%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX164^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:40:43 AM UTC 2026
% Result : Theorem 17.66s 3.02s
% Output : Refutation 17.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX164^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:09:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/1.03 % (2858996)Will run a generic schedule for satisfiability detection.
% 4.17/1.03 % (2859004)dis+10_1_sil=32000:sp=arity:random_seed=3682120965:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.17/1.03 % (2859001)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=187536213_2999 on theBenchmark for (2999ds/0Mi)
% 4.17/1.03 % (2859005)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3682831878:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.17/1.03 % (2859003)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=435171203:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.17/1.03 % (2859002)% WARNING: option uhcvi not known.
% 4.17/1.03 % (2859006)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=42355419:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.17/1.03 % (2859002)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2273994046:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.17/1.03 % (2859007)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3788979496:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.17/1.03 % (2859005)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.17/1.03 % (2859004)Instruction limit reached!
% 4.17/1.03 % (2859004)------------------------------
% 4.17/1.03 % (2859004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.03 % (2859004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.03 % (2859004)CaDiCaL version: 2.1.3
% 4.17/1.03 % (2859004)Termination reason: Instruction limit
% 4.17/1.03 % (2859004)Termination phase: Property scanning
% 4.17/1.03 % (2859004)Time elapsed: 0.026 s
% 4.17/1.03 % (2859004)Peak memory usage: 12 MB
% 4.17/1.03 % (2859004)Instructions burned: 109 (million)
% 4.17/1.03 % (2859002)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.17/1.03 % (2859015)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1502717116:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.17/1.03 % (2859005)Instruction limit reached!
% 4.17/1.03 % (2859005)------------------------------
% 4.17/1.03 % (2859005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.03 % (2859005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.03 % (2859005)CaDiCaL version: 2.1.3
% 4.17/1.03 % (2859005)Termination reason: Instruction limit
% 4.17/1.03 % (2859005)Termination phase: Property scanning
% 4.17/1.03 % (2859005)Time elapsed: 0.050 s
% 4.17/1.03 % (2859005)Peak memory usage: 12 MB
% 4.17/1.03 % (2859005)Instructions burned: 116 (million)
% 4.17/1.03 % (2859006)Instruction limit reached!
% 4.17/1.03 % (2859006)------------------------------
% 4.17/1.03 % (2859006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.03 % (2859006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.03 % (2859006)CaDiCaL version: 2.1.3
% 4.17/1.03 % (2859006)Termination reason: Instruction limit
% 4.17/1.03 % (2859006)Termination phase: Function definition elimination
% 4.17/1.03 % (2859006)Time elapsed: 0.057 s
% 4.17/1.03 % (2859006)Peak memory usage: 12 MB
% 4.17/1.03 % (2859006)Instructions burned: 134 (million)
% 4.17/1.03 % Exception at run slice level
% 4.17/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.03 % (2859017)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1779608446:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.17/1.03 % Exception at run slice level
% 4.17/1.03 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.17/1.03 % (2859007)Instruction limit reached!
% 4.17/1.03 % (2859007)------------------------------
% 4.17/1.03 % (2859007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.17/1.03 % (2859007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.03 % (2859007)CaDiCaL version: 2.1.3
% 4.17/1.03 % (2859007)Termination reason: Instruction limit
% 4.17/1.03 % (2859007)Termination phase: Property scanning
% 4.17/1.03 % (2859007)Time elapsed: 0.062 s
% 4.17/1.03 % (2859007)Peak memory usage: 12 MB
% 4.17/1.03 % (2859007)Instructions burned: 160 (million)
% 4.17/1.03 % (2859018)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3290687823:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 16.79/2.75 % (2859002)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.79/2.75 % (2859022)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3796423529:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.79/2.75 % (2859021)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=271178386:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 16.79/2.75 % (2859018)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.79/2.75 % (2859019)ott-21_1_sil=16000:fs=off:random_seed=1783962216:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 16.79/2.75 % (2859017)Instruction limit reached!
% 16.79/2.75 % (2859017)------------------------------
% 16.79/2.75 % (2859017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.79/2.75 % (2859017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.79/2.75 % (2859017)CaDiCaL version: 2.1.3
% 16.79/2.75 % (2859017)Termination reason: Instruction limit
% 16.79/2.75 % (2859017)Termination phase: Function definition elimination
% 16.79/2.75 % (2859017)Time elapsed: 0.056 s
% 16.79/2.75 % (2859017)Peak memory usage: 12 MB
% 16.79/2.75 % (2859017)Instructions burned: 133 (million)
% 16.79/2.75 % Exception at run slice level
% 16.79/2.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.79/2.75 % (2859028)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2579682779:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 16.79/2.75 % (2859027)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2875115168:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.79/2.75 % (2859018)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.79/2.75 % Exception at run slice level
% 16.79/2.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.79/2.75 % (2859019)Instruction limit reached!
% 16.79/2.75 % (2859019)------------------------------
% 16.79/2.75 % (2859019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.79/2.75 % (2859019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.79/2.75 % (2859019)CaDiCaL version: 2.1.3
% 16.79/2.75 % (2859019)Termination reason: Instruction limit
% 16.79/2.75 % (2859019)Termination phase: Property scanning
% 16.79/2.75 % (2859019)Time elapsed: 0.084 s
% 16.79/2.75 % (2859019)Peak memory usage: 12 MB
% 16.79/2.75 % (2859019)Instructions burned: 180 (million)
% 16.79/2.75 % (2859031)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1022840434:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 16.79/2.75 % (2859031)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.79/2.75 % (2859032)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4287401388:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 16.79/2.75 % (2859032)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.79/2.75 % (2859021)Instruction limit reached!
% 16.79/2.75 % (2859021)------------------------------
% 16.79/2.75 % (2859021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.79/2.75 % (2859021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.79/2.75 % (2859021)CaDiCaL version: 2.1.3
% 16.79/2.75 % (2859021)Termination reason: Instruction limit
% 16.79/2.75 % (2859021)Termination phase: Saturation
% 16.79/2.75 % (2859021)Time elapsed: 0.217 s
% 16.79/2.75 % (2859021)Peak memory usage: 15 MB
% 16.79/2.75 % (2859021)Instructions burned: 477 (million)
% 16.79/2.75 % (2859035)fmb+10_1_sil=64000:random_seed=849494601:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 16.79/2.75 % (2859031)Instruction limit reached!
% 16.79/2.75 % (2859031)------------------------------
% 16.79/2.75 % (2859031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.79/2.75 % (2859031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.79/2.75 % (2859031)CaDiCaL version: 2.1.3
% 16.79/2.75 % (2859031)Termination reason: Instruction limit
% 16.79/2.75 % (2859031)Termination phase: Saturation
% 16.79/2.75 % (2859031)Time elapsed: 0.177 s
% 17.66/3.02 % (2859031)Peak memory usage: 19 MB
% 17.66/3.02 % (2859031)Instructions burned: 694 (million)
% 17.66/3.02 % (2859035)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.66/3.02 % (2859037)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1261744046:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 17.66/3.02 % (2859018)Instruction limit reached!
% 17.66/3.02 % (2859018)------------------------------
% 17.66/3.02 % (2859018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859018)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859018)Termination reason: Instruction limit
% 17.66/3.02 % (2859018)Termination phase: Saturation
% 17.66/3.02 % (2859018)Time elapsed: 0.306 s
% 17.66/3.02 % (2859018)Peak memory usage: 18 MB
% 17.66/3.02 % (2859018)Instructions burned: 686 (million)
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859039)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3916179069:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 17.66/3.02 % (2859040)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3241312172:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859040)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.66/3.02 % (2859043)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2936384987:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 17.66/3.02 % (2859043)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 17.66/3.02 % (2859043)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859045)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3167173513:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859047)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3360530264:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 17.66/3.02 % (2859027)Instruction limit reached!
% 17.66/3.02 % (2859027)------------------------------
% 17.66/3.02 % (2859027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859027)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859027)Termination reason: Instruction limit
% 17.66/3.02 % (2859027)Termination phase: Saturation
% 17.66/3.02 % (2859027)Time elapsed: 0.525 s
% 17.66/3.02 % (2859027)Peak memory usage: 22 MB
% 17.66/3.02 % (2859027)Instructions burned: 1180 (million)
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859049)ott-2_1_sil=16000:newcnf=on:random_seed=3745696356:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 17.66/3.02 % (2859050)ott+10_1_sil=32000:tgt=ground:random_seed=2716541037:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 17.66/3.02 % (2859049)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 17.66/3.02 % (2859032)Instruction limit reached!
% 17.66/3.02 % (2859032)------------------------------
% 17.66/3.02 % (2859032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859032)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859032)Termination reason: Instruction limit
% 17.66/3.02 % (2859032)Termination phase: Saturation
% 17.66/3.02 % (2859032)Time elapsed: 0.500 s
% 17.66/3.02 % (2859032)Peak memory usage: 20 MB
% 17.66/3.02 % (2859032)Instructions burned: 880 (million)
% 17.66/3.02 % (2859053)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=122419588:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859055)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1776498257:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 17.66/3.02 % (2859043)Instruction limit reached!
% 17.66/3.02 % (2859043)------------------------------
% 17.66/3.02 % (2859043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859043)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859043)Termination reason: Instruction limit
% 17.66/3.02 % (2859043)Termination phase: Saturation
% 17.66/3.02 % (2859043)Time elapsed: 0.444 s
% 17.66/3.02 % (2859043)Peak memory usage: 20 MB
% 17.66/3.02 % (2859043)Instructions burned: 1476 (million)
% 17.66/3.02 % (2859057)dis+21_1_sil=32000:sas=cadical:random_seed=3321178857:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 17.66/3.02 % (2859055)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.66/3.02 % (2859049)Instruction limit reached!
% 17.66/3.02 % (2859049)------------------------------
% 17.66/3.02 % (2859049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859049)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859049)Termination reason: Instruction limit
% 17.66/3.02 % (2859049)Termination phase: Saturation
% 17.66/3.02 % (2859049)Time elapsed: 0.371 s
% 17.66/3.02 % (2859049)Peak memory usage: 19 MB
% 17.66/3.02 % (2859049)Instructions burned: 870 (million)
% 17.66/3.02 % (2859059)ott+11_1_sil=16000:gs=on:random_seed=4062472029:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 17.66/3.02 % (2859059)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 17.66/3.02 % (2859057)Instruction limit reached!
% 17.66/3.02 % (2859057)------------------------------
% 17.66/3.02 % (2859057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859057)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859057)Termination reason: Instruction limit
% 17.66/3.02 % (2859057)Termination phase: Saturation
% 17.66/3.02 % (2859057)Time elapsed: 0.992 s
% 17.66/3.02 % (2859057)Peak memory usage: 28 MB
% 17.66/3.02 % (2859057)Instructions burned: 3777 (million)
% 17.66/3.02 % (2859061)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=1740691165:fmbsr=1.6:i=67534_2980 on theBenchmark for (2980ds/67534Mi)
% 17.66/3.02 % Exception at run slice level
% 17.66/3.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 17.66/3.02 % (2859063)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=704647896:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2980 on theBenchmark for (2980ds/4591Mi)
% 17.66/3.02 % (2859059)Instruction limit reached!
% 17.66/3.02 % (2859059)------------------------------
% 17.66/3.02 % (2859059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859059)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859059)Termination reason: Instruction limit
% 17.66/3.02 % (2859059)Termination phase: Saturation
% 17.66/3.02 % (2859059)Time elapsed: 1.190 s
% 17.66/3.02 % (2859059)Peak memory usage: 30 MB
% 17.66/3.02 % (2859059)Instructions burned: 2253 (million)
% 17.66/3.02 % (2859065)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1232758262:i=29340_2976 on theBenchmark for (2976ds/29340Mi)
% 17.66/3.02 % (2859055)Instruction limit reached!
% 17.66/3.02 % (2859055)------------------------------
% 17.66/3.02 % (2859055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859055)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859055)Termination reason: Instruction limit
% 17.66/3.02 % (2859055)Termination phase: Saturation
% 17.66/3.02 % (2859055)Time elapsed: 1.595 s
% 17.66/3.02 % (2859055)Peak memory usage: 30 MB
% 17.66/3.02 % (2859055)Instructions burned: 3514 (million)
% 17.66/3.02 % (2859067)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2002484785:i=5211_2975 on theBenchmark for (2975ds/5211Mi)
% 17.66/3.02 % (2859002) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2858996-2859002"...
% 17.66/3.02 % (2859002)...printing done.
% 17.66/3.02 % (2859002)Refutation found. Thanks to Tanya!
% 17.66/3.02 % SZS status Theorem for theBenchmark
% 17.66/3.02 % SZS output start Proof for theBenchmark
% 17.66/3.02 thf(type_def_5, type, term: $tType).
% 17.66/3.02 thf(type_def_6, type, subst: $tType).
% 17.66/3.02 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 17.66/3.02 thf(type_def_8, type, d_term: $tType).
% 17.66/3.02 thf(type_def_9, type, d_subst: $tType).
% 17.66/3.02 thf(func_def_0, type, one: term).
% 17.66/3.02 thf(func_def_1, type, ap: (term > term > term)).
% 17.66/3.02 thf(func_def_2, type, lam: (term > term)).
% 17.66/3.02 thf(func_def_3, type, sub: (term > subst > term)).
% 17.66/3.02 thf(func_def_4, type, id: subst).
% 17.66/3.02 thf(func_def_5, type, sh: subst).
% 17.66/3.02 thf(func_def_6, type, push: (term > subst > subst)).
% 17.66/3.02 thf(func_def_7, type, comp: (subst > subst > subst)).
% 17.66/3.02 thf(func_def_8, type, var: (term > $o)).
% 17.66/3.02 thf(func_def_9, type, pushprop_lem1v2: $o).
% 17.66/3.02 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 17.66/3.02 thf(func_def_11, type, axmap: $o).
% 17.66/3.02 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 17.66/3.02 thf(func_def_13, type, shinj: $o).
% 17.66/3.02 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 17.66/3.02 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 17.66/3.02 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 17.66/3.02 thf(func_def_17, type, induction2lem: $o).
% 17.66/3.02 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 17.66/3.02 thf(func_def_19, type, axvarshift: $o).
% 17.66/3.02 thf(func_def_20, type, hoasapinj2: $o).
% 17.66/3.02 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 17.66/3.02 thf(func_def_22, type, hoasapinj1: $o).
% 17.66/3.02 thf(func_def_23, type, ulamvar1: $o).
% 17.66/3.02 thf(func_def_24, type, induction2lem_lthm: $o).
% 17.66/3.02 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 17.66/3.02 thf(func_def_26, type, apnotvar: $o).
% 17.66/3.02 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 17.66/3.02 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 17.66/3.02 thf(func_def_29, type, hoasinduction_lthm: $o).
% 17.66/3.02 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 17.66/3.02 thf(func_def_31, type, hoaslaminj: $o).
% 17.66/3.02 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 17.66/3.02 thf(func_def_33, type, induction2lem_gthm: $o).
% 17.66/3.02 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 17.66/3.02 thf(func_def_35, type, hoasinduction_lem3: $o).
% 17.66/3.02 thf(func_def_36, type, hoasinduction_lem2: $o).
% 17.66/3.02 thf(func_def_37, type, termmset_lthm: $o).
% 17.66/3.02 thf(func_def_38, type, hoasinduction_lem1: $o).
% 17.66/3.02 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 17.66/3.02 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 17.66/3.02 thf(func_def_41, type, hoasapnotvar: $o).
% 17.66/3.02 thf(func_def_42, type, hoasinduction_lem0: $o).
% 17.66/3.02 thf(func_def_43, type, hoasinduction: $o).
% 17.66/3.02 thf(func_def_44, type, hoasinduction_gthm: $o).
% 17.66/3.02 thf(func_def_45, type, axapp: $o).
% 17.66/3.02 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 17.66/3.02 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 17.66/3.02 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 17.66/3.02 thf(func_def_49, type, ulamvarind: $o).
% 17.66/3.02 thf(func_def_50, type, induction: $o).
% 17.66/3.02 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 17.66/3.02 thf(func_def_52, type, termmset_gthm: $o).
% 17.66/3.02 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 17.66/3.02 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 17.66/3.02 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 17.66/3.02 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 17.66/3.02 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 17.66/3.02 thf(func_def_58, type, pushprop_lem2v2: $o).
% 17.66/3.02 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 17.66/3.02 thf(func_def_60, type, axclos: $o).
% 17.66/3.02 thf(func_def_61, type, axassoc: $o).
% 17.66/3.02 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 17.66/3.02 thf(func_def_63, type, pushprop_lthm: $o).
% 17.66/3.02 thf(func_def_64, type, apinj2: $o).
% 17.66/3.02 thf(func_def_65, type, apinj1: $o).
% 17.66/3.02 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 17.66/3.02 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 17.66/3.02 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 17.66/3.02 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 17.66/3.02 thf(func_def_70, type, axvarcons: $o).
% 17.66/3.02 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 17.66/3.02 thf(func_def_72, type, axscons: $o).
% 17.66/3.02 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 17.66/3.02 thf(func_def_74, type, axidr: $o).
% 17.66/3.02 thf(func_def_75, type, pushprop_lem1: $o).
% 17.66/3.02 thf(func_def_76, type, laminj: $o).
% 17.66/3.02 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 17.66/3.02 thf(func_def_78, type, pushprop_lem0: $o).
% 17.66/3.02 thf(func_def_79, type, pushprop_gthm: $o).
% 17.66/3.02 thf(func_def_80, type, axabs: $o).
% 17.66/3.02 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 17.66/3.02 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 17.66/3.02 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 17.66/3.02 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 17.66/3.02 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 17.66/3.02 thf(func_def_86, type, lamnotap: $o).
% 17.66/3.02 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 17.66/3.02 thf(func_def_88, type, hoaslamnotvar: $o).
% 17.66/3.02 thf(func_def_89, type, axidl: $o).
% 17.66/3.02 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 17.66/3.02 thf(func_def_91, type, induction2_lthm: $o).
% 17.66/3.02 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 17.66/3.02 thf(func_def_93, type, substmonoid_lthm: $o).
% 17.66/3.02 thf(func_def_94, type, pushprop: $o).
% 17.66/3.02 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 17.66/3.02 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 17.66/3.02 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 17.66/3.02 thf(func_def_98, type, substmonoid: $o).
% 17.66/3.02 thf(func_def_99, type, lamnotvar: $o).
% 17.66/3.02 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 17.66/3.02 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 17.66/3.02 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 17.66/3.02 thf(func_def_103, type, induction2_gthm: $o).
% 17.66/3.02 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 17.66/3.02 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_106, type, hoaslamnotap: $o).
% 17.66/3.02 thf(func_def_107, type, substmonoid_gthm: $o).
% 17.66/3.02 thf(func_def_108, type, ulamvarsh: $o).
% 17.66/3.02 thf(func_def_109, type, induction2: $o).
% 17.66/3.02 thf(func_def_110, type, pushprop_lem3v2: $o).
% 17.66/3.02 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 17.66/3.02 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 17.66/3.02 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 17.66/3.02 thf(func_def_114, type, axshiftcons: $o).
% 17.66/3.02 thf(func_def_115, type, termmset: $o).
% 17.66/3.02 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 17.66/3.02 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 17.66/3.02 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 17.66/3.02 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 17.66/3.02 thf(func_def_120, type, axvarid: $o).
% 17.66/3.02 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 17.66/3.02 thf(func_def_122, type, d2term: (d_term > term)).
% 17.66/3.02 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 17.66/3.02 thf(func_def_124, type, d_one: d_term).
% 17.66/3.02 thf(func_def_125, type, d_id: d_subst).
% 17.66/3.02 thf(func_def_127, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 17.66/3.02 thf(func_def_128, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 17.66/3.02 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_131, type, db2: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_132, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 17.66/3.02 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_137, type, vIMP: ($o > $o > $o)).
% 17.66/3.02 thf(func_def_138, type, sP0: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_139, type, sP1: $o).
% 17.66/3.02 thf(func_def_140, type, sP2: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_141, type, sP3: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_142, type, sP4: $o).
% 17.66/3.02 thf(func_def_143, type, sP5: $o).
% 17.66/3.02 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_145, type, sP7: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_146, type, sP8: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_147, type, sP9: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_148, type, sP10: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_149, type, sP11: $o).
% 17.66/3.02 thf(func_def_150, type, sP12: $o).
% 17.66/3.02 thf(func_def_151, type, sP13: $o).
% 17.66/3.02 thf(func_def_152, type, sP14: $o).
% 17.66/3.02 thf(func_def_153, type, sP15: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_154, type, sP16: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_155, type, sP17: $o).
% 17.66/3.02 thf(func_def_156, type, sP18: $o).
% 17.66/3.02 thf(func_def_157, type, sP19: $o).
% 17.66/3.02 thf(func_def_158, type, sP20: $o).
% 17.66/3.02 thf(func_def_159, type, sP21: $o).
% 17.66/3.02 thf(func_def_160, type, sP22: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_161, type, sP23: $o).
% 17.66/3.02 thf(func_def_162, type, sP24: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_163, type, sP25: $o).
% 17.66/3.02 thf(func_def_164, type, sP26: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_165, type, sP27: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_166, type, sP28: $o).
% 17.66/3.02 thf(func_def_167, type, sP29: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_168, type, sP30: $o).
% 17.66/3.02 thf(func_def_169, type, sP31: $o).
% 17.66/3.02 thf(func_def_170, type, sP32: $o).
% 17.66/3.02 thf(func_def_171, type, sP33: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_172, type, sP34: $o).
% 17.66/3.02 thf(func_def_173, type, sP35: $o).
% 17.66/3.02 thf(func_def_174, type, sP36: $o).
% 17.66/3.02 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_176, type, sP38: $o).
% 17.66/3.02 thf(func_def_177, type, sP39: $o).
% 17.66/3.02 thf(func_def_178, type, sP40: $o).
% 17.66/3.02 thf(func_def_179, type, sP41: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_180, type, sP42: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_181, type, sP43: $o).
% 17.66/3.02 thf(func_def_182, type, sP44: $o).
% 17.66/3.02 thf(func_def_183, type, sP45: $o).
% 17.66/3.02 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_185, type, sP47: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_186, type, sP48: $o).
% 17.66/3.02 thf(func_def_187, type, sP49: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_188, type, sP50: $o).
% 17.66/3.02 thf(func_def_189, type, sP51: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_190, type, sP52: $o).
% 17.66/3.02 thf(func_def_191, type, sP53: ((term > $o) > $o)).
% 17.66/3.02 thf(func_def_192, type, sP54: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_193, type, sP55: ((subst > term > subst > $o) > $o)).
% 17.66/3.02 thf(func_def_194, type, sP56: $o).
% 17.66/3.02 thf(func_def_195, type, sP57: $o).
% 17.66/3.02 thf(func_def_196, type, sP58: $o).
% 17.66/3.02 thf(func_def_197, type, sK59: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_198, type, sK60: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_199, type, sK61: ((subst > term > subst > $o) > term > $o)).
% 17.66/3.02 thf(func_def_200, type, sK62: term).
% 17.66/3.02 thf(func_def_201, type, sK63: (term > $o)).
% 17.66/3.02 thf(func_def_202, type, sK64: term).
% 17.66/3.02 thf(func_def_203, type, sK65: (term > term)).
% 17.66/3.02 thf(func_def_204, type, sK66: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_205, type, sK67: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_206, type, sK68: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_207, type, sK69: term).
% 17.66/3.02 thf(func_def_208, type, sK70: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_209, type, sK71: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_210, type, sK72: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_211, type, sK73: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_212, type, sK74: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_213, type, sK75: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_214, type, sK76: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_215, type, sK77: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_216, type, sK78: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_217, type, sK79: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_218, type, sK80: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_219, type, sK81: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_220, type, sK82: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_221, type, sK83: (term > $o)).
% 17.66/3.02 thf(func_def_222, type, sK84: term).
% 17.66/3.02 thf(func_def_223, type, sK85: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_224, type, sK86: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_225, type, sK87: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_226, type, sK88: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_227, type, sK89: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_228, type, sK90: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_229, type, sK91: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_230, type, sK92: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_231, type, sK93: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_232, type, sK94: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_233, type, sK95: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_234, type, sK96: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_235, type, sK97: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_236, type, sK98: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_237, type, sK99: (term > $o)).
% 17.66/3.02 thf(func_def_238, type, sK100: term).
% 17.66/3.02 thf(func_def_239, type, sK101: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_240, type, sK102: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_241, type, sK103: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_242, type, sK104: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_243, type, sK105: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_244, type, sK106: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_245, type, sK107: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_246, type, sK108: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_247, type, sK109: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_248, type, sK110: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_249, type, sK111: term).
% 17.66/3.02 thf(func_def_250, type, sK112: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_251, type, sK113: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_252, type, sK114: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_253, type, sK115: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_254, type, sK116: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_255, type, sK117: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_256, type, sK118: (term > $o)).
% 17.66/3.02 thf(func_def_257, type, sK119: term).
% 17.66/3.02 thf(func_def_258, type, sK120: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_259, type, sK121: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_263, type, sK125: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_268, type, sK130: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_269, type, sK131: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_270, type, sK132: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_271, type, sK133: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_272, type, sK134: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_273, type, sK135: (term > $o)).
% 17.66/3.02 thf(func_def_274, type, sK136: term).
% 17.66/3.02 thf(func_def_275, type, sK137: (term > term)).
% 17.66/3.02 thf(func_def_276, type, sK138: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_277, type, sK139: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_278, type, sK140: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_279, type, sK141: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_281, type, sK143: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_282, type, sK144: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_283, type, sK145: term).
% 17.66/3.02 thf(func_def_284, type, sK146: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_285, type, sK147: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_286, type, sK148: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_287, type, sK149: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_288, type, sK150: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_289, type, sK151: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_290, type, sK152: (subst > (term > $o) > term)).
% 17.66/3.02 thf(func_def_291, type, sK153: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_292, type, sK154: (term > $o)).
% 17.66/3.02 thf(func_def_293, type, sK155: term).
% 17.66/3.02 thf(func_def_294, type, sK156: subst).
% 17.66/3.02 thf(func_def_295, type, sK157: (term > term)).
% 17.66/3.02 thf(func_def_296, type, sK158: term).
% 17.66/3.02 thf(func_def_297, type, sK159: (term > $o)).
% 17.66/3.02 thf(func_def_298, type, sK160: term).
% 17.66/3.02 thf(func_def_299, type, sK161: (term > term)).
% 17.66/3.02 thf(func_def_300, type, sK162: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_301, type, sK163: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_302, type, sK164: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_303, type, sK165: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_304, type, sK166: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_305, type, sK167: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_306, type, sK168: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_307, type, sK169: (term > $o)).
% 17.66/3.02 thf(func_def_308, type, sK170: term).
% 17.66/3.02 thf(func_def_309, type, sK171: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_310, type, sK172: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_311, type, sK173: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_312, type, sK174: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_313, type, sK175: (term > subst > term > term)).
% 17.66/3.02 thf(func_def_314, type, sK176: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_315, type, sK177: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_316, type, sK178: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_317, type, sK179: term).
