%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX170^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:38 AM UTC 2026
% Result : Theorem 6.46s 1.21s
% Output : Refutation 6.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX170^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n006.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:09:10 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.37 % (920298)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.77/0.37 % (920303)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3893809730:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.77/0.37 % (920309)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.77/0.37 % (920309)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
% 0.77/0.37 % (920304)lrs+10_16_si=on:nwc=1.5:random_seed=1610239500:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.77/0.37 % (920305)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2147030389:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.77/0.37 % (920307)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2127452194:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.77/0.37 % (920306)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=413476613: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)
% 0.77/0.37 % (920308)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2591743574:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.77/0.37 % (920309)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=2091368130:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.77/0.37 % (920305)Instruction limit reached!
% 0.77/0.37 % (920305)------------------------------
% 0.77/0.37 % (920305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.37 % (920305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.37 % (920305)CaDiCaL version: 2.1.3
% 0.77/0.37 % (920305)Termination reason: Instruction limit
% 0.77/0.37 % (920305)Termination phase: shuffling
% 0.77/0.37 % (920305)Time elapsed: 0.002 s
% 0.77/0.37 % (920305)Peak memory usage: 10 MB
% 0.77/0.37 % (920305)Instructions burned: 3 (million)
% 0.77/0.37 % (920304)Instruction limit reached!
% 0.77/0.37 % (920304)------------------------------
% 0.77/0.37 % (920304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.37 % (920304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.37 % (920304)CaDiCaL version: 2.1.3
% 0.77/0.37 % (920304)Termination reason: Instruction limit
% 0.77/0.37 % (920304)Termination phase: shuffling
% 0.77/0.37 % (920304)Time elapsed: 0.008 s
% 0.77/0.37 % (920304)Peak memory usage: 10 MB
% 0.77/0.37 % (920304)Instructions burned: 19 (million)
% 0.77/0.37 % (920307)Instruction limit reached!
% 0.77/0.37 % (920307)------------------------------
% 0.77/0.37 % (920307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.37 % (920307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.37 % (920307)CaDiCaL version: 2.1.3
% 0.77/0.37 % (920307)Termination reason: Instruction limit
% 0.77/0.37 % (920307)Termination phase: Property scanning
% 0.77/0.37 % (920307)Time elapsed: 0.011 s
% 0.77/0.37 % (920307)Peak memory usage: 10 MB
% 0.77/0.37 % (920307)Instructions burned: 25 (million)
% 0.77/0.37 % (920303)Instruction limit reached!
% 0.77/0.37 % (920303)------------------------------
% 0.77/0.37 % (920303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.37 % (920303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.37 % (920303)CaDiCaL version: 2.1.3
% 0.77/0.37 % (920303)Termination reason: Instruction limit
% 0.77/0.37 % (920303)Termination phase: Preprocessing 3
% 0.77/0.37 % (920303)Time elapsed: 0.022 s
% 0.77/0.37 % (920303)Peak memory usage: 13 MB
% 0.77/0.37 % (920303)Instructions burned: 87 (million)
% 0.77/0.37 % (920317)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2154828980:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.37 % (920317)Instruction limit reached!
% 0.77/0.37 % (920317)------------------------------
% 0.77/0.37 % (920317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.41 % (920317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.41 % (920317)CaDiCaL version: 2.1.3
% 0.77/0.41 % (920317)Termination reason: Instruction limit
% 0.77/0.41 % (920317)Termination phase: shuffling
% 0.77/0.41 % (920317)Time elapsed: 0.002 s
% 0.77/0.41 % (920317)Peak memory usage: 10 MB
% 0.77/0.41 % (920317)Instructions burned: 4 (million)
% 0.77/0.41 % (920320)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1475759563:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.77/0.41 % (920319)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.41 % (920320)Instruction limit reached!
% 0.77/0.41 % (920320)------------------------------
% 0.77/0.41 % (920320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.41 % (920320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.41 % (920320)CaDiCaL version: 2.1.3
% 0.77/0.41 % (920320)Termination reason: Instruction limit
% 0.77/0.41 % (920320)Termination phase: shuffling
% 0.77/0.41 % (920318)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1167436094:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.77/0.41 % (920320)Time elapsed: 0.003 s
% 0.77/0.41 % (920320)Peak memory usage: 10 MB
% 0.77/0.41 % (920320)Instructions burned: 13 (million)
% 0.77/0.41 % (920319)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=160839605:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.77/0.41 % (920318)Instruction limit reached!
% 0.77/0.41 % (920318)------------------------------
% 0.77/0.41 % (920318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.41 % (920318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.41 % (920318)CaDiCaL version: 2.1.3
% 0.77/0.41 % (920318)Termination reason: Instruction limit
% 0.77/0.41 % (920318)Termination phase: shuffling
% 0.77/0.41 % (920318)Time elapsed: 0.003 s
% 0.77/0.41 % (920318)Peak memory usage: 9 MB
% 0.77/0.41 % (920318)Instructions burned: 6 (million)
% 0.77/0.41 % (920308)Instruction limit reached!
% 0.77/0.41 % (920308)------------------------------
% 0.77/0.41 % (920308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.41 % (920308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.41 % (920308)CaDiCaL version: 2.1.3
% 0.77/0.41 % (920308)Termination reason: Instruction limit
% 0.77/0.41 % (920308)Termination phase: Preprocessing 3
% 0.77/0.41 % (920308)Time elapsed: 0.037 s
% 0.77/0.41 % (920308)Peak memory usage: 12 MB
% 0.77/0.41 % (920308)Instructions burned: 81 (million)
% 0.77/0.41 % (920319)Instruction limit reached!
% 0.77/0.41 % (920319)------------------------------
% 0.77/0.41 % (920319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.41 % (920319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.41 % (920319)CaDiCaL version: 2.1.3
% 0.77/0.41 % (920319)Termination reason: Instruction limit
% 0.77/0.41 % (920319)Termination phase: shuffling
% 0.77/0.41 % (920319)Time elapsed: 0.006 s
% 0.77/0.41 % (920319)Peak memory usage: 10 MB
% 0.77/0.41 % (920319)Instructions burned: 13 (million)
% 0.77/0.41 % (920325)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=1520898372:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.77/0.41 % (920323)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
% 0.77/0.41 % (920323)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.41 % (920323)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1071573369:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.77/0.41 % (920327)lrs+10_1_si=on:cs=on:random_seed=1931410122:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.77/0.41 % (920328)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.77/0.45 % (920327)Instruction limit reached!
% 0.77/0.45 % (920327)------------------------------
% 0.77/0.45 % (920327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.45 % (920327)CaDiCaL version: 2.1.3
% 0.77/0.45 % (920327)Termination reason: Instruction limit
% 0.77/0.45 % (920327)Termination phase: shuffling
% 0.77/0.45 % (920327)Time elapsed: 0.004 s
% 0.77/0.45 % (920327)Peak memory usage: 9 MB
% 0.77/0.45 % (920327)Instructions burned: 8 (million)
% 0.77/0.45 % (920329)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3729796506:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.77/0.45 % (920328)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=1947088307:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.45 % (920325)Instruction limit reached!
% 0.77/0.45 % (920325)------------------------------
% 0.77/0.45 % (920325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.45 % (920325)CaDiCaL version: 2.1.3
% 0.77/0.45 % (920325)Termination reason: Instruction limit
% 0.77/0.45 % (920325)Termination phase: Saturation
% 0.77/0.45 % (920325)Time elapsed: 0.020 s
% 0.77/0.45 % (920325)Peak memory usage: 12 MB
% 0.77/0.45 % (920325)Instructions burned: 89 (million)
% 0.77/0.45 % (920328)Instruction limit reached!
% 0.77/0.45 % (920328)------------------------------
% 0.77/0.45 % (920328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.45 % (920328)CaDiCaL version: 2.1.3
% 0.77/0.45 % (920328)Termination reason: Instruction limit
% 0.77/0.45 % (920328)Termination phase: shuffling
% 0.77/0.45 % (920328)Time elapsed: 0.002 s
% 0.77/0.45 % (920328)Peak memory usage: 9 MB
% 0.77/0.45 % (920328)Instructions burned: 5 (million)
% 0.77/0.45 % (920323)Instruction limit reached!
% 0.77/0.45 % (920323)------------------------------
% 0.77/0.45 % (920323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.45 % (920323)CaDiCaL version: 2.1.3
% 0.77/0.45 % (920323)Termination reason: Instruction limit
% 0.77/0.45 % (920323)Termination phase: shuffling
% 0.77/0.45 % (920323)Time elapsed: 0.013 s
% 0.77/0.45 % (920323)Peak memory usage: 10 MB
% 0.77/0.45 % (920323)Instructions burned: 28 (million)
% 0.77/0.45 % (920336)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3932966679:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.77/0.45 % (920309)Instruction limit reached!
% 0.77/0.45 % (920309)------------------------------
% 0.77/0.45 % (920309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.45 % (920309)CaDiCaL version: 2.1.3
% 0.77/0.45 % (920309)Termination reason: Instruction limit
% 0.77/0.45 % (920309)Termination phase: Property scanning
% 0.77/0.45 % (920309)Time elapsed: 0.070 s
% 0.77/0.45 % (920309)Peak memory usage: 13 MB
% 0.77/0.45 % (920309)Instructions burned: 159 (million)
% 0.77/0.45 % (920333)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=390786710:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.77/0.45 % (920329)Instruction limit reached!
% 0.77/0.45 % (920329)------------------------------
% 0.77/0.45 % (920329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.45 % (920329)CaDiCaL version: 2.1.3
% 0.77/0.45 % (920329)Termination reason: Instruction limit
% 0.77/0.45 % (920329)Termination phase: Saturation
% 0.77/0.45 % (920329)Time elapsed: 0.018 s
% 0.77/0.45 % (920329)Peak memory usage: 12 MB
% 0.77/0.45 % (920329)Instructions burned: 40 (million)
% 0.77/0.45 % (920336)Instruction limit reached!
% 0.77/0.45 % (920336)------------------------------
% 0.77/0.45 % (920336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.45 % (920336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/0.52 % (920336)CaDiCaL version: 2.1.3
% 1.50/0.52 % (920336)Termination reason: Instruction limit
% 1.50/0.52 % (920336)Termination phase: Property scanning
% 1.50/0.52 % (920336)Time elapsed: 0.006 s
% 1.50/0.52 % (920336)Peak memory usage: 10 MB
% 1.50/0.52 % (920336)Instructions burned: 26 (million)
% 1.50/0.52 % (920337)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=456600498:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.50/0.52 % (920338)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2545527219:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.50/0.52 % (920337)Instruction limit reached!
% 1.50/0.52 % (920337)------------------------------
% 1.50/0.52 % (920337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.50/0.52 % (920337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/0.52 % (920337)CaDiCaL version: 2.1.3
% 1.50/0.52 % (920337)Termination reason: Instruction limit
% 1.50/0.52 % (920337)Termination phase: shuffling
% 1.50/0.52 % (920337)Time elapsed: 0.007 s
% 1.50/0.52 % (920337)Peak memory usage: 10 MB
% 1.50/0.52 % (920337)Instructions burned: 15 (million)
% 1.50/0.52 % (920343)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3607562021:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.50/0.52 % (920340)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=983561557:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.50/0.52 % (920342)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2088950776:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.50/0.52 % (920343)Instruction limit reached!
% 1.50/0.52 % (920343)------------------------------
% 1.50/0.52 % (920343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.50/0.52 % (920343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/0.52 % (920343)CaDiCaL version: 2.1.3
% 1.50/0.52 % (920343)Termination reason: Instruction limit
% 1.50/0.52 % (920343)Termination phase: shuffling
% 1.50/0.52 % (920343)Time elapsed: 0.006 s
% 1.50/0.52 % (920343)Peak memory usage: 10 MB
% 1.50/0.52 % (920343)Instructions burned: 28 (million)
% 1.50/0.52 % (920340)Instruction limit reached!
% 1.50/0.52 % (920340)------------------------------
% 1.50/0.52 % (920340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.50/0.52 % (920340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/0.52 % (920340)CaDiCaL version: 2.1.3
% 1.50/0.52 % (920340)Termination reason: Instruction limit
% 1.50/0.52 % (920340)Termination phase: shuffling
% 1.50/0.52 % (920340)Time elapsed: 0.007 s
% 1.50/0.52 % (920340)Peak memory usage: 10 MB
% 1.50/0.52 % (920340)Instructions burned: 16 (million)
% 1.50/0.52 % (920342)Instruction limit reached!
% 1.50/0.52 % (920342)------------------------------
% 1.50/0.52 % (920342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.50/0.52 % (920342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.50/0.52 % (920342)CaDiCaL version: 2.1.3
% 1.50/0.52 % (920342)Termination reason: Instruction limit
% 1.50/0.52 % (920342)Termination phase: shuffling
% 1.50/0.52 % (920342)Time elapsed: 0.003 s
% 1.50/0.52 % (920342)Peak memory usage: 9 MB
% 1.50/0.52 % (920342)Instructions burned: 6 (million)
% 1.50/0.52 % (920350)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3800747024:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.50/0.52 % (920346)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2774065536:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.50/0.52 % (920351)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.50/0.52 % (920351)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.50/0.52 % (920352)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.50/0.52 % (920346)Instruction limit reached!
% 1.50/0.52 % (920346)------------------------------
% 1.50/0.52 % (920346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.58 % (920346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.58 % (920346)CaDiCaL version: 2.1.3
% 2.22/0.58 % (920346)Termination reason: Instruction limit
% 2.22/0.58 % (920346)Termination phase: Property scanning
% 2.22/0.58 % (920346)Time elapsed: 0.010 s
% 2.22/0.58 % (920346)Peak memory usage: 10 MB
% 2.22/0.58 % (920346)Instructions burned: 24 (million)
% 2.22/0.58 % (920351)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=423874373:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.22/0.58 % (920352)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=1355347166:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.22/0.58 % (920350)Instruction limit reached!
% 2.22/0.58 % (920350)------------------------------
% 2.22/0.58 % (920350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.58 % (920350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.58 % (920350)CaDiCaL version: 2.1.3
% 2.22/0.58 % (920350)Termination reason: Instruction limit
% 2.22/0.58 % (920350)Termination phase: Preprocessing 3
% 2.22/0.58 % (920350)Time elapsed: 0.015 s
% 2.22/0.58 % (920350)Peak memory usage: 12 MB
% 2.22/0.58 % (920350)Instructions burned: 64 (million)
% 2.22/0.58 % (920352)Instruction limit reached!
% 2.22/0.58 % (920352)------------------------------
% 2.22/0.58 % (920352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.58 % (920352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.58 % (920352)CaDiCaL version: 2.1.3
% 2.22/0.58 % (920352)Termination reason: Instruction limit
% 2.22/0.58 % (920352)Termination phase: shuffling
% 2.22/0.58 % (920352)Time elapsed: 0.004 s
% 2.22/0.58 % (920352)Peak memory usage: 10 MB
% 2.22/0.58 % (920352)Instructions burned: 9 (million)
% 2.22/0.58 % (920351)Instruction limit reached!
% 2.22/0.58 % (920351)------------------------------
% 2.22/0.58 % (920351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.58 % (920351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.58 % (920351)CaDiCaL version: 2.1.3
% 2.22/0.58 % (920351)Termination reason: Instruction limit
% 2.22/0.58 % (920351)Termination phase: shuffling
% 2.22/0.58 % (920351)Time elapsed: 0.007 s
% 2.22/0.58 % (920351)Peak memory usage: 10 MB
% 2.22/0.58 % (920351)Instructions burned: 15 (million)
% 2.22/0.58 % (920358)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2181242983:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.22/0.58 % (920358)Instruction limit reached!
% 2.22/0.58 % (920358)------------------------------
% 2.22/0.58 % (920358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.58 % (920358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.58 % (920358)CaDiCaL version: 2.1.3
% 2.22/0.58 % (920358)Termination reason: Instruction limit
% 2.22/0.58 % (920358)Termination phase: shuffling
% 2.22/0.58 % (920358)Time elapsed: 0.002 s
% 2.22/0.58 % (920358)Peak memory usage: 9 MB
% 2.22/0.58 % (920358)Instructions burned: 9 (million)
% 2.22/0.58 % (920357)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=1414859293:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.22/0.58 % (920359)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=277079001:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.22/0.58 % (920360)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1372248038:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.22/0.58 % (920362)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2030767302:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.22/0.58 % (920357)Instruction limit reached!
% 2.22/0.58 % (920357)------------------------------
% 2.22/0.58 % (920357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.58 % (920357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920357)CaDiCaL version: 2.1.3
% 2.52/0.65 % (920357)Termination reason: Instruction limit
% 2.52/0.65 % (920357)Termination phase: shuffling
% 2.52/0.65 % (920357)Time elapsed: 0.013 s
% 2.52/0.65 % (920357)Peak memory usage: 10 MB
% 2.52/0.65 % (920357)Instructions burned: 31 (million)
% 2.52/0.65 % (920359)Instruction limit reached!
% 2.52/0.65 % (920359)------------------------------
% 2.52/0.65 % (920359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.65 % (920359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920359)CaDiCaL version: 2.1.3
% 2.52/0.65 % (920359)Termination reason: Instruction limit
% 2.52/0.65 % (920359)Termination phase: shuffling
% 2.52/0.65 % (920359)Time elapsed: 0.010 s
% 2.52/0.65 % (920359)Peak memory usage: 10 MB
% 2.52/0.65 % (920359)Instructions burned: 23 (million)
% 2.52/0.65 % (920360)Instruction limit reached!
% 2.52/0.65 % (920360)------------------------------
% 2.52/0.65 % (920360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.65 % (920360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920360)CaDiCaL version: 2.1.3
% 2.52/0.65 % (920360)Termination reason: Instruction limit
% 2.52/0.65 % (920360)Termination phase: shuffling
% 2.52/0.65 % (920360)Time elapsed: 0.009 s
% 2.52/0.65 % (920360)Peak memory usage: 10 MB
% 2.52/0.65 % (920360)Instructions burned: 20 (million)
% 2.52/0.65 % (920367)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1960264795:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.52/0.65 % (920368)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4057679563:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.52/0.65 % (920369)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3317700836:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.52/0.65 % (920333)Instruction limit reached!
% 2.52/0.65 % (920333)------------------------------
% 2.52/0.65 % (920333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.65 % (920333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920333)CaDiCaL version: 2.1.3
% 2.52/0.65 % (920333)Termination reason: Instruction limit
% 2.52/0.65 % (920333)Termination phase: Saturation
% 2.52/0.65 % (920333)Time elapsed: 0.110 s
% 2.52/0.65 % (920333)Peak memory usage: 15 MB
% 2.52/0.65 % (920333)Instructions burned: 249 (million)
% 2.52/0.65 % (920369)Instruction limit reached!
% 2.52/0.65 % (920369)------------------------------
% 2.52/0.65 % (920369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.65 % (920369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920369)CaDiCaL version: 2.1.3
% 2.52/0.65 % (920369)Termination reason: Instruction limit
% 2.52/0.65 % (920369)Termination phase: Naming
% 2.52/0.65 % (920369)Time elapsed: 0.019 s
% 2.52/0.65 % (920369)Peak memory usage: 11 MB
% 2.52/0.65 % (920369)Instructions burned: 43 (million)
% 2.52/0.65 % (920373)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.52/0.65 % (920373)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=992911977:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.52/0.65 % (920373)Instruction limit reached!
% 2.52/0.65 % (920373)------------------------------
% 2.52/0.65 % (920373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.65 % (920374)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=257195331:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.52/0.65 % (920373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920373)CaDiCaL version: 2.1.3
% 2.52/0.65 % (920373)Termination reason: Instruction limit
% 2.52/0.65 % (920373)Termination phase: shuffling
% 2.52/0.65 % (920373)Time elapsed: 0.004 s
% 2.52/0.65 % (920373)Peak memory usage: 10 MB
% 2.52/0.65 % (920373)Instructions burned: 9 (million)
% 2.52/0.65 % (920338)Instruction limit reached!
% 2.52/0.65 % (920338)------------------------------
% 2.52/0.65 % (920338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.65 % (920338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.65 % (920338)CaDiCaL version: 2.1.3
% 2.71/0.73 % (920338)Termination reason: Instruction limit
% 2.71/0.73 % (920338)Termination phase: Saturation
% 2.71/0.73 % (920338)Time elapsed: 0.146 s
% 2.71/0.73 % (920338)Peak memory usage: 16 MB
% 2.71/0.73 % (920338)Instructions burned: 327 (million)
% 2.71/0.73 % (920377)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=1214429498: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)
% 2.71/0.73 % (920367)Instruction limit reached!
% 2.71/0.73 % (920367)------------------------------
% 2.71/0.73 % (920367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.71/0.73 % (920367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/0.73 % (920367)CaDiCaL version: 2.1.3
% 2.71/0.73 % (920367)Termination reason: Instruction limit
% 2.71/0.73 % (920367)Termination phase: Twee Goal Transformation
% 2.71/0.73 % (920367)Time elapsed: 0.062 s
% 2.71/0.73 % (920367)Peak memory usage: 13 MB
% 2.71/0.73 % (920367)Instructions burned: 144 (million)
% 2.71/0.73 % (920378)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.71/0.73 % (920378)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1891104121:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.71/0.73 % (920378)Instruction limit reached!
% 2.71/0.73 % (920378)------------------------------
% 2.71/0.73 % (920378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.71/0.73 % (920378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/0.73 % (920378)CaDiCaL version: 2.1.3
% 2.71/0.73 % (920378)Termination reason: Instruction limit
% 2.71/0.73 % (920378)Termination phase: shuffling
% 2.71/0.73 % (920378)Time elapsed: 0.003 s
% 2.71/0.73 % (920378)Peak memory usage: 10 MB
% 2.71/0.73 % (920378)Instructions burned: 6 (million)
% 2.71/0.73 % (920380)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1565437206:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.71/0.73 % (920368)Instruction limit reached!
% 2.71/0.73 % (920368)------------------------------
% 2.71/0.73 % (920368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.71/0.73 % (920368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/0.73 % (920368)CaDiCaL version: 2.1.3
% 2.71/0.73 % (920368)Termination reason: Instruction limit
% 2.71/0.73 % (920368)Termination phase: Property scanning
% 2.71/0.73 % (920368)Time elapsed: 0.082 s
% 2.71/0.73 % (920368)Peak memory usage: 13 MB
% 2.71/0.73 % (920368)Instructions burned: 194 (million)
% 2.71/0.73 % (920380)Instruction limit reached!
% 2.71/0.73 % (920380)------------------------------
% 2.71/0.73 % (920380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.71/0.73 % (920380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/0.73 % (920380)CaDiCaL version: 2.1.3
% 2.71/0.73 % (920380)Termination reason: Instruction limit
% 2.71/0.73 % (920380)Termination phase: shuffling
% 2.71/0.73 % (920380)Time elapsed: 0.010 s
% 2.71/0.73 % (920380)Peak memory usage: 10 MB
% 2.71/0.73 % (920380)Instructions burned: 24 (million)
% 2.71/0.73 % (920383)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2578920393:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.71/0.73 % (920384)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=2848239339:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.71/0.73 % (920383)Instruction limit reached!
% 2.71/0.73 % (920383)------------------------------
% 2.71/0.73 % (920383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.71/0.73 % (920383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/0.73 % (920383)CaDiCaL version: 2.1.3
% 2.71/0.73 % (920383)Termination reason: Instruction limit
% 2.71/0.73 % (920383)Termination phase: shuffling
% 2.71/0.73 % (920383)Time elapsed: 0.008 s
% 2.71/0.73 % (920383)Peak memory usage: 10 MB
% 2.71/0.73 % (920383)Instructions burned: 19 (million)
% 2.71/0.73 % (920385)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=1751976262:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.37/0.80 % (920374)Instruction limit reached!
% 3.37/0.80 % (920374)------------------------------
% 3.37/0.80 % (920374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.80 % (920374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.80 % (920374)CaDiCaL version: 2.1.3
% 3.37/0.80 % (920374)Termination reason: Instruction limit
% 3.37/0.80 % (920374)Termination phase: Saturation
% 3.37/0.80 % (920374)Time elapsed: 0.086 s
% 3.37/0.80 % (920374)Peak memory usage: 14 MB
% 3.37/0.80 % (920374)Instructions burned: 183 (million)
% 3.37/0.80 % (920388)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=3389214051: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)
% 3.37/0.80 % (920377)Instruction limit reached!
% 3.37/0.80 % (920377)------------------------------
% 3.37/0.80 % (920377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.80 % (920377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.80 % (920377)CaDiCaL version: 2.1.3
% 3.37/0.80 % (920377)Termination reason: Instruction limit
% 3.37/0.80 % (920377)Termination phase: Property scanning
% 3.37/0.80 % (920377)Time elapsed: 0.072 s
% 3.37/0.80 % (920377)Peak memory usage: 13 MB
% 3.37/0.80 % (920377)Instructions burned: 171 (million)
% 3.37/0.80 % (920390)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3483781320:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.37/0.80 % (920388)Instruction limit reached!
% 3.37/0.80 % (920388)------------------------------
% 3.37/0.80 % (920388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.80 % (920388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.80 % (920388)CaDiCaL version: 2.1.3
% 3.37/0.80 % (920388)Termination reason: Instruction limit
% 3.37/0.80 % (920388)Termination phase: SInE selection
% 3.37/0.80 % (920388)Time elapsed: 0.019 s
% 3.37/0.80 % (920388)Peak memory usage: 10 MB
% 3.37/0.80 % (920388)Instructions burned: 46 (million)
% 3.37/0.80 % (920392)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3753677994: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)
% 3.37/0.80 % (920392)Instruction limit reached!
% 3.37/0.80 % (920392)------------------------------
% 3.37/0.80 % (920392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.80 % (920392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.80 % (920392)CaDiCaL version: 2.1.3
% 3.37/0.80 % (920392)Termination reason: Instruction limit
% 3.37/0.80 % (920392)Termination phase: shuffling
% 3.37/0.80 % (920392)Time elapsed: 0.010 s
% 3.37/0.80 % (920392)Peak memory usage: 10 MB
% 3.37/0.80 % (920392)Instructions burned: 23 (million)
% 3.37/0.80 % (920394)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.37/0.80 % (920306)Instruction limit reached!
% 3.37/0.80 % (920306)------------------------------
% 3.37/0.80 % (920306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/0.80 % (920306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/0.80 % (920306)CaDiCaL version: 2.1.3
% 3.37/0.80 % (920306)Termination reason: Instruction limit
% 3.37/0.80 % (920306)Termination phase: Saturation
% 3.37/0.80 % (920306)Time elapsed: 0.336 s
% 3.37/0.80 % (920306)Peak memory usage: 18 MB
% 3.37/0.80 % (920306)Instructions burned: 634 (million)
% 3.37/0.80 % (920394)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2821811265:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.37/0.80 % (920396)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1281352507:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.37/0.80 % (920398)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=2064653758:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.67/0.95 % (920396)Instruction limit reached!
% 3.67/0.95 % (920396)------------------------------
% 3.67/0.95 % (920396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/0.95 % (920396)CaDiCaL version: 2.1.3
% 3.67/0.95 % (920396)Termination reason: Instruction limit
% 3.67/0.95 % (920396)Termination phase: shuffling
% 3.67/0.95 % (920396)Time elapsed: 0.006 s
% 3.67/0.95 % (920396)Peak memory usage: 10 MB
% 3.67/0.95 % (920396)Instructions burned: 14 (million)
% 3.67/0.95 % (920401)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1367727622:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.67/0.95 % (920398)Instruction limit reached!
% 3.67/0.95 % (920398)------------------------------
% 3.67/0.95 % (920398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/0.95 % (920398)CaDiCaL version: 2.1.3
% 3.67/0.95 % (920398)Termination reason: Instruction limit
% 3.67/0.95 % (920398)Termination phase: SInE selection
% 3.67/0.95 % (920398)Time elapsed: 0.028 s
% 3.67/0.95 % (920398)Peak memory usage: 11 MB
% 3.67/0.95 % (920398)Instructions burned: 67 (million)
% 3.67/0.95 % (920401)Instruction limit reached!
% 3.67/0.95 % (920401)------------------------------
% 3.67/0.95 % (920401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/0.95 % (920401)CaDiCaL version: 2.1.3
% 3.67/0.95 % (920401)Termination reason: Instruction limit
% 3.67/0.95 % (920401)Termination phase: Preprocessing 3
% 3.67/0.95 % (920401)Time elapsed: 0.023 s
% 3.67/0.95 % (920401)Peak memory usage: 11 MB
% 3.67/0.95 % (920401)Instructions burned: 53 (million)
% 3.67/0.95 % (920403)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=226235224:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.67/0.95 % (920362)Instruction limit reached!
% 3.67/0.95 % (920362)------------------------------
% 3.67/0.95 % (920362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/0.95 % (920362)CaDiCaL version: 2.1.3
% 3.67/0.95 % (920362)Termination reason: Instruction limit
% 3.67/0.95 % (920362)Termination phase: Saturation
% 3.67/0.95 % (920362)Time elapsed: 0.271 s
% 3.67/0.95 % (920362)Peak memory usage: 14 MB
% 3.67/0.95 % (920362)Instructions burned: 1243 (million)
% 3.67/0.95 % (920403)Instruction limit reached!
% 3.67/0.95 % (920403)------------------------------
% 3.67/0.95 % (920403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/0.95 % (920403)CaDiCaL version: 2.1.3
% 3.67/0.95 % (920403)Termination reason: Instruction limit
% 3.67/0.95 % (920403)Termination phase: Property scanning
% 3.67/0.95 % (920403)Time elapsed: 0.014 s
% 3.67/0.95 % (920403)Peak memory usage: 10 MB
% 3.67/0.95 % (920403)Instructions burned: 33 (million)
% 3.67/0.95 % (920404)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3649918163:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.67/0.95 % (920394)Instruction limit reached!
% 3.67/0.95 % (920394)------------------------------
% 3.67/0.95 % (920394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/0.95 % (920394)CaDiCaL version: 2.1.3
% 3.67/0.95 % (920394)Termination reason: Instruction limit
% 3.67/0.95 % (920394)Termination phase: Saturation
% 3.67/0.95 % (920394)Time elapsed: 0.084 s
% 3.67/0.95 % (920394)Peak memory usage: 14 MB
% 3.67/0.95 % (920394)Instructions burned: 201 (million)
% 3.67/0.95 % (920406)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=2468569747:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.67/0.95 % (920406)Instruction limit reached!
% 3.67/0.95 % (920406)------------------------------
% 3.67/0.95 % (920406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.67/0.95 % (920406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.03 % (920406)CaDiCaL version: 2.1.3
% 5.47/1.03 % (920406)Termination reason: Instruction limit
% 5.47/1.03 % (920406)Termination phase: Property scanning
% 5.47/1.03 % (920406)Time elapsed: 0.008 s
% 5.47/1.03 % (920406)Peak memory usage: 10 MB
% 5.47/1.03 % (920406)Instructions burned: 38 (million)
% 5.47/1.03 % (920409)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.47/1.03 % (920408)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=512129834:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.47/1.03 % (920390)Refutation not found, incomplete strategy
% 5.47/1.03 % (920390)------------------------------
% 5.47/1.03 % (920390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.03 % (920390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.03 % (920390)CaDiCaL version: 2.1.3
% 5.47/1.03 % (920390)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.03 % (920390)Time elapsed: 0.122 s
% 5.47/1.03 % (920390)Peak memory usage: 16 MB
% 5.47/1.03 % (920390)Instructions burned: 272 (million)
% 5.47/1.03 % (920390)------------------------------
% 5.47/1.03 % (920390)------------------------------
% 5.47/1.03 % (920409)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1882803390:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.47/1.03 % (920411)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1891469485:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 5.47/1.03 % (920384)Instruction limit reached!
% 5.47/1.03 % (920384)------------------------------
% 5.47/1.03 % (920384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.03 % (920384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.03 % (920384)CaDiCaL version: 2.1.3
% 5.47/1.03 % (920384)Termination reason: Instruction limit
% 5.47/1.03 % (920384)Termination phase: Saturation
% 5.47/1.03 % (920384)Time elapsed: 0.175 s
% 5.47/1.03 % (920384)Peak memory usage: 17 MB
% 5.47/1.03 % (920384)Instructions burned: 317 (million)
% 5.47/1.03 % (920414)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3881350386:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 5.47/1.03 % (920408)Instruction limit reached!
% 5.47/1.03 % (920408)------------------------------
% 5.47/1.03 % (920408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.03 % (920408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.03 % (920408)CaDiCaL version: 2.1.3
% 5.47/1.03 % (920408)Termination reason: Instruction limit
% 5.47/1.03 % (920408)Termination phase: Preprocessing 3
% 5.47/1.03 % (920408)Time elapsed: 0.030 s
% 5.47/1.03 % (920408)Peak memory usage: 12 MB
% 5.47/1.03 % (920408)Instructions burned: 67 (million)
% 5.47/1.03 % (920416)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3734007305:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 5.47/1.03 % (920404)Instruction limit reached!
% 5.47/1.03 % (920404)------------------------------
% 5.47/1.03 % (920404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.03 % (920404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.03 % (920404)CaDiCaL version: 2.1.3
% 5.47/1.03 % (920404)Termination reason: Instruction limit
% 5.47/1.03 % (920404)Termination phase: shuffling
% 5.47/1.03 % (920404)Time elapsed: 0.060 s
% 5.47/1.03 % (920404)Peak memory usage: 13 MB
% 5.47/1.03 % (920404)Instructions burned: 138 (million)
% 5.47/1.03 % (920418)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=119712593:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.47/1.03 % (920420)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=264835642:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.47/1.03 % (920411)Instruction limit reached!
% 5.47/1.03 % (920411)------------------------------
% 5.47/1.03 % (920411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.03 % (920411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.03 % (920411)CaDiCaL version: 2.1.3
% 5.47/1.03 % (920411)Termination reason: Instruction limit
% 5.47/1.03 % (920411)Termination phase: Saturation
% 5.47/1.03 % (920411)Time elapsed: 0.058 s
% 5.47/1.03 % (920411)Peak memory usage: 15 MB
% 5.47/1.09 % (920411)Instructions burned: 249 (million)
% 5.47/1.09 % (920414)Instruction limit reached!
% 5.47/1.09 % (920414)------------------------------
% 5.47/1.09 % (920414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.09 % (920414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.09 % (920414)CaDiCaL version: 2.1.3
% 5.47/1.09 % (920414)Termination reason: Instruction limit
% 5.47/1.09 % (920414)Termination phase: Property scanning
% 5.47/1.09 % (920414)Time elapsed: 0.044 s
% 5.47/1.09 % (920414)Peak memory usage: 12 MB
% 5.47/1.09 % (920414)Instructions burned: 99 (million)
% 5.47/1.09 % (920409)Instruction limit reached!
% 5.47/1.09 % (920409)------------------------------
% 5.47/1.09 % (920409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.09 % (920409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.09 % (920409)CaDiCaL version: 2.1.3
% 5.47/1.09 % (920409)Termination reason: Instruction limit
% 5.47/1.09 % (920409)Termination phase: Saturation
% 5.47/1.09 % (920409)Time elapsed: 0.074 s
% 5.47/1.09 % (920409)Peak memory usage: 12 MB
% 5.47/1.09 % (920409)Instructions burned: 180 (million)
% 5.47/1.09 % (920423)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1915179136:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.47/1.09 % (920424)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1677655250:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.47/1.09 % (920426)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4157351395:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 5.47/1.09 % (920423)Refutation not found, incomplete strategy
% 5.47/1.09 % (920423)------------------------------
% 5.47/1.09 % (920423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.09 % (920423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.09 % (920423)CaDiCaL version: 2.1.3
% 5.47/1.09 % (920423)Termination reason: Refutation not found, incomplete strategy
% 5.47/1.09 % (920423)Time elapsed: 0.020 s
% 5.47/1.09 % (920423)Peak memory usage: 13 MB
% 5.47/1.09 % (920423)Instructions burned: 83 (million)
% 5.47/1.09 % (920423)------------------------------
% 5.47/1.09 % (920423)------------------------------
% 5.47/1.09 % (920424)Instruction limit reached!
% 5.47/1.09 % (920424)------------------------------
% 5.47/1.09 % (920424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.09 % (920424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.09 % (920424)CaDiCaL version: 2.1.3
% 5.47/1.09 % (920424)Termination reason: Instruction limit
% 5.47/1.09 % (920424)Termination phase: Property scanning
% 5.47/1.09 % (920424)Time elapsed: 0.019 s
% 5.47/1.09 % (920424)Peak memory usage: 10 MB
% 5.47/1.09 % (920424)Instructions burned: 45 (million)
% 5.47/1.09 % (920429)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3865727415:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 5.47/1.09 % (920430)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2312781107:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 5.47/1.09 % (920430)Instruction limit reached!
% 5.47/1.09 % (920430)------------------------------
% 5.47/1.09 % (920430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.09 % (920430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.09 % (920430)CaDiCaL version: 2.1.3
% 5.47/1.09 % (920430)Termination reason: Instruction limit
% 5.47/1.09 % (920430)Termination phase: Property scanning
% 5.47/1.09 % (920430)Time elapsed: 0.042 s
% 5.47/1.09 % (920430)Peak memory usage: 12 MB
% 5.47/1.09 % (920430)Instructions burned: 95 (million)
% 5.47/1.09 % (920433)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=2115634722:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 5.47/1.09 % (920433)Instruction limit reached!
% 5.47/1.09 % (920433)------------------------------
% 5.47/1.09 % (920433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.47/1.09 % (920433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920433)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920433)Termination reason: Instruction limit
% 6.46/1.21 % (920433)Termination phase: Property scanning
% 6.46/1.21 % (920433)Time elapsed: 0.027 s
% 6.46/1.21 % (920433)Peak memory usage: 11 MB
% 6.46/1.21 % (920433)Instructions burned: 65 (million)
% 6.46/1.21 % (920416)Instruction limit reached!
% 6.46/1.21 % (920416)------------------------------
% 6.46/1.21 % (920416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920416)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920416)Termination reason: Instruction limit
% 6.46/1.21 % (920416)Termination phase: Saturation
% 6.46/1.21 % (920416)Time elapsed: 0.183 s
% 6.46/1.21 % (920416)Peak memory usage: 17 MB
% 6.46/1.21 % (920416)Instructions burned: 427 (million)
% 6.46/1.21 % (920429)Instruction limit reached!
% 6.46/1.21 % (920429)------------------------------
% 6.46/1.21 % (920429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920429)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920429)Termination reason: Instruction limit
% 6.46/1.21 % (920429)Termination phase: Saturation
% 6.46/1.21 % (920429)Time elapsed: 0.111 s
% 6.46/1.21 % (920429)Peak memory usage: 17 MB
% 6.46/1.21 % (920429)Instructions burned: 451 (million)
% 6.46/1.21 % (920437)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=662783382:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 6.46/1.21 % (920435)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=3555206593: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_2993 on theBenchmark for (2993ds/105Mi)
% 6.46/1.21 % (920436)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=2258355977:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 6.46/1.21 % (920385)Instruction limit reached!
% 6.46/1.21 % (920385)------------------------------
% 6.46/1.21 % (920385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920385)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920385)Termination reason: Instruction limit
% 6.46/1.21 % (920385)Termination phase: Saturation
% 6.46/1.21 % (920385)Time elapsed: 0.413 s
% 6.46/1.21 % (920385)Peak memory usage: 19 MB
% 6.46/1.21 % (920385)Instructions burned: 854 (million)
% 6.46/1.21 % (920426)Refutation not found, incomplete strategy
% 6.46/1.21 % (920426)------------------------------
% 6.46/1.21 % (920426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920426)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920426)Termination reason: Refutation not found, incomplete strategy
% 6.46/1.21 % (920426)Time elapsed: 0.175 s
% 6.46/1.21 % (920426)Peak memory usage: 17 MB
% 6.46/1.21 % (920426)Instructions burned: 374 (million)
% 6.46/1.21 % (920426)------------------------------
% 6.46/1.21 % (920426)------------------------------
% 6.46/1.21 % (920441)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3043887066:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.46/1.21 % (920435)Instruction limit reached!
% 6.46/1.21 % (920435)------------------------------
% 6.46/1.21 % (920435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920435)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920435)Termination reason: Instruction limit
% 6.46/1.21 % (920435)Termination phase: Saturation
% 6.46/1.21 % (920435)Time elapsed: 0.044 s
% 6.46/1.21 % (920435)Peak memory usage: 12 MB
% 6.46/1.21 % (920435)Instructions burned: 106 (million)
% 6.46/1.21 % (920442)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=140465110:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.46/1.21 % (920444)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=2749299759:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 6.46/1.21 % (920420)Instruction limit reached!
% 6.46/1.21 % (920420)------------------------------
% 6.46/1.21 % (920420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920420)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920420)Termination reason: Instruction limit
% 6.46/1.21 % (920420)Termination phase: Saturation
% 6.46/1.21 % (920420)Time elapsed: 0.246 s
% 6.46/1.21 % (920420)Peak memory usage: 18 MB
% 6.46/1.21 % (920420)Instructions burned: 516 (million)
% 6.46/1.21 % (920442)Instruction limit reached!
% 6.46/1.21 % (920442)------------------------------
% 6.46/1.21 % (920442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920442)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920442)Termination reason: Instruction limit
% 6.46/1.21 % (920442)Termination phase: Property scanning
% 6.46/1.21 % (920442)Time elapsed: 0.015 s
% 6.46/1.21 % (920442)Peak memory usage: 10 MB
% 6.46/1.21 % (920442)Instructions burned: 35 (million)
% 6.46/1.21 % (920437)Instruction limit reached!
% 6.46/1.21 % (920437)------------------------------
% 6.46/1.21 % (920437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920437)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920437)Termination reason: Instruction limit
% 6.46/1.21 % (920437)Termination phase: Saturation
% 6.46/1.21 % (920437)Time elapsed: 0.089 s
% 6.46/1.21 % (920437)Peak memory usage: 16 MB
% 6.46/1.21 % (920437)Instructions burned: 375 (million)
% 6.46/1.21 % (920448)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2570284194:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2992 on theBenchmark for (2992ds/22Mi)
% 6.46/1.21 % (920447)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=677415723:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2992 on theBenchmark for (2992ds/66Mi)
% 6.46/1.21 % (920449)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=3723280337:i=338:bd=all:ins=4:rtra=on_2992 on theBenchmark for (2992ds/338Mi)
% 6.46/1.21 % (920448)Instruction limit reached!
% 6.46/1.21 % (920448)------------------------------
% 6.46/1.21 % (920448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920448)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920448)Termination reason: Instruction limit
% 6.46/1.21 % (920448)Termination phase: shuffling
% 6.46/1.21 % (920448)Time elapsed: 0.009 s
% 6.46/1.21 % (920448)Peak memory usage: 10 MB
% 6.46/1.21 % (920448)Instructions burned: 22 (million)
% 6.46/1.21 % (920444)Instruction limit reached!
% 6.46/1.21 % (920444)------------------------------
% 6.46/1.21 % (920444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920444)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920444)Termination reason: Instruction limit
% 6.46/1.21 % (920444)Termination phase: Clausification
% 6.46/1.21 % (920444)Time elapsed: 0.041 s
% 6.46/1.21 % (920444)Peak memory usage: 13 MB
% 6.46/1.21 % (920444)Instructions burned: 91 (million)
% 6.46/1.21 % (920453)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2500304859:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 6.46/1.21 % (920454)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 6.46/1.21 % (920447)Instruction limit reached!
% 6.46/1.21 % (920447)------------------------------
% 6.46/1.21 % (920447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920447)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920447)Termination reason: Instruction limit
% 6.46/1.21 % (920447)Termination phase: Saturation
% 6.46/1.21 % (920447)Time elapsed: 0.032 s
% 6.46/1.21 % (920447)Peak memory usage: 13 MB
% 6.46/1.21 % (920447)Instructions burned: 68 (million)
% 6.46/1.21 % (920454)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2048524013:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 6.46/1.21 % (920453)Instruction limit reached!
% 6.46/1.21 % (920453)------------------------------
% 6.46/1.21 % (920453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920453)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920453)Termination reason: Instruction limit
% 6.46/1.21 % (920453)Termination phase: Property scanning
% 6.46/1.21 % (920453)Time elapsed: 0.012 s
% 6.46/1.21 % (920453)Peak memory usage: 10 MB
% 6.46/1.21 % (920453)Instructions burned: 28 (million)
% 6.46/1.21 % (920456)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=3684352431:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/340Mi)
% 6.46/1.21 % (920458)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=3559354449:i=227:sd=1:bd=all:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/227Mi)
% 6.46/1.21 % (920449)Instruction limit reached!
% 6.46/1.21 % (920449)------------------------------
% 6.46/1.21 % (920449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920449)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920449)Termination reason: Instruction limit
% 6.46/1.21 % (920449)Termination phase: Saturation
% 6.46/1.21 % (920449)Time elapsed: 0.075 s
% 6.46/1.21 % (920449)Peak memory usage: 18 MB
% 6.46/1.21 % (920449)Instructions burned: 342 (million)
% 6.46/1.21 % (920458)Refutation not found, incomplete strategy
% 6.46/1.21 % (920458)------------------------------
% 6.46/1.21 % (920458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920458)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920458)Termination reason: Refutation not found, incomplete strategy
% 6.46/1.21 % (920458)Time elapsed: 0.024 s
% 6.46/1.21 % (920458)Peak memory usage: 13 MB
% 6.46/1.21 % (920458)Instructions burned: 51 (million)
% 6.46/1.21 % (920458)------------------------------
% 6.46/1.21 % (920458)------------------------------
% 6.46/1.21 % (920461)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 6.46/1.21 % (920418) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-920298-920418"...
% 6.46/1.21 % (920454)Instruction limit reached!
% 6.46/1.21 % (920454)------------------------------
% 6.46/1.21 % (920454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.21 % (920454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.21 % (920454)CaDiCaL version: 2.1.3
% 6.46/1.21 % (920454)Termination reason: Instruction limit
% 6.46/1.21 % (920454)Termination phase: Saturation
% 6.46/1.21 % (920454)Time elapsed: 0.057 s
% 6.46/1.21 % (920454)Peak memory usage: 12 MB
% 6.46/1.21 % (920454)Instructions burned: 137 (million)
% 6.46/1.21 % (920461)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3918244972:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/373Mi)
% 6.46/1.21 % (920462)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1041122165:i=116:ep=RSTC:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/116Mi)
% 6.46/1.21 % (920464)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1638603744:i=575:rtra=on_2991 on theBenchmark for (2991ds/575Mi)
% 6.46/1.21 % (920418)...printing done.
% 6.46/1.21 % (920418)Refutation found. Thanks to Tanya!
% 6.46/1.21 % SZS status Theorem for theBenchmark
% 6.46/1.21 % SZS output start Proof for theBenchmark
% 6.46/1.21 thf(type_def_5, type, term: $tType).
% 6.46/1.21 thf(type_def_6, type, subst: $tType).
% 6.46/1.21 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 6.46/1.21 thf(type_def_8, type, d_term: $tType).
% 6.46/1.21 thf(type_def_9, type, d_subst: $tType).
% 6.46/1.21 thf(func_def_0, type, one: term).
% 6.46/1.21 thf(func_def_1, type, ap: (term > term > term)).
% 6.46/1.21 thf(func_def_2, type, lam: (term > term)).
% 6.46/1.21 thf(func_def_3, type, sub: (term > subst > term)).
% 6.46/1.21 thf(func_def_4, type, id: subst).
% 6.46/1.21 thf(func_def_5, type, sh: subst).
% 6.46/1.21 thf(func_def_6, type, push: (term > subst > subst)).
% 6.46/1.21 thf(func_def_7, type, comp: (subst > subst > subst)).
% 6.46/1.21 thf(func_def_8, type, var: (term > $o)).
% 6.46/1.21 thf(func_def_9, type, pushprop_lem1v2: $o).
% 6.46/1.21 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 6.46/1.21 thf(func_def_11, type, axmap: $o).
% 6.46/1.21 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 6.46/1.21 thf(func_def_13, type, shinj: $o).
% 6.46/1.21 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 6.46/1.21 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 6.46/1.21 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 6.46/1.21 thf(func_def_17, type, induction2lem: $o).
% 6.46/1.21 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 6.46/1.21 thf(func_def_19, type, axvarshift: $o).
% 6.46/1.21 thf(func_def_20, type, hoasapinj2: $o).
% 6.46/1.21 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 6.46/1.21 thf(func_def_22, type, hoasapinj1: $o).
% 6.46/1.21 thf(func_def_23, type, ulamvar1: $o).
% 6.46/1.21 thf(func_def_24, type, induction2lem_lthm: $o).
% 6.46/1.21 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 6.46/1.21 thf(func_def_26, type, apnotvar: $o).
% 6.46/1.21 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 6.46/1.21 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 6.46/1.21 thf(func_def_29, type, hoasinduction_lthm: $o).
% 6.46/1.21 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 6.46/1.21 thf(func_def_31, type, hoaslaminj: $o).
% 6.46/1.21 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 6.46/1.21 thf(func_def_33, type, induction2lem_gthm: $o).
% 6.46/1.21 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 6.46/1.21 thf(func_def_35, type, hoasinduction_lem3: $o).
% 6.46/1.21 thf(func_def_36, type, hoasinduction_lem2: $o).
% 6.46/1.21 thf(func_def_37, type, termmset_lthm: $o).
% 6.46/1.21 thf(func_def_38, type, hoasinduction_lem1: $o).
% 6.46/1.21 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 6.46/1.21 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 6.46/1.21 thf(func_def_41, type, hoasapnotvar: $o).
% 6.46/1.21 thf(func_def_42, type, hoasinduction_lem0: $o).
% 6.46/1.21 thf(func_def_43, type, hoasinduction: $o).
% 6.46/1.21 thf(func_def_44, type, hoasinduction_gthm: $o).
% 6.46/1.21 thf(func_def_45, type, axapp: $o).
% 6.46/1.21 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 6.46/1.21 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 6.46/1.21 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 6.46/1.21 thf(func_def_49, type, ulamvarind: $o).
% 6.46/1.21 thf(func_def_50, type, induction: $o).
% 6.46/1.21 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 6.46/1.21 thf(func_def_52, type, termmset_gthm: $o).
% 6.46/1.21 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 6.46/1.21 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 6.46/1.21 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 6.46/1.21 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 6.46/1.21 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 6.46/1.21 thf(func_def_58, type, pushprop_lem2v2: $o).
% 6.46/1.21 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 6.46/1.21 thf(func_def_60, type, axclos: $o).
% 6.46/1.21 thf(func_def_61, type, axassoc: $o).
% 6.46/1.21 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 6.46/1.21 thf(func_def_63, type, pushprop_lthm: $o).
% 6.46/1.21 thf(func_def_64, type, apinj2: $o).
% 6.46/1.21 thf(func_def_65, type, apinj1: $o).
% 6.46/1.21 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 6.46/1.21 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 6.46/1.21 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 6.46/1.21 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 6.46/1.21 thf(func_def_70, type, axvarcons: $o).
% 6.46/1.21 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 6.46/1.21 thf(func_def_72, type, axscons: $o).
% 6.46/1.21 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 6.46/1.21 thf(func_def_74, type, axidr: $o).
% 6.46/1.21 thf(func_def_75, type, pushprop_lem1: $o).
% 6.46/1.21 thf(func_def_76, type, laminj: $o).
% 6.46/1.21 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 6.46/1.21 thf(func_def_78, type, pushprop_lem0: $o).
% 6.46/1.21 thf(func_def_79, type, pushprop_gthm: $o).
% 6.46/1.21 thf(func_def_80, type, axabs: $o).
% 6.46/1.21 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 6.46/1.21 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 6.46/1.21 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 6.46/1.21 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 6.46/1.21 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 6.46/1.21 thf(func_def_86, type, lamnotap: $o).
% 6.46/1.21 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 6.46/1.21 thf(func_def_88, type, hoaslamnotvar: $o).
% 6.46/1.21 thf(func_def_89, type, axidl: $o).
% 6.46/1.21 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 6.46/1.21 thf(func_def_91, type, induction2_lthm: $o).
% 6.46/1.21 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 6.46/1.21 thf(func_def_93, type, substmonoid_lthm: $o).
% 6.46/1.21 thf(func_def_94, type, pushprop: $o).
% 6.46/1.21 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 6.46/1.21 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 6.46/1.21 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 6.46/1.21 thf(func_def_98, type, substmonoid: $o).
% 6.46/1.21 thf(func_def_99, type, lamnotvar: $o).
% 6.46/1.21 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 6.46/1.21 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 6.46/1.21 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 6.46/1.21 thf(func_def_103, type, induction2_gthm: $o).
% 6.46/1.21 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 6.46/1.21 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_106, type, hoaslamnotap: $o).
% 6.46/1.21 thf(func_def_107, type, substmonoid_gthm: $o).
% 6.46/1.21 thf(func_def_108, type, ulamvarsh: $o).
% 6.46/1.21 thf(func_def_109, type, induction2: $o).
% 6.46/1.21 thf(func_def_110, type, pushprop_lem3v2: $o).
% 6.46/1.21 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 6.46/1.21 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 6.46/1.21 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 6.46/1.21 thf(func_def_114, type, axshiftcons: $o).
% 6.46/1.21 thf(func_def_115, type, termmset: $o).
% 6.46/1.21 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 6.46/1.21 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 6.46/1.21 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 6.46/1.21 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 6.46/1.21 thf(func_def_120, type, axvarid: $o).
% 6.46/1.21 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 6.46/1.21 thf(func_def_122, type, d2term: (d_term > term)).
% 6.46/1.21 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 6.46/1.21 thf(func_def_124, type, d_one: d_term).
% 6.46/1.21 thf(func_def_125, type, d_id: d_subst).
% 6.46/1.21 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.46/1.21 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 6.46/1.21 thf(func_def_129, type, db3: !>[X0: $tType]:(X0)).
% 6.46/1.21 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)).
% 6.46/1.21 thf(func_def_131, type, db2: !>[X0: $tType]:(X0)).
% 6.46/1.21 thf(func_def_132, type, db0: !>[X0: $tType]:(X0)).
% 6.46/1.21 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.46/1.21 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.46/1.21 thf(func_def_137, type, db4: !>[X0: $tType]:(X0)).
% 6.46/1.21 thf(func_def_138, type, sP0: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_139, type, sP1: $o).
% 6.46/1.21 thf(func_def_140, type, sP2: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_141, type, sP3: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_142, type, sP4: $o).
% 6.46/1.21 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_144, type, sP6: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_145, type, sP7: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_146, type, sP8: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_147, type, sP9: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_148, type, sP10: $o).
% 6.46/1.21 thf(func_def_149, type, sP11: $o).
% 6.46/1.21 thf(func_def_150, type, sP12: $o).
% 6.46/1.21 thf(func_def_151, type, sP13: $o).
% 6.46/1.21 thf(func_def_152, type, sP14: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_153, type, sP15: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_154, type, sP16: $o).
% 6.46/1.21 thf(func_def_155, type, sP17: $o).
% 6.46/1.21 thf(func_def_156, type, sP18: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_157, type, sP19: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_158, type, sP20: $o).
% 6.46/1.21 thf(func_def_159, type, sP21: $o).
% 6.46/1.21 thf(func_def_160, type, sP22: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_161, type, sP23: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_162, type, sP24: $o).
% 6.46/1.21 thf(func_def_163, type, sP25: $o).
% 6.46/1.21 thf(func_def_164, type, sP26: $o).
% 6.46/1.21 thf(func_def_165, type, sP27: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_166, type, sP28: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_167, type, sP29: $o).
% 6.46/1.21 thf(func_def_168, type, sP30: $o).
% 6.46/1.21 thf(func_def_169, type, sP31: $o).
% 6.46/1.21 thf(func_def_170, type, sP32: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_171, type, sP33: $o).
% 6.46/1.21 thf(func_def_172, type, sP34: $o).
% 6.46/1.21 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_174, type, sP36: $o).
% 6.46/1.21 thf(func_def_175, type, sP37: $o).
% 6.46/1.21 thf(func_def_176, type, sP38: $o).
% 6.46/1.21 thf(func_def_177, type, sP39: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_178, type, sP40: $o).
% 6.46/1.21 thf(func_def_179, type, sP41: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_180, type, sP42: $o).
% 6.46/1.21 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_182, type, sP44: $o).
% 6.46/1.21 thf(func_def_183, type, sP45: $o).
% 6.46/1.21 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_185, type, sP47: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_186, type, sP48: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_187, type, sP49: ((term > $o) > $o)).
% 6.46/1.21 thf(func_def_188, type, sP50: $o).
% 6.46/1.21 thf(func_def_189, type, sP51: $o).
% 6.46/1.21 thf(func_def_190, type, sP52: $o).
% 6.46/1.21 thf(func_def_191, type, sP53: $o).
% 6.46/1.21 thf(func_def_192, type, sP54: $o).
% 6.46/1.21 thf(func_def_193, type, sP55: $o).
