%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX171^1 : 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 : n013.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 08:40:44 AM UTC 2026
% Result : Theorem 164.61s 23.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX171^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:09:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 3.95/1.00 % (2301573)Will run a generic schedule for satisfiability detection.
% 3.95/1.00 % (2301581)dis+10_1_sil=32000:sp=arity:random_seed=2331670202:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.95/1.00 % (2301579)% WARNING: option uhcvi not known.
% 3.95/1.00 % (2301578)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=411523383_2999 on theBenchmark for (2999ds/0Mi)
% 3.95/1.00 % (2301579)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2270617034:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.95/1.00 % (2301580)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1586298218:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.95/1.00 % (2301582)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3369525448:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.95/1.00 % (2301583)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1407715297:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.95/1.00 % (2301584)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2238393642:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.95/1.00 % (2301579)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.95/1.00 % (2301582)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.95/1.00 % (2301581)Instruction limit reached!
% 3.95/1.00 % (2301581)------------------------------
% 3.95/1.00 % (2301581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.00 % (2301581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.00 % (2301581)CaDiCaL version: 2.1.3
% 3.95/1.00 % (2301581)Termination reason: Instruction limit
% 3.95/1.00 % (2301581)Termination phase: Property scanning
% 3.95/1.00 % (2301581)Time elapsed: 0.024 s
% 3.95/1.00 % (2301581)Peak memory usage: 12 MB
% 3.95/1.00 % (2301581)Instructions burned: 108 (million)
% 3.95/1.00 % (2301592)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1573596703:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.95/1.00 % (2301582)Instruction limit reached!
% 3.95/1.00 % (2301582)------------------------------
% 3.95/1.00 % (2301582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.00 % (2301582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.00 % (2301582)CaDiCaL version: 2.1.3
% 3.95/1.00 % (2301582)Termination reason: Instruction limit
% 3.95/1.00 % (2301582)Termination phase: Property scanning
% 3.95/1.00 % (2301582)Time elapsed: 0.050 s
% 3.95/1.00 % (2301582)Peak memory usage: 12 MB
% 3.95/1.00 % (2301582)Instructions burned: 118 (million)
% 3.95/1.00 % (2301583)Instruction limit reached!
% 3.95/1.00 % (2301583)------------------------------
% 3.95/1.00 % (2301583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.00 % (2301583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.00 % (2301583)CaDiCaL version: 2.1.3
% 3.95/1.00 % (2301583)Termination reason: Instruction limit
% 3.95/1.00 % (2301583)Termination phase: Function definition elimination
% 3.95/1.00 % (2301583)Time elapsed: 0.055 s
% 3.95/1.00 % (2301583)Peak memory usage: 12 MB
% 3.95/1.00 % (2301583)Instructions burned: 132 (million)
% 3.95/1.00 % Exception at run slice level
% 3.95/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.95/1.00 % (2301584)Instruction limit reached!
% 3.95/1.00 % (2301584)------------------------------
% 3.95/1.00 % (2301584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.95/1.00 % (2301584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.00 % (2301584)CaDiCaL version: 2.1.3
% 3.95/1.00 % (2301584)Termination reason: Instruction limit
% 3.95/1.00 % (2301584)Termination phase: Property scanning
% 3.95/1.00 % (2301584)Time elapsed: 0.067 s
% 3.95/1.00 % (2301584)Peak memory usage: 13 MB
% 3.95/1.00 % (2301584)Instructions burned: 161 (million)
% 3.95/1.00 % (2301596)ott-21_1_sil=16000:fs=off:random_seed=2715286986:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.95/1.00 % (2301595)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=4238482279:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.95/1.00 % Exception at run slice level
% 3.95/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.77/2.71 % (2301579)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.77/2.71 % (2301597)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2216466053:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 16.77/2.71 % (2301594)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3246957359:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 16.77/2.71 % (2301595)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.77/2.71 % (2301600)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=840740101:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.77/2.71 % (2301596)Instruction limit reached!
% 16.77/2.71 % (2301596)------------------------------
% 16.77/2.71 % (2301596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.77/2.71 % (2301596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.77/2.71 % (2301596)CaDiCaL version: 2.1.3
% 16.77/2.71 % (2301596)Termination reason: Instruction limit
% 16.77/2.71 % (2301596)Termination phase: Property scanning
% 16.77/2.71 % (2301596)Time elapsed: 0.040 s
% 16.77/2.71 % (2301596)Peak memory usage: 12 MB
% 16.77/2.71 % (2301596)Instructions burned: 181 (million)
% 16.77/2.71 % (2301604)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3520562981:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.77/2.71 % (2301595)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 16.77/2.71 % Exception at run slice level
% 16.77/2.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.77/2.71 % (2301594)Instruction limit reached!
% 16.77/2.71 % (2301594)------------------------------
% 16.77/2.71 % (2301594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.77/2.71 % (2301594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.77/2.71 % (2301594)CaDiCaL version: 2.1.3
% 16.77/2.71 % (2301594)Termination reason: Instruction limit
% 16.77/2.71 % (2301594)Termination phase: Function definition elimination
% 16.77/2.71 % (2301594)Time elapsed: 0.088 s
% 16.77/2.71 % (2301594)Peak memory usage: 12 MB
% 16.77/2.71 % (2301594)Instructions burned: 131 (million)
% 16.77/2.71 % (2301606)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=137217748:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 16.77/2.71 % (2301607)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=2625413100: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)
% 16.77/2.71 % (2301607)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.77/2.71 % Exception at run slice level
% 16.77/2.71 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.77/2.71 % (2301610)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3882114374:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 16.77/2.71 % (2301597)Instruction limit reached!
% 16.77/2.71 % (2301597)------------------------------
% 16.77/2.71 % (2301597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.77/2.71 % (2301597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.77/2.71 % (2301597)CaDiCaL version: 2.1.3
% 16.77/2.71 % (2301597)Termination reason: Instruction limit
% 16.77/2.71 % (2301597)Termination phase: Saturation
% 16.77/2.71 % (2301597)Time elapsed: 0.223 s
% 16.77/2.71 % (2301597)Peak memory usage: 15 MB
% 16.77/2.71 % (2301597)Instructions burned: 479 (million)
% 16.77/2.71 % (2301610)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.77/2.71 % (2301612)fmb+10_1_sil=64000:random_seed=776568367:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 16.77/2.71 % (2301604)Instruction limit reached!
% 16.77/2.71 % (2301604)------------------------------
% 16.77/2.71 % (2301604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.77/2.71 % (2301604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.77/2.71 % (2301604)CaDiCaL version: 2.1.3
% 16.77/2.71 % (2301604)Termination reason: Instruction limit
% 16.77/2.71 % (2301604)Termination phase: Saturation
% 16.77/2.71 % (2301604)Time elapsed: 0.279 s
% 36.89/5.59 % (2301604)Peak memory usage: 22 MB
% 36.89/5.59 % (2301604)Instructions burned: 1180 (million)
% 36.89/5.59 % (2301612)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 36.89/5.59 % (2301595)Instruction limit reached!
% 36.89/5.59 % (2301595)------------------------------
% 36.89/5.59 % (2301595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.89/5.59 % (2301595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.89/5.59 % (2301595)CaDiCaL version: 2.1.3
% 36.89/5.59 % (2301595)Termination reason: Instruction limit
% 36.89/5.59 % (2301595)Termination phase: Saturation
% 36.89/5.59 % (2301595)Time elapsed: 0.343 s
% 36.89/5.59 % (2301595)Peak memory usage: 18 MB
% 36.89/5.59 % (2301595)Instructions burned: 685 (million)
% 36.89/5.59 % Exception at run slice level
% 36.89/5.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 36.89/5.59 % (2301614)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3854189142:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 36.89/5.59 % (2301616)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3228546073:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 36.89/5.59 % (2301615)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1385897286:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 36.89/5.59 % (2301616)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 36.89/5.59 % Exception at run slice level
% 36.89/5.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 36.89/5.59 % (2301620)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3799324137:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 36.89/5.59 % Exception at run slice level
% 36.89/5.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 36.89/5.59 % (2301607)Instruction limit reached!
% 36.89/5.59 % (2301607)------------------------------
% 36.89/5.59 % (2301607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.89/5.59 % (2301607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.89/5.59 % (2301607)CaDiCaL version: 2.1.3
% 36.89/5.59 % (2301607)Termination reason: Instruction limit
% 36.89/5.59 % (2301607)Termination phase: Saturation
% 36.89/5.59 % (2301607)Time elapsed: 0.321 s
% 36.89/5.59 % (2301607)Peak memory usage: 19 MB
% 36.89/5.59 % (2301607)Instructions burned: 694 (million)
% 36.89/5.59 % (2301622)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1148194745:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 36.89/5.59 % (2301623)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=15998435:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 36.89/5.59 % (2301620)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 36.89/5.59 % (2301620)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 36.89/5.59 % Exception at run slice level
% 36.89/5.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 36.89/5.59 % Exception at run slice level
% 36.89/5.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 36.89/5.59 % (2301626)ott-2_1_sil=16000:newcnf=on:random_seed=3097086992:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 36.89/5.59 % (2301627)ott+10_1_sil=32000:tgt=ground:random_seed=193129639:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 36.89/5.59 % (2301626)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 36.89/5.59 % (2301610)Instruction limit reached!
% 36.89/5.59 % (2301610)------------------------------
% 36.89/5.59 % (2301610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.89/5.59 % (2301610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.89/5.59 % (2301610)CaDiCaL version: 2.1.3
% 36.89/5.59 % (2301610)Termination reason: Instruction limit
% 36.89/5.59 % (2301610)Termination phase: Saturation
% 36.89/5.59 % (2301610)Time elapsed: 0.389 s
% 36.89/5.59 % (2301610)Peak memory usage: 20 MB
% 36.89/5.59 % (2301610)Instructions burned: 879 (million)
% 36.89/5.59 % (2301630)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1417185325:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 95.99/13.82 % Exception at run slice level
% 95.99/13.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 95.99/13.82 % (2301632)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=4069243130:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 95.99/13.82 % (2301632)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 95.99/13.82 % (2301626)Instruction limit reached!
% 95.99/13.82 % (2301626)------------------------------
% 95.99/13.82 % (2301626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 95.99/13.82 % (2301626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 95.99/13.82 % (2301626)CaDiCaL version: 2.1.3
% 95.99/13.82 % (2301626)Termination reason: Instruction limit
% 95.99/13.82 % (2301626)Termination phase: Saturation
% 95.99/13.82 % (2301626)Time elapsed: 0.386 s
% 95.99/13.82 % (2301626)Peak memory usage: 20 MB
% 95.99/13.82 % (2301626)Instructions burned: 871 (million)
% 95.99/13.82 % (2301634)dis+21_1_sil=32000:sas=cadical:random_seed=2546765350:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 95.99/13.82 % (2301620)Instruction limit reached!
% 95.99/13.82 % (2301620)------------------------------
% 95.99/13.82 % (2301620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 95.99/13.82 % (2301620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 95.99/13.82 % (2301620)CaDiCaL version: 2.1.3
% 95.99/13.82 % (2301620)Termination reason: Instruction limit
% 95.99/13.82 % (2301620)Termination phase: Saturation
% 95.99/13.82 % (2301620)Time elapsed: 0.699 s
% 95.99/13.82 % (2301620)Peak memory usage: 20 MB
% 95.99/13.82 % (2301620)Instructions burned: 1473 (million)
% 95.99/13.82 % (2301636)ott+11_1_sil=16000:gs=on:random_seed=2834360153:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2987 on theBenchmark for (2987ds/2251Mi)
% 95.99/13.82 % (2301636)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 95.99/13.82 % (2301616)Instruction limit reached!
% 95.99/13.82 % (2301616)------------------------------
% 95.99/13.82 % (2301616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 95.99/13.82 % (2301616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 95.99/13.82 % (2301616)CaDiCaL version: 2.1.3
% 95.99/13.82 % (2301616)Termination reason: Instruction limit
% 95.99/13.82 % (2301616)Termination phase: Saturation
% 95.99/13.82 % (2301616)Time elapsed: 1.393 s
% 95.99/13.82 % (2301616)Peak memory usage: 30 MB
% 95.99/13.82 % (2301616)Instructions burned: 5132 (million)
% 95.99/13.82 % (2301638)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3123539510:fmbsr=1.6:i=67534_2981 on theBenchmark for (2981ds/67534Mi)
% 95.99/13.82 % Exception at run slice level
% 95.99/13.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 95.99/13.82 % (2301640)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1551868699:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2980 on theBenchmark for (2980ds/4591Mi)
% 95.99/13.82 % (2301636)Instruction limit reached!
% 95.99/13.82 % (2301636)------------------------------
% 95.99/13.82 % (2301636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 95.99/13.82 % (2301636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 95.99/13.82 % (2301636)CaDiCaL version: 2.1.3
% 95.99/13.82 % (2301636)Termination reason: Instruction limit
% 95.99/13.82 % (2301636)Termination phase: Saturation
% 95.99/13.82 % (2301636)Time elapsed: 1.143 s
% 95.99/13.82 % (2301636)Peak memory usage: 30 MB
% 95.99/13.82 % (2301636)Instructions burned: 2253 (million)
% 95.99/13.82 % (2301642)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3177187217:i=29340_2975 on theBenchmark for (2975ds/29340Mi)
% 95.99/13.82 % (2301632)Instruction limit reached!
% 95.99/13.82 % (2301632)------------------------------
% 95.99/13.82 % (2301632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 95.99/13.82 % (2301632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 95.99/13.82 % (2301632)CaDiCaL version: 2.1.3
% 95.99/13.82 % (2301632)Termination reason: Instruction limit
% 95.99/13.82 % (2301632)Termination phase: Saturation
% 95.99/13.82 % (2301632)Time elapsed: 1.589 s
% 95.99/13.82 % (2301632)Peak memory usage: 30 MB
% 95.99/13.82 % (2301632)Instructions burned: 3512 (million)
% 95.99/13.82 % (2301644)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=3160800281:i=5211_2975 on theBenchmark for (2975ds/5211Mi)
% 116.42/16.73 % (2301634)Instruction limit reached!
% 116.42/16.73 % (2301634)------------------------------
% 116.42/16.73 % (2301634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 116.42/16.73 % (2301634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 116.42/16.73 % (2301634)CaDiCaL version: 2.1.3
% 116.42/16.73 % (2301634)Termination reason: Instruction limit
% 116.42/16.73 % (2301634)Termination phase: Saturation
% 116.42/16.73 % (2301634)Time elapsed: 1.666 s
% 116.42/16.73 % (2301634)Peak memory usage: 27 MB
% 116.42/16.73 % (2301634)Instructions burned: 3775 (million)
% 116.42/16.73 % (2301646)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=1640951750:i=5497:nm=2_2972 on theBenchmark for (2972ds/5497Mi)
% 116.42/16.73 % Exception at run slice level
% 116.42/16.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 116.42/16.73 % (2301648)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=1547916606:fmbsr=2:i=46332_2971 on theBenchmark for (2971ds/46332Mi)
% 116.42/16.73 % Exception at run slice level
% 116.42/16.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 116.42/16.73 % (2301650)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=3683343242:i=14071_2970 on theBenchmark for (2970ds/14071Mi)
% 116.42/16.73 % (2301627)Instruction limit reached!
% 116.42/16.73 % (2301627)------------------------------
% 116.42/16.73 % (2301627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 116.42/16.73 % (2301627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 116.42/16.73 % (2301627)CaDiCaL version: 2.1.3
% 116.42/16.73 % (2301627)Termination reason: Instruction limit
% 116.42/16.73 % (2301627)Termination phase: Saturation
% 116.42/16.73 % (2301627)Time elapsed: 2.287 s
% 116.42/16.73 % (2301627)Peak memory usage: 41 MB
% 116.42/16.73 % (2301627)Instructions burned: 5116 (million)
% 116.42/16.73 % (2301652)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2058392145:i=22565:add=on:rawr=on_2970 on theBenchmark for (2970ds/22565Mi)
% 116.42/16.73 % Exception at run slice level
% 116.42/16.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 116.42/16.73 % (2301654)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=3808452901:i=8173:av=off_2969 on theBenchmark for (2969ds/8173Mi)
% 116.42/16.73 % (2301640)Instruction limit reached!
% 116.42/16.73 % (2301640)------------------------------
% 116.42/16.73 % (2301640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 116.42/16.73 % (2301640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 116.42/16.73 % (2301640)CaDiCaL version: 2.1.3
% 116.42/16.73 % (2301640)Termination reason: Instruction limit
% 116.42/16.73 % (2301640)Termination phase: Saturation
% 116.42/16.73 % (2301640)Time elapsed: 1.177 s
% 116.42/16.73 % (2301640)Peak memory usage: 31 MB
% 116.42/16.73 % (2301640)Instructions burned: 4593 (million)
% 116.42/16.73 % (2301657)dis+10_16:1_sil=16000:random_seed=830774385:i=9155:fsr=off_2968 on theBenchmark for (2968ds/9155Mi)
% 116.42/16.73 % (2301644)Instruction limit reached!
% 116.42/16.73 % (2301644)------------------------------
% 116.42/16.73 % (2301644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 116.42/16.73 % (2301644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 116.42/16.73 % (2301644)CaDiCaL version: 2.1.3
% 116.42/16.73 % (2301644)Termination reason: Instruction limit
% 116.42/16.73 % (2301644)Termination phase: Saturation
% 116.42/16.73 % (2301644)Time elapsed: 2.404 s
% 116.42/16.73 % (2301644)Peak memory usage: 40 MB
% 116.42/16.73 % (2301644)Instructions burned: 5213 (million)
% 116.42/16.73 % (2301659)ott-3_8_sil=64000:random_seed=1581346352:i=20139:bs=on_2951 on theBenchmark for (2951ds/20139Mi)
% 116.42/16.73 % (2301657)Instruction limit reached!
% 116.42/16.73 % (2301657)------------------------------
% 116.42/16.73 % (2301657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 116.42/16.73 % (2301657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 116.42/16.73 % (2301657)CaDiCaL version: 2.1.3
% 116.42/16.73 % (2301657)Termination reason: Instruction limit
% 116.42/16.73 % (2301657)Termination phase: Saturation
% 116.42/16.73 % (2301657)Time elapsed: 2.214 s
% 116.42/16.73 % (2301657)Peak memory usage: 47 MB
% 116.42/16.73 % (2301657)Instructions burned: 9157 (million)
% 116.42/16.73 % (2301662)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=1408021368:fmbsr=2:i=32576_2946 on theBenchmark for (2946ds/32576Mi)
% 121.66/17.46 % Exception at run slice level
% 121.66/17.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 121.66/17.46 % (2301664)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=2335289473:i=11404_2946 on theBenchmark for (2946ds/11404Mi)
% 121.66/17.46 % (2301654)Instruction limit reached!
% 121.66/17.46 % (2301654)------------------------------
% 121.66/17.46 % (2301654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 121.66/17.46 % (2301654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 121.66/17.46 % (2301654)CaDiCaL version: 2.1.3
% 121.66/17.46 % (2301654)Termination reason: Instruction limit
% 121.66/17.46 % (2301654)Termination phase: Saturation
% 121.66/17.46 % (2301654)Time elapsed: 3.681 s
% 121.66/17.46 % (2301654)Peak memory usage: 45 MB
% 121.66/17.46 % (2301654)Instructions burned: 8174 (million)
% 121.66/17.46 % (2301666)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=1304771015:i=14134_2932 on theBenchmark for (2932ds/14134Mi)
% 121.66/17.46 % (2301666)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 121.66/17.46 % (2301664)Instruction limit reached!
% 121.66/17.46 % (2301664)------------------------------
% 121.66/17.46 % (2301664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 121.66/17.46 % (2301664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 121.66/17.46 % (2301664)CaDiCaL version: 2.1.3
% 121.66/17.46 % (2301664)Termination reason: Instruction limit
% 121.66/17.46 % (2301664)Termination phase: Saturation
% 121.66/17.46 % (2301664)Time elapsed: 2.774 s
% 121.66/17.46 % (2301664)Peak memory usage: 69 MB
% 121.66/17.46 % (2301664)Instructions burned: 11410 (million)
% 121.66/17.46 % (2301668)dis+33_16_sil=32000:sac=on:random_seed=2164656195:i=15851:nm=0_2918 on theBenchmark for (2918ds/15851Mi)
% 121.66/17.46 % (2301668)Instruction limit reached!
% 121.66/17.46 % (2301668)------------------------------
% 121.66/17.46 % (2301668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 121.66/17.46 % (2301668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 121.66/17.46 % (2301668)CaDiCaL version: 2.1.3
% 121.66/17.46 % (2301668)Termination reason: Instruction limit
% 121.66/17.46 % (2301668)Termination phase: Saturation
% 121.66/17.46 % (2301668)Time elapsed: 3.464 s
% 121.66/17.46 % (2301668)Peak memory usage: 19 MB
% 121.66/17.46 % (2301668)Instructions burned: 15856 (million)
% 121.66/17.46 % (2301670)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=1116119152:avsq=on:i=17627:add=on:amm=off_2883 on theBenchmark for (2883ds/17627Mi)
% 121.66/17.46 % (2301652)Instruction limit reached!
% 121.66/17.46 % (2301652)------------------------------
% 121.66/17.46 % (2301652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 121.66/17.46 % (2301652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 121.66/17.46 % (2301652)CaDiCaL version: 2.1.3
% 121.66/17.46 % (2301652)Termination reason: Instruction limit
% 121.66/17.46 % (2301652)Termination phase: Saturation
% 121.66/17.46 % (2301652)Time elapsed: 9.545 s
% 121.66/17.46 % (2301652)Peak memory usage: 52 MB
% 121.66/17.46 % (2301652)Instructions burned: 22567 (million)
% 121.66/17.46 % (2301672)ott+10_64_anc=all:sil=128000:sas=cadical:bsr=unit_only:nwc=1:cn=on:random_seed=1534034885:s2a=on:i=53295_2874 on theBenchmark for (2874ds/53295Mi)
% 121.66/17.47 % (2301666)Instruction limit reached!
% 121.66/17.47 % (2301666)------------------------------
% 121.66/17.47 % (2301666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 121.66/17.47 % (2301666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 121.66/17.47 % (2301666)CaDiCaL version: 2.1.3
% 121.66/17.47 % (2301666)Termination reason: Instruction limit
% 121.66/17.47 % (2301666)Termination phase: Saturation
% 121.66/17.47 % (2301666)Time elapsed: 6.362 s
% 121.66/17.47 % (2301666)Peak memory usage: 103 MB
% 121.66/17.47 % (2301666)Instructions burned: 14136 (million)
% 121.66/17.47 % (2301674)fmb+10_1_sil=32000:sas=cadical:fmbss=16:random_seed=249675471:i=26857:ins=20_2868 on theBenchmark for (2868ds/26857Mi)
% 121.66/17.47 % Exception at run slice level
% 121.66/17.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 121.66/17.47 % (2301676)ott+10_1_sil=64000:plsq=on:plsqc=4:bsr=unit_only:gs=on:random_seed=306779069:i=28120:bs=on:fsr=off_2867 on theBenchmark for (2867ds/28120Mi)
% 121.66/17.47 % (2301659)Instruction limit reached!
% 134.75/19.29 % (2301659)------------------------------
% 134.75/19.29 % (2301659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 134.75/19.29 % (2301659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 134.75/19.29 % (2301659)CaDiCaL version: 2.1.3
% 134.75/19.29 % (2301659)Termination reason: Instruction limit
% 134.75/19.29 % (2301659)Termination phase: Saturation
% 134.75/19.29 % (2301659)Time elapsed: 8.682 s
% 134.75/19.29 % (2301659)Peak memory usage: 60 MB
% 134.75/19.29 % (2301659)Instructions burned: 20141 (million)
% 134.75/19.29 % (2301678)fmb+10_1_sil=256000:fmbss=7:random_seed=761914454:fmbsr=1.6:i=182295_2864 on theBenchmark for (2864ds/182295Mi)
% 134.75/19.29 % Exception at run slice level
% 134.75/19.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 134.75/19.29 % (2301680)fmb+10_1_sil=128000:fmbss=21:newcnf=on:random_seed=353905043:i=44625:gsp=on_2863 on theBenchmark for (2863ds/44625Mi)
% 134.75/19.29 % (2301680)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 134.75/19.29 % (2301680)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 134.75/19.29 % Exception at run slice level
% 134.75/19.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 134.75/19.29 % (2301682)fmb+10_1_sil=256000:sas=cadical:fmbss=15:random_seed=2235101855:i=160505_2862 on theBenchmark for (2862ds/160505Mi)
% 134.75/19.29 % Exception at run slice level
% 134.75/19.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 134.75/19.29 % (2301684)fmb+10_1_sil=256000:tgt=full:fmbss=10:random_seed=533292365:fmbsr=1.3:i=225729_2861 on theBenchmark for (2861ds/225729Mi)
% 134.75/19.29 % Exception at run slice level
% 134.75/19.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 134.75/19.29 % (2301686)fmb+10_1_sil=256000:tgt=full:sas=cadical:fmbss=10:random_seed=2589854242:fmbsr=2:i=185024:ins=7_2860 on theBenchmark for (2860ds/185024Mi)
% 134.75/19.29 % Exception at run slice level
% 134.75/19.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 134.75/19.29 % (2301688)fmb+10_1_sas=cadical:si=on:bce=on:rp=on:random_seed=1643372493:rtra=on_2859 on theBenchmark for (2859ds/0Mi)
% 134.75/19.29 % Exception at run slice level
% 134.75/19.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 134.75/19.29 % (2301690)% WARNING: option uhcvi not known.
% 134.75/19.29 % (2301690)dis+11_61:31_drc=ordering:si=on:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2466376958:i=271062:add=off:rtra=on:rawr=on_2858 on theBenchmark for (2858ds/271062Mi)
% 134.75/19.29 % (2301690)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 134.75/19.29 % (2301690)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 134.75/19.29 % (2301642)Instruction limit reached!
% 134.75/19.29 % (2301642)------------------------------
% 134.75/19.29 % (2301642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 134.75/19.29 % (2301642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 134.75/19.29 % (2301642)CaDiCaL version: 2.1.3
% 134.75/19.29 % (2301642)Termination reason: Instruction limit
% 134.75/19.29 % (2301642)Termination phase: Saturation
% 134.75/19.29 % (2301642)Time elapsed: 13.484 s
% 134.75/19.29 % (2301642)Peak memory usage: 81 MB
% 134.75/19.29 % (2301642)Instructions burned: 29340 (million)
% 134.75/19.29 % (2301692)dis+10_161_sil=256000:plsq=on:si=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4052623642:i=176048:add=on:rtra=on:rawr=on_2840 on theBenchmark for (2840ds/176048Mi)
% 134.75/19.29 % (2301670)Instruction limit reached!
% 134.75/19.29 % (2301670)------------------------------
% 134.75/19.29 % (2301670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 134.75/19.29 % (2301670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 134.75/19.29 % (2301670)CaDiCaL version: 2.1.3
% 134.75/19.29 % (2301670)Termination reason: Instruction limit
% 134.75/19.29 % (2301670)Termination phase: Saturation
% 134.75/19.29 % (2301670)Time elapsed: 4.799 s
% 134.75/19.29 % (2301670)Peak memory usage: 94 MB
% 134.75/19.29 % (2301670)Instructions burned: 17628 (million)
% 134.75/19.29 % (2301694)dis+10_1_sil=32000:si=on:sp=arity:random_seed=2925252880:i=206:fgj=on:rtra=on_2835 on theBenchmark for (2835ds/206Mi)
% 164.61/23.49 % (2301694)Instruction limit reached!
% 164.61/23.49 % (2301694)------------------------------
% 164.61/23.49 % (2301694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301694)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301694)Termination reason: Instruction limit
% 164.61/23.49 % (2301694)Termination phase: Saturation
% 164.61/23.49 % (2301694)Time elapsed: 0.046 s
% 164.61/23.49 % (2301694)Peak memory usage: 14 MB
% 164.61/23.49 % (2301694)Instructions burned: 211 (million)
% 164.61/23.49 % (2301696)ott+31_1_sil=16000:si=on:lcm=predicate:bce=on:newcnf=on:random_seed=3673145712:i=232:rtra=on_2834 on theBenchmark for (2834ds/232Mi)
% 164.61/23.49 % (2301696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 164.61/23.49 % (2301696)Instruction limit reached!
% 164.61/23.49 % (2301696)------------------------------
% 164.61/23.49 % (2301696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301696)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301696)Termination reason: Instruction limit
% 164.61/23.49 % (2301696)Termination phase: Saturation
% 164.61/23.49 % (2301696)Time elapsed: 0.052 s
% 164.61/23.49 % (2301696)Peak memory usage: 14 MB
% 164.61/23.49 % (2301696)Instructions burned: 233 (million)
% 164.61/23.49 % (2301698)ott+1_1_to=lpo:sil=16000:si=on:sp=reverse_arity:erd=off:random_seed=3162198226:i=262:rtra=on_2833 on theBenchmark for (2833ds/262Mi)
% 164.61/23.49 % (2301698)Instruction limit reached!
% 164.61/23.49 % (2301698)------------------------------
% 164.61/23.49 % (2301698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301698)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301698)Termination reason: Instruction limit
% 164.61/23.49 % (2301698)Termination phase: Saturation
% 164.61/23.49 % (2301698)Time elapsed: 0.059 s
% 164.61/23.49 % (2301698)Peak memory usage: 15 MB
% 164.61/23.49 % (2301698)Instructions burned: 263 (million)
% 164.61/23.49 % (2301700)ott-3_16_to=lpo:sil=16000:si=on:sp=arity:fd=off:rp=on:random_seed=1128637690:i=318:bs=unit_only:nicw=on:fsr=off:rtra=on:amm=off_2833 on theBenchmark for (2833ds/318Mi)
% 164.61/23.49 % (2301700)Instruction limit reached!
% 164.61/23.49 % (2301700)------------------------------
% 164.61/23.49 % (2301700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301700)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301700)Termination reason: Instruction limit
% 164.61/23.49 % (2301700)Termination phase: Saturation
% 164.61/23.49 % (2301700)Time elapsed: 0.076 s
% 164.61/23.49 % (2301700)Peak memory usage: 16 MB
% 164.61/23.49 % (2301700)Instructions burned: 329 (million)
% 164.61/23.49 % (2301702)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:si=on:random_seed=3732384484:i=1428:nm=2:rtra=on_2832 on theBenchmark for (2832ds/1428Mi)
% 164.61/23.49 % Exception at run slice level
% 164.61/23.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 164.61/23.49 % (2301704)ott+32_1_sil=16000:bsd=on:si=on:sp=const_max:bce=on:random_seed=3535525556:i=262:bd=preordered:rtra=on:fsd=on_2831 on theBenchmark for (2831ds/262Mi)
% 164.61/23.49 % (2301704)Instruction limit reached!
% 164.61/23.49 % (2301704)------------------------------
% 164.61/23.49 % (2301704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301704)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301704)Termination reason: Instruction limit
% 164.61/23.49 % (2301704)Termination phase: Saturation
% 164.61/23.49 % (2301704)Time elapsed: 0.059 s
% 164.61/23.49 % (2301704)Peak memory usage: 15 MB
% 164.61/23.49 % (2301704)Instructions burned: 264 (million)
% 164.61/23.49 % (2301706)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:si=on:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4008178536:i=1368:slsql=off:bs=unit_only:nicw=on:rtra=on:rawr=on_2831 on theBenchmark for (2831ds/1368Mi)
% 164.61/23.49 % (2301706)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 164.61/23.49 % (2301706)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 164.61/23.49 % (2301706)Instruction limit reached!
% 164.61/23.49 % (2301706)------------------------------
% 164.61/23.49 % (2301706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301706)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301706)Termination reason: Instruction limit
% 164.61/23.49 % (2301706)Termination phase: Saturation
% 164.61/23.49 % (2301706)Time elapsed: 0.329 s
% 164.61/23.49 % (2301706)Peak memory usage: 20 MB
% 164.61/23.49 % (2301706)Instructions burned: 1371 (million)
% 164.61/23.49 % (2301708)ott-21_1_sil=16000:si=on:fs=off:random_seed=2643774283:i=360:av=off:fsr=off:rtra=on_2827 on theBenchmark for (2827ds/360Mi)
% 164.61/23.49 % (2301708)Instruction limit reached!
% 164.61/23.49 % (2301708)------------------------------
% 164.61/23.49 % (2301708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301708)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301708)Termination reason: Instruction limit
% 164.61/23.49 % (2301708)Termination phase: Saturation
% 164.61/23.49 % (2301708)Time elapsed: 0.079 s
% 164.61/23.49 % (2301708)Peak memory usage: 14 MB
% 164.61/23.49 % (2301708)Instructions burned: 361 (million)
% 164.61/23.49 % (2301710)dis+10_4_sil=64000:si=on:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1503934295:i=954:bd=all:rtra=on_2826 on theBenchmark for (2826ds/954Mi)
% 164.61/23.49 % (2301710)Instruction limit reached!
% 164.61/23.49 % (2301710)------------------------------
% 164.61/23.49 % (2301710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301710)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301710)Termination reason: Instruction limit
% 164.61/23.49 % (2301710)Termination phase: Saturation
% 164.61/23.49 % (2301710)Time elapsed: 0.273 s
% 164.61/23.49 % (2301710)Peak memory usage: 18 MB
% 164.61/23.49 % (2301710)Instructions burned: 957 (million)
% 164.61/23.49 % (2301712)fmb+10_1_sil=64000:si=on:erd=off:updr=off:random_seed=3998041251:fmbsr=1.3:i=1730:ins=25:rtra=on_2823 on theBenchmark for (2823ds/1730Mi)
% 164.61/23.49 % Exception at run slice level
% 164.61/23.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 164.61/23.49 % (2301714)ott+10_1_to=lpo:sil=64000:tgt=full:si=on:sp=arity:spb=goal_then_units:random_seed=1428443464:i=2358:rtra=on_2823 on theBenchmark for (2823ds/2358Mi)
% 164.61/23.49 % (2301714)Instruction limit reached!
% 164.61/23.49 % (2301714)------------------------------
% 164.61/23.49 % (2301714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301714)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301714)Termination reason: Instruction limit
% 164.61/23.49 % (2301714)Termination phase: Saturation
% 164.61/23.49 % (2301714)Time elapsed: 0.570 s
% 164.61/23.49 % (2301714)Peak memory usage: 25 MB
% 164.61/23.49 % (2301714)Instructions burned: 2362 (million)
% 164.61/23.49 % (2301716)fmb+10_1_sil=64000:si=on:erd=off:fmbss=14:random_seed=335612048:i=1778:ins=1:rtra=on_2817 on theBenchmark for (2817ds/1778Mi)
% 164.61/23.49 % Exception at run slice level
% 164.61/23.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 164.61/23.49 % (2301718)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:si=on:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1961897460:avsq=on:s2a=on:i=1384:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rtra=on:rawr=on_2816 on theBenchmark for (2816ds/1384Mi)
% 164.61/23.49 % (2301718)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 164.61/23.49 % (2301718)Instruction limit reached!
% 164.61/23.49 % (2301718)------------------------------
% 164.61/23.49 % (2301718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301718)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301718)Termination reason: Instruction limit
% 164.61/23.49 % (2301718)Termination phase: Saturation
% 164.61/23.49 % (2301718)Time elapsed: 0.650 s
% 164.61/23.49 % (2301718)Peak memory usage: 22 MB
% 164.61/23.49 % (2301718)Instructions burned: 1384 (million)
% 164.61/23.49 % (2301720)dis-10_1_anc=none:sil=64000:si=on:spb=goal:newcnf=on:cn=on:random_seed=2727132632:i=1758:kws=inv_precedence:fsr=off:rtra=on_2809 on theBenchmark for (2809ds/1758Mi)
% 164.61/23.49 % (2301720)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 164.61/23.49 % (2301720)Instruction limit reached!
% 164.61/23.49 % (2301720)------------------------------
% 164.61/23.49 % (2301720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 164.61/23.49 % (2301720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 164.61/23.49 % (2301720)CaDiCaL version: 2.1.3
% 164.61/23.49 % (2301720)Termination reason: Instruction limit
% 164.61/23.49 % (2301720)Termination phase: Saturation
% 164.61/23.49 % (2301720)Time elapsed: 0.818 s
% 164.61/23.49 % (2301720)Peak memory usage: 26 MB
% 164.61/23.49 % (2301720)Instructions burned: 1760 (million)
% 164.61/23.49 % (2301722)fmb+10_1_sil=64000:si=on:random_seed=3663514521:i=44122:nm=2:rtra=on:gsp=on_2801 on theBenchmark for (2801ds/44122Mi)
% 164.61/23.49 % (2301722)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 164.61/23.49 % Exception at run slice level
% 164.61/23.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 164.61/23.49 % (2301724)fmb+10_1_sil=16000:sas=cadical:si=on:fmbss=20:random_seed=1575365140:i=19030:nm=5:rtra=on_2800 on theBenchmark for (2800ds/19030Mi)
% 164.61/23.49 % Exception at run slice level
% 164.61/23.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 164.61/23.49 % (2301726)fmb+10_1_sil=64000:sas=cadical:si=on:fmbss=8:random_seed=548595969:fmbsr=1.7:i=1840:rtra=on_2799 on theBenchmark for (2799ds/1840Mi)
% 164.61/23.49 % Exception at run slice level
% 164.61/23.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 164.61/23.49 % (2301728)dis-4_1_sil=16000:drc=ordering:si=on:sp=const_frequency:sac=on:newcnf=on:random_seed=1546973946:i=10262:rtra=on_2798 on theBenchmark for (2798ds/10262Mi)
% 164.61/23.49 % (2301728)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 164.61/23.49 % (2301728) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2301573-2301728"...
% 164.61/23.49 % (2301728)...printing done.
% 164.61/23.49 % (2301728)Refutation found. Thanks to Tanya!
% 164.61/23.49 % SZS status Theorem for theBenchmark
% 164.61/23.49 % SZS output start Proof for theBenchmark
% 164.61/23.49 thf(type_def_5, type, term: $tType).
% 164.61/23.49 thf(type_def_6, type, subst: $tType).
% 164.61/23.49 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 164.61/23.49 thf(type_def_8, type, d_term: $tType).
% 164.61/23.49 thf(type_def_9, type, d_subst: $tType).
% 164.61/23.49 thf(func_def_0, type, one: term).
% 164.61/23.49 thf(func_def_1, type, ap: (term > term > term)).
% 164.61/23.49 thf(func_def_2, type, lam: (term > term)).
% 164.61/23.49 thf(func_def_3, type, sub: (term > subst > term)).
% 164.61/23.49 thf(func_def_4, type, id: subst).
% 164.61/23.49 thf(func_def_5, type, sh: subst).
% 164.61/23.49 thf(func_def_6, type, push: (term > subst > subst)).
% 164.61/23.49 thf(func_def_7, type, comp: (subst > subst > subst)).
% 164.61/23.49 thf(func_def_8, type, var: (term > $o)).
% 164.61/23.49 thf(func_def_9, type, pushprop_lem1v2: $o).
% 164.61/23.49 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 164.61/23.49 thf(func_def_11, type, axmap: $o).
% 164.61/23.49 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 164.61/23.49 thf(func_def_13, type, shinj: $o).
% 164.61/23.49 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 164.61/23.49 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 164.61/23.49 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 164.61/23.49 thf(func_def_17, type, induction2lem: $o).
% 164.61/23.49 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 164.61/23.49 thf(func_def_19, type, axvarshift: $o).
% 164.61/23.49 thf(func_def_20, type, hoasapinj2: $o).
% 164.61/23.49 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 164.61/23.49 thf(func_def_22, type, hoasapinj1: $o).
% 164.61/23.49 thf(func_def_23, type, ulamvar1: $o).
% 164.61/23.49 thf(func_def_24, type, induction2lem_lthm: $o).
% 164.61/23.49 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 164.61/23.49 thf(func_def_26, type, apnotvar: $o).
% 164.61/23.49 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 164.61/23.49 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 164.61/23.49 thf(func_def_29, type, hoasinduction_lthm: $o).
% 164.61/23.49 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 164.61/23.49 thf(func_def_31, type, hoaslaminj: $o).
% 164.61/23.49 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 164.61/23.49 thf(func_def_33, type, induction2lem_gthm: $o).
% 164.61/23.49 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 164.61/23.49 thf(func_def_35, type, hoasinduction_lem3: $o).
% 164.61/23.49 thf(func_def_36, type, hoasinduction_lem2: $o).
% 164.61/23.49 thf(func_def_37, type, termmset_lthm: $o).
% 164.61/23.49 thf(func_def_38, type, hoasinduction_lem1: $o).
% 164.61/23.49 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 164.61/23.49 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 164.61/23.49 thf(func_def_41, type, hoasapnotvar: $o).
% 164.61/23.49 thf(func_def_42, type, hoasinduction_lem0: $o).
% 164.61/23.49 thf(func_def_43, type, hoasinduction: $o).
% 164.61/23.49 thf(func_def_44, type, hoasinduction_gthm: $o).
% 164.61/23.49 thf(func_def_45, type, axapp: $o).
% 164.61/23.49 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 164.61/23.49 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 164.61/23.49 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 164.61/23.49 thf(func_def_49, type, ulamvarind: $o).
% 164.61/23.49 thf(func_def_50, type, induction: $o).
% 164.61/23.49 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 164.61/23.49 thf(func_def_52, type, termmset_gthm: $o).
% 164.61/23.49 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 164.61/23.49 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 164.61/23.49 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 164.61/23.49 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 164.61/23.49 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 164.61/23.49 thf(func_def_58, type, pushprop_lem2v2: $o).
% 164.61/23.49 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 164.61/23.49 thf(func_def_60, type, axclos: $o).
% 164.61/23.49 thf(func_def_61, type, axassoc: $o).
% 164.61/23.49 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 164.61/23.49 thf(func_def_63, type, pushprop_lthm: $o).
% 164.61/23.49 thf(func_def_64, type, apinj2: $o).
% 164.61/23.49 thf(func_def_65, type, apinj1: $o).
% 164.61/23.49 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 164.61/23.49 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 164.61/23.49 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 164.61/23.49 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 164.61/23.49 thf(func_def_70, type, axvarcons: $o).
% 164.61/23.49 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 164.61/23.49 thf(func_def_72, type, axscons: $o).
% 164.61/23.49 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 164.61/23.49 thf(func_def_74, type, axidr: $o).
% 164.61/23.49 thf(func_def_75, type, pushprop_lem1: $o).
% 164.61/23.49 thf(func_def_76, type, laminj: $o).
% 164.61/23.49 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 164.61/23.49 thf(func_def_78, type, pushprop_lem0: $o).
% 164.61/23.49 thf(func_def_79, type, pushprop_gthm: $o).
% 164.61/23.49 thf(func_def_80, type, axabs: $o).
% 164.61/23.49 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 164.61/23.49 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 164.61/23.49 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 164.61/23.49 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 164.61/23.49 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 164.61/23.49 thf(func_def_86, type, lamnotap: $o).
% 164.61/23.49 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 164.61/23.49 thf(func_def_88, type, hoaslamnotvar: $o).
% 164.61/23.49 thf(func_def_89, type, axidl: $o).
% 164.61/23.49 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 164.61/23.49 thf(func_def_91, type, induction2_lthm: $o).
% 164.61/23.49 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 164.61/23.49 thf(func_def_93, type, substmonoid_lthm: $o).
% 164.61/23.49 thf(func_def_94, type, pushprop: $o).
% 164.61/23.49 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 164.61/23.49 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 164.61/23.49 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 164.61/23.49 thf(func_def_98, type, substmonoid: $o).
% 164.61/23.49 thf(func_def_99, type, lamnotvar: $o).
% 164.61/23.49 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 164.61/23.49 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 164.61/23.49 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 164.61/23.49 thf(func_def_103, type, induction2_gthm: $o).
% 164.61/23.49 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 164.61/23.49 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_106, type, hoaslamnotap: $o).
% 164.61/23.49 thf(func_def_107, type, substmonoid_gthm: $o).
% 164.61/23.49 thf(func_def_108, type, ulamvarsh: $o).
% 164.61/23.49 thf(func_def_109, type, induction2: $o).
% 164.61/23.49 thf(func_def_110, type, pushprop_lem3v2: $o).
% 164.61/23.49 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 164.61/23.49 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 164.61/23.49 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 164.61/23.49 thf(func_def_114, type, axshiftcons: $o).
% 164.61/23.49 thf(func_def_115, type, termmset: $o).
% 164.61/23.49 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 164.61/23.49 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 164.61/23.49 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 164.61/23.49 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 164.61/23.49 thf(func_def_120, type, axvarid: $o).
% 164.61/23.49 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 164.61/23.49 thf(func_def_122, type, d2term: (d_term > term)).
% 164.61/23.49 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 164.61/23.49 thf(func_def_124, type, d_one: d_term).
% 164.61/23.49 thf(func_def_125, type, d_id: d_subst).
% 164.61/23.49 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 164.61/23.49 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 164.61/23.49 thf(func_def_129, type, db4: !>[X0: $tType]:(X0)).
% 164.61/23.49 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)).
% 164.61/23.49 thf(func_def_131, type, db2: !>[X0: $tType]:(X0)).
% 164.61/23.49 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 164.61/23.49 thf(func_def_133, type, db3: !>[X0: $tType]:(X0)).
% 164.61/23.49 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 164.61/23.49 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 164.61/23.49 thf(func_def_138, type, sP0: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_139, type, sP1: $o).
% 164.61/23.49 thf(func_def_140, type, sP2: $o).
% 164.61/23.49 thf(func_def_141, type, sP3: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_142, type, sP4: $o).
% 164.61/23.49 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_144, type, sP6: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_145, type, sP7: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_146, type, sP8: $o).
% 164.61/23.49 thf(func_def_147, type, sP9: $o).
% 164.61/23.49 thf(func_def_148, type, sP10: $o).
% 164.61/23.49 thf(func_def_149, type, sP11: $o).
% 164.61/23.49 thf(func_def_150, type, sP12: $o).
% 164.61/23.49 thf(func_def_151, type, sP13: $o).
% 164.61/23.49 thf(func_def_152, type, sP14: $o).
% 164.61/23.49 thf(func_def_153, type, sP15: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_154, type, sP16: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_155, type, sP17: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_156, type, sP18: $o).
% 164.61/23.49 thf(func_def_157, type, sP19: $o).
% 164.61/23.49 thf(func_def_158, type, sP20: $o).
% 164.61/23.49 thf(func_def_159, type, sP21: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_160, type, sP22: $o).
% 164.61/23.49 thf(func_def_161, type, sP23: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_162, type, sP24: $o).
% 164.61/23.49 thf(func_def_163, type, sP25: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_164, type, sP26: $o).
% 164.61/23.49 thf(func_def_165, type, sP27: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_166, type, sP28: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_167, type, sP29: $o).
% 164.61/23.49 thf(func_def_168, type, sP30: $o).
% 164.61/23.49 thf(func_def_169, type, sP31: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_171, type, sP33: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_172, type, sP34: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_173, type, sP35: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_174, type, sP36: $o).
% 164.61/23.49 thf(func_def_175, type, sP37: $o).
% 164.61/23.49 thf(func_def_176, type, sP38: $o).
% 164.61/23.49 thf(func_def_177, type, sP39: $o).
% 164.61/23.49 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_179, type, sP41: $o).
% 164.61/23.49 thf(func_def_180, type, sP42: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_181, type, sP43: ((term > $o) > $o)).
% 164.61/23.49 thf(func_def_182, type, sP44: $o).
% 164.61/23.49 thf(func_def_183, type, sP45: $o).
% 164.61/23.49 thf(func_def_184, type, sP46: $o).
% 164.61/23.49 thf(func_def_185, type, sP47: $o).
% 164.61/23.49 thf(func_def_186, type, sP48: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_187, type, sP49: $o).
% 164.61/23.49 thf(func_def_188, type, sP50: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_189, type, sP51: $o).
% 164.61/23.49 thf(func_def_190, type, sP52: $o).
% 164.61/23.49 thf(func_def_191, type, sP53: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_192, type, sP54: $o).
% 164.61/23.49 thf(func_def_193, type, sP55: $o).
% 164.61/23.49 thf(func_def_194, type, sP56: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_195, type, sP57: ((subst > term > subst > $o) > $o)).
% 164.61/23.49 thf(func_def_196, type, sP58: $o).
% 164.61/23.49 thf(func_def_197, type, sK59: term).
% 164.61/23.49 thf(func_def_198, type, sK60: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_199, type, sK61: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_200, type, sK62: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_201, type, sK63: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_202, type, sK64: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_203, type, sK65: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_204, type, sK66: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_205, type, sK67: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_206, type, sK68: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_207, type, sK69: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_208, type, sK70: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_209, type, sK71: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_210, type, sK72: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_211, type, sK73: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_212, type, sK74: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_213, type, sK75: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_214, type, sK76: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_215, type, sK77: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_216, type, sK78: term).
% 164.61/23.49 thf(func_def_217, type, sK79: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_218, type, sK80: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_219, type, sK81: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_220, type, sK82: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_221, type, sK83: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_222, type, sK84: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_223, type, sK85: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_225, type, sK87: (term > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_226, type, sK88: term).
% 164.61/23.49 thf(func_def_227, type, sK89: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_228, type, sK90: ((subst > term > subst > $o) > term > term)).
% 164.61/23.49 thf(func_def_229, type, sK91: term).
% 164.61/23.49 thf(func_def_230, type, sK92: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_231, type, sK93: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_232, type, sK94: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_233, type, sK95: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_234, type, sK96: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_235, type, sK97: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_236, type, sK98: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_237, type, sK99: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_238, type, sK100: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_240, type, sK102: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_241, type, sK103: term).
% 164.61/23.49 thf(func_def_242, type, sK104: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_243, type, sK105: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_244, type, sK106: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_245, type, sK107: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_246, type, sK108: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_247, type, sK109: (term > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_248, type, sK110: (term > $o)).
% 164.61/23.49 thf(func_def_249, type, sK111: term).
% 164.61/23.49 thf(func_def_250, type, sK112: term).
% 164.61/23.49 thf(func_def_251, type, sK113: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_252, type, sK114: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_253, type, sK115: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_254, type, sK116: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_255, type, sK117: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_256, type, sK118: ((subst > term > subst > $o) > (term > $o) > term)).
% 164.61/23.49 thf(func_def_257, type, sK119: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_258, type, sK120: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_263, type, sK125: term).
% 164.61/23.49 thf(func_def_264, type, sK126: term).
% 164.61/23.49 thf(func_def_265, type, sK127: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_270, type, sK132: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_271, type, sK133: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_272, type, sK134: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_273, type, sK135: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_274, type, sK136: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_275, type, sK137: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_276, type, sK138: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_277, type, sK139: term).
% 164.61/23.49 thf(func_def_278, type, sK140: (term > $o)).
% 164.61/23.49 thf(func_def_279, type, sK141: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_280, type, sK142: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_281, type, sK143: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_282, type, sK144: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_283, type, sK145: ((term > $o) > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_284, type, sK146: ((term > $o) > term > term)).
% 164.61/23.49 thf(func_def_285, type, sK147: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_286, type, sK148: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_287, type, sK149: term).
% 164.61/23.49 thf(func_def_288, type, sK150: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_289, type, sK151: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_290, type, sK152: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_291, type, sK153: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_292, type, sK154: (term > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_293, type, sK155: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_294, type, sK156: ((term > $o) > subst > term)).
% 164.61/23.49 thf(func_def_295, type, sK157: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_296, type, sK158: term).
% 164.61/23.49 thf(func_def_297, type, sK159: subst).
% 164.61/23.49 thf(func_def_298, type, sK160: term).
% 164.61/23.49 thf(func_def_299, type, sK161: (term > $o)).
% 164.61/23.49 thf(func_def_300, type, sK162: (term > term)).
% 164.61/23.49 thf(func_def_301, type, sK163: (term > $o)).
% 164.61/23.49 thf(func_def_302, type, sK164: term).
% 164.61/23.49 thf(func_def_303, type, sK165: (term > term)).
% 164.61/23.49 thf(func_def_304, type, sK166: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_305, type, sK167: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_306, type, sK168: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_307, type, sK169: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_308, type, sK170: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_309, type, sK171: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_310, type, sK172: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_311, type, sK173: term).
% 164.61/23.49 thf(func_def_312, type, sK174: (term > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_315, type, sK177: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_316, type, sK178: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_317, type, sK179: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_318, type, sK180: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_319, type, sK181: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_320, type, sK182: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_321, type, sK183: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_322, type, sK184: ((subst > term > term) > subst)).
% 164.61/23.49 thf(func_def_323, type, sK185: ((subst > term > term) > term)).
% 164.61/23.49 thf(func_def_324, type, sK186: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_325, type, sK187: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.49 thf(func_def_326, type, sK188: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_327, type, sK189: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_328, type, sK190: term).
% 164.61/23.49 thf(func_def_329, type, sK191: (term > $o)).
% 164.61/23.49 thf(func_def_330, type, sK192: (term > term)).
% 164.61/23.49 thf(func_def_331, type, sK193: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_332, type, sK194: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_333, type, sK195: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_334, type, sK196: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_335, type, sK197: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_336, type, sK198: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_337, type, sK199: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_338, type, sK200: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_339, type, sK201: term).
% 164.61/23.49 thf(func_def_340, type, sK202: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_341, type, sK203: term).
% 164.61/23.49 thf(func_def_342, type, sK204: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_343, type, sK205: term).
% 164.61/23.49 thf(func_def_344, type, sK206: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_348, type, sK210: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_349, type, sK211: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_350, type, sK212: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_351, type, sK213: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_352, type, sK214: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_353, type, sK215: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_354, type, sK216: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_355, type, sK217: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_356, type, sK218: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_357, type, sK219: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_358, type, sK220: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_359, type, sK221: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_360, type, sK222: ((subst > term > subst > $o) > subst)).
% 164.61/23.49 thf(func_def_361, type, sK223: ((subst > term > subst > $o) > term > term)).
% 164.61/23.49 thf(func_def_362, type, sK224: term).
% 164.61/23.49 thf(func_def_363, type, sK225: (subst > term > subst > $o)).
% 164.61/23.49 thf(func_def_364, type, sK226: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_365, type, sK227: ((term > $o) > term)).
% 164.61/23.49 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_368, type, sK230: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.49 thf(func_def_369, type, sK231: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_370, type, sK232: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_371, type, sK233: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_372, type, sK234: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_374, type, sK236: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_375, type, sK237: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_376, type, sK238: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_377, type, sK239: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_380, type, sK242: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_381, type, sK243: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_382, type, sK244: subst).
% 164.61/23.50 thf(func_def_383, type, sK245: term).
% 164.61/23.50 thf(func_def_384, type, sK246: subst).
% 164.61/23.50 thf(func_def_385, type, sK247: term).
% 164.61/23.50 thf(func_def_386, type, sK248: (term > $o)).
% 164.61/23.50 thf(func_def_387, type, sK249: subst).
% 164.61/23.50 thf(func_def_388, type, sK250: term).
% 164.61/23.50 thf(func_def_389, type, sK251: (term > $o)).
% 164.61/23.50 thf(func_def_390, type, sK252: subst).
% 164.61/23.50 thf(func_def_391, type, sK253: term).
% 164.61/23.50 thf(func_def_392, type, sK254: (term > term)).
% 164.61/23.50 thf(func_def_393, type, sK255: (subst > (term > $o) > term)).
% 164.61/23.50 thf(func_def_394, type, sK256: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_395, type, sK257: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_396, type, sK258: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_397, type, sK259: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_398, type, sK260: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_399, type, sK261: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_400, type, sK262: term).
% 164.61/23.50 thf(func_def_401, type, sK263: (term > $o)).
% 164.61/23.50 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_404, type, sK266: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_405, type, sK267: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_406, type, sK268: ((term > $o) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_407, type, sK269: ((term > $o) > term > term)).
% 164.61/23.50 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_409, type, sK271: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_410, type, sK272: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_411, type, sK273: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_412, type, sK274: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_413, type, sK275: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_414, type, sK276: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_415, type, sK277: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_416, type, sK278: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_417, type, sK279: (term > $o)).
% 164.61/23.50 thf(func_def_418, type, sK280: subst).
% 164.61/23.50 thf(func_def_419, type, sK281: term).
% 164.61/23.50 thf(func_def_420, type, sK282: (term > term)).
% 164.61/23.50 thf(func_def_421, type, sK283: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_422, type, sK284: (subst > (term > $o) > term)).
