155 : term, X156 : subst, X157 : (term > $o), X158 : (term > $o)] : (! [X159 : term] : (((X157 @ (sub @ X159 @ (push @ X155 @ X156)))) = ((X158 @ X159))))) = pushprop_p_and_p_prime) & pushprop_lem3v2 & ! [X160 : d_subst,X161 : d_subst] : ((((d2subst @ X160)) = ((d2subst @ X161))) => (X160 = X161)) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapinj2_gthm & substmonoid_gthm & hoaslamnotap_gthm & ~lamnotap & (induction2 <=> ! [X162 : term,X163 : (term > $o)] : (~ ! [X164 : term] : (~ ! [X165 : term] : (~(X163 @ X165) | (X163 @ (sub @ X164 @ (push @ X165 @ id)))) | (X163 @ (lam @ X164))) | ~ ! [X166 : term] : ((X163 @ X166) | ~(var @ X166)) | ~ ! [X167 : term,X168 : term] : (~(X163 @ X168) | (X163 @ (ap @ X167 @ X168)) | ~(X163 @ X167)) | (X163 @ X162))) & pushprop_lem0_gthm & hoasinduction_lem1_gthm & ((! [X169 : (subst > term > subst > $o)] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X169 @ id @ X171 @ id))) => (! [X172 : term,X173 : (term > $o)] : ((X173 @ X172) | ~ ! [X174 : term,X175 : term] : (~(X173 @ X174) | (X173 @ (ap @ X174 @ X175)) | ~(X173 @ X175)) | ~ ! [X176 : term] : ((X173 @ (lam @ X176)) | ~ ! [X177 : term] : ((X173 @ (sub @ X176 @ (push @ X177 @ id))) | ~(X173 @ X177))) | ~ ! [X178 : term] : ((X173 @ X178) | ~(var @ X178))) => (! [X179 : term] : (((sub @ X179 @ id)) = X179) => (! [X180 : (term > $o),X181 : (subst > term > subst > $o),X182 : term] : (~ ! [X183 : term] : ((X180 @ (sub @ X182 @ (push @ X183 @ id))) | ~(X180 @ X183)) | ~ ! [X184 : (subst > term > term)] : ((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id) | ~ ! [X185 : subst,X186 : term,X187 : subst] : (((X184 @ (comp @ X185 @ X187) @ (sub @ X186 @ X187))) = ((sub @ (X184 @ X185 @ X186) @ X187))) | ~ ! [X188 : term] : ((X181 @ id @ (X184 @ id @ X188) @ id) | ~(X181 @ id @ X188 @ id))) | ~ ! [X189 : term] : (((X180 @ X189)) = ((X181 @ id @ X189 @ id))) | (X180 @ (lam @ X182))) => ! [X190 : (subst > term > subst > $o),X191 : term] : (~ ! [X192 : term,X193 : term] : (~(X190 @ id @ X193 @ id) | (X190 @ id @ (ap @ (sub @ X192 @ id) @ X193) @ id) | ~(X190 @ id @ X192 @ id)) | ~ ! [X194 : (subst > term > term)] : (~ ! [X195 : subst,X196 : term,X197 : subst] : (((sub @ (X194 @ X195 @ X196) @ X197)) = ((X194 @ (comp @ X195 @ X197) @ (sub @ X196 @ X197)))) | (X190 @ id @ (lam @ (X194 @ sh @ one)) @ id) | ~ ! [X198 : term] : (~(X190 @ id @ X198 @ id) | (X190 @ id @ (X194 @ id @ X198) @ id))) | (X190 @ id @ X191 @ id)))))) <=> hoasinduction_no_psi_cond_lthm) & hoasinduction_lem3v2_gthm & pushprop_lem2v2_lthm & axabs & pushprop_gthm & (termmset <=> ! [X199 : term] : (((sub @ X199 @ id)) = X199)) & hoaslamnotvar_lthm & (! [X200 : term,X201 : term,X202 : term,X203 : term] : ((X202 = X203) | (((ap @ X200 @ X202)) != ((ap @ X201 @ X203)))) <=> apinj2) & hoasinduction_lem1v2 & ulamvarsh & (pushprop_lem1v2 <=> ! [X204 : subst,X205 : term,X206 : (term > $o),X207 : (term > $o)] : (~ ! [X208 : term] : (((X206 @ (sub @ X208 @ (push @ X205 @ X204)))) = ((X207 @ X208))) | (X207 @ one) | ~(X206 @ X205))) & pushprop_lem3v2_lthm & ! [X209 : d_term,X210 : d_term] : ((((d2term @ X209)) = ((d2term @ X210))) => (X209 = X210)) & hoasinduction_lem3_gthm & lamnotvar & (hoasinduction_lem3_lthm <=> (! [X211 : term] : (((sub @ X211 @ id)) = X211) => (! [X212 : term,X213 : (subst > term > subst > $o)] : (~ ! [X214 : term] : (~(X213 @ id @ X214 @ id) | (X213 @ id @ (sub @ X212 @ (push @ X214 @ id)) @ id)) | (X213 @ id @ (lam @ (sub @ X212 @ (push @ one @ sh))) @ id) | ~ ! [X215 : (subst > term > term)] : (~ ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (X215 @ X217 @ X216) @ X218)) = ((X215 @ (comp @ X217 @ X218) @ (sub @ X216 @ X218)))) | ~ ! [X219 : term] : (~(X213 @ id @ X219 @ id) | (X213 @ id @ (X215 @ id @ X219) @ id)) | (X213 @ id @ (lam @ (X215 @ sh @ one)) @ id))) => ! [X220 : term,X221 : (subst > term > subst > $o)] : (~ ! [X222 : subst,X223 : subst,X224 : term,X225 : subst] : (~(X221 @ (comp @ X223 @ X225) @ (sub @ X224 @ X225) @ X222) | (X221 @ X223 @ X224 @ (comp @ X225 @ X222))) | ~ ! [X226 : (subst > term > term)] : (~ ! [X227 : subst,X228 : term,X229 : subst] : (((sub @ (X226 @ X229 @ X228) @ X227)) = ((X226 @ (comp @ X229 @ X227) @ (sub @ X228 @ X227)))) | (X221 @ id @ (lam @ (X226 @ sh @ one)) @ id) | ~ ! [X230 : term] : (~(X221 @ id @ X230 @ id) | (X221 @ id @ (X226 @ id @ X230) @ id))) | ~ ! [X231 : term] : (~(X221 @ id @ X231 @ id) | (X221 @ id @ (sub @ X220 @ (push @ X231 @ id)) @ id)) | (X221 @ id @ (lam @ X220) @ id) | ~ ! [X232 : subst,X233 : subst,X234 : term,X235 : subst] : (~(X221 @ X232 @ X234 @ (comp @ X235 @ X233)) | (X221 @ (comp @ X232 @ X235) @ (sub @ X234 @ X235) @ X233)))))) & ulamvarind & (one = ((d2term @ d_one))) & (! [X236 : (term > $o),X237 : term,X238 : subst] : ~ ! [X239 : (term > $o)] : ~ ! [X240 : term] : (((X236 @ (sub @ X240 @ (push @ X237 @ X238)))) = ((X239 @ X240))) <=> pushprop_lem0) & (hoasinduction_lem2v2 <=> ! [X241 : term,X242 : term,X243 : (subst > term > subst > $o),X244 : (term > $o)] : (~ ! [X245 : term,X246 : subst,X247 : subst,X248 : subst] : ((X243 @ (comp @ X246 @ X248) @ (sub @ X245 @ X248) @ X247) | ~(X243 @ X246 @ X245 @ (comp @ X248 @ X247))) | (X244 @ (ap @ X241 @ X242)) | ~ ! [X249 : term] : (((X243 @ id @ X249 @ id)) = ((X244 @ X249))) | ~ ! [X250 : term,X251 : term] : (~(X243 @ id @ X251 @ id) | ~(X243 @ id @ X250 @ id) | (X243 @ id @ (ap @ (sub @ X251 @ id) @ X250) @ id)) | ~(X244 @ X241) | ~ ! [X252 : subst,X253 : term,X254 : subst,X255 : subst] : (~(X243 @ (comp @ X252 @ X255) @ (sub @ X253 @ X255) @ X254) | (X243 @ X252 @ X253 @ (comp @ X255 @ X254))) | ~(X244 @ X242))) & ((^[X256 : subst, X257 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasapinj2_lthm <=> (! [X258 : term,X259 : term,X260 : term,X261 : term] : ((((ap @ X258 @ X259)) != ((ap @ X260 @ X261))) | (X259 = X261)) => ! [X262 : term,X263 : term,X264 : term,X265 : term] : ((((ap @ (sub @ X262 @ id) @ X264)) != ((ap @ (sub @ X265 @ id) @ X263))) | (X263 = X264)))) & axvarshift & (substmonoid <=> (! [X266 : subst] : (((comp @ X266 @ id)) = X266) & ! [X267 : subst] : (((comp @ id @ X267)) = X267))) & hoasinduction_lem2v2_gthm & induction2_gthm & pushprop_lem2v2_gthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (laminj <=> ! [X268 : term,X269 : term] : ((X268 = X269) | (((lam @ X269)) != ((lam @ X268))))) & ! [X270 : d_term] : (d_one = X270) & (! [X271 : term] : ~ ! [X272 : (subst > term > term)] : ~ ! [X273 : subst,X274 : term] : (((X272 @ X273 @ X274)) = ((sub @ X271 @ (push @ X274 @ X273)))) <=> hoasinduction_lem3v2_f_lthm) & (! [X275 : (subst > term > subst > $o),X276 : term] : (~ ! [X277 : (subst > term > term)] : (~ ! [X278 : term] : (~(X275 @ id @ X278 @ id) | (X275 @ id @ (X277 @ id @ X278) @ id)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281)))) | (X275 @ id @ (lam @ (X277 @ sh @ one)) @ id)) | ~ ! [X282 : term] : ((X275 @ id @ (sub @ X276 @ (push @ X282 @ id)) @ id) | ~(X275 @ id @ X282 @ id)) | (X275 @ id @ (lam @ X276) @ id)) <=> hoasinduction_lem3a) & ((^[X283 : (subst > term > subst > $o), X284 : (term > $o)] : (! [X285 : term] : (((X284 @ X285)) = ((X283 @ id @ X285 @ id))))) = hoasinduction_p_and_p_prime) & (sh = ((d2subst @ d_id))) & (hoaslaminj <=> ! [X286 : subst,X287 : (subst > term > term),X288 : term,X289 : (subst > term > term)] : ((((lam @ (X287 @ sh @ one))) != ((lam @ (X289 @ sh @ one)))) | ~ ! [X290 : subst,X291 : term,X292 : subst] : (((sub @ (X287 @ X292 @ X291) @ X290)) = ((X287 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290)))) | ~ ! [X293 : subst,X294 : term,X295 : subst] : (((sub @ (X289 @ X295 @ X294) @ X293)) = ((X289 @ (comp @ X295 @ X293) @ (sub @ X294 @ X293)))) | (((X287 @ X286 @ X288)) = ((X289 @ X286 @ X288))))) & axclos & (! [X296 : (term > $o),X297 : term,X298 : (subst > term > subst > $o)] : (~ ! [X299 : term] : (((X298 @ id @ X299 @ id)) = ((X296 @ X299))) | ~ ! [X300 : (subst > term > term)] : (~ ! [X301 : term] : ((X298 @ id @ (X300 @ id @ X301) @ id) | ~(X298 @ id @ X301 @ id)) | (X298 @ id @ (lam @ (X300 @ sh @ one)) @ id) | ~ ! [X302 : term,X303 : subst,X304 : subst] : (((X300 @ (comp @ X303 @ X304) @ (sub @ X302 @ X304))) = ((sub @ (X300 @ X303 @ X302) @ X304)))) | (X296 @ (lam @ X297)) | ~ ! [X305 : term] : (~(X296 @ X305) | (X296 @ (sub @ X297 @ (push @ X305 @ id))))) <=> hoasinduction_lem3v2a) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X306 : term,X307 : term,X308 : (subst > term > term)] : (~ ! [X309 : term,X310 : subst,X311 : subst] : (((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X308 @ X311 @ X309) @ X310))) | (((ap @ (sub @ X307 @ id) @ X306)) != ((lam @ (X308 @ sh @ one))))) <=> hoaslamnotap) & (hoasinduction <=> ! [X312 : (subst > term > subst > $o),X313 : term] : (~ ! [X314 : term] : (~(var @ (sub @ X314 @ id)) | (X312 @ id @ X314 @ id)) | ~ ! [X315 : (subst > term > term)] : (~ ! [X316 : term] : (~(X312 @ id @ X316 @ id) | (X312 @ id @ (X315 @ id @ X316) @ id)) | (X312 @ id @ (lam @ (X315 @ sh @ one)) @ id) | ~ ! [X317 : subst,X318 : term,X319 : subst] : (((sub @ (X315 @ X319 @ X318) @ X317)) = ((X315 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317))))) | ~ ! [X320 : term,X321 : subst,X322 : subst,X323 : subst] : (~(X312 @ (comp @ X321 @ X323) @ (sub @ X320 @ X323) @ X322) | (X312 @ X321 @ X320 @ (comp @ X323 @ X322))) | ~ ! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : ((X312 @ (comp @ X324 @ X327) @ (sub @ X326 @ X327) @ X325) | ~(X312 @ X324 @ X326 @ (comp @ X327 @ X325))) | ~ ! [X328 : term,X329 : term] : ((X312 @ id @ (ap @ (sub @ X328 @ id) @ X329) @ id) | ~(X312 @ id @ X329 @ id) | ~(X312 @ id @ X328 @ id)) | (X312 @ id @ X313 @ id))) & hoasinduction_lem1_lthm & (hoasinduction_lem3aa_lthm <=> ! [X330 : (subst > term > subst > $o),X331 : term] : ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id) | ~ ! [X332 : (subst > term > term)] : (~ ! [X333 : term,X334 : subst,X335 : subst] : (((X332 @ (comp @ X334 @ X335) @ (sub @ X333 @ X335))) = ((sub @ (X332 @ X334 @ X333) @ X335))) | ~ ! [X336 : term] : ((X330 @ id @ (X332 @ id @ X336) @ id) | ~(X330 @ id @ X336 @ id)) | (X330 @ id @ (lam @ (X332 @ sh @ one)) @ id)) | ~ ! [X337 : term] : (~(X330 @ id @ X337 @ id) | (X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id)))) & (! [X338 : term,X339 : term,X340 : term,X341 : term] : ((((ap @ X341 @ X338)) != ((ap @ X339 @ X340))) | (X339 = X341)) <=> apinj1) & ((! [X342 : term] : (((sub @ X342 @ id)) = X342) => (! [X343 : term,X344 : (subst > term > subst > $o)] : (~ ! [X345 : term] : ((X344 @ id @ (sub @ X343 @ (push @ X345 @ id)) @ id) | ~(X344 @ id @ X345 @ id)) | (X344 @ id @ (lam @ (sub @ X343 @ (push @ one @ sh))) @ id) | ~ ! [X346 : (subst > term > term)] : ((X344 @ id @ (lam @ (X346 @ sh @ one)) @ id) | ~ ! [X347 : subst,X348 : term,X349 : subst] : (((X346 @ (comp @ X349 @ X347) @ (sub @ X348 @ X347))) = ((sub @ (X346 @ X349 @ X348) @ X347))) | ~ ! [X350 : term] : ((X344 @ id @ (X346 @ id @ X350) @ id) | ~(X344 @ id @ X350 @ id)))) => ! [X351 : term,X352 : (subst > term > subst > $o)] : (~ ! [X353 : (subst > term > term)] : ((X352 @ id @ (lam @ (X353 @ sh @ one)) @ id) | ~ ! [X354 : term] : (~(X352 @ id @ X354 @ id) | (X352 @ id @ (X353 @ id @ X354) @ id)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : term] : (~(X352 @ id @ X358 @ id) | (X352 @ id @ (sub @ X351 @ (push @ X358 @ id)) @ id)) | (X352 @ id @ (lam @ X351) @ id)))) <=> hoasinduction_lem3a_lthm) & pushprop_lthm & apnotvar & ((! [X359 : term] : ~ ! [X360 : (subst > term > term)] : ~ ! [X361 : subst,X362 : term] : (((sub @ X359 @ (push @ X362 @ X361))) = ((X360 @ X361 @ X362))) => (! [X363 : term] : (((sub @ X363 @ id)) = X363) => ! [X364 : term,X365 : (subst > term > subst > $o),X366 : (term > $o)] : (~ ! [X367 : term] : (((X365 @ id @ X367 @ id)) = ((X366 @ X367))) | ~ ! [X368 : (subst > term > term)] : ((X365 @ id @ (lam @ (X368 @ sh @ one)) @ id) | ~ ! [X369 : subst,X370 : subst,X371 : term] : (((X368 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370))) = ((sub @ (X368 @ X369 @ X371) @ X370))) | ~ ! [X372 : term] : (~(X365 @ id @ X372 @ id) | (X365 @ id @ (X368 @ id @ X372) @ id))) | ~ ! [X373 : term] : (~(X366 @ X373) | (X366 @ (sub @ X364 @ (push @ X373 @ id)))) | (X366 @ (lam @ X364))))) <=> hoasinduction_lem3v2a_lthm) & (induction2_lthm <=> (! [X374 : term] : (((sub @ X374 @ id)) = X374) => (! [X375 : subst,X376 : (term > $o),X377 : term] : (~ ! [X378 : term] : ((X376 @ (lam @ X378)) | ~ ! [X379 : term] : (~(X376 @ X379) | (X376 @ (sub @ X378 @ (push @ X379 @ id))))) | (X376 @ (sub @ X377 @ X375)) | ~ ! [X380 : term] : (~(var @ X380) | (X376 @ (sub @ X380 @ X375))) | ~ ! [X381 : term,X382 : term] : (~(X376 @ X381) | ~(X376 @ X382) | (X376 @ (ap @ X382 @ X381)))) => ! [X383 : (term > $o),X384 : term] : (~ ! [X385 : term,X386 : term] : (~(X383 @ X385) | (X383 @ (ap @ X386 @ X385)) | ~(X383 @ X386)) | (X383 @ X384) | ~ ! [X387 : term] : (~(var @ X387) | (X383 @ X387)) | ~ ! [X388 : term] : (~ ! [X389 : term] : (~(X383 @ X389) | (X383 @ (sub @ X388 @ (push @ X389 @ id)))) | (X383 @ (lam @ X388))))))) & hoaslamnotvar & hoasinduction_lem3a_gthm & (pushprop_lem1 <=> ! [X390 : subst,X391 : term,X392 : (term > $o),X393 : (term > $o),X394 : term] : (~(X392 @ X391) | (X393 @ (sub @ X391 @ (push @ X394 @ X390))))) & (hoaslaminj_lthm <=> (! [X395 : term,X396 : subst] : (((sub @ one @ (push @ X395 @ X396))) = X395) => (! [X397 : subst,X398 : term] : (((comp @ sh @ (push @ X398 @ X397))) = X397) => (! [X399 : term,X400 : term] : ((((lam @ X399)) != ((lam @ X400))) | (X399 = X400)) => ! [X401 : subst,X402 : (subst > term > term),X403 : term,X404 : (subst > term > term)] : ((((lam @ (X404 @ sh @ one))) != ((lam @ (X402 @ sh @ one)))) | ~ ! [X405 : subst,X406 : subst,X407 : term] : (((sub @ (X402 @ X405 @ X407) @ X406)) = ((X402 @ (comp @ X405 @ X406) @ (sub @ X407 @ X406)))) | (((X402 @ X401 @ X403)) = ((X404 @ X401 @ X403))) | ~ ! [X408 : subst,X409 : term,X410 : subst] : (((X404 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) = ((sub @ (X404 @ X408 @ X409) @ X410)))))))) & hoaslamnotvar_gthm & (! [X411 : subst,X412 : (term > $o),X413 : term] : ~ ! [X414 : (term > $o)] : ~ ! [X415 : term] : (((X414 @ X415)) = ((X412 @ (sub @ X415 @ (push @ X413 @ X411))))) <=> pushprop_lem0_lthm) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop_lthm_orig & (! [X416 : term,X417 : term,X418 : term,X419 : term] : ((((ap @ (sub @ X418 @ id) @ X417)) != ((ap @ (sub @ X416 @ id) @ X419))) | (X416 = X418)) <=> hoasapinj1) & hoasinduction_lem3b_gthm & (hoasinduction_lthm <=> (! [X420 : (term > $o),X421 : term] : (~ ! [X422 : term] : (~(var @ X422) | (X420 @ X422)) | ~ ! [X423 : term] : ((X420 @ (lam @ X423)) | ~ ! [X424 : term] : ((X420 @ (sub @ X423 @ (push @ X424 @ id))) | ~(X420 @ X424))) | ~ ! [X425 : term,X426 : term] : ((X420 @ (ap @ X426 @ X425)) | ~(X420 @ X426) | ~(X420 @ X425)) | (X420 @ X421)) => (! [X427 : (subst > term > subst > $o),X428 : term,X429 : term] : (~ ! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (~(X427 @ (comp @ X431 @ X430) @ (sub @ X432 @ X430) @ X433) | (X427 @ X431 @ X432 @ (comp @ X430 @ X433))) | ~ ! [X434 : subst,X435 : term,X436 : subst,X437 : subst] : (~(X427 @ X434 @ X435 @ (comp @ X436 @ X437)) | (X427 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436) @ X437)) | (X427 @ id @ (ap @ X429 @ X428) @ id) | ~(X427 @ id @ X428 @ id) | ~(X427 @ id @ X429 @ id) | ~ ! [X438 : term,X439 : term] : (~(X427 @ id @ X438 @ id) | (X427 @ id @ (ap @ (sub @ X439 @ id) @ X438) @ id) | ~(X427 @ id @ X439 @ id))) => (! [X440 : term,X441 : (subst > term > subst > $o)] : (~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((X441 @ X445 @ X443 @ (comp @ X444 @ X442)) | ~(X441 @ (comp @ X445 @ X444) @ (sub @ X443 @ X444) @ X442)) | (X441 @ id @ (lam @ X440) @ id) | ~ ! [X446 : (subst > term > term)] : ((X441 @ id @ (lam @ (X446 @ sh @ one)) @ id) | ~ ! [X447 : subst,X448 : term,X449 : subst] : (((X446 @ (comp @ X449 @ X447) @ (sub @ X448 @ X447))) = ((sub @ (X446 @ X449 @ X448) @ X447))) | ~ ! [X450 : term] : ((X441 @ id @ (X446 @ id @ X450) @ id) | ~(X441 @ id @ X450 @ id))) | ~ ! [X451 : term] : (~(X441 @ id @ X451 @ id) | (X441 @ id @ (sub @ X440 @ (push @ X451 @ id)) @ id)) | ~ ! [X452 : term,X453 : subst,X454 : subst,X455 : subst] : ((X441 @ (comp @ X455 @ X453) @ (sub @ X452 @ X453) @ X454) | ~(X441 @ X455 @ X452 @ (comp @ X453 @ X454)))) => ! [X456 : (subst > term > subst > $o),X457 : term] : (~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((X456 @ X460 @ X459 @ (comp @ X461 @ X458)) | ~(X456 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461) @ X458)) | (X456 @ id @ X457 @ id) | ~ ! [X462 : term] : (~(var @ (sub @ X462 @ id)) | (X456 @ id @ X462 @ id)) | ~ ! [X463 : term,X464 : term] : ((X456 @ id @ (ap @ (sub @ X464 @ id) @ X463) @ id) | ~(X456 @ id @ X464 @ id) | ~(X456 @ id @ X463 @ id)) | ~ ! [X465 : subst,X466 : subst,X467 : term,X468 : subst] : (~(X456 @ X465 @ X467 @ (comp @ X468 @ X466)) | (X456 @ (comp @ X465 @ X468) @ (sub @ X467 @ X468) @ X466)) | ~ ! [X469 : (subst > term > term)] : ((X456 @ id @ (lam @ (X469 @ sh @ one)) @ id) | ~ ! [X470 : subst,X471 : subst,X472 : term] : (((X469 @ (comp @ X471 @ X470) @ (sub @ X472 @ X470))) = ((sub @ (X469 @ X471 @ X472) @ X470))) | ~ ! [X473 : term] : ((X456 @ id @ (X469 @ id @ X473) @ id) | ~(X456 @ id @ X473 @ id)))))))) & (hoasapinj2 <=> ! [X474 : term,X475 : term,X476 : term,X477 : term] : ((X476 = X477) | (((ap @ (sub @ X475 @ id) @ X477)) != ((ap @ (sub @ X474 @ id) @ X476))))) & induction2lem_gthm & axmap & (axidl <=> ! [X478 : subst] : (((comp @ id @ X478)) = X478)) & ~(var @ (d2term @ d_one)) & hoaslaminj_gthm & hoasinduction_lem1v2_gthm & hoasapnotvar_gthm & pushprop_lem1_gthm & (! [X479 : term] : ~ ! [X480 : (subst > term > term)] : (((sub @ X479 @ (push @ one @ sh))) != ((X480 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & (id = ((d2subst @ d_id))) & (hoasinduction_lem3b <=> ! [X481 : term] : ~ ! [X482 : (subst > term > term)] : (((sub @ X481 @ (push @ one @ sh))) != ((X482 @ sh @ one)))) & hoasinduction_lem2_lthm & hoasinduction_lem2_gthm & hoasinduction_lem1 & pushprop_lem1v2_gthm & ! [X483 : subst] : ? [X484 : d_subst] : (((d2subst @ X484)) = X483) & (termmset_lthm <=> (! [X485 : term] : (((sub @ X485 @ id)) = X485) => ! [X486 : term] : (((sub @ X486 @ id)) = X486))) & (axvarid <=> ! [X487 : term] : (((sub @ X487 @ id)) = X487)) & (! [X488 : (subst > term > subst > $o),X489 : term,X490 : term] : (~(X488 @ id @ X490 @ id) | (X488 @ id @ (ap @ X490 @ X489) @ id) | ~(X488 @ id @ X489 @ id) | ~ ! [X491 : subst,X492 : subst,X493 : term,X494 : subst] : (~(X488 @ (comp @ X491 @ X492) @ (sub @ X493 @ X492) @ X494) | (X488 @ X491 @ X493 @ (comp @ X492 @ X494))) | ~ ! [X495 : term,X496 : term] : (~(X488 @ id @ X495 @ id) | (X488 @ id @ (ap @ (sub @ X495 @ id) @ X496) @ id) | ~(X488 @ id @ X496 @ id)) | ~ ! [X497 : subst,X498 : term,X499 : subst,X500 : subst] : ((X488 @ (comp @ X500 @ X497) @ (sub @ X498 @ X497) @ X499) | ~(X488 @ X500 @ X498 @ (comp @ X497 @ X499)))) <=> hoasinduction_lem2) & ((! [X501 : term] : (((sub @ X501 @ id)) = X501) => ! [X502 : (term > $o),X503 : (subst > term > subst > $o),X504 : term] : ((X502 @ (lam @ X504)) | ~ ! [X505 : term] : (((X502 @ X505)) = ((X503 @ id @ X505 @ id))) | ~ ! [X506 : subst,X507 : term,X508 : subst,X509 : subst] : (~(X503 @ X508 @ X507 @ (comp @ X509 @ X506)) | (X503 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509) @ X506)) | ~ ! [X510 : subst,X511 : subst,X512 : term,X513 : subst] : ((X503 @ X510 @ X512 @ (comp @ X511 @ X513)) | ~(X503 @ (comp @ X510 @ X511) @ (sub @ X512 @ X511) @ X513)) | ~ ! [X514 : (subst > term > term)] : ((X503 @ id @ (lam @ (X514 @ sh @ one)) @ id) | ~ ! [X515 : term] : ((X503 @ id @ (X514 @ id @ X515) @ id) | ~(X503 @ id @ X515 @ id)) | ~ ! [X516 : subst,X517 : subst,X518 : term] : (((sub @ (X514 @ X516 @ X518) @ X517)) = ((X514 @ (comp @ X516 @ X517) @ (sub @ X518 @ X517))))) | ~ ! [X519 : term] : ((X502 @ (sub @ X504 @ (push @ X519 @ id))) | ~(X502 @ X519)))) <=> hoasinduction_lem3v2_lthm) & (! [X520 : term,X521 : (subst > term > subst > $o)] : (~ ! [X522 : (subst > term > term),X523 : term] : (~ ! [X524 : subst,X525 : term,X526 : subst] : (((X522 @ (comp @ X524 @ X526) @ (sub @ X525 @ X526))) = ((sub @ X523 @ (push @ (sub @ X525 @ X526) @ (comp @ X524 @ X526))))) | ~ ! [X527 : term] : (~(X521 @ id @ X527 @ id) | (X521 @ id @ (X522 @ id @ X527) @ id)) | (X521 @ id @ (lam @ (X522 @ sh @ one)) @ id) | ~ ! [X528 : term,X529 : subst,X530 : subst] : (((sub @ (sub @ X523 @ (push @ X528 @ X529)) @ X530)) = ((sub @ (X522 @ X529 @ X528) @ X530)))) | (X521 @ id @ (lam @ (sub @ X520 @ (push @ one @ sh))) @ id) | ~ ! [X531 : term] : (~(X521 @ id @ X531 @ id) | (X521 @ id @ (sub @ X520 @ (push @ X531 @ id)) @ id))) <=> hoasinduction_lem3aaa) & ((! [X532 : subst] : (((comp @ id @ X532)) = X532) => (! [X533 : subst] : (((comp @ X533 @ id)) = X533) => (! [X534 : subst] : (((comp @ X534 @ id)) = X534) & ! [X535 : subst] : (((comp @ id @ X535)) = X535)))) <=> substmonoid_lthm) & (! [X536 : (term > $o),X537 : term] : (~ ! [X538 : term,X539 : term] : (~(X536 @ X539) | ~(X536 @ X538) | (X536 @ (ap @ X538 @ X539))) | ~ ! [X540 : term] : ((X536 @ (lam @ X540)) | ~(X536 @ X540)) | (X536 @ X537) | ~ ! [X541 : term] : ((X536 @ X541) | ~(var @ X541))) <=> induction) & (induction2lem <=> ! [X542 : subst,X543 : term,X544 : (term > $o)] : (~ ! [X545 : term] : (~ ! [X546 : term] : (~(X544 @ X546) | (X544 @ (sub @ X545 @ (push @ X546 @ id)))) | (X544 @ (lam @ X545))) | (X544 @ (sub @ X543 @ X542)) | ~ ! [X547 : term,X548 : term] : (~(X544 @ X548) | ~(X544 @ X547) | (X544 @ (ap @ X548 @ X547))) | ~ ! [X549 : term] : (~(var @ X549) | (X544 @ (sub @ X549 @ X542)))))),
% 2.91/0.81 inference(rectify,[],[f1])).