% 6.46/1.21 thf(func_def_194, type, sP56: ((subst > term > subst > $o) > $o)).
% 6.46/1.21 thf(func_def_195, type, sP57: $o).
% 6.46/1.21 thf(func_def_196, type, sP58: $o).
% 6.46/1.21 thf(func_def_197, type, sK59: (subst > term > term)).
% 6.46/1.21 thf(func_def_198, type, sK60: subst).
% 6.46/1.21 thf(func_def_199, type, sK61: (subst > term > term)).
% 6.46/1.21 thf(func_def_200, type, sK62: term).
% 6.46/1.21 thf(func_def_201, type, sK63: term).
% 6.46/1.21 thf(func_def_202, type, sK64: subst).
% 6.46/1.21 thf(func_def_203, type, sK65: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_204, type, sK66: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_205, type, sK67: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_206, type, sK68: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_207, type, sK69: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_208, type, sK70: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_209, type, sK71: term).
% 6.46/1.21 thf(func_def_210, type, sK72: subst).
% 6.46/1.21 thf(func_def_211, type, sK73: term).
% 6.46/1.21 thf(func_def_212, type, sK74: term).
% 6.46/1.21 thf(func_def_213, type, sK75: term).
% 6.46/1.21 thf(func_def_214, type, sK76: (term > $o)).
% 6.46/1.21 thf(func_def_215, type, sK77: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_216, type, sK78: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_217, type, sK79: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_218, type, sK80: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_219, type, sK81: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_220, type, sK82: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_221, type, sK83: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_222, type, sK84: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_223, type, sK85: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.46/1.21 thf(func_def_225, type, sK87: ((term > $o) > term > term)).
% 6.46/1.21 thf(func_def_226, type, sK88: term).
% 6.46/1.21 thf(func_def_227, type, sK89: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_228, type, sK90: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_229, type, sK91: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_230, type, sK92: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_231, type, sK93: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_232, type, sK94: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_233, type, sK95: term).
% 6.46/1.21 thf(func_def_234, type, sK96: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_235, type, sK97: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_236, type, sK98: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_237, type, sK99: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_238, type, sK100: (term > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_240, type, sK102: term).
% 6.46/1.21 thf(func_def_241, type, sK103: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_242, type, sK104: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_243, type, sK105: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_244, type, sK106: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_245, type, sK107: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_246, type, sK108: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_247, type, sK109: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(func_def_248, type, sK110: (term > $o)).
% 6.46/1.21 thf(func_def_249, type, sK111: term).
% 6.46/1.21 thf(func_def_250, type, sK112: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_251, type, sK113: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_252, type, sK114: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_253, type, sK115: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_254, type, sK116: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_255, type, sK117: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_256, type, sK118: (term > (term > $o) > term)).
% 6.46/1.21 thf(func_def_257, type, sK119: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.46/1.21 thf(func_def_258, type, sK120: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_259, type, sK121: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > term > $o)).
% 6.46/1.21 thf(func_def_261, type, sK123: term).
% 6.46/1.21 thf(func_def_262, type, sK124: (term > $o)).
% 6.46/1.21 thf(func_def_263, type, sK125: (term > term)).
% 6.46/1.21 thf(func_def_264, type, sK126: term).
% 6.46/1.21 thf(func_def_265, type, sK127: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_266, type, sK128: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_267, type, sK129: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_268, type, sK130: ((term > $o) > term > term)).
% 6.46/1.21 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_270, type, sK132: term).
% 6.46/1.21 thf(func_def_271, type, sK133: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_272, type, sK134: (term > $o)).
% 6.46/1.21 thf(func_def_273, type, sK135: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_274, type, sK136: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_275, type, sK137: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_276, type, sK138: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_277, type, sK139: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_278, type, sK140: term).
% 6.46/1.21 thf(func_def_279, type, sK141: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_281, type, sK143: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_282, type, sK144: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_283, type, sK145: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_284, type, sK146: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_285, type, sK147: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_286, type, sK148: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_288, type, sK150: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_289, type, sK151: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_290, type, sK152: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_291, type, sK153: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_292, type, sK154: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_293, type, sK155: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_294, type, sK156: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_296, type, sK158: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_297, type, sK159: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_298, type, sK160: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_299, type, sK161: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_300, type, sK162: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_301, type, sK163: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_302, type, sK164: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_303, type, sK165: term).
% 6.46/1.21 thf(func_def_304, type, sK166: term).
% 6.46/1.21 thf(func_def_305, type, sK167: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_306, type, sK168: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_307, type, sK169: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_308, type, sK170: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_309, type, sK171: (term > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_311, type, sK173: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_312, type, sK174: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_315, type, sK177: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(func_def_316, type, sK178: term).
% 6.46/1.21 thf(func_def_317, type, sK179: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_318, type, sK180: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_319, type, sK181: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_320, type, sK182: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_321, type, sK183: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_322, type, sK184: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_323, type, sK185: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_324, type, sK186: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_325, type, sK187: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_327, type, sK189: term).
% 6.46/1.21 thf(func_def_328, type, sK190: (term > $o)).
% 6.46/1.21 thf(func_def_329, type, sK191: (term > term)).
% 6.46/1.21 thf(func_def_330, type, sK192: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_331, type, sK193: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_332, type, sK194: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_333, type, sK195: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_334, type, sK196: (term > $o)).
% 6.46/1.21 thf(func_def_335, type, sK197: term).
% 6.46/1.21 thf(func_def_336, type, sK198: term).
% 6.46/1.21 thf(func_def_337, type, sK199: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_338, type, sK200: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_342, type, sK204: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_343, type, sK205: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_344, type, sK206: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.46/1.21 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_348, type, sK210: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_349, type, sK211: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_350, type, sK212: term).
% 6.46/1.21 thf(func_def_351, type, sK213: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_352, type, sK214: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_353, type, sK215: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_354, type, sK216: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_355, type, sK217: (term > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_356, type, sK218: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_357, type, sK219: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_358, type, sK220: term).
% 6.46/1.21 thf(func_def_359, type, sK221: (term > (subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_360, type, sK222: (term > (subst > term > term) > term)).
% 6.46/1.21 thf(func_def_361, type, sK223: (term > (subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_362, type, sK224: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_363, type, sK225: (term > (subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_364, type, sK226: (term > (subst > term > term) > term)).
% 6.46/1.21 thf(func_def_365, type, sK227: (term > (subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_368, type, sK230: (term > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_369, type, sK231: term).
% 6.46/1.21 thf(func_def_370, type, sK232: term).
% 6.46/1.21 thf(func_def_371, type, sK233: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_372, type, sK234: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_374, type, sK236: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_375, type, sK237: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_376, type, sK238: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_377, type, sK239: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_380, type, sK242: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_381, type, sK243: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_382, type, sK244: (term > subst > term > term)).
% 6.46/1.21 thf(func_def_383, type, sK245: (term > $o)).
% 6.46/1.21 thf(func_def_384, type, sK246: term).
% 6.46/1.21 thf(func_def_385, type, sK247: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_386, type, sK248: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_387, type, sK249: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_388, type, sK250: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_389, type, sK251: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_390, type, sK252: term).
% 6.46/1.21 thf(func_def_391, type, sK253: term).
% 6.46/1.21 thf(func_def_392, type, sK254: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_393, type, sK255: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_394, type, sK256: (term > (term > $o) > term)).
% 6.46/1.21 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.46/1.21 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_397, type, sK259: subst).
% 6.46/1.21 thf(func_def_398, type, sK260: term).
% 6.46/1.21 thf(func_def_399, type, sK261: (term > $o)).
% 6.46/1.21 thf(func_def_400, type, sK262: (term > term)).
% 6.46/1.21 thf(func_def_401, type, sK263: ((term > $o) > subst > term)).
% 6.46/1.21 thf(func_def_402, type, sK264: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_403, type, sK265: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_404, type, sK266: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_405, type, sK267: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_406, type, sK268: term).
% 6.46/1.21 thf(func_def_407, type, sK269: ((subst > term > subst > $o) > term > $o)).
% 6.46/1.21 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_409, type, sK271: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_410, type, sK272: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_411, type, sK273: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_412, type, sK274: term).
% 6.46/1.21 thf(func_def_413, type, sK275: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_414, type, sK276: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_415, type, sK277: term).
% 6.46/1.21 thf(func_def_416, type, sK278: (term > $o)).
% 6.46/1.21 thf(func_def_417, type, sK279: (term > term)).
% 6.46/1.21 thf(func_def_418, type, sK280: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_419, type, sK281: ((term > $o) > term > term)).
% 6.46/1.21 thf(func_def_420, type, sK282: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_421, type, sK283: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_422, type, sK284: term).
% 6.46/1.21 thf(func_def_423, type, sK285: (term > $o)).
% 6.46/1.21 thf(func_def_424, type, sK286: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_425, type, sK287: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_426, type, sK288: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_427, type, sK289: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_428, type, sK290: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_429, type, sK291: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_430, type, sK292: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_431, type, sK293: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_432, type, sK294: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_433, type, sK295: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_434, type, sK296: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_435, type, sK297: term).
% 6.46/1.21 thf(func_def_436, type, sK298: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_437, type, sK299: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_438, type, sK300: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_439, type, sK301: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_440, type, sK302: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_441, type, sK303: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(func_def_443, type, sK305: term).
% 6.46/1.21 thf(func_def_444, type, sK306: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(func_def_445, type, sK307: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_446, type, sK308: term).
% 6.46/1.21 thf(func_def_447, type, sK309: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_448, type, sK310: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_449, type, sK311: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_450, type, sK312: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_451, type, sK313: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_452, type, sK314: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_453, type, sK315: term).
% 6.46/1.21 thf(func_def_454, type, sK316: (term > $o)).
% 6.46/1.21 thf(func_def_455, type, sK317: ((term > $o) > term > term)).
% 6.46/1.21 thf(func_def_456, type, sK318: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_457, type, sK319: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_458, type, sK320: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_460, type, sK322: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_461, type, sK323: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_462, type, sK324: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_463, type, sK325: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_464, type, sK326: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_465, type, sK327: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_466, type, sK328: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_467, type, sK329: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_468, type, sK330: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_469, type, sK331: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_470, type, sK332: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_471, type, sK333: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_472, type, sK334: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_473, type, sK335: (subst > (term > $o) > term)).
% 6.46/1.21 thf(func_def_474, type, sK336: term).
% 6.46/1.21 thf(func_def_475, type, sK337: (term > $o)).
% 6.46/1.21 thf(func_def_476, type, sK338: subst).
% 6.46/1.21 thf(func_def_477, type, sK339: (term > term)).
% 6.46/1.21 thf(func_def_478, type, sK340: term).
% 6.46/1.21 thf(func_def_479, type, sK341: term).
% 6.46/1.21 thf(func_def_480, type, sK342: (term > $o)).
% 6.46/1.21 thf(func_def_481, type, sK343: (term > term)).
% 6.46/1.21 thf(func_def_482, type, sK344: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_483, type, sK345: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_484, type, sK346: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_485, type, sK347: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_486, type, sK348: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_487, type, sK349: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_488, type, sK350: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_489, type, sK351: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_490, type, sK352: subst).
% 6.46/1.21 thf(func_def_491, type, sK353: subst).
% 6.46/1.21 thf(func_def_492, type, sK354: term).
% 6.46/1.21 thf(func_def_493, type, sK355: term).
% 6.46/1.21 thf(func_def_494, type, sK356: subst).
% 6.46/1.21 thf(func_def_495, type, sK357: (term > $o)).
% 6.46/1.21 thf(func_def_496, type, sK358: term).
% 6.46/1.21 thf(func_def_497, type, sK359: term).
% 6.46/1.21 thf(func_def_498, type, sK360: (term > $o)).
% 6.46/1.21 thf(func_def_499, type, sK361: subst).
% 6.46/1.21 thf(func_def_500, type, sK362: (term > term)).
% 6.46/1.21 thf(func_def_501, type, sK363: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_502, type, sK364: (subst > (term > $o) > term)).
% 6.46/1.21 thf(func_def_503, type, sK365: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_504, type, sK366: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_505, type, sK367: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_506, type, sK368: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_509, type, sK371: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_510, type, sK372: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_515, type, sK377: term).
% 6.46/1.21 thf(func_def_516, type, sK378: term).
% 6.46/1.21 thf(func_def_517, type, sK379: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_518, type, sK380: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_519, type, sK381: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_520, type, sK382: term).
% 6.46/1.21 thf(func_def_521, type, sK383: (term > $o)).
% 6.46/1.21 thf(func_def_522, type, sK384: (term > term)).
% 6.46/1.21 thf(func_def_523, type, sK385: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_524, type, sK386: term).
% 6.46/1.21 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_526, type, sK388: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_527, type, sK389: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_528, type, sK390: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_532, type, sK394: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_534, type, sK396: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(func_def_535, type, sK397: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_538, type, sK400: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_539, type, sK401: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_541, type, sK403: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_543, type, sK405: term).
% 6.46/1.21 thf(func_def_544, type, sK406: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_545, type, sK407: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_546, type, sK408: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_547, type, sK409: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_548, type, sK410: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_549, type, sK411: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_550, type, sK412: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_552, type, sK414: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_553, type, sK415: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_554, type, sK416: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_555, type, sK417: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_556, type, sK418: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_557, type, sK419: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_558, type, sK420: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_559, type, sK421: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_560, type, sK422: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_561, type, sK423: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_562, type, sK424: term).
% 6.46/1.21 thf(func_def_563, type, sK425: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_564, type, sK426: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_565, type, sK427: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_566, type, sK428: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_568, type, sK430: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_569, type, sK431: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_570, type, sK432: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_571, type, sK433: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_572, type, sK434: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_573, type, sK435: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_574, type, sK436: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_575, type, sK437: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_576, type, sK438: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_577, type, sK439: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_578, type, sK440: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_579, type, sK441: term).
% 6.46/1.21 thf(func_def_580, type, sK442: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(func_def_582, type, sK444: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_584, type, sK446: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_585, type, sK447: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_586, type, sK448: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_587, type, sK449: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_588, type, sK450: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_589, type, sK451: ((subst > term > subst > $o) > subst)).
% 6.46/1.21 thf(func_def_590, type, sK452: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_591, type, sK453: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_592, type, sK454: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_593, type, sK455: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_595, type, sK457: subst).
% 6.46/1.21 thf(func_def_596, type, sK458: (term > $o)).
% 6.46/1.21 thf(func_def_597, type, sK459: term).
% 6.46/1.21 thf(func_def_598, type, sK460: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_599, type, sK461: (term > (term > $o) > subst > term > $o)).
% 6.46/1.21 thf(func_def_600, type, sK462: (subst > d_subst)).
% 6.46/1.21 thf(func_def_601, type, sK463: term).
% 6.46/1.21 thf(func_def_602, type, sK464: term).
% 6.46/1.21 thf(func_def_603, type, sK465: term).
% 6.46/1.21 thf(func_def_604, type, sK466: term).
% 6.46/1.21 thf(func_def_605, type, sK467: term).
% 6.46/1.21 thf(func_def_606, type, sK468: term).
% 6.46/1.21 thf(func_def_607, type, sK469: term).
% 6.46/1.21 thf(func_def_608, type, sK470: term).
% 6.46/1.21 thf(func_def_609, type, sK471: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_610, type, sK472: ((subst > term > subst > $o) > term)).
% 6.46/1.21 thf(func_def_611, type, sK473: term).
% 6.46/1.21 thf(func_def_612, type, sK474: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_613, type, sK475: (term > subst > term > term)).
% 6.46/1.21 thf(func_def_614, type, sK476: term).
% 6.46/1.21 thf(func_def_615, type, sK477: subst).
% 6.46/1.21 thf(func_def_616, type, sK478: subst).
% 6.46/1.21 thf(func_def_617, type, sK479: subst).
% 6.46/1.21 thf(func_def_618, type, sK480: subst).
% 6.46/1.21 thf(func_def_619, type, sK481: subst).
% 6.46/1.21 thf(func_def_620, type, sK482: subst).
% 6.46/1.21 thf(func_def_621, type, sK483: term).
% 6.46/1.21 thf(func_def_622, type, sK484: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_623, type, sK485: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_624, type, sK486: (term > subst > term > term)).
% 6.46/1.21 thf(func_def_625, type, sK487: term).
% 6.46/1.21 thf(func_def_626, type, sK488: (subst > term > term)).
% 6.46/1.21 thf(func_def_627, type, sK489: (subst > term > term)).
% 6.46/1.21 thf(func_def_628, type, sK490: subst).
% 6.46/1.21 thf(func_def_629, type, sK491: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_630, type, sK492: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_631, type, sK493: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_632, type, sK494: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_633, type, sK495: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_634, type, sK496: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_635, type, sK497: ((subst > term > subst > $o) > term > $o)).
% 6.46/1.21 thf(func_def_636, type, sK498: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_637, type, sK499: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_638, type, sK500: subst).
% 6.46/1.21 thf(func_def_639, type, sK501: term).
% 6.46/1.21 thf(func_def_640, type, sK502: term).
% 6.46/1.21 thf(func_def_641, type, sK503: term).
% 6.46/1.21 thf(func_def_642, type, sK504: term).
% 6.46/1.21 thf(func_def_643, type, sK505: term).
% 6.46/1.21 thf(func_def_644, type, sK506: term).
% 6.46/1.21 thf(func_def_645, type, sK507: term).
% 6.46/1.21 thf(func_def_646, type, sK508: ((term > $o) > (term > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_647, type, sK509: term).
% 6.46/1.21 thf(func_def_648, type, sK510: subst).
% 6.46/1.21 thf(func_def_649, type, sK511: (term > $o)).
% 6.46/1.21 thf(func_def_650, type, sK512: (term > $o)).
% 6.46/1.21 thf(func_def_651, type, sK513: term).
% 6.46/1.21 thf(func_def_652, type, sK514: term).
% 6.46/1.21 thf(func_def_653, type, sK515: term).
% 6.46/1.21 thf(func_def_654, type, sK516: term).
% 6.46/1.21 thf(func_def_655, type, sK517: term).
% 6.46/1.21 thf(func_def_656, type, sK518: term).
% 6.46/1.21 thf(func_def_657, type, sK519: term).
% 6.46/1.21 thf(func_def_658, type, sK520: term).
% 6.46/1.21 thf(func_def_659, type, sK521: term).
% 6.46/1.21 thf(func_def_660, type, sK522: term).
% 6.46/1.21 thf(func_def_661, type, sK523: term).
% 6.46/1.21 thf(func_def_662, type, sK524: term).
% 6.46/1.21 thf(func_def_663, type, sK525: term).
% 6.46/1.21 thf(func_def_664, type, sK526: subst).
% 6.46/1.21 thf(func_def_665, type, sK527: (term > $o)).
% 6.46/1.21 thf(func_def_666, type, sK528: (term > $o)).
% 6.46/1.21 thf(func_def_667, type, sK529: (term > subst > term > term)).
% 6.46/1.21 thf(func_def_668, type, sK530: term).
% 6.46/1.21 thf(func_def_669, type, sK531: term).
% 6.46/1.21 thf(func_def_670, type, sK532: term).
% 6.46/1.21 thf(func_def_671, type, sK533: term).
% 6.46/1.21 thf(func_def_672, type, sK534: term).
% 6.46/1.21 thf(func_def_673, type, sK535: term).
% 6.46/1.21 thf(func_def_674, type, sK536: term).
% 6.46/1.21 thf(func_def_675, type, sK537: subst).
% 6.46/1.21 thf(func_def_676, type, sK538: term).
% 6.46/1.21 thf(func_def_677, type, sK539: term).
% 6.46/1.21 thf(func_def_678, type, sK540: term).
% 6.46/1.21 thf(func_def_679, type, sK541: term).
% 6.46/1.21 thf(func_def_680, type, sK542: term).
% 6.46/1.21 thf(func_def_681, type, sK543: term).
% 6.46/1.21 thf(func_def_682, type, sK544: term).
% 6.46/1.21 thf(func_def_683, type, sK545: term).
% 6.46/1.21 thf(func_def_684, type, sK546: (term > d_term)).
% 6.46/1.21 thf(func_def_685, type, sK547: subst).
% 6.46/1.21 thf(func_def_686, type, sK548: term).
% 6.46/1.21 thf(func_def_687, type, sK549: term).
% 6.46/1.21 thf(func_def_688, type, sK550: (term > $o)).
% 6.46/1.21 thf(func_def_689, type, sK551: subst).
% 6.46/1.21 thf(func_def_690, type, sK552: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_691, type, sK553: (subst > (term > $o) > term > term > $o)).
% 6.46/1.21 thf(func_def_692, type, sK554: (term > subst > (term > $o) > (term > $o) > term)).
% 6.46/1.21 thf(func_def_693, type, sK555: subst).
% 6.46/1.21 thf(func_def_694, type, sK556: term).
% 6.46/1.21 thf(func_def_695, type, sK557: (term > $o)).
% 6.46/1.21 thf(func_def_696, type, sK558: (term > $o)).
% 6.46/1.21 thf(func_def_697, type, sK559: subst).
% 6.46/1.21 thf(func_def_698, type, sK560: term).
% 6.46/1.21 thf(func_def_699, type, sK561: term).
% 6.46/1.21 thf(func_def_700, type, sK562: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_701, type, sK563: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_702, type, sK564: (term > subst > term > term)).
% 6.46/1.21 thf(func_def_703, type, sK565: subst).
% 6.46/1.21 thf(func_def_704, type, sK566: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_705, type, sK567: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_706, type, sK568: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_707, type, sK569: term).
% 6.46/1.21 thf(func_def_708, type, sK570: (subst > term > term)).
% 6.46/1.21 thf(func_def_709, type, sK571: term).
% 6.46/1.21 thf(func_def_710, type, sK572: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_711, type, sK573: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_712, type, sK574: (term > $o)).
% 6.46/1.21 thf(func_def_713, type, sK575: term).
% 6.46/1.21 thf(func_def_714, type, sK576: ((subst > term > subst > $o) > term > $o)).
% 6.46/1.21 thf(func_def_715, type, sK577: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_716, type, sK578: ((term > $o) > term)).
% 6.46/1.21 thf(func_def_717, type, sK579: subst).
% 6.46/1.21 thf(func_def_718, type, sK580: (term > $o)).
% 6.46/1.21 thf(func_def_719, type, sK581: (term > $o)).
% 6.46/1.21 thf(func_def_720, type, sK582: term).
% 6.46/1.21 thf(func_def_721, type, sK583: term).
% 6.46/1.21 thf(func_def_722, type, sK584: term).
% 6.46/1.21 thf(func_def_723, type, sK585: subst).
% 6.46/1.21 thf(func_def_724, type, sK586: term).
% 6.46/1.21 thf(func_def_725, type, sK587: subst).
% 6.46/1.21 thf(func_def_726, type, sK588: subst).
% 6.46/1.21 thf(func_def_727, type, sK589: term).
% 6.46/1.21 thf(func_def_728, type, sK590: term).
% 6.46/1.21 thf(func_def_729, type, vNOT: ($o > $o)).
% 6.46/1.21 thf(func_def_730, type, sK591: (subst > term > subst > $o)).
% 6.46/1.21 thf(func_def_731, type, sK592: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_732, type, sK593: ((subst > term > term) > term)).
% 6.46/1.21 thf(func_def_733, type, sK594: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_734, type, sK595: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_735, type, sK596: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_736, type, sK597: ((subst > term > term) > subst)).
% 6.46/1.21 thf(func_def_737, type, sK598: term).
% 6.46/1.21 thf(func_def_738, type, sK599: ((subst > term > subst > $o) > subst > term > term)).
% 6.46/1.21 thf(func_def_739, type, sK600: ((subst > term > subst > $o) > term > term)).
% 6.46/1.21 thf(f1,axiom,(
% 6.46/1.21 hoasinduction_lem3_gthm & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & ulamvarind & hoasinduction_lem1 & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X13 : term,X14 : subst,X15 : term,X26 : (term > $o),X10 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & hoasinduction_lem2_gthm & (! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id)) <=> hoasinduction) & (laminj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13)))) => ! [X16 : term,X10 : (term > $o),X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))))))))) & pushprop_lthm_orig & induction2_gthm & (! [X20 : term,X19 : term,X13 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((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)] : ((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)))))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoasinduction_lem3a_lthm) & hoasinduction_lem1_lthm & pushprop_lem1v2_gthm & axapp & (hoasinduction_lem2 <=> ! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~(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 @ (ap @ X23 @ X24) @ id) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & (! [X11 : (term > $o),X48 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X48)) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) <=> hoasinduction_lem3v2) & (induction2lem <=> ! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)))) & hoasapnotvar_lthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X20 : term,X19 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)))) <=> hoasapinj1_lthm) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasinduction_gthm & (! [X13 : term,X14 : subst,X10 : (term > $o),X11 : (term > $o)] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13)) <=> pushprop_lem1v2) & ~(var @ (d2term @ d_one)) & hoaslamnotap_lthm & (hoasinduction_lem2v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X44 : term,X45 : term] : (~(X11 @ X44) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X13 : term,X14 : subst,X26 : 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))))) & ! [X1 : d_term] : (X1 = d_one) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (! [X13 : term,X19 : term,X20 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [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))))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))))))) <=> hoasinduction_no_psi_cond_lthm) & (hoasapinj2_lthm <=> (! [X15 : term,X13 : term,X20 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X15 : term,X19 : term,X13 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & ~ulamvar1 & (sh = ((d2subst @ d_id))) & (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))))) <=> hoasinduction_lem3v2a_lthm) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X14 : subst,X10 : (term > $o),X13 : term] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & pushprop & (! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ((! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) <=> substmonoid) & (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)))))))) & (hoaslaminj_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X33 : term,X31 : (subst > term > term),X32 : subst,X18 : (subst > term > term)] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one))))))))) & (hoasinduction_no_psi_cond <=> ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : ((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] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ X30 @ id))) & axvarshift & axclos & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & hoasapnotvar_gthm & hoasinduction_lem3a_gthm & (hoaslaminj <=> ! [X31 : (subst > term > term),X18 : (subst > term > term),X33 : term,X32 : subst] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))) & pushprop_gthm & (pushprop_lem1 <=> ! [X10 : (term > $o),X14 : subst,X26 : (term > $o),X15 : term,X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & termmset_gthm & hoasapinj2_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & (one = ((d2term @ d_one))) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & apnotvar & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & pushprop_lem1_gthm & (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [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))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & pushprop_lem0_gthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ulamvarsh & hoaslamnotvar_gthm & hoaslamnotvar & substmonoid_gthm & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aa_lthm) & (hoasinduction_lem3aa <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X35 : term,X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X38 : subst,X36 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X41 : subst,X39 : subst,X40 : term] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))))))) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & pushprop_lem3v2_lthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X26 : subst,X13 : term,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))) | (X11 @ (lam @ X48)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [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)))) <=> hoasinduction_lem3v2_lthm) & (! [X10 : (term > $o),X21 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21)) <=> induction) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (! [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))))) <=> hoaslamnotap) & hoasinduction_lem1v2_gthm & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & axassoc & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X16 : term,X17 : subst,X10 : (term > $o)] : (~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22))))) & hoasapinj1_gthm & (pushprop_lem0_lthm <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) <=> induction2) & hoasinduction_lem3b_gthm & hoaslaminj_gthm & hoasinduction_lem2v2_gthm & (! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & hoaslamnotap_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem3v2_gthm & hoasinduction_lem2_lthm & induction2lem_gthm & pushprop_lem3v2 & lamnotvar & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & ~lamnotap & pushprop_lem2v2 & hoasapnotvar & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_lthm <=> (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X25 : subst,X26 : 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)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id)) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X14 : 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,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))))))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [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))))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) <=> hoasinduction_lthm_3) & hoasinduction_lem1v2 & (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 @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ 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))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & pushprop_lem2v2_lthm & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (apinj2 <=> ! [X20 : term,X19 : term,X15 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & ! [X5 : d_subst] : (X5 = d_id) & (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) <=> hoasinduction_lem3v2a) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & axmap & hoaslamnotvar_lthm & axabs & pushprop_lem2v2_gthm & (! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ X43) @ id)) <=> hoasinduction_lem3a) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoasinduction_lem1_gthm & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & pushprop_lthm & (id = ((d2subst @ d_id))) & (hoasapinj2 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))),
% 6.46/1.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 6.46/1.22 thf(f2,conjecture,(
% 6.46/1.22 (hoasinduction_lem3a = ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : subst,X2 : subst,X3 : term] : (((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 @ X3) @ id))))),
% 6.46/1.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a)).
% 6.46/1.22 thf(f3,negated_conjecture,(
% 6.46/1.22 ~ (hoasinduction_lem3a = ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X4 : subst,X2 : subst,X3 : term] : (((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 @ X3) @ id))))),
% 6.46/1.22 inference(negated_conjecture,[status(cth)],[f2])).
% 6.46/1.22 thf(f4,plain,(
% 6.46/1.22 ~ (hoasinduction_lem3a = ! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (! [X2 : subst,X3 : subst,X4 : term] : (((sub @ (X1 @ X3 @ X4) @ X2)) = ((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ 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 @ X8) @ id))))),
% 6.46/1.22 inference(rectify,[],[f3])).
% 6.46/1.22 thf(f5,plain,(
% 6.46/1.22 ~ (hoasinduction_lem3a = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))),
% 6.46/1.22 inference(fool_elimination,[],[f4])).
% 6.46/1.22 thf(f6,plain,(
% 6.46/1.22 hoasinduction_lem3_gthm & (axidr <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & ulamvarind & hoasinduction_lem1 & ((! [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) = X1) => (! [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) = X4) => ! [X5 : term,X6 : subst,X7 : term,X8 : (term > $o),X9 : (term > $o)] : (~(X9 @ X5) | (X8 @ (sub @ X5 @ (push @ X7 @ X6)))))) <=> pushprop_lem1_lthm) & hoasinduction_lem2_gthm & (! [X10 : term,X11 : (subst > term > subst > $o)] : (~ ! [X12 : term] : ((X11 @ id @ X12 @ id) | ~(var @ (sub @ X12 @ id))) | ~ ! [X13 : subst,X14 : term,X15 : subst,X16 : subst] : (~(X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15) | (X11 @ X13 @ X14 @ (comp @ X16 @ X15))) | ~ ! [X17 : term,X18 : term] : (~(X11 @ id @ X17 @ id) | (X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id) | ~(X11 @ id @ X18 @ id)) | ~ ! [X19 : (subst > term > term)] : (~ ! [X20 : term] : ((X11 @ id @ (X19 @ id @ X20) @ id) | ~(X11 @ id @ X20 @ id)) | (X11 @ id @ (lam @ (X19 @ sh @ one)) @ id) | ~ ! [X21 : term,X22 : subst,X23 : subst] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22))))) | ~ ! [X24 : term,X25 : subst,X26 : subst,X27 : subst] : (~(X11 @ X27 @ X24 @ (comp @ X26 @ X25)) | (X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25)) | (X11 @ id @ X10 @ id)) <=> hoasinduction) & (laminj <=> ! [X28 : term,X29 : term] : ((X28 = X29) | (((lam @ X29)) != ((lam @ X28))))) & (! [X30 : (subst > term > subst > $o)] : ~ ! [X31 : (term > $o)] : ~ ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> hoasinduction_lem0_lthm) & (axidl <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & (induction2lem_lthm <=> (! [X34 : subst,X35 : term] : (((sub @ one @ (push @ X35 @ X34))) = X35) => (! [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) = X37) => (! [X38 : subst] : (((comp @ X38 @ id)) = X38) => (! [X39 : (term > $o),X40 : term] : ((X39 @ X40) | ~ ! [X41 : term] : ((X39 @ X41) | ~(var @ X41)) | ~ ! [X42 : term,X43 : term] : ((X39 @ (ap @ X42 @ X43)) | ~(X39 @ X43) | ~(X39 @ X42)) | ~ ! [X44 : term] : (~(X39 @ X44) | (X39 @ (lam @ X44)))) => ! [X45 : term,X46 : (term > $o),X47 : subst] : ((X46 @ (sub @ X45 @ X47)) | ~ ! [X48 : term,X49 : term] : (~(X46 @ X48) | ~(X46 @ X49) | (X46 @ (ap @ X49 @ X48))) | ~ ! [X50 : term] : (~ ! [X51 : term] : ((X46 @ (sub @ X50 @ (push @ X51 @ id))) | ~(X46 @ X51)) | (X46 @ (lam @ X50))) | ~ ! [X52 : term] : (~(var @ X52) | (X46 @ (sub @ X52 @ X47))))))))) & pushprop_lthm_orig & induction2_gthm & (! [X53 : term,X54 : term,X55 : term,X56 : term] : ((X55 = X56) | (((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54)))) <=> hoasapinj1) & ((! [X57 : term] : (((sub @ X57 @ id)) = X57) => (! [X58 : (subst > term > subst > $o),X59 : term] : ((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id) | ~ ! [X60 : term] : (~(X58 @ id @ X60 @ id) | (X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id)) | ~ ! [X61 : (subst > term > term)] : ((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id) | ~ ! [X62 : term] : ((X58 @ id @ (X61 @ id @ X62) @ id) | ~(X58 @ id @ X62 @ id)) | ~ ! [X63 : term,X64 : subst,X65 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) = ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))))) => ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : term] : ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id) | ~(X67 @ id @ X68 @ id)) | (X67 @ id @ (lam @ X66) @ id) | ~ ! [X69 : (subst > term > term)] : ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id) | ~ ! [X70 : term] : (~(X67 @ id @ X70 @ id) | (X67 @ id @ (X69 @ id @ X70) @ id)) | ~ ! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))))))) <=> hoasinduction_lem3a_lthm) & hoasinduction_lem1_lthm & pushprop_lem1v2_gthm & axapp & (hoasinduction_lem2 <=> ! [X74 : term,X75 : term,X76 : (subst > term > subst > $o)] : (~(X76 @ id @ X75 @ id) | ~ ! [X77 : term,X78 : term] : (~(X76 @ id @ X78 @ id) | (X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id) | ~(X76 @ id @ X77 @ id)) | ~(X76 @ id @ X74 @ id) | ~ ! [X79 : subst,X80 : term,X81 : subst,X82 : subst] : (~(X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79) | (X76 @ X81 @ X80 @ (comp @ X82 @ X79))) | (X76 @ id @ (ap @ X74 @ X75) @ id) | ~ ! [X83 : subst,X84 : subst,X85 : subst,X86 : term] : (~(X76 @ X84 @ X86 @ (comp @ X83 @ X85)) | (X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85)))) & (! [X87 : (term > $o),X88 : term,X89 : (subst > term > subst > $o)] : (~ ! [X90 : term] : (~(X87 @ X90) | (X87 @ (sub @ X88 @ (push @ X90 @ id)))) | ~ ! [X91 : subst,X92 : term,X93 : subst,X94 : subst] : ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93) | ~(X89 @ X94 @ X92 @ (comp @ X91 @ X93))) | ~ ! [X95 : term] : (((X87 @ X95)) = ((X89 @ id @ X95 @ id))) | ~ ! [X96 : (subst > term > term)] : (~ ! [X97 : term] : ((X89 @ id @ (X96 @ id @ X97) @ id) | ~(X89 @ id @ X97 @ id)) | (X89 @ id @ (lam @ (X96 @ sh @ one)) @ id) | ~ ! [X98 : subst,X99 : subst,X100 : term] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98)))) | (X87 @ (lam @ X88)) | ~ ! [X101 : subst,X102 : subst,X103 : subst,X104 : term] : (~(X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102) | (X89 @ X101 @ X104 @ (comp @ X103 @ X102)))) <=> hoasinduction_lem3v2) & (induction2lem <=> ! [X105 : subst,X106 : (term > $o),X107 : term] : (~ ! [X108 : term] : ((X106 @ (lam @ X108)) | ~ ! [X109 : term] : ((X106 @ (sub @ X108 @ (push @ X109 @ id))) | ~(X106 @ X109))) | ~ ! [X110 : term,X111 : term] : (~(X106 @ X111) | (X106 @ (ap @ X111 @ X110)) | ~(X106 @ X110)) | (X106 @ (sub @ X107 @ X105)) | ~ ! [X112 : term] : ((X106 @ (sub @ X112 @ X105)) | ~(var @ X112)))) & hoasapnotvar_lthm & ((! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : term,X115 : term,X116 : term,X117 : term] : ((X116 = X117) | (((ap @ X116 @ X115)) != ((ap @ X117 @ X114)))) => ! [X118 : term,X119 : term,X120 : term,X121 : term] : ((((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118))) | (X120 = X121)))) <=> hoasapinj1_lthm) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasinduction_gthm & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : ((X125 @ one) | ~ ! [X126 : term] : (((X125 @ X126)) = ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ~(X124 @ X122)) <=> pushprop_lem1v2) & ~(var @ (d2term @ d_one)) & hoaslamnotap_lthm & (hoasinduction_lem2v2 <=> ! [X127 : (subst > term > subst > $o),X128 : (term > $o),X129 : term,X130 : term] : (~(X128 @ X129) | ~ ! [X131 : term,X132 : term] : (~(X127 @ id @ X132 @ id) | (X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id) | ~(X127 @ id @ X131 @ id)) | ~ ! [X133 : term,X134 : subst,X135 : subst,X136 : subst] : (~(X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136) | (X127 @ X134 @ X133 @ (comp @ X135 @ X136))) | ~(X128 @ X130) | (X128 @ (ap @ X129 @ X130)) | ~ ! [X137 : term,X138 : subst,X139 : subst,X140 : subst] : (~(X127 @ X138 @ X137 @ (comp @ X139 @ X140)) | (X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)) | ~ ! [X141 : term] : (((X128 @ X141)) = ((X127 @ id @ X141 @ id))))) & ! [X142 : d_term] : (d_one = X142) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_lem3v2_f <=> ! [X143 : term] : ~ ! [X144 : (subst > term > term)] : ~ ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145)))) & (! [X147 : term,X148 : term,X149 : term,X150 : term] : ((((ap @ X147 @ X148)) != ((ap @ X150 @ X149))) | (X147 = X150)) <=> apinj1) & (! [X151 : term] : ~ ! [X152 : (subst > term > term)] : ~ ! [X153 : term,X154 : subst] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153))) <=> hoasinduction_lem3v2_f_lthm) & ((! [X155 : (subst > term > subst > $o)] : ~ ! [X156 : (term > $o)] : ~ ! [X157 : term] : (((X155 @ id @ X157 @ id)) = ((X156 @ X157))) => (! [X158 : term,X159 : (term > $o)] : ((X159 @ X158) | ~ ! [X160 : term,X161 : term] : (~(X159 @ X160) | ~(X159 @ X161) | (X159 @ (ap @ X160 @ X161))) | ~ ! [X162 : term] : ((X159 @ X162) | ~(var @ X162)) | ~ ! [X163 : term] : (~ ! [X164 : term] : (~(X159 @ X164) | (X159 @ (sub @ X163 @ (push @ X164 @ id)))) | (X159 @ (lam @ X163)))) => (! [X165 : term] : (((sub @ X165 @ id)) = X165) => (! [X166 : (term > $o),X167 : (subst > term > subst > $o),X168 : term] : (~ ! [X169 : (subst > term > term)] : (~ ! [X170 : term] : (~(X167 @ id @ X170 @ id) | (X167 @ id @ (X169 @ id @ X170) @ id)) | (X167 @ id @ (lam @ (X169 @ sh @ one)) @ id) | ~ ! [X171 : subst,X172 : subst,X173 : term] : (((sub @ (X169 @ X172 @ X173) @ X171)) = ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))) | ~ ! [X174 : term] : ((X166 @ (sub @ X168 @ (push @ X174 @ id))) | ~(X166 @ X174)) | (X166 @ (lam @ X168)) | ~ ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id)))) => ! [X176 : term,X177 : (subst > term > subst > $o)] : ((X177 @ id @ X176 @ id) | ~ ! [X178 : term,X179 : term] : (~(X177 @ id @ X179 @ id) | ~(X177 @ id @ X178 @ id) | (X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : subst,X182 : subst,X183 : term] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182)))) | (X177 @ id @ (lam @ (X180 @ sh @ one)) @ id) | ~ ! [X184 : term] : ((X177 @ id @ (X180 @ id @ X184) @ id) | ~(X177 @ id @ X184 @ id)))))))) <=> hoasinduction_no_psi_cond_lthm) & (hoasapinj2_lthm <=> (! [X185 : term,X186 : term,X187 : term,X188 : term] : ((((ap @ X186 @ X188)) != ((ap @ X185 @ X187))) | (X187 = X188)) => ! [X189 : term,X190 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190)))))) & ~ulamvar1 & (sh = ((d2subst @ d_id))) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> axshiftcons) & ((! [X195 : term] : ~ ! [X196 : (subst > term > term)] : ~ ! [X197 : subst,X198 : term] : (((X196 @ X197 @ X198)) = ((sub @ X195 @ (push @ X198 @ X197)))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => ! [X200 : term,X201 : (subst > term > subst > $o),X202 : (term > $o)] : (~ ! [X203 : term] : (((X201 @ id @ X203 @ id)) = ((X202 @ X203))) | ~ ! [X204 : (subst > term > term)] : (~ ! [X205 : subst,X206 : term,X207 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205)))) | ~ ! [X208 : term] : (~(X201 @ id @ X208 @ id) | (X201 @ id @ (X204 @ id @ X208) @ id)) | (X201 @ id @ (lam @ (X204 @ sh @ one)) @ id)) | (X202 @ (lam @ X200)) | ~ ! [X209 : term] : ((X202 @ (sub @ X200 @ (push @ X209 @ id))) | ~(X202 @ X209))))) <=> hoasinduction_lem3v2a_lthm) & ((! [X210 : term,X211 : subst] : (((sub @ one @ (push @ X210 @ X211))) = X210) => ! [X212 : (term > $o),X213 : subst,X214 : (term > $o),X215 : term] : (~ ! [X216 : term] : (((X212 @ X216)) = ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ~(X214 @ X215) | (X212 @ one))) <=> pushprop_lem1v2_lthm) & pushprop & (! [X217 : (term > $o),X218 : term,X219 : subst] : ~ ! [X220 : (term > $o)] : ~ ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221))) <=> pushprop_lem0) & ((! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223)) <=> substmonoid) & (pushprop_p_and_p_prime = (^[X224 : term, X225 : subst, X226 : (term > $o), X227 : (term > $o)] : (! [X228 : term] : (((X226 @ (sub @ X228 @ (push @ X224 @ X225)))) = ((X227 @ X228)))))) & (hoaslaminj_lthm <=> (! [X229 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X229))) = X230) => (! [X231 : term,X232 : subst] : (((comp @ sh @ (push @ X231 @ X232))) = X232) => (! [X233 : term,X234 : term] : ((X233 = X234) | (((lam @ X234)) != ((lam @ X233)))) => ! [X235 : term,X236 : (subst > term > term),X237 : subst,X238 : (subst > term > term)] : ((((X238 @ X237 @ X235)) = ((X236 @ X237 @ X235))) | ~ ! [X239 : subst,X240 : term,X241 : subst] : (((sub @ (X236 @ X239 @ X240) @ X241)) = ((X236 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241)))) | ~ ! [X242 : term,X243 : subst,X244 : subst] : (((X238 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243))) = ((sub @ (X238 @ X244 @ X242) @ X243))) | (((lam @ (X238 @ sh @ one))) != ((lam @ (X236 @ sh @ one))))))))) & (hoasinduction_no_psi_cond <=> ! [X245 : term,X246 : (subst > term > subst > $o)] : (~ ! [X247 : term,X248 : term] : (~(X246 @ id @ X247 @ id) | (X246 @ id @ (ap @ (sub @ X248 @ id) @ X247) @ id) | ~(X246 @ id @ X248 @ id)) | ~ ! [X249 : (subst > term > term)] : ((X246 @ id @ (lam @ (X249 @ sh @ one)) @ id) | ~ ! [X250 : term] : (~(X246 @ id @ X250 @ id) | (X246 @ id @ (X249 @ id @ X250) @ id)) | ~ ! [X251 : subst,X252 : subst,X253 : term] : (((sub @ (X249 @ X252 @ X253) @ X251)) = ((X249 @ (comp @ X252 @ X251) @ (sub @ X253 @ X251))))) | (X246 @ id @ X245 @ id))) & axvarshift & axclos & (! [X254 : term] : (((sub @ X254 @ id)) = X254) <=> axvarid) & hoasapnotvar_gthm & hoasinduction_lem3a_gthm & (hoaslaminj <=> ! [X255 : (subst > term > term),X256 : (subst > term > term),X257 : term,X258 : subst] : (~ ! [X259 : term,X260 : subst,X261 : subst] : (((sub @ (X256 @ X261 @ X259) @ X260)) = ((X256 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260)))) | (((X255 @ X258 @ X257)) = ((X256 @ X258 @ X257))) | ~ ! [X262 : subst,X263 : subst,X264 : term] : (((sub @ (X255 @ X263 @ X264) @ X262)) = ((X255 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262)))) | (((lam @ (X255 @ sh @ one))) != ((lam @ (X256 @ sh @ one)))))) & pushprop_gthm & (pushprop_lem1 <=> ! [X265 : (term > $o),X266 : subst,X267 : (term > $o),X268 : term,X269 : term] : (~(X265 @ X269) | (X267 @ (sub @ X269 @ (push @ X268 @ X266))))) & termmset_gthm & hoasapinj2_gthm & ((! [X270 : term] : (((sub @ X270 @ id)) = X270) => ! [X271 : term] : (((sub @ X271 @ id)) = X271)) <=> termmset_lthm) & (one = ((d2term @ d_one))) & ((! [X272 : subst] : (((comp @ id @ X272)) = X272) => (! [X273 : subst] : (((comp @ X273 @ id)) = X273) => (! [X274 : subst] : (((comp @ X274 @ id)) = X274) & ! [X275 : subst] : (((comp @ id @ X275)) = X275)))) <=> substmonoid_lthm) & (hoasinduction_lem3b <=> ! [X276 : term] : ~ ! [X277 : (subst > term > term)] : (((sub @ X276 @ (push @ one @ sh))) != ((X277 @ sh @ one)))) & apnotvar & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & pushprop_lem1_gthm & (! [X278 : (subst > term > subst > $o),X279 : term] : (~ ! [X280 : subst,X281 : term,X282 : subst,X283 : subst] : (~(X278 @ X282 @ X281 @ (comp @ X283 @ X280)) | (X278 @ (comp @ X282 @ X283) @ (sub @ X281 @ X283) @ X280)) | ~ ! [X284 : (subst > term > term)] : ((X278 @ id @ (lam @ (X284 @ sh @ one)) @ id) | ~ ! [X285 : subst,X286 : term,X287 : subst] : (((X284 @ (comp @ X285 @ X287) @ (sub @ X286 @ X287))) = ((sub @ (X284 @ X285 @ X286) @ X287))) | ~ ! [X288 : term] : ((X278 @ id @ (X284 @ id @ X288) @ id) | ~(X278 @ id @ X288 @ id))) | (X278 @ id @ (lam @ X279) @ id) | ~ ! [X289 : term] : ((X278 @ id @ (sub @ X279 @ (push @ X289 @ id)) @ id) | ~(X278 @ id @ X289 @ id)) | ~ ! [X290 : term,X291 : subst,X292 : subst,X293 : subst] : ((X278 @ X293 @ X290 @ (comp @ X292 @ X291)) | ~(X278 @ (comp @ X293 @ X292) @ (sub @ X290 @ X292) @ X291))) <=> hoasinduction_lem3) & pushprop_lem0_gthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ulamvarsh & hoaslamnotvar_gthm & hoaslamnotvar & substmonoid_gthm & (! [X294 : term,X295 : (subst > term > subst > $o)] : (~ ! [X296 : (subst > term > term)] : ((X295 @ id @ (lam @ (X296 @ sh @ one)) @ id) | ~ ! [X297 : subst,X298 : term,X299 : subst] : (((X296 @ (comp @ X299 @ X297) @ (sub @ X298 @ X297))) = ((sub @ (X296 @ X299 @ X298) @ X297))) | ~ ! [X300 : term] : (~(X295 @ id @ X300 @ id) | (X295 @ id @ (X296 @ id @ X300) @ id))) | (X295 @ id @ (lam @ (sub @ X294 @ (push @ one @ sh))) @ id) | ~ ! [X301 : term] : ((X295 @ id @ (sub @ X294 @ (push @ X301 @ id)) @ id) | ~(X295 @ id @ X301 @ id))) <=> hoasinduction_lem3aa_lthm) & (hoasinduction_lem3aa <=> ! [X302 : term,X303 : (subst > term > subst > $o)] : (~ ! [X304 : (subst > term > term)] : ((X303 @ id @ (lam @ (X304 @ sh @ one)) @ id) | ~ ! [X305 : subst,X306 : subst,X307 : term] : (((sub @ (X304 @ X305 @ X307) @ X306)) = ((X304 @ (comp @ X305 @ X306) @ (sub @ X307 @ X306)))) | ~ ! [X308 : term] : (~(X303 @ id @ X308 @ id) | (X303 @ id @ (X304 @ id @ X308) @ id))) | (X303 @ id @ (lam @ (sub @ X302 @ (push @ one @ sh))) @ id) | ~ ! [X309 : term] : ((X303 @ id @ (sub @ X302 @ (push @ X309 @ id)) @ id) | ~(X303 @ id @ X309 @ id)))) & ! [X310 : d_subst,X311 : d_subst] : ((((d2subst @ X310)) = ((d2subst @ X311))) => (X310 = X311)) & (hoasinduction_lem3aaa <=> ! [X312 : (subst > term > subst > $o),X313 : term] : (~ ! [X314 : term] : ((X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id) | ~(X312 @ id @ X314 @ id)) | (X312 @ id @ (lam @ (sub @ X313 @ (push @ one @ sh))) @ id) | ~ ! [X315 : term,X316 : (subst > term > term)] : (~ ! [X317 : term] : ((X312 @ id @ (X316 @ id @ X317) @ id) | ~(X312 @ id @ X317 @ id)) | ~ ! [X318 : subst,X319 : subst,X320 : term] : (((sub @ (X316 @ X319 @ X320) @ X318)) = ((sub @ (sub @ X315 @ (push @ X320 @ X319)) @ X318))) | (X312 @ id @ (lam @ (X316 @ sh @ one)) @ id) | ~ ! [X321 : subst,X322 : subst,X323 : term] : (((sub @ X315 @ (push @ (sub @ X323 @ X321) @ (comp @ X322 @ X321)))) = ((X316 @ (comp @ X322 @ X321) @ (sub @ X323 @ X321))))))) & (! [X324 : subst,X325 : term] : (((sub @ one @ (push @ X325 @ X324))) = X325) <=> axvarcons) & pushprop_lem3v2_lthm & ((! [X326 : term] : (((sub @ X326 @ id)) = X326) => ! [X327 : (subst > term > subst > $o),X328 : term,X329 : (term > $o)] : (~ ! [X330 : term] : ((X329 @ (sub @ X328 @ (push @ X330 @ id))) | ~(X329 @ X330)) | ~ ! [X331 : subst,X332 : term,X333 : subst,X334 : subst] : ((X327 @ X333 @ X332 @ (comp @ X331 @ X334)) | ~(X327 @ (comp @ X333 @ X331) @ (sub @ X332 @ X331) @ X334)) | ~ ! [X335 : term] : (((X329 @ X335)) = ((X327 @ id @ X335 @ id))) | (X329 @ (lam @ X328)) | ~ ! [X336 : subst,X337 : subst,X338 : subst,X339 : term] : ((X327 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336) | ~(X327 @ X338 @ X339 @ (comp @ X337 @ X336))) | ~ ! [X340 : (subst > term > term)] : (~ ! [X341 : subst,X342 : term,X343 : subst] : (((sub @ (X340 @ X341 @ X342) @ X343)) = ((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343)))) | ~ ! [X344 : term] : (~(X327 @ id @ X344 @ id) | (X327 @ id @ (X340 @ id @ X344) @ id)) | (X327 @ id @ (lam @ (X340 @ sh @ one)) @ id)))) <=> hoasinduction_lem3v2_lthm) & (! [X345 : (term > $o),X346 : term] : (~ ! [X347 : term,X348 : term] : (~(X345 @ X348) | (X345 @ (ap @ X348 @ X347)) | ~(X345 @ X347)) | ~ ! [X349 : term] : (~(var @ X349) | (X345 @ X349)) | ~ ! [X350 : term] : (~(X345 @ X350) | (X345 @ (lam @ X350))) | (X345 @ X346)) <=> induction) & (hoaslam = (^[X351 : subst, X352 : (subst > term > term)] : ((d2term @ d_one)))) & (! [X353 : (subst > term > term),X354 : term,X355 : term] : ((((ap @ (sub @ X355 @ id) @ X354)) != ((lam @ (X353 @ sh @ one)))) | ~ ! [X356 : subst,X357 : subst,X358 : term] : (((X353 @ (comp @ X357 @ X356) @ (sub @ X358 @ X356))) = ((sub @ (X353 @ X357 @ X358) @ X356)))) <=> hoaslamnotap) & hoasinduction_lem1v2_gthm & ! [X359 : d_term,X360 : d_term] : ((((d2term @ X359)) = ((d2term @ X360))) => (X359 = X360)) & axassoc & (induction2_lthm <=> (! [X361 : term] : (((sub @ X361 @ id)) = X361) => (! [X362 : term,X363 : subst,X364 : (term > $o)] : (~ ! [X365 : term] : ((X364 @ (sub @ X365 @ X363)) | ~(var @ X365)) | (X364 @ (sub @ X362 @ X363)) | ~ ! [X366 : term] : (~ ! [X367 : term] : (~(X364 @ X367) | (X364 @ (sub @ X366 @ (push @ X367 @ id)))) | (X364 @ (lam @ X366))) | ~ ! [X368 : term,X369 : term] : (~(X364 @ X368) | (X364 @ (ap @ X368 @ X369)) | ~(X364 @ X369))) => ! [X370 : term,X371 : (term > $o)] : (~ ! [X372 : term] : (~(var @ X372) | (X371 @ X372)) | ~ ! [X373 : term,X374 : term] : (~(X371 @ X374) | (X371 @ (ap @ X373 @ X374)) | ~(X371 @ X373)) | ~ ! [X375 : term] : (~ ! [X376 : term] : ((X371 @ (sub @ X375 @ (push @ X376 @ id))) | ~(X371 @ X376)) | (X371 @ (lam @ X375))) | (X371 @ X370))))) & hoasapinj1_gthm & (pushprop_lem0_lthm <=> ! [X377 : (term > $o),X378 : term,X379 : subst] : ~ ! [X380 : (term > $o)] : ~ ! [X381 : term] : (((X380 @ X381)) = ((X377 @ (sub @ X381 @ (push @ X378 @ X379)))))) & (! [X382 : (term > $o),X383 : term] : ((X382 @ X383) | ~ ! [X384 : term] : (~(var @ X384) | (X382 @ X384)) | ~ ! [X385 : term,X386 : term] : (~(X382 @ X386) | (X382 @ (ap @ X385 @ X386)) | ~(X382 @ X385)) | ~ ! [X387 : term] : ((X382 @ (lam @ X387)) | ~ ! [X388 : term] : (~(X382 @ X388) | (X382 @ (sub @ X387 @ (push @ X388 @ id)))))) <=> induction2) & hoasinduction_lem3b_gthm & hoaslaminj_gthm & hoasinduction_lem2v2_gthm & (! [X389 : term,X390 : term] : ((X389 = X390) | (((sub @ X389 @ sh)) != ((sub @ X390 @ sh)))) <=> shinj) & hoaslamnotap_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem3v2_gthm & hoasinduction_lem2_lthm & induction2lem_gthm & pushprop_lem3v2 & lamnotvar & (hoasinduction_p_and_p_prime = (^[X391 : (subst > term > subst > $o), X392 : (term > $o)] : (! [X393 : term] : (((X391 @ id @ X393 @ id)) = ((X392 @ X393)))))) & ~lamnotap & pushprop_lem2v2 & hoasapnotvar & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasinduction_lthm <=> (! [X394 : term,X395 : (term > $o)] : (~ ! [X396 : term,X397 : term] : (~(X395 @ X397) | (X395 @ (ap @ X396 @ X397)) | ~(X395 @ X396)) | (X395 @ X394) | ~ ! [X398 : term] : (~ ! [X399 : term] : (~(X395 @ X399) | (X395 @ (sub @ X398 @ (push @ X399 @ id)))) | (X395 @ (lam @ X398))) | ~ ! [X400 : term] : ((X395 @ X400) | ~(var @ X400))) => (! [X401 : (subst > term > subst > $o),X402 : term,X403 : term] : ((X401 @ id @ (ap @ X402 @ X403) @ id) | ~ ! [X404 : term,X405 : term] : (~(X401 @ id @ X405 @ id) | (X401 @ id @ (ap @ (sub @ X405 @ id) @ X404) @ id) | ~(X401 @ id @ X404 @ id)) | ~(X401 @ id @ X402 @ id) | ~(X401 @ id @ X403 @ id) | ~ ! [X406 : term,X407 : subst,X408 : subst,X409 : subst] : ((X401 @ (comp @ X407 @ X409) @ (sub @ X406 @ X409) @ X408) | ~(X401 @ X407 @ X406 @ (comp @ X409 @ X408))) | ~ ! [X410 : term,X411 : subst,X412 : subst,X413 : subst] : ((X401 @ X413 @ X410 @ (comp @ X412 @ X411)) | ~(X401 @ (comp @ X413 @ X412) @ (sub @ X410 @ X412) @ X411))) => (! [X414 : (subst > term > subst > $o),X415 : term] : (~ ! [X416 : (subst > term > term)] : (~ ! [X417 : term] : ((X414 @ id @ (X416 @ id @ X417) @ id) | ~(X414 @ id @ X417 @ id)) | (X414 @ id @ (lam @ (X416 @ sh @ one)) @ id) | ~ ! [X418 : term,X419 : subst,X420 : subst] : (((sub @ (X416 @ X420 @ X418) @ X419)) = ((X416 @ (comp @ X420 @ X419) @ (sub @ X418 @ X419))))) | ~ ! [X421 : subst,X422 : subst,X423 : subst,X424 : term] : ((X414 @ X421 @ X424 @ (comp @ X423 @ X422)) | ~(X414 @ (comp @ X421 @ X423) @ (sub @ X424 @ X423) @ X422)) | ~ ! [X425 : term] : (~(X414 @ id @ X425 @ id) | (X414 @ id @ (sub @ X415 @ (push @ X425 @ id)) @ id)) | ~ ! [X426 : subst,X427 : subst,X428 : subst,X429 : term] : (~(X414 @ X427 @ X429 @ (comp @ X428 @ X426)) | (X414 @ (comp @ X427 @ X428) @ (sub @ X429 @ X428) @ X426)) | (X414 @ id @ (lam @ X415) @ id)) => ! [X430 : term,X431 : (subst > term > subst > $o)] : (~ ! [X432 : term] : (~(var @ (sub @ X432 @ id)) | (X431 @ id @ X432 @ id)) | ~ ! [X433 : term,X434 : term] : (~(X431 @ id @ X434 @ id) | (X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id) | ~(X431 @ id @ X433 @ id)) | (X431 @ id @ X430 @ id) | ~ ! [X435 : subst,X436 : subst,X437 : subst,X438 : term] : ((X431 @ X435 @ X438 @ (comp @ X436 @ X437)) | ~(X431 @ (comp @ X435 @ X436) @ (sub @ X438 @ X436) @ X437)) | ~ ! [X439 : subst,X440 : subst,X441 : subst,X442 : term] : ((X431 @ (comp @ X440 @ X441) @ (sub @ X442 @ X441) @ X439) | ~(X431 @ X440 @ X442 @ (comp @ X441 @ X439))) | ~ ! [X443 : (subst > term > term)] : (~ ! [X444 : subst,X445 : term,X446 : subst] : (((sub @ (X443 @ X444 @ X445) @ X446)) = ((X443 @ (comp @ X444 @ X446) @ (sub @ X445 @ X446)))) | ~ ! [X447 : term] : (~(X431 @ id @ X447 @ id) | (X431 @ id @ (X443 @ id @ X447) @ id)) | (X431 @ id @ (lam @ (X443 @ sh @ one)) @ id))))))) & ((! [X448 : (subst > term > subst > $o)] : ~ ! [X449 : (term > $o)] : ~ ! [X450 : term] : (((X449 @ X450)) = ((X448 @ id @ X450 @ id))) => (! [X451 : term,X452 : (term > $o)] : ((X452 @ X451) | ~ ! [X453 : term] : (~ ! [X454 : term] : (~(X452 @ X454) | (X452 @ (sub @ X453 @ (push @ X454 @ id)))) | (X452 @ (lam @ X453))) | ~ ! [X455 : term,X456 : term] : (~(X452 @ X456) | (X452 @ (ap @ X456 @ X455)) | ~(X452 @ X455)) | ~ ! [X457 : term] : (~(var @ X457) | (X452 @ X457))) => (! [X458 : term] : (((sub @ X458 @ id)) = X458) => (! [X459 : term,X460 : (term > $o),X461 : (subst > term > subst > $o)] : (~ ! [X462 : term] : (((X461 @ id @ X462 @ id)) = ((X460 @ X462))) | ~ ! [X463 : term] : ((X460 @ (sub @ X459 @ (push @ X463 @ id))) | ~(X460 @ X463)) | (X460 @ (lam @ X459)) | ~ ! [X464 : (subst > term > term)] : (~ ! [X465 : term] : ((X461 @ id @ (X464 @ id @ X465) @ id) | ~(X461 @ id @ X465 @ id)) | (X461 @ id @ (lam @ (X464 @ sh @ one)) @ id) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))) = ((sub @ (X464 @ X466 @ X467) @ X468))))) => ! [X469 : (subst > term > subst > $o),X470 : term] : (~ ! [X471 : (subst > term > term)] : ((X469 @ id @ (lam @ (X471 @ sh @ one)) @ id) | ~ ! [X472 : term] : ((X469 @ id @ (X471 @ id @ X472) @ id) | ~(X469 @ id @ X472 @ id)) | ~ ! [X473 : subst,X474 : subst,X475 : term] : (((X471 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473))) = ((sub @ (X471 @ X474 @ X475) @ X473)))) | ~ ! [X476 : term] : ((X469 @ id @ X476 @ id) | ~(var @ (sub @ X476 @ id))) | ~ ! [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((X469 @ (comp @ X478 @ X479) @ (sub @ X477 @ X479) @ X480) | ~(X469 @ X478 @ X477 @ (comp @ X479 @ X480))) | (X469 @ id @ X470 @ id) | ~ ! [X481 : term,X482 : term] : (~(X469 @ id @ X482 @ id) | ~(X469 @ id @ X481 @ id) | (X469 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id)) | ~ ! [X483 : subst,X484 : subst,X485 : subst,X486 : term] : ((X469 @ X485 @ X486 @ (comp @ X483 @ X484)) | ~(X469 @ (comp @ X485 @ X483) @ (sub @ X486 @ X483) @ X484))))))) <=> hoasinduction_lthm_3) & hoasinduction_lem1v2 & (hoasinduction_lem3_lthm <=> (! [X487 : term] : (((sub @ X487 @ id)) = X487) => (! [X488 : term,X489 : (subst > term > subst > $o)] : ((X489 @ id @ (lam @ (sub @ X488 @ (push @ one @ sh))) @ id) | ~ ! [X490 : term] : ((X489 @ id @ (sub @ X488 @ (push @ X490 @ id)) @ id) | ~(X489 @ id @ X490 @ id)) | ~ ! [X491 : (subst > term > term)] : (~ ! [X492 : term] : ((X489 @ id @ (X491 @ id @ X492) @ id) | ~(X489 @ id @ X492 @ id)) | ~ ! [X493 : subst,X494 : subst,X495 : term] : (((sub @ (X491 @ X493 @ X495) @ X494)) = ((X491 @ (comp @ X493 @ X494) @ (sub @ X495 @ X494)))) | (X489 @ id @ (lam @ (X491 @ sh @ one)) @ id))) => ! [X496 : term,X497 : (subst > term > subst > $o)] : ((X497 @ id @ (lam @ X496) @ id) | ~ ! [X498 : subst,X499 : subst,X500 : term,X501 : subst] : (~(X497 @ X498 @ X500 @ (comp @ X501 @ X499)) | (X497 @ (comp @ X498 @ X501) @ (sub @ X500 @ X501) @ X499)) | ~ ! [X502 : term,X503 : subst,X504 : subst,X505 : subst] : (~(X497 @ (comp @ X505 @ X504) @ (sub @ X502 @ X504) @ X503) | (X497 @ X505 @ X502 @ (comp @ X504 @ X503))) | ~ ! [X506 : term] : ((X497 @ id @ (sub @ X496 @ (push @ X506 @ id)) @ id) | ~(X497 @ id @ X506 @ id)) | ~ ! [X507 : (subst > term > term)] : (~ ! [X508 : term] : ((X497 @ id @ (X507 @ id @ X508) @ id) | ~(X497 @ id @ X508 @ id)) | (X497 @ id @ (lam @ (X507 @ sh @ one)) @ id) | ~ ! [X509 : subst,X510 : subst,X511 : term] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) = ((sub @ (X507 @ X509 @ X511) @ X510)))))))) & pushprop_lem2v2_lthm & (hoasinduction_lem3b_lthm <=> ! [X512 : term] : ~ ! [X513 : (subst > term > term)] : (((X513 @ sh @ one)) != ((sub @ X512 @ (push @ one @ sh))))) & (apinj2 <=> ! [X514 : term,X515 : term,X516 : term,X517 : term] : ((X514 = X515) | (((ap @ X516 @ X514)) != ((ap @ X517 @ X515))))) & (! [X518 : subst] : (((push @ (sub @ one @ X518) @ (comp @ sh @ X518))) = X518) <=> axscons) & ! [X519 : term] : ? [X520 : d_term] : (((d2term @ X520)) = X519) & ! [X521 : d_subst] : (d_id = X521) & (! [X522 : (subst > term > subst > $o),X523 : term,X524 : (term > $o)] : ((X524 @ (lam @ X523)) | ~ ! [X525 : (subst > term > term)] : (~ ! [X526 : subst,X527 : subst,X528 : term] : (((sub @ (X525 @ X527 @ X528) @ X526)) = ((X525 @ (comp @ X527 @ X526) @ (sub @ X528 @ X526)))) | (X522 @ id @ (lam @ (X525 @ sh @ one)) @ id) | ~ ! [X529 : term] : (~(X522 @ id @ X529 @ id) | (X522 @ id @ (X525 @ id @ X529) @ id))) | ~ ! [X530 : term] : (((X524 @ X530)) = ((X522 @ id @ X530 @ id))) | ~ ! [X531 : term] : ((X524 @ (sub @ X523 @ (push @ X531 @ id))) | ~(X524 @ X531))) <=> hoasinduction_lem3v2a) & (termmset <=> ! [X532 : term] : (((sub @ X532 @ id)) = X532)) & axmap & hoaslamnotvar_lthm & axabs & pushprop_lem2v2_gthm & (! [X533 : term,X534 : (subst > term > subst > $o)] : (~ ! [X535 : term] : ((X534 @ id @ (sub @ X533 @ (push @ X535 @ id)) @ id) | ~(X534 @ id @ X535 @ id)) | ~ ! [X536 : (subst > term > term)] : ((X534 @ id @ (lam @ (X536 @ sh @ one)) @ id) | ~ ! [X537 : term] : ((X534 @ id @ (X536 @ id @ X537) @ id) | ~(X534 @ id @ X537 @ id)) | ~ ! [X538 : subst,X539 : term,X540 : subst] : (((X536 @ (comp @ X538 @ X540) @ (sub @ X539 @ X540))) = ((sub @ (X536 @ X538 @ X539) @ X540)))) | (X534 @ id @ (lam @ X533) @ id)) <=> hoasinduction_lem3a) & ! [X541 : subst] : ? [X542 : d_subst] : (((d2subst @ X542)) = X541) & hoasinduction_lem1_gthm & (hoasinduction_lem0 <=> ! [X543 : (subst > term > subst > $o)] : ~ ! [X544 : (term > $o)] : ~ ! [X545 : term] : (((X544 @ X545)) = ((X543 @ id @ X545 @ id)))) & pushprop_lthm & (id = ((d2subst @ d_id))) & (hoasapinj2 <=> ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X548 = X549) | (((ap @ (sub @ X547 @ id) @ X549)) != ((ap @ (sub @ X546 @ id) @ X548)))))),
% 6.46/1.22 inference(rectify,[],[f1])).