% 17.66/3.02 thf(func_def_318, type, sK180: term).
% 17.66/3.02 thf(func_def_319, type, sK181: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_320, type, sK182: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_321, type, sK183: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_322, type, sK184: term).
% 17.66/3.02 thf(func_def_323, type, sK185: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_324, type, sK186: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_325, type, sK187: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_327, type, sK189: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_328, type, sK190: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_329, type, sK191: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_330, type, sK192: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_331, type, sK193: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_332, type, sK194: term).
% 17.66/3.02 thf(func_def_333, type, sK195: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_334, type, sK196: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_335, type, sK197: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_336, type, sK198: term).
% 17.66/3.02 thf(func_def_337, type, sK199: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_338, type, sK200: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_339, type, sK201: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_340, type, sK202: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_341, type, sK203: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_342, type, sK204: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_343, type, sK205: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_344, type, sK206: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_346, type, sK208: (subst > term > term)).
% 17.66/3.02 thf(func_def_347, type, sK209: (subst > term > term)).
% 17.66/3.02 thf(func_def_348, type, sK210: subst).
% 17.66/3.02 thf(func_def_349, type, sK211: term).
% 17.66/3.02 thf(func_def_350, type, sK212: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_351, type, sK213: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_352, type, sK214: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_353, type, sK215: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_354, type, sK216: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_355, type, sK217: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_356, type, sK218: term).
% 17.66/3.02 thf(func_def_357, type, sK219: term).
% 17.66/3.02 thf(func_def_358, type, sK220: term).
% 17.66/3.02 thf(func_def_359, type, sK221: subst).
% 17.66/3.02 thf(func_def_360, type, sK222: term).
% 17.66/3.02 thf(func_def_361, type, sK223: subst).
% 17.66/3.02 thf(func_def_362, type, sK224: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_363, type, sK225: (term > $o)).
% 17.66/3.02 thf(func_def_364, type, sK226: term).
% 17.66/3.02 thf(func_def_365, type, sK227: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_366, type, sK228: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_367, type, sK229: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_368, type, sK230: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_369, type, sK231: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_370, type, sK232: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_371, type, sK233: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_372, type, sK234: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_373, type, sK235: (term > $o)).
% 17.66/3.02 thf(func_def_374, type, sK236: term).
% 17.66/3.02 thf(func_def_375, type, sK237: term).
% 17.66/3.02 thf(func_def_376, type, sK238: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_377, type, sK239: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_380, type, sK242: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_381, type, sK243: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_382, type, sK244: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_383, type, sK245: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_386, type, sK248: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_387, type, sK249: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_388, type, sK250: term).
% 17.66/3.02 thf(func_def_389, type, sK251: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_390, type, sK252: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_391, type, sK253: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_392, type, sK254: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_393, type, sK255: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_394, type, sK256: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_395, type, sK257: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_396, type, sK258: term).
% 17.66/3.02 thf(func_def_397, type, sK259: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_398, type, sK260: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_399, type, sK261: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_400, type, sK262: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_401, type, sK263: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_403, type, sK265: term).
% 17.66/3.02 thf(func_def_404, type, sK266: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_405, type, sK267: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_406, type, sK268: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_407, type, sK269: term).
% 17.66/3.02 thf(func_def_408, type, sK270: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_409, type, sK271: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_410, type, sK272: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_411, type, sK273: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_412, type, sK274: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_413, type, sK275: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_414, type, sK276: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_415, type, sK277: term).
% 17.66/3.02 thf(func_def_416, type, sK278: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_417, type, sK279: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_418, type, sK280: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_419, type, sK281: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_420, type, sK282: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_422, type, sK284: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_423, type, sK285: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_424, type, sK286: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_425, type, sK287: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_426, type, sK288: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_427, type, sK289: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_428, type, sK290: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_429, type, sK291: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_430, type, sK292: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_431, type, sK293: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_432, type, sK294: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_433, type, sK295: term).
% 17.66/3.02 thf(func_def_434, type, sK296: term).
% 17.66/3.02 thf(func_def_435, type, sK297: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_437, type, sK299: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_438, type, sK300: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_439, type, sK301: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_440, type, sK302: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_441, type, sK303: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_443, type, sK305: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_444, type, sK306: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_445, type, sK307: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_446, type, sK308: term).
% 17.66/3.02 thf(func_def_447, type, sK309: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_449, type, sK311: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_450, type, sK312: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_451, type, sK313: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_452, type, sK314: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_453, type, sK315: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_454, type, sK316: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_455, type, sK317: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_456, type, sK318: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_457, type, sK319: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_458, type, sK320: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_459, type, sK321: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_461, type, sK323: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_462, type, sK324: term).
% 17.66/3.02 thf(func_def_463, type, sK325: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_464, type, sK326: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_465, type, sK327: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_466, type, sK328: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_467, type, sK329: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_468, type, sK330: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_469, type, sK331: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_470, type, sK332: term).
% 17.66/3.02 thf(func_def_471, type, sK333: (term > (subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_472, type, sK334: (term > (subst > term > term) > term)).
% 17.66/3.02 thf(func_def_473, type, sK335: (term > (subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_474, type, sK336: (term > (subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_475, type, sK337: (term > (subst > term > term) > term)).
% 17.66/3.02 thf(func_def_476, type, sK338: (term > (subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_477, type, sK339: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_478, type, sK340: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_479, type, sK341: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_480, type, sK342: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_481, type, sK343: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_482, type, sK344: term).
% 17.66/3.02 thf(func_def_483, type, sK345: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_484, type, sK346: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_485, type, sK347: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_486, type, sK348: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_487, type, sK349: ((subst > term > subst > $o) > term > $o)).
% 17.66/3.02 thf(func_def_488, type, sK350: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_489, type, sK351: term).
% 17.66/3.02 thf(func_def_490, type, sK352: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_491, type, sK353: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_492, type, sK354: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_493, type, sK355: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_494, type, sK356: (term > $o)).
% 17.66/3.02 thf(func_def_495, type, sK357: term).
% 17.66/3.02 thf(func_def_496, type, sK358: (term > term)).
% 17.66/3.02 thf(func_def_497, type, sK359: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_498, type, sK360: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_499, type, sK361: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_500, type, sK362: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_501, type, sK363: (term > $o)).
% 17.66/3.02 thf(func_def_502, type, sK364: term).
% 17.66/3.02 thf(func_def_503, type, sK365: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_504, type, sK366: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_505, type, sK367: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_506, type, sK368: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_509, type, sK371: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_510, type, sK372: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_515, type, sK377: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_516, type, sK378: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_519, type, sK381: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_520, type, sK382: term).
% 17.66/3.02 thf(func_def_521, type, sK383: term).
% 17.66/3.02 thf(func_def_522, type, sK384: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_523, type, sK385: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_524, type, sK386: (term > $o)).
% 17.66/3.02 thf(func_def_525, type, sK387: term).
% 17.66/3.02 thf(func_def_526, type, sK388: (term > term)).
% 17.66/3.02 thf(func_def_527, type, sK389: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_528, type, sK390: term).
% 17.66/3.02 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_532, type, sK394: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_534, type, sK396: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_535, type, sK397: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_538, type, sK400: (term > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_539, type, sK401: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_541, type, sK403: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_544, type, sK406: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_545, type, sK407: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > subst)).
% 17.66/3.02 thf(func_def_547, type, sK409: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_548, type, sK410: term).
% 17.66/3.02 thf(func_def_549, type, sK411: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_550, type, sK412: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_551, type, sK413: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_552, type, sK414: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_553, type, sK415: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_554, type, sK416: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_555, type, sK417: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_556, type, sK418: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_557, type, sK419: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_558, type, sK420: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_559, type, sK421: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_560, type, sK422: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_561, type, sK423: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_562, type, sK424: ((subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_563, type, sK425: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_564, type, sK426: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_565, type, sK427: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_566, type, sK428: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_567, type, sK429: (term > $o)).
% 17.66/3.02 thf(func_def_568, type, sK430: term).
% 17.66/3.02 thf(func_def_569, type, sK431: subst).
% 17.66/3.02 thf(func_def_570, type, sK432: term).
% 17.66/3.02 thf(func_def_571, type, sK433: subst).
% 17.66/3.02 thf(func_def_572, type, sK434: term).
% 17.66/3.02 thf(func_def_573, type, sK435: subst).
% 17.66/3.02 thf(func_def_574, type, sK436: (term > $o)).
% 17.66/3.02 thf(func_def_575, type, sK437: term).
% 17.66/3.02 thf(func_def_576, type, sK438: subst).
% 17.66/3.02 thf(func_def_577, type, sK439: (term > term)).
% 17.66/3.02 thf(func_def_578, type, sK440: (subst > (term > $o) > term)).
% 17.66/3.02 thf(func_def_579, type, sK441: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_580, type, sK442: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_581, type, sK443: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_582, type, sK444: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_583, type, sK445: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_584, type, sK446: (term > $o)).
% 17.66/3.02 thf(func_def_585, type, sK447: term).
% 17.66/3.02 thf(func_def_586, type, sK448: subst).
% 17.66/3.02 thf(func_def_587, type, sK449: (term > term)).
% 17.66/3.02 thf(func_def_588, type, sK450: (subst > (term > $o) > term)).
% 17.66/3.02 thf(func_def_589, type, sK451: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_590, type, sK452: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_591, type, sK453: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_592, type, sK454: term).
% 17.66/3.02 thf(func_def_593, type, sK455: (term > $o)).
% 17.66/3.02 thf(func_def_594, type, sK456: term).
% 17.66/3.02 thf(func_def_595, type, sK457: subst).
% 17.66/3.02 thf(func_def_596, type, sK458: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_597, type, sK459: (subst > term > (term > $o) > term > $o)).
% 17.66/3.02 thf(func_def_598, type, sK460: term).
% 17.66/3.02 thf(func_def_599, type, sK461: term).
% 17.66/3.02 thf(func_def_600, type, sK462: subst).
% 17.66/3.02 thf(func_def_601, type, sK463: (term > $o)).
% 17.66/3.02 thf(func_def_602, type, sK464: (term > $o)).
% 17.66/3.02 thf(func_def_603, type, sK465: term).
% 17.66/3.02 thf(func_def_604, type, sK466: subst).
% 17.66/3.02 thf(func_def_605, type, sK467: term).
% 17.66/3.02 thf(func_def_606, type, sK468: term).
% 17.66/3.02 thf(func_def_607, type, sK469: subst).
% 17.66/3.02 thf(func_def_608, type, sK470: term).
% 17.66/3.02 thf(func_def_609, type, sK471: subst).
% 17.66/3.02 thf(func_def_610, type, sK472: (subst > term > term)).
% 17.66/3.02 thf(func_def_611, type, sK473: term).
% 17.66/3.02 thf(func_def_612, type, sK474: term).
% 17.66/3.02 thf(func_def_613, type, sK475: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_614, type, sK476: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_615, type, sK477: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_616, type, sK478: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_617, type, sK479: term).
% 17.66/3.02 thf(func_def_618, type, sK480: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_619, type, sK481: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_620, type, sK482: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_621, type, sK483: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_622, type, sK484: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_623, type, sK485: subst).
% 17.66/3.02 thf(func_def_624, type, sK486: subst).
% 17.66/3.02 thf(func_def_625, type, sK487: term).
% 17.66/3.02 thf(func_def_626, type, sK488: (term > subst > term > term)).
% 17.66/3.02 thf(func_def_627, type, sK489: subst).
% 17.66/3.02 thf(func_def_628, type, sK490: subst).
% 17.66/3.02 thf(func_def_629, type, sK491: subst).
% 17.66/3.02 thf(func_def_630, type, sK492: subst).
% 17.66/3.02 thf(func_def_631, type, sK493: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_632, type, sK494: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_633, type, sK495: ((subst > term > subst > $o) > term > $o)).
% 17.66/3.02 thf(func_def_634, type, sK496: subst).
% 17.66/3.02 thf(func_def_635, type, sK497: (term > $o)).
% 17.66/3.02 thf(func_def_636, type, sK498: term).
% 17.66/3.02 thf(func_def_637, type, sK499: subst).
% 17.66/3.02 thf(func_def_638, type, sK500: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_639, type, sK501: (subst > term > (term > $o) > term > $o)).
% 17.66/3.02 thf(func_def_640, type, sK502: term).
% 17.66/3.02 thf(func_def_641, type, sK503: term).
% 17.66/3.02 thf(func_def_642, type, sK504: (term > $o)).
% 17.66/3.02 thf(func_def_643, type, sK505: (term > $o)).
% 17.66/3.02 thf(func_def_644, type, sK506: term).
% 17.66/3.02 thf(func_def_645, type, sK507: subst).
% 17.66/3.02 thf(func_def_646, type, sK508: term).
% 17.66/3.02 thf(func_def_647, type, sK509: subst).
% 17.66/3.02 thf(func_def_648, type, sK510: subst).
% 17.66/3.02 thf(func_def_649, type, sK511: term).
% 17.66/3.02 thf(func_def_650, type, sK512: subst).
% 17.66/3.02 thf(func_def_651, type, sK513: term).
% 17.66/3.02 thf(func_def_652, type, sK514: term).
% 17.66/3.02 thf(func_def_653, type, sK515: term).
% 17.66/3.02 thf(func_def_654, type, sK516: term).
% 17.66/3.02 thf(func_def_655, type, sK517: term).
% 17.66/3.02 thf(func_def_656, type, sK518: term).
% 17.66/3.02 thf(func_def_657, type, sK519: term).
% 17.66/3.02 thf(func_def_658, type, sK520: term).
% 17.66/3.02 thf(func_def_659, type, sK521: term).
% 17.66/3.02 thf(func_def_660, type, sK522: term).
% 17.66/3.02 thf(func_def_661, type, sK523: term).
% 17.66/3.02 thf(func_def_662, type, sK524: term).
% 17.66/3.02 thf(func_def_663, type, sK525: term).
% 17.66/3.02 thf(func_def_664, type, sK526: term).
% 17.66/3.02 thf(func_def_665, type, sK527: term).
% 17.66/3.02 thf(func_def_666, type, sK528: term).
% 17.66/3.02 thf(func_def_667, type, sK529: term).
% 17.66/3.02 thf(func_def_668, type, sK530: term).
% 17.66/3.02 thf(func_def_669, type, sK531: term).
% 17.66/3.02 thf(func_def_670, type, sK532: term).
% 17.66/3.02 thf(func_def_671, type, sK533: term).
% 17.66/3.02 thf(func_def_672, type, sK534: term).
% 17.66/3.02 thf(func_def_673, type, sK535: term).
% 17.66/3.02 thf(func_def_674, type, sK536: term).
% 17.66/3.02 thf(func_def_675, type, sK537: term).
% 17.66/3.02 thf(func_def_676, type, sK538: (term > $o)).
% 17.66/3.02 thf(func_def_677, type, sK539: term).
% 17.66/3.02 thf(func_def_678, type, sK540: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_679, type, sK541: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_680, type, sK542: term).
% 17.66/3.02 thf(func_def_681, type, sK543: (term > subst > term > term)).
% 17.66/3.02 thf(func_def_682, type, sK544: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_683, type, sK545: ((term > $o) > term)).
% 17.66/3.02 thf(func_def_684, type, sK546: ((subst > term > subst > $o) > term > $o)).
% 17.66/3.02 thf(func_def_685, type, sK547: (term > $o)).
% 17.66/3.02 thf(func_def_686, type, sK548: (term > $o)).
% 17.66/3.02 thf(func_def_687, type, sK549: term).
% 17.66/3.02 thf(func_def_688, type, sK550: subst).
% 17.66/3.02 thf(func_def_689, type, sK551: (subst > term > (term > $o) > (term > $o) > term)).
% 17.66/3.02 thf(func_def_690, type, sK552: term).
% 17.66/3.02 thf(func_def_691, type, sK553: subst).
% 17.66/3.02 thf(func_def_692, type, sK554: term).
% 17.66/3.02 thf(func_def_693, type, sK555: term).
% 17.66/3.02 thf(func_def_694, type, sK556: (subst > term > term)).
% 17.66/3.02 thf(func_def_695, type, sK557: (subst > term > term)).
% 17.66/3.02 thf(func_def_696, type, sK558: subst).
% 17.66/3.02 thf(func_def_697, type, sK559: term).
% 17.66/3.02 thf(func_def_698, type, sK560: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_699, type, sK561: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_700, type, sK562: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_701, type, sK563: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_702, type, sK564: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_703, type, sK565: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_704, type, sK566: term).
% 17.66/3.02 thf(func_def_705, type, sK567: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_706, type, sK568: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_707, type, sK569: (term > subst > term > term)).
% 17.66/3.02 thf(func_def_708, type, sK570: term).
% 17.66/3.02 thf(func_def_709, type, sK571: term).
% 17.66/3.02 thf(func_def_710, type, sK572: term).
% 17.66/3.02 thf(func_def_711, type, sK573: term).
% 17.66/3.02 thf(func_def_712, type, sK574: term).
% 17.66/3.02 thf(func_def_713, type, sK575: term).
% 17.66/3.02 thf(func_def_714, type, sK576: term).
% 17.66/3.02 thf(func_def_715, type, sK577: term).
% 17.66/3.02 thf(func_def_716, type, sK578: term).
% 17.66/3.02 thf(func_def_717, type, sK579: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_718, type, sK580: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_719, type, sK581: (term > subst > term > term)).
% 17.66/3.02 thf(func_def_720, type, sK582: term).
% 17.66/3.02 thf(func_def_721, type, sK583: term).
% 17.66/3.02 thf(func_def_722, type, sK584: (term > $o)).
% 17.66/3.02 thf(func_def_723, type, sK585: (term > $o)).
% 17.66/3.02 thf(func_def_724, type, sK586: term).
% 17.66/3.02 thf(func_def_725, type, sK587: subst).
% 17.66/3.02 thf(func_def_726, type, sK588: (subst > term > (term > $o) > (term > $o) > term)).
% 17.66/3.02 thf(func_def_727, type, sK589: (subst > d_subst)).
% 17.66/3.02 thf(func_def_728, type, sK590: (term > d_term)).
% 17.66/3.02 thf(func_def_729, type, vNOT: ($o > $o)).
% 17.66/3.02 thf(func_def_730, type, sK591: (term > $o)).
% 17.66/3.02 thf(func_def_731, type, sK592: (subst > term > subst > $o)).
% 17.66/3.02 thf(func_def_732, type, sK593: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_733, type, sK594: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_734, type, sK595: ((subst > term > term) > term)).
% 17.66/3.02 thf(func_def_735, type, sK596: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_736, type, sK597: ((subst > term > term) > subst)).
% 17.66/3.02 thf(func_def_737, type, sK598: term).
% 17.66/3.02 thf(func_def_738, type, sK599: ((subst > term > subst > $o) > subst > term > term)).
% 17.66/3.02 thf(func_def_739, type, sK600: ((term > $o) > (subst > term > subst > $o) > term)).
% 17.66/3.02 thf(func_def_740, type, sK601: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_741, type, sK602: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_742, type, sK603: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_743, type, sK604: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_744, type, sK605: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_745, type, sK606: (term > (term > $o) > term)).
% 17.66/3.02 thf(func_def_747, type, db5: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_748, type, db7: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(func_def_749, type, db6: !>[X0: $tType]:(X0)).
% 17.66/3.02 thf(f1,axiom,(
% 17.66/3.02 (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [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] : ((X10 @ id @ X28 @ 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))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : ((X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) & hoasapnotvar_lthm & (pushprop_lem0_lthm <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (hoasinduction_lem3v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : ((X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X26 : (term > $o),X13 : term,X14 : subst,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & pushprop_lem2v2_gthm & pushprop_lem3v2 & (induction2 <=> ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))) & ulamvarsh & substmonoid_gthm & (hoaslamnotap <=> ! [X18 : (subst > term > term),X46 : term,X47 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem2v2_lthm & induction2_gthm & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ 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))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & hoasinduction_lem1_gthm & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [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))))))) & lamnotvar & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & hoasinduction_lem2_gthm & hoasinduction_lem3_gthm & pushprop & (substmonoid_lthm <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))))) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13))) => ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))))) & hoaslaminj_gthm & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & hoaslamnotvar & hoasapinj1_gthm & ~lamnotap & hoasinduction_lem1_lthm & hoasapinj2_gthm & hoasinduction_lem2_lthm & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & axabs & pushprop_gthm & (pushprop_lem0 <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (hoasinduction_lem3_lthm <=> (! [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 @ (sub @ X42 @ (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 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (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))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) & (laminj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & (pushprop_lem1 <=> ! [X10 : (term > $o),X26 : (term > $o),X13 : term,X14 : subst,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & hoasinduction_lem2v2_gthm & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X18 : (subst > term > term),X31 : (subst > term > term),X32 : subst,X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & (hoasinduction_lem3v2a <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & (hoasapinj2_lthm <=> (! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & (apinj1 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (apinj2 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & pushprop_lthm & (hoasinduction_lem2v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X44 : term,X45 : term] : ((X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~(X11 @ X44) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & axassoc & axclos & hoasinduction_lem3a_gthm & pushprop_lem2v2 & hoasinduction_lem3b_gthm & hoaslamnotvar_gthm & hoaslamnotap_gthm & pushprop_lem1v2_gthm & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((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)] : ((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))))))) & termmset_gthm & (hoasinduction_lem3a_lthm <=> (! [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 @ (sub @ X42 @ (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 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [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))))))))) & (induction <=> ! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))) & ulamvarind & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & pushprop_lem3v2_lthm & hoaslamnotvar_lthm & axapp & hoasinduction_gthm & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ 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))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & hoasapnotvar & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X11 : (term > $o),X13 : term,X14 : subst] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13)))) & hoaslamnotap_lthm & hoasinduction_lem1 & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem3 <=> ! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (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))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((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)] : ((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))))))) & induction2lem_gthm & (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X39 : subst,X40 : term,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X36 : subst,X37 : term,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))) & (hoaslaminj <=> ! [X18 : (subst > term > term),X31 : (subst > term > term),X32 : subst,X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ 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))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))))))) & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => (! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (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))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ id) | ~ ! [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))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & pushprop_lthm_orig & apnotvar & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => ! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))))))) & ~ulamvar1 & (hoasapinj1 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & hoasapnotvar_gthm & (hoasapinj2 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & axvarshift & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (induction2lem <=> ! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))) & hoasinduction_lem1v2_gthm & hoasinduction_lem1v2 & (shinj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & pushprop_lem0_gthm & axmap & pushprop_lem1_gthm & (pushprop_lem1v2 <=> ! [X10 : (term > $o),X11 : (term > $o),X13 : term,X14 : subst] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13))) & ~(var @ (d2term @ d_one)) & (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)))))))) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (sh = ((d2subst @ d_id))) & (id = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (one = ((d2term @ d_one))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ! [X5 : d_subst] : (X5 = d_id) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & ! [X1 : d_term] : (X1 = d_one) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1)))),
% 17.66/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 17.66/3.02 thf(f2,conjecture,(
% 17.66/3.02 (hoasinduction_lem3v2a = ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X2 : (subst > term > term)] : (! [X3 : subst,X4 : term,X5 : subst] : (((sub @ (X2 @ X3 @ X4) @ X5)) = ((X2 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) => (! [X4 : term] : ((X0 @ id @ X4 @ id) => (X0 @ id @ (X2 @ id @ X4) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X3 : subst, X4 : term] : ((X2 @ X3 @ X4)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X4 : term] : (! [X6 : term] : ((X1 @ X6) => (X1 @ (sub @ X4 @ (push @ X6 @ id)))) => (X1 @ (lam @ X4))))))),
% 17.66/3.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2a)).
% 17.66/3.02 thf(f3,negated_conjecture,(
% 17.66/3.02 ~ (hoasinduction_lem3v2a = ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X2 : (subst > term > term)] : (! [X3 : subst,X4 : term,X5 : subst] : (((sub @ (X2 @ X3 @ X4) @ X5)) = ((X2 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) => (! [X4 : term] : ((X0 @ id @ X4 @ id) => (X0 @ id @ (X2 @ id @ X4) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X3 : subst, X4 : term] : ((X2 @ X3 @ X4)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X4 : term] : (! [X6 : term] : ((X1 @ X6) => (X1 @ (sub @ X4 @ (push @ X6 @ id)))) => (X1 @ (lam @ X4))))))),
% 17.66/3.02 inference(negated_conjecture,[status(cth)],[f2])).