% 2.91/0.81 thf(f5,plain,(
% 2.91/0.81 ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : (($true = ((X4 @ X5))) | ~ ($true = ((var @ X5)))) | ~ ! [X6 : term,X7 : term] : (($true = ((X4 @ (ap @ X7 @ X6)))) | ~ ($true = ((X4 @ X6))) | ~ ($true = ((X4 @ X7)))) | (((X4 @ X3)) = $true) | ~ ! [X8 : term] : (($true = ((X4 @ (lam @ X8)))) | ~ ! [X9 : term] : (~ ($true = ((X4 @ X9))) | ($true = ((X4 @ (sub @ X8 @ (push @ X9 @ id)))))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (subst > term > subst > $o),X13 : (term > $o)] : (($true = ((X13 @ (lam @ X11)))) | ~ ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : (($true = ((X12 @ id @ (X15 @ id @ X16) @ id))) | ~ (((X12 @ id @ X16 @ id)) = $true)) | ($true = ((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))) | ~ ! [X17 : subst,X19 : term,X18 : subst] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) = ((sub @ (X15 @ X18 @ X19) @ X17)))) | ~ ! [X20 : term] : (~ (((X13 @ X20)) = $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X20 @ id))))))) => ! [X21 : term,X22 : (subst > term > subst > $o)] : (~ ! [X23 : term,X24 : term] : (($true = ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id))) | ~ (((X22 @ id @ X23 @ id)) = $true) | ~ ($true = ((X22 @ id @ X24 @ id)))) | ~ ! [X25 : subst,X26 : subst,X27 : subst,X28 : term] : (~ ($true = ((X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25))) | ($true = ((X22 @ X26 @ X28 @ (comp @ X27 @ X25))))) | ~ ! [X29 : term] : (~ ($true = ((var @ (sub @ X29 @ id)))) | ($true = ((X22 @ id @ X29 @ id)))) | ~ ! [X30 : (subst > term > term)] : (~ ! [X33 : term,X31 : subst,X32 : subst] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32)))) | ~ ! [X34 : term] : (($true = ((X22 @ id @ (X30 @ id @ X34) @ id))) | ~ ($true = ((X22 @ id @ X34 @ id)))) | (((X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) = $true)) | (((X22 @ id @ X21 @ id)) = $true) | ~ ! [X35 : term,X36 : subst,X37 : subst,X38 : subst] : (~ (((X22 @ X36 @ X35 @ (comp @ X38 @ X37))) = $true) | (((X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & ~ (ulamvar1 = $true) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X39 : term] : ~ ! [X40 : (subst > term > term)] : ~ ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42))))) & ((axvarcons = $true) <=> ! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> (axscons = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X49 : term,X48 : subst] : (((sub @ one @ (push @ X49 @ X48))) = X49) => (! [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) = X51) => ! [X52 : term,X53 : term,X54 : subst,X55 : (term > $o),X56 : (term > $o)] : (~ ($true = ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))))) & (! [X57 : term,X58 : (subst > term > subst > $o)] : (~ ! [X59 : (subst > term > term)] : (~ ! [X62 : subst,X60 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) | ~ ! [X63 : term] : ((((X58 @ id @ (X59 @ id @ X63) @ id)) = $true) | ~ ($true = ((X58 @ id @ X63 @ id)))) | ($true = ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id)))) | ~ ! [X64 : term] : (~ ($true = ((X58 @ id @ X64 @ id))) | ($true = ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id)))) | (((X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & (termmset_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X66 : term,X65 : subst] : (((sub @ one @ (push @ X66 @ X65))) = X66) => (! [X68 : subst,X67 : term] : (((comp @ sh @ (push @ X67 @ X68))) = X68) => (! [X69 : subst] : (((comp @ X69 @ id)) = X69) => (! [X70 : term,X71 : (term > $o)] : (~ ! [X72 : term] : (~ ($true = ((var @ X72))) | ($true = ((X71 @ X72)))) | ~ ! [X73 : term,X74 : term] : (~ ($true = ((X71 @ X74))) | ($true = ((X71 @ (ap @ X74 @ X73)))) | ~ (((X71 @ X73)) = $true)) | ($true = ((X71 @ X70))) | ~ ! [X75 : term] : (($true = ((X71 @ (lam @ X75)))) | ~ ($true = ((X71 @ X75))))) => ! [X76 : subst,X77 : term,X78 : (term > $o)] : (~ ! [X79 : term,X80 : term] : (~ (((X78 @ X79)) = $true) | (((X78 @ (ap @ X80 @ X79))) = $true) | ~ (((X78 @ X80)) = $true)) | ~ ! [X81 : term] : (~ ($true = ((var @ X81))) | ($true = ((X78 @ (sub @ X81 @ X76))))) | ($true = ((X78 @ (sub @ X77 @ X76)))) | ~ ! [X82 : term] : (~ ! [X83 : term] : (($true = ((X78 @ (sub @ X82 @ (push @ X83 @ id))))) | ~ ($true = ((X78 @ X83)))) | ($true = ((X78 @ (lam @ X82))))))))))) & ((shinj = $true) <=> ! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85))) & (hoasinduction_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) = X86) => ! [X88 : (term > $o),X89 : term,X90 : subst,X91 : (term > $o)] : ((((X88 @ one)) = $true) | ~ ($true = ((X91 @ X89))) | ~ ! [X92 : term] : (((X88 @ X92)) = ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))))) & ! [X93 : d_subst] : (d_id = X93) & (! [X94 : term,X95 : (subst > term > subst > $o)] : (~ ! [X96 : term] : (~ ($true = ((X95 @ id @ X96 @ id))) | ($true = ((X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id)))) | (((X95 @ id @ (lam @ X94) @ id)) = $true) | ~ ! [X97 : (subst > term > term)] : (~ ! [X98 : subst,X100 : subst,X99 : term] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98))) | ~ ! [X101 : term] : (~ ($true = ((X95 @ id @ X101 @ id))) | ($true = ((X95 @ id @ (X97 @ id @ X101) @ id)))) | (((X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) = $true)) | ~ ! [X102 : subst,X103 : subst,X104 : term,X105 : subst] : (($true = ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105))) | ~ ($true = ((X95 @ X103 @ X104 @ (comp @ X102 @ X105))))) | ~ ! [X106 : term,X107 : subst,X108 : subst,X109 : subst] : (($true = ((X95 @ X109 @ X106 @ (comp @ X107 @ X108)))) | ~ (((X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108)) = $true))) <=> (hoasinduction_lem3 = $true)) & (axapp = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & (! [X110 : (subst > term > subst > $o)] : ~ ! [X111 : (term > $o)] : ~ ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X113 : (subst > term > subst > $o)] : ~ ! [X114 : (term > $o)] : ~ ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id)))) & ((! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X119 : term,X120 : term,X118 : term,X117 : term] : ((((ap @ X117 @ X118)) != ((ap @ X120 @ X119))) | (X117 = X120)) => ! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)))) <=> (hoasapinj1_lthm = $true)) & ((axshiftcons = $true) <=> ! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X127 : term,X128 : (subst > term > subst > $o)] : (~ ! [X129 : (subst > term > term)] : ((((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id)) = $true) | ~ ! [X130 : term] : (($true = ((X128 @ id @ (X129 @ id @ X130) @ id))) | ~ ($true = ((X128 @ id @ X130 @ id)))) | ~ ! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133))))) | ($true = ((X128 @ id @ X127 @ id))) | ~ ! [X134 : term,X135 : term] : (~ ($true = ((X128 @ id @ X135 @ id))) | ($true = ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id))) | ~ (((X128 @ id @ X134 @ id)) = $true)))) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) <=> (axidr = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X137 : (subst > term > subst > $o),X138 : (term > $o),X139 : term] : (~ ! [X140 : (subst > term > term)] : (~ ! [X143 : subst,X142 : subst,X141 : term] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) | ~ ! [X144 : term] : (($true = ((X137 @ id @ (X140 @ id @ X144) @ id))) | ~ (((X137 @ id @ X144 @ id)) = $true)) | (((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) = $true)) | ~ ! [X145 : term] : (((X138 @ X145)) = ((X137 @ id @ X145 @ id))) | ~ ! [X146 : subst,X147 : term,X148 : subst,X149 : subst] : ((((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148)) = $true) | ~ ($true = ((X137 @ X149 @ X147 @ (comp @ X146 @ X148))))) | ~ ! [X150 : term] : (~ (((X138 @ X150)) = $true) | ($true = ((X138 @ (sub @ X139 @ (push @ X150 @ id)))))) | ~ ! [X151 : term,X152 : subst,X153 : subst,X154 : subst] : ((((X137 @ X152 @ X151 @ (comp @ X153 @ X154))) = $true) | ~ ($true = ((X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154)))) | ($true = ((X138 @ (lam @ X139))))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_lem3v2 = $true) & ! [X160 : d_subst,X161 : d_subst] : ((((d2subst @ X160)) = ((d2subst @ X161))) => (X160 = X161)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasapinj2_gthm = $true) & (substmonoid_gthm = $true) & (hoaslamnotap_gthm = $true) & ~ (lamnotap = $true) & ((induction2 = $true) <=> ! [X162 : term,X163 : (term > $o)] : (~ ! [X164 : term] : (~ ! [X165 : term] : (~ ($true = ((X163 @ X165))) | (((X163 @ (sub @ X164 @ (push @ X165 @ id)))) = $true)) | ($true = ((X163 @ (lam @ X164))))) | ~ ! [X166 : term] : (($true = ((X163 @ X166))) | ~ ($true = ((var @ X166)))) | ~ ! [X167 : term,X168 : term] : (~ ($true = ((X163 @ X168))) | ($true = ((X163 @ (ap @ X167 @ X168)))) | ~ (((X163 @ X167)) = $true)) | ($true = ((X163 @ X162))))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X169 : (subst > term > subst > $o)] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X169 @ id @ X171 @ id))) => (! [X172 : term,X173 : (term > $o)] : (($true = ((X173 @ X172))) | ~ ! [X174 : term,X175 : term] : (~ ($true = ((X173 @ X174))) | ($true = ((X173 @ (ap @ X174 @ X175)))) | ~ ($true = ((X173 @ X175)))) | ~ ! [X176 : term] : (($true = ((X173 @ (lam @ X176)))) | ~ ! [X177 : term] : (($true = ((X173 @ (sub @ X176 @ (push @ X177 @ id))))) | ~ (((X173 @ X177)) = $true))) | ~ ! [X178 : term] : (($true = ((X173 @ X178))) | ~ ($true = ((var @ X178))))) => (! [X179 : term] : (((sub @ X179 @ id)) = X179) => (! [X180 : (term > $o),X181 : (subst > term > subst > $o),X182 : term] : (~ ! [X183 : term] : (($true = ((X180 @ (sub @ X182 @ (push @ X183 @ id))))) | ~ ($true = ((X180 @ X183)))) | ~ ! [X184 : (subst > term > term)] : (($true = ((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id))) | ~ ! [X185 : subst,X186 : term,X187 : subst] : (((X184 @ (comp @ X185 @ X187) @ (sub @ X186 @ X187))) = ((sub @ (X184 @ X185 @ X186) @ X187))) | ~ ! [X188 : term] : (($true = ((X181 @ id @ (X184 @ id @ X188) @ id))) | ~ ($true = ((X181 @ id @ X188 @ id))))) | ~ ! [X189 : term] : (((X180 @ X189)) = ((X181 @ id @ X189 @ id))) | ($true = ((X180 @ (lam @ X182))))) => ! [X190 : (subst > term > subst > $o),X191 : term] : (~ ! [X192 : term,X193 : term] : (~ ($true = ((X190 @ id @ X193 @ id))) | ($true = ((X190 @ id @ (ap @ (sub @ X192 @ id) @ X193) @ id))) | ~ (((X190 @ id @ X192 @ id)) = $true)) | ~ ! [X194 : (subst > term > term)] : (~ ! [X195 : subst,X196 : term,X197 : subst] : (((sub @ (X194 @ X195 @ X196) @ X197)) = ((X194 @ (comp @ X195 @ X197) @ (sub @ X196 @ X197)))) | ($true = ((X190 @ id @ (lam @ (X194 @ sh @ one)) @ id))) | ~ ! [X198 : term] : (~ ($true = ((X190 @ id @ X198 @ id))) | ($true = ((X190 @ id @ (X194 @ id @ X198) @ id))))) | ($true = ((X190 @ id @ X191 @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (axabs = $true) & (pushprop_gthm = $true) & ((termmset = $true) <=> ! [X199 : term] : (((sub @ X199 @ id)) = X199)) & (hoaslamnotvar_lthm = $true) & (! [X200 : term,X201 : term,X202 : term,X203 : term] : ((X202 = X203) | (((ap @ X200 @ X202)) != ((ap @ X201 @ X203)))) <=> (apinj2 = $true)) & (hoasinduction_lem1v2 = $true) & (ulamvarsh = $true) & ((pushprop_lem1v2 = $true) <=> ! [X204 : subst,X205 : term,X206 : (term > $o),X207 : (term > $o)] : (~ ! [X208 : term] : (((X206 @ (sub @ X208 @ (push @ X205 @ X204)))) = ((X207 @ X208))) | (((X207 @ one)) = $true) | ~ (((X206 @ X205)) = $true))) & (pushprop_lem3v2_lthm = $true) & ! [X209 : d_term,X210 : d_term] : ((((d2term @ X209)) = ((d2term @ X210))) => (X209 = X210)) & (hoasinduction_lem3_gthm = $true) & (lamnotvar = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X211 : term] : (((sub @ X211 @ id)) = X211) => (! [X212 : term,X213 : (subst > term > subst > $o)] : (~ ! [X214 : term] : (~ ($true = ((X213 @ id @ X214 @ id))) | ($true = ((X213 @ id @ (sub @ X212 @ (push @ X214 @ id)) @ id)))) | ($true = ((X213 @ id @ (lam @ (sub @ X212 @ (push @ one @ sh))) @ id))) | ~ ! [X215 : (subst > term > term)] : (~ ! [X216 : term,X217 : subst,X218 : subst] : (((sub @ (X215 @ X217 @ X216) @ X218)) = ((X215 @ (comp @ X217 @ X218) @ (sub @ X216 @ X218)))) | ~ ! [X219 : term] : (~ ($true = ((X213 @ id @ X219 @ id))) | (((X213 @ id @ (X215 @ id @ X219) @ id)) = $true)) | ($true = ((X213 @ id @ (lam @ (X215 @ sh @ one)) @ id))))) => ! [X220 : term,X221 : (subst > term > subst > $o)] : (~ ! [X222 : subst,X223 : subst,X224 : term,X225 : subst] : (~ ($true = ((X221 @ (comp @ X223 @ X225) @ (sub @ X224 @ X225) @ X222))) | (((X221 @ X223 @ X224 @ (comp @ X225 @ X222))) = $true)) | ~ ! [X226 : (subst > term > term)] : (~ ! [X227 : subst,X228 : term,X229 : subst] : (((sub @ (X226 @ X229 @ X228) @ X227)) = ((X226 @ (comp @ X229 @ X227) @ (sub @ X228 @ X227)))) | (((X221 @ id @ (lam @ (X226 @ sh @ one)) @ id)) = $true) | ~ ! [X230 : term] : (~ ($true = ((X221 @ id @ X230 @ id))) | (((X221 @ id @ (X226 @ id @ X230) @ id)) = $true))) | ~ ! [X231 : term] : (~ ($true = ((X221 @ id @ X231 @ id))) | ($true = ((X221 @ id @ (sub @ X220 @ (push @ X231 @ id)) @ id)))) | ($true = ((X221 @ id @ (lam @ X220) @ id))) | ~ ! [X232 : subst,X233 : subst,X234 : term,X235 : subst] : (~ (((X221 @ X232 @ X234 @ (comp @ X235 @ X233))) = $true) | ($true = ((X221 @ (comp @ X232 @ X235) @ (sub @ X234 @ X235) @ X233)))))))) & (ulamvarind = $true) & (one = ((d2term @ d_one))) & (! [X236 : (term > $o),X237 : term,X238 : subst] : ~ ! [X239 : (term > $o)] : ~ ! [X240 : term] : (((X236 @ (sub @ X240 @ (push @ X237 @ X238)))) = ((X239 @ X240))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X241 : term,X242 : term,X243 : (subst > term > subst > $o),X244 : (term > $o)] : (~ ! [X245 : term,X246 : subst,X247 : subst,X248 : subst] : ((((X243 @ (comp @ X246 @ X248) @ (sub @ X245 @ X248) @ X247)) = $true) | ~ ($true = ((X243 @ X246 @ X245 @ (comp @ X248 @ X247))))) | ($true = ((X244 @ (ap @ X241 @ X242)))) | ~ ! [X249 : term] : (((X243 @ id @ X249 @ id)) = ((X244 @ X249))) | ~ ! [X250 : term,X251 : term] : (~ (((X243 @ id @ X251 @ id)) = $true) | ~ ($true = ((X243 @ id @ X250 @ id))) | ($true = ((X243 @ id @ (ap @ (sub @ X251 @ id) @ X250) @ id)))) | ~ ($true = ((X244 @ X241))) | ~ ! [X252 : subst,X253 : term,X254 : subst,X255 : subst] : (~ ($true = ((X243 @ (comp @ X252 @ X255) @ (sub @ X253 @ X255) @ X254))) | ($true = ((X243 @ X252 @ X253 @ (comp @ X255 @ X254))))) | ~ ($true = ((X244 @ X242))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj2_lthm = $true) <=> (! [X258 : term,X259 : term,X260 : term,X261 : term] : ((((ap @ X258 @ X259)) != ((ap @ X260 @ X261))) | (X259 = X261)) => ! [X262 : term,X263 : term,X264 : term,X265 : term] : ((((ap @ (sub @ X262 @ id) @ X264)) != ((ap @ (sub @ X265 @ id) @ X263))) | (X263 = X264)))) & (axvarshift = $true) & ((substmonoid = $true) <=> (! [X266 : subst] : (((comp @ X266 @ id)) = X266) & ! [X267 : subst] : (((comp @ id @ X267)) = X267))) & (hoasinduction_lem2v2_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((laminj = $true) <=> ! [X268 : term,X269 : term] : ((X268 = X269) | (((lam @ X269)) != ((lam @ X268))))) & ! [X270 : d_term] : (d_one = X270) & (! [X271 : term] : ~ ! [X272 : (subst > term > term)] : ~ ! [X273 : subst,X274 : term] : (((X272 @ X273 @ X274)) = ((sub @ X271 @ (push @ X274 @ X273)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X275 : (subst > term > subst > $o),X276 : term] : (~ ! [X277 : (subst > term > term)] : (~ ! [X278 : term] : (~ ($true = ((X275 @ id @ X278 @ id))) | ($true = ((X275 @ id @ (X277 @ id @ X278) @ id)))) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281)))) | (((X275 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true)) | ~ ! [X282 : term] : (($true = ((X275 @ id @ (sub @ X276 @ (push @ X282 @ id)) @ id))) | ~ ($true = ((X275 @ id @ X282 @ id)))) | ($true = ((X275 @ id @ (lam @ X276) @ id)))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = sh) & ((hoaslaminj = $true) <=> ! [X286 : subst,X287 : (subst > term > term),X288 : term,X289 : (subst > term > term)] : ((((lam @ (X287 @ sh @ one))) != ((lam @ (X289 @ sh @ one)))) | ~ ! [X290 : subst,X291 : term,X292 : subst] : (((sub @ (X287 @ X292 @ X291) @ X290)) = ((X287 @ (comp @ X292 @ X290) @ (sub @ X291 @ X290)))) | ~ ! [X293 : subst,X294 : term,X295 : subst] : (((sub @ (X289 @ X295 @ X294) @ X293)) = ((X289 @ (comp @ X295 @ X293) @ (sub @ X294 @ X293)))) | (((X287 @ X286 @ X288)) = ((X289 @ X286 @ X288))))) & (axclos = $true) & (! [X296 : (term > $o),X297 : term,X298 : (subst > term > subst > $o)] : (~ ! [X299 : term] : (((X298 @ id @ X299 @ id)) = ((X296 @ X299))) | ~ ! [X300 : (subst > term > term)] : (~ ! [X301 : term] : (($true = ((X298 @ id @ (X300 @ id @ X301) @ id))) | ~ ($true = ((X298 @ id @ X301 @ id)))) | ($true = ((X298 @ id @ (lam @ (X300 @ sh @ one)) @ id))) | ~ ! [X302 : term,X303 : subst,X304 : subst] : (((X300 @ (comp @ X303 @ X304) @ (sub @ X302 @ X304))) = ((sub @ (X300 @ X303 @ X302) @ X304)))) | (((X296 @ (lam @ X297))) = $true) | ~ ! [X305 : term] : (~ (((X296 @ X305)) = $true) | ($true = ((X296 @ (sub @ X297 @ (push @ X305 @ id))))))) <=> (hoasinduction_lem3v2a = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X306 : term,X307 : term,X308 : (subst > term > term)] : (~ ! [X309 : term,X310 : subst,X311 : subst] : (((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X308 @ X311 @ X309) @ X310))) | (((ap @ (sub @ X307 @ id) @ X306)) != ((lam @ (X308 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((hoasinduction = $true) <=> ! [X312 : (subst > term > subst > $o),X313 : term] : (~ ! [X314 : term] : (~ ($true = ((var @ (sub @ X314 @ id)))) | (((X312 @ id @ X314 @ id)) = $true)) | ~ ! [X315 : (subst > term > term)] : (~ ! [X316 : term] : (~ ($true = ((X312 @ id @ X316 @ id))) | ($true = ((X312 @ id @ (X315 @ id @ X316) @ id)))) | (((X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)) = $true) | ~ ! [X317 : subst,X318 : term,X319 : subst] : (((sub @ (X315 @ X319 @ X318) @ X317)) = ((X315 @ (comp @ X319 @ X317) @ (sub @ X318 @ X317))))) | ~ ! [X320 : term,X321 : subst,X322 : subst,X323 : subst] : (~ (((X312 @ (comp @ X321 @ X323) @ (sub @ X320 @ X323) @ X322)) = $true) | (((X312 @ X321 @ X320 @ (comp @ X323 @ X322))) = $true)) | ~ ! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (($true = ((X312 @ (comp @ X324 @ X327) @ (sub @ X326 @ X327) @ X325))) | ~ (((X312 @ X324 @ X326 @ (comp @ X327 @ X325))) = $true)) | ~ ! [X328 : term,X329 : term] : (($true = ((X312 @ id @ (ap @ (sub @ X328 @ id) @ X329) @ id))) | ~ (((X312 @ id @ X329 @ id)) = $true) | ~ ($true = ((X312 @ id @ X328 @ id)))) | (((X312 @ id @ X313 @ id)) = $true))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X330 : (subst > term > subst > $o),X331 : term] : ((((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X332 : (subst > term > term)] : (~ ! [X333 : term,X334 : subst,X335 : subst] : (((X332 @ (comp @ X334 @ X335) @ (sub @ X333 @ X335))) = ((sub @ (X332 @ X334 @ X333) @ X335))) | ~ ! [X336 : term] : (($true = ((X330 @ id @ (X332 @ id @ X336) @ id))) | ~ (((X330 @ id @ X336 @ id)) = $true)) | ($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id)))) | ~ ! [X337 : term] : (~ (((X330 @ id @ X337 @ id)) = $true) | (((X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id)) = $true)))) & (! [X338 : term,X339 : term,X340 : term,X341 : term] : ((((ap @ X341 @ X338)) != ((ap @ X339 @ X340))) | (X339 = X341)) <=> (apinj1 = $true)) & ((! [X342 : term] : (((sub @ X342 @ id)) = X342) => (! [X343 : term,X344 : (subst > term > subst > $o)] : (~ ! [X345 : term] : ((((X344 @ id @ (sub @ X343 @ (push @ X345 @ id)) @ id)) = $true) | ~ ($true = ((X344 @ id @ X345 @ id)))) | ($true = ((X344 @ id @ (lam @ (sub @ X343 @ (push @ one @ sh))) @ id))) | ~ ! [X346 : (subst > term > term)] : ((((X344 @ id @ (lam @ (X346 @ sh @ one)) @ id)) = $true) | ~ ! [X347 : subst,X348 : term,X349 : subst] : (((X346 @ (comp @ X349 @ X347) @ (sub @ X348 @ X347))) = ((sub @ (X346 @ X349 @ X348) @ X347))) | ~ ! [X350 : term] : (($true = ((X344 @ id @ (X346 @ id @ X350) @ id))) | ~ (((X344 @ id @ X350 @ id)) = $true)))) => ! [X351 : term,X352 : (subst > term > subst > $o)] : (~ ! [X353 : (subst > term > term)] : ((((X352 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : (~ ($true = ((X352 @ id @ X354 @ id))) | (((X352 @ id @ (X353 @ id @ X354) @ id)) = $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : term] : (~ ($true = ((X352 @ id @ X358 @ id))) | ($true = ((X352 @ id @ (sub @ X351 @ (push @ X358 @ id)) @ id)))) | ($true = ((X352 @ id @ (lam @ X351) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (pushprop_lthm = $true) & (apnotvar = $true) & ((! [X359 : term] : ~ ! [X360 : (subst > term > term)] : ~ ! [X361 : subst,X362 : term] : (((sub @ X359 @ (push @ X362 @ X361))) = ((X360 @ X361 @ X362))) => (! [X363 : term] : (((sub @ X363 @ id)) = X363) => ! [X364 : term,X365 : (subst > term > subst > $o),X366 : (term > $o)] : (~ ! [X367 : term] : (((X365 @ id @ X367 @ id)) = ((X366 @ X367))) | ~ ! [X368 : (subst > term > term)] : ((((X365 @ id @ (lam @ (X368 @ sh @ one)) @ id)) = $true) | ~ ! [X369 : subst,X370 : subst,X371 : term] : (((X368 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370))) = ((sub @ (X368 @ X369 @ X371) @ X370))) | ~ ! [X372 : term] : (~ ($true = ((X365 @ id @ X372 @ id))) | ($true = ((X365 @ id @ (X368 @ id @ X372) @ id))))) | ~ ! [X373 : term] : (~ (((X366 @ X373)) = $true) | ($true = ((X366 @ (sub @ X364 @ (push @ X373 @ id)))))) | ($true = ((X366 @ (lam @ X364))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((induction2_lthm = $true) <=> (! [X374 : term] : (((sub @ X374 @ id)) = X374) => (! [X375 : subst,X376 : (term > $o),X377 : term] : (~ ! [X378 : term] : (($true = ((X376 @ (lam @ X378)))) | ~ ! [X379 : term] : (~ ($true = ((X376 @ X379))) | ($true = ((X376 @ (sub @ X378 @ (push @ X379 @ id))))))) | (((X376 @ (sub @ X377 @ X375))) = $true) | ~ ! [X380 : term] : (~ ($true = ((var @ X380))) | (((X376 @ (sub @ X380 @ X375))) = $true)) | ~ ! [X381 : term,X382 : term] : (~ ($true = ((X376 @ X381))) | ~ ($true = ((X376 @ X382))) | ($true = ((X376 @ (ap @ X382 @ X381)))))) => ! [X383 : (term > $o),X384 : term] : (~ ! [X385 : term,X386 : term] : (~ ($true = ((X383 @ X385))) | (((X383 @ (ap @ X386 @ X385))) = $true) | ~ (((X383 @ X386)) = $true)) | ($true = ((X383 @ X384))) | ~ ! [X387 : term] : (~ (((var @ X387)) = $true) | ($true = ((X383 @ X387)))) | ~ ! [X388 : term] : (~ ! [X389 : term] : (~ ($true = ((X383 @ X389))) | (((X383 @ (sub @ X388 @ (push @ X389 @ id)))) = $true)) | (((X383 @ (lam @ X388))) = $true)))))) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X390 : subst,X391 : term,X392 : (term > $o),X393 : (term > $o),X394 : term] : (~ ($true = ((X392 @ X391))) | (((X393 @ (sub @ X391 @ (push @ X394 @ X390)))) = $true))) & ((hoaslaminj_lthm = $true) <=> (! [X395 : term,X396 : subst] : (((sub @ one @ (push @ X395 @ X396))) = X395) => (! [X397 : subst,X398 : term] : (((comp @ sh @ (push @ X398 @ X397))) = X397) => (! [X399 : term,X400 : term] : ((((lam @ X399)) != ((lam @ X400))) | (X399 = X400)) => ! [X401 : subst,X402 : (subst > term > term),X403 : term,X404 : (subst > term > term)] : ((((lam @ (X404 @ sh @ one))) != ((lam @ (X402 @ sh @ one)))) | ~ ! [X405 : subst,X406 : subst,X407 : term] : (((sub @ (X402 @ X405 @ X407) @ X406)) = ((X402 @ (comp @ X405 @ X406) @ (sub @ X407 @ X406)))) | (((X402 @ X401 @ X403)) = ((X404 @ X401 @ X403))) | ~ ! [X408 : subst,X409 : term,X410 : subst] : (((X404 @ (comp @ X408 @ X410) @ (sub @ X409 @ X410))) = ((sub @ (X404 @ X408 @ X409) @ X410)))))))) & (hoaslamnotvar_gthm = $true) & (! [X411 : subst,X412 : (term > $o),X413 : term] : ~ ! [X414 : (term > $o)] : ~ ! [X415 : term] : (((X414 @ X415)) = ((X412 @ (sub @ X415 @ (push @ X413 @ X411))))) <=> (pushprop_lem0_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm_orig = $true) & (! [X416 : term,X417 : term,X418 : term,X419 : term] : ((((ap @ (sub @ X418 @ id) @ X417)) != ((ap @ (sub @ X416 @ id) @ X419))) | (X416 = X418)) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X420 : (term > $o),X421 : term] : (~ ! [X422 : term] : (~ ($true = ((var @ X422))) | (((X420 @ X422)) = $true)) | ~ ! [X423 : term] : (($true = ((X420 @ (lam @ X423)))) | ~ ! [X424 : term] : ((((X420 @ (sub @ X423 @ (push @ X424 @ id)))) = $true) | ~ ($true = ((X420 @ X424))))) | ~ ! [X425 : term,X426 : term] : (($true = ((X420 @ (ap @ X426 @ X425)))) | ~ ($true = ((X420 @ X426))) | ~ ($true = ((X420 @ X425)))) | ($true = ((X420 @ X421)))) => (! [X427 : (subst > term > subst > $o),X428 : term,X429 : term] : (~ ! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (~ ($true = ((X427 @ (comp @ X431 @ X430) @ (sub @ X432 @ X430) @ X433))) | ($true = ((X427 @ X431 @ X432 @ (comp @ X430 @ X433))))) | ~ ! [X434 : subst,X435 : term,X436 : subst,X437 : subst] : (~ ($true = ((X427 @ X434 @ X435 @ (comp @ X436 @ X437)))) | ($true = ((X427 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436) @ X437)))) | (((X427 @ id @ (ap @ X429 @ X428) @ id)) = $true) | ~ ($true = ((X427 @ id @ X428 @ id))) | ~ (((X427 @ id @ X429 @ id)) = $true) | ~ ! [X438 : term,X439 : term] : (~ ($true = ((X427 @ id @ X438 @ id))) | ($true = ((X427 @ id @ (ap @ (sub @ X439 @ id) @ X438) @ id))) | ~ ($true = ((X427 @ id @ X439 @ id))))) => (! [X440 : term,X441 : (subst > term > subst > $o)] : (~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X441 @ X445 @ X443 @ (comp @ X444 @ X442))) = $true) | ~ (((X441 @ (comp @ X445 @ X444) @ (sub @ X443 @ X444) @ X442)) = $true)) | ($true = ((X441 @ id @ (lam @ X440) @ id))) | ~ ! [X446 : (subst > term > term)] : (($true = ((X441 @ id @ (lam @ (X446 @ sh @ one)) @ id))) | ~ ! [X447 : subst,X448 : term,X449 : subst] : (((X446 @ (comp @ X449 @ X447) @ (sub @ X448 @ X447))) = ((sub @ (X446 @ X449 @ X448) @ X447))) | ~ ! [X450 : term] : ((((X441 @ id @ (X446 @ id @ X450) @ id)) = $true) | ~ (((X441 @ id @ X450 @ id)) = $true))) | ~ ! [X451 : term] : (~ ($true = ((X441 @ id @ X451 @ id))) | (((X441 @ id @ (sub @ X440 @ (push @ X451 @ id)) @ id)) = $true)) | ~ ! [X452 : term,X453 : subst,X454 : subst,X455 : subst] : ((((X441 @ (comp @ X455 @ X453) @ (sub @ X452 @ X453) @ X454)) = $true) | ~ (((X441 @ X455 @ X452 @ (comp @ X453 @ X454))) = $true))) => ! [X456 : (subst > term > subst > $o),X457 : term] : (~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : (($true = ((X456 @ X460 @ X459 @ (comp @ X461 @ X458)))) | ~ ($true = ((X456 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461) @ X458)))) | ($true = ((X456 @ id @ X457 @ id))) | ~ ! [X462 : term] : (~ ($true = ((var @ (sub @ X462 @ id)))) | ($true = ((X456 @ id @ X462 @ id)))) | ~ ! [X463 : term,X464 : term] : ((((X456 @ id @ (ap @ (sub @ X464 @ id) @ X463) @ id)) = $true) | ~ (((X456 @ id @ X464 @ id)) = $true) | ~ ($true = ((X456 @ id @ X463 @ id)))) | ~ ! [X465 : subst,X466 : subst,X467 : term,X468 : subst] : (~ ($true = ((X456 @ X465 @ X467 @ (comp @ X468 @ X466)))) | (((X456 @ (comp @ X465 @ X468) @ (sub @ X467 @ X468) @ X466)) = $true)) | ~ ! [X469 : (subst > term > term)] : (($true = ((X456 @ id @ (lam @ (X469 @ sh @ one)) @ id))) | ~ ! [X470 : subst,X471 : subst,X472 : term] : (((X469 @ (comp @ X471 @ X470) @ (sub @ X472 @ X470))) = ((sub @ (X469 @ X471 @ X472) @ X470))) | ~ ! [X473 : term] : (($true = ((X456 @ id @ (X469 @ id @ X473) @ id))) | ~ (((X456 @ id @ X473 @ id)) = $true)))))))) & ((hoasapinj2 = $true) <=> ! [X474 : term,X475 : term,X476 : term,X477 : term] : ((X476 = X477) | (((ap @ (sub @ X475 @ id) @ X477)) != ((ap @ (sub @ X474 @ id) @ X476))))) & (induction2lem_gthm = $true) & (axmap = $true) & ((axidl = $true) <=> ! [X478 : subst] : (((comp @ id @ X478)) = X478)) & ~ (((var @ (d2term @ d_one))) = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & (! [X479 : term] : ~ ! [X480 : (subst > term > term)] : (((sub @ X479 @ (push @ one @ sh))) != ((X480 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3b = $true) <=> ! [X481 : term] : ~ ! [X482 : (subst > term > term)] : (((sub @ X481 @ (push @ one @ sh))) != ((X482 @ sh @ one)))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem1v2_gthm = $true) & ! [X483 : subst] : ? [X484 : d_subst] : (((d2subst @ X484)) = X483) & ((termmset_lthm = $true) <=> (! [X485 : term] : (((sub @ X485 @ id)) = X485) => ! [X486 : term] : (((sub @ X486 @ id)) = X486))) & ((axvarid = $true) <=> ! [X487 : term] : (((sub @ X487 @ id)) = X487)) & (! [X488 : (subst > term > subst > $o),X489 : term,X490 : term] : (~ ($true = ((X488 @ id @ X490 @ id))) | (((X488 @ id @ (ap @ X490 @ X489) @ id)) = $true) | ~ (((X488 @ id @ X489 @ id)) = $true) | ~ ! [X491 : subst,X492 : subst,X493 : term,X494 : subst] : (~ ($true = ((X488 @ (comp @ X491 @ X492) @ (sub @ X493 @ X492) @ X494))) | ($true = ((X488 @ X491 @ X493 @ (comp @ X492 @ X494))))) | ~ ! [X495 : term,X496 : term] : (~ (((X488 @ id @ X495 @ id)) = $true) | ($true = ((X488 @ id @ (ap @ (sub @ X495 @ id) @ X496) @ id))) | ~ ($true = ((X488 @ id @ X496 @ id)))) | ~ ! [X497 : subst,X498 : term,X499 : subst,X500 : subst] : ((((X488 @ (comp @ X500 @ X497) @ (sub @ X498 @ X497) @ X499)) = $true) | ~ ($true = ((X488 @ X500 @ X498 @ (comp @ X497 @ X499)))))) <=> (hoasinduction_lem2 = $true)) & ((! [X501 : term] : (((sub @ X501 @ id)) = X501) => ! [X502 : (term > $o),X503 : (subst > term > subst > $o),X504 : term] : (($true = ((X502 @ (lam @ X504)))) | ~ ! [X505 : term] : (((X502 @ X505)) = ((X503 @ id @ X505 @ id))) | ~ ! [X506 : subst,X507 : term,X508 : subst,X509 : subst] : (~ ($true = ((X503 @ X508 @ X507 @ (comp @ X509 @ X506)))) | (((X503 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509) @ X506)) = $true)) | ~ ! [X510 : subst,X511 : subst,X512 : term,X513 : subst] : (($true = ((X503 @ X510 @ X512 @ (comp @ X511 @ X513)))) | ~ ($true = ((X503 @ (comp @ X510 @ X511) @ (sub @ X512 @ X511) @ X513)))) | ~ ! [X514 : (subst > term > term)] : (($true = ((X503 @ id @ (lam @ (X514 @ sh @ one)) @ id))) | ~ ! [X515 : term] : ((((X503 @ id @ (X514 @ id @ X515) @ id)) = $true) | ~ ($true = ((X503 @ id @ X515 @ id)))) | ~ ! [X516 : subst,X517 : subst,X518 : term] : (((sub @ (X514 @ X516 @ X518) @ X517)) = ((X514 @ (comp @ X516 @ X517) @ (sub @ X518 @ X517))))) | ~ ! [X519 : term] : (($true = ((X502 @ (sub @ X504 @ (push @ X519 @ id))))) | ~ ($true = ((X502 @ X519)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X520 : term,X521 : (subst > term > subst > $o)] : (~ ! [X522 : (subst > term > term),X523 : term] : (~ ! [X524 : subst,X525 : term,X526 : subst] : (((X522 @ (comp @ X524 @ X526) @ (sub @ X525 @ X526))) = ((sub @ X523 @ (push @ (sub @ X525 @ X526) @ (comp @ X524 @ X526))))) | ~ ! [X527 : term] : (~ ($true = ((X521 @ id @ X527 @ id))) | ($true = ((X521 @ id @ (X522 @ id @ X527) @ id)))) | ($true = ((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id))) | ~ ! [X528 : term,X529 : subst,X530 : subst] : (((sub @ (sub @ X523 @ (push @ X528 @ X529)) @ X530)) = ((sub @ (X522 @ X529 @ X528) @ X530)))) | ($true = ((X521 @ id @ (lam @ (sub @ X520 @ (push @ one @ sh))) @ id))) | ~ ! [X531 : term] : (~ ($true = ((X521 @ id @ X531 @ id))) | ($true = ((X521 @ id @ (sub @ X520 @ (push @ X531 @ id)) @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ((! [X532 : subst] : (((comp @ id @ X532)) = X532) => (! [X533 : subst] : (((comp @ X533 @ id)) = X533) => (! [X534 : subst] : (((comp @ X534 @ id)) = X534) & ! [X535 : subst] : (((comp @ id @ X535)) = X535)))) <=> (substmonoid_lthm = $true)) & (! [X536 : (term > $o),X537 : term] : (~ ! [X538 : term,X539 : term] : (~ ($true = ((X536 @ X539))) | ~ ($true = ((X536 @ X538))) | ($true = ((X536 @ (ap @ X538 @ X539))))) | ~ ! [X540 : term] : (($true = ((X536 @ (lam @ X540)))) | ~ (((X536 @ X540)) = $true)) | ($true = ((X536 @ X537))) | ~ ! [X541 : term] : (($true = ((X536 @ X541))) | ~ ($true = ((var @ X541))))) <=> (induction = $true)) & ((induction2lem = $true) <=> ! [X542 : subst,X543 : term,X544 : (term > $o)] : (~ ! [X545 : term] : (~ ! [X546 : term] : (~ ($true = ((X544 @ X546))) | ($true = ((X544 @ (sub @ X545 @ (push @ X546 @ id)))))) | (((X544 @ (lam @ X545))) = $true)) | (((X544 @ (sub @ X543 @ X542))) = $true) | ~ ! [X547 : term,X548 : term] : (~ ($true = ((X544 @ X548))) | ~ ($true = ((X544 @ X547))) | ($true = ((X544 @ (ap @ X548 @ X547))))) | ~ ! [X549 : term] : (~ (((var @ X549)) = $true) | ($true = ((X544 @ (sub @ X549 @ X542)))))))),
% 2.91/0.81 inference(fool_elimination,[],[f4])).
% 2.91/0.81 thf(f6,plain,(
% 2.91/0.81 ~ (axclos = ! [X0 : subst,X1 : term,X2 : subst] : (((sub @ (sub @ X1 @ X0) @ X2)) = ((sub @ X1 @ (comp @ X0 @ X2)))))),
% 2.91/0.81 inference(rectify,[],[f3])).
% 2.91/0.81 thf(f7,plain,(
% 2.91/0.81 ~ (axclos = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sub @ Y1 @ Y2) @ Y0) = (sub @ Y1 @ (comp @ Y2 @ Y0)))))))))))),
% 2.91/0.81 inference(fool_elimination,[],[f6])).
% 2.91/0.81 thf(f8,plain,(
% 2.91/0.81 (axclos != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sub @ Y1 @ Y2) @ Y0) = (sub @ Y1 @ (comp @ Y2 @ Y0)))))))))))),
% 2.91/0.81 inference(flattening,[],[f7])).