% 6.46/1.22 thf(f7,plain,(
% 6.46/1.22 (hoasinduction_lem3_gthm = $true) & ((axidr = $true) <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & (ulamvarind = $true) & (hoasinduction_lem1 = $true) & ((! [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) = X1) => (! [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) = X4) => ! [X5 : term,X6 : subst,X7 : term,X8 : (term > $o),X9 : (term > $o)] : (~ (((X9 @ X5)) = $true) | (((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X10 : term,X11 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (($true = ((X11 @ id @ X12 @ id))) | ~ (((var @ (sub @ X12 @ id))) = $true)) | ~ ! [X13 : subst,X14 : term,X15 : subst,X16 : subst] : (~ (((X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15)) = $true) | (((X11 @ X13 @ X14 @ (comp @ X16 @ X15))) = $true)) | ~ ! [X17 : term,X18 : term] : (~ ($true = ((X11 @ id @ X17 @ id))) | ($true = ((X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id))) | ~ (((X11 @ id @ X18 @ id)) = $true)) | ~ ! [X19 : (subst > term > term)] : (~ ! [X20 : term] : ((((X11 @ id @ (X19 @ id @ X20) @ id)) = $true) | ~ ($true = ((X11 @ id @ X20 @ id)))) | (((X11 @ id @ (lam @ (X19 @ sh @ one)) @ id)) = $true) | ~ ! [X23 : subst,X22 : subst,X21 : term] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22))))) | ~ ! [X24 : term,X25 : subst,X26 : subst,X27 : subst] : (~ (((X11 @ X27 @ X24 @ (comp @ X26 @ X25))) = $true) | ($true = ((X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25)))) | ($true = ((X11 @ id @ X10 @ id)))) <=> (hoasinduction = $true)) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) <=> (laminj = $true)) & (! [X30 : (subst > term > subst > $o)] : ~ ! [X31 : (term > $o)] : ~ ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((axidl = $true) <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & ((induction2lem_lthm = $true) <=> (! [X35 : term,X34 : subst] : (((sub @ one @ (push @ X35 @ X34))) = X35) => (! [X37 : subst,X36 : term] : (((comp @ sh @ (push @ X36 @ X37))) = X37) => (! [X38 : subst] : (((comp @ X38 @ id)) = X38) => (! [X39 : (term > $o),X40 : term] : ((((X39 @ X40)) = $true) | ~ ! [X41 : term] : (($true = ((X39 @ X41))) | ~ (((var @ X41)) = $true)) | ~ ! [X42 : term,X43 : term] : ((((X39 @ (ap @ X42 @ X43))) = $true) | ~ (((X39 @ X43)) = $true) | ~ ($true = ((X39 @ X42)))) | ~ ! [X44 : term] : (~ ($true = ((X39 @ X44))) | ($true = ((X39 @ (lam @ X44)))))) => ! [X45 : term,X46 : (term > $o),X47 : subst] : (($true = ((X46 @ (sub @ X45 @ X47)))) | ~ ! [X48 : term,X49 : term] : (~ ($true = ((X46 @ X48))) | ~ ($true = ((X46 @ X49))) | (((X46 @ (ap @ X49 @ X48))) = $true)) | ~ ! [X50 : term] : (~ ! [X51 : term] : ((((X46 @ (sub @ X50 @ (push @ X51 @ id)))) = $true) | ~ ($true = ((X46 @ X51)))) | ($true = ((X46 @ (lam @ X50))))) | ~ ! [X52 : term] : (~ (((var @ X52)) = $true) | ($true = ((X46 @ (sub @ X52 @ X47))))))))))) & (pushprop_lthm_orig = $true) & (induction2_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56))) & ((! [X57 : term] : (((sub @ X57 @ id)) = X57) => (! [X58 : (subst > term > subst > $o),X59 : term] : ((((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X60 : term] : (~ (((X58 @ id @ X60 @ id)) = $true) | ($true = ((X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id)))) | ~ ! [X61 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id)) = $true) | ~ ! [X62 : term] : (($true = ((X58 @ id @ (X61 @ id @ X62) @ id))) | ~ (((X58 @ id @ X62 @ id)) = $true)) | ~ ! [X64 : subst,X63 : term,X65 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) = ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))))) => ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : term] : (($true = ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id))) | ~ ($true = ((X67 @ id @ X68 @ id)))) | ($true = ((X67 @ id @ (lam @ X66) @ id))) | ~ ! [X69 : (subst > term > term)] : (($true = ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id))) | ~ ! [X70 : term] : (~ (((X67 @ id @ X70 @ id)) = $true) | ($true = ((X67 @ id @ (X69 @ id @ X70) @ id)))) | ~ ! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (axapp = $true) & ((hoasinduction_lem2 = $true) <=> ! [X74 : term,X75 : term,X76 : (subst > term > subst > $o)] : (~ ($true = ((X76 @ id @ X75 @ id))) | ~ ! [X77 : term,X78 : term] : (~ (((X76 @ id @ X78 @ id)) = $true) | ($true = ((X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id))) | ~ ($true = ((X76 @ id @ X77 @ id)))) | ~ (((X76 @ id @ X74 @ id)) = $true) | ~ ! [X79 : subst,X80 : term,X81 : subst,X82 : subst] : (~ ($true = ((X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79))) | ($true = ((X76 @ X81 @ X80 @ (comp @ X82 @ X79))))) | ($true = ((X76 @ id @ (ap @ X74 @ X75) @ id))) | ~ ! [X83 : subst,X84 : subst,X85 : subst,X86 : term] : (~ ($true = ((X76 @ X84 @ X86 @ (comp @ X83 @ X85)))) | ($true = ((X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85)))))) & (! [X87 : (term > $o),X88 : term,X89 : (subst > term > subst > $o)] : (~ ! [X90 : term] : (~ (((X87 @ X90)) = $true) | (((X87 @ (sub @ X88 @ (push @ X90 @ id)))) = $true)) | ~ ! [X91 : subst,X92 : term,X93 : subst,X94 : subst] : (($true = ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93))) | ~ ($true = ((X89 @ X94 @ X92 @ (comp @ X91 @ X93))))) | ~ ! [X95 : term] : (((X87 @ X95)) = ((X89 @ id @ X95 @ id))) | ~ ! [X96 : (subst > term > term)] : (~ ! [X97 : term] : ((((X89 @ id @ (X96 @ id @ X97) @ id)) = $true) | ~ (((X89 @ id @ X97 @ id)) = $true)) | (((X89 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true) | ~ ! [X99 : subst,X100 : term,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98)))) | ($true = ((X87 @ (lam @ X88)))) | ~ ! [X101 : subst,X102 : subst,X103 : subst,X104 : term] : (~ ($true = ((X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102))) | ($true = ((X89 @ X101 @ X104 @ (comp @ X103 @ X102)))))) <=> (hoasinduction_lem3v2 = $true)) & ((induction2lem = $true) <=> ! [X105 : subst,X106 : (term > $o),X107 : term] : (~ ! [X108 : term] : (($true = ((X106 @ (lam @ X108)))) | ~ ! [X109 : term] : ((((X106 @ (sub @ X108 @ (push @ X109 @ id)))) = $true) | ~ ($true = ((X106 @ X109))))) | ~ ! [X110 : term,X111 : term] : (~ ($true = ((X106 @ X111))) | ($true = ((X106 @ (ap @ X111 @ X110)))) | ~ ($true = ((X106 @ X110)))) | ($true = ((X106 @ (sub @ X107 @ X105)))) | ~ ! [X112 : term] : (($true = ((X106 @ (sub @ X112 @ X105)))) | ~ ($true = ((var @ X112)))))) & (hoasapnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : term,X115 : term,X117 : term,X116 : term] : ((X116 = X117) | (((ap @ X116 @ X115)) != ((ap @ X117 @ X114)))) => ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_gthm = $true) & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (($true = ((X125 @ one))) | ~ ! [X126 : term] : (((X125 @ X126)) = ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ~ ($true = ((X124 @ X122)))) <=> (pushprop_lem1v2 = $true)) & ~ (((var @ (d2term @ d_one))) = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X127 : (subst > term > subst > $o),X128 : (term > $o),X129 : term,X130 : term] : (~ (((X128 @ X129)) = $true) | ~ ! [X131 : term,X132 : term] : (~ ($true = ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) | ~ ($true = ((X127 @ id @ X131 @ id)))) | ~ ! [X133 : term,X134 : subst,X135 : subst,X136 : subst] : (~ (((X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136)) = $true) | ($true = ((X127 @ X134 @ X133 @ (comp @ X135 @ X136))))) | ~ (((X128 @ X130)) = $true) | ($true = ((X128 @ (ap @ X129 @ X130)))) | ~ ! [X137 : term,X138 : subst,X139 : subst,X140 : subst] : (~ ($true = ((X127 @ X138 @ X137 @ (comp @ X139 @ X140)))) | ($true = ((X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)))) | ~ ! [X141 : term] : (((X128 @ X141)) = ((X127 @ id @ X141 @ id))))) & ! [X142 : d_term] : (d_one = X142) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X143 : term] : ~ ! [X144 : (subst > term > term)] : ~ ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145))) <=> (hoasinduction_lem3v2_f = $true)) & ((apinj1 = $true) <=> ! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X151 : term] : ~ ! [X152 : (subst > term > term)] : ~ ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153)))) & ((! [X155 : (subst > term > subst > $o)] : ~ ! [X156 : (term > $o)] : ~ ! [X157 : term] : (((X155 @ id @ X157 @ id)) = ((X156 @ X157))) => (! [X158 : term,X159 : (term > $o)] : (($true = ((X159 @ X158))) | ~ ! [X160 : term,X161 : term] : (~ ($true = ((X159 @ X160))) | ~ ($true = ((X159 @ X161))) | ($true = ((X159 @ (ap @ X160 @ X161))))) | ~ ! [X162 : term] : (($true = ((X159 @ X162))) | ~ ($true = ((var @ X162)))) | ~ ! [X163 : term] : (~ ! [X164 : term] : (~ ($true = ((X159 @ X164))) | ($true = ((X159 @ (sub @ X163 @ (push @ X164 @ id)))))) | ($true = ((X159 @ (lam @ X163)))))) => (! [X165 : term] : (((sub @ X165 @ id)) = X165) => (! [X166 : (term > $o),X167 : (subst > term > subst > $o),X168 : term] : (~ ! [X169 : (subst > term > term)] : (~ ! [X170 : term] : (~ ($true = ((X167 @ id @ X170 @ id))) | (((X167 @ id @ (X169 @ id @ X170) @ id)) = $true)) | (((X167 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ~ ! [X172 : subst,X173 : term,X171 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) = ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))) | ~ ! [X174 : term] : (($true = ((X166 @ (sub @ X168 @ (push @ X174 @ id))))) | ~ ($true = ((X166 @ X174)))) | (((X166 @ (lam @ X168))) = $true) | ~ ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id)))) => ! [X176 : term,X177 : (subst > term > subst > $o)] : ((((X177 @ id @ X176 @ id)) = $true) | ~ ! [X178 : term,X179 : term] : (~ ($true = ((X177 @ id @ X179 @ id))) | ~ (((X177 @ id @ X178 @ id)) = $true) | (((X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) = $true)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X182 : subst,X183 : term,X181 : subst] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182)))) | (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : term] : ((((X177 @ id @ (X180 @ id @ X184) @ id)) = $true) | ~ ($true = ((X177 @ id @ X184 @ id)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X187 : term,X186 : term,X188 : term,X185 : term] : ((((ap @ X186 @ X188)) != ((ap @ X185 @ X187))) | (X187 = X188)) => ! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192))) <=> (hoasapinj2_lthm = $true)) & ~ (ulamvar1 = $true) & (((d2subst @ d_id)) = sh) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> (axshiftcons = $true)) & ((! [X195 : term] : ~ ! [X196 : (subst > term > term)] : ~ ! [X198 : term,X197 : subst] : (((X196 @ X197 @ X198)) = ((sub @ X195 @ (push @ X198 @ X197)))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => ! [X200 : term,X201 : (subst > term > subst > $o),X202 : (term > $o)] : (~ ! [X203 : term] : (((X201 @ id @ X203 @ id)) = ((X202 @ X203))) | ~ ! [X204 : (subst > term > term)] : (~ ! [X206 : term,X207 : subst,X205 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205)))) | ~ ! [X208 : term] : (~ ($true = ((X201 @ id @ X208 @ id))) | (((X201 @ id @ (X204 @ id @ X208) @ id)) = $true)) | ($true = ((X201 @ id @ (lam @ (X204 @ sh @ one)) @ id)))) | (((X202 @ (lam @ X200))) = $true) | ~ ! [X209 : term] : ((((X202 @ (sub @ X200 @ (push @ X209 @ id)))) = $true) | ~ ($true = ((X202 @ X209))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) = X210) => ! [X212 : (term > $o),X213 : subst,X214 : (term > $o),X215 : term] : (~ ! [X216 : term] : (((X212 @ X216)) = ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ~ ($true = ((X214 @ X215))) | ($true = ((X212 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop = $true) & (! [X219 : subst,X217 : (term > $o),X218 : term] : ~ ! [X220 : (term > $o)] : ~ ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221))) <=> (pushprop_lem0 = $true)) & ((substmonoid = $true) <=> (! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((hoaslaminj_lthm = $true) <=> (! [X229 : subst,X230 : term] : (((sub @ one @ (push @ X230 @ X229))) = X230) => (! [X231 : term,X232 : subst] : (((comp @ sh @ (push @ X231 @ X232))) = X232) => (! [X233 : term,X234 : term] : ((X233 = X234) | (((lam @ X234)) != ((lam @ X233)))) => ! [X235 : term,X236 : (subst > term > term),X237 : subst,X238 : (subst > term > term)] : ((((X238 @ X237 @ X235)) = ((X236 @ X237 @ X235))) | ~ ! [X239 : subst,X240 : term,X241 : subst] : (((sub @ (X236 @ X239 @ X240) @ X241)) = ((X236 @ (comp @ X239 @ X241) @ (sub @ X240 @ X241)))) | ~ ! [X242 : term,X243 : subst,X244 : subst] : (((X238 @ (comp @ X244 @ X243) @ (sub @ X242 @ X243))) = ((sub @ (X238 @ X244 @ X242) @ X243))) | (((lam @ (X238 @ sh @ one))) != ((lam @ (X236 @ sh @ one))))))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X245 : term,X246 : (subst > term > subst > $o)] : (~ ! [X247 : term,X248 : term] : (~ (((X246 @ id @ X247 @ id)) = $true) | ($true = ((X246 @ id @ (ap @ (sub @ X248 @ id) @ X247) @ id))) | ~ ($true = ((X246 @ id @ X248 @ id)))) | ~ ! [X249 : (subst > term > term)] : (($true = ((X246 @ id @ (lam @ (X249 @ sh @ one)) @ id))) | ~ ! [X250 : term] : (~ ($true = ((X246 @ id @ X250 @ id))) | ($true = ((X246 @ id @ (X249 @ id @ X250) @ id)))) | ~ ! [X251 : subst,X252 : subst,X253 : term] : (((sub @ (X249 @ X252 @ X253) @ X251)) = ((X249 @ (comp @ X252 @ X251) @ (sub @ X253 @ X251))))) | ($true = ((X246 @ id @ X245 @ id))))) & (axvarshift = $true) & (axclos = $true) & (! [X254 : term] : (((sub @ X254 @ id)) = X254) <=> (axvarid = $true)) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoaslaminj = $true) <=> ! [X255 : (subst > term > term),X256 : (subst > term > term),X257 : term,X258 : subst] : (~ ! [X259 : term,X260 : subst,X261 : subst] : (((sub @ (X256 @ X261 @ X259) @ X260)) = ((X256 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260)))) | (((X255 @ X258 @ X257)) = ((X256 @ X258 @ X257))) | ~ ! [X262 : subst,X263 : subst,X264 : term] : (((sub @ (X255 @ X263 @ X264) @ X262)) = ((X255 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262)))) | (((lam @ (X255 @ sh @ one))) != ((lam @ (X256 @ sh @ one)))))) & (pushprop_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X265 : (term > $o),X266 : subst,X267 : (term > $o),X268 : term,X269 : term] : (~ ($true = ((X265 @ X269))) | ($true = ((X267 @ (sub @ X269 @ (push @ X268 @ X266))))))) & (termmset_gthm = $true) & (hoasapinj2_gthm = $true) & ((! [X270 : term] : (((sub @ X270 @ id)) = X270) => ! [X271 : term] : (((sub @ X271 @ id)) = X271)) <=> (termmset_lthm = $true)) & (one = ((d2term @ d_one))) & ((! [X272 : subst] : (((comp @ id @ X272)) = X272) => (! [X273 : subst] : (((comp @ X273 @ id)) = X273) => (! [X274 : subst] : (((comp @ X274 @ id)) = X274) & ! [X275 : subst] : (((comp @ id @ X275)) = X275)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X276 : term] : ~ ! [X277 : (subst > term > term)] : (((sub @ X276 @ (push @ one @ sh))) != ((X277 @ sh @ one)))) & (apnotvar = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem1_gthm = $true) & (! [X278 : (subst > term > subst > $o),X279 : term] : (~ ! [X280 : subst,X281 : term,X282 : subst,X283 : subst] : (~ ($true = ((X278 @ X282 @ X281 @ (comp @ X283 @ X280)))) | ($true = ((X278 @ (comp @ X282 @ X283) @ (sub @ X281 @ X283) @ X280)))) | ~ ! [X284 : (subst > term > term)] : ((((X278 @ id @ (lam @ (X284 @ sh @ one)) @ id)) = $true) | ~ ! [X285 : subst,X286 : term,X287 : subst] : (((X284 @ (comp @ X285 @ X287) @ (sub @ X286 @ X287))) = ((sub @ (X284 @ X285 @ X286) @ X287))) | ~ ! [X288 : term] : (($true = ((X278 @ id @ (X284 @ id @ X288) @ id))) | ~ ($true = ((X278 @ id @ X288 @ id))))) | (((X278 @ id @ (lam @ X279) @ id)) = $true) | ~ ! [X289 : term] : (($true = ((X278 @ id @ (sub @ X279 @ (push @ X289 @ id)) @ id))) | ~ (((X278 @ id @ X289 @ id)) = $true)) | ~ ! [X290 : term,X291 : subst,X292 : subst,X293 : subst] : ((((X278 @ X293 @ X290 @ (comp @ X292 @ X291))) = $true) | ~ ($true = ((X278 @ (comp @ X293 @ X292) @ (sub @ X290 @ X292) @ X291))))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarsh = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotvar = $true) & (substmonoid_gthm = $true) & (! [X294 : term,X295 : (subst > term > subst > $o)] : (~ ! [X296 : (subst > term > term)] : (($true = ((X295 @ id @ (lam @ (X296 @ sh @ one)) @ id))) | ~ ! [X297 : subst,X298 : term,X299 : subst] : (((X296 @ (comp @ X299 @ X297) @ (sub @ X298 @ X297))) = ((sub @ (X296 @ X299 @ X298) @ X297))) | ~ ! [X300 : term] : (~ ($true = ((X295 @ id @ X300 @ id))) | (((X295 @ id @ (X296 @ id @ X300) @ id)) = $true))) | ($true = ((X295 @ id @ (lam @ (sub @ X294 @ (push @ one @ sh))) @ id))) | ~ ! [X301 : term] : (($true = ((X295 @ id @ (sub @ X294 @ (push @ X301 @ id)) @ id))) | ~ ($true = ((X295 @ id @ X301 @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X302 : term,X303 : (subst > term > subst > $o)] : (~ ! [X304 : (subst > term > term)] : (($true = ((X303 @ id @ (lam @ (X304 @ sh @ one)) @ id))) | ~ ! [X305 : subst,X306 : subst,X307 : term] : (((sub @ (X304 @ X305 @ X307) @ X306)) = ((X304 @ (comp @ X305 @ X306) @ (sub @ X307 @ X306)))) | ~ ! [X308 : term] : (~ ($true = ((X303 @ id @ X308 @ id))) | ($true = ((X303 @ id @ (X304 @ id @ X308) @ id))))) | (((X303 @ id @ (lam @ (sub @ X302 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X309 : term] : (($true = ((X303 @ id @ (sub @ X302 @ (push @ X309 @ id)) @ id))) | ~ ($true = ((X303 @ id @ X309 @ id)))))) & ! [X310 : d_subst,X311 : d_subst] : ((((d2subst @ X310)) = ((d2subst @ X311))) => (X310 = X311)) & ((hoasinduction_lem3aaa = $true) <=> ! [X312 : (subst > term > subst > $o),X313 : term] : (~ ! [X314 : term] : (($true = ((X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id))) | ~ ($true = ((X312 @ id @ X314 @ id)))) | (((X312 @ id @ (lam @ (sub @ X313 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X315 : term,X316 : (subst > term > term)] : (~ ! [X317 : term] : ((((X312 @ id @ (X316 @ id @ X317) @ id)) = $true) | ~ ($true = ((X312 @ id @ X317 @ id)))) | ~ ! [X318 : subst,X319 : subst,X320 : term] : (((sub @ (X316 @ X319 @ X320) @ X318)) = ((sub @ (sub @ X315 @ (push @ X320 @ X319)) @ X318))) | ($true = ((X312 @ id @ (lam @ (X316 @ sh @ one)) @ id))) | ~ ! [X321 : subst,X322 : subst,X323 : term] : (((sub @ X315 @ (push @ (sub @ X323 @ X321) @ (comp @ X322 @ X321)))) = ((X316 @ (comp @ X322 @ X321) @ (sub @ X323 @ X321))))))) & (! [X324 : subst,X325 : term] : (((sub @ one @ (push @ X325 @ X324))) = X325) <=> (axvarcons = $true)) & (pushprop_lem3v2_lthm = $true) & ((! [X326 : term] : (((sub @ X326 @ id)) = X326) => ! [X327 : (subst > term > subst > $o),X328 : term,X329 : (term > $o)] : (~ ! [X330 : term] : ((((X329 @ (sub @ X328 @ (push @ X330 @ id)))) = $true) | ~ ($true = ((X329 @ X330)))) | ~ ! [X331 : subst,X332 : term,X333 : subst,X334 : subst] : (($true = ((X327 @ X333 @ X332 @ (comp @ X331 @ X334)))) | ~ (((X327 @ (comp @ X333 @ X331) @ (sub @ X332 @ X331) @ X334)) = $true)) | ~ ! [X335 : term] : (((X329 @ X335)) = ((X327 @ id @ X335 @ id))) | ($true = ((X329 @ (lam @ X328)))) | ~ ! [X336 : subst,X337 : subst,X338 : subst,X339 : term] : (($true = ((X327 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336))) | ~ ($true = ((X327 @ X338 @ X339 @ (comp @ X337 @ X336))))) | ~ ! [X340 : (subst > term > term)] : (~ ! [X341 : subst,X342 : term,X343 : subst] : (((sub @ (X340 @ X341 @ X342) @ X343)) = ((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343)))) | ~ ! [X344 : term] : (~ ($true = ((X327 @ id @ X344 @ id))) | ($true = ((X327 @ id @ (X340 @ id @ X344) @ id)))) | ($true = ((X327 @ id @ (lam @ (X340 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X345 : (term > $o),X346 : term] : (~ ! [X347 : term,X348 : term] : (~ (((X345 @ X348)) = $true) | (((X345 @ (ap @ X348 @ X347))) = $true) | ~ (((X345 @ X347)) = $true)) | ~ ! [X349 : term] : (~ ($true = ((var @ X349))) | ($true = ((X345 @ X349)))) | ~ ! [X350 : term] : (~ ($true = ((X345 @ X350))) | ($true = ((X345 @ (lam @ X350))))) | ($true = ((X345 @ X346)))) <=> (induction = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X353 : (subst > term > term),X354 : term,X355 : term] : ((((ap @ (sub @ X355 @ id) @ X354)) != ((lam @ (X353 @ sh @ one)))) | ~ ! [X356 : subst,X357 : subst,X358 : term] : (((X353 @ (comp @ X357 @ X356) @ (sub @ X358 @ X356))) = ((sub @ (X353 @ X357 @ X358) @ X356)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem1v2_gthm = $true) & ! [X359 : d_term,X360 : d_term] : ((((d2term @ X359)) = ((d2term @ X360))) => (X359 = X360)) & (axassoc = $true) & ((induction2_lthm = $true) <=> (! [X361 : term] : (((sub @ X361 @ id)) = X361) => (! [X362 : term,X363 : subst,X364 : (term > $o)] : (~ ! [X365 : term] : ((((X364 @ (sub @ X365 @ X363))) = $true) | ~ ($true = ((var @ X365)))) | (((X364 @ (sub @ X362 @ X363))) = $true) | ~ ! [X366 : term] : (~ ! [X367 : term] : (~ (((X364 @ X367)) = $true) | ($true = ((X364 @ (sub @ X366 @ (push @ X367 @ id)))))) | (((X364 @ (lam @ X366))) = $true)) | ~ ! [X368 : term,X369 : term] : (~ ($true = ((X364 @ X368))) | ($true = ((X364 @ (ap @ X368 @ X369)))) | ~ ($true = ((X364 @ X369))))) => ! [X370 : term,X371 : (term > $o)] : (~ ! [X372 : term] : (~ ($true = ((var @ X372))) | ($true = ((X371 @ X372)))) | ~ ! [X373 : term,X374 : term] : (~ (((X371 @ X374)) = $true) | ($true = ((X371 @ (ap @ X373 @ X374)))) | ~ ($true = ((X371 @ X373)))) | ~ ! [X375 : term] : (~ ! [X376 : term] : (($true = ((X371 @ (sub @ X375 @ (push @ X376 @ id))))) | ~ ($true = ((X371 @ X376)))) | ($true = ((X371 @ (lam @ X375))))) | ($true = ((X371 @ X370))))))) & (hoasapinj1_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X377 : (term > $o),X378 : term,X379 : subst] : ~ ! [X380 : (term > $o)] : ~ ! [X381 : term] : (((X380 @ X381)) = ((X377 @ (sub @ X381 @ (push @ X378 @ X379)))))) & (! [X382 : (term > $o),X383 : term] : ((((X382 @ X383)) = $true) | ~ ! [X384 : term] : (~ ($true = ((var @ X384))) | ($true = ((X382 @ X384)))) | ~ ! [X385 : term,X386 : term] : (~ ($true = ((X382 @ X386))) | ($true = ((X382 @ (ap @ X385 @ X386)))) | ~ (((X382 @ X385)) = $true)) | ~ ! [X387 : term] : ((((X382 @ (lam @ X387))) = $true) | ~ ! [X388 : term] : (~ ($true = ((X382 @ X388))) | ($true = ((X382 @ (sub @ X387 @ (push @ X388 @ id)))))))) <=> (induction2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X389 : term,X390 : term] : ((X389 = X390) | (((sub @ X389 @ sh)) != ((sub @ X390 @ sh)))) <=> (shinj = $true)) & (hoaslamnotap_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem3v2 = $true) & (lamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ~ (lamnotap = $true) & (pushprop_lem2v2 = $true) & (hoasapnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) <=> (! [X394 : term,X395 : (term > $o)] : (~ ! [X396 : term,X397 : term] : (~ (((X395 @ X397)) = $true) | ($true = ((X395 @ (ap @ X396 @ X397)))) | ~ (((X395 @ X396)) = $true)) | ($true = ((X395 @ X394))) | ~ ! [X398 : term] : (~ ! [X399 : term] : (~ ($true = ((X395 @ X399))) | ($true = ((X395 @ (sub @ X398 @ (push @ X399 @ id)))))) | ($true = ((X395 @ (lam @ X398))))) | ~ ! [X400 : term] : ((((X395 @ X400)) = $true) | ~ (((var @ X400)) = $true))) => (! [X401 : (subst > term > subst > $o),X402 : term,X403 : term] : ((((X401 @ id @ (ap @ X402 @ X403) @ id)) = $true) | ~ ! [X404 : term,X405 : term] : (~ (((X401 @ id @ X405 @ id)) = $true) | (((X401 @ id @ (ap @ (sub @ X405 @ id) @ X404) @ id)) = $true) | ~ ($true = ((X401 @ id @ X404 @ id)))) | ~ (((X401 @ id @ X402 @ id)) = $true) | ~ ($true = ((X401 @ id @ X403 @ id))) | ~ ! [X406 : term,X407 : subst,X408 : subst,X409 : subst] : ((((X401 @ (comp @ X407 @ X409) @ (sub @ X406 @ X409) @ X408)) = $true) | ~ ($true = ((X401 @ X407 @ X406 @ (comp @ X409 @ X408))))) | ~ ! [X410 : term,X411 : subst,X412 : subst,X413 : subst] : ((((X401 @ X413 @ X410 @ (comp @ X412 @ X411))) = $true) | ~ ($true = ((X401 @ (comp @ X413 @ X412) @ (sub @ X410 @ X412) @ X411))))) => (! [X414 : (subst > term > subst > $o),X415 : term] : (~ ! [X416 : (subst > term > term)] : (~ ! [X417 : term] : (($true = ((X414 @ id @ (X416 @ id @ X417) @ id))) | ~ (((X414 @ id @ X417 @ id)) = $true)) | (((X414 @ id @ (lam @ (X416 @ sh @ one)) @ id)) = $true) | ~ ! [X418 : term,X419 : subst,X420 : subst] : (((sub @ (X416 @ X420 @ X418) @ X419)) = ((X416 @ (comp @ X420 @ X419) @ (sub @ X418 @ X419))))) | ~ ! [X421 : subst,X422 : subst,X423 : subst,X424 : term] : (($true = ((X414 @ X421 @ X424 @ (comp @ X423 @ X422)))) | ~ (((X414 @ (comp @ X421 @ X423) @ (sub @ X424 @ X423) @ X422)) = $true)) | ~ ! [X425 : term] : (~ (((X414 @ id @ X425 @ id)) = $true) | ($true = ((X414 @ id @ (sub @ X415 @ (push @ X425 @ id)) @ id)))) | ~ ! [X426 : subst,X427 : subst,X428 : subst,X429 : term] : (~ ($true = ((X414 @ X427 @ X429 @ (comp @ X428 @ X426)))) | ($true = ((X414 @ (comp @ X427 @ X428) @ (sub @ X429 @ X428) @ X426)))) | (((X414 @ id @ (lam @ X415) @ id)) = $true)) => ! [X430 : term,X431 : (subst > term > subst > $o)] : (~ ! [X432 : term] : (~ ($true = ((var @ (sub @ X432 @ id)))) | ($true = ((X431 @ id @ X432 @ id)))) | ~ ! [X433 : term,X434 : term] : (~ ($true = ((X431 @ id @ X434 @ id))) | ($true = ((X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id))) | ~ ($true = ((X431 @ id @ X433 @ id)))) | ($true = ((X431 @ id @ X430 @ id))) | ~ ! [X435 : subst,X436 : subst,X437 : subst,X438 : term] : ((((X431 @ X435 @ X438 @ (comp @ X436 @ X437))) = $true) | ~ (((X431 @ (comp @ X435 @ X436) @ (sub @ X438 @ X436) @ X437)) = $true)) | ~ ! [X439 : subst,X440 : subst,X441 : subst,X442 : term] : (($true = ((X431 @ (comp @ X440 @ X441) @ (sub @ X442 @ X441) @ X439))) | ~ (((X431 @ X440 @ X442 @ (comp @ X441 @ X439))) = $true)) | ~ ! [X443 : (subst > term > term)] : (~ ! [X444 : subst,X445 : term,X446 : subst] : (((sub @ (X443 @ X444 @ X445) @ X446)) = ((X443 @ (comp @ X444 @ X446) @ (sub @ X445 @ X446)))) | ~ ! [X447 : term] : (~ (((X431 @ id @ X447 @ id)) = $true) | (((X431 @ id @ (X443 @ id @ X447) @ id)) = $true)) | (((X431 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true))))))) & ((! [X448 : (subst > term > subst > $o)] : ~ ! [X449 : (term > $o)] : ~ ! [X450 : term] : (((X449 @ X450)) = ((X448 @ id @ X450 @ id))) => (! [X451 : term,X452 : (term > $o)] : (($true = ((X452 @ X451))) | ~ ! [X453 : term] : (~ ! [X454 : term] : (~ (((X452 @ X454)) = $true) | ($true = ((X452 @ (sub @ X453 @ (push @ X454 @ id)))))) | ($true = ((X452 @ (lam @ X453))))) | ~ ! [X455 : term,X456 : term] : (~ (((X452 @ X456)) = $true) | (((X452 @ (ap @ X456 @ X455))) = $true) | ~ ($true = ((X452 @ X455)))) | ~ ! [X457 : term] : (~ ($true = ((var @ X457))) | (((X452 @ X457)) = $true))) => (! [X458 : term] : (((sub @ X458 @ id)) = X458) => (! [X459 : term,X460 : (term > $o),X461 : (subst > term > subst > $o)] : (~ ! [X462 : term] : (((X461 @ id @ X462 @ id)) = ((X460 @ X462))) | ~ ! [X463 : term] : (($true = ((X460 @ (sub @ X459 @ (push @ X463 @ id))))) | ~ ($true = ((X460 @ X463)))) | ($true = ((X460 @ (lam @ X459)))) | ~ ! [X464 : (subst > term > term)] : (~ ! [X465 : term] : (($true = ((X461 @ id @ (X464 @ id @ X465) @ id))) | ~ ($true = ((X461 @ id @ X465 @ id)))) | (((X461 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))) = ((sub @ (X464 @ X466 @ X467) @ X468))))) => ! [X469 : (subst > term > subst > $o),X470 : term] : (~ ! [X471 : (subst > term > term)] : ((((X469 @ id @ (lam @ (X471 @ sh @ one)) @ id)) = $true) | ~ ! [X472 : term] : (($true = ((X469 @ id @ (X471 @ id @ X472) @ id))) | ~ ($true = ((X469 @ id @ X472 @ id)))) | ~ ! [X473 : subst,X474 : subst,X475 : term] : (((X471 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473))) = ((sub @ (X471 @ X474 @ X475) @ X473)))) | ~ ! [X476 : term] : (($true = ((X469 @ id @ X476 @ id))) | ~ ($true = ((var @ (sub @ X476 @ id))))) | ~ ! [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((((X469 @ (comp @ X478 @ X479) @ (sub @ X477 @ X479) @ X480)) = $true) | ~ ($true = ((X469 @ X478 @ X477 @ (comp @ X479 @ X480))))) | ($true = ((X469 @ id @ X470 @ id))) | ~ ! [X481 : term,X482 : term] : (~ (((X469 @ id @ X482 @ id)) = $true) | ~ (((X469 @ id @ X481 @ id)) = $true) | (((X469 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id)) = $true)) | ~ ! [X483 : subst,X484 : subst,X485 : subst,X486 : term] : (($true = ((X469 @ X485 @ X486 @ (comp @ X483 @ X484)))) | ~ ($true = ((X469 @ (comp @ X485 @ X483) @ (sub @ X486 @ X483) @ X484))))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X487 : term] : (((sub @ X487 @ id)) = X487) => (! [X488 : term,X489 : (subst > term > subst > $o)] : (($true = ((X489 @ id @ (lam @ (sub @ X488 @ (push @ one @ sh))) @ id))) | ~ ! [X490 : term] : (($true = ((X489 @ id @ (sub @ X488 @ (push @ X490 @ id)) @ id))) | ~ (((X489 @ id @ X490 @ id)) = $true)) | ~ ! [X491 : (subst > term > term)] : (~ ! [X492 : term] : ((((X489 @ id @ (X491 @ id @ X492) @ id)) = $true) | ~ (((X489 @ id @ X492 @ id)) = $true)) | ~ ! [X493 : subst,X494 : subst,X495 : term] : (((sub @ (X491 @ X493 @ X495) @ X494)) = ((X491 @ (comp @ X493 @ X494) @ (sub @ X495 @ X494)))) | ($true = ((X489 @ id @ (lam @ (X491 @ sh @ one)) @ id))))) => ! [X496 : term,X497 : (subst > term > subst > $o)] : (($true = ((X497 @ id @ (lam @ X496) @ id))) | ~ ! [X498 : subst,X499 : subst,X500 : term,X501 : subst] : (~ ($true = ((X497 @ X498 @ X500 @ (comp @ X501 @ X499)))) | ($true = ((X497 @ (comp @ X498 @ X501) @ (sub @ X500 @ X501) @ X499)))) | ~ ! [X502 : term,X503 : subst,X504 : subst,X505 : subst] : (~ ($true = ((X497 @ (comp @ X505 @ X504) @ (sub @ X502 @ X504) @ X503))) | (((X497 @ X505 @ X502 @ (comp @ X504 @ X503))) = $true)) | ~ ! [X506 : term] : (($true = ((X497 @ id @ (sub @ X496 @ (push @ X506 @ id)) @ id))) | ~ ($true = ((X497 @ id @ X506 @ id)))) | ~ ! [X507 : (subst > term > term)] : (~ ! [X508 : term] : (($true = ((X497 @ id @ (X507 @ id @ X508) @ id))) | ~ (((X497 @ id @ X508 @ id)) = $true)) | ($true = ((X497 @ id @ (lam @ (X507 @ sh @ one)) @ id))) | ~ ! [X509 : subst,X510 : subst,X511 : term] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) = ((sub @ (X507 @ X509 @ X511) @ X510)))))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X512 : term] : ~ ! [X513 : (subst > term > term)] : (((X513 @ sh @ one)) != ((sub @ X512 @ (push @ one @ sh))))) & ((apinj2 = $true) <=> ! [X514 : term,X515 : term,X516 : term,X517 : term] : ((X514 = X515) | (((ap @ X516 @ X514)) != ((ap @ X517 @ X515))))) & (! [X518 : subst] : (((push @ (sub @ one @ X518) @ (comp @ sh @ X518))) = X518) <=> (axscons = $true)) & ! [X519 : term] : ? [X520 : d_term] : (((d2term @ X520)) = X519) & ! [X521 : d_subst] : (d_id = X521) & (! [X522 : (subst > term > subst > $o),X523 : term,X524 : (term > $o)] : ((((X524 @ (lam @ X523))) = $true) | ~ ! [X525 : (subst > term > term)] : (~ ! [X526 : subst,X527 : subst,X528 : term] : (((sub @ (X525 @ X527 @ X528) @ X526)) = ((X525 @ (comp @ X527 @ X526) @ (sub @ X528 @ X526)))) | ($true = ((X522 @ id @ (lam @ (X525 @ sh @ one)) @ id))) | ~ ! [X529 : term] : (~ ($true = ((X522 @ id @ X529 @ id))) | ($true = ((X522 @ id @ (X525 @ id @ X529) @ id))))) | ~ ! [X530 : term] : (((X524 @ X530)) = ((X522 @ id @ X530 @ id))) | ~ ! [X531 : term] : (($true = ((X524 @ (sub @ X523 @ (push @ X531 @ id))))) | ~ (((X524 @ X531)) = $true))) <=> (hoasinduction_lem3v2a = $true)) & ((termmset = $true) <=> ! [X532 : term] : (((sub @ X532 @ id)) = X532)) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & (! [X533 : term,X534 : (subst > term > subst > $o)] : (~ ! [X535 : term] : ((((X534 @ id @ (sub @ X533 @ (push @ X535 @ id)) @ id)) = $true) | ~ ($true = ((X534 @ id @ X535 @ id)))) | ~ ! [X536 : (subst > term > term)] : ((((X534 @ id @ (lam @ (X536 @ sh @ one)) @ id)) = $true) | ~ ! [X537 : term] : ((((X534 @ id @ (X536 @ id @ X537) @ id)) = $true) | ~ ($true = ((X534 @ id @ X537 @ id)))) | ~ ! [X538 : subst,X539 : term,X540 : subst] : (((X536 @ (comp @ X538 @ X540) @ (sub @ X539 @ X540))) = ((sub @ (X536 @ X538 @ X539) @ X540)))) | (((X534 @ id @ (lam @ X533) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & ! [X541 : subst] : ? [X542 : d_subst] : (((d2subst @ X542)) = X541) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X543 : (subst > term > subst > $o)] : ~ ! [X544 : (term > $o)] : ~ ! [X545 : term] : (((X544 @ X545)) = ((X543 @ id @ X545 @ id)))) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = id) & ((hoasapinj2 = $true) <=> ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X548 = X549) | (((ap @ (sub @ X547 @ id) @ X549)) != ((ap @ (sub @ X546 @ id) @ X548)))))),
% 6.46/1.22 inference(fool_elimination,[],[f6])).
% 6.46/1.22 thf(f8,plain,(
% 6.46/1.22 (hoasinduction_lem3a != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))),
% 6.46/1.22 inference(flattening,[],[f5])).