% 17.66/3.02 thf(f4,plain,(
% 17.66/3.02 (hoasinduction_lthm_3 <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((X3 @ X4) | ~ ! [X5 : term] : ((X3 @ (lam @ X5)) | ~ ! [X6 : term] : ((X3 @ (sub @ X5 @ (push @ X6 @ id))) | ~(X3 @ X6))) | ~ ! [X7 : term,X8 : term] : ((X3 @ (ap @ X7 @ X8)) | ~(X3 @ X8) | ~(X3 @ X7)) | ~ ! [X9 : term] : ((X3 @ X9) | ~(var @ X9))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((X12 @ (lam @ X13)) | ~ ! [X14 : term] : ((X12 @ (sub @ X13 @ (push @ X14 @ id))) | ~(X12 @ X14)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id) | ~ ! [X17 : term] : ((X11 @ id @ (X16 @ id @ X17) @ id) | ~(X11 @ id @ X17 @ id)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((X21 @ id @ X22 @ id) | ~ ! [X23 : (subst > term > term)] : ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id) | ~ ! [X24 : term] : ((X21 @ id @ (X23 @ id @ X24) @ id) | ~(X21 @ id @ X24 @ id)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id) | ~(X21 @ id @ X29 @ id) | ~(X21 @ id @ X28 @ id)) | ~ ! [X30 : term] : ((X21 @ id @ X30 @ id) | ~(var @ (sub @ X30 @ id))) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((X21 @ X31 @ X32 @ (comp @ X34 @ X33)) | ~(X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37) | ~(X21 @ X35 @ X36 @ (comp @ X38 @ X37))))))))) & (axvarid <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & (hoasinduction_lem3v2_lthm <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((X42 @ (lam @ X43)) | ~ ! [X44 : term] : ((X42 @ (sub @ X43 @ (push @ X44 @ id))) | ~(X42 @ X44)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id) | ~ ! [X47 : term] : ((X41 @ id @ (X46 @ id @ X47) @ id) | ~(X41 @ id @ X47 @ id)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((X41 @ X51 @ X52 @ (comp @ X54 @ X53)) | ~(X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57) | ~(X41 @ X55 @ X56 @ (comp @ X58 @ X57)))))) & hoasapnotvar_lthm & (pushprop_lem0_lthm <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & (termmset <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & (axshiftcons <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & (hoasinduction_lem3v2 <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((X68 @ (lam @ X69)) | ~ ! [X70 : term] : ((X68 @ (sub @ X69 @ (push @ X70 @ id))) | ~(X68 @ X70)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id) | ~ ! [X73 : term] : ((X67 @ id @ (X72 @ id @ X73) @ id) | ~(X67 @ id @ X73 @ id)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((X67 @ X77 @ X78 @ (comp @ X80 @ X79)) | ~(X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83) | ~(X67 @ X81 @ X82 @ (comp @ X84 @ X83))))) & (pushprop_lem1_lthm <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((X90 @ (sub @ X91 @ (push @ X93 @ X92))) | ~(X89 @ X91))))) & pushprop_lem2v2_gthm & pushprop_lem3v2 & (induction2 <=> ! [X94 : (term > $o),X95 : term] : ((X94 @ X95) | ~ ! [X96 : term] : ((X94 @ (lam @ X96)) | ~ ! [X97 : term] : ((X94 @ (sub @ X96 @ (push @ X97 @ id))) | ~(X94 @ X97))) | ~ ! [X98 : term,X99 : term] : ((X94 @ (ap @ X98 @ X99)) | ~(X94 @ X99) | ~(X94 @ X98)) | ~ ! [X100 : term] : ((X94 @ X100) | ~(var @ X100)))) & ulamvarsh & substmonoid_gthm & (hoaslamnotap <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem2v2_lthm & induction2_gthm & (hoasinduction_no_psi_cond <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((X107 @ id @ X108 @ id) | ~ ! [X109 : (subst > term > term)] : ((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id) | ~ ! [X110 : term] : ((X107 @ id @ (X109 @ id @ X110) @ id) | ~(X107 @ id @ X110 @ id)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id) | ~(X107 @ id @ X115 @ id) | ~(X107 @ id @ X114 @ id)))) & hoasinduction_lem1_gthm & (hoasinduction_lem3a <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((X116 @ id @ (lam @ X117) @ id) | ~ ! [X118 : term] : ((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id) | ~(X116 @ id @ X118 @ id)) | ~ ! [X119 : (subst > term > term)] : ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id) | ~ ! [X120 : term] : ((X116 @ id @ (X119 @ id @ X120) @ id) | ~(X116 @ id @ X120 @ id)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & lamnotvar & (substmonoid <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & (hoasinduction_lem3b <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & hoasinduction_lem2_gthm & hoasinduction_lem3_gthm & pushprop & (substmonoid_lthm <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & (hoasinduction_lem0_lthm <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & (induction2_lthm <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((X136 @ (sub @ X137 @ X138)) | ~ ! [X139 : term] : ((X136 @ (sub @ X139 @ X138)) | ~(var @ X139)) | ~ ! [X140 : term] : ((X136 @ (lam @ X140)) | ~ ! [X141 : term] : ((X136 @ (sub @ X140 @ (push @ X141 @ id))) | ~(X136 @ X141))) | ~ ! [X142 : term,X143 : term] : ((X136 @ (ap @ X142 @ X143)) | ~(X136 @ X143) | ~(X136 @ X142))) => ! [X144 : (term > $o),X145 : term] : ((X144 @ X145) | ~ ! [X146 : term] : ((X144 @ (lam @ X146)) | ~ ! [X147 : term] : ((X144 @ (sub @ X146 @ (push @ X147 @ id))) | ~(X144 @ X147))) | ~ ! [X148 : term,X149 : term] : ((X144 @ (ap @ X148 @ X149)) | ~(X144 @ X149) | ~(X144 @ X148)) | ~ ! [X150 : term] : ((X144 @ X150) | ~(var @ X150)))))) & hoaslaminj_gthm & (axidl <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & hoaslamnotvar & hoasapinj1_gthm & ~lamnotap & hoasinduction_lem1_lthm & hoasapinj2_gthm & hoasinduction_lem2_lthm & (hoasinduction_lem3v2a_lthm <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((X158 @ (lam @ X159)) | ~ ! [X160 : term] : ((X158 @ (sub @ X159 @ (push @ X160 @ id))) | ~(X158 @ X160)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id) | ~ ! [X163 : term] : ((X157 @ id @ (X162 @ id @ X163) @ id) | ~(X157 @ id @ X163 @ id)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & axabs & pushprop_gthm & (pushprop_lem0 <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & (hoasinduction_lem3_lthm <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id) | ~ ! [X175 : term] : ((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id) | ~(X173 @ id @ X175 @ id)) | ~ ! [X176 : (subst > term > term)] : ((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id) | ~ ! [X177 : term] : ((X173 @ id @ (X176 @ id @ X177) @ id) | ~(X173 @ id @ X177 @ id)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((X181 @ id @ (lam @ X182) @ id) | ~ ! [X183 : term] : ((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id) | ~(X181 @ id @ X183 @ id)) | ~ ! [X184 : (subst > term > term)] : ((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id) | ~ ! [X185 : term] : ((X181 @ id @ (X184 @ id @ X185) @ id) | ~(X181 @ id @ X185 @ id)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((X181 @ X189 @ X190 @ (comp @ X192 @ X191)) | ~(X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195) | ~(X181 @ X193 @ X194 @ (comp @ X196 @ X195))))))) & (laminj <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & (pushprop_lem1 <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((X200 @ (sub @ X201 @ (push @ X203 @ X202))) | ~(X199 @ X201))) & (axidr <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & hoasinduction_lem2v2_gthm & (axscons <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & (axvarcons <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & (hoaslaminj_lthm <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & (hoasapinj1_lthm <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & (hoasinduction_lem3v2a <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((X234 @ (lam @ X235)) | ~ ! [X236 : term] : ((X234 @ (sub @ X235 @ (push @ X236 @ id))) | ~(X234 @ X236)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id) | ~ ! [X239 : term] : ((X233 @ id @ (X238 @ id @ X239) @ id) | ~(X233 @ id @ X239 @ id)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & (hoasapinj2_lthm <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & (apinj1 <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & (apinj2 <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & pushprop_lthm & (hoasinduction_lem2v2 <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((X260 @ (ap @ X261 @ X262)) | ~(X260 @ X262) | ~(X260 @ X261) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id) | ~(X259 @ id @ X265 @ id) | ~(X259 @ id @ X264 @ id)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((X259 @ X266 @ X267 @ (comp @ X269 @ X268)) | ~(X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272) | ~(X259 @ X270 @ X271 @ (comp @ X273 @ X272))))) & axassoc & axclos & hoasinduction_lem3a_gthm & pushprop_lem2v2 & hoasinduction_lem3b_gthm & hoaslamnotvar_gthm & hoaslamnotap_gthm & pushprop_lem1v2_gthm & (hoasinduction_lem3aa <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id) | ~ ! [X276 : term] : ((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id) | ~(X274 @ id @ X276 @ id)) | ~ ! [X277 : (subst > term > term)] : ((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id) | ~ ! [X278 : term] : ((X274 @ id @ (X277 @ id @ X278) @ id) | ~(X274 @ id @ X278 @ id)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & termmset_gthm & (hoasinduction_lem3a_lthm <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id) | ~ ! [X285 : term] : ((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id) | ~(X283 @ id @ X285 @ id)) | ~ ! [X286 : (subst > term > term)] : ((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id) | ~ ! [X287 : term] : ((X283 @ id @ (X286 @ id @ X287) @ id) | ~(X283 @ id @ X287 @ id)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((X291 @ id @ (lam @ X292) @ id) | ~ ! [X293 : term] : ((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id) | ~(X291 @ id @ X293 @ id)) | ~ ! [X294 : (subst > term > term)] : ((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id) | ~ ! [X295 : term] : ((X291 @ id @ (X294 @ id @ X295) @ id) | ~(X291 @ id @ X295 @ id)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & (induction <=> ! [X299 : (term > $o),X300 : term] : ((X299 @ X300) | ~ ! [X301 : term] : ((X299 @ (lam @ X301)) | ~(X299 @ X301)) | ~ ! [X302 : term,X303 : term] : ((X299 @ (ap @ X302 @ X303)) | ~(X299 @ X303) | ~(X299 @ X302)) | ~ ! [X304 : term] : ((X299 @ X304) | ~(var @ X304)))) & ulamvarind & (hoasinduction_lem3b_lthm <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & pushprop_lem3v2_lthm & hoaslamnotvar_lthm & axapp & hoasinduction_gthm & (hoasinduction <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((X307 @ id @ X308 @ id) | ~ ! [X309 : (subst > term > term)] : ((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id) | ~ ! [X310 : term] : ((X307 @ id @ (X309 @ id @ X310) @ id) | ~(X307 @ id @ X310 @ id)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id) | ~(X307 @ id @ X315 @ id) | ~(X307 @ id @ X314 @ id)) | ~ ! [X316 : term] : ((X307 @ id @ X316 @ id) | ~(var @ (sub @ X316 @ id))) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((X307 @ X317 @ X318 @ (comp @ X320 @ X319)) | ~(X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323) | ~(X307 @ X321 @ X322 @ (comp @ X324 @ X323))))) & (hoasinduction_lem0 <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & hoasapnotvar & (pushprop_lem1v2_lthm <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((X331 @ one) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | ~(X330 @ X332)))) & hoaslamnotap_lthm & hoasinduction_lem1 & (termmset_lthm <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & (hoasinduction_lem2 <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((X337 @ id @ (ap @ X338 @ X339) @ id) | ~(X337 @ id @ X339 @ id) | ~(X337 @ id @ X338 @ id) | ~ ! [X340 : term,X341 : term] : ((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id) | ~(X337 @ id @ X341 @ id) | ~(X337 @ id @ X340 @ id)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((X337 @ X342 @ X343 @ (comp @ X345 @ X344)) | ~(X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348) | ~(X337 @ X346 @ X347 @ (comp @ X349 @ X348))))) & (hoasinduction_lem3 <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((X350 @ id @ (lam @ X351) @ id) | ~ ! [X352 : term] : ((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id) | ~(X350 @ id @ X352 @ id)) | ~ ! [X353 : (subst > term > term)] : ((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id) | ~ ! [X354 : term] : ((X350 @ id @ (X353 @ id @ X354) @ id) | ~(X350 @ id @ X354 @ id)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((X350 @ X358 @ X359 @ (comp @ X361 @ X360)) | ~(X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364) | ~(X350 @ X362 @ X363 @ (comp @ X365 @ X364))))) & (hoasinduction_lem3aa_lthm <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id) | ~ ! [X368 : term] : ((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id) | ~(X366 @ id @ X368 @ id)) | ~ ! [X369 : (subst > term > term)] : ((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id) | ~ ! [X370 : term] : ((X366 @ id @ (X369 @ id @ X370) @ id) | ~(X366 @ id @ X370 @ id)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & induction2lem_gthm & (hoasinduction_lem3aaa <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id) | ~ ! [X376 : term] : ((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id) | ~(X374 @ id @ X376 @ id)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (X374 @ id @ (lam @ (X377 @ sh @ one)) @ id) | ~ ! [X385 : term] : ((X374 @ id @ (X377 @ id @ X385) @ id) | ~(X374 @ id @ X385 @ id))))) & (hoaslaminj <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((X399 @ X400) | ~ ! [X401 : term] : ((X399 @ (lam @ X401)) | ~ ! [X402 : term] : ((X399 @ (sub @ X401 @ (push @ X402 @ id))) | ~(X399 @ X402))) | ~ ! [X403 : term,X404 : term] : ((X399 @ (ap @ X403 @ X404)) | ~(X399 @ X404) | ~(X399 @ X403)) | ~ ! [X405 : term] : ((X399 @ X405) | ~(var @ X405))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((X408 @ (lam @ X409)) | ~ ! [X410 : term] : ((X408 @ (sub @ X409 @ (push @ X410 @ id))) | ~(X408 @ X410)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id) | ~ ! [X413 : term] : ((X407 @ id @ (X412 @ id @ X413) @ id) | ~(X407 @ id @ X413 @ id)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((X417 @ id @ X418 @ id) | ~ ! [X419 : (subst > term > term)] : ((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id) | ~ ! [X420 : term] : ((X417 @ id @ (X419 @ id @ X420) @ id) | ~(X417 @ id @ X420 @ id)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id) | ~(X417 @ id @ X425 @ id) | ~(X417 @ id @ X424 @ id)))))))) & (hoasinduction_lthm <=> (! [X426 : (term > $o),X427 : term] : ((X426 @ X427) | ~ ! [X428 : term] : ((X426 @ (lam @ X428)) | ~ ! [X429 : term] : ((X426 @ (sub @ X428 @ (push @ X429 @ id))) | ~(X426 @ X429))) | ~ ! [X430 : term,X431 : term] : ((X426 @ (ap @ X430 @ X431)) | ~(X426 @ X431) | ~(X426 @ X430)) | ~ ! [X432 : term] : ((X426 @ X432) | ~(var @ X432))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((X433 @ id @ (ap @ X434 @ X435) @ id) | ~(X433 @ id @ X435 @ id) | ~(X433 @ id @ X434 @ id) | ~ ! [X436 : term,X437 : term] : ((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id) | ~(X433 @ id @ X437 @ id) | ~(X433 @ id @ X436 @ id)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((X433 @ X438 @ X439 @ (comp @ X441 @ X440)) | ~(X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444) | ~(X433 @ X442 @ X443 @ (comp @ X445 @ X444)))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((X446 @ id @ (lam @ X447) @ id) | ~ ! [X448 : term] : ((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id) | ~(X446 @ id @ X448 @ id)) | ~ ! [X449 : (subst > term > term)] : ((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id) | ~ ! [X450 : term] : ((X446 @ id @ (X449 @ id @ X450) @ id) | ~(X446 @ id @ X450 @ id)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((X446 @ X454 @ X455 @ (comp @ X457 @ X456)) | ~(X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460) | ~(X446 @ X458 @ X459 @ (comp @ X461 @ X460)))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((X462 @ id @ X463 @ id) | ~ ! [X464 : (subst > term > term)] : ((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id) | ~ ! [X465 : term] : ((X462 @ id @ (X464 @ id @ X465) @ id) | ~(X462 @ id @ X465 @ id)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id) | ~(X462 @ id @ X470 @ id) | ~(X462 @ id @ X469 @ id)) | ~ ! [X471 : term] : ((X462 @ id @ X471 @ id) | ~(var @ (sub @ X471 @ id))) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((X462 @ X472 @ X473 @ (comp @ X475 @ X474)) | ~(X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478) | ~(X462 @ X476 @ X477 @ (comp @ X479 @ X478)))))))) & (hoasinduction_lem3v2_f_lthm <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & pushprop_lthm_orig & apnotvar & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((X489 @ X490) | ~ ! [X491 : term] : ((X489 @ (lam @ X491)) | ~(X489 @ X491)) | ~ ! [X492 : term,X493 : term] : ((X489 @ (ap @ X492 @ X493)) | ~(X489 @ X493) | ~(X489 @ X492)) | ~ ! [X494 : term] : ((X489 @ X494) | ~(var @ X494))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((X495 @ (sub @ X496 @ X497)) | ~ ! [X498 : term] : ((X495 @ (sub @ X498 @ X497)) | ~(var @ X498)) | ~ ! [X499 : term] : ((X495 @ (lam @ X499)) | ~ ! [X500 : term] : ((X495 @ (sub @ X499 @ (push @ X500 @ id))) | ~(X495 @ X500))) | ~ ! [X501 : term,X502 : term] : ((X495 @ (ap @ X501 @ X502)) | ~(X495 @ X502) | ~(X495 @ X501)))))))) & ~ulamvar1 & (hoasapinj1 <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & hoasapnotvar_gthm & (hoasapinj2 <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & axvarshift & (hoasinduction_lem3v2_f <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & (induction2lem <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((X515 @ (sub @ X516 @ X517)) | ~ ! [X518 : term] : ((X515 @ (sub @ X518 @ X517)) | ~(var @ X518)) | ~ ! [X519 : term] : ((X515 @ (lam @ X519)) | ~ ! [X520 : term] : ((X515 @ (sub @ X519 @ (push @ X520 @ id))) | ~(X515 @ X520))) | ~ ! [X521 : term,X522 : term] : ((X515 @ (ap @ X521 @ X522)) | ~(X515 @ X522) | ~(X515 @ X521)))) & hoasinduction_lem1v2_gthm & hoasinduction_lem1v2 & (shinj <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & pushprop_lem0_gthm & axmap & pushprop_lem1_gthm & (pushprop_lem1v2 <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((X526 @ one) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | ~(X525 @ X527))) & ~(var @ (d2term @ d_one)) & (pushprop_p_and_p_prime = (^[X530 : term, X531 : subst, X532 : (term > $o), X533 : (term > $o)] : (! [X534 : term] : (((X533 @ X534)) = ((X532 @ (sub @ X534 @ (push @ X530 @ X531)))))))) & (hoasinduction_p_and_p_prime = (^[X535 : (subst > term > subst > $o), X536 : (term > $o)] : (! [X537 : term] : (((X536 @ X537)) = ((X535 @ id @ X537 @ id)))))) & (hoaslam = (^[X538 : subst, X539 : (subst > term > term)] : ((d2term @ d_one)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (sh = ((d2subst @ d_id))) & (id = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (one = ((d2term @ d_one))) & ! [X540 : d_subst,X541 : d_subst] : ((((d2subst @ X540)) = ((d2subst @ X541))) => (X540 = X541)) & ! [X542 : d_subst] : (d_id = X542) & ! [X543 : subst] : ? [X544 : d_subst] : (((d2subst @ X544)) = X543) & ! [X545 : d_term,X546 : d_term] : ((((d2term @ X545)) = ((d2term @ X546))) => (X545 = X546)) & ! [X547 : d_term] : (d_one = X547) & ! [X548 : term] : ? [X549 : d_term] : (((d2term @ X549)) = X548)),
% 17.66/3.02 inference(rectify,[],[f1])).
% 17.66/3.02 thf(f5,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | ~ (((X3 @ X6)) = $true))) | ~ ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | ~ (((X3 @ X8)) = $true) | ~ (((X3 @ X7)) = $true)) | ~ ! [X9 : term] : ((((X3 @ X9)) = $true) | ~ (((var @ X9)) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) = $true) | ~ ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | ~ (((X12 @ X14)) = $true)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) = $true) | ~ (((X11 @ id @ X17 @ id)) = $true)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | ~ (((X21 @ id @ X29 @ id)) = $true) | ~ (((X21 @ id @ X28 @ id)) = $true)) | ~ ! [X30 : term] : ((((X21 @ id @ X30 @ id)) = $true) | ~ (((var @ (sub @ X30 @ id))) = $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) = $true) | ~ (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) = $true) | ~ (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true)))))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ~ ! [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) = $true) | ~ (((X42 @ X44)) = $true)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | ~ (((X41 @ id @ X47 @ id)) = $true)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) = $true) | ~ (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) = $true) | ~ (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ~ ! [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) = $true) | ~ (((X68 @ X70)) = $true)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | ~ (((X67 @ id @ X73 @ id)) = $true)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) = $true) | ~ (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) = $true) | ~ (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | ~ (((X89 @ X91)) = $true))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X96 : term] : ((((X94 @ (lam @ X96))) = $true) | ~ ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | ~ (((X94 @ X97)) = $true))) | ~ ! [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) = $true) | ~ (((X94 @ X99)) = $true) | ~ (((X94 @ X98)) = $true)) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | ~ (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ~ ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ~ ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | ~ (((X107 @ id @ X110 @ id)) = $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) = $true) | ~ (((X107 @ id @ X115 @ id)) = $true) | ~ (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ~ ! [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) = $true) | ~ (((X116 @ id @ X118 @ id)) = $true)) | ~ ! [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) = $true) | ~ ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | ~ (((X116 @ id @ X120 @ id)) = $true)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) = $true) | ~ ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | ~ (((var @ X139)) = $true)) | ~ ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ~ ! [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ~ (((X136 @ X141)) = $true))) | ~ ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | ~ (((X136 @ X143)) = $true) | ~ (((X136 @ X142)) = $true))) => ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ~ ! [X146 : term] : ((((X144 @ (lam @ X146))) = $true) | ~ ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | ~ (((X144 @ X147)) = $true))) | ~ ! [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) = $true) | ~ (((X144 @ X149)) = $true) | ~ (((X144 @ X148)) = $true)) | ~ ! [X150 : term] : ((((X144 @ X150)) = $true) | ~ (((var @ X150)) = $true)))))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ~ (lamnotap = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) = $true) | ~ (((X158 @ X160)) = $true)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) = $true) | ~ ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | ~ (((X157 @ id @ X163 @ id)) = $true)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | ~ (((X173 @ id @ X175 @ id)) = $true)) | ~ ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) = $true) | ~ (((X173 @ id @ X177 @ id)) = $true)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ~ ! [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) = $true) | ~ (((X181 @ id @ X183 @ id)) = $true)) | ~ ! [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) = $true) | ~ ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | ~ (((X181 @ id @ X185 @ id)) = $true)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) = $true) | ~ (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) = $true) | ~ (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true)))))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | ~ (((X199 @ X201)) = $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | ~ (((X234 @ X236)) = $true)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | ~ (((X233 @ id @ X239 @ id)) = $true)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | ~ (((X260 @ X262)) = $true) | ~ (((X260 @ X261)) = $true) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) = $true) | ~ (((X259 @ id @ X265 @ id)) = $true) | ~ (((X259 @ id @ X264 @ id)) = $true)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) = $true) | ~ (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) = $true) | ~ (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) = $true) | ~ (((X274 @ id @ X276 @ id)) = $true)) | ~ ! [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | ~ (((X274 @ id @ X278 @ id)) = $true)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | ~ (((X283 @ id @ X285 @ id)) = $true)) | ~ ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ~ ! [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) = $true) | ~ (((X283 @ id @ X287 @ id)) = $true)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ~ ! [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) = $true) | ~ (((X291 @ id @ X293 @ id)) = $true)) | ~ ! [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | ~ (((X291 @ id @ X295 @ id)) = $true)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ~ ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | ~ (((X299 @ X301)) = $true)) | ~ ! [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) = $true) | ~ (((X299 @ X303)) = $true) | ~ (((X299 @ X302)) = $true)) | ~ ! [X304 : term] : ((((X299 @ X304)) = $true) | ~ (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ~ ! [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) = $true) | ~ ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | ~ (((X307 @ id @ X310 @ id)) = $true)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) = $true) | ~ (((X307 @ id @ X315 @ id)) = $true) | ~ (((X307 @ id @ X314 @ id)) = $true)) | ~ ! [X316 : term] : ((((X307 @ id @ X316 @ id)) = $true) | ~ (((var @ (sub @ X316 @ id))) = $true)) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) = $true) | ~ (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) = $true) | ~ (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | ~ (((X330 @ X332)) = $true)))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | ~ (((X337 @ id @ X339 @ id)) = $true) | ~ (((X337 @ id @ X338 @ id)) = $true) | ~ ! [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) = $true) | ~ (((X337 @ id @ X341 @ id)) = $true) | ~ (((X337 @ id @ X340 @ id)) = $true)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) = $true) | ~ (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) = $true) | ~ (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ~ ! [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) = $true) | ~ (((X350 @ id @ X352 @ id)) = $true)) | ~ ! [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | ~ (((X350 @ id @ X354 @ id)) = $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) = $true) | ~ (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) = $true) | ~ (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) = $true) | ~ (((X366 @ id @ X368 @ id)) = $true)) | ~ ! [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | ~ (((X366 @ id @ X370 @ id)) = $true)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) = $true) | ~ (((X374 @ id @ X376 @ id)) = $true)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | ~ (((X374 @ id @ X385 @ id)) = $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) = $true) | ~ ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ~ ! [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) = $true) | ~ (((X399 @ X402)) = $true))) | ~ ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | ~ (((X399 @ X404)) = $true) | ~ (((X399 @ X403)) = $true)) | ~ ! [X405 : term] : ((((X399 @ X405)) = $true) | ~ (((var @ X405)) = $true))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | ~ (((X408 @ X410)) = $true)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) = $true) | ~ (((X407 @ id @ X413 @ id)) = $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ~ ! [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | ~ (((X417 @ id @ X420 @ id)) = $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) = $true) | ~ (((X417 @ id @ X425 @ id)) = $true) | ~ (((X417 @ id @ X424 @ id)) = $true)))))))) & ((hoasinduction_lthm = $true) <=> (! [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) = $true) | ~ ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ~ ! [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) = $true) | ~ (((X426 @ X429)) = $true))) | ~ ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | ~ (((X426 @ X431)) = $true) | ~ (((X426 @ X430)) = $true)) | ~ ! [X432 : term] : ((((X426 @ X432)) = $true) | ~ (((var @ X432)) = $true))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) = $true) | ~ (((X433 @ id @ X435 @ id)) = $true) | ~ (((X433 @ id @ X434 @ id)) = $true) | ~ ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | ~ (((X433 @ id @ X437 @ id)) = $true) | ~ (((X433 @ id @ X436 @ id)) = $true)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | ~ (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) = $true)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | ~ (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) = $true))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) = $true) | ~ ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | ~ (((X446 @ id @ X448 @ id)) = $true)) | ~ ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) = $true) | ~ (((X446 @ id @ X450 @ id)) = $true)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | ~ (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) = $true)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | ~ (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) = $true))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ~ ! [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | ~ (((X462 @ id @ X465 @ id)) = $true)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) = $true) | ~ (((X462 @ id @ X470 @ id)) = $true) | ~ (((X462 @ id @ X469 @ id)) = $true)) | ~ ! [X471 : term] : ((((X462 @ id @ X471 @ id)) = $true) | ~ (((var @ (sub @ X471 @ id))) = $true)) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) = $true) | ~ (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) = $true) | ~ (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) = $true) | ~ ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | ~ (((X489 @ X491)) = $true)) | ~ ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | ~ (((X489 @ X493)) = $true) | ~ (((X489 @ X492)) = $true)) | ~ ! [X494 : term] : ((((X489 @ X494)) = $true) | ~ (((var @ X494)) = $true))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ~ ! [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) = $true) | ~ (((var @ X498)) = $true)) | ~ ! [X499 : term] : ((((X495 @ (lam @ X499))) = $true) | ~ ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | ~ (((X495 @ X500)) = $true))) | ~ ! [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) = $true) | ~ (((X495 @ X502)) = $true) | ~ (((X495 @ X501)) = $true)))))))) & ~ (ulamvar1 = $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ~ ! [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) = $true) | ~ (((var @ X518)) = $true)) | ~ ! [X519 : term] : ((((X515 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | ~ (((X515 @ X520)) = $true))) | ~ ! [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) = $true) | ~ (((X515 @ X522)) = $true) | ~ (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | ~ (((X525 @ X527)) = $true))) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X540 : d_subst,X541 : d_subst] : ((((d2subst @ X540)) = ((d2subst @ X541))) => (X540 = X541)) & ! [X542 : d_subst] : (d_id = X542) & ! [X543 : subst] : ? [X544 : d_subst] : (((d2subst @ X544)) = X543) & ! [X545 : d_term,X546 : d_term] : ((((d2term @ X545)) = ((d2term @ X546))) => (X545 = X546)) & ! [X547 : d_term] : (d_one = X547) & ! [X548 : term] : ? [X549 : d_term] : (((d2term @ X549)) = X548)),
% 17.66/3.02 inference(fool_elimination,[],[f4])).
% 17.66/3.02 thf(f6,plain,(
% 17.66/3.02 ~ (hoasinduction_lem3v2a = ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X2 : (subst > term > term)] : (! [X3 : subst,X4 : term,X5 : subst] : (((sub @ (X2 @ X3 @ X4) @ X5)) = ((X2 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) => (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (X2 @ id @ X6) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X7 : subst, X8 : term] : ((X2 @ X7 @ X8)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X9 : term] : (! [X10 : term] : ((X1 @ X10) => (X1 @ (sub @ X9 @ (push @ X10 @ id)))) => (X1 @ (lam @ X9))))))),
% 17.66/3.02 inference(rectify,[],[f3])).
