%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX167^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:40:37 AM UTC 2026
% Result : Theorem 6.34s 1.35s
% Output : Refutation 6.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX167^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n016.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 16:14:20 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.35 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.86/0.54 % (538987)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.86/0.54 % (538998)lrs+10_16_si=on:nwc=1.5:random_seed=4161769853:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.86/0.54 % (538997)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1949059875:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.86/0.54 % (538998)Instruction limit reached!
% 0.86/0.54 % (538998)------------------------------
% 0.86/0.54 % (538998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.54 % (538998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.54 % (538998)CaDiCaL version: 2.1.3
% 0.86/0.54 % (538998)Termination reason: Instruction limit
% 0.86/0.54 % (538998)Termination phase: shuffling
% 0.86/0.54 % (538998)Time elapsed: 0.008 s
% 0.86/0.54 % (538998)Peak memory usage: 10 MB
% 0.86/0.54 % (538998)Instructions burned: 18 (million)
% 0.86/0.54 % (539003)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.86/0.54 % (539003)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.86/0.54 % (538999)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4290347435:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.86/0.54 % (539000)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=2907156128:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.86/0.54 % (539001)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2180897438:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.86/0.54 % (539002)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1006947796:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.86/0.54 % (539003)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=1259325730:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.86/0.54 % (538999)Instruction limit reached!
% 0.86/0.54 % (538999)------------------------------
% 0.86/0.54 % (538999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.54 % (538999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.54 % (538999)CaDiCaL version: 2.1.3
% 0.86/0.54 % (538999)Termination reason: Instruction limit
% 0.86/0.54 % (538999)Termination phase: shuffling
% 0.86/0.54 % (538999)Time elapsed: 0.003 s
% 0.86/0.54 % (538999)Peak memory usage: 9 MB
% 0.86/0.54 % (538999)Instructions burned: 3 (million)
% 0.86/0.54 % (539009)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1458409460:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.86/0.54 % (539009)Instruction limit reached!
% 0.86/0.54 % (539009)------------------------------
% 0.86/0.54 % (539009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.54 % (539009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.54 % (539009)CaDiCaL version: 2.1.3
% 0.86/0.54 % (539009)Termination reason: Instruction limit
% 0.86/0.54 % (539009)Termination phase: shuffling
% 0.86/0.54 % (539009)Time elapsed: 0.001 s
% 0.86/0.54 % (539009)Peak memory usage: 10 MB
% 0.86/0.54 % (539009)Instructions burned: 2 (million)
% 0.86/0.54 % (539001)Instruction limit reached!
% 0.86/0.54 % (539001)------------------------------
% 0.86/0.54 % (539001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.54 % (539001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.54 % (539001)CaDiCaL version: 2.1.3
% 0.86/0.54 % (539001)Termination reason: Instruction limit
% 0.86/0.54 % (539001)Termination phase: shuffling
% 0.86/0.54 % (539001)Time elapsed: 0.020 s
% 0.86/0.54 % (539001)Peak memory usage: 10 MB
% 0.86/0.54 % (539001)Instructions burned: 24 (million)
% 0.86/0.54 % (538997)Instruction limit reached!
% 0.86/0.54 % (538997)------------------------------
% 0.86/0.54 % (538997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.54 % (538997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.58 % (538997)CaDiCaL version: 2.1.3
% 1.57/0.58 % (538997)Termination reason: Instruction limit
% 1.57/0.58 % (538997)Termination phase: Preprocessing 3
% 1.57/0.58 % (538997)Time elapsed: 0.040 s
% 1.57/0.58 % (538997)Peak memory usage: 13 MB
% 1.57/0.58 % (538997)Instructions burned: 87 (million)
% 1.57/0.58 % (539015)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2920260529:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.57/0.58 % (539015)Instruction limit reached!
% 1.57/0.58 % (539015)------------------------------
% 1.57/0.58 % (539015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.58 % (539015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.58 % (539015)CaDiCaL version: 2.1.3
% 1.57/0.58 % (539015)Termination reason: Instruction limit
% 1.57/0.58 % (539015)Termination phase: shuffling
% 1.57/0.58 % (539015)Time elapsed: 0.005 s
% 1.57/0.58 % (539015)Peak memory usage: 10 MB
% 1.57/0.58 % (539015)Instructions burned: 5 (million)
% 1.57/0.58 % (539020)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
% 1.57/0.58 % (539020)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.57/0.58 % (539018)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.57/0.58 % (539020)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1150107296:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.57/0.58 % (539018)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1032684256:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.57/0.58 % (539019)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2962371230:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.57/0.58 % (539018)Instruction limit reached!
% 1.57/0.58 % (539018)------------------------------
% 1.57/0.58 % (539018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.58 % (539018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.58 % (539018)CaDiCaL version: 2.1.3
% 1.57/0.58 % (539018)Termination reason: Instruction limit
% 1.57/0.58 % (539018)Termination phase: shuffling
% 1.57/0.58 % (539018)Time elapsed: 0.007 s
% 1.57/0.58 % (539018)Peak memory usage: 10 MB
% 1.57/0.58 % (539018)Instructions burned: 8 (million)
% 1.57/0.58 % (539020)Instruction limit reached!
% 1.57/0.58 % (539020)------------------------------
% 1.57/0.58 % (539020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.58 % (539020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.58 % (539020)CaDiCaL version: 2.1.3
% 1.57/0.58 % (539020)Termination reason: Instruction limit
% 1.57/0.58 % (539020)Termination phase: shuffling
% 1.57/0.58 % (539020)Time elapsed: 0.012 s
% 1.57/0.58 % (539020)Peak memory usage: 10 MB
% 1.57/0.58 % (539020)Instructions burned: 28 (million)
% 1.57/0.58 % (539002)Instruction limit reached!
% 1.57/0.58 % (539002)------------------------------
% 1.57/0.58 % (539002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.58 % (539002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.58 % (539002)CaDiCaL version: 2.1.3
% 1.57/0.58 % (539002)Termination reason: Instruction limit
% 1.57/0.58 % (539002)Termination phase: Preprocessing 3
% 1.57/0.58 % (539002)Time elapsed: 0.062 s
% 1.57/0.58 % (539002)Peak memory usage: 12 MB
% 1.57/0.58 % (539002)Instructions burned: 76 (million)
% 1.57/0.58 % (539019)Instruction limit reached!
% 1.57/0.58 % (539019)------------------------------
% 1.57/0.58 % (539019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.58 % (539019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.58 % (539019)CaDiCaL version: 2.1.3
% 1.57/0.58 % (539019)Termination reason: Instruction limit
% 1.57/0.58 % (539019)Termination phase: shuffling
% 1.57/0.58 % (539019)Time elapsed: 0.010 s
% 1.57/0.58 % (539019)Peak memory usage: 10 MB
% 1.57/0.58 % (539019)Instructions burned: 12 (million)
% 1.57/0.62 % (539022)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=3848844564:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.57/0.62 % (539028)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.57/0.62 % (539028)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=426854834:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.57/0.62 % (539028)Instruction limit reached!
% 1.57/0.62 % (539028)------------------------------
% 1.57/0.62 % (539028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.62 % (539028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.62 % (539028)CaDiCaL version: 2.1.3
% 1.57/0.62 % (539028)Termination reason: Instruction limit
% 1.57/0.62 % (539028)Termination phase: shuffling
% 1.57/0.62 % (539028)Time elapsed: 0.002 s
% 1.57/0.62 % (539028)Peak memory usage: 9 MB
% 1.57/0.62 % (539028)Instructions burned: 4 (million)
% 1.57/0.62 % (539027)lrs+10_1_si=on:cs=on:random_seed=196015002:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.57/0.62 % (539029)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1976652356:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.57/0.62 % (539030)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=349457945:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.57/0.62 % (539027)Instruction limit reached!
% 1.57/0.62 % (539027)------------------------------
% 1.57/0.62 % (539027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.62 % (539027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.62 % (539027)CaDiCaL version: 2.1.3
% 1.57/0.62 % (539027)Termination reason: Instruction limit
% 1.57/0.62 % (539027)Termination phase: shuffling
% 1.57/0.62 % (539027)Time elapsed: 0.007 s
% 1.57/0.62 % (539027)Peak memory usage: 10 MB
% 1.57/0.62 % (539027)Instructions burned: 8 (million)
% 1.57/0.62 % (539033)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2510063951:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.57/0.62 % (539037)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1470164778:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.57/0.62 % (539037)Instruction limit reached!
% 1.57/0.62 % (539037)------------------------------
% 1.57/0.62 % (539037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.62 % (539037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.62 % (539037)CaDiCaL version: 2.1.3
% 1.57/0.62 % (539037)Termination reason: Instruction limit
% 1.57/0.62 % (539037)Termination phase: shuffling
% 1.57/0.62 % (539037)Time elapsed: 0.004 s
% 1.57/0.62 % (539037)Peak memory usage: 10 MB
% 1.57/0.62 % (539037)Instructions burned: 18 (million)
% 1.57/0.62 % (539003)Instruction limit reached!
% 1.57/0.62 % (539003)------------------------------
% 1.57/0.62 % (539003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.62 % (539003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.62 % (539003)CaDiCaL version: 2.1.3
% 1.57/0.62 % (539003)Termination reason: Instruction limit
% 1.57/0.62 % (539003)Termination phase: Property scanning
% 1.57/0.62 % (539003)Time elapsed: 0.120 s
% 1.57/0.62 % (539003)Peak memory usage: 13 MB
% 1.57/0.62 % (539003)Instructions burned: 159 (million)
% 1.57/0.62 % (539033)Instruction limit reached!
% 1.57/0.62 % (539033)------------------------------
% 1.57/0.62 % (539033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.62 % (539033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.62 % (539033)CaDiCaL version: 2.1.3
% 1.57/0.62 % (539033)Termination reason: Instruction limit
% 1.57/0.62 % (539033)Termination phase: Property scanning
% 1.57/0.62 % (539033)Time elapsed: 0.013 s
% 1.57/0.62 % (539033)Peak memory usage: 10 MB
% 1.57/0.62 % (539033)Instructions burned: 26 (million)
% 1.57/0.62 % (539029)Instruction limit reached!
% 1.57/0.62 % (539029)------------------------------
% 2.04/0.65 % (539029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.65 % (539029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.65 % (539029)CaDiCaL version: 2.1.3
% 2.04/0.65 % (539029)Termination reason: Instruction limit
% 2.04/0.65 % (539029)Termination phase: Saturation
% 2.04/0.65 % (539029)Time elapsed: 0.027 s
% 2.04/0.65 % (539029)Peak memory usage: 11 MB
% 2.04/0.65 % (539029)Instructions burned: 39 (million)
% 2.04/0.65 % (539041)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=981003002:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.04/0.65 % (539022)Instruction limit reached!
% 2.04/0.65 % (539022)------------------------------
% 2.04/0.65 % (539022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.65 % (539022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.65 % (539022)CaDiCaL version: 2.1.3
% 2.04/0.65 % (539022)Termination reason: Instruction limit
% 2.04/0.65 % (539022)Termination phase: Saturation
% 2.04/0.65 % (539022)Time elapsed: 0.057 s
% 2.04/0.65 % (539022)Peak memory usage: 12 MB
% 2.04/0.65 % (539022)Instructions burned: 90 (million)
% 2.04/0.65 % (539042)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1498374976:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.04/0.65 % (539044)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1607037796:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.04/0.65 % (539043)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1352378273:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.04/0.65 % (539042)Instruction limit reached!
% 2.04/0.65 % (539042)------------------------------
% 2.04/0.65 % (539042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.65 % (539042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.65 % (539042)CaDiCaL version: 2.1.3
% 2.04/0.65 % (539042)Termination reason: Instruction limit
% 2.04/0.65 % (539042)Termination phase: shuffling
% 2.04/0.65 % (539042)Time elapsed: 0.006 s
% 2.04/0.65 % (539042)Peak memory usage: 10 MB
% 2.04/0.65 % (539042)Instructions burned: 14 (million)
% 2.04/0.65 % (539043)Instruction limit reached!
% 2.04/0.65 % (539043)------------------------------
% 2.04/0.65 % (539043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.65 % (539043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.65 % (539043)CaDiCaL version: 2.1.3
% 2.04/0.65 % (539043)Termination reason: Instruction limit
% 2.04/0.65 % (539043)Termination phase: shuffling
% 2.04/0.65 % (539043)Time elapsed: 0.002 s
% 2.04/0.65 % (539043)Peak memory usage: 9 MB
% 2.04/0.65 % (539043)Instructions burned: 3 (million)
% 2.04/0.65 % (539047)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2257005023:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.04/0.65 % (539044)Instruction limit reached!
% 2.04/0.65 % (539044)------------------------------
% 2.04/0.65 % (539044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.65 % (539044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.65 % (539044)CaDiCaL version: 2.1.3
% 2.04/0.65 % (539044)Termination reason: Instruction limit
% 2.04/0.65 % (539044)Termination phase: shuffling
% 2.04/0.65 % (539044)Time elapsed: 0.011 s
% 2.04/0.65 % (539044)Peak memory usage: 10 MB
% 2.04/0.65 % (539044)Instructions burned: 26 (million)
% 2.04/0.65 % (539052)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
% 2.04/0.65 % (539052)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.04/0.65 % (539047)Instruction limit reached!
% 2.04/0.65 % (539047)------------------------------
% 2.04/0.65 % (539047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.04/0.65 % (539047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.65 % (539047)CaDiCaL version: 2.1.3
% 2.04/0.65 % (539047)Termination reason: Instruction limit
% 2.04/0.65 % (539047)Termination phase: shuffling
% 2.18/0.72 % (539047)Time elapsed: 0.010 s
% 2.18/0.72 % (539047)Peak memory usage: 10 MB
% 2.18/0.72 % (539047)Instructions burned: 24 (million)
% 2.18/0.72 % (539051)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2582194795:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.18/0.72 % (539052)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=3624360597:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.18/0.72 % (539054)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.18/0.72 % (539054)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=3575191795:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.18/0.72 % (539052)Instruction limit reached!
% 2.18/0.72 % (539052)------------------------------
% 2.18/0.72 % (539052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.72 % (539052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.72 % (539052)CaDiCaL version: 2.1.3
% 2.18/0.72 % (539052)Termination reason: Instruction limit
% 2.18/0.72 % (539052)Termination phase: shuffling
% 2.18/0.72 % (539052)Time elapsed: 0.007 s
% 2.18/0.72 % (539052)Peak memory usage: 10 MB
% 2.18/0.72 % (539052)Instructions burned: 15 (million)
% 2.18/0.72 % (539054)Instruction limit reached!
% 2.18/0.72 % (539054)------------------------------
% 2.18/0.72 % (539054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.72 % (539054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.72 % (539054)CaDiCaL version: 2.1.3
% 2.18/0.72 % (539054)Termination reason: Instruction limit
% 2.18/0.72 % (539054)Termination phase: shuffling
% 2.18/0.72 % (539054)Time elapsed: 0.004 s
% 2.18/0.72 % (539054)Peak memory usage: 10 MB
% 2.18/0.72 % (539054)Instructions burned: 9 (million)
% 2.18/0.72 % (539056)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=633643690:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.18/0.72 % (539051)Instruction limit reached!
% 2.18/0.72 % (539051)------------------------------
% 2.18/0.72 % (539051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.72 % (539051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.72 % (539051)CaDiCaL version: 2.1.3
% 2.18/0.72 % (539051)Termination reason: Instruction limit
% 2.18/0.72 % (539051)Termination phase: Preprocessing 3
% 2.18/0.72 % (539051)Time elapsed: 0.027 s
% 2.18/0.72 % (539051)Peak memory usage: 12 MB
% 2.18/0.72 % (539051)Instructions burned: 62 (million)
% 2.18/0.72 % (539059)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3319258659:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.18/0.72 % (539060)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4050435562:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.18/0.72 % (539056)Instruction limit reached!
% 2.18/0.72 % (539056)------------------------------
% 2.18/0.72 % (539056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.72 % (539056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.72 % (539056)CaDiCaL version: 2.1.3
% 2.18/0.72 % (539056)Termination reason: Instruction limit
% 2.18/0.72 % (539056)Termination phase: shuffling
% 2.18/0.72 % (539056)Time elapsed: 0.013 s
% 2.18/0.72 % (539056)Peak memory usage: 10 MB
% 2.18/0.72 % (539056)Instructions burned: 31 (million)
% 2.18/0.72 % (539059)Instruction limit reached!
% 2.18/0.72 % (539059)------------------------------
% 2.18/0.72 % (539059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.72 % (539059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.72 % (539059)CaDiCaL version: 2.1.3
% 2.18/0.72 % (539059)Termination reason: Instruction limit
% 2.18/0.72 % (539059)Termination phase: shuffling
% 2.18/0.72 % (539059)Time elapsed: 0.003 s
% 2.18/0.72 % (539059)Peak memory usage: 9 MB
% 2.18/0.72 % (539059)Instructions burned: 8 (million)
% 2.18/0.72 % (539060)Instruction limit reached!
% 2.18/0.72 % (539060)------------------------------
% 2.18/0.79 % (539060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.79 % (539060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.79 % (539060)CaDiCaL version: 2.1.3
% 2.18/0.79 % (539060)Termination reason: Instruction limit
% 2.18/0.79 % (539060)Termination phase: shuffling
% 2.18/0.79 % (539060)Time elapsed: 0.011 s
% 2.18/0.79 % (539060)Peak memory usage: 10 MB
% 2.18/0.79 % (539060)Instructions burned: 24 (million)
% 2.18/0.79 % (539041)Instruction limit reached!
% 2.18/0.79 % (539041)------------------------------
% 2.18/0.79 % (539041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.79 % (539041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.79 % (539041)CaDiCaL version: 2.1.3
% 2.18/0.79 % (539041)Termination reason: Instruction limit
% 2.18/0.79 % (539041)Termination phase: Saturation
% 2.18/0.79 % (539041)Time elapsed: 0.078 s
% 2.18/0.79 % (539041)Peak memory usage: 16 MB
% 2.18/0.79 % (539041)Instructions burned: 331 (million)
% 2.18/0.79 % (539063)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2786604072:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.18/0.79 % (539065)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2211777933:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.18/0.79 % (539030)Instruction limit reached!
% 2.18/0.79 % (539030)------------------------------
% 2.18/0.79 % (539030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.79 % (539030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.79 % (539030)CaDiCaL version: 2.1.3
% 2.18/0.79 % (539030)Termination reason: Instruction limit
% 2.18/0.79 % (539030)Termination phase: Saturation
% 2.18/0.79 % (539030)Time elapsed: 0.120 s
% 2.18/0.79 % (539030)Peak memory usage: 15 MB
% 2.18/0.79 % (539030)Instructions burned: 250 (million)
% 2.18/0.79 % (539068)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3227833366:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.18/0.79 % (539063)Instruction limit reached!
% 2.18/0.79 % (539063)------------------------------
% 2.18/0.79 % (539063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.79 % (539063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.79 % (539063)CaDiCaL version: 2.1.3
% 2.18/0.79 % (539063)Termination reason: Instruction limit
% 2.18/0.79 % (539063)Termination phase: shuffling
% 2.18/0.79 % (539063)Time elapsed: 0.009 s
% 2.18/0.79 % (539063)Peak memory usage: 10 MB
% 2.18/0.79 % (539063)Instructions burned: 21 (million)
% 2.18/0.79 % (539066)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2853805883:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.18/0.79 % (539067)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4198580203:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.18/0.79 % (539068)Instruction limit reached!
% 2.18/0.79 % (539068)------------------------------
% 2.18/0.79 % (539068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.79 % (539068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.79 % (539068)CaDiCaL version: 2.1.3
% 2.18/0.79 % (539068)Termination reason: Instruction limit
% 2.18/0.79 % (539068)Termination phase: Preprocessing 3
% 2.18/0.79 % (539068)Time elapsed: 0.010 s
% 2.18/0.79 % (539068)Peak memory usage: 11 MB
% 2.18/0.79 % (539068)Instructions burned: 47 (million)
% 2.18/0.79 % (539071)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.18/0.79 % (539071)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4030871293:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.18/0.79 % (539074)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1613869054:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.18/0.79 % (539071)Instruction limit reached!
% 2.18/0.79 % (539071)------------------------------
% 2.18/0.79 % (539071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.18/0.79 % (539071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.18/0.79 % (539071)CaDiCaL version: 2.1.3
% 2.77/0.86 % (539071)Termination reason: Instruction limit
% 2.77/0.86 % (539071)Termination phase: shuffling
% 2.77/0.86 % (539071)Time elapsed: 0.004 s
% 2.77/0.86 % (539071)Peak memory usage: 10 MB
% 2.77/0.86 % (539071)Instructions burned: 9 (million)
% 2.77/0.86 % (539076)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=652993993:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.77/0.86 % (539080)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.77/0.86 % (539080)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3232147515:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.77/0.86 % (539080)Instruction limit reached!
% 2.77/0.86 % (539080)------------------------------
% 2.77/0.86 % (539080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.86 % (539080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.86 % (539080)CaDiCaL version: 2.1.3
% 2.77/0.86 % (539080)Termination reason: Instruction limit
% 2.77/0.86 % (539080)Termination phase: shuffling
% 2.77/0.86 % (539080)Time elapsed: 0.002 s
% 2.77/0.86 % (539080)Peak memory usage: 10 MB
% 2.77/0.86 % (539080)Instructions burned: 8 (million)
% 2.77/0.86 % (539084)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2488291605:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.77/0.86 % (539084)Instruction limit reached!
% 2.77/0.86 % (539084)------------------------------
% 2.77/0.86 % (539084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.86 % (539084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.86 % (539084)CaDiCaL version: 2.1.3
% 2.77/0.86 % (539084)Termination reason: Instruction limit
% 2.77/0.86 % (539084)Termination phase: shuffling
% 2.77/0.86 % (539084)Time elapsed: 0.005 s
% 2.77/0.86 % (539084)Peak memory usage: 10 MB
% 2.77/0.86 % (539084)Instructions burned: 24 (million)
% 2.77/0.86 % (539092)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=638481780:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.77/0.86 % (539092)Instruction limit reached!
% 2.77/0.86 % (539092)------------------------------
% 2.77/0.86 % (539092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.86 % (539092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.86 % (539092)CaDiCaL version: 2.1.3
% 2.77/0.86 % (539092)Termination reason: Instruction limit
% 2.77/0.86 % (539092)Termination phase: shuffling
% 2.77/0.86 % (539092)Time elapsed: 0.005 s
% 2.77/0.86 % (539092)Peak memory usage: 10 MB
% 2.77/0.86 % (539092)Instructions burned: 23 (million)
% 2.77/0.86 % (539066)Instruction limit reached!
% 2.77/0.86 % (539066)------------------------------
% 2.77/0.86 % (539066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.86 % (539066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.86 % (539066)CaDiCaL version: 2.1.3
% 2.77/0.86 % (539066)Termination reason: Instruction limit
% 2.77/0.86 % (539066)Termination phase: Property scanning
% 2.77/0.86 % (539066)Time elapsed: 0.065 s
% 2.77/0.86 % (539066)Peak memory usage: 13 MB
% 2.77/0.86 % (539066)Instructions burned: 146 (million)
% 2.77/0.86 % (539101)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2170252476:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.77/0.86 % (539102)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=408995854:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.77/0.86 % (539067)Instruction limit reached!
% 2.77/0.86 % (539067)------------------------------
% 2.77/0.86 % (539067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.77/0.86 % (539067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/0.86 % (539067)CaDiCaL version: 2.1.3
% 2.77/0.86 % (539067)Termination reason: Instruction limit
% 3.37/0.93 % (539067)Termination phase: Property scanning
% 3.37/0.93 % (539067)Time elapsed: 0.082 s
% 3.37/0.93 % (539067)Peak memory usage: 13 MB
% 3.37/0.93 % (539067)Instructions burned: 193 (million)
% 3.37/0.93 % (539076)Instruction limit reached!
% 3.37/0.93 % (539076)------------------------------
% 3.37/0.93 % (539076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.93 % (539076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.93 % (539076)CaDiCaL version: 2.1.3
% 3.37/0.93 % (539076)Termination reason: Instruction limit
% 3.37/0.93 % (539076)Termination phase: Property scanning
% 3.37/0.93 % (539076)Time elapsed: 0.073 s
% 3.37/0.93 % (539076)Peak memory usage: 13 MB
% 3.37/0.93 % (539076)Instructions burned: 171 (million)
% 3.37/0.93 % (539074)Instruction limit reached!
% 3.37/0.93 % (539074)------------------------------
% 3.37/0.93 % (539074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.93 % (539074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.93 % (539074)CaDiCaL version: 2.1.3
% 3.37/0.93 % (539074)Termination reason: Instruction limit
% 3.37/0.93 % (539074)Termination phase: Saturation
% 3.37/0.93 % (539074)Time elapsed: 0.082 s
% 3.37/0.93 % (539074)Peak memory usage: 15 MB
% 3.37/0.93 % (539074)Instructions burned: 181 (million)
% 3.37/0.93 % (539114)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3038180847:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.37/0.93 % (539117)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3186940737:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.37/0.93 % (539122)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3896953406:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.37/0.93 % (539114)Instruction limit reached!
% 3.37/0.93 % (539114)------------------------------
% 3.37/0.93 % (539114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.93 % (539114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.93 % (539114)CaDiCaL version: 2.1.3
% 3.37/0.93 % (539114)Termination reason: Instruction limit
% 3.37/0.93 % (539114)Termination phase: SInE selection
% 3.37/0.93 % (539114)Time elapsed: 0.019 s
% 3.37/0.93 % (539114)Peak memory usage: 10 MB
% 3.37/0.93 % (539114)Instructions burned: 45 (million)
% 3.37/0.93 % (539122)Instruction limit reached!
% 3.37/0.93 % (539122)------------------------------
% 3.37/0.93 % (539122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.93 % (539122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.93 % (539122)CaDiCaL version: 2.1.3
% 3.37/0.93 % (539122)Termination reason: Instruction limit
% 3.37/0.93 % (539122)Termination phase: shuffling
% 3.37/0.93 % (539122)Time elapsed: 0.010 s
% 3.37/0.93 % (539122)Peak memory usage: 10 MB
% 3.37/0.93 % (539122)Instructions burned: 22 (million)
% 3.37/0.93 % (539135)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.37/0.93 % (539135)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3756860831:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 3.37/0.93 % (539138)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3126177095:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 3.37/0.93 % (539000)Instruction limit reached!
% 3.37/0.93 % (539000)------------------------------
% 3.37/0.93 % (539000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.93 % (539000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.93 % (539000)CaDiCaL version: 2.1.3
% 3.37/0.93 % (539000)Termination reason: Instruction limit
% 3.37/0.93 % (539000)Termination phase: Saturation
% 3.37/0.93 % (539000)Time elapsed: 0.377 s
% 3.37/0.93 % (539000)Peak memory usage: 18 MB
% 3.37/0.93 % (539000)Instructions burned: 634 (million)
% 3.37/0.93 % (539138)Instruction limit reached!
% 3.37/0.93 % (539138)------------------------------
% 3.37/0.93 % (539138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.93 % (539138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.09 % (539138)CaDiCaL version: 2.1.3
% 4.84/1.09 % (539138)Termination reason: Instruction limit
% 4.84/1.09 % (539138)Termination phase: shuffling
% 4.84/1.09 % (539138)Time elapsed: 0.006 s
% 4.84/1.09 % (539138)Peak memory usage: 10 MB
% 4.84/1.09 % (539138)Instructions burned: 14 (million)
% 4.84/1.09 % (539101)Instruction limit reached!
% 4.84/1.09 % (539101)------------------------------
% 4.84/1.09 % (539101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.84/1.09 % (539101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.09 % (539101)CaDiCaL version: 2.1.3
% 4.84/1.09 % (539101)Termination reason: Instruction limit
% 4.84/1.09 % (539101)Termination phase: Saturation
% 4.84/1.09 % (539101)Time elapsed: 0.093 s
% 4.84/1.09 % (539101)Peak memory usage: 15 MB
% 4.84/1.09 % (539101)Instructions burned: 317 (million)
% 4.84/1.09 % (539153)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=648386424:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 4.84/1.09 % (539154)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2089067679:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 4.84/1.09 % (539162)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3423676131:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 4.84/1.09 % (539162)Instruction limit reached!
% 4.84/1.09 % (539162)------------------------------
% 4.84/1.09 % (539162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.84/1.09 % (539162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.09 % (539162)CaDiCaL version: 2.1.3
% 4.84/1.09 % (539162)Termination reason: Instruction limit
% 4.84/1.09 % (539162)Termination phase: Property scanning
% 4.84/1.09 % (539162)Time elapsed: 0.007 s
% 4.84/1.09 % (539162)Peak memory usage: 10 MB
% 4.84/1.09 % (539162)Instructions burned: 32 (million)
% 4.84/1.09 % (539154)Instruction limit reached!
% 4.84/1.09 % (539154)------------------------------
% 4.84/1.09 % (539154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.84/1.09 % (539154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.09 % (539154)CaDiCaL version: 2.1.3
% 4.84/1.09 % (539154)Termination reason: Instruction limit
% 4.84/1.09 % (539154)Termination phase: Preprocessing 3
% 4.84/1.09 % (539154)Time elapsed: 0.022 s
% 4.84/1.09 % (539154)Peak memory usage: 11 MB
% 4.84/1.09 % (539154)Instructions burned: 51 (million)
% 4.84/1.09 % (539173)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1282863865:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 4.84/1.09 % (539153)Instruction limit reached!
% 4.84/1.09 % (539153)------------------------------
% 4.84/1.09 % (539153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.84/1.09 % (539153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.09 % (539153)CaDiCaL version: 2.1.3
% 4.84/1.09 % (539153)Termination reason: Instruction limit
% 4.84/1.09 % (539153)Termination phase: Property scanning
% 4.84/1.09 % (539153)Time elapsed: 0.028 s
% 4.84/1.09 % (539153)Peak memory usage: 11 MB
% 4.84/1.09 % (539153)Instructions burned: 67 (million)
% 4.84/1.09 % (539180)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=508931620:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.84/1.09 % (539182)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3707957042:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 4.84/1.09 % (539173)Instruction limit reached!
% 4.84/1.09 % (539173)------------------------------
% 4.84/1.09 % (539173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.84/1.09 % (539173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.09 % (539173)CaDiCaL version: 2.1.3
% 4.84/1.09 % (539173)Termination reason: Instruction limit
% 4.84/1.09 % (539173)Termination phase: shuffling
% 4.84/1.09 % (539173)Time elapsed: 0.032 s
% 4.84/1.09 % (539173)Peak memory usage: 13 MB
% 4.84/1.09 % (539173)Instructions burned: 140 (million)
% 4.84/1.09 % (539135)Instruction limit reached!
% 4.84/1.09 % (539135)------------------------------
% 4.84/1.09 % (539135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.19 % (539135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.19 % (539135)CaDiCaL version: 2.1.3
% 5.43/1.19 % (539135)Termination reason: Instruction limit
% 5.43/1.19 % (539135)Termination phase: Saturation
% 5.43/1.19 % (539135)Time elapsed: 0.086 s
% 5.43/1.19 % (539135)Peak memory usage: 14 MB
% 5.43/1.19 % (539135)Instructions burned: 201 (million)
% 5.43/1.19 % (539180)Instruction limit reached!
% 5.43/1.19 % (539180)------------------------------
% 5.43/1.19 % (539180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.19 % (539180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.19 % (539180)CaDiCaL version: 2.1.3
% 5.43/1.19 % (539180)Termination reason: Instruction limit
% 5.43/1.19 % (539180)Termination phase: Property scanning
% 5.43/1.19 % (539180)Time elapsed: 0.015 s
% 5.43/1.19 % (539180)Peak memory usage: 10 MB
% 5.43/1.19 % (539180)Instructions burned: 34 (million)
% 5.43/1.19 % (539117)Refutation not found, incomplete strategy
% 5.43/1.19 % (539117)------------------------------
% 5.43/1.19 % (539117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.19 % (539117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.19 % (539117)CaDiCaL version: 2.1.3
% 5.43/1.19 % (539117)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.19 % (539117)Time elapsed: 0.123 s
% 5.43/1.19 % (539117)Peak memory usage: 16 MB
% 5.43/1.19 % (539117)Instructions burned: 271 (million)
% 5.43/1.19 % (539117)------------------------------
% 5.43/1.19 % (539117)------------------------------
% 5.43/1.19 % (539191)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.43/1.19 % (539191)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=495690940:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 5.43/1.19 % (539193)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2474985808:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.43/1.19 % (539192)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=448473625:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 5.43/1.19 % (539182)Instruction limit reached!
% 5.43/1.19 % (539182)------------------------------
% 5.43/1.19 % (539182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.19 % (539182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.19 % (539182)CaDiCaL version: 2.1.3
% 5.43/1.19 % (539182)Termination reason: Instruction limit
% 5.43/1.19 % (539182)Termination phase: Preprocessing 3
% 5.43/1.19 % (539182)Time elapsed: 0.030 s
% 5.43/1.19 % (539182)Peak memory usage: 12 MB
% 5.43/1.19 % (539182)Instructions burned: 67 (million)
% 5.43/1.19 % (539195)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3716385497:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.43/1.19 % (539206)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1980151536:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.43/1.19 % (539191)Instruction limit reached!
% 5.43/1.19 % (539191)------------------------------
% 5.43/1.19 % (539191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.19 % (539191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.19 % (539191)CaDiCaL version: 2.1.3
% 5.43/1.19 % (539191)Termination reason: Instruction limit
% 5.43/1.19 % (539191)Termination phase: Saturation
% 5.43/1.19 % (539191)Time elapsed: 0.040 s
% 5.43/1.19 % (539191)Peak memory usage: 12 MB
% 5.43/1.19 % (539191)Instructions burned: 182 (million)
% 5.43/1.19 % (539217)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2096655071:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.43/1.19 % (539193)Instruction limit reached!
% 5.43/1.19 % (539193)------------------------------
% 5.43/1.19 % (539193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.19 % (539193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.19 % (539193)CaDiCaL version: 2.1.3
% 5.43/1.19 % (539193)Termination reason: Instruction limit
% 5.43/1.19 % (539193)Termination phase: Property scanning
% 5.43/1.19 % (539193)Time elapsed: 0.043 s
% 5.43/1.19 % (539193)Peak memory usage: 12 MB
% 5.51/1.28 % (539193)Instructions burned: 97 (million)
% 5.51/1.28 % (539222)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3954765339:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.51/1.28 % (539192)Instruction limit reached!
% 5.51/1.28 % (539192)------------------------------
% 5.51/1.28 % (539192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.51/1.28 % (539192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/1.28 % (539192)CaDiCaL version: 2.1.3
% 5.51/1.28 % (539192)Termination reason: Instruction limit
% 5.51/1.28 % (539192)Termination phase: Saturation
% 5.51/1.28 % (539192)Time elapsed: 0.109 s
% 5.51/1.28 % (539192)Peak memory usage: 15 MB
% 5.51/1.28 % (539192)Instructions burned: 247 (million)
% 5.51/1.28 % (539222)Refutation not found, incomplete strategy
% 5.51/1.28 % (539222)------------------------------
% 5.51/1.28 % (539222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.51/1.28 % (539222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/1.28 % (539222)CaDiCaL version: 2.1.3
% 5.51/1.28 % (539222)Termination reason: Refutation not found, incomplete strategy
% 5.51/1.28 % (539222)Time elapsed: 0.047 s
% 5.51/1.28 % (539222)Peak memory usage: 13 MB
% 5.51/1.28 % (539222)Instructions burned: 102 (million)
% 5.51/1.28 % (539222)------------------------------
% 5.51/1.28 % (539222)------------------------------
% 5.51/1.28 % (539232)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2852740909:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 5.51/1.28 % (539231)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3852586142:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 5.51/1.28 % (539231)Instruction limit reached!
% 5.51/1.28 % (539231)------------------------------
% 5.51/1.28 % (539231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.51/1.28 % (539231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/1.28 % (539231)CaDiCaL version: 2.1.3
% 5.51/1.28 % (539231)Termination reason: Instruction limit
% 5.51/1.28 % (539231)Termination phase: Property scanning
% 5.51/1.28 % (539231)Time elapsed: 0.020 s
% 5.51/1.28 % (539231)Peak memory usage: 10 MB
% 5.51/1.28 % (539231)Instructions burned: 44 (million)
% 5.51/1.28 % (539235)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=732312087:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 5.51/1.28 % (539217)Instruction limit reached!
% 5.51/1.28 % (539217)------------------------------
% 5.51/1.28 % (539217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.51/1.28 % (539217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/1.28 % (539217)CaDiCaL version: 2.1.3
% 5.51/1.28 % (539217)Termination reason: Instruction limit
% 5.51/1.28 % (539217)Termination phase: Saturation
% 5.51/1.28 % (539217)Time elapsed: 0.133 s
% 5.51/1.28 % (539217)Peak memory usage: 18 MB
% 5.51/1.28 % (539217)Instructions burned: 517 (million)
% 5.51/1.28 % (539242)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1040800516:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 5.51/1.28 % (539195)Instruction limit reached!
% 5.51/1.28 % (539195)------------------------------
% 5.51/1.28 % (539195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.51/1.28 % (539195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/1.28 % (539195)CaDiCaL version: 2.1.3
% 5.51/1.28 % (539195)Termination reason: Instruction limit
% 5.51/1.28 % (539195)Termination phase: Saturation
% 5.51/1.28 % (539195)Time elapsed: 0.191 s
% 5.51/1.28 % (539195)Peak memory usage: 14 MB
% 5.51/1.28 % (539195)Instructions burned: 429 (million)
% 5.51/1.28 % (539242)Instruction limit reached!
% 5.51/1.28 % (539242)------------------------------
% 5.51/1.28 % (539242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.51/1.28 % (539242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/1.28 % (539242)CaDiCaL version: 2.1.3
% 5.51/1.28 % (539242)Termination reason: Instruction limit
% 5.51/1.28 % (539242)Termination phase: Property scanning
% 5.51/1.28 % (539242)Time elapsed: 0.023 s
% 5.51/1.28 % (539242)Peak memory usage: 12 MB
% 5.51/1.28 % (539242)Instructions burned: 97 (million)
% 6.34/1.35 % (539247)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=2722743180:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 6.34/1.35 % (539255)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1025785744:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 6.34/1.35 % (539102)Instruction limit reached!
% 6.34/1.35 % (539102)------------------------------
% 6.34/1.35 % (539102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539102)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539102)Termination reason: Instruction limit
% 6.34/1.35 % (539102)Termination phase: Saturation
% 6.34/1.35 % (539102)Time elapsed: 0.406 s
% 6.34/1.35 % (539102)Peak memory usage: 19 MB
% 6.34/1.35 % (539102)Instructions burned: 854 (million)
% 6.34/1.35 % (539255)Instruction limit reached!
% 6.34/1.35 % (539255)------------------------------
% 6.34/1.35 % (539255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539255)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539255)Termination reason: Instruction limit
% 6.34/1.35 % (539255)Termination phase: Saturation
% 6.34/1.35 % (539255)Time elapsed: 0.025 s
% 6.34/1.35 % (539255)Peak memory usage: 12 MB
% 6.34/1.35 % (539255)Instructions burned: 114 (million)
% 6.34/1.35 % (539247)Instruction limit reached!
% 6.34/1.35 % (539247)------------------------------
% 6.34/1.35 % (539247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539247)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539247)Termination reason: Instruction limit
% 6.34/1.35 % (539247)Termination phase: Property scanning
% 6.34/1.35 % (539247)Time elapsed: 0.028 s
% 6.34/1.35 % (539247)Peak memory usage: 11 MB
% 6.34/1.35 % (539247)Instructions burned: 68 (million)
% 6.34/1.35 % (539065)Instruction limit reached!
% 6.34/1.35 % (539065)------------------------------
% 6.34/1.35 % (539065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539065)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539065)Termination reason: Instruction limit
% 6.34/1.35 % (539065)Termination phase: Saturation
% 6.34/1.35 % (539065)Time elapsed: 0.509 s
% 6.34/1.35 % (539065)Peak memory usage: 13 MB
% 6.34/1.35 % (539065)Instructions burned: 1241 (million)
% 6.34/1.35 % (539283)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=524300281:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 6.34/1.35 % (539281)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=2874738908:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 6.34/1.35 % (539284)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=339399718:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.34/1.35 % (539289)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=566413565:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.34/1.35 % (539289)Instruction limit reached!
% 6.34/1.35 % (539289)------------------------------
% 6.34/1.35 % (539289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539289)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539289)Termination reason: Instruction limit
% 6.34/1.35 % (539289)Termination phase: Property scanning
% 6.34/1.35 % (539289)Time elapsed: 0.016 s
% 6.34/1.35 % (539289)Peak memory usage: 10 MB
% 6.34/1.35 % (539289)Instructions burned: 35 (million)
% 6.34/1.35 % (539298)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1838108161:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/91Mi)
% 6.34/1.35 % (539232)Refutation not found, incomplete strategy
% 6.34/1.35 % (539232)------------------------------
% 6.34/1.35 % (539232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539232)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539232)Termination reason: Refutation not found, incomplete strategy
% 6.34/1.35 % (539232)Time elapsed: 0.181 s
% 6.34/1.35 % (539232)Peak memory usage: 17 MB
% 6.34/1.35 % (539232)Instructions burned: 379 (million)
% 6.34/1.35 % (539232)------------------------------
% 6.34/1.35 % (539232)------------------------------
% 6.34/1.35 % (539300)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=1386274884:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2991 on theBenchmark for (2991ds/66Mi)
% 6.34/1.35 % (539298)Instruction limit reached!
% 6.34/1.35 % (539298)------------------------------
% 6.34/1.35 % (539298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539298)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539298)Termination reason: Instruction limit
% 6.34/1.35 % (539298)Termination phase: Preprocessing 3
% 6.34/1.35 % (539298)Time elapsed: 0.041 s
% 6.34/1.35 % (539298)Peak memory usage: 13 MB
% 6.34/1.35 % (539298)Instructions burned: 91 (million)
% 6.34/1.35 % (539283)Instruction limit reached!
% 6.34/1.35 % (539283)------------------------------
% 6.34/1.35 % (539283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539283)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539283)Termination reason: Instruction limit
% 6.34/1.35 % (539283)Termination phase: Saturation
% 6.34/1.35 % (539283)Time elapsed: 0.096 s
% 6.34/1.35 % (539283)Peak memory usage: 16 MB
% 6.34/1.35 % (539283)Instructions burned: 376 (million)
% 6.34/1.35 % (539303)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=2336647348:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 6.34/1.35 % (539300)Instruction limit reached!
% 6.34/1.35 % (539300)------------------------------
% 6.34/1.35 % (539300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539300)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539300)Termination reason: Instruction limit
% 6.34/1.35 % (539300)Termination phase: Saturation
% 6.34/1.35 % (539300)Time elapsed: 0.032 s
% 6.34/1.35 % (539300)Peak memory usage: 13 MB
% 6.34/1.35 % (539300)Instructions burned: 67 (million)
% 6.34/1.35 % (539302)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2080409927:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 6.34/1.35 % (539302)Instruction limit reached!
% 6.34/1.35 % (539302)------------------------------
% 6.34/1.35 % (539302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539302)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539302)Termination reason: Instruction limit
% 6.34/1.35 % (539302)Termination phase: shuffling
% 6.34/1.35 % (539302)Time elapsed: 0.010 s
% 6.34/1.35 % (539302)Peak memory usage: 10 MB
% 6.34/1.35 % (539302)Instructions burned: 22 (million)
% 6.34/1.35 % (539235)Instruction limit reached!
% 6.34/1.35 % (539235)------------------------------
% 6.34/1.35 % (539235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539235)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539235)Termination reason: Instruction limit
% 6.34/1.35 % (539235)Termination phase: Saturation
% 6.34/1.35 % (539235)Time elapsed: 0.209 s
% 6.34/1.35 % (539235)Peak memory usage: 17 MB
% 6.34/1.35 % (539235)Instructions burned: 450 (million)
% 6.34/1.35 % (539305)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3732989038:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 6.34/1.35 % (539307)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 6.34/1.35 % (539305)Instruction limit reached!
% 6.34/1.35 % (539305)------------------------------
% 6.34/1.35 % (539305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539305)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539305)Termination reason: Instruction limit
% 6.34/1.35 % (539305)Termination phase: Property scanning
% 6.34/1.35 % (539305)Time elapsed: 0.013 s
% 6.34/1.35 % (539305)Peak memory usage: 10 MB
% 6.34/1.35 % (539305)Instructions burned: 30 (million)
% 6.34/1.35 % (539307)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=3966239428:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2990 on theBenchmark for (2990ds/137Mi)
% 6.34/1.35 % (539308)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=1507847153:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2990 on theBenchmark for (2990ds/340Mi)
% 6.34/1.35 % (539206) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-538987-539206"...
% 6.34/1.35 % (539311)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=4235722923:i=227:sd=1:bd=all:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/227Mi)
% 6.34/1.35 % (539303)Instruction limit reached!
% 6.34/1.35 % (539303)------------------------------
% 6.34/1.35 % (539303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539303)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539303)Termination reason: Instruction limit
% 6.34/1.35 % (539303)Termination phase: Saturation
% 6.34/1.35 % (539303)Time elapsed: 0.084 s
% 6.34/1.35 % (539303)Peak memory usage: 19 MB
% 6.34/1.35 % (539303)Instructions burned: 341 (million)
% 6.34/1.35 % (539307)Instruction limit reached!
% 6.34/1.35 % (539307)------------------------------
% 6.34/1.35 % (539307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.35 % (539307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.35 % (539307)CaDiCaL version: 2.1.3
% 6.34/1.35 % (539307)Termination reason: Instruction limit
% 6.34/1.35 % (539307)Termination phase: Saturation
% 6.34/1.35 % (539307)Time elapsed: 0.058 s
% 6.34/1.35 % (539307)Peak memory usage: 12 MB
% 6.34/1.35 % (539307)Instructions burned: 139 (million)
% 6.34/1.35 % (539314)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 6.34/1.35 % (539314)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=1638999652:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/373Mi)
% 6.34/1.35 % (539206)...printing done.
% 6.34/1.35 % (539206)Refutation found. Thanks to Tanya!
% 6.34/1.35 % SZS status Theorem for theBenchmark
% 6.34/1.35 % SZS output start Proof for theBenchmark
% 6.34/1.35 thf(type_def_5, type, term: $tType).
% 6.34/1.35 thf(type_def_6, type, subst: $tType).
% 6.34/1.35 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 6.34/1.35 thf(type_def_8, type, d_term: $tType).
% 6.34/1.35 thf(type_def_9, type, d_subst: $tType).
% 6.34/1.35 thf(func_def_0, type, one: term).
% 6.34/1.35 thf(func_def_1, type, ap: (term > term > term)).
% 6.34/1.35 thf(func_def_2, type, lam: (term > term)).
% 6.34/1.35 thf(func_def_3, type, sub: (term > subst > term)).
% 6.34/1.35 thf(func_def_4, type, id: subst).
% 6.34/1.35 thf(func_def_5, type, sh: subst).
% 6.34/1.35 thf(func_def_6, type, push: (term > subst > subst)).
% 6.34/1.35 thf(func_def_7, type, comp: (subst > subst > subst)).
% 6.34/1.35 thf(func_def_8, type, var: (term > $o)).
% 6.34/1.35 thf(func_def_9, type, pushprop_lem1v2: $o).
% 6.34/1.35 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 6.34/1.35 thf(func_def_11, type, axmap: $o).
% 6.34/1.35 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 6.34/1.35 thf(func_def_13, type, shinj: $o).
% 6.34/1.35 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 6.34/1.35 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 6.34/1.35 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 6.34/1.35 thf(func_def_17, type, induction2lem: $o).
% 6.34/1.35 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 6.34/1.35 thf(func_def_19, type, axvarshift: $o).
% 6.34/1.35 thf(func_def_20, type, hoasapinj2: $o).
% 6.34/1.35 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 6.34/1.35 thf(func_def_22, type, hoasapinj1: $o).
% 6.34/1.35 thf(func_def_23, type, ulamvar1: $o).
% 6.34/1.35 thf(func_def_24, type, induction2lem_lthm: $o).
% 6.34/1.35 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 6.34/1.35 thf(func_def_26, type, apnotvar: $o).
% 6.34/1.35 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 6.34/1.35 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 6.34/1.35 thf(func_def_29, type, hoasinduction_lthm: $o).
% 6.34/1.35 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 6.34/1.35 thf(func_def_31, type, hoaslaminj: $o).
% 6.34/1.35 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 6.34/1.35 thf(func_def_33, type, induction2lem_gthm: $o).
% 6.34/1.35 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 6.34/1.35 thf(func_def_35, type, hoasinduction_lem3: $o).
% 6.34/1.35 thf(func_def_36, type, hoasinduction_lem2: $o).
% 6.34/1.35 thf(func_def_37, type, termmset_lthm: $o).
% 6.34/1.35 thf(func_def_38, type, hoasinduction_lem1: $o).
% 6.34/1.35 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 6.34/1.35 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 6.34/1.35 thf(func_def_41, type, hoasapnotvar: $o).
% 6.34/1.35 thf(func_def_42, type, hoasinduction_lem0: $o).
% 6.34/1.35 thf(func_def_43, type, hoasinduction: $o).
% 6.34/1.35 thf(func_def_44, type, hoasinduction_gthm: $o).
% 6.34/1.35 thf(func_def_45, type, axapp: $o).
% 6.34/1.35 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 6.34/1.35 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 6.34/1.35 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 6.34/1.35 thf(func_def_49, type, ulamvarind: $o).
% 6.34/1.35 thf(func_def_50, type, induction: $o).
% 6.34/1.35 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 6.34/1.35 thf(func_def_52, type, termmset_gthm: $o).
% 6.34/1.35 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 6.34/1.35 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 6.34/1.35 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 6.34/1.35 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 6.34/1.35 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 6.34/1.35 thf(func_def_58, type, pushprop_lem2v2: $o).
% 6.34/1.35 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 6.34/1.35 thf(func_def_60, type, axclos: $o).
% 6.34/1.35 thf(func_def_61, type, axassoc: $o).
% 6.34/1.35 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 6.34/1.35 thf(func_def_63, type, pushprop_lthm: $o).
% 6.34/1.35 thf(func_def_64, type, apinj2: $o).
% 6.34/1.35 thf(func_def_65, type, apinj1: $o).
% 6.34/1.35 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 6.34/1.35 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 6.34/1.35 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 6.34/1.35 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 6.34/1.35 thf(func_def_70, type, axvarcons: $o).
% 6.34/1.35 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 6.34/1.35 thf(func_def_72, type, axscons: $o).
% 6.34/1.35 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 6.34/1.35 thf(func_def_74, type, axidr: $o).
% 6.34/1.35 thf(func_def_75, type, pushprop_lem1: $o).
% 6.34/1.35 thf(func_def_76, type, laminj: $o).
% 6.34/1.35 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 6.34/1.35 thf(func_def_78, type, pushprop_lem0: $o).
% 6.34/1.35 thf(func_def_79, type, pushprop_gthm: $o).
% 6.34/1.35 thf(func_def_80, type, axabs: $o).
% 6.34/1.35 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 6.34/1.35 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 6.34/1.35 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 6.34/1.35 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 6.34/1.35 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 6.34/1.35 thf(func_def_86, type, lamnotap: $o).
% 6.34/1.35 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 6.34/1.35 thf(func_def_88, type, hoaslamnotvar: $o).
% 6.34/1.35 thf(func_def_89, type, axidl: $o).
% 6.34/1.35 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 6.34/1.35 thf(func_def_91, type, induction2_lthm: $o).
% 6.34/1.35 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 6.34/1.35 thf(func_def_93, type, substmonoid_lthm: $o).
% 6.34/1.35 thf(func_def_94, type, pushprop: $o).
% 6.34/1.35 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 6.34/1.35 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 6.34/1.35 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 6.34/1.35 thf(func_def_98, type, substmonoid: $o).
% 6.34/1.35 thf(func_def_99, type, lamnotvar: $o).
% 6.34/1.35 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 6.34/1.35 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 6.34/1.35 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 6.34/1.35 thf(func_def_103, type, induction2_gthm: $o).
% 6.34/1.35 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 6.34/1.35 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_106, type, hoaslamnotap: $o).
% 6.34/1.35 thf(func_def_107, type, substmonoid_gthm: $o).
% 6.34/1.35 thf(func_def_108, type, ulamvarsh: $o).
% 6.34/1.35 thf(func_def_109, type, induction2: $o).
% 6.34/1.35 thf(func_def_110, type, pushprop_lem3v2: $o).
% 6.34/1.35 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 6.34/1.35 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 6.34/1.35 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 6.34/1.35 thf(func_def_114, type, axshiftcons: $o).
% 6.34/1.35 thf(func_def_115, type, termmset: $o).
% 6.34/1.35 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 6.34/1.35 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 6.34/1.35 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 6.34/1.35 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 6.34/1.35 thf(func_def_120, type, axvarid: $o).
% 6.34/1.35 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 6.34/1.35 thf(func_def_122, type, d2term: (d_term > term)).
% 6.34/1.35 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 6.34/1.35 thf(func_def_124, type, d_one: d_term).
% 6.34/1.35 thf(func_def_125, type, d_id: d_subst).
% 6.34/1.35 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.34/1.35 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 6.34/1.35 thf(func_def_129, type, db3: !>[X0: $tType]:(X0)).
% 6.34/1.35 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 6.34/1.35 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 6.34/1.35 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 6.34/1.35 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.34/1.35 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.34/1.35 thf(func_def_137, type, db4: !>[X0: $tType]:(X0)).
% 6.34/1.35 thf(func_def_138, type, sP0: $o).
% 6.34/1.35 thf(func_def_139, type, sP1: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_140, type, sP2: $o).
% 6.34/1.35 thf(func_def_141, type, sP3: $o).
% 6.34/1.35 thf(func_def_142, type, sP4: $o).
% 6.34/1.35 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_145, type, sP7: $o).
% 6.34/1.35 thf(func_def_146, type, sP8: $o).
% 6.34/1.35 thf(func_def_147, type, sP9: $o).
% 6.34/1.35 thf(func_def_148, type, sP10: $o).
% 6.34/1.35 thf(func_def_149, type, sP11: $o).
% 6.34/1.35 thf(func_def_150, type, sP12: $o).
% 6.34/1.35 thf(func_def_151, type, sP13: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_152, type, sP14: $o).
% 6.34/1.35 thf(func_def_153, type, sP15: $o).
% 6.34/1.35 thf(func_def_154, type, sP16: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_155, type, sP17: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_156, type, sP18: $o).
% 6.34/1.35 thf(func_def_157, type, sP19: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_158, type, sP20: $o).
% 6.34/1.35 thf(func_def_159, type, sP21: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_160, type, sP22: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_161, type, sP23: $o).
% 6.34/1.35 thf(func_def_162, type, sP24: $o).
% 6.34/1.35 thf(func_def_163, type, sP25: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_164, type, sP26: $o).
% 6.34/1.35 thf(func_def_165, type, sP27: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_166, type, sP28: $o).
% 6.34/1.35 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_168, type, sP30: $o).
% 6.34/1.35 thf(func_def_169, type, sP31: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_171, type, sP33: $o).
% 6.34/1.35 thf(func_def_172, type, sP34: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_174, type, sP36: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_175, type, sP37: $o).
% 6.34/1.35 thf(func_def_176, type, sP38: $o).
% 6.34/1.35 thf(func_def_177, type, sP39: $o).
% 6.34/1.35 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_179, type, sP41: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_180, type, sP42: $o).
% 6.34/1.35 thf(func_def_181, type, sP43: $o).
% 6.34/1.35 thf(func_def_182, type, sP44: $o).
% 6.34/1.35 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_185, type, sP47: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_186, type, sP48: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_187, type, sP49: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_188, type, sP50: $o).
% 6.34/1.35 thf(func_def_189, type, sP51: $o).
% 6.34/1.35 thf(func_def_190, type, sP52: $o).
% 6.34/1.35 thf(func_def_191, type, sP53: $o).