% 6.46/1.22 thf(f9,plain,(
% 6.46/1.22 (hoasinduction_lem3_gthm = $true) & ((axidr = $true) <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & (ulamvarind = $true) & (hoasinduction_lem1 = $true) & ((! [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) = X1) => (! [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) = X4) => ! [X5 : term,X6 : subst,X7 : term,X8 : (term > $o),X9 : (term > $o)] : (~ (((X9 @ X5)) = $true) | (((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X10 : term,X11 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (($true = ((X11 @ id @ X12 @ id))) | ~ (((var @ (sub @ X12 @ id))) = $true)) | ~ ! [X13 : subst,X14 : term,X15 : subst,X16 : subst] : (~ (((X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15)) = $true) | (((X11 @ X13 @ X14 @ (comp @ X16 @ X15))) = $true)) | ~ ! [X17 : term,X18 : term] : (~ ($true = ((X11 @ id @ X17 @ id))) | ($true = ((X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id))) | ~ (((X11 @ id @ X18 @ id)) = $true)) | ~ ! [X19 : (subst > term > term)] : (~ ! [X20 : term] : ((((X11 @ id @ (X19 @ id @ X20) @ id)) = $true) | ~ ($true = ((X11 @ id @ X20 @ id)))) | (((X11 @ id @ (lam @ (X19 @ sh @ one)) @ id)) = $true) | ~ ! [X23 : subst,X22 : subst,X21 : term] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22))))) | ~ ! [X24 : term,X25 : subst,X26 : subst,X27 : subst] : (~ (((X11 @ X27 @ X24 @ (comp @ X26 @ X25))) = $true) | ($true = ((X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25)))) | ($true = ((X11 @ id @ X10 @ id)))) <=> (hoasinduction = $true)) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) <=> (laminj = $true)) & (! [X30 : (subst > term > subst > $o)] : ~ ! [X31 : (term > $o)] : ~ ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((axidl = $true) <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & ((induction2lem_lthm = $true) <=> (! [X35 : term,X34 : subst] : (((sub @ one @ (push @ X35 @ X34))) = X35) => (! [X37 : subst,X36 : term] : (((comp @ sh @ (push @ X36 @ X37))) = X37) => (! [X38 : subst] : (((comp @ X38 @ id)) = X38) => (! [X39 : (term > $o),X40 : term] : ((((X39 @ X40)) = $true) | ~ ! [X41 : term] : (($true = ((X39 @ X41))) | ~ (((var @ X41)) = $true)) | ~ ! [X42 : term,X43 : term] : ((((X39 @ (ap @ X42 @ X43))) = $true) | ~ (((X39 @ X43)) = $true) | ~ ($true = ((X39 @ X42)))) | ~ ! [X44 : term] : (~ ($true = ((X39 @ X44))) | ($true = ((X39 @ (lam @ X44)))))) => ! [X45 : term,X46 : (term > $o),X47 : subst] : (($true = ((X46 @ (sub @ X45 @ X47)))) | ~ ! [X48 : term,X49 : term] : (~ ($true = ((X46 @ X48))) | ~ ($true = ((X46 @ X49))) | (((X46 @ (ap @ X49 @ X48))) = $true)) | ~ ! [X50 : term] : (~ ! [X51 : term] : ((((X46 @ (sub @ X50 @ (push @ X51 @ id)))) = $true) | ~ ($true = ((X46 @ X51)))) | ($true = ((X46 @ (lam @ X50))))) | ~ ! [X52 : term] : (~ (((var @ X52)) = $true) | ($true = ((X46 @ (sub @ X52 @ X47))))))))))) & (pushprop_lthm_orig = $true) & (induction2_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56))) & ((! [X57 : term] : (((sub @ X57 @ id)) = X57) => (! [X58 : (subst > term > subst > $o),X59 : term] : ((((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X60 : term] : (~ (((X58 @ id @ X60 @ id)) = $true) | ($true = ((X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id)))) | ~ ! [X61 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id)) = $true) | ~ ! [X62 : term] : (($true = ((X58 @ id @ (X61 @ id @ X62) @ id))) | ~ (((X58 @ id @ X62 @ id)) = $true)) | ~ ! [X64 : subst,X63 : term,X65 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) = ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))))) => ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : term] : (($true = ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id))) | ~ ($true = ((X67 @ id @ X68 @ id)))) | ($true = ((X67 @ id @ (lam @ X66) @ id))) | ~ ! [X69 : (subst > term > term)] : (($true = ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id))) | ~ ! [X70 : term] : (~ (((X67 @ id @ X70 @ id)) = $true) | ($true = ((X67 @ id @ (X69 @ id @ X70) @ id)))) | ~ ! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (axapp = $true) & ((hoasinduction_lem2 = $true) <=> ! [X74 : term,X75 : term,X76 : (subst > term > subst > $o)] : (~ ($true = ((X76 @ id @ X75 @ id))) | ~ ! [X77 : term,X78 : term] : (~ (((X76 @ id @ X78 @ id)) = $true) | ($true = ((X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id))) | ~ ($true = ((X76 @ id @ X77 @ id)))) | ~ (((X76 @ id @ X74 @ id)) = $true) | ~ ! [X79 : subst,X80 : term,X81 : subst,X82 : subst] : (~ ($true = ((X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79))) | ($true = ((X76 @ X81 @ X80 @ (comp @ X82 @ X79))))) | ($true = ((X76 @ id @ (ap @ X74 @ X75) @ id))) | ~ ! [X83 : subst,X84 : subst,X85 : subst,X86 : term] : (~ ($true = ((X76 @ X84 @ X86 @ (comp @ X83 @ X85)))) | ($true = ((X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85)))))) & (! [X87 : (term > $o),X88 : term,X89 : (subst > term > subst > $o)] : (~ ! [X90 : term] : (~ (((X87 @ X90)) = $true) | (((X87 @ (sub @ X88 @ (push @ X90 @ id)))) = $true)) | ~ ! [X91 : subst,X92 : term,X93 : subst,X94 : subst] : (($true = ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93))) | ~ ($true = ((X89 @ X94 @ X92 @ (comp @ X91 @ X93))))) | ~ ! [X95 : term] : (((X87 @ X95)) = ((X89 @ id @ X95 @ id))) | ~ ! [X96 : (subst > term > term)] : (~ ! [X97 : term] : ((((X89 @ id @ (X96 @ id @ X97) @ id)) = $true) | ~ (((X89 @ id @ X97 @ id)) = $true)) | (((X89 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true) | ~ ! [X99 : subst,X100 : term,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98)))) | ($true = ((X87 @ (lam @ X88)))) | ~ ! [X101 : subst,X102 : subst,X103 : subst,X104 : term] : (~ ($true = ((X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102))) | ($true = ((X89 @ X101 @ X104 @ (comp @ X103 @ X102)))))) <=> (hoasinduction_lem3v2 = $true)) & ((induction2lem = $true) <=> ! [X105 : subst,X106 : (term > $o),X107 : term] : (~ ! [X108 : term] : (($true = ((X106 @ (lam @ X108)))) | ~ ! [X109 : term] : ((((X106 @ (sub @ X108 @ (push @ X109 @ id)))) = $true) | ~ ($true = ((X106 @ X109))))) | ~ ! [X110 : term,X111 : term] : (~ ($true = ((X106 @ X111))) | ($true = ((X106 @ (ap @ X111 @ X110)))) | ~ ($true = ((X106 @ X110)))) | ($true = ((X106 @ (sub @ X107 @ X105)))) | ~ ! [X112 : term] : (($true = ((X106 @ (sub @ X112 @ X105)))) | ~ ($true = ((var @ X112)))))) & (hoasapnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : term,X115 : term,X117 : term,X116 : term] : ((X116 = X117) | (((ap @ X116 @ X115)) != ((ap @ X117 @ X114)))) => ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_gthm = $true) & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (($true = ((X125 @ one))) | ~ ! [X126 : term] : (((X125 @ X126)) = ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ~ ($true = ((X124 @ X122)))) <=> (pushprop_lem1v2 = $true)) & ~ (((var @ (d2term @ d_one))) = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X127 : (subst > term > subst > $o),X128 : (term > $o),X129 : term,X130 : term] : (~ (((X128 @ X129)) = $true) | ~ ! [X131 : term,X132 : term] : (~ ($true = ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) | ~ ($true = ((X127 @ id @ X131 @ id)))) | ~ ! [X133 : term,X134 : subst,X135 : subst,X136 : subst] : (~ (((X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136)) = $true) | ($true = ((X127 @ X134 @ X133 @ (comp @ X135 @ X136))))) | ~ (((X128 @ X130)) = $true) | ($true = ((X128 @ (ap @ X129 @ X130)))) | ~ ! [X137 : term,X138 : subst,X139 : subst,X140 : subst] : (~ ($true = ((X127 @ X138 @ X137 @ (comp @ X139 @ X140)))) | ($true = ((X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)))) | ~ ! [X141 : term] : (((X128 @ X141)) = ((X127 @ id @ X141 @ id))))) & ! [X142 : d_term] : (d_one = X142) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X143 : term] : ~ ! [X144 : (subst > term > term)] : ~ ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145))) <=> (hoasinduction_lem3v2_f = $true)) & ((apinj1 = $true) <=> ! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X151 : term] : ~ ! [X152 : (subst > term > term)] : ~ ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153)))) & ((! [X155 : (subst > term > subst > $o)] : ~ ! [X156 : (term > $o)] : ~ ! [X157 : term] : (((X155 @ id @ X157 @ id)) = ((X156 @ X157))) => (! [X158 : term,X159 : (term > $o)] : (($true = ((X159 @ X158))) | ~ ! [X160 : term,X161 : term] : (~ ($true = ((X159 @ X160))) | ~ ($true = ((X159 @ X161))) | ($true = ((X159 @ (ap @ X160 @ X161))))) | ~ ! [X162 : term] : (($true = ((X159 @ X162))) | ~ ($true = ((var @ X162)))) | ~ ! [X163 : term] : (~ ! [X164 : term] : (~ ($true = ((X159 @ X164))) | ($true = ((X159 @ (sub @ X163 @ (push @ X164 @ id)))))) | ($true = ((X159 @ (lam @ X163)))))) => (! [X165 : term] : (((sub @ X165 @ id)) = X165) => (! [X166 : (term > $o),X167 : (subst > term > subst > $o),X168 : term] : (~ ! [X169 : (subst > term > term)] : (~ ! [X170 : term] : (~ ($true = ((X167 @ id @ X170 @ id))) | (((X167 @ id @ (X169 @ id @ X170) @ id)) = $true)) | (((X167 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ~ ! [X172 : subst,X173 : term,X171 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) = ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))) | ~ ! [X174 : term] : (($true = ((X166 @ (sub @ X168 @ (push @ X174 @ id))))) | ~ ($true = ((X166 @ X174)))) | (((X166 @ (lam @ X168))) = $true) | ~ ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id)))) => ! [X176 : term,X177 : (subst > term > subst > $o)] : ((((X177 @ id @ X176 @ id)) = $true) | ~ ! [X178 : term,X179 : term] : (~ ($true = ((X177 @ id @ X179 @ id))) | ~ (((X177 @ id @ X178 @ id)) = $true) | (((X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) = $true)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X182 : subst,X183 : term,X181 : subst] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182)))) | (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : term] : ((((X177 @ id @ (X180 @ id @ X184) @ id)) = $true) | ~ ($true = ((X177 @ id @ X184 @ id)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((! [X187 : term,X186 : term,X188 : term,X185 : term] : ((((ap @ X186 @ X188)) != ((ap @ X185 @ X187))) | (X187 = X188)) => ! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192))) <=> (hoasapinj2_lthm = $true)) & ~ (ulamvar1 = $true) & (((d2subst @ d_id)) = sh) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> (axshiftcons = $true)) & ((! [X195 : term] : ~ ! [X196 : (subst > term > term)] : ~ ! [X198 : term,X197 : subst] : (((X196 @ X197 @ X198)) = ((sub @ X195 @ (push @ X198 @ X197)))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => ! [X200 : term,X201 : (subst > term > subst > $o),X202 : (term > $o)] : (~ ! [X203 : term] : (((X201 @ id @ X203 @ id)) = ((X202 @ X203))) | ~ ! [X204 : (subst > term > term)] : (~ ! [X206 : term,X207 : subst,X205 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205)))) | ~ ! [X208 : term] : (~ ($true = ((X201 @ id @ X208 @ id))) | (((X201 @ id @ (X204 @ id @ X208) @ id)) = $true)) | ($true = ((X201 @ id @ (lam @ (X204 @ sh @ one)) @ id)))) | (((X202 @ (lam @ X200))) = $true) | ~ ! [X209 : term] : ((((X202 @ (sub @ X200 @ (push @ X209 @ id)))) = $true) | ~ ($true = ((X202 @ X209))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((! [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) = X210) => ! [X212 : (term > $o),X213 : subst,X214 : (term > $o),X215 : term] : (~ ! [X216 : term] : (((X212 @ X216)) = ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ~ ($true = ((X214 @ X215))) | ($true = ((X212 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop = $true) & (! [X219 : subst,X217 : (term > $o),X218 : term] : ~ ! [X220 : (term > $o)] : ~ ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221))) <=> (pushprop_lem0 = $true)) & ((substmonoid = $true) <=> (! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((hoaslaminj_lthm = $true) <=> (! [X224 : subst,X225 : term] : (((sub @ one @ (push @ X225 @ X224))) = X225) => (! [X227 : subst,X226 : term] : (((comp @ sh @ (push @ X226 @ X227))) = X227) => (! [X228 : term,X229 : term] : ((((lam @ X228)) != ((lam @ X229))) | (X228 = X229)) => ! [X233 : (subst > term > term),X232 : subst,X231 : (subst > term > term),X230 : term] : (~ ! [X236 : subst,X234 : subst,X235 : term] : (((X231 @ (comp @ X234 @ X236) @ (sub @ X235 @ X236))) = ((sub @ (X231 @ X234 @ X235) @ X236))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X231 @ sh @ one)))) | (((X231 @ X232 @ X230)) = ((X233 @ X232 @ X230))) | ~ ! [X237 : term,X239 : subst,X238 : subst] : (((sub @ (X233 @ X239 @ X237) @ X238)) = ((X233 @ (comp @ X239 @ X238) @ (sub @ X237 @ X238))))))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X240 : term,X241 : (subst > term > subst > $o)] : (~ ! [X242 : term,X243 : term] : (~ ($true = ((X241 @ id @ X242 @ id))) | ($true = ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) | ~ ($true = ((X241 @ id @ X243 @ id)))) | ~ ! [X244 : (subst > term > term)] : (($true = ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id))) | ~ ! [X245 : term] : (~ ($true = ((X241 @ id @ X245 @ id))) | (((X241 @ id @ (X244 @ id @ X245) @ id)) = $true)) | ~ ! [X246 : subst,X247 : subst,X248 : term] : (((sub @ (X244 @ X247 @ X248) @ X246)) = ((X244 @ (comp @ X247 @ X246) @ (sub @ X248 @ X246))))) | ($true = ((X241 @ id @ X240 @ id))))) & (axvarshift = $true) & (axclos = $true) & ((axvarid = $true) <=> ! [X249 : term] : (((sub @ X249 @ id)) = X249)) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoaslaminj = $true) <=> ! [X253 : subst,X250 : (subst > term > term),X252 : term,X251 : (subst > term > term)] : ((((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252))) | ~ ! [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) = ((sub @ (X250 @ X258 @ X259) @ X257))) | (((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ~ ! [X255 : subst,X254 : term,X256 : subst] : (((sub @ (X251 @ X256 @ X254) @ X255)) = ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))))) & (pushprop_gthm = $true) & ((pushprop_lem1 = $true) <=> ! [X260 : (term > $o),X261 : subst,X262 : (term > $o),X263 : term,X264 : term] : (~ ($true = ((X260 @ X264))) | ($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))))) & (termmset_gthm = $true) & (hoasapinj2_gthm = $true) & ((! [X265 : term] : (((sub @ X265 @ id)) = X265) => ! [X266 : term] : (((sub @ X266 @ id)) = X266)) <=> (termmset_lthm = $true)) & (one = ((d2term @ d_one))) & ((! [X267 : subst] : (((comp @ id @ X267)) = X267) => (! [X268 : subst] : (((comp @ X268 @ id)) = X268) => (! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)))) <=> (substmonoid_lthm = $true)) & (! [X271 : term] : ~ ! [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) != ((X272 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (apnotvar = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem1_gthm = $true) & (! [X273 : (subst > term > subst > $o),X274 : term] : (~ ! [X275 : subst,X276 : term,X277 : subst,X278 : subst] : (~ ($true = ((X273 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X273 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275)))) | ~ ! [X279 : (subst > term > term)] : ((((X273 @ id @ (lam @ (X279 @ sh @ one)) @ id)) = $true) | ~ ! [X280 : subst,X282 : subst,X281 : term] : (((sub @ (X279 @ X280 @ X281) @ X282)) = ((X279 @ (comp @ X280 @ X282) @ (sub @ X281 @ X282)))) | ~ ! [X283 : term] : ((((X273 @ id @ (X279 @ id @ X283) @ id)) = $true) | ~ (((X273 @ id @ X283 @ id)) = $true))) | ($true = ((X273 @ id @ (lam @ X274) @ id))) | ~ ! [X284 : term] : (($true = ((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id))) | ~ ($true = ((X273 @ id @ X284 @ id)))) | ~ ! [X285 : term,X286 : subst,X287 : subst,X288 : subst] : (($true = ((X273 @ X288 @ X285 @ (comp @ X287 @ X286)))) | ~ (((X273 @ (comp @ X288 @ X287) @ (sub @ X285 @ X287) @ X286)) = $true))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarsh = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotvar = $true) & (substmonoid_gthm = $true) & (! [X289 : term,X290 : (subst > term > subst > $o)] : (~ ! [X291 : (subst > term > term)] : ((((X290 @ id @ (lam @ (X291 @ sh @ one)) @ id)) = $true) | ~ ! [X292 : subst,X294 : subst,X293 : term] : (((sub @ (X291 @ X294 @ X293) @ X292)) = ((X291 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292)))) | ~ ! [X295 : term] : (~ (((X290 @ id @ X295 @ id)) = $true) | ($true = ((X290 @ id @ (X291 @ id @ X295) @ id))))) | (((X290 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X296 : term] : ((((X290 @ id @ (sub @ X289 @ (push @ X296 @ id)) @ id)) = $true) | ~ (((X290 @ id @ X296 @ id)) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X297 : term,X298 : (subst > term > subst > $o)] : (~ ! [X299 : (subst > term > term)] : ((((X298 @ id @ (lam @ (X299 @ sh @ one)) @ id)) = $true) | ~ ! [X302 : term,X301 : subst,X300 : subst] : (((sub @ (X299 @ X300 @ X302) @ X301)) = ((X299 @ (comp @ X300 @ X301) @ (sub @ X302 @ X301)))) | ~ ! [X303 : term] : (~ ($true = ((X298 @ id @ X303 @ id))) | (((X298 @ id @ (X299 @ id @ X303) @ id)) = $true))) | ($true = ((X298 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id))) | ~ ! [X304 : term] : (($true = ((X298 @ id @ (sub @ X297 @ (push @ X304 @ id)) @ id))) | ~ (((X298 @ id @ X304 @ id)) = $true)))) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) = ((d2subst @ X305))) => (X305 = X306)) & ((hoasinduction_lem3aaa = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : (~ ! [X309 : term] : (($true = ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id))) | ~ ($true = ((X307 @ id @ X309 @ id)))) | (((X307 @ id @ (lam @ (sub @ X308 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X310 : term,X311 : (subst > term > term)] : (~ ! [X312 : term] : (($true = ((X307 @ id @ (X311 @ id @ X312) @ id))) | ~ (((X307 @ id @ X312 @ id)) = $true)) | ~ ! [X314 : subst,X315 : term,X313 : subst] : (((sub @ (X311 @ X314 @ X315) @ X313)) = ((sub @ (sub @ X310 @ (push @ X315 @ X314)) @ X313))) | ($true = ((X307 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ~ ! [X317 : subst,X318 : term,X316 : subst] : (((X311 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316))) = ((sub @ X310 @ (push @ (sub @ X318 @ X316) @ (comp @ X317 @ X316)))))))) & (! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) <=> (axvarcons = $true)) & (pushprop_lem3v2_lthm = $true) & ((! [X321 : term] : (((sub @ X321 @ id)) = X321) => ! [X322 : (subst > term > subst > $o),X323 : term,X324 : (term > $o)] : (~ ! [X325 : term] : (($true = ((X324 @ (sub @ X323 @ (push @ X325 @ id))))) | ~ ($true = ((X324 @ X325)))) | ~ ! [X326 : subst,X327 : term,X328 : subst,X329 : subst] : (($true = ((X322 @ X328 @ X327 @ (comp @ X326 @ X329)))) | ~ (((X322 @ (comp @ X328 @ X326) @ (sub @ X327 @ X326) @ X329)) = $true)) | ~ ! [X330 : term] : (((X324 @ X330)) = ((X322 @ id @ X330 @ id))) | ($true = ((X324 @ (lam @ X323)))) | ~ ! [X331 : subst,X332 : subst,X333 : subst,X334 : term] : (($true = ((X322 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X331))) | ~ ($true = ((X322 @ X333 @ X334 @ (comp @ X332 @ X331))))) | ~ ! [X335 : (subst > term > term)] : (~ ! [X337 : term,X338 : subst,X336 : subst] : (((sub @ (X335 @ X336 @ X337) @ X338)) = ((X335 @ (comp @ X336 @ X338) @ (sub @ X337 @ X338)))) | ~ ! [X339 : term] : (~ ($true = ((X322 @ id @ X339 @ id))) | (((X322 @ id @ (X335 @ id @ X339) @ id)) = $true)) | ($true = ((X322 @ id @ (lam @ (X335 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X340 : (term > $o),X341 : term] : (~ ! [X342 : term,X343 : term] : (~ (((X340 @ X343)) = $true) | ($true = ((X340 @ (ap @ X343 @ X342)))) | ~ ($true = ((X340 @ X342)))) | ~ ! [X344 : term] : (~ ($true = ((var @ X344))) | ($true = ((X340 @ X344)))) | ~ ! [X345 : term] : (~ ($true = ((X340 @ X345))) | (((X340 @ (lam @ X345))) = $true)) | ($true = ((X340 @ X341)))) <=> (induction = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoaslamnotap = $true) <=> ! [X346 : (subst > term > term),X347 : term,X348 : term] : (~ ! [X350 : subst,X349 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) = ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347))))) & (hoasinduction_lem1v2_gthm = $true) & ! [X353 : d_term,X352 : d_term] : ((((d2term @ X352)) = ((d2term @ X353))) => (X352 = X353)) & (axassoc = $true) & ((induction2_lthm = $true) <=> (! [X354 : term] : (((sub @ X354 @ id)) = X354) => (! [X355 : term,X356 : subst,X357 : (term > $o)] : (~ ! [X358 : term] : (($true = ((X357 @ (sub @ X358 @ X356)))) | ~ (((var @ X358)) = $true)) | ($true = ((X357 @ (sub @ X355 @ X356)))) | ~ ! [X359 : term] : (~ ! [X360 : term] : (~ ($true = ((X357 @ X360))) | ($true = ((X357 @ (sub @ X359 @ (push @ X360 @ id)))))) | ($true = ((X357 @ (lam @ X359))))) | ~ ! [X361 : term,X362 : term] : (~ ($true = ((X357 @ X361))) | ($true = ((X357 @ (ap @ X361 @ X362)))) | ~ (((X357 @ X362)) = $true))) => ! [X363 : term,X364 : (term > $o)] : (~ ! [X365 : term] : (~ ($true = ((var @ X365))) | (((X364 @ X365)) = $true)) | ~ ! [X366 : term,X367 : term] : (~ (((X364 @ X367)) = $true) | ($true = ((X364 @ (ap @ X366 @ X367)))) | ~ ($true = ((X364 @ X366)))) | ~ ! [X368 : term] : (~ ! [X369 : term] : ((((X364 @ (sub @ X368 @ (push @ X369 @ id)))) = $true) | ~ ($true = ((X364 @ X369)))) | (((X364 @ (lam @ X368))) = $true)) | (((X364 @ X363)) = $true))))) & (hoasapinj1_gthm = $true) & (! [X371 : term,X370 : (term > $o),X372 : subst] : ~ ! [X373 : (term > $o)] : ~ ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374))) <=> (pushprop_lem0_lthm = $true)) & (! [X375 : (term > $o),X376 : term] : (($true = ((X375 @ X376))) | ~ ! [X377 : term] : (~ ($true = ((var @ X377))) | (((X375 @ X377)) = $true)) | ~ ! [X378 : term,X379 : term] : (~ ($true = ((X375 @ X379))) | ($true = ((X375 @ (ap @ X378 @ X379)))) | ~ (((X375 @ X378)) = $true)) | ~ ! [X380 : term] : ((((X375 @ (lam @ X380))) = $true) | ~ ! [X381 : term] : (~ ($true = ((X375 @ X381))) | (((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true)))) <=> (induction2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((shinj = $true) <=> ! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh))))) & (hoaslamnotap_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (induction2lem_gthm = $true) & (pushprop_lem3v2 = $true) & (lamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ~ (lamnotap = $true) & (pushprop_lem2v2 = $true) & (hoasapnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lthm = $true) <=> (! [X384 : term,X385 : (term > $o)] : (~ ! [X386 : term,X387 : term] : (~ ($true = ((X385 @ X387))) | (((X385 @ (ap @ X386 @ X387))) = $true) | ~ ($true = ((X385 @ X386)))) | ($true = ((X385 @ X384))) | ~ ! [X388 : term] : (~ ! [X389 : term] : (~ ($true = ((X385 @ X389))) | ($true = ((X385 @ (sub @ X388 @ (push @ X389 @ id)))))) | ($true = ((X385 @ (lam @ X388))))) | ~ ! [X390 : term] : ((((X385 @ X390)) = $true) | ~ ($true = ((var @ X390))))) => (! [X391 : (subst > term > subst > $o),X392 : term,X393 : term] : ((((X391 @ id @ (ap @ X392 @ X393) @ id)) = $true) | ~ ! [X394 : term,X395 : term] : (~ ($true = ((X391 @ id @ X395 @ id))) | (((X391 @ id @ (ap @ (sub @ X395 @ id) @ X394) @ id)) = $true) | ~ ($true = ((X391 @ id @ X394 @ id)))) | ~ ($true = ((X391 @ id @ X392 @ id))) | ~ (((X391 @ id @ X393 @ id)) = $true) | ~ ! [X396 : term,X397 : subst,X398 : subst,X399 : subst] : ((((X391 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398)) = $true) | ~ ($true = ((X391 @ X397 @ X396 @ (comp @ X399 @ X398))))) | ~ ! [X400 : term,X401 : subst,X402 : subst,X403 : subst] : (($true = ((X391 @ X403 @ X400 @ (comp @ X402 @ X401)))) | ~ ($true = ((X391 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401))))) => (! [X404 : (subst > term > subst > $o),X405 : term] : (~ ! [X406 : (subst > term > term)] : (~ ! [X407 : term] : (($true = ((X404 @ id @ (X406 @ id @ X407) @ id))) | ~ (((X404 @ id @ X407 @ id)) = $true)) | ($true = ((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id))) | ~ ! [X410 : subst,X408 : term,X409 : subst] : (((X406 @ (comp @ X410 @ X409) @ (sub @ X408 @ X409))) = ((sub @ (X406 @ X410 @ X408) @ X409)))) | ~ ! [X411 : subst,X412 : subst,X413 : subst,X414 : term] : (($true = ((X404 @ X411 @ X414 @ (comp @ X413 @ X412)))) | ~ ($true = ((X404 @ (comp @ X411 @ X413) @ (sub @ X414 @ X413) @ X412)))) | ~ ! [X415 : term] : (~ ($true = ((X404 @ id @ X415 @ id))) | (((X404 @ id @ (sub @ X405 @ (push @ X415 @ id)) @ id)) = $true)) | ~ ! [X416 : subst,X417 : subst,X418 : subst,X419 : term] : (~ ($true = ((X404 @ X417 @ X419 @ (comp @ X418 @ X416)))) | ($true = ((X404 @ (comp @ X417 @ X418) @ (sub @ X419 @ X418) @ X416)))) | (((X404 @ id @ (lam @ X405) @ id)) = $true)) => ! [X420 : term,X421 : (subst > term > subst > $o)] : (~ ! [X422 : term] : (~ (((var @ (sub @ X422 @ id))) = $true) | ($true = ((X421 @ id @ X422 @ id)))) | ~ ! [X423 : term,X424 : term] : (~ (((X421 @ id @ X424 @ id)) = $true) | (((X421 @ id @ (ap @ (sub @ X423 @ id) @ X424) @ id)) = $true) | ~ (((X421 @ id @ X423 @ id)) = $true)) | ($true = ((X421 @ id @ X420 @ id))) | ~ ! [X425 : subst,X426 : subst,X427 : subst,X428 : term] : ((((X421 @ X425 @ X428 @ (comp @ X426 @ X427))) = $true) | ~ ($true = ((X421 @ (comp @ X425 @ X426) @ (sub @ X428 @ X426) @ X427)))) | ~ ! [X429 : subst,X430 : subst,X431 : subst,X432 : term] : (($true = ((X421 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X429))) | ~ ($true = ((X421 @ X430 @ X432 @ (comp @ X431 @ X429))))) | ~ ! [X433 : (subst > term > term)] : (~ ! [X435 : term,X434 : subst,X436 : subst] : (((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X434 @ X435) @ X436))) | ~ ! [X437 : term] : (~ (((X421 @ id @ X437 @ id)) = $true) | ($true = ((X421 @ id @ (X433 @ id @ X437) @ id)))) | ($true = ((X421 @ id @ (lam @ (X433 @ sh @ one)) @ id))))))))) & ((! [X438 : (subst > term > subst > $o)] : ~ ! [X439 : (term > $o)] : ~ ! [X440 : term] : (((X439 @ X440)) = ((X438 @ id @ X440 @ id))) => (! [X441 : term,X442 : (term > $o)] : ((((X442 @ X441)) = $true) | ~ ! [X443 : term] : (~ ! [X444 : term] : (~ ($true = ((X442 @ X444))) | (((X442 @ (sub @ X443 @ (push @ X444 @ id)))) = $true)) | (((X442 @ (lam @ X443))) = $true)) | ~ ! [X445 : term,X446 : term] : (~ ($true = ((X442 @ X446))) | ($true = ((X442 @ (ap @ X446 @ X445)))) | ~ (((X442 @ X445)) = $true)) | ~ ! [X447 : term] : (~ (((var @ X447)) = $true) | ($true = ((X442 @ X447))))) => (! [X448 : term] : (((sub @ X448 @ id)) = X448) => (! [X449 : term,X450 : (term > $o),X451 : (subst > term > subst > $o)] : (~ ! [X452 : term] : (((X451 @ id @ X452 @ id)) = ((X450 @ X452))) | ~ ! [X453 : term] : ((((X450 @ (sub @ X449 @ (push @ X453 @ id)))) = $true) | ~ ($true = ((X450 @ X453)))) | ($true = ((X450 @ (lam @ X449)))) | ~ ! [X454 : (subst > term > term)] : (~ ! [X455 : term] : (($true = ((X451 @ id @ (X454 @ id @ X455) @ id))) | ~ ($true = ((X451 @ id @ X455 @ id)))) | (((X451 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ~ ! [X456 : subst,X457 : term,X458 : subst] : (((X454 @ (comp @ X456 @ X458) @ (sub @ X457 @ X458))) = ((sub @ (X454 @ X456 @ X457) @ X458))))) => ! [X459 : (subst > term > subst > $o),X460 : term] : (~ ! [X461 : (subst > term > term)] : (($true = ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id))) | ~ ! [X462 : term] : ((((X459 @ id @ (X461 @ id @ X462) @ id)) = $true) | ~ ($true = ((X459 @ id @ X462 @ id)))) | ~ ! [X463 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X463) @ (sub @ X465 @ X463))) = ((sub @ (X461 @ X464 @ X465) @ X463)))) | ~ ! [X466 : term] : ((((X459 @ id @ X466 @ id)) = $true) | ~ (((var @ (sub @ X466 @ id))) = $true)) | ~ ! [X467 : term,X468 : subst,X469 : subst,X470 : subst] : ((((X459 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469) @ X470)) = $true) | ~ ($true = ((X459 @ X468 @ X467 @ (comp @ X469 @ X470))))) | ($true = ((X459 @ id @ X460 @ id))) | ~ ! [X471 : term,X472 : term] : (~ ($true = ((X459 @ id @ X472 @ id))) | ~ ($true = ((X459 @ id @ X471 @ id))) | ($true = ((X459 @ id @ (ap @ (sub @ X471 @ id) @ X472) @ id)))) | ~ ! [X473 : subst,X474 : subst,X475 : subst,X476 : term] : (($true = ((X459 @ X475 @ X476 @ (comp @ X473 @ X474)))) | ~ ($true = ((X459 @ (comp @ X475 @ X473) @ (sub @ X476 @ X473) @ X474))))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X477 : term] : (((sub @ X477 @ id)) = X477) => (! [X478 : term,X479 : (subst > term > subst > $o)] : ((((X479 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X480 : term] : ((((X479 @ id @ (sub @ X478 @ (push @ X480 @ id)) @ id)) = $true) | ~ ($true = ((X479 @ id @ X480 @ id)))) | ~ ! [X481 : (subst > term > term)] : (~ ! [X482 : term] : (($true = ((X479 @ id @ (X481 @ id @ X482) @ id))) | ~ ($true = ((X479 @ id @ X482 @ id)))) | ~ ! [X485 : term,X484 : subst,X483 : subst] : (((sub @ (X481 @ X483 @ X485) @ X484)) = ((X481 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484)))) | (((X479 @ id @ (lam @ (X481 @ sh @ one)) @ id)) = $true))) => ! [X486 : term,X487 : (subst > term > subst > $o)] : (($true = ((X487 @ id @ (lam @ X486) @ id))) | ~ ! [X488 : subst,X489 : subst,X490 : term,X491 : subst] : (~ (((X487 @ X488 @ X490 @ (comp @ X491 @ X489))) = $true) | ($true = ((X487 @ (comp @ X488 @ X491) @ (sub @ X490 @ X491) @ X489)))) | ~ ! [X492 : term,X493 : subst,X494 : subst,X495 : subst] : (~ ($true = ((X487 @ (comp @ X495 @ X494) @ (sub @ X492 @ X494) @ X493))) | ($true = ((X487 @ X495 @ X492 @ (comp @ X494 @ X493))))) | ~ ! [X496 : term] : (($true = ((X487 @ id @ (sub @ X486 @ (push @ X496 @ id)) @ id))) | ~ (((X487 @ id @ X496 @ id)) = $true)) | ~ ! [X497 : (subst > term > term)] : (~ ! [X498 : term] : (($true = ((X487 @ id @ (X497 @ id @ X498) @ id))) | ~ ($true = ((X487 @ id @ X498 @ id)))) | ($true = ((X487 @ id @ (lam @ (X497 @ sh @ one)) @ id))) | ~ ! [X500 : subst,X501 : term,X499 : subst] : (((X497 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) = ((sub @ (X497 @ X499 @ X501) @ X500)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X502 : term] : ~ ! [X503 : (subst > term > term)] : (((X503 @ sh @ one)) != ((sub @ X502 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) <=> (apinj2 = $true)) & ((axscons = $true) <=> ! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508)) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & ! [X511 : d_subst] : (d_id = X511) & (! [X512 : (subst > term > subst > $o),X513 : term,X514 : (term > $o)] : (($true = ((X514 @ (lam @ X513)))) | ~ ! [X515 : (subst > term > term)] : (~ ! [X517 : subst,X518 : term,X516 : subst] : (((sub @ (X515 @ X517 @ X518) @ X516)) = ((X515 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516)))) | (((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id)) = $true) | ~ ! [X519 : term] : (~ (((X512 @ id @ X519 @ id)) = $true) | (((X512 @ id @ (X515 @ id @ X519) @ id)) = $true))) | ~ ! [X520 : term] : (((X514 @ X520)) = ((X512 @ id @ X520 @ id))) | ~ ! [X521 : term] : (($true = ((X514 @ (sub @ X513 @ (push @ X521 @ id))))) | ~ ($true = ((X514 @ X521))))) <=> (hoasinduction_lem3v2a = $true)) & (! [X522 : term] : (((sub @ X522 @ id)) = X522) <=> (termmset = $true)) & (axmap = $true) & (hoaslamnotvar_lthm = $true) & (axabs = $true) & (pushprop_lem2v2_gthm = $true) & (! [X523 : term,X524 : (subst > term > subst > $o)] : (~ ! [X525 : term] : ((((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) = $true) | ~ (((X524 @ id @ X525 @ id)) = $true)) | ~ ! [X526 : (subst > term > term)] : (($true = ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) | ~ ! [X527 : term] : (($true = ((X524 @ id @ (X526 @ id @ X527) @ id))) | ~ ($true = ((X524 @ id @ X527 @ id)))) | ~ ! [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530)))) | ($true = ((X524 @ id @ (lam @ X523) @ id)))) <=> (hoasinduction_lem3a = $true)) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (hoasinduction_lem1_gthm = $true) & (! [X533 : (subst > term > subst > $o)] : ~ ! [X534 : (term > $o)] : ~ ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lthm = $true) & (((d2subst @ d_id)) = id) & (! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) <=> (hoasapinj2 = $true))),
% 6.46/1.22 inference(rectify,[],[f7])).
% 6.46/1.22 thf(f10,plain,(
% 6.46/1.22 ((apinj1 = $true) <=> ! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149))))) & (! [X308 : term,X307 : (subst > term > subst > $o)] : (~ ! [X309 : term] : (($true = ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id))) | ($true != ((X307 @ id @ X309 @ id)))) | (((X307 @ id @ (lam @ (sub @ X308 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X310 : term,X311 : (subst > term > term)] : (($true = ((X307 @ id @ (lam @ (X311 @ sh @ one)) @ id))) | ~ ! [X317 : subst,X318 : term,X316 : subst] : (((X311 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316))) = ((sub @ X310 @ (push @ (sub @ X318 @ X316) @ (comp @ X317 @ X316))))) | ~ ! [X314 : subst,X315 : term,X313 : subst] : (((sub @ (X311 @ X314 @ X315) @ X313)) = ((sub @ (sub @ X310 @ (push @ X315 @ X314)) @ X313))) | ~ ! [X312 : term] : ((((X307 @ id @ X312 @ id)) != $true) | ($true = ((X307 @ id @ (X311 @ id @ X312) @ id)))))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem1_lthm = $true) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) = ((d2subst @ X305))) => (X305 = X306)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & ((induction = $true) <=> ! [X341 : term,X340 : (term > $o)] : (($true = ((X340 @ X341))) | ~ ! [X343 : term,X342 : term] : (($true = ((X340 @ (ap @ X343 @ X342)))) | ($true != ((X340 @ X342))) | (((X340 @ X343)) != $true)) | ~ ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344)))) | ~ ! [X345 : term] : (($true != ((X340 @ X345))) | (((X340 @ (lam @ X345))) = $true)))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X155 : (subst > term > subst > $o)] : ~ ! [X156 : (term > $o)] : ~ ! [X157 : term] : (((X155 @ id @ X157 @ id)) = ((X156 @ X157))) => (! [X158 : term,X159 : (term > $o)] : (~ ! [X161 : term,X160 : term] : (($true = ((X159 @ (ap @ X160 @ X161)))) | ($true != ((X159 @ X160))) | ($true != ((X159 @ X161)))) | ~ ! [X162 : term] : (($true != ((var @ X162))) | ($true = ((X159 @ X162)))) | ~ ! [X163 : term] : (($true = ((X159 @ (lam @ X163)))) | ~ ! [X164 : term] : (($true != ((X159 @ X164))) | ($true = ((X159 @ (sub @ X163 @ (push @ X164 @ id))))))) | ($true = ((X159 @ X158)))) => (! [X165 : term] : (((sub @ X165 @ id)) = X165) => (! [X168 : term,X166 : (term > $o),X167 : (subst > term > subst > $o)] : ((((X166 @ (lam @ X168))) = $true) | ~ ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id))) | ~ ! [X169 : (subst > term > term)] : ((((X167 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ~ ! [X172 : subst,X173 : term,X171 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) = ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171)))) | ~ ! [X170 : term] : ((((X167 @ id @ (X169 @ id @ X170) @ id)) = $true) | ($true != ((X167 @ id @ X170 @ id))))) | ~ ! [X174 : term] : (($true = ((X166 @ (sub @ X168 @ (push @ X174 @ id))))) | ($true != ((X166 @ X174))))) => ! [X177 : (subst > term > subst > $o),X176 : term] : ((((X177 @ id @ X176 @ id)) = $true) | ~ ! [X180 : (subst > term > term)] : (~ ! [X184 : term] : (($true != ((X177 @ id @ X184 @ id))) | (((X177 @ id @ (X180 @ id @ X184) @ id)) = $true)) | (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ~ ! [X182 : subst,X183 : term,X181 : subst] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182))))) | ~ ! [X178 : term,X179 : term] : ((((X177 @ id @ X178 @ id)) != $true) | (((X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) = $true) | ($true != ((X177 @ id @ X179 @ id)))))))))) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (induction2lem_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : term,X115 : term,X117 : term,X116 : term] : ((X116 = X117) | (((ap @ X116 @ X115)) != ((ap @ X117 @ X114)))) => ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((axidr = $true) <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lthm = $true) <=> (! [X384 : term,X385 : (term > $o)] : (~ ! [X388 : term] : (($true = ((X385 @ (lam @ X388)))) | ~ ! [X389 : term] : (($true = ((X385 @ (sub @ X388 @ (push @ X389 @ id))))) | ($true != ((X385 @ X389))))) | ~ ! [X390 : term] : (($true != ((var @ X390))) | (((X385 @ X390)) = $true)) | ($true = ((X385 @ X384))) | ~ ! [X387 : term,X386 : term] : (($true != ((X385 @ X387))) | ($true != ((X385 @ X386))) | (((X385 @ (ap @ X386 @ X387))) = $true))) => (! [X391 : (subst > term > subst > $o),X392 : term,X393 : term] : ((((X391 @ id @ X393 @ id)) != $true) | (((X391 @ id @ (ap @ X392 @ X393) @ id)) = $true) | ~ ! [X400 : term,X402 : subst,X403 : subst,X401 : subst] : (($true = ((X391 @ X403 @ X400 @ (comp @ X402 @ X401)))) | ($true != ((X391 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401)))) | ~ ! [X398 : subst,X399 : subst,X396 : term,X397 : subst] : ((((X391 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398)) = $true) | ($true != ((X391 @ X397 @ X396 @ (comp @ X399 @ X398))))) | ($true != ((X391 @ id @ X392 @ id))) | ~ ! [X394 : term,X395 : term] : ((((X391 @ id @ (ap @ (sub @ X395 @ id) @ X394) @ id)) = $true) | ($true != ((X391 @ id @ X395 @ id))) | ($true != ((X391 @ id @ X394 @ id))))) => (! [X405 : term,X404 : (subst > term > subst > $o)] : (~ ! [X412 : subst,X414 : term,X411 : subst,X413 : subst] : (($true != ((X404 @ (comp @ X411 @ X413) @ (sub @ X414 @ X413) @ X412))) | ($true = ((X404 @ X411 @ X414 @ (comp @ X413 @ X412))))) | ~ ! [X415 : term] : (($true != ((X404 @ id @ X415 @ id))) | (((X404 @ id @ (sub @ X405 @ (push @ X415 @ id)) @ id)) = $true)) | ~ ! [X406 : (subst > term > term)] : (~ ! [X410 : subst,X408 : term,X409 : subst] : (((X406 @ (comp @ X410 @ X409) @ (sub @ X408 @ X409))) = ((sub @ (X406 @ X410 @ X408) @ X409))) | ~ ! [X407 : term] : (($true = ((X404 @ id @ (X406 @ id @ X407) @ id))) | (((X404 @ id @ X407 @ id)) != $true)) | ($true = ((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)))) | ~ ! [X417 : subst,X418 : subst,X416 : subst,X419 : term] : (($true != ((X404 @ X417 @ X419 @ (comp @ X418 @ X416)))) | ($true = ((X404 @ (comp @ X417 @ X418) @ (sub @ X419 @ X418) @ X416)))) | (((X404 @ id @ (lam @ X405) @ id)) = $true)) => ! [X420 : term,X421 : (subst > term > subst > $o)] : (~ ! [X422 : term] : (($true = ((X421 @ id @ X422 @ id))) | (((var @ (sub @ X422 @ id))) != $true)) | ~ ! [X433 : (subst > term > term)] : (($true = ((X421 @ id @ (lam @ (X433 @ sh @ one)) @ id))) | ~ ! [X437 : term] : (($true = ((X421 @ id @ (X433 @ id @ X437) @ id))) | (((X421 @ id @ X437 @ id)) != $true)) | ~ ! [X435 : term,X434 : subst,X436 : subst] : (((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X434 @ X435) @ X436)))) | ~ ! [X432 : term,X430 : subst,X431 : subst,X429 : subst] : (($true != ((X421 @ X430 @ X432 @ (comp @ X431 @ X429)))) | ($true = ((X421 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X429)))) | ~ ! [X423 : term,X424 : term] : ((((X421 @ id @ X423 @ id)) != $true) | (((X421 @ id @ X424 @ id)) != $true) | (((X421 @ id @ (ap @ (sub @ X423 @ id) @ X424) @ id)) = $true)) | ($true = ((X421 @ id @ X420 @ id))) | ~ ! [X428 : term,X426 : subst,X425 : subst,X427 : subst] : ((((X421 @ X425 @ X428 @ (comp @ X426 @ X427))) = $true) | ($true != ((X421 @ (comp @ X425 @ X426) @ (sub @ X428 @ X426) @ X427))))))))) & (hoasinduction_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (axapp = $true) & (axmap = $true) & ((hoasinduction_lem3a = $true) <=> ! [X524 : (subst > term > subst > $o),X523 : term] : (($true = ((X524 @ id @ (lam @ X523) @ id))) | ~ ! [X526 : (subst > term > term)] : (~ ! [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530))) | ($true = ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) | ~ ! [X527 : term] : (($true != ((X524 @ id @ X527 @ id))) | ($true = ((X524 @ id @ (X526 @ id @ X527) @ id))))) | ~ ! [X525 : term] : ((((X524 @ id @ X525 @ id)) != $true) | (((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) = $true)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X224 : subst,X225 : term] : (((sub @ one @ (push @ X225 @ X224))) = X225) => (! [X227 : subst,X226 : term] : (((comp @ sh @ (push @ X226 @ X227))) = X227) => (! [X228 : term,X229 : term] : ((((lam @ X228)) != ((lam @ X229))) | (X228 = X229)) => ! [X233 : (subst > term > term),X232 : subst,X231 : (subst > term > term),X230 : term] : (~ ! [X236 : subst,X234 : subst,X235 : term] : (((X231 @ (comp @ X234 @ X236) @ (sub @ X235 @ X236))) = ((sub @ (X231 @ X234 @ X235) @ X236))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X231 @ sh @ one)))) | (((X231 @ X232 @ X230)) = ((X233 @ X232 @ X230))) | ~ ! [X237 : term,X239 : subst,X238 : subst] : (((sub @ (X233 @ X239 @ X237) @ X238)) = ((X233 @ (comp @ X239 @ X238) @ (sub @ X237 @ X238))))))))) & ((! [X265 : term] : (((sub @ X265 @ id)) = X265) => ! [X266 : term] : (((sub @ X266 @ id)) = X266)) <=> (termmset_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X346 : (subst > term > term),X347 : term,X348 : term] : (~ ! [X350 : subst,X349 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) = ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347))))) & (pushprop_gthm = $true) & ((! [X267 : subst] : (((comp @ id @ X267)) = X267) => (! [X268 : subst] : (((comp @ X268 @ id)) = X268) => (! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X321 : term] : (((sub @ X321 @ id)) = X321) => ! [X323 : term,X324 : (term > $o),X322 : (subst > term > subst > $o)] : (~ ! [X330 : term] : (((X324 @ X330)) = ((X322 @ id @ X330 @ id))) | ~ ! [X333 : subst,X334 : term,X331 : subst,X332 : subst] : (($true = ((X322 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X331))) | ($true != ((X322 @ X333 @ X334 @ (comp @ X332 @ X331))))) | ~ ! [X329 : subst,X328 : subst,X326 : subst,X327 : term] : (($true = ((X322 @ X328 @ X327 @ (comp @ X326 @ X329)))) | (((X322 @ (comp @ X328 @ X326) @ (sub @ X327 @ X326) @ X329)) != $true)) | ~ ! [X335 : (subst > term > term)] : (($true = ((X322 @ id @ (lam @ (X335 @ sh @ one)) @ id))) | ~ ! [X337 : term,X338 : subst,X336 : subst] : (((sub @ (X335 @ X336 @ X337) @ X338)) = ((X335 @ (comp @ X336 @ X338) @ (sub @ X337 @ X338)))) | ~ ! [X339 : term] : (($true != ((X322 @ id @ X339 @ id))) | (((X322 @ id @ (X335 @ id @ X339) @ id)) = $true))) | ($true = ((X324 @ (lam @ X323)))) | ~ ! [X325 : term] : (($true = ((X324 @ (sub @ X323 @ (push @ X325 @ id))))) | ($true != ((X324 @ X325))))))) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem2 = $true) <=> ! [X76 : (subst > term > subst > $o),X75 : term,X74 : term] : (($true = ((X76 @ id @ (ap @ X74 @ X75) @ id))) | ~ ! [X82 : subst,X79 : subst,X81 : subst,X80 : term] : (($true != ((X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79))) | ($true = ((X76 @ X81 @ X80 @ (comp @ X82 @ X79))))) | ($true != ((X76 @ id @ X75 @ id))) | ~ ! [X77 : term,X78 : term] : (($true = ((X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id))) | ($true != ((X76 @ id @ X77 @ id))) | (((X76 @ id @ X78 @ id)) != $true)) | ~ ! [X83 : subst,X85 : subst,X86 : term,X84 : subst] : (($true != ((X76 @ X84 @ X86 @ (comp @ X83 @ X85)))) | ($true = ((X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85)))) | (((X76 @ id @ X74 @ id)) != $true))) & ((! [X35 : term,X34 : subst] : (((sub @ one @ (push @ X35 @ X34))) = X35) => (! [X37 : subst,X36 : term] : (((comp @ sh @ (push @ X36 @ X37))) = X37) => (! [X38 : subst] : (((comp @ X38 @ id)) = X38) => (! [X39 : (term > $o),X40 : term] : (~ ! [X41 : term] : (($true = ((X39 @ X41))) | (((var @ X41)) != $true)) | (((X39 @ X40)) = $true) | ~ ! [X43 : term,X42 : term] : (($true != ((X39 @ X42))) | (((X39 @ (ap @ X42 @ X43))) = $true) | (((X39 @ X43)) != $true)) | ~ ! [X44 : term] : (($true = ((X39 @ (lam @ X44)))) | ($true != ((X39 @ X44))))) => ! [X46 : (term > $o),X47 : subst,X45 : term] : (($true = ((X46 @ (sub @ X45 @ X47)))) | ~ ! [X52 : term] : (($true = ((X46 @ (sub @ X52 @ X47)))) | (((var @ X52)) != $true)) | ~ ! [X50 : term] : (($true = ((X46 @ (lam @ X50)))) | ~ ! [X51 : term] : ((((X46 @ (sub @ X50 @ (push @ X51 @ id)))) = $true) | ($true != ((X46 @ X51))))) | ~ ! [X48 : term,X49 : term] : ((((X46 @ (ap @ X49 @ X48))) = $true) | ($true != ((X46 @ X48))) | ($true != ((X46 @ X49))))))))) <=> (induction2lem_lthm = $true)) & ((axscons = $true) <=> ! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) = X210) => ! [X215 : term,X213 : subst,X214 : (term > $o),X212 : (term > $o)] : (($true != ((X214 @ X215))) | ($true = ((X212 @ one))) | ~ ! [X216 : term] : (((X212 @ X216)) = ((X214 @ (sub @ X216 @ (push @ X215 @ X213)))))))) & (! [X512 : (subst > term > subst > $o),X514 : (term > $o),X513 : term] : (~ ! [X521 : term] : (($true = ((X514 @ (sub @ X513 @ (push @ X521 @ id))))) | ($true != ((X514 @ X521)))) | ($true = ((X514 @ (lam @ X513)))) | ~ ! [X515 : (subst > term > term)] : (~ ! [X519 : term] : ((((X512 @ id @ (X515 @ id @ X519) @ id)) = $true) | (((X512 @ id @ X519 @ id)) != $true)) | ~ ! [X517 : subst,X518 : term,X516 : subst] : (((sub @ (X515 @ X517 @ X518) @ X516)) = ((X515 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516)))) | (((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id)) = $true)) | ~ ! [X520 : term] : (((X514 @ X520)) = ((X512 @ id @ X520 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & ! [X353 : d_term,X352 : d_term] : ((((d2term @ X352)) = ((d2term @ X353))) => (X352 = X353)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X273 : (subst > term > subst > $o),X274 : term] : (~ ! [X279 : (subst > term > term)] : (~ ! [X280 : subst,X282 : subst,X281 : term] : (((sub @ (X279 @ X280 @ X281) @ X282)) = ((X279 @ (comp @ X280 @ X282) @ (sub @ X281 @ X282)))) | ~ ! [X283 : term] : ((((X273 @ id @ (X279 @ id @ X283) @ id)) = $true) | (((X273 @ id @ X283 @ id)) != $true)) | (((X273 @ id @ (lam @ (X279 @ sh @ one)) @ id)) = $true)) | ~ ! [X284 : term] : (($true != ((X273 @ id @ X284 @ id))) | ($true = ((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id)))) | ~ ! [X288 : subst,X286 : subst,X287 : subst,X285 : term] : (($true = ((X273 @ X288 @ X285 @ (comp @ X287 @ X286)))) | (((X273 @ (comp @ X288 @ X287) @ (sub @ X285 @ X287) @ X286)) != $true)) | ~ ! [X275 : subst,X276 : term,X278 : subst,X277 : subst] : (($true != ((X273 @ X277 @ X276 @ (comp @ X278 @ X275)))) | ($true = ((X273 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275)))) | ($true = ((X273 @ id @ (lam @ X274) @ id))))) & ((hoasinduction = $true) <=> ! [X10 : term,X11 : (subst > term > subst > $o)] : (~ ! [X12 : term] : ((((var @ (sub @ X12 @ id))) != $true) | ($true = ((X11 @ id @ X12 @ id)))) | ~ ! [X27 : subst,X25 : subst,X26 : subst,X24 : term] : ((((X11 @ X27 @ X24 @ (comp @ X26 @ X25))) != $true) | ($true = ((X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25)))) | ~ ! [X13 : subst,X15 : subst,X16 : subst,X14 : term] : ((((X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15)) != $true) | (((X11 @ X13 @ X14 @ (comp @ X16 @ X15))) = $true)) | ~ ! [X19 : (subst > term > term)] : (~ ! [X20 : term] : ((((X11 @ id @ (X19 @ id @ X20) @ id)) = $true) | ($true != ((X11 @ id @ X20 @ id)))) | ~ ! [X23 : subst,X22 : subst,X21 : term] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22)))) | (((X11 @ id @ (lam @ (X19 @ sh @ one)) @ id)) = $true)) | ($true = ((X11 @ id @ X10 @ id))) | ~ ! [X18 : term,X17 : term] : ((((X11 @ id @ X18 @ id)) != $true) | ($true = ((X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id))) | ($true != ((X11 @ id @ X17 @ id)))))) & ! [X511 : d_subst] : (d_id = X511) & ((induction2 = $true) <=> ! [X376 : term,X375 : (term > $o)] : (~ ! [X380 : term] : ((((X375 @ (lam @ X380))) = $true) | ~ ! [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true) | ($true != ((X375 @ X381))))) | ~ ! [X378 : term,X379 : term] : ((((X375 @ X378)) != $true) | ($true != ((X375 @ X379))) | ($true = ((X375 @ (ap @ X378 @ X379))))) | ~ ! [X377 : term] : (($true != ((var @ X377))) | (((X375 @ X377)) = $true)) | ($true = ((X375 @ X376))))) & (hoasinduction_lem3b_gthm = $true) & (induction2_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoaslaminj = $true) <=> ! [X253 : subst,X250 : (subst > term > term),X252 : term,X251 : (subst > term > term)] : ((((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252))) | ~ ! [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) = ((sub @ (X250 @ X258 @ X259) @ X257))) | (((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ~ ! [X255 : subst,X254 : term,X256 : subst] : (((sub @ (X251 @ X256 @ X254) @ X255)) = ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))))) & (axassoc = $true) & (pushprop_lthm = $true) & (pushprop_lem3v2 = $true) & (termmset_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X89 : (subst > term > subst > $o),X87 : (term > $o),X88 : term] : (~ ! [X95 : term] : (((X87 @ X95)) = ((X89 @ id @ X95 @ id))) | ($true = ((X87 @ (lam @ X88)))) | ~ ! [X90 : term] : ((((X87 @ (sub @ X88 @ (push @ X90 @ id)))) = $true) | (((X87 @ X90)) != $true)) | ~ ! [X96 : (subst > term > term)] : (~ ! [X97 : term] : ((((X89 @ id @ X97 @ id)) != $true) | (((X89 @ id @ (X96 @ id @ X97) @ id)) = $true)) | ~ ! [X99 : subst,X100 : term,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98))) | (((X89 @ id @ (lam @ (X96 @ sh @ one)) @ id)) = $true)) | ~ ! [X91 : subst,X94 : subst,X93 : subst,X92 : term] : (($true = ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93))) | ($true != ((X89 @ X94 @ X92 @ (comp @ X91 @ X93))))) | ~ ! [X104 : term,X102 : subst,X103 : subst,X101 : subst] : (($true != ((X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102))) | ($true = ((X89 @ X101 @ X104 @ (comp @ X103 @ X102))))))) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) <=> (laminj = $true)) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_gthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) | ($true != ((X260 @ X264)))) <=> (pushprop_lem1 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1v2 = $true) & ! [X142 : d_term] : (d_one = X142) & ((shinj = $true) <=> ! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh))))) & (! [X30 : (subst > term > subst > $o)] : ~ ! [X31 : (term > $o)] : ~ ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (! [X371 : term,X370 : (term > $o),X372 : subst] : ~ ! [X373 : (term > $o)] : ~ ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (axvarshift = $true) & (! [X289 : term,X290 : (subst > term > subst > $o)] : (~ ! [X296 : term] : ((((X290 @ id @ X296 @ id)) != $true) | (((X290 @ id @ (sub @ X289 @ (push @ X296 @ id)) @ id)) = $true)) | (((X290 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X291 : (subst > term > term)] : ((((X290 @ id @ (lam @ (X291 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : (($true = ((X290 @ id @ (X291 @ id @ X295) @ id))) | (((X290 @ id @ X295 @ id)) != $true)) | ~ ! [X292 : subst,X294 : subst,X293 : term] : (((sub @ (X291 @ X294 @ X293) @ X292)) = ((X291 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoaslamnotvar_lthm = $true) & ((! [X438 : (subst > term > subst > $o)] : ~ ! [X439 : (term > $o)] : ~ ! [X440 : term] : (((X439 @ X440)) = ((X438 @ id @ X440 @ id))) => (! [X441 : term,X442 : (term > $o)] : (~ ! [X443 : term] : (~ ! [X444 : term] : (($true != ((X442 @ X444))) | (((X442 @ (sub @ X443 @ (push @ X444 @ id)))) = $true)) | (((X442 @ (lam @ X443))) = $true)) | ~ ! [X446 : term,X445 : term] : (($true = ((X442 @ (ap @ X446 @ X445)))) | ($true != ((X442 @ X446))) | (((X442 @ X445)) != $true)) | ~ ! [X447 : term] : (($true = ((X442 @ X447))) | (((var @ X447)) != $true)) | (((X442 @ X441)) = $true)) => (! [X448 : term] : (((sub @ X448 @ id)) = X448) => (! [X449 : term,X451 : (subst > term > subst > $o),X450 : (term > $o)] : (~ ! [X454 : (subst > term > term)] : (~ ! [X456 : subst,X457 : term,X458 : subst] : (((X454 @ (comp @ X456 @ X458) @ (sub @ X457 @ X458))) = ((sub @ (X454 @ X456 @ X457) @ X458))) | ~ ! [X455 : term] : (($true != ((X451 @ id @ X455 @ id))) | ($true = ((X451 @ id @ (X454 @ id @ X455) @ id)))) | (((X451 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true)) | ~ ! [X452 : term] : (((X451 @ id @ X452 @ id)) = ((X450 @ X452))) | ~ ! [X453 : term] : ((((X450 @ (sub @ X449 @ (push @ X453 @ id)))) = $true) | ($true != ((X450 @ X453)))) | ($true = ((X450 @ (lam @ X449))))) => ! [X459 : (subst > term > subst > $o),X460 : term] : (~ ! [X472 : term,X471 : term] : (($true != ((X459 @ id @ X471 @ id))) | ($true != ((X459 @ id @ X472 @ id))) | ($true = ((X459 @ id @ (ap @ (sub @ X471 @ id) @ X472) @ id)))) | ($true = ((X459 @ id @ X460 @ id))) | ~ ! [X468 : subst,X467 : term,X469 : subst,X470 : subst] : (($true != ((X459 @ X468 @ X467 @ (comp @ X469 @ X470)))) | (((X459 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469) @ X470)) = $true)) | ~ ! [X461 : (subst > term > term)] : (~ ! [X462 : term] : ((((X459 @ id @ (X461 @ id @ X462) @ id)) = $true) | ($true != ((X459 @ id @ X462 @ id)))) | ~ ! [X463 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X463) @ (sub @ X465 @ X463))) = ((sub @ (X461 @ X464 @ X465) @ X463))) | ($true = ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id)))) | ~ ! [X466 : term] : ((((var @ (sub @ X466 @ id))) != $true) | (((X459 @ id @ X466 @ id)) = $true)) | ~ ! [X473 : subst,X476 : term,X475 : subst,X474 : subst] : (($true != ((X459 @ (comp @ X475 @ X473) @ (sub @ X476 @ X473) @ X474))) | ($true = ((X459 @ X475 @ X476 @ (comp @ X473 @ X474)))))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoasapinj2_gthm = $true) & (! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) <=> (hoasapinj2 = $true)) & (hoaslamnotvar = $true) & (! [X106 : (term > $o),X107 : term,X105 : subst] : (~ ! [X111 : term,X110 : term] : (($true != ((X106 @ X110))) | ($true = ((X106 @ (ap @ X111 @ X110)))) | ($true != ((X106 @ X111)))) | ($true = ((X106 @ (sub @ X107 @ X105)))) | ~ ! [X108 : term] : (($true = ((X106 @ (lam @ X108)))) | ~ ! [X109 : term] : ((((X106 @ (sub @ X108 @ (push @ X109 @ id)))) = $true) | ($true != ((X106 @ X109))))) | ~ ! [X112 : term] : (($true != ((var @ X112))) | ($true = ((X106 @ (sub @ X112 @ X105)))))) <=> (induction2lem = $true)) & (hoasinduction_lem2v2_gthm = $true) & (lamnotap != $true) & (lamnotvar = $true) & ((! [X187 : term,X186 : term,X188 : term,X185 : term] : ((((ap @ X186 @ X188)) != ((ap @ X185 @ X187))) | (X187 = X188)) => ! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192))) <=> (hoasapinj2_lthm = $true)) & ((axvarid = $true) <=> ! [X249 : term] : (((sub @ X249 @ id)) = X249)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aa = $true) <=> ! [X297 : term,X298 : (subst > term > subst > $o)] : (~ ! [X299 : (subst > term > term)] : ((((X298 @ id @ (lam @ (X299 @ sh @ one)) @ id)) = $true) | ~ ! [X302 : term,X301 : subst,X300 : subst] : (((sub @ (X299 @ X300 @ X302) @ X301)) = ((X299 @ (comp @ X300 @ X301) @ (sub @ X302 @ X301)))) | ~ ! [X303 : term] : ((((X298 @ id @ (X299 @ id @ X303) @ id)) = $true) | ($true != ((X298 @ id @ X303 @ id))))) | ($true = ((X298 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id))) | ~ ! [X304 : term] : ((((X298 @ id @ X304 @ id)) != $true) | ($true = ((X298 @ id @ (sub @ X297 @ (push @ X304 @ id)) @ id)))))) & (ulamvarind = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X522 : term] : (((sub @ X522 @ id)) = X522) <=> (termmset = $true)) & (axabs = $true) & (! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) <=> (apinj2 = $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X477 : term] : (((sub @ X477 @ id)) = X477) => (! [X478 : term,X479 : (subst > term > subst > $o)] : ((((X479 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X480 : term] : (($true != ((X479 @ id @ X480 @ id))) | (((X479 @ id @ (sub @ X478 @ (push @ X480 @ id)) @ id)) = $true)) | ~ ! [X481 : (subst > term > term)] : (~ ! [X485 : term,X484 : subst,X483 : subst] : (((sub @ (X481 @ X483 @ X485) @ X484)) = ((X481 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484)))) | (((X479 @ id @ (lam @ (X481 @ sh @ one)) @ id)) = $true) | ~ ! [X482 : term] : (($true = ((X479 @ id @ (X481 @ id @ X482) @ id))) | ($true != ((X479 @ id @ X482 @ id)))))) => ! [X486 : term,X487 : (subst > term > subst > $o)] : (~ ! [X488 : subst,X490 : term,X489 : subst,X491 : subst] : ((((X487 @ X488 @ X490 @ (comp @ X491 @ X489))) != $true) | ($true = ((X487 @ (comp @ X488 @ X491) @ (sub @ X490 @ X491) @ X489)))) | ($true = ((X487 @ id @ (lam @ X486) @ id))) | ~ ! [X492 : term,X493 : subst,X495 : subst,X494 : subst] : (($true = ((X487 @ X495 @ X492 @ (comp @ X494 @ X493)))) | ($true != ((X487 @ (comp @ X495 @ X494) @ (sub @ X492 @ X494) @ X493)))) | ~ ! [X497 : (subst > term > term)] : (($true = ((X487 @ id @ (lam @ (X497 @ sh @ one)) @ id))) | ~ ! [X500 : subst,X501 : term,X499 : subst] : (((X497 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) = ((sub @ (X497 @ X499 @ X501) @ X500))) | ~ ! [X498 : term] : (($true != ((X487 @ id @ X498 @ id))) | ($true = ((X487 @ id @ (X497 @ id @ X498) @ id))))) | ~ ! [X496 : term] : (($true = ((X487 @ id @ (sub @ X486 @ (push @ X496 @ id)) @ id))) | (((X487 @ id @ X496 @ id)) != $true)))))) & (! [X143 : term] : ~ ! [X144 : (subst > term > term)] : ~ ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X502 : term] : ~ ! [X503 : (subst > term > term)] : (((X503 @ sh @ one)) != ((sub @ X502 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasapnotvar = $true) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = id) & (! [X271 : term] : ~ ! [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) != ((X272 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (ulamvarsh = $true) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X151 : term] : ~ ! [X152 : (subst > term > term)] : ~ ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X127 : (subst > term > subst > $o),X130 : term,X128 : (term > $o),X129 : term] : (~ ! [X137 : term,X140 : subst,X139 : subst,X138 : subst] : (($true != ((X127 @ X138 @ X137 @ (comp @ X139 @ X140)))) | ($true = ((X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)))) | ~ ! [X132 : term,X131 : term] : (($true != ((X127 @ id @ X132 @ id))) | ($true = ((X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) | ($true != ((X127 @ id @ X131 @ id)))) | (((X128 @ X130)) != $true) | ~ ! [X134 : subst,X133 : term,X135 : subst,X136 : subst] : ((((X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136)) != $true) | ($true = ((X127 @ X134 @ X133 @ (comp @ X135 @ X136))))) | ($true = ((X128 @ (ap @ X129 @ X130)))) | (((X128 @ X129)) != $true) | ~ ! [X141 : term] : (((X128 @ X141)) = ((X127 @ id @ X141 @ id))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1 = $true) <=> ! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56))) & ((induction2_lthm = $true) <=> (! [X354 : term] : (((sub @ X354 @ id)) = X354) => (! [X357 : (term > $o),X355 : term,X356 : subst] : (~ ! [X358 : term] : ((((var @ X358)) != $true) | ($true = ((X357 @ (sub @ X358 @ X356))))) | ~ ! [X359 : term] : (~ ! [X360 : term] : (($true = ((X357 @ (sub @ X359 @ (push @ X360 @ id))))) | ($true != ((X357 @ X360)))) | ($true = ((X357 @ (lam @ X359))))) | ($true = ((X357 @ (sub @ X355 @ X356)))) | ~ ! [X361 : term,X362 : term] : (($true = ((X357 @ (ap @ X361 @ X362)))) | ($true != ((X357 @ X361))) | (((X357 @ X362)) != $true))) => ! [X363 : term,X364 : (term > $o)] : (~ ! [X365 : term] : (($true != ((var @ X365))) | (((X364 @ X365)) = $true)) | (((X364 @ X363)) = $true) | ~ ! [X368 : term] : (~ ! [X369 : term] : ((((X364 @ (sub @ X368 @ (push @ X369 @ id)))) = $true) | ($true != ((X364 @ X369)))) | (((X364 @ (lam @ X368))) = $true)) | ~ ! [X367 : term,X366 : term] : (($true != ((X364 @ X366))) | (((X364 @ X367)) != $true) | ($true = ((X364 @ (ap @ X366 @ X367))))))))) & (pushprop = $true) & ((! [X57 : term] : (((sub @ X57 @ id)) = X57) => (! [X59 : term,X58 : (subst > term > subst > $o)] : (~ ! [X61 : (subst > term > term)] : (~ ! [X64 : subst,X63 : term,X65 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) = ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))) | (((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id)) = $true) | ~ ! [X62 : term] : ((((X58 @ id @ X62 @ id)) != $true) | ($true = ((X58 @ id @ (X61 @ id @ X62) @ id))))) | (((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X60 : term] : ((((X58 @ id @ X60 @ id)) != $true) | ($true = ((X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id))))) => ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : term] : (($true = ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id))) | ($true != ((X67 @ id @ X68 @ id)))) | ($true = ((X67 @ id @ (lam @ X66) @ id))) | ~ ! [X69 : (subst > term > term)] : (~ ! [X70 : term] : (($true = ((X67 @ id @ (X69 @ id @ X70) @ id))) | (((X67 @ id @ X70 @ id)) != $true)) | ~ ! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))) | ($true = ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X122 : term,X125 : (term > $o),X124 : (term > $o),X123 : subst] : (~ ! [X126 : term] : (((X125 @ X126)) = ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ($true != ((X124 @ X122))) | ($true = ((X125 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) = X1) => (! [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) = X4) => ! [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true) | (((X9 @ X5)) != $true))))) & (ulamvar1 != $true) & (apnotvar = $true) & (pushprop_lem3v2_lthm = $true) & (axclos = $true) & (! [X533 : (subst > term > subst > $o)] : ~ ! [X534 : (term > $o)] : ~ ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) <=> (hoasinduction_lem0 = $true)) & (! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) <=> (axvarcons = $true)) & (hoasinduction_lem1_gthm = $true) & ((axidl = $true) <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & (! [X219 : subst,X217 : (term > $o),X218 : term] : ~ ! [X220 : (term > $o)] : ~ ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221))) <=> (pushprop_lem0 = $true)) & (pushprop_lem2v2_gthm = $true) & ((substmonoid = $true) <=> (! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X241 : (subst > term > subst > $o),X240 : term] : (~ ! [X244 : (subst > term > term)] : (($true = ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id))) | ~ ! [X245 : term] : (($true != ((X241 @ id @ X245 @ id))) | (((X241 @ id @ (X244 @ id @ X245) @ id)) = $true)) | ~ ! [X246 : subst,X247 : subst,X248 : term] : (((sub @ (X244 @ X247 @ X248) @ X246)) = ((X244 @ (comp @ X247 @ X246) @ (sub @ X248 @ X246))))) | ~ ! [X243 : term,X242 : term] : (($true != ((X241 @ id @ X243 @ id))) | ($true = ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) | ($true != ((X241 @ id @ X242 @ id)))) | ($true = ((X241 @ id @ X240 @ id))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X195 : term] : ~ ! [X196 : (subst > term > term)] : ~ ! [X198 : term,X197 : subst] : (((X196 @ X197 @ X198)) = ((sub @ X195 @ (push @ X198 @ X197)))) => (! [X199 : term] : (((sub @ X199 @ id)) = X199) => ! [X200 : term,X202 : (term > $o),X201 : (subst > term > subst > $o)] : (~ ! [X203 : term] : (((X201 @ id @ X203 @ id)) = ((X202 @ X203))) | ~ ! [X209 : term] : ((((X202 @ (sub @ X200 @ (push @ X209 @ id)))) = $true) | ($true != ((X202 @ X209)))) | (((X202 @ (lam @ X200))) = $true) | ~ ! [X204 : (subst > term > term)] : (~ ! [X208 : term] : ((((X201 @ id @ (X204 @ id @ X208) @ id)) = $true) | ($true != ((X201 @ id @ X208 @ id)))) | ($true = ((X201 @ id @ (lam @ (X204 @ sh @ one)) @ id))) | ~ ! [X206 : term,X207 : subst,X205 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205)))))))))),
% 6.46/1.22 inference(flattening,[],[f9])).