% 17.66/3.02 thf(f7,plain,(
% 17.66/3.02 ~ (hoasinduction_lem3v2a = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ (comp @ Y5 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2)))))))))))))),
% 17.66/3.02 inference(fool_elimination,[],[f6])).
% 17.66/3.02 thf(f8,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | ~ (((X3 @ X6)) = $true))) | ~ ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | ~ (((X3 @ X8)) = $true) | ~ (((X3 @ X7)) = $true)) | ~ ! [X9 : term] : ((((X3 @ X9)) = $true) | ~ (((var @ X9)) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) = $true) | ~ ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | ~ (((X12 @ X14)) = $true)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) = $true) | ~ (((X11 @ id @ X17 @ id)) = $true)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | ~ (((X21 @ id @ X29 @ id)) = $true) | ~ (((X21 @ id @ X28 @ id)) = $true)) | ~ ! [X30 : term] : ((((X21 @ id @ X30 @ id)) = $true) | ~ (((var @ (sub @ X30 @ id))) = $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) = $true) | ~ (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) = $true) | ~ (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true)))))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ~ ! [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) = $true) | ~ (((X42 @ X44)) = $true)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | ~ (((X41 @ id @ X47 @ id)) = $true)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) = $true) | ~ (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) = $true) | ~ (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ~ ! [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) = $true) | ~ (((X68 @ X70)) = $true)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | ~ (((X67 @ id @ X73 @ id)) = $true)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) = $true) | ~ (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) = $true) | ~ (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | ~ (((X89 @ X91)) = $true))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X96 : term] : ((((X94 @ (lam @ X96))) = $true) | ~ ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | ~ (((X94 @ X97)) = $true))) | ~ ! [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) = $true) | ~ (((X94 @ X99)) = $true) | ~ (((X94 @ X98)) = $true)) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | ~ (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ~ ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ~ ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | ~ (((X107 @ id @ X110 @ id)) = $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) = $true) | ~ (((X107 @ id @ X115 @ id)) = $true) | ~ (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ~ ! [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) = $true) | ~ (((X116 @ id @ X118 @ id)) = $true)) | ~ ! [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) = $true) | ~ ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | ~ (((X116 @ id @ X120 @ id)) = $true)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) = $true) | ~ ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | ~ (((var @ X139)) = $true)) | ~ ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ~ ! [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ~ (((X136 @ X141)) = $true))) | ~ ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | ~ (((X136 @ X143)) = $true) | ~ (((X136 @ X142)) = $true))) => ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ~ ! [X146 : term] : ((((X144 @ (lam @ X146))) = $true) | ~ ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | ~ (((X144 @ X147)) = $true))) | ~ ! [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) = $true) | ~ (((X144 @ X149)) = $true) | ~ (((X144 @ X148)) = $true)) | ~ ! [X150 : term] : ((((X144 @ X150)) = $true) | ~ (((var @ X150)) = $true)))))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ~ (lamnotap = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) = $true) | ~ (((X158 @ X160)) = $true)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) = $true) | ~ ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | ~ (((X157 @ id @ X163 @ id)) = $true)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | ~ (((X173 @ id @ X175 @ id)) = $true)) | ~ ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) = $true) | ~ (((X173 @ id @ X177 @ id)) = $true)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ~ ! [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) = $true) | ~ (((X181 @ id @ X183 @ id)) = $true)) | ~ ! [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) = $true) | ~ ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | ~ (((X181 @ id @ X185 @ id)) = $true)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) = $true) | ~ (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) = $true) | ~ (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true)))))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | ~ (((X199 @ X201)) = $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | ~ (((X234 @ X236)) = $true)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | ~ (((X233 @ id @ X239 @ id)) = $true)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | ~ (((X260 @ X262)) = $true) | ~ (((X260 @ X261)) = $true) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) = $true) | ~ (((X259 @ id @ X265 @ id)) = $true) | ~ (((X259 @ id @ X264 @ id)) = $true)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) = $true) | ~ (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) = $true) | ~ (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) = $true) | ~ (((X274 @ id @ X276 @ id)) = $true)) | ~ ! [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | ~ (((X274 @ id @ X278 @ id)) = $true)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | ~ (((X283 @ id @ X285 @ id)) = $true)) | ~ ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ~ ! [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) = $true) | ~ (((X283 @ id @ X287 @ id)) = $true)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ~ ! [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) = $true) | ~ (((X291 @ id @ X293 @ id)) = $true)) | ~ ! [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | ~ (((X291 @ id @ X295 @ id)) = $true)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ~ ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | ~ (((X299 @ X301)) = $true)) | ~ ! [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) = $true) | ~ (((X299 @ X303)) = $true) | ~ (((X299 @ X302)) = $true)) | ~ ! [X304 : term] : ((((X299 @ X304)) = $true) | ~ (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ~ ! [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) = $true) | ~ ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | ~ (((X307 @ id @ X310 @ id)) = $true)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) = $true) | ~ (((X307 @ id @ X315 @ id)) = $true) | ~ (((X307 @ id @ X314 @ id)) = $true)) | ~ ! [X316 : term] : ((((X307 @ id @ X316 @ id)) = $true) | ~ (((var @ (sub @ X316 @ id))) = $true)) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) = $true) | ~ (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) = $true) | ~ (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | ~ (((X330 @ X332)) = $true)))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | ~ (((X337 @ id @ X339 @ id)) = $true) | ~ (((X337 @ id @ X338 @ id)) = $true) | ~ ! [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) = $true) | ~ (((X337 @ id @ X341 @ id)) = $true) | ~ (((X337 @ id @ X340 @ id)) = $true)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) = $true) | ~ (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) = $true) | ~ (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ~ ! [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) = $true) | ~ (((X350 @ id @ X352 @ id)) = $true)) | ~ ! [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | ~ (((X350 @ id @ X354 @ id)) = $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) = $true) | ~ (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) = $true) | ~ (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) = $true) | ~ (((X366 @ id @ X368 @ id)) = $true)) | ~ ! [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | ~ (((X366 @ id @ X370 @ id)) = $true)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) = $true) | ~ (((X374 @ id @ X376 @ id)) = $true)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | ~ (((X374 @ id @ X385 @ id)) = $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) = $true) | ~ ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ~ ! [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) = $true) | ~ (((X399 @ X402)) = $true))) | ~ ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | ~ (((X399 @ X404)) = $true) | ~ (((X399 @ X403)) = $true)) | ~ ! [X405 : term] : ((((X399 @ X405)) = $true) | ~ (((var @ X405)) = $true))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | ~ (((X408 @ X410)) = $true)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) = $true) | ~ (((X407 @ id @ X413 @ id)) = $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ~ ! [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | ~ (((X417 @ id @ X420 @ id)) = $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) = $true) | ~ (((X417 @ id @ X425 @ id)) = $true) | ~ (((X417 @ id @ X424 @ id)) = $true)))))))) & ((hoasinduction_lthm = $true) <=> (! [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) = $true) | ~ ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ~ ! [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) = $true) | ~ (((X426 @ X429)) = $true))) | ~ ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | ~ (((X426 @ X431)) = $true) | ~ (((X426 @ X430)) = $true)) | ~ ! [X432 : term] : ((((X426 @ X432)) = $true) | ~ (((var @ X432)) = $true))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) = $true) | ~ (((X433 @ id @ X435 @ id)) = $true) | ~ (((X433 @ id @ X434 @ id)) = $true) | ~ ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | ~ (((X433 @ id @ X437 @ id)) = $true) | ~ (((X433 @ id @ X436 @ id)) = $true)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | ~ (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) = $true)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | ~ (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) = $true))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) = $true) | ~ ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | ~ (((X446 @ id @ X448 @ id)) = $true)) | ~ ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) = $true) | ~ (((X446 @ id @ X450 @ id)) = $true)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | ~ (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) = $true)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | ~ (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) = $true))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ~ ! [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | ~ (((X462 @ id @ X465 @ id)) = $true)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) = $true) | ~ (((X462 @ id @ X470 @ id)) = $true) | ~ (((X462 @ id @ X469 @ id)) = $true)) | ~ ! [X471 : term] : ((((X462 @ id @ X471 @ id)) = $true) | ~ (((var @ (sub @ X471 @ id))) = $true)) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) = $true) | ~ (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) = $true) | ~ (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) = $true) | ~ ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | ~ (((X489 @ X491)) = $true)) | ~ ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | ~ (((X489 @ X493)) = $true) | ~ (((X489 @ X492)) = $true)) | ~ ! [X494 : term] : ((((X489 @ X494)) = $true) | ~ (((var @ X494)) = $true))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ~ ! [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) = $true) | ~ (((var @ X498)) = $true)) | ~ ! [X499 : term] : ((((X495 @ (lam @ X499))) = $true) | ~ ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | ~ (((X495 @ X500)) = $true))) | ~ ! [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) = $true) | ~ (((X495 @ X502)) = $true) | ~ (((X495 @ X501)) = $true)))))))) & ~ (ulamvar1 = $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ~ ! [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) = $true) | ~ (((var @ X518)) = $true)) | ~ ! [X519 : term] : ((((X515 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | ~ (((X515 @ X520)) = $true))) | ~ ! [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) = $true) | ~ (((X515 @ X522)) = $true) | ~ (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | ~ (((X525 @ X527)) = $true))) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((((d2subst @ X530)) = ((d2subst @ X531))) => (X530 = X531)) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((((d2term @ X535)) = ((d2term @ X536))) => (X535 = X536)) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(rectify,[],[f5])).
% 17.66/3.02 thf(f9,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | (((X3 @ X6)) != $true))) | ~ ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)) | ~ ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) = $true) | ~ ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) = $true) | (((X11 @ id @ X17 @ id)) != $true)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | (((X21 @ id @ X29 @ id)) != $true) | (((X21 @ id @ X28 @ id)) != $true)) | ~ ! [X30 : term] : ((((X21 @ id @ X30 @ id)) = $true) | (((var @ (sub @ X30 @ id))) != $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) = $true) | (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) != $true)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) = $true) | (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) != $true)))))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ~ ! [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) = $true) | (((X42 @ X44)) != $true)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) = $true) | (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) != $true)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) = $true) | (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) != $true))))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ~ ! [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) = $true) | (((X68 @ X70)) != $true)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) = $true) | (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) != $true)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) = $true) | (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) != $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X96 : term] : ((((X94 @ (lam @ X96))) = $true) | ~ ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ~ ! [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) = $true) | (((X94 @ X99)) != $true) | (((X94 @ X98)) != $true)) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | (((var @ X100)) != $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ~ ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ~ ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) = $true) | (((X107 @ id @ X115 @ id)) != $true) | (((X107 @ id @ X114 @ id)) != $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ~ ! [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) = $true) | (((X116 @ id @ X118 @ id)) != $true)) | ~ ! [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) = $true) | ~ ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) = $true) | ~ ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) | ~ ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ~ ! [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | (((X136 @ X141)) != $true))) | ~ ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true))) => ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ~ ! [X146 : term] : ((((X144 @ (lam @ X146))) = $true) | ~ ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ~ ! [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) = $true) | (((X144 @ X149)) != $true) | (((X144 @ X148)) != $true)) | ~ ! [X150 : term] : ((((X144 @ X150)) = $true) | (((var @ X150)) != $true)))))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) = $true) | (((X158 @ X160)) != $true)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) = $true) | ~ ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) | ~ ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) = $true) | (((X173 @ id @ X177 @ id)) != $true)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ~ ! [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) = $true) | (((X181 @ id @ X183 @ id)) != $true)) | ~ ! [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) = $true) | ~ ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) = $true) | (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) != $true)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) = $true) | (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) != $true)))))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | (((X234 @ X236)) != $true)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) = $true) | (((X259 @ id @ X265 @ id)) != $true) | (((X259 @ id @ X264 @ id)) != $true)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) = $true) | (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) != $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) = $true) | (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) != $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) = $true) | (((X274 @ id @ X276 @ id)) != $true)) | ~ ! [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) | ~ ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ~ ! [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) = $true) | (((X283 @ id @ X287 @ id)) != $true)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ~ ! [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) = $true) | (((X291 @ id @ X293 @ id)) != $true)) | ~ ! [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ~ ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | (((X299 @ X301)) != $true)) | ~ ! [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) = $true) | (((X299 @ X303)) != $true) | (((X299 @ X302)) != $true)) | ~ ! [X304 : term] : ((((X299 @ X304)) = $true) | (((var @ X304)) != $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ~ ! [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) = $true) | ~ ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) = $true) | (((X307 @ id @ X315 @ id)) != $true) | (((X307 @ id @ X314 @ id)) != $true)) | ~ ! [X316 : term] : ((((X307 @ id @ X316 @ id)) = $true) | (((var @ (sub @ X316 @ id))) != $true)) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) = $true) | (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) != $true)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) = $true) | (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) != $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ~ ! [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) = $true) | (((X337 @ id @ X341 @ id)) != $true) | (((X337 @ id @ X340 @ id)) != $true)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) = $true) | (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) != $true)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) = $true) | (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) != $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ~ ! [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) = $true) | (((X350 @ id @ X352 @ id)) != $true)) | ~ ! [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) = $true) | (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) != $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) = $true) | (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) != $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) = $true) | (((X366 @ id @ X368 @ id)) != $true)) | ~ ! [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) = $true) | (((X374 @ id @ X376 @ id)) != $true)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) = $true) | ~ ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ~ ! [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) = $true) | (((X399 @ X402)) != $true))) | ~ ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)) | ~ ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) = $true) | (((X407 @ id @ X413 @ id)) != $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ~ ! [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) = $true) | (((X417 @ id @ X425 @ id)) != $true) | (((X417 @ id @ X424 @ id)) != $true)))))))) & ((hoasinduction_lthm = $true) <=> (! [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) = $true) | ~ ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ~ ! [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) = $true) | (((X426 @ X429)) != $true))) | ~ ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)) | ~ ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) = $true) | (((X433 @ id @ X435 @ id)) != $true) | (((X433 @ id @ X434 @ id)) != $true) | ~ ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) = $true) | ~ ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) | ~ ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) = $true) | (((X446 @ id @ X450 @ id)) != $true)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ~ ! [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) = $true) | (((X462 @ id @ X470 @ id)) != $true) | (((X462 @ id @ X469 @ id)) != $true)) | ~ ! [X471 : term] : ((((X462 @ id @ X471 @ id)) = $true) | (((var @ (sub @ X471 @ id))) != $true)) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) = $true) | (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) != $true)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) = $true) | (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) != $true))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) = $true) | ~ ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) | ~ ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)) | ~ ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ~ ! [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) = $true) | (((var @ X498)) != $true)) | ~ ! [X499 : term] : ((((X495 @ (lam @ X499))) = $true) | ~ ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ~ ! [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) = $true) | (((X495 @ X502)) != $true) | (((X495 @ X501)) != $true)))))))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ~ ! [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) = $true) | (((var @ X518)) != $true)) | ~ ! [X519 : term] : ((((X515 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ~ ! [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) = $true) | (((X515 @ X522)) != $true) | (((X515 @ X521)) != $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((((d2subst @ X530)) = ((d2subst @ X531))) => (X530 = X531)) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((((d2term @ X535)) = ((d2term @ X536))) => (X535 = X536)) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(flattening,[],[f8])).
% 17.66/3.02 thf(f10,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ (comp @ Y5 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2)))))))))))))),
% 17.66/3.02 inference(flattening,[],[f7])).
% 17.66/3.02 thf(f11,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) <=> ((((! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ? [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ X28 @ id)) = $true)) | ? [X30 : term] : ((((X21 @ id @ X30 @ id)) != $true) & (((var @ (sub @ X30 @ id))) = $true)) | ? [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) != $true) & (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ? [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) != $true) & (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true))) | ? [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) != $true) & ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) & ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true)) | ? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) != ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20))))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) != $true) & ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ? [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) != $true) & (((X3 @ X6)) = $true))) & ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)) & ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true)))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ? [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) != $true) & (((X42 @ X44)) = $true)) | ? [X45 : term] : (((X42 @ X45)) != ((X41 @ id @ X45 @ id))) | ? [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) != $true) & ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) & ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ? [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) != $true) & (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ? [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) != $true) & (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))) | ? [X40 : term] : (((sub @ X40 @ id)) != X40))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ? [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) != $true) & (((X68 @ X70)) = $true)) | ? [X71 : term] : (((X68 @ X71)) != ((X67 @ id @ X71 @ id))) | ? [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) != $true) & ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) & ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ? [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) != $true) & (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) != $true) & (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> ((! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88)) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ? [X96 : term] : ((((X94 @ (lam @ X96))) != $true) & ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ? [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) != $true) & (((X94 @ X99)) = $true) & (((X94 @ X98)) = $true)) | ? [X100 : term] : ((((X94 @ X100)) != $true) & (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ? [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) != $true) & (((X107 @ id @ X115 @ id)) = $true) & (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ? [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) != $true) & (((X116 @ id @ X118 @ id)) = $true)) | ? [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) != $true) & ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) & ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129)) | ? [X128 : subst] : (((comp @ id @ X128)) != X128))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> ((! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ? [X146 : term] : ((((X144 @ (lam @ X146))) != $true) & ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ? [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) != $true) & (((X144 @ X149)) = $true) & (((X144 @ X148)) = $true)) | ? [X150 : term] : ((((X144 @ X150)) != $true) & (((var @ X150)) = $true))) | ? [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) != $true) & ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) & ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ? [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) != $true) & (((X136 @ X141)) = $true))) & ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true)))) | ? [X135 : term] : (((sub @ X135 @ id)) != X135))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ? [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) != $true) & (((X158 @ X160)) = $true)) | ? [X161 : term] : (((X158 @ X161)) != ((X157 @ id @ X161 @ id))) | ? [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) != $true) & ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166)))))) | ? [X156 : term] : (((sub @ X156 @ id)) != X156)) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ? [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) != $true) & (((X181 @ id @ X183 @ id)) = $true)) | ? [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) != $true) & ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) & ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ? [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) != $true) & (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ? [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) != $true) & (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true))) | ? [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) != $true) & ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) & ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) != $true) & (((X173 @ id @ X177 @ id)) = $true)) | ? [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) != ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180))))))) | ? [X172 : term] : (((sub @ X172 @ id)) != X172))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (((! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))) | ? [X212 : term,X213 : term] : ((X212 != X213) & (((lam @ X212)) = ((lam @ X213))))) | ? [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) != X211)) | ? [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) != X208))) & ((hoasapinj1_lthm = $true) <=> ((! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228))))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ? [X263 : term] : (((X260 @ X263)) != ((X259 @ id @ X263 @ id))) | ? [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) != $true) & (((X259 @ id @ X265 @ id)) = $true) & (((X259 @ id @ X264 @ id)) = $true)) | ? [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) != $true) & (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ? [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) != $true) & (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ? [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) != $true) & (((X274 @ id @ X276 @ id)) = $true)) | ? [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true) & ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) & ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ? [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) != $true) & (((X291 @ id @ X293 @ id)) = $true)) | ? [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) & ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298)))))) | ? [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) != $true) & ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) & ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ? [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) != $true) & (((X283 @ id @ X287 @ id)) = $true)) | ? [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) != ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))))))) | ? [X282 : term] : (((sub @ X282 @ id)) != X282))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ? [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) != $true) & (((X299 @ X303)) = $true) & (((X299 @ X302)) = $true)) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ? [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) != $true) & ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) & ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ? [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) != $true) & (((X307 @ id @ X315 @ id)) = $true) & (((X307 @ id @ X314 @ id)) = $true)) | ? [X316 : term] : ((((X307 @ id @ X316 @ id)) != $true) & (((var @ (sub @ X316 @ id))) = $true)) | ? [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) != $true) & (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ? [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) != $true) & (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ? [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) != $true) & (((X337 @ id @ X341 @ id)) = $true) & (((X337 @ id @ X340 @ id)) = $true)) | ? [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) != $true) & (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ? [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) != $true) & (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ? [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) != $true) & (((X350 @ id @ X352 @ id)) = $true)) | ? [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true) & ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) & ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ? [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) != $true) & (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ? [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) != $true) & (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) != $true) & (((X366 @ id @ X368 @ id)) = $true)) | ? [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) & ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ? [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) != $true) & (((X374 @ id @ X376 @ id)) = $true)) | ? [X377 : (subst > term > term),X378 : term] : (! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) & ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) & (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true) & ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ? [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) != $true) & ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) & ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ? [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) != $true) & (((X417 @ id @ X425 @ id)) = $true) & (((X417 @ id @ X424 @ id)) = $true))) | ? [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) != $true) & ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) & ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) & ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ? [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) != $true) & (((X407 @ id @ X413 @ id)) = $true)) | ? [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) != ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416))))))) | ? [X406 : term] : (((sub @ X406 @ id)) != X406)) | ? [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) != $true) & ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ? [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) != $true) & (((X399 @ X402)) = $true))) & ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)) & ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true)))) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))))) & ((hoasinduction_lthm = $true) <=> (((! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ? [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) != $true) & ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ? [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) != $true) & (((X462 @ id @ X470 @ id)) = $true) & (((X462 @ id @ X469 @ id)) = $true)) | ? [X471 : term] : ((((X462 @ id @ X471 @ id)) != $true) & (((var @ (sub @ X471 @ id))) = $true)) | ? [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) != $true) & (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ? [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) != $true) & (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))) | ? [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) != $true) & ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) & ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ? [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) != $true) & (((X446 @ id @ X450 @ id)) = $true)) | ? [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) != ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) & ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) & ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true)))) | ? [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) != $true) & (((X433 @ id @ X435 @ id)) = $true) & (((X433 @ id @ X434 @ id)) = $true) & ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)) & ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) & ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true)))) | ? [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) != $true) & ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ? [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) != $true) & (((X426 @ X429)) = $true))) & ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)) & ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ? [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) != $true) & (((var @ X498)) = $true)) | ? [X499 : term] : ((((X495 @ (lam @ X499))) != $true) & ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ? [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) != $true) & (((X495 @ X502)) = $true) & (((X495 @ X501)) = $true))) | ? [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) != $true) & ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) & ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)) & ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true)))) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488)) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487)) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ? [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) != $true) & (((var @ X518)) = $true)) | ? [X519 : term] : ((((X515 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ? [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) != $true) & (((X515 @ X522)) = $true) & (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(ennf_transformation,[],[f9])).
% 17.66/3.02 thf(f12,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) <=> (! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ? [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ X28 @ id)) = $true)) | ? [X30 : term] : ((((X21 @ id @ X30 @ id)) != $true) & (((var @ (sub @ X30 @ id))) = $true)) | ? [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) != $true) & (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ? [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) != $true) & (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true))) | ? [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) != $true) & ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) & ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true)) | ? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) != ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) != $true) & ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ? [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) != $true) & (((X3 @ X6)) = $true))) & ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)) & ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ? [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) != $true) & (((X42 @ X44)) = $true)) | ? [X45 : term] : (((X42 @ X45)) != ((X41 @ id @ X45 @ id))) | ? [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) != $true) & ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) & ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ? [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) != $true) & (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ? [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) != $true) & (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))) | ? [X40 : term] : (((sub @ X40 @ id)) != X40))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ? [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) != $true) & (((X68 @ X70)) = $true)) | ? [X71 : term] : (((X68 @ X71)) != ((X67 @ id @ X71 @ id))) | ? [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) != $true) & ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) & ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ? [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) != $true) & (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) != $true) & (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ? [X96 : term] : ((((X94 @ (lam @ X96))) != $true) & ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ? [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) != $true) & (((X94 @ X99)) = $true) & (((X94 @ X98)) = $true)) | ? [X100 : term] : ((((X94 @ X100)) != $true) & (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ? [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) != $true) & (((X107 @ id @ X115 @ id)) = $true) & (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ? [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) != $true) & (((X116 @ id @ X118 @ id)) = $true)) | ? [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) != $true) & ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) & ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129) | ? [X128 : subst] : (((comp @ id @ X128)) != X128))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ? [X146 : term] : ((((X144 @ (lam @ X146))) != $true) & ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ? [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) != $true) & (((X144 @ X149)) = $true) & (((X144 @ X148)) = $true)) | ? [X150 : term] : ((((X144 @ X150)) != $true) & (((var @ X150)) = $true))) | ? [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) != $true) & ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) & ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ? [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) != $true) & (((X136 @ X141)) = $true))) & ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true))) | ? [X135 : term] : (((sub @ X135 @ id)) != X135))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ? [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) != $true) & (((X158 @ X160)) = $true)) | ? [X161 : term] : (((X158 @ X161)) != ((X157 @ id @ X161 @ id))) | ? [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) != $true) & ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166)))))) | ? [X156 : term] : (((sub @ X156 @ id)) != X156) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ? [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) != $true) & (((X181 @ id @ X183 @ id)) = $true)) | ? [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) != $true) & ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) & ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ? [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) != $true) & (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ? [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) != $true) & (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true))) | ? [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) != $true) & ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) & ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) != $true) & (((X173 @ id @ X177 @ id)) = $true)) | ? [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) != ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) | ? [X172 : term] : (((sub @ X172 @ id)) != X172))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))) | ? [X212 : term,X213 : term] : ((X212 != X213) & (((lam @ X212)) = ((lam @ X213)))) | ? [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) != X211) | ? [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) != X208))) & ((hoasapinj1_lthm = $true) <=> (! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228)))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ? [X263 : term] : (((X260 @ X263)) != ((X259 @ id @ X263 @ id))) | ? [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) != $true) & (((X259 @ id @ X265 @ id)) = $true) & (((X259 @ id @ X264 @ id)) = $true)) | ? [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) != $true) & (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ? [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) != $true) & (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ? [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) != $true) & (((X274 @ id @ X276 @ id)) = $true)) | ? [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true) & ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) & ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ? [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) != $true) & (((X291 @ id @ X293 @ id)) = $true)) | ? [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) & ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298)))))) | ? [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) != $true) & ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) & ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ? [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) != $true) & (((X283 @ id @ X287 @ id)) = $true)) | ? [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) != ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) | ? [X282 : term] : (((sub @ X282 @ id)) != X282))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ? [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) != $true) & (((X299 @ X303)) = $true) & (((X299 @ X302)) = $true)) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ? [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) != $true) & ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) & ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ? [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) != $true) & (((X307 @ id @ X315 @ id)) = $true) & (((X307 @ id @ X314 @ id)) = $true)) | ? [X316 : term] : ((((X307 @ id @ X316 @ id)) != $true) & (((var @ (sub @ X316 @ id))) = $true)) | ? [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) != $true) & (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ? [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) != $true) & (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ? [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) != $true) & (((X337 @ id @ X341 @ id)) = $true) & (((X337 @ id @ X340 @ id)) = $true)) | ? [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) != $true) & (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ? [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) != $true) & (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ? [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) != $true) & (((X350 @ id @ X352 @ id)) = $true)) | ? [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true) & ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) & ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ? [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) != $true) & (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ? [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) != $true) & (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) != $true) & (((X366 @ id @ X368 @ id)) = $true)) | ? [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) & ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ? [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) != $true) & (((X374 @ id @ X376 @ id)) = $true)) | ? [X377 : (subst > term > term),X378 : term] : (! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) & ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) & (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true) & ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ? [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) != $true) & ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) & ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ? [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) != $true) & (((X417 @ id @ X425 @ id)) = $true) & (((X417 @ id @ X424 @ id)) = $true))) | ? [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) != $true) & ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) & ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) & ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ? [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) != $true) & (((X407 @ id @ X413 @ id)) = $true)) | ? [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) != ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) | ? [X406 : term] : (((sub @ X406 @ id)) != X406) | ? [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) != $true) & ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ? [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) != $true) & (((X399 @ X402)) = $true))) & ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)) & ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true))) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))))) & ((hoasinduction_lthm = $true) <=> (! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ? [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) != $true) & ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ? [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) != $true) & (((X462 @ id @ X470 @ id)) = $true) & (((X462 @ id @ X469 @ id)) = $true)) | ? [X471 : term] : ((((X462 @ id @ X471 @ id)) != $true) & (((var @ (sub @ X471 @ id))) = $true)) | ? [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) != $true) & (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ? [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) != $true) & (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))) | ? [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) != $true) & ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) & ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ? [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) != $true) & (((X446 @ id @ X450 @ id)) = $true)) | ? [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) != ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) & ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) & ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true))) | ? [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) != $true) & (((X433 @ id @ X435 @ id)) = $true) & (((X433 @ id @ X434 @ id)) = $true) & ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)) & ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) & ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true))) | ? [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) != $true) & ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ? [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) != $true) & (((X426 @ X429)) = $true))) & ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)) & ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ? [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) != $true) & (((var @ X498)) = $true)) | ? [X499 : term] : ((((X495 @ (lam @ X499))) != $true) & ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ? [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) != $true) & (((X495 @ X502)) = $true) & (((X495 @ X501)) = $true))) | ? [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) != $true) & ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) & ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)) & ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true))) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ? [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) != $true) & (((var @ X518)) = $true)) | ? [X519 : term] : ((((X515 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ? [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) != $true) & (((X515 @ X522)) = $true) & (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(flattening,[],[f11])).