% 6.34/1.35 thf(func_def_192, type, sP54: $o).
% 6.34/1.35 thf(func_def_193, type, sP55: ((subst > term > subst > $o) > $o)).
% 6.34/1.35 thf(func_def_194, type, sP56: $o).
% 6.34/1.35 thf(func_def_195, type, sP57: ((term > $o) > $o)).
% 6.34/1.35 thf(func_def_196, type, sP58: $o).
% 6.34/1.35 thf(func_def_197, type, sK59: subst).
% 6.34/1.35 thf(func_def_198, type, sK60: term).
% 6.34/1.35 thf(func_def_199, type, sK61: (subst > term > term)).
% 6.34/1.35 thf(func_def_200, type, sK62: (subst > term > term)).
% 6.34/1.35 thf(func_def_201, type, sK63: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_202, type, sK64: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_203, type, sK65: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_204, type, sK66: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_205, type, sK67: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_206, type, sK68: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_207, type, sK69: term).
% 6.34/1.35 thf(func_def_208, type, sK70: subst).
% 6.34/1.35 thf(func_def_209, type, sK71: term).
% 6.34/1.35 thf(func_def_210, type, sK72: subst).
% 6.34/1.35 thf(func_def_211, type, sK73: term).
% 6.34/1.35 thf(func_def_212, type, sK74: term).
% 6.34/1.35 thf(func_def_213, type, sK75: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_214, type, sK76: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_215, type, sK77: term).
% 6.34/1.35 thf(func_def_216, type, sK78: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_217, type, sK79: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(func_def_218, type, sK80: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_219, type, sK81: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_220, type, sK82: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_221, type, sK83: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_222, type, sK84: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_223, type, sK85: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_225, type, sK87: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_226, type, sK88: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_227, type, sK89: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_228, type, sK90: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_229, type, sK91: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_230, type, sK92: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_231, type, sK93: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_232, type, sK94: term).
% 6.34/1.35 thf(func_def_233, type, sK95: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_234, type, sK96: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_235, type, sK97: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_236, type, sK98: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_237, type, sK99: (term > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_238, type, sK100: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_239, type, sK101: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_240, type, sK102: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_241, type, sK103: term).
% 6.34/1.35 thf(func_def_242, type, sK104: (term > $o)).
% 6.34/1.35 thf(func_def_243, type, sK105: (term > term)).
% 6.34/1.35 thf(func_def_244, type, sK106: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_245, type, sK107: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_246, type, sK108: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_247, type, sK109: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_248, type, sK110: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_249, type, sK111: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_250, type, sK112: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_251, type, sK113: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_252, type, sK114: term).
% 6.34/1.35 thf(func_def_253, type, sK115: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_254, type, sK116: term).
% 6.34/1.35 thf(func_def_255, type, sK117: term).
% 6.34/1.35 thf(func_def_256, type, sK118: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_257, type, sK119: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_258, type, sK120: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_263, type, sK125: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_266, type, sK128: (term > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_270, type, sK132: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_271, type, sK133: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_272, type, sK134: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_273, type, sK135: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_274, type, sK136: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_275, type, sK137: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_276, type, sK138: term).
% 6.34/1.35 thf(func_def_277, type, sK139: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_278, type, sK140: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_279, type, sK141: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_280, type, sK142: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_281, type, sK143: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_282, type, sK144: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_283, type, sK145: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_284, type, sK146: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_285, type, sK147: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_286, type, sK148: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_288, type, sK150: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_289, type, sK151: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_290, type, sK152: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_291, type, sK153: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_292, type, sK154: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_293, type, sK155: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_294, type, sK156: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > term > $o)).
% 6.34/1.35 thf(func_def_296, type, sK158: (term > $o)).
% 6.34/1.35 thf(func_def_297, type, sK159: term).
% 6.34/1.35 thf(func_def_298, type, sK160: (term > term)).
% 6.34/1.35 thf(func_def_299, type, sK161: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_300, type, sK162: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_301, type, sK163: term).
% 6.34/1.35 thf(func_def_302, type, sK164: term).
% 6.34/1.35 thf(func_def_303, type, sK165: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_304, type, sK166: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_305, type, sK167: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_306, type, sK168: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_307, type, sK169: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_308, type, sK170: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_309, type, sK171: ((term > $o) > term > term)).
% 6.34/1.35 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_311, type, sK173: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_312, type, sK174: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_313, type, sK175: term).
% 6.34/1.35 thf(func_def_314, type, sK176: (term > $o)).
% 6.34/1.35 thf(func_def_315, type, sK177: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_316, type, sK178: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_317, type, sK179: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_318, type, sK180: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_319, type, sK181: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_320, type, sK182: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_321, type, sK183: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_322, type, sK184: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_323, type, sK185: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_324, type, sK186: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_325, type, sK187: ((subst > term > subst > $o) > term > $o)).
% 6.34/1.35 thf(func_def_326, type, sK188: term).
% 6.34/1.35 thf(func_def_327, type, sK189: (term > $o)).
% 6.34/1.35 thf(func_def_328, type, sK190: term).
% 6.34/1.35 thf(func_def_329, type, sK191: (term > term)).
% 6.34/1.35 thf(func_def_330, type, sK192: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_331, type, sK193: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_332, type, sK194: term).
% 6.34/1.35 thf(func_def_333, type, sK195: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_334, type, sK196: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_335, type, sK197: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_336, type, sK198: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_337, type, sK199: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_338, type, sK200: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_342, type, sK204: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_343, type, sK205: (term > (term > $o) > term)).
% 6.34/1.35 thf(func_def_344, type, sK206: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_346, type, sK208: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_347, type, sK209: (term > $o)).
% 6.34/1.35 thf(func_def_348, type, sK210: term).
% 6.34/1.35 thf(func_def_349, type, sK211: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_350, type, sK212: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_351, type, sK213: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_352, type, sK214: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_353, type, sK215: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_354, type, sK216: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_355, type, sK217: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_356, type, sK218: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_357, type, sK219: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_358, type, sK220: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_359, type, sK221: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_360, type, sK222: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_361, type, sK223: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_362, type, sK224: (term > $o)).
% 6.34/1.35 thf(func_def_363, type, sK225: term).
% 6.34/1.35 thf(func_def_364, type, sK226: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_365, type, sK227: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_369, type, sK231: (term > (term > $o) > term)).
% 6.34/1.35 thf(func_def_370, type, sK232: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_371, type, sK233: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_372, type, sK234: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_374, type, sK236: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.34/1.35 thf(func_def_375, type, sK237: term).
% 6.34/1.35 thf(func_def_376, type, sK238: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_377, type, sK239: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_378, type, sK240: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_379, type, sK241: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_380, type, sK242: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_381, type, sK243: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_382, type, sK244: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_383, type, sK245: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_384, type, sK246: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_386, type, sK248: (term > $o)).
% 6.34/1.35 thf(func_def_387, type, sK249: term).
% 6.34/1.35 thf(func_def_388, type, sK250: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_389, type, sK251: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.34/1.35 thf(func_def_390, type, sK252: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_391, type, sK253: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_392, type, sK254: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_393, type, sK255: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_394, type, sK256: (term > (term > $o) > term)).
% 6.34/1.35 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_397, type, sK259: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_398, type, sK260: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_399, type, sK261: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_400, type, sK262: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_401, type, sK263: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_402, type, sK264: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_404, type, sK266: term).
% 6.34/1.35 thf(func_def_405, type, sK267: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_406, type, sK268: term).
% 6.34/1.35 thf(func_def_407, type, sK269: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_409, type, sK271: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_410, type, sK272: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_411, type, sK273: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_412, type, sK274: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_413, type, sK275: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_414, type, sK276: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_415, type, sK277: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_416, type, sK278: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_417, type, sK279: term).
% 6.34/1.35 thf(func_def_418, type, sK280: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_419, type, sK281: (term > $o)).
% 6.34/1.35 thf(func_def_420, type, sK282: term).
% 6.34/1.35 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_422, type, sK284: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_423, type, sK285: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_424, type, sK286: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_425, type, sK287: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_426, type, sK288: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_427, type, sK289: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_428, type, sK290: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_429, type, sK291: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_430, type, sK292: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_431, type, sK293: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_432, type, sK294: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_433, type, sK295: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_434, type, sK296: subst).
% 6.34/1.35 thf(func_def_435, type, sK297: term).
% 6.34/1.35 thf(func_def_436, type, sK298: subst).
% 6.34/1.35 thf(func_def_437, type, sK299: (term > $o)).
% 6.34/1.35 thf(func_def_438, type, sK300: term).
% 6.34/1.35 thf(func_def_439, type, sK301: term).
% 6.34/1.35 thf(func_def_440, type, sK302: subst).
% 6.34/1.35 thf(func_def_441, type, sK303: term).
% 6.34/1.35 thf(func_def_442, type, sK304: (term > $o)).
% 6.34/1.35 thf(func_def_443, type, sK305: subst).
% 6.34/1.35 thf(func_def_444, type, sK306: (term > term)).
% 6.34/1.35 thf(func_def_445, type, sK307: (subst > (term > $o) > term)).
% 6.34/1.35 thf(func_def_446, type, sK308: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_447, type, sK309: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_448, type, sK310: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_449, type, sK311: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_450, type, sK312: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_451, type, sK313: term).
% 6.34/1.35 thf(func_def_452, type, sK314: (term > $o)).
% 6.34/1.35 thf(func_def_453, type, sK315: (term > term)).
% 6.34/1.35 thf(func_def_454, type, sK316: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_455, type, sK317: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_456, type, sK318: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_457, type, sK319: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_458, type, sK320: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_459, type, sK321: term).
% 6.34/1.35 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_461, type, sK323: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_462, type, sK324: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_463, type, sK325: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_464, type, sK326: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_465, type, sK327: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_466, type, sK328: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_467, type, sK329: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_468, type, sK330: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_469, type, sK331: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_470, type, sK332: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_471, type, sK333: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_472, type, sK334: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_473, type, sK335: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_474, type, sK336: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_475, type, sK337: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_476, type, sK338: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_477, type, sK339: term).
% 6.34/1.35 thf(func_def_478, type, sK340: term).
% 6.34/1.35 thf(func_def_479, type, sK341: (term > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_480, type, sK342: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_481, type, sK343: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_482, type, sK344: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_483, type, sK345: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_484, type, sK346: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_485, type, sK347: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_486, type, sK348: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_487, type, sK349: ((subst > term > subst > $o) > subst)).
% 6.34/1.35 thf(func_def_488, type, sK350: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_489, type, sK351: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(func_def_490, type, sK352: term).
% 6.34/1.35 thf(func_def_491, type, sK353: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_492, type, sK354: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_493, type, sK355: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_494, type, sK356: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_495, type, sK357: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_496, type, sK358: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_497, type, sK359: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_498, type, sK360: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_499, type, sK361: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_501, type, sK363: (term > subst > term > term)).
% 6.34/1.35 thf(func_def_502, type, sK364: (term > $o)).
% 6.34/1.35 thf(func_def_503, type, sK365: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_504, type, sK366: term).
% 6.34/1.35 thf(func_def_505, type, sK367: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_506, type, sK368: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_507, type, sK369: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_508, type, sK370: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_509, type, sK371: term).
% 6.34/1.35 thf(func_def_510, type, sK372: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_511, type, sK373: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_512, type, sK374: (term > (term > $o) > term)).
% 6.34/1.35 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.34/1.35 thf(func_def_515, type, sK377: term).
% 6.34/1.35 thf(func_def_516, type, sK378: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_517, type, sK379: term).
% 6.34/1.35 thf(func_def_518, type, sK380: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_519, type, sK381: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_520, type, sK382: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_521, type, sK383: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_522, type, sK384: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_523, type, sK385: (term > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_524, type, sK386: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_525, type, sK387: term).
% 6.34/1.35 thf(func_def_526, type, sK388: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_527, type, sK389: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_528, type, sK390: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_529, type, sK391: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_531, type, sK393: (term > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_532, type, sK394: term).
% 6.34/1.35 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_534, type, sK396: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(func_def_535, type, sK397: term).
% 6.34/1.35 thf(func_def_536, type, sK398: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_537, type, sK399: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_538, type, sK400: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_539, type, sK401: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_540, type, sK402: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_541, type, sK403: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_542, type, sK404: ((term > $o) > subst > term)).
% 6.34/1.35 thf(func_def_543, type, sK405: term).
% 6.34/1.35 thf(func_def_544, type, sK406: subst).
% 6.34/1.35 thf(func_def_545, type, sK407: (term > $o)).
% 6.34/1.35 thf(func_def_546, type, sK408: (term > term)).
% 6.34/1.35 thf(func_def_547, type, sK409: term).
% 6.34/1.35 thf(func_def_548, type, sK410: term).
% 6.34/1.35 thf(func_def_549, type, sK411: (term > $o)).
% 6.34/1.35 thf(func_def_550, type, sK412: (term > term)).
% 6.34/1.35 thf(func_def_551, type, sK413: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_552, type, sK414: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_553, type, sK415: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_554, type, sK416: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_555, type, sK417: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_556, type, sK418: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_557, type, sK419: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_558, type, sK420: term).
% 6.34/1.35 thf(func_def_559, type, sK421: ((subst > term > term) > term > subst)).
% 6.34/1.35 thf(func_def_560, type, sK422: ((subst > term > term) > term > term)).
% 6.34/1.35 thf(func_def_561, type, sK423: ((subst > term > term) > term > subst)).
% 6.34/1.35 thf(func_def_562, type, sK424: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_563, type, sK425: ((subst > term > term) > term > subst)).
% 6.34/1.35 thf(func_def_564, type, sK426: ((subst > term > term) > term > term)).
% 6.34/1.35 thf(func_def_565, type, sK427: ((subst > term > term) > term > subst)).
% 6.34/1.35 thf(func_def_566, type, sK428: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_568, type, sK430: (term > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_569, type, sK431: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_570, type, sK432: term).
% 6.34/1.35 thf(func_def_571, type, sK433: (term > $o)).
% 6.34/1.35 thf(func_def_572, type, sK434: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_573, type, sK435: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_574, type, sK436: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_575, type, sK437: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_576, type, sK438: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_577, type, sK439: ((term > $o) > term > term)).
% 6.34/1.35 thf(func_def_578, type, sK440: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_579, type, sK441: (term > $o)).
% 6.34/1.35 thf(func_def_580, type, sK442: subst).
% 6.34/1.35 thf(func_def_581, type, sK443: term).
% 6.34/1.35 thf(func_def_582, type, sK444: (term > term)).
% 6.34/1.35 thf(func_def_583, type, sK445: (subst > (term > $o) > term)).
% 6.34/1.35 thf(func_def_584, type, sK446: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_585, type, sK447: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_586, type, sK448: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_587, type, sK449: term).
% 6.34/1.35 thf(func_def_588, type, sK450: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_589, type, sK451: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_590, type, sK452: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_591, type, sK453: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_592, type, sK454: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_593, type, sK455: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_595, type, sK457: subst).
% 6.34/1.35 thf(func_def_596, type, sK458: term).
% 6.34/1.35 thf(func_def_597, type, sK459: term).
% 6.34/1.35 thf(func_def_598, type, sK460: term).
% 6.34/1.35 thf(func_def_599, type, sK461: term).
% 6.34/1.35 thf(func_def_600, type, sK462: term).
% 6.34/1.35 thf(func_def_601, type, sK463: (term > $o)).
% 6.34/1.35 thf(func_def_602, type, sK464: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_603, type, sK465: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_604, type, sK466: term).
% 6.34/1.35 thf(func_def_605, type, sK467: term).
% 6.34/1.35 thf(func_def_606, type, sK468: term).
% 6.34/1.35 thf(func_def_607, type, sK469: term).
% 6.34/1.35 thf(func_def_608, type, sK470: subst).
% 6.34/1.35 thf(func_def_609, type, sK471: subst).
% 6.34/1.35 thf(func_def_610, type, sK472: term).
% 6.34/1.35 thf(func_def_611, type, sK473: term).
% 6.34/1.35 thf(func_def_612, type, sK474: term).
% 6.34/1.35 thf(func_def_613, type, sK475: term).
% 6.34/1.35 thf(func_def_614, type, sK476: ((term > $o) > (term > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_615, type, sK477: term).
% 6.34/1.35 thf(func_def_616, type, sK478: subst).
% 6.34/1.35 thf(func_def_617, type, sK479: (term > $o)).
% 6.34/1.35 thf(func_def_618, type, sK480: (term > $o)).
% 6.34/1.35 thf(func_def_619, type, sK481: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_620, type, sK482: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_621, type, sK483: ((subst > term > subst > $o) > term > $o)).
% 6.34/1.35 thf(func_def_622, type, sK484: term).
% 6.34/1.35 thf(func_def_623, type, sK485: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_624, type, sK486: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_625, type, sK487: (term > subst > term > term)).
% 6.34/1.35 thf(func_def_626, type, sK488: (term > d_term)).
% 6.34/1.35 thf(func_def_627, type, sK489: subst).
% 6.34/1.35 thf(func_def_628, type, sK490: subst).
% 6.34/1.35 thf(func_def_629, type, sK491: subst).
% 6.34/1.35 thf(func_def_630, type, sK492: subst).
% 6.34/1.35 thf(func_def_631, type, sK493: term).
% 6.34/1.35 thf(func_def_632, type, sK494: subst).
% 6.34/1.35 thf(func_def_633, type, sK495: term).
% 6.34/1.35 thf(func_def_634, type, sK496: term).
% 6.34/1.35 thf(func_def_635, type, sK497: subst).
% 6.34/1.35 thf(func_def_636, type, sK498: term).
% 6.34/1.35 thf(func_def_637, type, sK499: (term > $o)).
% 6.34/1.35 thf(func_def_638, type, sK500: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_639, type, sK501: ((term > $o) > term > subst > term > $o)).
% 6.34/1.35 thf(func_def_640, type, sK502: term).
% 6.34/1.35 thf(func_def_641, type, sK503: term).
% 6.34/1.35 thf(func_def_642, type, sK504: term).
% 6.34/1.35 thf(func_def_643, type, sK505: term).
% 6.34/1.35 thf(func_def_644, type, sK506: term).
% 6.34/1.35 thf(func_def_645, type, sK507: term).
% 6.34/1.35 thf(func_def_646, type, sK508: term).
% 6.34/1.35 thf(func_def_647, type, sK509: term).
% 6.34/1.35 thf(func_def_648, type, sK510: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_649, type, sK511: term).
% 6.34/1.35 thf(func_def_650, type, sK512: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_651, type, sK513: ((subst > term > subst > $o) > term)).
% 6.34/1.35 thf(func_def_652, type, sK514: (term > $o)).
% 6.34/1.35 thf(func_def_653, type, sK515: (term > $o)).
% 6.34/1.35 thf(func_def_654, type, sK516: term).
% 6.34/1.35 thf(func_def_655, type, sK517: subst).
% 6.34/1.35 thf(func_def_656, type, sK518: term).
% 6.34/1.35 thf(func_def_657, type, sK519: (term > subst > term > term)).
% 6.34/1.35 thf(func_def_658, type, sK520: term).
% 6.34/1.35 thf(func_def_659, type, sK521: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_660, type, sK522: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_661, type, sK523: term).
% 6.34/1.35 thf(func_def_662, type, sK524: (term > $o)).
% 6.34/1.35 thf(func_def_663, type, sK525: subst).
% 6.34/1.35 thf(func_def_664, type, sK526: term).
% 6.34/1.35 thf(func_def_665, type, sK527: term).
% 6.34/1.35 thf(func_def_666, type, sK528: (term > $o)).
% 6.34/1.35 thf(func_def_667, type, sK529: subst).
% 6.34/1.35 thf(func_def_668, type, sK530: term).
% 6.34/1.35 thf(func_def_669, type, sK531: subst).
% 6.34/1.35 thf(func_def_670, type, sK532: term).
% 6.34/1.35 thf(func_def_671, type, sK533: (subst > d_subst)).
% 6.34/1.35 thf(func_def_672, type, sK534: (term > subst > term > term)).
% 6.34/1.35 thf(func_def_673, type, sK535: term).
% 6.34/1.35 thf(func_def_674, type, sK536: term).
% 6.34/1.35 thf(func_def_675, type, sK537: term).
% 6.34/1.35 thf(func_def_676, type, sK538: term).
% 6.34/1.35 thf(func_def_677, type, sK539: term).
% 6.34/1.35 thf(func_def_678, type, sK540: term).
% 6.34/1.35 thf(func_def_679, type, sK541: term).
% 6.34/1.35 thf(func_def_680, type, sK542: term).
% 6.34/1.35 thf(func_def_681, type, sK543: term).
% 6.34/1.35 thf(func_def_682, type, sK544: subst).
% 6.34/1.35 thf(func_def_683, type, sK545: term).
% 6.34/1.35 thf(func_def_684, type, sK546: (term > subst > term > term)).
% 6.34/1.35 thf(func_def_685, type, sK547: (term > $o)).
% 6.34/1.35 thf(func_def_686, type, sK548: subst).
% 6.34/1.35 thf(func_def_687, type, sK549: term).
% 6.34/1.35 thf(func_def_688, type, sK550: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_689, type, sK551: (term > subst > (term > $o) > term > $o)).
% 6.34/1.35 thf(func_def_690, type, sK552: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_691, type, sK553: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_692, type, sK554: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_693, type, sK555: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_694, type, sK556: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_695, type, sK557: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_696, type, sK558: (subst > term > term)).
% 6.34/1.35 thf(func_def_697, type, sK559: term).
% 6.34/1.35 thf(func_def_698, type, sK560: subst).
% 6.34/1.35 thf(func_def_699, type, sK561: (subst > term > term)).
% 6.34/1.35 thf(func_def_700, type, sK562: term).
% 6.34/1.35 thf(func_def_701, type, sK563: term).
% 6.34/1.35 thf(func_def_702, type, sK564: term).
% 6.34/1.35 thf(func_def_703, type, sK565: term).
% 6.34/1.35 thf(func_def_704, type, sK566: term).
% 6.34/1.35 thf(func_def_705, type, sK567: term).
% 6.34/1.35 thf(func_def_706, type, sK568: term).
% 6.34/1.35 thf(func_def_707, type, sK569: term).
% 6.34/1.35 thf(func_def_708, type, sK570: term).
% 6.34/1.35 thf(func_def_709, type, sK571: term).
% 6.34/1.35 thf(func_def_710, type, sK572: (term > $o)).
% 6.34/1.35 thf(func_def_711, type, sK573: subst).
% 6.34/1.35 thf(func_def_712, type, sK574: (term > $o)).
% 6.34/1.35 thf(func_def_713, type, sK575: ((term > $o) > subst > (term > $o) > term > term)).
% 6.34/1.35 thf(func_def_714, type, sK576: subst).
% 6.34/1.35 thf(func_def_715, type, sK577: term).
% 6.34/1.35 thf(func_def_716, type, sK578: subst).
% 6.34/1.35 thf(func_def_717, type, sK579: term).
% 6.34/1.35 thf(func_def_718, type, sK580: subst).
% 6.34/1.35 thf(func_def_719, type, sK581: term).
% 6.34/1.35 thf(func_def_720, type, sK582: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_721, type, sK583: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_722, type, sK584: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_723, type, sK585: (subst > term > term)).
% 6.34/1.35 thf(func_def_724, type, sK586: term).
% 6.34/1.35 thf(func_def_725, type, sK587: term).
% 6.34/1.35 thf(func_def_726, type, sK588: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_727, type, sK589: ((term > $o) > term)).
% 6.34/1.35 thf(func_def_728, type, sK590: ((subst > term > subst > $o) > term > $o)).
% 6.34/1.35 thf(func_def_729, type, vNOT: ($o > $o)).
% 6.34/1.35 thf(func_def_730, type, sK591: (subst > term > subst > $o)).
% 6.34/1.35 thf(func_def_731, type, sK592: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_732, type, sK593: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_733, type, sK594: ((subst > term > term) > term)).
% 6.34/1.35 thf(func_def_734, type, sK595: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_735, type, sK596: ((subst > term > term) > subst)).
% 6.34/1.35 thf(func_def_736, type, sK597: term).
% 6.34/1.35 thf(func_def_737, type, sK598: ((subst > term > subst > $o) > subst > term > term)).
% 6.34/1.35 thf(func_def_738, type, sK599: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(func_def_739, type, sK600: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(func_def_740, type, sK601: ((subst > term > subst > $o) > term > term)).
% 6.34/1.35 thf(f1,axiom,(
% 6.34/1.35 hoasapinj1_gthm & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & pushprop & termmset_gthm & axapp & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [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)) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)))))))) & (induction2lem <=> ! [X17 : subst,X16 : term,X10 : (term > $o)] : (~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))))) & (one = ((d2term @ d_one))) & hoaslaminj_gthm & (id = ((d2subst @ d_id))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & axabs & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X31 : (subst > term > term),X33 : term,X18 : (subst > term > term),X32 : subst] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj2) & (! [X21 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13)))) <=> induction) & induction2_gthm & hoasinduction_lem1 & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ 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))))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem3v2_gthm & pushprop_lthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapnotvar_gthm & ! [X5 : d_subst] : (X5 = d_id) & hoaslamnotvar_gthm & ((! [X20 : term,X15 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X19 : term,X15 : term,X13 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj2_lthm) & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & hoasinduction_lem3a_gthm & (hoaslamnotap <=> ! [X18 : (subst > term > term),X47 : term,X46 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & pushprop_lem3v2_lthm & ~(var @ (d2term @ d_one)) & hoasinduction_lem2_gthm & hoasinduction_lem1v2 & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoaslamnotap_gthm & induction2lem_gthm & axvarshift & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)) => (! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [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 @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) & hoasinduction_lem1_lthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & hoasapinj2_gthm & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ulamvarind & (apinj2 <=> ! [X20 : term,X13 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X13 : term,X15 : term,X14 : subst,X26 : (term > $o),X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [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))) | (X11 @ (lam @ X29))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))))) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22))) & (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id)) <=> hoasinduction_lem2) & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasinduction_lem3v2a_lthm <=> (! [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)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))))) & axclos & (pushprop_lem1v2 <=> ! [X14 : subst,X11 : (term > $o),X13 : term,X10 : (term > $o)] : (~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & pushprop_gthm & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [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))) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & hoasinduction_lem2_lthm & hoasinduction_lem3b_gthm & hoasinduction_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))))) <=> induction2_lthm) & hoasinduction_lem2v2_gthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X14 : subst,X13 : term,X10 : (term > $o)] : (~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & pushprop_lem1_gthm & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & axmap & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X19 : term,X13 : term,X15 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)))) <=> hoasapinj1_lthm) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X1 : d_term] : (X1 = d_one) & pushprop_lem0_gthm & substmonoid_gthm & pushprop_lthm_orig & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & (hoasinduction_no_psi_cond <=> ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))) & hoasapnotvar_lthm & (! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (! [X13 : term,X14 : subst,X10 : (term > $o),X15 : term,X26 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & pushprop_lem2v2_lthm & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & hoaslamnotvar_lthm & hoasinduction_lem1_gthm & (laminj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))))) & (! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X35 : term,X18 : (subst > term > term)] : (~ ! [X40 : term,X41 : subst,X39 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X36 : subst,X37 : term,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aaa) & (! [X14 : subst,X13 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & pushprop_lem3v2 & hoaslamnotvar & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & ~ulamvar1 & lamnotvar & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)))) & (hoasinduction_lem2v2 <=> ! [X44 : term,X11 : (term > $o),X10 : (subst > term > subst > $o),X45 : term] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X11 @ X44) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))) & pushprop_lem2v2_gthm & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & pushprop_lem2v2 & (! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & ~lamnotap & (shinj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & (! [X20 : term,X19 : term,X13 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & axassoc & hoaslamnotap_lthm & (hoasinduction_lem3v2a <=> ! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [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,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))) & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,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)))) <=> hoasinduction_lem3v2) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) <=> substmonoid) & apnotvar & hoasapnotvar & (hoasapinj1 <=> ! [X20 : term,X13 : term,X19 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))) & pushprop_lem1v2_gthm & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X48 : term,X11 : (term > $o),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))))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))))))) & hoasinduction_lem1v2_gthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (sh = ((d2subst @ d_id))) & (hoaslaminj <=> ! [X32 : subst,X31 : (subst > term > term),X18 : (subst > term > term),X33 : term] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ X43) @ id))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoasinduction_lem3_gthm & ulamvarsh),
% 6.34/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 6.34/1.36 thf(f2,conjecture,(
% 6.34/1.36 (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : subst,X3 : term,X2 : subst] : (((sub @ (X1 @ X2 @ X3) @ X4)) = ((X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)))) => (! [X3 : term] : ((X0 @ id @ X3 @ id) => (X0 @ id @ (X1 @ id @ X3) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X2 : subst, X3 : term] : ((X1 @ X2 @ X3)))) @ id))) => ! [X3 : term] : (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (sub @ X3 @ (push @ X5 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X3 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aa)),
% 6.34/1.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa)).
% 6.34/1.36 thf(f3,negated_conjecture,(
% 6.34/1.36 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : subst,X3 : term,X2 : subst] : (((sub @ (X1 @ X2 @ X3) @ X4)) = ((X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)))) => (! [X3 : term] : ((X0 @ id @ X3 @ id) => (X0 @ id @ (X1 @ id @ X3) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X2 : subst, X3 : term] : ((X1 @ X2 @ X3)))) @ id))) => ! [X3 : term] : (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (sub @ X3 @ (push @ X5 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X3 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aa)),
% 6.34/1.36 inference(negated_conjecture,[status(cth)],[f2])).
% 6.34/1.36 thf(f4,plain,(
% 6.34/1.36 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X2 : subst,X3 : term,X4 : subst] : (((X1 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2))) = ((sub @ (X1 @ X4 @ X3) @ X2))) => (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (X1 @ id @ X5) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X6 : subst, X7 : term] : ((X1 @ X6 @ X7)))) @ id))) => ! [X8 : term] : (! [X9 : term] : ((X0 @ id @ X9 @ id) => (X0 @ id @ (sub @ X8 @ (push @ X9 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aa)),
% 6.34/1.36 inference(rectify,[],[f3])).
% 6.34/1.36 thf(f5,plain,(
% 6.34/1.36 ~ (hoasinduction_lem3aa = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.34/1.36 inference(fool_elimination,[],[f4])).
% 6.34/1.36 thf(f6,plain,(
% 6.34/1.36 hoasapinj1_gthm & (! [X0 : subst] : (((comp @ id @ X0)) = X0) <=> axidl) & pushprop & termmset_gthm & axapp & (hoasinduction_no_psi_cond_lthm <=> (! [X1 : (subst > term > subst > $o)] : ~ ! [X2 : (term > $o)] : ~ ! [X3 : term] : (((X2 @ X3)) = ((X1 @ id @ X3 @ id))) => (! [X4 : (term > $o),X5 : term] : ((X4 @ X5) | ~ ! [X6 : term] : ((X4 @ X6) | ~(var @ X6)) | ~ ! [X7 : term,X8 : term] : (~(X4 @ X7) | (X4 @ (ap @ X8 @ X7)) | ~(X4 @ X8)) | ~ ! [X9 : term] : (~ ! [X10 : term] : ((X4 @ (sub @ X9 @ (push @ X10 @ id))) | ~(X4 @ X10)) | (X4 @ (lam @ X9)))) => (! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : term,X13 : (subst > term > subst > $o),X14 : (term > $o)] : (~ ! [X15 : term] : (~(X14 @ X15) | (X14 @ (sub @ X12 @ (push @ X15 @ id)))) | (X14 @ (lam @ X12)) | ~ ! [X16 : (subst > term > term)] : (~ ! [X17 : subst,X18 : term,X19 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) = ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))) | ~ ! [X20 : term] : (~(X13 @ id @ X20 @ id) | (X13 @ id @ (X16 @ id @ X20) @ id)) | (X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) | ~ ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21)))) => ! [X22 : (subst > term > subst > $o),X23 : term] : (~ ! [X24 : (subst > term > term)] : (~ ! [X25 : term] : (~(X22 @ id @ X25 @ id) | (X22 @ id @ (X24 @ id @ X25) @ id)) | ~ ! [X26 : subst,X27 : term,X28 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) | (X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) | (X22 @ id @ X23 @ id) | ~ ! [X29 : term,X30 : term] : ((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id) | ~(X22 @ id @ X30 @ id) | ~(X22 @ id @ X29 @ id)))))))) & (induction2lem <=> ! [X31 : subst,X32 : term,X33 : (term > $o)] : (~ ! [X34 : term] : (~(var @ X34) | (X33 @ (sub @ X34 @ X31))) | (X33 @ (sub @ X32 @ X31)) | ~ ! [X35 : term,X36 : term] : (~(X33 @ X35) | (X33 @ (ap @ X36 @ X35)) | ~(X33 @ X36)) | ~ ! [X37 : term] : (~ ! [X38 : term] : ((X33 @ (sub @ X37 @ (push @ X38 @ id))) | ~(X33 @ X38)) | (X33 @ (lam @ X37))))) & (one = ((d2term @ d_one))) & hoaslaminj_gthm & (id = ((d2subst @ d_id))) & (! [X39 : term] : ~ ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ X39 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & axabs & (hoaslaminj_lthm <=> (! [X41 : term,X42 : subst] : (((sub @ one @ (push @ X41 @ X42))) = X41) => (! [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) = X44) => (! [X45 : term,X46 : term] : ((X45 = X46) | (((lam @ X46)) != ((lam @ X45)))) => ! [X47 : (subst > term > term),X48 : term,X49 : (subst > term > term),X50 : subst] : ((((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48))) | ~ ! [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) = ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | ~ ! [X54 : term,X55 : subst,X56 : subst] : (((sub @ (X47 @ X56 @ X54) @ X55)) = ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55))))))))) & (! [X57 : term,X58 : term,X59 : term,X60 : term] : ((X57 = X58) | (((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57)))) <=> hoasapinj2) & (! [X61 : term,X62 : (term > $o)] : (~ ! [X63 : term,X64 : term] : ((X62 @ (ap @ X64 @ X63)) | ~(X62 @ X63) | ~(X62 @ X64)) | (X62 @ X61) | ~ ! [X65 : term] : ((X62 @ X65) | ~(var @ X65)) | ~ ! [X66 : term] : (~(X62 @ X66) | (X62 @ (lam @ X66)))) <=> induction) & induction2_gthm & hoasinduction_lem1 & (hoasinduction_lem3aa_lthm <=> ! [X67 : (subst > term > subst > $o),X68 : term] : (~ ! [X69 : term] : (~(X67 @ id @ X69 @ id) | (X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) | (X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id) | ~ ! [X70 : (subst > term > term)] : (~ ! [X71 : term] : (~(X67 @ id @ X71 @ id) | (X67 @ id @ (X70 @ id @ X71) @ id)) | (X67 @ id @ (lam @ (X70 @ sh @ one)) @ id) | ~ ! [X72 : subst,X73 : subst,X74 : term] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72)))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem3v2_gthm & pushprop_lthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapnotvar_gthm & ! [X75 : d_subst] : (d_id = X75) & hoaslamnotvar_gthm & ((! [X76 : term,X77 : term,X78 : term,X79 : term] : ((X76 = X78) | (((ap @ X77 @ X76)) != ((ap @ X79 @ X78)))) => ! [X80 : term,X81 : term,X82 : term,X83 : term] : ((X80 = X83) | (((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))))) <=> hoasapinj2_lthm) & (hoasinduction_lem3v2_f <=> ! [X84 : term] : ~ ! [X85 : (subst > term > term)] : ~ ! [X86 : term,X87 : subst] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86)))) & hoasinduction_lem3a_gthm & (hoaslamnotap <=> ! [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))) | ~ ! [X91 : subst,X92 : subst,X93 : term] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X88 @ X92 @ X93) @ X91))))) & pushprop_lem3v2_lthm & ~(var @ (d2term @ d_one)) & hoasinduction_lem2_gthm & hoasinduction_lem1v2 & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoaslamnotap_gthm & induction2lem_gthm & axvarshift & (hoasinduction_lthm <=> (! [X94 : (term > $o),X95 : term] : (~ ! [X96 : term,X97 : term] : ((X94 @ (ap @ X96 @ X97)) | ~(X94 @ X97) | ~(X94 @ X96)) | ~ ! [X98 : term] : ((X94 @ (lam @ X98)) | ~ ! [X99 : term] : ((X94 @ (sub @ X98 @ (push @ X99 @ id))) | ~(X94 @ X99))) | ~ ! [X100 : term] : ((X94 @ X100) | ~(var @ X100)) | (X94 @ X95)) => (! [X101 : term,X102 : term,X103 : (subst > term > subst > $o)] : (~ ! [X104 : term,X105 : subst,X106 : subst,X107 : subst] : (~(X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107) | (X103 @ X105 @ X104 @ (comp @ X106 @ X107))) | (X103 @ id @ (ap @ X102 @ X101) @ id) | ~ ! [X108 : term,X109 : term] : (~(X103 @ id @ X109 @ id) | (X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id) | ~(X103 @ id @ X108 @ id)) | ~(X103 @ id @ X101 @ id) | ~(X103 @ id @ X102 @ id) | ~ ! [X110 : subst,X111 : subst,X112 : term,X113 : subst] : (~(X103 @ X110 @ X112 @ (comp @ X111 @ X113)) | (X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113))) => (! [X114 : (subst > term > subst > $o),X115 : term] : (~ ! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (~(X114 @ X118 @ X119 @ (comp @ X117 @ X116)) | (X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)) | ~ ! [X120 : term] : (~(X114 @ id @ X120 @ id) | (X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) | ~ ! [X121 : (subst > term > term)] : (~ ! [X122 : term] : ((X114 @ id @ (X121 @ id @ X122) @ id) | ~(X114 @ id @ X122 @ id)) | ~ ! [X123 : term,X124 : subst,X125 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) = ((sub @ (X121 @ X124 @ X123) @ X125))) | (X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) | (X114 @ id @ (lam @ X115) @ id) | ~ ! [X126 : subst,X127 : subst,X128 : subst,X129 : term] : ((X114 @ X127 @ X129 @ (comp @ X128 @ X126)) | ~(X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))) => ! [X130 : (subst > term > subst > $o),X131 : term] : (~ ! [X132 : (subst > term > term)] : (~ ! [X133 : subst,X134 : subst,X135 : term] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) | (X130 @ id @ (lam @ (X132 @ sh @ one)) @ id) | ~ ! [X136 : term] : (~(X130 @ id @ X136 @ id) | (X130 @ id @ (X132 @ id @ X136) @ id))) | ~ ! [X137 : term] : (~(var @ (sub @ X137 @ id)) | (X130 @ id @ X137 @ id)) | ~ ! [X138 : term,X139 : term] : (~(X130 @ id @ X138 @ id) | ~(X130 @ id @ X139 @ id) | (X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) | (X130 @ id @ X131 @ id) | ~ ! [X140 : term,X141 : subst,X142 : subst,X143 : subst] : ((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143) | ~(X130 @ X141 @ X140 @ (comp @ X142 @ X143))) | ~ ! [X144 : subst,X145 : term,X146 : subst,X147 : subst] : (~(X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146) | (X130 @ X147 @ X145 @ (comp @ X144 @ X146)))))))) & hoasinduction_lem1_lthm & (! [X148 : (subst > term > subst > $o)] : ~ ! [X149 : (term > $o)] : ~ ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id))) <=> hoasinduction_lem0) & hoasapinj2_gthm & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ulamvarind & (apinj2 <=> ! [X151 : term,X152 : term,X153 : term,X154 : term] : ((((ap @ X153 @ X151)) != ((ap @ X152 @ X154))) | (X151 = X154))) & (pushprop_lem1_lthm <=> (! [X155 : term,X156 : subst] : (((sub @ one @ (push @ X155 @ X156))) = X155) => (! [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) = X157) => ! [X159 : term,X160 : term,X161 : subst,X162 : (term > $o),X163 : (term > $o)] : ((X162 @ (sub @ X159 @ (push @ X160 @ X161))) | ~(X163 @ X159))))) & (hoasinduction_lthm_3 <=> (! [X164 : (subst > term > subst > $o)] : ~ ! [X165 : (term > $o)] : ~ ! [X166 : term] : (((X164 @ id @ X166 @ id)) = ((X165 @ X166))) => (! [X167 : term,X168 : (term > $o)] : (~ ! [X169 : term,X170 : term] : (~(X168 @ X169) | (X168 @ (ap @ X169 @ X170)) | ~(X168 @ X170)) | (X168 @ X167) | ~ ! [X171 : term] : ((X168 @ X171) | ~(var @ X171)) | ~ ! [X172 : term] : ((X168 @ (lam @ X172)) | ~ ! [X173 : term] : ((X168 @ (sub @ X172 @ (push @ X173 @ id))) | ~(X168 @ X173)))) => (! [X174 : term] : (((sub @ X174 @ id)) = X174) => (! [X175 : (subst > term > subst > $o),X176 : term,X177 : (term > $o)] : (~ ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) | ~ ! [X179 : term] : ((X177 @ (sub @ X176 @ (push @ X179 @ id))) | ~(X177 @ X179)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : subst,X182 : term,X183 : subst] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) = ((sub @ (X180 @ X181 @ X182) @ X183))) | (X175 @ id @ (lam @ (X180 @ sh @ one)) @ id) | ~ ! [X184 : term] : (~(X175 @ id @ X184 @ id) | (X175 @ id @ (X180 @ id @ X184) @ id))) | (X177 @ (lam @ X176))) => ! [X185 : (subst > term > subst > $o),X186 : term] : (~ ! [X187 : term,X188 : term] : (~(X185 @ id @ X188 @ id) | (X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id) | ~(X185 @ id @ X187 @ id)) | ~ ! [X189 : term] : ((X185 @ id @ X189 @ id) | ~(var @ (sub @ X189 @ id))) | ~ ! [X190 : subst,X191 : subst,X192 : subst,X193 : term] : ((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191) | ~(X185 @ X190 @ X193 @ (comp @ X192 @ X191))) | ~ ! [X194 : (subst > term > term)] : (~ ! [X195 : subst,X196 : subst,X197 : term] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196))) | (X185 @ id @ (lam @ (X194 @ sh @ one)) @ id) | ~ ! [X198 : term] : (~(X185 @ id @ X198 @ id) | (X185 @ id @ (X194 @ id @ X198) @ id))) | (X185 @ id @ X186 @ id) | ~ ! [X199 : subst,X200 : term,X201 : subst,X202 : subst] : (~(X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202) | (X185 @ X199 @ X200 @ (comp @ X201 @ X202))))))))) & ! [X203 : d_subst,X204 : d_subst] : ((((d2subst @ X204)) = ((d2subst @ X203))) => (X203 = X204)) & (induction2 <=> ! [X205 : term,X206 : (term > $o)] : (~ ! [X207 : term,X208 : term] : (~(X206 @ X208) | (X206 @ (ap @ X208 @ X207)) | ~(X206 @ X207)) | ~ ! [X209 : term] : (~(var @ X209) | (X206 @ X209)) | ~ ! [X210 : term] : ((X206 @ (lam @ X210)) | ~ ! [X211 : term] : (~(X206 @ X211) | (X206 @ (sub @ X210 @ (push @ X211 @ id))))) | (X206 @ X205))) & (! [X212 : term,X213 : term,X214 : (subst > term > subst > $o)] : (~ ! [X215 : term,X216 : term] : (~(X214 @ id @ X216 @ id) | ~(X214 @ id @ X215 @ id) | (X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id)) | (X214 @ id @ (ap @ X212 @ X213) @ id) | ~ ! [X217 : term,X218 : subst,X219 : subst,X220 : subst] : ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)) | ~(X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)) | ~(X214 @ id @ X212 @ id) | ~ ! [X221 : subst,X222 : term,X223 : subst,X224 : subst] : ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221) | ~(X214 @ X223 @ X222 @ (comp @ X224 @ X221))) | ~(X214 @ id @ X213 @ id)) <=> hoasinduction_lem2) & ((^[X225 : subst, X226 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasinduction_lem3v2a_lthm <=> (! [X227 : term] : ~ ! [X228 : (subst > term > term)] : ~ ! [X229 : subst,X230 : term] : (((sub @ X227 @ (push @ X230 @ X229))) = ((X228 @ X229 @ X230))) => (! [X231 : term] : (((sub @ X231 @ id)) = X231) => ! [X232 : term,X233 : (subst > term > subst > $o),X234 : (term > $o)] : (~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term] : ((X233 @ id @ (X235 @ id @ X236) @ id) | ~(X233 @ id @ X236 @ id)) | ~ ! [X237 : subst,X238 : subst,X239 : term] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237))) = ((sub @ (X235 @ X238 @ X239) @ X237))) | (X233 @ id @ (lam @ (X235 @ sh @ one)) @ id)) | ~ ! [X240 : term] : (((X233 @ id @ X240 @ id)) = ((X234 @ X240))) | (X234 @ (lam @ X232)) | ~ ! [X241 : term] : ((X234 @ (sub @ X232 @ (push @ X241 @ id))) | ~(X234 @ X241)))))) & axclos & (pushprop_lem1v2 <=> ! [X242 : subst,X243 : (term > $o),X244 : term,X245 : (term > $o)] : (~(X245 @ X244) | ~ ! [X246 : term] : (((X243 @ X246)) = ((X245 @ (sub @ X246 @ (push @ X244 @ X242))))) | (X243 @ one))) & (axvarid <=> ! [X247 : term] : (((sub @ X247 @ id)) = X247)) & pushprop_gthm & (hoasinduction <=> ! [X248 : (subst > term > subst > $o),X249 : term] : (~ ! [X250 : (subst > term > term)] : ((X248 @ id @ (lam @ (X250 @ sh @ one)) @ id) | ~ ! [X251 : subst,X252 : term,X253 : subst] : (((X250 @ (comp @ X251 @ X253) @ (sub @ X252 @ X253))) = ((sub @ (X250 @ X251 @ X252) @ X253))) | ~ ! [X254 : term] : ((X248 @ id @ (X250 @ id @ X254) @ id) | ~(X248 @ id @ X254 @ id))) | ~ ! [X255 : subst,X256 : subst,X257 : term,X258 : subst] : ((X248 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255) | ~(X248 @ X258 @ X257 @ (comp @ X256 @ X255))) | ~ ! [X259 : term] : ((X248 @ id @ X259 @ id) | ~(var @ (sub @ X259 @ id))) | ~ ! [X260 : term,X261 : term] : (~(X248 @ id @ X261 @ id) | ~(X248 @ id @ X260 @ id) | (X248 @ id @ (ap @ (sub @ X261 @ id) @ X260) @ id)) | (X248 @ id @ X249 @ id) | ~ ! [X262 : subst,X263 : term,X264 : subst,X265 : subst] : (~(X248 @ (comp @ X262 @ X265) @ (sub @ X263 @ X265) @ X264) | (X248 @ X262 @ X263 @ (comp @ X265 @ X264))))) & hoasinduction_lem2_lthm & hoasinduction_lem3b_gthm & hoasinduction_gthm & ((! [X266 : term] : (((sub @ X266 @ id)) = X266) => (! [X267 : (term > $o),X268 : subst,X269 : term] : ((X267 @ (sub @ X269 @ X268)) | ~ ! [X270 : term] : (~ ! [X271 : term] : ((X267 @ (sub @ X270 @ (push @ X271 @ id))) | ~(X267 @ X271)) | (X267 @ (lam @ X270))) | ~ ! [X272 : term] : ((X267 @ (sub @ X272 @ X268)) | ~(var @ X272)) | ~ ! [X273 : term,X274 : term] : (~(X267 @ X274) | (X267 @ (ap @ X274 @ X273)) | ~(X267 @ X273))) => ! [X275 : term,X276 : (term > $o)] : (~ ! [X277 : term,X278 : term] : (~(X276 @ X278) | (X276 @ (ap @ X278 @ X277)) | ~(X276 @ X277)) | ~ ! [X279 : term] : ((X276 @ (lam @ X279)) | ~ ! [X280 : term] : (~(X276 @ X280) | (X276 @ (sub @ X279 @ (push @ X280 @ id))))) | (X276 @ X275) | ~ ! [X281 : term] : (~(var @ X281) | (X276 @ X281))))) <=> induction2_lthm) & hoasinduction_lem2v2_gthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X282 : subst,X283 : term] : (((sub @ one @ (push @ X283 @ X282))) = X283) => ! [X284 : (term > $o),X285 : subst,X286 : term,X287 : (term > $o)] : (~(X287 @ X286) | ~ ! [X288 : term] : (((X284 @ X288)) = ((X287 @ (sub @ X288 @ (push @ X286 @ X285))))) | (X284 @ one))) <=> pushprop_lem1v2_lthm) & pushprop_lem1_gthm & ! [X289 : term] : ? [X290 : d_term] : (((d2term @ X290)) = X289) & (! [X291 : term,X292 : subst] : (((comp @ sh @ (push @ X291 @ X292))) = X292) <=> axshiftcons) & (axvarcons <=> ! [X293 : term,X294 : subst] : (((sub @ one @ (push @ X293 @ X294))) = X293)) & axmap & ((! [X295 : term] : (((sub @ X295 @ id)) = X295) => (! [X296 : term,X297 : term,X298 : term,X299 : term] : ((((ap @ X298 @ X299)) != ((ap @ X297 @ X296))) | (X297 = X298)) => ! [X300 : term,X301 : term,X302 : term,X303 : term] : ((((ap @ (sub @ X300 @ id) @ X303)) != ((ap @ (sub @ X302 @ id) @ X301))) | (X300 = X302)))) <=> hoasapinj1_lthm) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X304 : d_term] : (d_one = X304) & pushprop_lem0_gthm & substmonoid_gthm & pushprop_lthm_orig & (hoasinduction_lem3aa <=> ! [X305 : (subst > term > subst > $o),X306 : term] : (~ ! [X307 : (subst > term > term)] : ((X305 @ id @ (lam @ (X307 @ sh @ one)) @ id) | ~ ! [X308 : term] : (~(X305 @ id @ X308 @ id) | (X305 @ id @ (X307 @ id @ X308) @ id)) | ~ ! [X309 : subst,X310 : subst,X311 : term] : (((sub @ (X307 @ X309 @ X311) @ X310)) = ((X307 @ (comp @ X309 @ X310) @ (sub @ X311 @ X310))))) | (X305 @ id @ (lam @ (sub @ X306 @ (push @ one @ sh))) @ id) | ~ ! [X312 : term] : ((X305 @ id @ (sub @ X306 @ (push @ X312 @ id)) @ id) | ~(X305 @ id @ X312 @ id)))) & (hoasinduction_no_psi_cond <=> ! [X313 : term,X314 : (subst > term > subst > $o)] : (~ ! [X315 : (subst > term > term)] : ((X314 @ id @ (lam @ (X315 @ sh @ one)) @ id) | ~ ! [X316 : subst,X317 : term,X318 : subst] : (((sub @ (X315 @ X316 @ X317) @ X318)) = ((X315 @ (comp @ X316 @ X318) @ (sub @ X317 @ X318)))) | ~ ! [X319 : term] : (~(X314 @ id @ X319 @ id) | (X314 @ id @ (X315 @ id @ X319) @ id))) | (X314 @ id @ X313 @ id) | ~ ! [X320 : term,X321 : term] : (~(X314 @ id @ X321 @ id) | (X314 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id) | ~(X314 @ id @ X320 @ id)))) & hoasapnotvar_lthm & (! [X322 : (term > $o),X323 : term,X324 : subst] : ~ ! [X325 : (term > $o)] : ~ ! [X326 : term] : (((X325 @ X326)) = ((X322 @ (sub @ X326 @ (push @ X323 @ X324))))) <=> pushprop_lem0_lthm) & ((! [X327 : subst] : (((comp @ id @ X327)) = X327) => (! [X328 : subst] : (((comp @ X328 @ id)) = X328) => (! [X329 : subst] : (((comp @ id @ X329)) = X329) & ! [X330 : subst] : (((comp @ X330 @ id)) = X330)))) <=> substmonoid_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X331 : term] : ~ ! [X332 : (subst > term > term)] : ~ ! [X333 : subst,X334 : term] : (((sub @ X331 @ (push @ X334 @ X333))) = ((X332 @ X333 @ X334)))) & (! [X335 : term,X336 : subst,X337 : (term > $o),X338 : term,X339 : (term > $o)] : (~(X337 @ X335) | (X339 @ (sub @ X335 @ (push @ X338 @ X336)))) <=> pushprop_lem1) & (! [X340 : (subst > term > subst > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> hoasinduction_lem0_lthm) & pushprop_lem2v2_lthm & (termmset <=> ! [X343 : term] : (((sub @ X343 @ id)) = X343)) & hoaslamnotvar_lthm & hoasinduction_lem1_gthm & (laminj <=> ! [X344 : term,X345 : term] : ((X344 = X345) | (((lam @ X344)) != ((lam @ X345))))) & (hoasinduction_lem3_lthm <=> (! [X346 : term] : (((sub @ X346 @ id)) = X346) => (! [X347 : term,X348 : (subst > term > subst > $o)] : ((X348 @ id @ (lam @ (sub @ X347 @ (push @ one @ sh))) @ id) | ~ ! [X349 : term] : (~(X348 @ id @ X349 @ id) | (X348 @ id @ (sub @ X347 @ (push @ X349 @ id)) @ id)) | ~ ! [X350 : (subst > term > term)] : (~ ! [X351 : term] : ((X348 @ id @ (X350 @ id @ X351) @ id) | ~(X348 @ id @ X351 @ id)) | ~ ! [X352 : subst,X353 : subst,X354 : term] : (((sub @ (X350 @ X352 @ X354) @ X353)) = ((X350 @ (comp @ X352 @ X353) @ (sub @ X354 @ X353)))) | (X348 @ id @ (lam @ (X350 @ sh @ one)) @ id))) => ! [X355 : (subst > term > subst > $o),X356 : term] : (~ ! [X357 : (subst > term > term)] : (~ ! [X358 : term] : (~(X355 @ id @ X358 @ id) | (X355 @ id @ (X357 @ id @ X358) @ id)) | ~ ! [X359 : subst,X360 : subst,X361 : term] : (((X357 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359))) = ((sub @ (X357 @ X360 @ X361) @ X359))) | (X355 @ id @ (lam @ (X357 @ sh @ one)) @ id)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : (~(X355 @ X365 @ X363 @ (comp @ X362 @ X364)) | (X355 @ (comp @ X365 @ X362) @ (sub @ X363 @ X362) @ X364)) | ~ ! [X366 : term,X367 : subst,X368 : subst,X369 : subst] : (~(X355 @ (comp @ X367 @ X368) @ (sub @ X366 @ X368) @ X369) | (X355 @ X367 @ X366 @ (comp @ X368 @ X369))) | (X355 @ id @ (lam @ X356) @ id) | ~ ! [X370 : term] : ((X355 @ id @ (sub @ X356 @ (push @ X370 @ id)) @ id) | ~(X355 @ id @ X370 @ id)))))) & (! [X371 : term,X372 : (subst > term > subst > $o)] : (~ ! [X373 : term,X374 : (subst > term > term)] : (~ ! [X375 : term,X376 : subst,X377 : subst] : (((X374 @ (comp @ X377 @ X376) @ (sub @ X375 @ X376))) = ((sub @ X373 @ (push @ (sub @ X375 @ X376) @ (comp @ X377 @ X376))))) | ~ ! [X378 : subst,X379 : term,X380 : subst] : (((sub @ (X374 @ X378 @ X379) @ X380)) = ((sub @ (sub @ X373 @ (push @ X379 @ X378)) @ X380))) | ~ ! [X381 : term] : (~(X372 @ id @ X381 @ id) | (X372 @ id @ (X374 @ id @ X381) @ id)) | (X372 @ id @ (lam @ (X374 @ sh @ one)) @ id)) | (X372 @ id @ (lam @ (sub @ X371 @ (push @ one @ sh))) @ id) | ~ ! [X382 : term] : ((X372 @ id @ (sub @ X371 @ (push @ X382 @ id)) @ id) | ~(X372 @ id @ X382 @ id))) <=> hoasinduction_lem3aaa) & (! [X383 : subst,X384 : term,X385 : (term > $o)] : ~ ! [X386 : (term > $o)] : ~ ! [X387 : term] : (((X386 @ X387)) = ((X385 @ (sub @ X387 @ (push @ X384 @ X383))))) <=> pushprop_lem0) & pushprop_lem3v2 & hoaslamnotvar & (pushprop_p_and_p_prime = (^[X388 : term, X389 : subst, X390 : (term > $o), X391 : (term > $o)] : (! [X392 : term] : (((X391 @ X392)) = ((X390 @ (sub @ X392 @ (push @ X388 @ X389)))))))) & ~ulamvar1 & lamnotvar & ((^[X393 : (subst > term > subst > $o), X394 : (term > $o)] : (! [X395 : term] : (((X394 @ X395)) = ((X393 @ id @ X395 @ id))))) = hoasinduction_p_and_p_prime) & (hoasinduction_lem3a <=> ! [X396 : (subst > term > subst > $o),X397 : term] : ((X396 @ id @ (lam @ X397) @ id) | ~ ! [X398 : (subst > term > term)] : (~ ! [X399 : term] : ((X396 @ id @ (X398 @ id @ X399) @ id) | ~(X396 @ id @ X399 @ id)) | ~ ! [X400 : subst,X401 : subst,X402 : term] : (((X398 @ (comp @ X401 @ X400) @ (sub @ X402 @ X400))) = ((sub @ (X398 @ X401 @ X402) @ X400))) | (X396 @ id @ (lam @ (X398 @ sh @ one)) @ id)) | ~ ! [X403 : term] : (~(X396 @ id @ X403 @ id) | (X396 @ id @ (sub @ X397 @ (push @ X403 @ id)) @ id)))) & (hoasinduction_lem2v2 <=> ! [X404 : term,X405 : (term > $o),X406 : (subst > term > subst > $o),X407 : term] : (~ ! [X408 : term] : (((X405 @ X408)) = ((X406 @ id @ X408 @ id))) | ~ ! [X409 : subst,X410 : term,X411 : subst,X412 : subst] : (~(X406 @ (comp @ X412 @ X411) @ (sub @ X410 @ X411) @ X409) | (X406 @ X412 @ X410 @ (comp @ X411 @ X409))) | ~(X405 @ X407) | ~ ! [X413 : term,X414 : subst,X415 : subst,X416 : subst] : (~(X406 @ X416 @ X413 @ (comp @ X414 @ X415)) | (X406 @ (comp @ X416 @ X414) @ (sub @ X413 @ X414) @ X415)) | ~(X405 @ X404) | (X405 @ (ap @ X404 @ X407)) | ~ ! [X417 : term,X418 : term] : (~(X406 @ id @ X417 @ id) | ~(X406 @ id @ X418 @ id) | (X406 @ id @ (ap @ (sub @ X417 @ id) @ X418) @ id)))) & pushprop_lem2v2_gthm & ! [X419 : d_term,X420 : d_term] : ((((d2term @ X420)) = ((d2term @ X419))) => (X419 = X420)) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (! [X421 : subst] : (((comp @ X421 @ id)) = X421) <=> axidr) & (axscons <=> ! [X422 : subst] : (((push @ (sub @ one @ X422) @ (comp @ sh @ X422))) = X422)) & pushprop_lem2v2 & (! [X423 : (subst > term > subst > $o),X424 : term] : ((X423 @ id @ (lam @ X424) @ id) | ~ ! [X425 : (subst > term > term)] : (~ ! [X426 : term,X427 : subst,X428 : subst] : (((X425 @ (comp @ X428 @ X427) @ (sub @ X426 @ X427))) = ((sub @ (X425 @ X428 @ X426) @ X427))) | (X423 @ id @ (lam @ (X425 @ sh @ one)) @ id) | ~ ! [X429 : term] : (~(X423 @ id @ X429 @ id) | (X423 @ id @ (X425 @ id @ X429) @ id))) | ~ ! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (~(X423 @ X431 @ X432 @ (comp @ X433 @ X430)) | (X423 @ (comp @ X431 @ X433) @ (sub @ X432 @ X433) @ X430)) | ~ ! [X434 : term] : ((X423 @ id @ (sub @ X424 @ (push @ X434 @ id)) @ id) | ~(X423 @ id @ X434 @ id)) | ~ ! [X435 : subst,X436 : term,X437 : subst,X438 : subst] : ((X423 @ X435 @ X436 @ (comp @ X437 @ X438)) | ~(X423 @ (comp @ X435 @ X437) @ (sub @ X436 @ X437) @ X438))) <=> hoasinduction_lem3) & ~lamnotap & (shinj <=> ! [X439 : term,X440 : term] : ((X439 = X440) | (((sub @ X439 @ sh)) != ((sub @ X440 @ sh))))) & (! [X441 : term,X442 : term,X443 : term,X444 : term] : ((((ap @ X443 @ X442)) != ((ap @ X444 @ X441))) | (X443 = X444)) <=> apinj1) & axassoc & hoaslamnotap_lthm & (hoasinduction_lem3v2a <=> ! [X445 : (subst > term > subst > $o),X446 : term,X447 : (term > $o)] : (~ ! [X448 : term] : (((X447 @ X448)) = ((X445 @ id @ X448 @ id))) | ~ ! [X449 : (subst > term > term)] : ((X445 @ id @ (lam @ (X449 @ sh @ one)) @ id) | ~ ! [X450 : term] : ((X445 @ id @ (X449 @ id @ X450) @ id) | ~(X445 @ id @ X450 @ id)) | ~ ! [X451 : term,X452 : subst,X453 : subst] : (((sub @ (X449 @ X453 @ X451) @ X452)) = ((X449 @ (comp @ X453 @ X452) @ (sub @ X451 @ X452))))) | (X447 @ (lam @ X446)) | ~ ! [X454 : term] : ((X447 @ (sub @ X446 @ (push @ X454 @ id))) | ~(X447 @ X454)))) & (! [X455 : (term > $o),X456 : (subst > term > subst > $o),X457 : term] : (~ ! [X458 : subst,X459 : subst,X460 : subst,X461 : term] : (~(X456 @ X460 @ X461 @ (comp @ X459 @ X458)) | (X456 @ (comp @ X460 @ X459) @ (sub @ X461 @ X459) @ X458)) | ~ ! [X462 : subst,X463 : term,X464 : subst,X465 : subst] : ((X456 @ X465 @ X463 @ (comp @ X462 @ X464)) | ~(X456 @ (comp @ X465 @ X462) @ (sub @ X463 @ X462) @ X464)) | ~ ! [X466 : term] : (((X455 @ X466)) = ((X456 @ id @ X466 @ id))) | (X455 @ (lam @ X457)) | ~ ! [X467 : term] : ((X455 @ (sub @ X457 @ (push @ X467 @ id))) | ~(X455 @ X467)) | ~ ! [X468 : (subst > term > term)] : (~ ! [X469 : term,X470 : subst,X471 : subst] : (((X468 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471))) = ((sub @ (X468 @ X470 @ X469) @ X471))) | (X456 @ id @ (lam @ (X468 @ sh @ one)) @ id) | ~ ! [X472 : term] : (~(X456 @ id @ X472 @ id) | (X456 @ id @ (X468 @ id @ X472) @ id)))) <=> hoasinduction_lem3v2) & ((! [X473 : subst] : (((comp @ id @ X473)) = X473) & ! [X474 : subst] : (((comp @ X474 @ id)) = X474)) <=> substmonoid) & apnotvar & hoasapnotvar & (hoasapinj1 <=> ! [X475 : term,X476 : term,X477 : term,X478 : term] : ((((ap @ (sub @ X478 @ id) @ X475)) != ((ap @ (sub @ X476 @ id) @ X477))) | (X476 = X478))) & pushprop_lem1v2_gthm & (hoasinduction_lem3v2_lthm <=> (! [X479 : term] : (((sub @ X479 @ id)) = X479) => ! [X480 : term,X481 : (term > $o),X482 : (subst > term > subst > $o)] : (~ ! [X483 : (subst > term > term)] : ((X482 @ id @ (lam @ (X483 @ sh @ one)) @ id) | ~ ! [X484 : term] : (~(X482 @ id @ X484 @ id) | (X482 @ id @ (X483 @ id @ X484) @ id)) | ~ ! [X485 : subst,X486 : term,X487 : subst] : (((X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487))) = ((sub @ (X483 @ X485 @ X486) @ X487)))) | ~ ! [X488 : subst,X489 : term,X490 : subst,X491 : subst] : (~(X482 @ X491 @ X489 @ (comp @ X488 @ X490)) | (X482 @ (comp @ X491 @ X488) @ (sub @ X489 @ X488) @ X490)) | ~ ! [X492 : term] : (~(X481 @ X492) | (X481 @ (sub @ X480 @ (push @ X492 @ id)))) | (X481 @ (lam @ X480)) | ~ ! [X493 : term,X494 : subst,X495 : subst,X496 : subst] : ((X482 @ X495 @ X493 @ (comp @ X494 @ X496)) | ~(X482 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494) @ X496)) | ~ ! [X497 : term] : (((X481 @ X497)) = ((X482 @ id @ X497 @ id)))))) & (termmset_lthm <=> (! [X498 : term] : (((sub @ X498 @ id)) = X498) => ! [X499 : term] : (((sub @ X499 @ id)) = X499))) & (induction2lem_lthm <=> (! [X500 : subst,X501 : term] : (((sub @ one @ (push @ X501 @ X500))) = X501) => (! [X502 : subst,X503 : term] : (((comp @ sh @ (push @ X503 @ X502))) = X502) => (! [X504 : subst] : (((comp @ X504 @ id)) = X504) => (! [X505 : term,X506 : (term > $o)] : (~ ! [X507 : term] : ((X506 @ (lam @ X507)) | ~(X506 @ X507)) | ~ ! [X508 : term,X509 : term] : (~(X506 @ X509) | (X506 @ (ap @ X508 @ X509)) | ~(X506 @ X508)) | (X506 @ X505) | ~ ! [X510 : term] : ((X506 @ X510) | ~(var @ X510))) => ! [X511 : (term > $o),X512 : subst,X513 : term] : (~ ! [X514 : term] : (~ ! [X515 : term] : (~(X511 @ X515) | (X511 @ (sub @ X514 @ (push @ X515 @ id)))) | (X511 @ (lam @ X514))) | (X511 @ (sub @ X513 @ X512)) | ~ ! [X516 : term] : (~(var @ X516) | (X511 @ (sub @ X516 @ X512))) | ~ ! [X517 : term,X518 : term] : ((X511 @ (ap @ X517 @ X518)) | ~(X511 @ X518) | ~(X511 @ X517)))))))) & hoasinduction_lem1v2_gthm & ! [X519 : subst] : ? [X520 : d_subst] : (((d2subst @ X520)) = X519) & (sh = ((d2subst @ d_id))) & (hoaslaminj <=> ! [X521 : subst,X522 : (subst > term > term),X523 : (subst > term > term),X524 : term] : (~ ! [X525 : subst,X526 : term,X527 : subst] : (((X523 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X527 @ X526) @ X525))) | (((lam @ (X522 @ sh @ one))) != ((lam @ (X523 @ sh @ one)))) | ~ ! [X528 : subst,X529 : term,X530 : subst] : (((sub @ (X522 @ X528 @ X529) @ X530)) = ((X522 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530)))) | (((X523 @ X521 @ X524)) = ((X522 @ X521 @ X524))))) & (hoasinduction_lem3a_lthm <=> (! [X531 : term] : (((sub @ X531 @ id)) = X531) => (! [X532 : (subst > term > subst > $o),X533 : term] : (~ ! [X534 : (subst > term > term)] : (~ ! [X535 : subst,X536 : subst,X537 : term] : (((X534 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535))) = ((sub @ (X534 @ X536 @ X537) @ X535))) | ~ ! [X538 : term] : (~(X532 @ id @ X538 @ id) | (X532 @ id @ (X534 @ id @ X538) @ id)) | (X532 @ id @ (lam @ (X534 @ sh @ one)) @ id)) | ~ ! [X539 : term] : ((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id) | ~(X532 @ id @ X539 @ id)) | (X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id)) => ! [X540 : term,X541 : (subst > term > subst > $o)] : (~ ! [X542 : term] : (~(X541 @ id @ X542 @ id) | (X541 @ id @ (sub @ X540 @ (push @ X542 @ id)) @ id)) | ~ ! [X543 : (subst > term > term)] : (~ ! [X544 : term,X545 : subst,X546 : subst] : (((sub @ (X543 @ X546 @ X544) @ X545)) = ((X543 @ (comp @ X546 @ X545) @ (sub @ X544 @ X545)))) | (X541 @ id @ (lam @ (X543 @ sh @ one)) @ id) | ~ ! [X547 : term] : ((X541 @ id @ (X543 @ id @ X547) @ id) | ~(X541 @ id @ X547 @ id))) | (X541 @ id @ (lam @ X540) @ id))))) & (! [X548 : term] : ~ ! [X549 : (subst > term > term)] : (((X549 @ sh @ one)) != ((sub @ X548 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoasinduction_lem3_gthm & ulamvarsh),
% 6.34/1.36 inference(rectify,[],[f1])).