% 6.46/1.22 thf(f11,plain,(
% 6.46/1.22 ((apinj1 = $true) <=> ! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149))))) & (! [X307 : (subst > term > subst > $o),X308 : term] : (? [X311 : (subst > term > term),X310 : term] : (($true != ((X307 @ id @ (lam @ (X311 @ sh @ one)) @ id))) & ! [X317 : subst,X318 : term,X316 : subst] : (((X311 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316))) = ((sub @ X310 @ (push @ (sub @ X318 @ X316) @ (comp @ X317 @ X316))))) & ! [X312 : term] : ((((X307 @ id @ X312 @ id)) != $true) | ($true = ((X307 @ id @ (X311 @ id @ X312) @ id)))) & ! [X314 : subst,X315 : term,X313 : subst] : (((sub @ (X311 @ X314 @ X315) @ X313)) = ((sub @ (sub @ X310 @ (push @ X315 @ X314)) @ X313)))) | ? [X309 : term] : (($true = ((X307 @ id @ X309 @ id))) & ($true != ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id)))) | (((X307 @ id @ (lam @ (sub @ X308 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem1_lthm = $true) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) != ((d2subst @ X305))) | (X305 = X306)) & (hoasinduction_lem1 = $true) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X340 : (term > $o),X341 : term] : (? [X342 : term,X343 : term] : ((((X340 @ X343)) = $true) & ($true = ((X340 @ X342))) & ($true != ((X340 @ (ap @ X343 @ X342))))) | ($true = ((X340 @ X341))) | ? [X345 : term] : ((((X340 @ (lam @ X345))) != $true) & ($true = ((X340 @ X345)))) | ? [X344 : term] : (($true = ((var @ X344))) & ($true != ((X340 @ X344))))) <=> (induction = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X177 : (subst > term > subst > $o),X176 : term] : ((((X177 @ id @ X176 @ id)) = $true) | ? [X179 : term,X178 : term] : ((((X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) != $true) & (((X177 @ id @ X178 @ id)) = $true) & ($true = ((X177 @ id @ X179 @ id)))) | ? [X180 : (subst > term > term)] : (! [X182 : subst,X183 : term,X181 : subst] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182)))) & ! [X184 : term] : (($true != ((X177 @ id @ X184 @ id))) | (((X177 @ id @ (X180 @ id @ X184) @ id)) = $true)) & (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) != $true))) | ? [X167 : (subst > term > subst > $o),X168 : term,X166 : (term > $o)] : ((((X166 @ (lam @ X168))) != $true) & ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id))) & ! [X174 : term] : (($true = ((X166 @ (sub @ X168 @ (push @ X174 @ id))))) | ($true != ((X166 @ X174)))) & ! [X169 : (subst > term > term)] : ((((X167 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ? [X170 : term] : ((((X167 @ id @ (X169 @ id @ X170) @ id)) != $true) & ($true = ((X167 @ id @ X170 @ id)))) | ? [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) != ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))))) | ? [X165 : term] : (((sub @ X165 @ id)) != X165)) | ? [X158 : term,X159 : (term > $o)] : (! [X161 : term,X160 : term] : (($true = ((X159 @ (ap @ X160 @ X161)))) | ($true != ((X159 @ X160))) | ($true != ((X159 @ X161)))) & ($true != ((X159 @ X158))) & ! [X163 : term] : (? [X164 : term] : (($true = ((X159 @ X164))) & ($true != ((X159 @ (sub @ X163 @ (push @ X164 @ id)))))) | ($true = ((X159 @ (lam @ X163))))) & ! [X162 : term] : (($true != ((var @ X162))) | ($true = ((X159 @ X162)))))) | ? [X155 : (subst > term > subst > $o)] : ! [X156 : (term > $o)] : ? [X157 : term] : (((X155 @ id @ X157 @ id)) != ((X156 @ X157))))) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (induction2lem_gthm = $true) & ((hoasapinj1_lthm = $true) <=> ((! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118)))) | ? [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 != X117) & (((ap @ X116 @ X115)) = ((ap @ X117 @ X114))))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((axidr = $true) <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lthm = $true) <=> (((! [X421 : (subst > term > subst > $o),X420 : term] : (? [X433 : (subst > term > term)] : (($true != ((X421 @ id @ (lam @ (X433 @ sh @ one)) @ id))) & ! [X435 : term,X434 : subst,X436 : subst] : (((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X434 @ X435) @ X436))) & ! [X437 : term] : (($true = ((X421 @ id @ (X433 @ id @ X437) @ id))) | (((X421 @ id @ X437 @ id)) != $true))) | ? [X422 : term] : ((((var @ (sub @ X422 @ id))) = $true) & ($true != ((X421 @ id @ X422 @ id)))) | ? [X426 : subst,X428 : term,X425 : subst,X427 : subst] : (($true = ((X421 @ (comp @ X425 @ X426) @ (sub @ X428 @ X426) @ X427))) & (((X421 @ X425 @ X428 @ (comp @ X426 @ X427))) != $true)) | ($true = ((X421 @ id @ X420 @ id))) | ? [X424 : term,X423 : term] : ((((X421 @ id @ (ap @ (sub @ X423 @ id) @ X424) @ id)) != $true) & (((X421 @ id @ X423 @ id)) = $true) & (((X421 @ id @ X424 @ id)) = $true)) | ? [X429 : subst,X432 : term,X430 : subst,X431 : subst] : (($true != ((X421 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X429))) & ($true = ((X421 @ X430 @ X432 @ (comp @ X431 @ X429)))))) | ? [X405 : term,X404 : (subst > term > subst > $o)] : (! [X415 : term] : (($true != ((X404 @ id @ X415 @ id))) | (((X404 @ id @ (sub @ X405 @ (push @ X415 @ id)) @ id)) = $true)) & ! [X417 : subst,X418 : subst,X416 : subst,X419 : term] : (($true != ((X404 @ X417 @ X419 @ (comp @ X418 @ X416)))) | ($true = ((X404 @ (comp @ X417 @ X418) @ (sub @ X419 @ X418) @ X416)))) & ! [X406 : (subst > term > term)] : (? [X407 : term] : ((((X404 @ id @ X407 @ id)) = $true) & ($true != ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ? [X410 : subst,X409 : subst,X408 : term] : (((X406 @ (comp @ X410 @ X409) @ (sub @ X408 @ X409))) != ((sub @ (X406 @ X410 @ X408) @ X409))) | ($true = ((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)))) & ! [X412 : subst,X414 : term,X411 : subst,X413 : subst] : (($true != ((X404 @ (comp @ X411 @ X413) @ (sub @ X414 @ X413) @ X412))) | ($true = ((X404 @ X411 @ X414 @ (comp @ X413 @ X412))))) & (((X404 @ id @ (lam @ X405) @ id)) != $true))) | ? [X393 : term,X392 : term,X391 : (subst > term > subst > $o)] : ((((X391 @ id @ X393 @ id)) = $true) & ($true = ((X391 @ id @ X392 @ id))) & ! [X394 : term,X395 : term] : ((((X391 @ id @ (ap @ (sub @ X395 @ id) @ X394) @ id)) = $true) | ($true != ((X391 @ id @ X395 @ id))) | ($true != ((X391 @ id @ X394 @ id)))) & ! [X400 : term,X402 : subst,X403 : subst,X401 : subst] : (($true = ((X391 @ X403 @ X400 @ (comp @ X402 @ X401)))) | ($true != ((X391 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401)))) & ! [X398 : subst,X399 : subst,X396 : term,X397 : subst] : ((((X391 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398)) = $true) | ($true != ((X391 @ X397 @ X396 @ (comp @ X399 @ X398))))) & (((X391 @ id @ (ap @ X392 @ X393) @ id)) != $true))) | ? [X384 : term,X385 : (term > $o)] : (! [X390 : term] : (($true != ((var @ X390))) | (((X385 @ X390)) = $true)) & ($true != ((X385 @ X384))) & ! [X388 : term] : (? [X389 : term] : (($true != ((X385 @ (sub @ X388 @ (push @ X389 @ id))))) & ($true = ((X385 @ X389)))) | ($true = ((X385 @ (lam @ X388))))) & ! [X387 : term,X386 : term] : (($true != ((X385 @ X387))) | ($true != ((X385 @ X386))) | (((X385 @ (ap @ X386 @ X387))) = $true))))) & (hoasinduction_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (axapp = $true) & (axmap = $true) & (! [X524 : (subst > term > subst > $o),X523 : term] : (($true = ((X524 @ id @ (lam @ X523) @ id))) | ? [X525 : term] : ((((X524 @ id @ X525 @ id)) = $true) & (((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) != $true)) | ? [X526 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) & ! [X527 : term] : (($true != ((X524 @ id @ X527 @ id))) | ($true = ((X524 @ id @ (X526 @ id @ X527) @ id)))) & ! [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530))))) <=> (hoasinduction_lem3a = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X231 : (subst > term > term),X232 : subst,X233 : (subst > term > term),X230 : term] : (? [X236 : subst,X234 : subst,X235 : term] : (((X231 @ (comp @ X234 @ X236) @ (sub @ X235 @ X236))) != ((sub @ (X231 @ X234 @ X235) @ X236))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X231 @ sh @ one)))) | ? [X239 : subst,X238 : subst,X237 : term] : (((sub @ (X233 @ X239 @ X237) @ X238)) != ((X233 @ (comp @ X239 @ X238) @ (sub @ X237 @ X238)))) | (((X231 @ X232 @ X230)) = ((X233 @ X232 @ X230)))) | ? [X229 : term,X228 : term] : ((((lam @ X228)) = ((lam @ X229))) & (X228 != X229))) | ? [X226 : term,X227 : subst] : (((comp @ sh @ (push @ X226 @ X227))) != X227)) | ? [X225 : term,X224 : subst] : (((sub @ one @ (push @ X225 @ X224))) != X225))) & ((termmset_lthm = $true) <=> (! [X266 : term] : (((sub @ X266 @ id)) = X266) | ? [X265 : term] : (((sub @ X265 @ id)) != X265))) & (! [X348 : term,X346 : (subst > term > term),X347 : term] : (? [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) != ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347)))) <=> (hoaslamnotap = $true)) & (pushprop_gthm = $true) & ((((! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)) | ? [X268 : subst] : (((comp @ X268 @ id)) != X268)) | ? [X267 : subst] : (((comp @ id @ X267)) != X267)) <=> (substmonoid_lthm = $true)) & ((! [X323 : term,X324 : (term > $o),X322 : (subst > term > subst > $o)] : (? [X333 : subst,X331 : subst,X334 : term,X332 : subst] : (($true != ((X322 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X331))) & ($true = ((X322 @ X333 @ X334 @ (comp @ X332 @ X331))))) | ? [X328 : subst,X327 : term,X326 : subst,X329 : subst] : (($true != ((X322 @ X328 @ X327 @ (comp @ X326 @ X329)))) & (((X322 @ (comp @ X328 @ X326) @ (sub @ X327 @ X326) @ X329)) = $true)) | ? [X330 : term] : (((X324 @ X330)) != ((X322 @ id @ X330 @ id))) | ? [X335 : (subst > term > term)] : (! [X339 : term] : (($true != ((X322 @ id @ X339 @ id))) | (((X322 @ id @ (X335 @ id @ X339) @ id)) = $true)) & ($true != ((X322 @ id @ (lam @ (X335 @ sh @ one)) @ id))) & ! [X337 : term,X338 : subst,X336 : subst] : (((sub @ (X335 @ X336 @ X337) @ X338)) = ((X335 @ (comp @ X336 @ X338) @ (sub @ X337 @ X338))))) | ($true = ((X324 @ (lam @ X323)))) | ? [X325 : term] : (($true != ((X324 @ (sub @ X323 @ (push @ X325 @ id))))) & ($true = ((X324 @ X325))))) | ? [X321 : term] : (((sub @ X321 @ id)) != X321)) <=> (hoasinduction_lem3v2_lthm = $true)) & (((d2subst @ d_id)) = sh) & (! [X74 : term,X75 : term,X76 : (subst > term > subst > $o)] : (($true != ((X76 @ id @ X75 @ id))) | ? [X86 : term,X83 : subst,X85 : subst,X84 : subst] : (($true != ((X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85))) & ($true = ((X76 @ X84 @ X86 @ (comp @ X83 @ X85))))) | (((X76 @ id @ X74 @ id)) != $true) | ($true = ((X76 @ id @ (ap @ X74 @ X75) @ id))) | ? [X79 : subst,X80 : term,X82 : subst,X81 : subst] : (($true != ((X76 @ X81 @ X80 @ (comp @ X82 @ X79)))) & ($true = ((X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79)))) | ? [X78 : term,X77 : term] : (($true = ((X76 @ id @ X77 @ id))) & ($true != ((X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id))) & (((X76 @ id @ X78 @ id)) = $true))) <=> (hoasinduction_lem2 = $true)) & (((((! [X45 : term,X46 : (term > $o),X47 : subst] : (? [X50 : term] : (! [X51 : term] : ((((X46 @ (sub @ X50 @ (push @ X51 @ id)))) = $true) | ($true != ((X46 @ X51)))) & ($true != ((X46 @ (lam @ X50))))) | ($true = ((X46 @ (sub @ X45 @ X47)))) | ? [X52 : term] : ((((var @ X52)) = $true) & ($true != ((X46 @ (sub @ X52 @ X47))))) | ? [X48 : term,X49 : term] : (($true = ((X46 @ X49))) & ($true = ((X46 @ X48))) & (((X46 @ (ap @ X49 @ X48))) != $true))) | ? [X39 : (term > $o),X40 : term] : (! [X43 : term,X42 : term] : (($true != ((X39 @ X42))) | (((X39 @ (ap @ X42 @ X43))) = $true) | (((X39 @ X43)) != $true)) & ! [X41 : term] : (($true = ((X39 @ X41))) | (((var @ X41)) != $true)) & (((X39 @ X40)) != $true) & ! [X44 : term] : (($true = ((X39 @ (lam @ X44)))) | ($true != ((X39 @ X44)))))) | ? [X38 : subst] : (((comp @ X38 @ id)) != X38)) | ? [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) != X37)) | ? [X34 : subst,X35 : term] : (((sub @ one @ (push @ X35 @ X34))) != X35)) <=> (induction2lem_lthm = $true)) & ((axscons = $true) <=> ! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508)) & ((! [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true != ((X214 @ X215))) | ? [X216 : term] : (((X212 @ X216)) != ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ($true = ((X212 @ one)))) | ? [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) != X210)) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X514 : (term > $o),X513 : term,X512 : (subst > term > subst > $o)] : (? [X515 : (subst > term > term)] : (! [X517 : subst,X518 : term,X516 : subst] : (((sub @ (X515 @ X517 @ X518) @ X516)) = ((X515 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516)))) & ! [X519 : term] : ((((X512 @ id @ (X515 @ id @ X519) @ id)) = $true) | (((X512 @ id @ X519 @ id)) != $true)) & (((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id)) != $true)) | ? [X521 : term] : (($true != ((X514 @ (sub @ X513 @ (push @ X521 @ id))))) & ($true = ((X514 @ X521)))) | ($true = ((X514 @ (lam @ X513)))) | ? [X520 : term] : (((X514 @ X520)) != ((X512 @ id @ X520 @ id))))) & ! [X352 : d_term,X353 : d_term] : ((((d2term @ X352)) != ((d2term @ X353))) | (X352 = X353)) & (hoasapnotvar_lthm = $true) & (! [X274 : term,X273 : (subst > term > subst > $o)] : (($true = ((X273 @ id @ (lam @ X274) @ id))) | ? [X279 : (subst > term > term)] : (! [X280 : subst,X282 : subst,X281 : term] : (((sub @ (X279 @ X280 @ X281) @ X282)) = ((X279 @ (comp @ X280 @ X282) @ (sub @ X281 @ X282)))) & ! [X283 : term] : ((((X273 @ id @ (X279 @ id @ X283) @ id)) = $true) | (((X273 @ id @ X283 @ id)) != $true)) & (((X273 @ id @ (lam @ (X279 @ sh @ one)) @ id)) != $true)) | ? [X284 : term] : (($true != ((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id))) & ($true = ((X273 @ id @ X284 @ id)))) | ? [X278 : subst,X276 : term,X277 : subst,X275 : subst] : (($true != ((X273 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275))) & ($true = ((X273 @ X277 @ X276 @ (comp @ X278 @ X275))))) | ? [X286 : subst,X288 : subst,X285 : term,X287 : subst] : (($true != ((X273 @ X288 @ X285 @ (comp @ X287 @ X286)))) & (((X273 @ (comp @ X288 @ X287) @ (sub @ X285 @ X287) @ X286)) = $true))) <=> (hoasinduction_lem3 = $true)) & ((hoasinduction = $true) <=> ! [X11 : (subst > term > subst > $o),X10 : term] : (? [X12 : term] : (($true != ((X11 @ id @ X12 @ id))) & (((var @ (sub @ X12 @ id))) = $true)) | ? [X24 : term,X25 : subst,X26 : subst,X27 : subst] : (($true != ((X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25))) & (((X11 @ X27 @ X24 @ (comp @ X26 @ X25))) = $true)) | ($true = ((X11 @ id @ X10 @ id))) | ? [X17 : term,X18 : term] : (($true = ((X11 @ id @ X17 @ id))) & (((X11 @ id @ X18 @ id)) = $true) & ($true != ((X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id)))) | ? [X13 : subst,X14 : term,X16 : subst,X15 : subst] : ((((X11 @ X13 @ X14 @ (comp @ X16 @ X15))) != $true) & (((X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15)) = $true)) | ? [X19 : (subst > term > term)] : (! [X23 : subst,X22 : subst,X21 : term] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22)))) & ! [X20 : term] : ((((X11 @ id @ (X19 @ id @ X20) @ id)) = $true) | ($true != ((X11 @ id @ X20 @ id)))) & (((X11 @ id @ (lam @ (X19 @ sh @ one)) @ id)) != $true)))) & ! [X511 : d_subst] : (d_id = X511) & (! [X376 : term,X375 : (term > $o)] : (? [X380 : term] : ((((X375 @ (lam @ X380))) != $true) & ! [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true) | ($true != ((X375 @ X381))))) | ? [X379 : term,X378 : term] : ((((X375 @ X378)) = $true) & ($true = ((X375 @ X379))) & ($true != ((X375 @ (ap @ X378 @ X379))))) | ($true = ((X375 @ X376))) | ? [X377 : term] : ((((X375 @ X377)) != $true) & ($true = ((var @ X377))))) <=> (induction2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (induction2_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoaslaminj = $true) <=> ! [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ? [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) != ((sub @ (X250 @ X258 @ X259) @ X257))) | ? [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) != ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | (((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252))))) & (axassoc = $true) & (pushprop_lthm = $true) & (pushprop_lem3v2 = $true) & (termmset_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X89 : (subst > term > subst > $o),X88 : term,X87 : (term > $o)] : (? [X90 : term] : ((((X87 @ (sub @ X88 @ (push @ X90 @ id)))) != $true) & (((X87 @ X90)) = $true)) | ? [X96 : (subst > term > term)] : ((((X89 @ id @ (lam @ (X96 @ sh @ one)) @ id)) != $true) & ! [X99 : subst,X100 : term,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98))) & ! [X97 : term] : ((((X89 @ id @ X97 @ id)) != $true) | (((X89 @ id @ (X96 @ id @ X97) @ id)) = $true))) | ? [X102 : subst,X101 : subst,X104 : term,X103 : subst] : (($true != ((X89 @ X101 @ X104 @ (comp @ X103 @ X102)))) & ($true = ((X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102)))) | ? [X95 : term] : (((X87 @ X95)) != ((X89 @ id @ X95 @ id))) | ($true = ((X87 @ (lam @ X88)))) | ? [X92 : term,X93 : subst,X91 : subst,X94 : subst] : (($true = ((X89 @ X94 @ X92 @ (comp @ X91 @ X93)))) & ($true != ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93)))))) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) <=> (laminj = $true)) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_gthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3a_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) | ($true != ((X260 @ X264)))) <=> (pushprop_lem1 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1v2 = $true) & ! [X142 : d_term] : (d_one = X142) & ((shinj = $true) <=> ! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh))))) & (! [X30 : (subst > term > subst > $o)] : ? [X31 : (term > $o)] : ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X371 : term,X370 : (term > $o),X372 : subst] : ? [X373 : (term > $o)] : ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374)))) & (pushprop_lem2v2_lthm = $true) & (axvarshift = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X290 : (subst > term > subst > $o),X289 : term] : (? [X296 : term] : ((((X290 @ id @ X296 @ id)) = $true) & (((X290 @ id @ (sub @ X289 @ (push @ X296 @ id)) @ id)) != $true)) | ? [X291 : (subst > term > term)] : (! [X292 : subst,X294 : subst,X293 : term] : (((sub @ (X291 @ X294 @ X293) @ X292)) = ((X291 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292)))) & (((X290 @ id @ (lam @ (X291 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : (($true = ((X290 @ id @ (X291 @ id @ X295) @ id))) | (((X290 @ id @ X295 @ id)) != $true))) | (((X290 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) = $true))) & (hoaslamnotvar_lthm = $true) & (((((! [X459 : (subst > term > subst > $o),X460 : term] : (($true = ((X459 @ id @ X460 @ id))) | ? [X461 : (subst > term > term)] : (($true != ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id))) & ! [X462 : term] : ((((X459 @ id @ (X461 @ id @ X462) @ id)) = $true) | ($true != ((X459 @ id @ X462 @ id)))) & ! [X463 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X463) @ (sub @ X465 @ X463))) = ((sub @ (X461 @ X464 @ X465) @ X463)))) | ? [X466 : term] : ((((var @ (sub @ X466 @ id))) = $true) & (((X459 @ id @ X466 @ id)) != $true)) | ? [X472 : term,X471 : term] : (($true = ((X459 @ id @ X472 @ id))) & ($true = ((X459 @ id @ X471 @ id))) & ($true != ((X459 @ id @ (ap @ (sub @ X471 @ id) @ X472) @ id)))) | ? [X473 : subst,X476 : term,X474 : subst,X475 : subst] : (($true = ((X459 @ (comp @ X475 @ X473) @ (sub @ X476 @ X473) @ X474))) & ($true != ((X459 @ X475 @ X476 @ (comp @ X473 @ X474))))) | ? [X468 : subst,X469 : subst,X470 : subst,X467 : term] : (($true = ((X459 @ X468 @ X467 @ (comp @ X469 @ X470)))) & (((X459 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469) @ X470)) != $true))) | ? [X449 : term,X451 : (subst > term > subst > $o),X450 : (term > $o)] : (! [X452 : term] : (((X451 @ id @ X452 @ id)) = ((X450 @ X452))) & ! [X453 : term] : ((((X450 @ (sub @ X449 @ (push @ X453 @ id)))) = $true) | ($true != ((X450 @ X453)))) & ! [X454 : (subst > term > term)] : (? [X457 : term,X458 : subst,X456 : subst] : (((X454 @ (comp @ X456 @ X458) @ (sub @ X457 @ X458))) != ((sub @ (X454 @ X456 @ X457) @ X458))) | (((X451 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ? [X455 : term] : (($true != ((X451 @ id @ (X454 @ id @ X455) @ id))) & ($true = ((X451 @ id @ X455 @ id))))) & ($true != ((X450 @ (lam @ X449)))))) | ? [X448 : term] : (((sub @ X448 @ id)) != X448)) | ? [X441 : term,X442 : (term > $o)] : (! [X443 : term] : ((((X442 @ (lam @ X443))) = $true) | ? [X444 : term] : (($true = ((X442 @ X444))) & (((X442 @ (sub @ X443 @ (push @ X444 @ id)))) != $true))) & ! [X447 : term] : (($true = ((X442 @ X447))) | (((var @ X447)) != $true)) & (((X442 @ X441)) != $true) & ! [X446 : term,X445 : term] : (($true = ((X442 @ (ap @ X446 @ X445)))) | ($true != ((X442 @ X446))) | (((X442 @ X445)) != $true)))) | ? [X438 : (subst > term > subst > $o)] : ! [X439 : (term > $o)] : ? [X440 : term] : (((X439 @ X440)) != ((X438 @ id @ X440 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & (hoasapinj2_gthm = $true) & (! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) <=> (hoasapinj2 = $true)) & (hoaslamnotvar = $true) & ((induction2lem = $true) <=> ! [X105 : subst,X107 : term,X106 : (term > $o)] : (? [X112 : term] : (($true != ((X106 @ (sub @ X112 @ X105)))) & ($true = ((var @ X112)))) | ($true = ((X106 @ (sub @ X107 @ X105)))) | ? [X108 : term] : (($true != ((X106 @ (lam @ X108)))) & ! [X109 : term] : ((((X106 @ (sub @ X108 @ (push @ X109 @ id)))) = $true) | ($true != ((X106 @ X109))))) | ? [X110 : term,X111 : term] : (($true != ((X106 @ (ap @ X111 @ X110)))) & ($true = ((X106 @ X110))) & ($true = ((X106 @ X111)))))) & (hoasinduction_lem2v2_gthm = $true) & (lamnotap != $true) & (lamnotvar = $true) & ((! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192)) | ? [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) = ((ap @ X185 @ X187))) & (X187 != X188))) <=> (hoasapinj2_lthm = $true)) & ((axvarid = $true) <=> ! [X249 : term] : (((sub @ X249 @ id)) = X249)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aa = $true) <=> ! [X297 : term,X298 : (subst > term > subst > $o)] : (? [X299 : (subst > term > term)] : ((((X298 @ id @ (lam @ (X299 @ sh @ one)) @ id)) != $true) & ! [X303 : term] : ((((X298 @ id @ (X299 @ id @ X303) @ id)) = $true) | ($true != ((X298 @ id @ X303 @ id)))) & ! [X302 : term,X301 : subst,X300 : subst] : (((sub @ (X299 @ X300 @ X302) @ X301)) = ((X299 @ (comp @ X300 @ X301) @ (sub @ X302 @ X301))))) | ? [X304 : term] : (($true != ((X298 @ id @ (sub @ X297 @ (push @ X304 @ id)) @ id))) & (((X298 @ id @ X304 @ id)) = $true)) | ($true = ((X298 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id))))) & (ulamvarind = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X522 : term] : (((sub @ X522 @ id)) = X522) <=> (termmset = $true)) & (axabs = $true) & (! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) <=> (apinj2 = $true)) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X487 : (subst > term > subst > $o),X486 : term] : (? [X491 : subst,X488 : subst,X490 : term,X489 : subst] : (($true != ((X487 @ (comp @ X488 @ X491) @ (sub @ X490 @ X491) @ X489))) & (((X487 @ X488 @ X490 @ (comp @ X491 @ X489))) = $true)) | ? [X497 : (subst > term > term)] : (! [X500 : subst,X501 : term,X499 : subst] : (((X497 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) = ((sub @ (X497 @ X499 @ X501) @ X500))) & ($true != ((X487 @ id @ (lam @ (X497 @ sh @ one)) @ id))) & ! [X498 : term] : (($true != ((X487 @ id @ X498 @ id))) | ($true = ((X487 @ id @ (X497 @ id @ X498) @ id))))) | ? [X496 : term] : ((((X487 @ id @ X496 @ id)) = $true) & ($true != ((X487 @ id @ (sub @ X486 @ (push @ X496 @ id)) @ id)))) | ? [X492 : term,X495 : subst,X494 : subst,X493 : subst] : (($true = ((X487 @ (comp @ X495 @ X494) @ (sub @ X492 @ X494) @ X493))) & ($true != ((X487 @ X495 @ X492 @ (comp @ X494 @ X493))))) | ($true = ((X487 @ id @ (lam @ X486) @ id)))) | ? [X478 : term,X479 : (subst > term > subst > $o)] : (! [X481 : (subst > term > term)] : ((((X479 @ id @ (lam @ (X481 @ sh @ one)) @ id)) = $true) | ? [X482 : term] : (($true != ((X479 @ id @ (X481 @ id @ X482) @ id))) & ($true = ((X479 @ id @ X482 @ id)))) | ? [X483 : subst,X485 : term,X484 : subst] : (((sub @ (X481 @ X483 @ X485) @ X484)) != ((X481 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484))))) & ! [X480 : term] : (($true != ((X479 @ id @ X480 @ id))) | (((X479 @ id @ (sub @ X478 @ (push @ X480 @ id)) @ id)) = $true)) & (((X479 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)) != $true))) | ? [X477 : term] : (((sub @ X477 @ id)) != X477))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X143 : term] : ? [X144 : (subst > term > term)] : ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145)))) & (! [X502 : term] : ? [X503 : (subst > term > term)] : (((X503 @ sh @ one)) = ((sub @ X502 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasapnotvar = $true) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = id) & (! [X271 : term] : ? [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) = ((X272 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (ulamvarsh = $true) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X151 : term] : ? [X152 : (subst > term > term)] : ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153)))) & (pushprop_lem0_gthm = $true) & (! [X128 : (term > $o),X129 : term,X130 : term,X127 : (subst > term > subst > $o)] : (? [X136 : subst,X135 : subst,X134 : subst,X133 : term] : (($true != ((X127 @ X134 @ X133 @ (comp @ X135 @ X136)))) & (((X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136)) = $true)) | ($true = ((X128 @ (ap @ X129 @ X130)))) | ? [X131 : term,X132 : term] : (($true != ((X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) & ($true = ((X127 @ id @ X132 @ id))) & ($true = ((X127 @ id @ X131 @ id)))) | (((X128 @ X130)) != $true) | (((X128 @ X129)) != $true) | ? [X137 : term,X139 : subst,X140 : subst,X138 : subst] : (($true = ((X127 @ X138 @ X137 @ (comp @ X139 @ X140)))) & ($true != ((X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)))) | ? [X141 : term] : (((X128 @ X141)) != ((X127 @ id @ X141 @ id)))) <=> (hoasinduction_lem2v2 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1 = $true) <=> ! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56))) & ((induction2_lthm = $true) <=> ((! [X363 : term,X364 : (term > $o)] : ((((X364 @ X363)) = $true) | ? [X367 : term,X366 : term] : (($true = ((X364 @ X366))) & (((X364 @ X367)) = $true) & ($true != ((X364 @ (ap @ X366 @ X367))))) | ? [X368 : term] : (! [X369 : term] : ((((X364 @ (sub @ X368 @ (push @ X369 @ id)))) = $true) | ($true != ((X364 @ X369)))) & (((X364 @ (lam @ X368))) != $true)) | ? [X365 : term] : ((((X364 @ X365)) != $true) & ($true = ((var @ X365))))) | ? [X355 : term,X357 : (term > $o),X356 : subst] : (! [X359 : term] : (? [X360 : term] : (($true = ((X357 @ X360))) & ($true != ((X357 @ (sub @ X359 @ (push @ X360 @ id)))))) | ($true = ((X357 @ (lam @ X359))))) & ! [X361 : term,X362 : term] : (($true = ((X357 @ (ap @ X361 @ X362)))) | ($true != ((X357 @ X361))) | (((X357 @ X362)) != $true)) & ! [X358 : term] : ((((var @ X358)) != $true) | ($true = ((X357 @ (sub @ X358 @ X356))))) & ($true != ((X357 @ (sub @ X355 @ X356)))))) | ? [X354 : term] : (((sub @ X354 @ id)) != X354))) & (pushprop = $true) & (((! [X66 : term,X67 : (subst > term > subst > $o)] : (? [X69 : (subst > term > term)] : (! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))) & ($true != ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id))) & ! [X70 : term] : (($true = ((X67 @ id @ (X69 @ id @ X70) @ id))) | (((X67 @ id @ X70 @ id)) != $true))) | ($true = ((X67 @ id @ (lam @ X66) @ id))) | ? [X68 : term] : (($true != ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id))) & ($true = ((X67 @ id @ X68 @ id))))) | ? [X59 : term,X58 : (subst > term > subst > $o)] : (! [X60 : term] : ((((X58 @ id @ X60 @ id)) != $true) | ($true = ((X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id)))) & (((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id)) != $true) & ! [X61 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id)) = $true) | ? [X65 : subst,X63 : term,X64 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) != ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))) | ? [X62 : term] : (($true != ((X58 @ id @ (X61 @ id @ X62) @ id))) & (((X58 @ id @ X62 @ id)) = $true))))) | ? [X57 : term] : (((sub @ X57 @ id)) != X57)) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (? [X126 : term] : (((X125 @ X126)) != ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ($true != ((X124 @ X122))) | ($true = ((X125 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((pushprop_lem1_lthm = $true) <=> ((! [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true) | (((X9 @ X5)) != $true)) | ? [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) != X4)) | ? [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) != X1))) & (ulamvar1 != $true) & (apnotvar = $true) & (pushprop_lem3v2_lthm = $true) & (axclos = $true) & (! [X533 : (subst > term > subst > $o)] : ? [X534 : (term > $o)] : ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) <=> (hoasinduction_lem0 = $true)) & (! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) <=> (axvarcons = $true)) & (hoasinduction_lem1_gthm = $true) & ((axidl = $true) <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & ((pushprop_lem0 = $true) <=> ! [X219 : subst,X217 : (term > $o),X218 : term] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221)))) & (pushprop_lem2v2_gthm = $true) & ((substmonoid = $true) <=> (! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X240 : term,X241 : (subst > term > subst > $o)] : (? [X242 : term,X243 : term] : (($true != ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) & ($true = ((X241 @ id @ X242 @ id))) & ($true = ((X241 @ id @ X243 @ id)))) | ? [X244 : (subst > term > term)] : (! [X245 : term] : (($true != ((X241 @ id @ X245 @ id))) | (((X241 @ id @ (X244 @ id @ X245) @ id)) = $true)) & ! [X246 : subst,X247 : subst,X248 : term] : (((sub @ (X244 @ X247 @ X248) @ X246)) = ((X244 @ (comp @ X247 @ X246) @ (sub @ X248 @ X246)))) & ($true != ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id)))) | ($true = ((X241 @ id @ X240 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X202 : (term > $o),X200 : term,X201 : (subst > term > subst > $o)] : (? [X209 : term] : (($true = ((X202 @ X209))) & (((X202 @ (sub @ X200 @ (push @ X209 @ id)))) != $true)) | ? [X203 : term] : (((X201 @ id @ X203 @ id)) != ((X202 @ X203))) | (((X202 @ (lam @ X200))) = $true) | ? [X204 : (subst > term > term)] : (($true != ((X201 @ id @ (lam @ (X204 @ sh @ one)) @ id))) & ! [X208 : term] : ((((X201 @ id @ (X204 @ id @ X208) @ id)) = $true) | ($true != ((X201 @ id @ X208 @ id)))) & ! [X206 : term,X207 : subst,X205 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205)))))) | ? [X199 : term] : (((sub @ X199 @ id)) != X199)) | ? [X195 : term] : ! [X196 : (subst > term > term)] : ? [X197 : subst,X198 : term] : (((X196 @ X197 @ X198)) != ((sub @ X195 @ (push @ X198 @ X197))))))),
% 6.46/1.22 inference(ennf_transformation,[],[f10])).