% 2.91/0.81 thf(f9,plain,(
% 2.91/0.81 ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : (($true = ((X4 @ X5))) | ~ ($true = ((var @ X5)))) | ~ ! [X6 : term,X7 : term] : (($true = ((X4 @ (ap @ X7 @ X6)))) | ~ ($true = ((X4 @ X6))) | ~ ($true = ((X4 @ X7)))) | (((X4 @ X3)) = $true) | ~ ! [X8 : term] : (($true = ((X4 @ (lam @ X8)))) | ~ ! [X9 : term] : (~ ($true = ((X4 @ X9))) | ($true = ((X4 @ (sub @ X8 @ (push @ X9 @ id)))))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (subst > term > subst > $o),X13 : (term > $o)] : (($true = ((X13 @ (lam @ X11)))) | ~ ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : (($true = ((X12 @ id @ (X15 @ id @ X16) @ id))) | ~ (((X12 @ id @ X16 @ id)) = $true)) | ($true = ((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))) | ~ ! [X17 : subst,X19 : term,X18 : subst] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) = ((sub @ (X15 @ X18 @ X19) @ X17)))) | ~ ! [X20 : term] : (~ (((X13 @ X20)) = $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X20 @ id))))))) => ! [X21 : term,X22 : (subst > term > subst > $o)] : (~ ! [X23 : term,X24 : term] : (($true = ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id))) | ~ (((X22 @ id @ X23 @ id)) = $true) | ~ ($true = ((X22 @ id @ X24 @ id)))) | ~ ! [X25 : subst,X26 : subst,X27 : subst,X28 : term] : (~ ($true = ((X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25))) | ($true = ((X22 @ X26 @ X28 @ (comp @ X27 @ X25))))) | ~ ! [X29 : term] : (~ ($true = ((var @ (sub @ X29 @ id)))) | ($true = ((X22 @ id @ X29 @ id)))) | ~ ! [X30 : (subst > term > term)] : (~ ! [X33 : term,X31 : subst,X32 : subst] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32)))) | ~ ! [X34 : term] : (($true = ((X22 @ id @ (X30 @ id @ X34) @ id))) | ~ ($true = ((X22 @ id @ X34 @ id)))) | (((X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) = $true)) | (((X22 @ id @ X21 @ id)) = $true) | ~ ! [X35 : term,X36 : subst,X37 : subst,X38 : subst] : (~ (((X22 @ X36 @ X35 @ (comp @ X38 @ X37))) = $true) | (((X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & ~ (ulamvar1 = $true) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X39 : term] : ~ ! [X40 : (subst > term > term)] : ~ ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42))))) & ((axvarcons = $true) <=> ! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> (axscons = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X49 : term,X48 : subst] : (((sub @ one @ (push @ X49 @ X48))) = X49) => (! [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) = X51) => ! [X52 : term,X53 : term,X54 : subst,X55 : (term > $o),X56 : (term > $o)] : (~ ($true = ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))))) & (! [X57 : term,X58 : (subst > term > subst > $o)] : (~ ! [X59 : (subst > term > term)] : (~ ! [X62 : subst,X60 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) | ~ ! [X63 : term] : ((((X58 @ id @ (X59 @ id @ X63) @ id)) = $true) | ~ ($true = ((X58 @ id @ X63 @ id)))) | ($true = ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id)))) | ~ ! [X64 : term] : (~ ($true = ((X58 @ id @ X64 @ id))) | ($true = ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id)))) | (((X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & (termmset_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X66 : term,X65 : subst] : (((sub @ one @ (push @ X66 @ X65))) = X66) => (! [X68 : subst,X67 : term] : (((comp @ sh @ (push @ X67 @ X68))) = X68) => (! [X69 : subst] : (((comp @ X69 @ id)) = X69) => (! [X70 : term,X71 : (term > $o)] : (~ ! [X72 : term] : (~ ($true = ((var @ X72))) | ($true = ((X71 @ X72)))) | ~ ! [X73 : term,X74 : term] : (~ ($true = ((X71 @ X74))) | ($true = ((X71 @ (ap @ X74 @ X73)))) | ~ (((X71 @ X73)) = $true)) | ($true = ((X71 @ X70))) | ~ ! [X75 : term] : (($true = ((X71 @ (lam @ X75)))) | ~ ($true = ((X71 @ X75))))) => ! [X76 : subst,X77 : term,X78 : (term > $o)] : (~ ! [X79 : term,X80 : term] : (~ (((X78 @ X79)) = $true) | (((X78 @ (ap @ X80 @ X79))) = $true) | ~ (((X78 @ X80)) = $true)) | ~ ! [X81 : term] : (~ ($true = ((var @ X81))) | ($true = ((X78 @ (sub @ X81 @ X76))))) | ($true = ((X78 @ (sub @ X77 @ X76)))) | ~ ! [X82 : term] : (~ ! [X83 : term] : (($true = ((X78 @ (sub @ X82 @ (push @ X83 @ id))))) | ~ ($true = ((X78 @ X83)))) | ($true = ((X78 @ (lam @ X82))))))))))) & ((shinj = $true) <=> ! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85))) & (hoasinduction_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) = X86) => ! [X88 : (term > $o),X89 : term,X90 : subst,X91 : (term > $o)] : ((((X88 @ one)) = $true) | ~ ($true = ((X91 @ X89))) | ~ ! [X92 : term] : (((X88 @ X92)) = ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))))) & ! [X93 : d_subst] : (d_id = X93) & (! [X94 : term,X95 : (subst > term > subst > $o)] : (~ ! [X96 : term] : (~ ($true = ((X95 @ id @ X96 @ id))) | ($true = ((X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id)))) | (((X95 @ id @ (lam @ X94) @ id)) = $true) | ~ ! [X97 : (subst > term > term)] : (~ ! [X98 : subst,X100 : subst,X99 : term] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98))) | ~ ! [X101 : term] : (~ ($true = ((X95 @ id @ X101 @ id))) | ($true = ((X95 @ id @ (X97 @ id @ X101) @ id)))) | (((X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) = $true)) | ~ ! [X102 : subst,X103 : subst,X104 : term,X105 : subst] : (($true = ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105))) | ~ ($true = ((X95 @ X103 @ X104 @ (comp @ X102 @ X105))))) | ~ ! [X106 : term,X107 : subst,X108 : subst,X109 : subst] : (($true = ((X95 @ X109 @ X106 @ (comp @ X107 @ X108)))) | ~ (((X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108)) = $true))) <=> (hoasinduction_lem3 = $true)) & (axapp = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & (! [X110 : (subst > term > subst > $o)] : ~ ! [X111 : (term > $o)] : ~ ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X113 : (subst > term > subst > $o)] : ~ ! [X114 : (term > $o)] : ~ ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id)))) & ((! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X119 : term,X120 : term,X118 : term,X117 : term] : ((((ap @ X117 @ X118)) != ((ap @ X120 @ X119))) | (X117 = X120)) => ! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)))) <=> (hoasapinj1_lthm = $true)) & ((axshiftcons = $true) <=> ! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X127 : term,X128 : (subst > term > subst > $o)] : (~ ! [X129 : (subst > term > term)] : ((((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id)) = $true) | ~ ! [X130 : term] : (($true = ((X128 @ id @ (X129 @ id @ X130) @ id))) | ~ ($true = ((X128 @ id @ X130 @ id)))) | ~ ! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133))))) | ($true = ((X128 @ id @ X127 @ id))) | ~ ! [X134 : term,X135 : term] : (~ ($true = ((X128 @ id @ X135 @ id))) | ($true = ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id))) | ~ (((X128 @ id @ X134 @ id)) = $true)))) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) <=> (axidr = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X137 : (subst > term > subst > $o),X138 : (term > $o),X139 : term] : (~ ! [X140 : (subst > term > term)] : (~ ! [X143 : subst,X142 : subst,X141 : term] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) | ~ ! [X144 : term] : (($true = ((X137 @ id @ (X140 @ id @ X144) @ id))) | ~ (((X137 @ id @ X144 @ id)) = $true)) | (((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) = $true)) | ~ ! [X145 : term] : (((X138 @ X145)) = ((X137 @ id @ X145 @ id))) | ~ ! [X146 : subst,X147 : term,X148 : subst,X149 : subst] : ((((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148)) = $true) | ~ ($true = ((X137 @ X149 @ X147 @ (comp @ X146 @ X148))))) | ~ ! [X150 : term] : (~ (((X138 @ X150)) = $true) | ($true = ((X138 @ (sub @ X139 @ (push @ X150 @ id)))))) | ~ ! [X151 : term,X152 : subst,X153 : subst,X154 : subst] : ((((X137 @ X152 @ X151 @ (comp @ X153 @ X154))) = $true) | ~ ($true = ((X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154)))) | ($true = ((X138 @ (lam @ X139))))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_lem3v2 = $true) & ! [X155 : d_subst,X156 : d_subst] : ((((d2subst @ X155)) = ((d2subst @ X156))) => (X155 = X156)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasapinj2_gthm = $true) & (substmonoid_gthm = $true) & (hoaslamnotap_gthm = $true) & ~ (lamnotap = $true) & ((induction2 = $true) <=> ! [X157 : term,X158 : (term > $o)] : (~ ! [X159 : term] : (~ ! [X160 : term] : (~ ($true = ((X158 @ X160))) | ($true = ((X158 @ (sub @ X159 @ (push @ X160 @ id)))))) | (((X158 @ (lam @ X159))) = $true)) | ~ ! [X161 : term] : (($true = ((X158 @ X161))) | ~ ($true = ((var @ X161)))) | ~ ! [X162 : term,X163 : term] : (~ (((X158 @ X163)) = $true) | ($true = ((X158 @ (ap @ X162 @ X163)))) | ~ ($true = ((X158 @ X162)))) | ($true = ((X158 @ X157))))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X164 : (subst > term > subst > $o)] : ~ ! [X165 : (term > $o)] : ~ ! [X166 : term] : (((X165 @ X166)) = ((X164 @ id @ X166 @ id))) => (! [X167 : term,X168 : (term > $o)] : (($true = ((X168 @ X167))) | ~ ! [X169 : term,X170 : term] : (~ (((X168 @ X169)) = $true) | (((X168 @ (ap @ X169 @ X170))) = $true) | ~ ($true = ((X168 @ X170)))) | ~ ! [X171 : term] : (($true = ((X168 @ (lam @ X171)))) | ~ ! [X172 : term] : (($true = ((X168 @ (sub @ X171 @ (push @ X172 @ id))))) | ~ ($true = ((X168 @ X172))))) | ~ ! [X173 : term] : ((((X168 @ X173)) = $true) | ~ (((var @ X173)) = $true))) => (! [X174 : term] : (((sub @ X174 @ id)) = X174) => (! [X175 : (term > $o),X176 : (subst > term > subst > $o),X177 : term] : (~ ! [X178 : term] : (($true = ((X175 @ (sub @ X177 @ (push @ X178 @ id))))) | ~ ($true = ((X175 @ X178)))) | ~ ! [X179 : (subst > term > term)] : ((((X176 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ~ ! [X181 : term,X180 : subst,X182 : subst] : (((sub @ (X179 @ X180 @ X181) @ X182)) = ((X179 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182)))) | ~ ! [X183 : term] : ((((X176 @ id @ (X179 @ id @ X183) @ id)) = $true) | ~ (((X176 @ id @ X183 @ id)) = $true))) | ~ ! [X184 : term] : (((X176 @ id @ X184 @ id)) = ((X175 @ X184))) | (((X175 @ (lam @ X177))) = $true)) => ! [X185 : (subst > term > subst > $o),X186 : term] : (~ ! [X187 : term,X188 : term] : (~ ($true = ((X185 @ id @ X188 @ id))) | ($true = ((X185 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id))) | ~ ($true = ((X185 @ id @ X187 @ id)))) | ~ ! [X189 : (subst > term > term)] : (~ ! [X190 : subst,X192 : subst,X191 : term] : (((sub @ (X189 @ X190 @ X191) @ X192)) = ((X189 @ (comp @ X190 @ X192) @ (sub @ X191 @ X192)))) | ($true = ((X185 @ id @ (lam @ (X189 @ sh @ one)) @ id))) | ~ ! [X193 : term] : (~ ($true = ((X185 @ id @ X193 @ id))) | (((X185 @ id @ (X189 @ id @ X193) @ id)) = $true))) | (((X185 @ id @ X186 @ id)) = $true)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (axabs = $true) & (pushprop_gthm = $true) & (! [X194 : term] : (((sub @ X194 @ id)) = X194) <=> (termmset = $true)) & (hoaslamnotvar_lthm = $true) & ((apinj2 = $true) <=> ! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198))) & (hoasinduction_lem1v2 = $true) & (ulamvarsh = $true) & ((pushprop_lem1v2 = $true) <=> ! [X199 : subst,X200 : term,X201 : (term > $o),X202 : (term > $o)] : (~ ! [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) = ((X202 @ X203))) | ($true = ((X202 @ one))) | ~ ($true = ((X201 @ X200))))) & (pushprop_lem3v2_lthm = $true) & ! [X205 : d_term,X204 : d_term] : ((((d2term @ X204)) = ((d2term @ X205))) => (X204 = X205)) & (hoasinduction_lem3_gthm = $true) & (lamnotvar = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X206 : term] : (((sub @ X206 @ id)) = X206) => (! [X207 : term,X208 : (subst > term > subst > $o)] : (~ ! [X209 : term] : (~ (((X208 @ id @ X209 @ id)) = $true) | ($true = ((X208 @ id @ (sub @ X207 @ (push @ X209 @ id)) @ id)))) | ($true = ((X208 @ id @ (lam @ (sub @ X207 @ (push @ one @ sh))) @ id))) | ~ ! [X210 : (subst > term > term)] : (~ ! [X211 : term,X212 : subst,X213 : subst] : (((sub @ (X210 @ X212 @ X211) @ X213)) = ((X210 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213)))) | ~ ! [X214 : term] : (~ ($true = ((X208 @ id @ X214 @ id))) | ($true = ((X208 @ id @ (X210 @ id @ X214) @ id)))) | ($true = ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id))))) => ! [X215 : term,X216 : (subst > term > subst > $o)] : (~ ! [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (~ (((X216 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220) @ X217)) = $true) | ($true = ((X216 @ X218 @ X219 @ (comp @ X220 @ X217))))) | ~ ! [X221 : (subst > term > term)] : (~ ! [X223 : term,X224 : subst,X222 : subst] : (((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))) = ((sub @ (X221 @ X224 @ X223) @ X222))) | ($true = ((X216 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ~ ! [X225 : term] : (~ ($true = ((X216 @ id @ X225 @ id))) | (((X216 @ id @ (X221 @ id @ X225) @ id)) = $true))) | ~ ! [X226 : term] : (~ (((X216 @ id @ X226 @ id)) = $true) | ($true = ((X216 @ id @ (sub @ X215 @ (push @ X226 @ id)) @ id)))) | ($true = ((X216 @ id @ (lam @ X215) @ id))) | ~ ! [X227 : subst,X228 : subst,X229 : term,X230 : subst] : (~ ($true = ((X216 @ X227 @ X229 @ (comp @ X230 @ X228)))) | ($true = ((X216 @ (comp @ X227 @ X230) @ (sub @ X229 @ X230) @ X228)))))))) & (ulamvarind = $true) & (one = ((d2term @ d_one))) & (! [X233 : subst,X231 : (term > $o),X232 : term] : ~ ! [X234 : (term > $o)] : ~ ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X236 : term,X237 : term,X238 : (subst > term > subst > $o),X239 : (term > $o)] : (~ ! [X240 : term,X241 : subst,X242 : subst,X243 : subst] : (($true = ((X238 @ (comp @ X241 @ X243) @ (sub @ X240 @ X243) @ X242))) | ~ ($true = ((X238 @ X241 @ X240 @ (comp @ X243 @ X242))))) | ($true = ((X239 @ (ap @ X236 @ X237)))) | ~ ! [X244 : term] : (((X238 @ id @ X244 @ id)) = ((X239 @ X244))) | ~ ! [X245 : term,X246 : term] : (~ (((X238 @ id @ X246 @ id)) = $true) | ~ (((X238 @ id @ X245 @ id)) = $true) | (((X238 @ id @ (ap @ (sub @ X246 @ id) @ X245) @ id)) = $true)) | ~ ($true = ((X239 @ X236))) | ~ ! [X247 : subst,X248 : term,X249 : subst,X250 : subst] : (~ ($true = ((X238 @ (comp @ X247 @ X250) @ (sub @ X248 @ X250) @ X249))) | ($true = ((X238 @ X247 @ X248 @ (comp @ X250 @ X249))))) | ~ ($true = ((X239 @ X237))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X252 : term,X251 : term,X253 : term,X254 : term] : ((X252 = X254) | (((ap @ X253 @ X254)) != ((ap @ X251 @ X252)))) => ! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257))) <=> (hoasapinj2_lthm = $true)) & (axvarshift = $true) & ((substmonoid = $true) <=> (! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259))) & (hoasinduction_lem2v2_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) <=> (laminj = $true)) & ! [X263 : d_term] : (d_one = X263) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X264 : term] : ~ ! [X265 : (subst > term > term)] : ~ ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266))))) & (! [X268 : (subst > term > subst > $o),X269 : term] : (~ ! [X270 : (subst > term > term)] : (~ ! [X271 : term] : (~ (((X268 @ id @ X271 @ id)) = $true) | ($true = ((X268 @ id @ (X270 @ id @ X271) @ id)))) | ~ ! [X273 : term,X272 : subst,X274 : subst] : (((sub @ (X270 @ X272 @ X273) @ X274)) = ((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)))) | ($true = ((X268 @ id @ (lam @ (X270 @ sh @ one)) @ id)))) | ~ ! [X275 : term] : (($true = ((X268 @ id @ (sub @ X269 @ (push @ X275 @ id)) @ id))) | ~ ($true = ((X268 @ id @ X275 @ id)))) | ($true = ((X268 @ id @ (lam @ X269) @ id)))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((d2subst @ d_id)) = sh) & ((hoaslaminj = $true) <=> ! [X276 : subst,X277 : (subst > term > term),X279 : (subst > term > term),X278 : term] : ((((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ~ ! [X282 : subst,X280 : subst,X281 : term] : (((sub @ (X277 @ X282 @ X281) @ X280)) = ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280)))) | (((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ~ ! [X284 : term,X283 : subst,X285 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) = ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))))) & (axclos = $true) & (! [X286 : (term > $o),X287 : term,X288 : (subst > term > subst > $o)] : (~ ! [X289 : term] : (((X286 @ X289)) = ((X288 @ id @ X289 @ id))) | ~ ! [X290 : (subst > term > term)] : (~ ! [X291 : term] : (($true = ((X288 @ id @ (X290 @ id @ X291) @ id))) | ~ ($true = ((X288 @ id @ X291 @ id)))) | ($true = ((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id))) | ~ ! [X293 : subst,X294 : subst,X292 : term] : (((X290 @ (comp @ X293 @ X294) @ (sub @ X292 @ X294))) = ((sub @ (X290 @ X293 @ X292) @ X294)))) | ($true = ((X286 @ (lam @ X287)))) | ~ ! [X295 : term] : (~ ($true = ((X286 @ X295))) | ($true = ((X286 @ (sub @ X287 @ (push @ X295 @ id))))))) <=> (hoasinduction_lem3v2a = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoaslamnotap = $true) <=> ! [X298 : (subst > term > term),X297 : term,X296 : term] : (~ ! [X299 : term,X301 : subst,X300 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one)))))) & ((hoasinduction = $true) <=> ! [X302 : (subst > term > subst > $o),X303 : term] : (~ ! [X304 : term] : (~ (((var @ (sub @ X304 @ id))) = $true) | (((X302 @ id @ X304 @ id)) = $true)) | ~ ! [X305 : (subst > term > term)] : (~ ! [X306 : term] : (~ (((X302 @ id @ X306 @ id)) = $true) | (((X302 @ id @ (X305 @ id @ X306) @ id)) = $true)) | (((X302 @ id @ (lam @ (X305 @ sh @ one)) @ id)) = $true) | ~ ! [X308 : term,X307 : subst,X309 : subst] : (((X305 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307))) = ((sub @ (X305 @ X309 @ X308) @ X307)))) | ~ ! [X310 : term,X311 : subst,X312 : subst,X313 : subst] : (~ ($true = ((X302 @ (comp @ X311 @ X313) @ (sub @ X310 @ X313) @ X312))) | ($true = ((X302 @ X311 @ X310 @ (comp @ X313 @ X312))))) | ~ ! [X314 : subst,X315 : subst,X316 : term,X317 : subst] : (($true = ((X302 @ (comp @ X314 @ X317) @ (sub @ X316 @ X317) @ X315))) | ~ ($true = ((X302 @ X314 @ X316 @ (comp @ X317 @ X315))))) | ~ ! [X318 : term,X319 : term] : (($true = ((X302 @ id @ (ap @ (sub @ X318 @ id) @ X319) @ id))) | ~ ($true = ((X302 @ id @ X319 @ id))) | ~ ($true = ((X302 @ id @ X318 @ id)))) | ($true = ((X302 @ id @ X303 @ id))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X320 : (subst > term > subst > $o),X321 : term] : (($true = ((X320 @ id @ (lam @ (sub @ X321 @ (push @ one @ sh))) @ id))) | ~ ! [X322 : (subst > term > term)] : (~ ! [X325 : subst,X324 : subst,X323 : term] : (((X322 @ (comp @ X324 @ X325) @ (sub @ X323 @ X325))) = ((sub @ (X322 @ X324 @ X323) @ X325))) | ~ ! [X326 : term] : (($true = ((X320 @ id @ (X322 @ id @ X326) @ id))) | ~ ($true = ((X320 @ id @ X326 @ id)))) | ($true = ((X320 @ id @ (lam @ (X322 @ sh @ one)) @ id)))) | ~ ! [X327 : term] : (~ ($true = ((X320 @ id @ X327 @ id))) | ($true = ((X320 @ id @ (sub @ X321 @ (push @ X327 @ id)) @ id)))))) & (! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) <=> (apinj1 = $true)) & ((! [X332 : term] : (((sub @ X332 @ id)) = X332) => (! [X333 : term,X334 : (subst > term > subst > $o)] : (~ ! [X335 : term] : ((((X334 @ id @ (sub @ X333 @ (push @ X335 @ id)) @ id)) = $true) | ~ (((X334 @ id @ X335 @ id)) = $true)) | (((X334 @ id @ (lam @ (sub @ X333 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X336 : (subst > term > term)] : (($true = ((X334 @ id @ (lam @ (X336 @ sh @ one)) @ id))) | ~ ! [X338 : term,X339 : subst,X337 : subst] : (((X336 @ (comp @ X339 @ X337) @ (sub @ X338 @ X337))) = ((sub @ (X336 @ X339 @ X338) @ X337))) | ~ ! [X340 : term] : (($true = ((X334 @ id @ (X336 @ id @ X340) @ id))) | ~ ($true = ((X334 @ id @ X340 @ id)))))) => ! [X341 : term,X342 : (subst > term > subst > $o)] : (~ ! [X343 : (subst > term > term)] : (($true = ((X342 @ id @ (lam @ (X343 @ sh @ one)) @ id))) | ~ ! [X344 : term] : (~ (((X342 @ id @ X344 @ id)) = $true) | ($true = ((X342 @ id @ (X343 @ id @ X344) @ id)))) | ~ ! [X345 : subst,X346 : term,X347 : subst] : (((sub @ (X343 @ X345 @ X346) @ X347)) = ((X343 @ (comp @ X345 @ X347) @ (sub @ X346 @ X347))))) | ~ ! [X348 : term] : (~ ($true = ((X342 @ id @ X348 @ id))) | (((X342 @ id @ (sub @ X341 @ (push @ X348 @ id)) @ id)) = $true)) | ($true = ((X342 @ id @ (lam @ X341) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (pushprop_lthm = $true) & (apnotvar = $true) & ((! [X349 : term] : ~ ! [X350 : (subst > term > term)] : ~ ! [X352 : term,X351 : subst] : (((sub @ X349 @ (push @ X352 @ X351))) = ((X350 @ X351 @ X352))) => (! [X353 : term] : (((sub @ X353 @ id)) = X353) => ! [X354 : term,X355 : (subst > term > subst > $o),X356 : (term > $o)] : (~ ! [X357 : term] : (((X356 @ X357)) = ((X355 @ id @ X357 @ id))) | ~ ! [X358 : (subst > term > term)] : ((((X355 @ id @ (lam @ (X358 @ sh @ one)) @ id)) = $true) | ~ ! [X361 : term,X359 : subst,X360 : subst] : (((sub @ (X358 @ X359 @ X361) @ X360)) = ((X358 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360)))) | ~ ! [X362 : term] : (~ ($true = ((X355 @ id @ X362 @ id))) | ($true = ((X355 @ id @ (X358 @ id @ X362) @ id))))) | ~ ! [X363 : term] : (~ ($true = ((X356 @ X363))) | ($true = ((X356 @ (sub @ X354 @ (push @ X363 @ id)))))) | (((X356 @ (lam @ X354))) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((induction2_lthm = $true) <=> (! [X364 : term] : (((sub @ X364 @ id)) = X364) => (! [X365 : subst,X366 : (term > $o),X367 : term] : (~ ! [X368 : term] : ((((X366 @ (lam @ X368))) = $true) | ~ ! [X369 : term] : (~ (((X366 @ X369)) = $true) | (((X366 @ (sub @ X368 @ (push @ X369 @ id)))) = $true))) | (((X366 @ (sub @ X367 @ X365))) = $true) | ~ ! [X370 : term] : (~ ($true = ((var @ X370))) | ($true = ((X366 @ (sub @ X370 @ X365))))) | ~ ! [X371 : term,X372 : term] : (~ ($true = ((X366 @ X371))) | ~ (((X366 @ X372)) = $true) | (((X366 @ (ap @ X372 @ X371))) = $true))) => ! [X373 : (term > $o),X374 : term] : (~ ! [X375 : term,X376 : term] : (~ ($true = ((X373 @ X375))) | ($true = ((X373 @ (ap @ X376 @ X375)))) | ~ ($true = ((X373 @ X376)))) | ($true = ((X373 @ X374))) | ~ ! [X377 : term] : (~ ($true = ((var @ X377))) | (((X373 @ X377)) = $true)) | ~ ! [X378 : term] : (~ ! [X379 : term] : (~ (((X373 @ X379)) = $true) | ($true = ((X373 @ (sub @ X378 @ (push @ X379 @ id)))))) | ($true = ((X373 @ (lam @ X378))))))))) & (hoaslamnotvar = $true) & (hoasinduction_lem3a_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X380 : subst,X381 : term,X382 : (term > $o),X383 : (term > $o),X384 : term] : (~ ($true = ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & ((hoaslaminj_lthm = $true) <=> (! [X386 : subst,X385 : term] : (((sub @ one @ (push @ X385 @ X386))) = X385) => (! [X388 : term,X387 : subst] : (((comp @ sh @ (push @ X388 @ X387))) = X387) => (! [X390 : term,X389 : term] : ((((lam @ X389)) != ((lam @ X390))) | (X389 = X390)) => ! [X392 : (subst > term > term),X393 : term,X391 : subst,X394 : (subst > term > term)] : (~ ! [X396 : subst,X397 : term,X395 : subst] : (((sub @ (X392 @ X395 @ X397) @ X396)) = ((X392 @ (comp @ X395 @ X396) @ (sub @ X397 @ X396)))) | (((lam @ (X394 @ sh @ one))) != ((lam @ (X392 @ sh @ one)))) | ~ ! [X399 : term,X400 : subst,X398 : subst] : (((X394 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X394 @ X398 @ X399) @ X400))) | (((X392 @ X391 @ X393)) = ((X394 @ X391 @ X393)))))))) & (hoaslamnotvar_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X403 : term,X402 : (term > $o),X401 : subst] : ~ ! [X404 : (term > $o)] : ~ ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm_orig = $true) & (! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X410 : (term > $o),X411 : term] : (~ ! [X412 : term] : (~ ($true = ((var @ X412))) | ($true = ((X410 @ X412)))) | ~ ! [X413 : term] : (($true = ((X410 @ (lam @ X413)))) | ~ ! [X414 : term] : (($true = ((X410 @ (sub @ X413 @ (push @ X414 @ id))))) | ~ (((X410 @ X414)) = $true))) | ~ ! [X415 : term,X416 : term] : (($true = ((X410 @ (ap @ X416 @ X415)))) | ~ ($true = ((X410 @ X416))) | ~ (((X410 @ X415)) = $true)) | ($true = ((X410 @ X411)))) => (! [X417 : (subst > term > subst > $o),X418 : term,X419 : term] : (~ ! [X420 : subst,X421 : subst,X422 : term,X423 : subst] : (~ ($true = ((X417 @ (comp @ X421 @ X420) @ (sub @ X422 @ X420) @ X423))) | ($true = ((X417 @ X421 @ X422 @ (comp @ X420 @ X423))))) | ~ ! [X424 : subst,X425 : term,X426 : subst,X427 : subst] : (~ ($true = ((X417 @ X424 @ X425 @ (comp @ X426 @ X427)))) | ($true = ((X417 @ (comp @ X424 @ X426) @ (sub @ X425 @ X426) @ X427)))) | ($true = ((X417 @ id @ (ap @ X419 @ X418) @ id))) | ~ ($true = ((X417 @ id @ X418 @ id))) | ~ ($true = ((X417 @ id @ X419 @ id))) | ~ ! [X428 : term,X429 : term] : (~ ($true = ((X417 @ id @ X428 @ id))) | ($true = ((X417 @ id @ (ap @ (sub @ X429 @ id) @ X428) @ id))) | ~ (((X417 @ id @ X429 @ id)) = $true))) => (! [X430 : term,X431 : (subst > term > subst > $o)] : (~ ! [X432 : subst,X433 : term,X434 : subst,X435 : subst] : (($true = ((X431 @ X435 @ X433 @ (comp @ X434 @ X432)))) | ~ ($true = ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434) @ X432)))) | ($true = ((X431 @ id @ (lam @ X430) @ id))) | ~ ! [X436 : (subst > term > term)] : ((((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ~ ! [X439 : subst,X437 : subst,X438 : term] : (((X436 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437))) = ((sub @ (X436 @ X439 @ X438) @ X437))) | ~ ! [X440 : term] : (($true = ((X431 @ id @ (X436 @ id @ X440) @ id))) | ~ ($true = ((X431 @ id @ X440 @ id))))) | ~ ! [X441 : term] : (~ ($true = ((X431 @ id @ X441 @ id))) | ($true = ((X431 @ id @ (sub @ X430 @ (push @ X441 @ id)) @ id)))) | ~ ! [X442 : term,X443 : subst,X444 : subst,X445 : subst] : ((((X431 @ (comp @ X445 @ X443) @ (sub @ X442 @ X443) @ X444)) = $true) | ~ ($true = ((X431 @ X445 @ X442 @ (comp @ X443 @ X444)))))) => ! [X446 : (subst > term > subst > $o),X447 : term] : (~ ! [X448 : subst,X449 : term,X450 : subst,X451 : subst] : (($true = ((X446 @ X450 @ X449 @ (comp @ X451 @ X448)))) | ~ ($true = ((X446 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451) @ X448)))) | ($true = ((X446 @ id @ X447 @ id))) | ~ ! [X452 : term] : (~ ($true = ((var @ (sub @ X452 @ id)))) | (((X446 @ id @ X452 @ id)) = $true)) | ~ ! [X453 : term,X454 : term] : ((((X446 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id)) = $true) | ~ ($true = ((X446 @ id @ X454 @ id))) | ~ ($true = ((X446 @ id @ X453 @ id)))) | ~ ! [X455 : subst,X456 : subst,X457 : term,X458 : subst] : (~ (((X446 @ X455 @ X457 @ (comp @ X458 @ X456))) = $true) | (((X446 @ (comp @ X455 @ X458) @ (sub @ X457 @ X458) @ X456)) = $true)) | ~ ! [X459 : (subst > term > term)] : (($true = ((X446 @ id @ (lam @ (X459 @ sh @ one)) @ id))) | ~ ! [X460 : subst,X461 : subst,X462 : term] : (((X459 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460))) = ((sub @ (X459 @ X461 @ X462) @ X460))) | ~ ! [X463 : term] : (($true = ((X446 @ id @ (X459 @ id @ X463) @ id))) | ~ (((X446 @ id @ X463 @ id)) = $true)))))))) & ((hoasapinj2 = $true) <=> ! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467))) & (induction2lem_gthm = $true) & (axmap = $true) & ((axidl = $true) <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & ~ (((var @ (d2term @ d_one))) = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X469 : term] : ~ ! [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) != ((X470 @ sh @ one)))) & (((d2subst @ d_id)) = id) & (! [X471 : term] : ~ ! [X472 : (subst > term > term)] : (((X472 @ sh @ one)) != ((sub @ X471 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem1v2_gthm = $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & ((! [X475 : term] : (((sub @ X475 @ id)) = X475) => ! [X476 : term] : (((sub @ X476 @ id)) = X476)) <=> (termmset_lthm = $true)) & (! [X477 : term] : (((sub @ X477 @ id)) = X477) <=> (axvarid = $true)) & (! [X478 : (subst > term > subst > $o),X479 : term,X480 : term] : (~ ($true = ((X478 @ id @ X480 @ id))) | ($true = ((X478 @ id @ (ap @ X480 @ X479) @ id))) | ~ (((X478 @ id @ X479 @ id)) = $true) | ~ ! [X481 : subst,X482 : subst,X483 : term,X484 : subst] : (~ ($true = ((X478 @ (comp @ X481 @ X482) @ (sub @ X483 @ X482) @ X484))) | ($true = ((X478 @ X481 @ X483 @ (comp @ X482 @ X484))))) | ~ ! [X485 : term,X486 : term] : (~ ($true = ((X478 @ id @ X485 @ id))) | (((X478 @ id @ (ap @ (sub @ X485 @ id) @ X486) @ id)) = $true) | ~ ($true = ((X478 @ id @ X486 @ id)))) | ~ ! [X487 : subst,X488 : term,X489 : subst,X490 : subst] : (($true = ((X478 @ (comp @ X490 @ X487) @ (sub @ X488 @ X487) @ X489))) | ~ ($true = ((X478 @ X490 @ X488 @ (comp @ X487 @ X489)))))) <=> (hoasinduction_lem2 = $true)) & ((! [X491 : term] : (((sub @ X491 @ id)) = X491) => ! [X492 : (term > $o),X493 : (subst > term > subst > $o),X494 : term] : (($true = ((X492 @ (lam @ X494)))) | ~ ! [X495 : term] : (((X493 @ id @ X495 @ id)) = ((X492 @ X495))) | ~ ! [X496 : subst,X497 : term,X498 : subst,X499 : subst] : (~ ($true = ((X493 @ X498 @ X497 @ (comp @ X499 @ X496)))) | ($true = ((X493 @ (comp @ X498 @ X499) @ (sub @ X497 @ X499) @ X496)))) | ~ ! [X500 : subst,X501 : subst,X502 : term,X503 : subst] : (($true = ((X493 @ X500 @ X502 @ (comp @ X501 @ X503)))) | ~ (((X493 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) = $true)) | ~ ! [X504 : (subst > term > term)] : (($true = ((X493 @ id @ (lam @ (X504 @ sh @ one)) @ id))) | ~ ! [X505 : term] : ((((X493 @ id @ (X504 @ id @ X505) @ id)) = $true) | ~ ($true = ((X493 @ id @ X505 @ id)))) | ~ ! [X508 : term,X507 : subst,X506 : subst] : (((X504 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507))) = ((sub @ (X504 @ X506 @ X508) @ X507)))) | ~ ! [X509 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X509 @ id))))) | ~ ($true = ((X492 @ X509)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X510 : term,X511 : (subst > term > subst > $o)] : (~ ! [X512 : (subst > term > term),X513 : term] : (~ ! [X515 : term,X514 : subst,X516 : subst] : (((sub @ X513 @ (push @ (sub @ X515 @ X516) @ (comp @ X514 @ X516)))) = ((X512 @ (comp @ X514 @ X516) @ (sub @ X515 @ X516)))) | ~ ! [X517 : term] : (~ (((X511 @ id @ X517 @ id)) = $true) | ($true = ((X511 @ id @ (X512 @ id @ X517) @ id)))) | ($true = ((X511 @ id @ (lam @ (X512 @ sh @ one)) @ id))) | ~ ! [X520 : subst,X518 : term,X519 : subst] : (((sub @ (X512 @ X519 @ X518) @ X520)) = ((sub @ (sub @ X513 @ (push @ X518 @ X519)) @ X520)))) | (((X511 @ id @ (lam @ (sub @ X510 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X521 : term] : (~ ($true = ((X511 @ id @ X521 @ id))) | (((X511 @ id @ (sub @ X510 @ (push @ X521 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & ((! [X522 : subst] : (((comp @ id @ X522)) = X522) => (! [X523 : subst] : (((comp @ X523 @ id)) = X523) => (! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)))) <=> (substmonoid_lthm = $true)) & (! [X526 : (term > $o),X527 : term] : (~ ! [X528 : term,X529 : term] : (~ ($true = ((X526 @ X529))) | ~ ($true = ((X526 @ X528))) | ($true = ((X526 @ (ap @ X528 @ X529))))) | ~ ! [X530 : term] : (($true = ((X526 @ (lam @ X530)))) | ~ ($true = ((X526 @ X530)))) | ($true = ((X526 @ X527))) | ~ ! [X531 : term] : (($true = ((X526 @ X531))) | ~ ($true = ((var @ X531))))) <=> (induction = $true)) & ((induction2lem = $true) <=> ! [X532 : subst,X533 : term,X534 : (term > $o)] : (~ ! [X535 : term] : (~ ! [X536 : term] : (~ ($true = ((X534 @ X536))) | ($true = ((X534 @ (sub @ X535 @ (push @ X536 @ id)))))) | ($true = ((X534 @ (lam @ X535))))) | ($true = ((X534 @ (sub @ X533 @ X532)))) | ~ ! [X537 : term,X538 : term] : (~ ($true = ((X534 @ X538))) | ~ ($true = ((X534 @ X537))) | (((X534 @ (ap @ X538 @ X537))) = $true)) | ~ ! [X539 : term] : (~ ($true = ((var @ X539))) | ($true = ((X534 @ (sub @ X539 @ X532)))))))),
% 2.91/0.81 inference(rectify,[],[f5])).
% 2.91/0.81 thf(f10,plain,(
% 2.91/0.81 (hoasinduction_lem1_lthm = $true) & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : ((((X4 @ X3)) = $true) | ~ ! [X7 : term,X6 : term] : (($true != ((X4 @ X7))) | ($true = ((X4 @ (ap @ X7 @ X6)))) | ($true != ((X4 @ X6)))) | ~ ! [X5 : term] : (($true != ((var @ X5))) | ($true = ((X4 @ X5)))) | ~ ! [X8 : term] : (~ ! [X9 : term] : (($true != ((X4 @ X9))) | ($true = ((X4 @ (sub @ X8 @ (push @ X9 @ id)))))) | ($true = ((X4 @ (lam @ X8)))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X12 : (subst > term > subst > $o),X13 : (term > $o),X11 : term] : (~ ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) | ~ ! [X20 : term] : (($true = ((X13 @ (sub @ X11 @ (push @ X20 @ id))))) | (((X13 @ X20)) != $true)) | ($true = ((X13 @ (lam @ X11)))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : (($true = ((X12 @ id @ (X15 @ id @ X16) @ id))) | (((X12 @ id @ X16 @ id)) != $true)) | ~ ! [X17 : subst,X19 : term,X18 : subst] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) = ((sub @ (X15 @ X18 @ X19) @ X17))) | ($true = ((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))))) => ! [X22 : (subst > term > subst > $o),X21 : term] : (~ ! [X38 : subst,X36 : subst,X35 : term,X37 : subst] : ((((X22 @ X36 @ X35 @ (comp @ X38 @ X37))) != $true) | (((X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37)) = $true)) | ~ ! [X29 : term] : (($true = ((X22 @ id @ X29 @ id))) | ($true != ((var @ (sub @ X29 @ id))))) | (((X22 @ id @ X21 @ id)) = $true) | ~ ! [X24 : term,X23 : term] : ((((X22 @ id @ X23 @ id)) != $true) | ($true = ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id))) | ($true != ((X22 @ id @ X24 @ id)))) | ~ ! [X30 : (subst > term > term)] : (~ ! [X33 : term,X31 : subst,X32 : subst] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32)))) | ~ ! [X34 : term] : (($true = ((X22 @ id @ (X30 @ id @ X34) @ id))) | ($true != ((X22 @ id @ X34 @ id)))) | (((X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) = $true)) | ~ ! [X27 : subst,X26 : subst,X25 : subst,X28 : term] : (($true = ((X22 @ X26 @ X28 @ (comp @ X27 @ X25)))) | ($true != ((X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X386 : subst,X385 : term] : (((sub @ one @ (push @ X385 @ X386))) = X385) => (! [X388 : term,X387 : subst] : (((comp @ sh @ (push @ X388 @ X387))) = X387) => (! [X390 : term,X389 : term] : ((((lam @ X389)) != ((lam @ X390))) | (X389 = X390)) => ! [X392 : (subst > term > term),X393 : term,X391 : subst,X394 : (subst > term > term)] : (~ ! [X396 : subst,X397 : term,X395 : subst] : (((sub @ (X392 @ X395 @ X397) @ X396)) = ((X392 @ (comp @ X395 @ X396) @ (sub @ X397 @ X396)))) | (((lam @ (X394 @ sh @ one))) != ((lam @ (X392 @ sh @ one)))) | ~ ! [X399 : term,X400 : subst,X398 : subst] : (((X394 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) = ((sub @ (X394 @ X398 @ X399) @ X400))) | (((X392 @ X391 @ X393)) = ((X394 @ X391 @ X393)))))))) & ! [X205 : d_term,X204 : d_term] : ((((d2term @ X204)) = ((d2term @ X205))) => (X204 = X205)) & (hoaslamnotvar_lthm = $true) & (ulamvar1 != $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X128 : (subst > term > subst > $o),X127 : term] : (~ ! [X134 : term,X135 : term] : (($true = ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id))) | (((X128 @ id @ X134 @ id)) != $true) | ($true != ((X128 @ id @ X135 @ id)))) | ~ ! [X129 : (subst > term > term)] : ((((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id)) = $true) | ~ ! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133)))) | ~ ! [X130 : term] : (($true != ((X128 @ id @ X130 @ id))) | ($true = ((X128 @ id @ (X129 @ id @ X130) @ id))))) | ($true = ((X128 @ id @ X127 @ id))))) & ((hoasinduction_lem3aa = $true) <=> ! [X57 : term,X58 : (subst > term > subst > $o)] : (~ ! [X59 : (subst > term > term)] : (($true = ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id))) | ~ ! [X62 : subst,X60 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) | ~ ! [X63 : term] : ((((X58 @ id @ (X59 @ id @ X63) @ id)) = $true) | ($true != ((X58 @ id @ X63 @ id))))) | (((X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X64 : term] : (($true != ((X58 @ id @ X64 @ id))) | ($true = ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id)))))) & ((shinj = $true) <=> ! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85))) & (! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) <=> (hoasapinj1 = $true)) & (! [X137 : (subst > term > subst > $o),X139 : term,X138 : (term > $o)] : (~ ! [X154 : subst,X152 : subst,X151 : term,X153 : subst] : (($true != ((X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154))) | (((X137 @ X152 @ X151 @ (comp @ X153 @ X154))) = $true)) | ~ ! [X140 : (subst > term > term)] : (~ ! [X144 : term] : ((((X137 @ id @ X144 @ id)) != $true) | ($true = ((X137 @ id @ (X140 @ id @ X144) @ id)))) | ~ ! [X143 : subst,X142 : subst,X141 : term] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) | (((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) = $true)) | ($true = ((X138 @ (lam @ X139)))) | ~ ! [X145 : term] : (((X138 @ X145)) = ((X137 @ id @ X145 @ id))) | ~ ! [X146 : subst,X148 : subst,X147 : term,X149 : subst] : ((((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148)) = $true) | ($true != ((X137 @ X149 @ X147 @ (comp @ X146 @ X148))))) | ~ ! [X150 : term] : ((((X138 @ X150)) != $true) | ($true = ((X138 @ (sub @ X139 @ (push @ X150 @ id))))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X469 : term] : ~ ! [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) != ((X470 @ sh @ one)))) & ((axshiftcons = $true) <=> ! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125)) & (pushprop_lem0_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((pushprop_lem1_lthm = $true) <=> (! [X49 : term,X48 : subst] : (((sub @ one @ (push @ X49 @ X48))) = X49) => (! [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) = X51) => ! [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true != ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))))) & ((induction2lem = $true) <=> ! [X533 : term,X532 : subst,X534 : (term > $o)] : (~ ! [X539 : term] : (($true = ((X534 @ (sub @ X539 @ X532)))) | ($true != ((var @ X539)))) | ~ ! [X535 : term] : (($true = ((X534 @ (lam @ X535)))) | ~ ! [X536 : term] : (($true = ((X534 @ (sub @ X535 @ (push @ X536 @ id))))) | ($true != ((X534 @ X536))))) | ~ ! [X538 : term,X537 : term] : (($true != ((X534 @ X538))) | ($true != ((X534 @ X537))) | (((X534 @ (ap @ X538 @ X537))) = $true)) | ($true = ((X534 @ (sub @ X533 @ X532)))))) & (((var @ (d2term @ d_one))) != $true) & (hoaslaminj_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem2_lthm = $true) & (! [X94 : term,X95 : (subst > term > subst > $o)] : (~ ! [X103 : subst,X104 : term,X105 : subst,X102 : subst] : (($true = ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105))) | ($true != ((X95 @ X103 @ X104 @ (comp @ X102 @ X105))))) | ~ ! [X97 : (subst > term > term)] : ((((X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) = $true) | ~ ! [X101 : term] : (($true = ((X95 @ id @ (X97 @ id @ X101) @ id))) | ($true != ((X95 @ id @ X101 @ id)))) | ~ ! [X98 : subst,X100 : subst,X99 : term] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98)))) | ~ ! [X106 : term,X108 : subst,X109 : subst,X107 : subst] : (($true = ((X95 @ X109 @ X106 @ (comp @ X107 @ X108)))) | (((X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108)) != $true)) | (((X95 @ id @ (lam @ X94) @ id)) = $true) | ~ ! [X96 : term] : (($true = ((X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id))) | ($true != ((X95 @ id @ X96 @ id))))) <=> (hoasinduction_lem3 = $true)) & (! [X477 : term] : (((sub @ X477 @ id)) = X477) <=> (axvarid = $true)) & (! [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (~ ! [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) = ((X202 @ X203))) | ($true = ((X202 @ one))) | ($true != ((X201 @ X200)))) <=> (pushprop_lem1v2 = $true)) & (axapp = $true) & ((! [X475 : term] : (((sub @ X475 @ id)) = X475) => ! [X476 : term] : (((sub @ X476 @ id)) = X476)) <=> (termmset_lthm = $true)) & (axclos = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_gthm = $true) & ! [X263 : d_term] : (d_one = X263) & ((hoasinduction_lem3aaa = $true) <=> ! [X511 : (subst > term > subst > $o),X510 : term] : ((((X511 @ id @ (lam @ (sub @ X510 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X513 : term,X512 : (subst > term > term)] : (($true = ((X511 @ id @ (lam @ (X512 @ sh @ one)) @ id))) | ~ ! [X520 : subst,X518 : term,X519 : subst] : (((sub @ (X512 @ X519 @ X518) @ X520)) = ((sub @ (sub @ X513 @ (push @ X518 @ X519)) @ X520))) | ~ ! [X517 : term] : (($true = ((X511 @ id @ (X512 @ id @ X517) @ id))) | (((X511 @ id @ X517 @ id)) != $true)) | ~ ! [X515 : term,X514 : subst,X516 : subst] : (((sub @ X513 @ (push @ (sub @ X515 @ X516) @ (comp @ X514 @ X516)))) = ((X512 @ (comp @ X514 @ X516) @ (sub @ X515 @ X516))))) | ~ ! [X521 : term] : ((((X511 @ id @ (sub @ X510 @ (push @ X521 @ id)) @ id)) = $true) | ($true != ((X511 @ id @ X521 @ id)))))) & (((d2subst @ d_id)) = id) & (! [X480 : term,X478 : (subst > term > subst > $o),X479 : term] : ((((X478 @ id @ X479 @ id)) != $true) | ~ ! [X490 : subst,X489 : subst,X487 : subst,X488 : term] : (($true = ((X478 @ (comp @ X490 @ X487) @ (sub @ X488 @ X487) @ X489))) | ($true != ((X478 @ X490 @ X488 @ (comp @ X487 @ X489))))) | ($true != ((X478 @ id @ X480 @ id))) | ~ ! [X482 : subst,X484 : subst,X481 : subst,X483 : term] : (($true != ((X478 @ (comp @ X481 @ X482) @ (sub @ X483 @ X482) @ X484))) | ($true = ((X478 @ X481 @ X483 @ (comp @ X482 @ X484))))) | ($true = ((X478 @ id @ (ap @ X480 @ X479) @ id))) | ~ ! [X485 : term,X486 : term] : (($true != ((X478 @ id @ X486 @ id))) | (((X478 @ id @ (ap @ (sub @ X485 @ id) @ X486) @ id)) = $true) | ($true != ((X478 @ id @ X485 @ id))))) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((axidl = $true) <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X233 : subst,X231 : (term > $o),X232 : term] : ~ ! [X234 : (term > $o)] : ~ ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) <=> (pushprop_lem0 = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) = X86) => ! [X90 : subst,X89 : term,X88 : (term > $o),X91 : (term > $o)] : (~ ! [X92 : term] : (((X88 @ X92)) = ((X91 @ (sub @ X92 @ (push @ X89 @ X90))))) | ($true != ((X91 @ X89))) | (((X88 @ one)) = $true)))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X332 : term] : (((sub @ X332 @ id)) = X332) => (! [X333 : term,X334 : (subst > term > subst > $o)] : (~ ! [X336 : (subst > term > term)] : (($true = ((X334 @ id @ (lam @ (X336 @ sh @ one)) @ id))) | ~ ! [X340 : term] : (($true = ((X334 @ id @ (X336 @ id @ X340) @ id))) | ($true != ((X334 @ id @ X340 @ id)))) | ~ ! [X338 : term,X339 : subst,X337 : subst] : (((X336 @ (comp @ X339 @ X337) @ (sub @ X338 @ X337))) = ((sub @ (X336 @ X339 @ X338) @ X337)))) | (((X334 @ id @ (lam @ (sub @ X333 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X335 : term] : ((((X334 @ id @ X335 @ id)) != $true) | (((X334 @ id @ (sub @ X333 @ (push @ X335 @ id)) @ id)) = $true))) => ! [X342 : (subst > term > subst > $o),X341 : term] : (~ ! [X343 : (subst > term > term)] : (($true = ((X342 @ id @ (lam @ (X343 @ sh @ one)) @ id))) | ~ ! [X344 : term] : ((((X342 @ id @ X344 @ id)) != $true) | ($true = ((X342 @ id @ (X343 @ id @ X344) @ id)))) | ~ ! [X345 : subst,X346 : term,X347 : subst] : (((sub @ (X343 @ X345 @ X346) @ X347)) = ((X343 @ (comp @ X345 @ X347) @ (sub @ X346 @ X347))))) | ($true = ((X342 @ id @ (lam @ X341) @ id))) | ~ ! [X348 : term] : (($true != ((X342 @ id @ X348 @ id))) | (((X342 @ id @ (sub @ X341 @ (push @ X348 @ id)) @ id)) = $true)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axassoc = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X403 : term,X402 : (term > $o),X401 : subst] : ~ ! [X404 : (term > $o)] : ~ ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401)))))) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) <=> ! [X113 : (subst > term > subst > $o)] : ~ ! [X114 : (term > $o)] : ~ ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id)))) & ((! [X66 : term,X65 : subst] : (((sub @ one @ (push @ X66 @ X65))) = X66) => (! [X68 : subst,X67 : term] : (((comp @ sh @ (push @ X67 @ X68))) = X68) => (! [X69 : subst] : (((comp @ X69 @ id)) = X69) => (! [X71 : (term > $o),X70 : term] : (~ ! [X73 : term,X74 : term] : (($true = ((X71 @ (ap @ X74 @ X73)))) | ($true != ((X71 @ X74))) | (((X71 @ X73)) != $true)) | ($true = ((X71 @ X70))) | ~ ! [X75 : term] : (($true = ((X71 @ (lam @ X75)))) | ($true != ((X71 @ X75)))) | ~ ! [X72 : term] : (($true != ((var @ X72))) | ($true = ((X71 @ X72))))) => ! [X78 : (term > $o),X76 : subst,X77 : term] : (($true = ((X78 @ (sub @ X77 @ X76)))) | ~ ! [X79 : term,X80 : term] : ((((X78 @ X80)) != $true) | (((X78 @ X79)) != $true) | (((X78 @ (ap @ X80 @ X79))) = $true)) | ~ ! [X81 : term] : (($true = ((X78 @ (sub @ X81 @ X76)))) | ($true != ((var @ X81)))) | ~ ! [X82 : term] : (($true = ((X78 @ (lam @ X82)))) | ~ ! [X83 : term] : (($true != ((X78 @ X83))) | ($true = ((X78 @ (sub @ X82 @ (push @ X83 @ id)))))))))))) <=> (induction2lem_lthm = $true)) & (hoasapinj2_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true != ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & ((! [X252 : term,X251 : term,X253 : term,X254 : term] : ((X252 = X254) | (((ap @ X253 @ X254)) != ((ap @ X251 @ X252)))) => ! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257))) <=> (hoasapinj2_lthm = $true)) & (! [X286 : (term > $o),X287 : term,X288 : (subst > term > subst > $o)] : (~ ! [X289 : term] : (((X286 @ X289)) = ((X288 @ id @ X289 @ id))) | ~ ! [X290 : (subst > term > term)] : (~ ! [X293 : subst,X294 : subst,X292 : term] : (((X290 @ (comp @ X293 @ X294) @ (sub @ X292 @ X294))) = ((sub @ (X290 @ X293 @ X292) @ X294))) | ~ ! [X291 : term] : (($true = ((X288 @ id @ (X290 @ id @ X291) @ id))) | ($true != ((X288 @ id @ X291 @ id)))) | ($true = ((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id)))) | ~ ! [X295 : term] : (($true != ((X286 @ X295))) | ($true = ((X286 @ (sub @ X287 @ (push @ X295 @ id)))))) | ($true = ((X286 @ (lam @ X287))))) <=> (hoasinduction_lem3v2a = $true)) & ! [X155 : d_subst,X156 : d_subst] : ((((d2subst @ X155)) = ((d2subst @ X156))) => (X155 = X156)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop = $true) & ((! [X116 : term] : (((sub @ X116 @ id)) = X116) => (! [X119 : term,X120 : term,X118 : term,X117 : term] : ((((ap @ X117 @ X118)) != ((ap @ X120 @ X119))) | (X117 = X120)) => ! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem3v2 = $true) & (termmset_gthm = $true) & ! [X93 : d_subst] : (d_id = X93) & (apnotvar = $true) & (! [X526 : (term > $o),X527 : term] : (~ ! [X528 : term,X529 : term] : (($true = ((X526 @ (ap @ X528 @ X529)))) | ($true != ((X526 @ X529))) | ($true != ((X526 @ X528)))) | ~ ! [X530 : term] : (($true = ((X526 @ (lam @ X530)))) | ($true != ((X526 @ X530)))) | ($true = ((X526 @ X527))) | ~ ! [X531 : term] : (($true = ((X526 @ X531))) | ($true != ((var @ X531))))) <=> (induction = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) <=> (apinj1 = $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X269 : term,X268 : (subst > term > subst > $o)] : (($true = ((X268 @ id @ (lam @ X269) @ id))) | ~ ! [X275 : term] : (($true = ((X268 @ id @ (sub @ X269 @ (push @ X275 @ id)) @ id))) | ($true != ((X268 @ id @ X275 @ id)))) | ~ ! [X270 : (subst > term > term)] : (($true = ((X268 @ id @ (lam @ (X270 @ sh @ one)) @ id))) | ~ ! [X271 : term] : ((((X268 @ id @ X271 @ id)) != $true) | ($true = ((X268 @ id @ (X270 @ id @ X271) @ id)))) | ~ ! [X273 : term,X272 : subst,X274 : subst] : (((sub @ (X270 @ X272 @ X273) @ X274)) = ((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)))))) <=> (hoasinduction_lem3a = $true)) & (lamnotvar = $true) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X264 : term] : ~ ! [X265 : (subst > term > term)] : ~ ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266))))) & (lamnotap != $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) <=> ! [X302 : (subst > term > subst > $o),X303 : term] : (~ ! [X305 : (subst > term > term)] : (~ ! [X306 : term] : ((((X302 @ id @ (X305 @ id @ X306) @ id)) = $true) | (((X302 @ id @ X306 @ id)) != $true)) | (((X302 @ id @ (lam @ (X305 @ sh @ one)) @ id)) = $true) | ~ ! [X308 : term,X307 : subst,X309 : subst] : (((X305 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307))) = ((sub @ (X305 @ X309 @ X308) @ X307)))) | ~ ! [X312 : subst,X313 : subst,X311 : subst,X310 : term] : (($true != ((X302 @ (comp @ X311 @ X313) @ (sub @ X310 @ X313) @ X312))) | ($true = ((X302 @ X311 @ X310 @ (comp @ X313 @ X312))))) | ~ ! [X318 : term,X319 : term] : (($true != ((X302 @ id @ X319 @ id))) | ($true = ((X302 @ id @ (ap @ (sub @ X318 @ id) @ X319) @ id))) | ($true != ((X302 @ id @ X318 @ id)))) | ~ ! [X304 : term] : ((((X302 @ id @ X304 @ id)) = $true) | (((var @ (sub @ X304 @ id))) != $true)) | ($true = ((X302 @ id @ X303 @ id))) | ~ ! [X317 : subst,X315 : subst,X316 : term,X314 : subst] : (($true = ((X302 @ (comp @ X314 @ X317) @ (sub @ X316 @ X317) @ X315))) | ($true != ((X302 @ X314 @ X316 @ (comp @ X317 @ X315))))))) & (hoasapnotvar_gthm = $true) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> (axscons = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X206 : term] : (((sub @ X206 @ id)) = X206) => (! [X207 : term,X208 : (subst > term > subst > $o)] : (($true = ((X208 @ id @ (lam @ (sub @ X207 @ (push @ one @ sh))) @ id))) | ~ ! [X209 : term] : (($true = ((X208 @ id @ (sub @ X207 @ (push @ X209 @ id)) @ id))) | (((X208 @ id @ X209 @ id)) != $true)) | ~ ! [X210 : (subst > term > term)] : (($true = ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id))) | ~ ! [X211 : term,X212 : subst,X213 : subst] : (((sub @ (X210 @ X212 @ X211) @ X213)) = ((X210 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213)))) | ~ ! [X214 : term] : (($true = ((X208 @ id @ (X210 @ id @ X214) @ id))) | ($true != ((X208 @ id @ X214 @ id)))))) => ! [X215 : term,X216 : (subst > term > subst > $o)] : (($true = ((X216 @ id @ (lam @ X215) @ id))) | ~ ! [X226 : term] : (($true = ((X216 @ id @ (sub @ X215 @ (push @ X226 @ id)) @ id))) | (((X216 @ id @ X226 @ id)) != $true)) | ~ ! [X229 : term,X227 : subst,X230 : subst,X228 : subst] : (($true != ((X216 @ X227 @ X229 @ (comp @ X230 @ X228)))) | ($true = ((X216 @ (comp @ X227 @ X230) @ (sub @ X229 @ X230) @ X228)))) | ~ ! [X221 : (subst > term > term)] : (~ ! [X223 : term,X224 : subst,X222 : subst] : (((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))) = ((sub @ (X221 @ X224 @ X223) @ X222))) | ~ ! [X225 : term] : (($true != ((X216 @ id @ X225 @ id))) | (((X216 @ id @ (X221 @ id @ X225) @ id)) = $true)) | ($true = ((X216 @ id @ (lam @ (X221 @ sh @ one)) @ id)))) | ~ ! [X220 : subst,X219 : term,X218 : subst,X217 : subst] : ((((X216 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220) @ X217)) != $true) | ($true = ((X216 @ X218 @ X219 @ (comp @ X220 @ X217))))))))) & (pushprop_lthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X320 : (subst > term > subst > $o),X321 : term] : (~ ! [X322 : (subst > term > term)] : (~ ! [X326 : term] : (($true = ((X320 @ id @ (X322 @ id @ X326) @ id))) | ($true != ((X320 @ id @ X326 @ id)))) | ~ ! [X325 : subst,X324 : subst,X323 : term] : (((X322 @ (comp @ X324 @ X325) @ (sub @ X323 @ X325))) = ((sub @ (X322 @ X324 @ X323) @ X325))) | ($true = ((X320 @ id @ (lam @ (X322 @ sh @ one)) @ id)))) | ($true = ((X320 @ id @ (lam @ (sub @ X321 @ (push @ one @ sh))) @ id))) | ~ ! [X327 : term] : (($true != ((X320 @ id @ X327 @ id))) | ($true = ((X320 @ id @ (sub @ X321 @ (push @ X327 @ id)) @ id)))))) & (! [X471 : term] : ~ ! [X472 : (subst > term > term)] : (((X472 @ sh @ one)) != ((sub @ X471 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoasapnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X110 : (subst > term > subst > $o)] : ~ ! [X111 : (term > $o)] : ~ ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & (axmap = $true) & (one = ((d2term @ d_one))) & (! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) <=> (laminj = $true)) & (induction2lem_gthm = $true) & ((induction2_lthm = $true) <=> (! [X364 : term] : (((sub @ X364 @ id)) = X364) => (! [X365 : subst,X367 : term,X366 : (term > $o)] : (~ ! [X370 : term] : (($true = ((X366 @ (sub @ X370 @ X365)))) | ($true != ((var @ X370)))) | (((X366 @ (sub @ X367 @ X365))) = $true) | ~ ! [X372 : term,X371 : term] : (($true != ((X366 @ X371))) | (((X366 @ (ap @ X372 @ X371))) = $true) | (((X366 @ X372)) != $true)) | ~ ! [X368 : term] : ((((X366 @ (lam @ X368))) = $true) | ~ ! [X369 : term] : ((((X366 @ X369)) != $true) | (((X366 @ (sub @ X368 @ (push @ X369 @ id)))) = $true)))) => ! [X374 : term,X373 : (term > $o)] : (~ ! [X376 : term,X375 : term] : (($true != ((X373 @ X376))) | ($true = ((X373 @ (ap @ X376 @ X375)))) | ($true != ((X373 @ X375)))) | ~ ! [X377 : term] : (($true != ((var @ X377))) | (((X373 @ X377)) = $true)) | ~ ! [X378 : term] : (($true = ((X373 @ (lam @ X378)))) | ~ ! [X379 : term] : (($true = ((X373 @ (sub @ X378 @ (push @ X379 @ id))))) | (((X373 @ X379)) != $true))) | ($true = ((X373 @ X374))))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X349 : term] : ~ ! [X350 : (subst > term > term)] : ~ ! [X352 : term,X351 : subst] : (((sub @ X349 @ (push @ X352 @ X351))) = ((X350 @ X351 @ X352))) => (! [X353 : term] : (((sub @ X353 @ id)) = X353) => ! [X354 : term,X356 : (term > $o),X355 : (subst > term > subst > $o)] : (~ ! [X357 : term] : (((X356 @ X357)) = ((X355 @ id @ X357 @ id))) | (((X356 @ (lam @ X354))) = $true) | ~ ! [X358 : (subst > term > term)] : ((((X355 @ id @ (lam @ (X358 @ sh @ one)) @ id)) = $true) | ~ ! [X362 : term] : (($true != ((X355 @ id @ X362 @ id))) | ($true = ((X355 @ id @ (X358 @ id @ X362) @ id)))) | ~ ! [X361 : term,X359 : subst,X360 : subst] : (((sub @ (X358 @ X359 @ X361) @ X360)) = ((X358 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360))))) | ~ ! [X363 : term] : (($true = ((X356 @ (sub @ X354 @ (push @ X363 @ id))))) | ($true != ((X356 @ X363)))))))) & (pushprop_lthm_orig = $true) & ((substmonoid = $true) <=> (! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X238 : (subst > term > subst > $o),X239 : (term > $o),X237 : term,X236 : term] : (($true = ((X239 @ (ap @ X236 @ X237)))) | ~ ! [X245 : term,X246 : term] : ((((X238 @ id @ X246 @ id)) != $true) | (((X238 @ id @ X245 @ id)) != $true) | (((X238 @ id @ (ap @ (sub @ X246 @ id) @ X245) @ id)) = $true)) | ~ ! [X249 : subst,X248 : term,X250 : subst,X247 : subst] : (($true = ((X238 @ X247 @ X248 @ (comp @ X250 @ X249)))) | ($true != ((X238 @ (comp @ X247 @ X250) @ (sub @ X248 @ X250) @ X249)))) | ~ ! [X243 : subst,X242 : subst,X240 : term,X241 : subst] : (($true != ((X238 @ X241 @ X240 @ (comp @ X243 @ X242)))) | ($true = ((X238 @ (comp @ X241 @ X243) @ (sub @ X240 @ X243) @ X242)))) | ($true != ((X239 @ X237))) | ($true != ((X239 @ X236))) | ~ ! [X244 : term] : (((X238 @ id @ X244 @ id)) = ((X239 @ X244)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasapinj1_gthm = $true) & (! [X194 : term] : (((sub @ X194 @ id)) = X194) <=> (termmset = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (ulamvarsh = $true) & ((hoasapinj2 = $true) <=> ! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467))) & ((induction2 = $true) <=> ! [X158 : (term > $o),X157 : term] : (~ ! [X161 : term] : (($true != ((var @ X161))) | ($true = ((X158 @ X161)))) | ~ ! [X162 : term,X163 : term] : (($true = ((X158 @ (ap @ X162 @ X163)))) | (((X158 @ X163)) != $true) | ($true != ((X158 @ X162)))) | ($true = ((X158 @ X157))) | ~ ! [X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : (($true = ((X158 @ (sub @ X159 @ (push @ X160 @ id))))) | ($true != ((X158 @ X160))))))) & (ulamvarind = $true) & ((apinj2 = $true) <=> ! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198))) & (axabs = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X164 : (subst > term > subst > $o)] : ~ ! [X165 : (term > $o)] : ~ ! [X166 : term] : (((X165 @ X166)) = ((X164 @ id @ X166 @ id))) => (! [X168 : (term > $o),X167 : term] : (~ ! [X173 : term] : ((((var @ X173)) != $true) | (((X168 @ X173)) = $true)) | ~ ! [X169 : term,X170 : term] : (($true != ((X168 @ X170))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)) | ~ ! [X171 : term] : (~ ! [X172 : term] : (($true != ((X168 @ X172))) | ($true = ((X168 @ (sub @ X171 @ (push @ X172 @ id)))))) | ($true = ((X168 @ (lam @ X171))))) | ($true = ((X168 @ X167)))) => (! [X174 : term] : (((sub @ X174 @ id)) = X174) => (! [X177 : term,X176 : (subst > term > subst > $o),X175 : (term > $o)] : ((((X175 @ (lam @ X177))) = $true) | ~ ! [X178 : term] : (($true != ((X175 @ X178))) | ($true = ((X175 @ (sub @ X177 @ (push @ X178 @ id)))))) | ~ ! [X184 : term] : (((X176 @ id @ X184 @ id)) = ((X175 @ X184))) | ~ ! [X179 : (subst > term > term)] : (~ ! [X181 : term,X180 : subst,X182 : subst] : (((sub @ (X179 @ X180 @ X181) @ X182)) = ((X179 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182)))) | ~ ! [X183 : term] : ((((X176 @ id @ (X179 @ id @ X183) @ id)) = $true) | (((X176 @ id @ X183 @ id)) != $true)) | (((X176 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true))) => ! [X185 : (subst > term > subst > $o),X186 : term] : (~ ! [X188 : term,X187 : term] : (($true != ((X185 @ id @ X188 @ id))) | ($true != ((X185 @ id @ X187 @ id))) | ($true = ((X185 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)))) | (((X185 @ id @ X186 @ id)) = $true) | ~ ! [X189 : (subst > term > term)] : (($true = ((X185 @ id @ (lam @ (X189 @ sh @ one)) @ id))) | ~ ! [X190 : subst,X192 : subst,X191 : term] : (((sub @ (X189 @ X190 @ X191) @ X192)) = ((X189 @ (comp @ X190 @ X192) @ (sub @ X191 @ X192)))) | ~ ! [X193 : term] : ((((X185 @ id @ (X189 @ id @ X193) @ id)) = $true) | ($true != ((X185 @ id @ X193 @ id))))))))))) & (hoasinduction_lem1 = $true) & (hoasinduction_lem1_gthm = $true) & (hoasapnotvar_lthm = $true) & (induction2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X298 : (subst > term > term),X297 : term,X296 : term] : (~ ! [X299 : term,X301 : subst,X300 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one)))))) & ((hoaslaminj = $true) <=> ! [X276 : subst,X277 : (subst > term > term),X279 : (subst > term > term),X278 : term] : ((((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ~ ! [X282 : subst,X280 : subst,X281 : term] : (((sub @ (X277 @ X282 @ X281) @ X280)) = ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280)))) | (((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ~ ! [X284 : term,X283 : subst,X285 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) = ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))))) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) <=> (axidr = $true)) & ((axvarcons = $true) <=> ! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44)) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X39 : term] : ~ ! [X40 : (subst > term > term)] : ~ ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42))))) & ((! [X522 : subst] : (((comp @ id @ X522)) = X522) => (! [X523 : subst] : (((comp @ X523 @ id)) = X523) => (! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)))) <=> (substmonoid_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X491 : term] : (((sub @ X491 @ id)) = X491) => ! [X494 : term,X493 : (subst > term > subst > $o),X492 : (term > $o)] : (~ ! [X504 : (subst > term > term)] : (~ ! [X508 : term,X507 : subst,X506 : subst] : (((X504 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507))) = ((sub @ (X504 @ X506 @ X508) @ X507))) | ~ ! [X505 : term] : (($true != ((X493 @ id @ X505 @ id))) | (((X493 @ id @ (X504 @ id @ X505) @ id)) = $true)) | ($true = ((X493 @ id @ (lam @ (X504 @ sh @ one)) @ id)))) | ~ ! [X495 : term] : (((X493 @ id @ X495 @ id)) = ((X492 @ X495))) | ~ ! [X496 : subst,X499 : subst,X497 : term,X498 : subst] : (($true != ((X493 @ X498 @ X497 @ (comp @ X499 @ X496)))) | ($true = ((X493 @ (comp @ X498 @ X499) @ (sub @ X497 @ X499) @ X496)))) | ($true = ((X492 @ (lam @ X494)))) | ~ ! [X509 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X509 @ id))))) | ($true != ((X492 @ X509)))) | ~ ! [X501 : subst,X500 : subst,X502 : term,X503 : subst] : ((((X493 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) != $true) | ($true = ((X493 @ X500 @ X502 @ (comp @ X501 @ X503)))))))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X411 : term,X410 : (term > $o)] : (~ ! [X415 : term,X416 : term] : ((((X410 @ X415)) != $true) | ($true = ((X410 @ (ap @ X416 @ X415)))) | ($true != ((X410 @ X416)))) | ($true = ((X410 @ X411))) | ~ ! [X413 : term] : (~ ! [X414 : term] : (($true = ((X410 @ (sub @ X413 @ (push @ X414 @ id))))) | (((X410 @ X414)) != $true)) | ($true = ((X410 @ (lam @ X413))))) | ~ ! [X412 : term] : (($true != ((var @ X412))) | ($true = ((X410 @ X412))))) => (! [X419 : term,X418 : term,X417 : (subst > term > subst > $o)] : (($true != ((X417 @ id @ X418 @ id))) | ($true != ((X417 @ id @ X419 @ id))) | ~ ! [X427 : subst,X426 : subst,X424 : subst,X425 : term] : (($true != ((X417 @ X424 @ X425 @ (comp @ X426 @ X427)))) | ($true = ((X417 @ (comp @ X424 @ X426) @ (sub @ X425 @ X426) @ X427)))) | ~ ! [X428 : term,X429 : term] : ((((X417 @ id @ X429 @ id)) != $true) | ($true != ((X417 @ id @ X428 @ id))) | ($true = ((X417 @ id @ (ap @ (sub @ X429 @ id) @ X428) @ id)))) | ($true = ((X417 @ id @ (ap @ X419 @ X418) @ id))) | ~ ! [X421 : subst,X423 : subst,X422 : term,X420 : subst] : (($true != ((X417 @ (comp @ X421 @ X420) @ (sub @ X422 @ X420) @ X423))) | ($true = ((X417 @ X421 @ X422 @ (comp @ X420 @ X423)))))) => (! [X431 : (subst > term > subst > $o),X430 : term] : (($true = ((X431 @ id @ (lam @ X430) @ id))) | ~ ! [X441 : term] : (($true = ((X431 @ id @ (sub @ X430 @ (push @ X441 @ id)) @ id))) | ($true != ((X431 @ id @ X441 @ id)))) | ~ ! [X435 : subst,X434 : subst,X432 : subst,X433 : term] : (($true = ((X431 @ X435 @ X433 @ (comp @ X434 @ X432)))) | ($true != ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434) @ X432)))) | ~ ! [X436 : (subst > term > term)] : (~ ! [X439 : subst,X437 : subst,X438 : term] : (((X436 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437))) = ((sub @ (X436 @ X439 @ X438) @ X437))) | ~ ! [X440 : term] : (($true != ((X431 @ id @ X440 @ id))) | ($true = ((X431 @ id @ (X436 @ id @ X440) @ id)))) | (((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true)) | ~ ! [X444 : subst,X443 : subst,X445 : subst,X442 : term] : (($true != ((X431 @ X445 @ X442 @ (comp @ X443 @ X444)))) | (((X431 @ (comp @ X445 @ X443) @ (sub @ X442 @ X443) @ X444)) = $true))) => ! [X446 : (subst > term > subst > $o),X447 : term] : (~ ! [X457 : term,X455 : subst,X456 : subst,X458 : subst] : ((((X446 @ X455 @ X457 @ (comp @ X458 @ X456))) != $true) | (((X446 @ (comp @ X455 @ X458) @ (sub @ X457 @ X458) @ X456)) = $true)) | ~ ! [X454 : term,X453 : term] : ((((X446 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id)) = $true) | ($true != ((X446 @ id @ X454 @ id))) | ($true != ((X446 @ id @ X453 @ id)))) | ~ ! [X459 : (subst > term > term)] : (~ ! [X463 : term] : ((((X446 @ id @ X463 @ id)) != $true) | ($true = ((X446 @ id @ (X459 @ id @ X463) @ id)))) | ($true = ((X446 @ id @ (lam @ (X459 @ sh @ one)) @ id))) | ~ ! [X460 : subst,X461 : subst,X462 : term] : (((X459 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460))) = ((sub @ (X459 @ X461 @ X462) @ X460)))) | ~ ! [X452 : term] : (($true != ((var @ (sub @ X452 @ id)))) | (((X446 @ id @ X452 @ id)) = $true)) | ~ ! [X448 : subst,X449 : term,X450 : subst,X451 : subst] : (($true != ((X446 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451) @ X448))) | ($true = ((X446 @ X450 @ X449 @ (comp @ X451 @ X448))))) | ($true = ((X446 @ id @ X447 @ id))))))) <=> (hoasinduction_lthm = $true)) & (hoaslamnotap_gthm = $true)),
% 2.91/0.81 inference(flattening,[],[f9])).
% 2.91/0.81 thf(f11,plain,(
% 2.91/0.81 (hoasinduction_lem1_lthm = $true) & (((((! [X21 : term,X22 : (subst > term > subst > $o)] : (? [X36 : subst,X38 : subst,X35 : term,X37 : subst] : ((((X22 @ X36 @ X35 @ (comp @ X38 @ X37))) = $true) & (((X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37)) != $true)) | ? [X30 : (subst > term > term)] : (! [X34 : term] : (($true = ((X22 @ id @ (X30 @ id @ X34) @ id))) | ($true != ((X22 @ id @ X34 @ id)))) & (((X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) != $true) & ! [X33 : term,X31 : subst,X32 : subst] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32))))) | ? [X29 : term] : (($true != ((X22 @ id @ X29 @ id))) & ($true = ((var @ (sub @ X29 @ id))))) | ? [X24 : term,X23 : term] : ((((X22 @ id @ X23 @ id)) = $true) & ($true != ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id))) & ($true = ((X22 @ id @ X24 @ id)))) | (((X22 @ id @ X21 @ id)) = $true) | ? [X25 : subst,X28 : term,X27 : subst,X26 : subst] : (($true != ((X22 @ X26 @ X28 @ (comp @ X27 @ X25)))) & ($true = ((X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25))))) | ? [X13 : (term > $o),X11 : term,X12 : (subst > term > subst > $o)] : (! [X20 : term] : (($true = ((X13 @ (sub @ X11 @ (push @ X20 @ id))))) | (((X13 @ X20)) != $true)) & ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) & ($true != ((X13 @ (lam @ X11)))) & ! [X15 : (subst > term > term)] : (? [X16 : term] : (($true != ((X12 @ id @ (X15 @ id @ X16) @ id))) & (((X12 @ id @ X16 @ id)) = $true)) | ? [X17 : subst,X19 : term,X18 : subst] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) != ((sub @ (X15 @ X18 @ X19) @ X17))) | ($true = ((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X4 : (term > $o),X3 : term] : (! [X5 : term] : (($true != ((var @ X5))) | ($true = ((X4 @ X5)))) & (((X4 @ X3)) != $true) & ! [X7 : term,X6 : term] : (($true != ((X4 @ X7))) | ($true = ((X4 @ (ap @ X7 @ X6)))) | ($true != ((X4 @ X6)))) & ! [X8 : term] : (? [X9 : term] : (($true != ((X4 @ (sub @ X8 @ (push @ X9 @ id))))) & ($true = ((X4 @ X9)))) | ($true = ((X4 @ (lam @ X8))))))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & ((hoaslaminj_lthm = $true) <=> (((! [X394 : (subst > term > term),X391 : subst,X392 : (subst > term > term),X393 : term] : ((((lam @ (X394 @ sh @ one))) != ((lam @ (X392 @ sh @ one)))) | ? [X400 : subst,X399 : term,X398 : subst] : (((X394 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) != ((sub @ (X394 @ X398 @ X399) @ X400))) | (((X392 @ X391 @ X393)) = ((X394 @ X391 @ X393))) | ? [X397 : term,X396 : subst,X395 : subst] : (((sub @ (X392 @ X395 @ X397) @ X396)) != ((X392 @ (comp @ X395 @ X396) @ (sub @ X397 @ X396))))) | ? [X390 : term,X389 : term] : ((((lam @ X389)) = ((lam @ X390))) & (X389 != X390))) | ? [X387 : subst,X388 : term] : (((comp @ sh @ (push @ X388 @ X387))) != X387)) | ? [X386 : subst,X385 : term] : (((sub @ one @ (push @ X385 @ X386))) != X385))) & ! [X205 : d_term,X204 : d_term] : ((X204 = X205) | (((d2term @ X204)) != ((d2term @ X205)))) & (hoaslamnotvar_lthm = $true) & (ulamvar1 != $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X128 : (subst > term > subst > $o),X127 : term] : (($true = ((X128 @ id @ X127 @ id))) | ? [X134 : term,X135 : term] : (($true = ((X128 @ id @ X135 @ id))) & (((X128 @ id @ X134 @ id)) = $true) & ($true != ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) | ? [X129 : (subst > term > term)] : (! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133)))) & ! [X130 : term] : (($true != ((X128 @ id @ X130 @ id))) | ($true = ((X128 @ id @ (X129 @ id @ X130) @ id)))) & (((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id)) != $true)))) & (! [X58 : (subst > term > subst > $o),X57 : term] : (? [X64 : term] : (($true != ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id))) & ($true = ((X58 @ id @ X64 @ id)))) | ? [X59 : (subst > term > term)] : (! [X62 : subst,X60 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) & ($true != ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id))) & ! [X63 : term] : ((((X58 @ id @ (X59 @ id @ X63) @ id)) = $true) | ($true != ((X58 @ id @ X63 @ id))))) | (((X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & ((shinj = $true) <=> ! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85))) & (! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) <=> (hoasapinj1 = $true)) & (! [X137 : (subst > term > subst > $o),X139 : term,X138 : (term > $o)] : (? [X145 : term] : (((X138 @ X145)) != ((X137 @ id @ X145 @ id))) | ? [X140 : (subst > term > term)] : (! [X144 : term] : ((((X137 @ id @ X144 @ id)) != $true) | ($true = ((X137 @ id @ (X140 @ id @ X144) @ id)))) & ! [X143 : subst,X142 : subst,X141 : term] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) & (((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) != $true)) | ? [X146 : subst,X149 : subst,X147 : term,X148 : subst] : (($true = ((X137 @ X149 @ X147 @ (comp @ X146 @ X148)))) & (((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148)) != $true)) | ? [X154 : subst,X151 : term,X153 : subst,X152 : subst] : ((((X137 @ X152 @ X151 @ (comp @ X153 @ X154))) != $true) & ($true = ((X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154)))) | ? [X150 : term] : (($true != ((X138 @ (sub @ X139 @ (push @ X150 @ id))))) & (((X138 @ X150)) = $true)) | ($true = ((X138 @ (lam @ X139))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X469 : term] : ? [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) = ((X470 @ sh @ one)))) & ((axshiftcons = $true) <=> ! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125)) & (pushprop_lem0_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true != ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54)))))) | ? [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) != X51)) | ? [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) != X49))) & ((induction2lem = $true) <=> ! [X532 : subst,X533 : term,X534 : (term > $o)] : (? [X538 : term,X537 : term] : (($true = ((X534 @ X538))) & ($true = ((X534 @ X537))) & (((X534 @ (ap @ X538 @ X537))) != $true)) | ? [X539 : term] : (($true = ((var @ X539))) & ($true != ((X534 @ (sub @ X539 @ X532))))) | ($true = ((X534 @ (sub @ X533 @ X532)))) | ? [X535 : term] : (($true != ((X534 @ (lam @ X535)))) & ! [X536 : term] : (($true = ((X534 @ (sub @ X535 @ (push @ X536 @ id))))) | ($true != ((X534 @ X536))))))) & (((var @ (d2term @ d_one))) != $true) & (hoaslaminj_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X95 : (subst > term > subst > $o),X94 : term] : (? [X103 : subst,X102 : subst,X104 : term,X105 : subst] : (($true = ((X95 @ X103 @ X104 @ (comp @ X102 @ X105)))) & ($true != ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105)))) | (((X95 @ id @ (lam @ X94) @ id)) = $true) | ? [X109 : subst,X106 : term,X108 : subst,X107 : subst] : ((((X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108)) = $true) & ($true != ((X95 @ X109 @ X106 @ (comp @ X107 @ X108))))) | ? [X96 : term] : (($true = ((X95 @ id @ X96 @ id))) & ($true != ((X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id)))) | ? [X97 : (subst > term > term)] : (! [X101 : term] : (($true = ((X95 @ id @ (X97 @ id @ X101) @ id))) | ($true != ((X95 @ id @ X101 @ id)))) & (((X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) != $true) & ! [X98 : subst,X100 : subst,X99 : term] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98)))))) & (! [X477 : term] : (((sub @ X477 @ id)) = X477) <=> (axvarid = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (? [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) != ((X202 @ X203))) | ($true != ((X201 @ X200))) | ($true = ((X202 @ one))))) & (axapp = $true) & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) | ? [X475 : term] : (((sub @ X475 @ id)) != X475)) <=> (termmset_lthm = $true)) & (axclos = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_gthm = $true) & ! [X263 : d_term] : (d_one = X263) & (! [X510 : term,X511 : (subst > term > subst > $o)] : (? [X513 : term,X512 : (subst > term > term)] : (! [X520 : subst,X518 : term,X519 : subst] : (((sub @ (X512 @ X519 @ X518) @ X520)) = ((sub @ (sub @ X513 @ (push @ X518 @ X519)) @ X520))) & ! [X517 : term] : (($true = ((X511 @ id @ (X512 @ id @ X517) @ id))) | (((X511 @ id @ X517 @ id)) != $true)) & ! [X515 : term,X514 : subst,X516 : subst] : (((sub @ X513 @ (push @ (sub @ X515 @ X516) @ (comp @ X514 @ X516)))) = ((X512 @ (comp @ X514 @ X516) @ (sub @ X515 @ X516)))) & ($true != ((X511 @ id @ (lam @ (X512 @ sh @ one)) @ id)))) | ? [X521 : term] : (($true = ((X511 @ id @ X521 @ id))) & (((X511 @ id @ (sub @ X510 @ (push @ X521 @ id)) @ id)) != $true)) | (((X511 @ id @ (lam @ (sub @ X510 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem2 = $true) <=> ! [X480 : term,X479 : term,X478 : (subst > term > subst > $o)] : (? [X486 : term,X485 : term] : ((((X478 @ id @ (ap @ (sub @ X485 @ id) @ X486) @ id)) != $true) & ($true = ((X478 @ id @ X485 @ id))) & ($true = ((X478 @ id @ X486 @ id)))) | ($true = ((X478 @ id @ (ap @ X480 @ X479) @ id))) | ($true != ((X478 @ id @ X480 @ id))) | ? [X487 : subst,X490 : subst,X488 : term,X489 : subst] : (($true != ((X478 @ (comp @ X490 @ X487) @ (sub @ X488 @ X487) @ X489))) & ($true = ((X478 @ X490 @ X488 @ (comp @ X487 @ X489))))) | (((X478 @ id @ X479 @ id)) != $true) | ? [X483 : term,X481 : subst,X482 : subst,X484 : subst] : (($true != ((X478 @ X481 @ X483 @ (comp @ X482 @ X484)))) & ($true = ((X478 @ (comp @ X481 @ X482) @ (sub @ X483 @ X482) @ X484)))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((axidl = $true) <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X232 : term,X233 : subst,X231 : (term > $o)] : ? [X234 : (term > $o)] : ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) <=> (pushprop_lem0 = $true)) & ((! [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) = $true) | ($true != ((X91 @ X89))) | ? [X92 : term] : (((X88 @ X92)) != ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) | ? [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) != X86)) <=> (pushprop_lem1v2_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X342 : (subst > term > subst > $o),X341 : term] : (? [X343 : (subst > term > term)] : (! [X345 : subst,X346 : term,X347 : subst] : (((sub @ (X343 @ X345 @ X346) @ X347)) = ((X343 @ (comp @ X345 @ X347) @ (sub @ X346 @ X347)))) & ! [X344 : term] : ((((X342 @ id @ X344 @ id)) != $true) | ($true = ((X342 @ id @ (X343 @ id @ X344) @ id)))) & ($true != ((X342 @ id @ (lam @ (X343 @ sh @ one)) @ id)))) | ? [X348 : term] : ((((X342 @ id @ (sub @ X341 @ (push @ X348 @ id)) @ id)) != $true) & ($true = ((X342 @ id @ X348 @ id)))) | ($true = ((X342 @ id @ (lam @ X341) @ id)))) | ? [X334 : (subst > term > subst > $o),X333 : term] : (! [X335 : term] : ((((X334 @ id @ X335 @ id)) != $true) | (((X334 @ id @ (sub @ X333 @ (push @ X335 @ id)) @ id)) = $true)) & (((X334 @ id @ (lam @ (sub @ X333 @ (push @ one @ sh))) @ id)) != $true) & ! [X336 : (subst > term > term)] : (? [X337 : subst,X338 : term,X339 : subst] : (((X336 @ (comp @ X339 @ X337) @ (sub @ X338 @ X337))) != ((sub @ (X336 @ X339 @ X338) @ X337))) | ? [X340 : term] : (($true = ((X334 @ id @ X340 @ id))) & ($true != ((X334 @ id @ (X336 @ id @ X340) @ id)))) | ($true = ((X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)))))) | ? [X332 : term] : (((sub @ X332 @ id)) != X332))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (axassoc = $true) & (! [X402 : (term > $o),X401 : subst,X403 : term] : ? [X404 : (term > $o)] : ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401))))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = sh) & (! [X113 : (subst > term > subst > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id))) <=> (hoasinduction_lem0 = $true)) & (((((! [X78 : (term > $o),X76 : subst,X77 : term] : (? [X81 : term] : (($true != ((X78 @ (sub @ X81 @ X76)))) & ($true = ((var @ X81)))) | ? [X82 : term] : (! [X83 : term] : (($true != ((X78 @ X83))) | ($true = ((X78 @ (sub @ X82 @ (push @ X83 @ id)))))) & ($true != ((X78 @ (lam @ X82))))) | ? [X80 : term,X79 : term] : ((((X78 @ (ap @ X80 @ X79))) != $true) & (((X78 @ X79)) = $true) & (((X78 @ X80)) = $true)) | ($true = ((X78 @ (sub @ X77 @ X76))))) | ? [X70 : term,X71 : (term > $o)] : (($true != ((X71 @ X70))) & ! [X72 : term] : (($true != ((var @ X72))) | ($true = ((X71 @ X72)))) & ! [X75 : term] : (($true = ((X71 @ (lam @ X75)))) | ($true != ((X71 @ X75)))) & ! [X73 : term,X74 : term] : (($true = ((X71 @ (ap @ X74 @ X73)))) | ($true != ((X71 @ X74))) | (((X71 @ X73)) != $true)))) | ? [X69 : subst] : (((comp @ X69 @ id)) != X69)) | ? [X67 : term,X68 : subst] : (((comp @ sh @ (push @ X67 @ X68))) != X68)) | ? [X65 : subst,X66 : term] : (((sub @ one @ (push @ X66 @ X65))) != X66)) <=> (induction2lem_lthm = $true)) & (hoasapinj2_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true != ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & ((! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257)) | ? [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) = ((ap @ X251 @ X252))) & (X252 != X254))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X286 : (term > $o),X287 : term,X288 : (subst > term > subst > $o)] : (? [X289 : term] : (((X286 @ X289)) != ((X288 @ id @ X289 @ id))) | ($true = ((X286 @ (lam @ X287)))) | ? [X295 : term] : (($true != ((X286 @ (sub @ X287 @ (push @ X295 @ id))))) & ($true = ((X286 @ X295)))) | ? [X290 : (subst > term > term)] : (($true != ((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id))) & ! [X291 : term] : (($true = ((X288 @ id @ (X290 @ id @ X291) @ id))) | ($true != ((X288 @ id @ X291 @ id)))) & ! [X293 : subst,X294 : subst,X292 : term] : (((X290 @ (comp @ X293 @ X294) @ (sub @ X292 @ X294))) = ((sub @ (X290 @ X293 @ X292) @ X294)))))) & ! [X156 : d_subst,X155 : d_subst] : ((((d2subst @ X155)) != ((d2subst @ X156))) | (X155 = X156)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop = $true) & (((! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)) | ? [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 != X120) & (((ap @ X117 @ X118)) = ((ap @ X120 @ X119))))) | ? [X116 : term] : (((sub @ X116 @ id)) != X116)) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem3v2 = $true) & (termmset_gthm = $true) & ! [X93 : d_subst] : (d_id = X93) & (apnotvar = $true) & ((induction = $true) <=> ! [X526 : (term > $o),X527 : term] : (? [X529 : term,X528 : term] : (($true = ((X526 @ X529))) & ($true = ((X526 @ X528))) & ($true != ((X526 @ (ap @ X528 @ X529))))) | ? [X530 : term] : (($true != ((X526 @ (lam @ X530)))) & ($true = ((X526 @ X530)))) | ? [X531 : term] : (($true != ((X526 @ X531))) & ($true = ((var @ X531)))) | ($true = ((X526 @ X527))))) & (hoasinduction_lem2v2_gthm = $true) & (! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) <=> (apinj1 = $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X269 : term,X268 : (subst > term > subst > $o)] : (($true = ((X268 @ id @ (lam @ X269) @ id))) | ? [X270 : (subst > term > term)] : (! [X273 : term,X272 : subst,X274 : subst] : (((sub @ (X270 @ X272 @ X273) @ X274)) = ((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)))) & ! [X271 : term] : ((((X268 @ id @ X271 @ id)) != $true) | ($true = ((X268 @ id @ (X270 @ id @ X271) @ id)))) & ($true != ((X268 @ id @ (lam @ (X270 @ sh @ one)) @ id)))) | ? [X275 : term] : (($true = ((X268 @ id @ X275 @ id))) & ($true != ((X268 @ id @ (sub @ X269 @ (push @ X275 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (lamnotvar = $true) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X264 : term] : ? [X265 : (subst > term > term)] : ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266))))) & (lamnotap != $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) <=> ! [X302 : (subst > term > subst > $o),X303 : term] : (? [X304 : term] : ((((X302 @ id @ X304 @ id)) != $true) & (((var @ (sub @ X304 @ id))) = $true)) | ? [X315 : subst,X317 : subst,X314 : subst,X316 : term] : (($true = ((X302 @ X314 @ X316 @ (comp @ X317 @ X315)))) & ($true != ((X302 @ (comp @ X314 @ X317) @ (sub @ X316 @ X317) @ X315)))) | ? [X305 : (subst > term > term)] : ((((X302 @ id @ (lam @ (X305 @ sh @ one)) @ id)) != $true) & ! [X306 : term] : ((((X302 @ id @ (X305 @ id @ X306) @ id)) = $true) | (((X302 @ id @ X306 @ id)) != $true)) & ! [X308 : term,X307 : subst,X309 : subst] : (((X305 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307))) = ((sub @ (X305 @ X309 @ X308) @ X307)))) | ? [X313 : subst,X310 : term,X312 : subst,X311 : subst] : (($true = ((X302 @ (comp @ X311 @ X313) @ (sub @ X310 @ X313) @ X312))) & ($true != ((X302 @ X311 @ X310 @ (comp @ X313 @ X312))))) | ($true = ((X302 @ id @ X303 @ id))) | ? [X318 : term,X319 : term] : (($true = ((X302 @ id @ X319 @ id))) & ($true = ((X302 @ id @ X318 @ id))) & ($true != ((X302 @ id @ (ap @ (sub @ X318 @ id) @ X319) @ id)))))) & (hoasapnotvar_gthm = $true) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> (axscons = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X216 : (subst > term > subst > $o),X215 : term] : (($true = ((X216 @ id @ (lam @ X215) @ id))) | ? [X221 : (subst > term > term)] : (! [X225 : term] : (($true != ((X216 @ id @ X225 @ id))) | (((X216 @ id @ (X221 @ id @ X225) @ id)) = $true)) & ! [X223 : term,X224 : subst,X222 : subst] : (((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))) = ((sub @ (X221 @ X224 @ X223) @ X222))) & ($true != ((X216 @ id @ (lam @ (X221 @ sh @ one)) @ id)))) | ? [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (($true != ((X216 @ X218 @ X219 @ (comp @ X220 @ X217)))) & (((X216 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220) @ X217)) = $true)) | ? [X228 : subst,X227 : subst,X230 : subst,X229 : term] : (($true = ((X216 @ X227 @ X229 @ (comp @ X230 @ X228)))) & ($true != ((X216 @ (comp @ X227 @ X230) @ (sub @ X229 @ X230) @ X228)))) | ? [X226 : term] : (($true != ((X216 @ id @ (sub @ X215 @ (push @ X226 @ id)) @ id))) & (((X216 @ id @ X226 @ id)) = $true))) | ? [X208 : (subst > term > subst > $o),X207 : term] : (! [X210 : (subst > term > term)] : (? [X214 : term] : (($true = ((X208 @ id @ X214 @ id))) & ($true != ((X208 @ id @ (X210 @ id @ X214) @ id)))) | ($true = ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id))) | ? [X213 : subst,X212 : subst,X211 : term] : (((sub @ (X210 @ X212 @ X211) @ X213)) != ((X210 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213))))) & ($true != ((X208 @ id @ (lam @ (sub @ X207 @ (push @ one @ sh))) @ id))) & ! [X209 : term] : (($true = ((X208 @ id @ (sub @ X207 @ (push @ X209 @ id)) @ id))) | (((X208 @ id @ X209 @ id)) != $true)))) | ? [X206 : term] : (((sub @ X206 @ id)) != X206))) & (pushprop_lthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X321 : term,X320 : (subst > term > subst > $o)] : (($true = ((X320 @ id @ (lam @ (sub @ X321 @ (push @ one @ sh))) @ id))) | ? [X327 : term] : (($true != ((X320 @ id @ (sub @ X321 @ (push @ X327 @ id)) @ id))) & ($true = ((X320 @ id @ X327 @ id)))) | ? [X322 : (subst > term > term)] : (! [X325 : subst,X324 : subst,X323 : term] : (((X322 @ (comp @ X324 @ X325) @ (sub @ X323 @ X325))) = ((sub @ (X322 @ X324 @ X323) @ X325))) & ($true != ((X320 @ id @ (lam @ (X322 @ sh @ one)) @ id))) & ! [X326 : term] : (($true = ((X320 @ id @ (X322 @ id @ X326) @ id))) | ($true != ((X320 @ id @ X326 @ id)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X471 : term] : ? [X472 : (subst > term > term)] : (((X472 @ sh @ one)) = ((sub @ X471 @ (push @ one @ sh))))) & (hoasapnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id)))) & (pushprop_lem1v2_gthm = $true) & (axmap = $true) & (one = ((d2term @ d_one))) & (! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) <=> (laminj = $true)) & (induction2lem_gthm = $true) & ((induction2_lthm = $true) <=> ((! [X373 : (term > $o),X374 : term] : (($true = ((X373 @ X374))) | ? [X378 : term] : (($true != ((X373 @ (lam @ X378)))) & ! [X379 : term] : (($true = ((X373 @ (sub @ X378 @ (push @ X379 @ id))))) | (((X373 @ X379)) != $true))) | ? [X376 : term,X375 : term] : (($true = ((X373 @ X375))) & ($true = ((X373 @ X376))) & ($true != ((X373 @ (ap @ X376 @ X375))))) | ? [X377 : term] : ((((X373 @ X377)) != $true) & ($true = ((var @ X377))))) | ? [X366 : (term > $o),X367 : term,X365 : subst] : ((((X366 @ (sub @ X367 @ X365))) != $true) & ! [X368 : term] : ((((X366 @ (lam @ X368))) = $true) | ? [X369 : term] : ((((X366 @ (sub @ X368 @ (push @ X369 @ id)))) != $true) & (((X366 @ X369)) = $true))) & ! [X370 : term] : (($true = ((X366 @ (sub @ X370 @ X365)))) | ($true != ((var @ X370)))) & ! [X372 : term,X371 : term] : (($true != ((X366 @ X371))) | (((X366 @ (ap @ X372 @ X371))) = $true) | (((X366 @ X372)) != $true)))) | ? [X364 : term] : (((sub @ X364 @ id)) != X364))) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X355 : (subst > term > subst > $o),X356 : (term > $o),X354 : term] : (? [X363 : term] : (($true != ((X356 @ (sub @ X354 @ (push @ X363 @ id))))) & ($true = ((X356 @ X363)))) | ? [X357 : term] : (((X356 @ X357)) != ((X355 @ id @ X357 @ id))) | ? [X358 : (subst > term > term)] : (! [X361 : term,X359 : subst,X360 : subst] : (((sub @ (X358 @ X359 @ X361) @ X360)) = ((X358 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360)))) & (((X355 @ id @ (lam @ (X358 @ sh @ one)) @ id)) != $true) & ! [X362 : term] : (($true != ((X355 @ id @ X362 @ id))) | ($true = ((X355 @ id @ (X358 @ id @ X362) @ id))))) | (((X356 @ (lam @ X354))) = $true)) | ? [X353 : term] : (((sub @ X353 @ id)) != X353)) | ? [X349 : term] : ! [X350 : (subst > term > term)] : ? [X352 : term,X351 : subst] : (((sub @ X349 @ (push @ X352 @ X351))) != ((X350 @ X351 @ X352))))) & (pushprop_lthm_orig = $true) & ((substmonoid = $true) <=> (! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X237 : term,X236 : term,X238 : (subst > term > subst > $o),X239 : (term > $o)] : (? [X248 : term,X250 : subst,X247 : subst,X249 : subst] : (($true = ((X238 @ (comp @ X247 @ X250) @ (sub @ X248 @ X250) @ X249))) & ($true != ((X238 @ X247 @ X248 @ (comp @ X250 @ X249))))) | ? [X244 : term] : (((X238 @ id @ X244 @ id)) != ((X239 @ X244))) | ($true != ((X239 @ X236))) | ($true != ((X239 @ X237))) | ($true = ((X239 @ (ap @ X236 @ X237)))) | ? [X242 : subst,X241 : subst,X240 : term,X243 : subst] : (($true = ((X238 @ X241 @ X240 @ (comp @ X243 @ X242)))) & ($true != ((X238 @ (comp @ X241 @ X243) @ (sub @ X240 @ X243) @ X242)))) | ? [X245 : term,X246 : term] : ((((X238 @ id @ X246 @ id)) = $true) & (((X238 @ id @ X245 @ id)) = $true) & (((X238 @ id @ (ap @ (sub @ X246 @ id) @ X245) @ id)) != $true)))) & (hoasapinj1_gthm = $true) & (! [X194 : term] : (((sub @ X194 @ id)) = X194) <=> (termmset = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (ulamvarsh = $true) & ((hoasapinj2 = $true) <=> ! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467))) & ((induction2 = $true) <=> ! [X158 : (term > $o),X157 : term] : (($true = ((X158 @ X157))) | ? [X161 : term] : (($true != ((X158 @ X161))) & ($true = ((var @ X161)))) | ? [X163 : term,X162 : term] : ((((X158 @ X163)) = $true) & ($true = ((X158 @ X162))) & ($true != ((X158 @ (ap @ X162 @ X163))))) | ? [X159 : term] : ((((X158 @ (lam @ X159))) != $true) & ! [X160 : term] : (($true = ((X158 @ (sub @ X159 @ (push @ X160 @ id))))) | ($true != ((X158 @ X160))))))) & (ulamvarind = $true) & ((apinj2 = $true) <=> ! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198))) & (axabs = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X186 : term,X185 : (subst > term > subst > $o)] : ((((X185 @ id @ X186 @ id)) = $true) | ? [X189 : (subst > term > term)] : (! [X193 : term] : ((((X185 @ id @ (X189 @ id @ X193) @ id)) = $true) | ($true != ((X185 @ id @ X193 @ id)))) & ($true != ((X185 @ id @ (lam @ (X189 @ sh @ one)) @ id))) & ! [X190 : subst,X192 : subst,X191 : term] : (((sub @ (X189 @ X190 @ X191) @ X192)) = ((X189 @ (comp @ X190 @ X192) @ (sub @ X191 @ X192))))) | ? [X188 : term,X187 : term] : (($true = ((X185 @ id @ X187 @ id))) & ($true = ((X185 @ id @ X188 @ id))) & ($true != ((X185 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id))))) | ? [X177 : term,X176 : (subst > term > subst > $o),X175 : (term > $o)] : ((((X175 @ (lam @ X177))) != $true) & ! [X184 : term] : (((X176 @ id @ X184 @ id)) = ((X175 @ X184))) & ! [X179 : (subst > term > term)] : ((((X176 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ? [X183 : term] : ((((X176 @ id @ X183 @ id)) = $true) & (((X176 @ id @ (X179 @ id @ X183) @ id)) != $true)) | ? [X180 : subst,X181 : term,X182 : subst] : (((sub @ (X179 @ X180 @ X181) @ X182)) != ((X179 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182))))) & ! [X178 : term] : (($true != ((X175 @ X178))) | ($true = ((X175 @ (sub @ X177 @ (push @ X178 @ id)))))))) | ? [X174 : term] : (((sub @ X174 @ id)) != X174)) | ? [X167 : term,X168 : (term > $o)] : (! [X169 : term,X170 : term] : (($true != ((X168 @ X170))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)) & ! [X173 : term] : ((((var @ X173)) != $true) | (((X168 @ X173)) = $true)) & ($true != ((X168 @ X167))) & ! [X171 : term] : (? [X172 : term] : (($true != ((X168 @ (sub @ X171 @ (push @ X172 @ id))))) & ($true = ((X168 @ X172)))) | ($true = ((X168 @ (lam @ X171))))))) | ? [X164 : (subst > term > subst > $o)] : ! [X165 : (term > $o)] : ? [X166 : term] : (((X165 @ X166)) != ((X164 @ id @ X166 @ id))))) & (hoasinduction_lem1 = $true) & (hoasinduction_lem1_gthm = $true) & (hoasapnotvar_lthm = $true) & (induction2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X296 : term,X298 : (subst > term > term),X297 : term] : (? [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one)))))) & (! [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ? [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) != ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) | (((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ? [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) != ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280))))) <=> (hoaslaminj = $true)) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) <=> (axidr = $true)) & ((axvarcons = $true) <=> ! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44)) & (substmonoid_gthm = $true) & (! [X39 : term] : ? [X40 : (subst > term > term)] : ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42)))) <=> (hoasinduction_lem3v2_f = $true)) & ((((! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)) | ? [X523 : subst] : (((comp @ X523 @ id)) != X523)) | ? [X522 : subst] : (((comp @ id @ X522)) != X522)) <=> (substmonoid_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X491 : term] : (((sub @ X491 @ id)) != X491) | ! [X492 : (term > $o),X494 : term,X493 : (subst > term > subst > $o)] : (? [X501 : subst,X500 : subst,X503 : subst,X502 : term] : ((((X493 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) = $true) & ($true != ((X493 @ X500 @ X502 @ (comp @ X501 @ X503))))) | ? [X495 : term] : (((X493 @ id @ X495 @ id)) != ((X492 @ X495))) | ? [X504 : (subst > term > term)] : (! [X508 : term,X507 : subst,X506 : subst] : (((X504 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507))) = ((sub @ (X504 @ X506 @ X508) @ X507))) & ($true != ((X493 @ id @ (lam @ (X504 @ sh @ one)) @ id))) & ! [X505 : term] : (($true != ((X493 @ id @ X505 @ id))) | (((X493 @ id @ (X504 @ id @ X505) @ id)) = $true))) | ? [X509 : term] : (($true = ((X492 @ X509))) & ($true != ((X492 @ (sub @ X494 @ (push @ X509 @ id)))))) | ? [X497 : term,X498 : subst,X496 : subst,X499 : subst] : (($true != ((X493 @ (comp @ X498 @ X499) @ (sub @ X497 @ X499) @ X496))) & ($true = ((X493 @ X498 @ X497 @ (comp @ X499 @ X496))))) | ($true = ((X492 @ (lam @ X494))))))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((((! [X447 : term,X446 : (subst > term > subst > $o)] : (? [X454 : term,X453 : term] : ((((X446 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id)) != $true) & ($true = ((X446 @ id @ X453 @ id))) & ($true = ((X446 @ id @ X454 @ id)))) | ? [X452 : term] : (($true = ((var @ (sub @ X452 @ id)))) & (((X446 @ id @ X452 @ id)) != $true)) | ? [X456 : subst,X457 : term,X455 : subst,X458 : subst] : ((((X446 @ X455 @ X457 @ (comp @ X458 @ X456))) = $true) & (((X446 @ (comp @ X455 @ X458) @ (sub @ X457 @ X458) @ X456)) != $true)) | ($true = ((X446 @ id @ X447 @ id))) | ? [X448 : subst,X450 : subst,X451 : subst,X449 : term] : (($true != ((X446 @ X450 @ X449 @ (comp @ X451 @ X448)))) & ($true = ((X446 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451) @ X448)))) | ? [X459 : (subst > term > term)] : (! [X460 : subst,X461 : subst,X462 : term] : (((X459 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460))) = ((sub @ (X459 @ X461 @ X462) @ X460))) & ($true != ((X446 @ id @ (lam @ (X459 @ sh @ one)) @ id))) & ! [X463 : term] : ((((X446 @ id @ X463 @ id)) != $true) | ($true = ((X446 @ id @ (X459 @ id @ X463) @ id)))))) | ? [X430 : term,X431 : (subst > term > subst > $o)] : (! [X444 : subst,X443 : subst,X445 : subst,X442 : term] : (($true != ((X431 @ X445 @ X442 @ (comp @ X443 @ X444)))) | (((X431 @ (comp @ X445 @ X443) @ (sub @ X442 @ X443) @ X444)) = $true)) & ($true != ((X431 @ id @ (lam @ X430) @ id))) & ! [X436 : (subst > term > term)] : (? [X438 : term,X439 : subst,X437 : subst] : (((X436 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437))) != ((sub @ (X436 @ X439 @ X438) @ X437))) | (((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ? [X440 : term] : (($true != ((X431 @ id @ (X436 @ id @ X440) @ id))) & ($true = ((X431 @ id @ X440 @ id))))) & ! [X435 : subst,X434 : subst,X432 : subst,X433 : term] : (($true = ((X431 @ X435 @ X433 @ (comp @ X434 @ X432)))) | ($true != ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434) @ X432)))) & ! [X441 : term] : (($true = ((X431 @ id @ (sub @ X430 @ (push @ X441 @ id)) @ id))) | ($true != ((X431 @ id @ X441 @ id)))))) | ? [X417 : (subst > term > subst > $o),X418 : term,X419 : term] : (($true != ((X417 @ id @ (ap @ X419 @ X418) @ id))) & ($true = ((X417 @ id @ X419 @ id))) & ! [X421 : subst,X423 : subst,X422 : term,X420 : subst] : (($true != ((X417 @ (comp @ X421 @ X420) @ (sub @ X422 @ X420) @ X423))) | ($true = ((X417 @ X421 @ X422 @ (comp @ X420 @ X423))))) & ! [X427 : subst,X426 : subst,X424 : subst,X425 : term] : (($true != ((X417 @ X424 @ X425 @ (comp @ X426 @ X427)))) | ($true = ((X417 @ (comp @ X424 @ X426) @ (sub @ X425 @ X426) @ X427)))) & ($true = ((X417 @ id @ X418 @ id))) & ! [X428 : term,X429 : term] : ((((X417 @ id @ X429 @ id)) != $true) | ($true != ((X417 @ id @ X428 @ id))) | ($true = ((X417 @ id @ (ap @ (sub @ X429 @ id) @ X428) @ id)))))) | ? [X411 : term,X410 : (term > $o)] : (! [X415 : term,X416 : term] : ((((X410 @ X415)) != $true) | ($true = ((X410 @ (ap @ X416 @ X415)))) | ($true != ((X410 @ X416)))) & ($true != ((X410 @ X411))) & ! [X412 : term] : (($true != ((var @ X412))) | ($true = ((X410 @ X412)))) & ! [X413 : term] : (($true = ((X410 @ (lam @ X413)))) | ? [X414 : term] : ((((X410 @ X414)) = $true) & ($true != ((X410 @ (sub @ X413 @ (push @ X414 @ id))))))))) <=> (hoasinduction_lthm = $true)) & (hoaslamnotap_gthm = $true)),
% 2.91/0.81 inference(ennf_transformation,[],[f10])).
% 2.91/0.81 thf(f12,plain,(
% 2.91/0.81 (ulamvarsh = $true) & (hoaslamnotvar = $true) & (axclos = $true) & ((? [X366 : (term > $o),X367 : term,X365 : subst] : ((((X366 @ (sub @ X367 @ X365))) != $true) & ! [X368 : term] : ((((X366 @ (lam @ X368))) = $true) | ? [X369 : term] : ((((X366 @ (sub @ X368 @ (push @ X369 @ id)))) != $true) & (((X366 @ X369)) = $true))) & ! [X370 : term] : (($true = ((X366 @ (sub @ X370 @ X365)))) | ($true != ((var @ X370)))) & ! [X372 : term,X371 : term] : (($true != ((X366 @ X371))) | (((X366 @ (ap @ X372 @ X371))) = $true) | (((X366 @ X372)) != $true))) | ! [X373 : (term > $o),X374 : term] : (($true = ((X373 @ X374))) | ? [X378 : term] : (($true != ((X373 @ (lam @ X378)))) & ! [X379 : term] : (($true = ((X373 @ (sub @ X378 @ (push @ X379 @ id))))) | (((X373 @ X379)) != $true))) | ? [X376 : term,X375 : term] : (($true = ((X373 @ X375))) & ($true = ((X373 @ X376))) & ($true != ((X373 @ (ap @ X376 @ X375))))) | ? [X377 : term] : ((((X373 @ X377)) != $true) & ($true = ((var @ X377))))) | ? [X364 : term] : (((sub @ X364 @ id)) != X364)) <=> (induction2_lthm = $true)) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & ((? [X430 : term,X431 : (subst > term > subst > $o)] : (! [X444 : subst,X443 : subst,X445 : subst,X442 : term] : (($true != ((X431 @ X445 @ X442 @ (comp @ X443 @ X444)))) | (((X431 @ (comp @ X445 @ X443) @ (sub @ X442 @ X443) @ X444)) = $true)) & ($true != ((X431 @ id @ (lam @ X430) @ id))) & ! [X436 : (subst > term > term)] : (? [X438 : term,X439 : subst,X437 : subst] : (((X436 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437))) != ((sub @ (X436 @ X439 @ X438) @ X437))) | (((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ? [X440 : term] : (($true != ((X431 @ id @ (X436 @ id @ X440) @ id))) & ($true = ((X431 @ id @ X440 @ id))))) & ! [X435 : subst,X434 : subst,X432 : subst,X433 : term] : (($true = ((X431 @ X435 @ X433 @ (comp @ X434 @ X432)))) | ($true != ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434) @ X432)))) & ! [X441 : term] : (($true = ((X431 @ id @ (sub @ X430 @ (push @ X441 @ id)) @ id))) | ($true != ((X431 @ id @ X441 @ id))))) | ? [X411 : term,X410 : (term > $o)] : (! [X415 : term,X416 : term] : ((((X410 @ X415)) != $true) | ($true = ((X410 @ (ap @ X416 @ X415)))) | ($true != ((X410 @ X416)))) & ($true != ((X410 @ X411))) & ! [X412 : term] : (($true != ((var @ X412))) | ($true = ((X410 @ X412)))) & ! [X413 : term] : (($true = ((X410 @ (lam @ X413)))) | ? [X414 : term] : ((((X410 @ X414)) = $true) & ($true != ((X410 @ (sub @ X413 @ (push @ X414 @ id)))))))) | ! [X447 : term,X446 : (subst > term > subst > $o)] : (? [X454 : term,X453 : term] : ((((X446 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id)) != $true) & ($true = ((X446 @ id @ X453 @ id))) & ($true = ((X446 @ id @ X454 @ id)))) | ? [X452 : term] : (($true = ((var @ (sub @ X452 @ id)))) & (((X446 @ id @ X452 @ id)) != $true)) | ? [X456 : subst,X457 : term,X455 : subst,X458 : subst] : ((((X446 @ X455 @ X457 @ (comp @ X458 @ X456))) = $true) & (((X446 @ (comp @ X455 @ X458) @ (sub @ X457 @ X458) @ X456)) != $true)) | ($true = ((X446 @ id @ X447 @ id))) | ? [X448 : subst,X450 : subst,X451 : subst,X449 : term] : (($true != ((X446 @ X450 @ X449 @ (comp @ X451 @ X448)))) & ($true = ((X446 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451) @ X448)))) | ? [X459 : (subst > term > term)] : (! [X460 : subst,X461 : subst,X462 : term] : (((X459 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460))) = ((sub @ (X459 @ X461 @ X462) @ X460))) & ($true != ((X446 @ id @ (lam @ (X459 @ sh @ one)) @ id))) & ! [X463 : term] : ((((X446 @ id @ X463 @ id)) != $true) | ($true = ((X446 @ id @ (X459 @ id @ X463) @ id)))))) | ? [X417 : (subst > term > subst > $o),X418 : term,X419 : term] : (($true != ((X417 @ id @ (ap @ X419 @ X418) @ id))) & ($true = ((X417 @ id @ X419 @ id))) & ! [X421 : subst,X423 : subst,X422 : term,X420 : subst] : (($true != ((X417 @ (comp @ X421 @ X420) @ (sub @ X422 @ X420) @ X423))) | ($true = ((X417 @ X421 @ X422 @ (comp @ X420 @ X423))))) & ! [X427 : subst,X426 : subst,X424 : subst,X425 : term] : (($true != ((X417 @ X424 @ X425 @ (comp @ X426 @ X427)))) | ($true = ((X417 @ (comp @ X424 @ X426) @ (sub @ X425 @ X426) @ X427)))) & ($true = ((X417 @ id @ X418 @ id))) & ! [X428 : term,X429 : term] : ((((X417 @ id @ X429 @ id)) != $true) | ($true != ((X417 @ id @ X428 @ id))) | ($true = ((X417 @ id @ (ap @ (sub @ X429 @ id) @ X428) @ id)))))) <=> (hoasinduction_lthm = $true)) & (axassoc = $true) & (! [X321 : term,X320 : (subst > term > subst > $o)] : (($true = ((X320 @ id @ (lam @ (sub @ X321 @ (push @ one @ sh))) @ id))) | ? [X327 : term] : (($true != ((X320 @ id @ (sub @ X321 @ (push @ X327 @ id)) @ id))) & ($true = ((X320 @ id @ X327 @ id)))) | ? [X322 : (subst > term > term)] : (! [X325 : subst,X324 : subst,X323 : term] : (((X322 @ (comp @ X324 @ X325) @ (sub @ X323 @ X325))) = ((sub @ (X322 @ X324 @ X323) @ X325))) & ($true != ((X320 @ id @ (lam @ (X322 @ sh @ one)) @ id))) & ! [X326 : term] : (($true = ((X320 @ id @ (X322 @ id @ X326) @ id))) | ($true != ((X320 @ id @ X326 @ id)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X469 : term] : ? [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) = ((X470 @ sh @ one)))) & ((hoasapinj2 = $true) <=> ! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & ((axshiftcons = $true) <=> ! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125)) & ((induction = $true) <=> ! [X526 : (term > $o),X527 : term] : (? [X529 : term,X528 : term] : (($true = ((X526 @ X529))) & ($true = ((X526 @ X528))) & ($true != ((X526 @ (ap @ X528 @ X529))))) | ? [X530 : term] : (($true != ((X526 @ (lam @ X530)))) & ($true = ((X526 @ X530)))) | ? [X531 : term] : (($true != ((X526 @ X531))) & ($true = ((var @ X531)))) | ($true = ((X526 @ X527))))) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & ((? [X390 : term,X389 : term] : ((((lam @ X389)) = ((lam @ X390))) & (X389 != X390)) | ? [X386 : subst,X385 : term] : (((sub @ one @ (push @ X385 @ X386))) != X385) | ? [X387 : subst,X388 : term] : (((comp @ sh @ (push @ X388 @ X387))) != X387) | ! [X394 : (subst > term > term),X391 : subst,X392 : (subst > term > term),X393 : term] : ((((lam @ (X394 @ sh @ one))) != ((lam @ (X392 @ sh @ one)))) | ? [X400 : subst,X399 : term,X398 : subst] : (((X394 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) != ((sub @ (X394 @ X398 @ X399) @ X400))) | (((X392 @ X391 @ X393)) = ((X394 @ X391 @ X393))) | ? [X397 : term,X396 : subst,X395 : subst] : (((sub @ (X392 @ X395 @ X397) @ X396)) != ((X392 @ (comp @ X395 @ X396) @ (sub @ X397 @ X396)))))) <=> (hoaslaminj_lthm = $true)) & (! [X269 : term,X268 : (subst > term > subst > $o)] : (($true = ((X268 @ id @ (lam @ X269) @ id))) | ? [X270 : (subst > term > term)] : (! [X273 : term,X272 : subst,X274 : subst] : (((sub @ (X270 @ X272 @ X273) @ X274)) = ((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)))) & ! [X271 : term] : ((((X268 @ id @ X271 @ id)) != $true) | ($true = ((X268 @ id @ (X270 @ id @ X271) @ id)))) & ($true != ((X268 @ id @ (lam @ (X270 @ sh @ one)) @ id)))) | ? [X275 : term] : (($true = ((X268 @ id @ X275 @ id))) & ($true != ((X268 @ id @ (sub @ X269 @ (push @ X275 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id)))) & (hoasinduction_lem1v2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) <=> (laminj = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X480 : term,X479 : term,X478 : (subst > term > subst > $o)] : (? [X486 : term,X485 : term] : ((((X478 @ id @ (ap @ (sub @ X485 @ id) @ X486) @ id)) != $true) & ($true = ((X478 @ id @ X485 @ id))) & ($true = ((X478 @ id @ X486 @ id)))) | ($true = ((X478 @ id @ (ap @ X480 @ X479) @ id))) | ($true != ((X478 @ id @ X480 @ id))) | ? [X487 : subst,X490 : subst,X488 : term,X489 : subst] : (($true != ((X478 @ (comp @ X490 @ X487) @ (sub @ X488 @ X487) @ X489))) & ($true = ((X478 @ X490 @ X488 @ (comp @ X487 @ X489))))) | (((X478 @ id @ X479 @ id)) != $true) | ? [X483 : term,X481 : subst,X482 : subst,X484 : subst] : (($true != ((X478 @ X481 @ X483 @ (comp @ X482 @ X484)))) & ($true = ((X478 @ (comp @ X481 @ X482) @ (sub @ X483 @ X482) @ X484)))))) & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) | ? [X475 : term] : (((sub @ X475 @ id)) != X475)) <=> (termmset_lthm = $true)) & ((! [X78 : (term > $o),X76 : subst,X77 : term] : (? [X81 : term] : (($true != ((X78 @ (sub @ X81 @ X76)))) & ($true = ((var @ X81)))) | ? [X82 : term] : (! [X83 : term] : (($true != ((X78 @ X83))) | ($true = ((X78 @ (sub @ X82 @ (push @ X83 @ id)))))) & ($true != ((X78 @ (lam @ X82))))) | ? [X80 : term,X79 : term] : ((((X78 @ (ap @ X80 @ X79))) != $true) & (((X78 @ X79)) = $true) & (((X78 @ X80)) = $true)) | ($true = ((X78 @ (sub @ X77 @ X76))))) | ? [X69 : subst] : (((comp @ X69 @ id)) != X69) | ? [X67 : term,X68 : subst] : (((comp @ sh @ (push @ X67 @ X68))) != X68) | ? [X70 : term,X71 : (term > $o)] : (($true != ((X71 @ X70))) & ! [X72 : term] : (($true != ((var @ X72))) | ($true = ((X71 @ X72)))) & ! [X75 : term] : (($true = ((X71 @ (lam @ X75)))) | ($true != ((X71 @ X75)))) & ! [X73 : term,X74 : term] : (($true = ((X71 @ (ap @ X74 @ X73)))) | ($true != ((X71 @ X74))) | (((X71 @ X73)) != $true))) | ? [X65 : subst,X66 : term] : (((sub @ one @ (push @ X66 @ X65))) != X66)) <=> (induction2lem_lthm = $true)) & (! [X477 : term] : (((sub @ X477 @ id)) = X477) <=> (axvarid = $true)) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) <=> (axidr = $true)) & ((pushprop_lem1 = $true) <=> ! [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true != ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X93 : d_subst] : (d_id = X93) & ((hoasapinj1_lthm = $true) <=> (! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)) | ? [X116 : term] : (((sub @ X116 @ id)) != X116) | ? [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 != X120) & (((ap @ X117 @ X118)) = ((ap @ X120 @ X119)))))) & ((? [X349 : term] : ! [X350 : (subst > term > term)] : ? [X352 : term,X351 : subst] : (((sub @ X349 @ (push @ X352 @ X351))) != ((X350 @ X351 @ X352))) | ? [X353 : term] : (((sub @ X353 @ id)) != X353) | ! [X355 : (subst > term > subst > $o),X356 : (term > $o),X354 : term] : (? [X363 : term] : (($true != ((X356 @ (sub @ X354 @ (push @ X363 @ id))))) & ($true = ((X356 @ X363)))) | ? [X357 : term] : (((X356 @ X357)) != ((X355 @ id @ X357 @ id))) | ? [X358 : (subst > term > term)] : (! [X361 : term,X359 : subst,X360 : subst] : (((sub @ (X358 @ X359 @ X361) @ X360)) = ((X358 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360)))) & (((X355 @ id @ (lam @ (X358 @ sh @ one)) @ id)) != $true) & ! [X362 : term] : (($true != ((X355 @ id @ X362 @ id))) | ($true = ((X355 @ id @ (X358 @ id @ X362) @ id))))) | (((X356 @ (lam @ X354))) = $true))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (apnotvar = $true) & ((! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257)) | ? [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) = ((ap @ X251 @ X252))) & (X252 != X254))) <=> (hoasapinj2_lthm = $true)) & ((? [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) != X51) | ? [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) != X49) | ! [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true != ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))) <=> (pushprop_lem1_lthm = $true)) & ! [X263 : d_term] : (d_one = X263) & (induction2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> (axscons = $true)) & (! [X510 : term,X511 : (subst > term > subst > $o)] : (? [X513 : term,X512 : (subst > term > term)] : (! [X520 : subst,X518 : term,X519 : subst] : (((sub @ (X512 @ X519 @ X518) @ X520)) = ((sub @ (sub @ X513 @ (push @ X518 @ X519)) @ X520))) & ! [X517 : term] : (($true = ((X511 @ id @ (X512 @ id @ X517) @ id))) | (((X511 @ id @ X517 @ id)) != $true)) & ! [X515 : term,X514 : subst,X516 : subst] : (((sub @ X513 @ (push @ (sub @ X515 @ X516) @ (comp @ X514 @ X516)))) = ((X512 @ (comp @ X514 @ X516) @ (sub @ X515 @ X516)))) & ($true != ((X511 @ id @ (lam @ (X512 @ sh @ one)) @ id)))) | ? [X521 : term] : (($true = ((X511 @ id @ X521 @ id))) & (((X511 @ id @ (sub @ X510 @ (push @ X521 @ id)) @ id)) != $true)) | (((X511 @ id @ (lam @ (sub @ X510 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (termmset_gthm = $true) & (! [X402 : (term > $o),X401 : subst,X403 : term] : ? [X404 : (term > $o)] : ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401))))) <=> (pushprop_lem0_lthm = $true)) & (! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) <=> (apinj1 = $true)) & (axabs = $true) & ((substmonoid_lthm = $true) <=> ((! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)) | ? [X523 : subst] : (((comp @ X523 @ id)) != X523) | ? [X522 : subst] : (((comp @ id @ X522)) != X522))) & ((apinj2 = $true) <=> ! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198))) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X332 : term] : (((sub @ X332 @ id)) != X332) | ! [X342 : (subst > term > subst > $o),X341 : term] : (? [X343 : (subst > term > term)] : (! [X345 : subst,X346 : term,X347 : subst] : (((sub @ (X343 @ X345 @ X346) @ X347)) = ((X343 @ (comp @ X345 @ X347) @ (sub @ X346 @ X347)))) & ! [X344 : term] : ((((X342 @ id @ X344 @ id)) != $true) | ($true = ((X342 @ id @ (X343 @ id @ X344) @ id)))) & ($true != ((X342 @ id @ (lam @ (X343 @ sh @ one)) @ id)))) | ? [X348 : term] : ((((X342 @ id @ (sub @ X341 @ (push @ X348 @ id)) @ id)) != $true) & ($true = ((X342 @ id @ X348 @ id)))) | ($true = ((X342 @ id @ (lam @ X341) @ id)))) | ? [X334 : (subst > term > subst > $o),X333 : term] : (! [X335 : term] : ((((X334 @ id @ X335 @ id)) != $true) | (((X334 @ id @ (sub @ X333 @ (push @ X335 @ id)) @ id)) = $true)) & (((X334 @ id @ (lam @ (sub @ X333 @ (push @ one @ sh))) @ id)) != $true) & ! [X336 : (subst > term > term)] : (? [X337 : subst,X338 : term,X339 : subst] : (((X336 @ (comp @ X339 @ X337) @ (sub @ X338 @ X337))) != ((sub @ (X336 @ X339 @ X338) @ X337))) | ? [X340 : term] : (($true = ((X334 @ id @ X340 @ id))) & ($true != ((X334 @ id @ (X336 @ id @ X340) @ id)))) | ($true = ((X334 @ id @ (lam @ (X336 @ sh @ one)) @ id))))))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (ulamvar1 != $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X264 : term] : ? [X265 : (subst > term > term)] : ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ! [X156 : d_subst,X155 : d_subst] : ((((d2subst @ X155)) != ((d2subst @ X156))) | (X155 = X156)) & (induction2lem_gthm = $true) & (! [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ? [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) != ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) | (((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ? [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) != ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280))))) <=> (hoaslaminj = $true)) & (! [X113 : (subst > term > subst > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X167 : term,X168 : (term > $o)] : (! [X169 : term,X170 : term] : (($true != ((X168 @ X170))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)) & ! [X173 : term] : ((((var @ X173)) != $true) | (((X168 @ X173)) = $true)) & ($true != ((X168 @ X167))) & ! [X171 : term] : (? [X172 : term] : (($true != ((X168 @ (sub @ X171 @ (push @ X172 @ id))))) & ($true = ((X168 @ X172)))) | ($true = ((X168 @ (lam @ X171)))))) | ? [X174 : term] : (((sub @ X174 @ id)) != X174) | ! [X186 : term,X185 : (subst > term > subst > $o)] : ((((X185 @ id @ X186 @ id)) = $true) | ? [X189 : (subst > term > term)] : (! [X193 : term] : ((((X185 @ id @ (X189 @ id @ X193) @ id)) = $true) | ($true != ((X185 @ id @ X193 @ id)))) & ($true != ((X185 @ id @ (lam @ (X189 @ sh @ one)) @ id))) & ! [X190 : subst,X192 : subst,X191 : term] : (((sub @ (X189 @ X190 @ X191) @ X192)) = ((X189 @ (comp @ X190 @ X192) @ (sub @ X191 @ X192))))) | ? [X188 : term,X187 : term] : (($true = ((X185 @ id @ X187 @ id))) & ($true = ((X185 @ id @ X188 @ id))) & ($true != ((X185 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id))))) | ? [X164 : (subst > term > subst > $o)] : ! [X165 : (term > $o)] : ? [X166 : term] : (((X165 @ X166)) != ((X164 @ id @ X166 @ id))) | ? [X177 : term,X176 : (subst > term > subst > $o),X175 : (term > $o)] : ((((X175 @ (lam @ X177))) != $true) & ! [X184 : term] : (((X176 @ id @ X184 @ id)) = ((X175 @ X184))) & ! [X179 : (subst > term > term)] : ((((X176 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ? [X183 : term] : ((((X176 @ id @ X183 @ id)) = $true) & (((X176 @ id @ (X179 @ id @ X183) @ id)) != $true)) | ? [X180 : subst,X181 : term,X182 : subst] : (((sub @ (X179 @ X180 @ X181) @ X182)) != ((X179 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182))))) & ! [X178 : term] : (($true != ((X175 @ X178))) | ($true = ((X175 @ (sub @ X177 @ (push @ X178 @ id))))))))) & (axmap = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction = $true) <=> ! [X302 : (subst > term > subst > $o),X303 : term] : (? [X304 : term] : ((((X302 @ id @ X304 @ id)) != $true) & (((var @ (sub @ X304 @ id))) = $true)) | ? [X315 : subst,X317 : subst,X314 : subst,X316 : term] : (($true = ((X302 @ X314 @ X316 @ (comp @ X317 @ X315)))) & ($true != ((X302 @ (comp @ X314 @ X317) @ (sub @ X316 @ X317) @ X315)))) | ? [X305 : (subst > term > term)] : ((((X302 @ id @ (lam @ (X305 @ sh @ one)) @ id)) != $true) & ! [X306 : term] : ((((X302 @ id @ (X305 @ id @ X306) @ id)) = $true) | (((X302 @ id @ X306 @ id)) != $true)) & ! [X308 : term,X307 : subst,X309 : subst] : (((X305 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307))) = ((sub @ (X305 @ X309 @ X308) @ X307)))) | ? [X313 : subst,X310 : term,X312 : subst,X311 : subst] : (($true = ((X302 @ (comp @ X311 @ X313) @ (sub @ X310 @ X313) @ X312))) & ($true != ((X302 @ X311 @ X310 @ (comp @ X313 @ X312))))) | ($true = ((X302 @ id @ X303 @ id))) | ? [X318 : term,X319 : term] : (($true = ((X302 @ id @ X319 @ id))) & ($true = ((X302 @ id @ X318 @ id))) & ($true != ((X302 @ id @ (ap @ (sub @ X318 @ id) @ X319) @ id)))))) & ((induction2lem = $true) <=> ! [X532 : subst,X533 : term,X534 : (term > $o)] : (? [X538 : term,X537 : term] : (($true = ((X534 @ X538))) & ($true = ((X534 @ X537))) & (((X534 @ (ap @ X538 @ X537))) != $true)) | ? [X539 : term] : (($true = ((var @ X539))) & ($true != ((X534 @ (sub @ X539 @ X532))))) | ($true = ((X534 @ (sub @ X533 @ X532)))) | ? [X535 : term] : (($true != ((X534 @ (lam @ X535)))) & ! [X536 : term] : (($true = ((X534 @ (sub @ X535 @ (push @ X536 @ id))))) | ($true != ((X534 @ X536))))))) & ((shinj = $true) <=> ! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X205 : d_term,X204 : d_term] : ((X204 = X205) | (((d2term @ X204)) != ((d2term @ X205)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X286 : (term > $o),X287 : term,X288 : (subst > term > subst > $o)] : (? [X289 : term] : (((X286 @ X289)) != ((X288 @ id @ X289 @ id))) | ($true = ((X286 @ (lam @ X287)))) | ? [X295 : term] : (($true != ((X286 @ (sub @ X287 @ (push @ X295 @ id))))) & ($true = ((X286 @ X295)))) | ? [X290 : (subst > term > term)] : (($true != ((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id))) & ! [X291 : term] : (($true = ((X288 @ id @ (X290 @ id @ X291) @ id))) | ($true != ((X288 @ id @ X291 @ id)))) & ! [X293 : subst,X294 : subst,X292 : term] : (((X290 @ (comp @ X293 @ X294) @ (sub @ X292 @ X294))) = ((sub @ (X290 @ X293 @ X292) @ X294)))))) & (pushprop_lem2v2 = $true) & (axapp = $true) & ((axvarcons = $true) <=> ! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44)) & (hoasinduction_lem3v2_gthm = $true) & ((! [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) = $true) | ($true != ((X91 @ X89))) | ? [X92 : term] : (((X88 @ X92)) != ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) | ? [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) != X86)) <=> (pushprop_lem1v2_lthm = $true)) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X237 : term,X236 : term,X238 : (subst > term > subst > $o),X239 : (term > $o)] : (? [X248 : term,X250 : subst,X247 : subst,X249 : subst] : (($true = ((X238 @ (comp @ X247 @ X250) @ (sub @ X248 @ X250) @ X249))) & ($true != ((X238 @ X247 @ X248 @ (comp @ X250 @ X249))))) | ? [X244 : term] : (((X238 @ id @ X244 @ id)) != ((X239 @ X244))) | ($true != ((X239 @ X236))) | ($true != ((X239 @ X237))) | ($true = ((X239 @ (ap @ X236 @ X237)))) | ? [X242 : subst,X241 : subst,X240 : term,X243 : subst] : (($true = ((X238 @ X241 @ X240 @ (comp @ X243 @ X242)))) & ($true != ((X238 @ (comp @ X241 @ X243) @ (sub @ X240 @ X243) @ X242)))) | ? [X245 : term,X246 : term] : ((((X238 @ id @ X246 @ id)) = $true) & (((X238 @ id @ X245 @ id)) = $true) & (((X238 @ id @ (ap @ (sub @ X246 @ id) @ X245) @ id)) != $true)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X206 : term] : (((sub @ X206 @ id)) != X206) | ! [X216 : (subst > term > subst > $o),X215 : term] : (($true = ((X216 @ id @ (lam @ X215) @ id))) | ? [X221 : (subst > term > term)] : (! [X225 : term] : (($true != ((X216 @ id @ X225 @ id))) | (((X216 @ id @ (X221 @ id @ X225) @ id)) = $true)) & ! [X223 : term,X224 : subst,X222 : subst] : (((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))) = ((sub @ (X221 @ X224 @ X223) @ X222))) & ($true != ((X216 @ id @ (lam @ (X221 @ sh @ one)) @ id)))) | ? [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (($true != ((X216 @ X218 @ X219 @ (comp @ X220 @ X217)))) & (((X216 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220) @ X217)) = $true)) | ? [X228 : subst,X227 : subst,X230 : subst,X229 : term] : (($true = ((X216 @ X227 @ X229 @ (comp @ X230 @ X228)))) & ($true != ((X216 @ (comp @ X227 @ X230) @ (sub @ X229 @ X230) @ X228)))) | ? [X226 : term] : (($true != ((X216 @ id @ (sub @ X215 @ (push @ X226 @ id)) @ id))) & (((X216 @ id @ X226 @ id)) = $true))) | ? [X208 : (subst > term > subst > $o),X207 : term] : (! [X210 : (subst > term > term)] : (? [X214 : term] : (($true = ((X208 @ id @ X214 @ id))) & ($true != ((X208 @ id @ (X210 @ id @ X214) @ id)))) | ($true = ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id))) | ? [X213 : subst,X212 : subst,X211 : term] : (((sub @ (X210 @ X212 @ X211) @ X213)) != ((X210 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213))))) & ($true != ((X208 @ id @ (lam @ (sub @ X207 @ (push @ one @ sh))) @ id))) & ! [X209 : term] : (($true = ((X208 @ id @ (sub @ X207 @ (push @ X209 @ id)) @ id))) | (((X208 @ id @ X209 @ id)) != $true))))) & (hoasinduction_lem3a_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (? [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) != ((X202 @ X203))) | ($true != ((X201 @ X200))) | ($true = ((X202 @ one))))) & ((hoasinduction_lem3 = $true) <=> ! [X95 : (subst > term > subst > $o),X94 : term] : (? [X103 : subst,X102 : subst,X104 : term,X105 : subst] : (($true = ((X95 @ X103 @ X104 @ (comp @ X102 @ X105)))) & ($true != ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105)))) | (((X95 @ id @ (lam @ X94) @ id)) = $true) | ? [X109 : subst,X106 : term,X108 : subst,X107 : subst] : ((((X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108)) = $true) & ($true != ((X95 @ X109 @ X106 @ (comp @ X107 @ X108))))) | ? [X96 : term] : (($true = ((X95 @ id @ X96 @ id))) & ($true != ((X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id)))) | ? [X97 : (subst > term > term)] : (! [X101 : term] : (($true = ((X95 @ id @ (X97 @ id @ X101) @ id))) | ($true != ((X95 @ id @ X101 @ id)))) & (((X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) != $true) & ! [X98 : subst,X100 : subst,X99 : term] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98)))))) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X471 : term] : ? [X472 : (subst > term > term)] : (((X472 @ sh @ one)) = ((sub @ X471 @ (push @ one @ sh))))) & ((substmonoid = $true) <=> (! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259))) & (! [X58 : (subst > term > subst > $o),X57 : term] : (? [X64 : term] : (($true != ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id))) & ($true = ((X58 @ id @ X64 @ id)))) | ? [X59 : (subst > term > term)] : (! [X62 : subst,X60 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) & ($true != ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id))) & ! [X63 : term] : ((((X58 @ id @ (X59 @ id @ X63) @ id)) = $true) | ($true != ((X58 @ id @ X63 @ id))))) | (((X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X128 : (subst > term > subst > $o),X127 : term] : (($true = ((X128 @ id @ X127 @ id))) | ? [X134 : term,X135 : term] : (($true = ((X128 @ id @ X135 @ id))) & (((X128 @ id @ X134 @ id)) = $true) & ($true != ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) | ? [X129 : (subst > term > term)] : (! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133)))) & ! [X130 : term] : (($true != ((X128 @ id @ X130 @ id))) | ($true = ((X128 @ id @ (X129 @ id @ X130) @ id)))) & (((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id)) != $true)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X491 : term] : (((sub @ X491 @ id)) != X491) | ! [X492 : (term > $o),X494 : term,X493 : (subst > term > subst > $o)] : (? [X501 : subst,X500 : subst,X503 : subst,X502 : term] : ((((X493 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) = $true) & ($true != ((X493 @ X500 @ X502 @ (comp @ X501 @ X503))))) | ? [X495 : term] : (((X493 @ id @ X495 @ id)) != ((X492 @ X495))) | ? [X504 : (subst > term > term)] : (! [X508 : term,X507 : subst,X506 : subst] : (((X504 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507))) = ((sub @ (X504 @ X506 @ X508) @ X507))) & ($true != ((X493 @ id @ (lam @ (X504 @ sh @ one)) @ id))) & ! [X505 : term] : (($true != ((X493 @ id @ X505 @ id))) | (((X493 @ id @ (X504 @ id @ X505) @ id)) = $true))) | ? [X509 : term] : (($true = ((X492 @ X509))) & ($true != ((X492 @ (sub @ X494 @ (push @ X509 @ id)))))) | ? [X497 : term,X498 : subst,X496 : subst,X499 : subst] : (($true != ((X493 @ (comp @ X498 @ X499) @ (sub @ X497 @ X499) @ X496))) & ($true = ((X493 @ X498 @ X497 @ (comp @ X499 @ X496))))) | ($true = ((X492 @ (lam @ X494))))))) & (axvarshift = $true) & (! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) <=> (hoasapinj1 = $true)) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1 = $true) & ((induction2 = $true) <=> ! [X158 : (term > $o),X157 : term] : (($true = ((X158 @ X157))) | ? [X161 : term] : (($true != ((X158 @ X161))) & ($true = ((var @ X161)))) | ? [X163 : term,X162 : term] : ((((X158 @ X163)) = $true) & ($true = ((X158 @ X162))) & ($true != ((X158 @ (ap @ X162 @ X163))))) | ? [X159 : term] : ((((X158 @ (lam @ X159))) != $true) & ! [X160 : term] : (($true = ((X158 @ (sub @ X159 @ (push @ X160 @ id))))) | ($true != ((X158 @ X160))))))) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (! [X194 : term] : (((sub @ X194 @ id)) = X194) <=> (termmset = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X39 : term] : ? [X40 : (subst > term > term)] : ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42)))) <=> (hoasinduction_lem3v2_f = $true)) & ((hoaslamnotap = $true) <=> ! [X296 : term,X298 : (subst > term > term),X297 : term] : (? [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one)))))) & ((axidl = $true) <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & (hoasinduction_lem2_gthm = $true) & (! [X232 : term,X233 : subst,X231 : (term > $o)] : ? [X234 : (term > $o)] : ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) <=> (pushprop_lem0 = $true)) & (lamnotap != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X137 : (subst > term > subst > $o),X139 : term,X138 : (term > $o)] : (? [X145 : term] : (((X138 @ X145)) != ((X137 @ id @ X145 @ id))) | ? [X140 : (subst > term > term)] : (! [X144 : term] : ((((X137 @ id @ X144 @ id)) != $true) | ($true = ((X137 @ id @ (X140 @ id @ X144) @ id)))) & ! [X143 : subst,X142 : subst,X141 : term] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) & (((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) != $true)) | ? [X146 : subst,X149 : subst,X147 : term,X148 : subst] : (($true = ((X137 @ X149 @ X147 @ (comp @ X146 @ X148)))) & (((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148)) != $true)) | ? [X154 : subst,X151 : term,X153 : subst,X152 : subst] : ((((X137 @ X152 @ X151 @ (comp @ X153 @ X154))) != $true) & ($true = ((X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154)))) | ? [X150 : term] : (($true != ((X138 @ (sub @ X139 @ (push @ X150 @ id))))) & (((X138 @ X150)) = $true)) | ($true = ((X138 @ (lam @ X139))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X21 : term,X22 : (subst > term > subst > $o)] : (? [X36 : subst,X38 : subst,X35 : term,X37 : subst] : ((((X22 @ X36 @ X35 @ (comp @ X38 @ X37))) = $true) & (((X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37)) != $true)) | ? [X30 : (subst > term > term)] : (! [X34 : term] : (($true = ((X22 @ id @ (X30 @ id @ X34) @ id))) | ($true != ((X22 @ id @ X34 @ id)))) & (((X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) != $true) & ! [X33 : term,X31 : subst,X32 : subst] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32))))) | ? [X29 : term] : (($true != ((X22 @ id @ X29 @ id))) & ($true = ((var @ (sub @ X29 @ id))))) | ? [X24 : term,X23 : term] : ((((X22 @ id @ X23 @ id)) = $true) & ($true != ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id))) & ($true = ((X22 @ id @ X24 @ id)))) | (((X22 @ id @ X21 @ id)) = $true) | ? [X25 : subst,X28 : term,X27 : subst,X26 : subst] : (($true != ((X22 @ X26 @ X28 @ (comp @ X27 @ X25)))) & ($true = ((X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25))))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X13 : (term > $o),X11 : term,X12 : (subst > term > subst > $o)] : (! [X20 : term] : (($true = ((X13 @ (sub @ X11 @ (push @ X20 @ id))))) | (((X13 @ X20)) != $true)) & ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) & ($true != ((X13 @ (lam @ X11)))) & ! [X15 : (subst > term > term)] : (? [X16 : term] : (($true != ((X12 @ id @ (X15 @ id @ X16) @ id))) & (((X12 @ id @ X16 @ id)) = $true)) | ? [X17 : subst,X19 : term,X18 : subst] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) != ((sub @ (X15 @ X18 @ X19) @ X17))) | ($true = ((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))))) | ? [X4 : (term > $o),X3 : term] : (! [X5 : term] : (($true != ((var @ X5))) | ($true = ((X4 @ X5)))) & (((X4 @ X3)) != $true) & ! [X7 : term,X6 : term] : (($true != ((X4 @ X7))) | ($true = ((X4 @ (ap @ X7 @ X6)))) | ($true != ((X4 @ X6)))) & ! [X8 : term] : (? [X9 : term] : (($true != ((X4 @ (sub @ X8 @ (push @ X9 @ id))))) & ($true = ((X4 @ X9)))) | ($true = ((X4 @ (lam @ X8)))))))) & (hoasinduction_lem2_lthm = $true)),
% 2.91/0.81 inference(flattening,[],[f11])).