% 6.34/1.36 thf(f7,plain,(
% 6.34/1.36 (hoasapinj1_gthm = $true) & ((axidl = $true) <=> ! [X0 : subst] : (((comp @ id @ X0)) = X0)) & (pushprop = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X1 : (subst > term > subst > $o)] : ~ ! [X2 : (term > $o)] : ~ ! [X3 : term] : (((X2 @ X3)) = ((X1 @ id @ X3 @ id))) => (! [X4 : (term > $o),X5 : term] : (($true = ((X4 @ X5))) | ~ ! [X6 : term] : ((((X4 @ X6)) = $true) | ~ ($true = ((var @ X6)))) | ~ ! [X7 : term,X8 : term] : (~ ($true = ((X4 @ X7))) | (((X4 @ (ap @ X8 @ X7))) = $true) | ~ ($true = ((X4 @ X8)))) | ~ ! [X9 : term] : (~ ! [X10 : term] : ((((X4 @ (sub @ X9 @ (push @ X10 @ id)))) = $true) | ~ (((X4 @ X10)) = $true)) | (((X4 @ (lam @ X9))) = $true))) => (! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : term,X13 : (subst > term > subst > $o),X14 : (term > $o)] : (~ ! [X15 : term] : (~ ($true = ((X14 @ X15))) | (((X14 @ (sub @ X12 @ (push @ X15 @ id)))) = $true)) | (((X14 @ (lam @ X12))) = $true) | ~ ! [X16 : (subst > term > term)] : (~ ! [X18 : term,X19 : subst,X17 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) = ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))) | ~ ! [X20 : term] : (~ (((X13 @ id @ X20 @ id)) = $true) | (((X13 @ id @ (X16 @ id @ X20) @ id)) = $true)) | (((X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true)) | ~ ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21)))) => ! [X22 : (subst > term > subst > $o),X23 : term] : (~ ! [X24 : (subst > term > term)] : (~ ! [X25 : term] : (~ ($true = ((X22 @ id @ X25 @ id))) | (((X22 @ id @ (X24 @ id @ X25) @ id)) = $true)) | ~ ! [X28 : subst,X27 : term,X26 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)) | ($true = ((X22 @ id @ X23 @ id))) | ~ ! [X29 : term,X30 : term] : ((((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id)) = $true) | ~ (((X22 @ id @ X30 @ id)) = $true) | ~ (((X22 @ id @ X29 @ id)) = $true)))))))) & ((induction2lem = $true) <=> ! [X31 : subst,X32 : term,X33 : (term > $o)] : (~ ! [X34 : term] : (~ ($true = ((var @ X34))) | (((X33 @ (sub @ X34 @ X31))) = $true)) | (((X33 @ (sub @ X32 @ X31))) = $true) | ~ ! [X35 : term,X36 : term] : (~ (((X33 @ X35)) = $true) | ($true = ((X33 @ (ap @ X36 @ X35)))) | ~ (((X33 @ X36)) = $true)) | ~ ! [X37 : term] : (~ ! [X38 : term] : (($true = ((X33 @ (sub @ X37 @ (push @ X38 @ id))))) | ~ ($true = ((X33 @ X38)))) | (((X33 @ (lam @ X37))) = $true)))) & (one = ((d2term @ d_one))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = id) & (! [X39 : term] : ~ ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ X39 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (axabs = $true) & ((hoaslaminj_lthm = $true) <=> (! [X42 : subst,X41 : term] : (((sub @ one @ (push @ X41 @ X42))) = X41) => (! [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) = X44) => (! [X45 : term,X46 : term] : ((X45 = X46) | (((lam @ X46)) != ((lam @ X45)))) => ! [X50 : subst,X49 : (subst > term > term),X48 : term,X47 : (subst > term > term)] : ((((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one)))) | ~ ! [X55 : subst,X54 : term,X56 : subst] : (((sub @ (X47 @ X56 @ X54) @ X55)) = ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55)))) | ~ ! [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) = ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48)))))))) & ((hoasapinj2 = $true) <=> ! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58))) & (! [X61 : term,X62 : (term > $o)] : (~ ! [X63 : term,X64 : term] : ((((X62 @ (ap @ X64 @ X63))) = $true) | ~ ($true = ((X62 @ X63))) | ~ ($true = ((X62 @ X64)))) | (((X62 @ X61)) = $true) | ~ ! [X65 : term] : ((((X62 @ X65)) = $true) | ~ (((var @ X65)) = $true)) | ~ ! [X66 : term] : (~ ($true = ((X62 @ X66))) | (((X62 @ (lam @ X66))) = $true))) <=> (induction = $true)) & (induction2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : term] : (~ ! [X69 : term] : (~ (((X67 @ id @ X69 @ id)) = $true) | (((X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) = $true)) | (((X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X70 : (subst > term > term)] : (~ ! [X71 : term] : (~ (((X67 @ id @ X71 @ id)) = $true) | (((X67 @ id @ (X70 @ id @ X71) @ id)) = $true)) | ($true = ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ~ ! [X74 : term,X72 : subst,X73 : subst] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapnotvar_gthm = $true) & ! [X75 : d_subst] : (d_id = X75) & (hoaslamnotvar_gthm = $true) & ((! [X78 : term,X76 : term,X79 : term,X77 : term] : ((X76 = X78) | (((ap @ X77 @ X76)) != ((ap @ X79 @ X78)))) => ! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83))) <=> (hoasapinj2_lthm = $true)) & (! [X84 : term] : ~ ! [X85 : (subst > term > term)] : ~ ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_lem3a_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X89 : term,X90 : term,X88 : (subst > term > term)] : (~ ! [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X88 @ X92 @ X93) @ X91))) | (((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))))) & (pushprop_lem3v2_lthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lthm = $true) <=> (! [X94 : (term > $o),X95 : term] : (~ ! [X96 : term,X97 : term] : ((((X94 @ (ap @ X96 @ X97))) = $true) | ~ ($true = ((X94 @ X97))) | ~ (((X94 @ X96)) = $true)) | ~ ! [X98 : term] : ((((X94 @ (lam @ X98))) = $true) | ~ ! [X99 : term] : ((((X94 @ (sub @ X98 @ (push @ X99 @ id)))) = $true) | ~ ($true = ((X94 @ X99))))) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | ~ (((var @ X100)) = $true)) | (((X94 @ X95)) = $true)) => (! [X101 : term,X102 : term,X103 : (subst > term > subst > $o)] : (~ ! [X104 : term,X105 : subst,X106 : subst,X107 : subst] : (~ (((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107)) = $true) | (((X103 @ X105 @ X104 @ (comp @ X106 @ X107))) = $true)) | ($true = ((X103 @ id @ (ap @ X102 @ X101) @ id))) | ~ ! [X108 : term,X109 : term] : (~ (((X103 @ id @ X109 @ id)) = $true) | ($true = ((X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id))) | ~ ($true = ((X103 @ id @ X108 @ id)))) | ~ (((X103 @ id @ X101 @ id)) = $true) | ~ (((X103 @ id @ X102 @ id)) = $true) | ~ ! [X110 : subst,X111 : subst,X112 : term,X113 : subst] : (~ (((X103 @ X110 @ X112 @ (comp @ X111 @ X113))) = $true) | (((X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113)) = $true))) => (! [X114 : (subst > term > subst > $o),X115 : term] : (~ ! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (~ (((X114 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true = ((X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ~ ! [X120 : term] : (~ (((X114 @ id @ X120 @ id)) = $true) | (((X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) = $true)) | ~ ! [X121 : (subst > term > term)] : (~ ! [X122 : term] : (($true = ((X114 @ id @ (X121 @ id @ X122) @ id))) | ~ ($true = ((X114 @ id @ X122 @ id)))) | ~ ! [X124 : subst,X123 : term,X125 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) = ((sub @ (X121 @ X124 @ X123) @ X125))) | (((X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true)) | (((X114 @ id @ (lam @ X115) @ id)) = $true) | ~ ! [X126 : subst,X127 : subst,X128 : subst,X129 : term] : ((((X114 @ X127 @ X129 @ (comp @ X128 @ X126))) = $true) | ~ ($true = ((X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))))) => ! [X130 : (subst > term > subst > $o),X131 : term] : (~ ! [X132 : (subst > term > term)] : (~ ! [X133 : subst,X135 : term,X134 : subst] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) | (((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) = $true) | ~ ! [X136 : term] : (~ ($true = ((X130 @ id @ X136 @ id))) | (((X130 @ id @ (X132 @ id @ X136) @ id)) = $true))) | ~ ! [X137 : term] : (~ ($true = ((var @ (sub @ X137 @ id)))) | (((X130 @ id @ X137 @ id)) = $true)) | ~ ! [X138 : term,X139 : term] : (~ ($true = ((X130 @ id @ X138 @ id))) | ~ (((X130 @ id @ X139 @ id)) = $true) | (((X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) = $true)) | ($true = ((X130 @ id @ X131 @ id))) | ~ ! [X140 : term,X141 : subst,X142 : subst,X143 : subst] : ((((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143)) = $true) | ~ ($true = ((X130 @ X141 @ X140 @ (comp @ X142 @ X143))))) | ~ ! [X144 : subst,X145 : term,X146 : subst,X147 : subst] : (~ (((X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146)) = $true) | (((X130 @ X147 @ X145 @ (comp @ X144 @ X146))) = $true))))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X148 : (subst > term > subst > $o)] : ~ ! [X149 : (term > $o)] : ~ ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))) & (hoasapinj2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((apinj2 = $true) <=> ! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154))))) & ((pushprop_lem1_lthm = $true) <=> (! [X155 : term,X156 : subst] : (((sub @ one @ (push @ X155 @ X156))) = X155) => (! [X158 : term,X157 : subst] : (((comp @ sh @ (push @ X158 @ X157))) = X157) => ! [X159 : term,X160 : term,X161 : subst,X162 : (term > $o),X163 : (term > $o)] : ((((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true) | ~ ($true = ((X163 @ X159))))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X164 : (subst > term > subst > $o)] : ~ ! [X165 : (term > $o)] : ~ ! [X166 : term] : (((X164 @ id @ X166 @ id)) = ((X165 @ X166))) => (! [X167 : term,X168 : (term > $o)] : (~ ! [X169 : term,X170 : term] : (~ ($true = ((X168 @ X169))) | (((X168 @ (ap @ X169 @ X170))) = $true) | ~ (((X168 @ X170)) = $true)) | ($true = ((X168 @ X167))) | ~ ! [X171 : term] : ((((X168 @ X171)) = $true) | ~ ($true = ((var @ X171)))) | ~ ! [X172 : term] : ((((X168 @ (lam @ X172))) = $true) | ~ ! [X173 : term] : ((((X168 @ (sub @ X172 @ (push @ X173 @ id)))) = $true) | ~ ($true = ((X168 @ X173)))))) => (! [X174 : term] : (((sub @ X174 @ id)) = X174) => (! [X175 : (subst > term > subst > $o),X176 : term,X177 : (term > $o)] : (~ ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) | ~ ! [X179 : term] : ((((X177 @ (sub @ X176 @ (push @ X179 @ id)))) = $true) | ~ (((X177 @ X179)) = $true)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : subst,X183 : subst,X182 : term] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) = ((sub @ (X180 @ X181 @ X182) @ X183))) | (((X175 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : term] : (~ (((X175 @ id @ X184 @ id)) = $true) | (((X175 @ id @ (X180 @ id @ X184) @ id)) = $true))) | (((X177 @ (lam @ X176))) = $true)) => ! [X185 : (subst > term > subst > $o),X186 : term] : (~ ! [X187 : term,X188 : term] : (~ ($true = ((X185 @ id @ X188 @ id))) | (((X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id)) = $true) | ~ (((X185 @ id @ X187 @ id)) = $true)) | ~ ! [X189 : term] : (($true = ((X185 @ id @ X189 @ id))) | ~ ($true = ((var @ (sub @ X189 @ id))))) | ~ ! [X190 : subst,X191 : subst,X192 : subst,X193 : term] : ((((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191)) = $true) | ~ (((X185 @ X190 @ X193 @ (comp @ X192 @ X191))) = $true)) | ~ ! [X194 : (subst > term > term)] : (~ ! [X197 : term,X196 : subst,X195 : subst] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196))) | (((X185 @ id @ (lam @ (X194 @ sh @ one)) @ id)) = $true) | ~ ! [X198 : term] : (~ (((X185 @ id @ X198 @ id)) = $true) | (((X185 @ id @ (X194 @ id @ X198) @ id)) = $true))) | (((X185 @ id @ X186 @ id)) = $true) | ~ ! [X199 : subst,X200 : term,X201 : subst,X202 : subst] : (~ ($true = ((X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202))) | ($true = ((X185 @ X199 @ X200 @ (comp @ X201 @ X202))))))))))) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) = ((d2subst @ X203))) => (X203 = X204)) & ((induction2 = $true) <=> ! [X205 : term,X206 : (term > $o)] : (~ ! [X207 : term,X208 : term] : (~ ($true = ((X206 @ X208))) | ($true = ((X206 @ (ap @ X208 @ X207)))) | ~ (((X206 @ X207)) = $true)) | ~ ! [X209 : term] : (~ (((var @ X209)) = $true) | (((X206 @ X209)) = $true)) | ~ ! [X210 : term] : ((((X206 @ (lam @ X210))) = $true) | ~ ! [X211 : term] : (~ (((X206 @ X211)) = $true) | ($true = ((X206 @ (sub @ X210 @ (push @ X211 @ id))))))) | (((X206 @ X205)) = $true))) & (! [X212 : term,X213 : term,X214 : (subst > term > subst > $o)] : (~ ! [X215 : term,X216 : term] : (~ (((X214 @ id @ X216 @ id)) = $true) | ~ ($true = ((X214 @ id @ X215 @ id))) | ($true = ((X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id)))) | (((X214 @ id @ (ap @ X212 @ X213) @ id)) = $true) | ~ ! [X217 : term,X218 : subst,X219 : subst,X220 : subst] : (($true = ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)))) | ~ ($true = ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)))) | ~ (((X214 @ id @ X212 @ id)) = $true) | ~ ! [X221 : subst,X222 : term,X223 : subst,X224 : subst] : (($true = ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221))) | ~ (((X214 @ X223 @ X222 @ (comp @ X224 @ X221))) = $true)) | ~ (((X214 @ id @ X213 @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X227 : term] : ~ ! [X228 : (subst > term > term)] : ~ ! [X229 : subst,X230 : term] : (((sub @ X227 @ (push @ X230 @ X229))) = ((X228 @ X229 @ X230))) => (! [X231 : term] : (((sub @ X231 @ id)) = X231) => ! [X232 : term,X233 : (subst > term > subst > $o),X234 : (term > $o)] : (~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term] : ((((X233 @ id @ (X235 @ id @ X236) @ id)) = $true) | ~ (((X233 @ id @ X236 @ id)) = $true)) | ~ ! [X237 : subst,X238 : subst,X239 : term] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X239 @ X237))) = ((sub @ (X235 @ X238 @ X239) @ X237))) | ($true = ((X233 @ id @ (lam @ (X235 @ sh @ one)) @ id)))) | ~ ! [X240 : term] : (((X233 @ id @ X240 @ id)) = ((X234 @ X240))) | ($true = ((X234 @ (lam @ X232)))) | ~ ! [X241 : term] : (($true = ((X234 @ (sub @ X232 @ (push @ X241 @ id))))) | ~ (((X234 @ X241)) = $true)))))) & (axclos = $true) & ((pushprop_lem1v2 = $true) <=> ! [X242 : subst,X243 : (term > $o),X244 : term,X245 : (term > $o)] : (~ (((X245 @ X244)) = $true) | ~ ! [X246 : term] : (((X243 @ X246)) = ((X245 @ (sub @ X246 @ (push @ X244 @ X242))))) | ($true = ((X243 @ one))))) & ((axvarid = $true) <=> ! [X247 : term] : (((sub @ X247 @ id)) = X247)) & (pushprop_gthm = $true) & ((hoasinduction = $true) <=> ! [X248 : (subst > term > subst > $o),X249 : term] : (~ ! [X250 : (subst > term > term)] : ((((X248 @ id @ (lam @ (X250 @ sh @ one)) @ id)) = $true) | ~ ! [X251 : subst,X252 : term,X253 : subst] : (((X250 @ (comp @ X251 @ X253) @ (sub @ X252 @ X253))) = ((sub @ (X250 @ X251 @ X252) @ X253))) | ~ ! [X254 : term] : ((((X248 @ id @ (X250 @ id @ X254) @ id)) = $true) | ~ (((X248 @ id @ X254 @ id)) = $true))) | ~ ! [X255 : subst,X256 : subst,X257 : term,X258 : subst] : ((((X248 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255)) = $true) | ~ ($true = ((X248 @ X258 @ X257 @ (comp @ X256 @ X255))))) | ~ ! [X259 : term] : (($true = ((X248 @ id @ X259 @ id))) | ~ (((var @ (sub @ X259 @ id))) = $true)) | ~ ! [X260 : term,X261 : term] : (~ (((X248 @ id @ X261 @ id)) = $true) | ~ (((X248 @ id @ X260 @ id)) = $true) | ($true = ((X248 @ id @ (ap @ (sub @ X261 @ id) @ X260) @ id)))) | ($true = ((X248 @ id @ X249 @ id))) | ~ ! [X262 : subst,X263 : term,X264 : subst,X265 : subst] : (~ ($true = ((X248 @ (comp @ X262 @ X265) @ (sub @ X263 @ X265) @ X264))) | (((X248 @ X262 @ X263 @ (comp @ X265 @ X264))) = $true)))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_gthm = $true) & ((! [X266 : term] : (((sub @ X266 @ id)) = X266) => (! [X267 : (term > $o),X268 : subst,X269 : term] : ((((X267 @ (sub @ X269 @ X268))) = $true) | ~ ! [X270 : term] : (~ ! [X271 : term] : (($true = ((X267 @ (sub @ X270 @ (push @ X271 @ id))))) | ~ (((X267 @ X271)) = $true)) | (((X267 @ (lam @ X270))) = $true)) | ~ ! [X272 : term] : (($true = ((X267 @ (sub @ X272 @ X268)))) | ~ (((var @ X272)) = $true)) | ~ ! [X273 : term,X274 : term] : (~ ($true = ((X267 @ X274))) | ($true = ((X267 @ (ap @ X274 @ X273)))) | ~ (((X267 @ X273)) = $true))) => ! [X275 : term,X276 : (term > $o)] : (~ ! [X277 : term,X278 : term] : (~ (((X276 @ X278)) = $true) | ($true = ((X276 @ (ap @ X278 @ X277)))) | ~ (((X276 @ X277)) = $true)) | ~ ! [X279 : term] : ((((X276 @ (lam @ X279))) = $true) | ~ ! [X280 : term] : (~ (((X276 @ X280)) = $true) | ($true = ((X276 @ (sub @ X279 @ (push @ X280 @ id))))))) | (((X276 @ X275)) = $true) | ~ ! [X281 : term] : (~ (((var @ X281)) = $true) | ($true = ((X276 @ X281))))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X282 : subst,X283 : term] : (((sub @ one @ (push @ X283 @ X282))) = X283) => ! [X284 : (term > $o),X285 : subst,X286 : term,X287 : (term > $o)] : (~ (((X287 @ X286)) = $true) | ~ ! [X288 : term] : (((X284 @ X288)) = ((X287 @ (sub @ X288 @ (push @ X286 @ X285))))) | (((X284 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem1_gthm = $true) & ! [X289 : term] : ? [X290 : d_term] : (((d2term @ X290)) = X289) & (! [X291 : term,X292 : subst] : (((comp @ sh @ (push @ X291 @ X292))) = X292) <=> (axshiftcons = $true)) & ((axvarcons = $true) <=> ! [X293 : term,X294 : subst] : (((sub @ one @ (push @ X293 @ X294))) = X293)) & (axmap = $true) & ((! [X295 : term] : (((sub @ X295 @ id)) = X295) => (! [X296 : term,X297 : term,X298 : term,X299 : term] : ((((ap @ X298 @ X299)) != ((ap @ X297 @ X296))) | (X297 = X298)) => ! [X300 : term,X301 : term,X302 : term,X303 : term] : ((((ap @ (sub @ X300 @ id) @ X303)) != ((ap @ (sub @ X302 @ id) @ X301))) | (X300 = X302)))) <=> (hoasapinj1_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X304 : d_term] : (d_one = X304) & (pushprop_lem0_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X305 : (subst > term > subst > $o),X306 : term] : (~ ! [X307 : (subst > term > term)] : ((((X305 @ id @ (lam @ (X307 @ sh @ one)) @ id)) = $true) | ~ ! [X308 : term] : (~ (((X305 @ id @ X308 @ id)) = $true) | (((X305 @ id @ (X307 @ id @ X308) @ id)) = $true)) | ~ ! [X309 : subst,X310 : subst,X311 : term] : (((sub @ (X307 @ X309 @ X311) @ X310)) = ((X307 @ (comp @ X309 @ X310) @ (sub @ X311 @ X310))))) | ($true = ((X305 @ id @ (lam @ (sub @ X306 @ (push @ one @ sh))) @ id))) | ~ ! [X312 : term] : ((((X305 @ id @ (sub @ X306 @ (push @ X312 @ id)) @ id)) = $true) | ~ (((X305 @ id @ X312 @ id)) = $true)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X313 : term,X314 : (subst > term > subst > $o)] : (~ ! [X315 : (subst > term > term)] : ((((X314 @ id @ (lam @ (X315 @ sh @ one)) @ id)) = $true) | ~ ! [X316 : subst,X317 : term,X318 : subst] : (((sub @ (X315 @ X316 @ X317) @ X318)) = ((X315 @ (comp @ X316 @ X318) @ (sub @ X317 @ X318)))) | ~ ! [X319 : term] : (~ (((X314 @ id @ X319 @ id)) = $true) | (((X314 @ id @ (X315 @ id @ X319) @ id)) = $true))) | ($true = ((X314 @ id @ X313 @ id))) | ~ ! [X320 : term,X321 : term] : (~ ($true = ((X314 @ id @ X321 @ id))) | (((X314 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id)) = $true) | ~ ($true = ((X314 @ id @ X320 @ id)))))) & (hoasapnotvar_lthm = $true) & (! [X322 : (term > $o),X323 : term,X324 : subst] : ~ ! [X325 : (term > $o)] : ~ ! [X326 : term] : (((X325 @ X326)) = ((X322 @ (sub @ X326 @ (push @ X323 @ X324))))) <=> (pushprop_lem0_lthm = $true)) & ((! [X327 : subst] : (((comp @ id @ X327)) = X327) => (! [X328 : subst] : (((comp @ X328 @ id)) = X328) => (! [X329 : subst] : (((comp @ id @ X329)) = X329) & ! [X330 : subst] : (((comp @ X330 @ id)) = X330)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X331 : term] : ~ ! [X332 : (subst > term > term)] : ~ ! [X333 : subst,X334 : term] : (((sub @ X331 @ (push @ X334 @ X333))) = ((X332 @ X333 @ X334)))) & (! [X335 : term,X336 : subst,X337 : (term > $o),X338 : term,X339 : (term > $o)] : (~ (((X337 @ X335)) = $true) | ($true = ((X339 @ (sub @ X335 @ (push @ X338 @ X336)))))) <=> (pushprop_lem1 = $true)) & (! [X340 : (subst > term > subst > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X341 @ X342)) = ((X340 @ id @ X342 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((termmset = $true) <=> ! [X343 : term] : (((sub @ X343 @ id)) = X343)) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1_gthm = $true) & ((laminj = $true) <=> ! [X344 : term,X345 : term] : ((X344 = X345) | (((lam @ X344)) != ((lam @ X345))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X346 : term] : (((sub @ X346 @ id)) = X346) => (! [X347 : term,X348 : (subst > term > subst > $o)] : (($true = ((X348 @ id @ (lam @ (sub @ X347 @ (push @ one @ sh))) @ id))) | ~ ! [X349 : term] : (~ ($true = ((X348 @ id @ X349 @ id))) | ($true = ((X348 @ id @ (sub @ X347 @ (push @ X349 @ id)) @ id)))) | ~ ! [X350 : (subst > term > term)] : (~ ! [X351 : term] : ((((X348 @ id @ (X350 @ id @ X351) @ id)) = $true) | ~ (((X348 @ id @ X351 @ id)) = $true)) | ~ ! [X352 : subst,X353 : subst,X354 : term] : (((sub @ (X350 @ X352 @ X354) @ X353)) = ((X350 @ (comp @ X352 @ X353) @ (sub @ X354 @ X353)))) | ($true = ((X348 @ id @ (lam @ (X350 @ sh @ one)) @ id))))) => ! [X355 : (subst > term > subst > $o),X356 : term] : (~ ! [X357 : (subst > term > term)] : (~ ! [X358 : term] : (~ ($true = ((X355 @ id @ X358 @ id))) | (((X355 @ id @ (X357 @ id @ X358) @ id)) = $true)) | ~ ! [X359 : subst,X360 : subst,X361 : term] : (((X357 @ (comp @ X360 @ X359) @ (sub @ X361 @ X359))) = ((sub @ (X357 @ X360 @ X361) @ X359))) | (((X355 @ id @ (lam @ (X357 @ sh @ one)) @ id)) = $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : (~ ($true = ((X355 @ X365 @ X363 @ (comp @ X362 @ X364)))) | (((X355 @ (comp @ X365 @ X362) @ (sub @ X363 @ X362) @ X364)) = $true)) | ~ ! [X366 : term,X367 : subst,X368 : subst,X369 : subst] : (~ (((X355 @ (comp @ X367 @ X368) @ (sub @ X366 @ X368) @ X369)) = $true) | (((X355 @ X367 @ X366 @ (comp @ X368 @ X369))) = $true)) | (((X355 @ id @ (lam @ X356) @ id)) = $true) | ~ ! [X370 : term] : ((((X355 @ id @ (sub @ X356 @ (push @ X370 @ id)) @ id)) = $true) | ~ (((X355 @ id @ X370 @ id)) = $true)))))) & (! [X371 : term,X372 : (subst > term > subst > $o)] : (~ ! [X373 : term,X374 : (subst > term > term)] : (~ ! [X375 : term,X376 : subst,X377 : subst] : (((X374 @ (comp @ X377 @ X376) @ (sub @ X375 @ X376))) = ((sub @ X373 @ (push @ (sub @ X375 @ X376) @ (comp @ X377 @ X376))))) | ~ ! [X378 : subst,X379 : term,X380 : subst] : (((sub @ (X374 @ X378 @ X379) @ X380)) = ((sub @ (sub @ X373 @ (push @ X379 @ X378)) @ X380))) | ~ ! [X381 : term] : (~ ($true = ((X372 @ id @ X381 @ id))) | ($true = ((X372 @ id @ (X374 @ id @ X381) @ id)))) | (((X372 @ id @ (lam @ (X374 @ sh @ one)) @ id)) = $true)) | (((X372 @ id @ (lam @ (sub @ X371 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X382 : term] : ((((X372 @ id @ (sub @ X371 @ (push @ X382 @ id)) @ id)) = $true) | ~ (((X372 @ id @ X382 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (! [X383 : subst,X384 : term,X385 : (term > $o)] : ~ ! [X386 : (term > $o)] : ~ ! [X387 : term] : (((X386 @ X387)) = ((X385 @ (sub @ X387 @ (push @ X384 @ X383))))) <=> (pushprop_lem0 = $true)) & (pushprop_lem3v2 = $true) & (hoaslamnotvar = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ~ (ulamvar1 = $true) & (lamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3a = $true) <=> ! [X396 : (subst > term > subst > $o),X397 : term] : ((((X396 @ id @ (lam @ X397) @ id)) = $true) | ~ ! [X398 : (subst > term > term)] : (~ ! [X399 : term] : (($true = ((X396 @ id @ (X398 @ id @ X399) @ id))) | ~ (((X396 @ id @ X399 @ id)) = $true)) | ~ ! [X400 : subst,X401 : subst,X402 : term] : (((X398 @ (comp @ X401 @ X400) @ (sub @ X402 @ X400))) = ((sub @ (X398 @ X401 @ X402) @ X400))) | (((X396 @ id @ (lam @ (X398 @ sh @ one)) @ id)) = $true)) | ~ ! [X403 : term] : (~ (((X396 @ id @ X403 @ id)) = $true) | (((X396 @ id @ (sub @ X397 @ (push @ X403 @ id)) @ id)) = $true)))) & ((hoasinduction_lem2v2 = $true) <=> ! [X404 : term,X405 : (term > $o),X406 : (subst > term > subst > $o),X407 : term] : (~ ! [X408 : term] : (((X405 @ X408)) = ((X406 @ id @ X408 @ id))) | ~ ! [X409 : subst,X410 : term,X411 : subst,X412 : subst] : (~ (((X406 @ (comp @ X412 @ X411) @ (sub @ X410 @ X411) @ X409)) = $true) | (((X406 @ X412 @ X410 @ (comp @ X411 @ X409))) = $true)) | ~ (((X405 @ X407)) = $true) | ~ ! [X413 : term,X414 : subst,X415 : subst,X416 : subst] : (~ (((X406 @ X416 @ X413 @ (comp @ X414 @ X415))) = $true) | ($true = ((X406 @ (comp @ X416 @ X414) @ (sub @ X413 @ X414) @ X415)))) | ~ ($true = ((X405 @ X404))) | (((X405 @ (ap @ X404 @ X407))) = $true) | ~ ! [X417 : term,X418 : term] : (~ ($true = ((X406 @ id @ X417 @ id))) | ~ (((X406 @ id @ X418 @ id)) = $true) | (((X406 @ id @ (ap @ (sub @ X417 @ id) @ X418) @ id)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ! [X419 : d_term,X420 : d_term] : ((((d2term @ X420)) = ((d2term @ X419))) => (X419 = X420)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (! [X421 : subst] : (((comp @ X421 @ id)) = X421) <=> (axidr = $true)) & ((axscons = $true) <=> ! [X422 : subst] : (((push @ (sub @ one @ X422) @ (comp @ sh @ X422))) = X422)) & (pushprop_lem2v2 = $true) & (! [X423 : (subst > term > subst > $o),X424 : term] : ((((X423 @ id @ (lam @ X424) @ id)) = $true) | ~ ! [X425 : (subst > term > term)] : (~ ! [X426 : term,X427 : subst,X428 : subst] : (((X425 @ (comp @ X428 @ X427) @ (sub @ X426 @ X427))) = ((sub @ (X425 @ X428 @ X426) @ X427))) | ($true = ((X423 @ id @ (lam @ (X425 @ sh @ one)) @ id))) | ~ ! [X429 : term] : (~ (((X423 @ id @ X429 @ id)) = $true) | (((X423 @ id @ (X425 @ id @ X429) @ id)) = $true))) | ~ ! [X430 : subst,X431 : subst,X432 : term,X433 : subst] : (~ (((X423 @ X431 @ X432 @ (comp @ X433 @ X430))) = $true) | ($true = ((X423 @ (comp @ X431 @ X433) @ (sub @ X432 @ X433) @ X430)))) | ~ ! [X434 : term] : (($true = ((X423 @ id @ (sub @ X424 @ (push @ X434 @ id)) @ id))) | ~ (((X423 @ id @ X434 @ id)) = $true)) | ~ ! [X435 : subst,X436 : term,X437 : subst,X438 : subst] : (($true = ((X423 @ X435 @ X436 @ (comp @ X437 @ X438)))) | ~ (((X423 @ (comp @ X435 @ X437) @ (sub @ X436 @ X437) @ X438)) = $true))) <=> (hoasinduction_lem3 = $true)) & ~ (lamnotap = $true) & ((shinj = $true) <=> ! [X439 : term,X440 : term] : ((X439 = X440) | (((sub @ X439 @ sh)) != ((sub @ X440 @ sh))))) & (! [X441 : term,X442 : term,X443 : term,X444 : term] : ((((ap @ X443 @ X442)) != ((ap @ X444 @ X441))) | (X443 = X444)) <=> (apinj1 = $true)) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X445 : (subst > term > subst > $o),X446 : term,X447 : (term > $o)] : (~ ! [X448 : term] : (((X447 @ X448)) = ((X445 @ id @ X448 @ id))) | ~ ! [X449 : (subst > term > term)] : ((((X445 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X445 @ id @ (X449 @ id @ X450) @ id)) = $true) | ~ (((X445 @ id @ X450 @ id)) = $true)) | ~ ! [X451 : term,X452 : subst,X453 : subst] : (((sub @ (X449 @ X453 @ X451) @ X452)) = ((X449 @ (comp @ X453 @ X452) @ (sub @ X451 @ X452))))) | (((X447 @ (lam @ X446))) = $true) | ~ ! [X454 : term] : (($true = ((X447 @ (sub @ X446 @ (push @ X454 @ id))))) | ~ (((X447 @ X454)) = $true)))) & (! [X455 : (term > $o),X456 : (subst > term > subst > $o),X457 : term] : (~ ! [X458 : subst,X459 : subst,X460 : subst,X461 : term] : (~ (((X456 @ X460 @ X461 @ (comp @ X459 @ X458))) = $true) | (((X456 @ (comp @ X460 @ X459) @ (sub @ X461 @ X459) @ X458)) = $true)) | ~ ! [X462 : subst,X463 : term,X464 : subst,X465 : subst] : (($true = ((X456 @ X465 @ X463 @ (comp @ X462 @ X464)))) | ~ ($true = ((X456 @ (comp @ X465 @ X462) @ (sub @ X463 @ X462) @ X464)))) | ~ ! [X466 : term] : (((X455 @ X466)) = ((X456 @ id @ X466 @ id))) | (((X455 @ (lam @ X457))) = $true) | ~ ! [X467 : term] : (($true = ((X455 @ (sub @ X457 @ (push @ X467 @ id))))) | ~ ($true = ((X455 @ X467)))) | ~ ! [X468 : (subst > term > term)] : (~ ! [X469 : term,X470 : subst,X471 : subst] : (((X468 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471))) = ((sub @ (X468 @ X470 @ X469) @ X471))) | ($true = ((X456 @ id @ (lam @ (X468 @ sh @ one)) @ id))) | ~ ! [X472 : term] : (~ (((X456 @ id @ X472 @ id)) = $true) | (((X456 @ id @ (X468 @ id @ X472) @ id)) = $true)))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X473 : subst] : (((comp @ id @ X473)) = X473) & ! [X474 : subst] : (((comp @ X474 @ id)) = X474)) <=> (substmonoid = $true)) & (apnotvar = $true) & (hoasapnotvar = $true) & ((hoasapinj1 = $true) <=> ! [X475 : term,X476 : term,X477 : term,X478 : term] : ((((ap @ (sub @ X478 @ id) @ X475)) != ((ap @ (sub @ X476 @ id) @ X477))) | (X476 = X478))) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X479 : term] : (((sub @ X479 @ id)) = X479) => ! [X480 : term,X481 : (term > $o),X482 : (subst > term > subst > $o)] : (~ ! [X483 : (subst > term > term)] : (($true = ((X482 @ id @ (lam @ (X483 @ sh @ one)) @ id))) | ~ ! [X484 : term] : (~ (((X482 @ id @ X484 @ id)) = $true) | (((X482 @ id @ (X483 @ id @ X484) @ id)) = $true)) | ~ ! [X485 : subst,X486 : term,X487 : subst] : (((X483 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487))) = ((sub @ (X483 @ X485 @ X486) @ X487)))) | ~ ! [X488 : subst,X489 : term,X490 : subst,X491 : subst] : (~ (((X482 @ X491 @ X489 @ (comp @ X488 @ X490))) = $true) | ($true = ((X482 @ (comp @ X491 @ X488) @ (sub @ X489 @ X488) @ X490)))) | ~ ! [X492 : term] : (~ (((X481 @ X492)) = $true) | (((X481 @ (sub @ X480 @ (push @ X492 @ id)))) = $true)) | (((X481 @ (lam @ X480))) = $true) | ~ ! [X493 : term,X494 : subst,X495 : subst,X496 : subst] : (($true = ((X482 @ X495 @ X493 @ (comp @ X494 @ X496)))) | ~ (((X482 @ (comp @ X495 @ X494) @ (sub @ X493 @ X494) @ X496)) = $true)) | ~ ! [X497 : term] : (((X481 @ X497)) = ((X482 @ id @ X497 @ id)))))) & ((termmset_lthm = $true) <=> (! [X498 : term] : (((sub @ X498 @ id)) = X498) => ! [X499 : term] : (((sub @ X499 @ id)) = X499))) & ((induction2lem_lthm = $true) <=> (! [X500 : subst,X501 : term] : (((sub @ one @ (push @ X501 @ X500))) = X501) => (! [X502 : subst,X503 : term] : (((comp @ sh @ (push @ X503 @ X502))) = X502) => (! [X504 : subst] : (((comp @ X504 @ id)) = X504) => (! [X505 : term,X506 : (term > $o)] : (~ ! [X507 : term] : ((((X506 @ (lam @ X507))) = $true) | ~ ($true = ((X506 @ X507)))) | ~ ! [X508 : term,X509 : term] : (~ ($true = ((X506 @ X509))) | (((X506 @ (ap @ X508 @ X509))) = $true) | ~ (((X506 @ X508)) = $true)) | (((X506 @ X505)) = $true) | ~ ! [X510 : term] : ((((X506 @ X510)) = $true) | ~ (((var @ X510)) = $true))) => ! [X511 : (term > $o),X512 : subst,X513 : term] : (~ ! [X514 : term] : (~ ! [X515 : term] : (~ (((X511 @ X515)) = $true) | (((X511 @ (sub @ X514 @ (push @ X515 @ id)))) = $true)) | (((X511 @ (lam @ X514))) = $true)) | ($true = ((X511 @ (sub @ X513 @ X512)))) | ~ ! [X516 : term] : (~ (((var @ X516)) = $true) | (((X511 @ (sub @ X516 @ X512))) = $true)) | ~ ! [X517 : term,X518 : term] : ((((X511 @ (ap @ X517 @ X518))) = $true) | ~ ($true = ((X511 @ X518))) | ~ (((X511 @ X517)) = $true)))))))) & (hoasinduction_lem1v2_gthm = $true) & ! [X519 : subst] : ? [X520 : d_subst] : (((d2subst @ X520)) = X519) & (((d2subst @ d_id)) = sh) & ((hoaslaminj = $true) <=> ! [X521 : subst,X522 : (subst > term > term),X523 : (subst > term > term),X524 : term] : (~ ! [X525 : subst,X526 : term,X527 : subst] : (((X523 @ (comp @ X527 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X527 @ X526) @ X525))) | (((lam @ (X522 @ sh @ one))) != ((lam @ (X523 @ sh @ one)))) | ~ ! [X528 : subst,X529 : term,X530 : subst] : (((sub @ (X522 @ X528 @ X529) @ X530)) = ((X522 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530)))) | (((X523 @ X521 @ X524)) = ((X522 @ X521 @ X524))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X531 : term] : (((sub @ X531 @ id)) = X531) => (! [X532 : (subst > term > subst > $o),X533 : term] : (~ ! [X534 : (subst > term > term)] : (~ ! [X535 : subst,X536 : subst,X537 : term] : (((X534 @ (comp @ X536 @ X535) @ (sub @ X537 @ X535))) = ((sub @ (X534 @ X536 @ X537) @ X535))) | ~ ! [X538 : term] : (~ (((X532 @ id @ X538 @ id)) = $true) | ($true = ((X532 @ id @ (X534 @ id @ X538) @ id)))) | ($true = ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id)))) | ~ ! [X539 : term] : (($true = ((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id))) | ~ (((X532 @ id @ X539 @ id)) = $true)) | (((X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id)) = $true)) => ! [X540 : term,X541 : (subst > term > subst > $o)] : (~ ! [X542 : term] : (~ ($true = ((X541 @ id @ X542 @ id))) | (((X541 @ id @ (sub @ X540 @ (push @ X542 @ id)) @ id)) = $true)) | ~ ! [X543 : (subst > term > term)] : (~ ! [X544 : term,X545 : subst,X546 : subst] : (((sub @ (X543 @ X546 @ X544) @ X545)) = ((X543 @ (comp @ X546 @ X545) @ (sub @ X544 @ X545)))) | ($true = ((X541 @ id @ (lam @ (X543 @ sh @ one)) @ id))) | ~ ! [X547 : term] : ((((X541 @ id @ (X543 @ id @ X547) @ id)) = $true) | ~ (((X541 @ id @ X547 @ id)) = $true))) | (((X541 @ id @ (lam @ X540) @ id)) = $true))))) & (! [X548 : term] : ~ ! [X549 : (subst > term > term)] : (((X549 @ sh @ one)) != ((sub @ X548 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem3_gthm = $true) & (ulamvarsh = $true)),
% 6.34/1.36 inference(fool_elimination,[],[f6])).
% 6.34/1.36 thf(f8,plain,(
% 6.34/1.36 (hoasinduction_lem3aa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.34/1.36 inference(flattening,[],[f5])).