% 6.46/1.22 thf(f12,plain,(
% 6.46/1.22 ((hoaslaminj_lthm = $true) <=> (? [X226 : term,X227 : subst] : (((comp @ sh @ (push @ X226 @ X227))) != X227) | ! [X231 : (subst > term > term),X232 : subst,X233 : (subst > term > term),X230 : term] : (? [X236 : subst,X234 : subst,X235 : term] : (((X231 @ (comp @ X234 @ X236) @ (sub @ X235 @ X236))) != ((sub @ (X231 @ X234 @ X235) @ X236))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X231 @ sh @ one)))) | ? [X239 : subst,X238 : subst,X237 : term] : (((sub @ (X233 @ X239 @ X237) @ X238)) != ((X233 @ (comp @ X239 @ X238) @ (sub @ X237 @ X238)))) | (((X231 @ X232 @ X230)) = ((X233 @ X232 @ X230)))) | ? [X225 : term,X224 : subst] : (((sub @ one @ (push @ X225 @ X224))) != X225) | ? [X229 : term,X228 : term] : ((((lam @ X228)) = ((lam @ X229))) & (X228 != X229)))) & ((! [X323 : term,X324 : (term > $o),X322 : (subst > term > subst > $o)] : (? [X333 : subst,X331 : subst,X334 : term,X332 : subst] : (($true != ((X322 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X331))) & ($true = ((X322 @ X333 @ X334 @ (comp @ X332 @ X331))))) | ? [X328 : subst,X327 : term,X326 : subst,X329 : subst] : (($true != ((X322 @ X328 @ X327 @ (comp @ X326 @ X329)))) & (((X322 @ (comp @ X328 @ X326) @ (sub @ X327 @ X326) @ X329)) = $true)) | ? [X330 : term] : (((X324 @ X330)) != ((X322 @ id @ X330 @ id))) | ? [X335 : (subst > term > term)] : (! [X339 : term] : (($true != ((X322 @ id @ X339 @ id))) | (((X322 @ id @ (X335 @ id @ X339) @ id)) = $true)) & ($true != ((X322 @ id @ (lam @ (X335 @ sh @ one)) @ id))) & ! [X337 : term,X338 : subst,X336 : subst] : (((sub @ (X335 @ X336 @ X337) @ X338)) = ((X335 @ (comp @ X336 @ X338) @ (sub @ X337 @ X338))))) | ($true = ((X324 @ (lam @ X323)))) | ? [X325 : term] : (($true != ((X324 @ (sub @ X323 @ (push @ X325 @ id))))) & ($true = ((X324 @ X325))))) | ? [X321 : term] : (((sub @ X321 @ id)) != X321)) <=> (hoasinduction_lem3v2_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X219 : subst,X217 : (term > $o),X218 : term] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221)))) & (axvarshift = $true) & (lamnotap != $true) & ! [X511 : d_subst] : (d_id = X511) & (! [X524 : (subst > term > subst > $o),X523 : term] : (($true = ((X524 @ id @ (lam @ X523) @ id))) | ? [X525 : term] : ((((X524 @ id @ X525 @ id)) = $true) & (((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) != $true)) | ? [X526 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) & ! [X527 : term] : (($true != ((X524 @ id @ X527 @ id))) | ($true = ((X524 @ id @ (X526 @ id @ X527) @ id)))) & ! [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530))))) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X297 : term,X298 : (subst > term > subst > $o)] : (? [X299 : (subst > term > term)] : ((((X298 @ id @ (lam @ (X299 @ sh @ one)) @ id)) != $true) & ! [X303 : term] : ((((X298 @ id @ (X299 @ id @ X303) @ id)) = $true) | ($true != ((X298 @ id @ X303 @ id)))) & ! [X302 : term,X301 : subst,X300 : subst] : (((sub @ (X299 @ X300 @ X302) @ X301)) = ((X299 @ (comp @ X300 @ X301) @ (sub @ X302 @ X301))))) | ? [X304 : term] : (($true != ((X298 @ id @ (sub @ X297 @ (push @ X304 @ id)) @ id))) & (((X298 @ id @ X304 @ id)) = $true)) | ($true = ((X298 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X514 : (term > $o),X513 : term,X512 : (subst > term > subst > $o)] : (? [X515 : (subst > term > term)] : (! [X517 : subst,X518 : term,X516 : subst] : (((sub @ (X515 @ X517 @ X518) @ X516)) = ((X515 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516)))) & ! [X519 : term] : ((((X512 @ id @ (X515 @ id @ X519) @ id)) = $true) | (((X512 @ id @ X519 @ id)) != $true)) & (((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id)) != $true)) | ? [X521 : term] : (($true != ((X514 @ (sub @ X513 @ (push @ X521 @ id))))) & ($true = ((X514 @ X521)))) | ($true = ((X514 @ (lam @ X513)))) | ? [X520 : term] : (((X514 @ X520)) != ((X512 @ id @ X520 @ id))))) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((? [X441 : term,X442 : (term > $o)] : (! [X443 : term] : ((((X442 @ (lam @ X443))) = $true) | ? [X444 : term] : (($true = ((X442 @ X444))) & (((X442 @ (sub @ X443 @ (push @ X444 @ id)))) != $true))) & ! [X447 : term] : (($true = ((X442 @ X447))) | (((var @ X447)) != $true)) & (((X442 @ X441)) != $true) & ! [X446 : term,X445 : term] : (($true = ((X442 @ (ap @ X446 @ X445)))) | ($true != ((X442 @ X446))) | (((X442 @ X445)) != $true))) | ? [X449 : term,X451 : (subst > term > subst > $o),X450 : (term > $o)] : (! [X452 : term] : (((X451 @ id @ X452 @ id)) = ((X450 @ X452))) & ! [X453 : term] : ((((X450 @ (sub @ X449 @ (push @ X453 @ id)))) = $true) | ($true != ((X450 @ X453)))) & ! [X454 : (subst > term > term)] : (? [X457 : term,X458 : subst,X456 : subst] : (((X454 @ (comp @ X456 @ X458) @ (sub @ X457 @ X458))) != ((sub @ (X454 @ X456 @ X457) @ X458))) | (((X451 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ? [X455 : term] : (($true != ((X451 @ id @ (X454 @ id @ X455) @ id))) & ($true = ((X451 @ id @ X455 @ id))))) & ($true != ((X450 @ (lam @ X449))))) | ? [X448 : term] : (((sub @ X448 @ id)) != X448) | ? [X438 : (subst > term > subst > $o)] : ! [X439 : (term > $o)] : ? [X440 : term] : (((X439 @ X440)) != ((X438 @ id @ X440 @ id))) | ! [X459 : (subst > term > subst > $o),X460 : term] : (($true = ((X459 @ id @ X460 @ id))) | ? [X461 : (subst > term > term)] : (($true != ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id))) & ! [X462 : term] : ((((X459 @ id @ (X461 @ id @ X462) @ id)) = $true) | ($true != ((X459 @ id @ X462 @ id)))) & ! [X463 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X463) @ (sub @ X465 @ X463))) = ((sub @ (X461 @ X464 @ X465) @ X463)))) | ? [X466 : term] : ((((var @ (sub @ X466 @ id))) = $true) & (((X459 @ id @ X466 @ id)) != $true)) | ? [X472 : term,X471 : term] : (($true = ((X459 @ id @ X472 @ id))) & ($true = ((X459 @ id @ X471 @ id))) & ($true != ((X459 @ id @ (ap @ (sub @ X471 @ id) @ X472) @ id)))) | ? [X473 : subst,X476 : term,X474 : subst,X475 : subst] : (($true = ((X459 @ (comp @ X475 @ X473) @ (sub @ X476 @ X473) @ X474))) & ($true != ((X459 @ X475 @ X476 @ (comp @ X473 @ X474))))) | ? [X468 : subst,X469 : subst,X470 : subst,X467 : term] : (($true = ((X459 @ X468 @ X467 @ (comp @ X469 @ X470)))) & (((X459 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469) @ X470)) != $true)))) <=> (hoasinduction_lthm_3 = $true)) & (axmap = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192)) | ? [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) = ((ap @ X185 @ X187))) & (X187 != X188))) <=> (hoasapinj2_lthm = $true)) & (! [X240 : term,X241 : (subst > term > subst > $o)] : (? [X242 : term,X243 : term] : (($true != ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) & ($true = ((X241 @ id @ X242 @ id))) & ($true = ((X241 @ id @ X243 @ id)))) | ? [X244 : (subst > term > term)] : (! [X245 : term] : (($true != ((X241 @ id @ X245 @ id))) | (((X241 @ id @ (X244 @ id @ X245) @ id)) = $true)) & ! [X246 : subst,X247 : subst,X248 : term] : (((sub @ (X244 @ X247 @ X248) @ X246)) = ((X244 @ (comp @ X247 @ X246) @ (sub @ X248 @ X246)))) & ($true != ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id)))) | ($true = ((X241 @ id @ X240 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X271 : term] : ? [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) = ((X272 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & ((substmonoid = $true) <=> (! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223))) & ((? [X268 : subst] : (((comp @ X268 @ id)) != X268) | (! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)) | ? [X267 : subst] : (((comp @ id @ X267)) != X267)) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X143 : term] : ? [X144 : (subst > term > term)] : ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145)))) & (hoaslamnotap_gthm = $true) & ((? [X477 : term] : (((sub @ X477 @ id)) != X477) | ? [X478 : term,X479 : (subst > term > subst > $o)] : (! [X481 : (subst > term > term)] : ((((X479 @ id @ (lam @ (X481 @ sh @ one)) @ id)) = $true) | ? [X482 : term] : (($true != ((X479 @ id @ (X481 @ id @ X482) @ id))) & ($true = ((X479 @ id @ X482 @ id)))) | ? [X483 : subst,X485 : term,X484 : subst] : (((sub @ (X481 @ X483 @ X485) @ X484)) != ((X481 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484))))) & ! [X480 : term] : (($true != ((X479 @ id @ X480 @ id))) | (((X479 @ id @ (sub @ X478 @ (push @ X480 @ id)) @ id)) = $true)) & (((X479 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)) != $true)) | ! [X487 : (subst > term > subst > $o),X486 : term] : (? [X491 : subst,X488 : subst,X490 : term,X489 : subst] : (($true != ((X487 @ (comp @ X488 @ X491) @ (sub @ X490 @ X491) @ X489))) & (((X487 @ X488 @ X490 @ (comp @ X491 @ X489))) = $true)) | ? [X497 : (subst > term > term)] : (! [X500 : subst,X501 : term,X499 : subst] : (((X497 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) = ((sub @ (X497 @ X499 @ X501) @ X500))) & ($true != ((X487 @ id @ (lam @ (X497 @ sh @ one)) @ id))) & ! [X498 : term] : (($true != ((X487 @ id @ X498 @ id))) | ($true = ((X487 @ id @ (X497 @ id @ X498) @ id))))) | ? [X496 : term] : ((((X487 @ id @ X496 @ id)) = $true) & ($true != ((X487 @ id @ (sub @ X486 @ (push @ X496 @ id)) @ id)))) | ? [X492 : term,X495 : subst,X494 : subst,X493 : subst] : (($true = ((X487 @ (comp @ X495 @ X494) @ (sub @ X492 @ X494) @ X493))) & ($true != ((X487 @ X495 @ X492 @ (comp @ X494 @ X493))))) | ($true = ((X487 @ id @ (lam @ X486) @ id))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslamnotvar = $true) & (! [X376 : term,X375 : (term > $o)] : (? [X380 : term] : ((((X375 @ (lam @ X380))) != $true) & ! [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true) | ($true != ((X375 @ X381))))) | ? [X379 : term,X378 : term] : ((((X375 @ X378)) = $true) & ($true = ((X375 @ X379))) & ($true != ((X375 @ (ap @ X378 @ X379))))) | ($true = ((X375 @ X376))) | ? [X377 : term] : ((((X375 @ X377)) != $true) & ($true = ((var @ X377))))) <=> (induction2 = $true)) & (axclos = $true) & (pushprop_lem3v2 = $true) & ((hoaslaminj = $true) <=> ! [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ? [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) != ((sub @ (X250 @ X258 @ X259) @ X257))) | ? [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) != ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | (((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (ulamvar1 != $true) & (! [X30 : (subst > term > subst > $o)] : ? [X31 : (term > $o)] : ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X128 : (term > $o),X129 : term,X130 : term,X127 : (subst > term > subst > $o)] : (? [X136 : subst,X135 : subst,X134 : subst,X133 : term] : (($true != ((X127 @ X134 @ X133 @ (comp @ X135 @ X136)))) & (((X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136)) = $true)) | ($true = ((X128 @ (ap @ X129 @ X130)))) | ? [X131 : term,X132 : term] : (($true != ((X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) & ($true = ((X127 @ id @ X132 @ id))) & ($true = ((X127 @ id @ X131 @ id)))) | (((X128 @ X130)) != $true) | (((X128 @ X129)) != $true) | ? [X137 : term,X139 : subst,X140 : subst,X138 : subst] : (($true = ((X127 @ X138 @ X137 @ (comp @ X139 @ X140)))) & ($true != ((X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)))) | ? [X141 : term] : (((X128 @ X141)) != ((X127 @ id @ X141 @ id)))) <=> (hoasinduction_lem2v2 = $true)) & (axabs = $true) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) != ((d2subst @ X305))) | (X305 = X306)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X290 : (subst > term > subst > $o),X289 : term] : (? [X296 : term] : ((((X290 @ id @ X296 @ id)) = $true) & (((X290 @ id @ (sub @ X289 @ (push @ X296 @ id)) @ id)) != $true)) | ? [X291 : (subst > term > term)] : (! [X292 : subst,X294 : subst,X293 : term] : (((sub @ (X291 @ X294 @ X293) @ X292)) = ((X291 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292)))) & (((X290 @ id @ (lam @ (X291 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : (($true = ((X290 @ id @ (X291 @ id @ X295) @ id))) | (((X290 @ id @ X295 @ id)) != $true))) | (((X290 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) = $true))) & (induction2lem_gthm = $true) & ((shinj = $true) <=> ! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh))))) & ((axvarid = $true) <=> ! [X249 : term] : (((sub @ X249 @ id)) = X249)) & (pushprop_lem2v2 = $true) & (! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) <=> (apinj2 = $true)) & (hoasapinj1_gthm = $true) & (! [X307 : (subst > term > subst > $o),X308 : term] : (? [X311 : (subst > term > term),X310 : term] : (($true != ((X307 @ id @ (lam @ (X311 @ sh @ one)) @ id))) & ! [X317 : subst,X318 : term,X316 : subst] : (((X311 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316))) = ((sub @ X310 @ (push @ (sub @ X318 @ X316) @ (comp @ X317 @ X316))))) & ! [X312 : term] : ((((X307 @ id @ X312 @ id)) != $true) | ($true = ((X307 @ id @ (X311 @ id @ X312) @ id)))) & ! [X314 : subst,X315 : term,X313 : subst] : (((sub @ (X311 @ X314 @ X315) @ X313)) = ((sub @ (sub @ X310 @ (push @ X315 @ X314)) @ X313)))) | ? [X309 : term] : (($true = ((X307 @ id @ X309 @ id))) & ($true != ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id)))) | (((X307 @ id @ (lam @ (sub @ X308 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (hoasapnotvar_lthm = $true) & (! [X74 : term,X75 : term,X76 : (subst > term > subst > $o)] : (($true != ((X76 @ id @ X75 @ id))) | ? [X86 : term,X83 : subst,X85 : subst,X84 : subst] : (($true != ((X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85))) & ($true = ((X76 @ X84 @ X86 @ (comp @ X83 @ X85))))) | (((X76 @ id @ X74 @ id)) != $true) | ($true = ((X76 @ id @ (ap @ X74 @ X75) @ id))) | ? [X79 : subst,X80 : term,X82 : subst,X81 : subst] : (($true != ((X76 @ X81 @ X80 @ (comp @ X82 @ X79)))) & ($true = ((X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79)))) | ? [X78 : term,X77 : term] : (($true = ((X76 @ id @ X77 @ id))) & ($true != ((X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id))) & (((X76 @ id @ X78 @ id)) = $true))) <=> (hoasinduction_lem2 = $true)) & (axassoc = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_gthm = $true) & ((? [X199 : term] : (((sub @ X199 @ id)) != X199) | ? [X195 : term] : ! [X196 : (subst > term > term)] : ? [X197 : subst,X198 : term] : (((X196 @ X197 @ X198)) != ((sub @ X195 @ (push @ X198 @ X197)))) | ! [X202 : (term > $o),X200 : term,X201 : (subst > term > subst > $o)] : (? [X209 : term] : (($true = ((X202 @ X209))) & (((X202 @ (sub @ X200 @ (push @ X209 @ id)))) != $true)) | ? [X203 : term] : (((X201 @ id @ X203 @ id)) != ((X202 @ X203))) | (((X202 @ (lam @ X200))) = $true) | ? [X204 : (subst > term > term)] : (($true != ((X201 @ id @ (lam @ (X204 @ sh @ one)) @ id))) & ! [X208 : term] : ((((X201 @ id @ (X204 @ id @ X208) @ id)) = $true) | ($true != ((X201 @ id @ X208 @ id)))) & ! [X206 : term,X207 : subst,X205 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (? [X126 : term] : (((X125 @ X126)) != ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ($true != ((X124 @ X122))) | ($true = ((X125 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((induction2lem = $true) <=> ! [X105 : subst,X107 : term,X106 : (term > $o)] : (? [X112 : term] : (($true != ((X106 @ (sub @ X112 @ X105)))) & ($true = ((var @ X112)))) | ($true = ((X106 @ (sub @ X107 @ X105)))) | ? [X108 : term] : (($true != ((X106 @ (lam @ X108)))) & ! [X109 : term] : ((((X106 @ (sub @ X108 @ (push @ X109 @ id)))) = $true) | ($true != ((X106 @ X109))))) | ? [X110 : term,X111 : term] : (($true != ((X106 @ (ap @ X111 @ X110)))) & ($true = ((X106 @ X110))) & ($true = ((X106 @ X111)))))) & (hoaslamnotap_lthm = $true) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) <=> (laminj = $true)) & (hoasinduction_gthm = $true) & ((? [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 != X117) & (((ap @ X116 @ X115)) = ((ap @ X117 @ X114)))) | ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118)))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113)) <=> (hoasapinj1_lthm = $true)) & (hoasapnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) | ($true != ((X260 @ X264)))) <=> (pushprop_lem1 = $true)) & (! [X502 : term] : ? [X503 : (subst > term > term)] : (((X503 @ sh @ one)) = ((sub @ X502 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) <=> (hoasapinj2 = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X522 : term] : (((sub @ X522 @ id)) = X522) <=> (termmset = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X177 : (subst > term > subst > $o),X176 : term] : ((((X177 @ id @ X176 @ id)) = $true) | ? [X179 : term,X178 : term] : ((((X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) != $true) & (((X177 @ id @ X178 @ id)) = $true) & ($true = ((X177 @ id @ X179 @ id)))) | ? [X180 : (subst > term > term)] : (! [X182 : subst,X183 : term,X181 : subst] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182)))) & ! [X184 : term] : (($true != ((X177 @ id @ X184 @ id))) | (((X177 @ id @ (X180 @ id @ X184) @ id)) = $true)) & (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) != $true))) | ? [X167 : (subst > term > subst > $o),X168 : term,X166 : (term > $o)] : ((((X166 @ (lam @ X168))) != $true) & ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id))) & ! [X174 : term] : (($true = ((X166 @ (sub @ X168 @ (push @ X174 @ id))))) | ($true != ((X166 @ X174)))) & ! [X169 : (subst > term > term)] : ((((X167 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ? [X170 : term] : ((((X167 @ id @ (X169 @ id @ X170) @ id)) != $true) & ($true = ((X167 @ id @ X170 @ id)))) | ? [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) != ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171)))))) | ? [X158 : term,X159 : (term > $o)] : (! [X161 : term,X160 : term] : (($true = ((X159 @ (ap @ X160 @ X161)))) | ($true != ((X159 @ X160))) | ($true != ((X159 @ X161)))) & ($true != ((X159 @ X158))) & ! [X163 : term] : (? [X164 : term] : (($true = ((X159 @ X164))) & ($true != ((X159 @ (sub @ X163 @ (push @ X164 @ id)))))) | ($true = ((X159 @ (lam @ X163))))) & ! [X162 : term] : (($true != ((var @ X162))) | ($true = ((X159 @ X162))))) | ? [X155 : (subst > term > subst > $o)] : ! [X156 : (term > $o)] : ? [X157 : term] : (((X155 @ id @ X157 @ id)) != ((X156 @ X157))) | ? [X165 : term] : (((sub @ X165 @ id)) != X165))) & ((! [X66 : term,X67 : (subst > term > subst > $o)] : (? [X69 : (subst > term > term)] : (! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))) & ($true != ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id))) & ! [X70 : term] : (($true = ((X67 @ id @ (X69 @ id @ X70) @ id))) | (((X67 @ id @ X70 @ id)) != $true))) | ($true = ((X67 @ id @ (lam @ X66) @ id))) | ? [X68 : term] : (($true != ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id))) & ($true = ((X67 @ id @ X68 @ id))))) | ? [X59 : term,X58 : (subst > term > subst > $o)] : (! [X60 : term] : ((((X58 @ id @ X60 @ id)) != $true) | ($true = ((X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id)))) & (((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id)) != $true) & ! [X61 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id)) = $true) | ? [X65 : subst,X63 : term,X64 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) != ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))) | ? [X62 : term] : (($true != ((X58 @ id @ (X61 @ id @ X62) @ id))) & (((X58 @ id @ X62 @ id)) = $true)))) | ? [X57 : term] : (((sub @ X57 @ id)) != X57)) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X142 : d_term] : (d_one = X142) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> (axshiftcons = $true)) & ((apinj1 = $true) <=> ! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149))))) & ((hoasapinj1 = $true) <=> ! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56))) & (hoasinduction_lem2v2_gthm = $true) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) <=> (axvarcons = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem0_lthm = $true) <=> ! [X371 : term,X370 : (term > $o),X372 : subst] : ? [X373 : (term > $o)] : ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374)))) & (hoasinduction_lem1 = $true) & ((! [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true != ((X214 @ X215))) | ? [X216 : term] : (((X212 @ X216)) != ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ($true = ((X212 @ one)))) | ? [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) != X210)) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X352 : d_term,X353 : d_term] : ((((d2term @ X352)) != ((d2term @ X353))) | (X352 = X353)) & (hoasinduction_lem1_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X151 : term] : ? [X152 : (subst > term > term)] : ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153)))) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X89 : (subst > term > subst > $o),X88 : term,X87 : (term > $o)] : (? [X90 : term] : ((((X87 @ (sub @ X88 @ (push @ X90 @ id)))) != $true) & (((X87 @ X90)) = $true)) | ? [X96 : (subst > term > term)] : ((((X89 @ id @ (lam @ (X96 @ sh @ one)) @ id)) != $true) & ! [X99 : subst,X100 : term,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98))) & ! [X97 : term] : ((((X89 @ id @ X97 @ id)) != $true) | (((X89 @ id @ (X96 @ id @ X97) @ id)) = $true))) | ? [X102 : subst,X101 : subst,X104 : term,X103 : subst] : (($true != ((X89 @ X101 @ X104 @ (comp @ X103 @ X102)))) & ($true = ((X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102)))) | ? [X95 : term] : (((X87 @ X95)) != ((X89 @ id @ X95 @ id))) | ($true = ((X87 @ (lam @ X88)))) | ? [X92 : term,X93 : subst,X91 : subst,X94 : subst] : (($true = ((X89 @ X94 @ X92 @ (comp @ X91 @ X93)))) & ($true != ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93)))))) & (pushprop_lthm_orig = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((axidr = $true) <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & (! [X348 : term,X346 : (subst > term > term),X347 : term] : (? [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) != ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347)))) <=> (hoaslamnotap = $true)) & (induction2_gthm = $true) & (axapp = $true) & (! [X340 : (term > $o),X341 : term] : (? [X342 : term,X343 : term] : ((((X340 @ X343)) = $true) & ($true = ((X340 @ X342))) & ($true != ((X340 @ (ap @ X343 @ X342))))) | ($true = ((X340 @ X341))) | ? [X345 : term] : ((((X340 @ (lam @ X345))) != $true) & ($true = ((X340 @ X345)))) | ? [X344 : term] : (($true = ((var @ X344))) & ($true != ((X340 @ X344))))) <=> (induction = $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X533 : (subst > term > subst > $o)] : ? [X534 : (term > $o)] : ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true) | (((X9 @ X5)) != $true)) | ? [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) != X1) | ? [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) != X4))) & ((! [X363 : term,X364 : (term > $o)] : ((((X364 @ X363)) = $true) | ? [X367 : term,X366 : term] : (($true = ((X364 @ X366))) & (((X364 @ X367)) = $true) & ($true != ((X364 @ (ap @ X366 @ X367))))) | ? [X368 : term] : (! [X369 : term] : ((((X364 @ (sub @ X368 @ (push @ X369 @ id)))) = $true) | ($true != ((X364 @ X369)))) & (((X364 @ (lam @ X368))) != $true)) | ? [X365 : term] : ((((X364 @ X365)) != $true) & ($true = ((var @ X365))))) | ? [X355 : term,X357 : (term > $o),X356 : subst] : (! [X359 : term] : (? [X360 : term] : (($true = ((X357 @ X360))) & ($true != ((X357 @ (sub @ X359 @ (push @ X360 @ id)))))) | ($true = ((X357 @ (lam @ X359))))) & ! [X361 : term,X362 : term] : (($true = ((X357 @ (ap @ X361 @ X362)))) | ($true != ((X357 @ X361))) | (((X357 @ X362)) != $true)) & ! [X358 : term] : ((((var @ X358)) != $true) | ($true = ((X357 @ (sub @ X358 @ X356))))) & ($true != ((X357 @ (sub @ X355 @ X356))))) | ? [X354 : term] : (((sub @ X354 @ id)) != X354)) <=> (induction2_lthm = $true)) & ((axscons = $true) <=> ! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508)) & ((termmset_lthm = $true) <=> (! [X266 : term] : (((sub @ X266 @ id)) = X266) | ? [X265 : term] : (((sub @ X265 @ id)) != X265))) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((? [X38 : subst] : (((comp @ X38 @ id)) != X38) | ! [X45 : term,X46 : (term > $o),X47 : subst] : (? [X50 : term] : (! [X51 : term] : ((((X46 @ (sub @ X50 @ (push @ X51 @ id)))) = $true) | ($true != ((X46 @ X51)))) & ($true != ((X46 @ (lam @ X50))))) | ($true = ((X46 @ (sub @ X45 @ X47)))) | ? [X52 : term] : ((((var @ X52)) = $true) & ($true != ((X46 @ (sub @ X52 @ X47))))) | ? [X48 : term,X49 : term] : (($true = ((X46 @ X49))) & ($true = ((X46 @ X48))) & (((X46 @ (ap @ X49 @ X48))) != $true))) | ? [X34 : subst,X35 : term] : (((sub @ one @ (push @ X35 @ X34))) != X35) | ? [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) != X37) | ? [X39 : (term > $o),X40 : term] : (! [X43 : term,X42 : term] : (($true != ((X39 @ X42))) | (((X39 @ (ap @ X42 @ X43))) = $true) | (((X39 @ X43)) != $true)) & ! [X41 : term] : (($true = ((X39 @ X41))) | (((var @ X41)) != $true)) & (((X39 @ X40)) != $true) & ! [X44 : term] : (($true = ((X39 @ (lam @ X44)))) | ($true != ((X39 @ X44)))))) <=> (induction2lem_lthm = $true)) & (apnotvar = $true) & ((hoasinduction_lthm = $true) <=> (! [X421 : (subst > term > subst > $o),X420 : term] : (? [X433 : (subst > term > term)] : (($true != ((X421 @ id @ (lam @ (X433 @ sh @ one)) @ id))) & ! [X435 : term,X434 : subst,X436 : subst] : (((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X434 @ X435) @ X436))) & ! [X437 : term] : (($true = ((X421 @ id @ (X433 @ id @ X437) @ id))) | (((X421 @ id @ X437 @ id)) != $true))) | ? [X422 : term] : ((((var @ (sub @ X422 @ id))) = $true) & ($true != ((X421 @ id @ X422 @ id)))) | ? [X426 : subst,X428 : term,X425 : subst,X427 : subst] : (($true = ((X421 @ (comp @ X425 @ X426) @ (sub @ X428 @ X426) @ X427))) & (((X421 @ X425 @ X428 @ (comp @ X426 @ X427))) != $true)) | ($true = ((X421 @ id @ X420 @ id))) | ? [X424 : term,X423 : term] : ((((X421 @ id @ (ap @ (sub @ X423 @ id) @ X424) @ id)) != $true) & (((X421 @ id @ X423 @ id)) = $true) & (((X421 @ id @ X424 @ id)) = $true)) | ? [X429 : subst,X432 : term,X430 : subst,X431 : subst] : (($true != ((X421 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X429))) & ($true = ((X421 @ X430 @ X432 @ (comp @ X431 @ X429)))))) | ? [X405 : term,X404 : (subst > term > subst > $o)] : (! [X415 : term] : (($true != ((X404 @ id @ X415 @ id))) | (((X404 @ id @ (sub @ X405 @ (push @ X415 @ id)) @ id)) = $true)) & ! [X417 : subst,X418 : subst,X416 : subst,X419 : term] : (($true != ((X404 @ X417 @ X419 @ (comp @ X418 @ X416)))) | ($true = ((X404 @ (comp @ X417 @ X418) @ (sub @ X419 @ X418) @ X416)))) & ! [X406 : (subst > term > term)] : (? [X407 : term] : ((((X404 @ id @ X407 @ id)) = $true) & ($true != ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ? [X410 : subst,X409 : subst,X408 : term] : (((X406 @ (comp @ X410 @ X409) @ (sub @ X408 @ X409))) != ((sub @ (X406 @ X410 @ X408) @ X409))) | ($true = ((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)))) & ! [X412 : subst,X414 : term,X411 : subst,X413 : subst] : (($true != ((X404 @ (comp @ X411 @ X413) @ (sub @ X414 @ X413) @ X412))) | ($true = ((X404 @ X411 @ X414 @ (comp @ X413 @ X412))))) & (((X404 @ id @ (lam @ X405) @ id)) != $true)) | ? [X393 : term,X392 : term,X391 : (subst > term > subst > $o)] : ((((X391 @ id @ X393 @ id)) = $true) & ($true = ((X391 @ id @ X392 @ id))) & ! [X394 : term,X395 : term] : ((((X391 @ id @ (ap @ (sub @ X395 @ id) @ X394) @ id)) = $true) | ($true != ((X391 @ id @ X395 @ id))) | ($true != ((X391 @ id @ X394 @ id)))) & ! [X400 : term,X402 : subst,X403 : subst,X401 : subst] : (($true = ((X391 @ X403 @ X400 @ (comp @ X402 @ X401)))) | ($true != ((X391 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401)))) & ! [X398 : subst,X399 : subst,X396 : term,X397 : subst] : ((((X391 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398)) = $true) | ($true != ((X391 @ X397 @ X396 @ (comp @ X399 @ X398))))) & (((X391 @ id @ (ap @ X392 @ X393) @ id)) != $true)) | ? [X384 : term,X385 : (term > $o)] : (! [X390 : term] : (($true != ((var @ X390))) | (((X385 @ X390)) = $true)) & ($true != ((X385 @ X384))) & ! [X388 : term] : (? [X389 : term] : (($true != ((X385 @ (sub @ X388 @ (push @ X389 @ id))))) & ($true = ((X385 @ X389)))) | ($true = ((X385 @ (lam @ X388))))) & ! [X387 : term,X386 : term] : (($true != ((X385 @ X387))) | ($true != ((X385 @ X386))) | (((X385 @ (ap @ X386 @ X387))) = $true))))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) <=> ! [X11 : (subst > term > subst > $o),X10 : term] : (? [X12 : term] : (($true != ((X11 @ id @ X12 @ id))) & (((var @ (sub @ X12 @ id))) = $true)) | ? [X24 : term,X25 : subst,X26 : subst,X27 : subst] : (($true != ((X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25))) & (((X11 @ X27 @ X24 @ (comp @ X26 @ X25))) = $true)) | ($true = ((X11 @ id @ X10 @ id))) | ? [X17 : term,X18 : term] : (($true = ((X11 @ id @ X17 @ id))) & (((X11 @ id @ X18 @ id)) = $true) & ($true != ((X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id)))) | ? [X13 : subst,X14 : term,X16 : subst,X15 : subst] : ((((X11 @ X13 @ X14 @ (comp @ X16 @ X15))) != $true) & (((X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15)) = $true)) | ? [X19 : (subst > term > term)] : (! [X23 : subst,X22 : subst,X21 : term] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22)))) & ! [X20 : term] : ((((X11 @ id @ (X19 @ id @ X20) @ id)) = $true) | ($true != ((X11 @ id @ X20 @ id)))) & (((X11 @ id @ (lam @ (X19 @ sh @ one)) @ id)) != $true)))) & (ulamvarind = $true) & (! [X274 : term,X273 : (subst > term > subst > $o)] : (($true = ((X273 @ id @ (lam @ X274) @ id))) | ? [X279 : (subst > term > term)] : (! [X280 : subst,X282 : subst,X281 : term] : (((sub @ (X279 @ X280 @ X281) @ X282)) = ((X279 @ (comp @ X280 @ X282) @ (sub @ X281 @ X282)))) & ! [X283 : term] : ((((X273 @ id @ (X279 @ id @ X283) @ id)) = $true) | (((X273 @ id @ X283 @ id)) != $true)) & (((X273 @ id @ (lam @ (X279 @ sh @ one)) @ id)) != $true)) | ? [X284 : term] : (($true != ((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id))) & ($true = ((X273 @ id @ X284 @ id)))) | ? [X278 : subst,X276 : term,X277 : subst,X275 : subst] : (($true != ((X273 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275))) & ($true = ((X273 @ X277 @ X276 @ (comp @ X278 @ X275))))) | ? [X286 : subst,X288 : subst,X285 : term,X287 : subst] : (($true != ((X273 @ X288 @ X285 @ (comp @ X287 @ X286)))) & (((X273 @ (comp @ X288 @ X287) @ (sub @ X285 @ X287) @ X286)) = $true))) <=> (hoasinduction_lem3 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (termmset_gthm = $true)),
% 6.46/1.22 inference(flattening,[],[f11])).
% 6.46/1.22 thf(f13,definition,(
% 6.46/1.22 ! [X273 : (subst > term > subst > $o)] : ((((sP0 @ X273)) = $true) <=> ? [X279 : (subst > term > term)] : (! [X280 : subst,X282 : subst,X281 : term] : (((sub @ (X279 @ X280 @ X281) @ X282)) = ((X279 @ (comp @ X280 @ X282) @ (sub @ X281 @ X282)))) & ! [X283 : term] : ((((X273 @ id @ (X279 @ id @ X283) @ id)) = $true) | (((X273 @ id @ X283 @ id)) != $true)) & (((X273 @ id @ (lam @ (X279 @ sh @ one)) @ id)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f14,definition,(
% 6.46/1.22 (sP1 = $true) <=> ! [X274 : term,X273 : (subst > term > subst > $o)] : (($true = ((X273 @ id @ (lam @ X274) @ id))) | (((sP0 @ X273)) = $true) | ? [X284 : term] : (($true != ((X273 @ id @ (sub @ X274 @ (push @ X284 @ id)) @ id))) & ($true = ((X273 @ id @ X284 @ id)))) | ? [X278 : subst,X276 : term,X277 : subst,X275 : subst] : (($true != ((X273 @ (comp @ X277 @ X278) @ (sub @ X276 @ X278) @ X275))) & ($true = ((X273 @ X277 @ X276 @ (comp @ X278 @ X275))))) | ? [X286 : subst,X288 : subst,X285 : term,X287 : subst] : (($true != ((X273 @ X288 @ X285 @ (comp @ X287 @ X286)))) & (((X273 @ (comp @ X288 @ X287) @ (sub @ X285 @ X287) @ X286)) = $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f15,definition,(
% 6.46/1.22 ! [X11 : (subst > term > subst > $o)] : (($true = ((sP2 @ X11))) <=> ? [X19 : (subst > term > term)] : (! [X23 : subst,X22 : subst,X21 : term] : (((sub @ (X19 @ X23 @ X21) @ X22)) = ((X19 @ (comp @ X23 @ X22) @ (sub @ X21 @ X22)))) & ! [X20 : term] : ((((X11 @ id @ (X19 @ id @ X20) @ id)) = $true) | ($true != ((X11 @ id @ X20 @ id)))) & (((X11 @ id @ (lam @ (X19 @ sh @ one)) @ id)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f16,definition,(
% 6.46/1.22 ! [X11 : (subst > term > subst > $o)] : (($true = ((sP3 @ X11))) <=> ? [X17 : term,X18 : term] : (($true = ((X11 @ id @ X17 @ id))) & (((X11 @ id @ X18 @ id)) = $true) & ($true != ((X11 @ id @ (ap @ (sub @ X18 @ id) @ X17) @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f17,definition,(
% 6.46/1.22 ($true = sP4) <=> ! [X11 : (subst > term > subst > $o),X10 : term] : (? [X12 : term] : (($true != ((X11 @ id @ X12 @ id))) & (((var @ (sub @ X12 @ id))) = $true)) | ? [X24 : term,X25 : subst,X26 : subst,X27 : subst] : (($true != ((X11 @ (comp @ X27 @ X26) @ (sub @ X24 @ X26) @ X25))) & (((X11 @ X27 @ X24 @ (comp @ X26 @ X25))) = $true)) | ($true = ((X11 @ id @ X10 @ id))) | ($true = ((sP3 @ X11))) | ? [X13 : subst,X14 : term,X16 : subst,X15 : subst] : ((((X11 @ X13 @ X14 @ (comp @ X16 @ X15))) != $true) & (((X11 @ (comp @ X13 @ X16) @ (sub @ X14 @ X16) @ X15)) = $true)) | ($true = ((sP2 @ X11))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f18,definition,(
% 6.46/1.22 ! [X385 : (term > $o)] : (($true = ((sP5 @ X385))) <=> ! [X387 : term,X386 : term] : (($true != ((X385 @ X387))) | ($true != ((X385 @ X386))) | (((X385 @ (ap @ X386 @ X387))) = $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f19,definition,(
% 6.46/1.22 ! [X391 : (subst > term > subst > $o)] : (($true = ((sP6 @ X391))) <=> ! [X394 : term,X395 : term] : ((((X391 @ id @ (ap @ (sub @ X395 @ id) @ X394) @ id)) = $true) | ($true != ((X391 @ id @ X395 @ id))) | ($true != ((X391 @ id @ X394 @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f20,definition,(
% 6.46/1.22 ! [X404 : (subst > term > subst > $o)] : ((((sP7 @ X404)) = $true) <=> ! [X406 : (subst > term > term)] : (? [X407 : term] : ((((X404 @ id @ X407 @ id)) = $true) & ($true != ((X404 @ id @ (X406 @ id @ X407) @ id)))) | ? [X410 : subst,X409 : subst,X408 : term] : (((X406 @ (comp @ X410 @ X409) @ (sub @ X408 @ X409))) != ((sub @ (X406 @ X410 @ X408) @ X409))) | ($true = ((X404 @ id @ (lam @ (X406 @ sh @ one)) @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f21,definition,(
% 6.46/1.22 ! [X421 : (subst > term > subst > $o)] : (($true = ((sP8 @ X421))) <=> ? [X424 : term,X423 : term] : ((((X421 @ id @ (ap @ (sub @ X423 @ id) @ X424) @ id)) != $true) & (((X421 @ id @ X423 @ id)) = $true) & (((X421 @ id @ X424 @ id)) = $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f22,definition,(
% 6.46/1.22 ! [X421 : (subst > term > subst > $o)] : ((((sP9 @ X421)) = $true) <=> ? [X433 : (subst > term > term)] : (($true != ((X421 @ id @ (lam @ (X433 @ sh @ one)) @ id))) & ! [X435 : term,X434 : subst,X436 : subst] : (((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X433 @ X434 @ X435) @ X436))) & ! [X437 : term] : (($true = ((X421 @ id @ (X433 @ id @ X437) @ id))) | (((X421 @ id @ X437 @ id)) != $true))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f23,definition,(
% 6.46/1.22 (sP10 = $true) <=> ? [X405 : term,X404 : (subst > term > subst > $o)] : (! [X415 : term] : (($true != ((X404 @ id @ X415 @ id))) | (((X404 @ id @ (sub @ X405 @ (push @ X415 @ id)) @ id)) = $true)) & ! [X417 : subst,X418 : subst,X416 : subst,X419 : term] : (($true != ((X404 @ X417 @ X419 @ (comp @ X418 @ X416)))) | ($true = ((X404 @ (comp @ X417 @ X418) @ (sub @ X419 @ X418) @ X416)))) & (((sP7 @ X404)) = $true) & ! [X412 : subst,X414 : term,X411 : subst,X413 : subst] : (($true != ((X404 @ (comp @ X411 @ X413) @ (sub @ X414 @ X413) @ X412))) | ($true = ((X404 @ X411 @ X414 @ (comp @ X413 @ X412))))) & (((X404 @ id @ (lam @ X405) @ id)) != $true))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f24,definition,(
% 6.46/1.22 ($true = sP11) <=> ! [X421 : (subst > term > subst > $o),X420 : term] : ((((sP9 @ X421)) = $true) | ? [X422 : term] : ((((var @ (sub @ X422 @ id))) = $true) & ($true != ((X421 @ id @ X422 @ id)))) | ? [X426 : subst,X428 : term,X425 : subst,X427 : subst] : (($true = ((X421 @ (comp @ X425 @ X426) @ (sub @ X428 @ X426) @ X427))) & (((X421 @ X425 @ X428 @ (comp @ X426 @ X427))) != $true)) | ($true = ((X421 @ id @ X420 @ id))) | ($true = ((sP8 @ X421))) | ? [X429 : subst,X432 : term,X430 : subst,X431 : subst] : (($true != ((X421 @ (comp @ X430 @ X431) @ (sub @ X432 @ X431) @ X429))) & ($true = ((X421 @ X430 @ X432 @ (comp @ X431 @ X429))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f25,definition,(
% 6.46/1.22 ($true = sP12) <=> ? [X384 : term,X385 : (term > $o)] : (! [X390 : term] : (($true != ((var @ X390))) | (((X385 @ X390)) = $true)) & ($true != ((X385 @ X384))) & ! [X388 : term] : (? [X389 : term] : (($true != ((X385 @ (sub @ X388 @ (push @ X389 @ id))))) & ($true = ((X385 @ X389)))) | ($true = ((X385 @ (lam @ X388))))) & ($true = ((sP5 @ X385))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f26,definition,(
% 6.46/1.22 (sP13 = $true) <=> (($true = sP11) | (sP10 = $true) | ? [X393 : term,X392 : term,X391 : (subst > term > subst > $o)] : ((((X391 @ id @ X393 @ id)) = $true) & ($true = ((X391 @ id @ X392 @ id))) & ($true = ((sP6 @ X391))) & ! [X400 : term,X402 : subst,X403 : subst,X401 : subst] : (($true = ((X391 @ X403 @ X400 @ (comp @ X402 @ X401)))) | ($true != ((X391 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401)))) & ! [X398 : subst,X399 : subst,X396 : term,X397 : subst] : ((((X391 @ (comp @ X397 @ X399) @ (sub @ X396 @ X399) @ X398)) = $true) | ($true != ((X391 @ X397 @ X396 @ (comp @ X399 @ X398))))) & (((X391 @ id @ (ap @ X392 @ X393) @ id)) != $true)) | ($true = sP12))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f27,definition,(
% 6.46/1.22 ! [X39 : (term > $o)] : (($true = ((sP14 @ X39))) <=> ! [X43 : term,X42 : term] : (($true != ((X39 @ X42))) | (((X39 @ (ap @ X42 @ X43))) = $true) | (((X39 @ X43)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f28,definition,(
% 6.46/1.22 ! [X46 : (term > $o)] : (($true = ((sP15 @ X46))) <=> ? [X48 : term,X49 : term] : (($true = ((X46 @ X49))) & ($true = ((X46 @ X48))) & (((X46 @ (ap @ X49 @ X48))) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f29,definition,(
% 6.46/1.22 ($true = sP16) <=> ! [X45 : term,X46 : (term > $o),X47 : subst] : (? [X50 : term] : (! [X51 : term] : ((((X46 @ (sub @ X50 @ (push @ X51 @ id)))) = $true) | ($true != ((X46 @ X51)))) & ($true != ((X46 @ (lam @ X50))))) | ($true = ((X46 @ (sub @ X45 @ X47)))) | ? [X52 : term] : ((((var @ X52)) = $true) & ($true != ((X46 @ (sub @ X52 @ X47))))) | ($true = ((sP15 @ X46))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f30,definition,(
% 6.46/1.22 ($true = sP17) <=> (? [X38 : subst] : (((comp @ X38 @ id)) != X38) | ($true = sP16) | ? [X34 : subst,X35 : term] : (((sub @ one @ (push @ X35 @ X34))) != X35) | ? [X36 : term,X37 : subst] : (((comp @ sh @ (push @ X36 @ X37))) != X37) | ? [X39 : (term > $o),X40 : term] : (($true = ((sP14 @ X39))) & ! [X41 : term] : (($true = ((X39 @ X41))) | (((var @ X41)) != $true)) & (((X39 @ X40)) != $true) & ! [X44 : term] : (($true = ((X39 @ (lam @ X44)))) | ($true != ((X39 @ X44))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f31,definition,(
% 6.46/1.22 ! [X357 : (term > $o)] : ((((sP18 @ X357)) = $true) <=> ! [X361 : term,X362 : term] : (($true = ((X357 @ (ap @ X361 @ X362)))) | ($true != ((X357 @ X361))) | (((X357 @ X362)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f32,definition,(
% 6.46/1.22 ! [X364 : (term > $o)] : (($true = ((sP19 @ X364))) <=> ? [X367 : term,X366 : term] : (($true = ((X364 @ X366))) & (((X364 @ X367)) = $true) & ($true != ((X364 @ (ap @ X366 @ X367))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f33,definition,(
% 6.46/1.22 (sP20 = $true) <=> ! [X363 : term,X364 : (term > $o)] : ((((X364 @ X363)) = $true) | ($true = ((sP19 @ X364))) | ? [X368 : term] : (! [X369 : term] : ((((X364 @ (sub @ X368 @ (push @ X369 @ id)))) = $true) | ($true != ((X364 @ X369)))) & (((X364 @ (lam @ X368))) != $true)) | ? [X365 : term] : ((((X364 @ X365)) != $true) & ($true = ((var @ X365)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f34,definition,(
% 6.46/1.22 (sP21 = $true) <=> ((sP20 = $true) | ? [X355 : term,X357 : (term > $o),X356 : subst] : (! [X359 : term] : (? [X360 : term] : (($true = ((X357 @ X360))) & ($true != ((X357 @ (sub @ X359 @ (push @ X360 @ id)))))) | ($true = ((X357 @ (lam @ X359))))) & (((sP18 @ X357)) = $true) & ! [X358 : term] : ((((var @ X358)) != $true) | ($true = ((X357 @ (sub @ X358 @ X356))))) & ($true != ((X357 @ (sub @ X355 @ X356))))) | ? [X354 : term] : (((sub @ X354 @ id)) != X354))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f35,definition,(
% 6.46/1.22 ! [X340 : (term > $o)] : (($true = ((sP22 @ X340))) <=> ? [X342 : term,X343 : term] : ((((X340 @ X343)) = $true) & ($true = ((X340 @ X342))) & ($true != ((X340 @ (ap @ X343 @ X342))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f36,definition,(
% 6.46/1.22 ! [X89 : (subst > term > subst > $o)] : (($true = ((sP23 @ X89))) <=> ? [X96 : (subst > term > term)] : ((((X89 @ id @ (lam @ (X96 @ sh @ one)) @ id)) != $true) & ! [X99 : subst,X100 : term,X98 : subst] : (((X96 @ (comp @ X99 @ X98) @ (sub @ X100 @ X98))) = ((sub @ (X96 @ X99 @ X100) @ X98))) & ! [X97 : term] : ((((X89 @ id @ X97 @ id)) != $true) | (((X89 @ id @ (X96 @ id @ X97) @ id)) = $true))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f37,definition,(
% 6.46/1.22 ($true = sP24) <=> ! [X89 : (subst > term > subst > $o),X88 : term,X87 : (term > $o)] : (? [X90 : term] : ((((X87 @ (sub @ X88 @ (push @ X90 @ id)))) != $true) & (((X87 @ X90)) = $true)) | ($true = ((sP23 @ X89))) | ? [X102 : subst,X101 : subst,X104 : term,X103 : subst] : (($true != ((X89 @ X101 @ X104 @ (comp @ X103 @ X102)))) & ($true = ((X89 @ (comp @ X101 @ X103) @ (sub @ X104 @ X103) @ X102)))) | ? [X95 : term] : (((X87 @ X95)) != ((X89 @ id @ X95 @ id))) | ($true = ((X87 @ (lam @ X88)))) | ? [X92 : term,X93 : subst,X91 : subst,X94 : subst] : (($true = ((X89 @ X94 @ X92 @ (comp @ X91 @ X93)))) & ($true != ((X89 @ (comp @ X94 @ X91) @ (sub @ X92 @ X91) @ X93)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f38,definition,(
% 6.46/1.22 (sP25 = $true) <=> ? [X59 : term,X58 : (subst > term > subst > $o)] : (! [X60 : term] : ((((X58 @ id @ X60 @ id)) != $true) | ($true = ((X58 @ id @ (sub @ X59 @ (push @ X60 @ id)) @ id)))) & (((X58 @ id @ (lam @ (sub @ X59 @ (push @ one @ sh))) @ id)) != $true) & ! [X61 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X61 @ sh @ one)) @ id)) = $true) | ? [X65 : subst,X63 : term,X64 : subst] : (((sub @ (X61 @ X65 @ X63) @ X64)) != ((X61 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))) | ? [X62 : term] : (($true != ((X58 @ id @ (X61 @ id @ X62) @ id))) & (((X58 @ id @ X62 @ id)) = $true))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f39,definition,(
% 6.46/1.22 ($true = sP26) <=> (! [X66 : term,X67 : (subst > term > subst > $o)] : (? [X69 : (subst > term > term)] : (! [X71 : subst,X72 : term,X73 : subst] : (((X69 @ (comp @ X73 @ X71) @ (sub @ X72 @ X71))) = ((sub @ (X69 @ X73 @ X72) @ X71))) & ($true != ((X67 @ id @ (lam @ (X69 @ sh @ one)) @ id))) & ! [X70 : term] : (($true = ((X67 @ id @ (X69 @ id @ X70) @ id))) | (((X67 @ id @ X70 @ id)) != $true))) | ($true = ((X67 @ id @ (lam @ X66) @ id))) | ? [X68 : term] : (($true != ((X67 @ id @ (sub @ X66 @ (push @ X68 @ id)) @ id))) & ($true = ((X67 @ id @ X68 @ id))))) | (sP25 = $true) | ? [X57 : term] : (((sub @ X57 @ id)) != X57))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f40,definition,(
% 6.46/1.22 ! [X159 : (term > $o)] : (($true = ((sP27 @ X159))) <=> ! [X161 : term,X160 : term] : (($true = ((X159 @ (ap @ X160 @ X161)))) | ($true != ((X159 @ X160))) | ($true != ((X159 @ X161)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f41,definition,(
% 6.46/1.22 ! [X177 : (subst > term > subst > $o)] : ((((sP28 @ X177)) = $true) <=> ? [X180 : (subst > term > term)] : (! [X182 : subst,X183 : term,X181 : subst] : (((sub @ (X180 @ X181 @ X183) @ X182)) = ((X180 @ (comp @ X181 @ X182) @ (sub @ X183 @ X182)))) & ! [X184 : term] : (($true != ((X177 @ id @ X184 @ id))) | (((X177 @ id @ (X180 @ id @ X184) @ id)) = $true)) & (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f42,definition,(
% 6.46/1.22 ($true = sP29) <=> ? [X167 : (subst > term > subst > $o),X168 : term,X166 : (term > $o)] : ((((X166 @ (lam @ X168))) != $true) & ! [X175 : term] : (((X166 @ X175)) = ((X167 @ id @ X175 @ id))) & ! [X174 : term] : (($true = ((X166 @ (sub @ X168 @ (push @ X174 @ id))))) | ($true != ((X166 @ X174)))) & ! [X169 : (subst > term > term)] : ((((X167 @ id @ (lam @ (X169 @ sh @ one)) @ id)) = $true) | ? [X170 : term] : ((((X167 @ id @ (X169 @ id @ X170) @ id)) != $true) & ($true = ((X167 @ id @ X170 @ id)))) | ? [X173 : term,X171 : subst,X172 : subst] : (((sub @ (X169 @ X172 @ X173) @ X171)) != ((X169 @ (comp @ X172 @ X171) @ (sub @ X173 @ X171))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f43,definition,(
% 6.46/1.22 ($true = sP30) <=> ? [X158 : term,X159 : (term > $o)] : (($true = ((sP27 @ X159))) & ($true != ((X159 @ X158))) & ! [X163 : term] : (? [X164 : term] : (($true = ((X159 @ X164))) & ($true != ((X159 @ (sub @ X163 @ (push @ X164 @ id)))))) | ($true = ((X159 @ (lam @ X163))))) & ! [X162 : term] : (($true != ((var @ X162))) | ($true = ((X159 @ X162)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f44,definition,(
% 6.46/1.22 ($true = sP31) <=> (! [X177 : (subst > term > subst > $o),X176 : term] : ((((X177 @ id @ X176 @ id)) = $true) | ? [X179 : term,X178 : term] : ((((X177 @ id @ (ap @ (sub @ X178 @ id) @ X179) @ id)) != $true) & (((X177 @ id @ X178 @ id)) = $true) & ($true = ((X177 @ id @ X179 @ id)))) | (((sP28 @ X177)) = $true)) | ($true = sP29) | ($true = sP30) | ? [X155 : (subst > term > subst > $o)] : ! [X156 : (term > $o)] : ? [X157 : term] : (((X155 @ id @ X157 @ id)) != ((X156 @ X157))) | ? [X165 : term] : (((sub @ X165 @ id)) != X165))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f45,definition,(
% 6.46/1.22 ! [X106 : (term > $o)] : ((((sP32 @ X106)) = $true) <=> ? [X110 : term,X111 : term] : (($true != ((X106 @ (ap @ X111 @ X110)))) & ($true = ((X106 @ X110))) & ($true = ((X106 @ X111)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f46,definition,(
% 6.46/1.22 ($true = sP33) <=> ! [X105 : subst,X107 : term,X106 : (term > $o)] : (? [X112 : term] : (($true != ((X106 @ (sub @ X112 @ X105)))) & ($true = ((var @ X112)))) | ($true = ((X106 @ (sub @ X107 @ X105)))) | ? [X108 : term] : (($true != ((X106 @ (lam @ X108)))) & ! [X109 : term] : ((((X106 @ (sub @ X108 @ (push @ X109 @ id)))) = $true) | ($true != ((X106 @ X109))))) | (((sP32 @ X106)) = $true))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f47,definition,(
% 6.46/1.22 (sP34 = $true) <=> (? [X199 : term] : (((sub @ X199 @ id)) != X199) | ? [X195 : term] : ! [X196 : (subst > term > term)] : ? [X197 : subst,X198 : term] : (((X196 @ X197 @ X198)) != ((sub @ X195 @ (push @ X198 @ X197)))) | ! [X202 : (term > $o),X200 : term,X201 : (subst > term > subst > $o)] : (? [X209 : term] : (($true = ((X202 @ X209))) & (((X202 @ (sub @ X200 @ (push @ X209 @ id)))) != $true)) | ? [X203 : term] : (((X201 @ id @ X203 @ id)) != ((X202 @ X203))) | (((X202 @ (lam @ X200))) = $true) | ? [X204 : (subst > term > term)] : (($true != ((X201 @ id @ (lam @ (X204 @ sh @ one)) @ id))) & ! [X208 : term] : ((((X201 @ id @ (X204 @ id @ X208) @ id)) = $true) | ($true != ((X201 @ id @ X208 @ id)))) & ! [X206 : term,X207 : subst,X205 : subst] : (((sub @ (X204 @ X207 @ X206) @ X205)) = ((X204 @ (comp @ X207 @ X205) @ (sub @ X206 @ X205)))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f48,definition,(
% 6.46/1.22 ! [X76 : (subst > term > subst > $o)] : (($true = ((sP35 @ X76))) <=> ? [X78 : term,X77 : term] : (($true = ((X76 @ id @ X77 @ id))) & ($true != ((X76 @ id @ (ap @ (sub @ X77 @ id) @ X78) @ id))) & (((X76 @ id @ X78 @ id)) = $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f49,definition,(
% 6.46/1.22 ($true = sP36) <=> ! [X74 : term,X75 : term,X76 : (subst > term > subst > $o)] : (($true != ((X76 @ id @ X75 @ id))) | ? [X86 : term,X83 : subst,X85 : subst,X84 : subst] : (($true != ((X76 @ (comp @ X84 @ X83) @ (sub @ X86 @ X83) @ X85))) & ($true = ((X76 @ X84 @ X86 @ (comp @ X83 @ X85))))) | (((X76 @ id @ X74 @ id)) != $true) | ($true = ((X76 @ id @ (ap @ X74 @ X75) @ id))) | ? [X79 : subst,X80 : term,X82 : subst,X81 : subst] : (($true != ((X76 @ X81 @ X80 @ (comp @ X82 @ X79)))) & ($true = ((X76 @ (comp @ X81 @ X82) @ (sub @ X80 @ X82) @ X79)))) | ($true = ((sP35 @ X76))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f50,definition,(
% 6.46/1.22 ($true = sP37) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : (? [X311 : (subst > term > term),X310 : term] : (($true != ((X307 @ id @ (lam @ (X311 @ sh @ one)) @ id))) & ! [X317 : subst,X318 : term,X316 : subst] : (((X311 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316))) = ((sub @ X310 @ (push @ (sub @ X318 @ X316) @ (comp @ X317 @ X316))))) & ! [X312 : term] : ((((X307 @ id @ X312 @ id)) != $true) | ($true = ((X307 @ id @ (X311 @ id @ X312) @ id)))) & ! [X314 : subst,X315 : term,X313 : subst] : (((sub @ (X311 @ X314 @ X315) @ X313)) = ((sub @ (sub @ X310 @ (push @ X315 @ X314)) @ X313)))) | ? [X309 : term] : (($true = ((X307 @ id @ X309 @ id))) & ($true != ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id)))) | (((X307 @ id @ (lam @ (sub @ X308 @ (push @ one @ sh))) @ id)) = $true))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f51,definition,(
% 6.46/1.22 ($true = sP38) <=> ! [X290 : (subst > term > subst > $o),X289 : term] : (? [X296 : term] : ((((X290 @ id @ X296 @ id)) = $true) & (((X290 @ id @ (sub @ X289 @ (push @ X296 @ id)) @ id)) != $true)) | ? [X291 : (subst > term > term)] : (! [X292 : subst,X294 : subst,X293 : term] : (((sub @ (X291 @ X294 @ X293) @ X292)) = ((X291 @ (comp @ X294 @ X292) @ (sub @ X293 @ X292)))) & (((X290 @ id @ (lam @ (X291 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : (($true = ((X290 @ id @ (X291 @ id @ X295) @ id))) | (((X290 @ id @ X295 @ id)) != $true))) | (((X290 @ id @ (lam @ (sub @ X289 @ (push @ one @ sh))) @ id)) = $true))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f52,definition,(
% 6.46/1.22 ! [X127 : (subst > term > subst > $o)] : (($true = ((sP39 @ X127))) <=> ? [X131 : term,X132 : term] : (($true != ((X127 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) & ($true = ((X127 @ id @ X132 @ id))) & ($true = ((X127 @ id @ X131 @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f53,definition,(
% 6.46/1.22 ($true = sP40) <=> ! [X128 : (term > $o),X129 : term,X130 : term,X127 : (subst > term > subst > $o)] : (? [X136 : subst,X135 : subst,X134 : subst,X133 : term] : (($true != ((X127 @ X134 @ X133 @ (comp @ X135 @ X136)))) & (((X127 @ (comp @ X134 @ X135) @ (sub @ X133 @ X135) @ X136)) = $true)) | ($true = ((X128 @ (ap @ X129 @ X130)))) | ($true = ((sP39 @ X127))) | (((X128 @ X130)) != $true) | (((X128 @ X129)) != $true) | ? [X137 : term,X139 : subst,X140 : subst,X138 : subst] : (($true = ((X127 @ X138 @ X137 @ (comp @ X139 @ X140)))) & ($true != ((X127 @ (comp @ X138 @ X139) @ (sub @ X137 @ X139) @ X140)))) | ? [X141 : term] : (((X128 @ X141)) != ((X127 @ id @ X141 @ id))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f54,definition,(
% 6.46/1.22 ! [X375 : (term > $o)] : ((((sP41 @ X375)) = $true) <=> ? [X379 : term,X378 : term] : ((((X375 @ X378)) = $true) & ($true = ((X375 @ X379))) & ($true != ((X375 @ (ap @ X378 @ X379))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f55,definition,(
% 6.46/1.22 ($true = sP42) <=> ! [X376 : term,X375 : (term > $o)] : (? [X380 : term] : ((((X375 @ (lam @ X380))) != $true) & ! [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true) | ($true != ((X375 @ X381))))) | (((sP41 @ X375)) = $true) | ($true = ((X375 @ X376))) | ? [X377 : term] : ((((X375 @ X377)) != $true) & ($true = ((var @ X377)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f56,definition,(
% 6.46/1.22 ! [X487 : (subst > term > subst > $o)] : ((((sP43 @ X487)) = $true) <=> ? [X497 : (subst > term > term)] : (! [X500 : subst,X501 : term,X499 : subst] : (((X497 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) = ((sub @ (X497 @ X499 @ X501) @ X500))) & ($true != ((X487 @ id @ (lam @ (X497 @ sh @ one)) @ id))) & ! [X498 : term] : (($true != ((X487 @ id @ X498 @ id))) | ($true = ((X487 @ id @ (X497 @ id @ X498) @ id))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f57,definition,(
% 6.46/1.22 ($true = sP44) <=> ? [X478 : term,X479 : (subst > term > subst > $o)] : (! [X481 : (subst > term > term)] : ((((X479 @ id @ (lam @ (X481 @ sh @ one)) @ id)) = $true) | ? [X482 : term] : (($true != ((X479 @ id @ (X481 @ id @ X482) @ id))) & ($true = ((X479 @ id @ X482 @ id)))) | ? [X483 : subst,X485 : term,X484 : subst] : (((sub @ (X481 @ X483 @ X485) @ X484)) != ((X481 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484))))) & ! [X480 : term] : (($true != ((X479 @ id @ X480 @ id))) | (((X479 @ id @ (sub @ X478 @ (push @ X480 @ id)) @ id)) = $true)) & (((X479 @ id @ (lam @ (sub @ X478 @ (push @ one @ sh))) @ id)) != $true))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f58,definition,(
% 6.46/1.22 (sP45 = $true) <=> (? [X477 : term] : (((sub @ X477 @ id)) != X477) | ($true = sP44) | ! [X487 : (subst > term > subst > $o),X486 : term] : (? [X491 : subst,X488 : subst,X490 : term,X489 : subst] : (($true != ((X487 @ (comp @ X488 @ X491) @ (sub @ X490 @ X491) @ X489))) & (((X487 @ X488 @ X490 @ (comp @ X491 @ X489))) = $true)) | (((sP43 @ X487)) = $true) | ? [X496 : term] : ((((X487 @ id @ X496 @ id)) = $true) & ($true != ((X487 @ id @ (sub @ X486 @ (push @ X496 @ id)) @ id)))) | ? [X492 : term,X495 : subst,X494 : subst,X493 : subst] : (($true = ((X487 @ (comp @ X495 @ X494) @ (sub @ X492 @ X494) @ X493))) & ($true != ((X487 @ X495 @ X492 @ (comp @ X494 @ X493))))) | ($true = ((X487 @ id @ (lam @ X486) @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f59,definition,(
% 6.46/1.22 ! [X241 : (subst > term > subst > $o)] : (($true = ((sP46 @ X241))) <=> ? [X244 : (subst > term > term)] : (! [X245 : term] : (($true != ((X241 @ id @ X245 @ id))) | (((X241 @ id @ (X244 @ id @ X245) @ id)) = $true)) & ! [X246 : subst,X247 : subst,X248 : term] : (((sub @ (X244 @ X247 @ X248) @ X246)) = ((X244 @ (comp @ X247 @ X246) @ (sub @ X248 @ X246)))) & ($true != ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f60,definition,(
% 6.46/1.22 ! [X459 : (subst > term > subst > $o)] : ((((sP47 @ X459)) = $true) <=> ? [X472 : term,X471 : term] : (($true = ((X459 @ id @ X472 @ id))) & ($true = ((X459 @ id @ X471 @ id))) & ($true != ((X459 @ id @ (ap @ (sub @ X471 @ id) @ X472) @ id)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f61,definition,(
% 6.46/1.22 ! [X459 : (subst > term > subst > $o)] : (($true = ((sP48 @ X459))) <=> ? [X461 : (subst > term > term)] : (($true != ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id))) & ! [X462 : term] : ((((X459 @ id @ (X461 @ id @ X462) @ id)) = $true) | ($true != ((X459 @ id @ X462 @ id)))) & ! [X463 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X463) @ (sub @ X465 @ X463))) = ((sub @ (X461 @ X464 @ X465) @ X463)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f62,definition,(
% 6.46/1.22 ! [X442 : (term > $o)] : (($true = ((sP49 @ X442))) <=> ! [X446 : term,X445 : term] : (($true = ((X442 @ (ap @ X446 @ X445)))) | ($true != ((X442 @ X446))) | (((X442 @ X445)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f63,definition,(
% 6.46/1.22 ($true = sP50) <=> ! [X459 : (subst > term > subst > $o),X460 : term] : (($true = ((X459 @ id @ X460 @ id))) | ($true = ((sP48 @ X459))) | ? [X466 : term] : ((((var @ (sub @ X466 @ id))) = $true) & (((X459 @ id @ X466 @ id)) != $true)) | (((sP47 @ X459)) = $true) | ? [X473 : subst,X476 : term,X474 : subst,X475 : subst] : (($true = ((X459 @ (comp @ X475 @ X473) @ (sub @ X476 @ X473) @ X474))) & ($true != ((X459 @ X475 @ X476 @ (comp @ X473 @ X474))))) | ? [X468 : subst,X469 : subst,X470 : subst,X467 : term] : (($true = ((X459 @ X468 @ X467 @ (comp @ X469 @ X470)))) & (((X459 @ (comp @ X468 @ X469) @ (sub @ X467 @ X469) @ X470)) != $true)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f64,definition,(
% 6.46/1.22 ($true = sP51) <=> ? [X449 : term,X451 : (subst > term > subst > $o),X450 : (term > $o)] : (! [X452 : term] : (((X451 @ id @ X452 @ id)) = ((X450 @ X452))) & ! [X453 : term] : ((((X450 @ (sub @ X449 @ (push @ X453 @ id)))) = $true) | ($true != ((X450 @ X453)))) & ! [X454 : (subst > term > term)] : (? [X457 : term,X458 : subst,X456 : subst] : (((X454 @ (comp @ X456 @ X458) @ (sub @ X457 @ X458))) != ((sub @ (X454 @ X456 @ X457) @ X458))) | (((X451 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ? [X455 : term] : (($true != ((X451 @ id @ (X454 @ id @ X455) @ id))) & ($true = ((X451 @ id @ X455 @ id))))) & ($true != ((X450 @ (lam @ X449)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f65,definition,(
% 6.46/1.22 (sP52 = $true) <=> (? [X441 : term,X442 : (term > $o)] : (! [X443 : term] : ((((X442 @ (lam @ X443))) = $true) | ? [X444 : term] : (($true = ((X442 @ X444))) & (((X442 @ (sub @ X443 @ (push @ X444 @ id)))) != $true))) & ! [X447 : term] : (($true = ((X442 @ X447))) | (((var @ X447)) != $true)) & (((X442 @ X441)) != $true) & ($true = ((sP49 @ X442)))) | ($true = sP51) | ? [X448 : term] : (((sub @ X448 @ id)) != X448) | ? [X438 : (subst > term > subst > $o)] : ! [X439 : (term > $o)] : ? [X440 : term] : (((X439 @ X440)) != ((X438 @ id @ X440 @ id))) | ($true = sP50))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f66,definition,(
% 6.46/1.22 (sP53 = $true) <=> ! [X514 : (term > $o),X513 : term,X512 : (subst > term > subst > $o)] : (? [X515 : (subst > term > term)] : (! [X517 : subst,X518 : term,X516 : subst] : (((sub @ (X515 @ X517 @ X518) @ X516)) = ((X515 @ (comp @ X517 @ X516) @ (sub @ X518 @ X516)))) & ! [X519 : term] : ((((X512 @ id @ (X515 @ id @ X519) @ id)) = $true) | (((X512 @ id @ X519 @ id)) != $true)) & (((X512 @ id @ (lam @ (X515 @ sh @ one)) @ id)) != $true)) | ? [X521 : term] : (($true != ((X514 @ (sub @ X513 @ (push @ X521 @ id))))) & ($true = ((X514 @ X521)))) | ($true = ((X514 @ (lam @ X513)))) | ? [X520 : term] : (((X514 @ X520)) != ((X512 @ id @ X520 @ id))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f67,definition,(
% 6.46/1.22 ($true = sP54) <=> ! [X297 : term,X298 : (subst > term > subst > $o)] : (? [X299 : (subst > term > term)] : ((((X298 @ id @ (lam @ (X299 @ sh @ one)) @ id)) != $true) & ! [X303 : term] : ((((X298 @ id @ (X299 @ id @ X303) @ id)) = $true) | ($true != ((X298 @ id @ X303 @ id)))) & ! [X302 : term,X301 : subst,X300 : subst] : (((sub @ (X299 @ X300 @ X302) @ X301)) = ((X299 @ (comp @ X300 @ X301) @ (sub @ X302 @ X301))))) | ? [X304 : term] : (($true != ((X298 @ id @ (sub @ X297 @ (push @ X304 @ id)) @ id))) & (((X298 @ id @ X304 @ id)) = $true)) | ($true = ((X298 @ id @ (lam @ (sub @ X297 @ (push @ one @ sh))) @ id))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f68,definition,(
% 6.46/1.22 ($true = sP55) <=> ! [X524 : (subst > term > subst > $o),X523 : term] : (($true = ((X524 @ id @ (lam @ X523) @ id))) | ? [X525 : term] : ((((X524 @ id @ X525 @ id)) = $true) & (((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) != $true)) | ? [X526 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) & ! [X527 : term] : (($true != ((X524 @ id @ X527 @ id))) | ($true = ((X524 @ id @ (X526 @ id @ X527) @ id)))) & ! [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f69,definition,(
% 6.46/1.22 ! [X322 : (subst > term > subst > $o)] : ((((sP56 @ X322)) = $true) <=> ? [X335 : (subst > term > term)] : (! [X339 : term] : (($true != ((X322 @ id @ X339 @ id))) | (((X322 @ id @ (X335 @ id @ X339) @ id)) = $true)) & ($true != ((X322 @ id @ (lam @ (X335 @ sh @ one)) @ id))) & ! [X337 : term,X338 : subst,X336 : subst] : (((sub @ (X335 @ X336 @ X337) @ X338)) = ((X335 @ (comp @ X336 @ X338) @ (sub @ X337 @ X338))))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f70,definition,(
% 6.46/1.22 (sP57 = $true) <=> (! [X323 : term,X324 : (term > $o),X322 : (subst > term > subst > $o)] : (? [X333 : subst,X331 : subst,X334 : term,X332 : subst] : (($true != ((X322 @ (comp @ X333 @ X332) @ (sub @ X334 @ X332) @ X331))) & ($true = ((X322 @ X333 @ X334 @ (comp @ X332 @ X331))))) | ? [X328 : subst,X327 : term,X326 : subst,X329 : subst] : (($true != ((X322 @ X328 @ X327 @ (comp @ X326 @ X329)))) & (((X322 @ (comp @ X328 @ X326) @ (sub @ X327 @ X326) @ X329)) = $true)) | ? [X330 : term] : (((X324 @ X330)) != ((X322 @ id @ X330 @ id))) | (((sP56 @ X322)) = $true) | ($true = ((X324 @ (lam @ X323)))) | ? [X325 : term] : (($true != ((X324 @ (sub @ X323 @ (push @ X325 @ id))))) & ($true = ((X324 @ X325))))) | ? [X321 : term] : (((sub @ X321 @ id)) != X321))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f71,definition,(
% 6.46/1.22 (sP58 = $true) <=> (? [X226 : term,X227 : subst] : (((comp @ sh @ (push @ X226 @ X227))) != X227) | ! [X231 : (subst > term > term),X232 : subst,X233 : (subst > term > term),X230 : term] : (? [X236 : subst,X234 : subst,X235 : term] : (((X231 @ (comp @ X234 @ X236) @ (sub @ X235 @ X236))) != ((sub @ (X231 @ X234 @ X235) @ X236))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X231 @ sh @ one)))) | ? [X239 : subst,X238 : subst,X237 : term] : (((sub @ (X233 @ X239 @ X237) @ X238)) != ((X233 @ (comp @ X239 @ X238) @ (sub @ X237 @ X238)))) | (((X231 @ X232 @ X230)) = ((X233 @ X232 @ X230)))) | ? [X225 : term,X224 : subst] : (((sub @ one @ (push @ X225 @ X224))) != X225) | ? [X229 : term,X228 : term] : ((((lam @ X228)) = ((lam @ X229))) & (X228 != X229)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.46/1.22 thf(f72,plain,(
% 6.46/1.22 ((hoaslaminj_lthm = $true) <=> (sP58 = $true)) & ((sP57 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X219 : subst,X217 : (term > $o),X218 : term] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221)))) & (axvarshift = $true) & (lamnotap != $true) & ! [X511 : d_subst] : (d_id = X511) & (($true = sP55) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3aa = $true) <=> ($true = sP54)) & ((hoasinduction_lem3v2a = $true) <=> (sP53 = $true)) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP52 = $true) <=> (hoasinduction_lthm_3 = $true)) & (axmap = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192)) | ? [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) = ((ap @ X185 @ X187))) & (X187 != X188))) <=> (hoasapinj2_lthm = $true)) & (! [X240 : term,X241 : (subst > term > subst > $o)] : (? [X242 : term,X243 : term] : (($true != ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) & ($true = ((X241 @ id @ X242 @ id))) & ($true = ((X241 @ id @ X243 @ id)))) | ($true = ((sP46 @ X241))) | ($true = ((X241 @ id @ X240 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X271 : term] : ? [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) = ((X272 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & ((substmonoid = $true) <=> (! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223))) & ((? [X268 : subst] : (((comp @ X268 @ id)) != X268) | (! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)) | ? [X267 : subst] : (((comp @ id @ X267)) != X267)) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X143 : term] : ? [X144 : (subst > term > term)] : ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145)))) & (hoaslamnotap_gthm = $true) & ((sP45 = $true) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslamnotvar = $true) & (($true = sP42) <=> (induction2 = $true)) & (axclos = $true) & (pushprop_lem3v2 = $true) & ((hoaslaminj = $true) <=> ! [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ? [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) != ((sub @ (X250 @ X258 @ X259) @ X257))) | ? [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) != ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | (((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (ulamvar1 != $true) & (! [X30 : (subst > term > subst > $o)] : ? [X31 : (term > $o)] : ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X33 : subst] : (((comp @ id @ X33)) = X33)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP40) <=> (hoasinduction_lem2v2 = $true)) & (axabs = $true) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) != ((d2subst @ X305))) | (X305 = X306)) & ((hoasinduction_lem3aa_lthm = $true) <=> ($true = sP38)) & (induction2lem_gthm = $true) & ((shinj = $true) <=> ! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh))))) & ((axvarid = $true) <=> ! [X249 : term] : (((sub @ X249 @ id)) = X249)) & (pushprop_lem2v2 = $true) & (! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) <=> (apinj2 = $true)) & (hoasapinj1_gthm = $true) & (($true = sP37) <=> (hoasinduction_lem3aaa = $true)) & (hoasapnotvar_lthm = $true) & (($true = sP36) <=> (hoasinduction_lem2 = $true)) & (axassoc = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_gthm = $true) & ((sP34 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (? [X126 : term] : (((X125 @ X126)) != ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ($true != ((X124 @ X122))) | ($true = ((X125 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((induction2lem = $true) <=> ($true = sP33)) & (hoaslamnotap_lthm = $true) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) <=> (laminj = $true)) & (hoasinduction_gthm = $true) & ((? [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 != X117) & (((ap @ X116 @ X115)) = ((ap @ X117 @ X114)))) | ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118)))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113)) <=> (hoasapinj1_lthm = $true)) & (hoasapnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) | ($true != ((X260 @ X264)))) <=> (pushprop_lem1 = $true)) & (! [X502 : term] : ? [X503 : (subst > term > term)] : (((X503 @ sh @ one)) = ((sub @ X502 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) <=> (hoasapinj2 = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X522 : term] : (((sub @ X522 @ id)) = X522) <=> (termmset = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP31)) & (($true = sP26) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X142 : d_term] : (d_one = X142) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) <=> (axshiftcons = $true)) & ((apinj1 = $true) <=> ! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149))))) & ((hoasapinj1 = $true) <=> ! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56))) & (hoasinduction_lem2v2_gthm = $true) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) <=> (axvarcons = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem0_lthm = $true) <=> ! [X371 : term,X370 : (term > $o),X372 : subst] : ? [X373 : (term > $o)] : ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374)))) & (hoasinduction_lem1 = $true) & ((! [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true != ((X214 @ X215))) | ? [X216 : term] : (((X212 @ X216)) != ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ($true = ((X212 @ one)))) | ? [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) != X210)) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X352 : d_term,X353 : d_term] : ((((d2term @ X352)) != ((d2term @ X353))) | (X352 = X353)) & (hoasinduction_lem1_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X151 : term] : ? [X152 : (subst > term > term)] : ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153)))) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP24)) & (pushprop_lthm_orig = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((axidr = $true) <=> ! [X0 : subst] : (((comp @ X0 @ id)) = X0)) & (! [X348 : term,X346 : (subst > term > term),X347 : term] : (? [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) != ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347)))) <=> (hoaslamnotap = $true)) & (induction2_gthm = $true) & (axapp = $true) & (! [X340 : (term > $o),X341 : term] : (($true = ((sP22 @ X340))) | ($true = ((X340 @ X341))) | ? [X345 : term] : ((((X340 @ (lam @ X345))) != $true) & ($true = ((X340 @ X345)))) | ? [X344 : term] : (($true = ((var @ X344))) & ($true != ((X340 @ X344))))) <=> (induction = $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X533 : (subst > term > subst > $o)] : ? [X534 : (term > $o)] : ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true) | (((X9 @ X5)) != $true)) | ? [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) != X1) | ? [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) != X4))) & ((sP21 = $true) <=> (induction2_lthm = $true)) & ((axscons = $true) <=> ! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508)) & ((termmset_lthm = $true) <=> (! [X266 : term] : (((sub @ X266 @ id)) = X266) | ? [X265 : term] : (((sub @ X265 @ id)) != X265))) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (($true = sP17) <=> (induction2lem_lthm = $true)) & (apnotvar = $true) & ((hoasinduction_lthm = $true) <=> (sP13 = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) <=> ($true = sP4)) & (ulamvarind = $true) & ((sP1 = $true) <=> (hoasinduction_lem3 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (termmset_gthm = $true)),
% 6.46/1.22 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 6.46/1.22 thf(f84,plain,(
% 6.46/1.22 (($true = sP55) | ? [X524 : (subst > term > subst > $o),X523 : term] : (($true != ((X524 @ id @ (lam @ X523) @ id))) & ! [X525 : term] : ((((X524 @ id @ X525 @ id)) != $true) | (((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) = $true)) & ! [X526 : (subst > term > term)] : (($true = ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) | ? [X527 : term] : (($true = ((X524 @ id @ X527 @ id))) & ($true != ((X524 @ id @ (X526 @ id @ X527) @ id)))) | ? [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) != ((sub @ (X526 @ X528 @ X529) @ X530)))))) & (! [X524 : (subst > term > subst > $o),X523 : term] : (($true = ((X524 @ id @ (lam @ X523) @ id))) | ? [X525 : term] : ((((X524 @ id @ X525 @ id)) = $true) & (((X524 @ id @ (sub @ X523 @ (push @ X525 @ id)) @ id)) != $true)) | ? [X526 : (subst > term > term)] : (($true != ((X524 @ id @ (lam @ (X526 @ sh @ one)) @ id))) & ! [X527 : term] : (($true != ((X524 @ id @ X527 @ id))) | ($true = ((X524 @ id @ (X526 @ id @ X527) @ id)))) & ! [X529 : term,X528 : subst,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530))))) | ($true != sP55))),
% 6.46/1.22 inference(nnf_transformation,[],[f68])).