% 17.66/3.02 thf(f13,definition,(
% 17.66/3.02 ! [X515 : (term > $o)] : (($true = ((sP0 @ X515))) <=> ? [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) != $true) & (((X515 @ X522)) = $true) & (((X515 @ X521)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f14,definition,(
% 17.66/3.02 ($true = sP1) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ? [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) != $true) & (((var @ X518)) = $true)) | ? [X519 : term] : ((((X515 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ($true = ((sP0 @ X515))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f15,definition,(
% 17.66/3.02 ! [X489 : (term > $o)] : (($true = ((sP2 @ X489))) <=> ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f16,definition,(
% 17.66/3.02 ! [X495 : (term > $o)] : (($true = ((sP3 @ X495))) <=> ? [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) != $true) & (((X495 @ X502)) = $true) & (((X495 @ X501)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f17,definition,(
% 17.66/3.02 ($true = sP4) <=> ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ? [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) != $true) & (((var @ X498)) = $true)) | ? [X499 : term] : ((((X495 @ (lam @ X499))) != $true) & ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ($true = ((sP3 @ X495))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f18,definition,(
% 17.66/3.02 ($true = sP5) <=> (($true = sP4) | ? [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) != $true) & ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) & ($true = ((sP2 @ X489))) & ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true))) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f19,definition,(
% 17.66/3.02 ! [X426 : (term > $o)] : (($true = ((sP6 @ X426))) <=> ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f20,definition,(
% 17.66/3.02 ! [X433 : (subst > term > subst > $o)] : (($true = ((sP7 @ X433))) <=> ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f21,definition,(
% 17.66/3.02 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP8 @ X446))) <=> ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ? [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) != $true) & (((X446 @ id @ X450 @ id)) = $true)) | ? [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) != ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f22,definition,(
% 17.66/3.02 ! [X462 : (subst > term > subst > $o)] : (($true = ((sP9 @ X462))) <=> ? [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) != $true) & (((X462 @ id @ X470 @ id)) = $true) & (((X462 @ id @ X469 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f23,definition,(
% 17.66/3.02 ! [X462 : (subst > term > subst > $o)] : (($true = ((sP10 @ X462))) <=> ? [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) != $true) & ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f24,definition,(
% 17.66/3.02 ($true = sP11) <=> ? [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) != $true) & ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) & ($true = ((sP8 @ X446))) & ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) & ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f25,definition,(
% 17.66/3.02 ($true = sP12) <=> ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ($true = ((sP10 @ X462))) | ($true = ((sP9 @ X462))) | ? [X471 : term] : ((((X462 @ id @ X471 @ id)) != $true) & (((var @ (sub @ X471 @ id))) = $true)) | ? [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) != $true) & (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ? [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) != $true) & (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f26,definition,(
% 17.66/3.02 ($true = sP13) <=> ? [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) != $true) & ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ? [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) != $true) & (((X426 @ X429)) = $true))) & ($true = ((sP6 @ X426))) & ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f27,definition,(
% 17.66/3.02 ($true = sP14) <=> (($true = sP12) | ($true = sP11) | ? [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) != $true) & (((X433 @ id @ X435 @ id)) = $true) & (((X433 @ id @ X434 @ id)) = $true) & ($true = ((sP7 @ X433))) & ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) & ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true))) | ($true = sP13))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f28,definition,(
% 17.66/3.02 ! [X399 : (term > $o)] : (($true = ((sP15 @ X399))) <=> ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f29,definition,(
% 17.66/3.02 ! [X417 : (subst > term > subst > $o)] : (($true = ((sP16 @ X417))) <=> ? [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) != $true) & (((X417 @ id @ X425 @ id)) = $true) & (((X417 @ id @ X424 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f30,definition,(
% 17.66/3.02 ($true = sP17) <=> ? [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) != $true) & ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) & ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) & ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ? [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) != $true) & (((X407 @ id @ X413 @ id)) = $true)) | ? [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) != ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f31,definition,(
% 17.66/3.02 ($true = sP18) <=> ? [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) != $true) & ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ? [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) != $true) & (((X399 @ X402)) = $true))) & ($true = ((sP15 @ X399))) & ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f32,definition,(
% 17.66/3.02 ($true = sP19) <=> (! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ? [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) != $true) & ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) & ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ($true = ((sP16 @ X417)))) | ($true = sP17) | ? [X406 : term] : (((sub @ X406 @ id)) != X406) | ($true = sP18) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f33,definition,(
% 17.66/3.02 ($true = sP20) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ? [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) != $true) & (((X374 @ id @ X376 @ id)) = $true)) | ? [X377 : (subst > term > term),X378 : term] : (! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) & ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) & (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true) & ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f34,definition,(
% 17.66/3.02 ($true = sP21) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) != $true) & (((X366 @ id @ X368 @ id)) = $true)) | ? [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) & ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f35,definition,(
% 17.66/3.02 ! [X350 : (subst > term > subst > $o)] : (($true = ((sP22 @ X350))) <=> ? [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true) & ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) & ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f36,definition,(
% 17.66/3.02 ($true = sP23) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ? [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) != $true) & (((X350 @ id @ X352 @ id)) = $true)) | ($true = ((sP22 @ X350))) | ? [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) != $true) & (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ? [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) != $true) & (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f37,definition,(
% 17.66/3.02 ! [X337 : (subst > term > subst > $o)] : (($true = ((sP24 @ X337))) <=> ? [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) != $true) & (((X337 @ id @ X341 @ id)) = $true) & (((X337 @ id @ X340 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f38,definition,(
% 17.66/3.02 ($true = sP25) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ($true = ((sP24 @ X337))) | ? [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) != $true) & (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ? [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) != $true) & (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f39,definition,(
% 17.66/3.02 ! [X307 : (subst > term > subst > $o)] : (($true = ((sP26 @ X307))) <=> ? [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) != $true) & (((X307 @ id @ X315 @ id)) = $true) & (((X307 @ id @ X314 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f40,definition,(
% 17.66/3.02 ! [X307 : (subst > term > subst > $o)] : (($true = ((sP27 @ X307))) <=> ? [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) != $true) & ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) & ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f41,definition,(
% 17.66/3.02 ($true = sP28) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ($true = ((sP27 @ X307))) | ($true = ((sP26 @ X307))) | ? [X316 : term] : ((((X307 @ id @ X316 @ id)) != $true) & (((var @ (sub @ X316 @ id))) = $true)) | ? [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) != $true) & (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ? [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) != $true) & (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f42,definition,(
% 17.66/3.02 ! [X299 : (term > $o)] : (($true = ((sP29 @ X299))) <=> ? [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) != $true) & (((X299 @ X303)) = $true) & (((X299 @ X302)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f43,definition,(
% 17.66/3.02 ($true = sP30) <=> ? [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) != $true) & ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) & ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ? [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) != $true) & (((X283 @ id @ X287 @ id)) = $true)) | ? [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) != ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f44,definition,(
% 17.66/3.02 ($true = sP31) <=> (! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ? [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) != $true) & (((X291 @ id @ X293 @ id)) = $true)) | ? [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) & ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298)))))) | ($true = sP30) | ? [X282 : term] : (((sub @ X282 @ id)) != X282))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f45,definition,(
% 17.66/3.02 ($true = sP32) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ? [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) != $true) & (((X274 @ id @ X276 @ id)) = $true)) | ? [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true) & ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) & ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f46,definition,(
% 17.66/3.02 ! [X259 : (subst > term > subst > $o)] : (($true = ((sP33 @ X259))) <=> ? [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) != $true) & (((X259 @ id @ X265 @ id)) = $true) & (((X259 @ id @ X264 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f47,definition,(
% 17.66/3.02 ($true = sP34) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ? [X263 : term] : (((X260 @ X263)) != ((X259 @ id @ X263 @ id))) | ($true = ((sP33 @ X259))) | ? [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) != $true) & (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ? [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) != $true) & (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f48,definition,(
% 17.66/3.02 ($true = sP35) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f49,definition,(
% 17.66/3.02 ($true = sP36) <=> (! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))) | ? [X212 : term,X213 : term] : ((X212 != X213) & (((lam @ X212)) = ((lam @ X213)))) | ? [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) != X211) | ? [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) != X208))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f50,definition,(
% 17.66/3.02 ! [X181 : (subst > term > subst > $o)] : (($true = ((sP37 @ X181))) <=> ? [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) != $true) & ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) & ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f51,definition,(
% 17.66/3.02 ($true = sP38) <=> ? [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) != $true) & ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) & ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) != $true) & (((X173 @ id @ X177 @ id)) = $true)) | ? [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) != ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f52,definition,(
% 17.66/3.02 ($true = sP39) <=> (! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ? [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) != $true) & (((X181 @ id @ X183 @ id)) = $true)) | ($true = ((sP37 @ X181))) | ? [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) != $true) & (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ? [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) != $true) & (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true))) | ($true = sP38) | ? [X172 : term] : (((sub @ X172 @ id)) != X172))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f53,definition,(
% 17.66/3.02 ($true = sP40) <=> (! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ? [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) != $true) & (((X158 @ X160)) = $true)) | ? [X161 : term] : (((X158 @ X161)) != ((X157 @ id @ X161 @ id))) | ? [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) != $true) & ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166)))))) | ? [X156 : term] : (((sub @ X156 @ id)) != X156) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f54,definition,(
% 17.66/3.02 ! [X136 : (term > $o)] : (($true = ((sP41 @ X136))) <=> ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f55,definition,(
% 17.66/3.02 ! [X144 : (term > $o)] : (($true = ((sP42 @ X144))) <=> ? [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) != $true) & (((X144 @ X149)) = $true) & (((X144 @ X148)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f56,definition,(
% 17.66/3.02 ($true = sP43) <=> ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ? [X146 : term] : ((((X144 @ (lam @ X146))) != $true) & ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ($true = ((sP42 @ X144))) | ? [X150 : term] : ((((X144 @ X150)) != $true) & (((var @ X150)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f57,definition,(
% 17.66/3.02 ($true = sP44) <=> (($true = sP43) | ? [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) != $true) & ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) & ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ? [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) != $true) & (((X136 @ X141)) = $true))) & ($true = ((sP41 @ X136)))) | ? [X135 : term] : (((sub @ X135 @ id)) != X135))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f58,definition,(
% 17.66/3.02 ($true = sP45) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ? [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) != $true) & (((X116 @ id @ X118 @ id)) = $true)) | ? [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) != $true) & ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) & ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f59,definition,(
% 17.66/3.02 ! [X107 : (subst > term > subst > $o)] : (($true = ((sP46 @ X107))) <=> ? [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) != $true) & (((X107 @ id @ X115 @ id)) = $true) & (((X107 @ id @ X114 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f60,definition,(
% 17.66/3.02 ! [X94 : (term > $o)] : (($true = ((sP47 @ X94))) <=> ? [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) != $true) & (((X94 @ X99)) = $true) & (((X94 @ X98)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f61,definition,(
% 17.66/3.02 ($true = sP48) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ? [X96 : term] : ((((X94 @ (lam @ X96))) != $true) & ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ($true = ((sP47 @ X94))) | ? [X100 : term] : ((((X94 @ X100)) != $true) & (((var @ X100)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f62,definition,(
% 17.66/3.02 ! [X67 : (subst > term > subst > $o)] : (($true = ((sP49 @ X67))) <=> ? [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) != $true) & ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) & ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f63,definition,(
% 17.66/3.02 ($true = sP50) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ? [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) != $true) & (((X68 @ X70)) = $true)) | ? [X71 : term] : (((X68 @ X71)) != ((X67 @ id @ X71 @ id))) | ($true = ((sP49 @ X67))) | ? [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) != $true) & (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) != $true) & (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f64,definition,(
% 17.66/3.02 ! [X41 : (subst > term > subst > $o)] : (($true = ((sP51 @ X41))) <=> ? [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) != $true) & ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) & ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f65,definition,(
% 17.66/3.02 ($true = sP52) <=> (! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ? [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) != $true) & (((X42 @ X44)) = $true)) | ? [X45 : term] : (((X42 @ X45)) != ((X41 @ id @ X45 @ id))) | ($true = ((sP51 @ X41))) | ? [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) != $true) & (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ? [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) != $true) & (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))) | ? [X40 : term] : (((sub @ X40 @ id)) != X40))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f66,definition,(
% 17.66/3.02 ! [X3 : (term > $o)] : (($true = ((sP53 @ X3))) <=> ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f67,definition,(
% 17.66/3.02 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP54 @ X21))) <=> ? [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ X28 @ id)) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f68,definition,(
% 17.66/3.02 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP55 @ X21))) <=> ? [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f69,definition,(
% 17.66/3.02 ($true = sP56) <=> ? [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) != $true) & ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) & ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true)) | ? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) != ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20))))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f70,definition,(
% 17.66/3.02 ($true = sP57) <=> ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ($true = ((sP55 @ X21))) | ($true = ((sP54 @ X21))) | ? [X30 : term] : ((((X21 @ id @ X30 @ id)) != $true) & (((var @ (sub @ X30 @ id))) = $true)) | ? [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) != $true) & (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ? [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) != $true) & (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f71,definition,(
% 17.66/3.02 ($true = sP58) <=> (($true = sP57) | ($true = sP56) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) != $true) & ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ? [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) != $true) & (((X3 @ X6)) = $true))) & ($true = ((sP53 @ X3))) & ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 17.66/3.02 thf(f72,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) <=> ($true = sP58)) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> ($true = sP52)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP50)) & ((pushprop_lem1_lthm = $true) <=> (! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ($true = sP48)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ($true = ((sP46 @ X107))))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP45)) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129) | ? [X128 : subst] : (((comp @ id @ X128)) != X128))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> ($true = sP44)) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ($true = sP40)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> ($true = sP39)) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> ($true = sP36)) & ((hoasapinj1_lthm = $true) <=> (! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228)))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224))) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP35)) & ((hoasapinj2_lthm = $true) <=> (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP34)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ($true = sP32)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ($true = sP31)) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ($true = ((sP29 @ X299))) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ($true = sP28)) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335))) & ((hoasinduction_lem2 = $true) <=> ($true = sP25)) & ((hoasinduction_lem3 = $true) <=> ($true = sP23)) & ((hoasinduction_lem3aa_lthm = $true) <=> ($true = sP21)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP20)) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP19)) & ((hoasinduction_lthm = $true) <=> ($true = sP14)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> ($true = sP5)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ($true = sP1)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 17.66/3.02 thf(f148,plain,(
% 17.66/3.02 (($true = sP35) | ? [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) != $true) & ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | (((X234 @ X236)) != $true)) & ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) & ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ? [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) != $true) & (((X233 @ id @ X239 @ id)) = $true)) | ? [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) != ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & (! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242)))))) | ($true != sP35))),
% 17.66/3.02 inference(nnf_transformation,[],[f48])).
% 17.66/3.02 thf(f149,plain,(
% 17.66/3.02 (($true = sP35) | ? [X0 : (subst > term > subst > $o),X1 : (term > $o),X2 : term] : (($true != ((X1 @ (lam @ X2)))) & ! [X3 : term] : (($true = ((X1 @ (sub @ X2 @ (push @ X3 @ id))))) | ($true != ((X1 @ X3)))) & ! [X4 : term] : (((X0 @ id @ X4 @ id)) = ((X1 @ X4))) & ! [X5 : (subst > term > term)] : (($true = ((X0 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | ? [X6 : term] : (($true != ((X0 @ id @ (X5 @ id @ X6) @ id))) & ($true = ((X0 @ id @ X6 @ id)))) | ? [X7 : subst,X8 : term,X9 : subst] : (((sub @ (X5 @ X7 @ X8) @ X9)) != ((X5 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))))))) & (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X12 : term] : (($true = ((X11 @ (lam @ X12)))) | ? [X13 : term] : (($true != ((X11 @ (sub @ X12 @ (push @ X13 @ id))))) & ($true = ((X11 @ X13)))) | ? [X14 : term] : (((X11 @ X14)) != ((X10 @ id @ X14 @ id))) | ? [X15 : (subst > term > term)] : (($true != ((X10 @ id @ (lam @ (X15 @ sh @ one)) @ id))) & ! [X16 : term] : (($true = ((X10 @ id @ (X15 @ id @ X16) @ id))) | ($true != ((X10 @ id @ X16 @ id)))) & ! [X17 : subst,X18 : term,X19 : subst] : (((sub @ (X15 @ X17 @ X18) @ X19)) = ((X15 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))))) | ($true != sP35))),
% 17.66/3.02 inference(rectify,[],[f148])).
% 17.66/3.02 thf(f150,plain,(
% 17.66/3.02 (($true = sP35) | (($true != ((sK225 @ (lam @ sK226)))) & ! [X3 : term] : (($true = ((sK225 @ (sub @ sK226 @ (push @ X3 @ id))))) | ($true != ((sK225 @ X3)))) & ! [X4 : term] : (((sK224 @ id @ X4 @ id)) = ((sK225 @ X4))) & ! [X5 : (subst > term > term)] : (($true = ((sK224 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | (($true != ((sK224 @ id @ (X5 @ id @ (sK227 @ X5)) @ id))) & ($true = ((sK224 @ id @ (sK227 @ X5) @ id)))) | (((sub @ (X5 @ (sK228 @ X5) @ (sK229 @ X5)) @ (sK230 @ X5))) != ((X5 @ (comp @ (sK228 @ X5) @ (sK230 @ X5)) @ (sub @ (sK229 @ X5) @ (sK230 @ X5)))))))) & (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X12 : term] : (($true = ((X11 @ (lam @ X12)))) | (($true != ((X11 @ (sub @ X12 @ (push @ (sK231 @ X12 @ X11) @ id))))) & ($true = ((X11 @ (sK231 @ X12 @ X11))))) | (((X11 @ (sK232 @ X11 @ X10))) != ((X10 @ id @ (sK232 @ X11 @ X10) @ id))) | (($true != ((X10 @ id @ (lam @ (sK233 @ X10 @ sh @ one)) @ id))) & ! [X16 : term] : (($true = ((X10 @ id @ (sK233 @ X10 @ id @ X16) @ id))) | ($true != ((X10 @ id @ X16 @ id)))) & ! [X17 : subst,X18 : term,X19 : subst] : (((sub @ (sK233 @ X10 @ X17 @ X18) @ X19)) = ((sK233 @ X10 @ (comp @ X17 @ X19) @ (sub @ X18 @ X19)))))) | ($true != sP35))),
% 17.66/3.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK224,sK225,sK226,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK224),skolemize(X1,sK225),skolemize(X2,sK226),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16)],[f149])).
% 17.66/3.02 thf(f260,plain,(
% 17.66/3.02 (((hoasinduction_lthm_3 = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lthm_3 != $true))) & (((axvarid = $true) | ? [X39 : term] : (((sub @ X39 @ id)) != X39)) & (! [X39 : term] : (((sub @ X39 @ id)) = X39) | (axvarid != $true))) & (((hoasinduction_lem3v2_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2_lthm != $true))) & (hoasapnotvar_lthm = $true) & (((pushprop_lem0_lthm = $true) | ? [X59 : (term > $o),X60 : term,X61 : subst] : ! [X62 : (term > $o)] : ? [X63 : term] : (((X62 @ X63)) != ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & (! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61))))) | (pushprop_lem0_lthm != $true))) & (((termmset = $true) | ? [X64 : term] : (((sub @ X64 @ id)) != X64)) & (! [X64 : term] : (((sub @ X64 @ id)) = X64) | (termmset != $true))) & (((axshiftcons = $true) | ? [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) != X66)) & (! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66) | (axshiftcons != $true))) & (((hoasinduction_lem3v2 = $true) | ($true != sP50)) & (($true = sP50) | (hoasinduction_lem3v2 != $true))) & (((pushprop_lem1_lthm = $true) | (? [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) != $true) & (((X89 @ X91)) = $true)) & ! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) & ! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85))) & ((! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85)) | (pushprop_lem1_lthm != $true))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & (((induction2 = $true) | ($true != sP48)) & (($true = sP48) | (induction2 != $true))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (((hoaslamnotap = $true) | ? [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) = ((ap @ (sub @ X102 @ id) @ X103))) & ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))))) | (hoaslamnotap != $true))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) != $true) & ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ? [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) != $true) & (((X107 @ id @ X110 @ id)) = $true)) | ? [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) != ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) & ($true != ((sP46 @ X107))))) & (! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ($true = ((sP46 @ X107)))) | (hoasinduction_no_psi_cond != $true))) & (hoasinduction_lem1_gthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3a != $true))) & (lamnotvar = $true) & (((substmonoid = $true) | (? [X124 : subst] : (((comp @ X124 @ id)) != X124) | ? [X125 : subst] : (((comp @ id @ X125)) != X125))) & ((! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125)) | (substmonoid != $true))) & (((hoasinduction_lem3b = $true) | ? [X126 : term] : ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & (((substmonoid_lthm = $true) | ((? [X130 : subst] : (((comp @ X130 @ id)) != X130) | ? [X131 : subst] : (((comp @ id @ X131)) != X131)) & ! [X129 : subst] : (((comp @ X129 @ id)) = X129) & ! [X128 : subst] : (((comp @ id @ X128)) = X128))) & (((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129) | ? [X128 : subst] : (((comp @ id @ X128)) != X128)) | (substmonoid_lthm != $true))) & (((hoasinduction_lem0_lthm = $true) | ? [X132 : (subst > term > subst > $o)] : ! [X133 : (term > $o)] : ? [X134 : term] : (((X133 @ X134)) != ((X132 @ id @ X134 @ id)))) & (! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((induction2_lthm = $true) | ($true != sP44)) & (($true = sP44) | (induction2_lthm != $true))) & (hoaslaminj_gthm = $true) & (((axidl = $true) | ? [X151 : subst] : (((comp @ id @ X151)) != X151)) & (! [X151 : subst] : (((comp @ id @ X151)) = X151) | (axidl != $true))) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (((hoasinduction_lem3v2a_lthm = $true) | ($true != sP40)) & (($true = sP40) | (hoasinduction_lem3v2a_lthm != $true))) & (axabs = $true) & (pushprop_gthm = $true) & (((pushprop_lem0 = $true) | ? [X167 : (term > $o),X168 : term,X169 : subst] : ! [X170 : (term > $o)] : ? [X171 : term] : (((X170 @ X171)) != ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & (! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169))))) | (pushprop_lem0 != $true))) & (((hoasinduction_lem3_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3_lthm != $true))) & (((laminj = $true) | ? [X197 : term,X198 : term] : ((X197 != X198) & (((lam @ X197)) = ((lam @ X198))))) & (! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198)))) | (laminj != $true))) & (((pushprop_lem1 = $true) | ? [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) != $true) & (((X199 @ X201)) = $true))) & (! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true)) | (pushprop_lem1 != $true))) & (((axidr = $true) | ? [X204 : subst] : (((comp @ X204 @ id)) != X204)) & (! [X204 : subst] : (((comp @ X204 @ id)) = X204) | (axidr != $true))) & (hoasinduction_lem2v2_gthm = $true) & (((axscons = $true) | ? [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) != X205)) & (! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205) | (axscons != $true))) & (((axvarcons = $true) | ? [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) != X206)) & (! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206) | (axvarcons != $true))) & (((hoaslaminj_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoaslaminj_lthm != $true))) & (((hoasapinj1_lthm = $true) | (? [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 != X230) & (((ap @ (sub @ X229 @ id) @ X231)) = ((ap @ (sub @ X230 @ id) @ X232)))) & ! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) & ! [X224 : term] : (((sub @ X224 @ id)) = X224))) & ((! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228)))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224)) | (hoasapinj1_lthm != $true))) & (((hoasinduction_lem3v2a = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3v2a != $true))) & (((hoasapinj2_lthm = $true) | (? [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 != X250) & (((ap @ (sub @ X247 @ id) @ X249)) = ((ap @ (sub @ X248 @ id) @ X250)))) & ! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))))) & ((! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246))))) | (hoasapinj2_lthm != $true))) & (((apinj1 = $true) | ? [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 != X252) & (((ap @ X251 @ X253)) = ((ap @ X252 @ X254))))) & (! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254)))) | (apinj1 != $true))) & (((apinj2 = $true) | ? [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 != X258) & (((ap @ X255 @ X257)) = ((ap @ X256 @ X258))))) & (! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258)))) | (apinj2 != $true))) & (pushprop_lthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (((hoasinduction_lem3aa = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem3aa != $true))) & (termmset_gthm = $true) & (((hoasinduction_lem3a_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3a_lthm != $true))) & (((induction = $true) | ? [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) != $true) & ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | (((X299 @ X301)) != $true)) & ($true != ((sP29 @ X299))) & ! [X304 : term] : ((((X299 @ X304)) = $true) | (((var @ X304)) != $true)))) & (! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ($true = ((sP29 @ X299))) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true))) | (induction != $true))) & (ulamvarind = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X305 : term] : ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & (((hoasinduction = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction != $true))) & (((hoasinduction_lem0 = $true) | ? [X325 : (subst > term > subst > $o)] : ! [X326 : (term > $o)] : ? [X327 : term] : (((X326 @ X327)) != ((X325 @ id @ X327 @ id)))) & (! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id))) | (hoasinduction_lem0 != $true))) & (hoasapnotvar = $true) & (((pushprop_lem1v2_lthm = $true) | (? [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) != $true) & ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) & (((X330 @ X332)) = $true)) & ! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328))) & ((! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328)) | (pushprop_lem1v2_lthm != $true))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & (((termmset_lthm = $true) | (? [X336 : term] : (((sub @ X336 @ id)) != X336) & ! [X335 : term] : (((sub @ X335 @ id)) = X335))) & ((! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335)) | (termmset_lthm != $true))) & (((hoasinduction_lem2 = $true) | ($true != sP25)) & (($true = sP25) | (hoasinduction_lem2 != $true))) & (((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true))) & (((hoasinduction_lem3aa_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3aa_lthm != $true))) & (induction2lem_gthm = $true) & (((hoasinduction_lem3aaa = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem3aaa != $true))) & (((hoaslaminj = $true) | ? [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) != ((X387 @ X388 @ X389))) & (((lam @ (X386 @ sh @ one))) = ((lam @ (X387 @ sh @ one)))) & ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) & ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & (! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395))))) | (hoaslaminj != $true))) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_no_psi_cond_lthm != $true))) & (((hoasinduction_lthm = $true) | ($true != sP14)) & (($true = sP14) | (hoasinduction_lthm != $true))) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X480 : term] : ! [X481 : (subst > term > term)] : ? [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) != ((X481 @ X483 @ X482)))) & (! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482))) | (hoasinduction_lem3v2_f_lthm != $true))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (((induction2lem_lthm = $true) | ($true != sP5)) & (($true = sP5) | (induction2lem_lthm != $true))) & (ulamvar1 != $true) & (((hoasapinj1 = $true) | ? [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 != X504) & (((ap @ (sub @ X503 @ id) @ X505)) = ((ap @ (sub @ X504 @ id) @ X506))))) & (! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506)))) | (hoasapinj1 != $true))) & (hoasapnotvar_gthm = $true) & (((hoasapinj2 = $true) | ? [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 != X510) & (((ap @ (sub @ X507 @ id) @ X509)) = ((ap @ (sub @ X508 @ id) @ X510))))) & (! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510)))) | (hoasapinj2 != $true))) & (axvarshift = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X511 : term] : ! [X512 : (subst > term > term)] : ? [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) != ((X512 @ X514 @ X513)))) & (! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513))) | (hoasinduction_lem3v2_f != $true))) & (((induction2lem = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem != $true))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((shinj = $true) | ? [X523 : term,X524 : term] : ((X523 != X524) & (((sub @ X523 @ sh)) = ((sub @ X524 @ sh))))) & (! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh)))) | (shinj != $true))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & (((pushprop_lem1v2 = $true) | ? [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) != $true) & ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) & (((X525 @ X527)) = $true))) & (! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true)) | (pushprop_lem1v2 != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(nnf_transformation,[],[f72])).