% 6.34/1.36 thf(f9,plain,(
% 6.34/1.36 (hoasapinj1_gthm = $true) & ((axidl = $true) <=> ! [X0 : subst] : (((comp @ id @ X0)) = X0)) & (pushprop = $true) & (termmset_gthm = $true) & (axapp = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X1 : (subst > term > subst > $o)] : ~ ! [X2 : (term > $o)] : ~ ! [X3 : term] : (((X2 @ X3)) = ((X1 @ id @ X3 @ id))) => (! [X4 : (term > $o),X5 : term] : (($true = ((X4 @ X5))) | ~ ! [X6 : term] : ((((X4 @ X6)) = $true) | ~ ($true = ((var @ X6)))) | ~ ! [X7 : term,X8 : term] : (~ ($true = ((X4 @ X7))) | (((X4 @ (ap @ X8 @ X7))) = $true) | ~ ($true = ((X4 @ X8)))) | ~ ! [X9 : term] : (~ ! [X10 : term] : ((((X4 @ (sub @ X9 @ (push @ X10 @ id)))) = $true) | ~ (((X4 @ X10)) = $true)) | (((X4 @ (lam @ X9))) = $true))) => (! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X12 : term,X13 : (subst > term > subst > $o),X14 : (term > $o)] : (~ ! [X15 : term] : (~ ($true = ((X14 @ X15))) | (((X14 @ (sub @ X12 @ (push @ X15 @ id)))) = $true)) | (((X14 @ (lam @ X12))) = $true) | ~ ! [X16 : (subst > term > term)] : (~ ! [X18 : term,X19 : subst,X17 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) = ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))) | ~ ! [X20 : term] : (~ (((X13 @ id @ X20 @ id)) = $true) | (((X13 @ id @ (X16 @ id @ X20) @ id)) = $true)) | (((X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true)) | ~ ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21)))) => ! [X22 : (subst > term > subst > $o),X23 : term] : (~ ! [X24 : (subst > term > term)] : (~ ! [X25 : term] : (~ ($true = ((X22 @ id @ X25 @ id))) | (((X22 @ id @ (X24 @ id @ X25) @ id)) = $true)) | ~ ! [X28 : subst,X27 : term,X26 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)) | ($true = ((X22 @ id @ X23 @ id))) | ~ ! [X29 : term,X30 : term] : ((((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id)) = $true) | ~ (((X22 @ id @ X30 @ id)) = $true) | ~ (((X22 @ id @ X29 @ id)) = $true)))))))) & ((induction2lem = $true) <=> ! [X31 : subst,X32 : term,X33 : (term > $o)] : (~ ! [X34 : term] : (~ ($true = ((var @ X34))) | (((X33 @ (sub @ X34 @ X31))) = $true)) | (((X33 @ (sub @ X32 @ X31))) = $true) | ~ ! [X35 : term,X36 : term] : (~ (((X33 @ X35)) = $true) | ($true = ((X33 @ (ap @ X36 @ X35)))) | ~ (((X33 @ X36)) = $true)) | ~ ! [X37 : term] : (~ ! [X38 : term] : (($true = ((X33 @ (sub @ X37 @ (push @ X38 @ id))))) | ~ ($true = ((X33 @ X38)))) | (((X33 @ (lam @ X37))) = $true)))) & (one = ((d2term @ d_one))) & (hoaslaminj_gthm = $true) & (((d2subst @ d_id)) = id) & (! [X39 : term] : ~ ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ X39 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (axabs = $true) & ((hoaslaminj_lthm = $true) <=> (! [X42 : subst,X41 : term] : (((sub @ one @ (push @ X41 @ X42))) = X41) => (! [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) = X44) => (! [X45 : term,X46 : term] : ((X45 = X46) | (((lam @ X46)) != ((lam @ X45)))) => ! [X50 : subst,X49 : (subst > term > term),X48 : term,X47 : (subst > term > term)] : ((((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one)))) | ~ ! [X55 : subst,X54 : term,X56 : subst] : (((sub @ (X47 @ X56 @ X54) @ X55)) = ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55)))) | ~ ! [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) = ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48)))))))) & ((hoasapinj2 = $true) <=> ! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58))) & (! [X61 : term,X62 : (term > $o)] : (~ ! [X63 : term,X64 : term] : ((((X62 @ (ap @ X64 @ X63))) = $true) | ~ ($true = ((X62 @ X63))) | ~ ($true = ((X62 @ X64)))) | (((X62 @ X61)) = $true) | ~ ! [X65 : term] : ((((X62 @ X65)) = $true) | ~ (((var @ X65)) = $true)) | ~ ! [X66 : term] : (~ ($true = ((X62 @ X66))) | (((X62 @ (lam @ X66))) = $true))) <=> (induction = $true)) & (induction2_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : term] : (~ ! [X69 : term] : (~ (((X67 @ id @ X69 @ id)) = $true) | (((X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) = $true)) | (((X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X70 : (subst > term > term)] : (~ ! [X71 : term] : (~ (((X67 @ id @ X71 @ id)) = $true) | (((X67 @ id @ (X70 @ id @ X71) @ id)) = $true)) | ($true = ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ~ ! [X74 : term,X72 : subst,X73 : subst] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapnotvar_gthm = $true) & ! [X75 : d_subst] : (d_id = X75) & (hoaslamnotvar_gthm = $true) & ((! [X78 : term,X76 : term,X79 : term,X77 : term] : ((X76 = X78) | (((ap @ X77 @ X76)) != ((ap @ X79 @ X78)))) => ! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83))) <=> (hoasapinj2_lthm = $true)) & (! [X84 : term] : ~ ! [X85 : (subst > term > term)] : ~ ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_lem3a_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X89 : term,X90 : term,X88 : (subst > term > term)] : (~ ! [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X88 @ X92 @ X93) @ X91))) | (((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))))) & (pushprop_lem3v2_lthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (induction2lem_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lthm = $true) <=> (! [X94 : (term > $o),X95 : term] : (~ ! [X96 : term,X97 : term] : ((((X94 @ (ap @ X96 @ X97))) = $true) | ~ ($true = ((X94 @ X97))) | ~ (((X94 @ X96)) = $true)) | ~ ! [X98 : term] : ((((X94 @ (lam @ X98))) = $true) | ~ ! [X99 : term] : ((((X94 @ (sub @ X98 @ (push @ X99 @ id)))) = $true) | ~ ($true = ((X94 @ X99))))) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | ~ (((var @ X100)) = $true)) | (((X94 @ X95)) = $true)) => (! [X101 : term,X102 : term,X103 : (subst > term > subst > $o)] : (~ ! [X104 : term,X105 : subst,X106 : subst,X107 : subst] : (~ (((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107)) = $true) | (((X103 @ X105 @ X104 @ (comp @ X106 @ X107))) = $true)) | ($true = ((X103 @ id @ (ap @ X102 @ X101) @ id))) | ~ ! [X108 : term,X109 : term] : (~ (((X103 @ id @ X109 @ id)) = $true) | ($true = ((X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id))) | ~ ($true = ((X103 @ id @ X108 @ id)))) | ~ (((X103 @ id @ X101 @ id)) = $true) | ~ (((X103 @ id @ X102 @ id)) = $true) | ~ ! [X110 : subst,X111 : subst,X112 : term,X113 : subst] : (~ (((X103 @ X110 @ X112 @ (comp @ X111 @ X113))) = $true) | (((X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113)) = $true))) => (! [X114 : (subst > term > subst > $o),X115 : term] : (~ ! [X116 : subst,X117 : subst,X118 : subst,X119 : term] : (~ (((X114 @ X118 @ X119 @ (comp @ X117 @ X116))) = $true) | ($true = ((X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | ~ ! [X120 : term] : (~ (((X114 @ id @ X120 @ id)) = $true) | (((X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) = $true)) | ~ ! [X121 : (subst > term > term)] : (~ ! [X122 : term] : (($true = ((X114 @ id @ (X121 @ id @ X122) @ id))) | ~ ($true = ((X114 @ id @ X122 @ id)))) | ~ ! [X124 : subst,X123 : term,X125 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) = ((sub @ (X121 @ X124 @ X123) @ X125))) | (((X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true)) | (((X114 @ id @ (lam @ X115) @ id)) = $true) | ~ ! [X126 : subst,X127 : subst,X128 : subst,X129 : term] : ((((X114 @ X127 @ X129 @ (comp @ X128 @ X126))) = $true) | ~ ($true = ((X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))))) => ! [X130 : (subst > term > subst > $o),X131 : term] : (~ ! [X132 : (subst > term > term)] : (~ ! [X133 : subst,X135 : term,X134 : subst] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) | (((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) = $true) | ~ ! [X136 : term] : (~ ($true = ((X130 @ id @ X136 @ id))) | (((X130 @ id @ (X132 @ id @ X136) @ id)) = $true))) | ~ ! [X137 : term] : (~ ($true = ((var @ (sub @ X137 @ id)))) | (((X130 @ id @ X137 @ id)) = $true)) | ~ ! [X138 : term,X139 : term] : (~ ($true = ((X130 @ id @ X138 @ id))) | ~ (((X130 @ id @ X139 @ id)) = $true) | (((X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) = $true)) | ($true = ((X130 @ id @ X131 @ id))) | ~ ! [X140 : term,X141 : subst,X142 : subst,X143 : subst] : ((((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143)) = $true) | ~ ($true = ((X130 @ X141 @ X140 @ (comp @ X142 @ X143))))) | ~ ! [X144 : subst,X145 : term,X146 : subst,X147 : subst] : (~ (((X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146)) = $true) | (((X130 @ X147 @ X145 @ (comp @ X144 @ X146))) = $true))))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X148 : (subst > term > subst > $o)] : ~ ! [X149 : (term > $o)] : ~ ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))) & (hoasapinj2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((apinj2 = $true) <=> ! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154))))) & ((pushprop_lem1_lthm = $true) <=> (! [X155 : term,X156 : subst] : (((sub @ one @ (push @ X155 @ X156))) = X155) => (! [X158 : term,X157 : subst] : (((comp @ sh @ (push @ X158 @ X157))) = X157) => ! [X159 : term,X160 : term,X161 : subst,X162 : (term > $o),X163 : (term > $o)] : ((((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true) | ~ ($true = ((X163 @ X159))))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X164 : (subst > term > subst > $o)] : ~ ! [X165 : (term > $o)] : ~ ! [X166 : term] : (((X164 @ id @ X166 @ id)) = ((X165 @ X166))) => (! [X167 : term,X168 : (term > $o)] : (~ ! [X169 : term,X170 : term] : (~ ($true = ((X168 @ X169))) | (((X168 @ (ap @ X169 @ X170))) = $true) | ~ (((X168 @ X170)) = $true)) | ($true = ((X168 @ X167))) | ~ ! [X171 : term] : ((((X168 @ X171)) = $true) | ~ ($true = ((var @ X171)))) | ~ ! [X172 : term] : ((((X168 @ (lam @ X172))) = $true) | ~ ! [X173 : term] : ((((X168 @ (sub @ X172 @ (push @ X173 @ id)))) = $true) | ~ ($true = ((X168 @ X173)))))) => (! [X174 : term] : (((sub @ X174 @ id)) = X174) => (! [X175 : (subst > term > subst > $o),X176 : term,X177 : (term > $o)] : (~ ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) | ~ ! [X179 : term] : ((((X177 @ (sub @ X176 @ (push @ X179 @ id)))) = $true) | ~ (((X177 @ X179)) = $true)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : subst,X183 : subst,X182 : term] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) = ((sub @ (X180 @ X181 @ X182) @ X183))) | (((X175 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : term] : (~ (((X175 @ id @ X184 @ id)) = $true) | (((X175 @ id @ (X180 @ id @ X184) @ id)) = $true))) | (((X177 @ (lam @ X176))) = $true)) => ! [X185 : (subst > term > subst > $o),X186 : term] : (~ ! [X187 : term,X188 : term] : (~ ($true = ((X185 @ id @ X188 @ id))) | (((X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id)) = $true) | ~ (((X185 @ id @ X187 @ id)) = $true)) | ~ ! [X189 : term] : (($true = ((X185 @ id @ X189 @ id))) | ~ ($true = ((var @ (sub @ X189 @ id))))) | ~ ! [X190 : subst,X191 : subst,X192 : subst,X193 : term] : ((((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191)) = $true) | ~ (((X185 @ X190 @ X193 @ (comp @ X192 @ X191))) = $true)) | ~ ! [X194 : (subst > term > term)] : (~ ! [X197 : term,X196 : subst,X195 : subst] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196))) | (((X185 @ id @ (lam @ (X194 @ sh @ one)) @ id)) = $true) | ~ ! [X198 : term] : (~ (((X185 @ id @ X198 @ id)) = $true) | (((X185 @ id @ (X194 @ id @ X198) @ id)) = $true))) | (((X185 @ id @ X186 @ id)) = $true) | ~ ! [X199 : subst,X200 : term,X201 : subst,X202 : subst] : (~ ($true = ((X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202))) | ($true = ((X185 @ X199 @ X200 @ (comp @ X201 @ X202))))))))))) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) = ((d2subst @ X203))) => (X203 = X204)) & ((induction2 = $true) <=> ! [X205 : term,X206 : (term > $o)] : (~ ! [X207 : term,X208 : term] : (~ ($true = ((X206 @ X208))) | ($true = ((X206 @ (ap @ X208 @ X207)))) | ~ (((X206 @ X207)) = $true)) | ~ ! [X209 : term] : (~ (((var @ X209)) = $true) | (((X206 @ X209)) = $true)) | ~ ! [X210 : term] : ((((X206 @ (lam @ X210))) = $true) | ~ ! [X211 : term] : (~ (((X206 @ X211)) = $true) | ($true = ((X206 @ (sub @ X210 @ (push @ X211 @ id))))))) | (((X206 @ X205)) = $true))) & (! [X212 : term,X213 : term,X214 : (subst > term > subst > $o)] : (~ ! [X215 : term,X216 : term] : (~ (((X214 @ id @ X216 @ id)) = $true) | ~ ($true = ((X214 @ id @ X215 @ id))) | ($true = ((X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id)))) | (((X214 @ id @ (ap @ X212 @ X213) @ id)) = $true) | ~ ! [X217 : term,X218 : subst,X219 : subst,X220 : subst] : (($true = ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)))) | ~ ($true = ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)))) | ~ (((X214 @ id @ X212 @ id)) = $true) | ~ ! [X221 : subst,X222 : term,X223 : subst,X224 : subst] : (($true = ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221))) | ~ (((X214 @ X223 @ X222 @ (comp @ X224 @ X221))) = $true)) | ~ (((X214 @ id @ X213 @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X225 : term] : ~ ! [X226 : (subst > term > term)] : ~ ! [X228 : term,X227 : subst] : (((sub @ X225 @ (push @ X228 @ X227))) = ((X226 @ X227 @ X228))) => (! [X229 : term] : (((sub @ X229 @ id)) = X229) => ! [X230 : term,X231 : (subst > term > subst > $o),X232 : (term > $o)] : (~ ! [X233 : (subst > term > term)] : (~ ! [X234 : term] : (($true = ((X231 @ id @ (X233 @ id @ X234) @ id))) | ~ (((X231 @ id @ X234 @ id)) = $true)) | ~ ! [X235 : subst,X237 : term,X236 : subst] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235)))) | (((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) = $true)) | ~ ! [X238 : term] : (((X232 @ X238)) = ((X231 @ id @ X238 @ id))) | (((X232 @ (lam @ X230))) = $true) | ~ ! [X239 : term] : (($true = ((X232 @ (sub @ X230 @ (push @ X239 @ id))))) | ~ (((X232 @ X239)) = $true)))))) & (axclos = $true) & ((pushprop_lem1v2 = $true) <=> ! [X240 : subst,X241 : (term > $o),X242 : term,X243 : (term > $o)] : (~ ($true = ((X243 @ X242))) | ~ ! [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) = ((X241 @ X244))) | (((X241 @ one)) = $true))) & (! [X245 : term] : (((sub @ X245 @ id)) = X245) <=> (axvarid = $true)) & (pushprop_gthm = $true) & ((hoasinduction = $true) <=> ! [X246 : (subst > term > subst > $o),X247 : term] : (~ ! [X248 : (subst > term > term)] : (($true = ((X246 @ id @ (lam @ (X248 @ sh @ one)) @ id))) | ~ ! [X249 : subst,X250 : term,X251 : subst] : (((sub @ (X248 @ X249 @ X250) @ X251)) = ((X248 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251)))) | ~ ! [X252 : term] : ((((X246 @ id @ (X248 @ id @ X252) @ id)) = $true) | ~ (((X246 @ id @ X252 @ id)) = $true))) | ~ ! [X253 : subst,X254 : subst,X255 : term,X256 : subst] : (($true = ((X246 @ (comp @ X256 @ X254) @ (sub @ X255 @ X254) @ X253))) | ~ (((X246 @ X256 @ X255 @ (comp @ X254 @ X253))) = $true)) | ~ ! [X257 : term] : (($true = ((X246 @ id @ X257 @ id))) | ~ (((var @ (sub @ X257 @ id))) = $true)) | ~ ! [X258 : term,X259 : term] : (~ ($true = ((X246 @ id @ X259 @ id))) | ~ ($true = ((X246 @ id @ X258 @ id))) | (((X246 @ id @ (ap @ (sub @ X259 @ id) @ X258) @ id)) = $true)) | (((X246 @ id @ X247 @ id)) = $true) | ~ ! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (~ (((X246 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) = $true) | ($true = ((X246 @ X260 @ X261 @ (comp @ X263 @ X262))))))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_gthm = $true) & ((! [X264 : term] : (((sub @ X264 @ id)) = X264) => (! [X265 : (term > $o),X266 : subst,X267 : term] : ((((X265 @ (sub @ X267 @ X266))) = $true) | ~ ! [X268 : term] : (~ ! [X269 : term] : (($true = ((X265 @ (sub @ X268 @ (push @ X269 @ id))))) | ~ (((X265 @ X269)) = $true)) | (((X265 @ (lam @ X268))) = $true)) | ~ ! [X270 : term] : ((((X265 @ (sub @ X270 @ X266))) = $true) | ~ (((var @ X270)) = $true)) | ~ ! [X271 : term,X272 : term] : (~ (((X265 @ X272)) = $true) | (((X265 @ (ap @ X272 @ X271))) = $true) | ~ ($true = ((X265 @ X271))))) => ! [X273 : term,X274 : (term > $o)] : (~ ! [X275 : term,X276 : term] : (~ (((X274 @ X276)) = $true) | (((X274 @ (ap @ X276 @ X275))) = $true) | ~ (((X274 @ X275)) = $true)) | ~ ! [X277 : term] : (($true = ((X274 @ (lam @ X277)))) | ~ ! [X278 : term] : (~ (((X274 @ X278)) = $true) | (((X274 @ (sub @ X277 @ (push @ X278 @ id)))) = $true))) | (((X274 @ X273)) = $true) | ~ ! [X279 : term] : (~ (((var @ X279)) = $true) | (((X274 @ X279)) = $true))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) = X281) => ! [X282 : (term > $o),X283 : subst,X284 : term,X285 : (term > $o)] : (~ (((X285 @ X284)) = $true) | ~ ! [X286 : term] : (((X282 @ X286)) = ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) | ($true = ((X282 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem1_gthm = $true) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & (! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) <=> (axshiftcons = $true)) & ((axvarcons = $true) <=> ! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291)) & (axmap = $true) & ((! [X293 : term] : (((sub @ X293 @ id)) = X293) => (! [X295 : term,X294 : term,X297 : term,X296 : term] : ((X295 = X296) | (((ap @ X295 @ X294)) != ((ap @ X296 @ X297)))) => ! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300)))) <=> (hoasapinj1_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X302 : d_term] : (d_one = X302) & (pushprop_lem0_gthm = $true) & (substmonoid_gthm = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X303 : (subst > term > subst > $o),X304 : term] : (~ ! [X305 : (subst > term > term)] : (($true = ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id))) | ~ ! [X306 : term] : (~ (((X303 @ id @ X306 @ id)) = $true) | (((X303 @ id @ (X305 @ id @ X306) @ id)) = $true)) | ~ ! [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) = ((sub @ (X305 @ X307 @ X309) @ X308)))) | (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X310 : term] : (($true = ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id))) | ~ (((X303 @ id @ X310 @ id)) = $true)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X311 : term,X312 : (subst > term > subst > $o)] : (~ ! [X313 : (subst > term > term)] : (($true = ((X312 @ id @ (lam @ (X313 @ sh @ one)) @ id))) | ~ ! [X315 : term,X314 : subst,X316 : subst] : (((sub @ (X313 @ X314 @ X315) @ X316)) = ((X313 @ (comp @ X314 @ X316) @ (sub @ X315 @ X316)))) | ~ ! [X317 : term] : (~ (((X312 @ id @ X317 @ id)) = $true) | ($true = ((X312 @ id @ (X313 @ id @ X317) @ id))))) | ($true = ((X312 @ id @ X311 @ id))) | ~ ! [X318 : term,X319 : term] : (~ (((X312 @ id @ X319 @ id)) = $true) | (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) = $true) | ~ (((X312 @ id @ X318 @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & (! [X320 : (term > $o),X322 : subst,X321 : term] : ~ ! [X323 : (term > $o)] : ~ ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322))))) <=> (pushprop_lem0_lthm = $true)) & ((! [X325 : subst] : (((comp @ id @ X325)) = X325) => (! [X326 : subst] : (((comp @ X326 @ id)) = X326) => (! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327)))) <=> (substmonoid_lthm = $true)) & (! [X329 : term] : ~ ! [X330 : (subst > term > term)] : ~ ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X333 : term,X334 : subst,X335 : (term > $o),X336 : term,X337 : (term > $o)] : (~ ($true = ((X335 @ X333))) | ($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334)))))) <=> (pushprop_lem1 = $true)) & (! [X338 : (subst > term > subst > $o)] : ~ ! [X339 : (term > $o)] : ~ ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((termmset = $true) <=> ! [X341 : term] : (((sub @ X341 @ id)) = X341)) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1_gthm = $true) & ((laminj = $true) <=> ! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X344 : term] : (((sub @ X344 @ id)) = X344) => (! [X345 : term,X346 : (subst > term > subst > $o)] : ((((X346 @ id @ (lam @ (sub @ X345 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X347 : term] : (~ ($true = ((X346 @ id @ X347 @ id))) | (((X346 @ id @ (sub @ X345 @ (push @ X347 @ id)) @ id)) = $true)) | ~ ! [X348 : (subst > term > term)] : (~ ! [X349 : term] : (($true = ((X346 @ id @ (X348 @ id @ X349) @ id))) | ~ (((X346 @ id @ X349 @ id)) = $true)) | ~ ! [X350 : subst,X352 : term,X351 : subst] : (((X348 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351))) = ((sub @ (X348 @ X350 @ X352) @ X351))) | (((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id)) = $true))) => ! [X353 : (subst > term > subst > $o),X354 : term] : (~ ! [X355 : (subst > term > term)] : (~ ! [X356 : term] : (~ ($true = ((X353 @ id @ X356 @ id))) | (((X353 @ id @ (X355 @ id @ X356) @ id)) = $true)) | ~ ! [X358 : subst,X359 : term,X357 : subst] : (((sub @ (X355 @ X358 @ X359) @ X357)) = ((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357)))) | ($true = ((X353 @ id @ (lam @ (X355 @ sh @ one)) @ id)))) | ~ ! [X360 : subst,X361 : term,X362 : subst,X363 : subst] : (~ ($true = ((X353 @ X363 @ X361 @ (comp @ X360 @ X362)))) | (((X353 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362)) = $true)) | ~ ! [X364 : term,X365 : subst,X366 : subst,X367 : subst] : (~ (((X353 @ (comp @ X365 @ X366) @ (sub @ X364 @ X366) @ X367)) = $true) | (((X353 @ X365 @ X364 @ (comp @ X366 @ X367))) = $true)) | ($true = ((X353 @ id @ (lam @ X354) @ id))) | ~ ! [X368 : term] : ((((X353 @ id @ (sub @ X354 @ (push @ X368 @ id)) @ id)) = $true) | ~ (((X353 @ id @ X368 @ id)) = $true)))))) & (! [X369 : term,X370 : (subst > term > subst > $o)] : (~ ! [X371 : term,X372 : (subst > term > term)] : (~ ! [X375 : subst,X373 : term,X374 : subst] : (((X372 @ (comp @ X375 @ X374) @ (sub @ X373 @ X374))) = ((sub @ X371 @ (push @ (sub @ X373 @ X374) @ (comp @ X375 @ X374))))) | ~ ! [X378 : subst,X377 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X377) @ X378)) = ((sub @ (sub @ X371 @ (push @ X377 @ X376)) @ X378))) | ~ ! [X379 : term] : (~ (((X370 @ id @ X379 @ id)) = $true) | (((X370 @ id @ (X372 @ id @ X379) @ id)) = $true)) | (((X370 @ id @ (lam @ (X372 @ sh @ one)) @ id)) = $true)) | (((X370 @ id @ (lam @ (sub @ X369 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X380 : term] : ((((X370 @ id @ (sub @ X369 @ (push @ X380 @ id)) @ id)) = $true) | ~ ($true = ((X370 @ id @ X380 @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ((pushprop_lem0 = $true) <=> ! [X383 : (term > $o),X382 : term,X381 : subst] : ~ ! [X384 : (term > $o)] : ~ ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (pushprop_lem3v2 = $true) & (hoaslamnotvar = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ~ (ulamvar1 = $true) & (lamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3a = $true) <=> ! [X386 : (subst > term > subst > $o),X387 : term] : ((((X386 @ id @ (lam @ X387) @ id)) = $true) | ~ ! [X388 : (subst > term > term)] : (~ ! [X389 : term] : ((((X386 @ id @ (X388 @ id @ X389) @ id)) = $true) | ~ (((X386 @ id @ X389 @ id)) = $true)) | ~ ! [X392 : term,X391 : subst,X390 : subst] : (((sub @ (X388 @ X391 @ X392) @ X390)) = ((X388 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) | (((X386 @ id @ (lam @ (X388 @ sh @ one)) @ id)) = $true)) | ~ ! [X393 : term] : (~ (((X386 @ id @ X393 @ id)) = $true) | ($true = ((X386 @ id @ (sub @ X387 @ (push @ X393 @ id)) @ id)))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X394 : term,X395 : (term > $o),X396 : (subst > term > subst > $o),X397 : term] : (~ ! [X398 : term] : (((X396 @ id @ X398 @ id)) = ((X395 @ X398))) | ~ ! [X399 : subst,X400 : term,X401 : subst,X402 : subst] : (~ (((X396 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401) @ X399)) = $true) | (((X396 @ X402 @ X400 @ (comp @ X401 @ X399))) = $true)) | ~ (((X395 @ X397)) = $true) | ~ ! [X403 : term,X404 : subst,X405 : subst,X406 : subst] : (~ ($true = ((X396 @ X406 @ X403 @ (comp @ X404 @ X405)))) | (((X396 @ (comp @ X406 @ X404) @ (sub @ X403 @ X404) @ X405)) = $true)) | ~ (((X395 @ X394)) = $true) | (((X395 @ (ap @ X394 @ X397))) = $true) | ~ ! [X407 : term,X408 : term] : (~ (((X396 @ id @ X407 @ id)) = $true) | ~ (((X396 @ id @ X408 @ id)) = $true) | (((X396 @ id @ (ap @ (sub @ X407 @ id) @ X408) @ id)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ! [X409 : d_term,X410 : d_term] : ((((d2term @ X410)) = ((d2term @ X409))) => (X409 = X410)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (! [X411 : subst] : (((comp @ X411 @ id)) = X411) <=> (axidr = $true)) & ((axscons = $true) <=> ! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412)) & (pushprop_lem2v2 = $true) & (! [X413 : (subst > term > subst > $o),X414 : term] : (($true = ((X413 @ id @ (lam @ X414) @ id))) | ~ ! [X415 : (subst > term > term)] : (~ ! [X416 : term,X417 : subst,X418 : subst] : (((X415 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417))) = ((sub @ (X415 @ X418 @ X416) @ X417))) | (((X413 @ id @ (lam @ (X415 @ sh @ one)) @ id)) = $true) | ~ ! [X419 : term] : (~ (((X413 @ id @ X419 @ id)) = $true) | (((X413 @ id @ (X415 @ id @ X419) @ id)) = $true))) | ~ ! [X420 : subst,X421 : subst,X422 : term,X423 : subst] : (~ (((X413 @ X421 @ X422 @ (comp @ X423 @ X420))) = $true) | ($true = ((X413 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423) @ X420)))) | ~ ! [X424 : term] : ((((X413 @ id @ (sub @ X414 @ (push @ X424 @ id)) @ id)) = $true) | ~ ($true = ((X413 @ id @ X424 @ id)))) | ~ ! [X425 : subst,X426 : term,X427 : subst,X428 : subst] : (($true = ((X413 @ X425 @ X426 @ (comp @ X427 @ X428)))) | ~ ($true = ((X413 @ (comp @ X425 @ X427) @ (sub @ X426 @ X427) @ X428))))) <=> (hoasinduction_lem3 = $true)) & ~ (lamnotap = $true) & (! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) <=> (shinj = $true)) & (! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) <=> (apinj1 = $true)) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X435 : (subst > term > subst > $o),X436 : term,X437 : (term > $o)] : (~ ! [X438 : term] : (((X437 @ X438)) = ((X435 @ id @ X438 @ id))) | ~ ! [X439 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X439 @ sh @ one)) @ id)) = $true) | ~ ! [X440 : term] : ((((X435 @ id @ (X439 @ id @ X440) @ id)) = $true) | ~ (((X435 @ id @ X440 @ id)) = $true)) | ~ ! [X442 : subst,X441 : term,X443 : subst] : (((sub @ (X439 @ X443 @ X441) @ X442)) = ((X439 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))))) | (((X437 @ (lam @ X436))) = $true) | ~ ! [X444 : term] : ((((X437 @ (sub @ X436 @ (push @ X444 @ id)))) = $true) | ~ ($true = ((X437 @ X444)))))) & (! [X445 : (term > $o),X446 : (subst > term > subst > $o),X447 : term] : (~ ! [X448 : subst,X449 : subst,X450 : subst,X451 : term] : (~ ($true = ((X446 @ X450 @ X451 @ (comp @ X449 @ X448)))) | (((X446 @ (comp @ X450 @ X449) @ (sub @ X451 @ X449) @ X448)) = $true)) | ~ ! [X452 : subst,X453 : term,X454 : subst,X455 : subst] : ((((X446 @ X455 @ X453 @ (comp @ X452 @ X454))) = $true) | ~ ($true = ((X446 @ (comp @ X455 @ X452) @ (sub @ X453 @ X452) @ X454)))) | ~ ! [X456 : term] : (((X446 @ id @ X456 @ id)) = ((X445 @ X456))) | ($true = ((X445 @ (lam @ X447)))) | ~ ! [X457 : term] : ((((X445 @ (sub @ X447 @ (push @ X457 @ id)))) = $true) | ~ (((X445 @ X457)) = $true)) | ~ ! [X458 : (subst > term > term)] : (~ ! [X459 : term,X460 : subst,X461 : subst] : (((sub @ (X458 @ X460 @ X459) @ X461)) = ((X458 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461)))) | ($true = ((X446 @ id @ (lam @ (X458 @ sh @ one)) @ id))) | ~ ! [X462 : term] : (~ (((X446 @ id @ X462 @ id)) = $true) | ($true = ((X446 @ id @ (X458 @ id @ X462) @ id)))))) <=> (hoasinduction_lem3v2 = $true)) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (apnotvar = $true) & (hoasapnotvar = $true) & (! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) <=> (hoasapinj1 = $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X469 : term] : (((sub @ X469 @ id)) = X469) => ! [X470 : term,X471 : (term > $o),X472 : (subst > term > subst > $o)] : (~ ! [X473 : (subst > term > term)] : ((((X472 @ id @ (lam @ (X473 @ sh @ one)) @ id)) = $true) | ~ ! [X474 : term] : (~ (((X472 @ id @ X474 @ id)) = $true) | (((X472 @ id @ (X473 @ id @ X474) @ id)) = $true)) | ~ ! [X477 : subst,X476 : term,X475 : subst] : (((X473 @ (comp @ X475 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X473 @ X475 @ X476) @ X477)))) | ~ ! [X478 : subst,X479 : term,X480 : subst,X481 : subst] : (~ (((X472 @ X481 @ X479 @ (comp @ X478 @ X480))) = $true) | (((X472 @ (comp @ X481 @ X478) @ (sub @ X479 @ X478) @ X480)) = $true)) | ~ ! [X482 : term] : (~ ($true = ((X471 @ X482))) | ($true = ((X471 @ (sub @ X470 @ (push @ X482 @ id)))))) | ($true = ((X471 @ (lam @ X470)))) | ~ ! [X483 : term,X484 : subst,X485 : subst,X486 : subst] : ((((X472 @ X485 @ X483 @ (comp @ X484 @ X486))) = $true) | ~ (((X472 @ (comp @ X485 @ X484) @ (sub @ X483 @ X484) @ X486)) = $true)) | ~ ! [X487 : term] : (((X471 @ X487)) = ((X472 @ id @ X487 @ id)))))) & ((termmset_lthm = $true) <=> (! [X488 : term] : (((sub @ X488 @ id)) = X488) => ! [X489 : term] : (((sub @ X489 @ id)) = X489))) & ((induction2lem_lthm = $true) <=> (! [X490 : subst,X491 : term] : (((sub @ one @ (push @ X491 @ X490))) = X491) => (! [X492 : subst,X493 : term] : (((comp @ sh @ (push @ X493 @ X492))) = X492) => (! [X494 : subst] : (((comp @ X494 @ id)) = X494) => (! [X495 : term,X496 : (term > $o)] : (~ ! [X497 : term] : ((((X496 @ (lam @ X497))) = $true) | ~ (((X496 @ X497)) = $true)) | ~ ! [X498 : term,X499 : term] : (~ ($true = ((X496 @ X499))) | (((X496 @ (ap @ X498 @ X499))) = $true) | ~ (((X496 @ X498)) = $true)) | (((X496 @ X495)) = $true) | ~ ! [X500 : term] : ((((X496 @ X500)) = $true) | ~ ($true = ((var @ X500))))) => ! [X501 : (term > $o),X502 : subst,X503 : term] : (~ ! [X504 : term] : (~ ! [X505 : term] : (~ (((X501 @ X505)) = $true) | (((X501 @ (sub @ X504 @ (push @ X505 @ id)))) = $true)) | (((X501 @ (lam @ X504))) = $true)) | (((X501 @ (sub @ X503 @ X502))) = $true) | ~ ! [X506 : term] : (~ (((var @ X506)) = $true) | ($true = ((X501 @ (sub @ X506 @ X502))))) | ~ ! [X507 : term,X508 : term] : (($true = ((X501 @ (ap @ X507 @ X508)))) | ~ ($true = ((X501 @ X508))) | ~ (((X501 @ X507)) = $true)))))))) & (hoasinduction_lem1v2_gthm = $true) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & (((d2subst @ d_id)) = sh) & ((hoaslaminj = $true) <=> ! [X513 : (subst > term > term),X514 : term,X512 : (subst > term > term),X511 : subst] : (~ ! [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) = ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | ~ ! [X520 : subst,X519 : term,X518 : subst] : (((sub @ (X512 @ X518 @ X519) @ X520)) = ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514))) | (((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X521 : term] : (((sub @ X521 @ id)) = X521) => (! [X522 : (subst > term > subst > $o),X523 : term] : (~ ! [X524 : (subst > term > term)] : (~ ! [X525 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X525)) = ((X524 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | ~ ! [X528 : term] : (~ (((X522 @ id @ X528 @ id)) = $true) | (((X522 @ id @ (X524 @ id @ X528) @ id)) = $true)) | (((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)) = $true)) | ~ ! [X529 : term] : (($true = ((X522 @ id @ (sub @ X523 @ (push @ X529 @ id)) @ id))) | ~ (((X522 @ id @ X529 @ id)) = $true)) | (((X522 @ id @ (lam @ (sub @ X523 @ (push @ one @ sh))) @ id)) = $true)) => ! [X530 : term,X531 : (subst > term > subst > $o)] : (~ ! [X532 : term] : (~ ($true = ((X531 @ id @ X532 @ id))) | ($true = ((X531 @ id @ (sub @ X530 @ (push @ X532 @ id)) @ id)))) | ~ ! [X533 : (subst > term > term)] : (~ ! [X535 : subst,X536 : subst,X534 : term] : (((sub @ (X533 @ X536 @ X534) @ X535)) = ((X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535)))) | ($true = ((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id))) | ~ ! [X537 : term] : (($true = ((X531 @ id @ (X533 @ id @ X537) @ id))) | ~ ($true = ((X531 @ id @ X537 @ id))))) | (((X531 @ id @ (lam @ X530) @ id)) = $true))))) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ~ ! [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) != ((X539 @ sh @ one)))) & (hoasinduction_lem3_gthm = $true) & (ulamvarsh = $true)),
% 6.34/1.36 inference(rectify,[],[f7])).
% 6.34/1.36 thf(f10,plain,(
% 6.34/1.36 (! [X320 : (term > $o),X322 : subst,X321 : term] : ~ ! [X323 : (term > $o)] : ~ ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322))))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((axvarcons = $true) <=> ! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291)) & ((hoasinduction_lem3aaa = $true) <=> ! [X370 : (subst > term > subst > $o),X369 : term] : (~ ! [X380 : term] : (($true != ((X370 @ id @ X380 @ id))) | (((X370 @ id @ (sub @ X369 @ (push @ X380 @ id)) @ id)) = $true)) | ~ ! [X371 : term,X372 : (subst > term > term)] : (~ ! [X378 : subst,X377 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X377) @ X378)) = ((sub @ (sub @ X371 @ (push @ X377 @ X376)) @ X378))) | (((X370 @ id @ (lam @ (X372 @ sh @ one)) @ id)) = $true) | ~ ! [X375 : subst,X373 : term,X374 : subst] : (((X372 @ (comp @ X375 @ X374) @ (sub @ X373 @ X374))) = ((sub @ X371 @ (push @ (sub @ X373 @ X374) @ (comp @ X375 @ X374))))) | ~ ! [X379 : term] : ((((X370 @ id @ (X372 @ id @ X379) @ id)) = $true) | (((X370 @ id @ X379 @ id)) != $true))) | (((X370 @ id @ (lam @ (sub @ X369 @ (push @ one @ sh))) @ id)) = $true))) & ((! [X293 : term] : (((sub @ X293 @ id)) = X293) => (! [X295 : term,X294 : term,X297 : term,X296 : term] : ((X295 = X296) | (((ap @ X295 @ X294)) != ((ap @ X296 @ X297)))) => ! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300)))) <=> (hoasapinj1_lthm = $true)) & (! [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) | ($true != ((X335 @ X333)))) <=> (pushprop_lem1 = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj2 = $true) <=> ! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58))) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & ((! [X78 : term,X76 : term,X79 : term,X77 : term] : ((X76 = X78) | (((ap @ X77 @ X76)) != ((ap @ X79 @ X78)))) => ! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83))) <=> (hoasapinj2_lthm = $true)) & (axmap = $true) & (! [X245 : term] : (((sub @ X245 @ id)) = X245) <=> (axvarid = $true)) & (pushprop_lthm_orig = $true) & ((! [X325 : subst] : (((comp @ id @ X325)) = X325) => (! [X326 : subst] : (((comp @ X326 @ id)) = X326) => (! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327)))) <=> (substmonoid_lthm = $true)) & (! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) <=> (apinj1 = $true)) & (lamnotap != $true) & ! [X75 : d_subst] : (d_id = X75) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X68 : term,X67 : (subst > term > subst > $o)] : (~ ! [X70 : (subst > term > term)] : (($true = ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id))) | ~ ! [X71 : term] : ((((X67 @ id @ (X70 @ id @ X71) @ id)) = $true) | (((X67 @ id @ X71 @ id)) != $true)) | ~ ! [X74 : term,X72 : subst,X73 : subst] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72)))) | ~ ! [X69 : term] : ((((X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) = $true) | (((X67 @ id @ X69 @ id)) != $true)) | (((X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)) = $true))) & (hoasinduction_lem1 = $true) & (! [X213 : term,X212 : term,X214 : (subst > term > subst > $o)] : (~ ! [X216 : term,X215 : term] : (($true = ((X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))) | (((X214 @ id @ X216 @ id)) != $true) | ($true != ((X214 @ id @ X215 @ id)))) | (((X214 @ id @ X212 @ id)) != $true) | ~ ! [X218 : subst,X217 : term,X219 : subst,X220 : subst] : (($true = ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)))) | ($true != ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)))) | (((X214 @ id @ (ap @ X212 @ X213) @ id)) = $true) | ~ ! [X223 : subst,X224 : subst,X222 : term,X221 : subst] : (($true = ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221))) | (((X214 @ X223 @ X222 @ (comp @ X224 @ X221))) != $true)) | (((X214 @ id @ X213 @ id)) != $true)) <=> (hoasinduction_lem2 = $true)) & ! [X409 : d_term,X410 : d_term] : ((((d2term @ X410)) = ((d2term @ X409))) => (X409 = X410)) & (one = ((d2term @ d_one))) & (hoasinduction_lem1v2 = $true) & (pushprop_lthm = $true) & (! [X414 : term,X413 : (subst > term > subst > $o)] : (~ ! [X423 : subst,X422 : term,X421 : subst,X420 : subst] : (($true = ((X413 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423) @ X420))) | (((X413 @ X421 @ X422 @ (comp @ X423 @ X420))) != $true)) | ~ ! [X428 : subst,X426 : term,X425 : subst,X427 : subst] : (($true = ((X413 @ X425 @ X426 @ (comp @ X427 @ X428)))) | ($true != ((X413 @ (comp @ X425 @ X427) @ (sub @ X426 @ X427) @ X428)))) | ~ ! [X415 : (subst > term > term)] : (~ ! [X416 : term,X417 : subst,X418 : subst] : (((X415 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417))) = ((sub @ (X415 @ X418 @ X416) @ X417))) | (((X413 @ id @ (lam @ (X415 @ sh @ one)) @ id)) = $true) | ~ ! [X419 : term] : ((((X413 @ id @ (X415 @ id @ X419) @ id)) = $true) | (((X413 @ id @ X419 @ id)) != $true))) | ~ ! [X424 : term] : (($true != ((X413 @ id @ X424 @ id))) | (((X413 @ id @ (sub @ X414 @ (push @ X424 @ id)) @ id)) = $true)) | ($true = ((X413 @ id @ (lam @ X414) @ id)))) <=> (hoasinduction_lem3 = $true)) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) = X281) => ! [X282 : (term > $o),X284 : term,X285 : (term > $o),X283 : subst] : ((((X285 @ X284)) != $true) | ($true = ((X282 @ one))) | ~ ! [X286 : term] : (((X282 @ X286)) = ((X285 @ (sub @ X286 @ (push @ X284 @ X283)))))))) & (hoaslamnotap_lthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X42 : subst,X41 : term] : (((sub @ one @ (push @ X41 @ X42))) = X41) => (! [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) = X44) => (! [X45 : term,X46 : term] : ((X45 = X46) | (((lam @ X46)) != ((lam @ X45)))) => ! [X50 : subst,X49 : (subst > term > term),X48 : term,X47 : (subst > term > term)] : ((((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one)))) | ~ ! [X55 : subst,X54 : term,X56 : subst] : (((sub @ (X47 @ X56 @ X54) @ X55)) = ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55)))) | ~ ! [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) = ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48)))))))) & (! [X84 : term] : ~ ! [X85 : (subst > term > term)] : ~ ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86))) <=> (hoasinduction_lem3v2_f = $true)) & ((! [X164 : (subst > term > subst > $o)] : ~ ! [X165 : (term > $o)] : ~ ! [X166 : term] : (((X164 @ id @ X166 @ id)) = ((X165 @ X166))) => (! [X168 : (term > $o),X167 : term] : (($true = ((X168 @ X167))) | ~ ! [X170 : term,X169 : term] : (($true != ((X168 @ X169))) | (((X168 @ X170)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)) | ~ ! [X171 : term] : (($true != ((var @ X171))) | (((X168 @ X171)) = $true)) | ~ ! [X172 : term] : ((((X168 @ (lam @ X172))) = $true) | ~ ! [X173 : term] : ((((X168 @ (sub @ X172 @ (push @ X173 @ id)))) = $true) | ($true != ((X168 @ X173)))))) => (! [X174 : term] : (((sub @ X174 @ id)) = X174) => (! [X177 : (term > $o),X176 : term,X175 : (subst > term > subst > $o)] : (~ ! [X179 : term] : ((((X177 @ X179)) != $true) | (((X177 @ (sub @ X176 @ (push @ X179 @ id)))) = $true)) | ~ ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) | (((X177 @ (lam @ X176))) = $true) | ~ ! [X180 : (subst > term > term)] : (~ ! [X184 : term] : ((((X175 @ id @ X184 @ id)) != $true) | (((X175 @ id @ (X180 @ id @ X184) @ id)) = $true)) | ~ ! [X181 : subst,X183 : subst,X182 : term] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) = ((sub @ (X180 @ X181 @ X182) @ X183))) | (((X175 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true))) => ! [X185 : (subst > term > subst > $o),X186 : term] : (~ ! [X190 : subst,X193 : term,X191 : subst,X192 : subst] : ((((X185 @ X190 @ X193 @ (comp @ X192 @ X191))) != $true) | (((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191)) = $true)) | ~ ! [X201 : subst,X200 : term,X202 : subst,X199 : subst] : (($true = ((X185 @ X199 @ X200 @ (comp @ X201 @ X202)))) | ($true != ((X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202)))) | ~ ! [X189 : term] : (($true = ((X185 @ id @ X189 @ id))) | ($true != ((var @ (sub @ X189 @ id))))) | ~ ! [X194 : (subst > term > term)] : ((((X185 @ id @ (lam @ (X194 @ sh @ one)) @ id)) = $true) | ~ ! [X198 : term] : ((((X185 @ id @ (X194 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) | ~ ! [X197 : term,X196 : subst,X195 : subst] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196)))) | (((X185 @ id @ X186 @ id)) = $true) | ~ ! [X187 : term,X188 : term] : ((((X185 @ id @ X187 @ id)) != $true) | ($true != ((X185 @ id @ X188 @ id))) | (((X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ~ ! [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) != ((X539 @ sh @ one)))) & (axvarshift = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X387 : term,X386 : (subst > term > subst > $o)] : (~ ! [X388 : (subst > term > term)] : (~ ! [X392 : term,X391 : subst,X390 : subst] : (((sub @ (X388 @ X391 @ X392) @ X390)) = ((X388 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) | (((X386 @ id @ (lam @ (X388 @ sh @ one)) @ id)) = $true) | ~ ! [X389 : term] : ((((X386 @ id @ (X388 @ id @ X389) @ id)) = $true) | (((X386 @ id @ X389 @ id)) != $true))) | ~ ! [X393 : term] : (($true = ((X386 @ id @ (sub @ X387 @ (push @ X393 @ id)) @ id))) | (((X386 @ id @ X393 @ id)) != $true)) | (((X386 @ id @ (lam @ X387) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & (! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) <=> (hoasapinj1 = $true)) & ((termmset_lthm = $true) <=> (! [X488 : term] : (((sub @ X488 @ id)) = X488) => ! [X489 : term] : (((sub @ X489 @ id)) = X489))) & ((termmset = $true) <=> ! [X341 : term] : (((sub @ X341 @ id)) = X341)) & (pushprop_lem2v2_lthm = $true) & (! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) <=> (shinj = $true)) & (((d2subst @ d_id)) = id) & ((laminj = $true) <=> ! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343))) & (! [X411 : subst] : (((comp @ X411 @ id)) = X411) <=> (axidr = $true)) & (axclos = $true) & (lamnotvar = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((pushprop_lem1_lthm = $true) <=> (! [X155 : term,X156 : subst] : (((sub @ one @ (push @ X155 @ X156))) = X155) => (! [X158 : term,X157 : subst] : (((comp @ sh @ (push @ X158 @ X157))) = X157) => ! [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true != ((X163 @ X159))) | (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X225 : term] : ~ ! [X226 : (subst > term > term)] : ~ ! [X228 : term,X227 : subst] : (((sub @ X225 @ (push @ X228 @ X227))) = ((X226 @ X227 @ X228))) => (! [X229 : term] : (((sub @ X229 @ id)) = X229) => ! [X231 : (subst > term > subst > $o),X232 : (term > $o),X230 : term] : (~ ! [X238 : term] : (((X232 @ X238)) = ((X231 @ id @ X238 @ id))) | (((X232 @ (lam @ X230))) = $true) | ~ ! [X239 : term] : (($true = ((X232 @ (sub @ X230 @ (push @ X239 @ id))))) | (((X232 @ X239)) != $true)) | ~ ! [X233 : (subst > term > term)] : ((((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) = $true) | ~ ! [X234 : term] : ((((X231 @ id @ X234 @ id)) != $true) | ($true = ((X231 @ id @ (X233 @ id @ X234) @ id)))) | ~ ! [X235 : subst,X237 : term,X236 : subst] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235))))))))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1v2 = $true) <=> ! [X240 : subst,X241 : (term > $o),X243 : (term > $o),X242 : term] : (~ ! [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) = ((X241 @ X244))) | (((X241 @ one)) = $true) | ($true != ((X243 @ X242))))) & (hoaslamnotap_gthm = $true) & ((! [X344 : term] : (((sub @ X344 @ id)) = X344) => (! [X346 : (subst > term > subst > $o),X345 : term] : (~ ! [X348 : (subst > term > term)] : (~ ! [X350 : subst,X352 : term,X351 : subst] : (((X348 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351))) = ((sub @ (X348 @ X350 @ X352) @ X351))) | ~ ! [X349 : term] : (($true = ((X346 @ id @ (X348 @ id @ X349) @ id))) | (((X346 @ id @ X349 @ id)) != $true)) | (((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id)) = $true)) | ~ ! [X347 : term] : ((((X346 @ id @ (sub @ X345 @ (push @ X347 @ id)) @ id)) = $true) | ($true != ((X346 @ id @ X347 @ id)))) | (((X346 @ id @ (lam @ (sub @ X345 @ (push @ one @ sh))) @ id)) = $true)) => ! [X354 : term,X353 : (subst > term > subst > $o)] : (~ ! [X355 : (subst > term > term)] : (~ ! [X356 : term] : (($true != ((X353 @ id @ X356 @ id))) | (((X353 @ id @ (X355 @ id @ X356) @ id)) = $true)) | ($true = ((X353 @ id @ (lam @ (X355 @ sh @ one)) @ id))) | ~ ! [X358 : subst,X359 : term,X357 : subst] : (((sub @ (X355 @ X358 @ X359) @ X357)) = ((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357))))) | ~ ! [X368 : term] : ((((X353 @ id @ (sub @ X354 @ (push @ X368 @ id)) @ id)) = $true) | (((X353 @ id @ X368 @ id)) != $true)) | ~ ! [X363 : subst,X362 : subst,X360 : subst,X361 : term] : ((((X353 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362)) = $true) | ($true != ((X353 @ X363 @ X361 @ (comp @ X360 @ X362))))) | ~ ! [X366 : subst,X364 : term,X367 : subst,X365 : subst] : ((((X353 @ (comp @ X365 @ X366) @ (sub @ X364 @ X366) @ X367)) != $true) | (((X353 @ X365 @ X364 @ (comp @ X366 @ X367))) = $true)) | ($true = ((X353 @ id @ (lam @ X354) @ id)))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & ((! [X490 : subst,X491 : term] : (((sub @ one @ (push @ X491 @ X490))) = X491) => (! [X492 : subst,X493 : term] : (((comp @ sh @ (push @ X493 @ X492))) = X492) => (! [X494 : subst] : (((comp @ X494 @ id)) = X494) => (! [X495 : term,X496 : (term > $o)] : (~ ! [X497 : term] : ((((X496 @ (lam @ X497))) = $true) | (((X496 @ X497)) != $true)) | ~ ! [X500 : term] : (($true != ((var @ X500))) | (((X496 @ X500)) = $true)) | ~ ! [X498 : term,X499 : term] : ((((X496 @ (ap @ X498 @ X499))) = $true) | (((X496 @ X498)) != $true) | ($true != ((X496 @ X499)))) | (((X496 @ X495)) = $true)) => ! [X501 : (term > $o),X502 : subst,X503 : term] : (~ ! [X507 : term,X508 : term] : (($true != ((X501 @ X508))) | (((X501 @ X507)) != $true) | ($true = ((X501 @ (ap @ X507 @ X508))))) | ~ ! [X506 : term] : (($true = ((X501 @ (sub @ X506 @ X502)))) | (((var @ X506)) != $true)) | ~ ! [X504 : term] : (~ ! [X505 : term] : ((((X501 @ X505)) != $true) | (((X501 @ (sub @ X504 @ (push @ X505 @ id)))) = $true)) | (((X501 @ (lam @ X504))) = $true)) | (((X501 @ (sub @ X503 @ X502))) = $true)))))) <=> (induction2lem_lthm = $true)) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) = ((d2subst @ X203))) => (X203 = X204)) & (hoasinduction_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & (! [X338 : (subst > term > subst > $o)] : ~ ! [X339 : (term > $o)] : ~ ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((induction2 = $true) <=> ! [X205 : term,X206 : (term > $o)] : (~ ! [X210 : term] : (~ ! [X211 : term] : ((((X206 @ X211)) != $true) | ($true = ((X206 @ (sub @ X210 @ (push @ X211 @ id)))))) | (((X206 @ (lam @ X210))) = $true)) | (((X206 @ X205)) = $true) | ~ ! [X208 : term,X207 : term] : (($true = ((X206 @ (ap @ X208 @ X207)))) | (((X206 @ X207)) != $true) | ($true != ((X206 @ X208)))) | ~ ! [X209 : term] : ((((var @ X209)) != $true) | (((X206 @ X209)) = $true)))) & (pushprop = $true) & ((apinj2 = $true) <=> ! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X469 : term] : (((sub @ X469 @ id)) = X469) => ! [X470 : term,X471 : (term > $o),X472 : (subst > term > subst > $o)] : (~ ! [X473 : (subst > term > term)] : (~ ! [X477 : subst,X476 : term,X475 : subst] : (((X473 @ (comp @ X475 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X473 @ X475 @ X476) @ X477))) | (((X472 @ id @ (lam @ (X473 @ sh @ one)) @ id)) = $true) | ~ ! [X474 : term] : ((((X472 @ id @ (X473 @ id @ X474) @ id)) = $true) | (((X472 @ id @ X474 @ id)) != $true))) | ~ ! [X480 : subst,X481 : subst,X479 : term,X478 : subst] : ((((X472 @ (comp @ X481 @ X478) @ (sub @ X479 @ X478) @ X480)) = $true) | (((X472 @ X481 @ X479 @ (comp @ X478 @ X480))) != $true)) | ~ ! [X482 : term] : (($true != ((X471 @ X482))) | ($true = ((X471 @ (sub @ X470 @ (push @ X482 @ id)))))) | ~ ! [X484 : subst,X483 : term,X485 : subst,X486 : subst] : ((((X472 @ X485 @ X483 @ (comp @ X484 @ X486))) = $true) | (((X472 @ (comp @ X485 @ X484) @ (sub @ X483 @ X484) @ X486)) != $true)) | ($true = ((X471 @ (lam @ X470)))) | ~ ! [X487 : term] : (((X471 @ X487)) = ((X472 @ id @ X487 @ id)))))) & ((hoasinduction_lem0 = $true) <=> ! [X148 : (subst > term > subst > $o)] : ~ ! [X149 : (term > $o)] : ~ ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))) & (hoasapnotvar = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction = $true) <=> ! [X246 : (subst > term > subst > $o),X247 : term] : (~ ! [X255 : term,X256 : subst,X254 : subst,X253 : subst] : ((((X246 @ X256 @ X255 @ (comp @ X254 @ X253))) != $true) | ($true = ((X246 @ (comp @ X256 @ X254) @ (sub @ X255 @ X254) @ X253)))) | (((X246 @ id @ X247 @ id)) = $true) | ~ ! [X257 : term] : ((((var @ (sub @ X257 @ id))) != $true) | ($true = ((X246 @ id @ X257 @ id)))) | ~ ! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : ((((X246 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) != $true) | ($true = ((X246 @ X260 @ X261 @ (comp @ X263 @ X262))))) | ~ ! [X259 : term,X258 : term] : (($true != ((X246 @ id @ X259 @ id))) | (((X246 @ id @ (ap @ (sub @ X259 @ id) @ X258) @ id)) = $true) | ($true != ((X246 @ id @ X258 @ id)))) | ~ ! [X248 : (subst > term > term)] : (~ ! [X252 : term] : ((((X246 @ id @ X252 @ id)) != $true) | (((X246 @ id @ (X248 @ id @ X252) @ id)) = $true)) | ~ ! [X249 : subst,X250 : term,X251 : subst] : (((sub @ (X248 @ X249 @ X250) @ X251)) = ((X248 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251)))) | ($true = ((X246 @ id @ (lam @ (X248 @ sh @ one)) @ id)))))) & ((! [X1 : (subst > term > subst > $o)] : ~ ! [X2 : (term > $o)] : ~ ! [X3 : term] : (((X2 @ X3)) = ((X1 @ id @ X3 @ id))) => (! [X4 : (term > $o),X5 : term] : (~ ! [X6 : term] : (($true != ((var @ X6))) | (((X4 @ X6)) = $true)) | ~ ! [X7 : term,X8 : term] : (($true != ((X4 @ X8))) | ($true != ((X4 @ X7))) | (((X4 @ (ap @ X8 @ X7))) = $true)) | ($true = ((X4 @ X5))) | ~ ! [X9 : term] : ((((X4 @ (lam @ X9))) = $true) | ~ ! [X10 : term] : ((((X4 @ (sub @ X9 @ (push @ X10 @ id)))) = $true) | (((X4 @ X10)) != $true)))) => (! [X11 : term] : (((sub @ X11 @ id)) = X11) => (! [X13 : (subst > term > subst > $o),X14 : (term > $o),X12 : term] : (~ ! [X16 : (subst > term > term)] : ((((X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X20 : term] : ((((X13 @ id @ X20 @ id)) != $true) | (((X13 @ id @ (X16 @ id @ X20) @ id)) = $true)) | ~ ! [X18 : term,X19 : subst,X17 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) = ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19))))) | ~ ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21))) | ~ ! [X15 : term] : (($true != ((X14 @ X15))) | (((X14 @ (sub @ X12 @ (push @ X15 @ id)))) = $true)) | (((X14 @ (lam @ X12))) = $true)) => ! [X22 : (subst > term > subst > $o),X23 : term] : (~ ! [X29 : term,X30 : term] : ((((X22 @ id @ X30 @ id)) != $true) | (((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id)) = $true) | (((X22 @ id @ X29 @ id)) != $true)) | ~ ! [X24 : (subst > term > term)] : (~ ! [X28 : subst,X27 : term,X26 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) | ~ ! [X25 : term] : ((((X22 @ id @ (X24 @ id @ X25) @ id)) = $true) | ($true != ((X22 @ id @ X25 @ id)))) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)) | ($true = ((X22 @ id @ X23 @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X383 : (term > $o),X382 : term,X381 : subst] : ~ ! [X384 : (term > $o)] : ~ ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (axapp = $true) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (ulamvarind = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axabs = $true) & ((axidl = $true) <=> ! [X0 : subst] : (((comp @ id @ X0)) = X0)) & (! [X329 : term] : ~ ! [X330 : (subst > term > term)] : ~ ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((! [X521 : term] : (((sub @ X521 @ id)) = X521) => (! [X523 : term,X522 : (subst > term > subst > $o)] : (~ ! [X529 : term] : (($true = ((X522 @ id @ (sub @ X523 @ (push @ X529 @ id)) @ id))) | (((X522 @ id @ X529 @ id)) != $true)) | ~ ! [X524 : (subst > term > term)] : (~ ! [X525 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X525)) = ((X524 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | (((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)) = $true) | ~ ! [X528 : term] : ((((X522 @ id @ (X524 @ id @ X528) @ id)) = $true) | (((X522 @ id @ X528 @ id)) != $true))) | (((X522 @ id @ (lam @ (sub @ X523 @ (push @ one @ sh))) @ id)) = $true)) => ! [X531 : (subst > term > subst > $o),X530 : term] : (~ ! [X532 : term] : (($true = ((X531 @ id @ (sub @ X530 @ (push @ X532 @ id)) @ id))) | ($true != ((X531 @ id @ X532 @ id)))) | (((X531 @ id @ (lam @ X530) @ id)) = $true) | ~ ! [X533 : (subst > term > term)] : (~ ! [X537 : term] : (($true != ((X531 @ id @ X537 @ id))) | ($true = ((X531 @ id @ (X533 @ id @ X537) @ id)))) | ($true = ((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id))) | ~ ! [X535 : subst,X536 : subst,X534 : term] : (((sub @ (X533 @ X536 @ X534) @ X535)) = ((X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535)))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X303 : (subst > term > subst > $o),X304 : term] : (~ ! [X305 : (subst > term > term)] : (~ ! [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) = ((sub @ (X305 @ X307 @ X309) @ X308))) | ~ ! [X306 : term] : ((((X303 @ id @ X306 @ id)) != $true) | (((X303 @ id @ (X305 @ id @ X306) @ id)) = $true)) | ($true = ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id)))) | (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X310 : term] : ((((X303 @ id @ X310 @ id)) != $true) | ($true = ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((induction = $true) <=> ! [X61 : term,X62 : (term > $o)] : (~ ! [X65 : term] : ((((var @ X65)) != $true) | (((X62 @ X65)) = $true)) | (((X62 @ X61)) = $true) | ~ ! [X64 : term,X63 : term] : (($true != ((X62 @ X63))) | ($true != ((X62 @ X64))) | (((X62 @ (ap @ X64 @ X63))) = $true)) | ~ ! [X66 : term] : (($true != ((X62 @ X66))) | (((X62 @ (lam @ X66))) = $true)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | (((var @ X100)) != $true)) | ~ ! [X98 : term] : ((((X94 @ (lam @ X98))) = $true) | ~ ! [X99 : term] : ((((X94 @ (sub @ X98 @ (push @ X99 @ id)))) = $true) | ($true != ((X94 @ X99))))) | ~ ! [X97 : term,X96 : term] : ((((X94 @ (ap @ X96 @ X97))) = $true) | ($true != ((X94 @ X97))) | (((X94 @ X96)) != $true))) => (! [X101 : term,X102 : term,X103 : (subst > term > subst > $o)] : (($true = ((X103 @ id @ (ap @ X102 @ X101) @ id))) | ~ ! [X111 : subst,X110 : subst,X113 : subst,X112 : term] : ((((X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113)) = $true) | (((X103 @ X110 @ X112 @ (comp @ X111 @ X113))) != $true)) | ~ ! [X109 : term,X108 : term] : ((((X103 @ id @ X109 @ id)) != $true) | ($true != ((X103 @ id @ X108 @ id))) | ($true = ((X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id)))) | (((X103 @ id @ X102 @ id)) != $true) | ~ ! [X104 : term,X107 : subst,X106 : subst,X105 : subst] : ((((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107)) != $true) | (((X103 @ X105 @ X104 @ (comp @ X106 @ X107))) = $true)) | (((X103 @ id @ X101 @ id)) != $true)) => (! [X115 : term,X114 : (subst > term > subst > $o)] : (~ ! [X121 : (subst > term > term)] : (~ ! [X124 : subst,X123 : term,X125 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) = ((sub @ (X121 @ X124 @ X123) @ X125))) | ~ ! [X122 : term] : (($true = ((X114 @ id @ (X121 @ id @ X122) @ id))) | ($true != ((X114 @ id @ X122 @ id)))) | (((X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true)) | ~ ! [X117 : subst,X119 : term,X118 : subst,X116 : subst] : ((((X114 @ X118 @ X119 @ (comp @ X117 @ X116))) != $true) | ($true = ((X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))) | (((X114 @ id @ (lam @ X115) @ id)) = $true) | ~ ! [X120 : term] : ((((X114 @ id @ X120 @ id)) != $true) | (((X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) = $true)) | ~ ! [X126 : subst,X129 : term,X127 : subst,X128 : subst] : (($true != ((X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))) | (((X114 @ X127 @ X129 @ (comp @ X128 @ X126))) = $true))) => ! [X131 : term,X130 : (subst > term > subst > $o)] : (~ ! [X137 : term] : (($true != ((var @ (sub @ X137 @ id)))) | (((X130 @ id @ X137 @ id)) = $true)) | ~ ! [X139 : term,X138 : term] : ((((X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) = $true) | (((X130 @ id @ X139 @ id)) != $true) | ($true != ((X130 @ id @ X138 @ id)))) | ($true = ((X130 @ id @ X131 @ id))) | ~ ! [X132 : (subst > term > term)] : (~ ! [X133 : subst,X135 : term,X134 : subst] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) | ~ ! [X136 : term] : (($true != ((X130 @ id @ X136 @ id))) | (((X130 @ id @ (X132 @ id @ X136) @ id)) = $true)) | (((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) = $true)) | ~ ! [X147 : subst,X146 : subst,X144 : subst,X145 : term] : ((((X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146)) != $true) | (((X130 @ X147 @ X145 @ (comp @ X144 @ X146))) = $true)) | ~ ! [X141 : subst,X140 : term,X142 : subst,X143 : subst] : (($true != ((X130 @ X141 @ X140 @ (comp @ X142 @ X143)))) | (((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143)) = $true))))))) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X436 : term,X435 : (subst > term > subst > $o),X437 : (term > $o)] : (~ ! [X438 : term] : (((X437 @ X438)) = ((X435 @ id @ X438 @ id))) | ~ ! [X439 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X439 @ sh @ one)) @ id)) = $true) | ~ ! [X440 : term] : ((((X435 @ id @ (X439 @ id @ X440) @ id)) = $true) | (((X435 @ id @ X440 @ id)) != $true)) | ~ ! [X442 : subst,X441 : term,X443 : subst] : (((sub @ (X439 @ X443 @ X441) @ X442)) = ((X439 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442))))) | ~ ! [X444 : term] : (($true != ((X437 @ X444))) | (((X437 @ (sub @ X436 @ (push @ X444 @ id)))) = $true)) | (((X437 @ (lam @ X436))) = $true))) & (hoasinduction_lem3b_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X395 : (term > $o),X397 : term,X396 : (subst > term > subst > $o),X394 : term] : (~ ! [X400 : term,X402 : subst,X401 : subst,X399 : subst] : ((((X396 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401) @ X399)) != $true) | (((X396 @ X402 @ X400 @ (comp @ X401 @ X399))) = $true)) | ~ ! [X404 : subst,X403 : term,X405 : subst,X406 : subst] : ((((X396 @ (comp @ X406 @ X404) @ (sub @ X403 @ X404) @ X405)) = $true) | ($true != ((X396 @ X406 @ X403 @ (comp @ X404 @ X405))))) | ~ ! [X408 : term,X407 : term] : ((((X396 @ id @ X408 @ id)) != $true) | (((X396 @ id @ (ap @ (sub @ X407 @ id) @ X408) @ id)) = $true) | (((X396 @ id @ X407 @ id)) != $true)) | (((X395 @ (ap @ X394 @ X397))) = $true) | ~ ! [X398 : term] : (((X396 @ id @ X398 @ id)) = ((X395 @ X398))) | (((X395 @ X397)) != $true) | (((X395 @ X394)) != $true))) & (termmset_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X89 : term,X90 : term,X88 : (subst > term > term)] : (~ ! [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X88 @ X92 @ X93) @ X91))) | (((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))))) & ((axscons = $true) <=> ! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412)) & (hoasapinj1_gthm = $true) & (! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3v2 = $true) <=> ! [X445 : (term > $o),X447 : term,X446 : (subst > term > subst > $o)] : (~ ! [X449 : subst,X448 : subst,X450 : subst,X451 : term] : (($true != ((X446 @ X450 @ X451 @ (comp @ X449 @ X448)))) | (((X446 @ (comp @ X450 @ X449) @ (sub @ X451 @ X449) @ X448)) = $true)) | ~ ! [X458 : (subst > term > term)] : (~ ! [X459 : term,X460 : subst,X461 : subst] : (((sub @ (X458 @ X460 @ X459) @ X461)) = ((X458 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461)))) | ~ ! [X462 : term] : ((((X446 @ id @ X462 @ id)) != $true) | ($true = ((X446 @ id @ (X458 @ id @ X462) @ id)))) | ($true = ((X446 @ id @ (lam @ (X458 @ sh @ one)) @ id)))) | ~ ! [X453 : term,X454 : subst,X455 : subst,X452 : subst] : ((((X446 @ X455 @ X453 @ (comp @ X452 @ X454))) = $true) | ($true != ((X446 @ (comp @ X455 @ X452) @ (sub @ X453 @ X452) @ X454)))) | ~ ! [X456 : term] : (((X446 @ id @ X456 @ id)) = ((X445 @ X456))) | ($true = ((X445 @ (lam @ X447)))) | ~ ! [X457 : term] : ((((X445 @ (sub @ X447 @ (push @ X457 @ id)))) = $true) | (((X445 @ X457)) != $true)))) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & ((induction2lem = $true) <=> ! [X31 : subst,X33 : (term > $o),X32 : term] : (~ ! [X35 : term,X36 : term] : ((((X33 @ X36)) != $true) | ($true = ((X33 @ (ap @ X36 @ X35)))) | (((X33 @ X35)) != $true)) | (((X33 @ (sub @ X32 @ X31))) = $true) | ~ ! [X34 : term] : (($true != ((var @ X34))) | (((X33 @ (sub @ X34 @ X31))) = $true)) | ~ ! [X37 : term] : ((((X33 @ (lam @ X37))) = $true) | ~ ! [X38 : term] : (($true != ((X33 @ X38))) | ($true = ((X33 @ (sub @ X37 @ (push @ X38 @ id))))))))) & (! [X39 : term] : ~ ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ X39 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X302 : d_term] : (d_one = X302) & (apnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X312 : (subst > term > subst > $o),X311 : term] : (~ ! [X318 : term,X319 : term] : ((((X312 @ id @ X319 @ id)) != $true) | (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) = $true) | (((X312 @ id @ X318 @ id)) != $true)) | ($true = ((X312 @ id @ X311 @ id))) | ~ ! [X313 : (subst > term > term)] : (($true = ((X312 @ id @ (lam @ (X313 @ sh @ one)) @ id))) | ~ ! [X315 : term,X314 : subst,X316 : subst] : (((sub @ (X313 @ X314 @ X315) @ X316)) = ((X313 @ (comp @ X314 @ X316) @ (sub @ X315 @ X316)))) | ~ ! [X317 : term] : (($true = ((X312 @ id @ (X313 @ id @ X317) @ id))) | (((X312 @ id @ X317 @ id)) != $true))))) & (hoasinduction_lem3a_gthm = $true) & ((hoaslaminj = $true) <=> ! [X513 : (subst > term > term),X514 : term,X512 : (subst > term > term),X511 : subst] : (~ ! [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) = ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | ~ ! [X520 : subst,X519 : term,X518 : subst] : (((sub @ (X512 @ X518 @ X519) @ X520)) = ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514))) | (((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))))) & (hoasapinj2_gthm = $true) & (axassoc = $true) & ((! [X264 : term] : (((sub @ X264 @ id)) = X264) => (! [X266 : subst,X265 : (term > $o),X267 : term] : ((((X265 @ (sub @ X267 @ X266))) = $true) | ~ ! [X272 : term,X271 : term] : ((((X265 @ (ap @ X272 @ X271))) = $true) | ($true != ((X265 @ X271))) | (((X265 @ X272)) != $true)) | ~ ! [X270 : term] : ((((X265 @ (sub @ X270 @ X266))) = $true) | (((var @ X270)) != $true)) | ~ ! [X268 : term] : ((((X265 @ (lam @ X268))) = $true) | ~ ! [X269 : term] : (($true = ((X265 @ (sub @ X268 @ (push @ X269 @ id))))) | (((X265 @ X269)) != $true)))) => ! [X273 : term,X274 : (term > $o)] : (~ ! [X276 : term,X275 : term] : ((((X274 @ X275)) != $true) | (((X274 @ (ap @ X276 @ X275))) = $true) | (((X274 @ X276)) != $true)) | ~ ! [X277 : term] : (~ ! [X278 : term] : ((((X274 @ (sub @ X277 @ (push @ X278 @ id)))) = $true) | (((X274 @ X278)) != $true)) | ($true = ((X274 @ (lam @ X277))))) | (((X274 @ X273)) = $true) | ~ ! [X279 : term] : ((((X274 @ X279)) = $true) | (((var @ X279)) != $true))))) <=> (induction2_lthm = $true))),
% 6.34/1.36 inference(flattening,[],[f9])).