% 6.46/1.22 thf(f85,plain,(
% 6.46/1.22 (($true = sP55) | ? [X0 : (subst > term > subst > $o),X1 : term] : (($true != ((X0 @ id @ (lam @ X1) @ id))) & ! [X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | ($true = ((X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id)))) & ! [X3 : (subst > term > term)] : (($true = ((X0 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ? [X4 : term] : ((((X0 @ id @ X4 @ id)) = $true) & ($true != ((X0 @ id @ (X3 @ id @ X4) @ id)))) | ? [X5 : term,X6 : subst,X7 : subst] : (((sub @ (X3 @ X6 @ X5) @ X7)) != ((X3 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7))))))) & (! [X8 : (subst > term > subst > $o),X9 : term] : (($true = ((X8 @ id @ (lam @ X9) @ id))) | ? [X10 : term] : ((((X8 @ id @ X10 @ id)) = $true) & (((X8 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id)) != $true)) | ? [X11 : (subst > term > term)] : ((((X8 @ id @ (lam @ (X11 @ sh @ one)) @ id)) != $true) & ! [X12 : term] : (($true != ((X8 @ id @ X12 @ id))) | ($true = ((X8 @ id @ (X11 @ id @ X12) @ id)))) & ! [X13 : term,X14 : subst,X15 : subst] : (((sub @ (X11 @ X14 @ X13) @ X15)) = ((X11 @ (comp @ X14 @ X15) @ (sub @ X13 @ X15)))))) | ($true != sP55))),
% 6.46/1.22 inference(rectify,[],[f84])).
% 6.46/1.22 thf(f86,plain,(
% 6.46/1.22 (($true = sP55) | ((((sK94 @ id @ (lam @ sK95) @ id)) != $true) & ! [X2 : term] : (($true != ((sK94 @ id @ X2 @ id))) | (((sK94 @ id @ (sub @ sK95 @ (push @ X2 @ id)) @ id)) = $true)) & ! [X3 : (subst > term > term)] : (($true = ((sK94 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | (($true = ((sK94 @ id @ (sK96 @ X3) @ id))) & (((sK94 @ id @ (X3 @ id @ (sK96 @ X3)) @ id)) != $true)) | (((X3 @ (comp @ (sK98 @ X3) @ (sK99 @ X3)) @ (sub @ (sK97 @ X3) @ (sK99 @ X3)))) != ((sub @ (X3 @ (sK98 @ X3) @ (sK97 @ X3)) @ (sK99 @ X3))))))) & (! [X8 : (subst > term > subst > $o),X9 : term] : (($true = ((X8 @ id @ (lam @ X9) @ id))) | (($true = ((X8 @ id @ (sK100 @ X9 @ X8) @ id))) & (((X8 @ id @ (sub @ X9 @ (push @ (sK100 @ X9 @ X8) @ id)) @ id)) != $true)) | ((((X8 @ id @ (lam @ (sK101 @ X8 @ sh @ one)) @ id)) != $true) & ! [X12 : term] : (($true != ((X8 @ id @ X12 @ id))) | (((X8 @ id @ (sK101 @ X8 @ id @ X12) @ id)) = $true)) & ! [X13 : term,X14 : subst,X15 : subst] : (((sK101 @ X8 @ (comp @ X14 @ X15) @ (sub @ X13 @ X15))) = ((sub @ (sK101 @ X8 @ X14 @ X13) @ X15))))) | ($true != sP55))),
% 6.46/1.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK94,sK95,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK94),skolemize(X1,sK95),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20)],[f85])).
% 6.46/1.22 thf(f260,plain,(
% 6.46/1.22 (((hoaslaminj_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoaslaminj_lthm != $true))) & (((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true))) & (((pushprop_lem0 = $true) | ? [X219 : subst,X217 : (term > $o),X218 : term] : ! [X220 : (term > $o)] : ? [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) != ((X220 @ X221)))) & (! [X219 : subst,X217 : (term > $o),X218 : term] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221))) | (pushprop_lem0 != $true))) & (axvarshift = $true) & (lamnotap != $true) & ! [X511 : d_subst] : (d_id = X511) & ((($true = sP55) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP55))) & (((hoasinduction_lem3aa = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lem3aa != $true))) & (((hoasinduction_lem3v2a = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a != $true))) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true))) & (axmap = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (((! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192)) | ? [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) = ((ap @ X185 @ X187))) & (X187 != X188))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) = ((ap @ (sub @ X191 @ id) @ X190))) & (X190 != X192)) & ! [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) != ((ap @ X185 @ X187))) | (X187 = X188))))) & ((! [X240 : term,X241 : (subst > term > subst > $o)] : (? [X242 : term,X243 : term] : (($true != ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) & ($true = ((X241 @ id @ X242 @ id))) & ($true = ((X241 @ id @ X243 @ id)))) | ($true = ((sP46 @ X241))) | ($true = ((X241 @ id @ X240 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X240 : term,X241 : (subst > term > subst > $o)] : (! [X242 : term,X243 : term] : (($true = ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) | ($true != ((X241 @ id @ X242 @ id))) | ($true != ((X241 @ id @ X243 @ id)))) & ($true != ((sP46 @ X241))) & ($true != ((X241 @ id @ X240 @ id)))))) & ((! [X271 : term] : ? [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) = ((X272 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X271 : term] : ! [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) != ((X272 @ sh @ one))))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & (((substmonoid = $true) | (? [X222 : subst] : (((comp @ X222 @ id)) != X222) | ? [X223 : subst] : (((comp @ id @ X223)) != X223))) & ((! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223)) | (substmonoid != $true))) & (((? [X268 : subst] : (((comp @ X268 @ id)) != X268) | (! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)) | ? [X267 : subst] : (((comp @ id @ X267)) != X267)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X268 : subst] : (((comp @ X268 @ id)) = X268) & (? [X270 : subst] : (((comp @ id @ X270)) != X270) | ? [X269 : subst] : (((comp @ X269 @ id)) != X269)) & ! [X267 : subst] : (((comp @ id @ X267)) = X267)))) & (((hoasinduction_lem3v2_f = $true) | ? [X143 : term] : ! [X144 : (subst > term > term)] : ? [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) != ((X144 @ X146 @ X145)))) & (! [X143 : term] : ? [X144 : (subst > term > term)] : ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145))) | (hoasinduction_lem3v2_f != $true))) & (hoaslamnotap_gthm = $true) & (((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true))) & (hoaslamnotvar = $true) & ((($true = sP42) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP42))) & (axclos = $true) & (pushprop_lem3v2 = $true) & (((hoaslaminj = $true) | ? [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) = ((lam @ (X250 @ sh @ one)))) & ! [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) = ((sub @ (X250 @ X258 @ X259) @ X257))) & ! [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) = ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) & (((X251 @ X253 @ X252)) != ((X250 @ X253 @ X252))))) & (! [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ? [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) != ((sub @ (X250 @ X258 @ X259) @ X257))) | ? [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) != ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | (((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252)))) | (hoaslaminj != $true))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (ulamvar1 != $true) & ((! [X30 : (subst > term > subst > $o)] : ? [X31 : (term > $o)] : ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X30 : (subst > term > subst > $o)] : ! [X31 : (term > $o)] : ? [X32 : term] : (((X31 @ X32)) != ((X30 @ id @ X32 @ id))))) & (hoaslamnotvar_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((axidl = $true) | ? [X33 : subst] : (((comp @ id @ X33)) != X33)) & (! [X33 : subst] : (((comp @ id @ X33)) = X33) | (axidl != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((($true = sP40) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP40))) & (axabs = $true) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) != ((d2subst @ X305))) | (X305 = X306)) & (((hoasinduction_lem3aa_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3aa_lthm != $true))) & (induction2lem_gthm = $true) & (((shinj = $true) | ? [X382 : term,X383 : term] : ((X382 != X383) & (((sub @ X383 @ sh)) = ((sub @ X382 @ sh))))) & (! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh)))) | (shinj != $true))) & (((axvarid = $true) | ? [X249 : term] : (((sub @ X249 @ id)) != X249)) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) | (axvarid != $true))) & (pushprop_lem2v2 = $true) & ((! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 != X505) & (((ap @ X506 @ X504)) = ((ap @ X507 @ X505)))))) & (hoasapinj1_gthm = $true) & ((($true = sP37) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP37))) & (hoasapnotvar_lthm = $true) & ((($true = sP36) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP36))) & (axassoc = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_gthm = $true) & (((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true))) & ((! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (? [X126 : term] : (((X125 @ X126)) != ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ($true != ((X124 @ X122))) | ($true = ((X125 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (! [X126 : term] : (((X125 @ X126)) = ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) & ($true = ((X124 @ X122))) & ($true != ((X125 @ one)))))) & (((induction2lem = $true) | ($true != sP33)) & (($true = sP33) | (induction2lem != $true))) & (hoaslamnotap_lthm = $true) & ((! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) | (laminj != $true)) & ((laminj = $true) | ? [X29 : term,X28 : term] : ((((lam @ X29)) = ((lam @ X28))) & (X28 != X29)))) & (hoasinduction_gthm = $true) & (((? [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 != X117) & (((ap @ X116 @ X115)) = ((ap @ X117 @ X114)))) | ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118)))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 = X117) | (((ap @ X116 @ X115)) != ((ap @ X117 @ X114)))) & ? [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 != X121) & (((ap @ (sub @ X120 @ id) @ X119)) = ((ap @ (sub @ X121 @ id) @ X118)))) & ! [X113 : term] : (((sub @ X113 @ id)) = X113)))) & (hoasapnotvar = $true) & (hoaslamnotvar_lthm = $true) & ((! [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) | ($true != ((X260 @ X264)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true != ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) & ($true = ((X260 @ X264)))))) & ((! [X502 : term] : ? [X503 : (subst > term > term)] : (((X503 @ sh @ one)) = ((sub @ X502 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X502 : term] : ! [X503 : (subst > term > term)] : (((X503 @ sh @ one)) != ((sub @ X502 @ (push @ one @ sh)))))) & ((! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) = ((ap @ (sub @ X537 @ id) @ X539))) & (X538 != X539)))) & (pushprop_lem3v2_lthm = $true) & ((! [X522 : term] : (((sub @ X522 @ id)) = X522) | (termmset != $true)) & ((termmset = $true) | ? [X522 : term] : (((sub @ X522 @ id)) != X522))) & (hoasinduction_lem1_lthm = $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true))) & ((($true = sP26) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP26))) & ! [X142 : d_term] : (d_one = X142) & ((! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) != X194))) & (((apinj1 = $true) | ? [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 != X150) & (((ap @ X147 @ X148)) = ((ap @ X150 @ X149))))) & (! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149)))) | (apinj1 != $true))) & (((hoasapinj1 = $true) | ? [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) = ((ap @ (sub @ X55 @ id) @ X54))) & (X55 != X56))) & (! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56)) | (hoasapinj1 != $true))) & (hoasinduction_lem2v2_gthm = $true) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) != X320))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((pushprop_lem0_lthm = $true) | ? [X371 : term,X370 : (term > $o),X372 : subst] : ! [X373 : (term > $o)] : ? [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) != ((X373 @ X374)))) & (! [X371 : term,X370 : (term > $o),X372 : subst] : ? [X373 : (term > $o)] : ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374))) | (pushprop_lem0_lthm != $true))) & (hoasinduction_lem1 = $true) & (((! [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true != ((X214 @ X215))) | ? [X216 : term] : (((X212 @ X216)) != ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ($true = ((X212 @ one)))) | ? [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) != X210)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true = ((X214 @ X215))) & ! [X216 : term] : (((X212 @ X216)) = ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) & ($true != ((X212 @ one)))) & ! [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) = X210)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X352 : d_term,X353 : d_term] : ((((d2term @ X352)) != ((d2term @ X353))) | (X352 = X353)) & (hoasinduction_lem1_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X151 : term] : ! [X152 : (subst > term > term)] : ? [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) != ((X152 @ X154 @ X153)))) & (! [X151 : term] : ? [X152 : (subst > term > term)] : ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153))) | (hoasinduction_lem3v2_f_lthm != $true))) & (substmonoid_gthm = $true) & (((hoasinduction_lem3v2 = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_lem3v2 != $true))) & (pushprop_lthm_orig = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((axidr = $true) | ? [X0 : subst] : (((comp @ X0 @ id)) != X0)) & (! [X0 : subst] : (((comp @ X0 @ id)) = X0) | (axidr != $true))) & ((! [X348 : term,X346 : (subst > term > term),X347 : term] : (? [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) != ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X348 : term,X346 : (subst > term > term),X347 : term] : (! [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) = ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) & (((lam @ (X346 @ sh @ one))) = ((ap @ (sub @ X348 @ id) @ X347)))))) & (induction2_gthm = $true) & (axapp = $true) & ((! [X340 : (term > $o),X341 : term] : (($true = ((sP22 @ X340))) | ($true = ((X340 @ X341))) | ? [X345 : term] : ((((X340 @ (lam @ X345))) != $true) & ($true = ((X340 @ X345)))) | ? [X344 : term] : (($true = ((var @ X344))) & ($true != ((X340 @ X344))))) | (induction != $true)) & ((induction = $true) | ? [X340 : (term > $o),X341 : term] : (($true != ((sP22 @ X340))) & ($true != ((X340 @ X341))) & ! [X345 : term] : ((((X340 @ (lam @ X345))) = $true) | ($true != ((X340 @ X345)))) & ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344))))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapinj2_gthm = $true) & ((! [X533 : (subst > term > subst > $o)] : ? [X534 : (term > $o)] : ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X533 : (subst > term > subst > $o)] : ! [X534 : (term > $o)] : ? [X535 : term] : (((X533 @ id @ X535 @ id)) != ((X534 @ X535))))) & (pushprop_lem1_gthm = $true) & (((pushprop_lem1_lthm = $true) | (? [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) != $true) & (((X9 @ X5)) = $true)) & ! [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) = X1) & ! [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) = X4))) & ((! [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true) | (((X9 @ X5)) != $true)) | ? [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) != X1) | ? [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) != X4)) | (pushprop_lem1_lthm != $true))) & (((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true))) & (((axscons = $true) | ? [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) != X508)) & (! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508) | (axscons != $true))) & (((termmset_lthm = $true) | (? [X266 : term] : (((sub @ X266 @ id)) != X266) & ! [X265 : term] : (((sub @ X265 @ id)) = X265))) & ((! [X266 : term] : (((sub @ X266 @ id)) = X266) | ? [X265 : term] : (((sub @ X265 @ id)) != X265)) | (termmset_lthm != $true))) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & ((($true = sP17) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP17))) & (apnotvar = $true) & (((hoasinduction_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm != $true))) & (hoasinduction_lem3_gthm = $true) & (((hoasinduction = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction != $true))) & (ulamvarind = $true) & (((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (termmset_gthm = $true)),
% 6.46/1.22 inference(nnf_transformation,[],[f72])).
% 6.46/1.22 thf(f261,plain,(
% 6.46/1.22 ((hoaslaminj_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true)) & ((pushprop_lem0 = $true) | ? [X219 : subst,X217 : (term > $o),X218 : term] : ! [X220 : (term > $o)] : ? [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) != ((X220 @ X221)))) & (! [X219 : subst,X217 : (term > $o),X218 : term] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X218 @ X219)))) = ((X220 @ X221))) | (pushprop_lem0 != $true)) & (axvarshift = $true) & (lamnotap != $true) & ! [X511 : d_subst] : (d_id = X511) & (($true = sP55) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP55)) & ((hoasinduction_lem3aa = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3v2a = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X531 : subst] : ? [X532 : d_subst] : (((d2subst @ X532)) = X531) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & (axmap = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) != ((ap @ (sub @ X191 @ id) @ X190))) | (X190 = X192)) | ? [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) = ((ap @ X185 @ X187))) & (X187 != X188)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X191 : term,X189 : term,X192 : term,X190 : term] : ((((ap @ (sub @ X189 @ id) @ X192)) = ((ap @ (sub @ X191 @ id) @ X190))) & (X190 != X192)) & ! [X187 : term,X185 : term,X186 : term,X188 : term] : ((((ap @ X186 @ X188)) != ((ap @ X185 @ X187))) | (X187 = X188)))) & (! [X240 : term,X241 : (subst > term > subst > $o)] : (? [X242 : term,X243 : term] : (($true != ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) & ($true = ((X241 @ id @ X242 @ id))) & ($true = ((X241 @ id @ X243 @ id)))) | ($true = ((sP46 @ X241))) | ($true = ((X241 @ id @ X240 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X240 : term,X241 : (subst > term > subst > $o)] : (! [X242 : term,X243 : term] : (($true = ((X241 @ id @ (ap @ (sub @ X243 @ id) @ X242) @ id))) | ($true != ((X241 @ id @ X242 @ id))) | ($true != ((X241 @ id @ X243 @ id)))) & ($true != ((sP46 @ X241))) & ($true != ((X241 @ id @ X240 @ id))))) & (! [X271 : term] : ? [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) = ((X272 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X271 : term] : ! [X272 : (subst > term > term)] : (((sub @ X271 @ (push @ one @ sh))) != ((X272 @ sh @ one)))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & ((substmonoid = $true) | ? [X222 : subst] : (((comp @ X222 @ id)) != X222) | ? [X223 : subst] : (((comp @ id @ X223)) != X223)) & ((! [X222 : subst] : (((comp @ X222 @ id)) = X222) & ! [X223 : subst] : (((comp @ id @ X223)) = X223)) | (substmonoid != $true)) & (? [X268 : subst] : (((comp @ X268 @ id)) != X268) | (! [X270 : subst] : (((comp @ id @ X270)) = X270) & ! [X269 : subst] : (((comp @ X269 @ id)) = X269)) | ? [X267 : subst] : (((comp @ id @ X267)) != X267) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X268 : subst] : (((comp @ X268 @ id)) = X268) & (? [X270 : subst] : (((comp @ id @ X270)) != X270) | ? [X269 : subst] : (((comp @ X269 @ id)) != X269)) & ! [X267 : subst] : (((comp @ id @ X267)) = X267))) & ((hoasinduction_lem3v2_f = $true) | ? [X143 : term] : ! [X144 : (subst > term > term)] : ? [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) != ((X144 @ X146 @ X145)))) & (! [X143 : term] : ? [X144 : (subst > term > term)] : ! [X145 : term,X146 : subst] : (((sub @ X143 @ (push @ X145 @ X146))) = ((X144 @ X146 @ X145))) | (hoasinduction_lem3v2_f != $true)) & (hoaslamnotap_gthm = $true) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & (hoaslamnotvar = $true) & (($true = sP42) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP42)) & (axclos = $true) & (pushprop_lem3v2 = $true) & ((hoaslaminj = $true) | ? [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) = ((lam @ (X250 @ sh @ one)))) & ! [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) = ((sub @ (X250 @ X258 @ X259) @ X257))) & ! [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) = ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) & (((X251 @ X253 @ X252)) != ((X250 @ X253 @ X252))))) & (! [X252 : term,X251 : (subst > term > term),X250 : (subst > term > term),X253 : subst] : ((((lam @ (X251 @ sh @ one))) != ((lam @ (X250 @ sh @ one)))) | ? [X259 : term,X258 : subst,X257 : subst] : (((X250 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257))) != ((sub @ (X250 @ X258 @ X259) @ X257))) | ? [X255 : subst,X256 : subst,X254 : term] : (((sub @ (X251 @ X256 @ X254) @ X255)) != ((X251 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255)))) | (((X251 @ X253 @ X252)) = ((X250 @ X253 @ X252)))) | (hoaslaminj != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (ulamvar1 != $true) & (! [X30 : (subst > term > subst > $o)] : ? [X31 : (term > $o)] : ! [X32 : term] : (((X31 @ X32)) = ((X30 @ id @ X32 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X30 : (subst > term > subst > $o)] : ! [X31 : (term > $o)] : ? [X32 : term] : (((X31 @ X32)) != ((X30 @ id @ X32 @ id)))) & (hoaslamnotvar_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) | ? [X33 : subst] : (((comp @ id @ X33)) != X33)) & (! [X33 : subst] : (((comp @ id @ X33)) = X33) | (axidl != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP40) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP40)) & (axabs = $true) & ! [X306 : d_subst,X305 : d_subst] : ((((d2subst @ X306)) != ((d2subst @ X305))) | (X305 = X306)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((shinj = $true) | ? [X382 : term,X383 : term] : ((X382 != X383) & (((sub @ X383 @ sh)) = ((sub @ X382 @ sh))))) & (! [X382 : term,X383 : term] : ((X382 = X383) | (((sub @ X383 @ sh)) != ((sub @ X382 @ sh)))) | (shinj != $true)) & ((axvarid = $true) | ? [X249 : term] : (((sub @ X249 @ id)) != X249)) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) | (axvarid != $true)) & (pushprop_lem2v2 = $true) & (! [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 = X505) | (((ap @ X506 @ X504)) != ((ap @ X507 @ X505)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X505 : term,X506 : term,X507 : term,X504 : term] : ((X504 != X505) & (((ap @ X506 @ X504)) = ((ap @ X507 @ X505))))) & (hoasapinj1_gthm = $true) & (($true = sP37) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP37)) & (hoasapnotvar_lthm = $true) & (($true = sP36) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP36)) & (axassoc = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_gthm = $true) & ((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true)) & (! [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (? [X126 : term] : (((X125 @ X126)) != ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) | ($true != ((X124 @ X122))) | ($true = ((X125 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X122 : term,X123 : subst,X124 : (term > $o),X125 : (term > $o)] : (! [X126 : term] : (((X125 @ X126)) = ((X124 @ (sub @ X126 @ (push @ X122 @ X123))))) & ($true = ((X124 @ X122))) & ($true != ((X125 @ one))))) & ((induction2lem = $true) | ($true != sP33)) & (($true = sP33) | (induction2lem != $true)) & (hoaslamnotap_lthm = $true) & (! [X29 : term,X28 : term] : ((((lam @ X29)) != ((lam @ X28))) | (X28 = X29)) | (laminj != $true)) & ((laminj = $true) | ? [X29 : term,X28 : term] : ((((lam @ X29)) = ((lam @ X28))) & (X28 != X29))) & (hoasinduction_gthm = $true) & (? [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 != X117) & (((ap @ X116 @ X115)) = ((ap @ X117 @ X114)))) | ! [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 = X121) | (((ap @ (sub @ X120 @ id) @ X119)) != ((ap @ (sub @ X121 @ id) @ X118)))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X114 : term,X117 : term,X115 : term,X116 : term] : ((X116 = X117) | (((ap @ X116 @ X115)) != ((ap @ X117 @ X114)))) & ? [X119 : term,X118 : term,X120 : term,X121 : term] : ((X120 != X121) & (((ap @ (sub @ X120 @ id) @ X119)) = ((ap @ (sub @ X121 @ id) @ X118)))) & ! [X113 : term] : (((sub @ X113 @ id)) = X113))) & (hoasapnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true = ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) | ($true != ((X260 @ X264)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X263 : term,X264 : term,X261 : subst,X262 : (term > $o),X260 : (term > $o)] : (($true != ((X262 @ (sub @ X264 @ (push @ X263 @ X261))))) & ($true = ((X260 @ X264))))) & (! [X502 : term] : ? [X503 : (subst > term > term)] : (((X503 @ sh @ one)) = ((sub @ X502 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X502 : term] : ! [X503 : (subst > term > term)] : (((X503 @ sh @ one)) != ((sub @ X502 @ (push @ one @ sh))))) & (! [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) != ((ap @ (sub @ X537 @ id) @ X539))) | (X538 = X539)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X538 : term,X536 : term,X539 : term,X537 : term] : ((((ap @ (sub @ X536 @ id) @ X538)) = ((ap @ (sub @ X537 @ id) @ X539))) & (X538 != X539))) & (pushprop_lem3v2_lthm = $true) & (! [X522 : term] : (((sub @ X522 @ id)) = X522) | (termmset != $true)) & ((termmset = $true) | ? [X522 : term] : (((sub @ X522 @ id)) != X522)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true)) & (($true = sP26) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP26)) & ! [X142 : d_term] : (d_one = X142) & (! [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) = X194) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X193 : term,X194 : subst] : (((comp @ sh @ (push @ X193 @ X194))) != X194)) & ((apinj1 = $true) | ? [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 != X150) & (((ap @ X147 @ X148)) = ((ap @ X150 @ X149))))) & (! [X150 : term,X149 : term,X148 : term,X147 : term] : ((X147 = X150) | (((ap @ X147 @ X148)) != ((ap @ X150 @ X149)))) | (apinj1 != $true)) & ((hoasapinj1 = $true) | ? [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) = ((ap @ (sub @ X55 @ id) @ X54))) & (X55 != X56))) & (! [X53 : term,X54 : term,X56 : term,X55 : term] : ((((ap @ (sub @ X56 @ id) @ X53)) != ((ap @ (sub @ X55 @ id) @ X54))) | (X55 = X56)) | (hoasapinj1 != $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X509 : term] : ? [X510 : d_term] : (((d2term @ X510)) = X509) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) = X320) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X319 : subst,X320 : term] : (((sub @ one @ (push @ X320 @ X319))) != X320)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem0_lthm = $true) | ? [X371 : term,X370 : (term > $o),X372 : subst] : ! [X373 : (term > $o)] : ? [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) != ((X373 @ X374)))) & (! [X371 : term,X370 : (term > $o),X372 : subst] : ? [X373 : (term > $o)] : ! [X374 : term] : (((X370 @ (sub @ X374 @ (push @ X371 @ X372)))) = ((X373 @ X374))) | (pushprop_lem0_lthm != $true)) & (hoasinduction_lem1 = $true) & (! [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true != ((X214 @ X215))) | ? [X216 : term] : (((X212 @ X216)) != ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) | ($true = ((X212 @ one)))) | ? [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) != X210) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X212 : (term > $o),X214 : (term > $o),X213 : subst,X215 : term] : (($true = ((X214 @ X215))) & ! [X216 : term] : (((X212 @ X216)) = ((X214 @ (sub @ X216 @ (push @ X215 @ X213))))) & ($true != ((X212 @ one)))) & ! [X211 : subst,X210 : term] : (((sub @ one @ (push @ X210 @ X211))) = X210))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X352 : d_term,X353 : d_term] : ((((d2term @ X352)) != ((d2term @ X353))) | (X352 = X353)) & (hoasinduction_lem1_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X151 : term] : ! [X152 : (subst > term > term)] : ? [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) != ((X152 @ X154 @ X153)))) & (! [X151 : term] : ? [X152 : (subst > term > term)] : ! [X154 : subst,X153 : term] : (((sub @ X151 @ (push @ X153 @ X154))) = ((X152 @ X154 @ X153))) | (hoasinduction_lem3v2_f_lthm != $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_lem3v2 != $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((axidr = $true) | ? [X0 : subst] : (((comp @ X0 @ id)) != X0)) & (! [X0 : subst] : (((comp @ X0 @ id)) = X0) | (axidr != $true)) & (! [X348 : term,X346 : (subst > term > term),X347 : term] : (? [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) != ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) | (((lam @ (X346 @ sh @ one))) != ((ap @ (sub @ X348 @ id) @ X347)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X348 : term,X346 : (subst > term > term),X347 : term] : (! [X349 : subst,X350 : subst,X351 : term] : (((sub @ (X346 @ X350 @ X351) @ X349)) = ((X346 @ (comp @ X350 @ X349) @ (sub @ X351 @ X349)))) & (((lam @ (X346 @ sh @ one))) = ((ap @ (sub @ X348 @ id) @ X347))))) & (induction2_gthm = $true) & (axapp = $true) & (! [X340 : (term > $o),X341 : term] : (($true = ((sP22 @ X340))) | ($true = ((X340 @ X341))) | ? [X345 : term] : ((((X340 @ (lam @ X345))) != $true) & ($true = ((X340 @ X345)))) | ? [X344 : term] : (($true = ((var @ X344))) & ($true != ((X340 @ X344))))) | (induction != $true)) & ((induction = $true) | ? [X340 : (term > $o),X341 : term] : (($true != ((sP22 @ X340))) & ($true != ((X340 @ X341))) & ! [X345 : term] : ((((X340 @ (lam @ X345))) = $true) | ($true != ((X340 @ X345)))) & ! [X344 : term] : (($true != ((var @ X344))) | ($true = ((X340 @ X344)))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X533 : (subst > term > subst > $o)] : ? [X534 : (term > $o)] : ! [X535 : term] : (((X533 @ id @ X535 @ id)) = ((X534 @ X535))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X533 : (subst > term > subst > $o)] : ! [X534 : (term > $o)] : ? [X535 : term] : (((X533 @ id @ X535 @ id)) != ((X534 @ X535)))) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1_lthm = $true) | (? [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) != $true) & (((X9 @ X5)) = $true)) & ! [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) = X1) & ! [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) = X4))) & (! [X6 : subst,X8 : (term > $o),X9 : (term > $o),X7 : term,X5 : term] : ((((X8 @ (sub @ X5 @ (push @ X7 @ X6)))) = $true) | (((X9 @ X5)) != $true)) | ? [X1 : term,X2 : subst] : (((sub @ one @ (push @ X1 @ X2))) != X1) | ? [X3 : term,X4 : subst] : (((comp @ sh @ (push @ X3 @ X4))) != X4) | (pushprop_lem1_lthm != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true)) & ((axscons = $true) | ? [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) != X508)) & (! [X508 : subst] : (((push @ (sub @ one @ X508) @ (comp @ sh @ X508))) = X508) | (axscons != $true)) & ((termmset_lthm = $true) | (? [X266 : term] : (((sub @ X266 @ id)) != X266) & ! [X265 : term] : (((sub @ X265 @ id)) = X265))) & (! [X266 : term] : (((sub @ X266 @ id)) = X266) | ? [X265 : term] : (((sub @ X265 @ id)) != X265) | (termmset_lthm != $true)) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (($true = sP17) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP17)) & (apnotvar = $true) & ((hoasinduction_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction != $true)) & (ulamvarind = $true) & ((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (termmset_gthm = $true)),
% 6.46/1.22 inference(flattening,[],[f260])).
% 6.46/1.22 thf(f262,plain,(
% 6.46/1.22 ((hoaslaminj_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true)) & ((pushprop_lem0 = $true) | ? [X0 : subst,X1 : (term > $o),X2 : term] : ! [X3 : (term > $o)] : ? [X4 : term] : (((X1 @ (sub @ X4 @ (push @ X2 @ X0)))) != ((X3 @ X4)))) & (! [X5 : subst,X6 : (term > $o),X7 : term] : ? [X8 : (term > $o)] : ! [X9 : term] : (((X6 @ (sub @ X9 @ (push @ X7 @ X5)))) = ((X8 @ X9))) | (pushprop_lem0 != $true)) & (axvarshift = $true) & (lamnotap != $true) & ! [X10 : d_subst] : (d_id = X10) & (($true = sP55) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP55)) & ((hoasinduction_lem3aa = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3v2a = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X11 : subst] : ? [X12 : d_subst] : (((d2subst @ X12)) = X11) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & (axmap = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X13 : term,X14 : term,X15 : term,X16 : term] : ((((ap @ (sub @ X13 @ id) @ X16)) != ((ap @ (sub @ X14 @ id) @ X15))) | (X15 = X16)) | ? [X17 : term,X18 : term,X19 : term,X20 : term] : ((((ap @ X19 @ X20)) = ((ap @ X18 @ X17))) & (X17 != X20)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X21 : term,X22 : term,X23 : term,X24 : term] : ((((ap @ (sub @ X21 @ id) @ X24)) = ((ap @ (sub @ X22 @ id) @ X23))) & (X23 != X24)) & ! [X25 : term,X26 : term,X27 : term,X28 : term] : ((((ap @ X26 @ X25)) != ((ap @ X27 @ X28))) | (X25 = X28)))) & (! [X29 : term,X30 : (subst > term > subst > $o)] : (? [X31 : term,X32 : term] : (($true != ((X30 @ id @ (ap @ (sub @ X32 @ id) @ X31) @ id))) & (((X30 @ id @ X31 @ id)) = $true) & ($true = ((X30 @ id @ X32 @ id)))) | ($true = ((sP46 @ X30))) | ($true = ((X30 @ id @ X29 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X33 : term,X34 : (subst > term > subst > $o)] : (! [X35 : term,X36 : term] : ((((X34 @ id @ (ap @ (sub @ X36 @ id) @ X35) @ id)) = $true) | (((X34 @ id @ X35 @ id)) != $true) | ($true != ((X34 @ id @ X36 @ id)))) & ($true != ((sP46 @ X34))) & ($true != ((X34 @ id @ X33 @ id))))) & (! [X37 : term] : ? [X38 : (subst > term > term)] : (((X38 @ sh @ one)) = ((sub @ X37 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X39 : term] : ! [X40 : (subst > term > term)] : (((sub @ X39 @ (push @ one @ sh))) != ((X40 @ sh @ one)))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & ((substmonoid = $true) | ? [X41 : subst] : (((comp @ X41 @ id)) != X41) | ? [X42 : subst] : (((comp @ id @ X42)) != X42)) & ((! [X43 : subst] : (((comp @ X43 @ id)) = X43) & ! [X44 : subst] : (((comp @ id @ X44)) = X44)) | (substmonoid != $true)) & (? [X45 : subst] : (((comp @ X45 @ id)) != X45) | (! [X46 : subst] : (((comp @ id @ X46)) = X46) & ! [X47 : subst] : (((comp @ X47 @ id)) = X47)) | ? [X48 : subst] : (((comp @ id @ X48)) != X48) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X49 : subst] : (((comp @ X49 @ id)) = X49) & (? [X50 : subst] : (((comp @ id @ X50)) != X50) | ? [X51 : subst] : (((comp @ X51 @ id)) != X51)) & ! [X52 : subst] : (((comp @ id @ X52)) = X52))) & ((hoasinduction_lem3v2_f = $true) | ? [X53 : term] : ! [X54 : (subst > term > term)] : ? [X55 : term,X56 : subst] : (((X54 @ X56 @ X55)) != ((sub @ X53 @ (push @ X55 @ X56))))) & (! [X57 : term] : ? [X58 : (subst > term > term)] : ! [X59 : term,X60 : subst] : (((X58 @ X60 @ X59)) = ((sub @ X57 @ (push @ X59 @ X60)))) | (hoasinduction_lem3v2_f != $true)) & (hoaslamnotap_gthm = $true) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & (hoaslamnotvar = $true) & (($true = sP42) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP42)) & (axclos = $true) & (pushprop_lem3v2 = $true) & ((hoaslaminj = $true) | ? [X61 : term,X62 : (subst > term > term),X63 : (subst > term > term),X64 : subst] : ((((lam @ (X63 @ sh @ one))) = ((lam @ (X62 @ sh @ one)))) & ! [X65 : term,X66 : subst,X67 : subst] : (((sub @ (X63 @ X66 @ X65) @ X67)) = ((X63 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) & ! [X68 : subst,X69 : subst,X70 : term] : (((sub @ (X62 @ X69 @ X70) @ X68)) = ((X62 @ (comp @ X69 @ X68) @ (sub @ X70 @ X68)))) & (((X62 @ X64 @ X61)) != ((X63 @ X64 @ X61))))) & (! [X71 : term,X72 : (subst > term > term),X73 : (subst > term > term),X74 : subst] : ((((lam @ (X72 @ sh @ one))) != ((lam @ (X73 @ sh @ one)))) | ? [X75 : term,X76 : subst,X77 : subst] : (((X73 @ (comp @ X76 @ X77) @ (sub @ X75 @ X77))) != ((sub @ (X73 @ X76 @ X75) @ X77))) | ? [X78 : subst,X79 : subst,X80 : term] : (((sub @ (X72 @ X79 @ X80) @ X78)) != ((X72 @ (comp @ X79 @ X78) @ (sub @ X80 @ X78)))) | (((X73 @ X74 @ X71)) = ((X72 @ X74 @ X71)))) | (hoaslaminj != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (ulamvar1 != $true) & (! [X81 : (subst > term > subst > $o)] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X81 @ id @ X83 @ id)) = ((X82 @ X83))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X84 : (subst > term > subst > $o)] : ! [X85 : (term > $o)] : ? [X86 : term] : (((X85 @ X86)) != ((X84 @ id @ X86 @ id)))) & (hoaslamnotvar_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) | ? [X87 : subst] : (((comp @ id @ X87)) != X87)) & (! [X88 : subst] : (((comp @ id @ X88)) = X88) | (axidl != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP40) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP40)) & (axabs = $true) & ! [X89 : d_subst,X90 : d_subst] : ((((d2subst @ X90)) != ((d2subst @ X89))) | (X89 = X90)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((shinj = $true) | ? [X91 : term,X92 : term] : ((X91 != X92) & (((sub @ X92 @ sh)) = ((sub @ X91 @ sh))))) & (! [X93 : term,X94 : term] : ((X93 = X94) | (((sub @ X93 @ sh)) != ((sub @ X94 @ sh)))) | (shinj != $true)) & ((axvarid = $true) | ? [X95 : term] : (((sub @ X95 @ id)) != X95)) & (! [X96 : term] : (((sub @ X96 @ id)) = X96) | (axvarid != $true)) & (pushprop_lem2v2 = $true) & (! [X97 : term,X98 : term,X99 : term,X100 : term] : ((X97 = X100) | (((ap @ X99 @ X97)) != ((ap @ X98 @ X100)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X101 : term,X102 : term,X103 : term,X104 : term] : ((X101 != X104) & (((ap @ X103 @ X101)) = ((ap @ X102 @ X104))))) & (hoasapinj1_gthm = $true) & (($true = sP37) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP37)) & (hoasapnotvar_lthm = $true) & (($true = sP36) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP36)) & (axassoc = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_gthm = $true) & ((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true)) & (! [X105 : term,X106 : subst,X107 : (term > $o),X108 : (term > $o)] : (? [X109 : term] : (((X108 @ X109)) != ((X107 @ (sub @ X109 @ (push @ X105 @ X106))))) | ($true != ((X107 @ X105))) | ($true = ((X108 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X110 : term,X111 : subst,X112 : (term > $o),X113 : (term > $o)] : (! [X114 : term] : (((X112 @ (sub @ X114 @ (push @ X110 @ X111)))) = ((X113 @ X114))) & ($true = ((X112 @ X110))) & ($true != ((X113 @ one))))) & ((induction2lem = $true) | ($true != sP33)) & (($true = sP33) | (induction2lem != $true)) & (hoaslamnotap_lthm = $true) & (! [X115 : term,X116 : term] : ((((lam @ X115)) != ((lam @ X116))) | (X115 = X116)) | (laminj != $true)) & ((laminj = $true) | ? [X117 : term,X118 : term] : ((((lam @ X118)) = ((lam @ X117))) & (X117 != X118))) & (hoasinduction_gthm = $true) & (? [X119 : term,X120 : term,X121 : term,X122 : term] : ((X120 != X122) & (((ap @ X120 @ X119)) = ((ap @ X122 @ X121)))) | ! [X123 : term,X124 : term,X125 : term,X126 : term] : ((X125 = X126) | (((ap @ (sub @ X126 @ id) @ X124)) != ((ap @ (sub @ X125 @ id) @ X123)))) | ? [X127 : term] : (((sub @ X127 @ id)) != X127) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X128 : term,X129 : term,X130 : term,X131 : term] : ((X129 = X131) | (((ap @ X129 @ X128)) != ((ap @ X131 @ X130)))) & ? [X132 : term,X133 : term,X134 : term,X135 : term] : ((X134 != X135) & (((ap @ (sub @ X134 @ id) @ X132)) = ((ap @ (sub @ X135 @ id) @ X133)))) & ! [X136 : term] : (((sub @ X136 @ id)) = X136))) & (hoasapnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X137 : term,X138 : term,X139 : subst,X140 : (term > $o),X141 : (term > $o)] : ((((X140 @ (sub @ X138 @ (push @ X137 @ X139)))) = $true) | (((X141 @ X138)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X142 : term,X143 : term,X144 : subst,X145 : (term > $o),X146 : (term > $o)] : (($true != ((X145 @ (sub @ X143 @ (push @ X142 @ X144))))) & ($true = ((X146 @ X143))))) & (! [X147 : term] : ? [X148 : (subst > term > term)] : (((sub @ X147 @ (push @ one @ sh))) = ((X148 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X149 : term] : ! [X150 : (subst > term > term)] : (((sub @ X149 @ (push @ one @ sh))) != ((X150 @ sh @ one)))) & (! [X151 : term,X152 : term,X153 : term,X154 : term] : ((((ap @ (sub @ X152 @ id) @ X151)) != ((ap @ (sub @ X154 @ id) @ X153))) | (X151 = X153)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X155 : term,X156 : term,X157 : term,X158 : term] : ((((ap @ (sub @ X158 @ id) @ X157)) = ((ap @ (sub @ X156 @ id) @ X155))) & (X155 != X157))) & (pushprop_lem3v2_lthm = $true) & (! [X159 : term] : (((sub @ X159 @ id)) = X159) | (termmset != $true)) & ((termmset = $true) | ? [X160 : term] : (((sub @ X160 @ id)) != X160)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true)) & (($true = sP26) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP26)) & ! [X161 : d_term] : (d_one = X161) & (! [X162 : term,X163 : subst] : (((comp @ sh @ (push @ X162 @ X163))) = X163) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X164 : term,X165 : subst] : (((comp @ sh @ (push @ X164 @ X165))) != X165)) & ((apinj1 = $true) | ? [X166 : term,X167 : term,X168 : term,X169 : term] : ((X166 != X169) & (((ap @ X166 @ X167)) = ((ap @ X169 @ X168))))) & (! [X170 : term,X171 : term,X172 : term,X173 : term] : ((X170 = X173) | (((ap @ X173 @ X172)) != ((ap @ X170 @ X171)))) | (apinj1 != $true)) & ((hoasapinj1 = $true) | ? [X174 : term,X175 : term,X176 : term,X177 : term] : ((((ap @ (sub @ X176 @ id) @ X174)) = ((ap @ (sub @ X177 @ id) @ X175))) & (X176 != X177))) & (! [X178 : term,X179 : term,X180 : term,X181 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X180 = X181)) | (hoasapinj1 != $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X182 : term] : ? [X183 : d_term] : (((d2term @ X183)) = X182) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X184 : subst,X185 : term] : (((sub @ one @ (push @ X185 @ X184))) = X185) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) != X187)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem0_lthm = $true) | ? [X188 : term,X189 : (term > $o),X190 : subst] : ! [X191 : (term > $o)] : ? [X192 : term] : (((X189 @ (sub @ X192 @ (push @ X188 @ X190)))) != ((X191 @ X192)))) & (! [X193 : term,X194 : (term > $o),X195 : subst] : ? [X196 : (term > $o)] : ! [X197 : term] : (((X194 @ (sub @ X197 @ (push @ X193 @ X195)))) = ((X196 @ X197))) | (pushprop_lem0_lthm != $true)) & (hoasinduction_lem1 = $true) & (! [X198 : (term > $o),X199 : (term > $o),X200 : subst,X201 : term] : ((((X199 @ X201)) != $true) | ? [X202 : term] : (((X198 @ X202)) != ((X199 @ (sub @ X202 @ (push @ X201 @ X200))))) | ($true = ((X198 @ one)))) | ? [X203 : subst,X204 : term] : (((sub @ one @ (push @ X204 @ X203))) != X204) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X205 : (term > $o),X206 : (term > $o),X207 : subst,X208 : term] : ((((X206 @ X208)) = $true) & ! [X209 : term] : (((X205 @ X209)) = ((X206 @ (sub @ X209 @ (push @ X208 @ X207))))) & ($true != ((X205 @ one)))) & ! [X210 : subst,X211 : term] : (((sub @ one @ (push @ X211 @ X210))) = X211))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X212 : d_term,X213 : d_term] : ((((d2term @ X212)) != ((d2term @ X213))) | (X212 = X213)) & (hoasinduction_lem1_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X214 : term] : ! [X215 : (subst > term > term)] : ? [X216 : subst,X217 : term] : (((X215 @ X216 @ X217)) != ((sub @ X214 @ (push @ X217 @ X216))))) & (! [X218 : term] : ? [X219 : (subst > term > term)] : ! [X220 : subst,X221 : term] : (((X219 @ X220 @ X221)) = ((sub @ X218 @ (push @ X221 @ X220)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_lem3v2 != $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((axidr = $true) | ? [X222 : subst] : (((comp @ X222 @ id)) != X222)) & (! [X223 : subst] : (((comp @ X223 @ id)) = X223) | (axidr != $true)) & (! [X224 : term,X225 : (subst > term > term),X226 : term] : (? [X227 : subst,X228 : subst,X229 : term] : (((X225 @ (comp @ X228 @ X227) @ (sub @ X229 @ X227))) != ((sub @ (X225 @ X228 @ X229) @ X227))) | (((ap @ (sub @ X224 @ id) @ X226)) != ((lam @ (X225 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X230 : term,X231 : (subst > term > term),X232 : term] : (! [X233 : subst,X234 : subst,X235 : term] : (((X231 @ (comp @ X234 @ X233) @ (sub @ X235 @ X233))) = ((sub @ (X231 @ X234 @ X235) @ X233))) & (((lam @ (X231 @ sh @ one))) = ((ap @ (sub @ X230 @ id) @ X232))))) & (induction2_gthm = $true) & (axapp = $true) & (! [X236 : (term > $o),X237 : term] : (($true = ((sP22 @ X236))) | ($true = ((X236 @ X237))) | ? [X238 : term] : (($true != ((X236 @ (lam @ X238)))) & (((X236 @ X238)) = $true)) | ? [X239 : term] : (($true = ((var @ X239))) & (((X236 @ X239)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X240 : (term > $o),X241 : term] : (($true != ((sP22 @ X240))) & (((X240 @ X241)) != $true) & ! [X242 : term] : (($true = ((X240 @ (lam @ X242)))) | ($true != ((X240 @ X242)))) & ! [X243 : term] : (($true != ((var @ X243))) | (((X240 @ X243)) = $true)))) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X244 : (subst > term > subst > $o)] : ? [X245 : (term > $o)] : ! [X246 : term] : (((X244 @ id @ X246 @ id)) = ((X245 @ X246))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X247 : (subst > term > subst > $o)] : ! [X248 : (term > $o)] : ? [X249 : term] : (((X247 @ id @ X249 @ id)) != ((X248 @ X249)))) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1_lthm = $true) | (? [X250 : subst,X251 : (term > $o),X252 : (term > $o),X253 : term,X254 : term] : (($true != ((X251 @ (sub @ X254 @ (push @ X253 @ X250))))) & ($true = ((X252 @ X254)))) & ! [X255 : term,X256 : subst] : (((sub @ one @ (push @ X255 @ X256))) = X255) & ! [X257 : term,X258 : subst] : (((comp @ sh @ (push @ X257 @ X258))) = X258))) & (! [X259 : subst,X260 : (term > $o),X261 : (term > $o),X262 : term,X263 : term] : (($true = ((X260 @ (sub @ X263 @ (push @ X262 @ X259))))) | (((X261 @ X263)) != $true)) | ? [X264 : term,X265 : subst] : (((sub @ one @ (push @ X264 @ X265))) != X264) | ? [X266 : term,X267 : subst] : (((comp @ sh @ (push @ X266 @ X267))) != X267) | (pushprop_lem1_lthm != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true)) & ((axscons = $true) | ? [X268 : subst] : (((push @ (sub @ one @ X268) @ (comp @ sh @ X268))) != X268)) & (! [X269 : subst] : (((push @ (sub @ one @ X269) @ (comp @ sh @ X269))) = X269) | (axscons != $true)) & ((termmset_lthm = $true) | (? [X270 : term] : (((sub @ X270 @ id)) != X270) & ! [X271 : term] : (((sub @ X271 @ id)) = X271))) & (! [X272 : term] : (((sub @ X272 @ id)) = X272) | ? [X273 : term] : (((sub @ X273 @ id)) != X273) | (termmset_lthm != $true)) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (($true = sP17) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP17)) & (apnotvar = $true) & ((hoasinduction_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction != $true)) & (ulamvarind = $true) & ((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (termmset_gthm = $true)),
% 6.46/1.22 inference(rectify,[],[f261])).