% 2.91/0.81 thf(f13,definition,(
% 2.91/0.81 ! [X4 : (term > $o)] : (($true = ((sP0 @ X4))) <=> ! [X7 : term,X6 : term] : (($true != ((X4 @ X7))) | ($true = ((X4 @ (ap @ X7 @ X6)))) | ($true != ((X4 @ X6)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f14,definition,(
% 2.91/0.81 ! [X22 : (subst > term > subst > $o)] : (($true = ((sP1 @ X22))) <=> ? [X24 : term,X23 : term] : ((((X22 @ id @ X23 @ id)) = $true) & ($true != ((X22 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id))) & ($true = ((X22 @ id @ X24 @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f15,definition,(
% 2.91/0.81 ! [X22 : (subst > term > subst > $o)] : (($true = ((sP2 @ X22))) <=> ? [X30 : (subst > term > term)] : (! [X34 : term] : (($true = ((X22 @ id @ (X30 @ id @ X34) @ id))) | ($true != ((X22 @ id @ X34 @ id)))) & (((X22 @ id @ (lam @ (X30 @ sh @ one)) @ id)) != $true) & ! [X33 : term,X31 : subst,X32 : subst] : (((sub @ (X30 @ X31 @ X33) @ X32)) = ((X30 @ (comp @ X31 @ X32) @ (sub @ X33 @ X32))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f16,definition,(
% 2.91/0.81 ($true = sP3) <=> ? [X13 : (term > $o),X11 : term,X12 : (subst > term > subst > $o)] : (! [X20 : term] : (($true = ((X13 @ (sub @ X11 @ (push @ X20 @ id))))) | (((X13 @ X20)) != $true)) & ! [X14 : term] : (((X12 @ id @ X14 @ id)) = ((X13 @ X14))) & ($true != ((X13 @ (lam @ X11)))) & ! [X15 : (subst > term > term)] : (? [X16 : term] : (($true != ((X12 @ id @ (X15 @ id @ X16) @ id))) & (((X12 @ id @ X16 @ id)) = $true)) | ? [X17 : subst,X19 : term,X18 : subst] : (((X15 @ (comp @ X18 @ X17) @ (sub @ X19 @ X17))) != ((sub @ (X15 @ X18 @ X19) @ X17))) | ($true = ((X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f17,definition,(
% 2.91/0.81 ($true = sP4) <=> ! [X21 : term,X22 : (subst > term > subst > $o)] : (? [X36 : subst,X38 : subst,X35 : term,X37 : subst] : ((((X22 @ X36 @ X35 @ (comp @ X38 @ X37))) = $true) & (((X22 @ (comp @ X36 @ X38) @ (sub @ X35 @ X38) @ X37)) != $true)) | ($true = ((sP2 @ X22))) | ? [X29 : term] : (($true != ((X22 @ id @ X29 @ id))) & ($true = ((var @ (sub @ X29 @ id))))) | ($true = ((sP1 @ X22))) | (((X22 @ id @ X21 @ id)) = $true) | ? [X25 : subst,X28 : term,X27 : subst,X26 : subst] : (($true != ((X22 @ X26 @ X28 @ (comp @ X27 @ X25)))) & ($true = ((X22 @ (comp @ X26 @ X27) @ (sub @ X28 @ X27) @ X25)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f18,definition,(
% 2.91/0.81 ($true = sP5) <=> (($true = sP4) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ($true = sP3) | ? [X4 : (term > $o),X3 : term] : (! [X5 : term] : (($true != ((var @ X5))) | ($true = ((X4 @ X5)))) & (((X4 @ X3)) != $true) & ($true = ((sP0 @ X4))) & ! [X8 : term] : (? [X9 : term] : (($true != ((X4 @ (sub @ X8 @ (push @ X9 @ id))))) & ($true = ((X4 @ X9)))) | ($true = ((X4 @ (lam @ X8)))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f19,definition,(
% 2.91/0.81 ! [X137 : (subst > term > subst > $o)] : ((((sP6 @ X137)) = $true) <=> ? [X140 : (subst > term > term)] : (! [X144 : term] : ((((X137 @ id @ X144 @ id)) != $true) | ($true = ((X137 @ id @ (X140 @ id @ X144) @ id)))) & ! [X143 : subst,X142 : subst,X141 : term] : (((sub @ (X140 @ X143 @ X141) @ X142)) = ((X140 @ (comp @ X143 @ X142) @ (sub @ X141 @ X142)))) & (((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f20,definition,(
% 2.91/0.81 ($true = sP7) <=> ! [X137 : (subst > term > subst > $o),X139 : term,X138 : (term > $o)] : (? [X145 : term] : (((X138 @ X145)) != ((X137 @ id @ X145 @ id))) | (((sP6 @ X137)) = $true) | ? [X146 : subst,X149 : subst,X147 : term,X148 : subst] : (($true = ((X137 @ X149 @ X147 @ (comp @ X146 @ X148)))) & (((X137 @ (comp @ X149 @ X146) @ (sub @ X147 @ X146) @ X148)) != $true)) | ? [X154 : subst,X151 : term,X153 : subst,X152 : subst] : ((((X137 @ X152 @ X151 @ (comp @ X153 @ X154))) != $true) & ($true = ((X137 @ (comp @ X152 @ X153) @ (sub @ X151 @ X153) @ X154)))) | ? [X150 : term] : (($true != ((X138 @ (sub @ X139 @ (push @ X150 @ id))))) & (((X138 @ X150)) = $true)) | ($true = ((X138 @ (lam @ X139)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f21,definition,(
% 2.91/0.81 ! [X158 : (term > $o)] : (($true = ((sP8 @ X158))) <=> ? [X163 : term,X162 : term] : ((((X158 @ X163)) = $true) & ($true = ((X158 @ X162))) & ($true != ((X158 @ (ap @ X162 @ X163))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f22,definition,(
% 2.91/0.81 ($true = sP9) <=> ! [X158 : (term > $o),X157 : term] : (($true = ((X158 @ X157))) | ? [X161 : term] : (($true != ((X158 @ X161))) & ($true = ((var @ X161)))) | ($true = ((sP8 @ X158))) | ? [X159 : term] : ((((X158 @ (lam @ X159))) != $true) & ! [X160 : term] : (($true = ((X158 @ (sub @ X159 @ (push @ X160 @ id))))) | ($true != ((X158 @ X160))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f23,definition,(
% 2.91/0.81 ! [X493 : (subst > term > subst > $o)] : (($true = ((sP10 @ X493))) <=> ? [X504 : (subst > term > term)] : (! [X508 : term,X507 : subst,X506 : subst] : (((X504 @ (comp @ X506 @ X507) @ (sub @ X508 @ X507))) = ((sub @ (X504 @ X506 @ X508) @ X507))) & ($true != ((X493 @ id @ (lam @ (X504 @ sh @ one)) @ id))) & ! [X505 : term] : (($true != ((X493 @ id @ X505 @ id))) | (((X493 @ id @ (X504 @ id @ X505) @ id)) = $true))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f24,definition,(
% 2.91/0.81 ($true = sP11) <=> (? [X491 : term] : (((sub @ X491 @ id)) != X491) | ! [X492 : (term > $o),X494 : term,X493 : (subst > term > subst > $o)] : (? [X501 : subst,X500 : subst,X503 : subst,X502 : term] : ((((X493 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) = $true) & ($true != ((X493 @ X500 @ X502 @ (comp @ X501 @ X503))))) | ? [X495 : term] : (((X493 @ id @ X495 @ id)) != ((X492 @ X495))) | ($true = ((sP10 @ X493))) | ? [X509 : term] : (($true = ((X492 @ X509))) & ($true != ((X492 @ (sub @ X494 @ (push @ X509 @ id)))))) | ? [X497 : term,X498 : subst,X496 : subst,X499 : subst] : (($true != ((X493 @ (comp @ X498 @ X499) @ (sub @ X497 @ X499) @ X496))) & ($true = ((X493 @ X498 @ X497 @ (comp @ X499 @ X496))))) | ($true = ((X492 @ (lam @ X494))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f25,definition,(
% 2.91/0.81 ! [X128 : (subst > term > subst > $o)] : ((((sP12 @ X128)) = $true) <=> ? [X129 : (subst > term > term)] : (! [X131 : term,X132 : subst,X133 : subst] : (((sub @ (X129 @ X132 @ X131) @ X133)) = ((X129 @ (comp @ X132 @ X133) @ (sub @ X131 @ X133)))) & ! [X130 : term] : (($true != ((X128 @ id @ X130 @ id))) | ($true = ((X128 @ id @ (X129 @ id @ X130) @ id)))) & (((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id)) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f26,definition,(
% 2.91/0.81 (sP13 = $true) <=> ! [X58 : (subst > term > subst > $o),X57 : term] : (? [X64 : term] : (($true != ((X58 @ id @ (sub @ X57 @ (push @ X64 @ id)) @ id))) & ($true = ((X58 @ id @ X64 @ id)))) | ? [X59 : (subst > term > term)] : (! [X62 : subst,X60 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X60)) = ((X59 @ (comp @ X62 @ X60) @ (sub @ X61 @ X60)))) & ($true != ((X58 @ id @ (lam @ (X59 @ sh @ one)) @ id))) & ! [X63 : term] : ((((X58 @ id @ (X59 @ id @ X63) @ id)) = $true) | ($true != ((X58 @ id @ X63 @ id))))) | (((X58 @ id @ (lam @ (sub @ X57 @ (push @ one @ sh))) @ id)) = $true))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f27,definition,(
% 2.91/0.81 ! [X95 : (subst > term > subst > $o)] : ((((sP14 @ X95)) = $true) <=> ? [X97 : (subst > term > term)] : (! [X101 : term] : (($true = ((X95 @ id @ (X97 @ id @ X101) @ id))) | ($true != ((X95 @ id @ X101 @ id)))) & (((X95 @ id @ (lam @ (X97 @ sh @ one)) @ id)) != $true) & ! [X98 : subst,X100 : subst,X99 : term] : (((X97 @ (comp @ X100 @ X98) @ (sub @ X99 @ X98))) = ((sub @ (X97 @ X100 @ X99) @ X98)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f28,definition,(
% 2.91/0.81 ($true = sP15) <=> ! [X95 : (subst > term > subst > $o),X94 : term] : (? [X103 : subst,X102 : subst,X104 : term,X105 : subst] : (($true = ((X95 @ X103 @ X104 @ (comp @ X102 @ X105)))) & ($true != ((X95 @ (comp @ X103 @ X102) @ (sub @ X104 @ X102) @ X105)))) | (((X95 @ id @ (lam @ X94) @ id)) = $true) | ? [X109 : subst,X106 : term,X108 : subst,X107 : subst] : ((((X95 @ (comp @ X109 @ X107) @ (sub @ X106 @ X107) @ X108)) = $true) & ($true != ((X95 @ X109 @ X106 @ (comp @ X107 @ X108))))) | ? [X96 : term] : (($true = ((X95 @ id @ X96 @ id))) & ($true != ((X95 @ id @ (sub @ X94 @ (push @ X96 @ id)) @ id)))) | (((sP14 @ X95)) = $true))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f29,definition,(
% 2.91/0.81 ! [X216 : (subst > term > subst > $o)] : (($true = ((sP16 @ X216))) <=> ? [X221 : (subst > term > term)] : (! [X225 : term] : (($true != ((X216 @ id @ X225 @ id))) | (((X216 @ id @ (X221 @ id @ X225) @ id)) = $true)) & ! [X223 : term,X224 : subst,X222 : subst] : (((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))) = ((sub @ (X221 @ X224 @ X223) @ X222))) & ($true != ((X216 @ id @ (lam @ (X221 @ sh @ one)) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f30,definition,(
% 2.91/0.81 ($true = sP17) <=> ? [X208 : (subst > term > subst > $o),X207 : term] : (! [X210 : (subst > term > term)] : (? [X214 : term] : (($true = ((X208 @ id @ X214 @ id))) & ($true != ((X208 @ id @ (X210 @ id @ X214) @ id)))) | ($true = ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id))) | ? [X213 : subst,X212 : subst,X211 : term] : (((sub @ (X210 @ X212 @ X211) @ X213)) != ((X210 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213))))) & ($true != ((X208 @ id @ (lam @ (sub @ X207 @ (push @ one @ sh))) @ id))) & ! [X209 : term] : (($true = ((X208 @ id @ (sub @ X207 @ (push @ X209 @ id)) @ id))) | (((X208 @ id @ X209 @ id)) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f31,definition,(
% 2.91/0.81 (sP18 = $true) <=> (? [X206 : term] : (((sub @ X206 @ id)) != X206) | ! [X216 : (subst > term > subst > $o),X215 : term] : (($true = ((X216 @ id @ (lam @ X215) @ id))) | ($true = ((sP16 @ X216))) | ? [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (($true != ((X216 @ X218 @ X219 @ (comp @ X220 @ X217)))) & (((X216 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220) @ X217)) = $true)) | ? [X228 : subst,X227 : subst,X230 : subst,X229 : term] : (($true = ((X216 @ X227 @ X229 @ (comp @ X230 @ X228)))) & ($true != ((X216 @ (comp @ X227 @ X230) @ (sub @ X229 @ X230) @ X228)))) | ? [X226 : term] : (($true != ((X216 @ id @ (sub @ X215 @ (push @ X226 @ id)) @ id))) & (((X216 @ id @ X226 @ id)) = $true))) | ($true = sP17))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f32,definition,(
% 2.91/0.81 ! [X238 : (subst > term > subst > $o)] : (($true = ((sP19 @ X238))) <=> ? [X245 : term,X246 : term] : ((((X238 @ id @ X246 @ id)) = $true) & (((X238 @ id @ X245 @ id)) = $true) & (((X238 @ id @ (ap @ (sub @ X246 @ id) @ X245) @ id)) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f33,definition,(
% 2.91/0.81 ($true = sP20) <=> ! [X237 : term,X236 : term,X238 : (subst > term > subst > $o),X239 : (term > $o)] : (? [X248 : term,X250 : subst,X247 : subst,X249 : subst] : (($true = ((X238 @ (comp @ X247 @ X250) @ (sub @ X248 @ X250) @ X249))) & ($true != ((X238 @ X247 @ X248 @ (comp @ X250 @ X249))))) | ? [X244 : term] : (((X238 @ id @ X244 @ id)) != ((X239 @ X244))) | ($true != ((X239 @ X236))) | ($true != ((X239 @ X237))) | ($true = ((X239 @ (ap @ X236 @ X237)))) | ? [X242 : subst,X241 : subst,X240 : term,X243 : subst] : (($true = ((X238 @ X241 @ X240 @ (comp @ X243 @ X242)))) & ($true != ((X238 @ (comp @ X241 @ X243) @ (sub @ X240 @ X243) @ X242)))) | ($true = ((sP19 @ X238))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f34,definition,(
% 2.91/0.81 ($true = sP21) <=> ! [X286 : (term > $o),X287 : term,X288 : (subst > term > subst > $o)] : (? [X289 : term] : (((X286 @ X289)) != ((X288 @ id @ X289 @ id))) | ($true = ((X286 @ (lam @ X287)))) | ? [X295 : term] : (($true != ((X286 @ (sub @ X287 @ (push @ X295 @ id))))) & ($true = ((X286 @ X295)))) | ? [X290 : (subst > term > term)] : (($true != ((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id))) & ! [X291 : term] : (($true = ((X288 @ id @ (X290 @ id @ X291) @ id))) | ($true != ((X288 @ id @ X291 @ id)))) & ! [X293 : subst,X294 : subst,X292 : term] : (((X290 @ (comp @ X293 @ X294) @ (sub @ X292 @ X294))) = ((sub @ (X290 @ X293 @ X292) @ X294)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f35,definition,(
% 2.91/0.81 ! [X534 : (term > $o)] : (($true = ((sP22 @ X534))) <=> ? [X538 : term,X537 : term] : (($true = ((X534 @ X538))) & ($true = ((X534 @ X537))) & (((X534 @ (ap @ X538 @ X537))) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f36,definition,(
% 2.91/0.81 ($true = sP23) <=> ! [X532 : subst,X533 : term,X534 : (term > $o)] : (($true = ((sP22 @ X534))) | ? [X539 : term] : (($true = ((var @ X539))) & ($true != ((X534 @ (sub @ X539 @ X532))))) | ($true = ((X534 @ (sub @ X533 @ X532)))) | ? [X535 : term] : (($true != ((X534 @ (lam @ X535)))) & ! [X536 : term] : (($true = ((X534 @ (sub @ X535 @ (push @ X536 @ id))))) | ($true != ((X534 @ X536))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f37,definition,(
% 2.91/0.81 ! [X302 : (subst > term > subst > $o)] : (($true = ((sP24 @ X302))) <=> ? [X318 : term,X319 : term] : (($true = ((X302 @ id @ X319 @ id))) & ($true = ((X302 @ id @ X318 @ id))) & ($true != ((X302 @ id @ (ap @ (sub @ X318 @ id) @ X319) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f38,definition,(
% 2.91/0.81 ! [X302 : (subst > term > subst > $o)] : ((((sP25 @ X302)) = $true) <=> ? [X305 : (subst > term > term)] : ((((X302 @ id @ (lam @ (X305 @ sh @ one)) @ id)) != $true) & ! [X306 : term] : ((((X302 @ id @ (X305 @ id @ X306) @ id)) = $true) | (((X302 @ id @ X306 @ id)) != $true)) & ! [X308 : term,X307 : subst,X309 : subst] : (((X305 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307))) = ((sub @ (X305 @ X309 @ X308) @ X307)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f39,definition,(
% 2.91/0.81 ($true = sP26) <=> ! [X302 : (subst > term > subst > $o),X303 : term] : (? [X304 : term] : ((((X302 @ id @ X304 @ id)) != $true) & (((var @ (sub @ X304 @ id))) = $true)) | ? [X315 : subst,X317 : subst,X314 : subst,X316 : term] : (($true = ((X302 @ X314 @ X316 @ (comp @ X317 @ X315)))) & ($true != ((X302 @ (comp @ X314 @ X317) @ (sub @ X316 @ X317) @ X315)))) | (((sP25 @ X302)) = $true) | ? [X313 : subst,X310 : term,X312 : subst,X311 : subst] : (($true = ((X302 @ (comp @ X311 @ X313) @ (sub @ X310 @ X313) @ X312))) & ($true != ((X302 @ X311 @ X310 @ (comp @ X313 @ X312))))) | ($true = ((X302 @ id @ X303 @ id))) | ($true = ((sP24 @ X302))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f40,definition,(
% 2.91/0.81 ! [X185 : (subst > term > subst > $o)] : ((((sP27 @ X185)) = $true) <=> ? [X188 : term,X187 : term] : (($true = ((X185 @ id @ X187 @ id))) & ($true = ((X185 @ id @ X188 @ id))) & ($true != ((X185 @ id @ (ap @ (sub @ X187 @ id) @ X188) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f41,definition,(
% 2.91/0.81 ! [X168 : (term > $o)] : (($true = ((sP28 @ X168))) <=> ! [X169 : term,X170 : term] : (($true != ((X168 @ X170))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f42,definition,(
% 2.91/0.81 ($true = sP29) <=> ? [X177 : term,X176 : (subst > term > subst > $o),X175 : (term > $o)] : ((((X175 @ (lam @ X177))) != $true) & ! [X184 : term] : (((X176 @ id @ X184 @ id)) = ((X175 @ X184))) & ! [X179 : (subst > term > term)] : ((((X176 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ? [X183 : term] : ((((X176 @ id @ X183 @ id)) = $true) & (((X176 @ id @ (X179 @ id @ X183) @ id)) != $true)) | ? [X180 : subst,X181 : term,X182 : subst] : (((sub @ (X179 @ X180 @ X181) @ X182)) != ((X179 @ (comp @ X180 @ X182) @ (sub @ X181 @ X182))))) & ! [X178 : term] : (($true != ((X175 @ X178))) | ($true = ((X175 @ (sub @ X177 @ (push @ X178 @ id)))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f43,definition,(
% 2.91/0.81 ($true = sP30) <=> ! [X186 : term,X185 : (subst > term > subst > $o)] : ((((X185 @ id @ X186 @ id)) = $true) | ? [X189 : (subst > term > term)] : (! [X193 : term] : ((((X185 @ id @ (X189 @ id @ X193) @ id)) = $true) | ($true != ((X185 @ id @ X193 @ id)))) & ($true != ((X185 @ id @ (lam @ (X189 @ sh @ one)) @ id))) & ! [X190 : subst,X192 : subst,X191 : term] : (((sub @ (X189 @ X190 @ X191) @ X192)) = ((X189 @ (comp @ X190 @ X192) @ (sub @ X191 @ X192))))) | (((sP27 @ X185)) = $true))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f44,definition,(
% 2.91/0.81 ($true = sP31) <=> (? [X167 : term,X168 : (term > $o)] : (($true = ((sP28 @ X168))) & ! [X173 : term] : ((((var @ X173)) != $true) | (((X168 @ X173)) = $true)) & ($true != ((X168 @ X167))) & ! [X171 : term] : (? [X172 : term] : (($true != ((X168 @ (sub @ X171 @ (push @ X172 @ id))))) & ($true = ((X168 @ X172)))) | ($true = ((X168 @ (lam @ X171)))))) | ? [X174 : term] : (((sub @ X174 @ id)) != X174) | ($true = sP30) | ? [X164 : (subst > term > subst > $o)] : ! [X165 : (term > $o)] : ? [X166 : term] : (((X165 @ X166)) != ((X164 @ id @ X166 @ id))) | ($true = sP29))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f45,definition,(
% 2.91/0.81 ($true = sP32) <=> ? [X334 : (subst > term > subst > $o),X333 : term] : (! [X335 : term] : ((((X334 @ id @ X335 @ id)) != $true) | (((X334 @ id @ (sub @ X333 @ (push @ X335 @ id)) @ id)) = $true)) & (((X334 @ id @ (lam @ (sub @ X333 @ (push @ one @ sh))) @ id)) != $true) & ! [X336 : (subst > term > term)] : (? [X337 : subst,X338 : term,X339 : subst] : (((X336 @ (comp @ X339 @ X337) @ (sub @ X338 @ X337))) != ((sub @ (X336 @ X339 @ X338) @ X337))) | ? [X340 : term] : (($true = ((X334 @ id @ X340 @ id))) & ($true != ((X334 @ id @ (X336 @ id @ X340) @ id)))) | ($true = ((X334 @ id @ (lam @ (X336 @ sh @ one)) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f46,definition,(
% 2.91/0.81 (sP33 = $true) <=> (? [X332 : term] : (((sub @ X332 @ id)) != X332) | ! [X342 : (subst > term > subst > $o),X341 : term] : (? [X343 : (subst > term > term)] : (! [X345 : subst,X346 : term,X347 : subst] : (((sub @ (X343 @ X345 @ X346) @ X347)) = ((X343 @ (comp @ X345 @ X347) @ (sub @ X346 @ X347)))) & ! [X344 : term] : ((((X342 @ id @ X344 @ id)) != $true) | ($true = ((X342 @ id @ (X343 @ id @ X344) @ id)))) & ($true != ((X342 @ id @ (lam @ (X343 @ sh @ one)) @ id)))) | ? [X348 : term] : ((((X342 @ id @ (sub @ X341 @ (push @ X348 @ id)) @ id)) != $true) & ($true = ((X342 @ id @ X348 @ id)))) | ($true = ((X342 @ id @ (lam @ X341) @ id)))) | ($true = sP32))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f47,definition,(
% 2.91/0.81 (sP34 = $true) <=> ! [X510 : term,X511 : (subst > term > subst > $o)] : (? [X513 : term,X512 : (subst > term > term)] : (! [X520 : subst,X518 : term,X519 : subst] : (((sub @ (X512 @ X519 @ X518) @ X520)) = ((sub @ (sub @ X513 @ (push @ X518 @ X519)) @ X520))) & ! [X517 : term] : (($true = ((X511 @ id @ (X512 @ id @ X517) @ id))) | (((X511 @ id @ X517 @ id)) != $true)) & ! [X515 : term,X514 : subst,X516 : subst] : (((sub @ X513 @ (push @ (sub @ X515 @ X516) @ (comp @ X514 @ X516)))) = ((X512 @ (comp @ X514 @ X516) @ (sub @ X515 @ X516)))) & ($true != ((X511 @ id @ (lam @ (X512 @ sh @ one)) @ id)))) | ? [X521 : term] : (($true = ((X511 @ id @ X521 @ id))) & (((X511 @ id @ (sub @ X510 @ (push @ X521 @ id)) @ id)) != $true)) | (((X511 @ id @ (lam @ (sub @ X510 @ (push @ one @ sh))) @ id)) = $true))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f48,definition,(
% 2.91/0.81 (sP35 = $true) <=> (? [X349 : term] : ! [X350 : (subst > term > term)] : ? [X352 : term,X351 : subst] : (((sub @ X349 @ (push @ X352 @ X351))) != ((X350 @ X351 @ X352))) | ? [X353 : term] : (((sub @ X353 @ id)) != X353) | ! [X355 : (subst > term > subst > $o),X356 : (term > $o),X354 : term] : (? [X363 : term] : (($true != ((X356 @ (sub @ X354 @ (push @ X363 @ id))))) & ($true = ((X356 @ X363)))) | ? [X357 : term] : (((X356 @ X357)) != ((X355 @ id @ X357 @ id))) | ? [X358 : (subst > term > term)] : (! [X361 : term,X359 : subst,X360 : subst] : (((sub @ (X358 @ X359 @ X361) @ X360)) = ((X358 @ (comp @ X359 @ X360) @ (sub @ X361 @ X360)))) & (((X355 @ id @ (lam @ (X358 @ sh @ one)) @ id)) != $true) & ! [X362 : term] : (($true != ((X355 @ id @ X362 @ id))) | ($true = ((X355 @ id @ (X358 @ id @ X362) @ id))))) | (((X356 @ (lam @ X354))) = $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f49,definition,(
% 2.91/0.81 ! [X71 : (term > $o)] : (($true = ((sP36 @ X71))) <=> ! [X73 : term,X74 : term] : (($true = ((X71 @ (ap @ X74 @ X73)))) | ($true != ((X71 @ X74))) | (((X71 @ X73)) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f50,definition,(
% 2.91/0.81 ! [X78 : (term > $o)] : (($true = ((sP37 @ X78))) <=> ? [X80 : term,X79 : term] : ((((X78 @ (ap @ X80 @ X79))) != $true) & (((X78 @ X79)) = $true) & (((X78 @ X80)) = $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f51,definition,(
% 2.91/0.81 ($true = sP38) <=> ! [X78 : (term > $o),X76 : subst,X77 : term] : (? [X81 : term] : (($true != ((X78 @ (sub @ X81 @ X76)))) & ($true = ((var @ X81)))) | ? [X82 : term] : (! [X83 : term] : (($true != ((X78 @ X83))) | ($true = ((X78 @ (sub @ X82 @ (push @ X83 @ id)))))) & ($true != ((X78 @ (lam @ X82))))) | ($true = ((sP37 @ X78))) | ($true = ((X78 @ (sub @ X77 @ X76)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f52,definition,(
% 2.91/0.81 ($true = sP39) <=> (($true = sP38) | ? [X69 : subst] : (((comp @ X69 @ id)) != X69) | ? [X67 : term,X68 : subst] : (((comp @ sh @ (push @ X67 @ X68))) != X68) | ? [X70 : term,X71 : (term > $o)] : (($true != ((X71 @ X70))) & ! [X72 : term] : (($true != ((var @ X72))) | ($true = ((X71 @ X72)))) & ! [X75 : term] : (($true = ((X71 @ (lam @ X75)))) | ($true != ((X71 @ X75)))) & ($true = ((sP36 @ X71)))) | ? [X65 : subst,X66 : term] : (((sub @ one @ (push @ X66 @ X65))) != X66))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f53,definition,(
% 2.91/0.81 ! [X478 : (subst > term > subst > $o)] : (($true = ((sP40 @ X478))) <=> ? [X486 : term,X485 : term] : ((((X478 @ id @ (ap @ (sub @ X485 @ id) @ X486) @ id)) != $true) & ($true = ((X478 @ id @ X485 @ id))) & ($true = ((X478 @ id @ X486 @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f54,definition,(
% 2.91/0.81 ($true = sP41) <=> ! [X480 : term,X479 : term,X478 : (subst > term > subst > $o)] : (($true = ((sP40 @ X478))) | ($true = ((X478 @ id @ (ap @ X480 @ X479) @ id))) | ($true != ((X478 @ id @ X480 @ id))) | ? [X487 : subst,X490 : subst,X488 : term,X489 : subst] : (($true != ((X478 @ (comp @ X490 @ X487) @ (sub @ X488 @ X487) @ X489))) & ($true = ((X478 @ X490 @ X488 @ (comp @ X487 @ X489))))) | (((X478 @ id @ X479 @ id)) != $true) | ? [X483 : term,X481 : subst,X482 : subst,X484 : subst] : (($true != ((X478 @ X481 @ X483 @ (comp @ X482 @ X484)))) & ($true = ((X478 @ (comp @ X481 @ X482) @ (sub @ X483 @ X482) @ X484)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f55,definition,(
% 2.91/0.81 ($true = sP42) <=> ! [X269 : term,X268 : (subst > term > subst > $o)] : (($true = ((X268 @ id @ (lam @ X269) @ id))) | ? [X270 : (subst > term > term)] : (! [X273 : term,X272 : subst,X274 : subst] : (((sub @ (X270 @ X272 @ X273) @ X274)) = ((X270 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274)))) & ! [X271 : term] : ((((X268 @ id @ X271 @ id)) != $true) | ($true = ((X268 @ id @ (X270 @ id @ X271) @ id)))) & ($true != ((X268 @ id @ (lam @ (X270 @ sh @ one)) @ id)))) | ? [X275 : term] : (($true = ((X268 @ id @ X275 @ id))) & ($true != ((X268 @ id @ (sub @ X269 @ (push @ X275 @ id)) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f56,definition,(
% 2.91/0.81 ($true = sP43) <=> (? [X390 : term,X389 : term] : ((((lam @ X389)) = ((lam @ X390))) & (X389 != X390)) | ? [X386 : subst,X385 : term] : (((sub @ one @ (push @ X385 @ X386))) != X385) | ? [X387 : subst,X388 : term] : (((comp @ sh @ (push @ X388 @ X387))) != X387) | ! [X394 : (subst > term > term),X391 : subst,X392 : (subst > term > term),X393 : term] : ((((lam @ (X394 @ sh @ one))) != ((lam @ (X392 @ sh @ one)))) | ? [X400 : subst,X399 : term,X398 : subst] : (((X394 @ (comp @ X398 @ X400) @ (sub @ X399 @ X400))) != ((sub @ (X394 @ X398 @ X399) @ X400))) | (((X392 @ X391 @ X393)) = ((X394 @ X391 @ X393))) | ? [X397 : term,X396 : subst,X395 : subst] : (((sub @ (X392 @ X395 @ X397) @ X396)) != ((X392 @ (comp @ X395 @ X396) @ (sub @ X397 @ X396))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f57,definition,(
% 2.91/0.81 ! [X526 : (term > $o)] : ((((sP44 @ X526)) = $true) <=> ? [X529 : term,X528 : term] : (($true = ((X526 @ X529))) & ($true = ((X526 @ X528))) & ($true != ((X526 @ (ap @ X528 @ X529))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f58,definition,(
% 2.91/0.81 ($true = sP45) <=> ! [X321 : term,X320 : (subst > term > subst > $o)] : (($true = ((X320 @ id @ (lam @ (sub @ X321 @ (push @ one @ sh))) @ id))) | ? [X327 : term] : (($true != ((X320 @ id @ (sub @ X321 @ (push @ X327 @ id)) @ id))) & ($true = ((X320 @ id @ X327 @ id)))) | ? [X322 : (subst > term > term)] : (! [X325 : subst,X324 : subst,X323 : term] : (((X322 @ (comp @ X324 @ X325) @ (sub @ X323 @ X325))) = ((sub @ (X322 @ X324 @ X323) @ X325))) & ($true != ((X320 @ id @ (lam @ (X322 @ sh @ one)) @ id))) & ! [X326 : term] : (($true = ((X320 @ id @ (X322 @ id @ X326) @ id))) | ($true != ((X320 @ id @ X326 @ id))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f59,definition,(
% 2.91/0.81 ! [X417 : (subst > term > subst > $o)] : (($true = ((sP46 @ X417))) <=> ! [X428 : term,X429 : term] : ((((X417 @ id @ X429 @ id)) != $true) | ($true != ((X417 @ id @ X428 @ id))) | ($true = ((X417 @ id @ (ap @ (sub @ X429 @ id) @ X428) @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f60,definition,(
% 2.91/0.81 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP47 @ X446))) <=> ? [X459 : (subst > term > term)] : (! [X460 : subst,X461 : subst,X462 : term] : (((X459 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460))) = ((sub @ (X459 @ X461 @ X462) @ X460))) & ($true != ((X446 @ id @ (lam @ (X459 @ sh @ one)) @ id))) & ! [X463 : term] : ((((X446 @ id @ X463 @ id)) != $true) | ($true = ((X446 @ id @ (X459 @ id @ X463) @ id))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f61,definition,(
% 2.91/0.81 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP48 @ X446))) <=> ? [X454 : term,X453 : term] : ((((X446 @ id @ (ap @ (sub @ X454 @ id) @ X453) @ id)) != $true) & ($true = ((X446 @ id @ X453 @ id))) & ($true = ((X446 @ id @ X454 @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f62,definition,(
% 2.91/0.81 ! [X410 : (term > $o)] : (($true = ((sP49 @ X410))) <=> ! [X415 : term,X416 : term] : ((((X410 @ X415)) != $true) | ($true = ((X410 @ (ap @ X416 @ X415)))) | ($true != ((X410 @ X416)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f63,definition,(
% 2.91/0.81 ! [X431 : (subst > term > subst > $o)] : ((((sP50 @ X431)) = $true) <=> ! [X436 : (subst > term > term)] : (? [X438 : term,X439 : subst,X437 : subst] : (((X436 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437))) != ((sub @ (X436 @ X439 @ X438) @ X437))) | (((X431 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ? [X440 : term] : (($true != ((X431 @ id @ (X436 @ id @ X440) @ id))) & ($true = ((X431 @ id @ X440 @ id))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f64,definition,(
% 2.91/0.81 ($true = sP51) <=> ? [X430 : term,X431 : (subst > term > subst > $o)] : (! [X444 : subst,X443 : subst,X445 : subst,X442 : term] : (($true != ((X431 @ X445 @ X442 @ (comp @ X443 @ X444)))) | (((X431 @ (comp @ X445 @ X443) @ (sub @ X442 @ X443) @ X444)) = $true)) & ($true != ((X431 @ id @ (lam @ X430) @ id))) & (((sP50 @ X431)) = $true) & ! [X435 : subst,X434 : subst,X432 : subst,X433 : term] : (($true = ((X431 @ X435 @ X433 @ (comp @ X434 @ X432)))) | ($true != ((X431 @ (comp @ X435 @ X434) @ (sub @ X433 @ X434) @ X432)))) & ! [X441 : term] : (($true = ((X431 @ id @ (sub @ X430 @ (push @ X441 @ id)) @ id))) | ($true != ((X431 @ id @ X441 @ id)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f65,definition,(
% 2.91/0.81 ($true = sP52) <=> ! [X447 : term,X446 : (subst > term > subst > $o)] : (($true = ((sP48 @ X446))) | ? [X452 : term] : (($true = ((var @ (sub @ X452 @ id)))) & (((X446 @ id @ X452 @ id)) != $true)) | ? [X456 : subst,X457 : term,X455 : subst,X458 : subst] : ((((X446 @ X455 @ X457 @ (comp @ X458 @ X456))) = $true) & (((X446 @ (comp @ X455 @ X458) @ (sub @ X457 @ X458) @ X456)) != $true)) | ($true = ((X446 @ id @ X447 @ id))) | ? [X448 : subst,X450 : subst,X451 : subst,X449 : term] : (($true != ((X446 @ X450 @ X449 @ (comp @ X451 @ X448)))) & ($true = ((X446 @ (comp @ X450 @ X451) @ (sub @ X449 @ X451) @ X448)))) | ($true = ((sP47 @ X446))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f66,definition,(
% 2.91/0.81 ($true = sP53) <=> ? [X417 : (subst > term > subst > $o),X418 : term,X419 : term] : (($true != ((X417 @ id @ (ap @ X419 @ X418) @ id))) & ($true = ((X417 @ id @ X419 @ id))) & ! [X421 : subst,X423 : subst,X422 : term,X420 : subst] : (($true != ((X417 @ (comp @ X421 @ X420) @ (sub @ X422 @ X420) @ X423))) | ($true = ((X417 @ X421 @ X422 @ (comp @ X420 @ X423))))) & ! [X427 : subst,X426 : subst,X424 : subst,X425 : term] : (($true != ((X417 @ X424 @ X425 @ (comp @ X426 @ X427)))) | ($true = ((X417 @ (comp @ X424 @ X426) @ (sub @ X425 @ X426) @ X427)))) & ($true = ((X417 @ id @ X418 @ id))) & ($true = ((sP46 @ X417))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f67,definition,(
% 2.91/0.81 (sP54 = $true) <=> (($true = sP51) | ? [X411 : term,X410 : (term > $o)] : (($true = ((sP49 @ X410))) & ($true != ((X410 @ X411))) & ! [X412 : term] : (($true != ((var @ X412))) | ($true = ((X410 @ X412)))) & ! [X413 : term] : (($true = ((X410 @ (lam @ X413)))) | ? [X414 : term] : ((((X410 @ X414)) = $true) & ($true != ((X410 @ (sub @ X413 @ (push @ X414 @ id)))))))) | ($true = sP52) | ($true = sP53))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f68,definition,(
% 2.91/0.81 ! [X373 : (term > $o)] : ((((sP55 @ X373)) = $true) <=> ? [X376 : term,X375 : term] : (($true = ((X373 @ X375))) & ($true = ((X373 @ X376))) & ($true != ((X373 @ (ap @ X376 @ X375))))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f69,definition,(
% 2.91/0.81 ! [X366 : (term > $o)] : ((((sP56 @ X366)) = $true) <=> ! [X372 : term,X371 : term] : (($true != ((X366 @ X371))) | (((X366 @ (ap @ X372 @ X371))) = $true) | (((X366 @ X372)) != $true)))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f70,definition,(
% 2.91/0.81 ($true = sP57) <=> ! [X373 : (term > $o),X374 : term] : (($true = ((X373 @ X374))) | ? [X378 : term] : (($true != ((X373 @ (lam @ X378)))) & ! [X379 : term] : (($true = ((X373 @ (sub @ X378 @ (push @ X379 @ id))))) | (((X373 @ X379)) != $true))) | (((sP55 @ X373)) = $true) | ? [X377 : term] : ((((X373 @ X377)) != $true) & ($true = ((var @ X377)))))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f71,definition,(
% 2.91/0.81 ($true = sP58) <=> (? [X366 : (term > $o),X367 : term,X365 : subst] : ((((X366 @ (sub @ X367 @ X365))) != $true) & ! [X368 : term] : ((((X366 @ (lam @ X368))) = $true) | ? [X369 : term] : ((((X366 @ (sub @ X368 @ (push @ X369 @ id)))) != $true) & (((X366 @ X369)) = $true))) & ! [X370 : term] : (($true = ((X366 @ (sub @ X370 @ X365)))) | ($true != ((var @ X370)))) & (((sP56 @ X366)) = $true)) | ($true = sP57) | ? [X364 : term] : (((sub @ X364 @ id)) != X364))),
% 2.91/0.81 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.91/0.81 thf(f72,plain,(