% 6.34/1.36 thf(f11,plain,(
% 6.34/1.36 ((pushprop_lem0_lthm = $true) <=> ! [X322 : subst,X321 : term,X320 : (term > $o)] : ? [X323 : (term > $o)] : ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322)))))) & (pushprop_lem0_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((axvarcons = $true) <=> ! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291)) & (! [X370 : (subst > term > subst > $o),X369 : term] : ((((X370 @ id @ (lam @ (sub @ X369 @ (push @ one @ sh))) @ id)) = $true) | ? [X371 : term,X372 : (subst > term > term)] : (! [X375 : subst,X373 : term,X374 : subst] : (((X372 @ (comp @ X375 @ X374) @ (sub @ X373 @ X374))) = ((sub @ X371 @ (push @ (sub @ X373 @ X374) @ (comp @ X375 @ X374))))) & ! [X379 : term] : ((((X370 @ id @ (X372 @ id @ X379) @ id)) = $true) | (((X370 @ id @ X379 @ id)) != $true)) & ! [X378 : subst,X377 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X377) @ X378)) = ((sub @ (sub @ X371 @ (push @ X377 @ X376)) @ X378))) & (((X370 @ id @ (lam @ (X372 @ sh @ one)) @ id)) != $true)) | ? [X380 : term] : (($true = ((X370 @ id @ X380 @ id))) & (((X370 @ id @ (sub @ X369 @ (push @ X380 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (((! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300)) | ? [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) = ((ap @ X296 @ X297))) & (X295 != X296))) | ? [X293 : term] : (((sub @ X293 @ id)) != X293)) <=> (hoasapinj1_lthm = $true)) & (! [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) | ($true != ((X335 @ X333)))) <=> (pushprop_lem1 = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj2 = $true) <=> ! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58))) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & ((hoasapinj2_lthm = $true) <=> (! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83)) | ? [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 != X78) & (((ap @ X77 @ X76)) = ((ap @ X79 @ X78)))))) & (axmap = $true) & (! [X245 : term] : (((sub @ X245 @ id)) = X245) <=> (axvarid = $true)) & (pushprop_lthm_orig = $true) & ((((! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327)) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326)) | ? [X325 : subst] : (((comp @ id @ X325)) != X325)) <=> (substmonoid_lthm = $true)) & (! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) <=> (apinj1 = $true)) & (lamnotap != $true) & ! [X75 : d_subst] : (d_id = X75) & (hoasinduction_lem1_gthm = $true) & (! [X68 : term,X67 : (subst > term > subst > $o)] : (? [X69 : term] : ((((X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) != $true) & (((X67 @ id @ X69 @ id)) = $true)) | (((X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)) = $true) | ? [X70 : (subst > term > term)] : (! [X71 : term] : ((((X67 @ id @ (X70 @ id @ X71) @ id)) = $true) | (((X67 @ id @ X71 @ id)) != $true)) & ! [X74 : term,X72 : subst,X73 : subst] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72))) & ($true != ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X213 : term,X214 : (subst > term > subst > $o),X212 : term] : (? [X215 : term,X216 : term] : (($true != ((X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))) & (((X214 @ id @ X216 @ id)) = $true) & ($true = ((X214 @ id @ X215 @ id)))) | (((X214 @ id @ (ap @ X212 @ X213) @ id)) = $true) | (((X214 @ id @ X213 @ id)) != $true) | (((X214 @ id @ X212 @ id)) != $true) | ? [X222 : term,X221 : subst,X223 : subst,X224 : subst] : (($true != ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221))) & (((X214 @ X223 @ X222 @ (comp @ X224 @ X221))) = $true)) | ? [X217 : term,X219 : subst,X218 : subst,X220 : subst] : (($true != ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)))) & ($true = ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)))))) & ! [X410 : d_term,X409 : d_term] : ((((d2term @ X410)) != ((d2term @ X409))) | (X409 = X410)) & (one = ((d2term @ d_one))) & (hoasinduction_lem1v2 = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X414 : term,X413 : (subst > term > subst > $o)] : (? [X415 : (subst > term > term)] : (! [X416 : term,X417 : subst,X418 : subst] : (((X415 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417))) = ((sub @ (X415 @ X418 @ X416) @ X417))) & (((X413 @ id @ (lam @ (X415 @ sh @ one)) @ id)) != $true) & ! [X419 : term] : ((((X413 @ id @ (X415 @ id @ X419) @ id)) = $true) | (((X413 @ id @ X419 @ id)) != $true))) | ? [X424 : term] : (($true = ((X413 @ id @ X424 @ id))) & (((X413 @ id @ (sub @ X414 @ (push @ X424 @ id)) @ id)) != $true)) | ? [X422 : term,X423 : subst,X421 : subst,X420 : subst] : ((((X413 @ X421 @ X422 @ (comp @ X423 @ X420))) = $true) & ($true != ((X413 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423) @ X420)))) | ($true = ((X413 @ id @ (lam @ X414) @ id))) | ? [X425 : subst,X427 : subst,X426 : term,X428 : subst] : (($true != ((X413 @ X425 @ X426 @ (comp @ X427 @ X428)))) & ($true = ((X413 @ (comp @ X425 @ X427) @ (sub @ X426 @ X427) @ X428)))))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (? [X286 : term] : (((X282 @ X286)) != ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) | ($true = ((X282 @ one))) | (((X285 @ X284)) != $true)) | ? [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) != X281))) & (hoaslamnotap_lthm = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X50 : subst,X48 : term,X47 : (subst > term > term),X49 : (subst > term > term)] : (? [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) != ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | ? [X55 : subst,X56 : subst,X54 : term] : (((sub @ (X47 @ X56 @ X54) @ X55)) != ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48))) | (((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one))))) | ? [X46 : term,X45 : term] : ((X45 != X46) & (((lam @ X46)) = ((lam @ X45))))) | ? [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) != X44)) | ? [X41 : term,X42 : subst] : (((sub @ one @ (push @ X41 @ X42))) != X41))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X84 : term] : ? [X85 : (subst > term > term)] : ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86)))) & (((((! [X186 : term,X185 : (subst > term > subst > $o)] : (? [X194 : (subst > term > term)] : ((((X185 @ id @ (lam @ (X194 @ sh @ one)) @ id)) != $true) & ! [X198 : term] : ((((X185 @ id @ (X194 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) & ! [X197 : term,X196 : subst,X195 : subst] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196)))) | ? [X192 : subst,X191 : subst,X193 : term,X190 : subst] : ((((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191)) != $true) & (((X185 @ X190 @ X193 @ (comp @ X192 @ X191))) = $true)) | ? [X201 : subst,X199 : subst,X200 : term,X202 : subst] : (($true = ((X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202))) & ($true != ((X185 @ X199 @ X200 @ (comp @ X201 @ X202))))) | (((X185 @ id @ X186 @ id)) = $true) | ? [X189 : term] : (($true = ((var @ (sub @ X189 @ id)))) & ($true != ((X185 @ id @ X189 @ id)))) | ? [X187 : term,X188 : term] : ((((X185 @ id @ X187 @ id)) = $true) & ($true = ((X185 @ id @ X188 @ id))) & (((X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id)) != $true))) | ? [X175 : (subst > term > subst > $o),X177 : (term > $o),X176 : term] : (! [X179 : term] : ((((X177 @ X179)) != $true) | (((X177 @ (sub @ X176 @ (push @ X179 @ id)))) = $true)) & (((X177 @ (lam @ X176))) != $true) & ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) & ! [X180 : (subst > term > term)] : ((((X175 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ? [X183 : subst,X182 : term,X181 : subst] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) != ((sub @ (X180 @ X181 @ X182) @ X183))) | ? [X184 : term] : ((((X175 @ id @ X184 @ id)) = $true) & (((X175 @ id @ (X180 @ id @ X184) @ id)) != $true))))) | ? [X174 : term] : (((sub @ X174 @ id)) != X174)) | ? [X168 : (term > $o),X167 : term] : (! [X170 : term,X169 : term] : (($true != ((X168 @ X169))) | (((X168 @ X170)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)) & ! [X172 : term] : ((((X168 @ (lam @ X172))) = $true) | ? [X173 : term] : (($true = ((X168 @ X173))) & (((X168 @ (sub @ X172 @ (push @ X173 @ id)))) != $true))) & ($true != ((X168 @ X167))) & ! [X171 : term] : (($true != ((var @ X171))) | (((X168 @ X171)) = $true)))) | ? [X164 : (subst > term > subst > $o)] : ! [X165 : (term > $o)] : ? [X166 : term] : (((X164 @ id @ X166 @ id)) != ((X165 @ X166)))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ? [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) = ((X539 @ sh @ one)))) & (axvarshift = $true) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3a = $true) <=> ! [X386 : (subst > term > subst > $o),X387 : term] : (? [X388 : (subst > term > term)] : (! [X389 : term] : ((((X386 @ id @ (X388 @ id @ X389) @ id)) = $true) | (((X386 @ id @ X389 @ id)) != $true)) & ! [X392 : term,X391 : subst,X390 : subst] : (((sub @ (X388 @ X391 @ X392) @ X390)) = ((X388 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) & (((X386 @ id @ (lam @ (X388 @ sh @ one)) @ id)) != $true)) | ? [X393 : term] : ((((X386 @ id @ X393 @ id)) = $true) & ($true != ((X386 @ id @ (sub @ X387 @ (push @ X393 @ id)) @ id)))) | (((X386 @ id @ (lam @ X387) @ id)) = $true))) & (! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) <=> (hoasapinj1 = $true)) & ((? [X488 : term] : (((sub @ X488 @ id)) != X488) | ! [X489 : term] : (((sub @ X489 @ id)) = X489)) <=> (termmset_lthm = $true)) & ((termmset = $true) <=> ! [X341 : term] : (((sub @ X341 @ id)) = X341)) & (pushprop_lem2v2_lthm = $true) & (! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) <=> (shinj = $true)) & (((d2subst @ d_id)) = id) & ((laminj = $true) <=> ! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343))) & (! [X411 : subst] : (((comp @ X411 @ id)) = X411) <=> (axidr = $true)) & (axclos = $true) & (lamnotvar = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((pushprop_lem1_lthm = $true) <=> ((! [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true != ((X163 @ X159))) | (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true)) | ? [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) != X157)) | ? [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) != X155))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X232 : (term > $o),X231 : (subst > term > subst > $o),X230 : term] : (? [X239 : term] : (($true != ((X232 @ (sub @ X230 @ (push @ X239 @ id))))) & (((X232 @ X239)) = $true)) | ? [X233 : (subst > term > term)] : (! [X234 : term] : ((((X231 @ id @ X234 @ id)) != $true) | ($true = ((X231 @ id @ (X233 @ id @ X234) @ id)))) & ! [X235 : subst,X237 : term,X236 : subst] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235)))) & (((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) != $true)) | ? [X238 : term] : (((X232 @ X238)) != ((X231 @ id @ X238 @ id))) | (((X232 @ (lam @ X230))) = $true)) | ? [X229 : term] : (((sub @ X229 @ id)) != X229)) | ? [X225 : term] : ! [X226 : (subst > term > term)] : ? [X227 : subst,X228 : term] : (((sub @ X225 @ (push @ X228 @ X227))) != ((X226 @ X227 @ X228))))) & (((var @ (d2term @ d_one))) != $true) & (! [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (? [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) != ((X241 @ X244))) | ($true != ((X243 @ X242))) | (((X241 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (hoaslamnotap_gthm = $true) & (((! [X353 : (subst > term > subst > $o),X354 : term] : (? [X368 : term] : ((((X353 @ id @ X368 @ id)) = $true) & (((X353 @ id @ (sub @ X354 @ (push @ X368 @ id)) @ id)) != $true)) | ? [X366 : subst,X364 : term,X367 : subst,X365 : subst] : ((((X353 @ (comp @ X365 @ X366) @ (sub @ X364 @ X366) @ X367)) = $true) & (((X353 @ X365 @ X364 @ (comp @ X366 @ X367))) != $true)) | ? [X361 : term,X362 : subst,X363 : subst,X360 : subst] : ((((X353 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362)) != $true) & ($true = ((X353 @ X363 @ X361 @ (comp @ X360 @ X362))))) | ($true = ((X353 @ id @ (lam @ X354) @ id))) | ? [X355 : (subst > term > term)] : (! [X356 : term] : (($true != ((X353 @ id @ X356 @ id))) | (((X353 @ id @ (X355 @ id @ X356) @ id)) = $true)) & ! [X358 : subst,X359 : term,X357 : subst] : (((sub @ (X355 @ X358 @ X359) @ X357)) = ((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357)))) & ($true != ((X353 @ id @ (lam @ (X355 @ sh @ one)) @ id))))) | ? [X345 : term,X346 : (subst > term > subst > $o)] : (! [X348 : (subst > term > term)] : (? [X350 : subst,X352 : term,X351 : subst] : (((X348 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351))) != ((sub @ (X348 @ X350 @ X352) @ X351))) | ? [X349 : term] : (($true != ((X346 @ id @ (X348 @ id @ X349) @ id))) & (((X346 @ id @ X349 @ id)) = $true)) | (((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id)) = $true)) & (((X346 @ id @ (lam @ (sub @ X345 @ (push @ one @ sh))) @ id)) != $true) & ! [X347 : term] : ((((X346 @ id @ (sub @ X345 @ (push @ X347 @ id)) @ id)) = $true) | ($true != ((X346 @ id @ X347 @ id)))))) | ? [X344 : term] : (((sub @ X344 @ id)) != X344)) <=> (hoasinduction_lem3_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (((((! [X503 : term,X501 : (term > $o),X502 : subst] : (? [X506 : term] : (($true != ((X501 @ (sub @ X506 @ X502)))) & (((var @ X506)) = $true)) | ? [X504 : term] : ((((X501 @ (lam @ X504))) != $true) & ! [X505 : term] : ((((X501 @ X505)) != $true) | (((X501 @ (sub @ X504 @ (push @ X505 @ id)))) = $true))) | (((X501 @ (sub @ X503 @ X502))) = $true) | ? [X507 : term,X508 : term] : (($true = ((X501 @ X508))) & (((X501 @ X507)) = $true) & ($true != ((X501 @ (ap @ X507 @ X508)))))) | ? [X496 : (term > $o),X495 : term] : ((((X496 @ X495)) != $true) & ! [X500 : term] : (($true != ((var @ X500))) | (((X496 @ X500)) = $true)) & ! [X498 : term,X499 : term] : ((((X496 @ (ap @ X498 @ X499))) = $true) | (((X496 @ X498)) != $true) | ($true != ((X496 @ X499)))) & ! [X497 : term] : ((((X496 @ (lam @ X497))) = $true) | (((X496 @ X497)) != $true)))) | ? [X494 : subst] : (((comp @ X494 @ id)) != X494)) | ? [X493 : term,X492 : subst] : (((comp @ sh @ (push @ X493 @ X492))) != X492)) | ? [X490 : subst,X491 : term] : (((sub @ one @ (push @ X491 @ X490))) != X491)) <=> (induction2lem_lthm = $true)) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) != ((d2subst @ X203))) | (X203 = X204)) & (hoasinduction_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasapnotvar_gthm = $true) & (induction2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X338 : (subst > term > subst > $o)] : ? [X339 : (term > $o)] : ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id)))) & ((induction2 = $true) <=> ! [X205 : term,X206 : (term > $o)] : (? [X210 : term] : (! [X211 : term] : ((((X206 @ X211)) != $true) | ($true = ((X206 @ (sub @ X210 @ (push @ X211 @ id)))))) & (((X206 @ (lam @ X210))) != $true)) | ? [X208 : term,X207 : term] : ((((X206 @ X207)) = $true) & ($true != ((X206 @ (ap @ X208 @ X207)))) & ($true = ((X206 @ X208)))) | (((X206 @ X205)) = $true) | ? [X209 : term] : ((((var @ X209)) = $true) & (((X206 @ X209)) != $true)))) & (pushprop = $true) & ((apinj2 = $true) <=> ! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154))))) & ((! [X471 : (term > $o),X470 : term,X472 : (subst > term > subst > $o)] : (? [X484 : subst,X486 : subst,X485 : subst,X483 : term] : ((((X472 @ X485 @ X483 @ (comp @ X484 @ X486))) != $true) & (((X472 @ (comp @ X485 @ X484) @ (sub @ X483 @ X484) @ X486)) = $true)) | ($true = ((X471 @ (lam @ X470)))) | ? [X473 : (subst > term > term)] : (! [X477 : subst,X476 : term,X475 : subst] : (((X473 @ (comp @ X475 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X473 @ X475 @ X476) @ X477))) & (((X472 @ id @ (lam @ (X473 @ sh @ one)) @ id)) != $true) & ! [X474 : term] : ((((X472 @ id @ (X473 @ id @ X474) @ id)) = $true) | (((X472 @ id @ X474 @ id)) != $true))) | ? [X482 : term] : (($true != ((X471 @ (sub @ X470 @ (push @ X482 @ id))))) & ($true = ((X471 @ X482)))) | ? [X478 : subst,X481 : subst,X479 : term,X480 : subst] : ((((X472 @ X481 @ X479 @ (comp @ X478 @ X480))) = $true) & (((X472 @ (comp @ X481 @ X478) @ (sub @ X479 @ X478) @ X480)) != $true)) | ? [X487 : term] : (((X471 @ X487)) != ((X472 @ id @ X487 @ id)))) | ? [X469 : term] : (((sub @ X469 @ id)) != X469)) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X148 : (subst > term > subst > $o)] : ? [X149 : (term > $o)] : ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))) & (hoasapnotvar = $true) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction = $true) <=> ! [X246 : (subst > term > subst > $o),X247 : term] : (? [X257 : term] : (($true != ((X246 @ id @ X257 @ id))) & (((var @ (sub @ X257 @ id))) = $true)) | ? [X256 : subst,X254 : subst,X253 : subst,X255 : term] : (($true != ((X246 @ (comp @ X256 @ X254) @ (sub @ X255 @ X254) @ X253))) & (((X246 @ X256 @ X255 @ (comp @ X254 @ X253))) = $true)) | ? [X258 : term,X259 : term] : (($true = ((X246 @ id @ X259 @ id))) & ($true = ((X246 @ id @ X258 @ id))) & (((X246 @ id @ (ap @ (sub @ X259 @ id) @ X258) @ id)) != $true)) | (((X246 @ id @ X247 @ id)) = $true) | ? [X263 : subst,X260 : subst,X262 : subst,X261 : term] : ((((X246 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) = $true) & ($true != ((X246 @ X260 @ X261 @ (comp @ X263 @ X262))))) | ? [X248 : (subst > term > term)] : (! [X249 : subst,X250 : term,X251 : subst] : (((sub @ (X248 @ X249 @ X250) @ X251)) = ((X248 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251)))) & ($true != ((X246 @ id @ (lam @ (X248 @ sh @ one)) @ id))) & ! [X252 : term] : ((((X246 @ id @ X252 @ id)) != $true) | (((X246 @ id @ (X248 @ id @ X252) @ id)) = $true))))) & (((((! [X23 : term,X22 : (subst > term > subst > $o)] : (? [X24 : (subst > term > term)] : (! [X25 : term] : ((((X22 @ id @ (X24 @ id @ X25) @ id)) = $true) | ($true != ((X22 @ id @ X25 @ id)))) & ! [X28 : subst,X27 : term,X26 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) & (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) != $true)) | ($true = ((X22 @ id @ X23 @ id))) | ? [X30 : term,X29 : term] : ((((X22 @ id @ X29 @ id)) = $true) & (((X22 @ id @ X30 @ id)) = $true) & (((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id)) != $true))) | ? [X13 : (subst > term > subst > $o),X12 : term,X14 : (term > $o)] : (! [X15 : term] : (($true != ((X14 @ X15))) | (((X14 @ (sub @ X12 @ (push @ X15 @ id)))) = $true)) & ! [X16 : (subst > term > term)] : (? [X19 : subst,X18 : term,X17 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) != ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))) | ? [X20 : term] : ((((X13 @ id @ X20 @ id)) = $true) & (((X13 @ id @ (X16 @ id @ X20) @ id)) != $true)) | (((X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true)) & (((X14 @ (lam @ X12))) != $true) & ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21))))) | ? [X11 : term] : (((sub @ X11 @ id)) != X11)) | ? [X4 : (term > $o),X5 : term] : (! [X9 : term] : ((((X4 @ (lam @ X9))) = $true) | ? [X10 : term] : ((((X4 @ (sub @ X9 @ (push @ X10 @ id)))) != $true) & (((X4 @ X10)) = $true))) & ! [X6 : term] : (($true != ((var @ X6))) | (((X4 @ X6)) = $true)) & ! [X7 : term,X8 : term] : (($true != ((X4 @ X8))) | ($true != ((X4 @ X7))) | (((X4 @ (ap @ X8 @ X7))) = $true)) & ($true != ((X4 @ X5))))) | ? [X1 : (subst > term > subst > $o)] : ! [X2 : (term > $o)] : ? [X3 : term] : (((X2 @ X3)) != ((X1 @ id @ X3 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X383 : (term > $o),X381 : subst,X382 : term] : ? [X384 : (term > $o)] : ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (axapp = $true) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (ulamvarind = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (axabs = $true) & ((axidl = $true) <=> ! [X0 : subst] : (((comp @ id @ X0)) = X0)) & (! [X329 : term] : ? [X330 : (subst > term > term)] : ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasapnotvar_lthm = $true) & (((! [X531 : (subst > term > subst > $o),X530 : term] : ((((X531 @ id @ (lam @ X530) @ id)) = $true) | ? [X533 : (subst > term > term)] : (($true != ((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id))) & ! [X535 : subst,X536 : subst,X534 : term] : (((sub @ (X533 @ X536 @ X534) @ X535)) = ((X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535)))) & ! [X537 : term] : (($true != ((X531 @ id @ X537 @ id))) | ($true = ((X531 @ id @ (X533 @ id @ X537) @ id))))) | ? [X532 : term] : (($true = ((X531 @ id @ X532 @ id))) & ($true != ((X531 @ id @ (sub @ X530 @ (push @ X532 @ id)) @ id))))) | ? [X523 : term,X522 : (subst > term > subst > $o)] : ((((X522 @ id @ (lam @ (sub @ X523 @ (push @ one @ sh))) @ id)) != $true) & ! [X524 : (subst > term > term)] : (? [X525 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X525)) != ((X524 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | ? [X528 : term] : ((((X522 @ id @ X528 @ id)) = $true) & (((X522 @ id @ (X524 @ id @ X528) @ id)) != $true)) | (((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)) = $true)) & ! [X529 : term] : (($true = ((X522 @ id @ (sub @ X523 @ (push @ X529 @ id)) @ id))) | (((X522 @ id @ X529 @ id)) != $true)))) | ? [X521 : term] : (((sub @ X521 @ id)) != X521)) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X303 : (subst > term > subst > $o),X304 : term] : (? [X310 : term] : ((((X303 @ id @ X310 @ id)) = $true) & ($true != ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id)))) | ? [X305 : (subst > term > term)] : (! [X306 : term] : ((((X303 @ id @ X306 @ id)) != $true) | (((X303 @ id @ (X305 @ id @ X306) @ id)) = $true)) & ! [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) = ((sub @ (X305 @ X307 @ X309) @ X308))) & ($true != ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id)))) | (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & ((induction = $true) <=> ! [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) = $true) | ? [X65 : term] : ((((X62 @ X65)) != $true) & (((var @ X65)) = $true)) | ? [X66 : term] : (($true = ((X62 @ X66))) & (((X62 @ (lam @ X66))) != $true)) | ? [X64 : term,X63 : term] : (($true = ((X62 @ X63))) & ($true = ((X62 @ X64))) & (((X62 @ (ap @ X64 @ X63))) != $true)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lthm = $true) <=> (((! [X131 : term,X130 : (subst > term > subst > $o)] : (? [X137 : term] : ((((X130 @ id @ X137 @ id)) != $true) & ($true = ((var @ (sub @ X137 @ id))))) | ($true = ((X130 @ id @ X131 @ id))) | ? [X140 : term,X143 : subst,X141 : subst,X142 : subst] : (($true = ((X130 @ X141 @ X140 @ (comp @ X142 @ X143)))) & (((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143)) != $true)) | ? [X139 : term,X138 : term] : ((((X130 @ id @ X139 @ id)) = $true) & ($true = ((X130 @ id @ X138 @ id))) & (((X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) != $true)) | ? [X144 : subst,X145 : term,X147 : subst,X146 : subst] : ((((X130 @ X147 @ X145 @ (comp @ X144 @ X146))) != $true) & (((X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146)) = $true)) | ? [X132 : (subst > term > term)] : (! [X133 : subst,X135 : term,X134 : subst] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) & (((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) != $true) & ! [X136 : term] : (($true != ((X130 @ id @ X136 @ id))) | (((X130 @ id @ (X132 @ id @ X136) @ id)) = $true)))) | ? [X114 : (subst > term > subst > $o),X115 : term] : ((((X114 @ id @ (lam @ X115) @ id)) != $true) & ! [X120 : term] : ((((X114 @ id @ X120 @ id)) != $true) | (((X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) = $true)) & ! [X126 : subst,X129 : term,X127 : subst,X128 : subst] : (($true != ((X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))) | (((X114 @ X127 @ X129 @ (comp @ X128 @ X126))) = $true)) & ! [X121 : (subst > term > term)] : ((((X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true) | ? [X122 : term] : (($true != ((X114 @ id @ (X121 @ id @ X122) @ id))) & ($true = ((X114 @ id @ X122 @ id)))) | ? [X123 : term,X125 : subst,X124 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) != ((sub @ (X121 @ X124 @ X123) @ X125)))) & ! [X117 : subst,X119 : term,X118 : subst,X116 : subst] : ((((X114 @ X118 @ X119 @ (comp @ X117 @ X116))) != $true) | ($true = ((X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))))) | ? [X102 : term,X103 : (subst > term > subst > $o),X101 : term] : (! [X109 : term,X108 : term] : ((((X103 @ id @ X109 @ id)) != $true) | ($true != ((X103 @ id @ X108 @ id))) | ($true = ((X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id)))) & ($true != ((X103 @ id @ (ap @ X102 @ X101) @ id))) & (((X103 @ id @ X102 @ id)) = $true) & ! [X104 : term,X107 : subst,X106 : subst,X105 : subst] : ((((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107)) != $true) | (((X103 @ X105 @ X104 @ (comp @ X106 @ X107))) = $true)) & ! [X111 : subst,X110 : subst,X113 : subst,X112 : term] : ((((X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113)) = $true) | (((X103 @ X110 @ X112 @ (comp @ X111 @ X113))) != $true)) & (((X103 @ id @ X101 @ id)) = $true))) | ? [X95 : term,X94 : (term > $o)] : (! [X97 : term,X96 : term] : ((((X94 @ (ap @ X96 @ X97))) = $true) | ($true != ((X94 @ X97))) | (((X94 @ X96)) != $true)) & (((X94 @ X95)) != $true) & ! [X98 : term] : (? [X99 : term] : ((((X94 @ (sub @ X98 @ (push @ X99 @ id)))) != $true) & ($true = ((X94 @ X99)))) | (((X94 @ (lam @ X98))) = $true)) & ! [X100 : term] : ((((X94 @ X100)) = $true) | (((var @ X100)) != $true))))) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X435 : (subst > term > subst > $o),X436 : term,X437 : (term > $o)] : ((((X437 @ (lam @ X436))) = $true) | ? [X439 : (subst > term > term)] : (! [X442 : subst,X441 : term,X443 : subst] : (((sub @ (X439 @ X443 @ X441) @ X442)) = ((X439 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442)))) & ! [X440 : term] : ((((X435 @ id @ (X439 @ id @ X440) @ id)) = $true) | (((X435 @ id @ X440 @ id)) != $true)) & (((X435 @ id @ (lam @ (X439 @ sh @ one)) @ id)) != $true)) | ? [X444 : term] : ((((X437 @ (sub @ X436 @ (push @ X444 @ id)))) != $true) & ($true = ((X437 @ X444)))) | ? [X438 : term] : (((X437 @ X438)) != ((X435 @ id @ X438 @ id))))) & (hoasinduction_lem3b_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X397 : term,X396 : (subst > term > subst > $o),X395 : (term > $o),X394 : term] : (? [X402 : subst,X399 : subst,X401 : subst,X400 : term] : ((((X396 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401) @ X399)) = $true) & (((X396 @ X402 @ X400 @ (comp @ X401 @ X399))) != $true)) | (((X395 @ (ap @ X394 @ X397))) = $true) | ? [X398 : term] : (((X396 @ id @ X398 @ id)) != ((X395 @ X398))) | ? [X403 : term,X404 : subst,X406 : subst,X405 : subst] : ((((X396 @ (comp @ X406 @ X404) @ (sub @ X403 @ X404) @ X405)) != $true) & ($true = ((X396 @ X406 @ X403 @ (comp @ X404 @ X405))))) | ? [X408 : term,X407 : term] : ((((X396 @ id @ (ap @ (sub @ X407 @ id) @ X408) @ id)) != $true) & (((X396 @ id @ X407 @ id)) = $true) & (((X396 @ id @ X408 @ id)) = $true)) | (((X395 @ X394)) != $true) | (((X395 @ X397)) != $true))) & (termmset_gthm = $true) & (! [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))) | ? [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X88 @ X92 @ X93) @ X91)))) <=> (hoaslamnotap = $true)) & ((axscons = $true) <=> ! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412)) & (hoasapinj1_gthm = $true) & (! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X445 : (term > $o),X447 : term,X446 : (subst > term > subst > $o)] : (? [X456 : term] : (((X446 @ id @ X456 @ id)) != ((X445 @ X456))) | ? [X454 : subst,X455 : subst,X452 : subst,X453 : term] : (($true = ((X446 @ (comp @ X455 @ X452) @ (sub @ X453 @ X452) @ X454))) & (((X446 @ X455 @ X453 @ (comp @ X452 @ X454))) != $true)) | ? [X457 : term] : ((((X445 @ X457)) = $true) & (((X445 @ (sub @ X447 @ (push @ X457 @ id)))) != $true)) | ? [X458 : (subst > term > term)] : (($true != ((X446 @ id @ (lam @ (X458 @ sh @ one)) @ id))) & ! [X462 : term] : ((((X446 @ id @ X462 @ id)) != $true) | ($true = ((X446 @ id @ (X458 @ id @ X462) @ id)))) & ! [X459 : term,X460 : subst,X461 : subst] : (((sub @ (X458 @ X460 @ X459) @ X461)) = ((X458 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461))))) | ($true = ((X445 @ (lam @ X447)))) | ? [X450 : subst,X449 : subst,X451 : term,X448 : subst] : ((((X446 @ (comp @ X450 @ X449) @ (sub @ X451 @ X449) @ X448)) != $true) & ($true = ((X446 @ X450 @ X451 @ (comp @ X449 @ X448)))))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (! [X33 : (term > $o),X31 : subst,X32 : term] : ((((X33 @ (sub @ X32 @ X31))) = $true) | ? [X34 : term] : ((((X33 @ (sub @ X34 @ X31))) != $true) & ($true = ((var @ X34)))) | ? [X36 : term,X35 : term] : ((((X33 @ X36)) = $true) & (((X33 @ X35)) = $true) & ($true != ((X33 @ (ap @ X36 @ X35))))) | ? [X37 : term] : ((((X33 @ (lam @ X37))) != $true) & ! [X38 : term] : (($true != ((X33 @ X38))) | ($true = ((X33 @ (sub @ X37 @ (push @ X38 @ id)))))))) <=> (induction2lem = $true)) & (! [X39 : term] : ? [X40 : (subst > term > term)] : (((X40 @ sh @ one)) = ((sub @ X39 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X302 : d_term] : (d_one = X302) & (apnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X312 : (subst > term > subst > $o),X311 : term] : (? [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) = $true) & (((X312 @ id @ X318 @ id)) = $true) & (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) != $true)) | ? [X313 : (subst > term > term)] : (($true != ((X312 @ id @ (lam @ (X313 @ sh @ one)) @ id))) & ! [X315 : term,X314 : subst,X316 : subst] : (((sub @ (X313 @ X314 @ X315) @ X316)) = ((X313 @ (comp @ X314 @ X316) @ (sub @ X315 @ X316)))) & ! [X317 : term] : (($true = ((X312 @ id @ (X313 @ id @ X317) @ id))) | (((X312 @ id @ X317 @ id)) != $true))) | ($true = ((X312 @ id @ X311 @ id))))) & (hoasinduction_lem3a_gthm = $true) & (! [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))) | ? [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) != ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | ? [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) != ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514)))) <=> (hoaslaminj = $true)) & (hoasapinj2_gthm = $true) & (axassoc = $true) & (((! [X273 : term,X274 : (term > $o)] : (? [X275 : term,X276 : term] : ((((X274 @ X276)) = $true) & (((X274 @ X275)) = $true) & (((X274 @ (ap @ X276 @ X275))) != $true)) | ? [X279 : term] : ((((var @ X279)) = $true) & (((X274 @ X279)) != $true)) | ? [X277 : term] : (! [X278 : term] : ((((X274 @ (sub @ X277 @ (push @ X278 @ id)))) = $true) | (((X274 @ X278)) != $true)) & ($true != ((X274 @ (lam @ X277))))) | (((X274 @ X273)) = $true)) | ? [X267 : term,X266 : subst,X265 : (term > $o)] : ((((X265 @ (sub @ X267 @ X266))) != $true) & ! [X272 : term,X271 : term] : ((((X265 @ (ap @ X272 @ X271))) = $true) | ($true != ((X265 @ X271))) | (((X265 @ X272)) != $true)) & ! [X268 : term] : ((((X265 @ (lam @ X268))) = $true) | ? [X269 : term] : ((((X265 @ X269)) = $true) & ($true != ((X265 @ (sub @ X268 @ (push @ X269 @ id))))))) & ! [X270 : term] : ((((X265 @ (sub @ X270 @ X266))) = $true) | (((var @ X270)) != $true)))) | ? [X264 : term] : (((sub @ X264 @ id)) != X264)) <=> (induction2_lthm = $true))),
% 6.34/1.36 inference(ennf_transformation,[],[f10])).