% 17.66/3.02 thf(f261,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lthm_3 != $true)) & ((axvarid = $true) | ? [X39 : term] : (((sub @ X39 @ id)) != X39)) & (! [X39 : term] : (((sub @ X39 @ id)) = X39) | (axvarid != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X59 : (term > $o),X60 : term,X61 : subst] : ! [X62 : (term > $o)] : ? [X63 : term] : (((X62 @ X63)) != ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & (! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61))))) | (pushprop_lem0_lthm != $true)) & ((termmset = $true) | ? [X64 : term] : (((sub @ X64 @ id)) != X64)) & (! [X64 : term] : (((sub @ X64 @ id)) = X64) | (termmset != $true)) & ((axshiftcons = $true) | ? [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) != X66)) & (! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66) | (axshiftcons != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP50)) & (($true = sP50) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1_lthm = $true) | (? [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) != $true) & (((X89 @ X91)) = $true)) & ! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) & ! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85))) & (! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85) | (pushprop_lem1_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) | ($true != sP48)) & (($true = sP48) | (induction2 != $true)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) | ? [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) = ((ap @ (sub @ X102 @ id) @ X103))) & ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))))) | (hoaslamnotap != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) != $true) & ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ? [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) != $true) & (((X107 @ id @ X110 @ id)) = $true)) | ? [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) != ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) & ($true != ((sP46 @ X107))))) & (! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ($true = ((sP46 @ X107)))) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3a != $true)) & (lamnotvar = $true) & ((substmonoid = $true) | ? [X124 : subst] : (((comp @ X124 @ id)) != X124) | ? [X125 : subst] : (((comp @ id @ X125)) != X125)) & ((! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125)) | (substmonoid != $true)) & ((hoasinduction_lem3b = $true) | ? [X126 : term] : ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) | ((? [X130 : subst] : (((comp @ X130 @ id)) != X130) | ? [X131 : subst] : (((comp @ id @ X131)) != X131)) & ! [X129 : subst] : (((comp @ X129 @ id)) = X129) & ! [X128 : subst] : (((comp @ id @ X128)) = X128))) & ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129) | ? [X128 : subst] : (((comp @ id @ X128)) != X128) | (substmonoid_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X132 : (subst > term > subst > $o)] : ! [X133 : (term > $o)] : ? [X134 : term] : (((X133 @ X134)) != ((X132 @ id @ X134 @ id)))) & (! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP44)) & (($true = sP44) | (induction2_lthm != $true)) & (hoaslaminj_gthm = $true) & ((axidl = $true) | ? [X151 : subst] : (((comp @ id @ X151)) != X151)) & (! [X151 : subst] : (((comp @ id @ X151)) = X151) | (axidl != $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP40)) & (($true = sP40) | (hoasinduction_lem3v2a_lthm != $true)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) | ? [X167 : (term > $o),X168 : term,X169 : subst] : ! [X170 : (term > $o)] : ? [X171 : term] : (((X170 @ X171)) != ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & (! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3_lthm != $true)) & ((laminj = $true) | ? [X197 : term,X198 : term] : ((X197 != X198) & (((lam @ X197)) = ((lam @ X198))))) & (! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198)))) | (laminj != $true)) & ((pushprop_lem1 = $true) | ? [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) != $true) & (((X199 @ X201)) = $true))) & (! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true)) | (pushprop_lem1 != $true)) & ((axidr = $true) | ? [X204 : subst] : (((comp @ X204 @ id)) != X204)) & (! [X204 : subst] : (((comp @ X204 @ id)) = X204) | (axidr != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) | ? [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) != X205)) & (! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205) | (axscons != $true)) & ((axvarcons = $true) | ? [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) != X206)) & (! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206) | (axvarcons != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoaslaminj_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 != X230) & (((ap @ (sub @ X229 @ id) @ X231)) = ((ap @ (sub @ X230 @ id) @ X232)))) & ! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) & ! [X224 : term] : (((sub @ X224 @ id)) = X224))) & (! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228)))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3v2a != $true)) & ((hoasapinj2_lthm = $true) | (? [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 != X250) & (((ap @ (sub @ X247 @ id) @ X249)) = ((ap @ (sub @ X248 @ id) @ X250)))) & ! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))))) & (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))) | (hoasapinj2_lthm != $true)) & ((apinj1 = $true) | ? [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 != X252) & (((ap @ X251 @ X253)) = ((ap @ X252 @ X254))))) & (! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254)))) | (apinj1 != $true)) & ((apinj2 = $true) | ? [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 != X258) & (((ap @ X255 @ X257)) = ((ap @ X256 @ X258))))) & (! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258)))) | (apinj2 != $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem3aa != $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ? [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) != $true) & ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | (((X299 @ X301)) != $true)) & ($true != ((sP29 @ X299))) & ! [X304 : term] : ((((X299 @ X304)) = $true) | (((var @ X304)) != $true)))) & (! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ($true = ((sP29 @ X299))) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true))) | (induction != $true)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X305 : term] : ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction != $true)) & ((hoasinduction_lem0 = $true) | ? [X325 : (subst > term > subst > $o)] : ! [X326 : (term > $o)] : ? [X327 : term] : (((X326 @ X327)) != ((X325 @ id @ X327 @ id)))) & (! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) != $true) & ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) & (((X330 @ X332)) = $true)) & ! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328))) & (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328) | (pushprop_lem1v2_lthm != $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) | (? [X336 : term] : (((sub @ X336 @ id)) != X336) & ! [X335 : term] : (((sub @ X335 @ id)) = X335))) & (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335) | (termmset_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP25)) & (($true = sP25) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem3aaa != $true)) & ((hoaslaminj = $true) | ? [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) != ((X387 @ X388 @ X389))) & (((lam @ (X386 @ sh @ one))) = ((lam @ (X387 @ sh @ one)))) & ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) & ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & (! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395))))) | (hoaslaminj != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP14)) & (($true = sP14) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X480 : term] : ! [X481 : (subst > term > term)] : ? [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) != ((X481 @ X483 @ X482)))) & (! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) | ($true != sP5)) & (($true = sP5) | (induction2lem_lthm != $true)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) | ? [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 != X504) & (((ap @ (sub @ X503 @ id) @ X505)) = ((ap @ (sub @ X504 @ id) @ X506))))) & (! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506)))) | (hoasapinj1 != $true)) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) | ? [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 != X510) & (((ap @ (sub @ X507 @ id) @ X509)) = ((ap @ (sub @ X508 @ id) @ X510))))) & (! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510)))) | (hoasapinj2 != $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X511 : term] : ! [X512 : (subst > term > term)] : ? [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) != ((X512 @ X514 @ X513)))) & (! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513))) | (hoasinduction_lem3v2_f != $true)) & ((induction2lem = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) | ? [X523 : term,X524 : term] : ((X523 != X524) & (((sub @ X523 @ sh)) = ((sub @ X524 @ sh))))) & (! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh)))) | (shinj != $true)) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) != $true) & ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) & (((X525 @ X527)) = $true))) & (! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true)) | (pushprop_lem1v2 != $true)) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 17.66/3.02 inference(flattening,[],[f260])).
% 17.66/3.02 thf(f262,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lthm_3 != $true)) & ((axvarid = $true) | ? [X0 : term] : (((sub @ X0 @ id)) != X0)) & (! [X1 : term] : (((sub @ X1 @ id)) = X1) | (axvarid != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X2 : (term > $o),X3 : term,X4 : subst] : ! [X5 : (term > $o)] : ? [X6 : term] : (((X5 @ X6)) != ((X2 @ (sub @ X6 @ (push @ X3 @ X4)))))) & (! [X7 : (term > $o),X8 : term,X9 : subst] : ? [X10 : (term > $o)] : ! [X11 : term] : (((X10 @ X11)) = ((X7 @ (sub @ X11 @ (push @ X8 @ X9))))) | (pushprop_lem0_lthm != $true)) & ((termmset = $true) | ? [X12 : term] : (((sub @ X12 @ id)) != X12)) & (! [X13 : term] : (((sub @ X13 @ id)) = X13) | (termmset != $true)) & ((axshiftcons = $true) | ? [X14 : term,X15 : subst] : (((comp @ sh @ (push @ X14 @ X15))) != X15)) & (! [X16 : term,X17 : subst] : (((comp @ sh @ (push @ X16 @ X17))) = X17) | (axshiftcons != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP50)) & (($true = sP50) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1_lthm = $true) | (? [X18 : (term > $o),X19 : (term > $o),X20 : term,X21 : subst,X22 : term] : (($true != ((X19 @ (sub @ X20 @ (push @ X22 @ X21))))) & ($true = ((X18 @ X20)))) & ! [X23 : term,X24 : subst] : (((comp @ sh @ (push @ X23 @ X24))) = X24) & ! [X25 : term,X26 : subst] : (((sub @ one @ (push @ X25 @ X26))) = X25))) & (! [X27 : (term > $o),X28 : (term > $o),X29 : term,X30 : subst,X31 : term] : (($true = ((X28 @ (sub @ X29 @ (push @ X31 @ X30))))) | ($true != ((X27 @ X29)))) | ? [X32 : term,X33 : subst] : (((comp @ sh @ (push @ X32 @ X33))) != X33) | ? [X34 : term,X35 : subst] : (((sub @ one @ (push @ X34 @ X35))) != X34) | (pushprop_lem1_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) | ($true != sP48)) & (($true = sP48) | (induction2 != $true)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) | ? [X36 : (subst > term > term),X37 : term,X38 : term] : ((((lam @ (X36 @ sh @ one))) = ((ap @ (sub @ X37 @ id) @ X38))) & ! [X39 : subst,X40 : term,X41 : subst] : (((sub @ (X36 @ X39 @ X40) @ X41)) = ((X36 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)))))) & (! [X42 : (subst > term > term),X43 : term,X44 : term] : ((((lam @ (X42 @ sh @ one))) != ((ap @ (sub @ X43 @ id) @ X44))) | ? [X45 : subst,X46 : term,X47 : subst] : (((sub @ (X42 @ X45 @ X46) @ X47)) != ((X42 @ (comp @ X45 @ X47) @ (sub @ X46 @ X47))))) | (hoaslamnotap != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X48 : (subst > term > subst > $o),X49 : term] : (($true != ((X48 @ id @ X49 @ id))) & ! [X50 : (subst > term > term)] : (($true = ((X48 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | ? [X51 : term] : (($true != ((X48 @ id @ (X50 @ id @ X51) @ id))) & ($true = ((X48 @ id @ X51 @ id)))) | ? [X52 : subst,X53 : term,X54 : subst] : (((sub @ (X50 @ X52 @ X53) @ X54)) != ((X50 @ (comp @ X52 @ X54) @ (sub @ X53 @ X54))))) & ($true != ((sP46 @ X48))))) & (! [X55 : (subst > term > subst > $o),X56 : term] : (($true = ((X55 @ id @ X56 @ id))) | ? [X57 : (subst > term > term)] : (($true != ((X55 @ id @ (lam @ (X57 @ sh @ one)) @ id))) & ! [X58 : term] : (($true = ((X55 @ id @ (X57 @ id @ X58) @ id))) | ($true != ((X55 @ id @ X58 @ id)))) & ! [X59 : subst,X60 : term,X61 : subst] : (((sub @ (X57 @ X59 @ X60) @ X61)) = ((X57 @ (comp @ X59 @ X61) @ (sub @ X60 @ X61))))) | ($true = ((sP46 @ X55)))) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3a != $true)) & (lamnotvar = $true) & ((substmonoid = $true) | ? [X62 : subst] : (((comp @ X62 @ id)) != X62) | ? [X63 : subst] : (((comp @ id @ X63)) != X63)) & ((! [X64 : subst] : (((comp @ X64 @ id)) = X64) & ! [X65 : subst] : (((comp @ id @ X65)) = X65)) | (substmonoid != $true)) & ((hoasinduction_lem3b = $true) | ? [X66 : term] : ! [X67 : (subst > term > term)] : (((X67 @ sh @ one)) != ((sub @ X66 @ (push @ one @ sh))))) & (! [X68 : term] : ? [X69 : (subst > term > term)] : (((X69 @ sh @ one)) = ((sub @ X68 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) | ((? [X70 : subst] : (((comp @ X70 @ id)) != X70) | ? [X71 : subst] : (((comp @ id @ X71)) != X71)) & ! [X72 : subst] : (((comp @ X72 @ id)) = X72) & ! [X73 : subst] : (((comp @ id @ X73)) = X73))) & ((! [X74 : subst] : (((comp @ X74 @ id)) = X74) & ! [X75 : subst] : (((comp @ id @ X75)) = X75)) | ? [X76 : subst] : (((comp @ X76 @ id)) != X76) | ? [X77 : subst] : (((comp @ id @ X77)) != X77) | (substmonoid_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X78 : (subst > term > subst > $o)] : ! [X79 : (term > $o)] : ? [X80 : term] : (((X79 @ X80)) != ((X78 @ id @ X80 @ id)))) & (! [X81 : (subst > term > subst > $o)] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X82 @ X83)) = ((X81 @ id @ X83 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP44)) & (($true = sP44) | (induction2_lthm != $true)) & (hoaslaminj_gthm = $true) & ((axidl = $true) | ? [X84 : subst] : (((comp @ id @ X84)) != X84)) & (! [X85 : subst] : (((comp @ id @ X85)) = X85) | (axidl != $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP40)) & (($true = sP40) | (hoasinduction_lem3v2a_lthm != $true)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) | ? [X86 : (term > $o),X87 : term,X88 : subst] : ! [X89 : (term > $o)] : ? [X90 : term] : (((X89 @ X90)) != ((X86 @ (sub @ X90 @ (push @ X87 @ X88)))))) & (! [X91 : (term > $o),X92 : term,X93 : subst] : ? [X94 : (term > $o)] : ! [X95 : term] : (((X94 @ X95)) = ((X91 @ (sub @ X95 @ (push @ X92 @ X93))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3_lthm != $true)) & ((laminj = $true) | ? [X96 : term,X97 : term] : ((X96 != X97) & (((lam @ X96)) = ((lam @ X97))))) & (! [X98 : term,X99 : term] : ((X98 = X99) | (((lam @ X98)) != ((lam @ X99)))) | (laminj != $true)) & ((pushprop_lem1 = $true) | ? [X100 : (term > $o),X101 : (term > $o),X102 : term,X103 : subst,X104 : term] : (($true != ((X101 @ (sub @ X102 @ (push @ X104 @ X103))))) & ($true = ((X100 @ X102))))) & (! [X105 : (term > $o),X106 : (term > $o),X107 : term,X108 : subst,X109 : term] : (($true = ((X106 @ (sub @ X107 @ (push @ X109 @ X108))))) | ($true != ((X105 @ X107)))) | (pushprop_lem1 != $true)) & ((axidr = $true) | ? [X110 : subst] : (((comp @ X110 @ id)) != X110)) & (! [X111 : subst] : (((comp @ X111 @ id)) = X111) | (axidr != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) | ? [X112 : subst] : (((push @ (sub @ one @ X112) @ (comp @ sh @ X112))) != X112)) & (! [X113 : subst] : (((push @ (sub @ one @ X113) @ (comp @ sh @ X113))) = X113) | (axscons != $true)) & ((axvarcons = $true) | ? [X114 : term,X115 : subst] : (((sub @ one @ (push @ X114 @ X115))) != X114)) & (! [X116 : term,X117 : subst] : (((sub @ one @ (push @ X116 @ X117))) = X116) | (axvarcons != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoaslaminj_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X118 : term,X119 : term,X120 : term,X121 : term] : ((X118 != X119) & (((ap @ (sub @ X118 @ id) @ X120)) = ((ap @ (sub @ X119 @ id) @ X121)))) & ! [X122 : term,X123 : term,X124 : term,X125 : term] : ((X122 = X123) | (((ap @ X122 @ X124)) != ((ap @ X123 @ X125)))) & ! [X126 : term] : (((sub @ X126 @ id)) = X126))) & (! [X127 : term,X128 : term,X129 : term,X130 : term] : ((X127 = X128) | (((ap @ (sub @ X127 @ id) @ X129)) != ((ap @ (sub @ X128 @ id) @ X130)))) | ? [X131 : term,X132 : term,X133 : term,X134 : term] : ((X131 != X132) & (((ap @ X131 @ X133)) = ((ap @ X132 @ X134)))) | ? [X135 : term] : (((sub @ X135 @ id)) != X135) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3v2a != $true)) & ((hoasapinj2_lthm = $true) | (? [X136 : term,X137 : term,X138 : term,X139 : term] : ((X138 != X139) & (((ap @ (sub @ X136 @ id) @ X138)) = ((ap @ (sub @ X137 @ id) @ X139)))) & ! [X140 : term,X141 : term,X142 : term,X143 : term] : ((X142 = X143) | (((ap @ X140 @ X142)) != ((ap @ X141 @ X143)))))) & (! [X144 : term,X145 : term,X146 : term,X147 : term] : ((X146 = X147) | (((ap @ (sub @ X144 @ id) @ X146)) != ((ap @ (sub @ X145 @ id) @ X147)))) | ? [X148 : term,X149 : term,X150 : term,X151 : term] : ((X150 != X151) & (((ap @ X148 @ X150)) = ((ap @ X149 @ X151)))) | (hoasapinj2_lthm != $true)) & ((apinj1 = $true) | ? [X152 : term,X153 : term,X154 : term,X155 : term] : ((X152 != X153) & (((ap @ X152 @ X154)) = ((ap @ X153 @ X155))))) & (! [X156 : term,X157 : term,X158 : term,X159 : term] : ((X156 = X157) | (((ap @ X156 @ X158)) != ((ap @ X157 @ X159)))) | (apinj1 != $true)) & ((apinj2 = $true) | ? [X160 : term,X161 : term,X162 : term,X163 : term] : ((X162 != X163) & (((ap @ X160 @ X162)) = ((ap @ X161 @ X163))))) & (! [X164 : term,X165 : term,X166 : term,X167 : term] : ((X166 = X167) | (((ap @ X164 @ X166)) != ((ap @ X165 @ X167)))) | (apinj2 != $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem3aa != $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ? [X168 : (term > $o),X169 : term] : (($true != ((X168 @ X169))) & ! [X170 : term] : (($true = ((X168 @ (lam @ X170)))) | ($true != ((X168 @ X170)))) & ($true != ((sP29 @ X168))) & ! [X171 : term] : (($true = ((X168 @ X171))) | ($true != ((var @ X171)))))) & (! [X172 : (term > $o),X173 : term] : (($true = ((X172 @ X173))) | ? [X174 : term] : (($true != ((X172 @ (lam @ X174)))) & ($true = ((X172 @ X174)))) | ($true = ((sP29 @ X172))) | ? [X175 : term] : (($true != ((X172 @ X175))) & ($true = ((var @ X175))))) | (induction != $true)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X176 : term] : ! [X177 : (subst > term > term)] : (((X177 @ sh @ one)) != ((sub @ X176 @ (push @ one @ sh))))) & (! [X178 : term] : ? [X179 : (subst > term > term)] : (((X179 @ sh @ one)) = ((sub @ X178 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction != $true)) & ((hoasinduction_lem0 = $true) | ? [X180 : (subst > term > subst > $o)] : ! [X181 : (term > $o)] : ? [X182 : term] : (((X181 @ X182)) != ((X180 @ id @ X182 @ id)))) & (! [X183 : (subst > term > subst > $o)] : ? [X184 : (term > $o)] : ! [X185 : term] : (((X184 @ X185)) = ((X183 @ id @ X185 @ id))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X186 : (term > $o),X187 : (term > $o),X188 : term,X189 : subst] : (($true != ((X187 @ one))) & ! [X190 : term] : (((X187 @ X190)) = ((X186 @ (sub @ X190 @ (push @ X188 @ X189))))) & ($true = ((X186 @ X188)))) & ! [X191 : term,X192 : subst] : (((sub @ one @ (push @ X191 @ X192))) = X191))) & (! [X193 : (term > $o),X194 : (term > $o),X195 : term,X196 : subst] : (($true = ((X194 @ one))) | ? [X197 : term] : (((X194 @ X197)) != ((X193 @ (sub @ X197 @ (push @ X195 @ X196))))) | ($true != ((X193 @ X195)))) | ? [X198 : term,X199 : subst] : (((sub @ one @ (push @ X198 @ X199))) != X198) | (pushprop_lem1v2_lthm != $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) | (? [X200 : term] : (((sub @ X200 @ id)) != X200) & ! [X201 : term] : (((sub @ X201 @ id)) = X201))) & (! [X202 : term] : (((sub @ X202 @ id)) = X202) | ? [X203 : term] : (((sub @ X203 @ id)) != X203) | (termmset_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP25)) & (($true = sP25) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem3aaa != $true)) & ((hoaslaminj = $true) | ? [X204 : (subst > term > term),X205 : (subst > term > term),X206 : subst,X207 : term] : ((((X204 @ X206 @ X207)) != ((X205 @ X206 @ X207))) & (((lam @ (X204 @ sh @ one))) = ((lam @ (X205 @ sh @ one)))) & ! [X208 : subst,X209 : term,X210 : subst] : (((sub @ (X205 @ X208 @ X209) @ X210)) = ((X205 @ (comp @ X208 @ X210) @ (sub @ X209 @ X210)))) & ! [X211 : subst,X212 : term,X213 : subst] : (((sub @ (X204 @ X211 @ X212) @ X213)) = ((X204 @ (comp @ X211 @ X213) @ (sub @ X212 @ X213)))))) & (! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))) | (hoaslaminj != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP14)) & (($true = sP14) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X224 : term] : ! [X225 : (subst > term > term)] : ? [X226 : term,X227 : subst] : (((sub @ X224 @ (push @ X226 @ X227))) != ((X225 @ X227 @ X226)))) & (! [X228 : term] : ? [X229 : (subst > term > term)] : ! [X230 : term,X231 : subst] : (((sub @ X228 @ (push @ X230 @ X231))) = ((X229 @ X231 @ X230))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) | ($true != sP5)) & (($true = sP5) | (induction2lem_lthm != $true)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) | ? [X232 : term,X233 : term,X234 : term,X235 : term] : ((X232 != X233) & (((ap @ (sub @ X232 @ id) @ X234)) = ((ap @ (sub @ X233 @ id) @ X235))))) & (! [X236 : term,X237 : term,X238 : term,X239 : term] : ((X236 = X237) | (((ap @ (sub @ X236 @ id) @ X238)) != ((ap @ (sub @ X237 @ id) @ X239)))) | (hoasapinj1 != $true)) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) | ? [X240 : term,X241 : term,X242 : term,X243 : term] : ((X242 != X243) & (((ap @ (sub @ X240 @ id) @ X242)) = ((ap @ (sub @ X241 @ id) @ X243))))) & (! [X244 : term,X245 : term,X246 : term,X247 : term] : ((X246 = X247) | (((ap @ (sub @ X244 @ id) @ X246)) != ((ap @ (sub @ X245 @ id) @ X247)))) | (hoasapinj2 != $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X248 : term] : ! [X249 : (subst > term > term)] : ? [X250 : term,X251 : subst] : (((sub @ X248 @ (push @ X250 @ X251))) != ((X249 @ X251 @ X250)))) & (! [X252 : term] : ? [X253 : (subst > term > term)] : ! [X254 : term,X255 : subst] : (((sub @ X252 @ (push @ X254 @ X255))) = ((X253 @ X255 @ X254))) | (hoasinduction_lem3v2_f != $true)) & ((induction2lem = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) | ? [X256 : term,X257 : term] : ((X256 != X257) & (((sub @ X256 @ sh)) = ((sub @ X257 @ sh))))) & (! [X258 : term,X259 : term] : ((X258 = X259) | (((sub @ X258 @ sh)) != ((sub @ X259 @ sh)))) | (shinj != $true)) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X260 : (term > $o),X261 : (term > $o),X262 : term,X263 : subst] : (($true != ((X261 @ one))) & ! [X264 : term] : (((X261 @ X264)) = ((X260 @ (sub @ X264 @ (push @ X262 @ X263))))) & (((X260 @ X262)) = $true))) & (! [X265 : (term > $o),X266 : (term > $o),X267 : term,X268 : subst] : (($true = ((X266 @ one))) | ? [X269 : term] : (((X266 @ X269)) != ((X265 @ (sub @ X269 @ (push @ X267 @ X268))))) | ($true != ((X265 @ X267)))) | (pushprop_lem1v2 != $true)) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X270 : d_subst,X271 : d_subst] : ((X270 = X271) | (((d2subst @ X270)) != ((d2subst @ X271)))) & ! [X272 : d_subst] : (d_id = X272) & ! [X273 : subst] : ? [X274 : d_subst] : (((d2subst @ X274)) = X273) & ! [X275 : d_term,X276 : d_term] : ((X275 = X276) | (((d2term @ X275)) != ((d2term @ X276)))) & ! [X277 : d_term] : (d_one = X277) & ! [X278 : term] : ? [X279 : d_term] : (((d2term @ X279)) = X278)),
% 17.66/3.02 inference(rectify,[],[f261])).