% 164.61/23.50 thf(func_def_423, type, sK285: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_424, type, sK286: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_425, type, sK287: term).
% 164.61/23.50 thf(func_def_426, type, sK288: (term > $o)).
% 164.61/23.50 thf(func_def_427, type, sK289: (term > term)).
% 164.61/23.50 thf(func_def_428, type, sK290: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_429, type, sK291: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_430, type, sK292: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_431, type, sK293: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_432, type, sK294: term).
% 164.61/23.50 thf(func_def_433, type, sK295: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_434, type, sK296: ((subst > term > subst > $o) > term > $o)).
% 164.61/23.50 thf(func_def_435, type, sK297: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_437, type, sK299: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_438, type, sK300: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_439, type, sK301: term).
% 164.61/23.50 thf(func_def_440, type, sK302: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_441, type, sK303: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_442, type, sK304: term).
% 164.61/23.50 thf(func_def_443, type, sK305: (term > $o)).
% 164.61/23.50 thf(func_def_444, type, sK306: (term > term)).
% 164.61/23.50 thf(func_def_445, type, sK307: (term > (term > $o) > term)).
% 164.61/23.50 thf(func_def_446, type, sK308: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_447, type, sK309: ((subst > term > subst > $o) > (term > $o) > term)).
% 164.61/23.50 thf(func_def_448, type, sK310: (term > $o)).
% 164.61/23.50 thf(func_def_449, type, sK311: term).
% 164.61/23.50 thf(func_def_450, type, sK312: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_451, type, sK313: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_452, type, sK314: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_453, type, sK315: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_454, type, sK316: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_455, type, sK317: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_456, type, sK318: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_457, type, sK319: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_458, type, sK320: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_460, type, sK322: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_461, type, sK323: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_462, type, sK324: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_463, type, sK325: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_464, type, sK326: (term > subst > term > term)).
% 164.61/23.50 thf(func_def_465, type, sK327: term).
% 164.61/23.50 thf(func_def_466, type, sK328: (term > $o)).
% 164.61/23.50 thf(func_def_467, type, sK329: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_468, type, sK330: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_469, type, sK331: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_470, type, sK332: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_471, type, sK333: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_472, type, sK334: term).
% 164.61/23.50 thf(func_def_473, type, sK335: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_474, type, sK336: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_475, type, sK337: term).
% 164.61/23.50 thf(func_def_476, type, sK338: ((subst > term > subst > $o) > (term > $o) > term)).
% 164.61/23.50 thf(func_def_477, type, sK339: ((term > $o) > term > term)).
% 164.61/23.50 thf(func_def_478, type, sK340: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_479, type, sK341: subst).
% 164.61/23.50 thf(func_def_480, type, sK342: term).
% 164.61/23.50 thf(func_def_481, type, sK343: (subst > term > term)).
% 164.61/23.50 thf(func_def_482, type, sK344: (subst > term > term)).
% 164.61/23.50 thf(func_def_483, type, sK345: term).
% 164.61/23.50 thf(func_def_484, type, sK346: subst).
% 164.61/23.50 thf(func_def_485, type, sK347: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_486, type, sK348: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_487, type, sK349: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_488, type, sK350: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_489, type, sK351: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_490, type, sK352: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_491, type, sK353: term).
% 164.61/23.50 thf(func_def_492, type, sK354: subst).
% 164.61/23.50 thf(func_def_493, type, sK355: term).
% 164.61/23.50 thf(func_def_494, type, sK356: term).
% 164.61/23.50 thf(func_def_495, type, sK357: term).
% 164.61/23.50 thf(func_def_496, type, sK358: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_497, type, sK359: ((subst > term > term) > term > term)).
% 164.61/23.50 thf(func_def_498, type, sK360: ((subst > term > term) > term > subst)).
% 164.61/23.50 thf(func_def_499, type, sK361: ((subst > term > term) > term > subst)).
% 164.61/23.50 thf(func_def_500, type, sK362: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_501, type, sK363: ((subst > term > term) > term > subst)).
% 164.61/23.50 thf(func_def_502, type, sK364: ((subst > term > term) > term > term)).
% 164.61/23.50 thf(func_def_503, type, sK365: ((subst > term > term) > term > subst)).
% 164.61/23.50 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_505, type, sK367: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > term > term)).
% 164.61/23.50 thf(func_def_507, type, sK369: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_508, type, sK370: term).
% 164.61/23.50 thf(func_def_509, type, sK371: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_510, type, sK372: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_511, type, sK373: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_512, type, sK374: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_514, type, sK376: (term > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_515, type, sK377: ((subst > term > subst > $o) > term > $o)).
% 164.61/23.50 thf(func_def_516, type, sK378: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_517, type, sK379: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_518, type, sK380: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_519, type, sK381: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_520, type, sK382: term).
% 164.61/23.50 thf(func_def_521, type, sK383: term).
% 164.61/23.50 thf(func_def_522, type, sK384: (term > $o)).
% 164.61/23.50 thf(func_def_523, type, sK385: (term > term)).
% 164.61/23.50 thf(func_def_524, type, sK386: (term > (term > $o) > term)).
% 164.61/23.50 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_526, type, sK388: ((subst > term > subst > $o) > (term > $o) > term)).
% 164.61/23.50 thf(func_def_527, type, sK389: (term > $o)).
% 164.61/23.50 thf(func_def_528, type, sK390: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_529, type, sK391: term).
% 164.61/23.50 thf(func_def_530, type, sK392: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_531, type, sK393: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_532, type, sK394: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_533, type, sK395: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_534, type, sK396: term).
% 164.61/23.50 thf(func_def_535, type, sK397: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_538, type, sK400: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_539, type, sK401: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_541, type, sK403: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_544, type, sK406: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_545, type, sK407: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_547, type, sK409: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_548, type, sK410: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_549, type, sK411: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_550, type, sK412: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_552, type, sK414: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_553, type, sK415: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_554, type, sK416: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_555, type, sK417: term).
% 164.61/23.50 thf(func_def_556, type, sK418: (term > $o)).
% 164.61/23.50 thf(func_def_557, type, sK419: term).
% 164.61/23.50 thf(func_def_558, type, sK420: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_559, type, sK421: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_560, type, sK422: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_561, type, sK423: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_562, type, sK424: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_563, type, sK425: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_564, type, sK426: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_565, type, sK427: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_566, type, sK428: ((term > $o) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_567, type, sK429: ((term > $o) > term > term)).
% 164.61/23.50 thf(func_def_568, type, sK430: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_569, type, sK431: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_570, type, sK432: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_571, type, sK433: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_572, type, sK434: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_573, type, sK435: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_574, type, sK436: term).
% 164.61/23.50 thf(func_def_575, type, sK437: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_576, type, sK438: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_577, type, sK439: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_578, type, sK440: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_579, type, sK441: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_580, type, sK442: (term > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_581, type, sK443: term).
% 164.61/23.50 thf(func_def_582, type, sK444: (term > (subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_584, type, sK446: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_585, type, sK447: term).
% 164.61/23.50 thf(func_def_586, type, sK448: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_587, type, sK449: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_588, type, sK450: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_589, type, sK451: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_590, type, sK452: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_591, type, sK453: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_592, type, sK454: subst).
% 164.61/23.50 thf(func_def_593, type, sK455: subst).
% 164.61/23.50 thf(func_def_594, type, sK456: (term > $o)).
% 164.61/23.50 thf(func_def_595, type, sK457: (term > $o)).
% 164.61/23.50 thf(func_def_596, type, sK458: term).
% 164.61/23.50 thf(func_def_597, type, sK459: term).
% 164.61/23.50 thf(func_def_598, type, sK460: (subst > (term > $o) > term > term > $o)).
% 164.61/23.50 thf(func_def_599, type, sK461: term).
% 164.61/23.50 thf(func_def_600, type, sK462: (term > $o)).
% 164.61/23.50 thf(func_def_601, type, sK463: subst).
% 164.61/23.50 thf(func_def_602, type, sK464: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_603, type, sK465: term).
% 164.61/23.50 thf(func_def_604, type, sK466: term).
% 164.61/23.50 thf(func_def_605, type, sK467: term).
% 164.61/23.50 thf(func_def_606, type, sK468: term).
% 164.61/23.50 thf(func_def_607, type, sK469: term).
% 164.61/23.50 thf(func_def_608, type, sK470: term).
% 164.61/23.50 thf(func_def_609, type, sK471: term).
% 164.61/23.50 thf(func_def_610, type, sK472: term).
% 164.61/23.50 thf(func_def_611, type, sK473: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_612, type, sK474: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_613, type, sK475: ((subst > term > subst > $o) > term > $o)).
% 164.61/23.50 thf(func_def_614, type, sK476: subst).
% 164.61/23.50 thf(func_def_615, type, sK477: subst).
% 164.61/23.50 thf(func_def_616, type, sK478: subst).
% 164.61/23.50 thf(func_def_617, type, sK479: subst).
% 164.61/23.50 thf(func_def_618, type, sK480: term).
% 164.61/23.50 thf(func_def_619, type, sK481: (term > $o)).
% 164.61/23.50 thf(func_def_620, type, sK482: (term > $o)).
% 164.61/23.50 thf(func_def_621, type, sK483: subst).
% 164.61/23.50 thf(func_def_622, type, sK484: term).
% 164.61/23.50 thf(func_def_623, type, sK485: subst).
% 164.61/23.50 thf(func_def_624, type, sK486: term).
% 164.61/23.50 thf(func_def_625, type, sK487: term).
% 164.61/23.50 thf(func_def_626, type, sK488: subst).
% 164.61/23.50 thf(func_def_627, type, sK489: term).
% 164.61/23.50 thf(func_def_628, type, sK490: term).
% 164.61/23.50 thf(func_def_629, type, sK491: term).
% 164.61/23.50 thf(func_def_630, type, sK492: term).
% 164.61/23.50 thf(func_def_631, type, sK493: term).
% 164.61/23.50 thf(func_def_632, type, sK494: term).
% 164.61/23.50 thf(func_def_633, type, sK495: term).
% 164.61/23.50 thf(func_def_634, type, sK496: term).
% 164.61/23.50 thf(func_def_635, type, sK497: term).
% 164.61/23.50 thf(func_def_636, type, sK498: term).
% 164.61/23.50 thf(func_def_637, type, sK499: term).
% 164.61/23.50 thf(func_def_638, type, sK500: (term > subst > term > term)).
% 164.61/23.50 thf(func_def_639, type, sK501: term).
% 164.61/23.50 thf(func_def_640, type, sK502: subst).
% 164.61/23.50 thf(func_def_641, type, sK503: (term > subst > term > term)).
% 164.61/23.50 thf(func_def_642, type, sK504: term).
% 164.61/23.50 thf(func_def_643, type, sK505: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_644, type, sK506: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_645, type, sK507: term).
% 164.61/23.50 thf(func_def_646, type, sK508: term).
% 164.61/23.50 thf(func_def_647, type, sK509: (subst > term > term)).
% 164.61/23.50 thf(func_def_648, type, sK510: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_649, type, sK511: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_650, type, sK512: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_651, type, sK513: subst).
% 164.61/23.50 thf(func_def_652, type, sK514: (subst > d_subst)).
% 164.61/23.50 thf(func_def_653, type, sK515: term).
% 164.61/23.50 thf(func_def_654, type, sK516: term).
% 164.61/23.50 thf(func_def_655, type, sK517: term).
% 164.61/23.50 thf(func_def_656, type, sK518: term).
% 164.61/23.50 thf(func_def_657, type, sK519: subst).
% 164.61/23.50 thf(func_def_658, type, sK520: term).
% 164.61/23.50 thf(func_def_659, type, sK521: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_660, type, sK522: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_661, type, sK523: (term > subst > term > term)).
% 164.61/23.50 thf(func_def_662, type, sK524: (term > d_term)).
% 164.61/23.50 thf(func_def_663, type, sK525: term).
% 164.61/23.50 thf(func_def_664, type, sK526: term).
% 164.61/23.50 thf(func_def_665, type, sK527: term).
% 164.61/23.50 thf(func_def_666, type, sK528: subst).
% 164.61/23.50 thf(func_def_667, type, sK529: (subst > term > term)).
% 164.61/23.50 thf(func_def_668, type, sK530: (subst > term > term)).
% 164.61/23.50 thf(func_def_669, type, sK531: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_670, type, sK532: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_671, type, sK533: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_672, type, sK534: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_673, type, sK535: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_674, type, sK536: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_675, type, sK537: term).
% 164.61/23.50 thf(func_def_676, type, sK538: (term > subst > term > term)).
% 164.61/23.50 thf(func_def_677, type, sK539: term).
% 164.61/23.50 thf(func_def_678, type, sK540: term).
% 164.61/23.50 thf(func_def_679, type, sK541: term).
% 164.61/23.50 thf(func_def_680, type, sK542: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_681, type, sK543: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_682, type, sK544: term).
% 164.61/23.50 thf(func_def_683, type, sK545: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_684, type, sK546: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_685, type, sK547: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_686, type, sK548: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_687, type, sK549: (subst > (term > $o) > (term > $o) > term > term)).
% 164.61/23.50 thf(func_def_688, type, sK550: term).
% 164.61/23.50 thf(func_def_689, type, sK551: (term > $o)).
% 164.61/23.50 thf(func_def_690, type, sK552: (term > $o)).
% 164.61/23.50 thf(func_def_691, type, sK553: subst).
% 164.61/23.50 thf(func_def_692, type, sK554: term).
% 164.61/23.50 thf(func_def_693, type, sK555: term).
% 164.61/23.50 thf(func_def_694, type, sK556: (term > (term > $o) > subst > term > $o)).
% 164.61/23.50 thf(func_def_695, type, sK557: subst).
% 164.61/23.50 thf(func_def_696, type, sK558: (term > $o)).
% 164.61/23.50 thf(func_def_697, type, sK559: term).
% 164.61/23.50 thf(func_def_698, type, sK560: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_699, type, sK561: ((subst > term > subst > $o) > term > $o)).
% 164.61/23.50 thf(func_def_700, type, sK562: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_701, type, sK563: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_702, type, sK564: subst).
% 164.61/23.50 thf(func_def_703, type, sK565: term).
% 164.61/23.50 thf(func_def_704, type, sK566: term).
% 164.61/23.50 thf(func_def_705, type, sK567: (term > $o)).
% 164.61/23.50 thf(func_def_706, type, sK568: (term > $o)).
% 164.61/23.50 thf(func_def_707, type, sK569: subst).
% 164.61/23.50 thf(func_def_708, type, sK570: subst).
% 164.61/23.50 thf(func_def_709, type, sK571: term).
% 164.61/23.50 thf(func_def_710, type, sK572: (subst > (term > $o) > (term > $o) > term > term)).
% 164.61/23.50 thf(func_def_711, type, sK573: term).
% 164.61/23.50 thf(func_def_712, type, sK574: term).
% 164.61/23.50 thf(func_def_713, type, sK575: term).
% 164.61/23.50 thf(func_def_714, type, sK576: term).
% 164.61/23.50 thf(func_def_715, type, sK577: term).
% 164.61/23.50 thf(func_def_716, type, sK578: term).
% 164.61/23.50 thf(func_def_717, type, sK579: term).
% 164.61/23.50 thf(func_def_718, type, sK580: term).
% 164.61/23.50 thf(func_def_719, type, sK581: term).
% 164.61/23.50 thf(func_def_720, type, sK582: term).
% 164.61/23.50 thf(func_def_721, type, sK583: term).
% 164.61/23.50 thf(func_def_722, type, sK584: term).
% 164.61/23.50 thf(func_def_723, type, sK585: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_724, type, sK586: ((term > $o) > term)).
% 164.61/23.50 thf(func_def_725, type, sK587: term).
% 164.61/23.50 thf(func_def_726, type, sK588: (term > $o)).
% 164.61/23.50 thf(func_def_727, type, sK589: subst).
% 164.61/23.50 thf(func_def_728, type, sK590: subst).
% 164.61/23.50 thf(func_def_729, type, vNOT: ($o > $o)).
% 164.61/23.50 thf(func_def_730, type, sK591: (subst > term > subst > $o)).
% 164.61/23.50 thf(func_def_731, type, sK592: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_732, type, sK593: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_733, type, sK594: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_734, type, sK595: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_735, type, sK596: ((subst > term > term) > subst)).
% 164.61/23.50 thf(func_def_736, type, sK597: ((subst > term > term) > term)).
% 164.61/23.50 thf(func_def_737, type, sK598: term).
% 164.61/23.50 thf(func_def_738, type, sK599: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_739, type, sK600: ((subst > term > subst > $o) > subst > term > term)).
% 164.61/23.50 thf(func_def_740, type, sK601: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_741, type, sK602: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_742, type, sK603: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_743, type, sK604: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_744, type, sK605: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_745, type, sK606: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_746, type, sK607: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_747, type, sK608: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_748, type, sK609: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_749, type, sK610: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_750, type, sK611: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_751, type, sK612: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_752, type, sK613: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_753, type, sK614: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_754, type, sK615: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_755, type, sK616: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_756, type, sK617: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_757, type, sK618: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_758, type, sK619: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_759, type, sK620: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_760, type, sK621: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_761, type, sK622: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_762, type, sK623: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_763, type, sK624: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_764, type, sK625: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_765, type, sK626: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_766, type, sK627: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_767, type, sK628: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_768, type, sK629: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_769, type, sK630: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_770, type, sK631: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_771, type, sK632: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_772, type, sK633: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_773, type, sK634: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_774, type, sK635: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_775, type, sK636: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_776, type, sK637: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_777, type, sK638: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_778, type, sK639: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_779, type, sK640: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_780, type, sK641: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_781, type, sK642: ((subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_782, type, sK643: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_783, type, sK644: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_784, type, sK645: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_785, type, sK646: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_786, type, sK647: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_787, type, sK648: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_788, type, sK649: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_789, type, sK650: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_790, type, sK651: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_791, type, sK652: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_792, type, sK653: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_793, type, sK654: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_794, type, sK655: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_795, type, sK656: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_796, type, sK657: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_797, type, sK658: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_798, type, sK659: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_799, type, sK660: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_800, type, sK661: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_801, type, sK662: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_802, type, sK663: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_803, type, sK664: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_804, type, sK665: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_805, type, sK666: ((subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_807, type, db5: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_808, type, db7: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_809, type, db6: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_810, type, sK668: ((term > subst > term > subst > subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_811, type, sK669: ((term > subst > term > subst > subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_812, type, sK670: ((term > subst > term > subst > subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_813, type, sK671: ((term > subst > term > subst > subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_814, type, sK672: ((term > subst > term > subst > subst > term > subst > $o) > term)).
% 164.61/23.50 thf(func_def_815, type, sK673: ((term > subst > term > subst > subst > term > subst > $o) > subst)).
% 164.61/23.50 thf(func_def_816, type, sK674: ((term > subst > term > subst > subst > term > subst > $o) > subst > subst)).
% 164.61/23.50 thf(func_def_817, type, db8: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_818, type, db9: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_819, type, db13: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_820, type, db12: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_821, type, db11: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(func_def_822, type, db10: !>[X0: $tType]:(X0)).
% 164.61/23.50 thf(f1,axiom,(
% 164.61/23.50 ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) <=> hoasinduction_lthm_3) & hoaslamnotap_lthm & hoasinduction_lem2_gthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & (hoaslaminj <=> ! [X18 : (subst > term > term),X32 : subst,X31 : (subst > term > term),X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))) & (shinj <=> ! [X13 : term,X15 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & pushprop & (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)))) => ! [X32 : subst,X31 : (subst > term > term),X33 : term,X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : 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)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one))))))))) & hoasapinj2_gthm & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & (! [X10 : (term > $o),X22 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) <=> induction2) & (! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ! [X1 : d_term] : (X1 = d_one) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & substmonoid_gthm & hoasinduction_lem2v2_gthm & axvarshift & ~lamnotap & hoaslaminj_gthm & pushprop_gthm & hoasapinj1_gthm & (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))) => ! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & hoasapnotvar & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasapinj2_lthm <=> (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X20 : term,X19 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)))) & (pushprop_lem1v2 <=> ! [X11 : (term > $o),X13 : term,X14 : subst,X10 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & hoasinduction_lem3_gthm & lamnotvar & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (pushprop_lem0_lthm <=> ! [X14 : subst,X13 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (hoasinduction_lem3v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & hoaslamnotvar_lthm & (hoasinduction_lem2v2 <=> ! [X44 : term,X11 : (term > $o),X45 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X44))) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ~ulamvar1 & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem3b_gthm & axabs & pushprop_lthm & axapp & (apinj1 <=> ! [X15 : term,X20 : term,X13 : term,X19 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (sh = ((d2subst @ d_id))) & (hoasinduction_lem3a <=> ! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & induction2lem_gthm & axassoc & ~(var @ (d2term @ d_one)) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & hoasinduction_lem1v2_gthm & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))))))) & pushprop_lem3v2 & hoasinduction_lem3a_gthm & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X26 : (term > $o),X14 : subst,X15 : term,X13 : term,X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)))) <=> pushprop_lem1_lthm) & (pushprop_lem1 <=> ! [X26 : (term > $o),X10 : (term > $o),X13 : term,X14 : subst,X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & (hoasinduction_lem2 <=> ! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X10 @ id @ X24 @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & hoasapnotvar_gthm & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X21) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) => ! [X17 : subst,X16 : term,X10 : (term > $o)] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))))))))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ 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)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) & hoasinduction_gthm & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)))) & pushprop_lem3v2_lthm & (induction <=> ! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)))) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X14 : subst,X13 : term,X10 : (term > $o),X11 : (term > $o)] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) <=> pushprop_lem1v2_lthm) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & axclos & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X43) @ id))))) & (hoasapinj1 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (! [X15 : term,X19 : term,X13 : term,X20 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)) <=> hoasapinj2) & pushprop_lem2v2_gthm & hoaslamnotvar_gthm & (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))))))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2_lthm & axmap & pushprop_lem2v2 & (! [X47 : term,X46 : term,X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47)))) <=> hoaslamnotap) & ulamvarsh & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X19 : term,X15 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X19 : term,X13 : term,X15 : term,X20 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & (! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) <=> apinj2) & apnotvar & (id = ((d2subst @ d_id))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1_gthm & pushprop_lem1v2_gthm & (! [X17 : subst,X16 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))) <=> induction2lem) & ulamvarind & pushprop_lem0_gthm & (laminj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))) => ! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))))))) & pushprop_lthm_orig & hoaslamnotvar & ((^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) = pushprop_p_and_p_prime) & hoasinduction_lem2_lthm & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id))) & ! [X5 : d_subst] : (X5 = d_id) & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id)))))) & hoasapnotvar_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem1v2 & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3v2a) & (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))) & termmset_gthm & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & induction2_gthm & pushprop_lem1_gthm & (one = ((d2term @ d_one))) & hoasinduction_lem1 & hoaslamnotap_gthm & hoasinduction_lem1_lthm & (hoasinduction <=> ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X36 : subst,X38 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X39 : subst,X40 : term,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))))),
% 164.61/23.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 164.61/23.50 thf(f2,conjecture,(
% 164.61/23.50 (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X4 : subst,X2 : term,X3 : subst] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X3 : subst,X1 : subst,X2 : term,X4 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => (! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X5) @ id))) => (! [X6 : (subst > term > term)] : (! [X2 : term,X3 : subst,X1 : subst] : (((sub @ (X6 @ X1 @ X2) @ X3)) = ((X6 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X6 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X6 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (X0 @ id @ X2 @ id)))))) = hoasinduction)),
% 164.61/23.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction)).
% 164.61/23.50 thf(f3,negated_conjecture,(
% 164.61/23.50 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X4 : subst,X2 : term,X3 : subst] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X3 : subst,X1 : subst,X2 : term,X4 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => (! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X5) @ id))) => (! [X6 : (subst > term > term)] : (! [X2 : term,X3 : subst,X1 : subst] : (((sub @ (X6 @ X1 @ X2) @ X3)) = ((X6 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X6 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X6 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (X0 @ id @ X2 @ id)))))) = hoasinduction)),
% 164.61/23.50 inference(negated_conjecture,[status(cth)],[f2])).
% 164.61/23.50 thf(f4,plain,(
% 164.61/23.50 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : term,X4 : subst] : ((X0 @ X1 @ X3 @ (comp @ X2 @ X4)) => (X0 @ (comp @ X1 @ X2) @ (sub @ X3 @ X2) @ X4)) => (! [X5 : subst,X6 : subst,X7 : term,X8 : subst] : ((X0 @ (comp @ X6 @ X8) @ (sub @ X7 @ X8) @ X5) => (X0 @ X6 @ X7 @ (comp @ X8 @ X5))) => (! [X9 : term] : ((hoasvar @ id @ X9 @ id) => (X0 @ id @ X9 @ id)) => (! [X10 : term,X11 : term] : ((X0 @ id @ X10 @ id) => ((X0 @ id @ X11 @ id) => (X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id))) => (! [X12 : (subst > term > term)] : (! [X13 : term,X14 : subst,X15 : subst] : (((X12 @ (comp @ X15 @ X14) @ (sub @ X13 @ X14))) = ((sub @ (X12 @ X15 @ X13) @ X14))) => (! [X16 : term] : ((X0 @ id @ X16 @ id) => (X0 @ id @ (X12 @ id @ X16) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X17 : subst, X18 : term] : ((X12 @ X17 @ X18)))) @ id))) => ! [X19 : term] : (X0 @ id @ X19 @ id)))))) = hoasinduction)),
% 164.61/23.50 inference(rectify,[],[f3])).
% 164.61/23.50 thf(f5,plain,(
% 164.61/23.50 ~ (hoasinduction = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y2 @ (comp @ Y3 @ Y1)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3) @ Y1)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id))))))))))))),
% 164.61/23.50 inference(fool_elimination,[],[f4])).
% 164.61/23.50 thf(f6,plain,(
% 164.61/23.50 ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : (~ ! [X5 : term] : (~(var @ X5) | (X3 @ X5)) | ~ ! [X6 : term] : ((X3 @ (lam @ X6)) | ~ ! [X7 : term] : ((X3 @ (sub @ X6 @ (push @ X7 @ id))) | ~(X3 @ X7))) | (X3 @ X4) | ~ ! [X8 : term,X9 : term] : ((X3 @ (ap @ X9 @ X8)) | ~(X3 @ X8) | ~(X3 @ X9))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (subst > term > subst > $o),X13 : (term > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : subst,X16 : term,X17 : subst] : (((sub @ (X14 @ X15 @ X16) @ X17)) = ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)))) | (X12 @ id @ (lam @ (X14 @ sh @ one)) @ id) | ~ ! [X18 : term] : (~(X12 @ id @ X18 @ id) | (X12 @ id @ (X14 @ id @ X18) @ id))) | ~ ! [X19 : term] : (~(X13 @ X19) | (X13 @ (sub @ X11 @ (push @ X19 @ id)))) | (X13 @ (lam @ X11)) | ~ ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : subst,X24 : subst,X25 : subst,X26 : term] : ((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23) | ~(X21 @ X25 @ X26 @ (comp @ X24 @ X23))) | ~ ! [X27 : (subst > term > term)] : (~ ! [X28 : term] : (~(X21 @ id @ X28 @ id) | (X21 @ id @ (X27 @ id @ X28) @ id)) | ~ ! [X29 : term,X30 : subst,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) | (X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) | ~ ! [X32 : term] : ((X21 @ id @ X32 @ id) | ~(var @ (sub @ X32 @ id))) | (X21 @ id @ X22 @ id) | ~ ! [X33 : term,X34 : term] : (~(X21 @ id @ X33 @ id) | (X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id) | ~(X21 @ id @ X34 @ id)) | ~ ! [X35 : subst,X36 : subst,X37 : subst,X38 : term] : ((X21 @ X35 @ X38 @ (comp @ X37 @ X36)) | ~(X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))))))) <=> hoasinduction_lthm_3) & hoaslamnotap_lthm & hoasinduction_lem2_gthm & (! [X39 : (subst > term > subst > $o)] : ~ ! [X40 : (term > $o)] : ~ ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41))) <=> hoasinduction_lem0_lthm) & (hoaslaminj <=> ! [X42 : (subst > term > term),X43 : subst,X44 : (subst > term > term),X45 : term] : ((((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | ~ ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) = ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))) | ~ ! [X49 : subst,X50 : subst,X51 : term] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) = ((sub @ (X42 @ X49 @ X51) @ X50))) | (((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))))) & (shinj <=> ! [X52 : term,X53 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53))) & (axidr <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & pushprop & (hoaslaminj_lthm <=> (! [X55 : term,X56 : subst] : (((sub @ one @ (push @ X55 @ X56))) = X55) => (! [X57 : term,X58 : subst] : (((comp @ sh @ (push @ X57 @ X58))) = X58) => (! [X59 : term,X60 : term] : ((X59 = X60) | (((lam @ X59)) != ((lam @ X60)))) => ! [X61 : subst,X62 : (subst > term > term),X63 : term,X64 : (subst > term > term)] : (~ ! [X65 : term,X66 : subst,X67 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) = ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | ~ ! [X68 : subst,X69 : term,X70 : subst] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) = ((sub @ (X64 @ X68 @ X69) @ X70))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one))))))))) & hoasapinj2_gthm & (axidl <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & (! [X72 : (term > $o),X73 : term] : (~ ! [X74 : term,X75 : term] : (~(X72 @ X74) | (X72 @ (ap @ X75 @ X74)) | ~(X72 @ X75)) | (X72 @ X73) | ~ ! [X76 : term] : ((X72 @ X76) | ~(var @ X76)) | ~ ! [X77 : term] : ((X72 @ (lam @ X77)) | ~ ! [X78 : term] : ((X72 @ (sub @ X77 @ (push @ X78 @ id))) | ~(X72 @ X78)))) <=> induction2) & (! [X79 : (term > $o),X80 : term,X81 : subst] : ~ ! [X82 : (term > $o)] : ~ ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))) <=> pushprop_lem0) & ! [X84 : d_term] : (d_one = X84) & (! [X85 : term] : ~ ! [X86 : (subst > term > term)] : ~ ! [X87 : term,X88 : subst] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88)))) <=> hoasinduction_lem3v2_f) & substmonoid_gthm & hoasinduction_lem2v2_gthm & axvarshift & ~lamnotap & hoaslaminj_gthm & pushprop_gthm & hoasapinj1_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X89 : term] : ~ ! [X90 : (subst > term > term)] : ~ ! [X91 : term,X92 : subst] : (((sub @ X89 @ (push @ X91 @ X92))) = ((X90 @ X92 @ X91))) => (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term,X95 : (term > $o),X96 : (subst > term > subst > $o)] : (~ ! [X97 : term] : (((X95 @ X97)) = ((X96 @ id @ X97 @ id))) | (X95 @ (lam @ X94)) | ~ ! [X98 : term] : (~(X95 @ X98) | (X95 @ (sub @ X94 @ (push @ X98 @ id)))) | ~ ! [X99 : (subst > term > term)] : (~ ! [X100 : subst,X101 : term,X102 : subst] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) | (X96 @ id @ (lam @ (X99 @ sh @ one)) @ id) | ~ ! [X103 : term] : ((X96 @ id @ (X99 @ id @ X103) @ id) | ~(X96 @ id @ X103 @ id))))))) & (hoasinduction_lem3v2_lthm <=> (! [X104 : term] : (((sub @ X104 @ id)) = X104) => ! [X105 : (subst > term > subst > $o),X106 : term,X107 : (term > $o)] : (~ ! [X108 : subst,X109 : subst,X110 : term,X111 : subst] : (~(X105 @ X111 @ X110 @ (comp @ X108 @ X109)) | (X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)) | ~ ! [X112 : term] : (~(X107 @ X112) | (X107 @ (sub @ X106 @ (push @ X112 @ id)))) | ~ ! [X113 : subst,X114 : term,X115 : subst,X116 : subst] : (~(X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116) | (X105 @ X113 @ X114 @ (comp @ X115 @ X116))) | ~ ! [X117 : (subst > term > term)] : (~ ! [X118 : term] : ((X105 @ id @ (X117 @ id @ X118) @ id) | ~(X105 @ id @ X118 @ id)) | ~ ! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) | (X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) | (X107 @ (lam @ X106)) | ~ ! [X122 : term] : (((X107 @ X122)) = ((X105 @ id @ X122 @ id)))))) & hoasapnotvar & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasapinj2_lthm <=> (! [X123 : term,X124 : term,X125 : term,X126 : term] : ((X125 = X126) | (((ap @ X124 @ X125)) != ((ap @ X123 @ X126)))) => ! [X127 : term,X128 : term,X129 : term,X130 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128)))) & (pushprop_lem1v2 <=> ! [X131 : (term > $o),X132 : term,X133 : subst,X134 : (term > $o)] : ((X131 @ one) | ~(X134 @ X132) | ~ ! [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) = ((X131 @ X135))))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : ~ ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139))) <=> hoasinduction_lem3v2_f_lthm) & hoasinduction_lem3_gthm & lamnotvar & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (pushprop_lem0_lthm <=> ! [X142 : subst,X143 : term,X144 : (term > $o)] : ~ ! [X145 : (term > $o)] : ~ ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142)))))) & (axshiftcons <=> ! [X147 : term,X148 : subst] : (((comp @ sh @ (push @ X147 @ X148))) = X148)) & (hoasinduction_lem3v2 <=> ! [X149 : (subst > term > subst > $o),X150 : (term > $o),X151 : term] : (~ ! [X152 : (subst > term > term)] : (~ ! [X153 : term] : ((X149 @ id @ (X152 @ id @ X153) @ id) | ~(X149 @ id @ X153 @ id)) | (X149 @ id @ (lam @ (X152 @ sh @ one)) @ id) | ~ ! [X154 : subst,X155 : subst,X156 : term] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155)))) | ~ ! [X157 : term] : (~(X150 @ X157) | (X150 @ (sub @ X151 @ (push @ X157 @ id)))) | (X150 @ (lam @ X151)) | ~ ! [X158 : term] : (((X149 @ id @ X158 @ id)) = ((X150 @ X158))) | ~ ! [X159 : term,X160 : subst,X161 : subst,X162 : subst] : ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)) | ~(X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) | ~ ! [X163 : term,X164 : subst,X165 : subst,X166 : subst] : (~(X149 @ X166 @ X163 @ (comp @ X164 @ X165)) | (X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165)))) & hoaslamnotvar_lthm & (hoasinduction_lem2v2 <=> ! [X167 : term,X168 : (term > $o),X169 : term,X170 : (subst > term > subst > $o)] : (~ ! [X171 : term,X172 : term] : (~(X170 @ id @ X171 @ id) | (X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id) | ~(X170 @ id @ X172 @ id)) | ~ ! [X173 : term,X174 : subst,X175 : subst,X176 : subst] : (~(X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174) | (X170 @ X175 @ X173 @ (comp @ X176 @ X174))) | ~ ! [X177 : term] : (((X170 @ id @ X177 @ id)) = ((X168 @ X177))) | (X168 @ (ap @ X167 @ X169)) | ~(X168 @ X169) | ~ ! [X178 : subst,X179 : subst,X180 : subst,X181 : term] : ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179) | ~(X170 @ X180 @ X181 @ (comp @ X178 @ X179))) | ~(X168 @ X167))) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) = ((d2subst @ X183))) => (X182 = X183)) & ~ulamvar1 & (hoaslam = (^[X184 : subst, X185 : (subst > term > term)] : ((d2term @ d_one)))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem3b_gthm & axabs & pushprop_lthm & axapp & (apinj1 <=> ! [X186 : term,X187 : term,X188 : term,X189 : term] : ((X186 = X188) | (((ap @ X188 @ X189)) != ((ap @ X186 @ X187))))) & (! [X190 : term] : ~ ! [X191 : (subst > term > term)] : (((X191 @ sh @ one)) != ((sub @ X190 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (sh = ((d2subst @ d_id))) & (hoasinduction_lem3a <=> ! [X192 : term,X193 : (subst > term > subst > $o)] : ((X193 @ id @ (lam @ X192) @ id) | ~ ! [X194 : (subst > term > term)] : (~ ! [X195 : subst,X196 : subst,X197 : term] : (((sub @ (X194 @ X196 @ X197) @ X195)) = ((X194 @ (comp @ X196 @ X195) @ (sub @ X197 @ X195)))) | (X193 @ id @ (lam @ (X194 @ sh @ one)) @ id) | ~ ! [X198 : term] : ((X193 @ id @ (X194 @ id @ X198) @ id) | ~(X193 @ id @ X198 @ id))) | ~ ! [X199 : term] : ((X193 @ id @ (sub @ X192 @ (push @ X199 @ id)) @ id) | ~(X193 @ id @ X199 @ id)))) & induction2lem_gthm & axassoc & ~(var @ (d2term @ d_one)) & (hoasinduction_p_and_p_prime = (^[X200 : (subst > term > subst > $o), X201 : (term > $o)] : (! [X202 : term] : (((X200 @ id @ X202 @ id)) = ((X201 @ X202)))))) & hoasinduction_lem1v2_gthm & (hoasinduction_no_psi_cond_lthm <=> (! [X203 : (subst > term > subst > $o)] : ~ ! [X204 : (term > $o)] : ~ ! [X205 : term] : (((X203 @ id @ X205 @ id)) = ((X204 @ X205))) => (! [X206 : (term > $o),X207 : term] : ((X206 @ X207) | ~ ! [X208 : term] : ((X206 @ X208) | ~(var @ X208)) | ~ ! [X209 : term,X210 : term] : (~(X206 @ X209) | ~(X206 @ X210) | (X206 @ (ap @ X209 @ X210))) | ~ ! [X211 : term] : (~ ! [X212 : term] : (~(X206 @ X212) | (X206 @ (sub @ X211 @ (push @ X212 @ id)))) | (X206 @ (lam @ X211)))) => (! [X213 : term] : (((sub @ X213 @ id)) = X213) => (! [X214 : term,X215 : (subst > term > subst > $o),X216 : (term > $o)] : (~ ! [X217 : (subst > term > term)] : (~ ! [X218 : term,X219 : subst,X220 : subst] : (((sub @ (X217 @ X219 @ X218) @ X220)) = ((X217 @ (comp @ X219 @ X220) @ (sub @ X218 @ X220)))) | ~ ! [X221 : term] : (~(X215 @ id @ X221 @ id) | (X215 @ id @ (X217 @ id @ X221) @ id)) | (X215 @ id @ (lam @ (X217 @ sh @ one)) @ id)) | ~ ! [X222 : term] : (((X215 @ id @ X222 @ id)) = ((X216 @ X222))) | (X216 @ (lam @ X214)) | ~ ! [X223 : term] : (~(X216 @ X223) | (X216 @ (sub @ X214 @ (push @ X223 @ id))))) => ! [X224 : (subst > term > subst > $o),X225 : term] : (~ ! [X226 : (subst > term > term)] : (~ ! [X227 : subst,X228 : term,X229 : subst] : (((X226 @ (comp @ X229 @ X227) @ (sub @ X228 @ X227))) = ((sub @ (X226 @ X229 @ X228) @ X227))) | ~ ! [X230 : term] : (~(X224 @ id @ X230 @ id) | (X224 @ id @ (X226 @ id @ X230) @ id)) | (X224 @ id @ (lam @ (X226 @ sh @ one)) @ id)) | (X224 @ id @ X225 @ id) | ~ ! [X231 : term,X232 : term] : (~(X224 @ id @ X232 @ id) | ~(X224 @ id @ X231 @ id) | (X224 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)))))))) & pushprop_lem3v2 & hoasinduction_lem3a_gthm & (hoasinduction_lem3 <=> ! [X233 : term,X234 : (subst > term > subst > $o)] : (~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term,X237 : subst,X238 : subst] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X235 @ X238 @ X236) @ X237))) | ~ ! [X239 : term] : (~(X234 @ id @ X239 @ id) | (X234 @ id @ (X235 @ id @ X239) @ id)) | (X234 @ id @ (lam @ (X235 @ sh @ one)) @ id)) | ~ ! [X240 : subst,X241 : subst,X242 : subst,X243 : term] : ((X234 @ X241 @ X243 @ (comp @ X242 @ X240)) | ~(X234 @ (comp @ X241 @ X242) @ (sub @ X243 @ X242) @ X240)) | ~ ! [X244 : subst,X245 : subst,X246 : term,X247 : subst] : ((X234 @ (comp @ X244 @ X247) @ (sub @ X246 @ X247) @ X245) | ~(X234 @ X244 @ X246 @ (comp @ X247 @ X245))) | (X234 @ id @ (lam @ X233) @ id) | ~ ! [X248 : term] : ((X234 @ id @ (sub @ X233 @ (push @ X248 @ id)) @ id) | ~(X234 @ id @ X248 @ id)))) & ((! [X249 : subst,X250 : term] : (((sub @ one @ (push @ X250 @ X249))) = X250) => (! [X251 : subst,X252 : term] : (((comp @ sh @ (push @ X252 @ X251))) = X251) => ! [X253 : (term > $o),X254 : subst,X255 : term,X256 : term,X257 : (term > $o)] : ((X253 @ (sub @ X256 @ (push @ X255 @ X254))) | ~(X257 @ X256)))) <=> pushprop_lem1_lthm) & (pushprop_lem1 <=> ! [X258 : (term > $o),X259 : (term > $o),X260 : term,X261 : subst,X262 : term] : (~(X259 @ X260) | (X258 @ (sub @ X260 @ (push @ X262 @ X261))))) & (hoasinduction_lem2 <=> ! [X263 : term,X264 : term,X265 : (subst > term > subst > $o)] : ((X265 @ id @ (ap @ X263 @ X264) @ id) | ~ ! [X266 : subst,X267 : subst,X268 : term,X269 : subst] : ((X265 @ X269 @ X268 @ (comp @ X267 @ X266)) | ~(X265 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267) @ X266)) | ~(X265 @ id @ X263 @ id) | ~ ! [X270 : term,X271 : term] : (~(X265 @ id @ X270 @ id) | ~(X265 @ id @ X271 @ id) | (X265 @ id @ (ap @ (sub @ X270 @ id) @ X271) @ id)) | ~(X265 @ id @ X264 @ id) | ~ ! [X272 : subst,X273 : subst,X274 : subst,X275 : term] : ((X265 @ (comp @ X274 @ X273) @ (sub @ X275 @ X273) @ X272) | ~(X265 @ X274 @ X275 @ (comp @ X273 @ X272))))) & hoasapnotvar_gthm & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X276 : subst,X277 : term] : (((sub @ one @ (push @ X277 @ X276))) = X277) => (! [X278 : subst,X279 : term] : (((comp @ sh @ (push @ X279 @ X278))) = X278) => (! [X280 : subst] : (((comp @ X280 @ id)) = X280) => (! [X281 : term,X282 : (term > $o)] : (~ ! [X283 : term,X284 : term] : ((X282 @ (ap @ X283 @ X284)) | ~(X282 @ X284) | ~(X282 @ X283)) | (X282 @ X281) | ~ ! [X285 : term] : (~(var @ X285) | (X282 @ X285)) | ~ ! [X286 : term] : ((X282 @ (lam @ X286)) | ~(X282 @ X286))) => ! [X287 : subst,X288 : term,X289 : (term > $o)] : ((X289 @ (sub @ X288 @ X287)) | ~ ! [X290 : term,X291 : term] : (~(X289 @ X290) | (X289 @ (ap @ X290 @ X291)) | ~(X289 @ X291)) | ~ ! [X292 : term] : (~(var @ X292) | (X289 @ (sub @ X292 @ X287))) | ~ ! [X293 : term] : (~ ! [X294 : term] : (~(X289 @ X294) | (X289 @ (sub @ X293 @ (push @ X294 @ id)))) | (X289 @ (lam @ X293))))))))) & (! [X295 : term,X296 : (subst > term > subst > $o)] : (~ ! [X297 : (subst > term > term)] : ((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id) | ~ ! [X298 : term] : (~(X296 @ id @ X298 @ id) | (X296 @ id @ (X297 @ id @ X298) @ id)) | ~ ! [X299 : subst,X300 : subst,X301 : term] : (((sub @ (X297 @ X300 @ X301) @ X299)) = ((X297 @ (comp @ X300 @ X299) @ (sub @ X301 @ X299))))) | ~ ! [X302 : term] : ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id) | ~(X296 @ id @ X302 @ id)) | (X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa) & (hoasinduction_lem3_lthm <=> (! [X303 : term] : (((sub @ X303 @ id)) = X303) => (! [X304 : (subst > term > subst > $o),X305 : term] : (~ ! [X306 : term] : ((X304 @ id @ (sub @ X305 @ (push @ X306 @ id)) @ id) | ~(X304 @ id @ X306 @ id)) | ~ ! [X307 : (subst > term > term)] : (~ ! [X308 : term] : ((X304 @ id @ (X307 @ id @ X308) @ id) | ~(X304 @ id @ X308 @ id)) | (X304 @ id @ (lam @ (X307 @ sh @ one)) @ id) | ~ ! [X309 : subst,X310 : subst,X311 : term] : (((X307 @ (comp @ X309 @ X310) @ (sub @ X311 @ X310))) = ((sub @ (X307 @ X309 @ X311) @ X310)))) | (X304 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)) => ! [X312 : (subst > term > subst > $o),X313 : term] : (~ ! [X314 : term] : (~(X312 @ id @ X314 @ id) | (X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) | (X312 @ id @ (lam @ X313) @ id) | ~ ! [X315 : (subst > term > term)] : ((X312 @ id @ (lam @ (X315 @ sh @ one)) @ id) | ~ ! [X316 : subst,X317 : subst,X318 : term] : (((sub @ (X315 @ X317 @ X318) @ X316)) = ((X315 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316)))) | ~ ! [X319 : term] : (~(X312 @ id @ X319 @ id) | (X312 @ id @ (X315 @ id @ X319) @ id))) | ~ ! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : ((X312 @ X320 @ X321 @ (comp @ X323 @ X322)) | ~(X312 @ (comp @ X320 @ X323) @ (sub @ X321 @ X323) @ X322)) | ~ ! [X324 : term,X325 : subst,X326 : subst,X327 : subst] : ((X312 @ (comp @ X327 @ X326) @ (sub @ X324 @ X326) @ X325) | ~(X312 @ X327 @ X324 @ (comp @ X326 @ X325))))))) & hoasinduction_gthm & (hoasinduction_no_psi_cond <=> ! [X328 : (subst > term > subst > $o),X329 : term] : (~ ! [X330 : (subst > term > term)] : (~ ! [X331 : term,X332 : subst,X333 : subst] : (((sub @ (X330 @ X333 @ X331) @ X332)) = ((X330 @ (comp @ X333 @ X332) @ (sub @ X331 @ X332)))) | ~ ! [X334 : term] : ((X328 @ id @ (X330 @ id @ X334) @ id) | ~(X328 @ id @ X334 @ id)) | (X328 @ id @ (lam @ (X330 @ sh @ one)) @ id)) | (X328 @ id @ X329 @ id) | ~ ! [X335 : term,X336 : term] : ((X328 @ id @ (ap @ (sub @ X336 @ id) @ X335) @ id) | ~(X328 @ id @ X336 @ id) | ~(X328 @ id @ X335 @ id)))) & pushprop_lem3v2_lthm & (induction <=> ! [X337 : (term > $o),X338 : term] : (~ ! [X339 : term] : ((X337 @ X339) | ~(var @ X339)) | ~ ! [X340 : term,X341 : term] : (~(X337 @ X340) | (X337 @ (ap @ X340 @ X341)) | ~(X337 @ X341)) | (X337 @ X338) | ~ ! [X342 : term] : ((X337 @ (lam @ X342)) | ~(X337 @ X342)))) & ((! [X343 : term,X344 : subst] : (((sub @ one @ (push @ X343 @ X344))) = X343) => ! [X345 : subst,X346 : term,X347 : (term > $o),X348 : (term > $o)] : (~(X347 @ X346) | (X348 @ one) | ~ ! [X349 : term] : (((X348 @ X349)) = ((X347 @ (sub @ X349 @ (push @ X346 @ X345))))))) <=> pushprop_lem1v2_lthm) & (axscons <=> ! [X350 : subst] : (((push @ (sub @ one @ X350) @ (comp @ sh @ X350))) = X350)) & axclos & ! [X351 : subst] : ? [X352 : d_subst] : (((d2subst @ X352)) = X351) & (hoasinduction_lem3a_lthm <=> (! [X353 : term] : (((sub @ X353 @ id)) = X353) => (! [X354 : term,X355 : (subst > term > subst > $o)] : (~ ! [X356 : term] : ((X355 @ id @ (sub @ X354 @ (push @ X356 @ id)) @ id) | ~(X355 @ id @ X356 @ id)) | ~ ! [X357 : (subst > term > term)] : (~ ! [X358 : term] : (~(X355 @ id @ X358 @ id) | (X355 @ id @ (X357 @ id @ X358) @ id)) | ~ ! [X359 : term,X360 : subst,X361 : subst] : (((X357 @ (comp @ X361 @ X360) @ (sub @ X359 @ X360))) = ((sub @ (X357 @ X361 @ X359) @ X360))) | (X355 @ id @ (lam @ (X357 @ sh @ one)) @ id)) | (X355 @ id @ (lam @ (sub @ X354 @ (push @ one @ sh))) @ id)) => ! [X362 : term,X363 : (subst > term > subst > $o)] : (~ ! [X364 : term] : (~(X363 @ id @ X364 @ id) | (X363 @ id @ (sub @ X362 @ (push @ X364 @ id)) @ id)) | ~ ! [X365 : (subst > term > term)] : (~ ! [X366 : term,X367 : subst,X368 : subst] : (((sub @ (X365 @ X368 @ X366) @ X367)) = ((X365 @ (comp @ X368 @ X367) @ (sub @ X366 @ X367)))) | ~ ! [X369 : term] : ((X363 @ id @ (X365 @ id @ X369) @ id) | ~(X363 @ id @ X369 @ id)) | (X363 @ id @ (lam @ (X365 @ sh @ one)) @ id)) | (X363 @ id @ (lam @ X362) @ id))))) & (hoasapinj1 <=> ! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | (((ap @ (sub @ X370 @ id) @ X373)) != ((ap @ (sub @ X372 @ id) @ X371))))) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : ((((ap @ (sub @ X376 @ id) @ X375)) != ((ap @ (sub @ X374 @ id) @ X377))) | (X375 = X377)) <=> hoasapinj2) & pushprop_lem2v2_gthm & hoaslamnotvar_gthm & (substmonoid_lthm <=> (! [X378 : subst] : (((comp @ id @ X378)) = X378) => (! [X379 : subst] : (((comp @ X379 @ id)) = X379) => (! [X380 : subst] : (((comp @ X380 @ id)) = X380) & ! [X381 : subst] : (((comp @ id @ X381)) = X381))))) & (termmset_lthm <=> (! [X382 : term] : (((sub @ X382 @ id)) = X382) => ! [X383 : term] : (((sub @ X383 @ id)) = X383))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2_lthm & axmap & pushprop_lem2v2 & (! [X384 : term,X385 : term,X386 : (subst > term > term)] : (~ ! [X387 : term,X388 : subst,X389 : subst] : (((sub @ (X386 @ X388 @ X387) @ X389)) = ((X386 @ (comp @ X388 @ X389) @ (sub @ X387 @ X389)))) | (((lam @ (X386 @ sh @ one))) != ((ap @ (sub @ X385 @ id) @ X384)))) <=> hoaslamnotap) & ulamvarsh & (hoasinduction_lem0 <=> ! [X390 : (subst > term > subst > $o)] : ~ ! [X391 : (term > $o)] : ~ ! [X392 : term] : (((X391 @ X392)) = ((X390 @ id @ X392 @ id)))) & (! [X393 : term] : (((sub @ X393 @ id)) = X393) <=> axvarid) & (hoasapinj1_lthm <=> (! [X394 : term] : (((sub @ X394 @ id)) = X394) => (! [X395 : term,X396 : term,X397 : term,X398 : term] : ((((ap @ X395 @ X396)) != ((ap @ X397 @ X398))) | (X395 = X397)) => ! [X399 : term,X400 : term,X401 : term,X402 : term] : ((((ap @ (sub @ X400 @ id) @ X399)) != ((ap @ (sub @ X401 @ id) @ X402))) | (X400 = X401))))) & (! [X403 : term,X404 : term,X405 : term,X406 : term] : ((((ap @ X405 @ X403)) != ((ap @ X406 @ X404))) | (X403 = X404)) <=> apinj2) & apnotvar & (id = ((d2subst @ d_id))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1_gthm & pushprop_lem1v2_gthm & (! [X407 : subst,X408 : term,X409 : (term > $o)] : (~ ! [X410 : term] : (~ ! [X411 : term] : ((X409 @ (sub @ X410 @ (push @ X411 @ id))) | ~(X409 @ X411)) | (X409 @ (lam @ X410))) | ~ ! [X412 : term,X413 : term] : (~(X409 @ X412) | (X409 @ (ap @ X412 @ X413)) | ~(X409 @ X413)) | (X409 @ (sub @ X408 @ X407)) | ~ ! [X414 : term] : (~(var @ X414) | (X409 @ (sub @ X414 @ X407)))) <=> induction2lem) & ulamvarind & pushprop_lem0_gthm & (laminj <=> ! [X415 : term,X416 : term] : ((X415 = X416) | (((lam @ X416)) != ((lam @ X415))))) & (induction2_lthm <=> (! [X417 : term] : (((sub @ X417 @ id)) = X417) => (! [X418 : (term > $o),X419 : term,X420 : subst] : (~ ! [X421 : term,X422 : term] : (~(X418 @ X421) | ~(X418 @ X422) | (X418 @ (ap @ X421 @ X422))) | (X418 @ (sub @ X419 @ X420)) | ~ ! [X423 : term] : ((X418 @ (lam @ X423)) | ~ ! [X424 : term] : ((X418 @ (sub @ X423 @ (push @ X424 @ id))) | ~(X418 @ X424))) | ~ ! [X425 : term] : (~(var @ X425) | (X418 @ (sub @ X425 @ X420)))) => ! [X426 : term,X427 : (term > $o)] : ((X427 @ X426) | ~ ! [X428 : term] : (~(var @ X428) | (X427 @ X428)) | ~ ! [X429 : term] : ((X427 @ (lam @ X429)) | ~ ! [X430 : term] : ((X427 @ (sub @ X429 @ (push @ X430 @ id))) | ~(X427 @ X430))) | ~ ! [X431 : term,X432 : term] : (~(X427 @ X432) | ~(X427 @ X431) | (X427 @ (ap @ X431 @ X432))))))) & pushprop_lthm_orig & hoaslamnotvar & ((^[X433 : term, X434 : subst, X435 : (term > $o), X436 : (term > $o)] : (! [X437 : term] : (((X435 @ (sub @ X437 @ (push @ X433 @ X434)))) = ((X436 @ X437))))) = pushprop_p_and_p_prime) & hoasinduction_lem2_lthm & (hoasinduction_lem3aa_lthm <=> ! [X438 : (subst > term > subst > $o),X439 : term] : (~ ! [X440 : (subst > term > term)] : (~ ! [X441 : term] : ((X438 @ id @ (X440 @ id @ X441) @ id) | ~(X438 @ id @ X441 @ id)) | ~ ! [X442 : subst,X443 : term,X444 : subst] : (((sub @ (X440 @ X444 @ X443) @ X442)) = ((X440 @ (comp @ X444 @ X442) @ (sub @ X443 @ X442)))) | (X438 @ id @ (lam @ (X440 @ sh @ one)) @ id)) | ~ ! [X445 : term] : ((X438 @ id @ (sub @ X439 @ (push @ X445 @ id)) @ id) | ~(X438 @ id @ X445 @ id)) | (X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id))) & ! [X446 : d_subst] : (d_id = X446) & (hoasinduction_lthm <=> (! [X447 : (term > $o),X448 : term] : ((X447 @ X448) | ~ ! [X449 : term,X450 : term] : ((X447 @ (ap @ X450 @ X449)) | ~(X447 @ X449) | ~(X447 @ X450)) | ~ ! [X451 : term] : ((X447 @ (lam @ X451)) | ~ ! [X452 : term] : (~(X447 @ X452) | (X447 @ (sub @ X451 @ (push @ X452 @ id))))) | ~ ! [X453 : term] : (~(var @ X453) | (X447 @ X453))) => (! [X454 : term,X455 : term,X456 : (subst > term > subst > $o)] : ((X456 @ id @ (ap @ X455 @ X454) @ id) | ~ ! [X457 : subst,X458 : subst,X459 : term,X460 : subst] : (~(X456 @ X457 @ X459 @ (comp @ X460 @ X458)) | (X456 @ (comp @ X457 @ X460) @ (sub @ X459 @ X460) @ X458)) | ~ ! [X461 : subst,X462 : subst,X463 : term,X464 : subst] : (~(X456 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461) @ X464) | (X456 @ X462 @ X463 @ (comp @ X461 @ X464))) | ~(X456 @ id @ X454 @ id) | ~(X456 @ id @ X455 @ id) | ~ ! [X465 : term,X466 : term] : (~(X456 @ id @ X466 @ id) | (X456 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id) | ~(X456 @ id @ X465 @ id))) => (! [X467 : (subst > term > subst > $o),X468 : term] : (~ ! [X469 : (subst > term > term)] : (~ ! [X470 : term] : ((X467 @ id @ (X469 @ id @ X470) @ id) | ~(X467 @ id @ X470 @ id)) | ~ ! [X471 : term,X472 : subst,X473 : subst] : (((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) = ((sub @ (X469 @ X473 @ X471) @ X472))) | (X467 @ id @ (lam @ (X469 @ sh @ one)) @ id)) | (X467 @ id @ (lam @ X468) @ id) | ~ ! [X474 : term] : (~(X467 @ id @ X474 @ id) | (X467 @ id @ (sub @ X468 @ (push @ X474 @ id)) @ id)) | ~ ! [X475 : subst,X476 : term,X477 : subst,X478 : subst] : ((X467 @ (comp @ X475 @ X478) @ (sub @ X476 @ X478) @ X477) | ~(X467 @ X475 @ X476 @ (comp @ X478 @ X477))) | ~ ! [X479 : term,X480 : subst,X481 : subst,X482 : subst] : (~(X467 @ (comp @ X480 @ X481) @ (sub @ X479 @ X481) @ X482) | (X467 @ X480 @ X479 @ (comp @ X481 @ X482)))) => ! [X483 : (subst > term > subst > $o),X484 : term] : (~ ! [X485 : term] : ((X483 @ id @ X485 @ id) | ~(var @ (sub @ X485 @ id))) | ~ ! [X486 : subst,X487 : subst,X488 : subst,X489 : term] : ((X483 @ X488 @ X489 @ (comp @ X487 @ X486)) | ~(X483 @ (comp @ X488 @ X487) @ (sub @ X489 @ X487) @ X486)) | ~ ! [X490 : (subst > term > term)] : ((X483 @ id @ (lam @ (X490 @ sh @ one)) @ id) | ~ ! [X491 : term] : (~(X483 @ id @ X491 @ id) | (X483 @ id @ (X490 @ id @ X491) @ id)) | ~ ! [X492 : term,X493 : subst,X494 : subst] : (((X490 @ (comp @ X493 @ X494) @ (sub @ X492 @ X494))) = ((sub @ (X490 @ X493 @ X492) @ X494)))) | ~ ! [X495 : subst,X496 : term,X497 : subst,X498 : subst] : (~(X483 @ X498 @ X496 @ (comp @ X497 @ X495)) | (X483 @ (comp @ X498 @ X497) @ (sub @ X496 @ X497) @ X495)) | ~ ! [X499 : term,X500 : term] : (~(X483 @ id @ X500 @ id) | (X483 @ id @ (ap @ (sub @ X500 @ id) @ X499) @ id) | ~(X483 @ id @ X499 @ id)) | (X483 @ id @ X484 @ id)))))) & hoasapnotvar_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem1v2 & (! [X501 : (term > $o),X502 : (subst > term > subst > $o),X503 : term] : (~ ! [X504 : term] : ((X501 @ (sub @ X503 @ (push @ X504 @ id))) | ~(X501 @ X504)) | (X501 @ (lam @ X503)) | ~ ! [X505 : term] : (((X502 @ id @ X505 @ id)) = ((X501 @ X505))) | ~ ! [X506 : (subst > term > term)] : (~ ! [X507 : term] : (~(X502 @ id @ X507 @ id) | (X502 @ id @ (X506 @ id @ X507) @ id)) | (X502 @ id @ (lam @ (X506 @ sh @ one)) @ id) | ~ ! [X508 : subst,X509 : subst,X510 : term] : (((sub @ (X506 @ X509 @ X510) @ X508)) = ((X506 @ (comp @ X509 @ X508) @ (sub @ X510 @ X508)))))) <=> hoasinduction_lem3v2a) & (! [X511 : term,X512 : subst] : (((sub @ one @ (push @ X511 @ X512))) = X511) <=> axvarcons) & (substmonoid <=> (! [X513 : subst] : (((comp @ id @ X513)) = X513) & ! [X514 : subst] : (((comp @ X514 @ id)) = X514))) & termmset_gthm & (termmset <=> ! [X515 : term] : (((sub @ X515 @ id)) = X515)) & ! [X516 : d_term,X517 : d_term] : ((((d2term @ X516)) = ((d2term @ X517))) => (X516 = X517)) & induction2_gthm & pushprop_lem1_gthm & (one = ((d2term @ d_one))) & hoasinduction_lem1 & hoaslamnotap_gthm & hoasinduction_lem1_lthm & (hoasinduction <=> ! [X518 : term,X519 : (subst > term > subst > $o)] : (~ ! [X520 : term] : (~(var @ (sub @ X520 @ id)) | (X519 @ id @ X520 @ id)) | ~ ! [X521 : term,X522 : term] : (~(X519 @ id @ X521 @ id) | ~(X519 @ id @ X522 @ id) | (X519 @ id @ (ap @ (sub @ X522 @ id) @ X521) @ id)) | (X519 @ id @ X518 @ id) | ~ ! [X523 : term,X524 : subst,X525 : subst,X526 : subst] : ((X519 @ X524 @ X523 @ (comp @ X526 @ X525)) | ~(X519 @ (comp @ X524 @ X526) @ (sub @ X523 @ X526) @ X525)) | ~ ! [X527 : (subst > term > term)] : (~ ! [X528 : term] : ((X519 @ id @ (X527 @ id @ X528) @ id) | ~(X519 @ id @ X528 @ id)) | ~ ! [X529 : subst,X530 : subst,X531 : term] : (((X527 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529))) = ((sub @ (X527 @ X530 @ X531) @ X529))) | (X519 @ id @ (lam @ (X527 @ sh @ one)) @ id)) | ~ ! [X532 : term,X533 : subst,X534 : subst,X535 : subst] : ((X519 @ (comp @ X535 @ X533) @ (sub @ X532 @ X533) @ X534) | ~(X519 @ X535 @ X532 @ (comp @ X533 @ X534))))) & (hoasinduction_lem3b_lthm <=> ! [X536 : term] : ~ ! [X537 : (subst > term > term)] : (((sub @ X536 @ (push @ one @ sh))) != ((X537 @ sh @ one)))) & (hoasinduction_lem3aaa <=> ! [X538 : term,X539 : (subst > term > subst > $o)] : ((X539 @ id @ (lam @ (sub @ X538 @ (push @ one @ sh))) @ id) | ~ ! [X540 : (subst > term > term),X541 : term] : (~ ! [X542 : term] : (~(X539 @ id @ X542 @ id) | (X539 @ id @ (X540 @ id @ X542) @ id)) | ~ ! [X543 : subst,X544 : subst,X545 : term] : (((sub @ (sub @ X541 @ (push @ X545 @ X543)) @ X544)) = ((sub @ (X540 @ X543 @ X545) @ X544))) | ~ ! [X546 : subst,X547 : term,X548 : subst] : (((sub @ X541 @ (push @ (sub @ X547 @ X548) @ (comp @ X546 @ X548)))) = ((X540 @ (comp @ X546 @ X548) @ (sub @ X547 @ X548)))) | (X539 @ id @ (lam @ (X540 @ sh @ one)) @ id)) | ~ ! [X549 : term] : ((X539 @ id @ (sub @ X538 @ (push @ X549 @ id)) @ id) | ~(X539 @ id @ X549 @ id))))),
% 164.61/23.50 inference(rectify,[],[f1])).