% 6.34/1.36 thf(f12,plain,(
% 6.34/1.36 ((! [X50 : subst,X48 : term,X47 : (subst > term > term),X49 : (subst > term > term)] : (? [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) != ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | ? [X55 : subst,X56 : subst,X54 : term] : (((sub @ (X47 @ X56 @ X54) @ X55)) != ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48))) | (((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one))))) | ? [X41 : term,X42 : subst] : (((sub @ one @ (push @ X41 @ X42))) != X41) | ? [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) != X44) | ? [X46 : term,X45 : term] : ((X45 != X46) & (((lam @ X46)) = ((lam @ X45))))) <=> (hoaslaminj_lthm = $true)) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = id) & ((axscons = $true) <=> ! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412)) & (! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) <=> (apinj1 = $true)) & (hoaslamnotap_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((induction = $true) <=> ! [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) = $true) | ? [X65 : term] : ((((X62 @ X65)) != $true) & (((var @ X65)) = $true)) | ? [X66 : term] : (($true = ((X62 @ X66))) & (((X62 @ (lam @ X66))) != $true)) | ? [X64 : term,X63 : term] : (($true = ((X62 @ X63))) & ($true = ((X62 @ X64))) & (((X62 @ (ap @ X64 @ X63))) != $true)))) & ! [X302 : d_term] : (d_one = X302) & (axabs = $true) & (! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) <=> (hoasapinj1 = $true)) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & ((hoasinduction_lem3 = $true) <=> ! [X414 : term,X413 : (subst > term > subst > $o)] : (? [X415 : (subst > term > term)] : (! [X416 : term,X417 : subst,X418 : subst] : (((X415 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417))) = ((sub @ (X415 @ X418 @ X416) @ X417))) & (((X413 @ id @ (lam @ (X415 @ sh @ one)) @ id)) != $true) & ! [X419 : term] : ((((X413 @ id @ (X415 @ id @ X419) @ id)) = $true) | (((X413 @ id @ X419 @ id)) != $true))) | ? [X424 : term] : (($true = ((X413 @ id @ X424 @ id))) & (((X413 @ id @ (sub @ X414 @ (push @ X424 @ id)) @ id)) != $true)) | ? [X422 : term,X423 : subst,X421 : subst,X420 : subst] : ((((X413 @ X421 @ X422 @ (comp @ X423 @ X420))) = $true) & ($true != ((X413 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423) @ X420)))) | ($true = ((X413 @ id @ (lam @ X414) @ id))) | ? [X425 : subst,X427 : subst,X426 : term,X428 : subst] : (($true != ((X413 @ X425 @ X426 @ (comp @ X427 @ X428)))) & ($true = ((X413 @ (comp @ X425 @ X427) @ (sub @ X426 @ X427) @ X428)))))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58))) & (! [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (? [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) != ((X241 @ X244))) | ($true != ((X243 @ X242))) | (((X241 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X148 : (subst > term > subst > $o)] : ? [X149 : (term > $o)] : ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X84 : term] : ? [X85 : (subst > term > term)] : ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86)))) & (! [X303 : (subst > term > subst > $o),X304 : term] : (? [X310 : term] : ((((X303 @ id @ X310 @ id)) = $true) & ($true != ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id)))) | ? [X305 : (subst > term > term)] : (! [X306 : term] : ((((X303 @ id @ X306 @ id)) != $true) | (((X303 @ id @ (X305 @ id @ X306) @ id)) = $true)) & ! [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) = ((sub @ (X305 @ X307 @ X309) @ X308))) & ($true != ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id)))) | (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) <=> (! [X131 : term,X130 : (subst > term > subst > $o)] : (? [X137 : term] : ((((X130 @ id @ X137 @ id)) != $true) & ($true = ((var @ (sub @ X137 @ id))))) | ($true = ((X130 @ id @ X131 @ id))) | ? [X140 : term,X143 : subst,X141 : subst,X142 : subst] : (($true = ((X130 @ X141 @ X140 @ (comp @ X142 @ X143)))) & (((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143)) != $true)) | ? [X139 : term,X138 : term] : ((((X130 @ id @ X139 @ id)) = $true) & ($true = ((X130 @ id @ X138 @ id))) & (((X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) != $true)) | ? [X144 : subst,X145 : term,X147 : subst,X146 : subst] : ((((X130 @ X147 @ X145 @ (comp @ X144 @ X146))) != $true) & (((X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146)) = $true)) | ? [X132 : (subst > term > term)] : (! [X133 : subst,X135 : term,X134 : subst] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) & (((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) != $true) & ! [X136 : term] : (($true != ((X130 @ id @ X136 @ id))) | (((X130 @ id @ (X132 @ id @ X136) @ id)) = $true)))) | ? [X95 : term,X94 : (term > $o)] : (! [X97 : term,X96 : term] : ((((X94 @ (ap @ X96 @ X97))) = $true) | ($true != ((X94 @ X97))) | (((X94 @ X96)) != $true)) & (((X94 @ X95)) != $true) & ! [X98 : term] : (? [X99 : term] : ((((X94 @ (sub @ X98 @ (push @ X99 @ id)))) != $true) & ($true = ((X94 @ X99)))) | (((X94 @ (lam @ X98))) = $true)) & ! [X100 : term] : ((((X94 @ X100)) = $true) | (((var @ X100)) != $true))) | ? [X102 : term,X103 : (subst > term > subst > $o),X101 : term] : (! [X109 : term,X108 : term] : ((((X103 @ id @ X109 @ id)) != $true) | ($true != ((X103 @ id @ X108 @ id))) | ($true = ((X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id)))) & ($true != ((X103 @ id @ (ap @ X102 @ X101) @ id))) & (((X103 @ id @ X102 @ id)) = $true) & ! [X104 : term,X107 : subst,X106 : subst,X105 : subst] : ((((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107)) != $true) | (((X103 @ X105 @ X104 @ (comp @ X106 @ X107))) = $true)) & ! [X111 : subst,X110 : subst,X113 : subst,X112 : term] : ((((X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113)) = $true) | (((X103 @ X110 @ X112 @ (comp @ X111 @ X113))) != $true)) & (((X103 @ id @ X101 @ id)) = $true)) | ? [X114 : (subst > term > subst > $o),X115 : term] : ((((X114 @ id @ (lam @ X115) @ id)) != $true) & ! [X120 : term] : ((((X114 @ id @ X120 @ id)) != $true) | (((X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) = $true)) & ! [X126 : subst,X129 : term,X127 : subst,X128 : subst] : (($true != ((X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))) | (((X114 @ X127 @ X129 @ (comp @ X128 @ X126))) = $true)) & ! [X121 : (subst > term > term)] : ((((X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true) | ? [X122 : term] : (($true != ((X114 @ id @ (X121 @ id @ X122) @ id))) & ($true = ((X114 @ id @ X122 @ id)))) | ? [X123 : term,X125 : subst,X124 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) != ((sub @ (X121 @ X124 @ X123) @ X125)))) & ! [X117 : subst,X119 : term,X118 : subst,X116 : subst] : ((((X114 @ X118 @ X119 @ (comp @ X117 @ X116))) != $true) | ($true = ((X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116))))))) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & (((d2subst @ d_id)) = sh) & ((? [X4 : (term > $o),X5 : term] : (! [X9 : term] : ((((X4 @ (lam @ X9))) = $true) | ? [X10 : term] : ((((X4 @ (sub @ X9 @ (push @ X10 @ id)))) != $true) & (((X4 @ X10)) = $true))) & ! [X6 : term] : (($true != ((var @ X6))) | (((X4 @ X6)) = $true)) & ! [X7 : term,X8 : term] : (($true != ((X4 @ X8))) | ($true != ((X4 @ X7))) | (((X4 @ (ap @ X8 @ X7))) = $true)) & ($true != ((X4 @ X5)))) | ? [X1 : (subst > term > subst > $o)] : ! [X2 : (term > $o)] : ? [X3 : term] : (((X2 @ X3)) != ((X1 @ id @ X3 @ id))) | ? [X11 : term] : (((sub @ X11 @ id)) != X11) | ! [X23 : term,X22 : (subst > term > subst > $o)] : (? [X24 : (subst > term > term)] : (! [X25 : term] : ((((X22 @ id @ (X24 @ id @ X25) @ id)) = $true) | ($true != ((X22 @ id @ X25 @ id)))) & ! [X28 : subst,X27 : term,X26 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) & (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) != $true)) | ($true = ((X22 @ id @ X23 @ id))) | ? [X30 : term,X29 : term] : ((((X22 @ id @ X29 @ id)) = $true) & (((X22 @ id @ X30 @ id)) = $true) & (((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id)) != $true))) | ? [X13 : (subst > term > subst > $o),X12 : term,X14 : (term > $o)] : (! [X15 : term] : (($true != ((X14 @ X15))) | (((X14 @ (sub @ X12 @ (push @ X15 @ id)))) = $true)) & ! [X16 : (subst > term > term)] : (? [X19 : subst,X18 : term,X17 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) != ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))) | ? [X20 : term] : ((((X13 @ id @ X20 @ id)) = $true) & (((X13 @ id @ (X16 @ id @ X20) @ id)) != $true)) | (((X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true)) & (((X14 @ (lam @ X12))) != $true) & ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((? [X325 : subst] : (((comp @ id @ X325)) != X325) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326) | (! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327))) <=> (substmonoid_lthm = $true)) & (lamnotvar = $true) & ((axvarcons = $true) <=> ! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291)) & (hoasinduction_lem1v2_gthm = $true) & (axclos = $true) & (hoaslamnotap_lthm = $true) & ((? [X488 : term] : (((sub @ X488 @ id)) != X488) | ! [X489 : term] : (((sub @ X489 @ id)) = X489)) <=> (termmset_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X322 : subst,X321 : term,X320 : (term > $o)] : ? [X323 : (term > $o)] : ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322)))))) & ((! [X186 : term,X185 : (subst > term > subst > $o)] : (? [X194 : (subst > term > term)] : ((((X185 @ id @ (lam @ (X194 @ sh @ one)) @ id)) != $true) & ! [X198 : term] : ((((X185 @ id @ (X194 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) & ! [X197 : term,X196 : subst,X195 : subst] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196)))) | ? [X192 : subst,X191 : subst,X193 : term,X190 : subst] : ((((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191)) != $true) & (((X185 @ X190 @ X193 @ (comp @ X192 @ X191))) = $true)) | ? [X201 : subst,X199 : subst,X200 : term,X202 : subst] : (($true = ((X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202))) & ($true != ((X185 @ X199 @ X200 @ (comp @ X201 @ X202))))) | (((X185 @ id @ X186 @ id)) = $true) | ? [X189 : term] : (($true = ((var @ (sub @ X189 @ id)))) & ($true != ((X185 @ id @ X189 @ id)))) | ? [X187 : term,X188 : term] : ((((X185 @ id @ X187 @ id)) = $true) & ($true = ((X185 @ id @ X188 @ id))) & (((X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id)) != $true))) | ? [X175 : (subst > term > subst > $o),X177 : (term > $o),X176 : term] : (! [X179 : term] : ((((X177 @ X179)) != $true) | (((X177 @ (sub @ X176 @ (push @ X179 @ id)))) = $true)) & (((X177 @ (lam @ X176))) != $true) & ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) & ! [X180 : (subst > term > term)] : ((((X175 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ? [X183 : subst,X182 : term,X181 : subst] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) != ((sub @ (X180 @ X181 @ X182) @ X183))) | ? [X184 : term] : ((((X175 @ id @ X184 @ id)) = $true) & (((X175 @ id @ (X180 @ id @ X184) @ id)) != $true)))) | ? [X174 : term] : (((sub @ X174 @ id)) != X174) | ? [X168 : (term > $o),X167 : term] : (! [X170 : term,X169 : term] : (($true != ((X168 @ X169))) | (((X168 @ X170)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)) & ! [X172 : term] : ((((X168 @ (lam @ X172))) = $true) | ? [X173 : term] : (($true = ((X168 @ X173))) & (((X168 @ (sub @ X172 @ (push @ X173 @ id)))) != $true))) & ($true != ((X168 @ X167))) & ! [X171 : term] : (($true != ((var @ X171))) | (((X168 @ X171)) = $true))) | ? [X164 : (subst > term > subst > $o)] : ! [X165 : (term > $o)] : ? [X166 : term] : (((X164 @ id @ X166 @ id)) != ((X165 @ X166)))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83)) | ? [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 != X78) & (((ap @ X77 @ X76)) = ((ap @ X79 @ X78)))))) & ! [X410 : d_term,X409 : d_term] : ((((d2term @ X410)) != ((d2term @ X409))) | (X409 = X410)) & (termmset_gthm = $true) & ((! [X471 : (term > $o),X470 : term,X472 : (subst > term > subst > $o)] : (? [X484 : subst,X486 : subst,X485 : subst,X483 : term] : ((((X472 @ X485 @ X483 @ (comp @ X484 @ X486))) != $true) & (((X472 @ (comp @ X485 @ X484) @ (sub @ X483 @ X484) @ X486)) = $true)) | ($true = ((X471 @ (lam @ X470)))) | ? [X473 : (subst > term > term)] : (! [X477 : subst,X476 : term,X475 : subst] : (((X473 @ (comp @ X475 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X473 @ X475 @ X476) @ X477))) & (((X472 @ id @ (lam @ (X473 @ sh @ one)) @ id)) != $true) & ! [X474 : term] : ((((X472 @ id @ (X473 @ id @ X474) @ id)) = $true) | (((X472 @ id @ X474 @ id)) != $true))) | ? [X482 : term] : (($true != ((X471 @ (sub @ X470 @ (push @ X482 @ id))))) & ($true = ((X471 @ X482)))) | ? [X478 : subst,X481 : subst,X479 : term,X480 : subst] : ((((X472 @ X481 @ X479 @ (comp @ X478 @ X480))) = $true) & (((X472 @ (comp @ X481 @ X478) @ (sub @ X479 @ X478) @ X480)) != $true)) | ? [X487 : term] : (((X471 @ X487)) != ((X472 @ id @ X487 @ id)))) | ? [X469 : term] : (((sub @ X469 @ id)) != X469)) <=> (hoasinduction_lem3v2_lthm = $true)) & (pushprop_lthm_orig = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X312 : (subst > term > subst > $o),X311 : term] : (? [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) = $true) & (((X312 @ id @ X318 @ id)) = $true) & (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) != $true)) | ? [X313 : (subst > term > term)] : (($true != ((X312 @ id @ (lam @ (X313 @ sh @ one)) @ id))) & ! [X315 : term,X314 : subst,X316 : subst] : (((sub @ (X313 @ X314 @ X315) @ X316)) = ((X313 @ (comp @ X314 @ X316) @ (sub @ X315 @ X316)))) & ! [X317 : term] : (($true = ((X312 @ id @ (X313 @ id @ X317) @ id))) | (((X312 @ id @ X317 @ id)) != $true))) | ($true = ((X312 @ id @ X311 @ id))))) & (! [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) | ($true != ((X335 @ X333)))) <=> (pushprop_lem1 = $true)) & (lamnotap != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (! [X329 : term] : ? [X330 : (subst > term > term)] : ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X75 : d_subst] : (d_id = X75) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & ((termmset = $true) <=> ! [X341 : term] : (((sub @ X341 @ id)) = X341)) & (induction2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem1_lthm = $true) <=> (? [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) != X157) | ? [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) != X155) | ! [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true != ((X163 @ X159))) | (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true)))) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) != ((d2subst @ X203))) | (X203 = X204)) & (! [X39 : term] : ? [X40 : (subst > term > term)] : (((X40 @ sh @ one)) = ((sub @ X39 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (axvarshift = $true) & ((laminj = $true) <=> ! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343))) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) <=> (shinj = $true)) & (hoasapnotvar_lthm = $true) & (hoasapinj2_gthm = $true) & ((apinj2 = $true) <=> ! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154))))) & (! [X445 : (term > $o),X447 : term,X446 : (subst > term > subst > $o)] : (? [X456 : term] : (((X446 @ id @ X456 @ id)) != ((X445 @ X456))) | ? [X454 : subst,X455 : subst,X452 : subst,X453 : term] : (($true = ((X446 @ (comp @ X455 @ X452) @ (sub @ X453 @ X452) @ X454))) & (((X446 @ X455 @ X453 @ (comp @ X452 @ X454))) != $true)) | ? [X457 : term] : ((((X445 @ X457)) = $true) & (((X445 @ (sub @ X447 @ (push @ X457 @ id)))) != $true)) | ? [X458 : (subst > term > term)] : (($true != ((X446 @ id @ (lam @ (X458 @ sh @ one)) @ id))) & ! [X462 : term] : ((((X446 @ id @ X462 @ id)) != $true) | ($true = ((X446 @ id @ (X458 @ id @ X462) @ id)))) & ! [X459 : term,X460 : subst,X461 : subst] : (((sub @ (X458 @ X460 @ X459) @ X461)) = ((X458 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461))))) | ($true = ((X445 @ (lam @ X447)))) | ? [X450 : subst,X449 : subst,X451 : term,X448 : subst] : ((((X446 @ (comp @ X450 @ X449) @ (sub @ X451 @ X449) @ X448)) != $true) & ($true = ((X446 @ X450 @ X451 @ (comp @ X449 @ X448)))))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) <=> ! [X213 : term,X214 : (subst > term > subst > $o),X212 : term] : (? [X215 : term,X216 : term] : (($true != ((X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))) & (((X214 @ id @ X216 @ id)) = $true) & ($true = ((X214 @ id @ X215 @ id)))) | (((X214 @ id @ (ap @ X212 @ X213) @ id)) = $true) | (((X214 @ id @ X213 @ id)) != $true) | (((X214 @ id @ X212 @ id)) != $true) | ? [X222 : term,X221 : subst,X223 : subst,X224 : subst] : (($true != ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221))) & (((X214 @ X223 @ X222 @ (comp @ X224 @ X221))) = $true)) | ? [X217 : term,X219 : subst,X218 : subst,X220 : subst] : (($true != ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)))) & ($true = ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)))))) & (ulamvar1 != $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X397 : term,X396 : (subst > term > subst > $o),X395 : (term > $o),X394 : term] : (? [X402 : subst,X399 : subst,X401 : subst,X400 : term] : ((((X396 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401) @ X399)) = $true) & (((X396 @ X402 @ X400 @ (comp @ X401 @ X399))) != $true)) | (((X395 @ (ap @ X394 @ X397))) = $true) | ? [X398 : term] : (((X396 @ id @ X398 @ id)) != ((X395 @ X398))) | ? [X403 : term,X404 : subst,X406 : subst,X405 : subst] : ((((X396 @ (comp @ X406 @ X404) @ (sub @ X403 @ X404) @ X405)) != $true) & ($true = ((X396 @ X406 @ X403 @ (comp @ X404 @ X405))))) | ? [X408 : term,X407 : term] : ((((X396 @ id @ (ap @ (sub @ X407 @ id) @ X408) @ id)) != $true) & (((X396 @ id @ X407 @ id)) = $true) & (((X396 @ id @ X408 @ id)) = $true)) | (((X395 @ X394)) != $true) | (((X395 @ X397)) != $true))) & (pushprop = $true) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) <=> (! [X503 : term,X501 : (term > $o),X502 : subst] : (? [X506 : term] : (($true != ((X501 @ (sub @ X506 @ X502)))) & (((var @ X506)) = $true)) | ? [X504 : term] : ((((X501 @ (lam @ X504))) != $true) & ! [X505 : term] : ((((X501 @ X505)) != $true) | (((X501 @ (sub @ X504 @ (push @ X505 @ id)))) = $true))) | (((X501 @ (sub @ X503 @ X502))) = $true) | ? [X507 : term,X508 : term] : (($true = ((X501 @ X508))) & (((X501 @ X507)) = $true) & ($true != ((X501 @ (ap @ X507 @ X508)))))) | ? [X490 : subst,X491 : term] : (((sub @ one @ (push @ X491 @ X490))) != X491) | ? [X494 : subst] : (((comp @ X494 @ id)) != X494) | ? [X496 : (term > $o),X495 : term] : ((((X496 @ X495)) != $true) & ! [X500 : term] : (($true != ((var @ X500))) | (((X496 @ X500)) = $true)) & ! [X498 : term,X499 : term] : ((((X496 @ (ap @ X498 @ X499))) = $true) | (((X496 @ X498)) != $true) | ($true != ((X496 @ X499)))) & ! [X497 : term] : ((((X496 @ (lam @ X497))) = $true) | (((X496 @ X497)) != $true))) | ? [X493 : term,X492 : subst] : (((comp @ sh @ (push @ X493 @ X492))) != X492))) & ((induction2 = $true) <=> ! [X205 : term,X206 : (term > $o)] : (? [X210 : term] : (! [X211 : term] : ((((X206 @ X211)) != $true) | ($true = ((X206 @ (sub @ X210 @ (push @ X211 @ id)))))) & (((X206 @ (lam @ X210))) != $true)) | ? [X208 : term,X207 : term] : ((((X206 @ X207)) = $true) & ($true != ((X206 @ (ap @ X208 @ X207)))) & ($true = ((X206 @ X208)))) | (((X206 @ X205)) = $true) | ? [X209 : term] : ((((var @ X209)) = $true) & (((X206 @ X209)) != $true)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction = $true) <=> ! [X246 : (subst > term > subst > $o),X247 : term] : (? [X257 : term] : (($true != ((X246 @ id @ X257 @ id))) & (((var @ (sub @ X257 @ id))) = $true)) | ? [X256 : subst,X254 : subst,X253 : subst,X255 : term] : (($true != ((X246 @ (comp @ X256 @ X254) @ (sub @ X255 @ X254) @ X253))) & (((X246 @ X256 @ X255 @ (comp @ X254 @ X253))) = $true)) | ? [X258 : term,X259 : term] : (($true = ((X246 @ id @ X259 @ id))) & ($true = ((X246 @ id @ X258 @ id))) & (((X246 @ id @ (ap @ (sub @ X259 @ id) @ X258) @ id)) != $true)) | (((X246 @ id @ X247 @ id)) = $true) | ? [X263 : subst,X260 : subst,X262 : subst,X261 : term] : ((((X246 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) = $true) & ($true != ((X246 @ X260 @ X261 @ (comp @ X263 @ X262))))) | ? [X248 : (subst > term > term)] : (! [X249 : subst,X250 : term,X251 : subst] : (((sub @ (X248 @ X249 @ X250) @ X251)) = ((X248 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251)))) & ($true != ((X246 @ id @ (lam @ (X248 @ sh @ one)) @ id))) & ! [X252 : term] : ((((X246 @ id @ X252 @ id)) != $true) | (((X246 @ id @ (X248 @ id @ X252) @ id)) = $true))))) & (pushprop_lem0_gthm = $true) & ((? [X344 : term] : (((sub @ X344 @ id)) != X344) | ? [X345 : term,X346 : (subst > term > subst > $o)] : (! [X348 : (subst > term > term)] : (? [X350 : subst,X352 : term,X351 : subst] : (((X348 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351))) != ((sub @ (X348 @ X350 @ X352) @ X351))) | ? [X349 : term] : (($true != ((X346 @ id @ (X348 @ id @ X349) @ id))) & (((X346 @ id @ X349 @ id)) = $true)) | (((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id)) = $true)) & (((X346 @ id @ (lam @ (sub @ X345 @ (push @ one @ sh))) @ id)) != $true) & ! [X347 : term] : ((((X346 @ id @ (sub @ X345 @ (push @ X347 @ id)) @ id)) = $true) | ($true != ((X346 @ id @ X347 @ id))))) | ! [X353 : (subst > term > subst > $o),X354 : term] : (? [X368 : term] : ((((X353 @ id @ X368 @ id)) = $true) & (((X353 @ id @ (sub @ X354 @ (push @ X368 @ id)) @ id)) != $true)) | ? [X366 : subst,X364 : term,X367 : subst,X365 : subst] : ((((X353 @ (comp @ X365 @ X366) @ (sub @ X364 @ X366) @ X367)) = $true) & (((X353 @ X365 @ X364 @ (comp @ X366 @ X367))) != $true)) | ? [X361 : term,X362 : subst,X363 : subst,X360 : subst] : ((((X353 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362)) != $true) & ($true = ((X353 @ X363 @ X361 @ (comp @ X360 @ X362))))) | ($true = ((X353 @ id @ (lam @ X354) @ id))) | ? [X355 : (subst > term > term)] : (! [X356 : term] : (($true != ((X353 @ id @ X356 @ id))) | (((X353 @ id @ (X355 @ id @ X356) @ id)) = $true)) & ! [X358 : subst,X359 : term,X357 : subst] : (((sub @ (X355 @ X358 @ X359) @ X357)) = ((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357)))) & ($true != ((X353 @ id @ (lam @ (X355 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3_lthm = $true)) & ((axidl = $true) <=> ! [X0 : subst] : (((comp @ id @ X0)) = X0)) & (hoasinduction_lem2_lthm = $true) & (hoaslamnotvar = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ? [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) = ((X539 @ sh @ one)))) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & ((pushprop_lem0 = $true) <=> ! [X383 : (term > $o),X381 : subst,X382 : term] : ? [X384 : (term > $o)] : ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X225 : term] : ! [X226 : (subst > term > term)] : ? [X227 : subst,X228 : term] : (((sub @ X225 @ (push @ X228 @ X227))) != ((X226 @ X227 @ X228))) | ! [X232 : (term > $o),X231 : (subst > term > subst > $o),X230 : term] : (? [X239 : term] : (($true != ((X232 @ (sub @ X230 @ (push @ X239 @ id))))) & (((X232 @ X239)) = $true)) | ? [X233 : (subst > term > term)] : (! [X234 : term] : ((((X231 @ id @ X234 @ id)) != $true) | ($true = ((X231 @ id @ (X233 @ id @ X234) @ id)))) & ! [X235 : subst,X237 : term,X236 : subst] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235)))) & (((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) != $true)) | ? [X238 : term] : (((X232 @ X238)) != ((X231 @ id @ X238 @ id))) | (((X232 @ (lam @ X230))) = $true)) | ? [X229 : term] : (((sub @ X229 @ id)) != X229))) & ((hoasinduction_lem3a = $true) <=> ! [X386 : (subst > term > subst > $o),X387 : term] : (? [X388 : (subst > term > term)] : (! [X389 : term] : ((((X386 @ id @ (X388 @ id @ X389) @ id)) = $true) | (((X386 @ id @ X389 @ id)) != $true)) & ! [X392 : term,X391 : subst,X390 : subst] : (((sub @ (X388 @ X391 @ X392) @ X390)) = ((X388 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) & (((X386 @ id @ (lam @ (X388 @ sh @ one)) @ id)) != $true)) | ? [X393 : term] : ((((X386 @ id @ X393 @ id)) = $true) & ($true != ((X386 @ id @ (sub @ X387 @ (push @ X393 @ id)) @ id)))) | (((X386 @ id @ (lam @ X387) @ id)) = $true))) & (axmap = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))) | ? [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) != ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | ? [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) != ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514)))) <=> (hoaslaminj = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X531 : (subst > term > subst > $o),X530 : term] : ((((X531 @ id @ (lam @ X530) @ id)) = $true) | ? [X533 : (subst > term > term)] : (($true != ((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id))) & ! [X535 : subst,X536 : subst,X534 : term] : (((sub @ (X533 @ X536 @ X534) @ X535)) = ((X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535)))) & ! [X537 : term] : (($true != ((X531 @ id @ X537 @ id))) | ($true = ((X531 @ id @ (X533 @ id @ X537) @ id))))) | ? [X532 : term] : (($true = ((X531 @ id @ X532 @ id))) & ($true != ((X531 @ id @ (sub @ X530 @ (push @ X532 @ id)) @ id))))) | ? [X523 : term,X522 : (subst > term > subst > $o)] : ((((X522 @ id @ (lam @ (sub @ X523 @ (push @ one @ sh))) @ id)) != $true) & ! [X524 : (subst > term > term)] : (? [X525 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X525)) != ((X524 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | ? [X528 : term] : ((((X522 @ id @ X528 @ id)) = $true) & (((X522 @ id @ (X524 @ id @ X528) @ id)) != $true)) | (((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)) = $true)) & ! [X529 : term] : (($true = ((X522 @ id @ (sub @ X523 @ (push @ X529 @ id)) @ id))) | (((X522 @ id @ X529 @ id)) != $true))) | ? [X521 : term] : (((sub @ X521 @ id)) != X521)) <=> (hoasinduction_lem3a_lthm = $true)) & ((? [X293 : term] : (((sub @ X293 @ id)) != X293) | ? [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) = ((ap @ X296 @ X297))) & (X295 != X296)) | ! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300))) <=> (hoasapinj1_lthm = $true)) & ((? [X267 : term,X266 : subst,X265 : (term > $o)] : ((((X265 @ (sub @ X267 @ X266))) != $true) & ! [X272 : term,X271 : term] : ((((X265 @ (ap @ X272 @ X271))) = $true) | ($true != ((X265 @ X271))) | (((X265 @ X272)) != $true)) & ! [X268 : term] : ((((X265 @ (lam @ X268))) = $true) | ? [X269 : term] : ((((X265 @ X269)) = $true) & ($true != ((X265 @ (sub @ X268 @ (push @ X269 @ id))))))) & ! [X270 : term] : ((((X265 @ (sub @ X270 @ X266))) = $true) | (((var @ X270)) != $true))) | ! [X273 : term,X274 : (term > $o)] : (? [X275 : term,X276 : term] : ((((X274 @ X276)) = $true) & (((X274 @ X275)) = $true) & (((X274 @ (ap @ X276 @ X275))) != $true)) | ? [X279 : term] : ((((var @ X279)) = $true) & (((X274 @ X279)) != $true)) | ? [X277 : term] : (! [X278 : term] : ((((X274 @ (sub @ X277 @ (push @ X278 @ id)))) = $true) | (((X274 @ X278)) != $true)) & ($true != ((X274 @ (lam @ X277))))) | (((X274 @ X273)) = $true)) | ? [X264 : term] : (((sub @ X264 @ id)) != X264)) <=> (induction2_lthm = $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (? [X286 : term] : (((X282 @ X286)) != ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) | ($true = ((X282 @ one))) | (((X285 @ X284)) != $true)) | ? [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) != X281))) & (! [X411 : subst] : (((comp @ X411 @ id)) = X411) <=> (axidr = $true)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (ulamvarind = $true) & (! [X370 : (subst > term > subst > $o),X369 : term] : ((((X370 @ id @ (lam @ (sub @ X369 @ (push @ one @ sh))) @ id)) = $true) | ? [X371 : term,X372 : (subst > term > term)] : (! [X375 : subst,X373 : term,X374 : subst] : (((X372 @ (comp @ X375 @ X374) @ (sub @ X373 @ X374))) = ((sub @ X371 @ (push @ (sub @ X373 @ X374) @ (comp @ X375 @ X374))))) & ! [X379 : term] : ((((X370 @ id @ (X372 @ id @ X379) @ id)) = $true) | (((X370 @ id @ X379 @ id)) != $true)) & ! [X378 : subst,X377 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X377) @ X378)) = ((sub @ (sub @ X371 @ (push @ X377 @ X376)) @ X378))) & (((X370 @ id @ (lam @ (X372 @ sh @ one)) @ id)) != $true)) | ? [X380 : term] : (($true = ((X370 @ id @ X380 @ id))) & (((X370 @ id @ (sub @ X369 @ (push @ X380 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X435 : (subst > term > subst > $o),X436 : term,X437 : (term > $o)] : ((((X437 @ (lam @ X436))) = $true) | ? [X439 : (subst > term > term)] : (! [X442 : subst,X441 : term,X443 : subst] : (((sub @ (X439 @ X443 @ X441) @ X442)) = ((X439 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442)))) & ! [X440 : term] : ((((X435 @ id @ (X439 @ id @ X440) @ id)) = $true) | (((X435 @ id @ X440 @ id)) != $true)) & (((X435 @ id @ (lam @ (X439 @ sh @ one)) @ id)) != $true)) | ? [X444 : term] : ((((X437 @ (sub @ X436 @ (push @ X444 @ id)))) != $true) & ($true = ((X437 @ X444)))) | ? [X438 : term] : (((X437 @ X438)) != ((X435 @ id @ X438 @ id))))) & (! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) <=> (axshiftcons = $true)) & (! [X245 : term] : (((sub @ X245 @ id)) = X245) <=> (axvarid = $true)) & (hoasinduction_lem3v2_gthm = $true) & (axapp = $true) & (hoasapinj1_gthm = $true) & (! [X33 : (term > $o),X31 : subst,X32 : term] : ((((X33 @ (sub @ X32 @ X31))) = $true) | ? [X34 : term] : ((((X33 @ (sub @ X34 @ X31))) != $true) & ($true = ((var @ X34)))) | ? [X36 : term,X35 : term] : ((((X33 @ X36)) = $true) & (((X33 @ X35)) = $true) & ($true != ((X33 @ (ap @ X36 @ X35))))) | ? [X37 : term] : ((((X33 @ (lam @ X37))) != $true) & ! [X38 : term] : (($true != ((X33 @ X38))) | ($true = ((X33 @ (sub @ X37 @ (push @ X38 @ id)))))))) <=> (induction2lem = $true)) & (substmonoid_gthm = $true) & (! [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))) | ? [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X88 @ X92 @ X93) @ X91)))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X338 : (subst > term > subst > $o)] : ? [X339 : (term > $o)] : ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X68 : term,X67 : (subst > term > subst > $o)] : (? [X69 : term] : ((((X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) != $true) & (((X67 @ id @ X69 @ id)) = $true)) | (((X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)) = $true) | ? [X70 : (subst > term > term)] : (! [X71 : term] : ((((X67 @ id @ (X70 @ id @ X71) @ id)) = $true) | (((X67 @ id @ X71 @ id)) != $true)) & ! [X74 : term,X72 : subst,X73 : subst] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72))) & ($true != ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1v2 = $true)),
% 6.34/1.36 inference(flattening,[],[f11])).
% 6.34/1.36 thf(f13,definition,(
% 6.34/1.36 (sP0 = $true) <=> ! [X68 : term,X67 : (subst > term > subst > $o)] : (? [X69 : term] : ((((X67 @ id @ (sub @ X68 @ (push @ X69 @ id)) @ id)) != $true) & (((X67 @ id @ X69 @ id)) = $true)) | (((X67 @ id @ (lam @ (sub @ X68 @ (push @ one @ sh))) @ id)) = $true) | ? [X70 : (subst > term > term)] : (! [X71 : term] : ((((X67 @ id @ (X70 @ id @ X71) @ id)) = $true) | (((X67 @ id @ X71 @ id)) != $true)) & ! [X74 : term,X72 : subst,X73 : subst] : (((X70 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72))) = ((sub @ (X70 @ X73 @ X74) @ X72))) & ($true != ((X67 @ id @ (lam @ (X70 @ sh @ one)) @ id)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f14,definition,(
% 6.34/1.36 ! [X33 : (term > $o)] : ((((sP1 @ X33)) = $true) <=> ? [X36 : term,X35 : term] : ((((X33 @ X36)) = $true) & (((X33 @ X35)) = $true) & ($true != ((X33 @ (ap @ X36 @ X35))))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f15,definition,(
% 6.34/1.36 (sP2 = $true) <=> ! [X33 : (term > $o),X31 : subst,X32 : term] : ((((X33 @ (sub @ X32 @ X31))) = $true) | ? [X34 : term] : ((((X33 @ (sub @ X34 @ X31))) != $true) & ($true = ((var @ X34)))) | (((sP1 @ X33)) = $true) | ? [X37 : term] : ((((X33 @ (lam @ X37))) != $true) & ! [X38 : term] : (($true != ((X33 @ X38))) | ($true = ((X33 @ (sub @ X37 @ (push @ X38 @ id))))))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f16,definition,(
% 6.34/1.36 (sP3 = $true) <=> ! [X435 : (subst > term > subst > $o),X436 : term,X437 : (term > $o)] : ((((X437 @ (lam @ X436))) = $true) | ? [X439 : (subst > term > term)] : (! [X442 : subst,X441 : term,X443 : subst] : (((sub @ (X439 @ X443 @ X441) @ X442)) = ((X439 @ (comp @ X443 @ X442) @ (sub @ X441 @ X442)))) & ! [X440 : term] : ((((X435 @ id @ (X439 @ id @ X440) @ id)) = $true) | (((X435 @ id @ X440 @ id)) != $true)) & (((X435 @ id @ (lam @ (X439 @ sh @ one)) @ id)) != $true)) | ? [X444 : term] : ((((X437 @ (sub @ X436 @ (push @ X444 @ id)))) != $true) & ($true = ((X437 @ X444)))) | ? [X438 : term] : (((X437 @ X438)) != ((X435 @ id @ X438 @ id))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f17,definition,(
% 6.34/1.36 ($true = sP4) <=> ! [X370 : (subst > term > subst > $o),X369 : term] : ((((X370 @ id @ (lam @ (sub @ X369 @ (push @ one @ sh))) @ id)) = $true) | ? [X371 : term,X372 : (subst > term > term)] : (! [X375 : subst,X373 : term,X374 : subst] : (((X372 @ (comp @ X375 @ X374) @ (sub @ X373 @ X374))) = ((sub @ X371 @ (push @ (sub @ X373 @ X374) @ (comp @ X375 @ X374))))) & ! [X379 : term] : ((((X370 @ id @ (X372 @ id @ X379) @ id)) = $true) | (((X370 @ id @ X379 @ id)) != $true)) & ! [X378 : subst,X377 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X377) @ X378)) = ((sub @ (sub @ X371 @ (push @ X377 @ X376)) @ X378))) & (((X370 @ id @ (lam @ (X372 @ sh @ one)) @ id)) != $true)) | ? [X380 : term] : (($true = ((X370 @ id @ X380 @ id))) & (((X370 @ id @ (sub @ X369 @ (push @ X380 @ id)) @ id)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f18,definition,(
% 6.34/1.36 ! [X274 : (term > $o)] : ((((sP5 @ X274)) = $true) <=> ? [X275 : term,X276 : term] : ((((X274 @ X276)) = $true) & (((X274 @ X275)) = $true) & (((X274 @ (ap @ X276 @ X275))) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f19,definition,(
% 6.34/1.36 ! [X265 : (term > $o)] : ((((sP6 @ X265)) = $true) <=> ! [X272 : term,X271 : term] : ((((X265 @ (ap @ X272 @ X271))) = $true) | ($true != ((X265 @ X271))) | (((X265 @ X272)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f20,definition,(
% 6.34/1.36 (sP7 = $true) <=> ! [X273 : term,X274 : (term > $o)] : ((((sP5 @ X274)) = $true) | ? [X279 : term] : ((((var @ X279)) = $true) & (((X274 @ X279)) != $true)) | ? [X277 : term] : (! [X278 : term] : ((((X274 @ (sub @ X277 @ (push @ X278 @ id)))) = $true) | (((X274 @ X278)) != $true)) & ($true != ((X274 @ (lam @ X277))))) | (((X274 @ X273)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f21,definition,(
% 6.34/1.36 (sP8 = $true) <=> (? [X267 : term,X266 : subst,X265 : (term > $o)] : ((((X265 @ (sub @ X267 @ X266))) != $true) & (((sP6 @ X265)) = $true) & ! [X268 : term] : ((((X265 @ (lam @ X268))) = $true) | ? [X269 : term] : ((((X265 @ X269)) = $true) & ($true != ((X265 @ (sub @ X268 @ (push @ X269 @ id))))))) & ! [X270 : term] : ((((X265 @ (sub @ X270 @ X266))) = $true) | (((var @ X270)) != $true))) | (sP7 = $true) | ? [X264 : term] : (((sub @ X264 @ id)) != X264))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f22,definition,(
% 6.34/1.36 (sP9 = $true) <=> ? [X523 : term,X522 : (subst > term > subst > $o)] : ((((X522 @ id @ (lam @ (sub @ X523 @ (push @ one @ sh))) @ id)) != $true) & ! [X524 : (subst > term > term)] : (? [X525 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X525)) != ((X524 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | ? [X528 : term] : ((((X522 @ id @ X528 @ id)) = $true) & (((X522 @ id @ (X524 @ id @ X528) @ id)) != $true)) | (((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)) = $true)) & ! [X529 : term] : (($true = ((X522 @ id @ (sub @ X523 @ (push @ X529 @ id)) @ id))) | (((X522 @ id @ X529 @ id)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f23,definition,(
% 6.34/1.36 (sP10 = $true) <=> (! [X531 : (subst > term > subst > $o),X530 : term] : ((((X531 @ id @ (lam @ X530) @ id)) = $true) | ? [X533 : (subst > term > term)] : (($true != ((X531 @ id @ (lam @ (X533 @ sh @ one)) @ id))) & ! [X535 : subst,X536 : subst,X534 : term] : (((sub @ (X533 @ X536 @ X534) @ X535)) = ((X533 @ (comp @ X536 @ X535) @ (sub @ X534 @ X535)))) & ! [X537 : term] : (($true != ((X531 @ id @ X537 @ id))) | ($true = ((X531 @ id @ (X533 @ id @ X537) @ id))))) | ? [X532 : term] : (($true = ((X531 @ id @ X532 @ id))) & ($true != ((X531 @ id @ (sub @ X530 @ (push @ X532 @ id)) @ id))))) | (sP9 = $true) | ? [X521 : term] : (((sub @ X521 @ id)) != X521))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f24,definition,(
% 6.34/1.36 ($true = sP11) <=> ! [X386 : (subst > term > subst > $o),X387 : term] : (? [X388 : (subst > term > term)] : (! [X389 : term] : ((((X386 @ id @ (X388 @ id @ X389) @ id)) = $true) | (((X386 @ id @ X389 @ id)) != $true)) & ! [X392 : term,X391 : subst,X390 : subst] : (((sub @ (X388 @ X391 @ X392) @ X390)) = ((X388 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) & (((X386 @ id @ (lam @ (X388 @ sh @ one)) @ id)) != $true)) | ? [X393 : term] : ((((X386 @ id @ X393 @ id)) = $true) & ($true != ((X386 @ id @ (sub @ X387 @ (push @ X393 @ id)) @ id)))) | (((X386 @ id @ (lam @ X387) @ id)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f25,definition,(
% 6.34/1.36 ($true = sP12) <=> (? [X225 : term] : ! [X226 : (subst > term > term)] : ? [X227 : subst,X228 : term] : (((sub @ X225 @ (push @ X228 @ X227))) != ((X226 @ X227 @ X228))) | ! [X232 : (term > $o),X231 : (subst > term > subst > $o),X230 : term] : (? [X239 : term] : (($true != ((X232 @ (sub @ X230 @ (push @ X239 @ id))))) & (((X232 @ X239)) = $true)) | ? [X233 : (subst > term > term)] : (! [X234 : term] : ((((X231 @ id @ X234 @ id)) != $true) | ($true = ((X231 @ id @ (X233 @ id @ X234) @ id)))) & ! [X235 : subst,X237 : term,X236 : subst] : (((sub @ (X233 @ X236 @ X237) @ X235)) = ((X233 @ (comp @ X236 @ X235) @ (sub @ X237 @ X235)))) & (((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) != $true)) | ? [X238 : term] : (((X232 @ X238)) != ((X231 @ id @ X238 @ id))) | (((X232 @ (lam @ X230))) = $true)) | ? [X229 : term] : (((sub @ X229 @ id)) != X229))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f26,definition,(
% 6.34/1.36 ! [X353 : (subst > term > subst > $o)] : ((((sP13 @ X353)) = $true) <=> ? [X355 : (subst > term > term)] : (! [X356 : term] : (($true != ((X353 @ id @ X356 @ id))) | (((X353 @ id @ (X355 @ id @ X356) @ id)) = $true)) & ! [X358 : subst,X359 : term,X357 : subst] : (((sub @ (X355 @ X358 @ X359) @ X357)) = ((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357)))) & ($true != ((X353 @ id @ (lam @ (X355 @ sh @ one)) @ id)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f27,definition,(
% 6.34/1.36 ($true = sP14) <=> ? [X345 : term,X346 : (subst > term > subst > $o)] : (! [X348 : (subst > term > term)] : (? [X350 : subst,X352 : term,X351 : subst] : (((X348 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351))) != ((sub @ (X348 @ X350 @ X352) @ X351))) | ? [X349 : term] : (($true != ((X346 @ id @ (X348 @ id @ X349) @ id))) & (((X346 @ id @ X349 @ id)) = $true)) | (((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id)) = $true)) & (((X346 @ id @ (lam @ (sub @ X345 @ (push @ one @ sh))) @ id)) != $true) & ! [X347 : term] : ((((X346 @ id @ (sub @ X345 @ (push @ X347 @ id)) @ id)) = $true) | ($true != ((X346 @ id @ X347 @ id)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f28,definition,(
% 6.34/1.36 (sP15 = $true) <=> (? [X344 : term] : (((sub @ X344 @ id)) != X344) | ($true = sP14) | ! [X353 : (subst > term > subst > $o),X354 : term] : (? [X368 : term] : ((((X353 @ id @ X368 @ id)) = $true) & (((X353 @ id @ (sub @ X354 @ (push @ X368 @ id)) @ id)) != $true)) | ? [X366 : subst,X364 : term,X367 : subst,X365 : subst] : ((((X353 @ (comp @ X365 @ X366) @ (sub @ X364 @ X366) @ X367)) = $true) & (((X353 @ X365 @ X364 @ (comp @ X366 @ X367))) != $true)) | ? [X361 : term,X362 : subst,X363 : subst,X360 : subst] : ((((X353 @ (comp @ X363 @ X360) @ (sub @ X361 @ X360) @ X362)) != $true) & ($true = ((X353 @ X363 @ X361 @ (comp @ X360 @ X362))))) | ($true = ((X353 @ id @ (lam @ X354) @ id))) | (((sP13 @ X353)) = $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f29,definition,(
% 6.34/1.36 ! [X246 : (subst > term > subst > $o)] : ((((sP16 @ X246)) = $true) <=> ? [X248 : (subst > term > term)] : (! [X249 : subst,X250 : term,X251 : subst] : (((sub @ (X248 @ X249 @ X250) @ X251)) = ((X248 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251)))) & ($true != ((X246 @ id @ (lam @ (X248 @ sh @ one)) @ id))) & ! [X252 : term] : ((((X246 @ id @ X252 @ id)) != $true) | (((X246 @ id @ (X248 @ id @ X252) @ id)) = $true))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f30,definition,(
% 6.34/1.36 ! [X246 : (subst > term > subst > $o)] : ((((sP17 @ X246)) = $true) <=> ? [X258 : term,X259 : term] : (($true = ((X246 @ id @ X259 @ id))) & ($true = ((X246 @ id @ X258 @ id))) & (((X246 @ id @ (ap @ (sub @ X259 @ id) @ X258) @ id)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f31,definition,(
% 6.34/1.36 (sP18 = $true) <=> ! [X246 : (subst > term > subst > $o),X247 : term] : (? [X257 : term] : (($true != ((X246 @ id @ X257 @ id))) & (((var @ (sub @ X257 @ id))) = $true)) | ? [X256 : subst,X254 : subst,X253 : subst,X255 : term] : (($true != ((X246 @ (comp @ X256 @ X254) @ (sub @ X255 @ X254) @ X253))) & (((X246 @ X256 @ X255 @ (comp @ X254 @ X253))) = $true)) | (((sP17 @ X246)) = $true) | (((X246 @ id @ X247 @ id)) = $true) | ? [X263 : subst,X260 : subst,X262 : subst,X261 : term] : ((((X246 @ (comp @ X260 @ X263) @ (sub @ X261 @ X263) @ X262)) = $true) & ($true != ((X246 @ X260 @ X261 @ (comp @ X263 @ X262))))) | (((sP16 @ X246)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f32,definition,(
% 6.34/1.36 ! [X206 : (term > $o)] : (($true = ((sP19 @ X206))) <=> ? [X208 : term,X207 : term] : ((((X206 @ X207)) = $true) & ($true != ((X206 @ (ap @ X208 @ X207)))) & ($true = ((X206 @ X208)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f33,definition,(
% 6.34/1.36 (sP20 = $true) <=> ! [X205 : term,X206 : (term > $o)] : (? [X210 : term] : (! [X211 : term] : ((((X206 @ X211)) != $true) | ($true = ((X206 @ (sub @ X210 @ (push @ X211 @ id)))))) & (((X206 @ (lam @ X210))) != $true)) | ($true = ((sP19 @ X206))) | (((X206 @ X205)) = $true) | ? [X209 : term] : ((((var @ X209)) = $true) & (((X206 @ X209)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f34,definition,(
% 6.34/1.36 ! [X496 : (term > $o)] : ((((sP21 @ X496)) = $true) <=> ! [X498 : term,X499 : term] : ((((X496 @ (ap @ X498 @ X499))) = $true) | (((X496 @ X498)) != $true) | ($true != ((X496 @ X499)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f35,definition,(
% 6.34/1.36 ! [X501 : (term > $o)] : (($true = ((sP22 @ X501))) <=> ? [X507 : term,X508 : term] : (($true = ((X501 @ X508))) & (((X501 @ X507)) = $true) & ($true != ((X501 @ (ap @ X507 @ X508))))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f36,definition,(
% 6.34/1.36 ($true = sP23) <=> ! [X503 : term,X501 : (term > $o),X502 : subst] : (? [X506 : term] : (($true != ((X501 @ (sub @ X506 @ X502)))) & (((var @ X506)) = $true)) | ? [X504 : term] : ((((X501 @ (lam @ X504))) != $true) & ! [X505 : term] : ((((X501 @ X505)) != $true) | (((X501 @ (sub @ X504 @ (push @ X505 @ id)))) = $true))) | (((X501 @ (sub @ X503 @ X502))) = $true) | ($true = ((sP22 @ X501))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f37,definition,(
% 6.34/1.36 ($true = sP24) <=> (($true = sP23) | ? [X490 : subst,X491 : term] : (((sub @ one @ (push @ X491 @ X490))) != X491) | ? [X494 : subst] : (((comp @ X494 @ id)) != X494) | ? [X496 : (term > $o),X495 : term] : ((((X496 @ X495)) != $true) & ! [X500 : term] : (($true != ((var @ X500))) | (((X496 @ X500)) = $true)) & (((sP21 @ X496)) = $true) & ! [X497 : term] : ((((X496 @ (lam @ X497))) = $true) | (((X496 @ X497)) != $true))) | ? [X493 : term,X492 : subst] : (((comp @ sh @ (push @ X493 @ X492))) != X492))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f38,definition,(
% 6.34/1.36 ! [X396 : (subst > term > subst > $o)] : ((((sP25 @ X396)) = $true) <=> ? [X408 : term,X407 : term] : ((((X396 @ id @ (ap @ (sub @ X407 @ id) @ X408) @ id)) != $true) & (((X396 @ id @ X407 @ id)) = $true) & (((X396 @ id @ X408 @ id)) = $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f39,definition,(
% 6.34/1.36 (sP26 = $true) <=> ! [X397 : term,X396 : (subst > term > subst > $o),X395 : (term > $o),X394 : term] : (? [X402 : subst,X399 : subst,X401 : subst,X400 : term] : ((((X396 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401) @ X399)) = $true) & (((X396 @ X402 @ X400 @ (comp @ X401 @ X399))) != $true)) | (((X395 @ (ap @ X394 @ X397))) = $true) | ? [X398 : term] : (((X396 @ id @ X398 @ id)) != ((X395 @ X398))) | ? [X403 : term,X404 : subst,X406 : subst,X405 : subst] : ((((X396 @ (comp @ X406 @ X404) @ (sub @ X403 @ X404) @ X405)) != $true) & ($true = ((X396 @ X406 @ X403 @ (comp @ X404 @ X405))))) | (((sP25 @ X396)) = $true) | (((X395 @ X394)) != $true) | (((X395 @ X397)) != $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f40,definition,(
% 6.34/1.36 ! [X214 : (subst > term > subst > $o)] : ((((sP27 @ X214)) = $true) <=> ? [X215 : term,X216 : term] : (($true != ((X214 @ id @ (ap @ (sub @ X215 @ id) @ X216) @ id))) & (((X214 @ id @ X216 @ id)) = $true) & ($true = ((X214 @ id @ X215 @ id)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f41,definition,(
% 6.34/1.36 ($true = sP28) <=> ! [X213 : term,X214 : (subst > term > subst > $o),X212 : term] : ((((sP27 @ X214)) = $true) | (((X214 @ id @ (ap @ X212 @ X213) @ id)) = $true) | (((X214 @ id @ X213 @ id)) != $true) | (((X214 @ id @ X212 @ id)) != $true) | ? [X222 : term,X221 : subst,X223 : subst,X224 : subst] : (($true != ((X214 @ (comp @ X223 @ X224) @ (sub @ X222 @ X224) @ X221))) & (((X214 @ X223 @ X222 @ (comp @ X224 @ X221))) = $true)) | ? [X217 : term,X219 : subst,X218 : subst,X220 : subst] : (($true != ((X214 @ X218 @ X217 @ (comp @ X219 @ X220)))) & ($true = ((X214 @ (comp @ X218 @ X219) @ (sub @ X217 @ X219) @ X220)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f42,definition,(
% 6.34/1.36 ! [X446 : (subst > term > subst > $o)] : ((((sP29 @ X446)) = $true) <=> ? [X458 : (subst > term > term)] : (($true != ((X446 @ id @ (lam @ (X458 @ sh @ one)) @ id))) & ! [X462 : term] : ((((X446 @ id @ X462 @ id)) != $true) | ($true = ((X446 @ id @ (X458 @ id @ X462) @ id)))) & ! [X459 : term,X460 : subst,X461 : subst] : (((sub @ (X458 @ X460 @ X459) @ X461)) = ((X458 @ (comp @ X460 @ X461) @ (sub @ X459 @ X461))))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f43,definition,(
% 6.34/1.36 (sP30 = $true) <=> ! [X445 : (term > $o),X447 : term,X446 : (subst > term > subst > $o)] : (? [X456 : term] : (((X446 @ id @ X456 @ id)) != ((X445 @ X456))) | ? [X454 : subst,X455 : subst,X452 : subst,X453 : term] : (($true = ((X446 @ (comp @ X455 @ X452) @ (sub @ X453 @ X452) @ X454))) & (((X446 @ X455 @ X453 @ (comp @ X452 @ X454))) != $true)) | ? [X457 : term] : ((((X445 @ X457)) = $true) & (((X445 @ (sub @ X447 @ (push @ X457 @ id)))) != $true)) | (((sP29 @ X446)) = $true) | ($true = ((X445 @ (lam @ X447)))) | ? [X450 : subst,X449 : subst,X451 : term,X448 : subst] : ((((X446 @ (comp @ X450 @ X449) @ (sub @ X451 @ X449) @ X448)) != $true) & ($true = ((X446 @ X450 @ X451 @ (comp @ X449 @ X448))))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f44,definition,(
% 6.34/1.36 ! [X312 : (subst > term > subst > $o)] : ((((sP31 @ X312)) = $true) <=> ? [X313 : (subst > term > term)] : (($true != ((X312 @ id @ (lam @ (X313 @ sh @ one)) @ id))) & ! [X315 : term,X314 : subst,X316 : subst] : (((sub @ (X313 @ X314 @ X315) @ X316)) = ((X313 @ (comp @ X314 @ X316) @ (sub @ X315 @ X316)))) & ! [X317 : term] : (($true = ((X312 @ id @ (X313 @ id @ X317) @ id))) | (((X312 @ id @ X317 @ id)) != $true))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f45,definition,(
% 6.34/1.36 ! [X472 : (subst > term > subst > $o)] : (($true = ((sP32 @ X472))) <=> ? [X473 : (subst > term > term)] : (! [X477 : subst,X476 : term,X475 : subst] : (((X473 @ (comp @ X475 @ X477) @ (sub @ X476 @ X477))) = ((sub @ (X473 @ X475 @ X476) @ X477))) & (((X472 @ id @ (lam @ (X473 @ sh @ one)) @ id)) != $true) & ! [X474 : term] : ((((X472 @ id @ (X473 @ id @ X474) @ id)) = $true) | (((X472 @ id @ X474 @ id)) != $true))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f46,definition,(
% 6.34/1.36 ($true = sP33) <=> (! [X471 : (term > $o),X470 : term,X472 : (subst > term > subst > $o)] : (? [X484 : subst,X486 : subst,X485 : subst,X483 : term] : ((((X472 @ X485 @ X483 @ (comp @ X484 @ X486))) != $true) & (((X472 @ (comp @ X485 @ X484) @ (sub @ X483 @ X484) @ X486)) = $true)) | ($true = ((X471 @ (lam @ X470)))) | ($true = ((sP32 @ X472))) | ? [X482 : term] : (($true != ((X471 @ (sub @ X470 @ (push @ X482 @ id))))) & ($true = ((X471 @ X482)))) | ? [X478 : subst,X481 : subst,X479 : term,X480 : subst] : ((((X472 @ X481 @ X479 @ (comp @ X478 @ X480))) = $true) & (((X472 @ (comp @ X481 @ X478) @ (sub @ X479 @ X478) @ X480)) != $true)) | ? [X487 : term] : (((X471 @ X487)) != ((X472 @ id @ X487 @ id)))) | ? [X469 : term] : (((sub @ X469 @ id)) != X469))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f47,definition,(
% 6.34/1.36 ! [X168 : (term > $o)] : ((((sP34 @ X168)) = $true) <=> ! [X170 : term,X169 : term] : (($true != ((X168 @ X169))) | (((X168 @ X170)) != $true) | (((X168 @ (ap @ X169 @ X170))) = $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f48,definition,(
% 6.34/1.36 ! [X185 : (subst > term > subst > $o)] : (($true = ((sP35 @ X185))) <=> ? [X187 : term,X188 : term] : ((((X185 @ id @ X187 @ id)) = $true) & ($true = ((X185 @ id @ X188 @ id))) & (((X185 @ id @ (ap @ (sub @ X188 @ id) @ X187) @ id)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f49,definition,(
% 6.34/1.36 ! [X185 : (subst > term > subst > $o)] : ((((sP36 @ X185)) = $true) <=> ? [X194 : (subst > term > term)] : ((((X185 @ id @ (lam @ (X194 @ sh @ one)) @ id)) != $true) & ! [X198 : term] : ((((X185 @ id @ (X194 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) & ! [X197 : term,X196 : subst,X195 : subst] : (((X194 @ (comp @ X195 @ X196) @ (sub @ X197 @ X196))) = ((sub @ (X194 @ X195 @ X197) @ X196)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f50,definition,(
% 6.34/1.36 ($true = sP37) <=> ? [X175 : (subst > term > subst > $o),X177 : (term > $o),X176 : term] : (! [X179 : term] : ((((X177 @ X179)) != $true) | (((X177 @ (sub @ X176 @ (push @ X179 @ id)))) = $true)) & (((X177 @ (lam @ X176))) != $true) & ! [X178 : term] : (((X177 @ X178)) = ((X175 @ id @ X178 @ id))) & ! [X180 : (subst > term > term)] : ((((X175 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ? [X183 : subst,X182 : term,X181 : subst] : (((X180 @ (comp @ X181 @ X183) @ (sub @ X182 @ X183))) != ((sub @ (X180 @ X181 @ X182) @ X183))) | ? [X184 : term] : ((((X175 @ id @ X184 @ id)) = $true) & (((X175 @ id @ (X180 @ id @ X184) @ id)) != $true))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f51,definition,(
% 6.34/1.36 (sP38 = $true) <=> ! [X186 : term,X185 : (subst > term > subst > $o)] : ((((sP36 @ X185)) = $true) | ? [X192 : subst,X191 : subst,X193 : term,X190 : subst] : ((((X185 @ (comp @ X190 @ X192) @ (sub @ X193 @ X192) @ X191)) != $true) & (((X185 @ X190 @ X193 @ (comp @ X192 @ X191))) = $true)) | ? [X201 : subst,X199 : subst,X200 : term,X202 : subst] : (($true = ((X185 @ (comp @ X199 @ X201) @ (sub @ X200 @ X201) @ X202))) & ($true != ((X185 @ X199 @ X200 @ (comp @ X201 @ X202))))) | (((X185 @ id @ X186 @ id)) = $true) | ? [X189 : term] : (($true = ((var @ (sub @ X189 @ id)))) & ($true != ((X185 @ id @ X189 @ id)))) | ($true = ((sP35 @ X185))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f52,definition,(
% 6.34/1.36 (sP39 = $true) <=> ((sP38 = $true) | ($true = sP37) | ? [X174 : term] : (((sub @ X174 @ id)) != X174) | ? [X168 : (term > $o),X167 : term] : ((((sP34 @ X168)) = $true) & ! [X172 : term] : ((((X168 @ (lam @ X172))) = $true) | ? [X173 : term] : (($true = ((X168 @ X173))) & (((X168 @ (sub @ X172 @ (push @ X173 @ id)))) != $true))) & ($true != ((X168 @ X167))) & ! [X171 : term] : (($true != ((var @ X171))) | (((X168 @ X171)) = $true))) | ? [X164 : (subst > term > subst > $o)] : ! [X165 : (term > $o)] : ? [X166 : term] : (((X164 @ id @ X166 @ id)) != ((X165 @ X166))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f53,definition,(
% 6.34/1.36 ! [X22 : (subst > term > subst > $o)] : ((((sP40 @ X22)) = $true) <=> ? [X30 : term,X29 : term] : ((((X22 @ id @ X29 @ id)) = $true) & (((X22 @ id @ X30 @ id)) = $true) & (((X22 @ id @ (ap @ (sub @ X30 @ id) @ X29) @ id)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f54,definition,(
% 6.34/1.36 ! [X4 : (term > $o)] : (($true = ((sP41 @ X4))) <=> ! [X7 : term,X8 : term] : (($true != ((X4 @ X8))) | ($true != ((X4 @ X7))) | (((X4 @ (ap @ X8 @ X7))) = $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f55,definition,(
% 6.34/1.36 ($true = sP42) <=> ? [X13 : (subst > term > subst > $o),X12 : term,X14 : (term > $o)] : (! [X15 : term] : (($true != ((X14 @ X15))) | (((X14 @ (sub @ X12 @ (push @ X15 @ id)))) = $true)) & ! [X16 : (subst > term > term)] : (? [X19 : subst,X18 : term,X17 : subst] : (((sub @ (X16 @ X17 @ X18) @ X19)) != ((X16 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))) | ? [X20 : term] : ((((X13 @ id @ X20 @ id)) = $true) & (((X13 @ id @ (X16 @ id @ X20) @ id)) != $true)) | (((X13 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true)) & (((X14 @ (lam @ X12))) != $true) & ! [X21 : term] : (((X13 @ id @ X21 @ id)) = ((X14 @ X21))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f56,definition,(
% 6.34/1.36 ($true = sP43) <=> ! [X23 : term,X22 : (subst > term > subst > $o)] : (? [X24 : (subst > term > term)] : (! [X25 : term] : ((((X22 @ id @ (X24 @ id @ X25) @ id)) = $true) | ($true != ((X22 @ id @ X25 @ id)))) & ! [X28 : subst,X27 : term,X26 : subst] : (((sub @ (X24 @ X28 @ X27) @ X26)) = ((X24 @ (comp @ X28 @ X26) @ (sub @ X27 @ X26)))) & (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) != $true)) | ($true = ((X22 @ id @ X23 @ id))) | (((sP40 @ X22)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f57,definition,(
% 6.34/1.36 (sP44 = $true) <=> (? [X4 : (term > $o),X5 : term] : (! [X9 : term] : ((((X4 @ (lam @ X9))) = $true) | ? [X10 : term] : ((((X4 @ (sub @ X9 @ (push @ X10 @ id)))) != $true) & (((X4 @ X10)) = $true))) & ! [X6 : term] : (($true != ((var @ X6))) | (((X4 @ X6)) = $true)) & ($true = ((sP41 @ X4))) & ($true != ((X4 @ X5)))) | ? [X1 : (subst > term > subst > $o)] : ! [X2 : (term > $o)] : ? [X3 : term] : (((X2 @ X3)) != ((X1 @ id @ X3 @ id))) | ? [X11 : term] : (((sub @ X11 @ id)) != X11) | ($true = sP43) | ($true = sP42))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f58,definition,(
% 6.34/1.36 ! [X114 : (subst > term > subst > $o)] : (($true = ((sP45 @ X114))) <=> ! [X121 : (subst > term > term)] : ((((X114 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true) | ? [X122 : term] : (($true != ((X114 @ id @ (X121 @ id @ X122) @ id))) & ($true = ((X114 @ id @ X122 @ id)))) | ? [X123 : term,X125 : subst,X124 : subst] : (((X121 @ (comp @ X124 @ X125) @ (sub @ X123 @ X125))) != ((sub @ (X121 @ X124 @ X123) @ X125)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f59,definition,(
% 6.34/1.36 ! [X103 : (subst > term > subst > $o)] : ((((sP46 @ X103)) = $true) <=> ! [X109 : term,X108 : term] : ((((X103 @ id @ X109 @ id)) != $true) | ($true != ((X103 @ id @ X108 @ id))) | ($true = ((X103 @ id @ (ap @ (sub @ X108 @ id) @ X109) @ id)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f60,definition,(
% 6.34/1.36 ! [X94 : (term > $o)] : ((((sP47 @ X94)) = $true) <=> ! [X97 : term,X96 : term] : ((((X94 @ (ap @ X96 @ X97))) = $true) | ($true != ((X94 @ X97))) | (((X94 @ X96)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f61,definition,(
% 6.34/1.36 ! [X130 : (subst > term > subst > $o)] : ((((sP48 @ X130)) = $true) <=> ? [X132 : (subst > term > term)] : (! [X133 : subst,X135 : term,X134 : subst] : (((X132 @ (comp @ X133 @ X134) @ (sub @ X135 @ X134))) = ((sub @ (X132 @ X133 @ X135) @ X134))) & (((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) != $true) & ! [X136 : term] : (($true != ((X130 @ id @ X136 @ id))) | (((X130 @ id @ (X132 @ id @ X136) @ id)) = $true))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f62,definition,(
% 6.34/1.36 ! [X130 : (subst > term > subst > $o)] : (($true = ((sP49 @ X130))) <=> ? [X139 : term,X138 : term] : ((((X130 @ id @ X139 @ id)) = $true) & ($true = ((X130 @ id @ X138 @ id))) & (((X130 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f63,definition,(
% 6.34/1.36 (sP50 = $true) <=> ? [X114 : (subst > term > subst > $o),X115 : term] : ((((X114 @ id @ (lam @ X115) @ id)) != $true) & ! [X120 : term] : ((((X114 @ id @ X120 @ id)) != $true) | (((X114 @ id @ (sub @ X115 @ (push @ X120 @ id)) @ id)) = $true)) & ! [X126 : subst,X129 : term,X127 : subst,X128 : subst] : (($true != ((X114 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128) @ X126))) | (((X114 @ X127 @ X129 @ (comp @ X128 @ X126))) = $true)) & ($true = ((sP45 @ X114))) & ! [X117 : subst,X119 : term,X118 : subst,X116 : subst] : ((((X114 @ X118 @ X119 @ (comp @ X117 @ X116))) != $true) | ($true = ((X114 @ (comp @ X118 @ X117) @ (sub @ X119 @ X117) @ X116)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f64,definition,(
% 6.34/1.36 (sP51 = $true) <=> ! [X131 : term,X130 : (subst > term > subst > $o)] : (? [X137 : term] : ((((X130 @ id @ X137 @ id)) != $true) & ($true = ((var @ (sub @ X137 @ id))))) | ($true = ((X130 @ id @ X131 @ id))) | ? [X140 : term,X143 : subst,X141 : subst,X142 : subst] : (($true = ((X130 @ X141 @ X140 @ (comp @ X142 @ X143)))) & (((X130 @ (comp @ X141 @ X142) @ (sub @ X140 @ X142) @ X143)) != $true)) | ($true = ((sP49 @ X130))) | ? [X144 : subst,X145 : term,X147 : subst,X146 : subst] : ((((X130 @ X147 @ X145 @ (comp @ X144 @ X146))) != $true) & (((X130 @ (comp @ X147 @ X144) @ (sub @ X145 @ X144) @ X146)) = $true)) | (((sP48 @ X130)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f65,definition,(
% 6.34/1.36 (sP52 = $true) <=> ? [X102 : term,X103 : (subst > term > subst > $o),X101 : term] : ((((sP46 @ X103)) = $true) & ($true != ((X103 @ id @ (ap @ X102 @ X101) @ id))) & (((X103 @ id @ X102 @ id)) = $true) & ! [X104 : term,X107 : subst,X106 : subst,X105 : subst] : ((((X103 @ (comp @ X105 @ X106) @ (sub @ X104 @ X106) @ X107)) != $true) | (((X103 @ X105 @ X104 @ (comp @ X106 @ X107))) = $true)) & ! [X111 : subst,X110 : subst,X113 : subst,X112 : term] : ((((X103 @ (comp @ X110 @ X111) @ (sub @ X112 @ X111) @ X113)) = $true) | (((X103 @ X110 @ X112 @ (comp @ X111 @ X113))) != $true)) & (((X103 @ id @ X101 @ id)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f66,definition,(
% 6.34/1.36 (sP53 = $true) <=> ((sP51 = $true) | ? [X95 : term,X94 : (term > $o)] : ((((sP47 @ X94)) = $true) & (((X94 @ X95)) != $true) & ! [X98 : term] : (? [X99 : term] : ((((X94 @ (sub @ X98 @ (push @ X99 @ id)))) != $true) & ($true = ((X94 @ X99)))) | (((X94 @ (lam @ X98))) = $true)) & ! [X100 : term] : ((((X94 @ X100)) = $true) | (((var @ X100)) != $true))) | (sP52 = $true) | (sP50 = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f67,definition,(
% 6.34/1.36 (sP54 = $true) <=> ! [X303 : (subst > term > subst > $o),X304 : term] : (? [X310 : term] : ((((X303 @ id @ X310 @ id)) = $true) & ($true != ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id)))) | ? [X305 : (subst > term > term)] : (! [X306 : term] : ((((X303 @ id @ X306 @ id)) != $true) | (((X303 @ id @ (X305 @ id @ X306) @ id)) = $true)) & ! [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) = ((sub @ (X305 @ X307 @ X309) @ X308))) & ($true != ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id)))) | (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f68,definition,(
% 6.34/1.36 ! [X413 : (subst > term > subst > $o)] : ((((sP55 @ X413)) = $true) <=> ? [X415 : (subst > term > term)] : (! [X416 : term,X417 : subst,X418 : subst] : (((X415 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417))) = ((sub @ (X415 @ X418 @ X416) @ X417))) & (((X413 @ id @ (lam @ (X415 @ sh @ one)) @ id)) != $true) & ! [X419 : term] : ((((X413 @ id @ (X415 @ id @ X419) @ id)) = $true) | (((X413 @ id @ X419 @ id)) != $true))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f69,definition,(
% 6.34/1.36 (sP56 = $true) <=> ! [X414 : term,X413 : (subst > term > subst > $o)] : ((((sP55 @ X413)) = $true) | ? [X424 : term] : (($true = ((X413 @ id @ X424 @ id))) & (((X413 @ id @ (sub @ X414 @ (push @ X424 @ id)) @ id)) != $true)) | ? [X422 : term,X423 : subst,X421 : subst,X420 : subst] : ((((X413 @ X421 @ X422 @ (comp @ X423 @ X420))) = $true) & ($true != ((X413 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423) @ X420)))) | ($true = ((X413 @ id @ (lam @ X414) @ id))) | ? [X425 : subst,X427 : subst,X426 : term,X428 : subst] : (($true != ((X413 @ X425 @ X426 @ (comp @ X427 @ X428)))) & ($true = ((X413 @ (comp @ X425 @ X427) @ (sub @ X426 @ X427) @ X428)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f70,definition,(
% 6.34/1.36 ! [X62 : (term > $o)] : ((((sP57 @ X62)) = $true) <=> ? [X64 : term,X63 : term] : (($true = ((X62 @ X63))) & ($true = ((X62 @ X64))) & (((X62 @ (ap @ X64 @ X63))) != $true)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f71,definition,(
% 6.34/1.36 (sP58 = $true) <=> (! [X50 : subst,X48 : term,X47 : (subst > term > term),X49 : (subst > term > term)] : (? [X51 : term,X52 : subst,X53 : subst] : (((sub @ (X49 @ X52 @ X51) @ X53)) != ((X49 @ (comp @ X52 @ X53) @ (sub @ X51 @ X53)))) | ? [X55 : subst,X56 : subst,X54 : term] : (((sub @ (X47 @ X56 @ X54) @ X55)) != ((X47 @ (comp @ X56 @ X55) @ (sub @ X54 @ X55)))) | (((X47 @ X50 @ X48)) = ((X49 @ X50 @ X48))) | (((lam @ (X47 @ sh @ one))) != ((lam @ (X49 @ sh @ one))))) | ? [X41 : term,X42 : subst] : (((sub @ one @ (push @ X41 @ X42))) != X41) | ? [X43 : term,X44 : subst] : (((comp @ sh @ (push @ X43 @ X44))) != X44) | ? [X46 : term,X45 : term] : ((X45 != X46) & (((lam @ X46)) = ((lam @ X45)))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.34/1.36 thf(f72,plain,(
% 6.34/1.36 ((sP58 = $true) <=> (hoaslaminj_lthm = $true)) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = id) & ((axscons = $true) <=> ! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412)) & (! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) <=> (apinj1 = $true)) & (hoaslamnotap_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((induction = $true) <=> ! [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) = $true) | ? [X65 : term] : ((((X62 @ X65)) != $true) & (((var @ X65)) = $true)) | ? [X66 : term] : (($true = ((X62 @ X66))) & (((X62 @ (lam @ X66))) != $true)) | (((sP57 @ X62)) = $true))) & ! [X302 : d_term] : (d_one = X302) & (axabs = $true) & (! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) <=> (hoasapinj1 = $true)) & ((substmonoid = $true) <=> (! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463))) & ((hoasinduction_lem3 = $true) <=> (sP56 = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58))) & (! [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (? [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) != ((X241 @ X244))) | ($true != ((X243 @ X242))) | (((X241 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X148 : (subst > term > subst > $o)] : ? [X149 : (term > $o)] : ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id)))) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X84 : term] : ? [X85 : (subst > term > term)] : ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86)))) & ((sP54 = $true) <=> (hoasinduction_lem3aa = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) <=> (sP53 = $true)) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & (((d2subst @ d_id)) = sh) & ((sP44 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((? [X325 : subst] : (((comp @ id @ X325)) != X325) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326) | (! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327))) <=> (substmonoid_lthm = $true)) & (lamnotvar = $true) & ((axvarcons = $true) <=> ! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291)) & (hoasinduction_lem1v2_gthm = $true) & (axclos = $true) & (hoaslamnotap_lthm = $true) & ((? [X488 : term] : (((sub @ X488 @ id)) != X488) | ! [X489 : term] : (((sub @ X489 @ id)) = X489)) <=> (termmset_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X322 : subst,X321 : term,X320 : (term > $o)] : ? [X323 : (term > $o)] : ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322)))))) & ((sP39 = $true) <=> (hoasinduction_lthm_3 = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83)) | ? [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 != X78) & (((ap @ X77 @ X76)) = ((ap @ X79 @ X78)))))) & ! [X410 : d_term,X409 : d_term] : ((((d2term @ X410)) != ((d2term @ X409))) | (X409 = X410)) & (termmset_gthm = $true) & (($true = sP33) <=> (hoasinduction_lem3v2_lthm = $true)) & (pushprop_lthm_orig = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X312 : (subst > term > subst > $o),X311 : term] : (? [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) = $true) & (((X312 @ id @ X318 @ id)) = $true) & (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) != $true)) | (((sP31 @ X312)) = $true) | ($true = ((X312 @ id @ X311 @ id))))) & (! [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) | ($true != ((X335 @ X333)))) <=> (pushprop_lem1 = $true)) & (lamnotap != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (! [X329 : term] : ? [X330 : (subst > term > term)] : ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X75 : d_subst] : (d_id = X75) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & ((termmset = $true) <=> ! [X341 : term] : (((sub @ X341 @ id)) = X341)) & (induction2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem1_lthm = $true) <=> (? [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) != X157) | ? [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) != X155) | ! [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true != ((X163 @ X159))) | (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true)))) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) != ((d2subst @ X203))) | (X203 = X204)) & (! [X39 : term] : ? [X40 : (subst > term > term)] : (((X40 @ sh @ one)) = ((sub @ X39 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (axvarshift = $true) & ((laminj = $true) <=> ! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343))) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) <=> (shinj = $true)) & (hoasapnotvar_lthm = $true) & (hoasapinj2_gthm = $true) & ((apinj2 = $true) <=> ! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154))))) & ((sP30 = $true) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) <=> ($true = sP28)) & (ulamvar1 != $true) & ((hoasinduction_lem2v2 = $true) <=> (sP26 = $true)) & (pushprop = $true) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) <=> ($true = sP24)) & ((induction2 = $true) <=> (sP20 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction = $true) <=> (sP18 = $true)) & (pushprop_lem0_gthm = $true) & ((sP15 = $true) <=> (hoasinduction_lem3_lthm = $true)) & ((axidl = $true) <=> ! [X0 : subst] : (((comp @ id @ X0)) = X0)) & (hoasinduction_lem2_lthm = $true) & (hoaslamnotvar = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X538 : term] : ? [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) = ((X539 @ sh @ one)))) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & ((pushprop_lem0 = $true) <=> ! [X383 : (term > $o),X381 : subst,X382 : term] : ? [X384 : (term > $o)] : ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ($true = sP12)) & ((hoasinduction_lem3a = $true) <=> ($true = sP11)) & (axmap = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))) | ? [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) != ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | ? [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) != ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514)))) <=> (hoaslaminj = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((sP10 = $true) <=> (hoasinduction_lem3a_lthm = $true)) & ((? [X293 : term] : (((sub @ X293 @ id)) != X293) | ? [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) = ((ap @ X296 @ X297))) & (X295 != X296)) | ! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300))) <=> (hoasapinj1_lthm = $true)) & ((sP8 = $true) <=> (induction2_lthm = $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (? [X286 : term] : (((X282 @ X286)) != ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) | ($true = ((X282 @ one))) | (((X285 @ X284)) != $true)) | ? [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) != X281))) & (! [X411 : subst] : (((comp @ X411 @ id)) = X411) <=> (axidr = $true)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (ulamvarind = $true) & (($true = sP4) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2a = $true) <=> (sP3 = $true)) & (! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) <=> (axshiftcons = $true)) & (! [X245 : term] : (((sub @ X245 @ id)) = X245) <=> (axvarid = $true)) & (hoasinduction_lem3v2_gthm = $true) & (axapp = $true) & (hoasapinj1_gthm = $true) & ((sP2 = $true) <=> (induction2lem = $true)) & (substmonoid_gthm = $true) & (! [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))) | ? [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X88 @ X92 @ X93) @ X91)))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X338 : (subst > term > subst > $o)] : ? [X339 : (term > $o)] : ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP0 = $true) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1v2 = $true)),
% 6.34/1.36 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])).