% 2.91/0.81 (ulamvarsh = $true) & (hoaslamnotvar = $true) & (axclos = $true) & (($true = sP58) <=> (induction2_lthm = $true)) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & ((sP54 = $true) <=> (hoasinduction_lthm = $true)) & (axassoc = $true) & (($true = sP45) <=> (hoasinduction_lem3aa_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X469 : term] : ? [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) = ((X470 @ sh @ one)))) & ((hoasapinj2 = $true) <=> ! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & ((axshiftcons = $true) <=> ! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125)) & ((induction = $true) <=> ! [X526 : (term > $o),X527 : term] : ((((sP44 @ X526)) = $true) | ? [X530 : term] : (($true != ((X526 @ (lam @ X530)))) & ($true = ((X526 @ X530)))) | ? [X531 : term] : (($true != ((X526 @ X531))) & ($true = ((var @ X531)))) | ($true = ((X526 @ X527))))) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP43) <=> (hoaslaminj_lthm = $true)) & (($true = sP42) <=> (hoasinduction_lem3a = $true)) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id)))) & (hoasinduction_lem1v2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) <=> (laminj = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ($true = sP41)) & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) | ? [X475 : term] : (((sub @ X475 @ id)) != X475)) <=> (termmset_lthm = $true)) & (($true = sP39) <=> (induction2lem_lthm = $true)) & (! [X477 : term] : (((sub @ X477 @ id)) = X477) <=> (axvarid = $true)) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) <=> (axidr = $true)) & ((pushprop_lem1 = $true) <=> ! [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true != ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X93 : d_subst] : (d_id = X93) & ((hoasapinj1_lthm = $true) <=> (! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)) | ? [X116 : term] : (((sub @ X116 @ id)) != X116) | ? [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 != X120) & (((ap @ X117 @ X118)) = ((ap @ X120 @ X119)))))) & ((sP35 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (apnotvar = $true) & ((! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257)) | ? [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) = ((ap @ X251 @ X252))) & (X252 != X254))) <=> (hoasapinj2_lthm = $true)) & ((? [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) != X51) | ? [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) != X49) | ! [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true != ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))) <=> (pushprop_lem1_lthm = $true)) & ! [X263 : d_term] : (d_one = X263) & (induction2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) <=> (axscons = $true)) & ((sP34 = $true) <=> (hoasinduction_lem3aaa = $true)) & (termmset_gthm = $true) & (! [X402 : (term > $o),X401 : subst,X403 : term] : ? [X404 : (term > $o)] : ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401))))) <=> (pushprop_lem0_lthm = $true)) & (! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) <=> (apinj1 = $true)) & (axabs = $true) & ((substmonoid_lthm = $true) <=> ((! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)) | ? [X523 : subst] : (((comp @ X523 @ id)) != X523) | ? [X522 : subst] : (((comp @ id @ X522)) != X522))) & ((apinj2 = $true) <=> ! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198))) & ((hoasinduction_lem3a_lthm = $true) <=> (sP33 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (ulamvar1 != $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X264 : term] : ? [X265 : (subst > term > term)] : ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ! [X156 : d_subst,X155 : d_subst] : ((((d2subst @ X155)) != ((d2subst @ X156))) | (X155 = X156)) & (induction2lem_gthm = $true) & (! [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ? [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) != ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) | (((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ? [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) != ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280))))) <=> (hoaslaminj = $true)) & (! [X113 : (subst > term > subst > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP31)) & (axmap = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction = $true) <=> ($true = sP26)) & ((induction2lem = $true) <=> ($true = sP23)) & ((shinj = $true) <=> ! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X205 : d_term,X204 : d_term] : ((X204 = X205) | (((d2term @ X204)) != ((d2term @ X205)))) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP21)) & (pushprop_lem2v2 = $true) & (axapp = $true) & ((axvarcons = $true) <=> ! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44)) & (hoasinduction_lem3v2_gthm = $true) & ((! [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) = $true) | ($true != ((X91 @ X89))) | ? [X92 : term] : (((X88 @ X92)) != ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) | ? [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) != X86)) <=> (pushprop_lem1v2_lthm = $true)) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP20)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3_lthm = $true) <=> (sP18 = $true)) & (hoasinduction_lem3a_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (? [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) != ((X202 @ X203))) | ($true != ((X201 @ X200))) | ($true = ((X202 @ one))))) & ((hoasinduction_lem3 = $true) <=> ($true = sP15)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X471 : term] : ? [X472 : (subst > term > term)] : (((X472 @ sh @ one)) = ((sub @ X471 @ (push @ one @ sh))))) & ((substmonoid = $true) <=> (! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259))) & ((sP13 = $true) <=> (hoasinduction_lem3aa = $true)) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X128 : (subst > term > subst > $o),X127 : term] : (($true = ((X128 @ id @ X127 @ id))) | ? [X134 : term,X135 : term] : (($true = ((X128 @ id @ X135 @ id))) & (((X128 @ id @ X134 @ id)) = $true) & ($true != ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) | (((sP12 @ X128)) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) <=> ($true = sP11)) & (axvarshift = $true) & (! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) <=> (hoasapinj1 = $true)) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1 = $true) & ((induction2 = $true) <=> ($true = sP9)) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (! [X194 : term] : (((sub @ X194 @ id)) = X194) <=> (termmset = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X39 : term] : ? [X40 : (subst > term > term)] : ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42)))) <=> (hoasinduction_lem3v2_f = $true)) & ((hoaslamnotap = $true) <=> ! [X296 : term,X298 : (subst > term > term),X297 : term] : (? [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one)))))) & ((axidl = $true) <=> ! [X468 : subst] : (((comp @ id @ X468)) = X468)) & (hoasinduction_lem2_gthm = $true) & (! [X232 : term,X233 : subst,X231 : (term > $o)] : ? [X234 : (term > $o)] : ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) <=> (pushprop_lem0 = $true)) & (lamnotap != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (($true = sP7) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lthm_3 = $true) <=> ($true = sP5)) & (hoasinduction_lem2_lthm = $true)),
% 2.91/0.81 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])).
% 2.91/0.81 thf(f260,plain,(
% 2.91/0.81 (ulamvarsh = $true) & (hoaslamnotvar = $true) & (axclos = $true) & ((($true = sP58) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP58))) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & (((sP54 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP54 != $true))) & (axassoc = $true) & ((($true = sP45) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP45))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasinduction_lem3b_lthm = $true) | ? [X469 : term] : ! [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) != ((X470 @ sh @ one)))) & (! [X469 : term] : ? [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) = ((X470 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (((hoasapinj2 = $true) | ? [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) = ((ap @ (sub @ X464 @ id) @ X466))) & (X466 != X467))) & (! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467)) | (hoasapinj2 != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & (((axshiftcons = $true) | ? [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) != X125)) & (! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125) | (axshiftcons != $true))) & (((induction = $true) | ? [X526 : (term > $o),X527 : term] : ((((sP44 @ X526)) != $true) & ! [X530 : term] : (($true = ((X526 @ (lam @ X530)))) | ($true != ((X526 @ X530)))) & ! [X531 : term] : (($true = ((X526 @ X531))) | ($true != ((var @ X531)))) & ($true != ((X526 @ X527))))) & (! [X526 : (term > $o),X527 : term] : ((((sP44 @ X526)) = $true) | ? [X530 : term] : (($true != ((X526 @ (lam @ X530)))) & ($true = ((X526 @ X530)))) | ? [X531 : term] : (($true != ((X526 @ X531))) & ($true = ((var @ X531)))) | ($true = ((X526 @ X527)))) | (induction != $true))) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & ((($true = sP43) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP43))) & ((($true = sP42) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP42))) & (pushprop_gthm = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X110 : (subst > term > subst > $o)] : ! [X111 : (term > $o)] : ? [X112 : term] : (((X111 @ X112)) != ((X110 @ id @ X112 @ id)))) & (! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id))) | (hoasinduction_lem0_lthm != $true))) & (hoasinduction_lem1v2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & ((! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) | (laminj != $true)) & ((laminj = $true) | ? [X262 : term,X261 : term] : ((X261 != X262) & (((lam @ X262)) = ((lam @ X261)))))) & (hoasinduction_lem1_gthm = $true) & (((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true))) & (((! [X476 : term] : (((sub @ X476 @ id)) = X476) | ? [X475 : term] : (((sub @ X475 @ id)) != X475)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X476 : term] : (((sub @ X476 @ id)) != X476) & ! [X475 : term] : (((sub @ X475 @ id)) = X475)))) & ((($true = sP39) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP39))) & ((! [X477 : term] : (((sub @ X477 @ id)) = X477) | (axvarid != $true)) & ((axvarid = $true) | ? [X477 : term] : (((sub @ X477 @ id)) != X477))) & ((! [X136 : subst] : (((comp @ X136 @ id)) = X136) | (axidr != $true)) & ((axidr = $true) | ? [X136 : subst] : (((comp @ X136 @ id)) != X136))) & (((pushprop_lem1 = $true) | ? [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true = ((X382 @ X381))) & ($true != ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & (! [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true != ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380)))))) | (pushprop_lem1 != $true))) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X93 : d_subst] : (d_id = X93) & (((hoasapinj1_lthm = $true) | (? [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) = ((ap @ (sub @ X122 @ id) @ X121))) & (X122 != X124)) & ! [X116 : term] : (((sub @ X116 @ id)) = X116) & ! [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 = X120) | (((ap @ X117 @ X118)) != ((ap @ X120 @ X119)))))) & ((! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)) | ? [X116 : term] : (((sub @ X116 @ id)) != X116) | ? [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 != X120) & (((ap @ X117 @ X118)) = ((ap @ X120 @ X119))))) | (hoasapinj1_lthm != $true))) & (((sP35 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP35 != $true))) & (apnotvar = $true) & (((! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257)) | ? [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) = ((ap @ X251 @ X252))) & (X252 != X254))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) = ((ap @ (sub @ X258 @ id) @ X256))) & (X256 != X257)) & ! [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) != ((ap @ X251 @ X252))) | (X252 = X254))))) & (((? [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) != X51) | ? [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) != X49) | ! [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true != ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) = X51) & ! [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) = X49) & ? [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true = ((X55 @ X53))) & ($true != ((X56 @ (sub @ X53 @ (push @ X52 @ X54))))))))) & ! [X263 : d_term] : (d_one = X263) & (induction2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) | (axscons != $true)) & ((axscons = $true) | ? [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) != X47))) & (((sP34 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP34 != $true))) & (termmset_gthm = $true) & ((! [X402 : (term > $o),X401 : subst,X403 : term] : ? [X404 : (term > $o)] : ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X402 : (term > $o),X401 : subst,X403 : term] : ! [X404 : (term > $o)] : ? [X405 : term] : (((X404 @ X405)) != ((X402 @ (sub @ X405 @ (push @ X403 @ X401))))))) & ((! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 != X331) & (((ap @ X329 @ X330)) = ((ap @ X331 @ X328)))))) & (axabs = $true) & (((substmonoid_lthm = $true) | ((? [X524 : subst] : (((comp @ X524 @ id)) != X524) | ? [X525 : subst] : (((comp @ id @ X525)) != X525)) & ! [X523 : subst] : (((comp @ X523 @ id)) = X523) & ! [X522 : subst] : (((comp @ id @ X522)) = X522))) & (((! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)) | ? [X523 : subst] : (((comp @ X523 @ id)) != X523) | ? [X522 : subst] : (((comp @ id @ X522)) != X522)) | (substmonoid_lthm != $true))) & (((apinj2 = $true) | ? [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) = ((ap @ X196 @ X198))) & (X197 != X198))) & (! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198)) | (apinj2 != $true))) & (((hoasinduction_lem3a_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3a_lthm != $true))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (ulamvar1 != $true) & (hoaslaminj_gthm = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X264 : term] : ! [X265 : (subst > term > term)] : ? [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) != ((sub @ X264 @ (push @ X267 @ X266))))) & (! [X264 : term] : ? [X265 : (subst > term > term)] : ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266)))) | (hoasinduction_lem3v2_f_lthm != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ! [X156 : d_subst,X155 : d_subst] : ((((d2subst @ X155)) != ((d2subst @ X156))) | (X155 = X156)) & (induction2lem_gthm = $true) & ((! [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ? [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) != ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) | (((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ? [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) != ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) = ((lam @ (X277 @ sh @ one)))) & ! [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) = ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) & (((X277 @ X276 @ X278)) != ((X279 @ X276 @ X278))) & ! [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) = ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280))))))) & ((! [X113 : (subst > term > subst > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X113 : (subst > term > subst > $o)] : ! [X114 : (term > $o)] : ? [X115 : term] : (((X114 @ X115)) != ((X113 @ id @ X115 @ id))))) & (hoaslamnotvar_lthm = $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true))) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (((hoasinduction = $true) | ($true != sP26)) & (($true = sP26) | (hoasinduction != $true))) & (((induction2lem = $true) | ($true != sP23)) & (($true = sP23) | (induction2lem != $true))) & (((shinj = $true) | ? [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) = ((sub @ X85 @ sh))) & (X84 != X85))) & (! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85)) | (shinj != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X205 : d_term,X204 : d_term] : ((X204 = X205) | (((d2term @ X204)) != ((d2term @ X205)))) & (((hoasinduction_lem3v2a = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3v2a != $true))) & (pushprop_lem2v2 = $true) & (axapp = $true) & (((axvarcons = $true) | ? [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) != X44)) & (! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44) | (axvarcons != $true))) & (hoasinduction_lem3v2_gthm = $true) & (((! [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) = $true) | ($true != ((X91 @ X89))) | ? [X92 : term] : (((X88 @ X92)) != ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) | ? [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) != X86)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) != $true) & ($true = ((X91 @ X89))) & ! [X92 : term] : (((X88 @ X92)) = ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) & ! [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) = X86)))) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem2v2 != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true))) & (hoasinduction_lem3a_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1_lthm = $true) & (((pushprop_lem1v2 = $true) | ? [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (! [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) = ((X202 @ X203))) & ($true = ((X201 @ X200))) & ($true != ((X202 @ one))))) & (! [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (? [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) != ((X202 @ X203))) | ($true != ((X201 @ X200))) | ($true = ((X202 @ one)))) | (pushprop_lem1v2 != $true))) & (((hoasinduction_lem3 = $true) | ($true != sP15)) & (($true = sP15) | (hoasinduction_lem3 != $true))) & (hoasapinj1_gthm = $true) & (((hoasinduction_lem3b = $true) | ? [X471 : term] : ! [X472 : (subst > term > term)] : (((X472 @ sh @ one)) != ((sub @ X471 @ (push @ one @ sh))))) & (! [X471 : term] : ? [X472 : (subst > term > term)] : (((X472 @ sh @ one)) = ((sub @ X471 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (((substmonoid = $true) | (? [X260 : subst] : (((comp @ id @ X260)) != X260) | ? [X259 : subst] : (((comp @ X259 @ id)) != X259))) & ((! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259)) | (substmonoid != $true))) & (((sP13 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP13 != $true))) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X128 : (subst > term > subst > $o),X127 : term] : (($true != ((X128 @ id @ X127 @ id))) & ! [X134 : term,X135 : term] : (($true != ((X128 @ id @ X135 @ id))) | (((X128 @ id @ X134 @ id)) != $true) | ($true = ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) & (((sP12 @ X128)) != $true))) & (! [X128 : (subst > term > subst > $o),X127 : term] : (($true = ((X128 @ id @ X127 @ id))) | ? [X134 : term,X135 : term] : (($true = ((X128 @ id @ X135 @ id))) & (((X128 @ id @ X134 @ id)) = $true) & ($true != ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) | (((sP12 @ X128)) = $true)) | (hoasinduction_no_psi_cond != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true))) & (axvarshift = $true) & ((! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) = ((ap @ (sub @ X408 @ id) @ X407))) & (X406 != X408)))) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1 = $true) & (((induction2 = $true) | ($true != sP9)) & (($true = sP9) | (induction2 != $true))) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & ((! [X194 : term] : (((sub @ X194 @ id)) = X194) | (termmset != $true)) & ((termmset = $true) | ? [X194 : term] : (((sub @ X194 @ id)) != X194))) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((! [X39 : term] : ? [X40 : (subst > term > term)] : ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X39 : term] : ! [X40 : (subst > term > term)] : ? [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) != ((sub @ X39 @ (push @ X41 @ X42)))))) & (((hoaslamnotap = $true) | ? [X296 : term,X298 : (subst > term > term),X297 : term] : (! [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X298 @ X301 @ X299) @ X300))) & (((ap @ (sub @ X297 @ id) @ X296)) = ((lam @ (X298 @ sh @ one)))))) & (! [X296 : term,X298 : (subst > term > term),X297 : term] : (? [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one))))) | (hoaslamnotap != $true))) & (((axidl = $true) | ? [X468 : subst] : (((comp @ id @ X468)) != X468)) & (! [X468 : subst] : (((comp @ id @ X468)) = X468) | (axidl != $true))) & (hoasinduction_lem2_gthm = $true) & ((! [X232 : term,X233 : subst,X231 : (term > $o)] : ? [X234 : (term > $o)] : ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X232 : term,X233 : subst,X231 : (term > $o)] : ! [X234 : (term > $o)] : ? [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) != ((X234 @ X235))))) & (lamnotap != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((($true = sP7) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP7))) & (((hoasinduction_lthm_3 = $true) | ($true != sP5)) & (($true = sP5) | (hoasinduction_lthm_3 != $true))) & (hoasinduction_lem2_lthm = $true)),
% 2.91/0.81 inference(nnf_transformation,[],[f72])).
% 2.91/0.81 thf(f261,plain,(
% 2.91/0.81 (ulamvarsh = $true) & (hoaslamnotvar = $true) & (axclos = $true) & (($true = sP58) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP58)) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & ((sP54 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP54 != $true)) & (axassoc = $true) & (($true = sP45) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP45)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) | ? [X469 : term] : ! [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) != ((X470 @ sh @ one)))) & (! [X469 : term] : ? [X470 : (subst > term > term)] : (((sub @ X469 @ (push @ one @ sh))) = ((X470 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasapinj2 = $true) | ? [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) = ((ap @ (sub @ X464 @ id) @ X466))) & (X466 != X467))) & (! [X464 : term,X467 : term,X465 : term,X466 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((ap @ (sub @ X464 @ id) @ X466))) | (X466 = X467)) | (hoasapinj2 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & ((axshiftcons = $true) | ? [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) != X125)) & (! [X125 : subst,X126 : term] : (((comp @ sh @ (push @ X126 @ X125))) = X125) | (axshiftcons != $true)) & ((induction = $true) | ? [X526 : (term > $o),X527 : term] : ((((sP44 @ X526)) != $true) & ! [X530 : term] : (($true = ((X526 @ (lam @ X530)))) | ($true != ((X526 @ X530)))) & ! [X531 : term] : (($true = ((X526 @ X531))) | ($true != ((var @ X531)))) & ($true != ((X526 @ X527))))) & (! [X526 : (term > $o),X527 : term] : ((((sP44 @ X526)) = $true) | ? [X530 : term] : (($true != ((X526 @ (lam @ X530)))) & ($true = ((X526 @ X530)))) | ? [X531 : term] : (($true != ((X526 @ X531))) & ($true = ((var @ X531)))) | ($true = ((X526 @ X527)))) | (induction != $true)) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP43) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP43)) & (($true = sP42) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP42)) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X110 : (subst > term > subst > $o)] : ! [X111 : (term > $o)] : ? [X112 : term] : (((X111 @ X112)) != ((X110 @ id @ X112 @ id)))) & (! [X110 : (subst > term > subst > $o)] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X111 @ X112)) = ((X110 @ id @ X112 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X262 : term,X261 : term] : ((X261 = X262) | (((lam @ X262)) != ((lam @ X261)))) | (laminj != $true)) & ((laminj = $true) | ? [X262 : term,X261 : term] : ((X261 != X262) & (((lam @ X262)) = ((lam @ X261))))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true)) & (! [X476 : term] : (((sub @ X476 @ id)) = X476) | ? [X475 : term] : (((sub @ X475 @ id)) != X475) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X476 : term] : (((sub @ X476 @ id)) != X476) & ! [X475 : term] : (((sub @ X475 @ id)) = X475))) & (($true = sP39) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP39)) & (! [X477 : term] : (((sub @ X477 @ id)) = X477) | (axvarid != $true)) & ((axvarid = $true) | ? [X477 : term] : (((sub @ X477 @ id)) != X477)) & (! [X136 : subst] : (((comp @ X136 @ id)) = X136) | (axidr != $true)) & ((axidr = $true) | ? [X136 : subst] : (((comp @ X136 @ id)) != X136)) & ((pushprop_lem1 = $true) | ? [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true = ((X382 @ X381))) & ($true != ((X383 @ (sub @ X381 @ (push @ X384 @ X380))))))) & (! [X381 : term,X380 : subst,X383 : (term > $o),X384 : term,X382 : (term > $o)] : (($true != ((X382 @ X381))) | ($true = ((X383 @ (sub @ X381 @ (push @ X384 @ X380)))))) | (pushprop_lem1 != $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X93 : d_subst] : (d_id = X93) & ((hoasapinj1_lthm = $true) | (? [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) = ((ap @ (sub @ X122 @ id) @ X121))) & (X122 != X124)) & ! [X116 : term] : (((sub @ X116 @ id)) = X116) & ! [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 = X120) | (((ap @ X117 @ X118)) != ((ap @ X120 @ X119)))))) & (! [X123 : term,X121 : term,X124 : term,X122 : term] : ((((ap @ (sub @ X124 @ id) @ X123)) != ((ap @ (sub @ X122 @ id) @ X121))) | (X122 = X124)) | ? [X116 : term] : (((sub @ X116 @ id)) != X116) | ? [X119 : term,X120 : term,X117 : term,X118 : term] : ((X117 != X120) & (((ap @ X117 @ X118)) = ((ap @ X120 @ X119)))) | (hoasapinj1_lthm != $true)) & ((sP35 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP35 != $true)) & (apnotvar = $true) & (! [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) != ((ap @ (sub @ X258 @ id) @ X256))) | (X256 = X257)) | ? [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) = ((ap @ X251 @ X252))) & (X252 != X254)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X255 : term,X258 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X255 @ id) @ X257)) = ((ap @ (sub @ X258 @ id) @ X256))) & (X256 != X257)) & ! [X254 : term,X252 : term,X253 : term,X251 : term] : ((((ap @ X253 @ X254)) != ((ap @ X251 @ X252))) | (X252 = X254)))) & (? [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) != X51) | ? [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) != X49) | ! [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true != ((X55 @ X53))) | ($true = ((X56 @ (sub @ X53 @ (push @ X52 @ X54)))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X50 : term,X51 : subst] : (((comp @ sh @ (push @ X50 @ X51))) = X51) & ! [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) = X49) & ? [X53 : term,X55 : (term > $o),X56 : (term > $o),X54 : subst,X52 : term] : (($true = ((X55 @ X53))) & ($true != ((X56 @ (sub @ X53 @ (push @ X52 @ X54)))))))) & ! [X263 : d_term] : (d_one = X263) & (induction2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) = X47) | (axscons != $true)) & ((axscons = $true) | ? [X47 : subst] : (((push @ (sub @ one @ X47) @ (comp @ sh @ X47))) != X47)) & ((sP34 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP34 != $true)) & (termmset_gthm = $true) & (! [X402 : (term > $o),X401 : subst,X403 : term] : ? [X404 : (term > $o)] : ! [X405 : term] : (((X404 @ X405)) = ((X402 @ (sub @ X405 @ (push @ X403 @ X401))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X402 : (term > $o),X401 : subst,X403 : term] : ! [X404 : (term > $o)] : ? [X405 : term] : (((X404 @ X405)) != ((X402 @ (sub @ X405 @ (push @ X403 @ X401)))))) & (! [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 = X331) | (((ap @ X329 @ X330)) != ((ap @ X331 @ X328)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X329 : term,X328 : term,X330 : term,X331 : term] : ((X329 != X331) & (((ap @ X329 @ X330)) = ((ap @ X331 @ X328))))) & (axabs = $true) & ((substmonoid_lthm = $true) | ((? [X524 : subst] : (((comp @ X524 @ id)) != X524) | ? [X525 : subst] : (((comp @ id @ X525)) != X525)) & ! [X523 : subst] : (((comp @ X523 @ id)) = X523) & ! [X522 : subst] : (((comp @ id @ X522)) = X522))) & ((! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)) | ? [X523 : subst] : (((comp @ X523 @ id)) != X523) | ? [X522 : subst] : (((comp @ id @ X522)) != X522) | (substmonoid_lthm != $true)) & ((apinj2 = $true) | ? [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) = ((ap @ X196 @ X198))) & (X197 != X198))) & (! [X195 : term,X197 : term,X196 : term,X198 : term] : ((((ap @ X195 @ X197)) != ((ap @ X196 @ X198))) | (X197 = X198)) | (apinj2 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3a_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (ulamvar1 != $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X264 : term] : ! [X265 : (subst > term > term)] : ? [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) != ((sub @ X264 @ (push @ X267 @ X266))))) & (! [X264 : term] : ? [X265 : (subst > term > term)] : ! [X266 : subst,X267 : term] : (((X265 @ X266 @ X267)) = ((sub @ X264 @ (push @ X267 @ X266)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ! [X156 : d_subst,X155 : d_subst] : ((((d2subst @ X155)) != ((d2subst @ X156))) | (X155 = X156)) & (induction2lem_gthm = $true) & (! [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) != ((lam @ (X277 @ sh @ one)))) | ? [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) != ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) | (((X277 @ X276 @ X278)) = ((X279 @ X276 @ X278))) | ? [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) != ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X277 : (subst > term > term),X279 : (subst > term > term),X278 : term,X276 : subst] : ((((lam @ (X279 @ sh @ one))) = ((lam @ (X277 @ sh @ one)))) & ! [X285 : subst,X284 : term,X283 : subst] : (((sub @ (X279 @ X285 @ X284) @ X283)) = ((X279 @ (comp @ X285 @ X283) @ (sub @ X284 @ X283)))) & (((X277 @ X276 @ X278)) != ((X279 @ X276 @ X278))) & ! [X281 : term,X280 : subst,X282 : subst] : (((sub @ (X277 @ X282 @ X281) @ X280)) = ((X277 @ (comp @ X282 @ X280) @ (sub @ X281 @ X280)))))) & (! [X113 : (subst > term > subst > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X113 @ id @ X115 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X113 : (subst > term > subst > $o)] : ! [X114 : (term > $o)] : ? [X115 : term] : (((X114 @ X115)) != ((X113 @ id @ X115 @ id)))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true)) & (axmap = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction = $true) | ($true != sP26)) & (($true = sP26) | (hoasinduction != $true)) & ((induction2lem = $true) | ($true != sP23)) & (($true = sP23) | (induction2lem != $true)) & ((shinj = $true) | ? [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) = ((sub @ X85 @ sh))) & (X84 != X85))) & (! [X85 : term,X84 : term] : ((((sub @ X84 @ sh)) != ((sub @ X85 @ sh))) | (X84 = X85)) | (shinj != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X205 : d_term,X204 : d_term] : ((X204 = X205) | (((d2term @ X204)) != ((d2term @ X205)))) & ((hoasinduction_lem3v2a = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3v2a != $true)) & (pushprop_lem2v2 = $true) & (axapp = $true) & ((axvarcons = $true) | ? [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) != X44)) & (! [X43 : subst,X44 : term] : (((sub @ one @ (push @ X44 @ X43))) = X44) | (axvarcons != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) = $true) | ($true != ((X91 @ X89))) | ? [X92 : term] : (((X88 @ X92)) != ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) | ? [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) != X86) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X91 : (term > $o),X88 : (term > $o),X90 : subst,X89 : term] : ((((X88 @ one)) != $true) & ($true = ((X91 @ X89))) & ! [X92 : term] : (((X88 @ X92)) = ((X91 @ (sub @ X92 @ (push @ X89 @ X90)))))) & ! [X87 : subst,X86 : term] : (((sub @ one @ (push @ X86 @ X87))) = X86))) & ! [X45 : term] : ? [X46 : d_term] : (((d2term @ X46)) = X45) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem2v2 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2 = $true) | ? [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (! [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) = ((X202 @ X203))) & ($true = ((X201 @ X200))) & ($true != ((X202 @ one))))) & (! [X201 : (term > $o),X199 : subst,X200 : term,X202 : (term > $o)] : (? [X203 : term] : (((X201 @ (sub @ X203 @ (push @ X200 @ X199)))) != ((X202 @ X203))) | ($true != ((X201 @ X200))) | ($true = ((X202 @ one)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP15)) & (($true = sP15) | (hoasinduction_lem3 != $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X471 : term] : ! [X472 : (subst > term > term)] : (((X472 @ sh @ one)) != ((sub @ X471 @ (push @ one @ sh))))) & (! [X471 : term] : ? [X472 : (subst > term > term)] : (((X472 @ sh @ one)) = ((sub @ X471 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((substmonoid = $true) | ? [X260 : subst] : (((comp @ id @ X260)) != X260) | ? [X259 : subst] : (((comp @ X259 @ id)) != X259)) & ((! [X260 : subst] : (((comp @ id @ X260)) = X260) & ! [X259 : subst] : (((comp @ X259 @ id)) = X259)) | (substmonoid != $true)) & ((sP13 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP13 != $true)) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X128 : (subst > term > subst > $o),X127 : term] : (($true != ((X128 @ id @ X127 @ id))) & ! [X134 : term,X135 : term] : (($true != ((X128 @ id @ X135 @ id))) | (((X128 @ id @ X134 @ id)) != $true) | ($true = ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) & (((sP12 @ X128)) != $true))) & (! [X128 : (subst > term > subst > $o),X127 : term] : (($true = ((X128 @ id @ X127 @ id))) | ? [X134 : term,X135 : term] : (($true = ((X128 @ id @ X135 @ id))) & (((X128 @ id @ X134 @ id)) = $true) & ($true != ((X128 @ id @ (ap @ (sub @ X134 @ id) @ X135) @ id)))) | (((sP12 @ X128)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true)) & (axvarshift = $true) & (! [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) != ((ap @ (sub @ X408 @ id) @ X407))) | (X406 = X408)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X408 : term,X409 : term,X406 : term,X407 : term] : ((((ap @ (sub @ X406 @ id) @ X409)) = ((ap @ (sub @ X408 @ id) @ X407))) & (X406 != X408))) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1 = $true) & ((induction2 = $true) | ($true != sP9)) & (($true = sP9) | (induction2 != $true)) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (! [X194 : term] : (((sub @ X194 @ id)) = X194) | (termmset != $true)) & ((termmset = $true) | ? [X194 : term] : (((sub @ X194 @ id)) != X194)) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X39 : term] : ? [X40 : (subst > term > term)] : ! [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) = ((sub @ X39 @ (push @ X41 @ X42)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X39 : term] : ! [X40 : (subst > term > term)] : ? [X41 : term,X42 : subst] : (((X40 @ X42 @ X41)) != ((sub @ X39 @ (push @ X41 @ X42))))) & ((hoaslamnotap = $true) | ? [X296 : term,X298 : (subst > term > term),X297 : term] : (! [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X298 @ X301 @ X299) @ X300))) & (((ap @ (sub @ X297 @ id) @ X296)) = ((lam @ (X298 @ sh @ one)))))) & (! [X296 : term,X298 : (subst > term > term),X297 : term] : (? [X299 : term,X300 : subst,X301 : subst] : (((X298 @ (comp @ X301 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X298 @ X301 @ X299) @ X300))) | (((ap @ (sub @ X297 @ id) @ X296)) != ((lam @ (X298 @ sh @ one))))) | (hoaslamnotap != $true)) & ((axidl = $true) | ? [X468 : subst] : (((comp @ id @ X468)) != X468)) & (! [X468 : subst] : (((comp @ id @ X468)) = X468) | (axidl != $true)) & (hoasinduction_lem2_gthm = $true) & (! [X232 : term,X233 : subst,X231 : (term > $o)] : ? [X234 : (term > $o)] : ! [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) = ((X234 @ X235))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X232 : term,X233 : subst,X231 : (term > $o)] : ! [X234 : (term > $o)] : ? [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) != ((X234 @ X235)))) & (lamnotap != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (($true = sP7) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP7)) & ((hoasinduction_lthm_3 = $true) | ($true != sP5)) & (($true = sP5) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem2_lthm = $true)),
% 2.91/0.81 inference(flattening,[],[f260])).