% 164.61/23.50 thf(f7,plain,(
% 164.61/23.50 ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : (~ ! [X5 : term] : (~ ($true = ((var @ X5))) | (((X3 @ X5)) = $true)) | ~ ! [X6 : term] : ((((X3 @ (lam @ X6))) = $true) | ~ ! [X7 : term] : ((((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true) | ~ (((X3 @ X7)) = $true))) | ($true = ((X3 @ X4))) | ~ ! [X8 : term,X9 : term] : (($true = ((X3 @ (ap @ X9 @ X8)))) | ~ (((X3 @ X8)) = $true) | ~ ($true = ((X3 @ X9))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (subst > term > subst > $o),X13 : (term > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : subst,X17 : subst,X16 : term] : (((sub @ (X14 @ X15 @ X16) @ X17)) = ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)))) | (((X12 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ~ ! [X18 : term] : (~ (((X12 @ id @ X18 @ id)) = $true) | ($true = ((X12 @ id @ (X14 @ id @ X18) @ id))))) | ~ ! [X19 : term] : (~ (((X13 @ X19)) = $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X19 @ id)))))) | ($true = ((X13 @ (lam @ X11)))) | ~ ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : subst,X24 : subst,X25 : subst,X26 : term] : ((((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23)) = $true) | ~ ($true = ((X21 @ X25 @ X26 @ (comp @ X24 @ X23))))) | ~ ! [X27 : (subst > term > term)] : (~ ! [X28 : term] : (~ ($true = ((X21 @ id @ X28 @ id))) | (((X21 @ id @ (X27 @ id @ X28) @ id)) = $true)) | ~ ! [X30 : subst,X29 : term,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) | (((X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) = $true)) | ~ ! [X32 : term] : (($true = ((X21 @ id @ X32 @ id))) | ~ (((var @ (sub @ X32 @ id))) = $true)) | ($true = ((X21 @ id @ X22 @ id))) | ~ ! [X33 : term,X34 : term] : (~ ($true = ((X21 @ id @ X33 @ id))) | (((X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id)) = $true) | ~ (((X21 @ id @ X34 @ id)) = $true)) | ~ ! [X35 : subst,X36 : subst,X37 : subst,X38 : term] : ((((X21 @ X35 @ X38 @ (comp @ X37 @ X36))) = $true) | ~ ($true = ((X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X39 : (subst > term > subst > $o)] : ~ ! [X40 : (term > $o)] : ~ ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41)))) & ((hoaslaminj = $true) <=> ! [X43 : subst,X45 : term,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | (((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | ~ ! [X50 : subst,X51 : term,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) = ((sub @ (X42 @ X49 @ X51) @ X50))) | ~ ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) = ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) <=> (shinj = $true)) & ((axidr = $true) <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) <=> (! [X56 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X56))) = X55) => (! [X58 : subst,X57 : term] : (((comp @ sh @ (push @ X57 @ X58))) = X58) => (! [X60 : term,X59 : term] : ((X59 = X60) | (((lam @ X59)) != ((lam @ X60)))) => ! [X63 : term,X62 : (subst > term > term),X61 : subst,X64 : (subst > term > term)] : (~ ! [X67 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) = ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | ~ ! [X68 : subst,X70 : subst,X69 : term] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) = ((sub @ (X64 @ X68 @ X69) @ X70))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63)))))))) & (hoasapinj2_gthm = $true) & ((axidl = $true) <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & (! [X72 : (term > $o),X73 : term] : (~ ! [X74 : term,X75 : term] : (~ ($true = ((X72 @ X74))) | ($true = ((X72 @ (ap @ X75 @ X74)))) | ~ (((X72 @ X75)) = $true)) | (((X72 @ X73)) = $true) | ~ ! [X76 : term] : (($true = ((X72 @ X76))) | ~ ($true = ((var @ X76)))) | ~ ! [X77 : term] : ((((X72 @ (lam @ X77))) = $true) | ~ ! [X78 : term] : ((((X72 @ (sub @ X77 @ (push @ X78 @ id)))) = $true) | ~ (((X72 @ X78)) = $true)))) <=> (induction2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X81 : subst,X80 : term,X79 : (term > $o)] : ~ ! [X82 : (term > $o)] : ~ ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81)))))) & ! [X84 : d_term] : (d_one = X84) & ((hoasinduction_lem3v2_f = $true) <=> ! [X85 : term] : ~ ! [X86 : (subst > term > term)] : ~ ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88))))) & (substmonoid_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (axvarshift = $true) & ~ (lamnotap = $true) & (hoaslaminj_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X89 : term] : ~ ! [X90 : (subst > term > term)] : ~ ! [X92 : subst,X91 : term] : (((sub @ X89 @ (push @ X91 @ X92))) = ((X90 @ X92 @ X91))) => (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term,X95 : (term > $o),X96 : (subst > term > subst > $o)] : (~ ! [X97 : term] : (((X95 @ X97)) = ((X96 @ id @ X97 @ id))) | (((X95 @ (lam @ X94))) = $true) | ~ ! [X98 : term] : (~ ($true = ((X95 @ X98))) | ($true = ((X95 @ (sub @ X94 @ (push @ X98 @ id)))))) | ~ ! [X99 : (subst > term > term)] : (~ ! [X100 : subst,X102 : subst,X101 : term] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) | (((X96 @ id @ (lam @ (X99 @ sh @ one)) @ id)) = $true) | ~ ! [X103 : term] : ((((X96 @ id @ (X99 @ id @ X103) @ id)) = $true) | ~ ($true = ((X96 @ id @ X103 @ id))))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X104 : term] : (((sub @ X104 @ id)) = X104) => ! [X105 : (subst > term > subst > $o),X106 : term,X107 : (term > $o)] : (~ ! [X108 : subst,X109 : subst,X110 : term,X111 : subst] : (~ ($true = ((X105 @ X111 @ X110 @ (comp @ X108 @ X109)))) | ($true = ((X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)))) | ~ ! [X112 : term] : (~ ($true = ((X107 @ X112))) | ($true = ((X107 @ (sub @ X106 @ (push @ X112 @ id)))))) | ~ ! [X113 : subst,X114 : term,X115 : subst,X116 : subst] : (~ ($true = ((X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116))) | (((X105 @ X113 @ X114 @ (comp @ X115 @ X116))) = $true)) | ~ ! [X117 : (subst > term > term)] : (~ ! [X118 : term] : ((((X105 @ id @ (X117 @ id @ X118) @ id)) = $true) | ~ (((X105 @ id @ X118 @ id)) = $true)) | ~ ! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) | (((X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) = $true)) | ($true = ((X107 @ (lam @ X106)))) | ~ ! [X122 : term] : (((X107 @ X122)) = ((X105 @ id @ X122 @ id)))))) & (hoasapnotvar = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X125 : term,X126 : term,X124 : term,X123 : term] : ((((ap @ X124 @ X125)) != ((ap @ X123 @ X126))) | (X125 = X126)) => ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) <=> (hoasapinj2_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X131 : (term > $o),X132 : term,X133 : subst,X134 : (term > $o)] : ((((X131 @ one)) = $true) | ~ (((X134 @ X132)) = $true) | ~ ! [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) = ((X131 @ X135))))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : ~ ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (lamnotvar = $true) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ~ ! [X145 : (term > $o)] : ~ ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) <=> (pushprop_lem0_lthm = $true)) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) <=> (axshiftcons = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X149 : (subst > term > subst > $o),X150 : (term > $o),X151 : term] : (~ ! [X152 : (subst > term > term)] : (~ ! [X153 : term] : ((((X149 @ id @ (X152 @ id @ X153) @ id)) = $true) | ~ (((X149 @ id @ X153 @ id)) = $true)) | ($true = ((X149 @ id @ (lam @ (X152 @ sh @ one)) @ id))) | ~ ! [X154 : subst,X156 : term,X155 : subst] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155)))) | ~ ! [X157 : term] : (~ ($true = ((X150 @ X157))) | (((X150 @ (sub @ X151 @ (push @ X157 @ id)))) = $true)) | ($true = ((X150 @ (lam @ X151)))) | ~ ! [X158 : term] : (((X149 @ id @ X158 @ id)) = ((X150 @ X158))) | ~ ! [X159 : term,X160 : subst,X161 : subst,X162 : subst] : (($true = ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)))) | ~ (((X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) = $true)) | ~ ! [X163 : term,X164 : subst,X165 : subst,X166 : subst] : (~ (((X149 @ X166 @ X163 @ (comp @ X164 @ X165))) = $true) | ($true = ((X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165)))))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X167 : term,X168 : (term > $o),X169 : term,X170 : (subst > term > subst > $o)] : (~ ! [X171 : term,X172 : term] : (~ ($true = ((X170 @ id @ X171 @ id))) | (((X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id)) = $true) | ~ (((X170 @ id @ X172 @ id)) = $true)) | ~ ! [X173 : term,X174 : subst,X175 : subst,X176 : subst] : (~ ($true = ((X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174))) | (((X170 @ X175 @ X173 @ (comp @ X176 @ X174))) = $true)) | ~ ! [X177 : term] : (((X170 @ id @ X177 @ id)) = ((X168 @ X177))) | (((X168 @ (ap @ X167 @ X169))) = $true) | ~ (((X168 @ X169)) = $true) | ~ ! [X178 : subst,X179 : subst,X180 : subst,X181 : term] : (($true = ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179))) | ~ ($true = ((X170 @ X180 @ X181 @ (comp @ X178 @ X179))))) | ~ ($true = ((X168 @ X167))))) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) = ((d2subst @ X183))) => (X182 = X183)) & ~ (ulamvar1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3b_gthm = $true) & (axabs = $true) & (pushprop_lthm = $true) & (axapp = $true) & ((apinj1 = $true) <=> ! [X186 : term,X187 : term,X188 : term,X189 : term] : ((X186 = X188) | (((ap @ X188 @ X189)) != ((ap @ X186 @ X187))))) & (! [X190 : term] : ~ ! [X191 : (subst > term > term)] : (((X191 @ sh @ one)) != ((sub @ X190 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem3a = $true) <=> ! [X192 : term,X193 : (subst > term > subst > $o)] : ((((X193 @ id @ (lam @ X192) @ id)) = $true) | ~ ! [X194 : (subst > term > term)] : (~ ! [X195 : subst,X196 : subst,X197 : term] : (((sub @ (X194 @ X196 @ X197) @ X195)) = ((X194 @ (comp @ X196 @ X195) @ (sub @ X197 @ X195)))) | (((X193 @ id @ (lam @ (X194 @ sh @ one)) @ id)) = $true) | ~ ! [X198 : term] : ((((X193 @ id @ (X194 @ id @ X198) @ id)) = $true) | ~ ($true = ((X193 @ id @ X198 @ id))))) | ~ ! [X199 : term] : ((((X193 @ id @ (sub @ X192 @ (push @ X199 @ id)) @ id)) = $true) | ~ (((X193 @ id @ X199 @ id)) = $true)))) & (induction2lem_gthm = $true) & (axassoc = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X203 : (subst > term > subst > $o)] : ~ ! [X204 : (term > $o)] : ~ ! [X205 : term] : (((X203 @ id @ X205 @ id)) = ((X204 @ X205))) => (! [X206 : (term > $o),X207 : term] : ((((X206 @ X207)) = $true) | ~ ! [X208 : term] : (($true = ((X206 @ X208))) | ~ ($true = ((var @ X208)))) | ~ ! [X209 : term,X210 : term] : (~ ($true = ((X206 @ X209))) | ~ (((X206 @ X210)) = $true) | ($true = ((X206 @ (ap @ X209 @ X210))))) | ~ ! [X211 : term] : (~ ! [X212 : term] : (~ ($true = ((X206 @ X212))) | ($true = ((X206 @ (sub @ X211 @ (push @ X212 @ id)))))) | ($true = ((X206 @ (lam @ X211)))))) => (! [X213 : term] : (((sub @ X213 @ id)) = X213) => (! [X214 : term,X215 : (subst > term > subst > $o),X216 : (term > $o)] : (~ ! [X217 : (subst > term > term)] : (~ ! [X218 : term,X219 : subst,X220 : subst] : (((sub @ (X217 @ X219 @ X218) @ X220)) = ((X217 @ (comp @ X219 @ X220) @ (sub @ X218 @ X220)))) | ~ ! [X221 : term] : (~ ($true = ((X215 @ id @ X221 @ id))) | (((X215 @ id @ (X217 @ id @ X221) @ id)) = $true)) | ($true = ((X215 @ id @ (lam @ (X217 @ sh @ one)) @ id)))) | ~ ! [X222 : term] : (((X215 @ id @ X222 @ id)) = ((X216 @ X222))) | ($true = ((X216 @ (lam @ X214)))) | ~ ! [X223 : term] : (~ (((X216 @ X223)) = $true) | (((X216 @ (sub @ X214 @ (push @ X223 @ id)))) = $true))) => ! [X224 : (subst > term > subst > $o),X225 : term] : (~ ! [X226 : (subst > term > term)] : (~ ! [X227 : subst,X228 : term,X229 : subst] : (((X226 @ (comp @ X229 @ X227) @ (sub @ X228 @ X227))) = ((sub @ (X226 @ X229 @ X228) @ X227))) | ~ ! [X230 : term] : (~ (((X224 @ id @ X230 @ id)) = $true) | (((X224 @ id @ (X226 @ id @ X230) @ id)) = $true)) | ($true = ((X224 @ id @ (lam @ (X226 @ sh @ one)) @ id)))) | (((X224 @ id @ X225 @ id)) = $true) | ~ ! [X231 : term,X232 : term] : (~ (((X224 @ id @ X232 @ id)) = $true) | ~ (((X224 @ id @ X231 @ id)) = $true) | ($true = ((X224 @ id @ (ap @ (sub @ X232 @ id) @ X231) @ id)))))))))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X233 : term,X234 : (subst > term > subst > $o)] : (~ ! [X235 : (subst > term > term)] : (~ ! [X236 : term,X237 : subst,X238 : subst] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X235 @ X238 @ X236) @ X237))) | ~ ! [X239 : term] : (~ (((X234 @ id @ X239 @ id)) = $true) | (((X234 @ id @ (X235 @ id @ X239) @ id)) = $true)) | ($true = ((X234 @ id @ (lam @ (X235 @ sh @ one)) @ id)))) | ~ ! [X240 : subst,X241 : subst,X242 : subst,X243 : term] : (($true = ((X234 @ X241 @ X243 @ (comp @ X242 @ X240)))) | ~ (((X234 @ (comp @ X241 @ X242) @ (sub @ X243 @ X242) @ X240)) = $true)) | ~ ! [X244 : subst,X245 : subst,X246 : term,X247 : subst] : (($true = ((X234 @ (comp @ X244 @ X247) @ (sub @ X246 @ X247) @ X245))) | ~ ($true = ((X234 @ X244 @ X246 @ (comp @ X247 @ X245))))) | ($true = ((X234 @ id @ (lam @ X233) @ id))) | ~ ! [X248 : term] : ((((X234 @ id @ (sub @ X233 @ (push @ X248 @ id)) @ id)) = $true) | ~ (((X234 @ id @ X248 @ id)) = $true)))) & ((! [X249 : subst,X250 : term] : (((sub @ one @ (push @ X250 @ X249))) = X250) => (! [X251 : subst,X252 : term] : (((comp @ sh @ (push @ X252 @ X251))) = X251) => ! [X253 : (term > $o),X254 : subst,X255 : term,X256 : term,X257 : (term > $o)] : ((((X253 @ (sub @ X256 @ (push @ X255 @ X254)))) = $true) | ~ (((X257 @ X256)) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X258 : (term > $o),X259 : (term > $o),X260 : term,X261 : subst,X262 : term] : (~ ($true = ((X259 @ X260))) | ($true = ((X258 @ (sub @ X260 @ (push @ X262 @ X261))))))) & ((hoasinduction_lem2 = $true) <=> ! [X263 : term,X264 : term,X265 : (subst > term > subst > $o)] : ((((X265 @ id @ (ap @ X263 @ X264) @ id)) = $true) | ~ ! [X266 : subst,X267 : subst,X268 : term,X269 : subst] : (($true = ((X265 @ X269 @ X268 @ (comp @ X267 @ X266)))) | ~ (((X265 @ (comp @ X269 @ X267) @ (sub @ X268 @ X267) @ X266)) = $true)) | ~ (((X265 @ id @ X263 @ id)) = $true) | ~ ! [X270 : term,X271 : term] : (~ (((X265 @ id @ X270 @ id)) = $true) | ~ ($true = ((X265 @ id @ X271 @ id))) | ($true = ((X265 @ id @ (ap @ (sub @ X270 @ id) @ X271) @ id)))) | ~ ($true = ((X265 @ id @ X264 @ id))) | ~ ! [X272 : subst,X273 : subst,X274 : subst,X275 : term] : ((((X265 @ (comp @ X274 @ X273) @ (sub @ X275 @ X273) @ X272)) = $true) | ~ ($true = ((X265 @ X274 @ X275 @ (comp @ X273 @ X272))))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X276 : subst,X277 : term] : (((sub @ one @ (push @ X277 @ X276))) = X277) => (! [X278 : subst,X279 : term] : (((comp @ sh @ (push @ X279 @ X278))) = X278) => (! [X280 : subst] : (((comp @ X280 @ id)) = X280) => (! [X281 : term,X282 : (term > $o)] : (~ ! [X283 : term,X284 : term] : ((((X282 @ (ap @ X283 @ X284))) = $true) | ~ (((X282 @ X284)) = $true) | ~ (((X282 @ X283)) = $true)) | (((X282 @ X281)) = $true) | ~ ! [X285 : term] : (~ ($true = ((var @ X285))) | (((X282 @ X285)) = $true)) | ~ ! [X286 : term] : (($true = ((X282 @ (lam @ X286)))) | ~ (((X282 @ X286)) = $true))) => ! [X287 : subst,X288 : term,X289 : (term > $o)] : (($true = ((X289 @ (sub @ X288 @ X287)))) | ~ ! [X290 : term,X291 : term] : (~ ($true = ((X289 @ X290))) | ($true = ((X289 @ (ap @ X290 @ X291)))) | ~ ($true = ((X289 @ X291)))) | ~ ! [X292 : term] : (~ ($true = ((var @ X292))) | (((X289 @ (sub @ X292 @ X287))) = $true)) | ~ ! [X293 : term] : (~ ! [X294 : term] : (~ (((X289 @ X294)) = $true) | (((X289 @ (sub @ X293 @ (push @ X294 @ id)))) = $true)) | ($true = ((X289 @ (lam @ X293))))))))))) & (! [X295 : term,X296 : (subst > term > subst > $o)] : (~ ! [X297 : (subst > term > term)] : ((((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ~ ! [X298 : term] : (~ ($true = ((X296 @ id @ X298 @ id))) | ($true = ((X296 @ id @ (X297 @ id @ X298) @ id)))) | ~ ! [X299 : subst,X300 : subst,X301 : term] : (((sub @ (X297 @ X300 @ X301) @ X299)) = ((X297 @ (comp @ X300 @ X299) @ (sub @ X301 @ X299))))) | ~ ! [X302 : term] : (($true = ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id))) | ~ ($true = ((X296 @ id @ X302 @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X303 : term] : (((sub @ X303 @ id)) = X303) => (! [X304 : (subst > term > subst > $o),X305 : term] : (~ ! [X306 : term] : (($true = ((X304 @ id @ (sub @ X305 @ (push @ X306 @ id)) @ id))) | ~ ($true = ((X304 @ id @ X306 @ id)))) | ~ ! [X307 : (subst > term > term)] : (~ ! [X308 : term] : ((((X304 @ id @ (X307 @ id @ X308) @ id)) = $true) | ~ ($true = ((X304 @ id @ X308 @ id)))) | ($true = ((X304 @ id @ (lam @ (X307 @ sh @ one)) @ id))) | ~ ! [X309 : subst,X310 : subst,X311 : term] : (((X307 @ (comp @ X309 @ X310) @ (sub @ X311 @ X310))) = ((sub @ (X307 @ X309 @ X311) @ X310)))) | ($true = ((X304 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) => ! [X312 : (subst > term > subst > $o),X313 : term] : (~ ! [X314 : term] : (~ (((X312 @ id @ X314 @ id)) = $true) | (((X312 @ id @ (sub @ X313 @ (push @ X314 @ id)) @ id)) = $true)) | (((X312 @ id @ (lam @ X313) @ id)) = $true) | ~ ! [X315 : (subst > term > term)] : ((((X312 @ id @ (lam @ (X315 @ sh @ one)) @ id)) = $true) | ~ ! [X316 : subst,X317 : subst,X318 : term] : (((sub @ (X315 @ X317 @ X318) @ X316)) = ((X315 @ (comp @ X317 @ X316) @ (sub @ X318 @ X316)))) | ~ ! [X319 : term] : (~ (((X312 @ id @ X319 @ id)) = $true) | ($true = ((X312 @ id @ (X315 @ id @ X319) @ id))))) | ~ ! [X320 : subst,X321 : term,X322 : subst,X323 : subst] : (($true = ((X312 @ X320 @ X321 @ (comp @ X323 @ X322)))) | ~ (((X312 @ (comp @ X320 @ X323) @ (sub @ X321 @ X323) @ X322)) = $true)) | ~ ! [X324 : term,X325 : subst,X326 : subst,X327 : subst] : ((((X312 @ (comp @ X327 @ X326) @ (sub @ X324 @ X326) @ X325)) = $true) | ~ (((X312 @ X327 @ X324 @ (comp @ X326 @ X325))) = $true)))))) & (hoasinduction_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X328 : (subst > term > subst > $o),X329 : term] : (~ ! [X330 : (subst > term > term)] : (~ ! [X331 : term,X332 : subst,X333 : subst] : (((sub @ (X330 @ X333 @ X331) @ X332)) = ((X330 @ (comp @ X333 @ X332) @ (sub @ X331 @ X332)))) | ~ ! [X334 : term] : (($true = ((X328 @ id @ (X330 @ id @ X334) @ id))) | ~ ($true = ((X328 @ id @ X334 @ id)))) | (((X328 @ id @ (lam @ (X330 @ sh @ one)) @ id)) = $true)) | (((X328 @ id @ X329 @ id)) = $true) | ~ ! [X335 : term,X336 : term] : (($true = ((X328 @ id @ (ap @ (sub @ X336 @ id) @ X335) @ id))) | ~ ($true = ((X328 @ id @ X336 @ id))) | ~ ($true = ((X328 @ id @ X335 @ id)))))) & (pushprop_lem3v2_lthm = $true) & ((induction = $true) <=> ! [X337 : (term > $o),X338 : term] : (~ ! [X339 : term] : ((((X337 @ X339)) = $true) | ~ (((var @ X339)) = $true)) | ~ ! [X340 : term,X341 : term] : (~ (((X337 @ X340)) = $true) | (((X337 @ (ap @ X340 @ X341))) = $true) | ~ (((X337 @ X341)) = $true)) | ($true = ((X337 @ X338))) | ~ ! [X342 : term] : ((((X337 @ (lam @ X342))) = $true) | ~ ($true = ((X337 @ X342)))))) & ((! [X343 : term,X344 : subst] : (((sub @ one @ (push @ X343 @ X344))) = X343) => ! [X345 : subst,X346 : term,X347 : (term > $o),X348 : (term > $o)] : (~ ($true = ((X347 @ X346))) | ($true = ((X348 @ one))) | ~ ! [X349 : term] : (((X348 @ X349)) = ((X347 @ (sub @ X349 @ (push @ X346 @ X345))))))) <=> (pushprop_lem1v2_lthm = $true)) & ((axscons = $true) <=> ! [X350 : subst] : (((push @ (sub @ one @ X350) @ (comp @ sh @ X350))) = X350)) & (axclos = $true) & ! [X351 : subst] : ? [X352 : d_subst] : (((d2subst @ X352)) = X351) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X353 : term] : (((sub @ X353 @ id)) = X353) => (! [X354 : term,X355 : (subst > term > subst > $o)] : (~ ! [X356 : term] : (($true = ((X355 @ id @ (sub @ X354 @ (push @ X356 @ id)) @ id))) | ~ (((X355 @ id @ X356 @ id)) = $true)) | ~ ! [X357 : (subst > term > term)] : (~ ! [X358 : term] : (~ ($true = ((X355 @ id @ X358 @ id))) | ($true = ((X355 @ id @ (X357 @ id @ X358) @ id)))) | ~ ! [X359 : term,X360 : subst,X361 : subst] : (((X357 @ (comp @ X361 @ X360) @ (sub @ X359 @ X360))) = ((sub @ (X357 @ X361 @ X359) @ X360))) | ($true = ((X355 @ id @ (lam @ (X357 @ sh @ one)) @ id)))) | ($true = ((X355 @ id @ (lam @ (sub @ X354 @ (push @ one @ sh))) @ id)))) => ! [X362 : term,X363 : (subst > term > subst > $o)] : (~ ! [X364 : term] : (~ ($true = ((X363 @ id @ X364 @ id))) | ($true = ((X363 @ id @ (sub @ X362 @ (push @ X364 @ id)) @ id)))) | ~ ! [X365 : (subst > term > term)] : (~ ! [X366 : term,X367 : subst,X368 : subst] : (((sub @ (X365 @ X368 @ X366) @ X367)) = ((X365 @ (comp @ X368 @ X367) @ (sub @ X366 @ X367)))) | ~ ! [X369 : term] : (($true = ((X363 @ id @ (X365 @ id @ X369) @ id))) | ~ ($true = ((X363 @ id @ X369 @ id)))) | (((X363 @ id @ (lam @ (X365 @ sh @ one)) @ id)) = $true)) | (((X363 @ id @ (lam @ X362) @ id)) = $true))))) & ((hoasapinj1 = $true) <=> ! [X370 : term,X371 : term,X372 : term,X373 : term] : ((X370 = X372) | (((ap @ (sub @ X370 @ id) @ X373)) != ((ap @ (sub @ X372 @ id) @ X371))))) & (! [X374 : term,X375 : term,X376 : term,X377 : term] : ((((ap @ (sub @ X376 @ id) @ X375)) != ((ap @ (sub @ X374 @ id) @ X377))) | (X375 = X377)) <=> (hoasapinj2 = $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X378 : subst] : (((comp @ id @ X378)) = X378) => (! [X379 : subst] : (((comp @ X379 @ id)) = X379) => (! [X380 : subst] : (((comp @ X380 @ id)) = X380) & ! [X381 : subst] : (((comp @ id @ X381)) = X381))))) & ((termmset_lthm = $true) <=> (! [X382 : term] : (((sub @ X382 @ id)) = X382) => ! [X383 : term] : (((sub @ X383 @ id)) = X383))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_lthm = $true) & (axmap = $true) & (pushprop_lem2v2 = $true) & (! [X384 : term,X385 : term,X386 : (subst > term > term)] : (~ ! [X387 : term,X388 : subst,X389 : subst] : (((sub @ (X386 @ X388 @ X387) @ X389)) = ((X386 @ (comp @ X388 @ X389) @ (sub @ X387 @ X389)))) | (((lam @ (X386 @ sh @ one))) != ((ap @ (sub @ X385 @ id) @ X384)))) <=> (hoaslamnotap = $true)) & (ulamvarsh = $true) & ((hoasinduction_lem0 = $true) <=> ! [X390 : (subst > term > subst > $o)] : ~ ! [X391 : (term > $o)] : ~ ! [X392 : term] : (((X391 @ X392)) = ((X390 @ id @ X392 @ id)))) & (! [X393 : term] : (((sub @ X393 @ id)) = X393) <=> (axvarid = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X394 : term] : (((sub @ X394 @ id)) = X394) => (! [X395 : term,X396 : term,X397 : term,X398 : term] : ((((ap @ X395 @ X396)) != ((ap @ X397 @ X398))) | (X395 = X397)) => ! [X399 : term,X400 : term,X401 : term,X402 : term] : ((((ap @ (sub @ X400 @ id) @ X399)) != ((ap @ (sub @ X401 @ id) @ X402))) | (X400 = X401))))) & (! [X403 : term,X404 : term,X405 : term,X406 : term] : ((((ap @ X405 @ X403)) != ((ap @ X406 @ X404))) | (X403 = X404)) <=> (apinj2 = $true)) & (apnotvar = $true) & (((d2subst @ d_id)) = id) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X407 : subst,X408 : term,X409 : (term > $o)] : (~ ! [X410 : term] : (~ ! [X411 : term] : (($true = ((X409 @ (sub @ X410 @ (push @ X411 @ id))))) | ~ (((X409 @ X411)) = $true)) | ($true = ((X409 @ (lam @ X410))))) | ~ ! [X412 : term,X413 : term] : (~ ($true = ((X409 @ X412))) | ($true = ((X409 @ (ap @ X412 @ X413)))) | ~ (((X409 @ X413)) = $true)) | ($true = ((X409 @ (sub @ X408 @ X407)))) | ~ ! [X414 : term] : (~ ($true = ((var @ X414))) | ($true = ((X409 @ (sub @ X414 @ X407)))))) <=> (induction2lem = $true)) & (ulamvarind = $true) & (pushprop_lem0_gthm = $true) & ((laminj = $true) <=> ! [X415 : term,X416 : term] : ((X415 = X416) | (((lam @ X416)) != ((lam @ X415))))) & ((induction2_lthm = $true) <=> (! [X417 : term] : (((sub @ X417 @ id)) = X417) => (! [X418 : (term > $o),X419 : term,X420 : subst] : (~ ! [X421 : term,X422 : term] : (~ (((X418 @ X421)) = $true) | ~ (((X418 @ X422)) = $true) | ($true = ((X418 @ (ap @ X421 @ X422))))) | ($true = ((X418 @ (sub @ X419 @ X420)))) | ~ ! [X423 : term] : ((((X418 @ (lam @ X423))) = $true) | ~ ! [X424 : term] : ((((X418 @ (sub @ X423 @ (push @ X424 @ id)))) = $true) | ~ (((X418 @ X424)) = $true))) | ~ ! [X425 : term] : (~ (((var @ X425)) = $true) | (((X418 @ (sub @ X425 @ X420))) = $true))) => ! [X426 : term,X427 : (term > $o)] : (($true = ((X427 @ X426))) | ~ ! [X428 : term] : (~ (((var @ X428)) = $true) | (((X427 @ X428)) = $true)) | ~ ! [X429 : term] : (($true = ((X427 @ (lam @ X429)))) | ~ ! [X430 : term] : ((((X427 @ (sub @ X429 @ (push @ X430 @ id)))) = $true) | ~ (((X427 @ X430)) = $true))) | ~ ! [X431 : term,X432 : term] : (~ (((X427 @ X432)) = $true) | ~ (((X427 @ X431)) = $true) | (((X427 @ (ap @ X431 @ X432))) = $true)))))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X438 : (subst > term > subst > $o),X439 : term] : (~ ! [X440 : (subst > term > term)] : (~ ! [X441 : term] : ((((X438 @ id @ (X440 @ id @ X441) @ id)) = $true) | ~ ($true = ((X438 @ id @ X441 @ id)))) | ~ ! [X442 : subst,X443 : term,X444 : subst] : (((sub @ (X440 @ X444 @ X443) @ X442)) = ((X440 @ (comp @ X444 @ X442) @ (sub @ X443 @ X442)))) | (((X438 @ id @ (lam @ (X440 @ sh @ one)) @ id)) = $true)) | ~ ! [X445 : term] : ((((X438 @ id @ (sub @ X439 @ (push @ X445 @ id)) @ id)) = $true) | ~ ($true = ((X438 @ id @ X445 @ id)))) | (((X438 @ id @ (lam @ (sub @ X439 @ (push @ one @ sh))) @ id)) = $true))) & ! [X446 : d_subst] : (d_id = X446) & ((hoasinduction_lthm = $true) <=> (! [X447 : (term > $o),X448 : term] : ((((X447 @ X448)) = $true) | ~ ! [X449 : term,X450 : term] : ((((X447 @ (ap @ X450 @ X449))) = $true) | ~ (((X447 @ X449)) = $true) | ~ (((X447 @ X450)) = $true)) | ~ ! [X451 : term] : (($true = ((X447 @ (lam @ X451)))) | ~ ! [X452 : term] : (~ (((X447 @ X452)) = $true) | ($true = ((X447 @ (sub @ X451 @ (push @ X452 @ id))))))) | ~ ! [X453 : term] : (~ ($true = ((var @ X453))) | ($true = ((X447 @ X453))))) => (! [X454 : term,X455 : term,X456 : (subst > term > subst > $o)] : (($true = ((X456 @ id @ (ap @ X455 @ X454) @ id))) | ~ ! [X457 : subst,X458 : subst,X459 : term,X460 : subst] : (~ ($true = ((X456 @ X457 @ X459 @ (comp @ X460 @ X458)))) | ($true = ((X456 @ (comp @ X457 @ X460) @ (sub @ X459 @ X460) @ X458)))) | ~ ! [X461 : subst,X462 : subst,X463 : term,X464 : subst] : (~ (((X456 @ (comp @ X462 @ X461) @ (sub @ X463 @ X461) @ X464)) = $true) | (((X456 @ X462 @ X463 @ (comp @ X461 @ X464))) = $true)) | ~ (((X456 @ id @ X454 @ id)) = $true) | ~ (((X456 @ id @ X455 @ id)) = $true) | ~ ! [X465 : term,X466 : term] : (~ (((X456 @ id @ X466 @ id)) = $true) | ($true = ((X456 @ id @ (ap @ (sub @ X466 @ id) @ X465) @ id))) | ~ ($true = ((X456 @ id @ X465 @ id))))) => (! [X467 : (subst > term > subst > $o),X468 : term] : (~ ! [X469 : (subst > term > term)] : (~ ! [X470 : term] : (($true = ((X467 @ id @ (X469 @ id @ X470) @ id))) | ~ ($true = ((X467 @ id @ X470 @ id)))) | ~ ! [X471 : term,X472 : subst,X473 : subst] : (((X469 @ (comp @ X473 @ X472) @ (sub @ X471 @ X472))) = ((sub @ (X469 @ X473 @ X471) @ X472))) | (((X467 @ id @ (lam @ (X469 @ sh @ one)) @ id)) = $true)) | ($true = ((X467 @ id @ (lam @ X468) @ id))) | ~ ! [X474 : term] : (~ (((X467 @ id @ X474 @ id)) = $true) | (((X467 @ id @ (sub @ X468 @ (push @ X474 @ id)) @ id)) = $true)) | ~ ! [X475 : subst,X476 : term,X477 : subst,X478 : subst] : ((((X467 @ (comp @ X475 @ X478) @ (sub @ X476 @ X478) @ X477)) = $true) | ~ (((X467 @ X475 @ X476 @ (comp @ X478 @ X477))) = $true)) | ~ ! [X479 : term,X480 : subst,X481 : subst,X482 : subst] : (~ (((X467 @ (comp @ X480 @ X481) @ (sub @ X479 @ X481) @ X482)) = $true) | ($true = ((X467 @ X480 @ X479 @ (comp @ X481 @ X482)))))) => ! [X483 : (subst > term > subst > $o),X484 : term] : (~ ! [X485 : term] : (($true = ((X483 @ id @ X485 @ id))) | ~ (((var @ (sub @ X485 @ id))) = $true)) | ~ ! [X486 : subst,X487 : subst,X488 : subst,X489 : term] : ((((X483 @ X488 @ X489 @ (comp @ X487 @ X486))) = $true) | ~ ($true = ((X483 @ (comp @ X488 @ X487) @ (sub @ X489 @ X487) @ X486)))) | ~ ! [X490 : (subst > term > term)] : (($true = ((X483 @ id @ (lam @ (X490 @ sh @ one)) @ id))) | ~ ! [X491 : term] : (~ (((X483 @ id @ X491 @ id)) = $true) | (((X483 @ id @ (X490 @ id @ X491) @ id)) = $true)) | ~ ! [X492 : term,X493 : subst,X494 : subst] : (((X490 @ (comp @ X493 @ X494) @ (sub @ X492 @ X494))) = ((sub @ (X490 @ X493 @ X492) @ X494)))) | ~ ! [X495 : subst,X496 : term,X497 : subst,X498 : subst] : (~ (((X483 @ X498 @ X496 @ (comp @ X497 @ X495))) = $true) | ($true = ((X483 @ (comp @ X498 @ X497) @ (sub @ X496 @ X497) @ X495)))) | ~ ! [X499 : term,X500 : term] : (~ (((X483 @ id @ X500 @ id)) = $true) | (((X483 @ id @ (ap @ (sub @ X500 @ id) @ X499) @ id)) = $true) | ~ ($true = ((X483 @ id @ X499 @ id)))) | ($true = ((X483 @ id @ X484 @ id)))))))) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2 = $true) & (! [X501 : (term > $o),X502 : (subst > term > subst > $o),X503 : term] : (~ ! [X504 : term] : (($true = ((X501 @ (sub @ X503 @ (push @ X504 @ id))))) | ~ (((X501 @ X504)) = $true)) | (((X501 @ (lam @ X503))) = $true) | ~ ! [X505 : term] : (((X502 @ id @ X505 @ id)) = ((X501 @ X505))) | ~ ! [X506 : (subst > term > term)] : (~ ! [X507 : term] : (~ (((X502 @ id @ X507 @ id)) = $true) | (((X502 @ id @ (X506 @ id @ X507) @ id)) = $true)) | (((X502 @ id @ (lam @ (X506 @ sh @ one)) @ id)) = $true) | ~ ! [X508 : subst,X509 : subst,X510 : term] : (((sub @ (X506 @ X509 @ X510) @ X508)) = ((X506 @ (comp @ X509 @ X508) @ (sub @ X510 @ X508)))))) <=> (hoasinduction_lem3v2a = $true)) & (! [X511 : term,X512 : subst] : (((sub @ one @ (push @ X511 @ X512))) = X511) <=> (axvarcons = $true)) & ((substmonoid = $true) <=> (! [X513 : subst] : (((comp @ id @ X513)) = X513) & ! [X514 : subst] : (((comp @ X514 @ id)) = X514))) & (termmset_gthm = $true) & ((termmset = $true) <=> ! [X515 : term] : (((sub @ X515 @ id)) = X515)) & ! [X516 : d_term,X517 : d_term] : ((((d2term @ X516)) = ((d2term @ X517))) => (X516 = X517)) & (induction2_gthm = $true) & (pushprop_lem1_gthm = $true) & (one = ((d2term @ d_one))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction = $true) <=> ! [X518 : term,X519 : (subst > term > subst > $o)] : (~ ! [X520 : term] : (~ (((var @ (sub @ X520 @ id))) = $true) | ($true = ((X519 @ id @ X520 @ id)))) | ~ ! [X521 : term,X522 : term] : (~ ($true = ((X519 @ id @ X521 @ id))) | ~ (((X519 @ id @ X522 @ id)) = $true) | (((X519 @ id @ (ap @ (sub @ X522 @ id) @ X521) @ id)) = $true)) | ($true = ((X519 @ id @ X518 @ id))) | ~ ! [X523 : term,X524 : subst,X525 : subst,X526 : subst] : (($true = ((X519 @ X524 @ X523 @ (comp @ X526 @ X525)))) | ~ ($true = ((X519 @ (comp @ X524 @ X526) @ (sub @ X523 @ X526) @ X525)))) | ~ ! [X527 : (subst > term > term)] : (~ ! [X528 : term] : ((((X519 @ id @ (X527 @ id @ X528) @ id)) = $true) | ~ ($true = ((X519 @ id @ X528 @ id)))) | ~ ! [X529 : subst,X530 : subst,X531 : term] : (((X527 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529))) = ((sub @ (X527 @ X530 @ X531) @ X529))) | (((X519 @ id @ (lam @ (X527 @ sh @ one)) @ id)) = $true)) | ~ ! [X532 : term,X533 : subst,X534 : subst,X535 : subst] : ((((X519 @ (comp @ X535 @ X533) @ (sub @ X532 @ X533) @ X534)) = $true) | ~ ($true = ((X519 @ X535 @ X532 @ (comp @ X533 @ X534))))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X536 : term] : ~ ! [X537 : (subst > term > term)] : (((sub @ X536 @ (push @ one @ sh))) != ((X537 @ sh @ one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X538 : term,X539 : (subst > term > subst > $o)] : (($true = ((X539 @ id @ (lam @ (sub @ X538 @ (push @ one @ sh))) @ id))) | ~ ! [X540 : (subst > term > term),X541 : term] : (~ ! [X542 : term] : (~ (((X539 @ id @ X542 @ id)) = $true) | ($true = ((X539 @ id @ (X540 @ id @ X542) @ id)))) | ~ ! [X543 : subst,X544 : subst,X545 : term] : (((sub @ (sub @ X541 @ (push @ X545 @ X543)) @ X544)) = ((sub @ (X540 @ X543 @ X545) @ X544))) | ~ ! [X546 : subst,X547 : term,X548 : subst] : (((sub @ X541 @ (push @ (sub @ X547 @ X548) @ (comp @ X546 @ X548)))) = ((X540 @ (comp @ X546 @ X548) @ (sub @ X547 @ X548)))) | ($true = ((X539 @ id @ (lam @ (X540 @ sh @ one)) @ id)))) | ~ ! [X549 : term] : ((((X539 @ id @ (sub @ X538 @ (push @ X549 @ id)) @ id)) = $true) | ~ (((X539 @ id @ X549 @ id)) = $true))))),
% 164.61/23.50 inference(fool_elimination,[],[f6])).
% 164.61/23.50 thf(f8,plain,(
% 164.61/23.50 (hoasinduction != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y2 @ (comp @ Y3 @ Y1)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3) @ Y1)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id))))))))))))),
% 164.61/23.50 inference(flattening,[],[f5])).