% 6.34/1.36 thf(f86,plain,(
% 6.34/1.36 ((sP54 = $true) | ? [X303 : (subst > term > subst > $o),X304 : term] : (! [X310 : term] : ((((X303 @ id @ X310 @ id)) != $true) | ($true = ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id)))) & ! [X305 : (subst > term > term)] : (? [X306 : term] : ((((X303 @ id @ X306 @ id)) = $true) & (((X303 @ id @ (X305 @ id @ X306) @ id)) != $true)) | ? [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) != ((sub @ (X305 @ X307 @ X309) @ X308))) | ($true = ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id)))) & (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) != $true))) & (! [X303 : (subst > term > subst > $o),X304 : term] : (? [X310 : term] : ((((X303 @ id @ X310 @ id)) = $true) & ($true != ((X303 @ id @ (sub @ X304 @ (push @ X310 @ id)) @ id)))) | ? [X305 : (subst > term > term)] : (! [X306 : term] : ((((X303 @ id @ X306 @ id)) != $true) | (((X303 @ id @ (X305 @ id @ X306) @ id)) = $true)) & ! [X309 : term,X308 : subst,X307 : subst] : (((X305 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308))) = ((sub @ (X305 @ X307 @ X309) @ X308))) & ($true != ((X303 @ id @ (lam @ (X305 @ sh @ one)) @ id)))) | (((X303 @ id @ (lam @ (sub @ X304 @ (push @ one @ sh))) @ id)) = $true)) | (sP54 != $true))),
% 6.34/1.36 inference(nnf_transformation,[],[f67])).
% 6.34/1.36 thf(f87,plain,(
% 6.34/1.36 ((sP54 = $true) | ? [X0 : (subst > term > subst > $o),X1 : term] : (! [X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | ($true = ((X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id)))) & ! [X3 : (subst > term > term)] : (? [X4 : term] : ((((X0 @ id @ X4 @ id)) = $true) & ($true != ((X0 @ id @ (X3 @ id @ X4) @ id)))) | ? [X5 : term,X6 : subst,X7 : subst] : (((X3 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) != ((sub @ (X3 @ X7 @ X5) @ X6))) | (((X0 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) & (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) != $true))) & (! [X8 : (subst > term > subst > $o),X9 : term] : (? [X10 : term] : ((((X8 @ id @ X10 @ id)) = $true) & ($true != ((X8 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id)))) | ? [X11 : (subst > term > term)] : (! [X12 : term] : ((((X8 @ id @ X12 @ id)) != $true) | (((X8 @ id @ (X11 @ id @ X12) @ id)) = $true)) & ! [X13 : term,X14 : subst,X15 : subst] : (((X11 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14))) = ((sub @ (X11 @ X15 @ X13) @ X14))) & (((X8 @ id @ (lam @ (X11 @ sh @ one)) @ id)) != $true)) | (((X8 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id)) = $true)) | (sP54 != $true))),
% 6.34/1.36 inference(rectify,[],[f86])).
% 6.34/1.36 thf(f88,plain,(
% 6.34/1.36 ((sP54 = $true) | (! [X2 : term] : ((((sK93 @ id @ X2 @ id)) != $true) | (((sK93 @ id @ (sub @ sK94 @ (push @ X2 @ id)) @ id)) = $true)) & ! [X3 : (subst > term > term)] : (((((sK93 @ id @ (sK95 @ X3) @ id)) = $true) & (((sK93 @ id @ (X3 @ id @ (sK95 @ X3)) @ id)) != $true)) | (((sub @ (X3 @ (sK98 @ X3) @ (sK96 @ X3)) @ (sK97 @ X3))) != ((X3 @ (comp @ (sK98 @ X3) @ (sK97 @ X3)) @ (sub @ (sK96 @ X3) @ (sK97 @ X3))))) | ($true = ((sK93 @ id @ (lam @ (X3 @ sh @ one)) @ id)))) & (((sK93 @ id @ (lam @ (sub @ sK94 @ (push @ one @ sh))) @ id)) != $true))) & (! [X8 : (subst > term > subst > $o),X9 : term] : ((($true = ((X8 @ id @ (sK99 @ X9 @ X8) @ id))) & ($true != ((X8 @ id @ (sub @ X9 @ (push @ (sK99 @ X9 @ X8) @ id)) @ id)))) | (! [X12 : term] : ((((X8 @ id @ X12 @ id)) != $true) | ($true = ((X8 @ id @ (sK100 @ X8 @ id @ X12) @ id)))) & ! [X13 : term,X14 : subst,X15 : subst] : (((sK100 @ X8 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14))) = ((sub @ (sK100 @ X8 @ X15 @ X13) @ X14))) & ($true != ((X8 @ id @ (lam @ (sK100 @ X8 @ sh @ one)) @ id)))) | (((X8 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id)) = $true)) | (sP54 != $true))),
% 6.34/1.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK93,sK94,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK93),skolemize(X1,sK94),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18)],[f87])).
% 6.34/1.36 thf(f260,plain,(
% 6.34/1.36 (((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP58 != $true))) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = id) & (((axscons = $true) | ? [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) != X412)) & (! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412) | (axscons != $true))) & ((! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) = ((ap @ X433 @ X432))) & (X433 != X434)))) & (hoaslamnotap_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((induction = $true) | ? [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) != $true) & ! [X65 : term] : ((((X62 @ X65)) = $true) | (((var @ X65)) != $true)) & ! [X66 : term] : (($true != ((X62 @ X66))) | (((X62 @ (lam @ X66))) = $true)) & (((sP57 @ X62)) != $true))) & (! [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) = $true) | ? [X65 : term] : ((((X62 @ X65)) != $true) & (((var @ X65)) = $true)) | ? [X66 : term] : (($true = ((X62 @ X66))) & (((X62 @ (lam @ X66))) != $true)) | (((sP57 @ X62)) = $true)) | (induction != $true))) & ! [X302 : d_term] : (d_one = X302) & (axabs = $true) & ((! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) = ((ap @ (sub @ X466 @ id) @ X467))) & (X466 != X468)))) & (((substmonoid = $true) | (? [X464 : subst] : (((comp @ X464 @ id)) != X464) | ? [X463 : subst] : (((comp @ id @ X463)) != X463))) & ((! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463)) | (substmonoid != $true))) & (((hoasinduction_lem3 = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3 != $true))) & (hoasinduction_lem3_gthm = $true) & (((hoasapinj2 = $true) | ? [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) = ((ap @ (sub @ X60 @ id) @ X57))) & (X57 != X58))) & (! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58)) | (hoasapinj2 != $true))) & ((! [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (? [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) != ((X241 @ X244))) | ($true != ((X243 @ X242))) | (((X241 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (! [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) = ((X241 @ X244))) & ($true = ((X243 @ X242))) & (((X241 @ one)) != $true)))) & (((hoasinduction_lem0 = $true) | ? [X148 : (subst > term > subst > $o)] : ! [X149 : (term > $o)] : ? [X150 : term] : (((X149 @ X150)) != ((X148 @ id @ X150 @ id)))) & (! [X148 : (subst > term > subst > $o)] : ? [X149 : (term > $o)] : ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id))) | (hoasinduction_lem0 != $true))) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X84 : term] : ! [X85 : (subst > term > term)] : ? [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) != ((X85 @ X87 @ X86)))) & (! [X84 : term] : ? [X85 : (subst > term > term)] : ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86))) | (hoasinduction_lem3v2_f != $true))) & (((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((hoasinduction_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lthm != $true))) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & (((d2subst @ d_id)) = sh) & (((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true))) & (((? [X325 : subst] : (((comp @ id @ X325)) != X325) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326) | (! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X325 : subst] : (((comp @ id @ X325)) = X325) & ! [X326 : subst] : (((comp @ X326 @ id)) = X326) & (? [X328 : subst] : (((comp @ X328 @ id)) != X328) | ? [X327 : subst] : (((comp @ id @ X327)) != X327))))) & (lamnotvar = $true) & (((axvarcons = $true) | ? [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) != X291)) & (! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291) | (axvarcons != $true))) & (hoasinduction_lem1v2_gthm = $true) & (axclos = $true) & (hoaslamnotap_lthm = $true) & (((? [X488 : term] : (((sub @ X488 @ id)) != X488) | ! [X489 : term] : (((sub @ X489 @ id)) = X489)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X488 : term] : (((sub @ X488 @ id)) = X488) & ? [X489 : term] : (((sub @ X489 @ id)) != X489)))) & (((pushprop_lem0_lthm = $true) | ? [X322 : subst,X321 : term,X320 : (term > $o)] : ! [X323 : (term > $o)] : ? [X324 : term] : (((X323 @ X324)) != ((X320 @ (sub @ X324 @ (push @ X321 @ X322)))))) & (! [X322 : subst,X321 : term,X320 : (term > $o)] : ? [X323 : (term > $o)] : ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322))))) | (pushprop_lem0_lthm != $true))) & (((sP39 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP39 != $true))) & (((hoasapinj2_lthm = $true) | (? [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) = ((ap @ (sub @ X82 @ id) @ X80))) & (X80 != X83)) & ! [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 = X78) | (((ap @ X77 @ X76)) != ((ap @ X79 @ X78)))))) & ((! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83)) | ? [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 != X78) & (((ap @ X77 @ X76)) = ((ap @ X79 @ X78))))) | (hoasapinj2_lthm != $true))) & ! [X410 : d_term,X409 : d_term] : ((((d2term @ X410)) != ((d2term @ X409))) | (X409 = X410)) & (termmset_gthm = $true) & ((($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33))) & (pushprop_lthm_orig = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X312 : (subst > term > subst > $o),X311 : term] : (! [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) != $true) | (((X312 @ id @ X318 @ id)) != $true) | (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) = $true)) & (((sP31 @ X312)) != $true) & ($true != ((X312 @ id @ X311 @ id))))) & (! [X312 : (subst > term > subst > $o),X311 : term] : (? [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) = $true) & (((X312 @ id @ X318 @ id)) = $true) & (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) != $true)) | (((sP31 @ X312)) = $true) | ($true = ((X312 @ id @ X311 @ id)))) | (hoasinduction_no_psi_cond != $true))) & ((! [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) | ($true != ((X335 @ X333)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true != ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) & ($true = ((X335 @ X333)))))) & (lamnotap != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((! [X329 : term] : ? [X330 : (subst > term > term)] : ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X329 : term] : ! [X330 : (subst > term > term)] : ? [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) != ((sub @ X329 @ (push @ X332 @ X331)))))) & (hoasinduction_lem1_gthm = $true) & ! [X75 : d_subst] : (d_id = X75) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & (((termmset = $true) | ? [X341 : term] : (((sub @ X341 @ id)) != X341)) & (! [X341 : term] : (((sub @ X341 @ id)) = X341) | (termmset != $true))) & (induction2_gthm = $true) & (apnotvar = $true) & (((pushprop_lem1_lthm = $true) | (! [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) = X157) & ! [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) = X155) & ? [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true = ((X163 @ X159))) & (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) != $true)))) & ((? [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) != X157) | ? [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) != X155) | ! [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true != ((X163 @ X159))) | (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true))) | (pushprop_lem1_lthm != $true))) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) != ((d2subst @ X203))) | (X203 = X204)) & ((! [X39 : term] : ? [X40 : (subst > term > term)] : (((X40 @ sh @ one)) = ((sub @ X39 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X39 : term] : ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ X39 @ (push @ one @ sh)))))) & (axvarshift = $true) & (((laminj = $true) | ? [X342 : term,X343 : term] : ((((lam @ X342)) = ((lam @ X343))) & (X342 != X343))) & (! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343)) | (laminj != $true))) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem3b_gthm = $true) & ((! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) | (shinj != $true)) & ((shinj = $true) | ? [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) = ((sub @ X430 @ sh))) & (X429 != X430)))) & (hoasapnotvar_lthm = $true) & (hoasapinj2_gthm = $true) & (((apinj2 = $true) | ? [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 != X154) & (((ap @ X153 @ X151)) = ((ap @ X152 @ X154))))) & (! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154)))) | (apinj2 != $true))) & (((sP30 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP30 != $true))) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction_lem2 != $true))) & (ulamvar1 != $true) & (((hoasinduction_lem2v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem2v2 != $true))) & (pushprop = $true) & (ulamvarsh = $true) & (((induction2lem_lthm = $true) | ($true != sP24)) & (($true = sP24) | (induction2lem_lthm != $true))) & (((induction2 = $true) | (sP20 != $true)) & ((sP20 = $true) | (induction2 != $true))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true))) & (pushprop_lem0_gthm = $true) & (((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true))) & (((axidl = $true) | ? [X0 : subst] : (((comp @ id @ X0)) != X0)) & (! [X0 : subst] : (((comp @ id @ X0)) = X0) | (axidl != $true))) & (hoasinduction_lem2_lthm = $true) & (hoaslamnotvar = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((hoasinduction_lem3b = $true) | ? [X538 : term] : ! [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) != ((X539 @ sh @ one)))) & (! [X538 : term] : ? [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) = ((X539 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & (((pushprop_lem0 = $true) | ? [X383 : (term > $o),X381 : subst,X382 : term] : ! [X384 : (term > $o)] : ? [X385 : term] : (((X384 @ X385)) != ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (! [X383 : (term > $o),X381 : subst,X382 : term] : ? [X384 : (term > $o)] : ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381))))) | (pushprop_lem0 != $true))) & (hoasinduction_lem1 = $true) & (((hoasinduction_lem3v2a_lthm = $true) | ($true != sP12)) & (($true = sP12) | (hoasinduction_lem3v2a_lthm != $true))) & (((hoasinduction_lem3a = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3a != $true))) & (axmap = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((! [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))) | ? [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) != ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | ? [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) != ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) = ((lam @ (X513 @ sh @ one)))) & ! [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) = ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) & ! [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) = ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) & (((X512 @ X511 @ X514)) != ((X513 @ X511 @ X514)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true))) & (((? [X293 : term] : (((sub @ X293 @ id)) != X293) | ? [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) = ((ap @ X296 @ X297))) & (X295 != X296)) | ! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X293 : term] : (((sub @ X293 @ id)) = X293) & ! [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) != ((ap @ X296 @ X297))) | (X295 = X296)) & ? [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) = ((ap @ (sub @ X300 @ id) @ X299))) & (X298 != X300))))) & (((sP8 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP8 != $true))) & (induction2lem_gthm = $true) & (((pushprop_lem1v2_lthm = $true) | (? [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (! [X286 : term] : (((X282 @ X286)) = ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) & ($true != ((X282 @ one))) & (((X285 @ X284)) = $true)) & ! [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) = X281))) & ((! [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (? [X286 : term] : (((X282 @ X286)) != ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) | ($true = ((X282 @ one))) | (((X285 @ X284)) != $true)) | ? [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) != X281)) | (pushprop_lem1v2_lthm != $true))) & ((! [X411 : subst] : (((comp @ X411 @ id)) = X411) | (axidr != $true)) & ((axidr = $true) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (ulamvarind = $true) & ((($true = sP4) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP4))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((hoasinduction_lem3v2a = $true) | (sP3 != $true)) & ((sP3 = $true) | (hoasinduction_lem3v2a != $true))) & ((! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) != X290))) & ((! [X245 : term] : (((sub @ X245 @ id)) = X245) | (axvarid != $true)) & ((axvarid = $true) | ? [X245 : term] : (((sub @ X245 @ id)) != X245))) & (hoasinduction_lem3v2_gthm = $true) & (axapp = $true) & (hoasapinj1_gthm = $true) & (((sP2 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP2 != $true))) & (substmonoid_gthm = $true) & ((! [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))) | ? [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X88 @ X92 @ X93) @ X91)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) = ((lam @ (X88 @ sh @ one)))) & ! [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X88 @ X92 @ X93) @ X91)))))) & (((hoasinduction_lem0_lthm = $true) | ? [X338 : (subst > term > subst > $o)] : ! [X339 : (term > $o)] : ? [X340 : term] : (((X339 @ X340)) != ((X338 @ id @ X340 @ id)))) & (! [X338 : (subst > term > subst > $o)] : ? [X339 : (term > $o)] : ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true))) & (hoasinduction_lem1v2 = $true)),
% 6.34/1.36 inference(nnf_transformation,[],[f72])).
% 6.34/1.36 thf(f261,plain,(
% 6.34/1.36 ((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP58 != $true)) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = id) & ((axscons = $true) | ? [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) != X412)) & (! [X412 : subst] : (((push @ (sub @ one @ X412) @ (comp @ sh @ X412))) = X412) | (axscons != $true)) & (! [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) != ((ap @ X433 @ X432))) | (X433 = X434)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X432 : term,X431 : term,X434 : term,X433 : term] : ((((ap @ X434 @ X431)) = ((ap @ X433 @ X432))) & (X433 != X434))) & (hoaslamnotap_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((induction = $true) | ? [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) != $true) & ! [X65 : term] : ((((X62 @ X65)) = $true) | (((var @ X65)) != $true)) & ! [X66 : term] : (($true != ((X62 @ X66))) | (((X62 @ (lam @ X66))) = $true)) & (((sP57 @ X62)) != $true))) & (! [X61 : term,X62 : (term > $o)] : ((((X62 @ X61)) = $true) | ? [X65 : term] : ((((X62 @ X65)) != $true) & (((var @ X65)) = $true)) | ? [X66 : term] : (($true = ((X62 @ X66))) & (((X62 @ (lam @ X66))) != $true)) | (((sP57 @ X62)) = $true)) | (induction != $true)) & ! [X302 : d_term] : (d_one = X302) & (axabs = $true) & (! [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) != ((ap @ (sub @ X466 @ id) @ X467))) | (X466 = X468)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X466 : term,X467 : term,X465 : term,X468 : term] : ((((ap @ (sub @ X468 @ id) @ X465)) = ((ap @ (sub @ X466 @ id) @ X467))) & (X466 != X468))) & ((substmonoid = $true) | ? [X464 : subst] : (((comp @ X464 @ id)) != X464) | ? [X463 : subst] : (((comp @ id @ X463)) != X463)) & ((! [X464 : subst] : (((comp @ X464 @ id)) = X464) & ! [X463 : subst] : (((comp @ id @ X463)) = X463)) | (substmonoid != $true)) & ((hoasinduction_lem3 = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) | ? [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) = ((ap @ (sub @ X60 @ id) @ X57))) & (X57 != X58))) & (! [X57 : term,X58 : term,X60 : term,X59 : term] : ((((ap @ (sub @ X59 @ id) @ X58)) != ((ap @ (sub @ X60 @ id) @ X57))) | (X57 = X58)) | (hoasapinj2 != $true)) & (! [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (? [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) != ((X241 @ X244))) | ($true != ((X243 @ X242))) | (((X241 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X242 : term,X240 : subst,X241 : (term > $o),X243 : (term > $o)] : (! [X244 : term] : (((X243 @ (sub @ X244 @ (push @ X242 @ X240)))) = ((X241 @ X244))) & ($true = ((X243 @ X242))) & (((X241 @ one)) != $true))) & ((hoasinduction_lem0 = $true) | ? [X148 : (subst > term > subst > $o)] : ! [X149 : (term > $o)] : ? [X150 : term] : (((X149 @ X150)) != ((X148 @ id @ X150 @ id)))) & (! [X148 : (subst > term > subst > $o)] : ? [X149 : (term > $o)] : ! [X150 : term] : (((X149 @ X150)) = ((X148 @ id @ X150 @ id))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X84 : term] : ! [X85 : (subst > term > term)] : ? [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) != ((X85 @ X87 @ X86)))) & (! [X84 : term] : ? [X85 : (subst > term > term)] : ! [X87 : subst,X86 : term] : (((sub @ X84 @ (push @ X86 @ X87))) = ((X85 @ X87 @ X86))) | (hoasinduction_lem3v2_f != $true)) & ((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lthm != $true)) & ! [X287 : term] : ? [X288 : d_term] : (((d2term @ X288)) = X287) & (((d2subst @ d_id)) = sh) & ((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true)) & (? [X325 : subst] : (((comp @ id @ X325)) != X325) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326) | (! [X328 : subst] : (((comp @ X328 @ id)) = X328) & ! [X327 : subst] : (((comp @ id @ X327)) = X327)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X325 : subst] : (((comp @ id @ X325)) = X325) & ! [X326 : subst] : (((comp @ X326 @ id)) = X326) & (? [X328 : subst] : (((comp @ X328 @ id)) != X328) | ? [X327 : subst] : (((comp @ id @ X327)) != X327)))) & (lamnotvar = $true) & ((axvarcons = $true) | ? [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) != X291)) & (! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291) | (axvarcons != $true)) & (hoasinduction_lem1v2_gthm = $true) & (axclos = $true) & (hoaslamnotap_lthm = $true) & (? [X488 : term] : (((sub @ X488 @ id)) != X488) | ! [X489 : term] : (((sub @ X489 @ id)) = X489) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X488 : term] : (((sub @ X488 @ id)) = X488) & ? [X489 : term] : (((sub @ X489 @ id)) != X489))) & ((pushprop_lem0_lthm = $true) | ? [X322 : subst,X321 : term,X320 : (term > $o)] : ! [X323 : (term > $o)] : ? [X324 : term] : (((X323 @ X324)) != ((X320 @ (sub @ X324 @ (push @ X321 @ X322)))))) & (! [X322 : subst,X321 : term,X320 : (term > $o)] : ? [X323 : (term > $o)] : ! [X324 : term] : (((X323 @ X324)) = ((X320 @ (sub @ X324 @ (push @ X321 @ X322))))) | (pushprop_lem0_lthm != $true)) & ((sP39 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP39 != $true)) & ((hoasapinj2_lthm = $true) | (? [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) = ((ap @ (sub @ X82 @ id) @ X80))) & (X80 != X83)) & ! [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 = X78) | (((ap @ X77 @ X76)) != ((ap @ X79 @ X78)))))) & (! [X83 : term,X80 : term,X81 : term,X82 : term] : ((((ap @ (sub @ X81 @ id) @ X83)) != ((ap @ (sub @ X82 @ id) @ X80))) | (X80 = X83)) | ? [X78 : term,X79 : term,X77 : term,X76 : term] : ((X76 != X78) & (((ap @ X77 @ X76)) = ((ap @ X79 @ X78)))) | (hoasapinj2_lthm != $true)) & ! [X410 : d_term,X409 : d_term] : ((((d2term @ X410)) != ((d2term @ X409))) | (X409 = X410)) & (termmset_gthm = $true) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (pushprop_lthm_orig = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X312 : (subst > term > subst > $o),X311 : term] : (! [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) != $true) | (((X312 @ id @ X318 @ id)) != $true) | (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) = $true)) & (((sP31 @ X312)) != $true) & ($true != ((X312 @ id @ X311 @ id))))) & (! [X312 : (subst > term > subst > $o),X311 : term] : (? [X319 : term,X318 : term] : ((((X312 @ id @ X319 @ id)) = $true) & (((X312 @ id @ X318 @ id)) = $true) & (((X312 @ id @ (ap @ (sub @ X319 @ id) @ X318) @ id)) != $true)) | (((sP31 @ X312)) = $true) | ($true = ((X312 @ id @ X311 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (! [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true = ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) | ($true != ((X335 @ X333)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X335 : (term > $o),X337 : (term > $o),X333 : term,X334 : subst,X336 : term] : (($true != ((X337 @ (sub @ X333 @ (push @ X336 @ X334))))) & ($true = ((X335 @ X333))))) & (lamnotap != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (! [X329 : term] : ? [X330 : (subst > term > term)] : ! [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) = ((sub @ X329 @ (push @ X332 @ X331)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X329 : term] : ! [X330 : (subst > term > term)] : ? [X332 : term,X331 : subst] : (((X330 @ X331 @ X332)) != ((sub @ X329 @ (push @ X332 @ X331))))) & (hoasinduction_lem1_gthm = $true) & ! [X75 : d_subst] : (d_id = X75) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & ((termmset = $true) | ? [X341 : term] : (((sub @ X341 @ id)) != X341)) & (! [X341 : term] : (((sub @ X341 @ id)) = X341) | (termmset != $true)) & (induction2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem1_lthm = $true) | (! [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) = X157) & ! [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) = X155) & ? [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true = ((X163 @ X159))) & (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) != $true)))) & (? [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) != X157) | ? [X156 : subst,X155 : term] : (((sub @ one @ (push @ X155 @ X156))) != X155) | ! [X162 : (term > $o),X161 : subst,X159 : term,X160 : term,X163 : (term > $o)] : (($true != ((X163 @ X159))) | (((X162 @ (sub @ X159 @ (push @ X160 @ X161)))) = $true)) | (pushprop_lem1_lthm != $true)) & ! [X509 : subst] : ? [X510 : d_subst] : (((d2subst @ X510)) = X509) & ! [X204 : d_subst,X203 : d_subst] : ((((d2subst @ X204)) != ((d2subst @ X203))) | (X203 = X204)) & (! [X39 : term] : ? [X40 : (subst > term > term)] : (((X40 @ sh @ one)) = ((sub @ X39 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X39 : term] : ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ X39 @ (push @ one @ sh))))) & (axvarshift = $true) & ((laminj = $true) | ? [X342 : term,X343 : term] : ((((lam @ X342)) = ((lam @ X343))) & (X342 != X343))) & (! [X342 : term,X343 : term] : ((((lam @ X342)) != ((lam @ X343))) | (X342 = X343)) | (laminj != $true)) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) != ((sub @ X430 @ sh))) | (X429 = X430)) | (shinj != $true)) & ((shinj = $true) | ? [X430 : term,X429 : term] : ((((sub @ X429 @ sh)) = ((sub @ X430 @ sh))) & (X429 != X430))) & (hoasapnotvar_lthm = $true) & (hoasapinj2_gthm = $true) & ((apinj2 = $true) | ? [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 != X154) & (((ap @ X153 @ X151)) = ((ap @ X152 @ X154))))) & (! [X152 : term,X154 : term,X153 : term,X151 : term] : ((X151 = X154) | (((ap @ X153 @ X151)) != ((ap @ X152 @ X154)))) | (apinj2 != $true)) & ((sP30 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP30 != $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction_lem2 != $true)) & (ulamvar1 != $true) & ((hoasinduction_lem2v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem2v2 != $true)) & (pushprop = $true) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) | ($true != sP24)) & (($true = sP24) | (induction2lem_lthm != $true)) & ((induction2 = $true) | (sP20 != $true)) & ((sP20 = $true) | (induction2 != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true)) & (pushprop_lem0_gthm = $true) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((axidl = $true) | ? [X0 : subst] : (((comp @ id @ X0)) != X0)) & (! [X0 : subst] : (((comp @ id @ X0)) = X0) | (axidl != $true)) & (hoasinduction_lem2_lthm = $true) & (hoaslamnotvar = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X538 : term] : ! [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) != ((X539 @ sh @ one)))) & (! [X538 : term] : ? [X539 : (subst > term > term)] : (((sub @ X538 @ (push @ one @ sh))) = ((X539 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & ((pushprop_lem0 = $true) | ? [X383 : (term > $o),X381 : subst,X382 : term] : ! [X384 : (term > $o)] : ? [X385 : term] : (((X384 @ X385)) != ((X383 @ (sub @ X385 @ (push @ X382 @ X381)))))) & (! [X383 : (term > $o),X381 : subst,X382 : term] : ? [X384 : (term > $o)] : ! [X385 : term] : (((X384 @ X385)) = ((X383 @ (sub @ X385 @ (push @ X382 @ X381))))) | (pushprop_lem0 != $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP12)) & (($true = sP12) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3a != $true)) & (axmap = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) != ((lam @ (X513 @ sh @ one)))) | ? [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) != ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | ? [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) != ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) | (((X512 @ X511 @ X514)) = ((X513 @ X511 @ X514)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X512 : (subst > term > term),X514 : term,X511 : subst,X513 : (subst > term > term)] : ((((lam @ (X512 @ sh @ one))) = ((lam @ (X513 @ sh @ one)))) & ! [X520 : subst,X518 : subst,X519 : term] : (((sub @ (X512 @ X518 @ X519) @ X520)) = ((X512 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) & ! [X516 : term,X517 : subst,X515 : subst] : (((sub @ (X513 @ X517 @ X516) @ X515)) = ((X513 @ (comp @ X517 @ X515) @ (sub @ X516 @ X515)))) & (((X512 @ X511 @ X514)) != ((X513 @ X511 @ X514))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true)) & (? [X293 : term] : (((sub @ X293 @ id)) != X293) | ? [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) = ((ap @ X296 @ X297))) & (X295 != X296)) | ! [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) != ((ap @ (sub @ X300 @ id) @ X299))) | (X298 = X300)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X293 : term] : (((sub @ X293 @ id)) = X293) & ! [X297 : term,X296 : term,X294 : term,X295 : term] : ((((ap @ X295 @ X294)) != ((ap @ X296 @ X297))) | (X295 = X296)) & ? [X298 : term,X300 : term,X301 : term,X299 : term] : ((((ap @ (sub @ X298 @ id) @ X301)) = ((ap @ (sub @ X300 @ id) @ X299))) & (X298 != X300)))) & ((sP8 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP8 != $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (! [X286 : term] : (((X282 @ X286)) = ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) & ($true != ((X282 @ one))) & (((X285 @ X284)) = $true)) & ! [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) = X281))) & (! [X284 : term,X285 : (term > $o),X283 : subst,X282 : (term > $o)] : (? [X286 : term] : (((X282 @ X286)) != ((X285 @ (sub @ X286 @ (push @ X284 @ X283))))) | ($true = ((X282 @ one))) | (((X285 @ X284)) != $true)) | ? [X280 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X280))) != X281) | (pushprop_lem1v2_lthm != $true)) & (! [X411 : subst] : (((comp @ X411 @ id)) = X411) | (axidr != $true)) & ((axidr = $true) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (ulamvarind = $true) & (($true = sP4) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP4)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2a = $true) | (sP3 != $true)) & ((sP3 = $true) | (hoasinduction_lem3v2a != $true)) & (! [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) = X290) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X289 : term,X290 : subst] : (((comp @ sh @ (push @ X289 @ X290))) != X290)) & (! [X245 : term] : (((sub @ X245 @ id)) = X245) | (axvarid != $true)) & ((axvarid = $true) | ? [X245 : term] : (((sub @ X245 @ id)) != X245)) & (hoasinduction_lem3v2_gthm = $true) & (axapp = $true) & (hoasapinj1_gthm = $true) & ((sP2 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP2 != $true)) & (substmonoid_gthm = $true) & (! [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) != ((lam @ (X88 @ sh @ one)))) | ? [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X88 @ X92 @ X93) @ X91)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X88 : (subst > term > term),X89 : term,X90 : term] : ((((ap @ (sub @ X90 @ id) @ X89)) = ((lam @ (X88 @ sh @ one)))) & ! [X93 : term,X92 : subst,X91 : subst] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X88 @ X92 @ X93) @ X91))))) & ((hoasinduction_lem0_lthm = $true) | ? [X338 : (subst > term > subst > $o)] : ! [X339 : (term > $o)] : ? [X340 : term] : (((X339 @ X340)) != ((X338 @ id @ X340 @ id)))) & (! [X338 : (subst > term > subst > $o)] : ? [X339 : (term > $o)] : ! [X340 : term] : (((X339 @ X340)) = ((X338 @ id @ X340 @ id))) | (hoasinduction_lem0_lthm != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & (hoasinduction_lem1v2 = $true)),
% 6.34/1.36 inference(flattening,[],[f260])).
% 6.34/1.36 thf(f262,plain,(
% 6.34/1.36 ((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP58 != $true)) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = id) & ((axscons = $true) | ? [X0 : subst] : (((push @ (sub @ one @ X0) @ (comp @ sh @ X0))) != X0)) & (! [X1 : subst] : (((push @ (sub @ one @ X1) @ (comp @ sh @ X1))) = X1) | (axscons != $true)) & (! [X2 : term,X3 : term,X4 : term,X5 : term] : ((((ap @ X5 @ X2)) != ((ap @ X4 @ X3))) | (X4 = X5)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X6 : term,X7 : term,X8 : term,X9 : term] : ((((ap @ X9 @ X6)) = ((ap @ X8 @ X7))) & (X8 != X9))) & (hoaslamnotap_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((induction = $true) | ? [X10 : term,X11 : (term > $o)] : ((((X11 @ X10)) != $true) & ! [X12 : term] : ((((X11 @ X12)) = $true) | ($true != ((var @ X12)))) & ! [X13 : term] : ((((X11 @ X13)) != $true) | (((X11 @ (lam @ X13))) = $true)) & (((sP57 @ X11)) != $true))) & (! [X14 : term,X15 : (term > $o)] : ((((X15 @ X14)) = $true) | ? [X16 : term] : ((((X15 @ X16)) != $true) & (((var @ X16)) = $true)) | ? [X17 : term] : (($true = ((X15 @ X17))) & (((X15 @ (lam @ X17))) != $true)) | (((sP57 @ X15)) = $true)) | (induction != $true)) & ! [X18 : d_term] : (d_one = X18) & (axabs = $true) & (! [X19 : term,X20 : term,X21 : term,X22 : term] : ((((ap @ (sub @ X19 @ id) @ X20)) != ((ap @ (sub @ X22 @ id) @ X21))) | (X19 = X22)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X23 : term,X24 : term,X25 : term,X26 : term] : ((((ap @ (sub @ X26 @ id) @ X25)) = ((ap @ (sub @ X23 @ id) @ X24))) & (X23 != X26))) & ((substmonoid = $true) | ? [X27 : subst] : (((comp @ X27 @ id)) != X27) | ? [X28 : subst] : (((comp @ id @ X28)) != X28)) & ((! [X29 : subst] : (((comp @ X29 @ id)) = X29) & ! [X30 : subst] : (((comp @ id @ X30)) = X30)) | (substmonoid != $true)) & ((hoasinduction_lem3 = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) | ? [X31 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X32)) = ((ap @ (sub @ X33 @ id) @ X31))) & (X31 != X32))) & (! [X35 : term,X36 : term,X37 : term,X38 : term] : ((((ap @ (sub @ X38 @ id) @ X36)) != ((ap @ (sub @ X37 @ id) @ X35))) | (X35 = X36)) | (hoasapinj2 != $true)) & (! [X39 : term,X40 : subst,X41 : (term > $o),X42 : (term > $o)] : (? [X43 : term] : (((X42 @ (sub @ X43 @ (push @ X39 @ X40)))) != ((X41 @ X43))) | (((X42 @ X39)) != $true) | (((X41 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X44 : term,X45 : subst,X46 : (term > $o),X47 : (term > $o)] : (! [X48 : term] : (((X46 @ X48)) = ((X47 @ (sub @ X48 @ (push @ X44 @ X45))))) & (((X47 @ X44)) = $true) & ($true != ((X46 @ one))))) & ((hoasinduction_lem0 = $true) | ? [X49 : (subst > term > subst > $o)] : ! [X50 : (term > $o)] : ? [X51 : term] : (((X49 @ id @ X51 @ id)) != ((X50 @ X51)))) & (! [X52 : (subst > term > subst > $o)] : ? [X53 : (term > $o)] : ! [X54 : term] : (((X52 @ id @ X54 @ id)) = ((X53 @ X54))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X55 : term] : ! [X56 : (subst > term > term)] : ? [X57 : subst,X58 : term] : (((sub @ X55 @ (push @ X58 @ X57))) != ((X56 @ X57 @ X58)))) & (! [X59 : term] : ? [X60 : (subst > term > term)] : ! [X61 : subst,X62 : term] : (((sub @ X59 @ (push @ X62 @ X61))) = ((X60 @ X61 @ X62))) | (hoasinduction_lem3v2_f != $true)) & ((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lthm != $true)) & ! [X63 : term] : ? [X64 : d_term] : (((d2term @ X64)) = X63) & (((d2subst @ d_id)) = sh) & ((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true)) & (? [X65 : subst] : (((comp @ id @ X65)) != X65) | ? [X66 : subst] : (((comp @ X66 @ id)) != X66) | (! [X67 : subst] : (((comp @ X67 @ id)) = X67) & ! [X68 : subst] : (((comp @ id @ X68)) = X68)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X69 : subst] : (((comp @ id @ X69)) = X69) & ! [X70 : subst] : (((comp @ X70 @ id)) = X70) & (? [X71 : subst] : (((comp @ X71 @ id)) != X71) | ? [X72 : subst] : (((comp @ id @ X72)) != X72)))) & (lamnotvar = $true) & ((axvarcons = $true) | ? [X73 : term,X74 : subst] : (((sub @ one @ (push @ X73 @ X74))) != X73)) & (! [X75 : term,X76 : subst] : (((sub @ one @ (push @ X75 @ X76))) = X75) | (axvarcons != $true)) & (hoasinduction_lem1v2_gthm = $true) & (axclos = $true) & (hoaslamnotap_lthm = $true) & (? [X77 : term] : (((sub @ X77 @ id)) != X77) | ! [X78 : term] : (((sub @ X78 @ id)) = X78) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X79 : term] : (((sub @ X79 @ id)) = X79) & ? [X80 : term] : (((sub @ X80 @ id)) != X80))) & ((pushprop_lem0_lthm = $true) | ? [X81 : subst,X82 : term,X83 : (term > $o)] : ! [X84 : (term > $o)] : ? [X85 : term] : (((X83 @ (sub @ X85 @ (push @ X82 @ X81)))) != ((X84 @ X85)))) & (! [X86 : subst,X87 : term,X88 : (term > $o)] : ? [X89 : (term > $o)] : ! [X90 : term] : (((X88 @ (sub @ X90 @ (push @ X87 @ X86)))) = ((X89 @ X90))) | (pushprop_lem0_lthm != $true)) & ((sP39 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP39 != $true)) & ((hoasapinj2_lthm = $true) | (? [X91 : term,X92 : term,X93 : term,X94 : term] : ((((ap @ (sub @ X94 @ id) @ X92)) = ((ap @ (sub @ X93 @ id) @ X91))) & (X91 != X92)) & ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X98) | (((ap @ X97 @ X98)) != ((ap @ X96 @ X95)))))) & (! [X99 : term,X100 : term,X101 : term,X102 : term] : ((((ap @ (sub @ X102 @ id) @ X100)) != ((ap @ (sub @ X101 @ id) @ X99))) | (X99 = X100)) | ? [X103 : term,X104 : term,X105 : term,X106 : term] : ((X103 != X106) & (((ap @ X105 @ X106)) = ((ap @ X104 @ X103)))) | (hoasapinj2_lthm != $true)) & ! [X107 : d_term,X108 : d_term] : ((((d2term @ X108)) != ((d2term @ X107))) | (X107 = X108)) & (termmset_gthm = $true) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (pushprop_lthm_orig = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X109 : (subst > term > subst > $o),X110 : term] : (! [X111 : term,X112 : term] : ((((X109 @ id @ X111 @ id)) != $true) | (((X109 @ id @ X112 @ id)) != $true) | (((X109 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id)) = $true)) & (((sP31 @ X109)) != $true) & (((X109 @ id @ X110 @ id)) != $true))) & (! [X113 : (subst > term > subst > $o),X114 : term] : (? [X115 : term,X116 : term] : ((((X113 @ id @ X115 @ id)) = $true) & (((X113 @ id @ X116 @ id)) = $true) & (((X113 @ id @ (ap @ (sub @ X115 @ id) @ X116) @ id)) != $true)) | (((sP31 @ X113)) = $true) | (((X113 @ id @ X114 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X117 : (term > $o),X118 : (term > $o),X119 : term,X120 : subst,X121 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X121 @ X120))))) | ($true != ((X117 @ X119)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X122 : (term > $o),X123 : (term > $o),X124 : term,X125 : subst,X126 : term] : (($true != ((X123 @ (sub @ X124 @ (push @ X126 @ X125))))) & ($true = ((X122 @ X124))))) & (lamnotap != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (! [X127 : term] : ? [X128 : (subst > term > term)] : ! [X129 : term,X130 : subst] : (((sub @ X127 @ (push @ X129 @ X130))) = ((X128 @ X130 @ X129))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X131 : term] : ! [X132 : (subst > term > term)] : ? [X133 : term,X134 : subst] : (((sub @ X131 @ (push @ X133 @ X134))) != ((X132 @ X134 @ X133)))) & (hoasinduction_lem1_gthm = $true) & ! [X135 : d_subst] : (d_id = X135) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & ((termmset = $true) | ? [X136 : term] : (((sub @ X136 @ id)) != X136)) & (! [X137 : term] : (((sub @ X137 @ id)) = X137) | (termmset != $true)) & (induction2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem1_lthm = $true) | (! [X138 : subst,X139 : term] : (((comp @ sh @ (push @ X139 @ X138))) = X138) & ! [X140 : subst,X141 : term] : (((sub @ one @ (push @ X141 @ X140))) = X141) & ? [X142 : (term > $o),X143 : subst,X144 : term,X145 : term,X146 : (term > $o)] : ((((X146 @ X144)) = $true) & ($true != ((X142 @ (sub @ X144 @ (push @ X145 @ X143)))))))) & (? [X147 : subst,X148 : term] : (((comp @ sh @ (push @ X148 @ X147))) != X147) | ? [X149 : subst,X150 : term] : (((sub @ one @ (push @ X150 @ X149))) != X150) | ! [X151 : (term > $o),X152 : subst,X153 : term,X154 : term,X155 : (term > $o)] : ((((X155 @ X153)) != $true) | ($true = ((X151 @ (sub @ X153 @ (push @ X154 @ X152)))))) | (pushprop_lem1_lthm != $true)) & ! [X156 : subst] : ? [X157 : d_subst] : (((d2subst @ X157)) = X156) & ! [X158 : d_subst,X159 : d_subst] : ((((d2subst @ X159)) != ((d2subst @ X158))) | (X158 = X159)) & (! [X160 : term] : ? [X161 : (subst > term > term)] : (((X161 @ sh @ one)) = ((sub @ X160 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X162 : term] : ! [X163 : (subst > term > term)] : (((sub @ X162 @ (push @ one @ sh))) != ((X163 @ sh @ one)))) & (axvarshift = $true) & ((laminj = $true) | ? [X164 : term,X165 : term] : ((((lam @ X165)) = ((lam @ X164))) & (X164 != X165))) & (! [X166 : term,X167 : term] : ((((lam @ X167)) != ((lam @ X166))) | (X166 = X167)) | (laminj != $true)) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X168 : term,X169 : term] : ((((sub @ X168 @ sh)) != ((sub @ X169 @ sh))) | (X168 = X169)) | (shinj != $true)) & ((shinj = $true) | ? [X170 : term,X171 : term] : ((((sub @ X171 @ sh)) = ((sub @ X170 @ sh))) & (X170 != X171))) & (hoasapnotvar_lthm = $true) & (hoasapinj2_gthm = $true) & ((apinj2 = $true) | ? [X172 : term,X173 : term,X174 : term,X175 : term] : ((X173 != X175) & (((ap @ X174 @ X175)) = ((ap @ X172 @ X173))))) & (! [X176 : term,X177 : term,X178 : term,X179 : term] : ((X177 = X179) | (((ap @ X176 @ X177)) != ((ap @ X178 @ X179)))) | (apinj2 != $true)) & ((sP30 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP30 != $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction_lem2 != $true)) & (ulamvar1 != $true) & ((hoasinduction_lem2v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem2v2 != $true)) & (pushprop = $true) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) | ($true != sP24)) & (($true = sP24) | (induction2lem_lthm != $true)) & ((induction2 = $true) | (sP20 != $true)) & ((sP20 = $true) | (induction2 != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true)) & (pushprop_lem0_gthm = $true) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((axidl = $true) | ? [X180 : subst] : (((comp @ id @ X180)) != X180)) & (! [X181 : subst] : (((comp @ id @ X181)) = X181) | (axidl != $true)) & (hoasinduction_lem2_lthm = $true) & (hoaslamnotvar = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X182 : term] : ! [X183 : (subst > term > term)] : (((sub @ X182 @ (push @ one @ sh))) != ((X183 @ sh @ one)))) & (! [X184 : term] : ? [X185 : (subst > term > term)] : (((sub @ X184 @ (push @ one @ sh))) = ((X185 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & ((pushprop_lem0 = $true) | ? [X186 : (term > $o),X187 : subst,X188 : term] : ! [X189 : (term > $o)] : ? [X190 : term] : (((X189 @ X190)) != ((X186 @ (sub @ X190 @ (push @ X188 @ X187)))))) & (! [X191 : (term > $o),X192 : subst,X193 : term] : ? [X194 : (term > $o)] : ! [X195 : term] : (((X191 @ (sub @ X195 @ (push @ X193 @ X192)))) = ((X194 @ X195))) | (pushprop_lem0 != $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP12)) & (($true = sP12) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3a != $true)) & (axmap = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X196 : (subst > term > term),X197 : term,X198 : subst,X199 : (subst > term > term)] : ((((lam @ (X196 @ sh @ one))) != ((lam @ (X199 @ sh @ one)))) | ? [X200 : subst,X201 : subst,X202 : term] : (((X196 @ (comp @ X201 @ X200) @ (sub @ X202 @ X200))) != ((sub @ (X196 @ X201 @ X202) @ X200))) | ? [X203 : term,X204 : subst,X205 : subst] : (((X199 @ (comp @ X204 @ X205) @ (sub @ X203 @ X205))) != ((sub @ (X199 @ X204 @ X203) @ X205))) | (((X199 @ X198 @ X197)) = ((X196 @ X198 @ X197)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X206 : (subst > term > term),X207 : term,X208 : subst,X209 : (subst > term > term)] : ((((lam @ (X206 @ sh @ one))) = ((lam @ (X209 @ sh @ one)))) & ! [X210 : subst,X211 : subst,X212 : term] : (((X206 @ (comp @ X211 @ X210) @ (sub @ X212 @ X210))) = ((sub @ (X206 @ X211 @ X212) @ X210))) & ! [X213 : term,X214 : subst,X215 : subst] : (((X209 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215))) = ((sub @ (X209 @ X214 @ X213) @ X215))) & (((X209 @ X208 @ X207)) != ((X206 @ X208 @ X207))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true)) & (? [X216 : term] : (((sub @ X216 @ id)) != X216) | ? [X217 : term,X218 : term,X219 : term,X220 : term] : ((((ap @ X220 @ X219)) = ((ap @ X218 @ X217))) & (X218 != X220)) | ! [X221 : term,X222 : term,X223 : term,X224 : term] : ((((ap @ (sub @ X221 @ id) @ X223)) != ((ap @ (sub @ X222 @ id) @ X224))) | (X221 = X222)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X225 : term] : (((sub @ X225 @ id)) = X225) & ! [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ X227 @ X226)) != ((ap @ X229 @ X228))) | (X227 = X229)) & ? [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ (sub @ X231 @ id) @ X233)) = ((ap @ (sub @ X230 @ id) @ X232))) & (X230 != X231)))) & ((sP8 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP8 != $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X234 : term,X235 : (term > $o),X236 : subst,X237 : (term > $o)] : (! [X238 : term] : (((X237 @ X238)) = ((X235 @ (sub @ X238 @ (push @ X234 @ X236))))) & (((X237 @ one)) != $true) & ($true = ((X235 @ X234)))) & ! [X239 : subst,X240 : term] : (((sub @ one @ (push @ X240 @ X239))) = X240))) & (! [X241 : term,X242 : (term > $o),X243 : subst,X244 : (term > $o)] : (? [X245 : term] : (((X242 @ (sub @ X245 @ (push @ X241 @ X243)))) != ((X244 @ X245))) | ($true = ((X244 @ one))) | (((X242 @ X241)) != $true)) | ? [X246 : subst,X247 : term] : (((sub @ one @ (push @ X247 @ X246))) != X247) | (pushprop_lem1v2_lthm != $true)) & (! [X248 : subst] : (((comp @ X248 @ id)) = X248) | (axidr != $true)) & ((axidr = $true) | ? [X249 : subst] : (((comp @ X249 @ id)) != X249)) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (ulamvarind = $true) & (($true = sP4) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP4)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2a = $true) | (sP3 != $true)) & ((sP3 = $true) | (hoasinduction_lem3v2a != $true)) & (! [X250 : term,X251 : subst] : (((comp @ sh @ (push @ X250 @ X251))) = X251) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X252 : term,X253 : subst] : (((comp @ sh @ (push @ X252 @ X253))) != X253)) & (! [X254 : term] : (((sub @ X254 @ id)) = X254) | (axvarid != $true)) & ((axvarid = $true) | ? [X255 : term] : (((sub @ X255 @ id)) != X255)) & (hoasinduction_lem3v2_gthm = $true) & (axapp = $true) & (hoasapinj1_gthm = $true) & ((sP2 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP2 != $true)) & (substmonoid_gthm = $true) & (! [X256 : (subst > term > term),X257 : term,X258 : term] : ((((ap @ (sub @ X258 @ id) @ X257)) != ((lam @ (X256 @ sh @ one)))) | ? [X259 : term,X260 : subst,X261 : subst] : (((sub @ (X256 @ X260 @ X259) @ X261)) != ((X256 @ (comp @ X260 @ X261) @ (sub @ X259 @ X261))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X262 : (subst > term > term),X263 : term,X264 : term] : ((((ap @ (sub @ X264 @ id) @ X263)) = ((lam @ (X262 @ sh @ one)))) & ! [X265 : term,X266 : subst,X267 : subst] : (((sub @ (X262 @ X266 @ X265) @ X267)) = ((X262 @ (comp @ X266 @ X267) @ (sub @ X265 @ X267)))))) & ((hoasinduction_lem0_lthm = $true) | ? [X268 : (subst > term > subst > $o)] : ! [X269 : (term > $o)] : ? [X270 : term] : (((X268 @ id @ X270 @ id)) != ((X269 @ X270)))) & (! [X271 : (subst > term > subst > $o)] : ? [X272 : (term > $o)] : ! [X273 : term] : (((X271 @ id @ X273 @ id)) = ((X272 @ X273))) | (hoasinduction_lem0_lthm != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & (hoasinduction_lem1v2 = $true)),
% 6.34/1.36 inference(rectify,[],[f261])).