% 17.66/3.02 thf(f263,plain,(
% 17.66/3.02 ((hoasinduction_lthm_3 = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lthm_3 != $true)) & ((axvarid = $true) | (sK454 != ((sub @ sK454 @ id)))) & (! [X1 : term] : (((sub @ X1 @ id)) = X1) | (axvarid != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ! [X5 : (term > $o)] : (((X5 @ (sK458 @ X5))) != ((sK455 @ (sub @ (sK458 @ X5) @ (push @ sK456 @ sK457)))))) & (! [X7 : (term > $o),X8 : term,X9 : subst] : ! [X11 : term] : (((X7 @ (sub @ X11 @ (push @ X8 @ X9)))) = ((sK459 @ X9 @ X8 @ X7 @ X11))) | (pushprop_lem0_lthm != $true)) & ((termmset = $true) | (sK460 != ((sub @ sK460 @ id)))) & (! [X13 : term] : (((sub @ X13 @ id)) = X13) | (termmset != $true)) & ((axshiftcons = $true) | (sK462 != ((comp @ sh @ (push @ sK461 @ sK462))))) & (! [X16 : term,X17 : subst] : (((comp @ sh @ (push @ X16 @ X17))) = X17) | (axshiftcons != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP50)) & (($true = sP50) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1_lthm = $true) | ((($true != ((sK464 @ (sub @ sK465 @ (push @ sK467 @ sK466))))) & ($true = ((sK463 @ sK465)))) & ! [X23 : term,X24 : subst] : (((comp @ sh @ (push @ X23 @ X24))) = X24) & ! [X25 : term,X26 : subst] : (((sub @ one @ (push @ X25 @ X26))) = X25))) & (! [X27 : (term > $o),X28 : (term > $o),X29 : term,X30 : subst,X31 : term] : (($true = ((X28 @ (sub @ X29 @ (push @ X31 @ X30))))) | ($true != ((X27 @ X29)))) | (sK469 != ((comp @ sh @ (push @ sK468 @ sK469)))) | (sK470 != ((sub @ one @ (push @ sK470 @ sK471)))) | (pushprop_lem1_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) | ($true != sP48)) & (($true = sP48) | (induction2 != $true)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) | ((((lam @ (sK472 @ sh @ one))) = ((ap @ (sub @ sK473 @ id) @ sK474))) & ! [X39 : subst,X40 : term,X41 : subst] : (((sub @ (sK472 @ X39 @ X40) @ X41)) = ((sK472 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)))))) & (! [X42 : (subst > term > term),X43 : term,X44 : term] : ((((lam @ (X42 @ sh @ one))) != ((ap @ (sub @ X43 @ id) @ X44))) | (((sub @ (X42 @ (sK475 @ X42) @ (sK476 @ X42)) @ (sK477 @ X42))) != ((X42 @ (comp @ (sK475 @ X42) @ (sK477 @ X42)) @ (sub @ (sK476 @ X42) @ (sK477 @ X42)))))) | (hoaslamnotap != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | (($true != ((sK478 @ id @ sK479 @ id))) & ! [X50 : (subst > term > term)] : (($true = ((sK478 @ id @ (lam @ (X50 @ sh @ one)) @ id))) | (($true != ((sK478 @ id @ (X50 @ id @ (sK480 @ X50)) @ id))) & ($true = ((sK478 @ id @ (sK480 @ X50) @ id)))) | (((sub @ (X50 @ (sK481 @ X50) @ (sK482 @ X50)) @ (sK483 @ X50))) != ((X50 @ (comp @ (sK481 @ X50) @ (sK483 @ X50)) @ (sub @ (sK482 @ X50) @ (sK483 @ X50)))))) & ($true != ((sP46 @ sK478))))) & (! [X55 : (subst > term > subst > $o),X56 : term] : (($true = ((X55 @ id @ X56 @ id))) | (($true != ((X55 @ id @ (lam @ (sK484 @ X55 @ sh @ one)) @ id))) & ! [X58 : term] : (($true = ((X55 @ id @ (sK484 @ X55 @ id @ X58) @ id))) | ($true != ((X55 @ id @ X58 @ id)))) & ! [X59 : subst,X60 : term,X61 : subst] : (((sub @ (sK484 @ X55 @ X59 @ X60) @ X61)) = ((sK484 @ X55 @ (comp @ X59 @ X61) @ (sub @ X60 @ X61))))) | ($true = ((sP46 @ X55)))) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3a != $true)) & (lamnotvar = $true) & ((substmonoid = $true) | (sK485 != ((comp @ sK485 @ id))) | (sK486 != ((comp @ id @ sK486)))) & ((! [X64 : subst] : (((comp @ X64 @ id)) = X64) & ! [X65 : subst] : (((comp @ id @ X65)) = X65)) | (substmonoid != $true)) & ((hoasinduction_lem3b = $true) | ! [X67 : (subst > term > term)] : (((X67 @ sh @ one)) != ((sub @ sK487 @ (push @ one @ sh))))) & (! [X68 : term] : (((sub @ X68 @ (push @ one @ sh))) = ((sK488 @ X68 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) | (((sK489 != ((comp @ sK489 @ id))) | (sK490 != ((comp @ id @ sK490)))) & ! [X72 : subst] : (((comp @ X72 @ id)) = X72) & ! [X73 : subst] : (((comp @ id @ X73)) = X73))) & ((! [X74 : subst] : (((comp @ X74 @ id)) = X74) & ! [X75 : subst] : (((comp @ id @ X75)) = X75)) | (sK491 != ((comp @ sK491 @ id))) | (sK492 != ((comp @ id @ sK492))) | (substmonoid_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X79 : (term > $o)] : (((X79 @ (sK494 @ X79))) != ((sK493 @ id @ (sK494 @ X79) @ id)))) & (! [X81 : (subst > term > subst > $o)] : ! [X83 : term] : (((X81 @ id @ X83 @ id)) = ((sK495 @ X81 @ X83))) | (hoasinduction_lem0_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP44)) & (($true = sP44) | (induction2_lthm != $true)) & (hoaslaminj_gthm = $true) & ((axidl = $true) | (sK496 != ((comp @ id @ sK496)))) & (! [X85 : subst] : (((comp @ id @ X85)) = X85) | (axidl != $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP40)) & (($true = sP40) | (hoasinduction_lem3v2a_lthm != $true)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) | ! [X89 : (term > $o)] : (((X89 @ (sK500 @ X89))) != ((sK497 @ (sub @ (sK500 @ X89) @ (push @ sK498 @ sK499)))))) & (! [X91 : (term > $o),X92 : term,X93 : subst] : ! [X95 : term] : (((X91 @ (sub @ X95 @ (push @ X92 @ X93)))) = ((sK501 @ X93 @ X92 @ X91 @ X95))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3_lthm = $true) | ($true != sP39)) & (($true = sP39) | (hoasinduction_lem3_lthm != $true)) & ((laminj = $true) | ((sK502 != sK503) & (((lam @ sK502)) = ((lam @ sK503))))) & (! [X98 : term,X99 : term] : ((X98 = X99) | (((lam @ X98)) != ((lam @ X99)))) | (laminj != $true)) & ((pushprop_lem1 = $true) | (($true != ((sK505 @ (sub @ sK506 @ (push @ sK508 @ sK507))))) & ($true = ((sK504 @ sK506))))) & (! [X105 : (term > $o),X106 : (term > $o),X107 : term,X108 : subst,X109 : term] : (($true = ((X106 @ (sub @ X107 @ (push @ X109 @ X108))))) | ($true != ((X105 @ X107)))) | (pushprop_lem1 != $true)) & ((axidr = $true) | (sK509 != ((comp @ sK509 @ id)))) & (! [X111 : subst] : (((comp @ X111 @ id)) = X111) | (axidr != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) | (sK510 != ((push @ (sub @ one @ sK510) @ (comp @ sh @ sK510))))) & (! [X113 : subst] : (((push @ (sub @ one @ X113) @ (comp @ sh @ X113))) = X113) | (axscons != $true)) & ((axvarcons = $true) | (sK511 != ((sub @ one @ (push @ sK511 @ sK512))))) & (! [X116 : term,X117 : subst] : (((sub @ one @ (push @ X116 @ X117))) = X116) | (axvarcons != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoaslaminj_lthm != $true)) & ((hoasapinj1_lthm = $true) | (((sK513 != sK514) & (((ap @ (sub @ sK513 @ id) @ sK515)) = ((ap @ (sub @ sK514 @ id) @ sK516)))) & ! [X122 : term,X123 : term,X124 : term,X125 : term] : ((X122 = X123) | (((ap @ X122 @ X124)) != ((ap @ X123 @ X125)))) & ! [X126 : term] : (((sub @ X126 @ id)) = X126))) & (! [X127 : term,X128 : term,X129 : term,X130 : term] : ((X127 = X128) | (((ap @ (sub @ X127 @ id) @ X129)) != ((ap @ (sub @ X128 @ id) @ X130)))) | ((sK517 != sK518) & (((ap @ sK517 @ sK519)) = ((ap @ sK518 @ sK520)))) | (sK521 != ((sub @ sK521 @ id))) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3v2a != $true)) & ((hoasapinj2_lthm = $true) | (((sK524 != sK525) & (((ap @ (sub @ sK522 @ id) @ sK524)) = ((ap @ (sub @ sK523 @ id) @ sK525)))) & ! [X140 : term,X141 : term,X142 : term,X143 : term] : ((X142 = X143) | (((ap @ X140 @ X142)) != ((ap @ X141 @ X143)))))) & (! [X144 : term,X145 : term,X146 : term,X147 : term] : ((X146 = X147) | (((ap @ (sub @ X144 @ id) @ X146)) != ((ap @ (sub @ X145 @ id) @ X147)))) | ((sK528 != sK529) & (((ap @ sK526 @ sK528)) = ((ap @ sK527 @ sK529)))) | (hoasapinj2_lthm != $true)) & ((apinj1 = $true) | ((sK530 != sK531) & (((ap @ sK530 @ sK532)) = ((ap @ sK531 @ sK533))))) & (! [X156 : term,X157 : term,X158 : term,X159 : term] : ((X156 = X157) | (((ap @ X156 @ X158)) != ((ap @ X157 @ X159)))) | (apinj1 != $true)) & ((apinj2 = $true) | ((sK536 != sK537) & (((ap @ sK534 @ sK536)) = ((ap @ sK535 @ sK537))))) & (! [X164 : term,X165 : term,X166 : term,X167 : term] : ((X166 = X167) | (((ap @ X164 @ X166)) != ((ap @ X165 @ X167)))) | (apinj2 != $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_lem3aa != $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | (($true != ((sK538 @ sK539))) & ! [X170 : term] : (($true = ((sK538 @ (lam @ X170)))) | ($true != ((sK538 @ X170)))) & ($true != ((sP29 @ sK538))) & ! [X171 : term] : (($true = ((sK538 @ X171))) | ($true != ((var @ X171)))))) & (! [X172 : (term > $o),X173 : term] : (($true = ((X172 @ X173))) | (($true != ((X172 @ (lam @ (sK540 @ X172))))) & ($true = ((X172 @ (sK540 @ X172))))) | ($true = ((sP29 @ X172))) | (($true != ((X172 @ (sK541 @ X172)))) & ($true = ((var @ (sK541 @ X172)))))) | (induction != $true)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X177 : (subst > term > term)] : (((X177 @ sh @ one)) != ((sub @ sK542 @ (push @ one @ sh))))) & (! [X178 : term] : (((sub @ X178 @ (push @ one @ sh))) = ((sK543 @ X178 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) | ($true != sP28)) & (($true = sP28) | (hoasinduction != $true)) & ((hoasinduction_lem0 = $true) | ! [X181 : (term > $o)] : (((X181 @ (sK545 @ X181))) != ((sK544 @ id @ (sK545 @ X181) @ id)))) & (! [X183 : (subst > term > subst > $o)] : ! [X185 : term] : (((X183 @ id @ X185 @ id)) = ((sK546 @ X183 @ X185))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) | ((($true != ((sK548 @ one))) & ! [X190 : term] : (((sK548 @ X190)) = ((sK547 @ (sub @ X190 @ (push @ sK549 @ sK550))))) & ($true = ((sK547 @ sK549)))) & ! [X191 : term,X192 : subst] : (((sub @ one @ (push @ X191 @ X192))) = X191))) & (! [X193 : (term > $o),X194 : (term > $o),X195 : term,X196 : subst] : (($true = ((X194 @ one))) | (((X194 @ (sK551 @ X196 @ X195 @ X194 @ X193))) != ((X193 @ (sub @ (sK551 @ X196 @ X195 @ X194 @ X193) @ (push @ X195 @ X196))))) | ($true != ((X193 @ X195)))) | (sK552 != ((sub @ one @ (push @ sK552 @ sK553)))) | (pushprop_lem1v2_lthm != $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) | ((sK554 != ((sub @ sK554 @ id))) & ! [X201 : term] : (((sub @ X201 @ id)) = X201))) & (! [X202 : term] : (((sub @ X202 @ id)) = X202) | (sK555 != ((sub @ sK555 @ id))) | (termmset_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP25)) & (($true = sP25) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP20)) & (($true = sP20) | (hoasinduction_lem3aaa != $true)) & ((hoaslaminj = $true) | ((((sK556 @ sK558 @ sK559)) != ((sK557 @ sK558 @ sK559))) & (((lam @ (sK556 @ sh @ one))) = ((lam @ (sK557 @ sh @ one)))) & ! [X208 : subst,X209 : term,X210 : subst] : (((sub @ (sK557 @ X208 @ X209) @ X210)) = ((sK557 @ (comp @ X208 @ X210) @ (sub @ X209 @ X210)))) & ! [X211 : subst,X212 : term,X213 : subst] : (((sub @ (sK556 @ X211 @ X212) @ X213)) = ((sK556 @ (comp @ X211 @ X213) @ (sub @ X212 @ X213)))))) & (! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | (((sub @ (X215 @ (sK560 @ X215) @ (sK561 @ X215)) @ (sK562 @ X215))) != ((X215 @ (comp @ (sK560 @ X215) @ (sK562 @ X215)) @ (sub @ (sK561 @ X215) @ (sK562 @ X215))))) | (((sub @ (X214 @ (sK563 @ X214) @ (sK564 @ X214)) @ (sK565 @ X214))) != ((X214 @ (comp @ (sK563 @ X214) @ (sK565 @ X214)) @ (sub @ (sK564 @ X214) @ (sK565 @ X214)))))) | (hoaslaminj != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP14)) & (($true = sP14) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X225 : (subst > term > term)] : (((sub @ sK566 @ (push @ (sK567 @ X225) @ (sK568 @ X225)))) != ((X225 @ (sK568 @ X225) @ (sK567 @ X225))))) & (! [X228 : term] : ! [X230 : term,X231 : subst] : (((sub @ X228 @ (push @ X230 @ X231))) = ((sK569 @ X228 @ X231 @ X230))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) | ($true != sP5)) & (($true = sP5) | (induction2lem_lthm != $true)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) | ((sK570 != sK571) & (((ap @ (sub @ sK570 @ id) @ sK572)) = ((ap @ (sub @ sK571 @ id) @ sK573))))) & (! [X236 : term,X237 : term,X238 : term,X239 : term] : ((X236 = X237) | (((ap @ (sub @ X236 @ id) @ X238)) != ((ap @ (sub @ X237 @ id) @ X239)))) | (hoasapinj1 != $true)) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) | ((sK576 != sK577) & (((ap @ (sub @ sK574 @ id) @ sK576)) = ((ap @ (sub @ sK575 @ id) @ sK577))))) & (! [X244 : term,X245 : term,X246 : term,X247 : term] : ((X246 = X247) | (((ap @ (sub @ X244 @ id) @ X246)) != ((ap @ (sub @ X245 @ id) @ X247)))) | (hoasapinj2 != $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X249 : (subst > term > term)] : (((sub @ sK578 @ (push @ (sK579 @ X249) @ (sK580 @ X249)))) != ((X249 @ (sK580 @ X249) @ (sK579 @ X249))))) & (! [X252 : term] : ! [X254 : term,X255 : subst] : (((sub @ X252 @ (push @ X254 @ X255))) = ((sK581 @ X252 @ X255 @ X254))) | (hoasinduction_lem3v2_f != $true)) & ((induction2lem = $true) | ($true != sP1)) & (($true = sP1) | (induction2lem != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) | ((sK582 != sK583) & (((sub @ sK582 @ sh)) = ((sub @ sK583 @ sh))))) & (! [X258 : term,X259 : term] : ((X258 = X259) | (((sub @ X258 @ sh)) != ((sub @ X259 @ sh)))) | (shinj != $true)) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) | (($true != ((sK585 @ one))) & ! [X264 : term] : (((sK585 @ X264)) = ((sK584 @ (sub @ X264 @ (push @ sK586 @ sK587))))) & ($true = ((sK584 @ sK586))))) & (! [X265 : (term > $o),X266 : (term > $o),X267 : term,X268 : subst] : (($true = ((X266 @ one))) | (((X266 @ (sK588 @ X268 @ X267 @ X266 @ X265))) != ((X265 @ (sub @ (sK588 @ X268 @ X267 @ X266 @ X265) @ (push @ X267 @ X268))))) | ($true != ((X265 @ X267)))) | (pushprop_lem1v2 != $true)) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X270 : d_subst,X271 : d_subst] : ((X270 = X271) | (((d2subst @ X270)) != ((d2subst @ X271)))) & ! [X272 : d_subst] : (d_id = X272) & ! [X273 : subst] : (((d2subst @ (sK589 @ X273))) = X273) & ! [X275 : d_term,X276 : d_term] : ((X275 = X276) | (((d2term @ X275)) != ((d2term @ X276)))) & ! [X277 : d_term] : (d_one = X277) & ! [X278 : term] : (((d2term @ (sK590 @ X278))) = X278)),
% 17.66/3.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,vAPP,vAPP,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,vAPP,vAPP,vAPP,sK478,sK479,vAPP,vAPP,vAPP,vAPP,vAPP,sK485,sK486,sK487,vAPP,sK489,sK490,sK491,sK492,sK493,vAPP,vAPP,sK496,sK497,sK498,sK499,vAPP,vAPP,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,vAPP,vAPP,sK542,vAPP,sK544,vAPP,vAPP,sK547,sK548,sK549,sK550,vAPP,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK566,vAPP,vAPP,vAPP,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,vAPP,vAPP,vAPP,sK582,sK583,sK584,sK585,sK586,sK587,vAPP,vAPP,vAPP]),skolemize(X0,sK454),skolemize(X2,sK455),skolemize(X3,sK456),skolemize(X4,sK457),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X12,sK460),skolemize(X14,sK461),skolemize(X15,sK462),skolemize(X18,sK463),skolemize(X19,sK464),skolemize(X20,sK465),skolemize(X21,sK466),skolemize(X22,sK467),skolemize(X32,sK468),skolemize(X33,sK469),skolemize(X34,sK470),skolemize(X35,sK471),skolemize(X36,sK472),skolemize(X37,sK473),skolemize(X38,sK474),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X48,sK478),skolemize(X49,sK479),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X62,sK485),skolemize(X63,sK486),skolemize(X66,sK487),skolemize(X17,sK67 @ X16),skolemize(X70,sK489),skolemize(X71,sK490),skolemize(X76,sK491),skolemize(X77,sK492),skolemize(X78,sK493),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X84,sK496),skolemize(X86,sK497),skolemize(X87,sK498),skolemize(X88,sK499),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X96,sK502),skolemize(X97,sK503),skolemize(X100,sK504),skolemize(X101,sK505),skolemize(X102,sK506),skolemize(X103,sK507),skolemize(X104,sK508),skolemize(X110,sK509),skolemize(X112,sK510),skolemize(X114,sK511),skolemize(X115,sK512),skolemize(X118,sK513),skolemize(X119,sK514),skolemize(X120,sK515),skolemize(X121,sK516),skolemize(X131,sK517),skolemize(X132,sK518),skolemize(X133,sK519),skolemize(X134,sK520),skolemize(X135,sK521),skolemize(X136,sK522),skolemize(X137,sK523),skolemize(X138,sK524),skolemize(X139,sK525),skolemize(X148,sK526),skolemize(X149,sK527),skolemize(X150,sK528),skolemize(X151,sK529),skolemize(X152,sK530),skolemize(X153,sK531),skolemize(X154,sK532),skolemize(X155,sK533),skolemize(X160,sK534),skolemize(X161,sK535),skolemize(X162,sK536),skolemize(X163,sK537),skolemize(X168,sK538),skolemize(X169,sK539),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X176,sK542),skolemize(X17,sK67 @ X16),skolemize(X180,sK544),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X186,sK547),skolemize(X187,sK548),skolemize(X188,sK549),skolemize(X189,sK550),skolemize(X17,sK67 @ X16),skolemize(X198,sK552),skolemize(X199,sK553),skolemize(X200,sK554),skolemize(X203,sK555),skolemize(X204,sK556),skolemize(X205,sK557),skolemize(X206,sK558),skolemize(X207,sK559),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X224,sK566),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X232,sK570),skolemize(X233,sK571),skolemize(X234,sK572),skolemize(X235,sK573),skolemize(X240,sK574),skolemize(X241,sK575),skolemize(X242,sK576),skolemize(X243,sK577),skolemize(X248,sK578),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X256,sK582),skolemize(X257,sK583),skolemize(X260,sK584),skolemize(X261,sK585),skolemize(X262,sK586),skolemize(X263,sK587),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16),skolemize(X17,sK67 @ X16)],[f262])).
% 17.66/3.02 thf(f467,plain,(
% 17.66/3.02 ( ! [X5 : (subst > term > term)] : (($true = sP35) | ($true = ((sK224 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | ($true = ((sK224 @ id @ (sK227 @ X5) @ id))) | (((sub @ (X5 @ (sK228 @ X5) @ (sK229 @ X5)) @ (sK230 @ X5))) != ((X5 @ (comp @ (sK228 @ X5) @ (sK230 @ X5)) @ (sub @ (sK229 @ X5) @ (sK230 @ X5)))))) )),
% 17.66/3.02 inference(cnf_transformation,[],[f150])).
% 17.66/3.02 thf(f469,plain,(
% 17.66/3.02 ( ! [X4 : term] : (($true = sP35) | (((sK224 @ id @ X4 @ id)) = ((sK225 @ X4)))) )),
% 17.66/3.02 inference(cnf_transformation,[],[f150])).
% 17.66/3.02 thf(f471,plain,(
% 17.66/3.02 ($true = sP35) | ($true != ((sK225 @ (lam @ sK226))))),
% 17.66/3.02 inference(cnf_transformation,[],[f150])).
% 17.66/3.02 thf(f752,plain,(
% 17.66/3.02 ( ! [X278 : term] : ((((d2term @ (sK590 @ X278))) = X278)) )),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f753,plain,(
% 17.66/3.02 ( ! [X277 : d_term] : ((d_one = X277)) )),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f755,plain,(
% 17.66/3.02 ( ! [X273 : subst] : ((((d2subst @ (sK589 @ X273))) = X273)) )),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f756,plain,(
% 17.66/3.02 ( ! [X272 : d_subst] : ((d_id = X272)) )),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f758,plain,(
% 17.66/3.02 (one = ((d2term @ d_one)))),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f767,plain,(
% 17.66/3.02 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f768,plain,(
% 17.66/3.02 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id))))))))),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f879,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $true) | ($true != sP35)),
% 17.66/3.02 inference(cnf_transformation,[],[f263])).
% 17.66/3.02 thf(f978,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ (comp @ Y5 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ (hoaslam @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => ((hoasinduction_p_and_p_prime @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2)))))))))))))),
% 17.66/3.02 inference(cnf_transformation,[],[f10])).
% 17.66/3.02 thf(f981,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ (comp @ Y5 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2)))))))))))))),
% 17.66/3.02 inference(definition_unfolding,[],[f978,f767,f768])).
% 17.66/3.02 thf(f983,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ (comp @ Y5 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2)))))))))))))),
% 17.66/3.02 inference(xor_proxy_clausification,[],[f981])).
% 17.66/3.02 thf(f984,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : term > $o]: (!! @ (subst > term > subst > $o) @ (^[Y1 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y2 : subst > term > term]: ((!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (!! @ subst @ (^[Y5 : subst]: ((sub @ (Y2 @ Y5 @ Y4) @ Y3) = (Y2 @ (comp @ Y5 @ Y3) @ (sub @ Y4 @ Y3))))))))) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ id @ Y3 @ id) => (Y1 @ id @ (Y2 @ id @ Y3) @ id)))) => (Y1 @ id @ ((^[Y3 : subst]: ((^[Y4 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y3 : subst]: ((^[Y4 : term]: (Y2 @ Y3 @ Y4))))) @ id))))) => (((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ id @ Y4 @ id))))))) @ Y1 @ Y0) => (!! @ term @ (^[Y2 : term]: ((!! @ term @ (^[Y3 : term]: ((Y0 @ Y3) => (Y0 @ (sub @ Y2 @ (push @ Y3 @ id)))))) => (Y0 @ (lam @ Y2)))))))))) @ sK591)))),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f983])).
% 17.66/3.02 thf(f985,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (d2term @ d_one) @ id))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ Y1) = (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((sK591 @ Y2) => (sK591 @ (sub @ Y1 @ (push @ Y2 @ id)))))) => (sK591 @ (lam @ Y1)))))))))))),
% 17.66/3.02 inference(beta-eta_normalization,[],[f984])).
% 17.66/3.02 thf(f986,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (d2term @ d_one) @ id))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ Y1) = (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((sK591 @ Y2) => (sK591 @ (sub @ Y1 @ (push @ Y2 @ id)))))) => (sK591 @ (lam @ Y1)))))))) @ sK592)))),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f985])).
% 17.66/3.02 thf(f987,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (d2term @ d_one) @ id))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ Y0) = (sK592 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ Y1) => (sK591 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK591 @ (lam @ Y0)))))))))),
% 17.66/3.02 inference(beta-eta_normalization,[],[f986])).
% 17.66/3.02 thf(f988,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = (((!! @ term @ (^[Y0 : term]: ((sK591 @ Y0) = (sK592 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ Y1) => (sK591 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK591 @ (lam @ Y0))))))))),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f987])).
% 17.66/3.02 thf(f989,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($true = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (d2term @ d_one) @ id)))))))),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f987])).
% 17.66/3.02 thf(f990,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($true = (((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK592 @ id @ Y1 @ id) => (sK592 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK592 @ id @ (d2term @ d_one) @ id)))) @ X1)))) )),
% 17.66/3.02 inference(pi_proxy_clausification,[],[f989])).