% 164.61/23.50 thf(f9,plain,(
% 164.61/23.50 ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : (term > $o),X4 : term] : (~ ! [X5 : term] : (~ ($true = ((var @ X5))) | (((X3 @ X5)) = $true)) | ~ ! [X6 : term] : ((((X3 @ (lam @ X6))) = $true) | ~ ! [X7 : term] : ((((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true) | ~ (((X3 @ X7)) = $true))) | ($true = ((X3 @ X4))) | ~ ! [X8 : term,X9 : term] : (($true = ((X3 @ (ap @ X9 @ X8)))) | ~ (((X3 @ X8)) = $true) | ~ ($true = ((X3 @ X9))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : term,X12 : (subst > term > subst > $o),X13 : (term > $o)] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : subst,X17 : subst,X16 : term] : (((sub @ (X14 @ X15 @ X16) @ X17)) = ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)))) | (((X12 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ~ ! [X18 : term] : (~ (((X12 @ id @ X18 @ id)) = $true) | ($true = ((X12 @ id @ (X14 @ id @ X18) @ id))))) | ~ ! [X19 : term] : (~ (((X13 @ X19)) = $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X19 @ id)))))) | ($true = ((X13 @ (lam @ X11)))) | ~ ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : subst,X24 : subst,X25 : subst,X26 : term] : ((((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23)) = $true) | ~ ($true = ((X21 @ X25 @ X26 @ (comp @ X24 @ X23))))) | ~ ! [X27 : (subst > term > term)] : (~ ! [X28 : term] : (~ ($true = ((X21 @ id @ X28 @ id))) | (((X21 @ id @ (X27 @ id @ X28) @ id)) = $true)) | ~ ! [X30 : subst,X29 : term,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) | (((X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) = $true)) | ~ ! [X32 : term] : (($true = ((X21 @ id @ X32 @ id))) | ~ (((var @ (sub @ X32 @ id))) = $true)) | ($true = ((X21 @ id @ X22 @ id))) | ~ ! [X33 : term,X34 : term] : (~ ($true = ((X21 @ id @ X33 @ id))) | (((X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id)) = $true) | ~ (((X21 @ id @ X34 @ id)) = $true)) | ~ ! [X35 : subst,X36 : subst,X37 : subst,X38 : term] : ((((X21 @ X35 @ X38 @ (comp @ X37 @ X36))) = $true) | ~ ($true = ((X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X39 : (subst > term > subst > $o)] : ~ ! [X40 : (term > $o)] : ~ ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41)))) & ((hoaslaminj = $true) <=> ! [X43 : subst,X45 : term,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | (((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | ~ ! [X50 : subst,X51 : term,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) = ((sub @ (X42 @ X49 @ X51) @ X50))) | ~ ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) = ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) <=> (shinj = $true)) & ((axidr = $true) <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & (pushprop = $true) & ((hoaslaminj_lthm = $true) <=> (! [X56 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X56))) = X55) => (! [X58 : subst,X57 : term] : (((comp @ sh @ (push @ X57 @ X58))) = X58) => (! [X60 : term,X59 : term] : ((X59 = X60) | (((lam @ X59)) != ((lam @ X60)))) => ! [X63 : term,X62 : (subst > term > term),X61 : subst,X64 : (subst > term > term)] : (~ ! [X67 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) = ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | ~ ! [X68 : subst,X70 : subst,X69 : term] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) = ((sub @ (X64 @ X68 @ X69) @ X70))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63)))))))) & (hoasapinj2_gthm = $true) & ((axidl = $true) <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & (! [X72 : (term > $o),X73 : term] : (~ ! [X74 : term,X75 : term] : (~ ($true = ((X72 @ X74))) | ($true = ((X72 @ (ap @ X75 @ X74)))) | ~ (((X72 @ X75)) = $true)) | (((X72 @ X73)) = $true) | ~ ! [X76 : term] : (($true = ((X72 @ X76))) | ~ ($true = ((var @ X76)))) | ~ ! [X77 : term] : ((((X72 @ (lam @ X77))) = $true) | ~ ! [X78 : term] : ((((X72 @ (sub @ X77 @ (push @ X78 @ id)))) = $true) | ~ (((X72 @ X78)) = $true)))) <=> (induction2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X81 : subst,X80 : term,X79 : (term > $o)] : ~ ! [X82 : (term > $o)] : ~ ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81)))))) & ! [X84 : d_term] : (d_one = X84) & ((hoasinduction_lem3v2_f = $true) <=> ! [X85 : term] : ~ ! [X86 : (subst > term > term)] : ~ ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88))))) & (substmonoid_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (axvarshift = $true) & ~ (lamnotap = $true) & (hoaslaminj_gthm = $true) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X89 : term] : ~ ! [X90 : (subst > term > term)] : ~ ! [X92 : subst,X91 : term] : (((sub @ X89 @ (push @ X91 @ X92))) = ((X90 @ X92 @ X91))) => (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term,X95 : (term > $o),X96 : (subst > term > subst > $o)] : (~ ! [X97 : term] : (((X95 @ X97)) = ((X96 @ id @ X97 @ id))) | (((X95 @ (lam @ X94))) = $true) | ~ ! [X98 : term] : (~ ($true = ((X95 @ X98))) | ($true = ((X95 @ (sub @ X94 @ (push @ X98 @ id)))))) | ~ ! [X99 : (subst > term > term)] : (~ ! [X100 : subst,X102 : subst,X101 : term] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) | (((X96 @ id @ (lam @ (X99 @ sh @ one)) @ id)) = $true) | ~ ! [X103 : term] : ((((X96 @ id @ (X99 @ id @ X103) @ id)) = $true) | ~ ($true = ((X96 @ id @ X103 @ id))))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X104 : term] : (((sub @ X104 @ id)) = X104) => ! [X105 : (subst > term > subst > $o),X106 : term,X107 : (term > $o)] : (~ ! [X108 : subst,X109 : subst,X110 : term,X111 : subst] : (~ ($true = ((X105 @ X111 @ X110 @ (comp @ X108 @ X109)))) | ($true = ((X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)))) | ~ ! [X112 : term] : (~ ($true = ((X107 @ X112))) | ($true = ((X107 @ (sub @ X106 @ (push @ X112 @ id)))))) | ~ ! [X113 : subst,X114 : term,X115 : subst,X116 : subst] : (~ ($true = ((X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116))) | (((X105 @ X113 @ X114 @ (comp @ X115 @ X116))) = $true)) | ~ ! [X117 : (subst > term > term)] : (~ ! [X118 : term] : ((((X105 @ id @ (X117 @ id @ X118) @ id)) = $true) | ~ (((X105 @ id @ X118 @ id)) = $true)) | ~ ! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) | (((X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) = $true)) | ($true = ((X107 @ (lam @ X106)))) | ~ ! [X122 : term] : (((X107 @ X122)) = ((X105 @ id @ X122 @ id)))))) & (hoasapnotvar = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X125 : term,X126 : term,X124 : term,X123 : term] : ((((ap @ X124 @ X125)) != ((ap @ X123 @ X126))) | (X125 = X126)) => ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) <=> (hoasapinj2_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X131 : (term > $o),X132 : term,X133 : subst,X134 : (term > $o)] : ((((X131 @ one)) = $true) | ~ (((X134 @ X132)) = $true) | ~ ! [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) = ((X131 @ X135))))) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : ~ ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (lamnotvar = $true) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ~ ! [X145 : (term > $o)] : ~ ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) <=> (pushprop_lem0_lthm = $true)) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) <=> (axshiftcons = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X149 : (subst > term > subst > $o),X150 : (term > $o),X151 : term] : (~ ! [X152 : (subst > term > term)] : (~ ! [X153 : term] : ((((X149 @ id @ (X152 @ id @ X153) @ id)) = $true) | ~ (((X149 @ id @ X153 @ id)) = $true)) | ($true = ((X149 @ id @ (lam @ (X152 @ sh @ one)) @ id))) | ~ ! [X154 : subst,X156 : term,X155 : subst] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155)))) | ~ ! [X157 : term] : (~ ($true = ((X150 @ X157))) | (((X150 @ (sub @ X151 @ (push @ X157 @ id)))) = $true)) | ($true = ((X150 @ (lam @ X151)))) | ~ ! [X158 : term] : (((X149 @ id @ X158 @ id)) = ((X150 @ X158))) | ~ ! [X159 : term,X160 : subst,X161 : subst,X162 : subst] : (($true = ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)))) | ~ (((X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) = $true)) | ~ ! [X163 : term,X164 : subst,X165 : subst,X166 : subst] : (~ (((X149 @ X166 @ X163 @ (comp @ X164 @ X165))) = $true) | ($true = ((X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165)))))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X167 : term,X168 : (term > $o),X169 : term,X170 : (subst > term > subst > $o)] : (~ ! [X171 : term,X172 : term] : (~ ($true = ((X170 @ id @ X171 @ id))) | (((X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id)) = $true) | ~ (((X170 @ id @ X172 @ id)) = $true)) | ~ ! [X173 : term,X174 : subst,X175 : subst,X176 : subst] : (~ ($true = ((X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174))) | (((X170 @ X175 @ X173 @ (comp @ X176 @ X174))) = $true)) | ~ ! [X177 : term] : (((X170 @ id @ X177 @ id)) = ((X168 @ X177))) | (((X168 @ (ap @ X167 @ X169))) = $true) | ~ (((X168 @ X169)) = $true) | ~ ! [X178 : subst,X179 : subst,X180 : subst,X181 : term] : (($true = ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179))) | ~ ($true = ((X170 @ X180 @ X181 @ (comp @ X178 @ X179))))) | ~ ($true = ((X168 @ X167))))) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) = ((d2subst @ X183))) => (X182 = X183)) & ~ (ulamvar1 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3b_gthm = $true) & (axabs = $true) & (pushprop_lthm = $true) & (axapp = $true) & ((apinj1 = $true) <=> ! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186))) & ((hoasinduction_lem3b = $true) <=> ! [X188 : term] : ~ ! [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) != ((X189 @ sh @ one)))) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem3a = $true) <=> ! [X190 : term,X191 : (subst > term > subst > $o)] : (($true = ((X191 @ id @ (lam @ X190) @ id))) | ~ ! [X192 : (subst > term > term)] : (~ ! [X194 : subst,X195 : term,X193 : subst] : (((X192 @ (comp @ X194 @ X193) @ (sub @ X195 @ X193))) = ((sub @ (X192 @ X194 @ X195) @ X193))) | ($true = ((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id))) | ~ ! [X196 : term] : ((((X191 @ id @ (X192 @ id @ X196) @ id)) = $true) | ~ (((X191 @ id @ X196 @ id)) = $true))) | ~ ! [X197 : term] : ((((X191 @ id @ (sub @ X190 @ (push @ X197 @ id)) @ id)) = $true) | ~ (((X191 @ id @ X197 @ id)) = $true)))) & (induction2lem_gthm = $true) & (axassoc = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X198 : (subst > term > subst > $o)] : ~ ! [X199 : (term > $o)] : ~ ! [X200 : term] : (((X198 @ id @ X200 @ id)) = ((X199 @ X200))) => (! [X201 : (term > $o),X202 : term] : ((((X201 @ X202)) = $true) | ~ ! [X203 : term] : ((((X201 @ X203)) = $true) | ~ ($true = ((var @ X203)))) | ~ ! [X204 : term,X205 : term] : (~ ($true = ((X201 @ X204))) | ~ (((X201 @ X205)) = $true) | ($true = ((X201 @ (ap @ X204 @ X205))))) | ~ ! [X206 : term] : (~ ! [X207 : term] : (~ (((X201 @ X207)) = $true) | ($true = ((X201 @ (sub @ X206 @ (push @ X207 @ id)))))) | ($true = ((X201 @ (lam @ X206)))))) => (! [X208 : term] : (((sub @ X208 @ id)) = X208) => (! [X209 : term,X210 : (subst > term > subst > $o),X211 : (term > $o)] : (~ ! [X212 : (subst > term > term)] : (~ ! [X214 : subst,X215 : subst,X213 : term] : (((sub @ (X212 @ X214 @ X213) @ X215)) = ((X212 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)))) | ~ ! [X216 : term] : (~ ($true = ((X210 @ id @ X216 @ id))) | (((X210 @ id @ (X212 @ id @ X216) @ id)) = $true)) | (((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id)) = $true)) | ~ ! [X217 : term] : (((X210 @ id @ X217 @ id)) = ((X211 @ X217))) | ($true = ((X211 @ (lam @ X209)))) | ~ ! [X218 : term] : (~ (((X211 @ X218)) = $true) | ($true = ((X211 @ (sub @ X209 @ (push @ X218 @ id))))))) => ! [X219 : (subst > term > subst > $o),X220 : term] : (~ ! [X221 : (subst > term > term)] : (~ ! [X222 : subst,X223 : term,X224 : subst] : (((sub @ (X221 @ X224 @ X223) @ X222)) = ((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222)))) | ~ ! [X225 : term] : (~ ($true = ((X219 @ id @ X225 @ id))) | (((X219 @ id @ (X221 @ id @ X225) @ id)) = $true)) | ($true = ((X219 @ id @ (lam @ (X221 @ sh @ one)) @ id)))) | ($true = ((X219 @ id @ X220 @ id))) | ~ ! [X226 : term,X227 : term] : (~ (((X219 @ id @ X227 @ id)) = $true) | ~ ($true = ((X219 @ id @ X226 @ id))) | (((X219 @ id @ (ap @ (sub @ X227 @ id) @ X226) @ id)) = $true)))))))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X228 : term,X229 : (subst > term > subst > $o)] : (~ ! [X230 : (subst > term > term)] : (~ ! [X232 : subst,X233 : subst,X231 : term] : (((sub @ (X230 @ X233 @ X231) @ X232)) = ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) | ~ ! [X234 : term] : (~ ($true = ((X229 @ id @ X234 @ id))) | (((X229 @ id @ (X230 @ id @ X234) @ id)) = $true)) | (((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id)) = $true)) | ~ ! [X235 : subst,X236 : subst,X237 : subst,X238 : term] : ((((X229 @ X236 @ X238 @ (comp @ X237 @ X235))) = $true) | ~ ($true = ((X229 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237) @ X235)))) | ~ ! [X239 : subst,X240 : subst,X241 : term,X242 : subst] : ((((X229 @ (comp @ X239 @ X242) @ (sub @ X241 @ X242) @ X240)) = $true) | ~ (((X229 @ X239 @ X241 @ (comp @ X242 @ X240))) = $true)) | ($true = ((X229 @ id @ (lam @ X228) @ id))) | ~ ! [X243 : term] : ((((X229 @ id @ (sub @ X228 @ (push @ X243 @ id)) @ id)) = $true) | ~ (((X229 @ id @ X243 @ id)) = $true)))) & ((! [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) = X245) => (! [X247 : term,X246 : subst] : (((comp @ sh @ (push @ X247 @ X246))) = X246) => ! [X248 : (term > $o),X249 : subst,X250 : term,X251 : term,X252 : (term > $o)] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | ~ (((X252 @ X251)) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X253 : (term > $o),X254 : (term > $o),X255 : term,X256 : subst,X257 : term] : (~ (((X254 @ X255)) = $true) | (((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true))) & ((hoasinduction_lem2 = $true) <=> ! [X258 : term,X259 : term,X260 : (subst > term > subst > $o)] : (($true = ((X260 @ id @ (ap @ X258 @ X259) @ id))) | ~ ! [X261 : subst,X262 : subst,X263 : term,X264 : subst] : ((((X260 @ X264 @ X263 @ (comp @ X262 @ X261))) = $true) | ~ ($true = ((X260 @ (comp @ X264 @ X262) @ (sub @ X263 @ X262) @ X261)))) | ~ (((X260 @ id @ X258 @ id)) = $true) | ~ ! [X265 : term,X266 : term] : (~ ($true = ((X260 @ id @ X265 @ id))) | ~ ($true = ((X260 @ id @ X266 @ id))) | ($true = ((X260 @ id @ (ap @ (sub @ X265 @ id) @ X266) @ id)))) | ~ ($true = ((X260 @ id @ X259 @ id))) | ~ ! [X267 : subst,X268 : subst,X269 : subst,X270 : term] : (($true = ((X260 @ (comp @ X269 @ X268) @ (sub @ X270 @ X268) @ X267))) | ~ ($true = ((X260 @ X269 @ X270 @ (comp @ X268 @ X267))))))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X272 : term,X271 : subst] : (((sub @ one @ (push @ X272 @ X271))) = X272) => (! [X273 : subst,X274 : term] : (((comp @ sh @ (push @ X274 @ X273))) = X273) => (! [X275 : subst] : (((comp @ X275 @ id)) = X275) => (! [X276 : term,X277 : (term > $o)] : (~ ! [X278 : term,X279 : term] : (($true = ((X277 @ (ap @ X278 @ X279)))) | ~ (((X277 @ X279)) = $true) | ~ (((X277 @ X278)) = $true)) | ($true = ((X277 @ X276))) | ~ ! [X280 : term] : (~ ($true = ((var @ X280))) | ($true = ((X277 @ X280)))) | ~ ! [X281 : term] : (($true = ((X277 @ (lam @ X281)))) | ~ (((X277 @ X281)) = $true))) => ! [X282 : subst,X283 : term,X284 : (term > $o)] : ((((X284 @ (sub @ X283 @ X282))) = $true) | ~ ! [X285 : term,X286 : term] : (~ (((X284 @ X285)) = $true) | ($true = ((X284 @ (ap @ X285 @ X286)))) | ~ ($true = ((X284 @ X286)))) | ~ ! [X287 : term] : (~ ($true = ((var @ X287))) | (((X284 @ (sub @ X287 @ X282))) = $true)) | ~ ! [X288 : term] : (~ ! [X289 : term] : (~ ($true = ((X284 @ X289))) | ($true = ((X284 @ (sub @ X288 @ (push @ X289 @ id)))))) | ($true = ((X284 @ (lam @ X288))))))))))) & (! [X290 : term,X291 : (subst > term > subst > $o)] : (~ ! [X292 : (subst > term > term)] : (($true = ((X291 @ id @ (lam @ (X292 @ sh @ one)) @ id))) | ~ ! [X293 : term] : (~ (((X291 @ id @ X293 @ id)) = $true) | (((X291 @ id @ (X292 @ id @ X293) @ id)) = $true)) | ~ ! [X294 : subst,X295 : subst,X296 : term] : (((X292 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))) = ((sub @ (X292 @ X295 @ X296) @ X294)))) | ~ ! [X297 : term] : (($true = ((X291 @ id @ (sub @ X290 @ (push @ X297 @ id)) @ id))) | ~ (((X291 @ id @ X297 @ id)) = $true)) | ($true = ((X291 @ id @ (lam @ (sub @ X290 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X298 : term] : (((sub @ X298 @ id)) = X298) => (! [X299 : (subst > term > subst > $o),X300 : term] : (~ ! [X301 : term] : ((((X299 @ id @ (sub @ X300 @ (push @ X301 @ id)) @ id)) = $true) | ~ ($true = ((X299 @ id @ X301 @ id)))) | ~ ! [X302 : (subst > term > term)] : (~ ! [X303 : term] : ((((X299 @ id @ (X302 @ id @ X303) @ id)) = $true) | ~ ($true = ((X299 @ id @ X303 @ id)))) | (((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ~ ! [X306 : term,X305 : subst,X304 : subst] : (((X302 @ (comp @ X304 @ X305) @ (sub @ X306 @ X305))) = ((sub @ (X302 @ X304 @ X306) @ X305)))) | ($true = ((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id)))) => ! [X307 : (subst > term > subst > $o),X308 : term] : (~ ! [X309 : term] : (~ ($true = ((X307 @ id @ X309 @ id))) | ($true = ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id)))) | ($true = ((X307 @ id @ (lam @ X308) @ id))) | ~ ! [X310 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X310 @ sh @ one)) @ id)) = $true) | ~ ! [X312 : subst,X311 : subst,X313 : term] : (((X310 @ (comp @ X312 @ X311) @ (sub @ X313 @ X311))) = ((sub @ (X310 @ X312 @ X313) @ X311))) | ~ ! [X314 : term] : (~ ($true = ((X307 @ id @ X314 @ id))) | ($true = ((X307 @ id @ (X310 @ id @ X314) @ id))))) | ~ ! [X315 : subst,X316 : term,X317 : subst,X318 : subst] : (($true = ((X307 @ X315 @ X316 @ (comp @ X318 @ X317)))) | ~ ($true = ((X307 @ (comp @ X315 @ X318) @ (sub @ X316 @ X318) @ X317)))) | ~ ! [X319 : term,X320 : subst,X321 : subst,X322 : subst] : ((((X307 @ (comp @ X322 @ X321) @ (sub @ X319 @ X321) @ X320)) = $true) | ~ ($true = ((X307 @ X322 @ X319 @ (comp @ X321 @ X320))))))))) & (hoasinduction_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X323 : (subst > term > subst > $o),X324 : term] : (~ ! [X325 : (subst > term > term)] : (~ ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327)))) | ~ ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ~ ($true = ((X323 @ id @ X329 @ id)))) | ($true = ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id)))) | (((X323 @ id @ X324 @ id)) = $true) | ~ ! [X330 : term,X331 : term] : (($true = ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) | ~ (((X323 @ id @ X331 @ id)) = $true) | ~ ($true = ((X323 @ id @ X330 @ id)))))) & (pushprop_lem3v2_lthm = $true) & ((induction = $true) <=> ! [X332 : (term > $o),X333 : term] : (~ ! [X334 : term] : ((((X332 @ X334)) = $true) | ~ (((var @ X334)) = $true)) | ~ ! [X335 : term,X336 : term] : (~ ($true = ((X332 @ X335))) | ($true = ((X332 @ (ap @ X335 @ X336)))) | ~ (((X332 @ X336)) = $true)) | (((X332 @ X333)) = $true) | ~ ! [X337 : term] : (($true = ((X332 @ (lam @ X337)))) | ~ (((X332 @ X337)) = $true)))) & ((! [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) = X338) => ! [X340 : subst,X341 : term,X342 : (term > $o),X343 : (term > $o)] : (~ (((X342 @ X341)) = $true) | (((X343 @ one)) = $true) | ~ ! [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) = ((X343 @ X344))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) <=> (axscons = $true)) & (axclos = $true) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X348 : term] : (((sub @ X348 @ id)) = X348) => (! [X349 : term,X350 : (subst > term > subst > $o)] : (~ ! [X351 : term] : ((((X350 @ id @ (sub @ X349 @ (push @ X351 @ id)) @ id)) = $true) | ~ (((X350 @ id @ X351 @ id)) = $true)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : term] : (~ (((X350 @ id @ X353 @ id)) = $true) | (((X350 @ id @ (X352 @ id @ X353) @ id)) = $true)) | ~ ! [X355 : subst,X354 : term,X356 : subst] : (((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X356 @ X354) @ X355))) | ($true = ((X350 @ id @ (lam @ (X352 @ sh @ one)) @ id)))) | ($true = ((X350 @ id @ (lam @ (sub @ X349 @ (push @ one @ sh))) @ id)))) => ! [X357 : term,X358 : (subst > term > subst > $o)] : (~ ! [X359 : term] : (~ ($true = ((X358 @ id @ X359 @ id))) | (((X358 @ id @ (sub @ X357 @ (push @ X359 @ id)) @ id)) = $true)) | ~ ! [X360 : (subst > term > term)] : (~ ! [X363 : subst,X361 : term,X362 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) | ~ ! [X364 : term] : (($true = ((X358 @ id @ (X360 @ id @ X364) @ id))) | ~ ($true = ((X358 @ id @ X364 @ id)))) | (((X358 @ id @ (lam @ (X360 @ sh @ one)) @ id)) = $true)) | (((X358 @ id @ (lam @ X357) @ id)) = $true))))) & ((hoasapinj1 = $true) <=> ! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367))) & (! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) <=> (hoasapinj2 = $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X373 : subst] : (((comp @ id @ X373)) = X373) => (! [X374 : subst] : (((comp @ X374 @ id)) = X374) => (! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376))))) & ((! [X377 : term] : (((sub @ X377 @ id)) = X377) => ! [X378 : term] : (((sub @ X378 @ id)) = X378)) <=> (termmset_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_lthm = $true) & (axmap = $true) & (pushprop_lem2v2 = $true) & (! [X379 : term,X380 : term,X381 : (subst > term > term)] : ((((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one)))) | ~ ! [X383 : subst,X382 : term,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) = ((sub @ (X381 @ X383 @ X382) @ X384)))) <=> (hoaslamnotap = $true)) & (ulamvarsh = $true) & (! [X385 : (subst > term > subst > $o)] : ~ ! [X386 : (term > $o)] : ~ ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) <=> (hoasinduction_lem0 = $true)) & ((axvarid = $true) <=> ! [X388 : term] : (((sub @ X388 @ id)) = X388)) & ((hoasapinj1_lthm = $true) <=> (! [X389 : term] : (((sub @ X389 @ id)) = X389) => (! [X391 : term,X392 : term,X390 : term,X393 : term] : ((X390 = X392) | (((ap @ X390 @ X391)) != ((ap @ X392 @ X393)))) => ! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396))))) & ((apinj2 = $true) <=> ! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399))) & (apnotvar = $true) & (((d2subst @ d_id)) = id) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X402 : subst,X403 : term,X404 : (term > $o)] : (~ ! [X405 : term] : (~ ! [X406 : term] : (($true = ((X404 @ (sub @ X405 @ (push @ X406 @ id))))) | ~ ($true = ((X404 @ X406)))) | (((X404 @ (lam @ X405))) = $true)) | ~ ! [X407 : term,X408 : term] : (~ (((X404 @ X407)) = $true) | ($true = ((X404 @ (ap @ X407 @ X408)))) | ~ (((X404 @ X408)) = $true)) | ($true = ((X404 @ (sub @ X403 @ X402)))) | ~ ! [X409 : term] : (~ ($true = ((var @ X409))) | (((X404 @ (sub @ X409 @ X402))) = $true))) <=> (induction2lem = $true)) & (ulamvarind = $true) & (pushprop_lem0_gthm = $true) & (! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) <=> (laminj = $true)) & ((induction2_lthm = $true) <=> (! [X412 : term] : (((sub @ X412 @ id)) = X412) => (! [X413 : (term > $o),X414 : term,X415 : subst] : (~ ! [X416 : term,X417 : term] : (~ ($true = ((X413 @ X416))) | ~ ($true = ((X413 @ X417))) | ($true = ((X413 @ (ap @ X416 @ X417))))) | (((X413 @ (sub @ X414 @ X415))) = $true) | ~ ! [X418 : term] : (($true = ((X413 @ (lam @ X418)))) | ~ ! [X419 : term] : ((((X413 @ (sub @ X418 @ (push @ X419 @ id)))) = $true) | ~ (((X413 @ X419)) = $true))) | ~ ! [X420 : term] : (~ (((var @ X420)) = $true) | ($true = ((X413 @ (sub @ X420 @ X415)))))) => ! [X421 : term,X422 : (term > $o)] : (($true = ((X422 @ X421))) | ~ ! [X423 : term] : (~ ($true = ((var @ X423))) | ($true = ((X422 @ X423)))) | ~ ! [X424 : term] : (($true = ((X422 @ (lam @ X424)))) | ~ ! [X425 : term] : ((((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true) | ~ (((X422 @ X425)) = $true))) | ~ ! [X426 : term,X427 : term] : (~ (((X422 @ X427)) = $true) | ~ ($true = ((X422 @ X426))) | (((X422 @ (ap @ X426 @ X427))) = $true)))))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X428 : (subst > term > subst > $o),X429 : term] : (~ ! [X430 : (subst > term > term)] : (~ ! [X431 : term] : (($true = ((X428 @ id @ (X430 @ id @ X431) @ id))) | ~ (((X428 @ id @ X431 @ id)) = $true)) | ~ ! [X432 : subst,X433 : term,X434 : subst] : (((X430 @ (comp @ X434 @ X432) @ (sub @ X433 @ X432))) = ((sub @ (X430 @ X434 @ X433) @ X432))) | (((X428 @ id @ (lam @ (X430 @ sh @ one)) @ id)) = $true)) | ~ ! [X435 : term] : (($true = ((X428 @ id @ (sub @ X429 @ (push @ X435 @ id)) @ id))) | ~ (((X428 @ id @ X435 @ id)) = $true)) | ($true = ((X428 @ id @ (lam @ (sub @ X429 @ (push @ one @ sh))) @ id))))) & ! [X436 : d_subst] : (d_id = X436) & ((hoasinduction_lthm = $true) <=> (! [X437 : (term > $o),X438 : term] : ((((X437 @ X438)) = $true) | ~ ! [X439 : term,X440 : term] : (($true = ((X437 @ (ap @ X440 @ X439)))) | ~ ($true = ((X437 @ X439))) | ~ (((X437 @ X440)) = $true)) | ~ ! [X441 : term] : (($true = ((X437 @ (lam @ X441)))) | ~ ! [X442 : term] : (~ ($true = ((X437 @ X442))) | (((X437 @ (sub @ X441 @ (push @ X442 @ id)))) = $true))) | ~ ! [X443 : term] : (~ (((var @ X443)) = $true) | (((X437 @ X443)) = $true))) => (! [X444 : term,X445 : term,X446 : (subst > term > subst > $o)] : (($true = ((X446 @ id @ (ap @ X445 @ X444) @ id))) | ~ ! [X447 : subst,X448 : subst,X449 : term,X450 : subst] : (~ (((X446 @ X447 @ X449 @ (comp @ X450 @ X448))) = $true) | (((X446 @ (comp @ X447 @ X450) @ (sub @ X449 @ X450) @ X448)) = $true)) | ~ ! [X451 : subst,X452 : subst,X453 : term,X454 : subst] : (~ (((X446 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451) @ X454)) = $true) | (((X446 @ X452 @ X453 @ (comp @ X451 @ X454))) = $true)) | ~ ($true = ((X446 @ id @ X444 @ id))) | ~ (((X446 @ id @ X445 @ id)) = $true) | ~ ! [X455 : term,X456 : term] : (~ ($true = ((X446 @ id @ X456 @ id))) | (((X446 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id)) = $true) | ~ (((X446 @ id @ X455 @ id)) = $true))) => (! [X457 : (subst > term > subst > $o),X458 : term] : (~ ! [X459 : (subst > term > term)] : (~ ! [X460 : term] : ((((X457 @ id @ (X459 @ id @ X460) @ id)) = $true) | ~ (((X457 @ id @ X460 @ id)) = $true)) | ~ ! [X463 : subst,X462 : subst,X461 : term] : (((X459 @ (comp @ X463 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X459 @ X463 @ X461) @ X462))) | (((X457 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true)) | (((X457 @ id @ (lam @ X458) @ id)) = $true) | ~ ! [X464 : term] : (~ (((X457 @ id @ X464 @ id)) = $true) | ($true = ((X457 @ id @ (sub @ X458 @ (push @ X464 @ id)) @ id)))) | ~ ! [X465 : subst,X466 : term,X467 : subst,X468 : subst] : ((((X457 @ (comp @ X465 @ X468) @ (sub @ X466 @ X468) @ X467)) = $true) | ~ (((X457 @ X465 @ X466 @ (comp @ X468 @ X467))) = $true)) | ~ ! [X469 : term,X470 : subst,X471 : subst,X472 : subst] : (~ (((X457 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471) @ X472)) = $true) | (((X457 @ X470 @ X469 @ (comp @ X471 @ X472))) = $true))) => ! [X473 : (subst > term > subst > $o),X474 : term] : (~ ! [X475 : term] : ((((X473 @ id @ X475 @ id)) = $true) | ~ ($true = ((var @ (sub @ X475 @ id))))) | ~ ! [X476 : subst,X477 : subst,X478 : subst,X479 : term] : ((((X473 @ X478 @ X479 @ (comp @ X477 @ X476))) = $true) | ~ ($true = ((X473 @ (comp @ X478 @ X477) @ (sub @ X479 @ X477) @ X476)))) | ~ ! [X480 : (subst > term > term)] : (($true = ((X473 @ id @ (lam @ (X480 @ sh @ one)) @ id))) | ~ ! [X481 : term] : (~ ($true = ((X473 @ id @ X481 @ id))) | (((X473 @ id @ (X480 @ id @ X481) @ id)) = $true)) | ~ ! [X484 : subst,X482 : term,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ~ ! [X485 : subst,X486 : term,X487 : subst,X488 : subst] : (~ (((X473 @ X488 @ X486 @ (comp @ X487 @ X485))) = $true) | ($true = ((X473 @ (comp @ X488 @ X487) @ (sub @ X486 @ X487) @ X485)))) | ~ ! [X489 : term,X490 : term] : (~ (((X473 @ id @ X490 @ id)) = $true) | (((X473 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id)) = $true) | ~ (((X473 @ id @ X489 @ id)) = $true)) | ($true = ((X473 @ id @ X474 @ id)))))))) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2 = $true) & (! [X491 : (term > $o),X492 : (subst > term > subst > $o),X493 : term] : (~ ! [X494 : term] : ((((X491 @ (sub @ X493 @ (push @ X494 @ id)))) = $true) | ~ (((X491 @ X494)) = $true)) | ($true = ((X491 @ (lam @ X493)))) | ~ ! [X495 : term] : (((X491 @ X495)) = ((X492 @ id @ X495 @ id))) | ~ ! [X496 : (subst > term > term)] : (~ ! [X497 : term] : (~ (((X492 @ id @ X497 @ id)) = $true) | (((X492 @ id @ (X496 @ id @ X497) @ id)) = $true)) | ($true = ((X492 @ id @ (lam @ (X496 @ sh @ one)) @ id))) | ~ ! [X500 : term,X498 : subst,X499 : subst] : (((sub @ (X496 @ X499 @ X500) @ X498)) = ((X496 @ (comp @ X499 @ X498) @ (sub @ X500 @ X498)))))) <=> (hoasinduction_lem3v2a = $true)) & ((axvarcons = $true) <=> ! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501)) & ((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) <=> (substmonoid = $true)) & (termmset_gthm = $true) & (! [X505 : term] : (((sub @ X505 @ id)) = X505) <=> (termmset = $true)) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) = ((d2term @ X507))) => (X506 = X507)) & (induction2_gthm = $true) & (pushprop_lem1_gthm = $true) & (one = ((d2term @ d_one))) & (hoasinduction_lem1 = $true) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction = $true) <=> ! [X508 : term,X509 : (subst > term > subst > $o)] : (~ ! [X510 : term] : (~ (((var @ (sub @ X510 @ id))) = $true) | (((X509 @ id @ X510 @ id)) = $true)) | ~ ! [X511 : term,X512 : term] : (~ ($true = ((X509 @ id @ X511 @ id))) | ~ (((X509 @ id @ X512 @ id)) = $true) | ($true = ((X509 @ id @ (ap @ (sub @ X512 @ id) @ X511) @ id)))) | ($true = ((X509 @ id @ X508 @ id))) | ~ ! [X513 : term,X514 : subst,X515 : subst,X516 : subst] : (($true = ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) | ~ ($true = ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) | ~ ! [X517 : (subst > term > term)] : (~ ! [X518 : term] : (($true = ((X509 @ id @ (X517 @ id @ X518) @ id))) | ~ (((X509 @ id @ X518 @ id)) = $true)) | ~ ! [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) = ((sub @ (X517 @ X520 @ X521) @ X519))) | ($true = ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id)))) | ~ ! [X522 : term,X523 : subst,X524 : subst,X525 : subst] : (($true = ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524))) | ~ (((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) = $true)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X526 : term] : ~ ! [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) != ((X527 @ sh @ one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X528 : term,X529 : (subst > term > subst > $o)] : ((((X529 @ id @ (lam @ (sub @ X528 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X530 : (subst > term > term),X531 : term] : (~ ! [X532 : term] : (~ (((X529 @ id @ X532 @ id)) = $true) | (((X529 @ id @ (X530 @ id @ X532) @ id)) = $true)) | ~ ! [X535 : term,X534 : subst,X533 : subst] : (((sub @ (sub @ X531 @ (push @ X535 @ X533)) @ X534)) = ((sub @ (X530 @ X533 @ X535) @ X534))) | ~ ! [X538 : subst,X537 : term,X536 : subst] : (((sub @ X531 @ (push @ (sub @ X537 @ X538) @ (comp @ X536 @ X538)))) = ((X530 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538)))) | ($true = ((X529 @ id @ (lam @ (X530 @ sh @ one)) @ id)))) | ~ ! [X539 : term] : ((((X529 @ id @ (sub @ X528 @ (push @ X539 @ id)) @ id)) = $true) | ~ (((X529 @ id @ X539 @ id)) = $true))))),
% 164.61/23.50 inference(rectify,[],[f7])).
% 164.61/23.50 thf(f10,plain,(
% 164.61/23.50 (ulamvarind = $true) & (lamnotap != $true) & ((! [X438 : term,X437 : (term > $o)] : (~ ! [X443 : term] : ((((var @ X443)) != $true) | (((X437 @ X443)) = $true)) | ~ ! [X441 : term] : (~ ! [X442 : term] : ((((X437 @ (sub @ X441 @ (push @ X442 @ id)))) = $true) | ($true != ((X437 @ X442)))) | ($true = ((X437 @ (lam @ X441))))) | ~ ! [X439 : term,X440 : term] : (($true = ((X437 @ (ap @ X440 @ X439)))) | (((X437 @ X440)) != $true) | ($true != ((X437 @ X439)))) | (((X437 @ X438)) = $true)) => (! [X445 : term,X446 : (subst > term > subst > $o),X444 : term] : (($true != ((X446 @ id @ X444 @ id))) | ~ ! [X454 : subst,X453 : term,X452 : subst,X451 : subst] : ((((X446 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451) @ X454)) != $true) | (((X446 @ X452 @ X453 @ (comp @ X451 @ X454))) = $true)) | ~ ! [X448 : subst,X447 : subst,X450 : subst,X449 : term] : ((((X446 @ X447 @ X449 @ (comp @ X450 @ X448))) != $true) | (((X446 @ (comp @ X447 @ X450) @ (sub @ X449 @ X450) @ X448)) = $true)) | ~ ! [X456 : term,X455 : term] : ((((X446 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id)) = $true) | (((X446 @ id @ X455 @ id)) != $true) | ($true != ((X446 @ id @ X456 @ id)))) | ($true = ((X446 @ id @ (ap @ X445 @ X444) @ id))) | (((X446 @ id @ X445 @ id)) != $true)) => (! [X457 : (subst > term > subst > $o),X458 : term] : (~ ! [X468 : subst,X465 : subst,X466 : term,X467 : subst] : ((((X457 @ (comp @ X465 @ X468) @ (sub @ X466 @ X468) @ X467)) = $true) | (((X457 @ X465 @ X466 @ (comp @ X468 @ X467))) != $true)) | ~ ! [X464 : term] : ((((X457 @ id @ X464 @ id)) != $true) | ($true = ((X457 @ id @ (sub @ X458 @ (push @ X464 @ id)) @ id)))) | ~ ! [X469 : term,X471 : subst,X470 : subst,X472 : subst] : ((((X457 @ X470 @ X469 @ (comp @ X471 @ X472))) = $true) | (((X457 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471) @ X472)) != $true)) | (((X457 @ id @ (lam @ X458) @ id)) = $true) | ~ ! [X459 : (subst > term > term)] : (~ ! [X463 : subst,X462 : subst,X461 : term] : (((X459 @ (comp @ X463 @ X462) @ (sub @ X461 @ X462))) = ((sub @ (X459 @ X463 @ X461) @ X462))) | ~ ! [X460 : term] : ((((X457 @ id @ X460 @ id)) != $true) | (((X457 @ id @ (X459 @ id @ X460) @ id)) = $true)) | (((X457 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true))) => ! [X474 : term,X473 : (subst > term > subst > $o)] : (~ ! [X486 : term,X485 : subst,X487 : subst,X488 : subst] : (($true = ((X473 @ (comp @ X488 @ X487) @ (sub @ X486 @ X487) @ X485))) | (((X473 @ X488 @ X486 @ (comp @ X487 @ X485))) != $true)) | ~ ! [X480 : (subst > term > term)] : (($true = ((X473 @ id @ (lam @ (X480 @ sh @ one)) @ id))) | ~ ! [X481 : term] : (($true != ((X473 @ id @ X481 @ id))) | (((X473 @ id @ (X480 @ id @ X481) @ id)) = $true)) | ~ ! [X484 : subst,X482 : term,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ~ ! [X475 : term] : (($true != ((var @ (sub @ X475 @ id)))) | (((X473 @ id @ X475 @ id)) = $true)) | ($true = ((X473 @ id @ X474 @ id))) | ~ ! [X476 : subst,X479 : term,X477 : subst,X478 : subst] : (($true != ((X473 @ (comp @ X478 @ X477) @ (sub @ X479 @ X477) @ X476))) | (((X473 @ X478 @ X479 @ (comp @ X477 @ X476))) = $true)) | ~ ! [X490 : term,X489 : term] : ((((X473 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id)) = $true) | (((X473 @ id @ X489 @ id)) != $true) | (((X473 @ id @ X490 @ id)) != $true)))))) <=> (hoasinduction_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotap_gthm = $true) & (! [X324 : term,X323 : (subst > term > subst > $o)] : ((((X323 @ id @ X324 @ id)) = $true) | ~ ! [X325 : (subst > term > term)] : (~ ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327)))) | ~ ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ($true != ((X323 @ id @ X329 @ id)))) | ($true = ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id)))) | ~ ! [X330 : term,X331 : term] : ((((X323 @ id @ X331 @ id)) != $true) | ($true = ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) | ($true != ((X323 @ id @ X330 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & ((axvarid = $true) <=> ! [X388 : term] : (((sub @ X388 @ id)) = X388)) & (hoasinduction_lem2_gthm = $true) & (apnotvar = $true) & (! [X404 : (term > $o),X402 : subst,X403 : term] : (~ ! [X409 : term] : (($true != ((var @ X409))) | (((X404 @ (sub @ X409 @ X402))) = $true)) | ($true = ((X404 @ (sub @ X403 @ X402)))) | ~ ! [X408 : term,X407 : term] : (($true = ((X404 @ (ap @ X407 @ X408)))) | (((X404 @ X408)) != $true) | (((X404 @ X407)) != $true)) | ~ ! [X405 : term] : (~ ! [X406 : term] : (($true != ((X404 @ X406))) | ($true = ((X404 @ (sub @ X405 @ (push @ X406 @ id)))))) | (((X404 @ (lam @ X405))) = $true))) <=> (induction2lem = $true)) & ((induction2lem_lthm = $true) <=> (! [X272 : term,X271 : subst] : (((sub @ one @ (push @ X272 @ X271))) = X272) => (! [X273 : subst,X274 : term] : (((comp @ sh @ (push @ X274 @ X273))) = X273) => (! [X275 : subst] : (((comp @ X275 @ id)) = X275) => (! [X277 : (term > $o),X276 : term] : (($true = ((X277 @ X276))) | ~ ! [X280 : term] : (($true != ((var @ X280))) | ($true = ((X277 @ X280)))) | ~ ! [X281 : term] : (($true = ((X277 @ (lam @ X281)))) | (((X277 @ X281)) != $true)) | ~ ! [X279 : term,X278 : term] : (($true = ((X277 @ (ap @ X278 @ X279)))) | (((X277 @ X279)) != $true) | (((X277 @ X278)) != $true))) => ! [X282 : subst,X284 : (term > $o),X283 : term] : (~ ! [X288 : term] : (($true = ((X284 @ (lam @ X288)))) | ~ ! [X289 : term] : (($true != ((X284 @ X289))) | ($true = ((X284 @ (sub @ X288 @ (push @ X289 @ id))))))) | ~ ! [X286 : term,X285 : term] : ((((X284 @ X285)) != $true) | ($true != ((X284 @ X286))) | ($true = ((X284 @ (ap @ X285 @ X286))))) | (((X284 @ (sub @ X283 @ X282))) = $true) | ~ ! [X287 : term] : ((((X284 @ (sub @ X287 @ X282))) = $true) | ($true != ((var @ X287)))))))))) & (pushprop_lem0_gthm = $true) & (one = ((d2term @ d_one))) & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X4 : term,X3 : (term > $o)] : (~ ! [X9 : term,X8 : term] : (($true = ((X3 @ (ap @ X9 @ X8)))) | ($true != ((X3 @ X9))) | (((X3 @ X8)) != $true)) | ($true = ((X3 @ X4))) | ~ ! [X6 : term] : ((((X3 @ (lam @ X6))) = $true) | ~ ! [X7 : term] : ((((X3 @ X7)) != $true) | (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) = $true))) | ~ ! [X5 : term] : ((((X3 @ X5)) = $true) | ($true != ((var @ X5))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X12 : (subst > term > subst > $o),X13 : (term > $o),X11 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X18 : term] : ((((X12 @ id @ X18 @ id)) != $true) | ($true = ((X12 @ id @ (X14 @ id @ X18) @ id)))) | ~ ! [X15 : subst,X17 : subst,X16 : term] : (((sub @ (X14 @ X15 @ X16) @ X17)) = ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17)))) | (((X12 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true)) | ($true = ((X13 @ (lam @ X11)))) | ~ ! [X19 : term] : ((((X13 @ X19)) != $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X19 @ id)))))) | ~ ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id)))) => ! [X22 : term,X21 : (subst > term > subst > $o)] : (~ ! [X27 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) = $true) | ~ ! [X30 : subst,X29 : term,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) | ~ ! [X28 : term] : ((((X21 @ id @ (X27 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id))))) | ~ ! [X35 : subst,X38 : term,X37 : subst,X36 : subst] : (($true != ((X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))) | (((X21 @ X35 @ X38 @ (comp @ X37 @ X36))) = $true)) | ~ ! [X34 : term,X33 : term] : ((((X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id)) = $true) | (((X21 @ id @ X34 @ id)) != $true) | ($true != ((X21 @ id @ X33 @ id)))) | ($true = ((X21 @ id @ X22 @ id))) | ~ ! [X23 : subst,X25 : subst,X24 : subst,X26 : term] : (($true != ((X21 @ X25 @ X26 @ (comp @ X24 @ X23)))) | (((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23)) = $true)) | ~ ! [X32 : term] : ((((var @ (sub @ X32 @ id))) != $true) | ($true = ((X21 @ id @ X32 @ id))))))))) <=> (hoasinduction_lthm_3 = $true)) & (axapp = $true) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = sh) & (induction2lem_gthm = $true) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X526 : term] : ~ ! [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) != ((X527 @ sh @ one)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X290 : term,X291 : (subst > term > subst > $o)] : (~ ! [X292 : (subst > term > term)] : (~ ! [X293 : term] : ((((X291 @ id @ X293 @ id)) != $true) | (((X291 @ id @ (X292 @ id @ X293) @ id)) = $true)) | ~ ! [X294 : subst,X295 : subst,X296 : term] : (((X292 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))) = ((sub @ (X292 @ X295 @ X296) @ X294))) | ($true = ((X291 @ id @ (lam @ (X292 @ sh @ one)) @ id)))) | ~ ! [X297 : term] : ((((X291 @ id @ X297 @ id)) != $true) | ($true = ((X291 @ id @ (sub @ X290 @ (push @ X297 @ id)) @ id)))) | ($true = ((X291 @ id @ (lam @ (sub @ X290 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & (ulamvar1 != $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X89 : term] : ~ ! [X90 : (subst > term > term)] : ~ ! [X92 : subst,X91 : term] : (((sub @ X89 @ (push @ X91 @ X92))) = ((X90 @ X92 @ X91))) => (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term,X96 : (subst > term > subst > $o),X95 : (term > $o)] : (~ ! [X98 : term] : (($true = ((X95 @ (sub @ X94 @ (push @ X98 @ id))))) | ($true != ((X95 @ X98)))) | ~ ! [X97 : term] : (((X95 @ X97)) = ((X96 @ id @ X97 @ id))) | (((X95 @ (lam @ X94))) = $true) | ~ ! [X99 : (subst > term > term)] : ((((X96 @ id @ (lam @ (X99 @ sh @ one)) @ id)) = $true) | ~ ! [X100 : subst,X102 : subst,X101 : term] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) | ~ ! [X103 : term] : (($true != ((X96 @ id @ X103 @ id))) | (((X96 @ id @ (X99 @ id @ X103) @ id)) = $true))))))) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & (hoasapnotvar_lthm = $true) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) = ((d2subst @ X183))) => (X182 = X183)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X198 : (subst > term > subst > $o)] : ~ ! [X199 : (term > $o)] : ~ ! [X200 : term] : (((X198 @ id @ X200 @ id)) = ((X199 @ X200))) => (! [X202 : term,X201 : (term > $o)] : (~ ! [X206 : term] : (($true = ((X201 @ (lam @ X206)))) | ~ ! [X207 : term] : (($true = ((X201 @ (sub @ X206 @ (push @ X207 @ id))))) | (((X201 @ X207)) != $true))) | ~ ! [X204 : term,X205 : term] : (($true != ((X201 @ X204))) | (((X201 @ X205)) != $true) | ($true = ((X201 @ (ap @ X204 @ X205))))) | (((X201 @ X202)) = $true) | ~ ! [X203 : term] : ((((X201 @ X203)) = $true) | ($true != ((var @ X203))))) => (! [X208 : term] : (((sub @ X208 @ id)) = X208) => (! [X210 : (subst > term > subst > $o),X211 : (term > $o),X209 : term] : (~ ! [X217 : term] : (((X210 @ id @ X217 @ id)) = ((X211 @ X217))) | ~ ! [X212 : (subst > term > term)] : ((((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id)) = $true) | ~ ! [X216 : term] : ((((X210 @ id @ (X212 @ id @ X216) @ id)) = $true) | ($true != ((X210 @ id @ X216 @ id)))) | ~ ! [X214 : subst,X215 : subst,X213 : term] : (((sub @ (X212 @ X214 @ X213) @ X215)) = ((X212 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215))))) | ($true = ((X211 @ (lam @ X209)))) | ~ ! [X218 : term] : ((((X211 @ X218)) != $true) | ($true = ((X211 @ (sub @ X209 @ (push @ X218 @ id))))))) => ! [X220 : term,X219 : (subst > term > subst > $o)] : (~ ! [X221 : (subst > term > term)] : (~ ! [X222 : subst,X223 : term,X224 : subst] : (((sub @ (X221 @ X224 @ X223) @ X222)) = ((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222)))) | ($true = ((X219 @ id @ (lam @ (X221 @ sh @ one)) @ id))) | ~ ! [X225 : term] : (($true != ((X219 @ id @ X225 @ id))) | (((X219 @ id @ (X221 @ id @ X225) @ id)) = $true))) | ~ ! [X226 : term,X227 : term] : ((((X219 @ id @ X227 @ id)) != $true) | (((X219 @ id @ (ap @ (sub @ X227 @ id) @ X226) @ id)) = $true) | ($true != ((X219 @ id @ X226 @ id)))) | ($true = ((X219 @ id @ X220 @ id))))))))) & (! [X150 : (term > $o),X149 : (subst > term > subst > $o),X151 : term] : (~ ! [X165 : subst,X164 : subst,X163 : term,X166 : subst] : ((((X149 @ X166 @ X163 @ (comp @ X164 @ X165))) != $true) | ($true = ((X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165)))) | ~ ! [X157 : term] : ((((X150 @ (sub @ X151 @ (push @ X157 @ id)))) = $true) | ($true != ((X150 @ X157)))) | ~ ! [X158 : term] : (((X149 @ id @ X158 @ id)) = ((X150 @ X158))) | ($true = ((X150 @ (lam @ X151)))) | ~ ! [X152 : (subst > term > term)] : (($true = ((X149 @ id @ (lam @ (X152 @ sh @ one)) @ id))) | ~ ! [X153 : term] : ((((X149 @ id @ X153 @ id)) != $true) | (((X149 @ id @ (X152 @ id @ X153) @ id)) = $true)) | ~ ! [X154 : subst,X156 : term,X155 : subst] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155)))) | ~ ! [X161 : subst,X162 : subst,X159 : term,X160 : subst] : (($true = ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)))) | (((X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X85 : term] : ~ ! [X86 : (subst > term > term)] : ~ ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88))))) & (pushprop_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem3v2 = $true) & (substmonoid_gthm = $true) & (! [X229 : (subst > term > subst > $o),X228 : term] : (~ ! [X243 : term] : ((((X229 @ id @ (sub @ X228 @ (push @ X243 @ id)) @ id)) = $true) | (((X229 @ id @ X243 @ id)) != $true)) | ($true = ((X229 @ id @ (lam @ X228) @ id))) | ~ ! [X241 : term,X242 : subst,X240 : subst,X239 : subst] : ((((X229 @ (comp @ X239 @ X242) @ (sub @ X241 @ X242) @ X240)) = $true) | (((X229 @ X239 @ X241 @ (comp @ X242 @ X240))) != $true)) | ~ ! [X230 : (subst > term > term)] : (~ ! [X234 : term] : ((((X229 @ id @ (X230 @ id @ X234) @ id)) = $true) | ($true != ((X229 @ id @ X234 @ id)))) | ~ ! [X232 : subst,X233 : subst,X231 : term] : (((sub @ (X230 @ X233 @ X231) @ X232)) = ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) | (((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id)) = $true)) | ~ ! [X236 : subst,X237 : subst,X238 : term,X235 : subst] : ((((X229 @ X236 @ X238 @ (comp @ X237 @ X235))) = $true) | ($true != ((X229 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237) @ X235))))) <=> (hoasinduction_lem3 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X133 : subst,X132 : term,X131 : (term > $o),X134 : (term > $o)] : ((((X131 @ one)) = $true) | ~ ! [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) = ((X131 @ X135))) | (((X134 @ X132)) != $true))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem3a_gthm = $true) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ~ ! [X145 : (term > $o)] : ~ ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X389 : term] : (((sub @ X389 @ id)) = X389) => (! [X391 : term,X392 : term,X390 : term,X393 : term] : ((X390 = X392) | (((ap @ X390 @ X391)) != ((ap @ X392 @ X393)))) => ! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396))))) & (! [X73 : term,X72 : (term > $o)] : (~ ! [X76 : term] : (($true != ((var @ X76))) | ($true = ((X72 @ X76)))) | (((X72 @ X73)) = $true) | ~ ! [X75 : term,X74 : term] : ((((X72 @ X75)) != $true) | ($true = ((X72 @ (ap @ X75 @ X74)))) | ($true != ((X72 @ X74)))) | ~ ! [X77 : term] : ((((X72 @ (lam @ X77))) = $true) | ~ ! [X78 : term] : ((((X72 @ X78)) != $true) | (((X72 @ (sub @ X77 @ (push @ X78 @ id)))) = $true)))) <=> (induction2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X348 : term] : (((sub @ X348 @ id)) = X348) => (! [X349 : term,X350 : (subst > term > subst > $o)] : (~ ! [X352 : (subst > term > term)] : (~ ! [X355 : subst,X354 : term,X356 : subst] : (((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355))) = ((sub @ (X352 @ X356 @ X354) @ X355))) | ($true = ((X350 @ id @ (lam @ (X352 @ sh @ one)) @ id))) | ~ ! [X353 : term] : ((((X350 @ id @ X353 @ id)) != $true) | (((X350 @ id @ (X352 @ id @ X353) @ id)) = $true))) | ($true = ((X350 @ id @ (lam @ (sub @ X349 @ (push @ one @ sh))) @ id))) | ~ ! [X351 : term] : ((((X350 @ id @ X351 @ id)) != $true) | (((X350 @ id @ (sub @ X349 @ (push @ X351 @ id)) @ id)) = $true))) => ! [X357 : term,X358 : (subst > term > subst > $o)] : ((((X358 @ id @ (lam @ X357) @ id)) = $true) | ~ ! [X359 : term] : (($true != ((X358 @ id @ X359 @ id))) | (((X358 @ id @ (sub @ X357 @ (push @ X359 @ id)) @ id)) = $true)) | ~ ! [X360 : (subst > term > term)] : (~ ! [X363 : subst,X361 : term,X362 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) | ~ ! [X364 : term] : (($true = ((X358 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X358 @ id @ X364 @ id)))) | (((X358 @ id @ (lam @ (X360 @ sh @ one)) @ id)) = $true)))))) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X528 : term,X529 : (subst > term > subst > $o)] : (~ ! [X539 : term] : ((((X529 @ id @ (sub @ X528 @ (push @ X539 @ id)) @ id)) = $true) | (((X529 @ id @ X539 @ id)) != $true)) | (((X529 @ id @ (lam @ (sub @ X528 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X531 : term,X530 : (subst > term > term)] : (~ ! [X538 : subst,X537 : term,X536 : subst] : (((sub @ X531 @ (push @ (sub @ X537 @ X538) @ (comp @ X536 @ X538)))) = ((X530 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538)))) | ~ ! [X535 : term,X534 : subst,X533 : subst] : (((sub @ (sub @ X531 @ (push @ X535 @ X533)) @ X534)) = ((sub @ (X530 @ X533 @ X535) @ X534))) | ($true = ((X529 @ id @ (lam @ (X530 @ sh @ one)) @ id))) | ~ ! [X532 : term] : ((((X529 @ id @ X532 @ id)) != $true) | (((X529 @ id @ (X530 @ id @ X532) @ id)) = $true)))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X191 : (subst > term > subst > $o),X190 : term] : (~ ! [X197 : term] : ((((X191 @ id @ (sub @ X190 @ (push @ X197 @ id)) @ id)) = $true) | (((X191 @ id @ X197 @ id)) != $true)) | ($true = ((X191 @ id @ (lam @ X190) @ id))) | ~ ! [X192 : (subst > term > term)] : (($true = ((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id))) | ~ ! [X196 : term] : ((((X191 @ id @ X196 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X196) @ id)) = $true)) | ~ ! [X194 : subst,X195 : term,X193 : subst] : (((X192 @ (comp @ X194 @ X193) @ (sub @ X195 @ X193))) = ((sub @ (X192 @ X194 @ X195) @ X193)))))) & (ulamvarsh = $true) & ((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) <=> (substmonoid = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & (! [X136 : term] : ~ ! [X137 : (subst > term > term)] : ~ ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((axvarcons = $true) <=> ! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X377 : term] : (((sub @ X377 @ id)) = X377) => ! [X378 : term] : (((sub @ X378 @ id)) = X378)) <=> (termmset_lthm = $true)) & ((induction2_lthm = $true) <=> (! [X412 : term] : (((sub @ X412 @ id)) = X412) => (! [X413 : (term > $o),X415 : subst,X414 : term] : (~ ! [X420 : term] : (($true = ((X413 @ (sub @ X420 @ X415)))) | (((var @ X420)) != $true)) | (((X413 @ (sub @ X414 @ X415))) = $true) | ~ ! [X416 : term,X417 : term] : (($true != ((X413 @ X417))) | ($true = ((X413 @ (ap @ X416 @ X417)))) | ($true != ((X413 @ X416)))) | ~ ! [X418 : term] : (~ ! [X419 : term] : ((((X413 @ (sub @ X418 @ (push @ X419 @ id)))) = $true) | (((X413 @ X419)) != $true)) | ($true = ((X413 @ (lam @ X418)))))) => ! [X422 : (term > $o),X421 : term] : (~ ! [X424 : term] : (($true = ((X422 @ (lam @ X424)))) | ~ ! [X425 : term] : ((((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true) | (((X422 @ X425)) != $true))) | ~ ! [X423 : term] : (($true = ((X422 @ X423))) | ($true != ((var @ X423)))) | ($true = ((X422 @ X421))) | ~ ! [X426 : term,X427 : term] : (($true != ((X422 @ X426))) | (((X422 @ (ap @ X426 @ X427))) = $true) | (((X422 @ X427)) != $true)))))) & (((var @ (d2term @ d_one))) != $true) & (! [X385 : (subst > term > subst > $o)] : ~ ! [X386 : (term > $o)] : ~ ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) <=> (hoasinduction_lem0 = $true)) & (axassoc = $true) & (pushprop_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X104 : term] : (((sub @ X104 @ id)) = X104) => ! [X107 : (term > $o),X105 : (subst > term > subst > $o),X106 : term] : (~ ! [X117 : (subst > term > term)] : ((((X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) = $true) | ~ ! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) | ~ ! [X118 : term] : ((((X105 @ id @ (X117 @ id @ X118) @ id)) = $true) | (((X105 @ id @ X118 @ id)) != $true))) | ~ ! [X116 : subst,X115 : subst,X114 : term,X113 : subst] : ((((X105 @ X113 @ X114 @ (comp @ X115 @ X116))) = $true) | ($true != ((X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116)))) | ($true = ((X107 @ (lam @ X106)))) | ~ ! [X112 : term] : (($true = ((X107 @ (sub @ X106 @ (push @ X112 @ id))))) | ($true != ((X107 @ X112)))) | ~ ! [X111 : subst,X109 : subst,X110 : term,X108 : subst] : (($true != ((X105 @ X111 @ X110 @ (comp @ X108 @ X109)))) | ($true = ((X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)))) | ~ ! [X122 : term] : (((X107 @ X122)) = ((X105 @ id @ X122 @ id)))))) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X43 : subst,X45 : term,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | (((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | ~ ! [X50 : subst,X51 : term,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) = ((sub @ (X42 @ X49 @ X51) @ X50))) | ~ ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) = ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & ((axidl = $true) <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & ! [X436 : d_subst] : (d_id = X436) & ((hoasinduction = $true) <=> ! [X508 : term,X509 : (subst > term > subst > $o)] : (~ ! [X517 : (subst > term > term)] : (($true = ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id))) | ~ ! [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) = ((sub @ (X517 @ X520 @ X521) @ X519))) | ~ ! [X518 : term] : (($true = ((X509 @ id @ (X517 @ id @ X518) @ id))) | (((X509 @ id @ X518 @ id)) != $true))) | ~ ! [X514 : subst,X513 : term,X516 : subst,X515 : subst] : (($true = ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) | ($true != ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) | ($true = ((X509 @ id @ X508 @ id))) | ~ ! [X523 : subst,X524 : subst,X522 : term,X525 : subst] : (($true = ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524))) | (((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) != $true)) | ~ ! [X510 : term] : ((((var @ (sub @ X510 @ id))) != $true) | (((X509 @ id @ X510 @ id)) = $true)) | ~ ! [X512 : term,X511 : term] : ((((X509 @ id @ X512 @ id)) != $true) | ($true != ((X509 @ id @ X511 @ id))) | ($true = ((X509 @ id @ (ap @ (sub @ X512 @ id) @ X511) @ id)))))) & (! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) <=> (hoasapinj2 = $true)) & ((! [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) = X338) => ! [X343 : (term > $o),X340 : subst,X341 : term,X342 : (term > $o)] : ((((X343 @ one)) = $true) | ~ ! [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) = ((X343 @ X344))) | (((X342 @ X341)) != $true))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X170 : (subst > term > subst > $o),X169 : term,X168 : (term > $o),X167 : term] : ((((X168 @ (ap @ X167 @ X169))) = $true) | ~ ! [X177 : term] : (((X170 @ id @ X177 @ id)) = ((X168 @ X177))) | (((X168 @ X169)) != $true) | ~ ! [X176 : subst,X174 : subst,X173 : term,X175 : subst] : ((((X170 @ X175 @ X173 @ (comp @ X176 @ X174))) = $true) | ($true != ((X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174)))) | ~ ! [X172 : term,X171 : term] : ((((X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id)) = $true) | ($true != ((X170 @ id @ X171 @ id))) | (((X170 @ id @ X172 @ id)) != $true)) | ($true != ((X168 @ X167))) | ~ ! [X178 : subst,X180 : subst,X179 : subst,X181 : term] : (($true = ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179))) | ($true != ((X170 @ X180 @ X181 @ (comp @ X178 @ X179))))))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop = $true) & ((! [X298 : term] : (((sub @ X298 @ id)) = X298) => (! [X299 : (subst > term > subst > $o),X300 : term] : (~ ! [X301 : term] : ((((X299 @ id @ (sub @ X300 @ (push @ X301 @ id)) @ id)) = $true) | ($true != ((X299 @ id @ X301 @ id)))) | ~ ! [X302 : (subst > term > term)] : ((((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ~ ! [X306 : term,X305 : subst,X304 : subst] : (((X302 @ (comp @ X304 @ X305) @ (sub @ X306 @ X305))) = ((sub @ (X302 @ X304 @ X306) @ X305))) | ~ ! [X303 : term] : ((((X299 @ id @ (X302 @ id @ X303) @ id)) = $true) | ($true != ((X299 @ id @ X303 @ id))))) | ($true = ((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id)))) => ! [X308 : term,X307 : (subst > term > subst > $o)] : (($true = ((X307 @ id @ (lam @ X308) @ id))) | ~ ! [X316 : term,X318 : subst,X315 : subst,X317 : subst] : (($true != ((X307 @ (comp @ X315 @ X318) @ (sub @ X316 @ X318) @ X317))) | ($true = ((X307 @ X315 @ X316 @ (comp @ X318 @ X317))))) | ~ ! [X319 : term,X322 : subst,X320 : subst,X321 : subst] : ((((X307 @ (comp @ X322 @ X321) @ (sub @ X319 @ X321) @ X320)) = $true) | ($true != ((X307 @ X322 @ X319 @ (comp @ X321 @ X320))))) | ~ ! [X310 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X310 @ sh @ one)) @ id)) = $true) | ~ ! [X314 : term] : (($true = ((X307 @ id @ (X310 @ id @ X314) @ id))) | ($true != ((X307 @ id @ X314 @ id)))) | ~ ! [X312 : subst,X311 : subst,X313 : term] : (((X310 @ (comp @ X312 @ X311) @ (sub @ X313 @ X311))) = ((sub @ (X310 @ X312 @ X313) @ X311)))) | ~ ! [X309 : term] : (($true = ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id))) | ($true != ((X307 @ id @ X309 @ id))))))) <=> (hoasinduction_lem3_lthm = $true)) & (axclos = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X428 : (subst > term > subst > $o),X429 : term] : (($true = ((X428 @ id @ (lam @ (sub @ X429 @ (push @ one @ sh))) @ id))) | ~ ! [X430 : (subst > term > term)] : (~ ! [X431 : term] : (($true = ((X428 @ id @ (X430 @ id @ X431) @ id))) | (((X428 @ id @ X431 @ id)) != $true)) | ~ ! [X432 : subst,X433 : term,X434 : subst] : (((X430 @ (comp @ X434 @ X432) @ (sub @ X433 @ X432))) = ((sub @ (X430 @ X434 @ X433) @ X432))) | (((X428 @ id @ (lam @ (X430 @ sh @ one)) @ id)) = $true)) | ~ ! [X435 : term] : ((((X428 @ id @ X435 @ id)) != $true) | ($true = ((X428 @ id @ (sub @ X429 @ (push @ X435 @ id)) @ id)))))) & ((pushprop_lem0 = $true) <=> ! [X81 : subst,X80 : term,X79 : (term > $o)] : ~ ! [X82 : (term > $o)] : ~ ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81)))))) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axmap = $true) & ((hoasinduction_lem2 = $true) <=> ! [X260 : (subst > term > subst > $o),X258 : term,X259 : term] : (~ ! [X263 : term,X262 : subst,X264 : subst,X261 : subst] : (($true != ((X260 @ (comp @ X264 @ X262) @ (sub @ X263 @ X262) @ X261))) | (((X260 @ X264 @ X263 @ (comp @ X262 @ X261))) = $true)) | (((X260 @ id @ X258 @ id)) != $true) | ~ ! [X265 : term,X266 : term] : (($true = ((X260 @ id @ (ap @ (sub @ X265 @ id) @ X266) @ id))) | ($true != ((X260 @ id @ X265 @ id))) | ($true != ((X260 @ id @ X266 @ id)))) | ($true != ((X260 @ id @ X259 @ id))) | ~ ! [X269 : subst,X270 : term,X267 : subst,X268 : subst] : (($true != ((X260 @ X269 @ X270 @ (comp @ X268 @ X267)))) | ($true = ((X260 @ (comp @ X269 @ X268) @ (sub @ X270 @ X268) @ X267)))) | ($true = ((X260 @ id @ (ap @ X258 @ X259) @ id))))) & (hoasapinj1_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (~ ! [X496 : (subst > term > term)] : (~ ! [X500 : term,X498 : subst,X499 : subst] : (((sub @ (X496 @ X499 @ X500) @ X498)) = ((X496 @ (comp @ X499 @ X498) @ (sub @ X500 @ X498)))) | ($true = ((X492 @ id @ (lam @ (X496 @ sh @ one)) @ id))) | ~ ! [X497 : term] : ((((X492 @ id @ X497 @ id)) != $true) | (((X492 @ id @ (X496 @ id @ X497) @ id)) = $true))) | ~ ! [X494 : term] : ((((X491 @ (sub @ X493 @ (push @ X494 @ id)))) = $true) | (((X491 @ X494)) != $true)) | ~ ! [X495 : term] : (((X491 @ X495)) = ((X492 @ id @ X495 @ id))) | ($true = ((X491 @ (lam @ X493)))))) & (hoaslamnotvar = $true) & (! [X332 : (term > $o),X333 : term] : (~ ! [X334 : term] : ((((X332 @ X334)) = $true) | (((var @ X334)) != $true)) | (((X332 @ X333)) = $true) | ~ ! [X337 : term] : (($true = ((X332 @ (lam @ X337)))) | (((X332 @ X337)) != $true)) | ~ ! [X335 : term,X336 : term] : (($true = ((X332 @ (ap @ X335 @ X336)))) | (((X332 @ X336)) != $true) | ($true != ((X332 @ X335))))) <=> (induction = $true)) & (hoaslamnotap_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) = X245) => (! [X247 : term,X246 : subst] : (((comp @ sh @ (push @ X247 @ X246))) = X246) => ! [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | (((X252 @ X251)) != $true)))) <=> (pushprop_lem1_lthm = $true)) & (hoasapnotvar = $true) & ((apinj1 = $true) <=> ! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186))) & (! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) <=> (axscons = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X188 : term] : ~ ! [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) != ((X189 @ sh @ one)))) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) <=> (shinj = $true)) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasapinj1 = $true) <=> ! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367))) & (hoasinduction_lem1 = $true) & (hoaslamnotvar_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X373 : subst] : (((comp @ id @ X373)) = X373) => (! [X374 : subst] : (((comp @ X374 @ id)) = X374) => (! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376))))) & (termmset_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X379 : term,X380 : term,X381 : (subst > term > term)] : ((((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one)))) | ~ ! [X383 : subst,X382 : term,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) = ((sub @ (X381 @ X383 @ X382) @ X384)))) <=> (hoaslamnotap = $true)) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) = ((d2term @ X507))) => (X506 = X507)) & ((axidr = $true) <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & (! [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true) | (((X254 @ X255)) != $true)) <=> (pushprop_lem1 = $true)) & (lamnotvar = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X39 : (subst > term > subst > $o)] : ~ ! [X40 : (term > $o)] : ~ ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41)))) & ! [X84 : d_term] : (d_one = X84) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) <=> (axshiftcons = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X56 : subst,X55 : term] : (((sub @ one @ (push @ X55 @ X56))) = X55) => (! [X58 : subst,X57 : term] : (((comp @ sh @ (push @ X57 @ X58))) = X58) => (! [X60 : term,X59 : term] : ((X59 = X60) | (((lam @ X59)) != ((lam @ X60)))) => ! [X63 : term,X62 : (subst > term > term),X61 : subst,X64 : (subst > term > term)] : (~ ! [X67 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) = ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | ~ ! [X68 : subst,X70 : subst,X69 : term] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) = ((sub @ (X64 @ X68 @ X69) @ X70))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one)))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63)))))))) & (! [X505 : term] : (((sub @ X505 @ id)) = X505) <=> (termmset = $true)) & ((! [X125 : term,X126 : term,X124 : term,X123 : term] : ((((ap @ X124 @ X125)) != ((ap @ X123 @ X126))) | (X125 = X126)) => ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((apinj2 = $true) <=> ! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399))) & (! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) <=> (laminj = $true))),
% 164.61/23.50 inference(flattening,[],[f9])).