% 6.46/1.22 thf(f263,plain,(
% 6.46/1.22 ((hoaslaminj_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoaslaminj_lthm != $true)) & ((sP57 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP57 != $true)) & ((pushprop_lem0 = $true) | ! [X3 : (term > $o)] : (((X3 @ (sK460 @ X3))) != ((sK458 @ (sub @ (sK460 @ X3) @ (push @ sK459 @ sK457)))))) & (! [X5 : subst,X6 : (term > $o),X7 : term] : ! [X9 : term] : (((X6 @ (sub @ X9 @ (push @ X7 @ X5)))) = ((sK461 @ X7 @ X6 @ X5 @ X9))) | (pushprop_lem0 != $true)) & (axvarshift = $true) & (lamnotap != $true) & ! [X10 : d_subst] : (d_id = X10) & (($true = sP55) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP55)) & ((hoasinduction_lem3aa = $true) | ($true != sP54)) & (($true = sP54) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3v2a = $true) | (sP53 != $true)) & ((sP53 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X11 : subst] : (((d2subst @ (sK462 @ X11))) = X11) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP52 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP52 != $true)) & (axmap = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X13 : term,X14 : term,X15 : term,X16 : term] : ((((ap @ (sub @ X13 @ id) @ X16)) != ((ap @ (sub @ X14 @ id) @ X15))) | (X15 = X16)) | ((((ap @ sK464 @ sK463)) = ((ap @ sK465 @ sK466))) & (sK466 != sK463)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((((ap @ (sub @ sK468 @ id) @ sK469)) = ((ap @ (sub @ sK467 @ id) @ sK470))) & (sK469 != sK470)) & ! [X25 : term,X26 : term,X27 : term,X28 : term] : ((((ap @ X26 @ X25)) != ((ap @ X27 @ X28))) | (X25 = X28)))) & (! [X29 : term,X30 : (subst > term > subst > $o)] : ((($true != ((X30 @ id @ (ap @ (sub @ (sK472 @ X30) @ id) @ (sK471 @ X30)) @ id))) & ($true = ((X30 @ id @ (sK471 @ X30) @ id))) & (((X30 @ id @ (sK472 @ X30) @ id)) = $true)) | ($true = ((sP46 @ X30))) | ($true = ((X30 @ id @ X29 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X35 : term,X36 : term] : (($true = ((sK474 @ id @ (ap @ (sub @ X36 @ id) @ X35) @ id))) | ($true != ((sK474 @ id @ X35 @ id))) | ($true != ((sK474 @ id @ X36 @ id)))) & ($true != ((sP46 @ sK474))) & ($true != ((sK474 @ id @ sK473 @ id))))) & (! [X37 : term] : (((sub @ X37 @ (push @ one @ sh))) = ((sK475 @ X37 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X40 : (subst > term > term)] : (((X40 @ sh @ one)) != ((sub @ sK476 @ (push @ one @ sh))))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & ((substmonoid = $true) | (sK477 != ((comp @ sK477 @ id))) | (sK478 != ((comp @ id @ sK478)))) & ((! [X43 : subst] : (((comp @ X43 @ id)) = X43) & ! [X44 : subst] : (((comp @ id @ X44)) = X44)) | (substmonoid != $true)) & ((sK479 != ((comp @ sK479 @ id))) | (! [X46 : subst] : (((comp @ id @ X46)) = X46) & ! [X47 : subst] : (((comp @ X47 @ id)) = X47)) | (((comp @ id @ sK480)) != sK480) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X49 : subst] : (((comp @ X49 @ id)) = X49) & ((((comp @ id @ sK481)) != sK481) | (((comp @ sK482 @ id)) != sK482)) & ! [X52 : subst] : (((comp @ id @ X52)) = X52))) & ((hoasinduction_lem3v2_f = $true) | ! [X54 : (subst > term > term)] : (((X54 @ (sK485 @ X54) @ (sK484 @ X54))) != ((sub @ sK483 @ (push @ (sK484 @ X54) @ (sK485 @ X54)))))) & (! [X57 : term] : ! [X59 : term,X60 : subst] : (((sK486 @ X57 @ X60 @ X59)) = ((sub @ X57 @ (push @ X59 @ X60)))) | (hoasinduction_lem3v2_f != $true)) & (hoaslamnotap_gthm = $true) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & (hoaslamnotvar = $true) & (($true = sP42) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP42)) & (axclos = $true) & (pushprop_lem3v2 = $true) & ((hoaslaminj = $true) | ((((lam @ (sK488 @ sh @ one))) = ((lam @ (sK489 @ sh @ one)))) & ! [X65 : term,X66 : subst,X67 : subst] : (((sub @ (sK489 @ X66 @ X65) @ X67)) = ((sK489 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) & ! [X68 : subst,X69 : subst,X70 : term] : (((sK488 @ (comp @ X69 @ X68) @ (sub @ X70 @ X68))) = ((sub @ (sK488 @ X69 @ X70) @ X68))) & (((sK488 @ sK490 @ sK487)) != ((sK489 @ sK490 @ sK487))))) & (! [X71 : term,X72 : (subst > term > term),X73 : (subst > term > term),X74 : subst] : ((((lam @ (X72 @ sh @ one))) != ((lam @ (X73 @ sh @ one)))) | (((sub @ (X73 @ (sK492 @ X73) @ (sK491 @ X73)) @ (sK493 @ X73))) != ((X73 @ (comp @ (sK492 @ X73) @ (sK493 @ X73)) @ (sub @ (sK491 @ X73) @ (sK493 @ X73))))) | (((sub @ (X72 @ (sK495 @ X72) @ (sK496 @ X72)) @ (sK494 @ X72))) != ((X72 @ (comp @ (sK495 @ X72) @ (sK494 @ X72)) @ (sub @ (sK496 @ X72) @ (sK494 @ X72))))) | (((X73 @ X74 @ X71)) = ((X72 @ X74 @ X71)))) | (hoaslaminj != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (ulamvar1 != $true) & (! [X81 : (subst > term > subst > $o)] : ! [X83 : term] : (((sK497 @ X81 @ X83)) = ((X81 @ id @ X83 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X85 : (term > $o)] : (((sK498 @ id @ (sK499 @ X85) @ id)) != ((X85 @ (sK499 @ X85))))) & (hoaslamnotvar_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) | (((comp @ id @ sK500)) != sK500)) & (! [X88 : subst] : (((comp @ id @ X88)) = X88) | (axidl != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP40) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP40)) & (axabs = $true) & ! [X89 : d_subst,X90 : d_subst] : ((((d2subst @ X90)) != ((d2subst @ X89))) | (X89 = X90)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP38)) & (($true = sP38) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((shinj = $true) | ((sK502 != sK501) & (((sub @ sK502 @ sh)) = ((sub @ sK501 @ sh))))) & (! [X93 : term,X94 : term] : ((X93 = X94) | (((sub @ X93 @ sh)) != ((sub @ X94 @ sh)))) | (shinj != $true)) & ((axvarid = $true) | (((sub @ sK503 @ id)) != sK503)) & (! [X96 : term] : (((sub @ X96 @ id)) = X96) | (axvarid != $true)) & (pushprop_lem2v2 = $true) & (! [X97 : term,X98 : term,X99 : term,X100 : term] : ((X97 = X100) | (((ap @ X99 @ X97)) != ((ap @ X98 @ X100)))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK507 != sK504) & (((ap @ sK505 @ sK507)) = ((ap @ sK506 @ sK504))))) & (hoasapinj1_gthm = $true) & (($true = sP37) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP37)) & (hoasapnotvar_lthm = $true) & (($true = sP36) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP36)) & (axassoc = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_gthm = $true) & ((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true)) & (! [X105 : term,X106 : subst,X107 : (term > $o),X108 : (term > $o)] : ((((X107 @ (sub @ (sK508 @ X108 @ X107 @ X106 @ X105) @ (push @ X105 @ X106)))) != ((X108 @ (sK508 @ X108 @ X107 @ X106 @ X105)))) | ($true != ((X107 @ X105))) | ($true = ((X108 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X114 : term] : (((sK512 @ X114)) = ((sK511 @ (sub @ X114 @ (push @ sK509 @ sK510))))) & ($true = ((sK511 @ sK509))) & ($true != ((sK512 @ one))))) & ((induction2lem = $true) | ($true != sP33)) & (($true = sP33) | (induction2lem != $true)) & (hoaslamnotap_lthm = $true) & (! [X115 : term,X116 : term] : ((((lam @ X115)) != ((lam @ X116))) | (X115 = X116)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK513)) = ((lam @ sK514))) & (sK513 != sK514))) & (hoasinduction_gthm = $true) & (((sK518 != sK516) & (((ap @ sK518 @ sK517)) = ((ap @ sK516 @ sK515)))) | ! [X123 : term,X124 : term,X125 : term,X126 : term] : ((X125 = X126) | (((ap @ (sub @ X126 @ id) @ X124)) != ((ap @ (sub @ X125 @ id) @ X123)))) | (((sub @ sK519 @ id)) != sK519) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X128 : term,X129 : term,X130 : term,X131 : term] : ((X129 = X131) | (((ap @ X129 @ X128)) != ((ap @ X131 @ X130)))) & ((sK522 != sK523) & (((ap @ (sub @ sK523 @ id) @ sK521)) = ((ap @ (sub @ sK522 @ id) @ sK520)))) & ! [X136 : term] : (((sub @ X136 @ id)) = X136))) & (hoasapnotvar = $true) & (hoaslamnotvar_lthm = $true) & (! [X137 : term,X138 : term,X139 : subst,X140 : (term > $o),X141 : (term > $o)] : ((((X140 @ (sub @ X138 @ (push @ X137 @ X139)))) = $true) | (((X141 @ X138)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK527 @ (sub @ sK525 @ (push @ sK524 @ sK526)))) != $true) & ($true = ((sK528 @ sK525))))) & (! [X147 : term] : (((sub @ X147 @ (push @ one @ sh))) = ((sK529 @ X147 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X150 : (subst > term > term)] : (((X150 @ sh @ one)) != ((sub @ sK530 @ (push @ one @ sh))))) & (! [X151 : term,X152 : term,X153 : term,X154 : term] : ((((ap @ (sub @ X152 @ id) @ X151)) != ((ap @ (sub @ X154 @ id) @ X153))) | (X151 = X153)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK534 @ id) @ sK533)) = ((ap @ (sub @ sK532 @ id) @ sK531))) & (sK533 != sK531))) & (pushprop_lem3v2_lthm = $true) & (! [X159 : term] : (((sub @ X159 @ id)) = X159) | (termmset != $true)) & ((termmset = $true) | (sK535 != ((sub @ sK535 @ id)))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_no_psi_cond_lthm != $true)) & (($true = sP26) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP26)) & ! [X161 : d_term] : (d_one = X161) & (! [X162 : term,X163 : subst] : (((comp @ sh @ (push @ X162 @ X163))) = X163) | (axshiftcons != $true)) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK536 @ sK537))) != sK537)) & ((apinj1 = $true) | ((sK541 != sK538) & (((ap @ sK541 @ sK540)) = ((ap @ sK538 @ sK539))))) & (! [X170 : term,X171 : term,X172 : term,X173 : term] : ((X170 = X173) | (((ap @ X173 @ X172)) != ((ap @ X170 @ X171)))) | (apinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK544 @ id) @ sK542)) = ((ap @ (sub @ sK545 @ id) @ sK543))) & (sK544 != sK545))) & (! [X178 : term,X179 : term,X180 : term,X181 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X180 = X181)) | (hoasapinj1 != $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X182 : term] : (((d2term @ (sK546 @ X182))) = X182) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (! [X184 : subst,X185 : term] : (((sub @ one @ (push @ X185 @ X184))) = X185) | (axvarcons != $true)) & ((axvarcons = $true) | (sK548 != ((sub @ one @ (push @ sK548 @ sK547))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((pushprop_lem0_lthm = $true) | ! [X191 : (term > $o)] : (((sK550 @ (sub @ (sK552 @ X191) @ (push @ sK549 @ sK551)))) != ((X191 @ (sK552 @ X191))))) & (! [X193 : term,X194 : (term > $o),X195 : subst] : ! [X197 : term] : (((sK553 @ X195 @ X194 @ X193 @ X197)) = ((X194 @ (sub @ X197 @ (push @ X193 @ X195))))) | (pushprop_lem0_lthm != $true)) & (hoasinduction_lem1 = $true) & (! [X198 : (term > $o),X199 : (term > $o),X200 : subst,X201 : term] : ((((X199 @ X201)) != $true) | (((X199 @ (sub @ (sK554 @ X201 @ X200 @ X199 @ X198) @ (push @ X201 @ X200)))) != ((X198 @ (sK554 @ X201 @ X200 @ X199 @ X198)))) | ($true = ((X198 @ one)))) | (((sub @ one @ (push @ sK556 @ sK555))) != sK556) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((($true = ((sK558 @ sK560))) & ! [X209 : term] : (((sK558 @ (sub @ X209 @ (push @ sK560 @ sK559)))) = ((sK557 @ X209))) & ($true != ((sK557 @ one)))) & ! [X210 : subst,X211 : term] : (((sub @ one @ (push @ X211 @ X210))) = X211))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X212 : d_term,X213 : d_term] : ((((d2term @ X212)) != ((d2term @ X213))) | (X212 = X213)) & (hoasinduction_lem1_gthm = $true) & (ulamvarsh = $true) & (hoasinduction_lem1v2 = $true) & (pushprop = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X215 : (subst > term > term)] : (((sub @ sK561 @ (push @ (sK563 @ X215) @ (sK562 @ X215)))) != ((X215 @ (sK562 @ X215) @ (sK563 @ X215))))) & (! [X218 : term] : ! [X220 : subst,X221 : term] : (((sK564 @ X218 @ X220 @ X221)) = ((sub @ X218 @ (push @ X221 @ X220)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2 = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_lem3v2 != $true)) & (pushprop_lthm_orig = $true) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & ((axidr = $true) | (sK565 != ((comp @ sK565 @ id)))) & (! [X223 : subst] : (((comp @ X223 @ id)) = X223) | (axidr != $true)) & (! [X224 : term,X225 : (subst > term > term),X226 : term] : ((((sub @ (X225 @ (sK567 @ X225) @ (sK568 @ X225)) @ (sK566 @ X225))) != ((X225 @ (comp @ (sK567 @ X225) @ (sK566 @ X225)) @ (sub @ (sK568 @ X225) @ (sK566 @ X225))))) | (((ap @ (sub @ X224 @ id) @ X226)) != ((lam @ (X225 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X233 : subst,X234 : subst,X235 : term] : (((sK570 @ (comp @ X234 @ X233) @ (sub @ X235 @ X233))) = ((sub @ (sK570 @ X234 @ X235) @ X233))) & (((lam @ (sK570 @ sh @ one))) = ((ap @ (sub @ sK569 @ id) @ sK571))))) & (induction2_gthm = $true) & (axapp = $true) & (! [X236 : (term > $o),X237 : term] : (($true = ((sP22 @ X236))) | ($true = ((X236 @ X237))) | (($true != ((X236 @ (lam @ (sK572 @ X236))))) & ($true = ((X236 @ (sK572 @ X236))))) | ((((var @ (sK573 @ X236))) = $true) & (((X236 @ (sK573 @ X236))) != $true))) | (induction != $true)) & ((induction = $true) | (($true != ((sP22 @ sK574))) & ($true != ((sK574 @ sK575))) & ! [X242 : term] : ((((sK574 @ (lam @ X242))) = $true) | ($true != ((sK574 @ X242)))) & ! [X243 : term] : (($true != ((var @ X243))) | ($true = ((sK574 @ X243)))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X244 : (subst > term > subst > $o)] : ! [X246 : term] : (((X244 @ id @ X246 @ id)) = ((sK576 @ X244 @ X246))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X248 : (term > $o)] : (((sK577 @ id @ (sK578 @ X248) @ id)) != ((X248 @ (sK578 @ X248))))) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1_lthm = $true) | (((((sK580 @ (sub @ sK583 @ (push @ sK582 @ sK579)))) != $true) & ($true = ((sK581 @ sK583)))) & ! [X255 : term,X256 : subst] : (((sub @ one @ (push @ X255 @ X256))) = X255) & ! [X257 : term,X258 : subst] : (((comp @ sh @ (push @ X257 @ X258))) = X258))) & (! [X259 : subst,X260 : (term > $o),X261 : (term > $o),X262 : term,X263 : term] : (($true = ((X260 @ (sub @ X263 @ (push @ X262 @ X259))))) | (((X261 @ X263)) != $true)) | (sK584 != ((sub @ one @ (push @ sK584 @ sK585)))) | (sK587 != ((comp @ sh @ (push @ sK586 @ sK587)))) | (pushprop_lem1_lthm != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP21 != $true)) & ((axscons = $true) | (sK588 != ((push @ (sub @ one @ sK588) @ (comp @ sh @ sK588))))) & (! [X269 : subst] : (((push @ (sub @ one @ X269) @ (comp @ sh @ X269))) = X269) | (axscons != $true)) & ((termmset_lthm = $true) | ((((sub @ sK589 @ id)) != sK589) & ! [X271 : term] : (((sub @ X271 @ id)) = X271))) & (! [X272 : term] : (((sub @ X272 @ id)) = X272) | (sK590 != ((sub @ sK590 @ id))) | (termmset_lthm != $true)) & (pushprop_lem1v2_gthm = $true) & (one = ((d2term @ d_one))) & (($true = sP17) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP17)) & (apnotvar = $true) & ((hoasinduction_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) | ($true != sP4)) & (($true = sP4) | (hoasinduction != $true)) & (ulamvarind = $true) & ((sP1 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP1 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (termmset_gthm = $true)),
% 6.46/1.22 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,vAPP,vAPP,vAPP,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,vAPP,vAPP,sK473,sK474,vAPP,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,vAPP,vAPP,vAPP,sK487,sK488,sK489,sK490,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK498,vAPP,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,vAPP,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,vAPP,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,vAPP,sK547,sK548,sK549,sK550,sK551,vAPP,vAPP,vAPP,sK555,sK556,sK557,sK558,sK559,sK560,sK561,vAPP,vAPP,vAPP,sK565,vAPP,vAPP,vAPP,sK569,sK570,sK571,vAPP,vAPP,sK574,sK575,vAPP,sK577,vAPP,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590]),skolemize(X0,sK457),skolemize(X1,sK458),skolemize(X2,sK459),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X17,sK463),skolemize(X18,sK464),skolemize(X19,sK465),skolemize(X20,sK466),skolemize(X21,sK467),skolemize(X22,sK468),skolemize(X23,sK469),skolemize(X24,sK470),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X33,sK473),skolemize(X34,sK474),skolemize(X27,sK70 @ X20),skolemize(X39,sK476),skolemize(X41,sK477),skolemize(X42,sK478),skolemize(X45,sK479),skolemize(X48,sK480),skolemize(X50,sK481),skolemize(X51,sK482),skolemize(X53,sK483),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X61,sK487),skolemize(X62,sK488),skolemize(X63,sK489),skolemize(X64,sK490),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X84,sK498),skolemize(X27,sK70 @ X20),skolemize(X87,sK500),skolemize(X91,sK501),skolemize(X92,sK502),skolemize(X95,sK503),skolemize(X101,sK504),skolemize(X102,sK505),skolemize(X103,sK506),skolemize(X104,sK507),skolemize(X27,sK70 @ X20),skolemize(X110,sK509),skolemize(X111,sK510),skolemize(X112,sK511),skolemize(X113,sK512),skolemize(X117,sK513),skolemize(X118,sK514),skolemize(X119,sK515),skolemize(X120,sK516),skolemize(X121,sK517),skolemize(X122,sK518),skolemize(X127,sK519),skolemize(X132,sK520),skolemize(X133,sK521),skolemize(X134,sK522),skolemize(X135,sK523),skolemize(X142,sK524),skolemize(X143,sK525),skolemize(X144,sK526),skolemize(X145,sK527),skolemize(X146,sK528),skolemize(X27,sK70 @ X20),skolemize(X149,sK530),skolemize(X155,sK531),skolemize(X156,sK532),skolemize(X157,sK533),skolemize(X158,sK534),skolemize(X160,sK535),skolemize(X164,sK536),skolemize(X165,sK537),skolemize(X166,sK538),skolemize(X167,sK539),skolemize(X168,sK540),skolemize(X169,sK541),skolemize(X174,sK542),skolemize(X175,sK543),skolemize(X176,sK544),skolemize(X177,sK545),skolemize(X27,sK70 @ X20),skolemize(X186,sK547),skolemize(X187,sK548),skolemize(X188,sK549),skolemize(X189,sK550),skolemize(X190,sK551),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X203,sK555),skolemize(X204,sK556),skolemize(X205,sK557),skolemize(X206,sK558),skolemize(X207,sK559),skolemize(X208,sK560),skolemize(X214,sK561),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X222,sK565),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X230,sK569),skolemize(X231,sK570),skolemize(X232,sK571),skolemize(X27,sK70 @ X20),skolemize(X27,sK70 @ X20),skolemize(X240,sK574),skolemize(X241,sK575),skolemize(X27,sK70 @ X20),skolemize(X247,sK577),skolemize(X27,sK70 @ X20),skolemize(X250,sK579),skolemize(X251,sK580),skolemize(X252,sK581),skolemize(X253,sK582),skolemize(X254,sK583),skolemize(X264,sK584),skolemize(X265,sK585),skolemize(X266,sK586),skolemize(X267,sK587),skolemize(X268,sK588),skolemize(X270,sK589),skolemize(X273,sK590)],[f262])).
% 6.46/1.22 thf(f264,plain,(
% 6.46/1.22 (hoasinduction_lem3a != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))),
% 6.46/1.22 inference(cnf_transformation,[],[f8])).
% 6.46/1.22 thf(f301,plain,(
% 6.46/1.22 ( ! [X3 : (subst > term > term)] : ((((X3 @ (comp @ (sK98 @ X3) @ (sK99 @ X3)) @ (sub @ (sK97 @ X3) @ (sK99 @ X3)))) != ((sub @ (X3 @ (sK98 @ X3) @ (sK97 @ X3)) @ (sK99 @ X3)))) | ($true = ((sK94 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ($true = sP55) | ($true = ((sK94 @ id @ (sK96 @ X3) @ id)))) )),
% 6.46/1.22 inference(cnf_transformation,[],[f86])).
% 6.46/1.22 thf(f303,plain,(
% 6.46/1.22 ($true = sP55) | (((sK94 @ id @ (lam @ sK95) @ id)) != $true)),
% 6.46/1.22 inference(cnf_transformation,[],[f86])).
% 6.46/1.22 thf(f755,plain,(
% 6.46/1.22 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 6.46/1.22 inference(cnf_transformation,[],[f263])).
% 6.46/1.22 thf(f767,plain,(
% 6.46/1.22 (one = ((d2term @ d_one)))),
% 6.46/1.22 inference(cnf_transformation,[],[f263])).
% 6.46/1.22 thf(f833,plain,(
% 6.46/1.22 ( ! [X182 : term] : ((((d2term @ (sK546 @ X182))) = X182)) )),
% 6.46/1.22 inference(cnf_transformation,[],[f263])).
% 6.46/1.22 thf(f843,plain,(
% 6.46/1.22 ( ! [X161 : d_term] : ((d_one = X161)) )),
% 6.46/1.22 inference(cnf_transformation,[],[f263])).
% 6.46/1.22 thf(f968,plain,(
% 6.46/1.22 ($true != sP55) | (hoasinduction_lem3a = $true)),
% 6.46/1.22 inference(cnf_transformation,[],[f263])).
% 6.46/1.22 thf(f969,plain,(
% 6.46/1.22 ($true = sP55) | (hoasinduction_lem3a != $true)),
% 6.46/1.22 inference(cnf_transformation,[],[f263])).
% 6.46/1.22 thf(f981,plain,(
% 6.46/1.22 (hoasinduction_lem3a != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))),
% 6.46/1.22 inference(definition_unfolding,[],[f264,f755])).
% 6.46/1.22 thf(f1118,plain,(
% 6.46/1.22 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))) = $true) | (hoasinduction_lem3a = $true)),
% 6.46/1.22 inference(xor_proxy_clausification,[],[f981])).
% 6.46/1.22 thf(f1119,plain,(
% 6.46/1.22 (hoasinduction_lem3a = $false) | (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))) = $false)),
% 6.46/1.22 inference(xor_proxy_clausification,[],[f981])).
% 6.46/1.22 thf(f1120,plain,(
% 6.46/1.22 ((((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))) @ sK591)) = $false) | (hoasinduction_lem3a = $false)),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1119])).
% 6.46/1.22 thf(f1121,plain,(
% 6.46/1.22 ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ 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 @ Y0) @ id)))))) = $false) | (hoasinduction_lem3a = $false)),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1120])).
% 6.46/1.22 thf(f1122,plain,(
% 6.46/1.22 (hoasinduction_lem3a = $false) | (((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ Y0) @ id))))) = $false)),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1121])).
% 6.46/1.22 thf(f1123,plain,(
% 6.46/1.22 (hoasinduction_lem3a = $false) | ($true = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))))))),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1121])).
% 6.46/1.22 thf(f1124,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3a = $false) | ($true = (((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) @ X1)))) )),
% 6.46/1.22 inference(pi_proxy_clausification,[],[f1123])).
% 6.46/1.22 thf(f1125,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) | (hoasinduction_lem3a = $false)) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1124])).
% 6.46/1.22 thf(f1126,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))))) = $false) | (hoasinduction_lem3a = $false) | ($true = (((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1125])).
% 6.46/1.22 thf(f1127,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ (sK592 @ X1))) = $false) | (hoasinduction_lem3a = $false)) )),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1126])).
% 6.46/1.22 thf(f1128,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ (sK592 @ X1))) = $false) | (hoasinduction_lem3a = $false) | (((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))))) = $false)) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1127])).
% 6.46/1.22 thf(f1129,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ Y2) = (X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2)))))))) @ (sK592 @ X1))) = $false) | ((((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK593 @ X1))) = $false) | (hoasinduction_lem3a = $false)) )),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1128])).
% 6.46/1.22 thf(f1130,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (((((sK591 @ id @ (sK593 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK593 @ X1)) @ id))) = $false) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y0 @ (sK592 @ X1)) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK592 @ X1) @ Y1))))))))) | (hoasinduction_lem3a = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1129])).
% 6.46/1.22 thf(f1132,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y0 @ (sK592 @ X1)) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK592 @ X1) @ Y1))))))))) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (hoasinduction_lem3a = $false)) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1130])).
% 6.46/1.22 thf(f1133,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (((((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y0 @ (sK592 @ X1)) @ Y1) = (X1 @ (comp @ Y0 @ Y1) @ (sub @ (sK592 @ X1) @ Y1)))))) @ (sK594 @ X1))) = $false) | (hoasinduction_lem3a = $false) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1132])).
% 6.46/1.22 thf(f1134,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction_lem3a = $false) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (((!! @ subst @ (^[Y0 : subst]: ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ Y0) = (X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK592 @ X1) @ Y0)))))) = $false)) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1133])).
% 6.46/1.22 thf(f1135,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((^[Y0 : subst]: ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ Y0) = (X1 @ (comp @ (sK594 @ X1) @ Y0) @ (sub @ (sK592 @ X1) @ Y0)))) @ (sK595 @ X1))) = $false) | (hoasinduction_lem3a = $false)) )),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1134])).
% 6.46/1.22 thf(f1136,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3a = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | ($false = (((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1)) = (X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1))))))) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1135])).
% 6.46/1.22 thf(f1137,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (hoasinduction_lem3a = $false) | (((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1)))) != ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1))))) )),
% 6.46/1.22 inference(equality_proxy_clausification,[],[f1136])).
% 6.46/1.22 thf(f1143,plain,(
% 6.46/1.22 ((((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ Y0) @ id))) @ sK598)) = $false) | (hoasinduction_lem3a = $false)),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1122])).
% 6.46/1.22 thf(f1144,plain,(
% 6.46/1.22 ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (sub @ sK598 @ (push @ Y0 @ id)) @ id)))) => (sK591 @ id @ (lam @ sK598) @ id))) = $false) | (hoasinduction_lem3a = $false)),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1143])).
% 6.46/1.22 thf(f1145,plain,(
% 6.46/1.22 ($false = ((sK591 @ id @ (lam @ sK598) @ id))) | (hoasinduction_lem3a = $false)),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1144])).
% 6.46/1.22 thf(f1150,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > subst > $o)] : (($true = (((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y3 @ Y2) @ Y4) = (Y1 @ (comp @ Y3 @ Y4) @ (sub @ Y2 @ Y4))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))) @ X1))) | (hoasinduction_lem3a = $true)) )),
% 6.46/1.22 inference(pi_proxy_clausification,[],[f1118])).
% 6.46/1.22 thf(f1151,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ Y0) @ id)))))) = $true)) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1150])).
% 6.46/1.22 thf(f1152,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | (((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ Y0) @ id))))) = $true) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id)))))) = $false)) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1151])).
% 6.46/1.22 thf(f1153,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : (($true = (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ Y0) @ id))) @ X2))) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id)))))) = $false) | (hoasinduction_lem3a = $true)) )),
% 6.46/1.22 inference(pi_proxy_clausification,[],[f1152])).
% 6.46/1.22 thf(f1154,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ($true = (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ Y0) @ id))) @ X2))) | ((((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id)))) @ (sK599 @ X1))) = $false)) )),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1153])).
% 6.46/1.22 thf(f1155,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : (($true = (((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ X2) @ id)))) | ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK599 @ X1 @ Y1 @ Y0) @ Y2) = (sK599 @ X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => ((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ Y0) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id)))) = $false) | (hoasinduction_lem3a = $true)) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1154])).
% 6.46/1.22 thf(f1156,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : ((((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id))))) = $false) | ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK599 @ X1 @ Y1 @ Y0) @ Y2) = (sK599 @ X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => ((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ Y0) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id)))) = $false) | ($true = ((X1 @ id @ (lam @ X2) @ id))) | (hoasinduction_lem3a = $true)) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1155])).
% 6.46/1.22 thf(f1157,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : (((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK599 @ X1 @ Y1 @ Y0) @ Y2) = (sK599 @ X1 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => ((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ Y0) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id)))) = $false) | ($true = ((X1 @ id @ (lam @ X2) @ id))) | ((((^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id))) @ (sK600 @ X1 @ X2))) = $false) | (hoasinduction_lem3a = $true)) )),
% 6.46/1.22 inference(sigma_proxy_clausification,[],[f1156])).
% 6.46/1.22 thf(f1158,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ((((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ Y0) @ id)))) => (X1 @ id @ (d2term @ d_one) @ id))) = $false) | ($true = ((X1 @ id @ (lam @ X2) @ id))) | ((((^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id))) @ (sK600 @ X1 @ X2))) = $false)) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1157])).
% 6.46/1.22 thf(f1174,plain,(
% 6.46/1.22 ( ! [X2 : term,X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ((((^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id))) @ (sK600 @ X1 @ X2))) = $false) | ($true = ((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ Y0) @ id)))))) | ($true = ((X1 @ id @ (lam @ X2) @ id)))) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1158])).
% 6.46/1.22 thf(f1175,plain,(
% 6.46/1.22 ( ! [X2 : term,X3 : term,X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ((((^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id))) @ (sK600 @ X1 @ X2))) = $false) | ($true = (((^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ Y0) @ id))) @ X3))) | ($true = ((X1 @ id @ (lam @ X2) @ id)))) )),
% 6.46/1.22 inference(pi_proxy_clausification,[],[f1174])).
% 6.46/1.22 thf(f1176,plain,(
% 6.46/1.22 ( ! [X2 : term,X3 : term,X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ($true = ((X1 @ id @ (lam @ X2) @ id))) | ((((X1 @ id @ (sK600 @ X1 @ X2) @ id) => (X1 @ id @ (sub @ X2 @ (push @ (sK600 @ X1 @ X2) @ id)) @ id))) = $false) | ($true = (((X1 @ id @ X3 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ X3) @ id))))) )),
% 6.46/1.22 inference(beta-eta_normalization,[],[f1175])).
% 6.46/1.22 thf(f1178,plain,(
% 6.46/1.22 ( ! [X2 : term,X3 : term,X1 : (subst > term > subst > $o)] : ((hoasinduction_lem3a = $true) | ($true = (((X1 @ id @ X3 @ id) => (X1 @ id @ (sK599 @ X1 @ id @ X3) @ id)))) | ($true = ((X1 @ id @ (lam @ X2) @ id))) | ($true = ((X1 @ id @ (sK600 @ X1 @ X2) @ id)))) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1176])).
% 6.46/1.22 thf(f1179,plain,(
% 6.46/1.22 ( ! [X2 : term,X3 : term,X1 : (subst > term > subst > $o)] : (($true = ((X1 @ id @ (lam @ X2) @ id))) | (hoasinduction_lem3a = $true) | (((X1 @ id @ X3 @ id)) = $false) | ($true = ((X1 @ id @ (sK599 @ X1 @ id @ X3) @ id))) | ($true = ((X1 @ id @ (sK600 @ X1 @ X2) @ id)))) )),
% 6.46/1.22 inference(imp_proxy_clausification,[],[f1178])).
% 6.46/1.22 thf(f1413,definition,(
% 6.46/1.22 spl601_54 <=> ($true = sP55)),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_54])],[avatar_definition])).
% 6.46/1.22 thf(f2080,definition,(
% 6.46/1.22 spl601_210 <=> (hoasinduction_lem3a = $true)),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_210])],[avatar_definition])).
% 6.46/1.22 thf(f2081,plain,(
% 6.46/1.22 (hoasinduction_lem3a = $true) | ~spl601_210),
% 6.46/1.22 inference(avatar_component_clause,[],[f2080])).
% 6.46/1.22 thf(f2083,plain,(
% 6.46/1.22 ~spl601_210 | spl601_54),
% 6.46/1.22 inference(avatar_split_clause,[],[f969,f1413,f2080])).
% 6.46/1.22 thf(f2093,definition,(
% 6.46/1.22 spl601_213 <=> (((sK94 @ id @ (lam @ sK95) @ id)) = $true)),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_213])],[avatar_definition])).
% 6.46/1.22 thf(f2095,plain,(
% 6.46/1.22 (((sK94 @ id @ (lam @ sK95) @ id)) != $true) | spl601_213),
% 6.46/1.22 inference(avatar_component_clause,[],[f2093])).
% 6.46/1.22 thf(f2096,plain,(
% 6.46/1.22 spl601_54 | ~spl601_213),
% 6.46/1.22 inference(avatar_split_clause,[],[f303,f2093,f1413])).
% 6.46/1.22 thf(f2199,plain,(
% 6.46/1.22 spl601_210 | ~spl601_54),
% 6.46/1.22 inference(avatar_split_clause,[],[f968,f1413,f2080])).
% 6.46/1.22 thf(f3344,definition,(
% 6.46/1.22 spl601_501 <=> ! [X3 : (subst > term > term)] : ((((X3 @ (comp @ (sK98 @ X3) @ (sK99 @ X3)) @ (sub @ (sK97 @ X3) @ (sK99 @ X3)))) != ((sub @ (X3 @ (sK98 @ X3) @ (sK97 @ X3)) @ (sK99 @ X3)))) | ($true = ((sK94 @ id @ (sK96 @ X3) @ id))) | ($true = ((sK94 @ id @ (lam @ (X3 @ sh @ one)) @ id))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_501])],[avatar_definition])).
% 6.46/1.22 thf(f3345,plain,(
% 6.46/1.22 ( ! [X3 : (subst > term > term)] : (($true = ((sK94 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ($true = ((sK94 @ id @ (sK96 @ X3) @ id))) | (((X3 @ (comp @ (sK98 @ X3) @ (sK99 @ X3)) @ (sub @ (sK97 @ X3) @ (sK99 @ X3)))) != ((sub @ (X3 @ (sK98 @ X3) @ (sK97 @ X3)) @ (sK99 @ X3))))) ) | ~spl601_501),
% 6.46/1.22 inference(avatar_component_clause,[],[f3344])).
% 6.46/1.22 thf(f3346,plain,(
% 6.46/1.22 spl601_54 | spl601_501),
% 6.46/1.22 inference(avatar_split_clause,[],[f301,f3344,f1413])).
% 6.46/1.22 thf(f3709,definition,(
% 6.46/1.22 spl601_584 <=> (hoasinduction_lem3a = $false)),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_584])],[avatar_definition])).
% 6.46/1.22 thf(f3711,plain,(
% 6.46/1.22 (hoasinduction_lem3a = $false) | ~spl601_584),
% 6.46/1.22 inference(avatar_component_clause,[],[f3709])).
% 6.46/1.22 thf(f3713,definition,(
% 6.46/1.22 spl601_585 <=> ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id))) | (((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1)))) != ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1)))))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_585])],[avatar_definition])).
% 6.46/1.22 thf(f3714,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : ((((X1 @ (comp @ (sK594 @ X1) @ (sK595 @ X1)) @ (sub @ (sK592 @ X1) @ (sK595 @ X1)))) != ((sub @ (X1 @ (sK594 @ X1) @ (sK592 @ X1)) @ (sK595 @ X1)))) | ($true = ((sK591 @ id @ (sK593 @ X1) @ id)))) ) | ~spl601_585),
% 6.46/1.22 inference(avatar_component_clause,[],[f3713])).
% 6.46/1.22 thf(f3716,definition,(
% 6.46/1.22 spl601_586 <=> ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_586])],[avatar_definition])).
% 6.46/1.22 thf(f3718,plain,(
% 6.46/1.22 ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl601_586),
% 6.46/1.22 inference(avatar_component_clause,[],[f3716])).
% 6.46/1.22 thf(f3719,plain,(
% 6.46/1.22 spl601_584 | spl601_585 | spl601_586),
% 6.46/1.22 inference(avatar_split_clause,[],[f1137,f3716,f3713,f3709])).
% 6.46/1.22 thf(f3729,definition,(
% 6.46/1.22 spl601_589 <=> ($false = ((sK591 @ id @ (lam @ sK598) @ id)))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_589])],[avatar_definition])).
% 6.46/1.22 thf(f3731,plain,(
% 6.46/1.22 ($false = ((sK591 @ id @ (lam @ sK598) @ id))) | ~spl601_589),
% 6.46/1.22 inference(avatar_component_clause,[],[f3729])).
% 6.46/1.22 thf(f3732,plain,(
% 6.46/1.22 spl601_589 | spl601_584),
% 6.46/1.22 inference(avatar_split_clause,[],[f1145,f3709,f3729])).
% 6.46/1.22 thf(f3742,definition,(
% 6.46/1.22 spl601_592 <=> ! [X2 : term,X1 : (subst > term > subst > $o),X3 : term] : (($true = ((X1 @ id @ (lam @ X2) @ id))) | ($true = ((X1 @ id @ (sK600 @ X1 @ X2) @ id))) | ($true = ((X1 @ id @ (sK599 @ X1 @ id @ X3) @ id))) | (((X1 @ id @ X3 @ id)) = $false))),
% 6.46/1.22 introduced(definition,[new_symbols(definition,[spl601_592])],[avatar_definition])).
% 6.46/1.22 thf(f3743,plain,(
% 6.46/1.22 ( ! [X2 : term,X3 : term,X1 : (subst > term > subst > $o)] : (($true = ((X1 @ id @ (sK599 @ X1 @ id @ X3) @ id))) | ($true = ((X1 @ id @ (lam @ X2) @ id))) | ($true = ((X1 @ id @ (sK600 @ X1 @ X2) @ id))) | (((X1 @ id @ X3 @ id)) = $false)) ) | ~spl601_592),
% 6.46/1.22 inference(avatar_component_clause,[],[f3742])).
% 6.46/1.22 thf(f3744,plain,(
% 6.46/1.22 spl601_210 | spl601_592),
% 6.46/1.22 inference(avatar_split_clause,[],[f1179,f3742,f2080])).
% 6.46/1.22 thf(f4336,plain,(
% 6.46/1.22 ( ! [X182 : term] : ((((d2term @ d_one)) = X182)) )),
% 6.46/1.22 inference(forward_demodulation,[],[f833,f843])).
% 6.46/1.22 thf(f4343,plain,(
% 6.46/1.22 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 6.46/1.22 inference(superposition,[],[f4336,f4336])).
% 6.46/1.22 thf(f4356,plain,(
% 6.46/1.22 ( ! [X2 : term,X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ (sK600 @ X0 @ X2) @ id)) = $true) | ($true = ((X0 @ id @ (lam @ X2) @ id))) | ($true = ((X0 @ id @ (d2term @ d_one) @ id))) | (((X0 @ id @ X1 @ id)) = $false)) ) | ~spl601_592),
% 6.46/1.22 inference(superposition,[],[f3743,f4336])).
% 6.46/1.22 thf(f4371,plain,(
% 6.46/1.22 ( ! [X2 : term,X0 : (subst > term > subst > $o),X1 : term] : (($true = ((X0 @ id @ (lam @ X2) @ id))) | (((X0 @ id @ X1 @ id)) = $false) | ($true = ((X0 @ id @ (d2term @ d_one) @ id))) | ($true = ((X0 @ id @ (d2term @ d_one) @ id)))) ) | ~spl601_592),
% 6.46/1.22 inference(forward_demodulation,[],[f4356,f4336])).
% 6.46/1.22 thf(f4372,plain,(
% 6.46/1.22 ( ! [X2 : term,X0 : (subst > term > subst > $o),X1 : term] : (($true = ((X0 @ id @ (lam @ X2) @ id))) | (((X0 @ id @ X1 @ id)) = $false) | ($true = ((X0 @ id @ (d2term @ d_one) @ id)))) ) | ~spl601_592),
% 6.46/1.22 inference(duplicate_literal_removal,[],[f4371])).
% 6.46/1.22 thf(f4392,plain,(
% 6.46/1.22 ( ! [X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ X1 @ id)) = $false) | ($true = ((X0 @ id @ (d2term @ d_one) @ id))) | ($true = ((X0 @ id @ (d2term @ d_one) @ id)))) ) | ~spl601_592),
% 6.46/1.22 inference(forward_demodulation,[],[f4372,f4336])).
% 6.46/1.22 thf(f4393,plain,(
% 6.46/1.22 ( ! [X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ X1 @ id)) = $false) | ($true = ((X0 @ id @ (d2term @ d_one) @ id)))) ) | ~spl601_592),
% 6.46/1.22 inference(duplicate_literal_removal,[],[f4392])).
% 6.46/1.22 thf(f4408,plain,(
% 6.46/1.22 ( ! [X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ one @ id)) = $true) | (((X0 @ id @ X1 @ id)) = $false)) ) | ~spl601_592),
% 6.46/1.22 inference(forward_demodulation,[],[f4393,f767])).
% 6.46/1.22 thf(f6262,plain,(
% 6.46/1.22 (((sK94 @ id @ (d2term @ d_one) @ id)) != $true) | spl601_213),
% 6.46/1.22 inference(forward_demodulation,[],[f2095,f4336])).
% 6.46/1.22 thf(f6263,plain,(
% 6.46/1.22 ($true != ((sK94 @ id @ one @ id))) | spl601_213),
% 6.46/1.22 inference(forward_demodulation,[],[f6262,f767])).
% 6.46/1.22 thf(f6268,plain,(
% 6.46/1.22 ( ! [X0 : term] : ((((sK94 @ id @ X0 @ id)) = $false) | ($true != $true)) ) | (spl601_213 | ~spl601_592)),
% 6.46/1.22 inference(superposition,[],[f6263,f4408])).
% 6.46/1.22 thf(f6278,plain,(
% 6.46/1.22 ( ! [X0 : term] : ((((sK94 @ id @ X0 @ id)) = $false)) ) | (spl601_213 | ~spl601_592)),
% 6.46/1.22 inference(trivial_inequality_removal,[],[f6268])).
% 6.46/1.22 thf(f10756,plain,(
% 6.46/1.22 ( ! [X3 : (subst > term > term)] : (($true = ((sK94 @ id @ (lam @ (X3 @ sh @ one)) @ id))) | ($true = ((sK94 @ id @ (sK96 @ X3) @ id)))) ) | ~spl601_501),
% 6.46/1.22 inference(forward_subsumption_resolution,[],[f3345,f4343])).
% 6.46/1.22 thf(f10757,plain,(
% 6.46/1.22 ( ! [X3 : (subst > term > term)] : (($true = $false) | ($true = ((sK94 @ id @ (sK96 @ X3) @ id)))) ) | (spl601_213 | ~spl601_501 | ~spl601_592)),
% 6.46/1.22 inference(forward_demodulation,[],[f10756,f6278])).
% 6.46/1.22 thf(f10758,plain,(
% 6.46/1.22 ( ! [X3 : (subst > term > term)] : (($true = ((sK94 @ id @ (sK96 @ X3) @ id)))) ) | (spl601_213 | ~spl601_501 | ~spl601_592)),
% 6.46/1.22 inference(trivial_inequality_removal,[],[f10757])).
% 6.46/1.22 thf(f10759,plain,(
% 6.46/1.22 ($true = $false) | (spl601_213 | ~spl601_501 | ~spl601_592)),
% 6.46/1.22 inference(forward_demodulation,[],[f10758,f6278])).
% 6.46/1.22 thf(f10760,plain,(
% 6.46/1.22 $false | (spl601_213 | ~spl601_501 | ~spl601_592)),
% 6.46/1.22 inference(trivial_inequality_removal,[],[f10759])).
% 6.46/1.22 thf(f10761,plain,(
% 6.46/1.22 spl601_213 | ~spl601_501 | ~spl601_592),
% 6.46/1.22 inference(avatar_contradiction_clause,[],[f10760])).
% 6.46/1.22 thf(f10764,plain,(
% 6.46/1.22 ($true = $false) | (~spl601_210 | ~spl601_584)),
% 6.46/1.22 inference(forward_demodulation,[],[f2081,f3711])).
% 6.46/1.22 thf(f10765,plain,(
% 6.46/1.22 $false | (~spl601_210 | ~spl601_584)),
% 6.46/1.22 inference(trivial_inequality_removal,[],[f10764])).
% 6.46/1.22 thf(f10766,plain,(
% 6.46/1.22 ~spl601_210 | ~spl601_584),
% 6.46/1.22 inference(avatar_contradiction_clause,[],[f10765])).
% 6.46/1.22 thf(f10780,plain,(
% 6.46/1.22 (((sK591 @ id @ (d2term @ d_one) @ id)) = $false) | ~spl601_589),
% 6.46/1.22 inference(forward_demodulation,[],[f3731,f4336])).
% 6.46/1.22 thf(f10781,plain,(
% 6.46/1.22 ($true = ((sK591 @ id @ one @ id))) | ~spl601_586),
% 6.46/1.22 inference(forward_demodulation,[],[f3718,f767])).
% 6.46/1.22 thf(f10782,plain,(
% 6.46/1.22 (((sK591 @ id @ one @ id)) = $false) | ~spl601_589),
% 6.46/1.22 inference(forward_demodulation,[],[f10780,f767])).
% 6.46/1.22 thf(f10834,plain,(
% 6.46/1.22 ($true = $false) | (~spl601_586 | ~spl601_589)),
% 6.46/1.22 inference(superposition,[],[f10782,f10781])).
% 6.46/1.22 thf(f10882,plain,(
% 6.46/1.22 $false | (~spl601_586 | ~spl601_589)),
% 6.46/1.22 inference(trivial_inequality_removal,[],[f10834])).
% 6.46/1.22 thf(f10883,plain,(
% 6.46/1.22 ~spl601_586 | ~spl601_589),
% 6.46/1.22 inference(avatar_contradiction_clause,[],[f10882])).
% 6.46/1.22 thf(f10892,plain,(
% 6.46/1.22 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK593 @ X1) @ id)))) ) | ~spl601_585),
% 6.46/1.22 inference(forward_subsumption_resolution,[],[f3714,f4343])).
% 6.46/1.22 thf(f10899,plain,(
% 6.46/1.22 ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl601_585),
% 6.46/1.22 inference(forward_demodulation,[],[f10892,f4336])).
% 6.46/1.22 thf(f10902,plain,(
% 6.46/1.22 ($true = ((sK591 @ id @ one @ id))) | ~spl601_585),
% 6.46/1.22 inference(forward_demodulation,[],[f10899,f767])).
% 6.46/1.22 thf(f10904,plain,(
% 6.46/1.22 ($true = $false) | (~spl601_585 | ~spl601_589)),
% 6.46/1.22 inference(forward_demodulation,[],[f10902,f10782])).
% 6.46/1.22 thf(f10905,plain,(
% 6.46/1.22 $false | (~spl601_585 | ~spl601_589)),
% 6.46/1.22 inference(trivial_inequality_removal,[],[f10904])).
% 6.46/1.22 thf(f10906,plain,(
% 6.46/1.22 ~spl601_585 | ~spl601_589),
% 6.46/1.22 inference(avatar_contradiction_clause,[],[f10905])).
% 6.46/1.22 cnf(s154, plain, spl601_54 | ~spl601_210, inference(sat_conversion,[],[f2083])).
% 6.46/1.22 cnf(s157, plain, spl601_54 | ~spl601_213, inference(sat_conversion,[],[f2096])).
% 6.46/1.22 cnf(s181, plain, ~spl601_54 | spl601_210, inference(sat_conversion,[],[f2199])).
% 6.46/1.22 cnf(s461, plain, spl601_54 | spl601_501, inference(sat_conversion,[],[f3346])).
% 6.46/1.22 cnf(s555, plain, spl601_584 | spl601_585 | spl601_586, inference(sat_conversion,[],[f3719])).
% 6.46/1.22 cnf(s558, plain, spl601_584 | spl601_589, inference(sat_conversion,[],[f3732])).
% 6.46/1.22 cnf(s561, plain, spl601_210 | spl601_592, inference(sat_conversion,[],[f3744])).
% 6.46/1.22 cnf(s800, plain, spl601_213 | ~spl601_501 | ~spl601_592, inference(sat_conversion,[],[f10761])).
% 6.46/1.22 cnf(s801, plain, ~spl601_210 | ~spl601_584, inference(sat_conversion,[],[f10766])).
% 6.46/1.22 cnf(s803, plain, ~spl601_586 | ~spl601_589, inference(sat_conversion,[],[f10883])).
% 6.46/1.22 cnf(s806, plain, ~spl601_585 | ~spl601_589, inference(sat_conversion,[],[f10906])).
% 6.46/1.22 cnf(s879, plain, spl601_54, inference(rat,[],[s561,s800,s154,s157,s461])).
% 6.46/1.22 cnf(s885, plain, spl601_210, inference(rat,[],[s181,s879])).
% 6.46/1.22 cnf(s887, plain, ~spl601_584, inference(rat,[],[s801,s885])).
% 6.46/1.22 cnf(s888, plain, spl601_589, inference(rat,[],[s558,s887])).
% 6.46/1.22 cnf(s890, plain, ~spl601_585, inference(rat,[],[s806,s888])).
% 6.46/1.22 cnf(s891, plain, ~spl601_586, inference(rat,[],[s803,s888])).
% 6.46/1.22 cnf(s892, plain, $false, inference(rat,[],[s555,s887,s890,s891])).
% 6.46/1.22 thf(f10907,plain,(
% 6.46/1.22 $false),
% 6.46/1.22 inference(avatar_sat_refutation,[],[s892])).
% 6.46/1.22 % SZS output end Proof for theBenchmark
% 6.46/1.22 % (920418)------------------------------
% 6.46/1.22 % (920418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.46/1.22 % (920418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.22 % (920418)CaDiCaL version: 2.1.3
% 6.46/1.22 % (920418)Termination reason: Refutation
% 6.46/1.22 % (920418)Time elapsed: 0.421 s
% 6.46/1.22 % (920418)Peak memory usage: 19 MB
% 6.46/1.22 % (920418)Instructions burned: 883 (million)
% 6.46/1.22 % (920298)Success in time 0.959 s
% 6.46/1.22 % Vampire exiting
%------------------------------------------------------------------------------