% 2.91/0.81 thf(f262,plain,(
% 2.91/0.81 (ulamvarsh = $true) & (hoaslamnotvar = $true) & (axclos = $true) & (($true = sP58) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP58)) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & ((sP54 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP54 != $true)) & (axassoc = $true) & (($true = sP45) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP45)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) | ? [X0 : term] : ! [X1 : (subst > term > term)] : (((X1 @ sh @ one)) != ((sub @ X0 @ (push @ one @ sh))))) & (! [X2 : term] : ? [X3 : (subst > term > term)] : (((X3 @ sh @ one)) = ((sub @ X2 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasapinj2 = $true) | ? [X4 : term,X5 : term,X6 : term,X7 : term] : ((((ap @ (sub @ X6 @ id) @ X5)) = ((ap @ (sub @ X4 @ id) @ X7))) & (X5 != X7))) & (! [X8 : term,X9 : term,X10 : term,X11 : term] : ((((ap @ (sub @ X10 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X11))) | (X9 = X11)) | (hoasapinj2 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & ((axshiftcons = $true) | ? [X12 : subst,X13 : term] : (((comp @ sh @ (push @ X13 @ X12))) != X12)) & (! [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) = X14) | (axshiftcons != $true)) & ((induction = $true) | ? [X16 : (term > $o),X17 : term] : (($true != ((sP44 @ X16))) & ! [X18 : term] : (($true = ((X16 @ (lam @ X18)))) | (((X16 @ X18)) != $true)) & ! [X19 : term] : ((((X16 @ X19)) = $true) | ($true != ((var @ X19)))) & (((X16 @ X17)) != $true))) & (! [X20 : (term > $o),X21 : term] : (($true = ((sP44 @ X20))) | ? [X22 : term] : ((((X20 @ (lam @ X22))) != $true) & (((X20 @ X22)) = $true)) | ? [X23 : term] : ((((X20 @ X23)) != $true) & ($true = ((var @ X23)))) | ($true = ((X20 @ X21)))) | (induction != $true)) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP43) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP43)) & (($true = sP42) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP42)) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X24 : (subst > term > subst > $o)] : ! [X25 : (term > $o)] : ? [X26 : term] : (((X25 @ X26)) != ((X24 @ id @ X26 @ id)))) & (! [X27 : (subst > term > subst > $o)] : ? [X28 : (term > $o)] : ! [X29 : term] : (((X28 @ X29)) = ((X27 @ id @ X29 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X30 : term,X31 : term] : ((X30 = X31) | (((lam @ X30)) != ((lam @ X31)))) | (laminj != $true)) & ((laminj = $true) | ? [X32 : term,X33 : term] : ((X32 != X33) & (((lam @ X32)) = ((lam @ X33))))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true)) & (! [X34 : term] : (((sub @ X34 @ id)) = X34) | ? [X35 : term] : (((sub @ X35 @ id)) != X35) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X36 : term] : (((sub @ X36 @ id)) != X36) & ! [X37 : term] : (((sub @ X37 @ id)) = X37))) & (($true = sP39) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP39)) & (! [X38 : term] : (((sub @ X38 @ id)) = X38) | (axvarid != $true)) & ((axvarid = $true) | ? [X39 : term] : (((sub @ X39 @ id)) != X39)) & (! [X40 : subst] : (((comp @ X40 @ id)) = X40) | (axidr != $true)) & ((axidr = $true) | ? [X41 : subst] : (((comp @ X41 @ id)) != X41)) & ((pushprop_lem1 = $true) | ? [X42 : term,X43 : subst,X44 : (term > $o),X45 : term,X46 : (term > $o)] : (($true = ((X46 @ X42))) & ($true != ((X44 @ (sub @ X42 @ (push @ X45 @ X43))))))) & (! [X47 : term,X48 : subst,X49 : (term > $o),X50 : term,X51 : (term > $o)] : (($true != ((X51 @ X47))) | ($true = ((X49 @ (sub @ X47 @ (push @ X50 @ X48)))))) | (pushprop_lem1 != $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X52 : d_subst] : (d_id = X52) & ((hoasapinj1_lthm = $true) | (? [X53 : term,X54 : term,X55 : term,X56 : term] : ((((ap @ (sub @ X55 @ id) @ X53)) = ((ap @ (sub @ X56 @ id) @ X54))) & (X55 != X56)) & ! [X57 : term] : (((sub @ X57 @ id)) = X57) & ! [X58 : term,X59 : term,X60 : term,X61 : term] : ((X59 = X60) | (((ap @ X60 @ X61)) != ((ap @ X59 @ X58)))))) & (! [X62 : term,X63 : term,X64 : term,X65 : term] : ((((ap @ (sub @ X65 @ id) @ X63)) != ((ap @ (sub @ X64 @ id) @ X62))) | (X64 = X65)) | ? [X66 : term] : (((sub @ X66 @ id)) != X66) | ? [X67 : term,X68 : term,X69 : term,X70 : term] : ((X68 != X69) & (((ap @ X69 @ X70)) = ((ap @ X68 @ X67)))) | (hoasapinj1_lthm != $true)) & ((sP35 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP35 != $true)) & (apnotvar = $true) & (! [X71 : term,X72 : term,X73 : term,X74 : term] : ((((ap @ (sub @ X71 @ id) @ X74)) != ((ap @ (sub @ X72 @ id) @ X73))) | (X73 = X74)) | ? [X75 : term,X76 : term,X77 : term,X78 : term] : ((((ap @ X78 @ X76)) = ((ap @ X77 @ X75))) & (X75 != X76)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X79 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X80 @ id) @ X81)) = ((ap @ (sub @ X79 @ id) @ X82))) & (X81 != X82)) & ! [X83 : term,X84 : term,X85 : term,X86 : term] : ((((ap @ X86 @ X84)) != ((ap @ X85 @ X83))) | (X83 = X84)))) & (? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X89 : subst,X90 : term] : (((sub @ one @ (push @ X90 @ X89))) != X90) | ! [X91 : term,X92 : (term > $o),X93 : (term > $o),X94 : subst,X95 : term] : (($true != ((X92 @ X91))) | ($true = ((X93 @ (sub @ X91 @ (push @ X95 @ X94)))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X96 : term,X97 : subst] : (((comp @ sh @ (push @ X96 @ X97))) = X97) & ! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) & ? [X100 : term,X101 : (term > $o),X102 : (term > $o),X103 : subst,X104 : term] : (($true = ((X101 @ X100))) & ($true != ((X102 @ (sub @ X100 @ (push @ X104 @ X103)))))))) & ! [X105 : d_term] : (d_one = X105) & (induction2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X106 : subst] : (((push @ (sub @ one @ X106) @ (comp @ sh @ X106))) = X106) | (axscons != $true)) & ((axscons = $true) | ? [X107 : subst] : (((push @ (sub @ one @ X107) @ (comp @ sh @ X107))) != X107)) & ((sP34 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP34 != $true)) & (termmset_gthm = $true) & (! [X108 : (term > $o),X109 : subst,X110 : term] : ? [X111 : (term > $o)] : ! [X112 : term] : (((X111 @ X112)) = ((X108 @ (sub @ X112 @ (push @ X110 @ X109))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X113 : (term > $o),X114 : subst,X115 : term] : ! [X116 : (term > $o)] : ? [X117 : term] : (((X116 @ X117)) != ((X113 @ (sub @ X117 @ (push @ X115 @ X114)))))) & (! [X118 : term,X119 : term,X120 : term,X121 : term] : ((X118 = X121) | (((ap @ X118 @ X120)) != ((ap @ X121 @ X119)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X122 : term,X123 : term,X124 : term,X125 : term] : ((X122 != X125) & (((ap @ X125 @ X123)) = ((ap @ X122 @ X124))))) & (axabs = $true) & ((substmonoid_lthm = $true) | ((? [X126 : subst] : (((comp @ X126 @ id)) != X126) | ? [X127 : subst] : (((comp @ id @ X127)) != X127)) & ! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129))) & ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X132 : subst] : (((comp @ X132 @ id)) != X132) | ? [X133 : subst] : (((comp @ id @ X133)) != X133) | (substmonoid_lthm != $true)) & ((apinj2 = $true) | ? [X134 : term,X135 : term,X136 : term,X137 : term] : ((((ap @ X136 @ X137)) = ((ap @ X134 @ X135))) & (X135 != X137))) & (! [X138 : term,X139 : term,X140 : term,X141 : term] : ((((ap @ X138 @ X139)) != ((ap @ X140 @ X141))) | (X139 = X141)) | (apinj2 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3a_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (ulamvar1 != $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X142 : term] : ! [X143 : (subst > term > term)] : ? [X144 : subst,X145 : term] : (((sub @ X142 @ (push @ X145 @ X144))) != ((X143 @ X144 @ X145)))) & (! [X146 : term] : ? [X147 : (subst > term > term)] : ! [X148 : subst,X149 : term] : (((X147 @ X148 @ X149)) = ((sub @ X146 @ (push @ X149 @ X148)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ! [X150 : d_subst,X151 : d_subst] : ((((d2subst @ X150)) != ((d2subst @ X151))) | (X150 = X151)) & (induction2lem_gthm = $true) & (! [X152 : (subst > term > term),X153 : (subst > term > term),X154 : term,X155 : subst] : ((((lam @ (X152 @ sh @ one))) != ((lam @ (X153 @ sh @ one)))) | ? [X156 : subst,X157 : term,X158 : subst] : (((X153 @ (comp @ X156 @ X158) @ (sub @ X157 @ X158))) != ((sub @ (X153 @ X156 @ X157) @ X158))) | (((X152 @ X155 @ X154)) = ((X153 @ X155 @ X154))) | ? [X159 : term,X160 : subst,X161 : subst] : (((X152 @ (comp @ X161 @ X160) @ (sub @ X159 @ X160))) != ((sub @ (X152 @ X161 @ X159) @ X160)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X162 : (subst > term > term),X163 : (subst > term > term),X164 : term,X165 : subst] : ((((lam @ (X162 @ sh @ one))) = ((lam @ (X163 @ sh @ one)))) & ! [X166 : subst,X167 : term,X168 : subst] : (((X163 @ (comp @ X166 @ X168) @ (sub @ X167 @ X168))) = ((sub @ (X163 @ X166 @ X167) @ X168))) & (((X162 @ X165 @ X164)) != ((X163 @ X165 @ X164))) & ! [X169 : term,X170 : subst,X171 : subst] : (((sub @ (X162 @ X171 @ X169) @ X170)) = ((X162 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170)))))) & (! [X172 : (subst > term > subst > $o)] : ? [X173 : (term > $o)] : ! [X174 : term] : (((X173 @ X174)) = ((X172 @ id @ X174 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X175 : (subst > term > subst > $o)] : ! [X176 : (term > $o)] : ? [X177 : term] : (((X176 @ X177)) != ((X175 @ id @ X177 @ id)))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true)) & (axmap = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction = $true) | ($true != sP26)) & (($true = sP26) | (hoasinduction != $true)) & ((induction2lem = $true) | ($true != sP23)) & (($true = sP23) | (induction2lem != $true)) & ((shinj = $true) | ? [X178 : term,X179 : term] : ((((sub @ X178 @ sh)) = ((sub @ X179 @ sh))) & (X178 != X179))) & (! [X180 : term,X181 : term] : ((((sub @ X181 @ sh)) != ((sub @ X180 @ sh))) | (X180 = X181)) | (shinj != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X182 : d_term,X183 : d_term] : ((X182 = X183) | (((d2term @ X183)) != ((d2term @ X182)))) & ((hoasinduction_lem3v2a = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3v2a != $true)) & (pushprop_lem2v2 = $true) & (axapp = $true) & ((axvarcons = $true) | ? [X184 : subst,X185 : term] : (((sub @ one @ (push @ X185 @ X184))) != X185)) & (! [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) = X187) | (axvarcons != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X188 : (term > $o),X189 : (term > $o),X190 : subst,X191 : term] : (($true = ((X189 @ one))) | (((X188 @ X191)) != $true) | ? [X192 : term] : (((X189 @ X192)) != ((X188 @ (sub @ X192 @ (push @ X191 @ X190)))))) | ? [X193 : subst,X194 : term] : (((sub @ one @ (push @ X194 @ X193))) != X194) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X195 : (term > $o),X196 : (term > $o),X197 : subst,X198 : term] : ((((X196 @ one)) != $true) & (((X195 @ X198)) = $true) & ! [X199 : term] : (((X195 @ (sub @ X199 @ (push @ X198 @ X197)))) = ((X196 @ X199)))) & ! [X200 : subst,X201 : term] : (((sub @ one @ (push @ X201 @ X200))) = X201))) & ! [X202 : term] : ? [X203 : d_term] : (((d2term @ X203)) = X202) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem2v2 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2 = $true) | ? [X204 : (term > $o),X205 : subst,X206 : term,X207 : (term > $o)] : (! [X208 : term] : (((X204 @ (sub @ X208 @ (push @ X206 @ X205)))) = ((X207 @ X208))) & (((X204 @ X206)) = $true) & (((X207 @ one)) != $true))) & (! [X209 : (term > $o),X210 : subst,X211 : term,X212 : (term > $o)] : (? [X213 : term] : (((X212 @ X213)) != ((X209 @ (sub @ X213 @ (push @ X211 @ X210))))) | ($true != ((X209 @ X211))) | ($true = ((X212 @ one)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP15)) & (($true = sP15) | (hoasinduction_lem3 != $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X214 : term] : ! [X215 : (subst > term > term)] : (((sub @ X214 @ (push @ one @ sh))) != ((X215 @ sh @ one)))) & (! [X216 : term] : ? [X217 : (subst > term > term)] : (((X217 @ sh @ one)) = ((sub @ X216 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((substmonoid = $true) | ? [X218 : subst] : (((comp @ id @ X218)) != X218) | ? [X219 : subst] : (((comp @ X219 @ id)) != X219)) & ((! [X220 : subst] : (((comp @ id @ X220)) = X220) & ! [X221 : subst] : (((comp @ X221 @ id)) = X221)) | (substmonoid != $true)) & ((sP13 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP13 != $true)) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X222 : (subst > term > subst > $o),X223 : term] : (($true != ((X222 @ id @ X223 @ id))) & ! [X224 : term,X225 : term] : (($true != ((X222 @ id @ X225 @ id))) | ($true != ((X222 @ id @ X224 @ id))) | ($true = ((X222 @ id @ (ap @ (sub @ X224 @ id) @ X225) @ id)))) & ($true != ((sP12 @ X222))))) & (! [X226 : (subst > term > subst > $o),X227 : term] : (($true = ((X226 @ id @ X227 @ id))) | ? [X228 : term,X229 : term] : ((((X226 @ id @ X229 @ id)) = $true) & (((X226 @ id @ X228 @ id)) = $true) & ($true != ((X226 @ id @ (ap @ (sub @ X228 @ id) @ X229) @ id)))) | (((sP12 @ X226)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true)) & (axvarshift = $true) & (! [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ (sub @ X232 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X233))) | (X230 = X232)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X234 : term,X235 : term,X236 : term,X237 : term] : ((((ap @ (sub @ X236 @ id) @ X235)) = ((ap @ (sub @ X234 @ id) @ X237))) & (X234 != X236))) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1 = $true) & ((induction2 = $true) | ($true != sP9)) & (($true = sP9) | (induction2 != $true)) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ! [X238 : subst] : ? [X239 : d_subst] : (((d2subst @ X239)) = X238) & (! [X240 : term] : (((sub @ X240 @ id)) = X240) | (termmset != $true)) & ((termmset = $true) | ? [X241 : term] : (((sub @ X241 @ id)) != X241)) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X242 : term] : ? [X243 : (subst > term > term)] : ! [X244 : term,X245 : subst] : (((sub @ X242 @ (push @ X244 @ X245))) = ((X243 @ X245 @ X244))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X246 : term] : ! [X247 : (subst > term > term)] : ? [X248 : term,X249 : subst] : (((X247 @ X249 @ X248)) != ((sub @ X246 @ (push @ X248 @ X249))))) & ((hoaslamnotap = $true) | ? [X250 : term,X251 : (subst > term > term),X252 : term] : (! [X253 : term,X254 : subst,X255 : subst] : (((sub @ (X251 @ X255 @ X253) @ X254)) = ((X251 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254)))) & (((lam @ (X251 @ sh @ one))) = ((ap @ (sub @ X252 @ id) @ X250))))) & (! [X256 : term,X257 : (subst > term > term),X258 : term] : (? [X259 : term,X260 : subst,X261 : subst] : (((sub @ (X257 @ X261 @ X259) @ X260)) != ((X257 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260)))) | (((lam @ (X257 @ sh @ one))) != ((ap @ (sub @ X258 @ id) @ X256)))) | (hoaslamnotap != $true)) & ((axidl = $true) | ? [X262 : subst] : (((comp @ id @ X262)) != X262)) & (! [X263 : subst] : (((comp @ id @ X263)) = X263) | (axidl != $true)) & (hoasinduction_lem2_gthm = $true) & (! [X264 : term,X265 : subst,X266 : (term > $o)] : ? [X267 : (term > $o)] : ! [X268 : term] : (((X267 @ X268)) = ((X266 @ (sub @ X268 @ (push @ X264 @ X265))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X269 : term,X270 : subst,X271 : (term > $o)] : ! [X272 : (term > $o)] : ? [X273 : term] : (((X272 @ X273)) != ((X271 @ (sub @ X273 @ (push @ X269 @ X270)))))) & (lamnotap != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (($true = sP7) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP7)) & ((hoasinduction_lthm_3 = $true) | ($true != sP5)) & (($true = sP5) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem2_lthm = $true)),
% 2.91/0.81 inference(rectify,[],[f261])).
% 2.91/0.81 thf(f263,plain,(
% 2.91/0.81 (ulamvarsh = $true) & (hoaslamnotvar = $true) & (axclos = $true) & (($true = sP58) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP58)) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3_gthm = $true) & ((sP54 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP54 != $true)) & (axassoc = $true) & (($true = sP45) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP45)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) | ! [X1 : (subst > term > term)] : (((sub @ sK457 @ (push @ one @ sh))) != ((X1 @ sh @ one)))) & (! [X2 : term] : (((sK458 @ X2 @ sh @ one)) = ((sub @ X2 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK459 @ id) @ sK462)) = ((ap @ (sub @ sK461 @ id) @ sK460))) & (sK460 != sK462))) & (! [X8 : term,X9 : term,X10 : term,X11 : term] : ((((ap @ (sub @ X10 @ id) @ X9)) != ((ap @ (sub @ X8 @ id) @ X11))) | (X9 = X11)) | (hoasapinj2 != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & ((axshiftcons = $true) | (sK463 != ((comp @ sh @ (push @ sK464 @ sK463))))) & (! [X14 : subst,X15 : term] : (((comp @ sh @ (push @ X15 @ X14))) = X14) | (axshiftcons != $true)) & ((induction = $true) | (($true != ((sP44 @ sK465))) & ! [X18 : term] : (($true = ((sK465 @ (lam @ X18)))) | (((sK465 @ X18)) != $true)) & ! [X19 : term] : ((((sK465 @ X19)) = $true) | ($true != ((var @ X19)))) & (((sK465 @ sK466)) != $true))) & (! [X20 : (term > $o),X21 : term] : (($true = ((sP44 @ X20))) | (($true != ((X20 @ (lam @ (sK467 @ X20))))) & (((X20 @ (sK467 @ X20))) = $true)) | (($true != ((X20 @ (sK468 @ X20)))) & ($true = ((var @ (sK468 @ X20))))) | ($true = ((X20 @ X21)))) | (induction != $true)) & (ulamvarind = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP43) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP43)) & (($true = sP42) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP42)) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X25 : (term > $o)] : (((sK469 @ id @ (sK470 @ X25) @ id)) != ((X25 @ (sK470 @ X25))))) & (! [X27 : (subst > term > subst > $o)] : ! [X29 : term] : (((sK471 @ X27 @ X29)) = ((X27 @ id @ X29 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X30 : term,X31 : term] : ((X30 = X31) | (((lam @ X30)) != ((lam @ X31)))) | (laminj != $true)) & ((laminj = $true) | ((sK472 != sK473) & (((lam @ sK472)) = ((lam @ sK473))))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem2 != $true)) & (! [X34 : term] : (((sub @ X34 @ id)) = X34) | (((sub @ sK474 @ id)) != sK474) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK475 @ id)) != sK475) & ! [X37 : term] : (((sub @ X37 @ id)) = X37))) & (($true = sP39) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP39)) & (! [X38 : term] : (((sub @ X38 @ id)) = X38) | (axvarid != $true)) & ((axvarid = $true) | (sK476 != ((sub @ sK476 @ id)))) & (! [X40 : subst] : (((comp @ X40 @ id)) = X40) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK477 @ id)) != sK477)) & ((pushprop_lem1 = $true) | (($true = ((sK482 @ sK478))) & ($true != ((sK480 @ (sub @ sK478 @ (push @ sK481 @ sK479))))))) & (! [X47 : term,X48 : subst,X49 : (term > $o),X50 : term,X51 : (term > $o)] : (($true != ((X51 @ X47))) | ($true = ((X49 @ (sub @ X47 @ (push @ X50 @ X48)))))) | (pushprop_lem1 != $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X52 : d_subst] : (d_id = X52) & ((hoasapinj1_lthm = $true) | (((((ap @ (sub @ sK485 @ id) @ sK483)) = ((ap @ (sub @ sK486 @ id) @ sK484))) & (sK485 != sK486)) & ! [X57 : term] : (((sub @ X57 @ id)) = X57) & ! [X58 : term,X59 : term,X60 : term,X61 : term] : ((X59 = X60) | (((ap @ X60 @ X61)) != ((ap @ X59 @ X58)))))) & (! [X62 : term,X63 : term,X64 : term,X65 : term] : ((((ap @ (sub @ X65 @ id) @ X63)) != ((ap @ (sub @ X64 @ id) @ X62))) | (X64 = X65)) | (((sub @ sK487 @ id)) != sK487) | ((sK489 != sK490) & (((ap @ sK489 @ sK488)) = ((ap @ sK490 @ sK491)))) | (hoasapinj1_lthm != $true)) & ((sP35 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP35 != $true)) & (apnotvar = $true) & (! [X71 : term,X72 : term,X73 : term,X74 : term] : ((((ap @ (sub @ X71 @ id) @ X74)) != ((ap @ (sub @ X72 @ id) @ X73))) | (X73 = X74)) | ((((ap @ sK494 @ sK492)) = ((ap @ sK495 @ sK493))) & (sK493 != sK492)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((((ap @ (sub @ sK497 @ id) @ sK498)) = ((ap @ (sub @ sK496 @ id) @ sK499))) & (sK499 != sK498)) & ! [X83 : term,X84 : term,X85 : term,X86 : term] : ((((ap @ X86 @ X84)) != ((ap @ X85 @ X83))) | (X83 = X84)))) & ((((comp @ sh @ (push @ sK500 @ sK501))) != sK501) | (((sub @ one @ (push @ sK503 @ sK502))) != sK503) | ! [X91 : term,X92 : (term > $o),X93 : (term > $o),X94 : subst,X95 : term] : (($true != ((X92 @ X91))) | ($true = ((X93 @ (sub @ X91 @ (push @ X95 @ X94)))))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X96 : term,X97 : subst] : (((comp @ sh @ (push @ X96 @ X97))) = X97) & ! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) & (($true = ((sK505 @ sK504))) & ($true != ((sK506 @ (sub @ sK504 @ (push @ sK508 @ sK507)))))))) & ! [X105 : d_term] : (d_one = X105) & (induction2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X106 : subst] : (((push @ (sub @ one @ X106) @ (comp @ sh @ X106))) = X106) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK509) @ (comp @ sh @ sK509))) != sK509)) & ((sP34 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP34 != $true)) & (termmset_gthm = $true) & (! [X108 : (term > $o),X109 : subst,X110 : term] : ! [X112 : term] : (((sK510 @ X110 @ X109 @ X108 @ X112)) = ((X108 @ (sub @ X112 @ (push @ X110 @ X109))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X116 : (term > $o)] : (((X116 @ (sK514 @ X116))) != ((sK511 @ (sub @ (sK514 @ X116) @ (push @ sK513 @ sK512)))))) & (! [X118 : term,X119 : term,X120 : term,X121 : term] : ((X118 = X121) | (((ap @ X118 @ X120)) != ((ap @ X121 @ X119)))) | (apinj1 != $true)) & ((apinj1 = $true) | ((sK515 != sK518) & (((ap @ sK515 @ sK517)) = ((ap @ sK518 @ sK516))))) & (axabs = $true) & ((substmonoid_lthm = $true) | (((sK519 != ((comp @ sK519 @ id))) | (((comp @ id @ sK520)) != sK520)) & ! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129))) & ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | (sK521 != ((comp @ sK521 @ id))) | (sK522 != ((comp @ id @ sK522))) | (substmonoid_lthm != $true)) & ((apinj2 = $true) | ((((ap @ sK525 @ sK526)) = ((ap @ sK523 @ sK524))) & (sK524 != sK526))) & (! [X138 : term,X139 : term,X140 : term,X141 : term] : ((((ap @ X138 @ X139)) != ((ap @ X140 @ X141))) | (X139 = X141)) | (apinj2 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3a_lthm != $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (ulamvar1 != $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X143 : (subst > term > term)] : (((X143 @ (sK528 @ X143) @ (sK529 @ X143))) != ((sub @ sK527 @ (push @ (sK529 @ X143) @ (sK528 @ X143)))))) & (! [X146 : term] : ! [X148 : subst,X149 : term] : (((sK530 @ X146 @ X148 @ X149)) = ((sub @ X146 @ (push @ X149 @ X148)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & ! [X150 : d_subst,X151 : d_subst] : ((((d2subst @ X150)) != ((d2subst @ X151))) | (X150 = X151)) & (induction2lem_gthm = $true) & (! [X152 : (subst > term > term),X153 : (subst > term > term),X154 : term,X155 : subst] : ((((lam @ (X152 @ sh @ one))) != ((lam @ (X153 @ sh @ one)))) | (((X153 @ (comp @ (sK531 @ X153) @ (sK533 @ X153)) @ (sub @ (sK532 @ X153) @ (sK533 @ X153)))) != ((sub @ (X153 @ (sK531 @ X153) @ (sK532 @ X153)) @ (sK533 @ X153)))) | (((X152 @ X155 @ X154)) = ((X153 @ X155 @ X154))) | (((sub @ (X152 @ (sK536 @ X152) @ (sK534 @ X152)) @ (sK535 @ X152))) != ((X152 @ (comp @ (sK536 @ X152) @ (sK535 @ X152)) @ (sub @ (sK534 @ X152) @ (sK535 @ X152)))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((lam @ (sK538 @ sh @ one))) = ((lam @ (sK537 @ sh @ one)))) & ! [X166 : subst,X167 : term,X168 : subst] : (((sub @ (sK538 @ X166 @ X167) @ X168)) = ((sK538 @ (comp @ X166 @ X168) @ (sub @ X167 @ X168)))) & (((sK538 @ sK540 @ sK539)) != ((sK537 @ sK540 @ sK539))) & ! [X169 : term,X170 : subst,X171 : subst] : (((sK537 @ (comp @ X171 @ X170) @ (sub @ X169 @ X170))) = ((sub @ (sK537 @ X171 @ X169) @ X170))))) & (! [X172 : (subst > term > subst > $o)] : ! [X174 : term] : (((sK541 @ X172 @ X174)) = ((X172 @ id @ X174 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X176 : (term > $o)] : (((X176 @ (sK543 @ X176))) != ((sK542 @ id @ (sK543 @ X176) @ id)))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true)) & (axmap = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction = $true) | ($true != sP26)) & (($true = sP26) | (hoasinduction != $true)) & ((induction2lem = $true) | ($true != sP23)) & (($true = sP23) | (induction2lem != $true)) & ((shinj = $true) | ((((sub @ sK544 @ sh)) = ((sub @ sK545 @ sh))) & (sK544 != sK545))) & (! [X180 : term,X181 : term] : ((((sub @ X181 @ sh)) != ((sub @ X180 @ sh))) | (X180 = X181)) | (shinj != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X182 : d_term,X183 : d_term] : ((X182 = X183) | (((d2term @ X183)) != ((d2term @ X182)))) & ((hoasinduction_lem3v2a = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3v2a != $true)) & (pushprop_lem2v2 = $true) & (axapp = $true) & ((axvarcons = $true) | (((sub @ one @ (push @ sK547 @ sK546))) != sK547)) & (! [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) = X187) | (axvarcons != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X188 : (term > $o),X189 : (term > $o),X190 : subst,X191 : term] : (($true = ((X189 @ one))) | (((X188 @ X191)) != $true) | (((X189 @ (sK548 @ X191 @ X190 @ X189 @ X188))) != ((X188 @ (sub @ (sK548 @ X191 @ X190 @ X189 @ X188) @ (push @ X191 @ X190)))))) | (sK550 != ((sub @ one @ (push @ sK550 @ sK549)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((($true != ((sK552 @ one))) & ($true = ((sK551 @ sK554))) & ! [X199 : term] : (((sK551 @ (sub @ X199 @ (push @ sK554 @ sK553)))) = ((sK552 @ X199)))) & ! [X200 : subst,X201 : term] : (((sub @ one @ (push @ X201 @ X200))) = X201))) & ! [X202 : term] : (((d2term @ (sK555 @ X202))) = X202) & (hoasapnotvar_lthm = $true) & (hoasinduction_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem2v2 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2 = $true) | (! [X208 : term] : (((sK556 @ (sub @ X208 @ (push @ sK558 @ sK557)))) = ((sK559 @ X208))) & (((sK556 @ sK558)) = $true) & ($true != ((sK559 @ one))))) & (! [X209 : (term > $o),X210 : subst,X211 : term,X212 : (term > $o)] : ((((X209 @ (sub @ (sK560 @ X212 @ X211 @ X210 @ X209) @ (push @ X211 @ X210)))) != ((X212 @ (sK560 @ X212 @ X211 @ X210 @ X209)))) | ($true != ((X209 @ X211))) | ($true = ((X212 @ one)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP15)) & (($true = sP15) | (hoasinduction_lem3 != $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3b = $true) | ! [X215 : (subst > term > term)] : (((X215 @ sh @ one)) != ((sub @ sK561 @ (push @ one @ sh))))) & (! [X216 : term] : (((sK562 @ X216 @ sh @ one)) = ((sub @ X216 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((substmonoid = $true) | (sK563 != ((comp @ id @ sK563))) | (((comp @ sK564 @ id)) != sK564)) & ((! [X220 : subst] : (((comp @ id @ X220)) = X220) & ! [X221 : subst] : (((comp @ X221 @ id)) = X221)) | (substmonoid != $true)) & ((sP13 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP13 != $true)) & (substmonoid_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) | ((((sK565 @ id @ sK566 @ id)) != $true) & ! [X224 : term,X225 : term] : (($true != ((sK565 @ id @ X225 @ id))) | ($true != ((sK565 @ id @ X224 @ id))) | ($true = ((sK565 @ id @ (ap @ (sub @ X224 @ id) @ X225) @ id)))) & (((sP12 @ sK565)) != $true))) & (! [X226 : (subst > term > subst > $o),X227 : term] : (($true = ((X226 @ id @ X227 @ id))) | ((((X226 @ id @ (sK568 @ X226) @ id)) = $true) & ($true = ((X226 @ id @ (sK567 @ X226) @ id))) & ($true != ((X226 @ id @ (ap @ (sub @ (sK567 @ X226) @ id) @ (sK568 @ X226)) @ id)))) | (((sP12 @ X226)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3v2_lthm != $true)) & (axvarshift = $true) & (! [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ (sub @ X232 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X233))) | (X230 = X232)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK569 @ id) @ sK572)) = ((ap @ (sub @ sK571 @ id) @ sK570))) & (sK571 != sK569))) & (lamnotvar = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1 = $true) & ((induction2 = $true) | ($true != sP9)) & (($true = sP9) | (induction2 != $true)) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ! [X238 : subst] : (((d2subst @ (sK573 @ X238))) = X238) & (! [X240 : term] : (((sub @ X240 @ id)) = X240) | (termmset != $true)) & ((termmset = $true) | (sK574 != ((sub @ sK574 @ id)))) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X242 : term] : ! [X244 : term,X245 : subst] : (((sK575 @ X242 @ X245 @ X244)) = ((sub @ X242 @ (push @ X244 @ X245)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X247 : (subst > term > term)] : (((X247 @ (sK578 @ X247) @ (sK577 @ X247))) != ((sub @ sK576 @ (push @ (sK577 @ X247) @ (sK578 @ X247)))))) & ((hoaslamnotap = $true) | (! [X253 : term,X254 : subst,X255 : subst] : (((sub @ (sK580 @ X255 @ X253) @ X254)) = ((sK580 @ (comp @ X255 @ X254) @ (sub @ X253 @ X254)))) & (((lam @ (sK580 @ sh @ one))) = ((ap @ (sub @ sK581 @ id) @ sK579))))) & (! [X256 : term,X257 : (subst > term > term),X258 : term] : ((((sub @ (X257 @ (sK584 @ X257) @ (sK582 @ X257)) @ (sK583 @ X257))) != ((X257 @ (comp @ (sK584 @ X257) @ (sK583 @ X257)) @ (sub @ (sK582 @ X257) @ (sK583 @ X257))))) | (((lam @ (X257 @ sh @ one))) != ((ap @ (sub @ X258 @ id) @ X256)))) | (hoaslamnotap != $true)) & ((axidl = $true) | (sK585 != ((comp @ id @ sK585)))) & (! [X263 : subst] : (((comp @ id @ X263)) = X263) | (axidl != $true)) & (hoasinduction_lem2_gthm = $true) & (! [X264 : term,X265 : subst,X266 : (term > $o)] : ! [X268 : term] : (((sK586 @ X266 @ X265 @ X264 @ X268)) = ((X266 @ (sub @ X268 @ (push @ X264 @ X265))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X272 : (term > $o)] : (((sK589 @ (sub @ (sK590 @ X272) @ (push @ sK587 @ sK588)))) != ((X272 @ (sK590 @ X272))))) & (lamnotap != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (($true = sP7) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP7)) & ((hoasinduction_lthm_3 = $true) | ($true != sP5)) & (($true = sP5) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem2_lthm = $true)),
% 2.91/0.81 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,vAPP,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,vAPP,vAPP,sK469,vAPP,vAPP,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,vAPP,sK511,sK512,sK513,vAPP,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK537,sK538,sK539,sK540,vAPP,sK542,vAPP,sK544,sK545,sK546,sK547,vAPP,sK549,sK550,sK551,sK552,sK553,sK554,vAPP,sK556,sK557,sK558,sK559,vAPP,sK561,vAPP,sK563,sK564,sK565,sK566,vAPP,vAPP,sK569,sK570,sK571,sK572,vAPP,sK574,vAPP,sK576,vAPP,vAPP,sK579,sK580,sK581,vAPP,vAPP,vAPP,sK585,vAPP,sK587,sK588,sK589,vAPP]),skolemize(X0,sK457),skolemize(X11,sK64 @ X10),skolemize(X4,sK459),skolemize(X5,sK460),skolemize(X6,sK461),skolemize(X7,sK462),skolemize(X12,sK463),skolemize(X13,sK464),skolemize(X16,sK465),skolemize(X17,sK466),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X24,sK469),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X32,sK472),skolemize(X33,sK473),skolemize(X35,sK474),skolemize(X36,sK475),skolemize(X39,sK476),skolemize(X41,sK477),skolemize(X42,sK478),skolemize(X43,sK479),skolemize(X44,sK480),skolemize(X45,sK481),skolemize(X46,sK482),skolemize(X53,sK483),skolemize(X54,sK484),skolemize(X55,sK485),skolemize(X56,sK486),skolemize(X66,sK487),skolemize(X67,sK488),skolemize(X68,sK489),skolemize(X69,sK490),skolemize(X70,sK491),skolemize(X75,sK492),skolemize(X76,sK493),skolemize(X77,sK494),skolemize(X78,sK495),skolemize(X79,sK496),skolemize(X80,sK497),skolemize(X81,sK498),skolemize(X82,sK499),skolemize(X87,sK500),skolemize(X88,sK501),skolemize(X89,sK502),skolemize(X90,sK503),skolemize(X100,sK504),skolemize(X101,sK505),skolemize(X102,sK506),skolemize(X103,sK507),skolemize(X104,sK508),skolemize(X107,sK509),skolemize(X11,sK64 @ X10),skolemize(X113,sK511),skolemize(X114,sK512),skolemize(X115,sK513),skolemize(X11,sK64 @ X10),skolemize(X122,sK515),skolemize(X123,sK516),skolemize(X124,sK517),skolemize(X125,sK518),skolemize(X126,sK519),skolemize(X127,sK520),skolemize(X132,sK521),skolemize(X133,sK522),skolemize(X134,sK523),skolemize(X135,sK524),skolemize(X136,sK525),skolemize(X137,sK526),skolemize(X142,sK527),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X162,sK537),skolemize(X163,sK538),skolemize(X164,sK539),skolemize(X165,sK540),skolemize(X11,sK64 @ X10),skolemize(X175,sK542),skolemize(X11,sK64 @ X10),skolemize(X178,sK544),skolemize(X179,sK545),skolemize(X184,sK546),skolemize(X185,sK547),skolemize(X11,sK64 @ X10),skolemize(X193,sK549),skolemize(X194,sK550),skolemize(X195,sK551),skolemize(X196,sK552),skolemize(X197,sK553),skolemize(X198,sK554),skolemize(X11,sK64 @ X10),skolemize(X204,sK556),skolemize(X205,sK557),skolemize(X206,sK558),skolemize(X207,sK559),skolemize(X11,sK64 @ X10),skolemize(X214,sK561),skolemize(X11,sK64 @ X10),skolemize(X218,sK563),skolemize(X219,sK564),skolemize(X222,sK565),skolemize(X223,sK566),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X234,sK569),skolemize(X235,sK570),skolemize(X236,sK571),skolemize(X237,sK572),skolemize(X11,sK64 @ X10),skolemize(X241,sK574),skolemize(X11,sK64 @ X10),skolemize(X246,sK576),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X250,sK579),skolemize(X251,sK580),skolemize(X252,sK581),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X11,sK64 @ X10),skolemize(X262,sK585),skolemize(X11,sK64 @ X10),skolemize(X269,sK587),skolemize(X270,sK588),skolemize(X271,sK589),skolemize(X11,sK64 @ X10)],[f262])).
% 2.91/0.81 thf(f824,plain,(
% 2.91/0.81 ( ! [X202 : term] : ((((d2term @ (sK555 @ X202))) = X202)) )),
% 2.91/0.81 inference(cnf_transformation,[],[f263])).
% 2.91/0.81 thf(f891,plain,(
% 2.91/0.81 ( ! [X105 : d_term] : ((d_one = X105)) )),
% 2.91/0.81 inference(cnf_transformation,[],[f263])).
% 2.91/0.81 thf(f975,plain,(
% 2.91/0.81 (axclos = $true)),
% 2.91/0.81 inference(cnf_transformation,[],[f263])).
% 2.91/0.81 thf(f978,plain,(
% 2.91/0.81 (axclos != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sub @ Y1 @ Y2) @ Y0) = (sub @ Y1 @ (comp @ Y2 @ Y0)))))))))))),
% 2.91/0.81 inference(cnf_transformation,[],[f8])).
% 2.91/0.81 thf(f981,plain,(
% 2.91/0.81 (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sub @ Y1 @ Y2) @ Y0) = (sub @ Y1 @ (comp @ Y2 @ Y0)))))))))) != $true)),
% 2.91/0.81 inference(definition_unfolding,[],[f978,f975])).
% 2.91/0.81 thf(f992,plain,(
% 2.91/0.81 ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sub @ Y1 @ Y2) @ Y0) = (sub @ Y1 @ (comp @ Y2 @ Y0)))))))) @ sK591)))),
% 2.91/0.81 inference(sigma_proxy_clausification,[],[f981])).
% 2.91/0.81 thf(f993,plain,(
% 2.91/0.81 ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sub @ Y0 @ Y1) @ sK591) = (sub @ Y0 @ (comp @ Y1 @ sK591)))))))))),
% 2.91/0.81 inference(beta-eta_normalization,[],[f992])).
% 2.91/0.81 thf(f994,plain,(
% 2.91/0.81 ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sub @ Y0 @ Y1) @ sK591) = (sub @ Y0 @ (comp @ Y1 @ sK591)))))) @ sK592)) = $false)),
% 2.91/0.81 inference(sigma_proxy_clausification,[],[f993])).
% 2.91/0.81 thf(f995,plain,(
% 2.91/0.81 ($false = ((!! @ subst @ (^[Y0 : subst]: ((sub @ (sub @ sK592 @ Y0) @ sK591) = (sub @ sK592 @ (comp @ Y0 @ sK591)))))))),
% 2.91/0.81 inference(beta-eta_normalization,[],[f994])).
% 2.91/0.81 thf(f996,plain,(
% 2.91/0.81 ((((^[Y0 : subst]: ((sub @ (sub @ sK592 @ Y0) @ sK591) = (sub @ sK592 @ (comp @ Y0 @ sK591)))) @ sK593)) = $false)),
% 2.91/0.81 inference(sigma_proxy_clausification,[],[f995])).
% 2.91/0.81 thf(f997,plain,(
% 2.91/0.81 ($false = (((sub @ (sub @ sK592 @ sK593) @ sK591) = (sub @ sK592 @ (comp @ sK593 @ sK591)))))),
% 2.91/0.81 inference(beta-eta_normalization,[],[f996])).
% 2.91/0.81 thf(f998,plain,(
% 2.91/0.81 (((sub @ sK592 @ (comp @ sK593 @ sK591))) != ((sub @ (sub @ sK592 @ sK593) @ sK591)))),
% 2.91/0.81 inference(equality_proxy_clausification,[],[f997])).
% 2.91/0.81 thf(f3953,plain,(
% 2.91/0.81 ( ! [X202 : term] : ((((d2term @ d_one)) = X202)) )),
% 2.91/0.81 inference(forward_demodulation,[],[f824,f891])).
% 2.91/0.81 thf(f3964,plain,(
% 2.91/0.81 (((d2term @ d_one)) != ((sub @ sK592 @ (comp @ sK593 @ sK591))))),
% 2.91/0.81 inference(superposition,[],[f998,f3953])).
% 2.91/0.81 thf(f3965,plain,(
% 2.91/0.81 $false),
% 2.91/0.81 inference(forward_subsumption_resolution,[],[f3964,f3953])).
% 2.91/0.81 % SZS output end Proof for theBenchmark
% 2.91/0.81 % (1434175)------------------------------
% 2.91/0.81 % (1434175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.91/0.81 % (1434175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/0.81 % (1434175)CaDiCaL version: 2.1.3
% 2.91/0.81 % (1434175)Termination reason: Refutation
% 2.91/0.81 % (1434175)Time elapsed: 0.182 s
% 2.91/0.81 % (1434175)Peak memory usage: 16 MB
% 2.91/0.81 % (1434175)Instructions burned: 405 (million)
% 2.91/0.81 % (1434135)Success in time 0.385 s
% 2.91/0.81 % Vampire exiting
%------------------------------------------------------------------------------