% 164.61/23.50 thf(f11,plain,(
% 164.61/23.50 (ulamvarind = $true) & (lamnotap != $true) & ((((! [X473 : (subst > term > subst > $o),X474 : term] : (? [X489 : term,X490 : term] : ((((X473 @ id @ X490 @ id)) = $true) & (((X473 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id)) != $true) & (((X473 @ id @ X489 @ id)) = $true)) | ? [X480 : (subst > term > term)] : (! [X481 : term] : (($true != ((X473 @ id @ X481 @ id))) | (((X473 @ id @ (X480 @ id @ X481) @ id)) = $true)) & ($true != ((X473 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X484 : subst,X482 : term,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ($true = ((X473 @ id @ X474 @ id))) | ? [X488 : subst,X486 : term,X487 : subst,X485 : subst] : ((((X473 @ X488 @ X486 @ (comp @ X487 @ X485))) = $true) & ($true != ((X473 @ (comp @ X488 @ X487) @ (sub @ X486 @ X487) @ X485)))) | ? [X476 : subst,X478 : subst,X477 : subst,X479 : term] : (($true = ((X473 @ (comp @ X478 @ X477) @ (sub @ X479 @ X477) @ X476))) & (((X473 @ X478 @ X479 @ (comp @ X477 @ X476))) != $true)) | ? [X475 : term] : ((((X473 @ id @ X475 @ id)) != $true) & ($true = ((var @ (sub @ X475 @ id)))))) | ? [X458 : term,X457 : (subst > term > subst > $o)] : (! [X459 : (subst > term > term)] : (? [X461 : term,X462 : subst,X463 : subst] : (((X459 @ (comp @ X463 @ X462) @ (sub @ X461 @ X462))) != ((sub @ (X459 @ X463 @ X461) @ X462))) | ? [X460 : term] : ((((X457 @ id @ X460 @ id)) = $true) & (((X457 @ id @ (X459 @ id @ X460) @ id)) != $true)) | (((X457 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true)) & ! [X468 : subst,X465 : subst,X466 : term,X467 : subst] : ((((X457 @ (comp @ X465 @ X468) @ (sub @ X466 @ X468) @ X467)) = $true) | (((X457 @ X465 @ X466 @ (comp @ X468 @ X467))) != $true)) & ! [X469 : term,X471 : subst,X470 : subst,X472 : subst] : ((((X457 @ X470 @ X469 @ (comp @ X471 @ X472))) = $true) | (((X457 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471) @ X472)) != $true)) & ! [X464 : term] : ((((X457 @ id @ X464 @ id)) != $true) | ($true = ((X457 @ id @ (sub @ X458 @ (push @ X464 @ id)) @ id)))) & (((X457 @ id @ (lam @ X458) @ id)) != $true))) | ? [X444 : term,X446 : (subst > term > subst > $o),X445 : term] : ((((X446 @ id @ X445 @ id)) = $true) & ! [X456 : term,X455 : term] : ((((X446 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id)) = $true) | (((X446 @ id @ X455 @ id)) != $true) | ($true != ((X446 @ id @ X456 @ id)))) & ! [X448 : subst,X447 : subst,X450 : subst,X449 : term] : ((((X446 @ X447 @ X449 @ (comp @ X450 @ X448))) != $true) | (((X446 @ (comp @ X447 @ X450) @ (sub @ X449 @ X450) @ X448)) = $true)) & ! [X454 : subst,X453 : term,X452 : subst,X451 : subst] : ((((X446 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451) @ X454)) != $true) | (((X446 @ X452 @ X453 @ (comp @ X451 @ X454))) = $true)) & ($true != ((X446 @ id @ (ap @ X445 @ X444) @ id))) & ($true = ((X446 @ id @ X444 @ id))))) | ? [X438 : term,X437 : (term > $o)] : (! [X443 : term] : ((((var @ X443)) != $true) | (((X437 @ X443)) = $true)) & (((X437 @ X438)) != $true) & ! [X441 : term] : (($true = ((X437 @ (lam @ X441)))) | ? [X442 : term] : (($true = ((X437 @ X442))) & (((X437 @ (sub @ X441 @ (push @ X442 @ id)))) != $true))) & ! [X439 : term,X440 : term] : (($true = ((X437 @ (ap @ X440 @ X439)))) | (((X437 @ X440)) != $true) | ($true != ((X437 @ X439)))))) <=> (hoasinduction_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotap_gthm = $true) & (! [X323 : (subst > term > subst > $o),X324 : term] : (? [X325 : (subst > term > term)] : (($true != ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) & ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ($true != ((X323 @ id @ X329 @ id)))) & ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) | (((X323 @ id @ X324 @ id)) = $true) | ? [X331 : term,X330 : term] : (($true != ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) & (((X323 @ id @ X331 @ id)) = $true) & ($true = ((X323 @ id @ X330 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & ((axvarid = $true) <=> ! [X388 : term] : (((sub @ X388 @ id)) = X388)) & (hoasinduction_lem2_gthm = $true) & (apnotvar = $true) & ((induction2lem = $true) <=> ! [X404 : (term > $o),X402 : subst,X403 : term] : (? [X405 : term] : (! [X406 : term] : (($true != ((X404 @ X406))) | ($true = ((X404 @ (sub @ X405 @ (push @ X406 @ id)))))) & (((X404 @ (lam @ X405))) != $true)) | ? [X409 : term] : ((((X404 @ (sub @ X409 @ X402))) != $true) & ($true = ((var @ X409)))) | ($true = ((X404 @ (sub @ X403 @ X402)))) | ? [X408 : term,X407 : term] : (($true != ((X404 @ (ap @ X407 @ X408)))) & (((X404 @ X407)) = $true) & (((X404 @ X408)) = $true)))) & ((induction2lem_lthm = $true) <=> ((((! [X284 : (term > $o),X282 : subst,X283 : term] : (? [X287 : term] : ((((X284 @ (sub @ X287 @ X282))) != $true) & ($true = ((var @ X287)))) | (((X284 @ (sub @ X283 @ X282))) = $true) | ? [X286 : term,X285 : term] : (($true != ((X284 @ (ap @ X285 @ X286)))) & (((X284 @ X285)) = $true) & ($true = ((X284 @ X286)))) | ? [X288 : term] : (! [X289 : term] : (($true != ((X284 @ X289))) | ($true = ((X284 @ (sub @ X288 @ (push @ X289 @ id)))))) & ($true != ((X284 @ (lam @ X288)))))) | ? [X276 : term,X277 : (term > $o)] : (! [X279 : term,X278 : term] : (($true = ((X277 @ (ap @ X278 @ X279)))) | (((X277 @ X279)) != $true) | (((X277 @ X278)) != $true)) & ! [X281 : term] : (($true = ((X277 @ (lam @ X281)))) | (((X277 @ X281)) != $true)) & ($true != ((X277 @ X276))) & ! [X280 : term] : (($true != ((var @ X280))) | ($true = ((X277 @ X280)))))) | ? [X275 : subst] : (((comp @ X275 @ id)) != X275)) | ? [X274 : term,X273 : subst] : (((comp @ sh @ (push @ X274 @ X273))) != X273)) | ? [X271 : subst,X272 : term] : (((sub @ one @ (push @ X272 @ X271))) != X272))) & (pushprop_lem0_gthm = $true) & (one = ((d2term @ d_one))) & (((((! [X22 : term,X21 : (subst > term > subst > $o)] : (? [X34 : term,X33 : term] : (($true = ((X21 @ id @ X33 @ id))) & (((X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id)) != $true) & (((X21 @ id @ X34 @ id)) = $true)) | ($true = ((X21 @ id @ X22 @ id))) | ? [X32 : term] : ((((var @ (sub @ X32 @ id))) = $true) & ($true != ((X21 @ id @ X32 @ id)))) | ? [X37 : subst,X38 : term,X36 : subst,X35 : subst] : (($true = ((X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))) & (((X21 @ X35 @ X38 @ (comp @ X37 @ X36))) != $true)) | ? [X25 : subst,X26 : term,X23 : subst,X24 : subst] : (($true = ((X21 @ X25 @ X26 @ (comp @ X24 @ X23)))) & (((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23)) != $true)) | ? [X27 : (subst > term > term)] : (! [X28 : term] : ((((X21 @ id @ (X27 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id)))) & ! [X30 : subst,X29 : term,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) & (((X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) != $true))) | ? [X13 : (term > $o),X12 : (subst > term > subst > $o),X11 : term] : (! [X19 : term] : ((((X13 @ X19)) != $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X19 @ id)))))) & ! [X14 : (subst > term > term)] : ((((X12 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X18 : term] : (($true != ((X12 @ id @ (X14 @ id @ X18) @ id))) & (((X12 @ id @ X18 @ id)) = $true)) | ? [X17 : subst,X15 : subst,X16 : term] : (((sub @ (X14 @ X15 @ X16) @ X17)) != ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17))))) & ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id))) & ($true != ((X13 @ (lam @ X11)))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X4 : term,X3 : (term > $o)] : (! [X9 : term,X8 : term] : (($true = ((X3 @ (ap @ X9 @ X8)))) | ($true != ((X3 @ X9))) | (((X3 @ X8)) != $true)) & ($true != ((X3 @ X4))) & ! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & ! [X5 : term] : ((((X3 @ X5)) = $true) | ($true != ((var @ X5)))))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2)))) <=> (hoasinduction_lthm_3 = $true)) & (axapp = $true) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = sh) & (induction2lem_gthm = $true) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X526 : term] : ? [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) = ((X527 @ sh @ one)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X291 : (subst > term > subst > $o),X290 : term] : (($true = ((X291 @ id @ (lam @ (sub @ X290 @ (push @ one @ sh))) @ id))) | ? [X297 : term] : ((((X291 @ id @ X297 @ id)) = $true) & ($true != ((X291 @ id @ (sub @ X290 @ (push @ X297 @ id)) @ id)))) | ? [X292 : (subst > term > term)] : (! [X293 : term] : ((((X291 @ id @ X293 @ id)) != $true) | (((X291 @ id @ (X292 @ id @ X293) @ id)) = $true)) & ! [X294 : subst,X295 : subst,X296 : term] : (((X292 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))) = ((sub @ (X292 @ X295 @ X296) @ X294))) & ($true != ((X291 @ id @ (lam @ (X292 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & (ulamvar1 != $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X94 : term,X95 : (term > $o),X96 : (subst > term > subst > $o)] : (? [X97 : term] : (((X95 @ X97)) != ((X96 @ id @ X97 @ id))) | ? [X98 : term] : (($true = ((X95 @ X98))) & ($true != ((X95 @ (sub @ X94 @ (push @ X98 @ id)))))) | ? [X99 : (subst > term > term)] : (! [X100 : subst,X102 : subst,X101 : term] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) & ! [X103 : term] : (($true != ((X96 @ id @ X103 @ id))) | (((X96 @ id @ (X99 @ id @ X103) @ id)) = $true)) & (((X96 @ id @ (lam @ (X99 @ sh @ one)) @ id)) != $true)) | (((X95 @ (lam @ X94))) = $true)) | ? [X93 : term] : (((sub @ X93 @ id)) != X93)) | ? [X89 : term] : ! [X90 : (subst > term > term)] : ? [X91 : term,X92 : subst] : (((sub @ X89 @ (push @ X91 @ X92))) != ((X90 @ X92 @ X91))))) & (hoasinduction_lem3_gthm = $true) & (axabs = $true) & (hoasapnotvar_lthm = $true) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) != ((d2subst @ X183))) | (X182 = X183)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X220 : term,X219 : (subst > term > subst > $o)] : (? [X226 : term,X227 : term] : ((((X219 @ id @ X227 @ id)) = $true) & ($true = ((X219 @ id @ X226 @ id))) & (((X219 @ id @ (ap @ (sub @ X227 @ id) @ X226) @ id)) != $true)) | ? [X221 : (subst > term > term)] : (! [X225 : term] : (($true != ((X219 @ id @ X225 @ id))) | (((X219 @ id @ (X221 @ id @ X225) @ id)) = $true)) & ($true != ((X219 @ id @ (lam @ (X221 @ sh @ one)) @ id))) & ! [X222 : subst,X223 : term,X224 : subst] : (((sub @ (X221 @ X224 @ X223) @ X222)) = ((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))))) | ($true = ((X219 @ id @ X220 @ id)))) | ? [X211 : (term > $o),X209 : term,X210 : (subst > term > subst > $o)] : (! [X218 : term] : ((((X211 @ X218)) != $true) | ($true = ((X211 @ (sub @ X209 @ (push @ X218 @ id)))))) & ! [X212 : (subst > term > term)] : (? [X213 : term,X215 : subst,X214 : subst] : (((sub @ (X212 @ X214 @ X213) @ X215)) != ((X212 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)))) | (((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id)) = $true) | ? [X216 : term] : (($true = ((X210 @ id @ X216 @ id))) & (((X210 @ id @ (X212 @ id @ X216) @ id)) != $true))) & ! [X217 : term] : (((X210 @ id @ X217 @ id)) = ((X211 @ X217))) & ($true != ((X211 @ (lam @ X209)))))) | ? [X208 : term] : (((sub @ X208 @ id)) != X208)) | ? [X202 : term,X201 : (term > $o)] : (! [X204 : term,X205 : term] : (($true != ((X201 @ X204))) | (((X201 @ X205)) != $true) | ($true = ((X201 @ (ap @ X204 @ X205))))) & ! [X203 : term] : ((((X201 @ X203)) = $true) | ($true != ((var @ X203)))) & (((X201 @ X202)) != $true) & ! [X206 : term] : (? [X207 : term] : (($true != ((X201 @ (sub @ X206 @ (push @ X207 @ id))))) & (((X201 @ X207)) = $true)) | ($true = ((X201 @ (lam @ X206))))))) | ? [X198 : (subst > term > subst > $o)] : ! [X199 : (term > $o)] : ? [X200 : term] : (((X198 @ id @ X200 @ id)) != ((X199 @ X200))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X149 : (subst > term > subst > $o),X151 : term,X150 : (term > $o)] : (? [X160 : subst,X161 : subst,X162 : subst,X159 : term] : (($true != ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)))) & (((X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) = $true)) | ? [X158 : term] : (((X149 @ id @ X158 @ id)) != ((X150 @ X158))) | ? [X157 : term] : (($true = ((X150 @ X157))) & (((X150 @ (sub @ X151 @ (push @ X157 @ id)))) != $true)) | ? [X152 : (subst > term > term)] : (! [X153 : term] : ((((X149 @ id @ X153 @ id)) != $true) | (((X149 @ id @ (X152 @ id @ X153) @ id)) = $true)) & ! [X154 : subst,X156 : term,X155 : subst] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155))) & ($true != ((X149 @ id @ (lam @ (X152 @ sh @ one)) @ id)))) | ? [X166 : subst,X165 : subst,X163 : term,X164 : subst] : (($true != ((X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165))) & (((X149 @ X166 @ X163 @ (comp @ X164 @ X165))) = $true)) | ($true = ((X150 @ (lam @ X151)))))) & (axvarshift = $true) & (! [X85 : term] : ? [X86 : (subst > term > term)] : ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem3v2 = $true) & (substmonoid_gthm = $true) & (! [X229 : (subst > term > subst > $o),X228 : term] : (? [X243 : term] : ((((X229 @ id @ X243 @ id)) = $true) & (((X229 @ id @ (sub @ X228 @ (push @ X243 @ id)) @ id)) != $true)) | ? [X239 : subst,X241 : term,X242 : subst,X240 : subst] : ((((X229 @ X239 @ X241 @ (comp @ X242 @ X240))) = $true) & (((X229 @ (comp @ X239 @ X242) @ (sub @ X241 @ X242) @ X240)) != $true)) | ($true = ((X229 @ id @ (lam @ X228) @ id))) | ? [X230 : (subst > term > term)] : (! [X232 : subst,X233 : subst,X231 : term] : (((sub @ (X230 @ X233 @ X231) @ X232)) = ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) & (((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id)) != $true) & ! [X234 : term] : ((((X229 @ id @ (X230 @ id @ X234) @ id)) = $true) | ($true != ((X229 @ id @ X234 @ id))))) | ? [X238 : term,X236 : subst,X235 : subst,X237 : subst] : (($true = ((X229 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237) @ X235))) & (((X229 @ X236 @ X238 @ (comp @ X237 @ X235))) != $true))) <=> (hoasinduction_lem3 = $true)) & (! [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) != $true) | ? [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) != ((X131 @ X135))) | (((X131 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem3a_gthm = $true) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ? [X145 : (term > $o)] : ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396)) | ? [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 != X392) & (((ap @ X390 @ X391)) = ((ap @ X392 @ X393))))) | ? [X389 : term] : (((sub @ X389 @ id)) != X389))) & (! [X73 : term,X72 : (term > $o)] : (? [X76 : term] : (($true = ((var @ X76))) & ($true != ((X72 @ X76)))) | ? [X74 : term,X75 : term] : ((((X72 @ X75)) = $true) & ($true = ((X72 @ X74))) & ($true != ((X72 @ (ap @ X75 @ X74))))) | (((X72 @ X73)) = $true) | ? [X77 : term] : ((((X72 @ (lam @ X77))) != $true) & ! [X78 : term] : ((((X72 @ X78)) != $true) | (((X72 @ (sub @ X77 @ (push @ X78 @ id)))) = $true)))) <=> (induction2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X358 : (subst > term > subst > $o),X357 : term] : (? [X360 : (subst > term > term)] : (! [X363 : subst,X361 : term,X362 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) & ! [X364 : term] : (($true = ((X358 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X358 @ id @ X364 @ id)))) & (((X358 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true)) | ? [X359 : term] : (($true = ((X358 @ id @ X359 @ id))) & (((X358 @ id @ (sub @ X357 @ (push @ X359 @ id)) @ id)) != $true)) | (((X358 @ id @ (lam @ X357) @ id)) = $true)) | ? [X350 : (subst > term > subst > $o),X349 : term] : (! [X351 : term] : ((((X350 @ id @ X351 @ id)) != $true) | (((X350 @ id @ (sub @ X349 @ (push @ X351 @ id)) @ id)) = $true)) & ($true != ((X350 @ id @ (lam @ (sub @ X349 @ (push @ one @ sh))) @ id))) & ! [X352 : (subst > term > term)] : (? [X353 : term] : ((((X350 @ id @ (X352 @ id @ X353) @ id)) != $true) & (((X350 @ id @ X353 @ id)) = $true)) | ? [X356 : subst,X354 : term,X355 : subst] : (((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355))) != ((sub @ (X352 @ X356 @ X354) @ X355))) | ($true = ((X350 @ id @ (lam @ (X352 @ sh @ one)) @ id)))))) | ? [X348 : term] : (((sub @ X348 @ id)) != X348))) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X528 : term,X529 : (subst > term > subst > $o)] : (? [X531 : term,X530 : (subst > term > term)] : (! [X535 : term,X534 : subst,X533 : subst] : (((sub @ (sub @ X531 @ (push @ X535 @ X533)) @ X534)) = ((sub @ (X530 @ X533 @ X535) @ X534))) & ! [X532 : term] : ((((X529 @ id @ X532 @ id)) != $true) | (((X529 @ id @ (X530 @ id @ X532) @ id)) = $true)) & ($true != ((X529 @ id @ (lam @ (X530 @ sh @ one)) @ id))) & ! [X538 : subst,X537 : term,X536 : subst] : (((sub @ X531 @ (push @ (sub @ X537 @ X538) @ (comp @ X536 @ X538)))) = ((X530 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538))))) | ? [X539 : term] : ((((X529 @ id @ X539 @ id)) = $true) & (((X529 @ id @ (sub @ X528 @ (push @ X539 @ id)) @ id)) != $true)) | (((X529 @ id @ (lam @ (sub @ X528 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X191 : (subst > term > subst > $o),X190 : term] : (? [X192 : (subst > term > term)] : (($true != ((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : term,X193 : subst] : (((X192 @ (comp @ X194 @ X193) @ (sub @ X195 @ X193))) = ((sub @ (X192 @ X194 @ X195) @ X193))) & ! [X196 : term] : ((((X191 @ id @ X196 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X196) @ id)) = $true))) | ($true = ((X191 @ id @ (lam @ X190) @ id))) | ? [X197 : term] : ((((X191 @ id @ X197 @ id)) = $true) & (((X191 @ id @ (sub @ X190 @ (push @ X197 @ id)) @ id)) != $true)))) & (ulamvarsh = $true) & ((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) <=> (substmonoid = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X136 : term] : ? [X137 : (subst > term > term)] : ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139)))) & ((axvarcons = $true) <=> ! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1_gthm = $true) & ((? [X377 : term] : (((sub @ X377 @ id)) != X377) | ! [X378 : term] : (((sub @ X378 @ id)) = X378)) <=> (termmset_lthm = $true)) & ((induction2_lthm = $true) <=> ((! [X422 : (term > $o),X421 : term] : (? [X424 : term] : (($true != ((X422 @ (lam @ X424)))) & ! [X425 : term] : ((((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true) | (((X422 @ X425)) != $true))) | ? [X423 : term] : (($true = ((var @ X423))) & ($true != ((X422 @ X423)))) | ($true = ((X422 @ X421))) | ? [X426 : term,X427 : term] : (($true = ((X422 @ X426))) & (((X422 @ X427)) = $true) & (((X422 @ (ap @ X426 @ X427))) != $true))) | ? [X415 : subst,X414 : term,X413 : (term > $o)] : (! [X420 : term] : (($true = ((X413 @ (sub @ X420 @ X415)))) | (((var @ X420)) != $true)) & (((X413 @ (sub @ X414 @ X415))) != $true) & ! [X418 : term] : (? [X419 : term] : ((((X413 @ X419)) = $true) & (((X413 @ (sub @ X418 @ (push @ X419 @ id)))) != $true)) | ($true = ((X413 @ (lam @ X418))))) & ! [X416 : term,X417 : term] : (($true != ((X413 @ X417))) | ($true = ((X413 @ (ap @ X416 @ X417)))) | ($true != ((X413 @ X416)))))) | ? [X412 : term] : (((sub @ X412 @ id)) != X412))) & (((var @ (d2term @ d_one))) != $true) & (! [X385 : (subst > term > subst > $o)] : ? [X386 : (term > $o)] : ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) <=> (hoasinduction_lem0 = $true)) & (axassoc = $true) & (pushprop_lthm = $true) & ((? [X104 : term] : (((sub @ X104 @ id)) != X104) | ! [X105 : (subst > term > subst > $o),X106 : term,X107 : (term > $o)] : (? [X108 : subst,X109 : subst,X111 : subst,X110 : term] : (($true = ((X105 @ X111 @ X110 @ (comp @ X108 @ X109)))) & ($true != ((X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)))) | ? [X114 : term,X115 : subst,X113 : subst,X116 : subst] : ((((X105 @ X113 @ X114 @ (comp @ X115 @ X116))) != $true) & ($true = ((X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116)))) | ? [X117 : (subst > term > term)] : (! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) & (((X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) != $true) & ! [X118 : term] : ((((X105 @ id @ (X117 @ id @ X118) @ id)) = $true) | (((X105 @ id @ X118 @ id)) != $true))) | ? [X122 : term] : (((X107 @ X122)) != ((X105 @ id @ X122 @ id))) | ($true = ((X107 @ (lam @ X106)))) | ? [X112 : term] : (($true = ((X107 @ X112))) & ($true != ((X107 @ (sub @ X106 @ (push @ X112 @ id)))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | (((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | ? [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) != ((sub @ (X42 @ X49 @ X51) @ X50))) | ? [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) != ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & ((axidl = $true) <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & ! [X436 : d_subst] : (d_id = X436) & ((hoasinduction = $true) <=> ! [X508 : term,X509 : (subst > term > subst > $o)] : (? [X522 : term,X525 : subst,X524 : subst,X523 : subst] : ((((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) = $true) & ($true != ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524)))) | ? [X514 : subst,X515 : subst,X516 : subst,X513 : term] : (($true != ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) & ($true = ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) | ? [X517 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id))) & ! [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) = ((sub @ (X517 @ X520 @ X521) @ X519))) & ! [X518 : term] : (($true = ((X509 @ id @ (X517 @ id @ X518) @ id))) | (((X509 @ id @ X518 @ id)) != $true))) | ? [X510 : term] : ((((var @ (sub @ X510 @ id))) = $true) & (((X509 @ id @ X510 @ id)) != $true)) | ($true = ((X509 @ id @ X508 @ id))) | ? [X512 : term,X511 : term] : ((((X509 @ id @ X512 @ id)) = $true) & ($true != ((X509 @ id @ (ap @ (sub @ X512 @ id) @ X511) @ id))) & ($true = ((X509 @ id @ X511 @ id)))))) & (! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) <=> (hoasapinj2 = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (? [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) != X338) | ! [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) != $true) | ? [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) != ((X343 @ X344))) | (((X343 @ one)) = $true)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X168 : (term > $o),X167 : term,X169 : term,X170 : (subst > term > subst > $o)] : (? [X175 : subst,X174 : subst,X173 : term,X176 : subst] : (($true = ((X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174))) & (((X170 @ X175 @ X173 @ (comp @ X176 @ X174))) != $true)) | ? [X177 : term] : (((X170 @ id @ X177 @ id)) != ((X168 @ X177))) | ? [X181 : term,X178 : subst,X180 : subst,X179 : subst] : (($true != ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179))) & ($true = ((X170 @ X180 @ X181 @ (comp @ X178 @ X179))))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X167 @ X169))) = $true) | ? [X172 : term,X171 : term] : ((((X170 @ id @ X172 @ id)) = $true) & (((X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id)) != $true) & ($true = ((X170 @ id @ X171 @ id)))) | ($true != ((X168 @ X167)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop = $true) & (((! [X307 : (subst > term > subst > $o),X308 : term] : (? [X310 : (subst > term > term)] : (! [X312 : subst,X311 : subst,X313 : term] : (((X310 @ (comp @ X312 @ X311) @ (sub @ X313 @ X311))) = ((sub @ (X310 @ X312 @ X313) @ X311))) & ! [X314 : term] : (($true = ((X307 @ id @ (X310 @ id @ X314) @ id))) | ($true != ((X307 @ id @ X314 @ id)))) & (((X307 @ id @ (lam @ (X310 @ sh @ one)) @ id)) != $true)) | ? [X317 : subst,X316 : term,X318 : subst,X315 : subst] : (($true = ((X307 @ (comp @ X315 @ X318) @ (sub @ X316 @ X318) @ X317))) & ($true != ((X307 @ X315 @ X316 @ (comp @ X318 @ X317))))) | ? [X320 : subst,X322 : subst,X319 : term,X321 : subst] : ((((X307 @ (comp @ X322 @ X321) @ (sub @ X319 @ X321) @ X320)) != $true) & ($true = ((X307 @ X322 @ X319 @ (comp @ X321 @ X320))))) | ($true = ((X307 @ id @ (lam @ X308) @ id))) | ? [X309 : term] : (($true = ((X307 @ id @ X309 @ id))) & ($true != ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id))))) | ? [X300 : term,X299 : (subst > term > subst > $o)] : (! [X302 : (subst > term > term)] : ((((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ? [X304 : subst,X306 : term,X305 : subst] : (((X302 @ (comp @ X304 @ X305) @ (sub @ X306 @ X305))) != ((sub @ (X302 @ X304 @ X306) @ X305))) | ? [X303 : term] : (($true = ((X299 @ id @ X303 @ id))) & (((X299 @ id @ (X302 @ id @ X303) @ id)) != $true))) & ($true != ((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id))) & ! [X301 : term] : ((((X299 @ id @ (sub @ X300 @ (push @ X301 @ id)) @ id)) = $true) | ($true != ((X299 @ id @ X301 @ id)))))) | ? [X298 : term] : (((sub @ X298 @ id)) != X298)) <=> (hoasinduction_lem3_lthm = $true)) & (axclos = $true) & (! [X428 : (subst > term > subst > $o),X429 : term] : (($true = ((X428 @ id @ (lam @ (sub @ X429 @ (push @ one @ sh))) @ id))) | ? [X430 : (subst > term > term)] : (! [X432 : subst,X433 : term,X434 : subst] : (((X430 @ (comp @ X434 @ X432) @ (sub @ X433 @ X432))) = ((sub @ (X430 @ X434 @ X433) @ X432))) & (((X428 @ id @ (lam @ (X430 @ sh @ one)) @ id)) != $true) & ! [X431 : term] : (($true = ((X428 @ id @ (X430 @ id @ X431) @ id))) | (((X428 @ id @ X431 @ id)) != $true))) | ? [X435 : term] : ((((X428 @ id @ X435 @ id)) = $true) & ($true != ((X428 @ id @ (sub @ X429 @ (push @ X435 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X80 : term,X79 : (term > $o),X81 : subst] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))) <=> (pushprop_lem0 = $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axmap = $true) & ((hoasinduction_lem2 = $true) <=> ! [X258 : term,X259 : term,X260 : (subst > term > subst > $o)] : (($true = ((X260 @ id @ (ap @ X258 @ X259) @ id))) | ? [X266 : term,X265 : term] : (($true = ((X260 @ id @ X265 @ id))) & ($true = ((X260 @ id @ X266 @ id))) & ($true != ((X260 @ id @ (ap @ (sub @ X265 @ id) @ X266) @ id)))) | ? [X270 : term,X267 : subst,X268 : subst,X269 : subst] : (($true != ((X260 @ (comp @ X269 @ X268) @ (sub @ X270 @ X268) @ X267))) & ($true = ((X260 @ X269 @ X270 @ (comp @ X268 @ X267))))) | ? [X264 : subst,X262 : subst,X261 : subst,X263 : term] : ((((X260 @ X264 @ X263 @ (comp @ X262 @ X261))) != $true) & ($true = ((X260 @ (comp @ X264 @ X262) @ (sub @ X263 @ X262) @ X261)))) | ($true != ((X260 @ id @ X259 @ id))) | (((X260 @ id @ X258 @ id)) != $true))) & (hoasapinj1_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (? [X495 : term] : (((X491 @ X495)) != ((X492 @ id @ X495 @ id))) | ($true = ((X491 @ (lam @ X493)))) | ? [X494 : term] : ((((X491 @ X494)) = $true) & (((X491 @ (sub @ X493 @ (push @ X494 @ id)))) != $true)) | ? [X496 : (subst > term > term)] : (! [X500 : term,X498 : subst,X499 : subst] : (((sub @ (X496 @ X499 @ X500) @ X498)) = ((X496 @ (comp @ X499 @ X498) @ (sub @ X500 @ X498)))) & ($true != ((X492 @ id @ (lam @ (X496 @ sh @ one)) @ id))) & ! [X497 : term] : ((((X492 @ id @ X497 @ id)) != $true) | (((X492 @ id @ (X496 @ id @ X497) @ id)) = $true))))) & (hoaslamnotvar = $true) & (! [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) = $true) | ? [X336 : term,X335 : term] : ((((X332 @ X336)) = $true) & ($true = ((X332 @ X335))) & ($true != ((X332 @ (ap @ X335 @ X336))))) | ? [X337 : term] : (($true != ((X332 @ (lam @ X337)))) & (((X332 @ X337)) = $true)) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X332 @ X334)) != $true))) <=> (induction = $true)) & (hoaslamnotap_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((! [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | (((X252 @ X251)) != $true)) | ? [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) != X246)) | ? [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) != X245)) <=> (pushprop_lem1_lthm = $true)) & (hoasapnotvar = $true) & ((apinj1 = $true) <=> ! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186))) & (! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) <=> (axscons = $true)) & (! [X188 : term] : ? [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) = ((X189 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) <=> (shinj = $true)) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasapinj1 = $true) <=> ! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367))) & (hoasinduction_lem1 = $true) & (hoaslamnotvar_gthm = $true) & ((substmonoid_lthm = $true) <=> (((! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376)) | ? [X374 : subst] : (((comp @ X374 @ id)) != X374)) | ? [X373 : subst] : (((comp @ id @ X373)) != X373))) & (termmset_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslamnotap = $true) <=> ! [X380 : term,X379 : term,X381 : (subst > term > term)] : (? [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) != ((sub @ (X381 @ X383 @ X382) @ X384))) | (((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one)))))) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) != ((d2term @ X507))) | (X506 = X507)) & ((axidr = $true) <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & (! [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true) | (((X254 @ X255)) != $true)) <=> (pushprop_lem1 = $true)) & (lamnotvar = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X39 : (subst > term > subst > $o)] : ? [X40 : (term > $o)] : ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41)))) & ! [X84 : d_term] : (d_one = X84) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) <=> (axshiftcons = $true)) & ((hoaslaminj_lthm = $true) <=> (((! [X61 : subst,X63 : term,X64 : (subst > term > term),X62 : (subst > term > term)] : (? [X67 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) != ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63))) | ? [X69 : term,X70 : subst,X68 : subst] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) != ((sub @ (X64 @ X68 @ X69) @ X70))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one))))) | ? [X60 : term,X59 : term] : ((((lam @ X59)) = ((lam @ X60))) & (X59 != X60))) | ? [X57 : term,X58 : subst] : (((comp @ sh @ (push @ X57 @ X58))) != X58)) | ? [X55 : term,X56 : subst] : (((sub @ one @ (push @ X55 @ X56))) != X55))) & (! [X505 : term] : (((sub @ X505 @ id)) = X505) <=> (termmset = $true)) & ((? [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 != X126) & (((ap @ X124 @ X125)) = ((ap @ X123 @ X126)))) | ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((apinj2 = $true) <=> ! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399))) & (! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) <=> (laminj = $true))),
% 164.61/23.50 inference(ennf_transformation,[],[f10])).