% 17.66/3.02 thf(f991,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($true = (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y1) @ Y0) = (X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (d2term @ d_one) @ id)))))) )),
% 17.66/3.02 inference(beta-eta_normalization,[],[f990])).
% 17.66/3.02 thf(f992,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y1) @ Y0) = (X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))))) | ($true = (((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (d2term @ d_one) @ id))))) )),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f991])).
% 17.66/3.02 thf(f993,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y1) @ Y0) = (X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0)))))))) @ (sK593 @ X1)))) | ($true = (((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))) => (sK592 @ id @ (d2term @ d_one) @ id))))) )),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f992])).
% 17.66/3.02 thf(f994,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y1) @ Y0) = (X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0)))))))) @ (sK593 @ X1)))) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id)))))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f993])).
% 17.66/3.02 thf(f995,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y1) @ Y0) = (X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0)))))))) @ (sK593 @ X1)))) | ($false = (((^[Y0 : term]: ((sK592 @ id @ Y0 @ id) => (sK592 @ id @ (X1 @ id @ Y0) @ id))) @ (sK594 @ X1)))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f994])).
% 17.66/3.02 thf(f996,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ (sK593 @ X1)) = (X1 @ (comp @ Y1 @ (sK593 @ X1)) @ (sub @ Y0 @ (sK593 @ X1)))))))))) | ($false = (((sK592 @ id @ (sK594 @ X1) @ id) => (sK592 @ id @ (X1 @ id @ (sK594 @ X1)) @ id)))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(beta-eta_normalization,[],[f995])).
% 17.66/3.02 thf(f997,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ (sK593 @ X1)) = (X1 @ (comp @ Y1 @ (sK593 @ X1)) @ (sub @ Y0 @ (sK593 @ X1))))))) @ (sK595 @ X1)))) | ($false = (((sK592 @ id @ (sK594 @ X1) @ id) => (sK592 @ id @ (X1 @ id @ (sK594 @ X1)) @ id)))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f996])).
% 17.66/3.02 thf(f999,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (X1 @ Y1 @ Y0) @ (sK593 @ X1)) = (X1 @ (comp @ Y1 @ (sK593 @ X1)) @ (sub @ Y0 @ (sK593 @ X1))))))) @ (sK595 @ X1)))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f997])).
% 17.66/3.02 thf(f1000,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = ((!! @ subst @ (^[Y0 : subst]: ((sub @ (X1 @ Y0 @ (sK595 @ X1)) @ (sK593 @ X1)) = (X1 @ (comp @ Y0 @ (sK593 @ X1)) @ (sub @ (sK595 @ X1) @ (sK593 @ X1)))))))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(beta-eta_normalization,[],[f999])).
% 17.66/3.02 thf(f1001,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : subst]: ((sub @ (X1 @ Y0 @ (sK595 @ X1)) @ (sK593 @ X1)) = (X1 @ (comp @ Y0 @ (sK593 @ X1)) @ (sub @ (sK595 @ X1) @ (sK593 @ X1))))) @ (sK596 @ X1)))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f1000])).
% 17.66/3.02 thf(f1002,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | ($false = (((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK593 @ X1)) = (X1 @ (comp @ (sK596 @ X1) @ (sK593 @ X1)) @ (sub @ (sK595 @ X1) @ (sK593 @ X1)))))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(beta-eta_normalization,[],[f1001])).
% 17.66/3.02 thf(f1003,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((hoasinduction_lem3v2a = $false) | (((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK593 @ X1))) != ((X1 @ (comp @ (sK596 @ X1) @ (sK593 @ X1)) @ (sub @ (sK595 @ X1) @ (sK593 @ X1))))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id))) | ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))) )),
% 17.66/3.02 inference(equality_proxy_clausification,[],[f1002])).
% 17.66/3.02 thf(f1008,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ Y1) => (sK591 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK591 @ (lam @ Y0)))))))),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f988])).
% 17.66/3.02 thf(f1009,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($true = ((!! @ term @ (^[Y0 : term]: ((sK591 @ Y0) = (sK592 @ id @ Y0 @ id))))))),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f988])).
% 17.66/3.02 thf(f1010,plain,(
% 17.66/3.02 ( ! [X1 : term] : ((hoasinduction_lem3v2a = $false) | ($true = (((^[Y0 : term]: ((sK591 @ Y0) = (sK592 @ id @ Y0 @ id))) @ X1)))) )),
% 17.66/3.02 inference(pi_proxy_clausification,[],[f1009])).
% 17.66/3.02 thf(f1011,plain,(
% 17.66/3.02 ( ! [X1 : term] : ((hoasinduction_lem3v2a = $false) | ($true = (((sK591 @ X1) = (sK592 @ id @ X1 @ id))))) )),
% 17.66/3.02 inference(beta-eta_normalization,[],[f1010])).
% 17.66/3.02 thf(f1012,plain,(
% 17.66/3.02 ( ! [X1 : term] : ((hoasinduction_lem3v2a = $false) | (((sK591 @ X1)) = ((sK592 @ id @ X1 @ id)))) )),
% 17.66/3.02 inference(equality_proxy_clausification,[],[f1011])).
% 17.66/3.02 thf(f1013,plain,(
% 17.66/3.02 ( ! [X1 : term] : ((hoasinduction_lem3v2a = $false) | ($true = ((sK591 @ X1))) | ($false = ((sK592 @ id @ X1 @ id)))) )),
% 17.66/3.02 inference(iff_proxy_clausification,[],[f1012])).
% 17.66/3.02 thf(f1015,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ Y1) => (sK591 @ (sub @ Y0 @ (push @ Y1 @ id)))))) => (sK591 @ (lam @ Y0)))) @ sK598)))),
% 17.66/3.02 inference(sigma_proxy_clausification,[],[f1008])).
% 17.66/3.02 thf(f1016,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = (((!! @ term @ (^[Y0 : term]: ((sK591 @ Y0) => (sK591 @ (sub @ sK598 @ (push @ Y0 @ id)))))) => (sK591 @ (lam @ sK598)))))),
% 17.66/3.02 inference(beta-eta_normalization,[],[f1015])).
% 17.66/3.02 thf(f1017,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ($false = ((sK591 @ (lam @ sK598))))),
% 17.66/3.02 inference(imp_proxy_clausification,[],[f1016])).
% 17.66/3.02 thf(f1166,plain,(
% 17.66/3.02 ( ! [X4 : term] : (($true = sP35) | (((sK224 @ id @ X4 @ id)) = $false) | ($true = ((sK225 @ X4)))) )),
% 17.66/3.02 inference(iff_proxy_clausification,[],[f469])).
% 17.66/3.02 thf(f1244,definition,(
% 17.66/3.02 spl607_1 <=> ($true = ((sK592 @ id @ (d2term @ d_one) @ id)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_1])],[avatar_definition])).
% 17.66/3.02 thf(f1245,plain,(
% 17.66/3.02 ($true != ((sK592 @ id @ (d2term @ d_one) @ id))) | spl607_1),
% 17.66/3.02 inference(avatar_component_clause,[],[f1244])).
% 17.66/3.02 thf(f1246,plain,(
% 17.66/3.02 ($true = ((sK592 @ id @ (d2term @ d_one) @ id))) | ~spl607_1),
% 17.66/3.02 inference(avatar_component_clause,[],[f1244])).
% 17.66/3.02 thf(f1248,definition,(
% 17.66/3.02 spl607_2 <=> ! [X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK593 @ X1))) != ((X1 @ (comp @ (sK596 @ X1) @ (sK593 @ X1)) @ (sub @ (sK595 @ X1) @ (sK593 @ X1))))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_2])],[avatar_definition])).
% 17.66/3.02 thf(f1249,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK596 @ X1) @ (sK595 @ X1)) @ (sK593 @ X1))) != ((X1 @ (comp @ (sK596 @ X1) @ (sK593 @ X1)) @ (sub @ (sK595 @ X1) @ (sK593 @ X1))))) | ($true = ((sK592 @ id @ (sK594 @ X1) @ id)))) ) | ~spl607_2),
% 17.66/3.02 inference(avatar_component_clause,[],[f1248])).
% 17.66/3.02 thf(f1251,definition,(
% 17.66/3.02 spl607_3 <=> (hoasinduction_lem3v2a = $false)),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_3])],[avatar_definition])).
% 17.66/3.02 thf(f1253,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $false) | ~spl607_3),
% 17.66/3.02 inference(avatar_component_clause,[],[f1251])).
% 17.66/3.02 thf(f1254,plain,(
% 17.66/3.02 spl607_1 | spl607_2 | spl607_3),
% 17.66/3.02 inference(avatar_split_clause,[],[f1003,f1251,f1248,f1244])).
% 17.66/3.02 thf(f1264,definition,(
% 17.66/3.02 spl607_6 <=> ! [X1 : term] : (($true = ((sK591 @ X1))) | ($false = ((sK592 @ id @ X1 @ id))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_6])],[avatar_definition])).
% 17.66/3.02 thf(f1265,plain,(
% 17.66/3.02 ( ! [X1 : term] : (($false = ((sK592 @ id @ X1 @ id))) | ($true = ((sK591 @ X1)))) ) | ~spl607_6),
% 17.66/3.02 inference(avatar_component_clause,[],[f1264])).
% 17.66/3.02 thf(f1266,plain,(
% 17.66/3.02 spl607_6 | spl607_3),
% 17.66/3.02 inference(avatar_split_clause,[],[f1013,f1251,f1264])).
% 17.66/3.02 thf(f1272,definition,(
% 17.66/3.02 spl607_8 <=> ($false = ((sK591 @ (lam @ sK598))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_8])],[avatar_definition])).
% 17.66/3.02 thf(f1274,plain,(
% 17.66/3.02 ($false = ((sK591 @ (lam @ sK598)))) | ~spl607_8),
% 17.66/3.02 inference(avatar_component_clause,[],[f1272])).
% 17.66/3.02 thf(f1275,plain,(
% 17.66/3.02 spl607_8 | spl607_3),
% 17.66/3.02 inference(avatar_split_clause,[],[f1017,f1251,f1272])).
% 17.66/3.02 thf(f1280,definition,(
% 17.66/3.02 spl607_10 <=> (hoasinduction_lem3v2a = $true)),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_10])],[avatar_definition])).
% 17.66/3.02 thf(f1282,plain,(
% 17.66/3.02 (hoasinduction_lem3v2a = $true) | ~spl607_10),
% 17.66/3.02 inference(avatar_component_clause,[],[f1280])).
% 17.66/3.02 thf(f1770,definition,(
% 17.66/3.02 spl607_120 <=> ($true = sP35)),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_120])],[avatar_definition])).
% 17.66/3.02 thf(f1774,plain,(
% 17.66/3.02 ~spl607_120 | spl607_10),
% 17.66/3.02 inference(avatar_split_clause,[],[f879,f1280,f1770])).
% 17.66/3.02 thf(f3211,definition,(
% 17.66/3.02 spl607_453 <=> ! [X5 : (subst > term > term)] : (($true = ((sK224 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | (((sub @ (X5 @ (sK228 @ X5) @ (sK229 @ X5)) @ (sK230 @ X5))) != ((X5 @ (comp @ (sK228 @ X5) @ (sK230 @ X5)) @ (sub @ (sK229 @ X5) @ (sK230 @ X5))))) | ($true = ((sK224 @ id @ (sK227 @ X5) @ id))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_453])],[avatar_definition])).
% 17.66/3.02 thf(f3212,plain,(
% 17.66/3.02 ( ! [X5 : (subst > term > term)] : (($true = ((sK224 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | (((sub @ (X5 @ (sK228 @ X5) @ (sK229 @ X5)) @ (sK230 @ X5))) != ((X5 @ (comp @ (sK228 @ X5) @ (sK230 @ X5)) @ (sub @ (sK229 @ X5) @ (sK230 @ X5))))) | ($true = ((sK224 @ id @ (sK227 @ X5) @ id)))) ) | ~spl607_453),
% 17.66/3.02 inference(avatar_component_clause,[],[f3211])).
% 17.66/3.02 thf(f3213,plain,(
% 17.66/3.02 spl607_453 | spl607_120),
% 17.66/3.02 inference(avatar_split_clause,[],[f467,f1770,f3211])).
% 17.66/3.02 thf(f3219,definition,(
% 17.66/3.02 spl607_455 <=> ! [X4 : term] : ((((sK224 @ id @ X4 @ id)) = $false) | ($true = ((sK225 @ X4))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_455])],[avatar_definition])).
% 17.66/3.02 thf(f3220,plain,(
% 17.66/3.02 ( ! [X4 : term] : ((((sK224 @ id @ X4 @ id)) = $false) | ($true = ((sK225 @ X4)))) ) | ~spl607_455),
% 17.66/3.02 inference(avatar_component_clause,[],[f3219])).
% 17.66/3.02 thf(f3221,plain,(
% 17.66/3.02 spl607_455 | spl607_120),
% 17.66/3.02 inference(avatar_split_clause,[],[f1166,f1770,f3219])).
% 17.66/3.02 thf(f3231,definition,(
% 17.66/3.02 spl607_458 <=> ($true = ((sK225 @ (lam @ sK226))))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_458])],[avatar_definition])).
% 17.66/3.02 thf(f3233,plain,(
% 17.66/3.02 ($true != ((sK225 @ (lam @ sK226)))) | spl607_458),
% 17.66/3.02 inference(avatar_component_clause,[],[f3231])).
% 17.66/3.02 thf(f3234,plain,(
% 17.66/3.02 ~spl607_458 | spl607_120),
% 17.66/3.02 inference(avatar_split_clause,[],[f471,f1770,f3231])).
% 17.66/3.02 thf(f4031,plain,(
% 17.66/3.02 ($true = $false) | (~spl607_3 | ~spl607_10)),
% 17.66/3.02 inference(forward_demodulation,[],[f1282,f1253])).
% 17.66/3.02 thf(f4032,plain,(
% 17.66/3.02 $false | (~spl607_3 | ~spl607_10)),
% 17.66/3.02 inference(trivial_inequality_removal,[],[f4031])).
% 17.66/3.02 thf(f4033,plain,(
% 17.66/3.02 ~spl607_3 | ~spl607_10),
% 17.66/3.02 inference(avatar_contradiction_clause,[],[f4032])).
% 17.66/3.02 thf(f4067,plain,(
% 17.66/3.02 ( ! [X278 : term] : ((((d2term @ d_one)) = X278)) )),
% 17.66/3.02 inference(forward_demodulation,[],[f752,f753])).
% 17.66/3.02 thf(f4069,plain,(
% 17.66/3.02 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 17.66/3.02 inference(constrained_superposition,[],[f4067,f4067])).
% 17.66/3.02 thf(f4072,plain,(
% 17.66/3.02 ( ! [X273 : subst] : ((((d2subst @ d_id)) = X273)) )),
% 17.66/3.02 inference(forward_demodulation,[],[f755,f756])).
% 17.66/3.02 thf(f4074,plain,(
% 17.66/3.02 ( ! [X0 : subst,X1 : subst] : ((X0 = X1)) )),
% 17.66/3.02 inference(constrained_superposition,[],[f4072,f4072])).
% 17.66/3.02 thf(f5531,definition,(
% 17.66/3.02 spl607_666 <=> ! [X3 : term] : ($true != ((sK225 @ X3)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_666])],[avatar_definition])).
% 17.66/3.02 thf(f5532,plain,(
% 17.66/3.02 ( ! [X3 : term] : (($true != ((sK225 @ X3)))) ) | ~spl607_666),
% 17.66/3.02 inference(avatar_component_clause,[],[f5531])).
% 17.66/3.02 thf(f5538,plain,(
% 17.66/3.02 ($true = ((sK592 @ id @ one @ id))) | ~spl607_1),
% 17.66/3.02 inference(forward_demodulation,[],[f1246,f758])).
% 17.66/3.02 thf(f5542,definition,(
% 17.66/3.02 spl607_668 <=> ! [X1 : term] : ($false = ((sK591 @ X1)))),
% 17.66/3.02 introduced(definition,[new_symbols(definition,[spl607_668])],[avatar_definition])).
% 17.66/3.02 thf(f5543,plain,(
% 17.66/3.02 ( ! [X1 : term] : (($false = ((sK591 @ X1)))) ) | ~spl607_668),
% 17.66/3.02 inference(avatar_component_clause,[],[f5542])).
% 17.66/3.02 thf(f5642,plain,(
% 17.66/3.02 ( ! [X0 : term] : (($false = ((sK591 @ X0)))) ) | ~spl607_8),
% 17.66/3.02 inference(constrained_superposition,[],[f1274,f4069])).
% 17.66/3.02 thf(f5645,plain,(
% 17.66/3.02 spl607_668 | ~spl607_8),
% 17.66/3.02 inference(avatar_split_clause,[],[f5642,f1272,f5542])).
% 17.66/3.02 thf(f5665,plain,(
% 17.66/3.02 ( ! [X0 : term] : (($true = ((sK592 @ id @ X0 @ id)))) ) | ~spl607_1),
% 17.66/3.02 inference(constrained_superposition,[],[f5538,f4069])).
% 17.66/3.02 thf(f5672,plain,(
% 17.66/3.02 ( ! [X0 : subst,X1 : term] : (($true = ((sK592 @ X0 @ X1 @ X0)))) ) | ~spl607_1),
% 17.66/3.02 inference(constrained_superposition,[],[f5665,f4074])).
% 17.66/3.02 thf(f6541,plain,(
% 17.66/3.02 ( ! [X0 : term] : (($true = $false) | ($true = ((sK591 @ X0)))) ) | (~spl607_1 | ~spl607_6)),
% 17.66/3.02 inference(constrained_superposition,[],[f5672,f1265])).
% 17.66/3.02 thf(f6542,plain,(
% 17.66/3.02 ( ! [X0 : term] : (($true = ((sK591 @ X0)))) ) | (~spl607_1 | ~spl607_6)),
% 17.66/3.02 inference(trivial_inequality_removal,[],[f6541])).
% 17.66/3.02 thf(f6554,plain,(
% 17.66/3.02 ($true != ((sK592 @ id @ one @ id))) | spl607_1),
% 17.66/3.02 inference(forward_demodulation,[],[f1245,f758])).
% 17.66/3.02 thf(f19735,plain,(
% 17.66/3.02 ( ! [X5 : (subst > term > term)] : (($true = ((sK224 @ id @ (lam @ (X5 @ sh @ one)) @ id))) | ($true = ((sK224 @ id @ (sK227 @ X5) @ id)))) ) | ~spl607_453),
% 17.66/3.02 inference(forward_subsumption_resolution,[],[f3212,f4069])).
% 17.66/3.02 thf(f19736,plain,(
% 17.66/3.02 ( ! [X5 : (subst > term > term)] : (($true = ((sK224 @ id @ (d2term @ d_one) @ id))) | ($true = ((sK224 @ id @ (sK227 @ X5) @ id)))) ) | ~spl607_453),
% 17.66/3.02 inference(forward_demodulation,[],[f19735,f4067])).
% 17.66/3.02 thf(f19737,plain,(
% 17.66/3.02 ( ! [X5 : (subst > term > term)] : (($true = ((sK224 @ id @ one @ id))) | ($true = ((sK224 @ id @ (sK227 @ X5) @ id)))) ) | ~spl607_453),
% 17.66/3.02 inference(forward_demodulation,[],[f19736,f758])).
% 17.66/3.02 thf(f20980,plain,(
% 17.66/3.02 ($true = ((sK224 @ id @ (d2term @ d_one) @ id))) | ($true = ((sK224 @ id @ one @ id))) | ~spl607_453),
% 17.66/3.02 inference(forward_demodulation,[],[f19737,f4067])).
% 17.66/3.02 thf(f20997,plain,(
% 17.66/3.02 ($true = ((sK224 @ id @ one @ id))) | ($true = ((sK224 @ id @ one @ id))) | ~spl607_453),
% 17.66/3.02 inference(forward_demodulation,[],[f20980,f758])).
% 17.66/3.02 thf(f20998,plain,(
% 17.66/3.02 ($true = ((sK224 @ id @ one @ id))) | ~spl607_453),
% 17.66/3.02 inference(duplicate_literal_removal,[],[f20997])).
% 17.66/3.02 thf(f73209,plain,(
% 17.66/3.02 ( ! [X4 : term] : ((((sK224 @ id @ X4 @ id)) = $false)) ) | (~spl607_455 | ~spl607_666)),
% 17.66/3.02 inference(forward_subsumption_resolution,[],[f3220,f5532])).
% 17.66/3.02 thf(f73241,plain,(
% 17.66/3.02 ($true = $false) | (~spl607_453 | ~spl607_455 | ~spl607_666)),
% 17.66/3.02 inference(constrained_superposition,[],[f73209,f20998])).
% 17.66/3.02 thf(f73443,plain,(
% 17.66/3.02 $false | (~spl607_453 | ~spl607_455 | ~spl607_666)),
% 17.66/3.02 inference(trivial_inequality_removal,[],[f73241])).
% 17.66/3.02 thf(f73444,plain,(
% 17.66/3.02 ~spl607_453 | ~spl607_455 | ~spl607_666),
% 17.66/3.02 inference(avatar_contradiction_clause,[],[f73443])).
% 17.66/3.02 thf(f73798,plain,(
% 17.66/3.02 ( ! [X0 : term] : (($true != ((sK225 @ X0)))) ) | spl607_458),
% 17.66/3.02 inference(constrained_superposition,[],[f3233,f4069])).
% 17.66/3.02 thf(f73872,plain,(
% 17.66/3.02 spl607_666 | spl607_458),
% 17.66/3.02 inference(avatar_split_clause,[],[f73798,f3231,f5531])).
% 17.66/3.02 thf(f73894,plain,(
% 17.66/3.02 ( ! [X1 : (subst > term > term)] : (($true = ((sK592 @ id @ (sK594 @ X1) @ id)))) ) | ~spl607_2),
% 17.66/3.02 inference(forward_subsumption_resolution,[],[f1249,f4069])).
% 17.66/3.02 thf(f73904,plain,(
% 17.66/3.02 ($true = ((sK592 @ id @ (d2term @ d_one) @ id))) | ~spl607_2),
% 17.66/3.02 inference(forward_demodulation,[],[f73894,f4067])).
% 17.66/3.02 thf(f73906,plain,(
% 17.66/3.02 ($true = ((sK592 @ id @ one @ id))) | ~spl607_2),
% 17.66/3.02 inference(forward_demodulation,[],[f73904,f758])).
% 17.66/3.02 thf(f76043,plain,(
% 17.66/3.02 $false | (spl607_1 | ~spl607_2)),
% 17.66/3.02 inference(forward_subsumption_resolution,[],[f73906,f6554])).
% 17.66/3.02 thf(f76044,plain,(
% 17.66/3.02 spl607_1 | ~spl607_2),
% 17.66/3.02 inference(avatar_contradiction_clause,[],[f76043])).
% 17.66/3.02 thf(f77225,plain,(
% 17.66/3.02 ($true = $false) | (~spl607_1 | ~spl607_6 | ~spl607_668)),
% 17.66/3.02 inference(forward_demodulation,[],[f6542,f5543])).
% 17.66/3.02 thf(f77226,plain,(
% 17.66/3.02 $false | (~spl607_1 | ~spl607_6 | ~spl607_668)),
% 17.66/3.02 inference(trivial_inequality_removal,[],[f77225])).
% 17.66/3.02 thf(f77227,plain,(
% 17.66/3.02 ~spl607_1 | ~spl607_6 | ~spl607_668),
% 17.66/3.02 inference(avatar_contradiction_clause,[],[f77226])).
% 17.66/3.02 cnf(s1, plain, spl607_1 | spl607_2 | spl607_3, inference(sat_conversion,[],[f1254])).
% 17.66/3.02 cnf(s4, plain, spl607_3 | spl607_6, inference(sat_conversion,[],[f1266])).
% 17.66/3.02 cnf(s6, plain, spl607_3 | spl607_8, inference(sat_conversion,[],[f1275])).
% 17.66/3.02 cnf(s103, plain, spl607_10 | ~spl607_120, inference(sat_conversion,[],[f1774])).
% 17.66/3.02 cnf(s425, plain, spl607_120 | spl607_453, inference(sat_conversion,[],[f3213])).
% 17.66/3.02 cnf(s427, plain, spl607_120 | spl607_455, inference(sat_conversion,[],[f3221])).
% 17.66/3.02 cnf(s430, plain, spl607_120 | ~spl607_458, inference(sat_conversion,[],[f3234])).
% 17.66/3.02 cnf(s622, plain, ~spl607_3 | ~spl607_10, inference(sat_conversion,[],[f4033])).
% 17.66/3.02 cnf(s681, plain, ~spl607_8 | spl607_668, inference(sat_conversion,[],[f5645])).
% 17.66/3.02 cnf(s2668, plain, ~spl607_453 | ~spl607_455 | ~spl607_666, inference(sat_conversion,[],[f73444])).
% 17.66/3.02 cnf(s2679, plain, spl607_458 | spl607_666, inference(sat_conversion,[],[f73872])).
% 17.66/3.02 cnf(s2807, plain, spl607_1 | ~spl607_2, inference(sat_conversion,[],[f76044])).
% 17.66/3.02 cnf(s2823, plain, ~spl607_1 | ~spl607_6 | ~spl607_668, inference(sat_conversion,[],[f77227])).
% 17.66/3.02 cnf(s2986, plain, spl607_120, inference(rat,[],[s2668,s2679,s425,s427,s430])).
% 17.66/3.02 cnf(s2999, plain, spl607_10, inference(rat,[],[s103,s2986])).
% 17.66/3.02 cnf(s3000, plain, ~spl607_3, inference(rat,[],[s622,s2999])).
% 17.66/3.02 cnf(s3001, plain, spl607_8, inference(rat,[],[s6,s3000])).
% 17.66/3.02 cnf(s3003, plain, spl607_6, inference(rat,[],[s4,s3000])).
% 17.66/3.02 cnf(s3005, plain, spl607_668, inference(rat,[],[s681,s3001])).
% 17.66/3.02 cnf(s3007, plain, ~spl607_1, inference(rat,[],[s2823,s3003,s3005])).
% 17.66/3.02 cnf(s3008, plain, ~spl607_2, inference(rat,[],[s2807,s3007])).
% 17.66/3.02 cnf(s3010, plain, $false, inference(rat,[],[s1,s3000,s3007,s3008])).
% 17.66/3.02 thf(f79298,plain,(
% 17.66/3.02 $false),
% 17.66/3.02 inference(avatar_sat_refutation,[],[s3010])).
% 17.66/3.02 % SZS output end Proof for theBenchmark
% 17.66/3.02 % (2859002)------------------------------
% 17.66/3.02 % (2859002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.66/3.02 % (2859002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.66/3.02 % (2859002)CaDiCaL version: 2.1.3
% 17.66/3.02 % (2859002)Termination reason: Refutation
% 17.66/3.02 % (2859002)Time elapsed: 2.712 s
% 17.66/3.02 % (2859002)Peak memory usage: 34 MB
% 17.66/3.02 % (2859002)Instructions burned: 6004 (million)
% 17.66/3.02 % (2858996)Success in time 2.782 s
% 17.66/3.02 % Vampire exiting
%------------------------------------------------------------------------------