% 6.34/1.36 thf(f263,plain,(
% 6.34/1.36 ((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP58 != $true)) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = id) & ((axscons = $true) | (((push @ (sub @ one @ sK457) @ (comp @ sh @ sK457))) != sK457)) & (! [X1 : subst] : (((push @ (sub @ one @ X1) @ (comp @ sh @ X1))) = X1) | (axscons != $true)) & (! [X2 : term,X3 : term,X4 : term,X5 : term] : ((((ap @ X5 @ X2)) != ((ap @ X4 @ X3))) | (X4 = X5)) | (apinj1 != $true)) & ((apinj1 = $true) | ((((ap @ sK460 @ sK459)) = ((ap @ sK461 @ sK458))) & (sK460 != sK461))) & (hoaslamnotap_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((induction = $true) | ((((sK463 @ sK462)) != $true) & ! [X12 : term] : ((((sK463 @ X12)) = $true) | ($true != ((var @ X12)))) & ! [X13 : term] : (($true != ((sK463 @ X13))) | (((sK463 @ (lam @ X13))) = $true)) & ($true != ((sP57 @ sK463))))) & (! [X14 : term,X15 : (term > $o)] : ((((X15 @ X14)) = $true) | ((((X15 @ (sK464 @ X15))) != $true) & (((var @ (sK464 @ X15))) = $true)) | ((((X15 @ (sK465 @ X15))) = $true) & (((X15 @ (lam @ (sK465 @ X15)))) != $true)) | (((sP57 @ X15)) = $true)) | (induction != $true)) & ! [X18 : d_term] : (d_one = X18) & (axabs = $true) & (! [X19 : term,X20 : term,X21 : term,X22 : term] : ((((ap @ (sub @ X19 @ id) @ X20)) != ((ap @ (sub @ X22 @ id) @ X21))) | (X19 = X22)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK469 @ id) @ sK468)) = ((ap @ (sub @ sK466 @ id) @ sK467))) & (sK469 != sK466))) & ((substmonoid = $true) | (((comp @ sK470 @ id)) != sK470) | (((comp @ id @ sK471)) != sK471)) & ((! [X29 : subst] : (((comp @ X29 @ id)) = X29) & ! [X30 : subst] : (((comp @ id @ X30)) = X30)) | (substmonoid != $true)) & ((hoasinduction_lem3 = $true) | (sP56 != $true)) & ((sP56 = $true) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK474 @ id) @ sK472)) = ((ap @ (sub @ sK475 @ id) @ sK473))) & (sK473 != sK472))) & (! [X35 : term,X36 : term,X37 : term,X38 : term] : ((((ap @ (sub @ X38 @ id) @ X36)) != ((ap @ (sub @ X37 @ id) @ X35))) | (X35 = X36)) | (hoasapinj2 != $true)) & (! [X39 : term,X40 : subst,X41 : (term > $o),X42 : (term > $o)] : ((((X42 @ (sub @ (sK476 @ X42 @ X41 @ X40 @ X39) @ (push @ X39 @ X40)))) != ((X41 @ (sK476 @ X42 @ X41 @ X40 @ X39)))) | (((X42 @ X39)) != $true) | (((X41 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X48 : term] : (((sK480 @ (sub @ X48 @ (push @ sK477 @ sK478)))) = ((sK479 @ X48))) & ($true = ((sK480 @ sK477))) & (((sK479 @ one)) != $true))) & ((hoasinduction_lem0 = $true) | ! [X50 : (term > $o)] : (((sK481 @ id @ (sK482 @ X50) @ id)) != ((X50 @ (sK482 @ X50))))) & (! [X52 : (subst > term > subst > $o)] : ! [X54 : term] : (((X52 @ id @ X54 @ id)) = ((sK483 @ X52 @ X54))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X56 : (subst > term > term)] : (((X56 @ (sK485 @ X56) @ (sK486 @ X56))) != ((sub @ sK484 @ (push @ (sK486 @ X56) @ (sK485 @ X56)))))) & (! [X59 : term] : ! [X61 : subst,X62 : term] : (((sK487 @ X59 @ X61 @ X62)) = ((sub @ X59 @ (push @ X62 @ X61)))) | (hoasinduction_lem3v2_f != $true)) & ((sP54 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP54 != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lthm != $true)) & ! [X63 : term] : (((d2term @ (sK488 @ X63))) = X63) & (((d2subst @ d_id)) = sh) & ((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true)) & ((((comp @ id @ sK489)) != sK489) | (((comp @ sK490 @ id)) != sK490) | (! [X67 : subst] : (((comp @ X67 @ id)) = X67) & ! [X68 : subst] : (((comp @ id @ X68)) = X68)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X69 : subst] : (((comp @ id @ X69)) = X69) & ! [X70 : subst] : (((comp @ X70 @ id)) = X70) & ((((comp @ sK491 @ id)) != sK491) | (((comp @ id @ sK492)) != sK492)))) & (lamnotvar = $true) & ((axvarcons = $true) | (sK493 != ((sub @ one @ (push @ sK493 @ sK494))))) & (! [X75 : term,X76 : subst] : (((sub @ one @ (push @ X75 @ X76))) = X75) | (axvarcons != $true)) & (hoasinduction_lem1v2_gthm = $true) & (axclos = $true) & (hoaslamnotap_lthm = $true) & ((sK495 != ((sub @ sK495 @ id))) | ! [X78 : term] : (((sub @ X78 @ id)) = X78) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X79 : term] : (((sub @ X79 @ id)) = X79) & (sK496 != ((sub @ sK496 @ id))))) & ((pushprop_lem0_lthm = $true) | ! [X84 : (term > $o)] : (((sK499 @ (sub @ (sK500 @ X84) @ (push @ sK498 @ sK497)))) != ((X84 @ (sK500 @ X84))))) & (! [X86 : subst,X87 : term,X88 : (term > $o)] : ! [X90 : term] : (((sK501 @ X88 @ X87 @ X86 @ X90)) = ((X88 @ (sub @ X90 @ (push @ X87 @ X86))))) | (pushprop_lem0_lthm != $true)) & ((sP39 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP39 != $true)) & ((hoasapinj2_lthm = $true) | (((((ap @ (sub @ sK504 @ id) @ sK502)) = ((ap @ (sub @ sK505 @ id) @ sK503))) & (sK502 != sK503)) & ! [X95 : term,X96 : term,X97 : term,X98 : term] : ((X95 = X98) | (((ap @ X97 @ X98)) != ((ap @ X96 @ X95)))))) & (! [X99 : term,X100 : term,X101 : term,X102 : term] : ((((ap @ (sub @ X102 @ id) @ X100)) != ((ap @ (sub @ X101 @ id) @ X99))) | (X99 = X100)) | ((sK506 != sK509) & (((ap @ sK508 @ sK509)) = ((ap @ sK507 @ sK506)))) | (hoasapinj2_lthm != $true)) & ! [X107 : d_term,X108 : d_term] : ((((d2term @ X108)) != ((d2term @ X107))) | (X107 = X108)) & (termmset_gthm = $true) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (pushprop_lthm_orig = $true) & ((hoasinduction_no_psi_cond = $true) | (! [X111 : term,X112 : term] : (($true != ((sK510 @ id @ X111 @ id))) | (((sK510 @ id @ X112 @ id)) != $true) | (((sK510 @ id @ (ap @ (sub @ X111 @ id) @ X112) @ id)) = $true)) & ($true != ((sP31 @ sK510))) & ($true != ((sK510 @ id @ sK511 @ id))))) & (! [X113 : (subst > term > subst > $o),X114 : term] : ((($true = ((X113 @ id @ (sK512 @ X113) @ id))) & (((X113 @ id @ (sK513 @ X113) @ id)) = $true) & (((X113 @ id @ (ap @ (sub @ (sK512 @ X113) @ id) @ (sK513 @ X113)) @ id)) != $true)) | (((sP31 @ X113)) = $true) | (((X113 @ id @ X114 @ id)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X117 : (term > $o),X118 : (term > $o),X119 : term,X120 : subst,X121 : term] : (($true = ((X118 @ (sub @ X119 @ (push @ X121 @ X120))))) | ($true != ((X117 @ X119)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true != ((sK515 @ (sub @ sK516 @ (push @ sK518 @ sK517))))) & (((sK514 @ sK516)) = $true))) & (lamnotap != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (! [X127 : term] : ! [X129 : term,X130 : subst] : (((sub @ X127 @ (push @ X129 @ X130))) = ((sK519 @ X127 @ X130 @ X129))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X132 : (subst > term > term)] : (((X132 @ (sK522 @ X132) @ (sK521 @ X132))) != ((sub @ sK520 @ (push @ (sK521 @ X132) @ (sK522 @ X132)))))) & (hoasinduction_lem1_gthm = $true) & ! [X135 : d_subst] : (d_id = X135) & (pushprop_lem3v2 = $true) & (axassoc = $true) & (hoasinduction_lem2_gthm = $true) & ((termmset = $true) | (sK523 != ((sub @ sK523 @ id)))) & (! [X137 : term] : (((sub @ X137 @ id)) = X137) | (termmset != $true)) & (induction2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem1_lthm = $true) | (! [X138 : subst,X139 : term] : (((comp @ sh @ (push @ X139 @ X138))) = X138) & ! [X140 : subst,X141 : term] : (((sub @ one @ (push @ X141 @ X140))) = X141) & ((((sK528 @ sK526)) = $true) & (((sK524 @ (sub @ sK526 @ (push @ sK527 @ sK525)))) != $true)))) & ((sK529 != ((comp @ sh @ (push @ sK530 @ sK529)))) | (sK532 != ((sub @ one @ (push @ sK532 @ sK531)))) | ! [X151 : (term > $o),X152 : subst,X153 : term,X154 : term,X155 : (term > $o)] : ((((X155 @ X153)) != $true) | ($true = ((X151 @ (sub @ X153 @ (push @ X154 @ X152)))))) | (pushprop_lem1_lthm != $true)) & ! [X156 : subst] : (((d2subst @ (sK533 @ X156))) = X156) & ! [X158 : d_subst,X159 : d_subst] : ((((d2subst @ X159)) != ((d2subst @ X158))) | (X158 = X159)) & (! [X160 : term] : (((sK534 @ X160 @ sh @ one)) = ((sub @ X160 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X163 : (subst > term > term)] : (((sub @ sK535 @ (push @ one @ sh))) != ((X163 @ sh @ one)))) & (axvarshift = $true) & ((laminj = $true) | ((((lam @ sK536)) = ((lam @ sK537))) & (sK536 != sK537))) & (! [X166 : term,X167 : term] : ((((lam @ X167)) != ((lam @ X166))) | (X166 = X167)) | (laminj != $true)) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem3b_gthm = $true) & (! [X168 : term,X169 : term] : ((((sub @ X168 @ sh)) != ((sub @ X169 @ sh))) | (X168 = X169)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK539 @ sh)) = ((sub @ sK538 @ sh))) & (sK539 != sK538))) & (hoasapnotvar_lthm = $true) & (hoasapinj2_gthm = $true) & ((apinj2 = $true) | ((sK541 != sK543) & (((ap @ sK540 @ sK541)) = ((ap @ sK542 @ sK543))))) & (! [X176 : term,X177 : term,X178 : term,X179 : term] : ((X177 = X179) | (((ap @ X176 @ X177)) != ((ap @ X178 @ X179)))) | (apinj2 != $true)) & ((sP30 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP30 != $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction_lem2 != $true)) & (ulamvar1 != $true) & ((hoasinduction_lem2v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem2v2 != $true)) & (pushprop = $true) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) | ($true != sP24)) & (($true = sP24) | (induction2lem_lthm != $true)) & ((induction2 = $true) | (sP20 != $true)) & ((sP20 = $true) | (induction2 != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true)) & (pushprop_lem0_gthm = $true) & ((sP15 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP15 != $true)) & ((axidl = $true) | (sK544 != ((comp @ id @ sK544)))) & (! [X181 : subst] : (((comp @ id @ X181)) = X181) | (axidl != $true)) & (hoasinduction_lem2_lthm = $true) & (hoaslamnotvar = $true) & (hoaslaminj_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3b = $true) | ! [X183 : (subst > term > term)] : (((sub @ sK545 @ (push @ one @ sh))) != ((X183 @ sh @ one)))) & (! [X184 : term] : (((sub @ X184 @ (push @ one @ sh))) = ((sK546 @ X184 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & ((pushprop_lem0 = $true) | ! [X189 : (term > $o)] : (((X189 @ (sK550 @ X189))) != ((sK547 @ (sub @ (sK550 @ X189) @ (push @ sK549 @ sK548)))))) & (! [X191 : (term > $o),X192 : subst,X193 : term] : ! [X195 : term] : (((X191 @ (sub @ X195 @ (push @ X193 @ X192)))) = ((sK551 @ X193 @ X192 @ X191 @ X195))) | (pushprop_lem0 != $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP12)) & (($true = sP12) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP11)) & (($true = sP11) | (hoasinduction_lem3a != $true)) & (axmap = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X196 : (subst > term > term),X197 : term,X198 : subst,X199 : (subst > term > term)] : ((((lam @ (X196 @ sh @ one))) != ((lam @ (X199 @ sh @ one)))) | (((X196 @ (comp @ (sK553 @ X196) @ (sK552 @ X196)) @ (sub @ (sK554 @ X196) @ (sK552 @ X196)))) != ((sub @ (X196 @ (sK553 @ X196) @ (sK554 @ X196)) @ (sK552 @ X196)))) | (((X199 @ (comp @ (sK556 @ X199) @ (sK557 @ X199)) @ (sub @ (sK555 @ X199) @ (sK557 @ X199)))) != ((sub @ (X199 @ (sK556 @ X199) @ (sK555 @ X199)) @ (sK557 @ X199)))) | (((X199 @ X198 @ X197)) = ((X196 @ X198 @ X197)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((lam @ (sK558 @ sh @ one))) = ((lam @ (sK561 @ sh @ one)))) & ! [X210 : subst,X211 : subst,X212 : term] : (((sK558 @ (comp @ X211 @ X210) @ (sub @ X212 @ X210))) = ((sub @ (sK558 @ X211 @ X212) @ X210))) & ! [X213 : term,X214 : subst,X215 : subst] : (((sub @ (sK561 @ X214 @ X213) @ X215)) = ((sK561 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)))) & (((sK558 @ sK560 @ sK559)) != ((sK561 @ sK560 @ sK559))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true)) & ((((sub @ sK562 @ id)) != sK562) | ((((ap @ sK564 @ sK563)) = ((ap @ sK566 @ sK565))) & (sK564 != sK566)) | ! [X221 : term,X222 : term,X223 : term,X224 : term] : ((((ap @ (sub @ X221 @ id) @ X223)) != ((ap @ (sub @ X222 @ id) @ X224))) | (X221 = X222)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X225 : term] : (((sub @ X225 @ id)) = X225) & ! [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ X227 @ X226)) != ((ap @ X229 @ X228))) | (X227 = X229)) & ((((ap @ (sub @ sK567 @ id) @ sK569)) = ((ap @ (sub @ sK568 @ id) @ sK570))) & (sK567 != sK568)))) & ((sP8 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP8 != $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) | ((! [X238 : term] : (((sK572 @ (sub @ X238 @ (push @ sK571 @ sK573)))) = ((sK574 @ X238))) & (((sK574 @ one)) != $true) & ($true = ((sK572 @ sK571)))) & ! [X239 : subst,X240 : term] : (((sub @ one @ (push @ X240 @ X239))) = X240))) & (! [X241 : term,X242 : (term > $o),X243 : subst,X244 : (term > $o)] : ((((X244 @ (sK575 @ X244 @ X243 @ X242 @ X241))) != ((X242 @ (sub @ (sK575 @ X244 @ X243 @ X242 @ X241) @ (push @ X241 @ X243))))) | ($true = ((X244 @ one))) | (((X242 @ X241)) != $true)) | (((sub @ one @ (push @ sK577 @ sK576))) != sK577) | (pushprop_lem1v2_lthm != $true)) & (! [X248 : subst] : (((comp @ X248 @ id)) = X248) | (axidr != $true)) & ((axidr = $true) | (sK578 != ((comp @ sK578 @ id)))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_gthm = $true) & (ulamvarind = $true) & (($true = sP4) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP4)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2a = $true) | (sP3 != $true)) & ((sP3 = $true) | (hoasinduction_lem3v2a != $true)) & (! [X250 : term,X251 : subst] : (((comp @ sh @ (push @ X250 @ X251))) = X251) | (axshiftcons != $true)) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK579 @ sK580))) != sK580)) & (! [X254 : term] : (((sub @ X254 @ id)) = X254) | (axvarid != $true)) & ((axvarid = $true) | (((sub @ sK581 @ id)) != sK581)) & (hoasinduction_lem3v2_gthm = $true) & (axapp = $true) & (hoasapinj1_gthm = $true) & ((sP2 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP2 != $true)) & (substmonoid_gthm = $true) & (! [X256 : (subst > term > term),X257 : term,X258 : term] : ((((ap @ (sub @ X258 @ id) @ X257)) != ((lam @ (X256 @ sh @ one)))) | (((X256 @ (comp @ (sK583 @ X256) @ (sK584 @ X256)) @ (sub @ (sK582 @ X256) @ (sK584 @ X256)))) != ((sub @ (X256 @ (sK583 @ X256) @ (sK582 @ X256)) @ (sK584 @ X256))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ((((ap @ (sub @ sK587 @ id) @ sK586)) = ((lam @ (sK585 @ sh @ one)))) & ! [X265 : term,X266 : subst,X267 : subst] : (((sK585 @ (comp @ X266 @ X267) @ (sub @ X265 @ X267))) = ((sub @ (sK585 @ X266 @ X265) @ X267))))) & ((hoasinduction_lem0_lthm = $true) | ! [X269 : (term > $o)] : (((sK588 @ id @ (sK589 @ X269) @ id)) != ((X269 @ (sK589 @ X269))))) & (! [X271 : (subst > term > subst > $o)] : ! [X273 : term] : (((X271 @ id @ X273 @ id)) = ((sK590 @ X271 @ X273))) | (hoasinduction_lem0_lthm != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP0 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP0 != $true)) & (hoasinduction_lem1v2 = $true)),
% 6.34/1.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,vAPP,vAPP,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,sK475,vAPP,sK477,sK478,sK479,sK480,sK481,vAPP,vAPP,sK484,vAPP,vAPP,vAPP,vAPP,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,vAPP,vAPP,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,vAPP,vAPP,sK514,sK515,sK516,sK517,sK518,vAPP,sK520,vAPP,vAPP,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,vAPP,vAPP,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,vAPP,sK547,sK548,sK549,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,vAPP,sK576,sK577,sK578,sK579,sK580,sK581,vAPP,vAPP,vAPP,sK585,sK586,sK587,sK588,vAPP,vAPP]),skolemize(X0,sK457),skolemize(X6,sK458),skolemize(X7,sK459),skolemize(X8,sK460),skolemize(X9,sK461),skolemize(X10,sK462),skolemize(X11,sK463),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X23,sK466),skolemize(X24,sK467),skolemize(X25,sK468),skolemize(X26,sK469),skolemize(X27,sK470),skolemize(X28,sK471),skolemize(X31,sK472),skolemize(X32,sK473),skolemize(X33,sK474),skolemize(X34,sK475),skolemize(X25,sK68 @ X18),skolemize(X44,sK477),skolemize(X45,sK478),skolemize(X46,sK479),skolemize(X47,sK480),skolemize(X49,sK481),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X55,sK484),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X65,sK489),skolemize(X66,sK490),skolemize(X71,sK491),skolemize(X72,sK492),skolemize(X73,sK493),skolemize(X74,sK494),skolemize(X77,sK495),skolemize(X80,sK496),skolemize(X81,sK497),skolemize(X82,sK498),skolemize(X83,sK499),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X91,sK502),skolemize(X92,sK503),skolemize(X93,sK504),skolemize(X94,sK505),skolemize(X103,sK506),skolemize(X104,sK507),skolemize(X105,sK508),skolemize(X106,sK509),skolemize(X109,sK510),skolemize(X110,sK511),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X122,sK514),skolemize(X123,sK515),skolemize(X124,sK516),skolemize(X125,sK517),skolemize(X126,sK518),skolemize(X25,sK68 @ X18),skolemize(X131,sK520),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X136,sK523),skolemize(X142,sK524),skolemize(X143,sK525),skolemize(X144,sK526),skolemize(X145,sK527),skolemize(X146,sK528),skolemize(X147,sK529),skolemize(X148,sK530),skolemize(X149,sK531),skolemize(X150,sK532),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X162,sK535),skolemize(X164,sK536),skolemize(X165,sK537),skolemize(X170,sK538),skolemize(X171,sK539),skolemize(X172,sK540),skolemize(X173,sK541),skolemize(X174,sK542),skolemize(X175,sK543),skolemize(X180,sK544),skolemize(X182,sK545),skolemize(X25,sK68 @ X18),skolemize(X186,sK547),skolemize(X187,sK548),skolemize(X188,sK549),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X206,sK558),skolemize(X207,sK559),skolemize(X208,sK560),skolemize(X209,sK561),skolemize(X216,sK562),skolemize(X217,sK563),skolemize(X218,sK564),skolemize(X219,sK565),skolemize(X220,sK566),skolemize(X230,sK567),skolemize(X231,sK568),skolemize(X232,sK569),skolemize(X233,sK570),skolemize(X234,sK571),skolemize(X235,sK572),skolemize(X236,sK573),skolemize(X237,sK574),skolemize(X25,sK68 @ X18),skolemize(X246,sK576),skolemize(X247,sK577),skolemize(X249,sK578),skolemize(X252,sK579),skolemize(X253,sK580),skolemize(X255,sK581),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18),skolemize(X262,sK585),skolemize(X263,sK586),skolemize(X264,sK587),skolemize(X268,sK588),skolemize(X25,sK68 @ X18),skolemize(X25,sK68 @ X18)],[f262])).
% 6.34/1.36 thf(f264,plain,(
% 6.34/1.36 (hoasinduction_lem3aa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.34/1.36 inference(cnf_transformation,[],[f8])).
% 6.34/1.36 thf(f302,plain,(
% 6.34/1.36 (((sK93 @ id @ (lam @ (sub @ sK94 @ (push @ one @ sh))) @ id)) != $true) | (sP54 = $true)),
% 6.34/1.36 inference(cnf_transformation,[],[f88])).
% 6.34/1.36 thf(f304,plain,(
% 6.34/1.36 ( ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK98 @ X3) @ (sK96 @ X3)) @ (sK97 @ X3))) != ((X3 @ (comp @ (sK98 @ X3) @ (sK97 @ X3)) @ (sub @ (sK96 @ X3) @ (sK97 @ X3))))) | (sP54 = $true) | (((sK93 @ id @ (sK95 @ X3) @ id)) = $true) | ($true = ((sK93 @ id @ (lam @ (X3 @ sh @ one)) @ id)))) )),
% 6.34/1.36 inference(cnf_transformation,[],[f88])).
% 6.34/1.36 thf(f305,plain,(
% 6.34/1.36 ( ! [X2 : term] : ((sP54 = $true) | (((sK93 @ id @ (sub @ sK94 @ (push @ X2 @ id)) @ id)) = $true) | (((sK93 @ id @ X2 @ id)) != $true)) )),
% 6.34/1.36 inference(cnf_transformation,[],[f88])).
% 6.34/1.36 thf(f757,plain,(
% 6.34/1.36 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 6.34/1.36 inference(cnf_transformation,[],[f263])).
% 6.34/1.36 thf(f930,plain,(
% 6.34/1.36 ( ! [X63 : term] : ((((d2term @ (sK488 @ X63))) = X63)) )),
% 6.34/1.36 inference(cnf_transformation,[],[f263])).
% 6.34/1.36 thf(f934,plain,(
% 6.34/1.36 (sP54 != $true) | (hoasinduction_lem3aa = $true)),
% 6.34/1.36 inference(cnf_transformation,[],[f263])).
% 6.34/1.36 thf(f959,plain,(
% 6.34/1.36 ( ! [X18 : d_term] : ((d_one = X18)) )),
% 6.34/1.36 inference(cnf_transformation,[],[f263])).
% 6.34/1.36 thf(f976,plain,(
% 6.34/1.36 (one = ((d2term @ d_one)))),
% 6.34/1.36 inference(cnf_transformation,[],[f263])).
% 6.34/1.36 thf(f981,plain,(
% 6.34/1.36 (hoasinduction_lem3aa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.34/1.36 inference(definition_unfolding,[],[f264,f757])).
% 6.34/1.36 thf(f1107,plain,(
% 6.34/1.36 (hoasinduction_lem3aa = $false) | (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))) = $false)),
% 6.34/1.36 inference(xor_proxy_clausification,[],[f981])).
% 6.34/1.36 thf(f1108,plain,(
% 6.34/1.36 (hoasinduction_lem3aa = $false) | ((((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y1 @ (comp @ Y2 @ Y4) @ (sub @ Y3 @ Y4)) = (sub @ (Y1 @ Y2 @ Y3) @ Y4)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))) @ sK591)) = $false)),
% 6.34/1.36 inference(sigma_proxy_clausification,[],[f1107])).
% 6.34/1.36 thf(f1109,plain,(
% 6.34/1.36 ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))))) = $false) | (hoasinduction_lem3aa = $false)),
% 6.34/1.36 inference(beta-eta_normalization,[],[f1108])).
% 6.34/1.36 thf(f1110,plain,(
% 6.34/1.36 (hoasinduction_lem3aa = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))))))),
% 6.34/1.36 inference(imp_proxy_clausification,[],[f1109])).
% 6.34/1.36 thf(f1111,plain,(
% 6.34/1.36 ($true = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))))) | (hoasinduction_lem3aa = $false)),
% 6.34/1.36 inference(imp_proxy_clausification,[],[f1109])).
% 6.34/1.36 thf(f1112,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3aa = $false) | ((((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((Y0 @ (comp @ Y1 @ Y3) @ (sub @ Y2 @ Y3)) = (sub @ (Y0 @ Y1 @ Y2) @ Y3)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) @ X1)) = $true)) )),
% 6.34/1.36 inference(pi_proxy_clausification,[],[f1111])).
% 6.34/1.36 thf(f1113,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2)))))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) | (hoasinduction_lem3aa = $false)) )),
% 6.34/1.36 inference(beta-eta_normalization,[],[f1112])).
% 6.34/1.36 thf(f1114,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2))))))))) = $false) | (hoasinduction_lem3aa = $false) | ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))) = $true)) )),
% 6.34/1.36 inference(imp_proxy_clausification,[],[f1113])).
% 6.34/1.36 thf(f1115,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3aa = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2))))))) @ (sK592 @ X1)))) | ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))) = $true)) )),
% 6.34/1.36 inference(sigma_proxy_clausification,[],[f1114])).
% 6.34/1.36 thf(f1116,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))))) = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2))))))) @ (sK592 @ X1)))) | (hoasinduction_lem3aa = $false)) )),
% 6.34/1.36 inference(imp_proxy_clausification,[],[f1115])).
% 6.34/1.36 thf(f1117,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((X1 @ (comp @ Y0 @ Y2) @ (sub @ Y1 @ Y2)) = (sub @ (X1 @ Y0 @ Y1) @ Y2))))))) @ (sK592 @ X1)))) | ((((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK593 @ X1))) = $false) | (hoasinduction_lem3aa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.34/1.36 inference(sigma_proxy_clausification,[],[f1116])).
% 6.34/1.36 thf(f1118,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ (sK592 @ X1) @ Y1) @ (sub @ Y0 @ Y1)) = (sub @ (X1 @ (sK592 @ X1) @ Y0) @ Y1)))))))) | ((((sK591 @ id @ (sK593 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK593 @ X1)) @ id))) = $false) | (hoasinduction_lem3aa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.34/1.36 inference(beta-eta_normalization,[],[f1117])).
% 6.34/1.36 thf(f1119,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3aa = $false) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ (sK592 @ X1) @ Y1) @ (sub @ Y0 @ Y1)) = (sub @ (X1 @ (sK592 @ X1) @ Y0) @ Y1))))) @ (sK594 @ X1))) = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((sK591 @ id @ (sK593 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK593 @ X1)) @ id))) = $false)) )),
% 6.34/1.36 inference(sigma_proxy_clausification,[],[f1118])).
% 6.34/1.36 thf(f1121,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((X1 @ (comp @ (sK592 @ X1) @ Y1) @ (sub @ Y0 @ Y1)) = (sub @ (X1 @ (sK592 @ X1) @ Y0) @ Y1))))) @ (sK594 @ X1))) = $false) | (hoasinduction_lem3aa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.34/1.36 inference(imp_proxy_clausification,[],[f1119])).
% 6.34/1.36 thf(f1122,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: ((X1 @ (comp @ (sK592 @ X1) @ Y0) @ (sub @ (sK594 @ X1) @ Y0)) = (sub @ (X1 @ (sK592 @ X1) @ (sK594 @ X1)) @ Y0))))) = $false) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (hoasinduction_lem3aa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.34/1.36 inference(beta-eta_normalization,[],[f1121])).
% 6.34/1.36 thf(f1123,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | ((((^[Y0 : subst]: ((X1 @ (comp @ (sK592 @ X1) @ Y0) @ (sub @ (sK594 @ X1) @ Y0)) = (sub @ (X1 @ (sK592 @ X1) @ (sK594 @ X1)) @ Y0))) @ (sK595 @ X1))) = $false) | (hoasinduction_lem3aa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.34/1.36 inference(sigma_proxy_clausification,[],[f1122])).
% 6.34/1.36 thf(f1124,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3aa = $false) | ((((X1 @ (comp @ (sK592 @ X1) @ (sK595 @ X1)) @ (sub @ (sK594 @ X1) @ (sK595 @ X1))) = (sub @ (X1 @ (sK592 @ X1) @ (sK594 @ X1)) @ (sK595 @ X1)))) = $false) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.34/1.36 inference(beta-eta_normalization,[],[f1123])).
% 6.34/1.36 thf(f1125,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (((sub @ (X1 @ (sK592 @ X1) @ (sK594 @ X1)) @ (sK595 @ X1))) != ((X1 @ (comp @ (sK592 @ X1) @ (sK595 @ X1)) @ (sub @ (sK594 @ X1) @ (sK595 @ X1))))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction_lem3aa = $false)) )),
% 6.34/1.36 inference(equality_proxy_clausification,[],[f1124])).
% 6.34/1.36 thf(f1130,plain,(
% 6.34/1.36 (hoasinduction_lem3aa = $false) | ((((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))) @ sK597)) = $false)),
% 6.34/1.36 inference(sigma_proxy_clausification,[],[f1110])).
% 6.34/1.36 thf(f1131,plain,(
% 6.34/1.36 ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (sub @ sK597 @ (push @ Y0 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ sK597 @ (push @ one @ sh))) @ id))) = $false) | (hoasinduction_lem3aa = $false)),
% 6.34/1.36 inference(beta-eta_normalization,[],[f1130])).
% 6.34/1.36 thf(f1132,plain,(
% 6.34/1.36 (((sK591 @ id @ (lam @ (sub @ sK597 @ (push @ one @ sh))) @ id)) = $false) | (hoasinduction_lem3aa = $false)),
% 6.34/1.36 inference(imp_proxy_clausification,[],[f1131])).
% 6.34/1.36 thf(f1500,definition,(
% 6.34/1.36 spl602_74 <=> ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK98 @ X3) @ (sK96 @ X3)) @ (sK97 @ X3))) != ((X3 @ (comp @ (sK98 @ X3) @ (sK97 @ X3)) @ (sub @ (sK96 @ X3) @ (sK97 @ X3))))) | ($true = ((sK93 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | (((sK93 @ id @ (sK95 @ X3) @ id)) = $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_74])],[avatar_definition])).
% 6.34/1.36 thf(f1501,plain,(
% 6.34/1.36 ( ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK98 @ X3) @ (sK96 @ X3)) @ (sK97 @ X3))) != ((X3 @ (comp @ (sK98 @ X3) @ (sK97 @ X3)) @ (sub @ (sK96 @ X3) @ (sK97 @ X3))))) | ($true = ((sK93 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | (((sK93 @ id @ (sK95 @ X3) @ id)) = $true)) ) | ~spl602_74),
% 6.34/1.36 inference(avatar_component_clause,[],[f1500])).
% 6.34/1.36 thf(f1503,definition,(
% 6.34/1.36 spl602_75 <=> (sP54 = $true)),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_75])],[avatar_definition])).
% 6.34/1.36 thf(f1506,plain,(
% 6.34/1.36 spl602_74 | spl602_75),
% 6.34/1.36 inference(avatar_split_clause,[],[f304,f1503,f1500])).
% 6.34/1.36 thf(f1563,definition,(
% 6.34/1.36 spl602_89 <=> (hoasinduction_lem3aa = $true)),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_89])],[avatar_definition])).
% 6.34/1.36 thf(f1565,plain,(
% 6.34/1.36 (hoasinduction_lem3aa = $true) | ~spl602_89),
% 6.34/1.36 inference(avatar_component_clause,[],[f1563])).
% 6.34/1.36 thf(f1566,plain,(
% 6.34/1.36 ~spl602_75 | spl602_89),
% 6.34/1.36 inference(avatar_split_clause,[],[f934,f1563,f1503])).
% 6.34/1.36 thf(f2545,definition,(
% 6.34/1.36 spl602_318 <=> ! [X2 : term] : ((((sK93 @ id @ (sub @ sK94 @ (push @ X2 @ id)) @ id)) = $true) | (((sK93 @ id @ X2 @ id)) != $true))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_318])],[avatar_definition])).
% 6.34/1.36 thf(f2546,plain,(
% 6.34/1.36 ( ! [X2 : term] : ((((sK93 @ id @ X2 @ id)) != $true) | (((sK93 @ id @ (sub @ sK94 @ (push @ X2 @ id)) @ id)) = $true)) ) | ~spl602_318),
% 6.34/1.36 inference(avatar_component_clause,[],[f2545])).
% 6.34/1.36 thf(f2547,plain,(
% 6.34/1.36 spl602_318 | spl602_75),
% 6.34/1.36 inference(avatar_split_clause,[],[f305,f1503,f2545])).
% 6.34/1.36 thf(f2635,definition,(
% 6.34/1.36 spl602_338 <=> (((sK93 @ id @ (lam @ (sub @ sK94 @ (push @ one @ sh))) @ id)) = $true)),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_338])],[avatar_definition])).
% 6.34/1.36 thf(f2637,plain,(
% 6.34/1.36 (((sK93 @ id @ (lam @ (sub @ sK94 @ (push @ one @ sh))) @ id)) != $true) | spl602_338),
% 6.34/1.36 inference(avatar_component_clause,[],[f2635])).
% 6.34/1.36 thf(f2638,plain,(
% 6.34/1.36 ~spl602_338 | spl602_75),
% 6.34/1.36 inference(avatar_split_clause,[],[f302,f1503,f2635])).
% 6.34/1.36 thf(f3466,definition,(
% 6.34/1.36 spl602_529 <=> ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (((sub @ (X1 @ (sK592 @ X1) @ (sK594 @ X1)) @ (sK595 @ X1))) != ((X1 @ (comp @ (sK592 @ X1) @ (sK595 @ X1)) @ (sub @ (sK594 @ X1) @ (sK595 @ X1))))))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_529])],[avatar_definition])).
% 6.34/1.36 thf(f3467,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (((sub @ (X1 @ (sK592 @ X1) @ (sK594 @ X1)) @ (sK595 @ X1))) != ((X1 @ (comp @ (sK592 @ X1) @ (sK595 @ X1)) @ (sub @ (sK594 @ X1) @ (sK595 @ X1)))))) ) | ~spl602_529),
% 6.34/1.36 inference(avatar_component_clause,[],[f3466])).
% 6.34/1.36 thf(f3469,definition,(
% 6.34/1.36 spl602_530 <=> (hoasinduction_lem3aa = $false)),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_530])],[avatar_definition])).
% 6.34/1.36 thf(f3471,plain,(
% 6.34/1.36 (hoasinduction_lem3aa = $false) | ~spl602_530),
% 6.34/1.36 inference(avatar_component_clause,[],[f3469])).
% 6.34/1.36 thf(f3473,definition,(
% 6.34/1.36 spl602_531 <=> ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_531])],[avatar_definition])).
% 6.34/1.36 thf(f3475,plain,(
% 6.34/1.36 ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl602_531),
% 6.34/1.36 inference(avatar_component_clause,[],[f3473])).
% 6.34/1.36 thf(f3476,plain,(
% 6.34/1.36 spl602_529 | spl602_530 | spl602_531),
% 6.34/1.36 inference(avatar_split_clause,[],[f1125,f3473,f3469,f3466])).
% 6.34/1.36 thf(f3486,definition,(
% 6.34/1.36 spl602_534 <=> (((sK591 @ id @ (lam @ (sub @ sK597 @ (push @ one @ sh))) @ id)) = $false)),
% 6.34/1.36 introduced(definition,[new_symbols(definition,[spl602_534])],[avatar_definition])).
% 6.34/1.36 thf(f3488,plain,(
% 6.34/1.36 (((sK591 @ id @ (lam @ (sub @ sK597 @ (push @ one @ sh))) @ id)) = $false) | ~spl602_534),
% 6.34/1.36 inference(avatar_component_clause,[],[f3486])).
% 6.34/1.36 thf(f3489,plain,(
% 6.34/1.36 spl602_534 | spl602_530),
% 6.34/1.36 inference(avatar_split_clause,[],[f1132,f3469,f3486])).
% 6.34/1.36 thf(f4392,plain,(
% 6.34/1.36 ( ! [X63 : term] : ((((d2term @ d_one)) = X63)) )),
% 6.34/1.36 inference(forward_demodulation,[],[f930,f959])).
% 6.34/1.36 thf(f4399,plain,(
% 6.34/1.36 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 6.34/1.36 inference(superposition,[],[f4392,f4392])).
% 6.34/1.36 thf(f7692,plain,(
% 6.34/1.36 (((sK93 @ id @ (d2term @ d_one) @ id)) != $true) | spl602_338),
% 6.34/1.36 inference(forward_demodulation,[],[f2637,f4392])).
% 6.34/1.36 thf(f7693,plain,(
% 6.34/1.36 (((sK93 @ id @ one @ id)) != $true) | spl602_338),
% 6.34/1.36 inference(forward_demodulation,[],[f7692,f976])).
% 6.34/1.36 thf(f8624,plain,(
% 6.34/1.36 ( ! [X2 : term] : ((((sK93 @ id @ (d2term @ d_one) @ id)) = $true) | (((sK93 @ id @ X2 @ id)) != $true)) ) | ~spl602_318),
% 6.34/1.36 inference(forward_demodulation,[],[f2546,f4392])).
% 6.34/1.36 thf(f8625,plain,(
% 6.34/1.36 ( ! [X2 : term] : ((((sK93 @ id @ one @ id)) = $true) | (((sK93 @ id @ X2 @ id)) != $true)) ) | ~spl602_318),
% 6.34/1.36 inference(forward_demodulation,[],[f8624,f976])).
% 6.34/1.36 thf(f8626,plain,(
% 6.34/1.36 ( ! [X2 : term] : ((((sK93 @ id @ X2 @ id)) != $true)) ) | (~spl602_318 | spl602_338)),
% 6.34/1.36 inference(forward_subsumption_resolution,[],[f8625,f7693])).
% 6.34/1.36 thf(f11081,plain,(
% 6.34/1.36 ( ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK98 @ X3) @ (sK96 @ X3)) @ (sK97 @ X3))) != ((X3 @ (comp @ (sK98 @ X3) @ (sK97 @ X3)) @ (sub @ (sK96 @ X3) @ (sK97 @ X3))))) | (((sK93 @ id @ (sK95 @ X3) @ id)) = $true)) ) | (~spl602_74 | ~spl602_318 | spl602_338)),
% 6.34/1.36 inference(forward_subsumption_resolution,[],[f1501,f8626])).
% 6.34/1.36 thf(f11082,plain,(
% 6.34/1.36 ( ! [X3 : (subst > term > term)] : ((((sK93 @ id @ (sK95 @ X3) @ id)) = $true)) ) | (~spl602_74 | ~spl602_318 | spl602_338)),
% 6.34/1.36 inference(forward_subsumption_resolution,[],[f11081,f4399])).
% 6.34/1.36 thf(f11083,plain,(
% 6.34/1.36 $false | (~spl602_74 | ~spl602_318 | spl602_338)),
% 6.34/1.36 inference(forward_subsumption_resolution,[],[f11082,f8626])).
% 6.34/1.36 thf(f11084,plain,(
% 6.34/1.36 ~spl602_74 | ~spl602_318 | spl602_338),
% 6.34/1.36 inference(avatar_contradiction_clause,[],[f11083])).
% 6.34/1.36 thf(f11089,plain,(
% 6.34/1.36 ($true = $false) | (~spl602_89 | ~spl602_530)),
% 6.34/1.36 inference(forward_demodulation,[],[f1565,f3471])).
% 6.34/1.36 thf(f11090,plain,(
% 6.34/1.36 $false | (~spl602_89 | ~spl602_530)),
% 6.34/1.36 inference(trivial_inequality_removal,[],[f11089])).
% 6.34/1.36 thf(f11091,plain,(
% 6.34/1.36 ~spl602_89 | ~spl602_530),
% 6.34/1.36 inference(avatar_contradiction_clause,[],[f11090])).
% 6.34/1.36 thf(f11109,plain,(
% 6.34/1.36 ($false = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl602_534),
% 6.34/1.36 inference(forward_demodulation,[],[f3488,f4392])).
% 6.34/1.36 thf(f11110,plain,(
% 6.34/1.36 (((sK591 @ id @ one @ id)) = $true) | ~spl602_531),
% 6.34/1.36 inference(forward_demodulation,[],[f3475,f976])).
% 6.34/1.36 thf(f11111,plain,(
% 6.34/1.36 (((sK591 @ id @ one @ id)) = $false) | ~spl602_534),
% 6.34/1.36 inference(forward_demodulation,[],[f11109,f976])).
% 6.34/1.36 thf(f11167,plain,(
% 6.34/1.36 ($true = $false) | (~spl602_531 | ~spl602_534)),
% 6.34/1.36 inference(superposition,[],[f11111,f11110])).
% 6.34/1.36 thf(f11214,plain,(
% 6.34/1.36 $false | (~spl602_531 | ~spl602_534)),
% 6.34/1.36 inference(trivial_inequality_removal,[],[f11167])).
% 6.34/1.36 thf(f11215,plain,(
% 6.34/1.36 ~spl602_531 | ~spl602_534),
% 6.34/1.36 inference(avatar_contradiction_clause,[],[f11214])).
% 6.34/1.36 thf(f11224,plain,(
% 6.34/1.36 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id)))) ) | ~spl602_529),
% 6.34/1.36 inference(forward_subsumption_resolution,[],[f3467,f4399])).
% 6.34/1.36 thf(f11227,plain,(
% 6.34/1.36 ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl602_529),
% 6.34/1.36 inference(forward_demodulation,[],[f11224,f4392])).
% 6.34/1.36 thf(f11229,plain,(
% 6.34/1.36 (((sK591 @ id @ one @ id)) = $true) | ~spl602_529),
% 6.34/1.36 inference(forward_demodulation,[],[f11227,f976])).
% 6.34/1.36 thf(f11231,plain,(
% 6.34/1.36 ($true = $false) | (~spl602_529 | ~spl602_534)),
% 6.34/1.36 inference(forward_demodulation,[],[f11229,f11111])).
% 6.34/1.36 thf(f11232,plain,(
% 6.34/1.36 $false | (~spl602_529 | ~spl602_534)),
% 6.34/1.36 inference(trivial_inequality_removal,[],[f11231])).
% 6.34/1.36 thf(f11233,plain,(
% 6.34/1.36 ~spl602_529 | ~spl602_534),
% 6.34/1.36 inference(avatar_contradiction_clause,[],[f11232])).
% 6.34/1.36 cnf(s40, plain, spl602_74 | spl602_75, inference(sat_conversion,[],[f1506])).
% 6.34/1.36 cnf(s50, plain, ~spl602_75 | spl602_89, inference(sat_conversion,[],[f1566])).
% 6.34/1.36 cnf(s258, plain, spl602_75 | spl602_318, inference(sat_conversion,[],[f2547])).
% 6.34/1.36 cnf(s282, plain, spl602_75 | ~spl602_338, inference(sat_conversion,[],[f2638])).
% 6.34/1.36 cnf(s489, plain, spl602_529 | spl602_530 | spl602_531, inference(sat_conversion,[],[f3476])).
% 6.34/1.36 cnf(s492, plain, spl602_530 | spl602_534, inference(sat_conversion,[],[f3489])).
% 6.34/1.36 cnf(s747, plain, ~spl602_74 | ~spl602_318 | spl602_338, inference(sat_conversion,[],[f11084])).
% 6.34/1.36 cnf(s748, plain, ~spl602_89 | ~spl602_530, inference(sat_conversion,[],[f11091])).
% 6.34/1.36 cnf(s750, plain, ~spl602_531 | ~spl602_534, inference(sat_conversion,[],[f11215])).
% 6.34/1.36 cnf(s751, plain, ~spl602_529 | ~spl602_534, inference(sat_conversion,[],[f11233])).
% 6.34/1.36 cnf(s801, plain, spl602_530, inference(rat,[],[s489,s750,s751,s492])).
% 6.34/1.36 cnf(s802, plain, ~spl602_89, inference(rat,[],[s748,s801])).
% 6.34/1.36 cnf(s809, plain, ~spl602_75, inference(rat,[],[s50,s802])).
% 6.34/1.36 cnf(s811, plain, ~spl602_338, inference(rat,[],[s282,s809])).
% 6.34/1.36 cnf(s812, plain, spl602_318, inference(rat,[],[s258,s809])).
% 6.34/1.36 cnf(s813, plain, spl602_74, inference(rat,[],[s40,s809])).
% 6.34/1.36 cnf(s814, plain, $false, inference(rat,[],[s747,s811,s812,s813])).
% 6.34/1.36 thf(f11234,plain,(
% 6.34/1.36 $false),
% 6.34/1.36 inference(avatar_sat_refutation,[],[s814])).
% 6.34/1.36 % SZS output end Proof for theBenchmark
% 6.34/1.36 % (539206)------------------------------
% 6.34/1.36 % (539206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.34/1.36 % (539206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.36 % (539206)CaDiCaL version: 2.1.3
% 6.34/1.36 % (539206)Termination reason: Refutation
% 6.34/1.36 % (539206)Time elapsed: 0.441 s
% 6.34/1.36 % (539206)Peak memory usage: 19 MB
% 6.34/1.36 % (539206)Instructions burned: 920 (million)
% 6.34/1.36 % (538987)Success in time 0.993 s
% 6.34/1.36 % Vampire exiting
%------------------------------------------------------------------------------