% 164.61/23.50 thf(f12,plain,(
% 164.61/23.50 (axassoc = $true) & (axapp = $true) & ((axidl = $true) <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & (! [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true) | (((X254 @ X255)) != $true)) <=> (pushprop_lem1 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction = $true) <=> ! [X508 : term,X509 : (subst > term > subst > $o)] : (? [X522 : term,X525 : subst,X524 : subst,X523 : subst] : ((((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) = $true) & ($true != ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524)))) | ? [X514 : subst,X515 : subst,X516 : subst,X513 : term] : (($true != ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) & ($true = ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) | ? [X517 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id))) & ! [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) = ((sub @ (X517 @ X520 @ X521) @ X519))) & ! [X518 : term] : (($true = ((X509 @ id @ (X517 @ id @ X518) @ id))) | (((X509 @ id @ X518 @ id)) != $true))) | ? [X510 : term] : ((((var @ (sub @ X510 @ id))) = $true) & (((X509 @ id @ X510 @ id)) != $true)) | ($true = ((X509 @ id @ X508 @ id))) | ? [X512 : term,X511 : term] : ((((X509 @ id @ X512 @ id)) = $true) & ($true != ((X509 @ id @ (ap @ (sub @ X512 @ id) @ X511) @ id))) & ($true = ((X509 @ id @ X511 @ id)))))) & (! [X80 : term,X79 : (term > $o),X81 : subst] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))) <=> (pushprop_lem0 = $true)) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X307 : (subst > term > subst > $o),X308 : term] : (? [X310 : (subst > term > term)] : (! [X312 : subst,X311 : subst,X313 : term] : (((X310 @ (comp @ X312 @ X311) @ (sub @ X313 @ X311))) = ((sub @ (X310 @ X312 @ X313) @ X311))) & ! [X314 : term] : (($true = ((X307 @ id @ (X310 @ id @ X314) @ id))) | ($true != ((X307 @ id @ X314 @ id)))) & (((X307 @ id @ (lam @ (X310 @ sh @ one)) @ id)) != $true)) | ? [X317 : subst,X316 : term,X318 : subst,X315 : subst] : (($true = ((X307 @ (comp @ X315 @ X318) @ (sub @ X316 @ X318) @ X317))) & ($true != ((X307 @ X315 @ X316 @ (comp @ X318 @ X317))))) | ? [X320 : subst,X322 : subst,X319 : term,X321 : subst] : ((((X307 @ (comp @ X322 @ X321) @ (sub @ X319 @ X321) @ X320)) != $true) & ($true = ((X307 @ X322 @ X319 @ (comp @ X321 @ X320))))) | ($true = ((X307 @ id @ (lam @ X308) @ id))) | ? [X309 : term] : (($true = ((X307 @ id @ X309 @ id))) & ($true != ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id))))) | ? [X298 : term] : (((sub @ X298 @ id)) != X298) | ? [X300 : term,X299 : (subst > term > subst > $o)] : (! [X302 : (subst > term > term)] : ((((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ? [X304 : subst,X306 : term,X305 : subst] : (((X302 @ (comp @ X304 @ X305) @ (sub @ X306 @ X305))) != ((sub @ (X302 @ X304 @ X306) @ X305))) | ? [X303 : term] : (($true = ((X299 @ id @ X303 @ id))) & (((X299 @ id @ (X302 @ id @ X303) @ id)) != $true))) & ($true != ((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id))) & ! [X301 : term] : ((((X299 @ id @ (sub @ X300 @ (push @ X301 @ id)) @ id)) = $true) | ($true != ((X299 @ id @ X301 @ id))))))) & (hoasinduction_lem2_lthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) <=> ! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186))) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X191 : (subst > term > subst > $o),X190 : term] : (? [X192 : (subst > term > term)] : (($true != ((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : term,X193 : subst] : (((X192 @ (comp @ X194 @ X193) @ (sub @ X195 @ X193))) = ((sub @ (X192 @ X194 @ X195) @ X193))) & ! [X196 : term] : ((((X191 @ id @ X196 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X196) @ id)) = $true))) | ($true = ((X191 @ id @ (lam @ X190) @ id))) | ? [X197 : term] : ((((X191 @ id @ X197 @ id)) = $true) & (((X191 @ id @ (sub @ X190 @ (push @ X197 @ id)) @ id)) != $true)))) & ((hoasapinj1 = $true) <=> ! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367))) & (! [X168 : (term > $o),X167 : term,X169 : term,X170 : (subst > term > subst > $o)] : (? [X175 : subst,X174 : subst,X173 : term,X176 : subst] : (($true = ((X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174))) & (((X170 @ X175 @ X173 @ (comp @ X176 @ X174))) != $true)) | ? [X177 : term] : (((X170 @ id @ X177 @ id)) != ((X168 @ X177))) | ? [X181 : term,X178 : subst,X180 : subst,X179 : subst] : (($true != ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179))) & ($true = ((X170 @ X180 @ X181 @ (comp @ X178 @ X179))))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X167 @ X169))) = $true) | ? [X172 : term,X171 : term] : ((((X170 @ id @ X172 @ id)) = $true) & (((X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id)) != $true) & ($true = ((X170 @ id @ X171 @ id)))) | ($true != ((X168 @ X167)))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X39 : (subst > term > subst > $o)] : ? [X40 : (term > $o)] : ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (induction2_gthm = $true) & (((! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376)) | ? [X374 : subst] : (((comp @ X374 @ id)) != X374) | ? [X373 : subst] : (((comp @ id @ X373)) != X373)) <=> (substmonoid_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem2 = $true) <=> ! [X258 : term,X259 : term,X260 : (subst > term > subst > $o)] : (($true = ((X260 @ id @ (ap @ X258 @ X259) @ id))) | ? [X266 : term,X265 : term] : (($true = ((X260 @ id @ X265 @ id))) & ($true = ((X260 @ id @ X266 @ id))) & ($true != ((X260 @ id @ (ap @ (sub @ X265 @ id) @ X266) @ id)))) | ? [X270 : term,X267 : subst,X268 : subst,X269 : subst] : (($true != ((X260 @ (comp @ X269 @ X268) @ (sub @ X270 @ X268) @ X267))) & ($true = ((X260 @ X269 @ X270 @ (comp @ X268 @ X267))))) | ? [X264 : subst,X262 : subst,X261 : subst,X263 : term] : ((((X260 @ X264 @ X263 @ (comp @ X262 @ X261))) != $true) & ($true = ((X260 @ (comp @ X264 @ X262) @ (sub @ X263 @ X262) @ X261)))) | ($true != ((X260 @ id @ X259 @ id))) | (((X260 @ id @ X258 @ id)) != $true))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (? [X495 : term] : (((X491 @ X495)) != ((X492 @ id @ X495 @ id))) | ($true = ((X491 @ (lam @ X493)))) | ? [X494 : term] : ((((X491 @ X494)) = $true) & (((X491 @ (sub @ X493 @ (push @ X494 @ id)))) != $true)) | ? [X496 : (subst > term > term)] : (! [X500 : term,X498 : subst,X499 : subst] : (((sub @ (X496 @ X499 @ X500) @ X498)) = ((X496 @ (comp @ X499 @ X498) @ (sub @ X500 @ X498)))) & ($true != ((X492 @ id @ (lam @ (X496 @ sh @ one)) @ id))) & ! [X497 : term] : ((((X492 @ id @ X497 @ id)) != $true) | (((X492 @ id @ (X496 @ id @ X497) @ id)) = $true))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((pushprop_lem1_lthm = $true) <=> (! [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | (((X252 @ X251)) != $true)) | ? [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) != X246) | ? [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) != X245))) & (lamnotvar = $true) & (! [X505 : term] : (((sub @ X505 @ id)) = X505) <=> (termmset = $true)) & (! [X291 : (subst > term > subst > $o),X290 : term] : (($true = ((X291 @ id @ (lam @ (sub @ X290 @ (push @ one @ sh))) @ id))) | ? [X297 : term] : ((((X291 @ id @ X297 @ id)) = $true) & ($true != ((X291 @ id @ (sub @ X290 @ (push @ X297 @ id)) @ id)))) | ? [X292 : (subst > term > term)] : (! [X293 : term] : ((((X291 @ id @ X293 @ id)) != $true) | (((X291 @ id @ (X292 @ id @ X293) @ id)) = $true)) & ! [X294 : subst,X295 : subst,X296 : term] : (((X292 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))) = ((sub @ (X292 @ X295 @ X296) @ X294))) & ($true != ((X291 @ id @ (lam @ (X292 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((? [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 != X392) & (((ap @ X390 @ X391)) = ((ap @ X392 @ X393)))) | ? [X389 : term] : (((sub @ X389 @ id)) != X389) | ! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) <=> (? [X412 : term] : (((sub @ X412 @ id)) != X412) | ! [X422 : (term > $o),X421 : term] : (? [X424 : term] : (($true != ((X422 @ (lam @ X424)))) & ! [X425 : term] : ((((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true) | (((X422 @ X425)) != $true))) | ? [X423 : term] : (($true = ((var @ X423))) & ($true != ((X422 @ X423)))) | ($true = ((X422 @ X421))) | ? [X426 : term,X427 : term] : (($true = ((X422 @ X426))) & (((X422 @ X427)) = $true) & (((X422 @ (ap @ X426 @ X427))) != $true))) | ? [X415 : subst,X414 : term,X413 : (term > $o)] : (! [X420 : term] : (($true = ((X413 @ (sub @ X420 @ X415)))) | (((var @ X420)) != $true)) & (((X413 @ (sub @ X414 @ X415))) != $true) & ! [X418 : term] : (? [X419 : term] : ((((X413 @ X419)) = $true) & (((X413 @ (sub @ X418 @ (push @ X419 @ id)))) != $true)) | ($true = ((X413 @ (lam @ X418))))) & ! [X416 : term,X417 : term] : (($true != ((X413 @ X417))) | ($true = ((X413 @ (ap @ X416 @ X417)))) | ($true != ((X413 @ X416))))))) & (hoasinduction_lem3_gthm = $true) & (lamnotap != $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X526 : term] : ? [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) = ((X527 @ sh @ one)))) & (axabs = $true) & ! [X84 : d_term] : (d_one = X84) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X229 : (subst > term > subst > $o),X228 : term] : (? [X243 : term] : ((((X229 @ id @ X243 @ id)) = $true) & (((X229 @ id @ (sub @ X228 @ (push @ X243 @ id)) @ id)) != $true)) | ? [X239 : subst,X241 : term,X242 : subst,X240 : subst] : ((((X229 @ X239 @ X241 @ (comp @ X242 @ X240))) = $true) & (((X229 @ (comp @ X239 @ X242) @ (sub @ X241 @ X242) @ X240)) != $true)) | ($true = ((X229 @ id @ (lam @ X228) @ id))) | ? [X230 : (subst > term > term)] : (! [X232 : subst,X233 : subst,X231 : term] : (((sub @ (X230 @ X233 @ X231) @ X232)) = ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) & (((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id)) != $true) & ! [X234 : term] : ((((X229 @ id @ (X230 @ id @ X234) @ id)) = $true) | ($true != ((X229 @ id @ X234 @ id))))) | ? [X238 : term,X236 : subst,X235 : subst,X237 : subst] : (($true = ((X229 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237) @ X235))) & (((X229 @ X236 @ X238 @ (comp @ X237 @ X235))) != $true))) <=> (hoasinduction_lem3 = $true)) & ((axvarcons = $true) <=> ! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501)) & (substmonoid_gthm = $true) & ((hoasinduction_lthm = $true) <=> (? [X438 : term,X437 : (term > $o)] : (! [X443 : term] : ((((var @ X443)) != $true) | (((X437 @ X443)) = $true)) & (((X437 @ X438)) != $true) & ! [X441 : term] : (($true = ((X437 @ (lam @ X441)))) | ? [X442 : term] : (($true = ((X437 @ X442))) & (((X437 @ (sub @ X441 @ (push @ X442 @ id)))) != $true))) & ! [X439 : term,X440 : term] : (($true = ((X437 @ (ap @ X440 @ X439)))) | (((X437 @ X440)) != $true) | ($true != ((X437 @ X439))))) | ! [X473 : (subst > term > subst > $o),X474 : term] : (? [X489 : term,X490 : term] : ((((X473 @ id @ X490 @ id)) = $true) & (((X473 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id)) != $true) & (((X473 @ id @ X489 @ id)) = $true)) | ? [X480 : (subst > term > term)] : (! [X481 : term] : (($true != ((X473 @ id @ X481 @ id))) | (((X473 @ id @ (X480 @ id @ X481) @ id)) = $true)) & ($true != ((X473 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X484 : subst,X482 : term,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))) | ($true = ((X473 @ id @ X474 @ id))) | ? [X488 : subst,X486 : term,X487 : subst,X485 : subst] : ((((X473 @ X488 @ X486 @ (comp @ X487 @ X485))) = $true) & ($true != ((X473 @ (comp @ X488 @ X487) @ (sub @ X486 @ X487) @ X485)))) | ? [X476 : subst,X478 : subst,X477 : subst,X479 : term] : (($true = ((X473 @ (comp @ X478 @ X477) @ (sub @ X479 @ X477) @ X476))) & (((X473 @ X478 @ X479 @ (comp @ X477 @ X476))) != $true)) | ? [X475 : term] : ((((X473 @ id @ X475 @ id)) != $true) & ($true = ((var @ (sub @ X475 @ id)))))) | ? [X458 : term,X457 : (subst > term > subst > $o)] : (! [X459 : (subst > term > term)] : (? [X461 : term,X462 : subst,X463 : subst] : (((X459 @ (comp @ X463 @ X462) @ (sub @ X461 @ X462))) != ((sub @ (X459 @ X463 @ X461) @ X462))) | ? [X460 : term] : ((((X457 @ id @ X460 @ id)) = $true) & (((X457 @ id @ (X459 @ id @ X460) @ id)) != $true)) | (((X457 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true)) & ! [X468 : subst,X465 : subst,X466 : term,X467 : subst] : ((((X457 @ (comp @ X465 @ X468) @ (sub @ X466 @ X468) @ X467)) = $true) | (((X457 @ X465 @ X466 @ (comp @ X468 @ X467))) != $true)) & ! [X469 : term,X471 : subst,X470 : subst,X472 : subst] : ((((X457 @ X470 @ X469 @ (comp @ X471 @ X472))) = $true) | (((X457 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471) @ X472)) != $true)) & ! [X464 : term] : ((((X457 @ id @ X464 @ id)) != $true) | ($true = ((X457 @ id @ (sub @ X458 @ (push @ X464 @ id)) @ id)))) & (((X457 @ id @ (lam @ X458) @ id)) != $true)) | ? [X444 : term,X446 : (subst > term > subst > $o),X445 : term] : ((((X446 @ id @ X445 @ id)) = $true) & ! [X456 : term,X455 : term] : ((((X446 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id)) = $true) | (((X446 @ id @ X455 @ id)) != $true) | ($true != ((X446 @ id @ X456 @ id)))) & ! [X448 : subst,X447 : subst,X450 : subst,X449 : term] : ((((X446 @ X447 @ X449 @ (comp @ X450 @ X448))) != $true) | (((X446 @ (comp @ X447 @ X450) @ (sub @ X449 @ X450) @ X448)) = $true)) & ! [X454 : subst,X453 : term,X452 : subst,X451 : subst] : ((((X446 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451) @ X454)) != $true) | (((X446 @ X452 @ X453 @ (comp @ X451 @ X454))) = $true)) & ($true != ((X446 @ id @ (ap @ X445 @ X444) @ id))) & ($true = ((X446 @ id @ X444 @ id)))))) & (! [X85 : term] : ? [X86 : (subst > term > term)] : ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88)))) <=> (hoasinduction_lem3v2_f = $true)) & (ulamvarsh = $true) & (termmset_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslamnotap = $true) <=> ! [X380 : term,X379 : term,X381 : (subst > term > term)] : (? [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) != ((sub @ (X381 @ X383 @ X382) @ X384))) | (((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one)))))) & ((axidr = $true) <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & (hoasinduction_lem1v2_gthm = $true) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) != ((d2subst @ X183))) | (X182 = X183)) & ((? [X275 : subst] : (((comp @ X275 @ id)) != X275) | ? [X274 : term,X273 : subst] : (((comp @ sh @ (push @ X274 @ X273))) != X273) | ? [X276 : term,X277 : (term > $o)] : (! [X279 : term,X278 : term] : (($true = ((X277 @ (ap @ X278 @ X279)))) | (((X277 @ X279)) != $true) | (((X277 @ X278)) != $true)) & ! [X281 : term] : (($true = ((X277 @ (lam @ X281)))) | (((X277 @ X281)) != $true)) & ($true != ((X277 @ X276))) & ! [X280 : term] : (($true != ((var @ X280))) | ($true = ((X277 @ X280))))) | ! [X284 : (term > $o),X282 : subst,X283 : term] : (? [X287 : term] : ((((X284 @ (sub @ X287 @ X282))) != $true) & ($true = ((var @ X287)))) | (((X284 @ (sub @ X283 @ X282))) = $true) | ? [X286 : term,X285 : term] : (($true != ((X284 @ (ap @ X285 @ X286)))) & (((X284 @ X285)) = $true) & ($true = ((X284 @ X286)))) | ? [X288 : term] : (! [X289 : term] : (($true != ((X284 @ X289))) | ($true = ((X284 @ (sub @ X288 @ (push @ X289 @ id)))))) & ($true != ((X284 @ (lam @ X288)))))) | ? [X271 : subst,X272 : term] : (((sub @ one @ (push @ X272 @ X271))) != X272)) <=> (induction2lem_lthm = $true)) & ((apinj2 = $true) <=> ! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X149 : (subst > term > subst > $o),X151 : term,X150 : (term > $o)] : (? [X160 : subst,X161 : subst,X162 : subst,X159 : term] : (($true != ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)))) & (((X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) = $true)) | ? [X158 : term] : (((X149 @ id @ X158 @ id)) != ((X150 @ X158))) | ? [X157 : term] : (($true = ((X150 @ X157))) & (((X150 @ (sub @ X151 @ (push @ X157 @ id)))) != $true)) | ? [X152 : (subst > term > term)] : (! [X153 : term] : ((((X149 @ id @ X153 @ id)) != $true) | (((X149 @ id @ (X152 @ id @ X153) @ id)) = $true)) & ! [X154 : subst,X156 : term,X155 : subst] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155))) & ($true != ((X149 @ id @ (lam @ (X152 @ sh @ one)) @ id)))) | ? [X166 : subst,X165 : subst,X163 : term,X164 : subst] : (($true != ((X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165))) & (((X149 @ X166 @ X163 @ (comp @ X164 @ X165))) = $true)) | ($true = ((X150 @ (lam @ X151)))))) & ((induction2lem = $true) <=> ! [X404 : (term > $o),X402 : subst,X403 : term] : (? [X405 : term] : (! [X406 : term] : (($true != ((X404 @ X406))) | ($true = ((X404 @ (sub @ X405 @ (push @ X406 @ id)))))) & (((X404 @ (lam @ X405))) != $true)) | ? [X409 : term] : ((((X404 @ (sub @ X409 @ X402))) != $true) & ($true = ((var @ X409)))) | ($true = ((X404 @ (sub @ X403 @ X402)))) | ? [X408 : term,X407 : term] : (($true != ((X404 @ (ap @ X407 @ X408)))) & (((X404 @ X407)) = $true) & (((X404 @ X408)) = $true)))) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (pushprop = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) <=> (axscons = $true)) & (hoasinduction_lem1v2 = $true) & (! [X73 : term,X72 : (term > $o)] : (? [X76 : term] : (($true = ((var @ X76))) & ($true != ((X72 @ X76)))) | ? [X74 : term,X75 : term] : ((((X72 @ X75)) = $true) & ($true = ((X72 @ X74))) & ($true != ((X72 @ (ap @ X75 @ X74))))) | (((X72 @ X73)) = $true) | ? [X77 : term] : ((((X72 @ (lam @ X77))) != $true) & ! [X78 : term] : ((((X72 @ X78)) != $true) | (((X72 @ (sub @ X77 @ (push @ X78 @ id)))) = $true)))) <=> (induction2 = $true)) & (pushprop_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X136 : term] : ? [X137 : (subst > term > term)] : ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139)))) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((? [X377 : term] : (((sub @ X377 @ id)) != X377) | ! [X378 : term] : (((sub @ X378 @ id)) = X378)) <=> (termmset_lthm = $true)) & ((hoaslaminj = $true) <=> ! [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | (((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | ? [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) != ((sub @ (X42 @ X49 @ X51) @ X50))) | ? [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) != ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (((d2subst @ d_id)) = sh) & ((axvarid = $true) <=> ! [X388 : term] : (((sub @ X388 @ id)) = X388)) & (! [X188 : term] : ? [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) = ((X189 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((! [X220 : term,X219 : (subst > term > subst > $o)] : (? [X226 : term,X227 : term] : ((((X219 @ id @ X227 @ id)) = $true) & ($true = ((X219 @ id @ X226 @ id))) & (((X219 @ id @ (ap @ (sub @ X227 @ id) @ X226) @ id)) != $true)) | ? [X221 : (subst > term > term)] : (! [X225 : term] : (($true != ((X219 @ id @ X225 @ id))) | (((X219 @ id @ (X221 @ id @ X225) @ id)) = $true)) & ($true != ((X219 @ id @ (lam @ (X221 @ sh @ one)) @ id))) & ! [X222 : subst,X223 : term,X224 : subst] : (((sub @ (X221 @ X224 @ X223) @ X222)) = ((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))))) | ($true = ((X219 @ id @ X220 @ id)))) | ? [X198 : (subst > term > subst > $o)] : ! [X199 : (term > $o)] : ? [X200 : term] : (((X198 @ id @ X200 @ id)) != ((X199 @ X200))) | ? [X211 : (term > $o),X209 : term,X210 : (subst > term > subst > $o)] : (! [X218 : term] : ((((X211 @ X218)) != $true) | ($true = ((X211 @ (sub @ X209 @ (push @ X218 @ id)))))) & ! [X212 : (subst > term > term)] : (? [X213 : term,X215 : subst,X214 : subst] : (((sub @ (X212 @ X214 @ X213) @ X215)) != ((X212 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)))) | (((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id)) = $true) | ? [X216 : term] : (($true = ((X210 @ id @ X216 @ id))) & (((X210 @ id @ (X212 @ id @ X216) @ id)) != $true))) & ! [X217 : term] : (((X210 @ id @ X217 @ id)) = ((X211 @ X217))) & ($true != ((X211 @ (lam @ X209))))) | ? [X202 : term,X201 : (term > $o)] : (! [X204 : term,X205 : term] : (($true != ((X201 @ X204))) | (((X201 @ X205)) != $true) | ($true = ((X201 @ (ap @ X204 @ X205))))) & ! [X203 : term] : ((((X201 @ X203)) = $true) | ($true != ((var @ X203)))) & (((X201 @ X202)) != $true) & ! [X206 : term] : (? [X207 : term] : (($true != ((X201 @ (sub @ X206 @ (push @ X207 @ id))))) & (((X201 @ X207)) = $true)) | ($true = ((X201 @ (lam @ X206)))))) | ? [X208 : term] : (((sub @ X208 @ id)) != X208)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) <=> (laminj = $true)) & (hoasinduction_lem1 = $true) & (! [X323 : (subst > term > subst > $o),X324 : term] : (? [X325 : (subst > term > term)] : (($true != ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) & ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ($true != ((X323 @ id @ X329 @ id)))) & ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) | (((X323 @ id @ X324 @ id)) = $true) | ? [X331 : term,X330 : term] : (($true != ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) & (((X323 @ id @ X331 @ id)) = $true) & ($true = ((X323 @ id @ X330 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) != $true) | ? [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) != ((X131 @ X135))) | (((X131 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) <=> (shinj = $true)) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & (one = ((d2term @ d_one))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem2v2_gthm = $true) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ? [X145 : (term > $o)] : ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) <=> (pushprop_lem0_lthm = $true)) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & ((? [X89 : term] : ! [X90 : (subst > term > term)] : ? [X91 : term,X92 : subst] : (((sub @ X89 @ (push @ X91 @ X92))) != ((X90 @ X92 @ X91))) | ? [X93 : term] : (((sub @ X93 @ id)) != X93) | ! [X94 : term,X95 : (term > $o),X96 : (subst > term > subst > $o)] : (? [X97 : term] : (((X95 @ X97)) != ((X96 @ id @ X97 @ id))) | ? [X98 : term] : (($true = ((X95 @ X98))) & ($true != ((X95 @ (sub @ X94 @ (push @ X98 @ id)))))) | ? [X99 : (subst > term > term)] : (! [X100 : subst,X102 : subst,X101 : term] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) & ! [X103 : term] : (($true != ((X96 @ id @ X103 @ id))) | (((X96 @ id @ (X99 @ id @ X103) @ id)) = $true)) & (((X96 @ id @ (lam @ (X99 @ sh @ one)) @ id)) != $true)) | (((X95 @ (lam @ X94))) = $true))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoaslaminj_lthm = $true) <=> (? [X57 : term,X58 : subst] : (((comp @ sh @ (push @ X57 @ X58))) != X58) | ! [X61 : subst,X63 : term,X64 : (subst > term > term),X62 : (subst > term > term)] : (? [X67 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) != ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63))) | ? [X69 : term,X70 : subst,X68 : subst] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) != ((sub @ (X64 @ X68 @ X69) @ X70))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one))))) | ? [X55 : term,X56 : subst] : (((sub @ one @ (push @ X55 @ X56))) != X55) | ? [X60 : term,X59 : term] : ((((lam @ X59)) = ((lam @ X60))) & (X59 != X60)))) & (! [X385 : (subst > term > subst > $o)] : ? [X386 : (term > $o)] : ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) <=> (hoasinduction_lem0 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) <=> (axshiftcons = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) != X338) | ! [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) != $true) | ? [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) != ((X343 @ X344))) | (((X343 @ one)) = $true)))) & (axvarshift = $true) & (! [X528 : term,X529 : (subst > term > subst > $o)] : (? [X531 : term,X530 : (subst > term > term)] : (! [X535 : term,X534 : subst,X533 : subst] : (((sub @ (sub @ X531 @ (push @ X535 @ X533)) @ X534)) = ((sub @ (X530 @ X533 @ X535) @ X534))) & ! [X532 : term] : ((((X529 @ id @ X532 @ id)) != $true) | (((X529 @ id @ (X530 @ id @ X532) @ id)) = $true)) & ($true != ((X529 @ id @ (lam @ (X530 @ sh @ one)) @ id))) & ! [X538 : subst,X537 : term,X536 : subst] : (((sub @ X531 @ (push @ (sub @ X537 @ X538) @ (comp @ X536 @ X538)))) = ((X530 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538))))) | ? [X539 : term] : ((((X529 @ id @ X539 @ id)) = $true) & (((X529 @ id @ (sub @ X528 @ (push @ X539 @ id)) @ id)) != $true)) | (((X529 @ id @ (lam @ (sub @ X528 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (! [X428 : (subst > term > subst > $o),X429 : term] : (($true = ((X428 @ id @ (lam @ (sub @ X429 @ (push @ one @ sh))) @ id))) | ? [X430 : (subst > term > term)] : (! [X432 : subst,X433 : term,X434 : subst] : (((X430 @ (comp @ X434 @ X432) @ (sub @ X433 @ X432))) = ((sub @ (X430 @ X434 @ X433) @ X432))) & (((X428 @ id @ (lam @ (X430 @ sh @ one)) @ id)) != $true) & ! [X431 : term] : (($true = ((X428 @ id @ (X430 @ id @ X431) @ id))) | (((X428 @ id @ X431 @ id)) != $true))) | ? [X435 : term] : ((((X428 @ id @ X435 @ id)) = $true) & ($true != ((X428 @ id @ (sub @ X429 @ (push @ X435 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasapinj2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | ? [X13 : (term > $o),X12 : (subst > term > subst > $o),X11 : term] : (! [X19 : term] : ((((X13 @ X19)) != $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X19 @ id)))))) & ! [X14 : (subst > term > term)] : ((((X12 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X18 : term] : (($true != ((X12 @ id @ (X14 @ id @ X18) @ id))) & (((X12 @ id @ X18 @ id)) = $true)) | ? [X17 : subst,X15 : subst,X16 : term] : (((sub @ (X14 @ X15 @ X16) @ X17)) != ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17))))) & ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id))) & ($true != ((X13 @ (lam @ X11))))) | ! [X22 : term,X21 : (subst > term > subst > $o)] : (? [X34 : term,X33 : term] : (($true = ((X21 @ id @ X33 @ id))) & (((X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id)) != $true) & (((X21 @ id @ X34 @ id)) = $true)) | ($true = ((X21 @ id @ X22 @ id))) | ? [X32 : term] : ((((var @ (sub @ X32 @ id))) = $true) & ($true != ((X21 @ id @ X32 @ id)))) | ? [X37 : subst,X38 : term,X36 : subst,X35 : subst] : (($true = ((X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))) & (((X21 @ X35 @ X38 @ (comp @ X37 @ X36))) != $true)) | ? [X25 : subst,X26 : term,X23 : subst,X24 : subst] : (($true = ((X21 @ X25 @ X26 @ (comp @ X24 @ X23)))) & (((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23)) != $true)) | ? [X27 : (subst > term > term)] : (! [X28 : term] : ((((X21 @ id @ (X27 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id)))) & ! [X30 : subst,X29 : term,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) & (((X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) != $true))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X4 : term,X3 : (term > $o)] : (! [X9 : term,X8 : term] : (($true = ((X3 @ (ap @ X9 @ X8)))) | ($true != ((X3 @ X9))) | (((X3 @ X8)) != $true)) & ($true != ((X3 @ X4))) & ! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & ! [X5 : term] : ((((X3 @ X5)) = $true) | ($true != ((var @ X5)))))) <=> (hoasinduction_lthm_3 = $true)) & ((? [X104 : term] : (((sub @ X104 @ id)) != X104) | ! [X105 : (subst > term > subst > $o),X106 : term,X107 : (term > $o)] : (? [X108 : subst,X109 : subst,X111 : subst,X110 : term] : (($true = ((X105 @ X111 @ X110 @ (comp @ X108 @ X109)))) & ($true != ((X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)))) | ? [X114 : term,X115 : subst,X113 : subst,X116 : subst] : ((((X105 @ X113 @ X114 @ (comp @ X115 @ X116))) != $true) & ($true = ((X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116)))) | ? [X117 : (subst > term > term)] : (! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) & (((X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) != $true) & ! [X118 : term] : ((((X105 @ id @ (X117 @ id @ X118) @ id)) = $true) | (((X105 @ id @ X118 @ id)) != $true))) | ? [X122 : term] : (((X107 @ X122)) != ((X105 @ id @ X122 @ id))) | ($true = ((X107 @ (lam @ X106)))) | ? [X112 : term] : (($true = ((X107 @ X112))) & ($true != ((X107 @ (sub @ X106 @ (push @ X112 @ id)))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) <=> (hoasapinj2 = $true)) & (hoaslamnotvar_lthm = $true) & ((? [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 != X126) & (((ap @ X124 @ X125)) = ((ap @ X123 @ X126)))) | ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) <=> (hoasapinj2_lthm = $true)) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) != ((d2term @ X507))) | (X506 = X507)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (apnotvar = $true) & ((! [X358 : (subst > term > subst > $o),X357 : term] : (? [X360 : (subst > term > term)] : (! [X363 : subst,X361 : term,X362 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) & ! [X364 : term] : (($true = ((X358 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X358 @ id @ X364 @ id)))) & (((X358 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true)) | ? [X359 : term] : (($true = ((X358 @ id @ X359 @ id))) & (((X358 @ id @ (sub @ X357 @ (push @ X359 @ id)) @ id)) != $true)) | (((X358 @ id @ (lam @ X357) @ id)) = $true)) | ? [X350 : (subst > term > subst > $o),X349 : term] : (! [X351 : term] : ((((X350 @ id @ X351 @ id)) != $true) | (((X350 @ id @ (sub @ X349 @ (push @ X351 @ id)) @ id)) = $true)) & ($true != ((X350 @ id @ (lam @ (sub @ X349 @ (push @ one @ sh))) @ id))) & ! [X352 : (subst > term > term)] : (? [X353 : term] : ((((X350 @ id @ (X352 @ id @ X353) @ id)) != $true) & (((X350 @ id @ X353 @ id)) = $true)) | ? [X356 : subst,X354 : term,X355 : subst] : (((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355))) != ((sub @ (X352 @ X356 @ X354) @ X355))) | ($true = ((X350 @ id @ (lam @ (X352 @ sh @ one)) @ id))))) | ? [X348 : term] : (((sub @ X348 @ id)) != X348)) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) = $true) | ? [X336 : term,X335 : term] : ((((X332 @ X336)) = $true) & ($true = ((X332 @ X335))) & ($true != ((X332 @ (ap @ X335 @ X336))))) | ? [X337 : term] : (($true != ((X332 @ (lam @ X337)))) & (((X332 @ X337)) = $true)) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X332 @ X334)) != $true))) <=> (induction = $true)) & ((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) <=> (substmonoid = $true)) & ! [X436 : d_subst] : (d_id = X436)),
% 164.61/23.50 inference(flattening,[],[f11])).
% 164.61/23.50 thf(f13,definition,(
% 164.61/23.50 ! [X332 : (term > $o)] : (($true = ((sP0 @ X332))) <=> ? [X336 : term,X335 : term] : ((((X332 @ X336)) = $true) & ($true = ((X332 @ X335))) & ($true != ((X332 @ (ap @ X335 @ X336))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f14,definition,(
% 164.61/23.50 (sP1 = $true) <=> ? [X350 : (subst > term > subst > $o),X349 : term] : (! [X351 : term] : ((((X350 @ id @ X351 @ id)) != $true) | (((X350 @ id @ (sub @ X349 @ (push @ X351 @ id)) @ id)) = $true)) & ($true != ((X350 @ id @ (lam @ (sub @ X349 @ (push @ one @ sh))) @ id))) & ! [X352 : (subst > term > term)] : (? [X353 : term] : ((((X350 @ id @ (X352 @ id @ X353) @ id)) != $true) & (((X350 @ id @ X353 @ id)) = $true)) | ? [X356 : subst,X354 : term,X355 : subst] : (((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355))) != ((sub @ (X352 @ X356 @ X354) @ X355))) | ($true = ((X350 @ id @ (lam @ (X352 @ sh @ one)) @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f15,definition,(
% 164.61/23.50 ($true = sP2) <=> (! [X358 : (subst > term > subst > $o),X357 : term] : (? [X360 : (subst > term > term)] : (! [X363 : subst,X361 : term,X362 : subst] : (((X360 @ (comp @ X363 @ X362) @ (sub @ X361 @ X362))) = ((sub @ (X360 @ X363 @ X361) @ X362))) & ! [X364 : term] : (($true = ((X358 @ id @ (X360 @ id @ X364) @ id))) | ($true != ((X358 @ id @ X364 @ id)))) & (((X358 @ id @ (lam @ (X360 @ sh @ one)) @ id)) != $true)) | ? [X359 : term] : (($true = ((X358 @ id @ X359 @ id))) & (((X358 @ id @ (sub @ X357 @ (push @ X359 @ id)) @ id)) != $true)) | (((X358 @ id @ (lam @ X357) @ id)) = $true)) | (sP1 = $true) | ? [X348 : term] : (((sub @ X348 @ id)) != X348))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f16,definition,(
% 164.61/23.50 ! [X105 : (subst > term > subst > $o)] : ((((sP3 @ X105)) = $true) <=> ? [X117 : (subst > term > term)] : (! [X119 : subst,X120 : term,X121 : subst] : (((X117 @ (comp @ X121 @ X119) @ (sub @ X120 @ X119))) = ((sub @ (X117 @ X121 @ X120) @ X119))) & (((X105 @ id @ (lam @ (X117 @ sh @ one)) @ id)) != $true) & ! [X118 : term] : ((((X105 @ id @ (X117 @ id @ X118) @ id)) = $true) | (((X105 @ id @ X118 @ id)) != $true))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f17,definition,(
% 164.61/23.50 (sP4 = $true) <=> (? [X104 : term] : (((sub @ X104 @ id)) != X104) | ! [X105 : (subst > term > subst > $o),X106 : term,X107 : (term > $o)] : (? [X108 : subst,X109 : subst,X111 : subst,X110 : term] : (($true = ((X105 @ X111 @ X110 @ (comp @ X108 @ X109)))) & ($true != ((X105 @ (comp @ X111 @ X108) @ (sub @ X110 @ X108) @ X109)))) | ? [X114 : term,X115 : subst,X113 : subst,X116 : subst] : ((((X105 @ X113 @ X114 @ (comp @ X115 @ X116))) != $true) & ($true = ((X105 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115) @ X116)))) | (((sP3 @ X105)) = $true) | ? [X122 : term] : (((X107 @ X122)) != ((X105 @ id @ X122 @ id))) | ($true = ((X107 @ (lam @ X106)))) | ? [X112 : term] : (($true = ((X107 @ X112))) & ($true != ((X107 @ (sub @ X106 @ (push @ X112 @ id))))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f18,definition,(
% 164.61/23.50 ! [X3 : (term > $o)] : ((((sP5 @ X3)) = $true) <=> ! [X9 : term,X8 : term] : (($true = ((X3 @ (ap @ X9 @ X8)))) | ($true != ((X3 @ X9))) | (((X3 @ X8)) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f19,definition,(
% 164.61/23.50 ! [X21 : (subst > term > subst > $o)] : ((((sP6 @ X21)) = $true) <=> ? [X27 : (subst > term > term)] : (! [X28 : term] : ((((X21 @ id @ (X27 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id)))) & ! [X30 : subst,X29 : term,X31 : subst] : (((X27 @ (comp @ X31 @ X30) @ (sub @ X29 @ X30))) = ((sub @ (X27 @ X31 @ X29) @ X30))) & (((X21 @ id @ (lam @ (X27 @ sh @ one)) @ id)) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f20,definition,(
% 164.61/23.50 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP7 @ X21))) <=> ? [X34 : term,X33 : term] : (($true = ((X21 @ id @ X33 @ id))) & (((X21 @ id @ (ap @ (sub @ X33 @ id) @ X34) @ id)) != $true) & (((X21 @ id @ X34 @ id)) = $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f21,definition,(
% 164.61/23.50 (sP8 = $true) <=> ! [X22 : term,X21 : (subst > term > subst > $o)] : (($true = ((sP7 @ X21))) | ($true = ((X21 @ id @ X22 @ id))) | ? [X32 : term] : ((((var @ (sub @ X32 @ id))) = $true) & ($true != ((X21 @ id @ X32 @ id)))) | ? [X37 : subst,X38 : term,X36 : subst,X35 : subst] : (($true = ((X21 @ (comp @ X35 @ X37) @ (sub @ X38 @ X37) @ X36))) & (((X21 @ X35 @ X38 @ (comp @ X37 @ X36))) != $true)) | ? [X25 : subst,X26 : term,X23 : subst,X24 : subst] : (($true = ((X21 @ X25 @ X26 @ (comp @ X24 @ X23)))) & (((X21 @ (comp @ X25 @ X24) @ (sub @ X26 @ X24) @ X23)) != $true)) | (((sP6 @ X21)) = $true))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f22,definition,(
% 164.61/23.50 (sP9 = $true) <=> ? [X13 : (term > $o),X12 : (subst > term > subst > $o),X11 : term] : (! [X19 : term] : ((((X13 @ X19)) != $true) | ($true = ((X13 @ (sub @ X11 @ (push @ X19 @ id)))))) & ! [X14 : (subst > term > term)] : ((((X12 @ id @ (lam @ (X14 @ sh @ one)) @ id)) = $true) | ? [X18 : term] : (($true != ((X12 @ id @ (X14 @ id @ X18) @ id))) & (((X12 @ id @ X18 @ id)) = $true)) | ? [X17 : subst,X15 : subst,X16 : term] : (((sub @ (X14 @ X15 @ X16) @ X17)) != ((X14 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17))))) & ! [X20 : term] : (((X13 @ X20)) = ((X12 @ id @ X20 @ id))) & ($true != ((X13 @ (lam @ X11)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f23,definition,(
% 164.61/23.50 ($true = sP10) <=> (? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | (sP9 = $true) | (sP8 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X4 : term,X3 : (term > $o)] : ((((sP5 @ X3)) = $true) & ($true != ((X3 @ X4))) & ! [X6 : term] : (? [X7 : term] : ((((X3 @ X7)) = $true) & (((X3 @ (sub @ X6 @ (push @ X7 @ id)))) != $true)) | (((X3 @ (lam @ X6))) = $true)) & ! [X5 : term] : ((((X3 @ X5)) = $true) | ($true != ((var @ X5))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f24,definition,(
% 164.61/23.50 (sP11 = $true) <=> ! [X428 : (subst > term > subst > $o),X429 : term] : (($true = ((X428 @ id @ (lam @ (sub @ X429 @ (push @ one @ sh))) @ id))) | ? [X430 : (subst > term > term)] : (! [X432 : subst,X433 : term,X434 : subst] : (((X430 @ (comp @ X434 @ X432) @ (sub @ X433 @ X432))) = ((sub @ (X430 @ X434 @ X433) @ X432))) & (((X428 @ id @ (lam @ (X430 @ sh @ one)) @ id)) != $true) & ! [X431 : term] : (($true = ((X428 @ id @ (X430 @ id @ X431) @ id))) | (((X428 @ id @ X431 @ id)) != $true))) | ? [X435 : term] : ((((X428 @ id @ X435 @ id)) = $true) & ($true != ((X428 @ id @ (sub @ X429 @ (push @ X435 @ id)) @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f25,definition,(
% 164.61/23.50 (sP12 = $true) <=> ! [X528 : term,X529 : (subst > term > subst > $o)] : (? [X531 : term,X530 : (subst > term > term)] : (! [X535 : term,X534 : subst,X533 : subst] : (((sub @ (sub @ X531 @ (push @ X535 @ X533)) @ X534)) = ((sub @ (X530 @ X533 @ X535) @ X534))) & ! [X532 : term] : ((((X529 @ id @ X532 @ id)) != $true) | (((X529 @ id @ (X530 @ id @ X532) @ id)) = $true)) & ($true != ((X529 @ id @ (lam @ (X530 @ sh @ one)) @ id))) & ! [X538 : subst,X537 : term,X536 : subst] : (((sub @ X531 @ (push @ (sub @ X537 @ X538) @ (comp @ X536 @ X538)))) = ((X530 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538))))) | ? [X539 : term] : ((((X529 @ id @ X539 @ id)) = $true) & (((X529 @ id @ (sub @ X528 @ (push @ X539 @ id)) @ id)) != $true)) | (((X529 @ id @ (lam @ (sub @ X528 @ (push @ one @ sh))) @ id)) = $true))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f26,definition,(
% 164.61/23.50 ($true = sP13) <=> (? [X57 : term,X58 : subst] : (((comp @ sh @ (push @ X57 @ X58))) != X58) | ! [X61 : subst,X63 : term,X64 : (subst > term > term),X62 : (subst > term > term)] : (? [X67 : subst,X65 : term,X66 : subst] : (((sub @ (X62 @ X67 @ X65) @ X66)) != ((X62 @ (comp @ X67 @ X66) @ (sub @ X65 @ X66)))) | (((X62 @ X61 @ X63)) = ((X64 @ X61 @ X63))) | ? [X69 : term,X70 : subst,X68 : subst] : (((X64 @ (comp @ X68 @ X70) @ (sub @ X69 @ X70))) != ((sub @ (X64 @ X68 @ X69) @ X70))) | (((lam @ (X64 @ sh @ one))) != ((lam @ (X62 @ sh @ one))))) | ? [X55 : term,X56 : subst] : (((sub @ one @ (push @ X55 @ X56))) != X55) | ? [X60 : term,X59 : term] : ((((lam @ X59)) = ((lam @ X60))) & (X59 != X60)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f27,definition,(
% 164.61/23.50 (sP14 = $true) <=> (? [X89 : term] : ! [X90 : (subst > term > term)] : ? [X91 : term,X92 : subst] : (((sub @ X89 @ (push @ X91 @ X92))) != ((X90 @ X92 @ X91))) | ? [X93 : term] : (((sub @ X93 @ id)) != X93) | ! [X94 : term,X95 : (term > $o),X96 : (subst > term > subst > $o)] : (? [X97 : term] : (((X95 @ X97)) != ((X96 @ id @ X97 @ id))) | ? [X98 : term] : (($true = ((X95 @ X98))) & ($true != ((X95 @ (sub @ X94 @ (push @ X98 @ id)))))) | ? [X99 : (subst > term > term)] : (! [X100 : subst,X102 : subst,X101 : term] : (((sub @ (X99 @ X100 @ X101) @ X102)) = ((X99 @ (comp @ X100 @ X102) @ (sub @ X101 @ X102)))) & ! [X103 : term] : (($true != ((X96 @ id @ X103 @ id))) | (((X96 @ id @ (X99 @ id @ X103) @ id)) = $true)) & (((X96 @ id @ (lam @ (X99 @ sh @ one)) @ id)) != $true)) | (((X95 @ (lam @ X94))) = $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f28,definition,(
% 164.61/23.50 ! [X323 : (subst > term > subst > $o)] : ((((sP15 @ X323)) = $true) <=> ? [X331 : term,X330 : term] : (($true != ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) & (((X323 @ id @ X331 @ id)) = $true) & ($true = ((X323 @ id @ X330 @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f29,definition,(
% 164.61/23.50 ! [X201 : (term > $o)] : ((((sP16 @ X201)) = $true) <=> ! [X204 : term,X205 : term] : (($true != ((X201 @ X204))) | (((X201 @ X205)) != $true) | ($true = ((X201 @ (ap @ X204 @ X205))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f30,definition,(
% 164.61/23.50 ! [X219 : (subst > term > subst > $o)] : (($true = ((sP17 @ X219))) <=> ? [X221 : (subst > term > term)] : (! [X225 : term] : (($true != ((X219 @ id @ X225 @ id))) | (((X219 @ id @ (X221 @ id @ X225) @ id)) = $true)) & ($true != ((X219 @ id @ (lam @ (X221 @ sh @ one)) @ id))) & ! [X222 : subst,X223 : term,X224 : subst] : (((sub @ (X221 @ X224 @ X223) @ X222)) = ((X221 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f31,definition,(
% 164.61/23.50 ($true = sP18) <=> ? [X211 : (term > $o),X209 : term,X210 : (subst > term > subst > $o)] : (! [X218 : term] : ((((X211 @ X218)) != $true) | ($true = ((X211 @ (sub @ X209 @ (push @ X218 @ id)))))) & ! [X212 : (subst > term > term)] : (? [X213 : term,X215 : subst,X214 : subst] : (((sub @ (X212 @ X214 @ X213) @ X215)) != ((X212 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215)))) | (((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id)) = $true) | ? [X216 : term] : (($true = ((X210 @ id @ X216 @ id))) & (((X210 @ id @ (X212 @ id @ X216) @ id)) != $true))) & ! [X217 : term] : (((X210 @ id @ X217 @ id)) = ((X211 @ X217))) & ($true != ((X211 @ (lam @ X209)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f32,definition,(
% 164.61/23.50 (sP19 = $true) <=> ? [X202 : term,X201 : (term > $o)] : ((((sP16 @ X201)) = $true) & ! [X203 : term] : ((((X201 @ X203)) = $true) | ($true != ((var @ X203)))) & (((X201 @ X202)) != $true) & ! [X206 : term] : (? [X207 : term] : (($true != ((X201 @ (sub @ X206 @ (push @ X207 @ id))))) & (((X201 @ X207)) = $true)) | ($true = ((X201 @ (lam @ X206))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f33,definition,(
% 164.61/23.50 (sP20 = $true) <=> (! [X220 : term,X219 : (subst > term > subst > $o)] : (? [X226 : term,X227 : term] : ((((X219 @ id @ X227 @ id)) = $true) & ($true = ((X219 @ id @ X226 @ id))) & (((X219 @ id @ (ap @ (sub @ X227 @ id) @ X226) @ id)) != $true)) | ($true = ((sP17 @ X219))) | ($true = ((X219 @ id @ X220 @ id)))) | ? [X198 : (subst > term > subst > $o)] : ! [X199 : (term > $o)] : ? [X200 : term] : (((X198 @ id @ X200 @ id)) != ((X199 @ X200))) | ($true = sP18) | (sP19 = $true) | ? [X208 : term] : (((sub @ X208 @ id)) != X208))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f34,definition,(
% 164.61/23.50 ! [X72 : (term > $o)] : ((((sP21 @ X72)) = $true) <=> ? [X74 : term,X75 : term] : ((((X72 @ X75)) = $true) & ($true = ((X72 @ X74))) & ($true != ((X72 @ (ap @ X75 @ X74))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f35,definition,(
% 164.61/23.50 ($true = sP22) <=> ! [X73 : term,X72 : (term > $o)] : (? [X76 : term] : (($true = ((var @ X76))) & ($true != ((X72 @ X76)))) | (((sP21 @ X72)) = $true) | (((X72 @ X73)) = $true) | ? [X77 : term] : ((((X72 @ (lam @ X77))) != $true) & ! [X78 : term] : ((((X72 @ X78)) != $true) | (((X72 @ (sub @ X77 @ (push @ X78 @ id)))) = $true))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f36,definition,(
% 164.61/23.50 ! [X404 : (term > $o)] : (($true = ((sP23 @ X404))) <=> ? [X408 : term,X407 : term] : (($true != ((X404 @ (ap @ X407 @ X408)))) & (((X404 @ X407)) = $true) & (((X404 @ X408)) = $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f37,definition,(
% 164.61/23.50 (sP24 = $true) <=> ! [X404 : (term > $o),X402 : subst,X403 : term] : (? [X405 : term] : (! [X406 : term] : (($true != ((X404 @ X406))) | ($true = ((X404 @ (sub @ X405 @ (push @ X406 @ id)))))) & (((X404 @ (lam @ X405))) != $true)) | ? [X409 : term] : ((((X404 @ (sub @ X409 @ X402))) != $true) & ($true = ((var @ X409)))) | ($true = ((X404 @ (sub @ X403 @ X402)))) | ($true = ((sP23 @ X404))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f38,definition,(
% 164.61/23.50 ! [X149 : (subst > term > subst > $o)] : ((((sP25 @ X149)) = $true) <=> ? [X152 : (subst > term > term)] : (! [X153 : term] : ((((X149 @ id @ X153 @ id)) != $true) | (((X149 @ id @ (X152 @ id @ X153) @ id)) = $true)) & ! [X154 : subst,X156 : term,X155 : subst] : (((X152 @ (comp @ X154 @ X155) @ (sub @ X156 @ X155))) = ((sub @ (X152 @ X154 @ X156) @ X155))) & ($true != ((X149 @ id @ (lam @ (X152 @ sh @ one)) @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f39,definition,(
% 164.61/23.50 (sP26 = $true) <=> ! [X149 : (subst > term > subst > $o),X151 : term,X150 : (term > $o)] : (? [X160 : subst,X161 : subst,X162 : subst,X159 : term] : (($true != ((X149 @ X160 @ X159 @ (comp @ X162 @ X161)))) & (((X149 @ (comp @ X160 @ X162) @ (sub @ X159 @ X162) @ X161)) = $true)) | ? [X158 : term] : (((X149 @ id @ X158 @ id)) != ((X150 @ X158))) | ? [X157 : term] : (($true = ((X150 @ X157))) & (((X150 @ (sub @ X151 @ (push @ X157 @ id)))) != $true)) | (((sP25 @ X149)) = $true) | ? [X166 : subst,X165 : subst,X163 : term,X164 : subst] : (($true != ((X149 @ (comp @ X166 @ X164) @ (sub @ X163 @ X164) @ X165))) & (((X149 @ X166 @ X163 @ (comp @ X164 @ X165))) = $true)) | ($true = ((X150 @ (lam @ X151)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f40,definition,(
% 164.61/23.50 ! [X284 : (term > $o)] : (($true = ((sP27 @ X284))) <=> ? [X286 : term,X285 : term] : (($true != ((X284 @ (ap @ X285 @ X286)))) & (((X284 @ X285)) = $true) & ($true = ((X284 @ X286)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f41,definition,(
% 164.61/23.50 ! [X277 : (term > $o)] : (($true = ((sP28 @ X277))) <=> ! [X279 : term,X278 : term] : (($true = ((X277 @ (ap @ X278 @ X279)))) | (((X277 @ X279)) != $true) | (((X277 @ X278)) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f42,definition,(
% 164.61/23.50 ($true = sP29) <=> ! [X284 : (term > $o),X282 : subst,X283 : term] : (? [X287 : term] : ((((X284 @ (sub @ X287 @ X282))) != $true) & ($true = ((var @ X287)))) | (((X284 @ (sub @ X283 @ X282))) = $true) | ($true = ((sP27 @ X284))) | ? [X288 : term] : (! [X289 : term] : (($true != ((X284 @ X289))) | ($true = ((X284 @ (sub @ X288 @ (push @ X289 @ id)))))) & ($true != ((X284 @ (lam @ X288))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f43,definition,(
% 164.61/23.50 (sP30 = $true) <=> (? [X275 : subst] : (((comp @ X275 @ id)) != X275) | ? [X274 : term,X273 : subst] : (((comp @ sh @ (push @ X274 @ X273))) != X273) | ? [X276 : term,X277 : (term > $o)] : (($true = ((sP28 @ X277))) & ! [X281 : term] : (($true = ((X277 @ (lam @ X281)))) | (((X277 @ X281)) != $true)) & ($true != ((X277 @ X276))) & ! [X280 : term] : (($true != ((var @ X280))) | ($true = ((X277 @ X280))))) | ($true = sP29) | ? [X271 : subst,X272 : term] : (((sub @ one @ (push @ X272 @ X271))) != X272))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f44,definition,(
% 164.61/23.50 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP31 @ X446))) <=> ! [X456 : term,X455 : term] : ((((X446 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id)) = $true) | (((X446 @ id @ X455 @ id)) != $true) | ($true != ((X446 @ id @ X456 @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f45,definition,(
% 164.61/23.50 ! [X457 : (subst > term > subst > $o)] : ((((sP32 @ X457)) = $true) <=> ! [X459 : (subst > term > term)] : (? [X461 : term,X462 : subst,X463 : subst] : (((X459 @ (comp @ X463 @ X462) @ (sub @ X461 @ X462))) != ((sub @ (X459 @ X463 @ X461) @ X462))) | ? [X460 : term] : ((((X457 @ id @ X460 @ id)) = $true) & (((X457 @ id @ (X459 @ id @ X460) @ id)) != $true)) | (((X457 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f46,definition,(
% 164.61/23.50 ! [X473 : (subst > term > subst > $o)] : ((((sP33 @ X473)) = $true) <=> ? [X480 : (subst > term > term)] : (! [X481 : term] : (($true != ((X473 @ id @ X481 @ id))) | (((X473 @ id @ (X480 @ id @ X481) @ id)) = $true)) & ($true != ((X473 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X484 : subst,X482 : term,X483 : subst] : (((sub @ (X480 @ X483 @ X482) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X482 @ X484))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f47,definition,(
% 164.61/23.50 ! [X473 : (subst > term > subst > $o)] : ((((sP34 @ X473)) = $true) <=> ? [X489 : term,X490 : term] : ((((X473 @ id @ X490 @ id)) = $true) & (((X473 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id)) != $true) & (((X473 @ id @ X489 @ id)) = $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f48,definition,(
% 164.61/23.50 ! [X437 : (term > $o)] : (($true = ((sP35 @ X437))) <=> ! [X439 : term,X440 : term] : (($true = ((X437 @ (ap @ X440 @ X439)))) | (((X437 @ X440)) != $true) | ($true != ((X437 @ X439)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f49,definition,(
% 164.61/23.50 (sP36 = $true) <=> ? [X458 : term,X457 : (subst > term > subst > $o)] : ((((sP32 @ X457)) = $true) & ! [X468 : subst,X465 : subst,X466 : term,X467 : subst] : ((((X457 @ (comp @ X465 @ X468) @ (sub @ X466 @ X468) @ X467)) = $true) | (((X457 @ X465 @ X466 @ (comp @ X468 @ X467))) != $true)) & ! [X469 : term,X471 : subst,X470 : subst,X472 : subst] : ((((X457 @ X470 @ X469 @ (comp @ X471 @ X472))) = $true) | (((X457 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471) @ X472)) != $true)) & ! [X464 : term] : ((((X457 @ id @ X464 @ id)) != $true) | ($true = ((X457 @ id @ (sub @ X458 @ (push @ X464 @ id)) @ id)))) & (((X457 @ id @ (lam @ X458) @ id)) != $true))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f50,definition,(
% 164.61/23.50 (sP37 = $true) <=> ! [X473 : (subst > term > subst > $o),X474 : term] : ((((sP34 @ X473)) = $true) | (((sP33 @ X473)) = $true) | ($true = ((X473 @ id @ X474 @ id))) | ? [X488 : subst,X486 : term,X487 : subst,X485 : subst] : ((((X473 @ X488 @ X486 @ (comp @ X487 @ X485))) = $true) & ($true != ((X473 @ (comp @ X488 @ X487) @ (sub @ X486 @ X487) @ X485)))) | ? [X476 : subst,X478 : subst,X477 : subst,X479 : term] : (($true = ((X473 @ (comp @ X478 @ X477) @ (sub @ X479 @ X477) @ X476))) & (((X473 @ X478 @ X479 @ (comp @ X477 @ X476))) != $true)) | ? [X475 : term] : ((((X473 @ id @ X475 @ id)) != $true) & ($true = ((var @ (sub @ X475 @ id))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f51,definition,(
% 164.61/23.50 ($true = sP38) <=> ? [X444 : term,X446 : (subst > term > subst > $o),X445 : term] : ((((X446 @ id @ X445 @ id)) = $true) & ($true = ((sP31 @ X446))) & ! [X448 : subst,X447 : subst,X450 : subst,X449 : term] : ((((X446 @ X447 @ X449 @ (comp @ X450 @ X448))) != $true) | (((X446 @ (comp @ X447 @ X450) @ (sub @ X449 @ X450) @ X448)) = $true)) & ! [X454 : subst,X453 : term,X452 : subst,X451 : subst] : ((((X446 @ (comp @ X452 @ X451) @ (sub @ X453 @ X451) @ X454)) != $true) | (((X446 @ X452 @ X453 @ (comp @ X451 @ X454))) = $true)) & ($true != ((X446 @ id @ (ap @ X445 @ X444) @ id))) & ($true = ((X446 @ id @ X444 @ id))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f52,definition,(
% 164.61/23.50 (sP39 = $true) <=> (? [X438 : term,X437 : (term > $o)] : (! [X443 : term] : ((((var @ X443)) != $true) | (((X437 @ X443)) = $true)) & (((X437 @ X438)) != $true) & ! [X441 : term] : (($true = ((X437 @ (lam @ X441)))) | ? [X442 : term] : (($true = ((X437 @ X442))) & (((X437 @ (sub @ X441 @ (push @ X442 @ id)))) != $true))) & ($true = ((sP35 @ X437)))) | (sP37 = $true) | (sP36 = $true) | ($true = sP38))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f53,definition,(
% 164.61/23.50 ! [X229 : (subst > term > subst > $o)] : (($true = ((sP40 @ X229))) <=> ? [X230 : (subst > term > term)] : (! [X232 : subst,X233 : subst,X231 : term] : (((sub @ (X230 @ X233 @ X231) @ X232)) = ((X230 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) & (((X229 @ id @ (lam @ (X230 @ sh @ one)) @ id)) != $true) & ! [X234 : term] : ((((X229 @ id @ (X230 @ id @ X234) @ id)) = $true) | ($true != ((X229 @ id @ X234 @ id))))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f54,definition,(
% 164.61/23.50 (sP41 = $true) <=> ! [X229 : (subst > term > subst > $o),X228 : term] : (? [X243 : term] : ((((X229 @ id @ X243 @ id)) = $true) & (((X229 @ id @ (sub @ X228 @ (push @ X243 @ id)) @ id)) != $true)) | ? [X239 : subst,X241 : term,X242 : subst,X240 : subst] : ((((X229 @ X239 @ X241 @ (comp @ X242 @ X240))) = $true) & (((X229 @ (comp @ X239 @ X242) @ (sub @ X241 @ X242) @ X240)) != $true)) | ($true = ((X229 @ id @ (lam @ X228) @ id))) | ($true = ((sP40 @ X229))) | ? [X238 : term,X236 : subst,X235 : subst,X237 : subst] : (($true = ((X229 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237) @ X235))) & (((X229 @ X236 @ X238 @ (comp @ X237 @ X235))) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f55,definition,(
% 164.61/23.50 ! [X413 : (term > $o)] : ((((sP42 @ X413)) = $true) <=> ! [X416 : term,X417 : term] : (($true != ((X413 @ X417))) | ($true = ((X413 @ (ap @ X416 @ X417)))) | ($true != ((X413 @ X416)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f56,definition,(
% 164.61/23.50 ! [X422 : (term > $o)] : ((((sP43 @ X422)) = $true) <=> ? [X426 : term,X427 : term] : (($true = ((X422 @ X426))) & (((X422 @ X427)) = $true) & (((X422 @ (ap @ X426 @ X427))) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f57,definition,(
% 164.61/23.50 ($true = sP44) <=> ! [X422 : (term > $o),X421 : term] : (? [X424 : term] : (($true != ((X422 @ (lam @ X424)))) & ! [X425 : term] : ((((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true) | (((X422 @ X425)) != $true))) | ? [X423 : term] : (($true = ((var @ X423))) & ($true != ((X422 @ X423)))) | ($true = ((X422 @ X421))) | (((sP43 @ X422)) = $true))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f58,definition,(
% 164.61/23.50 ($true = sP45) <=> (? [X412 : term] : (((sub @ X412 @ id)) != X412) | ($true = sP44) | ? [X415 : subst,X414 : term,X413 : (term > $o)] : (! [X420 : term] : (($true = ((X413 @ (sub @ X420 @ X415)))) | (((var @ X420)) != $true)) & (((X413 @ (sub @ X414 @ X415))) != $true) & ! [X418 : term] : (? [X419 : term] : ((((X413 @ X419)) = $true) & (((X413 @ (sub @ X418 @ (push @ X419 @ id)))) != $true)) | ($true = ((X413 @ (lam @ X418))))) & (((sP42 @ X413)) = $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f59,definition,(
% 164.61/23.50 (sP46 = $true) <=> ! [X291 : (subst > term > subst > $o),X290 : term] : (($true = ((X291 @ id @ (lam @ (sub @ X290 @ (push @ one @ sh))) @ id))) | ? [X297 : term] : ((((X291 @ id @ X297 @ id)) = $true) & ($true != ((X291 @ id @ (sub @ X290 @ (push @ X297 @ id)) @ id)))) | ? [X292 : (subst > term > term)] : (! [X293 : term] : ((((X291 @ id @ X293 @ id)) != $true) | (((X291 @ id @ (X292 @ id @ X293) @ id)) = $true)) & ! [X294 : subst,X295 : subst,X296 : term] : (((X292 @ (comp @ X295 @ X294) @ (sub @ X296 @ X294))) = ((sub @ (X292 @ X295 @ X296) @ X294))) & ($true != ((X291 @ id @ (lam @ (X292 @ sh @ one)) @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f60,definition,(
% 164.61/23.50 ($true = sP47) <=> ! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (? [X495 : term] : (((X491 @ X495)) != ((X492 @ id @ X495 @ id))) | ($true = ((X491 @ (lam @ X493)))) | ? [X494 : term] : ((((X491 @ X494)) = $true) & (((X491 @ (sub @ X493 @ (push @ X494 @ id)))) != $true)) | ? [X496 : (subst > term > term)] : (! [X500 : term,X498 : subst,X499 : subst] : (((sub @ (X496 @ X499 @ X500) @ X498)) = ((X496 @ (comp @ X499 @ X498) @ (sub @ X500 @ X498)))) & ($true != ((X492 @ id @ (lam @ (X496 @ sh @ one)) @ id))) & ! [X497 : term] : ((((X492 @ id @ X497 @ id)) != $true) | (((X492 @ id @ (X496 @ id @ X497) @ id)) = $true))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f61,definition,(
% 164.61/23.50 ! [X260 : (subst > term > subst > $o)] : (($true = ((sP48 @ X260))) <=> ? [X266 : term,X265 : term] : (($true = ((X260 @ id @ X265 @ id))) & ($true = ((X260 @ id @ X266 @ id))) & ($true != ((X260 @ id @ (ap @ (sub @ X265 @ id) @ X266) @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f62,definition,(
% 164.61/23.50 ($true = sP49) <=> ! [X258 : term,X259 : term,X260 : (subst > term > subst > $o)] : (($true = ((X260 @ id @ (ap @ X258 @ X259) @ id))) | ($true = ((sP48 @ X260))) | ? [X270 : term,X267 : subst,X268 : subst,X269 : subst] : (($true != ((X260 @ (comp @ X269 @ X268) @ (sub @ X270 @ X268) @ X267))) & ($true = ((X260 @ X269 @ X270 @ (comp @ X268 @ X267))))) | ? [X264 : subst,X262 : subst,X261 : subst,X263 : term] : ((((X260 @ X264 @ X263 @ (comp @ X262 @ X261))) != $true) & ($true = ((X260 @ (comp @ X264 @ X262) @ (sub @ X263 @ X262) @ X261)))) | ($true != ((X260 @ id @ X259 @ id))) | (((X260 @ id @ X258 @ id)) != $true))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f63,definition,(
% 164.61/23.50 ! [X170 : (subst > term > subst > $o)] : (($true = ((sP50 @ X170))) <=> ? [X172 : term,X171 : term] : ((((X170 @ id @ X172 @ id)) = $true) & (((X170 @ id @ (ap @ (sub @ X171 @ id) @ X172) @ id)) != $true) & ($true = ((X170 @ id @ X171 @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f64,definition,(
% 164.61/23.50 (sP51 = $true) <=> ! [X168 : (term > $o),X167 : term,X169 : term,X170 : (subst > term > subst > $o)] : (? [X175 : subst,X174 : subst,X173 : term,X176 : subst] : (($true = ((X170 @ (comp @ X175 @ X176) @ (sub @ X173 @ X176) @ X174))) & (((X170 @ X175 @ X173 @ (comp @ X176 @ X174))) != $true)) | ? [X177 : term] : (((X170 @ id @ X177 @ id)) != ((X168 @ X177))) | ? [X181 : term,X178 : subst,X180 : subst,X179 : subst] : (($true != ((X170 @ (comp @ X180 @ X178) @ (sub @ X181 @ X178) @ X179))) & ($true = ((X170 @ X180 @ X181 @ (comp @ X178 @ X179))))) | (((X168 @ X169)) != $true) | (((X168 @ (ap @ X167 @ X169))) = $true) | ($true = ((sP50 @ X170))) | ($true != ((X168 @ X167))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f65,definition,(
% 164.61/23.50 (sP52 = $true) <=> ! [X191 : (subst > term > subst > $o),X190 : term] : (? [X192 : (subst > term > term)] : (($true != ((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id))) & ! [X194 : subst,X195 : term,X193 : subst] : (((X192 @ (comp @ X194 @ X193) @ (sub @ X195 @ X193))) = ((sub @ (X192 @ X194 @ X195) @ X193))) & ! [X196 : term] : ((((X191 @ id @ X196 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X196) @ id)) = $true))) | ($true = ((X191 @ id @ (lam @ X190) @ id))) | ? [X197 : term] : ((((X191 @ id @ X197 @ id)) = $true) & (((X191 @ id @ (sub @ X190 @ (push @ X197 @ id)) @ id)) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f66,definition,(
% 164.61/23.50 ! [X307 : (subst > term > subst > $o)] : ((((sP53 @ X307)) = $true) <=> ? [X310 : (subst > term > term)] : (! [X312 : subst,X311 : subst,X313 : term] : (((X310 @ (comp @ X312 @ X311) @ (sub @ X313 @ X311))) = ((sub @ (X310 @ X312 @ X313) @ X311))) & ! [X314 : term] : (($true = ((X307 @ id @ (X310 @ id @ X314) @ id))) | ($true != ((X307 @ id @ X314 @ id)))) & (((X307 @ id @ (lam @ (X310 @ sh @ one)) @ id)) != $true)))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f67,definition,(
% 164.61/23.50 ($true = sP54) <=> ? [X300 : term,X299 : (subst > term > subst > $o)] : (! [X302 : (subst > term > term)] : ((((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id)) = $true) | ? [X304 : subst,X306 : term,X305 : subst] : (((X302 @ (comp @ X304 @ X305) @ (sub @ X306 @ X305))) != ((sub @ (X302 @ X304 @ X306) @ X305))) | ? [X303 : term] : (($true = ((X299 @ id @ X303 @ id))) & (((X299 @ id @ (X302 @ id @ X303) @ id)) != $true))) & ($true != ((X299 @ id @ (lam @ (sub @ X300 @ (push @ one @ sh))) @ id))) & ! [X301 : term] : ((((X299 @ id @ (sub @ X300 @ (push @ X301 @ id)) @ id)) = $true) | ($true != ((X299 @ id @ X301 @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f68,definition,(
% 164.61/23.50 (sP55 = $true) <=> (! [X307 : (subst > term > subst > $o),X308 : term] : ((((sP53 @ X307)) = $true) | ? [X317 : subst,X316 : term,X318 : subst,X315 : subst] : (($true = ((X307 @ (comp @ X315 @ X318) @ (sub @ X316 @ X318) @ X317))) & ($true != ((X307 @ X315 @ X316 @ (comp @ X318 @ X317))))) | ? [X320 : subst,X322 : subst,X319 : term,X321 : subst] : ((((X307 @ (comp @ X322 @ X321) @ (sub @ X319 @ X321) @ X320)) != $true) & ($true = ((X307 @ X322 @ X319 @ (comp @ X321 @ X320))))) | ($true = ((X307 @ id @ (lam @ X308) @ id))) | ? [X309 : term] : (($true = ((X307 @ id @ X309 @ id))) & ($true != ((X307 @ id @ (sub @ X308 @ (push @ X309 @ id)) @ id))))) | ? [X298 : term] : (((sub @ X298 @ id)) != X298) | ($true = sP54))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f69,definition,(
% 164.61/23.50 ! [X509 : (subst > term > subst > $o)] : (($true = ((sP56 @ X509))) <=> ? [X512 : term,X511 : term] : ((((X509 @ id @ X512 @ id)) = $true) & ($true != ((X509 @ id @ (ap @ (sub @ X512 @ id) @ X511) @ id))) & ($true = ((X509 @ id @ X511 @ id)))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f70,definition,(
% 164.61/23.50 ! [X509 : (subst > term > subst > $o)] : ((((sP57 @ X509)) = $true) <=> ? [X517 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id))) & ! [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) = ((sub @ (X517 @ X520 @ X521) @ X519))) & ! [X518 : term] : (($true = ((X509 @ id @ (X517 @ id @ X518) @ id))) | (((X509 @ id @ X518 @ id)) != $true))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f71,definition,(
% 164.61/23.50 (sP58 = $true) <=> ! [X508 : term,X509 : (subst > term > subst > $o)] : (? [X522 : term,X525 : subst,X524 : subst,X523 : subst] : ((((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) = $true) & ($true != ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524)))) | ? [X514 : subst,X515 : subst,X516 : subst,X513 : term] : (($true != ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) & ($true = ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) | (((sP57 @ X509)) = $true) | ? [X510 : term] : ((((var @ (sub @ X510 @ id))) = $true) & (((X509 @ id @ X510 @ id)) != $true)) | ($true = ((X509 @ id @ X508 @ id))) | ($true = ((sP56 @ X509))))),
% 164.61/23.50 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 164.61/23.50 thf(f72,plain,(
% 164.61/23.50 (axassoc = $true) & (axapp = $true) & ((axidl = $true) <=> ! [X71 : subst] : (((comp @ id @ X71)) = X71)) & (! [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true) | (((X254 @ X255)) != $true)) <=> (pushprop_lem1 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction = $true) <=> (sP58 = $true)) & (! [X80 : term,X79 : (term > $o),X81 : subst] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))) <=> (pushprop_lem0 = $true)) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (sP55 = $true)) & (hoasinduction_lem2_lthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) <=> ! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186))) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3a = $true) <=> (sP52 = $true)) & ((hoasapinj1 = $true) <=> ! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367))) & ((sP51 = $true) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X39 : (subst > term > subst > $o)] : ? [X40 : (term > $o)] : ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (induction2_gthm = $true) & (((! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376)) | ? [X374 : subst] : (((comp @ X374 @ id)) != X374) | ? [X373 : subst] : (((comp @ id @ X373)) != X373)) <=> (substmonoid_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem2 = $true) <=> ($true = sP49)) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP47)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((pushprop_lem1_lthm = $true) <=> (! [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | (((X252 @ X251)) != $true)) | ? [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) != X246) | ? [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) != X245))) & (lamnotvar = $true) & (! [X505 : term] : (((sub @ X505 @ id)) = X505) <=> (termmset = $true)) & ((sP46 = $true) <=> (hoasinduction_lem3aa = $true)) & ((? [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 != X392) & (((ap @ X390 @ X391)) = ((ap @ X392 @ X393)))) | ? [X389 : term] : (((sub @ X389 @ id)) != X389) | ! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) <=> ($true = sP45)) & (hoasinduction_lem3_gthm = $true) & (lamnotap != $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X526 : term] : ? [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) = ((X527 @ sh @ one)))) & (axabs = $true) & ! [X84 : d_term] : (d_one = X84) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP41 = $true) <=> (hoasinduction_lem3 = $true)) & ((axvarcons = $true) <=> ! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501)) & (substmonoid_gthm = $true) & ((hoasinduction_lthm = $true) <=> (sP39 = $true)) & (! [X85 : term] : ? [X86 : (subst > term > term)] : ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88)))) <=> (hoasinduction_lem3v2_f = $true)) & (ulamvarsh = $true) & (termmset_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslamnotap = $true) <=> ! [X380 : term,X379 : term,X381 : (subst > term > term)] : (? [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) != ((sub @ (X381 @ X383 @ X382) @ X384))) | (((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one)))))) & ((axidr = $true) <=> ! [X54 : subst] : (((comp @ X54 @ id)) = X54)) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & (hoasinduction_lem1v2_gthm = $true) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) != ((d2subst @ X183))) | (X182 = X183)) & ((sP30 = $true) <=> (induction2lem_lthm = $true)) & ((apinj2 = $true) <=> ! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2 = $true) <=> (sP26 = $true)) & ((induction2lem = $true) <=> (sP24 = $true)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (pushprop = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) <=> (axscons = $true)) & (hoasinduction_lem1v2 = $true) & (($true = sP22) <=> (induction2 = $true)) & (pushprop_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X136 : term] : ? [X137 : (subst > term > term)] : ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139)))) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((? [X377 : term] : (((sub @ X377 @ id)) != X377) | ! [X378 : term] : (((sub @ X378 @ id)) = X378)) <=> (termmset_lthm = $true)) & ((hoaslaminj = $true) <=> ! [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | (((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | ? [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) != ((sub @ (X42 @ X49 @ X51) @ X50))) | ? [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) != ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (((d2subst @ d_id)) = sh) & ((axvarid = $true) <=> ! [X388 : term] : (((sub @ X388 @ id)) = X388)) & (! [X188 : term] : ? [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) = ((X189 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((sP20 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) <=> (laminj = $true)) & (hoasinduction_lem1 = $true) & (! [X323 : (subst > term > subst > $o),X324 : term] : (? [X325 : (subst > term > term)] : (($true != ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) & ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ($true != ((X323 @ id @ X329 @ id)))) & ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) | (((X323 @ id @ X324 @ id)) = $true) | (((sP15 @ X323)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) != $true) | ? [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) != ((X131 @ X135))) | (((X131 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) <=> (shinj = $true)) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & (one = ((d2term @ d_one))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem2v2_gthm = $true) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ? [X145 : (term > $o)] : ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) <=> (pushprop_lem0_lthm = $true)) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & ((sP14 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoaslaminj_lthm = $true) <=> ($true = sP13)) & (! [X385 : (subst > term > subst > $o)] : ? [X386 : (term > $o)] : ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) <=> (hoasinduction_lem0 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) <=> (axshiftcons = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) != X338) | ! [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) != $true) | ? [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) != ((X343 @ X344))) | (((X343 @ one)) = $true)))) & (axvarshift = $true) & ((sP12 = $true) <=> (hoasinduction_lem3aaa = $true)) & ((sP11 = $true) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasapinj2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP10) <=> (hoasinduction_lthm_3 = $true)) & ((sP4 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) <=> (hoasapinj2 = $true)) & (hoaslamnotvar_lthm = $true) & ((? [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 != X126) & (((ap @ X124 @ X125)) = ((ap @ X123 @ X126)))) | ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) <=> (hoasapinj2_lthm = $true)) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) != ((d2term @ X507))) | (X506 = X507)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (apnotvar = $true) & (($true = sP2) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) = $true) | ($true = ((sP0 @ X332))) | ? [X337 : term] : (($true != ((X332 @ (lam @ X337)))) & (((X332 @ X337)) = $true)) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X332 @ X334)) != $true))) <=> (induction = $true)) & ((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) <=> (substmonoid = $true)) & ! [X436 : d_subst] : (d_id = X436)),
% 164.61/23.50 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])).
% 164.61/23.50 thf(f73,plain,(
% 164.61/23.50 ((sP58 = $true) | ? [X508 : term,X509 : (subst > term > subst > $o)] : (! [X522 : term,X525 : subst,X524 : subst,X523 : subst] : ((((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) != $true) | ($true = ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524)))) & ! [X514 : subst,X515 : subst,X516 : subst,X513 : term] : (($true = ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) | ($true != ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) & (((sP57 @ X509)) != $true) & ! [X510 : term] : ((((var @ (sub @ X510 @ id))) != $true) | (((X509 @ id @ X510 @ id)) = $true)) & ($true != ((X509 @ id @ X508 @ id))) & ($true != ((sP56 @ X509))))) & (! [X508 : term,X509 : (subst > term > subst > $o)] : (? [X522 : term,X525 : subst,X524 : subst,X523 : subst] : ((((X509 @ X525 @ X522 @ (comp @ X523 @ X524))) = $true) & ($true != ((X509 @ (comp @ X525 @ X523) @ (sub @ X522 @ X523) @ X524)))) | ? [X514 : subst,X515 : subst,X516 : subst,X513 : term] : (($true != ((X509 @ X514 @ X513 @ (comp @ X516 @ X515)))) & ($true = ((X509 @ (comp @ X514 @ X516) @ (sub @ X513 @ X516) @ X515)))) | (((sP57 @ X509)) = $true) | ? [X510 : term] : ((((var @ (sub @ X510 @ id))) = $true) & (((X509 @ id @ X510 @ id)) != $true)) | ($true = ((X509 @ id @ X508 @ id))) | ($true = ((sP56 @ X509)))) | (sP58 != $true))),
% 164.61/23.50 inference(nnf_transformation,[],[f71])).
% 164.61/23.50 thf(f74,plain,(
% 164.61/23.50 ((sP58 = $true) | ? [X0 : term,X1 : (subst > term > subst > $o)] : (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true != ((X1 @ X3 @ X2 @ (comp @ X5 @ X4)))) | ($true = ((X1 @ (comp @ X3 @ X5) @ (sub @ X2 @ X5) @ X4)))) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((X1 @ X6 @ X9 @ (comp @ X8 @ X7))) = $true) | ($true != ((X1 @ (comp @ X6 @ X8) @ (sub @ X9 @ X8) @ X7)))) & (((sP57 @ X1)) != $true) & ! [X10 : term] : (($true != ((var @ (sub @ X10 @ id)))) | (((X1 @ id @ X10 @ id)) = $true)) & ($true != ((X1 @ id @ X0 @ id))) & ($true != ((sP56 @ X1))))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : (? [X13 : term,X14 : subst,X15 : subst,X16 : subst] : (($true = ((X12 @ X14 @ X13 @ (comp @ X16 @ X15)))) & ($true != ((X12 @ (comp @ X14 @ X16) @ (sub @ X13 @ X16) @ X15)))) | ? [X17 : subst,X18 : subst,X19 : subst,X20 : term] : ((((X12 @ X17 @ X20 @ (comp @ X19 @ X18))) != $true) & ($true = ((X12 @ (comp @ X17 @ X19) @ (sub @ X20 @ X19) @ X18)))) | ($true = ((sP57 @ X12))) | ? [X21 : term] : (($true = ((var @ (sub @ X21 @ id)))) & ($true != ((X12 @ id @ X21 @ id)))) | (((X12 @ id @ X11 @ id)) = $true) | ($true = ((sP56 @ X12)))) | (sP58 != $true))),
% 164.61/23.50 inference(rectify,[],[f73])).
% 164.61/23.50 thf(f75,plain,(
% 164.61/23.50 ((sP58 = $true) | (! [X2 : term,X3 : subst,X4 : subst,X5 : subst] : (($true != ((sK60 @ X3 @ X2 @ (comp @ X5 @ X4)))) | ($true = ((sK60 @ (comp @ X3 @ X5) @ (sub @ X2 @ X5) @ X4)))) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : (($true = ((sK60 @ X6 @ X9 @ (comp @ X8 @ X7)))) | (((sK60 @ (comp @ X6 @ X8) @ (sub @ X9 @ X8) @ X7)) != $true)) & ($true != ((sP57 @ sK60))) & ! [X10 : term] : (($true != ((var @ (sub @ X10 @ id)))) | ($true = ((sK60 @ id @ X10 @ id)))) & (((sK60 @ id @ sK59 @ id)) != $true) & (((sP56 @ sK60)) != $true))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : (((((X12 @ (sK62 @ X12) @ (sK61 @ X12) @ (comp @ (sK64 @ X12) @ (sK63 @ X12)))) = $true) & ($true != ((X12 @ (comp @ (sK62 @ X12) @ (sK64 @ X12)) @ (sub @ (sK61 @ X12) @ (sK64 @ X12)) @ (sK63 @ X12))))) | (($true != ((X12 @ (sK65 @ X12) @ (sK68 @ X12) @ (comp @ (sK67 @ X12) @ (sK66 @ X12))))) & ($true = ((X12 @ (comp @ (sK65 @ X12) @ (sK67 @ X12)) @ (sub @ (sK68 @ X12) @ (sK67 @ X12)) @ (sK66 @ X12))))) | ($true = ((sP57 @ X12))) | (($true = ((var @ (sub @ (sK69 @ X12) @ id)))) & (((X12 @ id @ (sK69 @ X12) @ id)) != $true)) | (((X12 @ id @ X11 @ id)) = $true) | ($true = ((sP56 @ X12)))) | (sP58 != $true))),
% 164.61/23.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK59,sK60,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK59),skolemize(X1,sK60),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12)],[f74])).
% 164.61/23.50 thf(f76,plain,(
% 164.61/23.50 ! [X509 : (subst > term > subst > $o)] : (((((sP57 @ X509)) = $true) | ! [X517 : (subst > term > term)] : (($true = ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id))) | ? [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) != ((sub @ (X517 @ X520 @ X521) @ X519))) | ? [X518 : term] : (($true != ((X509 @ id @ (X517 @ id @ X518) @ id))) & (((X509 @ id @ X518 @ id)) = $true)))) & (? [X517 : (subst > term > term)] : (($true != ((X509 @ id @ (lam @ (X517 @ sh @ one)) @ id))) & ! [X521 : term,X519 : subst,X520 : subst] : (((X517 @ (comp @ X520 @ X519) @ (sub @ X521 @ X519))) = ((sub @ (X517 @ X520 @ X521) @ X519))) & ! [X518 : term] : (($true = ((X509 @ id @ (X517 @ id @ X518) @ id))) | (((X509 @ id @ X518 @ id)) != $true))) | (((sP57 @ X509)) != $true)))),
% 164.61/23.50 inference(nnf_transformation,[],[f70])).
% 164.61/23.50 thf(f77,plain,(
% 164.61/23.50 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP57 @ X0))) | ! [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ? [X2 : term,X3 : subst,X4 : subst] : (((sub @ (X1 @ X4 @ X2) @ X3)) != ((X1 @ (comp @ X4 @ X3) @ (sub @ X2 @ X3)))) | ? [X5 : term] : ((((X0 @ id @ (X1 @ id @ X5) @ id)) != $true) & (((X0 @ id @ X5 @ id)) = $true)))) & (? [X6 : (subst > term > term)] : (($true != ((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id))) & ! [X7 : term,X8 : subst,X9 : subst] : (((X6 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8))) = ((sub @ (X6 @ X9 @ X7) @ X8))) & ! [X10 : term] : (($true = ((X0 @ id @ (X6 @ id @ X10) @ id))) | ($true != ((X0 @ id @ X10 @ id))))) | ($true != ((sP57 @ X0)))))),
% 164.61/23.50 inference(rectify,[],[f76])).
% 164.61/23.50 thf(f78,plain,(
% 164.61/23.50 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP57 @ X0))) | ! [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((X1 @ (comp @ (sK72 @ X1) @ (sK71 @ X1)) @ (sub @ (sK70 @ X1) @ (sK71 @ X1)))) != ((sub @ (X1 @ (sK72 @ X1) @ (sK70 @ X1)) @ (sK71 @ X1)))) | ((((X0 @ id @ (X1 @ id @ (sK73 @ X1 @ X0)) @ id)) != $true) & ($true = ((X0 @ id @ (sK73 @ X1 @ X0) @ id)))))) & ((($true != ((X0 @ id @ (lam @ (sK74 @ X0 @ sh @ one)) @ id))) & ! [X7 : term,X8 : subst,X9 : subst] : (((sK74 @ X0 @ (comp @ X9 @ X8) @ (sub @ X7 @ X8))) = ((sub @ (sK74 @ X0 @ X9 @ X7) @ X8))) & ! [X10 : term] : ((((X0 @ id @ (sK74 @ X0 @ id @ X10) @ id)) = $true) | ($true != ((X0 @ id @ X10 @ id))))) | ($true != ((sP57 @ X0)))))),
% 164.61/23.50 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12)],[f77])).
% 164.61/23.50 thf(f207,plain,(
% 164.61/23.50 ! [X323 : (subst > term > subst > $o)] : (((((sP15 @ X323)) = $true) | ! [X331 : term,X330 : term] : (($true = ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) | (((X323 @ id @ X331 @ id)) != $true) | ($true != ((X323 @ id @ X330 @ id))))) & (? [X331 : term,X330 : term] : (($true != ((X323 @ id @ (ap @ (sub @ X331 @ id) @ X330) @ id))) & (((X323 @ id @ X331 @ id)) = $true) & ($true = ((X323 @ id @ X330 @ id)))) | (((sP15 @ X323)) != $true)))),
% 164.61/23.50 inference(nnf_transformation,[],[f28])).
% 164.61/23.50 thf(f208,plain,(
% 164.61/23.50 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP15 @ X0))) | ! [X1 : term,X2 : term] : ((((X0 @ id @ (ap @ (sub @ X1 @ id) @ X2) @ id)) = $true) | (((X0 @ id @ X1 @ id)) != $true) | (((X0 @ id @ X2 @ id)) != $true))) & (? [X3 : term,X4 : term] : (($true != ((X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id))) & ($true = ((X0 @ id @ X3 @ id))) & ($true = ((X0 @ id @ X4 @ id)))) | ($true != ((sP15 @ X0)))))),
% 164.61/23.50 inference(rectify,[],[f207])).
% 164.61/23.50 thf(f209,plain,(
% 164.61/23.50 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP15 @ X0))) | ! [X1 : term,X2 : term] : ((((X0 @ id @ (ap @ (sub @ X1 @ id) @ X2) @ id)) = $true) | (((X0 @ id @ X1 @ id)) != $true) | (((X0 @ id @ X2 @ id)) != $true))) & ((($true != ((X0 @ id @ (ap @ (sub @ (sK324 @ X0) @ id) @ (sK325 @ X0)) @ id))) & (((X0 @ id @ (sK324 @ X0) @ id)) = $true) & ($true = ((X0 @ id @ (sK325 @ X0) @ id)))) | ($true != ((sP15 @ X0)))))),
% 164.61/23.50 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12)],[f208])).
% 164.61/23.50 thf(f260,plain,(
% 164.61/23.50 (axassoc = $true) & (axapp = $true) & (((axidl = $true) | ? [X71 : subst] : (((comp @ id @ X71)) != X71)) & (! [X71 : subst] : (((comp @ id @ X71)) = X71) | (axidl != $true))) & ((! [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true) | (((X254 @ X255)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) != $true) & (((X254 @ X255)) = $true)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true))) & ((! [X80 : term,X79 : (term > $o),X81 : subst] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X80 : term,X79 : (term > $o),X81 : subst] : ! [X82 : (term > $o)] : ? [X83 : term] : (((X82 @ X83)) != ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))))) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & (((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true))) & (hoasinduction_lem2_lthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & (((apinj1 = $true) | ? [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) = ((ap @ X184 @ X185))) & (X184 != X186))) & (! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186)) | (apinj1 != $true))) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & (((hoasinduction_lem3a = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a != $true))) & (((hoasapinj1 = $true) | ? [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) = ((ap @ (sub @ X365 @ id) @ X368))) & (X365 != X367))) & (! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367)) | (hoasapinj1 != $true))) & (((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true))) & (pushprop_lthm_orig = $true) & (hoaslamnotap_gthm = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X39 : (subst > term > subst > $o)] : ! [X40 : (term > $o)] : ? [X41 : term] : (((X39 @ id @ X41 @ id)) != ((X40 @ X41)))) & (! [X39 : (subst > term > subst > $o)] : ? [X40 : (term > $o)] : ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41))) | (hoasinduction_lem0_lthm != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (induction2_gthm = $true) & ((((! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376)) | ? [X374 : subst] : (((comp @ X374 @ id)) != X374) | ? [X373 : subst] : (((comp @ id @ X373)) != X373)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X375 : subst] : (((comp @ X375 @ id)) != X375) | ? [X376 : subst] : (((comp @ id @ X376)) != X376)) & ! [X374 : subst] : (((comp @ X374 @ id)) = X374) & ! [X373 : subst] : (((comp @ id @ X373)) = X373)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((hoasinduction_lem2 = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction_lem2 != $true))) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & (((hoasinduction_lem3v2a = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2a != $true))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (((pushprop_lem1_lthm = $true) | (? [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true != ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) & (((X252 @ X251)) = $true)) & ! [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) = X246) & ! [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) = X245))) & ((! [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | (((X252 @ X251)) != $true)) | ? [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) != X246) | ? [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) != X245)) | (pushprop_lem1_lthm != $true))) & (lamnotvar = $true) & ((! [X505 : term] : (((sub @ X505 @ id)) = X505) | (termmset != $true)) & ((termmset = $true) | ? [X505 : term] : (((sub @ X505 @ id)) != X505))) & (((sP46 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP46 != $true))) & (((? [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 != X392) & (((ap @ X390 @ X391)) = ((ap @ X392 @ X393)))) | ? [X389 : term] : (((sub @ X389 @ id)) != X389) | ! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 = X392) | (((ap @ X390 @ X391)) != ((ap @ X392 @ X393)))) & ! [X389 : term] : (((sub @ X389 @ id)) = X389) & ? [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) = ((ap @ (sub @ X396 @ id) @ X397))) & (X395 != X396))))) & (pushprop_lem3v2 = $true) & (((induction2_lthm = $true) | ($true != sP45)) & (($true = sP45) | (induction2_lthm != $true))) & (hoasinduction_lem3_gthm = $true) & (lamnotap != $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X526 : term] : ! [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) != ((X527 @ sh @ one)))) & (! [X526 : term] : ? [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) = ((X527 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (axabs = $true) & ! [X84 : d_term] : (d_one = X84) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (((sP41 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP41 != $true))) & (((axvarcons = $true) | ? [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) != X501)) & (! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501) | (axvarcons != $true))) & (substmonoid_gthm = $true) & (((hoasinduction_lthm = $true) | (sP39 != $true)) & ((sP39 = $true) | (hoasinduction_lthm != $true))) & ((! [X85 : term] : ? [X86 : (subst > term > term)] : ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X85 : term] : ! [X86 : (subst > term > term)] : ? [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) != ((sub @ X85 @ (push @ X87 @ X88)))))) & (ulamvarsh = $true) & (termmset_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((hoaslamnotap = $true) | ? [X380 : term,X379 : term,X381 : (subst > term > term)] : (! [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) = ((sub @ (X381 @ X383 @ X382) @ X384))) & (((ap @ (sub @ X380 @ id) @ X379)) = ((lam @ (X381 @ sh @ one)))))) & (! [X380 : term,X379 : term,X381 : (subst > term > term)] : (? [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) != ((sub @ (X381 @ X383 @ X382) @ X384))) | (((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one))))) | (hoaslamnotap != $true))) & (((axidr = $true) | ? [X54 : subst] : (((comp @ X54 @ id)) != X54)) & (! [X54 : subst] : (((comp @ X54 @ id)) = X54) | (axidr != $true))) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & (hoasinduction_lem1v2_gthm = $true) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) != ((d2subst @ X183))) | (X182 = X183)) & (((sP30 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP30 != $true))) & (((apinj2 = $true) | ? [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) = ((ap @ X400 @ X398))) & (X398 != X399))) & (! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399)) | (apinj2 != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoaslamnotap_lthm = $true) & (((hoasinduction_lem3v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3v2 != $true))) & (((induction2lem = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem != $true))) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (pushprop = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) | (axscons != $true)) & ((axscons = $true) | ? [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) != X345))) & (hoasinduction_lem1v2 = $true) & ((($true = sP22) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP22))) & (pushprop_gthm = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X136 : term] : ! [X137 : (subst > term > term)] : ? [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) != ((X137 @ X138 @ X139)))) & (! [X136 : term] : ? [X137 : (subst > term > term)] : ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139))) | (hoasinduction_lem3v2_f_lthm != $true))) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((? [X377 : term] : (((sub @ X377 @ id)) != X377) | ! [X378 : term] : (((sub @ X378 @ id)) = X378)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X377 : term] : (((sub @ X377 @ id)) = X377) & ? [X378 : term] : (((sub @ X378 @ id)) != X378)))) & (((hoaslaminj = $true) | ? [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) = ((lam @ (X44 @ sh @ one)))) & (((X42 @ X43 @ X45)) != ((X44 @ X43 @ X45))) & ! [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) = ((sub @ (X42 @ X49 @ X51) @ X50))) & ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) = ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & (! [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | (((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | ? [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) != ((sub @ (X42 @ X49 @ X51) @ X50))) | ? [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) != ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46))))) | (hoaslaminj != $true))) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (((d2subst @ d_id)) = sh) & (((axvarid = $true) | ? [X388 : term] : (((sub @ X388 @ id)) != X388)) & (! [X388 : term] : (((sub @ X388 @ id)) = X388) | (axvarid != $true))) & ((! [X188 : term] : ? [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) = ((X189 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X188 : term] : ! [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) != ((X189 @ sh @ one))))) & (((sP20 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP20 != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) | (laminj != $true)) & ((laminj = $true) | ? [X410 : term,X411 : term] : ((X410 != X411) & (((lam @ X410)) = ((lam @ X411)))))) & (hoasinduction_lem1 = $true) & ((! [X323 : (subst > term > subst > $o),X324 : term] : (? [X325 : (subst > term > term)] : (($true != ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) & ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ($true != ((X323 @ id @ X329 @ id)))) & ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) | (((X323 @ id @ X324 @ id)) = $true) | (((sP15 @ X323)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X323 : (subst > term > subst > $o),X324 : term] : (! [X325 : (subst > term > term)] : (($true = ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) | ? [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) != $true) & ($true = ((X323 @ id @ X329 @ id)))) | ? [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) != ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) & (((X323 @ id @ X324 @ id)) != $true) & (((sP15 @ X323)) != $true)))) & (pushprop_lem3v2_lthm = $true) & ((! [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) != $true) | ? [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) != ((X131 @ X135))) | (((X131 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) = $true) & ! [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) = ((X131 @ X135))) & (((X131 @ one)) != $true)))) & ((! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) | (shinj != $true)) & ((shinj = $true) | ? [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) = ((sub @ X53 @ sh))) & (X52 != X53)))) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & (one = ((d2term @ d_one))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem2v2_gthm = $true) & ((! [X142 : subst,X144 : (term > $o),X143 : term] : ? [X145 : (term > $o)] : ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X142 : subst,X144 : (term > $o),X143 : term] : ! [X145 : (term > $o)] : ? [X146 : term] : (((X145 @ X146)) != ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))))) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & (((sP14 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP14 != $true))) & (((hoaslaminj_lthm = $true) | ($true != sP13)) & (($true = sP13) | (hoaslaminj_lthm != $true))) & ((! [X385 : (subst > term > subst > $o)] : ? [X386 : (term > $o)] : ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X385 : (subst > term > subst > $o)] : ! [X386 : (term > $o)] : ? [X387 : term] : (((X386 @ X387)) != ((X385 @ id @ X387 @ id))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) != X148))) & (hoasinduction_lem1_lthm = $true) & (((pushprop_lem1v2_lthm = $true) | (! [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) = X338) & ? [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) = $true) & ! [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) = ((X343 @ X344))) & (((X343 @ one)) != $true)))) & ((? [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) != X338) | ! [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) != $true) | ? [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) != ((X343 @ X344))) | (((X343 @ one)) = $true))) | (pushprop_lem1v2_lthm != $true))) & (axvarshift = $true) & (((sP12 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP12 != $true))) & (((sP11 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP11 != $true))) & (hoasapinj2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10))) & (((sP4 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP4 != $true))) & ((! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 != X372) & (((ap @ (sub @ X371 @ id) @ X370)) = ((ap @ (sub @ X369 @ id) @ X372)))))) & (hoaslamnotvar_lthm = $true) & (((? [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 != X126) & (((ap @ X124 @ X125)) = ((ap @ X123 @ X126)))) | ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 = X126) | (((ap @ X124 @ X125)) != ((ap @ X123 @ X126)))) & ? [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) = ((ap @ (sub @ X129 @ id) @ X127))) & (X127 != X128))))) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) != ((d2term @ X507))) | (X506 = X507)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (apnotvar = $true) & ((($true = sP2) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP2))) & ((! [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) = $true) | ($true = ((sP0 @ X332))) | ? [X337 : term] : (($true != ((X332 @ (lam @ X337)))) & (((X332 @ X337)) = $true)) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X332 @ X334)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) != $true) & ($true != ((sP0 @ X332))) & ! [X337 : term] : (($true = ((X332 @ (lam @ X337)))) | (((X332 @ X337)) != $true)) & ! [X334 : term] : ((((var @ X334)) != $true) | (((X332 @ X334)) = $true))))) & (((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X504 : subst] : (((comp @ X504 @ id)) != X504) | ? [X503 : subst] : (((comp @ id @ X503)) != X503)))) & ! [X436 : d_subst] : (d_id = X436)),
% 164.61/23.50 inference(nnf_transformation,[],[f72])).
% 164.61/23.50 thf(f261,plain,(
% 164.61/23.50 (axassoc = $true) & (axapp = $true) & ((axidl = $true) | ? [X71 : subst] : (((comp @ id @ X71)) != X71)) & (! [X71 : subst] : (((comp @ id @ X71)) = X71) | (axidl != $true)) & (! [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) = $true) | (((X254 @ X255)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X256 : subst,X254 : (term > $o),X253 : (term > $o),X257 : term,X255 : term] : ((((X253 @ (sub @ X255 @ (push @ X257 @ X256)))) != $true) & (((X254 @ X255)) = $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true)) & (! [X80 : term,X79 : (term > $o),X81 : subst] : ? [X82 : (term > $o)] : ! [X83 : term] : (((X82 @ X83)) = ((X79 @ (sub @ X83 @ (push @ X80 @ X81))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X80 : term,X79 : (term > $o),X81 : subst] : ! [X82 : (term > $o)] : ? [X83 : term] : (((X82 @ X83)) != ((X79 @ (sub @ X83 @ (push @ X80 @ X81)))))) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem2_lthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) | ? [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) = ((ap @ X184 @ X185))) & (X184 != X186))) & (! [X187 : term,X185 : term,X184 : term,X186 : term] : ((((ap @ X186 @ X187)) != ((ap @ X184 @ X185))) | (X184 = X186)) | (apinj1 != $true)) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3a = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasapinj1 = $true) | ? [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) = ((ap @ (sub @ X365 @ id) @ X368))) & (X365 != X367))) & (! [X366 : term,X367 : term,X368 : term,X365 : term] : ((((ap @ (sub @ X367 @ id) @ X366)) != ((ap @ (sub @ X365 @ id) @ X368))) | (X365 = X367)) | (hoasapinj1 != $true)) & ((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X39 : (subst > term > subst > $o)] : ! [X40 : (term > $o)] : ? [X41 : term] : (((X39 @ id @ X41 @ id)) != ((X40 @ X41)))) & (! [X39 : (subst > term > subst > $o)] : ? [X40 : (term > $o)] : ! [X41 : term] : (((X39 @ id @ X41 @ id)) = ((X40 @ X41))) | (hoasinduction_lem0_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (induction2_gthm = $true) & ((! [X375 : subst] : (((comp @ X375 @ id)) = X375) & ! [X376 : subst] : (((comp @ id @ X376)) = X376)) | ? [X374 : subst] : (((comp @ X374 @ id)) != X374) | ? [X373 : subst] : (((comp @ id @ X373)) != X373) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X375 : subst] : (((comp @ X375 @ id)) != X375) | ? [X376 : subst] : (((comp @ id @ X376)) != X376)) & ! [X374 : subst] : (((comp @ X374 @ id)) = X374) & ! [X373 : subst] : (((comp @ id @ X373)) = X373))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem2 = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction_lem2 != $true)) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2a = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2a != $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((pushprop_lem1_lthm = $true) | (? [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true != ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) & (((X252 @ X251)) = $true)) & ! [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) = X246) & ! [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) = X245))) & (! [X251 : term,X248 : (term > $o),X252 : (term > $o),X249 : subst,X250 : term] : (($true = ((X248 @ (sub @ X251 @ (push @ X250 @ X249))))) | (((X252 @ X251)) != $true)) | ? [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) != X246) | ? [X245 : term,X244 : subst] : (((sub @ one @ (push @ X245 @ X244))) != X245) | (pushprop_lem1_lthm != $true)) & (lamnotvar = $true) & (! [X505 : term] : (((sub @ X505 @ id)) = X505) | (termmset != $true)) & ((termmset = $true) | ? [X505 : term] : (((sub @ X505 @ id)) != X505)) & ((sP46 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP46 != $true)) & (? [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 != X392) & (((ap @ X390 @ X391)) = ((ap @ X392 @ X393)))) | ? [X389 : term] : (((sub @ X389 @ id)) != X389) | ! [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) != ((ap @ (sub @ X396 @ id) @ X397))) | (X395 = X396)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X390 : term,X393 : term,X392 : term,X391 : term] : ((X390 = X392) | (((ap @ X390 @ X391)) != ((ap @ X392 @ X393)))) & ! [X389 : term] : (((sub @ X389 @ id)) = X389) & ? [X395 : term,X396 : term,X397 : term,X394 : term] : ((((ap @ (sub @ X395 @ id) @ X394)) = ((ap @ (sub @ X396 @ id) @ X397))) & (X395 != X396)))) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) | ($true != sP45)) & (($true = sP45) | (induction2_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (lamnotap != $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X526 : term] : ! [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) != ((X527 @ sh @ one)))) & (! [X526 : term] : ? [X527 : (subst > term > term)] : (((sub @ X526 @ (push @ one @ sh))) = ((X527 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (axabs = $true) & ! [X84 : d_term] : (d_one = X84) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP41 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((axvarcons = $true) | ? [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) != X501)) & (! [X501 : term,X502 : subst] : (((sub @ one @ (push @ X501 @ X502))) = X501) | (axvarcons != $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lthm = $true) | (sP39 != $true)) & ((sP39 = $true) | (hoasinduction_lthm != $true)) & (! [X85 : term] : ? [X86 : (subst > term > term)] : ! [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) = ((sub @ X85 @ (push @ X87 @ X88)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X85 : term] : ! [X86 : (subst > term > term)] : ? [X88 : subst,X87 : term] : (((X86 @ X88 @ X87)) != ((sub @ X85 @ (push @ X87 @ X88))))) & (ulamvarsh = $true) & (termmset_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslamnotap = $true) | ? [X380 : term,X379 : term,X381 : (subst > term > term)] : (! [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) = ((sub @ (X381 @ X383 @ X382) @ X384))) & (((ap @ (sub @ X380 @ id) @ X379)) = ((lam @ (X381 @ sh @ one)))))) & (! [X380 : term,X379 : term,X381 : (subst > term > term)] : (? [X382 : term,X383 : subst,X384 : subst] : (((X381 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384))) != ((sub @ (X381 @ X383 @ X382) @ X384))) | (((ap @ (sub @ X380 @ id) @ X379)) != ((lam @ (X381 @ sh @ one))))) | (hoaslamnotap != $true)) & ((axidr = $true) | ? [X54 : subst] : (((comp @ X54 @ id)) != X54)) & (! [X54 : subst] : (((comp @ X54 @ id)) = X54) | (axidr != $true)) & ! [X346 : subst] : ? [X347 : d_subst] : (((d2subst @ X347)) = X346) & (hoasinduction_lem1v2_gthm = $true) & ! [X182 : d_subst,X183 : d_subst] : ((((d2subst @ X182)) != ((d2subst @ X183))) | (X182 = X183)) & ((sP30 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP30 != $true)) & ((apinj2 = $true) | ? [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) = ((ap @ X400 @ X398))) & (X398 != X399))) & (! [X398 : term,X400 : term,X401 : term,X399 : term] : ((((ap @ X401 @ X399)) != ((ap @ X400 @ X398))) | (X398 = X399)) | (apinj2 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3v2 != $true)) & ((induction2lem = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem != $true)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (pushprop = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) = X345) | (axscons != $true)) & ((axscons = $true) | ? [X345 : subst] : (((push @ (sub @ one @ X345) @ (comp @ sh @ X345))) != X345)) & (hoasinduction_lem1v2 = $true) & (($true = sP22) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP22)) & (pushprop_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X136 : term] : ! [X137 : (subst > term > term)] : ? [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) != ((X137 @ X138 @ X139)))) & (! [X136 : term] : ? [X137 : (subst > term > term)] : ! [X138 : subst,X139 : term] : (((sub @ X136 @ (push @ X139 @ X138))) = ((X137 @ X138 @ X139))) | (hoasinduction_lem3v2_f_lthm != $true)) & ! [X140 : term] : ? [X141 : d_term] : (((d2term @ X141)) = X140) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (? [X377 : term] : (((sub @ X377 @ id)) != X377) | ! [X378 : term] : (((sub @ X378 @ id)) = X378) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X377 : term] : (((sub @ X377 @ id)) = X377) & ? [X378 : term] : (((sub @ X378 @ id)) != X378))) & ((hoaslaminj = $true) | ? [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) = ((lam @ (X44 @ sh @ one)))) & (((X42 @ X43 @ X45)) != ((X44 @ X43 @ X45))) & ! [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) = ((sub @ (X42 @ X49 @ X51) @ X50))) & ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) = ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46)))))) & (! [X45 : term,X43 : subst,X42 : (subst > term > term),X44 : (subst > term > term)] : ((((lam @ (X42 @ sh @ one))) != ((lam @ (X44 @ sh @ one)))) | (((X42 @ X43 @ X45)) = ((X44 @ X43 @ X45))) | ? [X51 : term,X50 : subst,X49 : subst] : (((X42 @ (comp @ X49 @ X50) @ (sub @ X51 @ X50))) != ((sub @ (X42 @ X49 @ X51) @ X50))) | ? [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X44 @ X48 @ X47) @ X46)) != ((X44 @ (comp @ X48 @ X46) @ (sub @ X47 @ X46))))) | (hoaslaminj != $true)) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (((d2subst @ d_id)) = sh) & ((axvarid = $true) | ? [X388 : term] : (((sub @ X388 @ id)) != X388)) & (! [X388 : term] : (((sub @ X388 @ id)) = X388) | (axvarid != $true)) & (! [X188 : term] : ? [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) = ((X189 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X188 : term] : ! [X189 : (subst > term > term)] : (((sub @ X188 @ (push @ one @ sh))) != ((X189 @ sh @ one)))) & ((sP20 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP20 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X410 : term,X411 : term] : ((X410 = X411) | (((lam @ X410)) != ((lam @ X411)))) | (laminj != $true)) & ((laminj = $true) | ? [X410 : term,X411 : term] : ((X410 != X411) & (((lam @ X410)) = ((lam @ X411))))) & (hoasinduction_lem1 = $true) & (! [X323 : (subst > term > subst > $o),X324 : term] : (? [X325 : (subst > term > term)] : (($true != ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) & ! [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) = $true) | ($true != ((X323 @ id @ X329 @ id)))) & ! [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) = ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) | (((X323 @ id @ X324 @ id)) = $true) | (((sP15 @ X323)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X323 : (subst > term > subst > $o),X324 : term] : (! [X325 : (subst > term > term)] : (($true = ((X323 @ id @ (lam @ (X325 @ sh @ one)) @ id))) | ? [X329 : term] : ((((X323 @ id @ (X325 @ id @ X329) @ id)) != $true) & ($true = ((X323 @ id @ X329 @ id)))) | ? [X327 : subst,X328 : subst,X326 : term] : (((sub @ (X325 @ X328 @ X326) @ X327)) != ((X325 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))))) & (((X323 @ id @ X324 @ id)) != $true) & (((sP15 @ X323)) != $true))) & (pushprop_lem3v2_lthm = $true) & (! [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) != $true) | ? [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) != ((X131 @ X135))) | (((X131 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X132 : term,X131 : (term > $o),X134 : (term > $o),X133 : subst] : ((((X134 @ X132)) = $true) & ! [X135 : term] : (((X134 @ (sub @ X135 @ (push @ X132 @ X133)))) = ((X131 @ X135))) & (((X131 @ one)) != $true))) & (! [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) | (shinj != $true)) & ((shinj = $true) | ? [X53 : term,X52 : term] : ((((sub @ X52 @ sh)) = ((sub @ X53 @ sh))) & (X52 != X53))) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & (one = ((d2term @ d_one))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem2v2_gthm = $true) & (! [X142 : subst,X144 : (term > $o),X143 : term] : ? [X145 : (term > $o)] : ! [X146 : term] : (((X145 @ X146)) = ((X144 @ (sub @ X146 @ (push @ X143 @ X142))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X142 : subst,X144 : (term > $o),X143 : term] : ! [X145 : (term > $o)] : ? [X146 : term] : (((X145 @ X146)) != ((X144 @ (sub @ X146 @ (push @ X143 @ X142)))))) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & ((sP14 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP14 != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP13)) & (($true = sP13) | (hoaslaminj_lthm != $true)) & (! [X385 : (subst > term > subst > $o)] : ? [X386 : (term > $o)] : ! [X387 : term] : (((X386 @ X387)) = ((X385 @ id @ X387 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X385 : (subst > term > subst > $o)] : ! [X386 : (term > $o)] : ? [X387 : term] : (((X386 @ X387)) != ((X385 @ id @ X387 @ id)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) = X148) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X148 : subst,X147 : term] : (((comp @ sh @ (push @ X147 @ X148))) != X148)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) = X338) & ? [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) = $true) & ! [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) = ((X343 @ X344))) & (((X343 @ one)) != $true)))) & (? [X339 : subst,X338 : term] : (((sub @ one @ (push @ X338 @ X339))) != X338) | ! [X341 : term,X342 : (term > $o),X343 : (term > $o),X340 : subst] : ((((X342 @ X341)) != $true) | ? [X344 : term] : (((X342 @ (sub @ X344 @ (push @ X341 @ X340)))) != ((X343 @ X344))) | (((X343 @ one)) = $true)) | (pushprop_lem1v2_lthm != $true)) & (axvarshift = $true) & ((sP12 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP12 != $true)) & ((sP11 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP11 != $true)) & (hoasapinj2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10)) & ((sP4 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP4 != $true)) & (! [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 = X372) | (((ap @ (sub @ X371 @ id) @ X370)) != ((ap @ (sub @ X369 @ id) @ X372)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X371 : term,X370 : term,X369 : term,X372 : term] : ((X370 != X372) & (((ap @ (sub @ X371 @ id) @ X370)) = ((ap @ (sub @ X369 @ id) @ X372))))) & (hoaslamnotvar_lthm = $true) & (? [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 != X126) & (((ap @ X124 @ X125)) = ((ap @ X123 @ X126)))) | ! [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) != ((ap @ (sub @ X129 @ id) @ X127))) | (X127 = X128)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X123 : term,X126 : term,X125 : term,X124 : term] : ((X125 = X126) | (((ap @ X124 @ X125)) != ((ap @ X123 @ X126)))) & ? [X130 : term,X129 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X130 @ id) @ X128)) = ((ap @ (sub @ X129 @ id) @ X127))) & (X127 != X128)))) & ! [X506 : d_term,X507 : d_term] : ((((d2term @ X506)) != ((d2term @ X507))) | (X506 = X507)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (apnotvar = $true) & (($true = sP2) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP2)) & (! [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) = $true) | ($true = ((sP0 @ X332))) | ? [X337 : term] : (($true != ((X332 @ (lam @ X337)))) & (((X332 @ X337)) = $true)) | ? [X334 : term] : ((((var @ X334)) = $true) & (((X332 @ X334)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X333 : term,X332 : (term > $o)] : ((((X332 @ X333)) != $true) & ($true != ((sP0 @ X332))) & ! [X337 : term] : (($true = ((X332 @ (lam @ X337)))) | (((X332 @ X337)) != $true)) & ! [X334 : term] : ((((var @ X334)) != $true) | (((X332 @ X334)) = $true)))) & ((! [X504 : subst] : (((comp @ X504 @ id)) = X504) & ! [X503 : subst] : (((comp @ id @ X503)) = X503)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X504 : subst] : (((comp @ X504 @ id)) != X504) | ? [X503 : subst] : (((comp @ id @ X503)) != X503)) & ! [X436 : d_subst] : (d_id = X436)),
% 0.22/23.50 inference(flattening,[],[f260])).
% 0.22/23.50 thf(f262,plain,(
% 0.22/23.50 (axassoc = $true) & (axapp = $true) & ((axidl = $true) | ? [X0 : subst] : (((comp @ id @ X0)) != X0)) & (! [X1 : subst] : (((comp @ id @ X1)) = X1) | (axidl != $true)) & (! [X2 : subst,X3 : (term > $o),X4 : (term > $o),X5 : term,X6 : term] : ((((X4 @ (sub @ X6 @ (push @ X5 @ X2)))) = $true) | (((X3 @ X6)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X7 : subst,X8 : (term > $o),X9 : (term > $o),X10 : term,X11 : term] : (($true != ((X9 @ (sub @ X11 @ (push @ X10 @ X7))))) & ($true = ((X8 @ X11))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true)) & (! [X12 : term,X13 : (term > $o),X14 : subst] : ? [X15 : (term > $o)] : ! [X16 : term] : (((X13 @ (sub @ X16 @ (push @ X12 @ X14)))) = ((X15 @ X16))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X17 : term,X18 : (term > $o),X19 : subst] : ! [X20 : (term > $o)] : ? [X21 : term] : (((X18 @ (sub @ X21 @ (push @ X17 @ X19)))) != ((X20 @ X21)))) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem2_lthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) | ? [X22 : term,X23 : term,X24 : term,X25 : term] : ((((ap @ X24 @ X23)) = ((ap @ X25 @ X22))) & (X24 != X25))) & (! [X26 : term,X27 : term,X28 : term,X29 : term] : ((((ap @ X29 @ X26)) != ((ap @ X28 @ X27))) | (X28 = X29)) | (apinj1 != $true)) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3a = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasapinj1 = $true) | ? [X30 : term,X31 : term,X32 : term,X33 : term] : ((((ap @ (sub @ X31 @ id) @ X30)) = ((ap @ (sub @ X33 @ id) @ X32))) & (X31 != X33))) & (! [X34 : term,X35 : term,X36 : term,X37 : term] : ((((ap @ (sub @ X35 @ id) @ X34)) != ((ap @ (sub @ X37 @ id) @ X36))) | (X35 = X37)) | (hoasapinj1 != $true)) & ((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X38 : (subst > term > subst > $o)] : ! [X39 : (term > $o)] : ? [X40 : term] : (((X39 @ X40)) != ((X38 @ id @ X40 @ id)))) & (! [X41 : (subst > term > subst > $o)] : ? [X42 : (term > $o)] : ! [X43 : term] : (((X42 @ X43)) = ((X41 @ id @ X43 @ id))) | (hoasinduction_lem0_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (induction2_gthm = $true) & ((! [X44 : subst] : (((comp @ X44 @ id)) = X44) & ! [X45 : subst] : (((comp @ id @ X45)) = X45)) | ? [X46 : subst] : (((comp @ X46 @ id)) != X46) | ? [X47 : subst] : (((comp @ id @ X47)) != X47) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X48 : subst] : (((comp @ X48 @ id)) != X48) | ? [X49 : subst] : (((comp @ id @ X49)) != X49)) & ! [X50 : subst] : (((comp @ X50 @ id)) = X50) & ! [X51 : subst] : (((comp @ id @ X51)) = X51))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem2 = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction_lem2 != $true)) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2a = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2a != $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((pushprop_lem1_lthm = $true) | (? [X52 : term,X53 : (term > $o),X54 : (term > $o),X55 : subst,X56 : term] : (($true != ((X53 @ (sub @ X52 @ (push @ X56 @ X55))))) & ($true = ((X54 @ X52)))) & ! [X57 : subst,X58 : term] : (((comp @ sh @ (push @ X58 @ X57))) = X57) & ! [X59 : term,X60 : subst] : (((sub @ one @ (push @ X59 @ X60))) = X59))) & (! [X61 : term,X62 : (term > $o),X63 : (term > $o),X64 : subst,X65 : term] : (($true = ((X62 @ (sub @ X61 @ (push @ X65 @ X64))))) | (((X63 @ X61)) != $true)) | ? [X66 : subst,X67 : term] : (((comp @ sh @ (push @ X67 @ X66))) != X66) | ? [X68 : term,X69 : subst] : (((sub @ one @ (push @ X68 @ X69))) != X68) | (pushprop_lem1_lthm != $true)) & (lamnotvar = $true) & (! [X70 : term] : (((sub @ X70 @ id)) = X70) | (termmset != $true)) & ((termmset = $true) | ? [X71 : term] : (((sub @ X71 @ id)) != X71)) & ((sP46 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP46 != $true)) & (? [X72 : term,X73 : term,X74 : term,X75 : term] : ((X72 != X74) & (((ap @ X74 @ X73)) = ((ap @ X72 @ X75)))) | ? [X76 : term] : (((sub @ X76 @ id)) != X76) | ! [X77 : term,X78 : term,X79 : term,X80 : term] : ((((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79))) | (X77 = X78)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X81 : term,X82 : term,X83 : term,X84 : term] : ((X81 = X83) | (((ap @ X83 @ X82)) != ((ap @ X81 @ X84)))) & ! [X85 : term] : (((sub @ X85 @ id)) = X85) & ? [X86 : term,X87 : term,X88 : term,X89 : term] : ((((ap @ (sub @ X87 @ id) @ X88)) = ((ap @ (sub @ X86 @ id) @ X89))) & (X86 != X87)))) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) | ($true != sP45)) & (($true = sP45) | (induction2_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (lamnotap != $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X90 : term] : ! [X91 : (subst > term > term)] : (((sub @ X90 @ (push @ one @ sh))) != ((X91 @ sh @ one)))) & (! [X92 : term] : ? [X93 : (subst > term > term)] : (((sub @ X92 @ (push @ one @ sh))) = ((X93 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (axabs = $true) & ! [X94 : d_term] : (d_one = X94) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP41 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((axvarcons = $true) | ? [X95 : term,X96 : subst] : (((sub @ one @ (push @ X95 @ X96))) != X95)) & (! [X97 : term,X98 : subst] : (((sub @ one @ (push @ X97 @ X98))) = X97) | (axvarcons != $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lthm = $true) | (sP39 != $true)) & ((sP39 = $true) | (hoasinduction_lthm != $true)) & (! [X99 : term] : ? [X100 : (subst > term > term)] : ! [X101 : subst,X102 : term] : (((sub @ X99 @ (push @ X102 @ X101))) = ((X100 @ X101 @ X102))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X103 : term] : ! [X104 : (subst > term > term)] : ? [X105 : subst,X106 : term] : (((X104 @ X105 @ X106)) != ((sub @ X103 @ (push @ X106 @ X105))))) & (ulamvarsh = $true) & (termmset_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslamnotap = $true) | ? [X107 : term,X108 : term,X109 : (subst > term > term)] : (! [X110 : term,X111 : subst,X112 : subst] : (((sub @ (X109 @ X111 @ X110) @ X112)) = ((X109 @ (comp @ X111 @ X112) @ (sub @ X110 @ X112)))) & (((ap @ (sub @ X107 @ id) @ X108)) = ((lam @ (X109 @ sh @ one)))))) & (! [X113 : term,X114 : term,X115 : (subst > term > term)] : (? [X116 : term,X117 : subst,X118 : subst] : (((sub @ (X115 @ X117 @ X116) @ X118)) != ((X115 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118)))) | (((ap @ (sub @ X113 @ id) @ X114)) != ((lam @ (X115 @ sh @ one))))) | (hoaslamnotap != $true)) & ((axidr = $true) | ? [X119 : subst] : (((comp @ X119 @ id)) != X119)) & (! [X120 : subst] : (((comp @ X120 @ id)) = X120) | (axidr != $true)) & ! [X121 : subst] : ? [X122 : d_subst] : (((d2subst @ X122)) = X121) & (hoasinduction_lem1v2_gthm = $true) & ! [X123 : d_subst,X124 : d_subst] : ((((d2subst @ X124)) != ((d2subst @ X123))) | (X123 = X124)) & ((sP30 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP30 != $true)) & ((apinj2 = $true) | ? [X125 : term,X126 : term,X127 : term,X128 : term] : ((((ap @ X127 @ X128)) = ((ap @ X126 @ X125))) & (X125 != X128))) & (! [X129 : term,X130 : term,X131 : term,X132 : term] : ((((ap @ X130 @ X129)) != ((ap @ X131 @ X132))) | (X129 = X132)) | (apinj2 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3v2 != $true)) & ((induction2lem = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem != $true)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (pushprop = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X133 : subst] : (((push @ (sub @ one @ X133) @ (comp @ sh @ X133))) = X133) | (axscons != $true)) & ((axscons = $true) | ? [X134 : subst] : (((push @ (sub @ one @ X134) @ (comp @ sh @ X134))) != X134)) & (hoasinduction_lem1v2 = $true) & (($true = sP22) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP22)) & (pushprop_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X135 : term] : ! [X136 : (subst > term > term)] : ? [X137 : subst,X138 : term] : (((X136 @ X137 @ X138)) != ((sub @ X135 @ (push @ X138 @ X137))))) & (! [X139 : term] : ? [X140 : (subst > term > term)] : ! [X141 : subst,X142 : term] : (((sub @ X139 @ (push @ X142 @ X141))) = ((X140 @ X141 @ X142))) | (hoasinduction_lem3v2_f_lthm != $true)) & ! [X143 : term] : ? [X144 : d_term] : (((d2term @ X144)) = X143) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (? [X145 : term] : (((sub @ X145 @ id)) != X145) | ! [X146 : term] : (((sub @ X146 @ id)) = X146) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X147 : term] : (((sub @ X147 @ id)) = X147) & ? [X148 : term] : (((sub @ X148 @ id)) != X148))) & ((hoaslaminj = $true) | ? [X149 : term,X150 : subst,X151 : (subst > term > term),X152 : (subst > term > term)] : ((((lam @ (X151 @ sh @ one))) = ((lam @ (X152 @ sh @ one)))) & (((X151 @ X150 @ X149)) != ((X152 @ X150 @ X149))) & ! [X153 : term,X154 : subst,X155 : subst] : (((X151 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154))) = ((sub @ (X151 @ X155 @ X153) @ X154))) & ! [X156 : subst,X157 : term,X158 : subst] : (((X152 @ (comp @ X158 @ X156) @ (sub @ X157 @ X156))) = ((sub @ (X152 @ X158 @ X157) @ X156))))) & (! [X159 : term,X160 : subst,X161 : (subst > term > term),X162 : (subst > term > term)] : ((((lam @ (X161 @ sh @ one))) != ((lam @ (X162 @ sh @ one)))) | (((X161 @ X160 @ X159)) = ((X162 @ X160 @ X159))) | ? [X163 : term,X164 : subst,X165 : subst] : (((X161 @ (comp @ X165 @ X164) @ (sub @ X163 @ X164))) != ((sub @ (X161 @ X165 @ X163) @ X164))) | ? [X166 : subst,X167 : term,X168 : subst] : (((sub @ (X162 @ X168 @ X167) @ X166)) != ((X162 @ (comp @ X168 @ X166) @ (sub @ X167 @ X166))))) | (hoaslaminj != $true)) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (((d2subst @ d_id)) = sh) & ((axvarid = $true) | ? [X169 : term] : (((sub @ X169 @ id)) != X169)) & (! [X170 : term] : (((sub @ X170 @ id)) = X170) | (axvarid != $true)) & (! [X171 : term] : ? [X172 : (subst > term > term)] : (((X172 @ sh @ one)) = ((sub @ X171 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X173 : term] : ! [X174 : (subst > term > term)] : (((sub @ X173 @ (push @ one @ sh))) != ((X174 @ sh @ one)))) & ((sP20 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP20 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X175 : term,X176 : term] : ((X175 = X176) | (((lam @ X175)) != ((lam @ X176)))) | (laminj != $true)) & ((laminj = $true) | ? [X177 : term,X178 : term] : ((X177 != X178) & (((lam @ X178)) = ((lam @ X177))))) & (hoasinduction_lem1 = $true) & (! [X179 : (subst > term > subst > $o),X180 : term] : (? [X181 : (subst > term > term)] : ((((X179 @ id @ (lam @ (X181 @ sh @ one)) @ id)) != $true) & ! [X182 : term] : (($true = ((X179 @ id @ (X181 @ id @ X182) @ id))) | ($true != ((X179 @ id @ X182 @ id)))) & ! [X183 : subst,X184 : subst,X185 : term] : (((X181 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183))) = ((sub @ (X181 @ X184 @ X185) @ X183)))) | (((X179 @ id @ X180 @ id)) = $true) | (((sP15 @ X179)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X186 : (subst > term > subst > $o),X187 : term] : (! [X188 : (subst > term > term)] : (($true = ((X186 @ id @ (lam @ (X188 @ sh @ one)) @ id))) | ? [X189 : term] : ((((X186 @ id @ (X188 @ id @ X189) @ id)) != $true) & (((X186 @ id @ X189 @ id)) = $true)) | ? [X190 : subst,X191 : subst,X192 : term] : (((sub @ (X188 @ X191 @ X192) @ X190)) != ((X188 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190))))) & ($true != ((X186 @ id @ X187 @ id))) & (((sP15 @ X186)) != $true))) & (pushprop_lem3v2_lthm = $true) & (! [X193 : term,X194 : (term > $o),X195 : (term > $o),X196 : subst] : (($true != ((X195 @ X193))) | ? [X197 : term] : (((X194 @ X197)) != ((X195 @ (sub @ X197 @ (push @ X193 @ X196))))) | (((X194 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X198 : term,X199 : (term > $o),X200 : (term > $o),X201 : subst] : (($true = ((X200 @ X198))) & ! [X202 : term] : (((X200 @ (sub @ X202 @ (push @ X198 @ X201)))) = ((X199 @ X202))) & ($true != ((X199 @ one))))) & (! [X203 : term,X204 : term] : ((((sub @ X203 @ sh)) != ((sub @ X204 @ sh))) | (X203 = X204)) | (shinj != $true)) & ((shinj = $true) | ? [X205 : term,X206 : term] : ((((sub @ X205 @ sh)) = ((sub @ X206 @ sh))) & (X205 != X206))) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & (one = ((d2term @ d_one))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem2v2_gthm = $true) & (! [X207 : subst,X208 : (term > $o),X209 : term] : ? [X210 : (term > $o)] : ! [X211 : term] : (((X208 @ (sub @ X211 @ (push @ X209 @ X207)))) = ((X210 @ X211))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X212 : subst,X213 : (term > $o),X214 : term] : ! [X215 : (term > $o)] : ? [X216 : term] : (((X213 @ (sub @ X216 @ (push @ X214 @ X212)))) != ((X215 @ X216)))) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & ((sP14 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP14 != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP13)) & (($true = sP13) | (hoaslaminj_lthm != $true)) & (! [X217 : (subst > term > subst > $o)] : ? [X218 : (term > $o)] : ! [X219 : term] : (((X217 @ id @ X219 @ id)) = ((X218 @ X219))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X220 : (subst > term > subst > $o)] : ! [X221 : (term > $o)] : ? [X222 : term] : (((X220 @ id @ X222 @ id)) != ((X221 @ X222)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X223 : subst,X224 : term] : (((comp @ sh @ (push @ X224 @ X223))) = X223) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X225 : subst,X226 : term] : (((comp @ sh @ (push @ X226 @ X225))) != X225)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X227 : subst,X228 : term] : (((sub @ one @ (push @ X228 @ X227))) = X228) & ? [X229 : term,X230 : (term > $o),X231 : (term > $o),X232 : subst] : (($true = ((X230 @ X229))) & ! [X233 : term] : (((X230 @ (sub @ X233 @ (push @ X229 @ X232)))) = ((X231 @ X233))) & (((X231 @ one)) != $true)))) & (? [X234 : subst,X235 : term] : (((sub @ one @ (push @ X235 @ X234))) != X235) | ! [X236 : term,X237 : (term > $o),X238 : (term > $o),X239 : subst] : ((((X237 @ X236)) != $true) | ? [X240 : term] : (((X238 @ X240)) != ((X237 @ (sub @ X240 @ (push @ X236 @ X239))))) | (((X238 @ one)) = $true)) | (pushprop_lem1v2_lthm != $true)) & (axvarshift = $true) & ((sP12 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP12 != $true)) & ((sP11 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP11 != $true)) & (hoasapinj2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10)) & ((sP4 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP4 != $true)) & (! [X241 : term,X242 : term,X243 : term,X244 : term] : ((X242 = X244) | (((ap @ (sub @ X241 @ id) @ X242)) != ((ap @ (sub @ X243 @ id) @ X244)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X245 : term,X246 : term,X247 : term,X248 : term] : ((X246 != X248) & (((ap @ (sub @ X245 @ id) @ X246)) = ((ap @ (sub @ X247 @ id) @ X248))))) & (hoaslamnotvar_lthm = $true) & (? [X249 : term,X250 : term,X251 : term,X252 : term] : ((X250 != X251) & (((ap @ X252 @ X251)) = ((ap @ X249 @ X250)))) | ! [X253 : term,X254 : term,X255 : term,X256 : term] : ((((ap @ (sub @ X253 @ id) @ X256)) != ((ap @ (sub @ X254 @ id) @ X255))) | (X255 = X256)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X257 : term,X258 : term,X259 : term,X260 : term] : ((X258 = X259) | (((ap @ X260 @ X259)) != ((ap @ X257 @ X258)))) & ? [X261 : term,X262 : term,X263 : term,X264 : term] : ((((ap @ (sub @ X261 @ id) @ X264)) = ((ap @ (sub @ X262 @ id) @ X263))) & (X263 != X264)))) & ! [X265 : d_term,X266 : d_term] : ((((d2term @ X266)) != ((d2term @ X265))) | (X265 = X266)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (apnotvar = $true) & (($true = sP2) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP2)) & (! [X267 : term,X268 : (term > $o)] : (($true = ((X268 @ X267))) | ($true = ((sP0 @ X268))) | ? [X269 : term] : (($true != ((X268 @ (lam @ X269)))) & (((X268 @ X269)) = $true)) | ? [X270 : term] : (($true = ((var @ X270))) & ($true != ((X268 @ X270))))) | (induction != $true)) & ((induction = $true) | ? [X271 : term,X272 : (term > $o)] : (($true != ((X272 @ X271))) & (((sP0 @ X272)) != $true) & ! [X273 : term] : ((((X272 @ (lam @ X273))) = $true) | (((X272 @ X273)) != $true)) & ! [X274 : term] : (($true != ((var @ X274))) | (((X272 @ X274)) = $true)))) & ((! [X275 : subst] : (((comp @ X275 @ id)) = X275) & ! [X276 : subst] : (((comp @ id @ X276)) = X276)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X277 : subst] : (((comp @ X277 @ id)) != X277) | ? [X278 : subst] : (((comp @ id @ X278)) != X278)) & ! [X279 : d_subst] : (d_id = X279)),
% 0.22/23.50 inference(rectify,[],[f261])).
% 0.22/23.50 thf(f263,plain,(
% 0.22/23.50 (axassoc = $true) & (axapp = $true) & ((axidl = $true) | (((comp @ id @ sK454)) != sK454)) & (! [X1 : subst] : (((comp @ id @ X1)) = X1) | (axidl != $true)) & (! [X2 : subst,X3 : (term > $o),X4 : (term > $o),X5 : term,X6 : term] : ((((X4 @ (sub @ X6 @ (push @ X5 @ X2)))) = $true) | (((X3 @ X6)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true != ((sK457 @ (sub @ sK459 @ (push @ sK458 @ sK455))))) & (((sK456 @ sK459)) = $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction != $true)) & (! [X12 : term,X13 : (term > $o),X14 : subst] : ! [X16 : term] : (((sK460 @ X14 @ X13 @ X12 @ X16)) = ((X13 @ (sub @ X16 @ (push @ X12 @ X14))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X20 : (term > $o)] : (((sK462 @ (sub @ (sK464 @ X20) @ (push @ sK461 @ sK463)))) != ((X20 @ (sK464 @ X20))))) & (axmap = $true) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoasinduction_lem2_lthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & ((apinj1 = $true) | ((((ap @ sK468 @ sK465)) = ((ap @ sK467 @ sK466))) & (sK468 != sK467))) & (! [X26 : term,X27 : term,X28 : term,X29 : term] : ((((ap @ X29 @ X26)) != ((ap @ X28 @ X27))) | (X28 = X29)) | (apinj1 != $true)) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ((hoasinduction_lem3a = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK472 @ id) @ sK471)) = ((ap @ (sub @ sK470 @ id) @ sK469))) & (sK472 != sK470))) & (! [X34 : term,X35 : term,X36 : term,X37 : term] : ((((ap @ (sub @ X35 @ id) @ X34)) != ((ap @ (sub @ X37 @ id) @ X36))) | (X35 = X37)) | (hoasapinj1 != $true)) & ((sP51 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP51 != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X39 : (term > $o)] : (((X39 @ (sK474 @ X39))) != ((sK473 @ id @ (sK474 @ X39) @ id)))) & (! [X41 : (subst > term > subst > $o)] : ! [X43 : term] : (((X41 @ id @ X43 @ id)) = ((sK475 @ X41 @ X43))) | (hoasinduction_lem0_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (induction2_gthm = $true) & ((! [X44 : subst] : (((comp @ X44 @ id)) = X44) & ! [X45 : subst] : (((comp @ id @ X45)) = X45)) | (sK476 != ((comp @ sK476 @ id))) | (sK477 != ((comp @ id @ sK477))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (((sK478 != ((comp @ sK478 @ id))) | (((comp @ id @ sK479)) != sK479)) & ! [X50 : subst] : (((comp @ X50 @ id)) = X50) & ! [X51 : subst] : (((comp @ id @ X51)) = X51))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem2 = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction_lem2 != $true)) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2a = $true) | ($true != sP47)) & (($true = sP47) | (hoasinduction_lem3v2a != $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((pushprop_lem1_lthm = $true) | ((($true != ((sK481 @ (sub @ sK480 @ (push @ sK484 @ sK483))))) & ($true = ((sK482 @ sK480)))) & ! [X57 : subst,X58 : term] : (((comp @ sh @ (push @ X58 @ X57))) = X57) & ! [X59 : term,X60 : subst] : (((sub @ one @ (push @ X59 @ X60))) = X59))) & (! [X61 : term,X62 : (term > $o),X63 : (term > $o),X64 : subst,X65 : term] : (($true = ((X62 @ (sub @ X61 @ (push @ X65 @ X64))))) | (((X63 @ X61)) != $true)) | (sK485 != ((comp @ sh @ (push @ sK486 @ sK485)))) | (((sub @ one @ (push @ sK487 @ sK488))) != sK487) | (pushprop_lem1_lthm != $true)) & (lamnotvar = $true) & (! [X70 : term] : (((sub @ X70 @ id)) = X70) | (termmset != $true)) & ((termmset = $true) | (sK489 != ((sub @ sK489 @ id)))) & ((sP46 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP46 != $true)) & (((sK490 != sK492) & (((ap @ sK490 @ sK493)) = ((ap @ sK492 @ sK491)))) | (sK494 != ((sub @ sK494 @ id))) | ! [X77 : term,X78 : term,X79 : term,X80 : term] : ((((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79))) | (X77 = X78)) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X81 : term,X82 : term,X83 : term,X84 : term] : ((X81 = X83) | (((ap @ X83 @ X82)) != ((ap @ X81 @ X84)))) & ! [X85 : term] : (((sub @ X85 @ id)) = X85) & ((((ap @ (sub @ sK496 @ id) @ sK497)) = ((ap @ (sub @ sK495 @ id) @ sK498))) & (sK496 != sK495)))) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) | ($true != sP45)) & (($true = sP45) | (induction2_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (lamnotap != $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X91 : (subst > term > term)] : (((sub @ sK499 @ (push @ one @ sh))) != ((X91 @ sh @ one)))) & (! [X92 : term] : (((sK500 @ X92 @ sh @ one)) = ((sub @ X92 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (axabs = $true) & ! [X94 : d_term] : (d_one = X94) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP41 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP41 != $true)) & ((axvarcons = $true) | (((sub @ one @ (push @ sK501 @ sK502))) != sK501)) & (! [X97 : term,X98 : subst] : (((sub @ one @ (push @ X97 @ X98))) = X97) | (axvarcons != $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lthm = $true) | (sP39 != $true)) & ((sP39 = $true) | (hoasinduction_lthm != $true)) & (! [X99 : term] : ! [X101 : subst,X102 : term] : (((sub @ X99 @ (push @ X102 @ X101))) = ((sK503 @ X99 @ X101 @ X102))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X104 : (subst > term > term)] : (((X104 @ (sK505 @ X104) @ (sK506 @ X104))) != ((sub @ sK504 @ (push @ (sK506 @ X104) @ (sK505 @ X104)))))) & (ulamvarsh = $true) & (termmset_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslamnotap = $true) | (! [X110 : term,X111 : subst,X112 : subst] : (((sK509 @ (comp @ X111 @ X112) @ (sub @ X110 @ X112))) = ((sub @ (sK509 @ X111 @ X110) @ X112))) & (((ap @ (sub @ sK507 @ id) @ sK508)) = ((lam @ (sK509 @ sh @ one)))))) & (! [X113 : term,X114 : term,X115 : (subst > term > term)] : ((((sub @ (X115 @ (sK511 @ X115) @ (sK510 @ X115)) @ (sK512 @ X115))) != ((X115 @ (comp @ (sK511 @ X115) @ (sK512 @ X115)) @ (sub @ (sK510 @ X115) @ (sK512 @ X115))))) | (((ap @ (sub @ X113 @ id) @ X114)) != ((lam @ (X115 @ sh @ one))))) | (hoaslamnotap != $true)) & ((axidr = $true) | (sK513 != ((comp @ sK513 @ id)))) & (! [X120 : subst] : (((comp @ X120 @ id)) = X120) | (axidr != $true)) & ! [X121 : subst] : (((d2subst @ (sK514 @ X121))) = X121) & (hoasinduction_lem1v2_gthm = $true) & ! [X123 : d_subst,X124 : d_subst] : ((((d2subst @ X124)) != ((d2subst @ X123))) | (X123 = X124)) & ((sP30 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP30 != $true)) & ((apinj2 = $true) | ((((ap @ sK517 @ sK518)) = ((ap @ sK516 @ sK515))) & (sK515 != sK518))) & (! [X129 : term,X130 : term,X131 : term,X132 : term] : ((((ap @ X130 @ X129)) != ((ap @ X131 @ X132))) | (X129 = X132)) | (apinj2 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasapnotvar = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2 = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3v2 != $true)) & ((induction2lem = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem != $true)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (pushprop = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X133 : subst] : (((push @ (sub @ one @ X133) @ (comp @ sh @ X133))) = X133) | (axscons != $true)) & ((axscons = $true) | (sK519 != ((push @ (sub @ one @ sK519) @ (comp @ sh @ sK519))))) & (hoasinduction_lem1v2 = $true) & (($true = sP22) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP22)) & (pushprop_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X136 : (subst > term > term)] : (((X136 @ (sK521 @ X136) @ (sK522 @ X136))) != ((sub @ sK520 @ (push @ (sK522 @ X136) @ (sK521 @ X136)))))) & (! [X139 : term] : ! [X141 : subst,X142 : term] : (((sub @ X139 @ (push @ X142 @ X141))) = ((sK523 @ X139 @ X141 @ X142))) | (hoasinduction_lem3v2_f_lthm != $true)) & ! [X143 : term] : (((d2term @ (sK524 @ X143))) = X143) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((((sub @ sK525 @ id)) != sK525) | ! [X146 : term] : (((sub @ X146 @ id)) = X146) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X147 : term] : (((sub @ X147 @ id)) = X147) & (sK526 != ((sub @ sK526 @ id))))) & ((hoaslaminj = $true) | ((((lam @ (sK530 @ sh @ one))) = ((lam @ (sK529 @ sh @ one)))) & (((sK529 @ sK528 @ sK527)) != ((sK530 @ sK528 @ sK527))) & ! [X153 : term,X154 : subst,X155 : subst] : (((sub @ (sK529 @ X155 @ X153) @ X154)) = ((sK529 @ (comp @ X155 @ X154) @ (sub @ X153 @ X154)))) & ! [X156 : subst,X157 : term,X158 : subst] : (((sub @ (sK530 @ X158 @ X157) @ X156)) = ((sK530 @ (comp @ X158 @ X156) @ (sub @ X157 @ X156)))))) & (! [X159 : term,X160 : subst,X161 : (subst > term > term),X162 : (subst > term > term)] : ((((lam @ (X161 @ sh @ one))) != ((lam @ (X162 @ sh @ one)))) | (((X161 @ X160 @ X159)) = ((X162 @ X160 @ X159))) | (((sub @ (X161 @ (sK533 @ X161) @ (sK531 @ X161)) @ (sK532 @ X161))) != ((X161 @ (comp @ (sK533 @ X161) @ (sK532 @ X161)) @ (sub @ (sK531 @ X161) @ (sK532 @ X161))))) | (((sub @ (X162 @ (sK536 @ X162) @ (sK535 @ X162)) @ (sK534 @ X162))) != ((X162 @ (comp @ (sK536 @ X162) @ (sK534 @ X162)) @ (sub @ (sK535 @ X162) @ (sK534 @ X162)))))) | (hoaslaminj != $true)) & (hoasinduction_lem2_gthm = $true) & (ulamvar1 != $true) & (((d2subst @ d_id)) = sh) & ((axvarid = $true) | (sK537 != ((sub @ sK537 @ id)))) & (! [X170 : term] : (((sub @ X170 @ id)) = X170) | (axvarid != $true)) & (! [X171 : term] : (((sub @ X171 @ (push @ one @ sh))) = ((sK538 @ X171 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X174 : (subst > term > term)] : (((X174 @ sh @ one)) != ((sub @ sK539 @ (push @ one @ sh))))) & ((sP20 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP20 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X175 : term,X176 : term] : ((X175 = X176) | (((lam @ X175)) != ((lam @ X176)))) | (laminj != $true)) & ((laminj = $true) | ((sK541 != sK540) & (((lam @ sK541)) = ((lam @ sK540))))) & (hoasinduction_lem1 = $true) & (! [X179 : (subst > term > subst > $o),X180 : term] : ((($true != ((X179 @ id @ (lam @ (sK542 @ X179 @ sh @ one)) @ id))) & ! [X182 : term] : (($true = ((X179 @ id @ (sK542 @ X179 @ id @ X182) @ id))) | ($true != ((X179 @ id @ X182 @ id)))) & ! [X183 : subst,X184 : subst,X185 : term] : (((sK542 @ X179 @ (comp @ X184 @ X183) @ (sub @ X185 @ X183))) = ((sub @ (sK542 @ X179 @ X184 @ X185) @ X183)))) | (((X179 @ id @ X180 @ id)) = $true) | (((sP15 @ X179)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X188 : (subst > term > term)] : (($true = ((sK543 @ id @ (lam @ (X188 @ sh @ one)) @ id))) | (($true != ((sK543 @ id @ (X188 @ id @ (sK545 @ X188)) @ id))) & ($true = ((sK543 @ id @ (sK545 @ X188) @ id)))) | (((X188 @ (comp @ (sK547 @ X188) @ (sK546 @ X188)) @ (sub @ (sK548 @ X188) @ (sK546 @ X188)))) != ((sub @ (X188 @ (sK547 @ X188) @ (sK548 @ X188)) @ (sK546 @ X188))))) & ($true != ((sK543 @ id @ sK544 @ id))) & (((sP15 @ sK543)) != $true))) & (pushprop_lem3v2_lthm = $true) & (! [X193 : term,X194 : (term > $o),X195 : (term > $o),X196 : subst] : (($true != ((X195 @ X193))) | (((X194 @ (sK549 @ X196 @ X195 @ X194 @ X193))) != ((X195 @ (sub @ (sK549 @ X196 @ X195 @ X194 @ X193) @ (push @ X193 @ X196))))) | (((X194 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true = ((sK552 @ sK550))) & ! [X202 : term] : (((sK552 @ (sub @ X202 @ (push @ sK550 @ sK553)))) = ((sK551 @ X202))) & ($true != ((sK551 @ one))))) & (! [X203 : term,X204 : term] : ((((sub @ X203 @ sh)) != ((sub @ X204 @ sh))) | (X203 = X204)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK554 @ sh)) = ((sub @ sK555 @ sh))) & (sK555 != sK554))) & (hoasinduction_gthm = $true) & (hoaslamnotvar = $true) & (one = ((d2term @ d_one))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem2v2_gthm = $true) & (! [X207 : subst,X208 : (term > $o),X209 : term] : ! [X211 : term] : (((X208 @ (sub @ X211 @ (push @ X209 @ X207)))) = ((sK556 @ X209 @ X208 @ X207 @ X211))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X215 : (term > $o)] : (((sK558 @ (sub @ (sK560 @ X215) @ (push @ sK559 @ sK557)))) != ((X215 @ (sK560 @ X215))))) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & ((sP14 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP14 != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP13)) & (($true = sP13) | (hoaslaminj_lthm != $true)) & (! [X217 : (subst > term > subst > $o)] : ! [X219 : term] : (((X217 @ id @ X219 @ id)) = ((sK561 @ X217 @ X219))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X221 : (term > $o)] : (((X221 @ (sK563 @ X221))) != ((sK562 @ id @ (sK563 @ X221) @ id)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X223 : subst,X224 : term] : (((comp @ sh @ (push @ X224 @ X223))) = X223) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK564 != ((comp @ sh @ (push @ sK565 @ sK564))))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X227 : subst,X228 : term] : (((sub @ one @ (push @ X228 @ X227))) = X228) & (($true = ((sK567 @ sK566))) & ! [X233 : term] : (((sK567 @ (sub @ X233 @ (push @ sK566 @ sK569)))) = ((sK568 @ X233))) & (((sK568 @ one)) != $true)))) & ((((sub @ one @ (push @ sK571 @ sK570))) != sK571) | ! [X236 : term,X237 : (term > $o),X238 : (term > $o),X239 : subst] : ((((X237 @ X236)) != $true) | (((X237 @ (sub @ (sK572 @ X239 @ X238 @ X237 @ X236) @ (push @ X236 @ X239)))) != ((X238 @ (sK572 @ X239 @ X238 @ X237 @ X236)))) | (((X238 @ one)) = $true)) | (pushprop_lem1v2_lthm != $true)) & (axvarshift = $true) & ((sP12 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP12 != $true)) & ((sP11 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP11 != $true)) & (hoasapinj2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (($true = sP10) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP10)) & ((sP4 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP4 != $true)) & (! [X241 : term,X242 : term,X243 : term,X244 : term] : ((X242 = X244) | (((ap @ (sub @ X241 @ id) @ X242)) != ((ap @ (sub @ X243 @ id) @ X244)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((sK576 != sK574) & (((ap @ (sub @ sK575 @ id) @ sK576)) = ((ap @ (sub @ sK573 @ id) @ sK574))))) & (hoaslamnotvar_lthm = $true) & (((sK579 != sK578) & (((ap @ sK577 @ sK578)) = ((ap @ sK580 @ sK579)))) | ! [X253 : term,X254 : term,X255 : term,X256 : term] : ((((ap @ (sub @ X253 @ id) @ X256)) != ((ap @ (sub @ X254 @ id) @ X255))) | (X255 = X256)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X257 : term,X258 : term,X259 : term,X260 : term] : ((X258 = X259) | (((ap @ X260 @ X259)) != ((ap @ X257 @ X258)))) & ((((ap @ (sub @ sK582 @ id) @ sK583)) = ((ap @ (sub @ sK581 @ id) @ sK584))) & (sK583 != sK584)))) & ! [X265 : d_term,X266 : d_term] : ((((d2term @ X266)) != ((d2term @ X265))) | (X265 = X266)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (apnotvar = $true) & (($true = sP2) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP2)) & (! [X267 : term,X268 : (term > $o)] : (($true = ((X268 @ X267))) | ($true = ((sP0 @ X268))) | ((((X268 @ (lam @ (sK585 @ X268)))) != $true) & ($true = ((X268 @ (sK585 @ X268))))) | ((((var @ (sK586 @ X268))) = $true) & (((X268 @ (sK586 @ X268))) != $true))) | (induction != $true)) & ((induction = $true) | ((((sK588 @ sK587)) != $true) & ($true != ((sP0 @ sK588))) & ! [X273 : term] : (($true = ((sK588 @ (lam @ X273)))) | ($true != ((sK588 @ X273)))) & ! [X274 : term] : (($true != ((var @ X274))) | (((sK588 @ X274)) = $true)))) & ((! [X275 : subst] : (((comp @ X275 @ id)) = X275) & ! [X276 : subst] : (((comp @ id @ X276)) = X276)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ sK589 @ id)) != sK589) | (sK590 != ((comp @ id @ sK590)))) & ! [X279 : d_subst] : (d_id = X279)),
% 0.22/23.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,vAPP,sK461,sK462,sK463,vAPP,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,vAPP,vAPP,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,vAPP,sK501,sK502,vAPP,sK504,vAPP,vAPP,sK507,sK508,sK509,vAPP,vAPP,vAPP,sK513,vAPP,sK515,sK516,sK517,sK518,sK519,sK520,vAPP,vAPP,vAPP,vAPP,sK525,sK526,sK527,sK528,sK529,sK530,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK537,vAPP,sK539,sK540,sK541,vAPP,sK543,sK544,vAPP,vAPP,vAPP,vAPP,vAPP,sK550,sK551,sK552,sK553,sK554,sK555,vAPP,sK557,sK558,sK559,vAPP,vAPP,sK562,vAPP,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,vAPP,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,vAPP,vAPP,sK587,sK588,sK589,sK590]),skolemize(X0,sK454),skolemize(X7,sK455),skolemize(X8,sK456),skolemize(X9,sK457),skolemize(X10,sK458),skolemize(X11,sK459),skolemize(X21,sK69 @ X12),skolemize(X17,sK461),skolemize(X18,sK462),skolemize(X19,sK463),skolemize(X21,sK69 @ X12),skolemize(X22,sK465),skolemize(X23,sK466),skolemize(X24,sK467),skolemize(X25,sK468),skolemize(X30,sK469),skolemize(X31,sK470),skolemize(X32,sK471),skolemize(X33,sK472),skolemize(X38,sK473),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X46,sK476),skolemize(X47,sK477),skolemize(X48,sK478),skolemize(X49,sK479),skolemize(X52,sK480),skolemize(X53,sK481),skolemize(X54,sK482),skolemize(X55,sK483),skolemize(X56,sK484),skolemize(X66,sK485),skolemize(X67,sK486),skolemize(X68,sK487),skolemize(X69,sK488),skolemize(X71,sK489),skolemize(X72,sK490),skolemize(X73,sK491),skolemize(X74,sK492),skolemize(X75,sK493),skolemize(X76,sK494),skolemize(X86,sK495),skolemize(X87,sK496),skolemize(X88,sK497),skolemize(X89,sK498),skolemize(X90,sK499),skolemize(X21,sK69 @ X12),skolemize(X95,sK501),skolemize(X96,sK502),skolemize(X21,sK69 @ X12),skolemize(X103,sK504),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X107,sK507),skolemize(X108,sK508),skolemize(X109,sK509),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X119,sK513),skolemize(X21,sK69 @ X12),skolemize(X125,sK515),skolemize(X126,sK516),skolemize(X127,sK517),skolemize(X128,sK518),skolemize(X134,sK519),skolemize(X135,sK520),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X145,sK525),skolemize(X148,sK526),skolemize(X149,sK527),skolemize(X150,sK528),skolemize(X151,sK529),skolemize(X152,sK530),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X169,sK537),skolemize(X21,sK69 @ X12),skolemize(X173,sK539),skolemize(X177,sK540),skolemize(X178,sK541),skolemize(X21,sK69 @ X12),skolemize(X186,sK543),skolemize(X187,sK544),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X198,sK550),skolemize(X199,sK551),skolemize(X200,sK552),skolemize(X201,sK553),skolemize(X205,sK554),skolemize(X206,sK555),skolemize(X21,sK69 @ X12),skolemize(X212,sK557),skolemize(X213,sK558),skolemize(X214,sK559),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X220,sK562),skolemize(X21,sK69 @ X12),skolemize(X225,sK564),skolemize(X226,sK565),skolemize(X229,sK566),skolemize(X230,sK567),skolemize(X231,sK568),skolemize(X232,sK569),skolemize(X234,sK570),skolemize(X235,sK571),skolemize(X21,sK69 @ X12),skolemize(X245,sK573),skolemize(X246,sK574),skolemize(X247,sK575),skolemize(X248,sK576),skolemize(X249,sK577),skolemize(X250,sK578),skolemize(X251,sK579),skolemize(X252,sK580),skolemize(X261,sK581),skolemize(X262,sK582),skolemize(X263,sK583),skolemize(X264,sK584),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X271,sK587),skolemize(X272,sK588),skolemize(X277,sK589),skolemize(X278,sK590)],[f262])).
% 0.22/23.50 thf(f273,plain,(
% 0.22/23.50 (((sK60 @ id @ sK59 @ id)) != $true) | (sP58 = $true)),
% 0.22/23.50 inference(cnf_transformation,[],[f75])).
% 0.22/23.50 thf(f275,plain,(
% 0.22/23.50 ($true != ((sP57 @ sK60))) | (sP58 = $true)),
% 0.22/23.50 inference(cnf_transformation,[],[f75])).
% 0.22/23.50 thf(f281,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ($true = ((X0 @ id @ (sK73 @ X1 @ X0) @ id))) | ($true = ((sP57 @ X0))) | (((X1 @ (comp @ (sK72 @ X1) @ (sK71 @ X1)) @ (sub @ (sK70 @ X1) @ (sK71 @ X1)))) != ((sub @ (X1 @ (sK72 @ X1) @ (sK70 @ X1)) @ (sK71 @ X1))))) )),
% 0.22/23.50 inference(cnf_transformation,[],[f78])).
% 0.22/23.50 thf(f607,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true = ((X0 @ id @ (sK325 @ X0) @ id))) | ($true != ((sP15 @ X0)))) )),
% 0.22/23.50 inference(cnf_transformation,[],[f209])).
% 0.22/23.50 thf(f609,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true != ((sP15 @ X0))) | ($true != ((X0 @ id @ (ap @ (sub @ (sK324 @ X0) @ id) @ (sK325 @ X0)) @ id)))) )),
% 0.22/23.50 inference(cnf_transformation,[],[f209])).
% 0.22/23.50 thf(f752,plain,(
% 0.22/23.50 ( ! [X279 : d_subst] : ((d_id = X279)) )),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f811,plain,(
% 0.22/23.50 (one = ((d2term @ d_one)))),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f823,plain,(
% 0.22/23.50 (hoasinduction_no_psi_cond = $true) | ($true != ((sK543 @ id @ sK544 @ id)))),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f824,plain,(
% 0.22/23.50 ( ! [X188 : (subst > term > term)] : ((((X188 @ (comp @ (sK547 @ X188) @ (sK546 @ X188)) @ (sub @ (sK548 @ X188) @ (sK546 @ X188)))) != ((sub @ (X188 @ (sK547 @ X188) @ (sK548 @ X188)) @ (sK546 @ X188)))) | ($true = ((sK543 @ id @ (lam @ (X188 @ sh @ one)) @ id))) | ($true = ((sK543 @ id @ (sK545 @ X188) @ id))) | (hoasinduction_no_psi_cond = $true)) )),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f828,plain,(
% 0.22/23.50 ( ! [X180 : term,X179 : (subst > term > subst > $o)] : ((((sP15 @ X179)) = $true) | (((X179 @ id @ X180 @ id)) = $true) | (hoasinduction_no_psi_cond != $true) | ($true != ((X179 @ id @ (lam @ (sK542 @ X179 @ sh @ one)) @ id)))) )),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f854,plain,(
% 0.22/23.50 ( ! [X143 : term] : ((((d2term @ (sK524 @ X143))) = X143)) )),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f882,plain,(
% 0.22/23.50 ( ! [X121 : subst] : ((((d2subst @ (sK514 @ X121))) = X121)) )),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f903,plain,(
% 0.22/23.50 ( ! [X94 : d_term] : ((d_one = X94)) )),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f935,plain,(
% 0.22/23.50 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f969,plain,(
% 0.22/23.50 (hoasinduction = $true) | (sP58 != $true)),
% 0.22/23.50 inference(cnf_transformation,[],[f263])).
% 0.22/23.50 thf(f978,plain,(
% 0.22/23.50 (hoasinduction != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y2 @ (comp @ Y3 @ Y1)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3) @ Y1)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id))))))))))))),
% 0.22/23.50 inference(cnf_transformation,[],[f8])).
% 0.22/23.50 thf(f981,plain,(
% 0.22/23.50 (hoasinduction != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y2 @ (comp @ Y3 @ Y1)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3) @ Y1)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id))))))))))))),
% 0.22/23.50 inference(definition_unfolding,[],[f978,f935])).
% 0.22/23.50 thf(f997,plain,(
% 0.22/23.50 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y2 @ (comp @ Y3 @ Y1)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3) @ Y1)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id))))))))))) = $false) | (hoasinduction = $false)),
% 0.22/23.50 inference(xor_proxy_clausification,[],[f981])).
% 0.22/23.50 thf(f998,plain,(
% 0.22/23.50 (hoasinduction = $false) | ((((^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y2 @ (comp @ Y3 @ Y1)) => (Y0 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3) @ Y1)))))))))) => ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1) @ Y4) => (Y0 @ Y3 @ Y2 @ (comp @ Y1 @ Y4))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => ((!! @ term @ (^[Y1 : term]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => ((Y0 @ id @ Y1 @ id) => (Y0 @ id @ (hoasap @ id @ Y2 @ id @ Y1) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id))))))))) @ sK591)) = $false)),
% 0.22/23.50 inference(sigma_proxy_clausification,[],[f997])).
% 0.22/23.50 thf(f999,plain,(
% 0.22/23.50 (hoasinduction = $false) | ((((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK591 @ Y3 @ Y1 @ (comp @ Y2 @ Y0)) => (sK591 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2) @ Y0)))))))))) => ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK591 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0) @ Y3) => (sK591 @ Y2 @ Y1 @ (comp @ Y0 @ Y3))))))))))) => ((!! @ term @ (^[Y0 : term]: ((hoasvar @ id @ Y0 @ id) => (sK591 @ id @ Y0 @ id)))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id))))))))) = $false)),
% 0.22/23.50 inference(beta-eta_normalization,[],[f998])).
% 0.22/23.50 thf(f1000,plain,(
% 0.22/23.50 ($false = (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK591 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0) @ Y3) => (sK591 @ Y2 @ Y1 @ (comp @ Y0 @ Y3))))))))))) => ((!! @ term @ (^[Y0 : term]: ((hoasvar @ id @ Y0 @ id) => (sK591 @ id @ Y0 @ id)))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id))))))))) | (hoasinduction = $false)),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f999])).
% 0.22/23.50 thf(f1011,plain,(
% 0.22/23.50 (hoasinduction = $false) | ((((!! @ term @ (^[Y0 : term]: ((hoasvar @ id @ Y0 @ id) => (sK591 @ id @ Y0 @ id)))) => ((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id))))))) = $false)),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1000])).
% 0.22/23.50 thf(f1022,plain,(
% 0.22/23.50 ((((!! @ term @ (^[Y0 : term]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (hoasap @ id @ Y1 @ id @ Y0) @ id))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id)))))) = $false) | (hoasinduction = $false)),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1011])).
% 0.22/23.50 thf(f1027,plain,(
% 0.22/23.50 (hoasinduction = $false) | ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id))))) = $false)),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1022])).
% 0.22/23.50 thf(f1035,plain,(
% 0.22/23.50 (hoasinduction = $false) | ($false = ((!! @ term @ (^[Y0 : term]: (sK591 @ id @ Y0 @ id)))))),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1027])).
% 0.22/23.50 thf(f1036,plain,(
% 0.22/23.50 (hoasinduction = $false) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))))) = $true)),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1027])).
% 0.22/23.50 thf(f1037,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((hoasinduction = $false) | ($true = (((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) @ X1)))) )),
% 0.22/23.50 inference(pi_proxy_clausification,[],[f1036])).
% 0.22/23.50 thf(f1038,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((hoasinduction = $false) | ($true = (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)) = (sub @ (X1 @ Y0 @ Y2) @ Y1)))))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))))) )),
% 0.22/23.50 inference(beta-eta_normalization,[],[f1037])).
% 0.22/23.50 thf(f1039,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((hoasinduction = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)) = (sub @ (X1 @ Y0 @ Y2) @ Y1))))))))) = $false) | ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))) = $true)) )),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1038])).
% 0.22/23.50 thf(f1040,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))) = $true) | (hoasinduction = $false) | ($false = (((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)) = (sub @ (X1 @ Y0 @ Y2) @ Y1))))))) @ (sK592 @ X1))))) )),
% 0.22/23.50 inference(sigma_proxy_clausification,[],[f1039])).
% 0.22/23.50 thf(f1041,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))))) | (hoasinduction = $false) | ($false = (((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)) = (sub @ (X1 @ Y0 @ Y2) @ Y1))))))) @ (sK592 @ X1))))) )),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1040])).
% 0.22/23.50 thf(f1042,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((hoasinduction = $false) | ($false = (((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((X1 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)) = (sub @ (X1 @ Y0 @ Y2) @ Y1))))))) @ (sK592 @ X1)))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK593 @ X1))) = $false)) )),
% 0.22/23.50 inference(sigma_proxy_clausification,[],[f1041])).
% 0.22/23.50 thf(f1043,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (((((sK591 @ id @ (sK593 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK593 @ X1)) @ id))) = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((X1 @ (comp @ (sK592 @ X1) @ Y0) @ (sub @ Y1 @ Y0)) = (sub @ (X1 @ (sK592 @ X1) @ Y1) @ Y0))))))) = $false) | (hoasinduction = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 0.22/23.50 inference(beta-eta_normalization,[],[f1042])).
% 0.22/23.50 thf(f1045,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((X1 @ (comp @ (sK592 @ X1) @ Y0) @ (sub @ Y1 @ Y0)) = (sub @ (X1 @ (sK592 @ X1) @ Y1) @ Y0))))))) = $false) | (hoasinduction = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true)) )),
% 0.22/23.50 inference(imp_proxy_clausification,[],[f1043])).
% 0.22/23.50 thf(f1046,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction = $false) | ((((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((X1 @ (comp @ (sK592 @ X1) @ Y0) @ (sub @ Y1 @ Y0)) = (sub @ (X1 @ (sK592 @ X1) @ Y1) @ Y0))))) @ (sK594 @ X1))) = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true)) )),
% 0.22/23.50 inference(sigma_proxy_clausification,[],[f1045])).
% 0.22/23.50 thf(f1047,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((hoasinduction = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = ((!! @ term @ (^[Y0 : term]: ((X1 @ (comp @ (sK592 @ X1) @ (sK594 @ X1)) @ (sub @ Y0 @ (sK594 @ X1))) = (sub @ (X1 @ (sK592 @ X1) @ Y0) @ (sK594 @ X1)))))))) )),
% 0.22/23.50 inference(beta-eta_normalization,[],[f1046])).
% 0.22/23.50 thf(f1048,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (($false = (((^[Y0 : term]: ((X1 @ (comp @ (sK592 @ X1) @ (sK594 @ X1)) @ (sub @ Y0 @ (sK594 @ X1))) = (sub @ (X1 @ (sK592 @ X1) @ Y0) @ (sK594 @ X1)))) @ (sK595 @ X1)))) | (hoasinduction = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 0.22/23.50 inference(sigma_proxy_clausification,[],[f1047])).
% 0.22/23.50 thf(f1049,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | ((((X1 @ (comp @ (sK592 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1))) = (sub @ (X1 @ (sK592 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1)))) = $false)) )),
% 0.22/23.50 inference(beta-eta_normalization,[],[f1048])).
% 0.22/23.50 thf(f1050,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((hoasinduction = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (((X1 @ (comp @ (sK592 @ X1) @ (sK594 @ X1)) @ (sub @ (sK595 @ X1) @ (sK594 @ X1)))) != ((sub @ (X1 @ (sK592 @ X1) @ (sK595 @ X1)) @ (sK594 @ X1))))) )),
% 0.22/23.50 inference(equality_proxy_clausification,[],[f1049])).
% 0.22/23.50 thf(f1056,plain,(
% 0.22/23.50 ((((^[Y0 : term]: (sK591 @ id @ Y0 @ id)) @ sK598)) = $false) | (hoasinduction = $false)),
% 0.22/23.50 inference(sigma_proxy_clausification,[],[f1035])).
% 0.22/23.50 thf(f1057,plain,(
% 0.22/23.50 (((sK591 @ id @ sK598 @ id)) = $false) | (hoasinduction = $false)),
% 0.22/23.50 inference(beta-eta_normalization,[],[f1056])).
% 0.22/23.50 thf(f1479,definition,(
% 0.22/23.50 spl667_1 <=> (((sK591 @ id @ sK598 @ id)) = $false)),
% 0.22/23.50 introduced(definition,[new_symbols(definition,[spl667_1])],[avatar_definition])).
% 0.22/23.50 thf(f1481,plain,(
% 0.22/23.50 (((sK591 @ id @ sK598 @ id)) = $false) | ~spl667_1),
% 0.22/23.50 inference(avatar_component_clause,[],[f1479])).
% 0.22/23.50 thf(f1483,definition,(
% 0.22/23.50 spl667_2 <=> (hoasinduction = $false)),
% 0.22/23.50 introduced(definition,[new_symbols(definition,[spl667_2])],[avatar_definition])).
% 0.22/23.50 thf(f1484,plain,(
% 0.22/23.50 (hoasinduction != $false) | spl667_2),
% 0.22/23.50 inference(avatar_component_clause,[],[f1483])).
% 0.22/23.50 thf(f1485,plain,(
% 0.22/23.50 (hoasinduction = $false) | ~spl667_2),
% 0.22/23.50 inference(avatar_component_clause,[],[f1483])).
% 0.22/23.50 thf(f1486,plain,(
% 0.22/23.50 spl667_1 | spl667_2),
% 0.22/23.50 inference(avatar_split_clause,[],[f1057,f1483,f1479])).
% 0.22/23.50 thf(f1852,plain,(
% 0.22/23.50 (sP58 != $true) | ($true = $false) | ~spl667_2),
% 0.22/23.50 inference(forward_demodulation,[],[f969,f1485])).
% 0.22/23.50 thf(f1853,plain,(
% 0.22/23.50 (sP58 != $true) | ~spl667_2),
% 0.22/23.50 inference(trivial_inequality_removal,[],[f1852])).
% 0.22/23.50 thf(f2124,plain,(
% 0.22/23.50 ( ! [X143 : term] : ((((d2term @ d_one)) = X143)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f854,f903])).
% 0.22/23.50 thf(f2131,plain,(
% 0.22/23.50 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 0.22/23.50 inference(constrained_superposition,[],[f2124,f2124])).
% 0.22/23.50 thf(f2137,plain,(
% 0.22/23.50 ( ! [X121 : subst] : ((((d2subst @ d_id)) = X121)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f882,f752])).
% 0.22/23.50 thf(f2144,plain,(
% 0.22/23.50 ( ! [X0 : subst,X1 : subst] : ((X0 = X1)) )),
% 0.22/23.50 inference(constrained_superposition,[],[f2137,f2137])).
% 0.22/23.50 thf(f2270,plain,(
% 0.22/23.50 ($true != ((sP57 @ sK60))) | ~spl667_2),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f275,f1853])).
% 0.22/23.50 thf(f2470,definition,(
% 0.22/23.50 spl667_85 <=> (hoasinduction_no_psi_cond = $true)),
% 0.22/23.50 introduced(definition,[new_symbols(definition,[spl667_85])],[avatar_definition])).
% 0.22/23.50 thf(f2471,plain,(
% 0.22/23.50 (hoasinduction_no_psi_cond != $true) | spl667_85),
% 0.22/23.50 inference(avatar_component_clause,[],[f2470])).
% 0.22/23.50 thf(f2664,plain,(
% 0.22/23.50 (((sK60 @ id @ sK59 @ id)) != $true) | ~spl667_2),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f273,f1853])).
% 0.22/23.50 thf(f2739,definition,(
% 0.22/23.50 spl667_87 <=> ($true = ((sK543 @ id @ sK544 @ id)))),
% 0.22/23.50 introduced(definition,[new_symbols(definition,[spl667_87])],[avatar_definition])).
% 0.22/23.50 thf(f2741,plain,(
% 0.22/23.50 ($true != ((sK543 @ id @ sK544 @ id))) | spl667_87),
% 0.22/23.50 inference(avatar_component_clause,[],[f2739])).
% 0.22/23.50 thf(f2742,plain,(
% 0.22/23.50 ~spl667_87 | spl667_85),
% 0.22/23.50 inference(avatar_split_clause,[],[f823,f2470,f2739])).
% 0.22/23.50 thf(f2743,plain,(
% 0.22/23.50 ( ! [X0 : term] : ((((sK543 @ id @ X0 @ id)) != $true)) ) | spl667_87),
% 0.22/23.50 inference(constrained_superposition,[],[f2741,f2131])).
% 0.22/23.50 thf(f8804,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true != ((sP15 @ X0))) | (((X0 @ id @ (d2term @ d_one) @ id)) = $true)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f607,f2124])).
% 0.22/23.50 thf(f8805,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true != ((sP15 @ X0))) | ($true = ((X0 @ id @ one @ id)))) )),
% 0.22/23.50 inference(forward_demodulation,[],[f8804,f811])).
% 0.22/23.50 thf(f15364,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true != ((sP15 @ X0))) | (((X0 @ id @ (d2term @ d_one) @ id)) != $true)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f609,f2124])).
% 0.22/23.50 thf(f15365,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true != ((X0 @ id @ one @ id))) | ($true != ((sP15 @ X0)))) )),
% 0.22/23.50 inference(forward_demodulation,[],[f15364,f811])).
% 0.22/23.50 thf(f15366,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true != ((sP15 @ X0)))) )),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f15365,f8805])).
% 0.22/23.50 thf(f31293,plain,(
% 0.22/23.50 ( ! [X180 : term,X179 : (subst > term > subst > $o)] : ((((X179 @ id @ X180 @ id)) = $true) | (hoasinduction_no_psi_cond != $true) | ($true != ((X179 @ id @ (lam @ (sK542 @ X179 @ sh @ one)) @ id)))) )),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f828,f15366])).
% 0.22/23.50 thf(f31294,plain,(
% 0.22/23.50 ( ! [X180 : term,X179 : (subst > term > subst > $o)] : ((hoasinduction_no_psi_cond != $true) | ($true != ((X179 @ id @ (d2term @ d_one) @ id))) | (((X179 @ id @ X180 @ id)) = $true)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f31293,f2124])).
% 0.22/23.50 thf(f31295,plain,(
% 0.22/23.50 ( ! [X180 : term,X179 : (subst > term > subst > $o)] : ((((X179 @ id @ X180 @ id)) = $true) | ($true != ((X179 @ id @ one @ id))) | (hoasinduction_no_psi_cond != $true)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f31294,f811])).
% 0.22/23.50 thf(f31297,definition,(
% 0.22/23.50 spl667_104 <=> ! [X179 : (subst > term > subst > $o),X180 : term] : ((((X179 @ id @ X180 @ id)) = $true) | ($true != ((X179 @ id @ one @ id))))),
% 0.22/23.50 introduced(definition,[new_symbols(definition,[spl667_104])],[avatar_definition])).
% 0.22/23.50 thf(f31298,plain,(
% 0.22/23.50 ( ! [X180 : term,X179 : (subst > term > subst > $o)] : (($true != ((X179 @ id @ one @ id))) | (((X179 @ id @ X180 @ id)) = $true)) ) | ~spl667_104),
% 0.22/23.50 inference(avatar_component_clause,[],[f31297])).
% 0.22/23.50 thf(f31299,plain,(
% 0.22/23.50 ~spl667_85 | spl667_104),
% 0.22/23.50 inference(avatar_split_clause,[],[f31295,f31297,f2470])).
% 0.22/23.50 thf(f35778,plain,(
% 0.22/23.50 ( ! [X188 : (subst > term > term)] : ((((X188 @ (comp @ (sK547 @ X188) @ (sK546 @ X188)) @ (sub @ (sK548 @ X188) @ (sK546 @ X188)))) != ((sub @ (X188 @ (sK547 @ X188) @ (sK548 @ X188)) @ (sK546 @ X188)))) | ($true = ((sK543 @ id @ (sK545 @ X188) @ id))) | ($true = ((sK543 @ id @ (lam @ (X188 @ sh @ one)) @ id)))) ) | spl667_85),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f824,f2471])).
% 0.22/23.50 thf(f35779,plain,(
% 0.22/23.50 ( ! [X188 : (subst > term > term)] : (($true = ((sK543 @ id @ (sK545 @ X188) @ id))) | ($true = ((sK543 @ id @ (lam @ (X188 @ sh @ one)) @ id)))) ) | spl667_85),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f35778,f2131])).
% 0.22/23.50 thf(f35780,plain,(
% 0.22/23.50 ( ! [X188 : (subst > term > term)] : (($true = ((sK543 @ id @ (lam @ (X188 @ sh @ one)) @ id)))) ) | (spl667_85 | spl667_87)),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f35779,f2743])).
% 0.22/23.50 thf(f35781,plain,(
% 0.22/23.50 $false | (spl667_85 | spl667_87)),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f35780,f2743])).
% 0.22/23.50 thf(f35782,plain,(
% 0.22/23.50 spl667_85 | spl667_87),
% 0.22/23.50 inference(avatar_contradiction_clause,[],[f35781])).
% 0.22/23.50 thf(f36703,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ($true = ((X0 @ id @ (sK73 @ X1 @ X0) @ id))) | ($true = ((sP57 @ X0)))) )),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f281,f2131])).
% 0.22/23.50 thf(f36704,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : (($true = ((sP57 @ X0))) | (((X0 @ id @ (d2term @ d_one) @ id)) = $true) | ($true = ((X0 @ id @ (sK73 @ X1 @ X0) @ id)))) )),
% 0.22/23.50 inference(forward_demodulation,[],[f36703,f2124])).
% 0.22/23.50 thf(f36705,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : (($true = ((sP57 @ X0))) | ($true = ((X0 @ id @ one @ id))) | ($true = ((X0 @ id @ (sK73 @ X1 @ X0) @ id)))) )),
% 0.22/23.50 inference(forward_demodulation,[],[f36704,f811])).
% 0.22/23.50 thf(f36706,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : (($true = ((X0 @ id @ (sK73 @ X1 @ X0) @ id))) | ($true = ((sP57 @ X0)))) ) | ~spl667_104),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f36705,f31298])).
% 0.22/23.50 thf(f36707,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (d2term @ d_one) @ id)) = $true) | ($true = ((sP57 @ X0)))) ) | ~spl667_104),
% 0.22/23.50 inference(forward_demodulation,[],[f36706,f2124])).
% 0.22/23.50 thf(f36708,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > $o)] : (($true = ((X0 @ id @ one @ id))) | ($true = ((sP57 @ X0)))) ) | ~spl667_104),
% 0.22/23.50 inference(forward_demodulation,[],[f36707,f811])).
% 0.22/23.50 thf(f37035,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > subst),X1 : (subst > term > subst > term)] : ((((sP57 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (sK60 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : subst]: ((^[Y4 : term]: ((^[Y5 : subst]: (Y5)))))) @ Y0 @ Y1 @ Y2))))))))) = $true) | (sK59 != ((X1 @ id @ one @ id))) | ($true != $true) | (id != ((X0 @ id @ one @ id)))) ) | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(constrained_superposition,[],[f2664,f36708])).
% 0.22/23.50 thf(f37589,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > subst),X1 : (subst > term > subst > term)] : ((((sP57 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (sK60 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : subst]: ((^[Y4 : term]: ((^[Y5 : subst]: (Y5)))))) @ Y0 @ Y1 @ Y2))))))))) = $true) | (id != ((X0 @ id @ one @ id))) | (sK59 != ((X1 @ id @ one @ id)))) ) | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(trivial_inequality_removal,[],[f37035])).
% 0.22/23.50 thf(f37590,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > subst),X1 : (subst > term > subst > term)] : ((((sP57 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (sK60 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2) @ Y2)))))))) = $true) | (id != ((X0 @ id @ one @ id))) | (sK59 != ((X1 @ id @ one @ id)))) ) | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(beta-eta_normalization,[],[f37589])).
% 0.22/23.50 thf(f37809,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > subst),X1 : (subst > term > subst > term)] : ((((sP57 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (sK60 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2) @ Y2)))))))) = $true) | (sK59 != ((X1 @ id @ one @ id)))) ) | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f37590,f2144])).
% 0.22/23.50 thf(f37893,plain,(
% 0.22/23.50 ( ! [X0 : (subst > term > subst > subst),X1 : (subst > term > subst > term)] : ((((sP57 @ (^[Y0 : subst]: ((^[Y1 : term]: ((^[Y2 : subst]: (sK60 @ (X0 @ Y0 @ Y1 @ Y2) @ (X1 @ Y0 @ Y1 @ Y2) @ Y2)))))))) = $true)) ) | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f37809,f2131])).
% 0.22/23.50 thf(f52576,plain,(
% 0.22/23.50 ($true != $true) | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(constrained_superposition,[],[f2270,f37893])).
% 0.22/23.50 thf(f52609,plain,(
% 0.22/23.50 $false | (~spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(trivial_inequality_removal,[],[f52576])).
% 0.22/23.50 thf(f52610,plain,(
% 0.22/23.50 ~spl667_2 | ~spl667_104),
% 0.22/23.50 inference(avatar_contradiction_clause,[],[f52609])).
% 0.22/23.50 thf(f52663,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | (hoasinduction = $false)) )),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f1050,f2131])).
% 0.22/23.50 thf(f52678,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ one @ id)) = $true) | (hoasinduction = $false) | (((sK591 @ id @ (sK593 @ X1) @ id)) = $true)) )),
% 0.22/23.50 inference(forward_demodulation,[],[f52663,f811])).
% 0.22/23.50 thf(f52986,plain,(
% 0.22/23.50 ( ! [X0 : term] : ((((sK591 @ id @ X0 @ id)) = $false)) ) | ~spl667_1),
% 0.22/23.50 inference(constrained_superposition,[],[f1481,f2131])).
% 0.22/23.50 thf(f55451,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (sK593 @ X1) @ id)) = $true) | (hoasinduction = $false)) ) | ~spl667_104),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f52678,f31298])).
% 0.22/23.50 thf(f55479,plain,(
% 0.22/23.50 ( ! [X1 : (subst > term > term)] : ((((sK591 @ id @ (sK593 @ X1) @ id)) = $true)) ) | (spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(forward_subsumption_resolution,[],[f55451,f1484])).
% 0.22/23.50 thf(f55504,plain,(
% 0.22/23.50 ($true = $false) | (~spl667_1 | spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(forward_demodulation,[],[f55479,f52986])).
% 0.22/23.50 thf(f55505,plain,(
% 0.22/23.50 $false | (~spl667_1 | spl667_2 | ~spl667_104)),
% 0.22/23.50 inference(trivial_inequality_removal,[],[f55504])).
% 0.22/23.50 thf(f55506,plain,(
% 0.22/23.50 ~spl667_1 | spl667_2 | ~spl667_104),
% 0.22/23.50 inference(avatar_contradiction_clause,[],[f55505])).
% 0.22/23.50 cnf(s1, plain, spl667_1 | spl667_2, inference(sat_conversion,[],[f1486])).
% 0.22/23.50 cnf(s89, plain, spl667_85 | ~spl667_87, inference(sat_conversion,[],[f2742])).
% 0.22/23.50 cnf(s106, plain, ~spl667_85 | spl667_104, inference(sat_conversion,[],[f31299])).
% 0.22/23.50 cnf(s111, plain, spl667_85 | spl667_87, inference(sat_conversion,[],[f35782])).
% 0.22/23.50 cnf(s115, plain, ~spl667_2 | ~spl667_104, inference(sat_conversion,[],[f52610])).
% 0.22/23.50 cnf(s119, plain, ~spl667_1 | spl667_2 | ~spl667_104, inference(sat_conversion,[],[f55506])).
% 0.22/23.50 cnf(s142, plain, spl667_85, inference(rat,[],[s89,s111])).
% 0.22/23.50 cnf(s143, plain, spl667_104, inference(rat,[],[s106,s142])).
% 0.22/23.50 cnf(s144, plain, ~spl667_2, inference(rat,[],[s115,s143])).
% 0.22/23.50 cnf(s145, plain, ~spl667_1, inference(rat,[],[s119,s143,s144])).
% 0.22/23.50 cnf(s147, plain, $false, inference(rat,[],[s1,s144,s145])).
% 0.22/23.50 thf(f55571,plain,(
% 0.22/23.50 $false),
% 0.22/23.50 inference(avatar_sat_refutation,[],[s147])).
% 0.22/23.50 % SZS output end Proof for theBenchmark
% 0.22/23.50 % (2301728)------------------------------
% 0.22/23.50 % (2301728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/23.50 % (2301728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/23.50 % (2301728)CaDiCaL version: 2.1.3
% 0.22/23.50 % (2301728)Termination reason: Refutation
% 0.22/23.50 % (2301728)Time elapsed: 3.049 s
% 0.22/23.50 % (2301728)Peak memory usage: 34 MB
% 0.22/23.50 % (2301728)Instructions burned: 6674 (million)
% 0.22/23.50 % (2301573)Success in time 23.263 s
% 0.22/23.50 % Vampire exiting
%------------------------------------------------------------------------------