%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX156^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:40:41 AM UTC 2026
% Result : Theorem 8.63s 1.67s
% Output : Refutation 8.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX156^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:09:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.25/0.95 % (1232915)Will run a generic schedule for satisfiability detection.
% 4.25/0.95 % (1232936)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1901843448_2999 on theBenchmark for (2999ds/0Mi)
% 4.25/0.95 % (1232937)% WARNING: option uhcvi not known.
% 4.25/0.95 % (1232937)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=14671095:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.25/0.95 % (1232939)dis+10_1_sil=32000:sp=arity:random_seed=2881160507:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.25/0.95 % (1232940)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3631642536:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.25/0.95 % (1232938)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1518335071:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.25/0.95 % (1232942)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=439320581:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.25/0.95 % (1232943)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2795072701:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.25/0.95 % (1232937)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.25/0.95 % (1232940)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.25/0.95 % Exception at run slice level
% 4.25/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.25/0.95 % (1232939)Instruction limit reached!
% 4.25/0.95 % (1232939)------------------------------
% 4.25/0.95 % (1232939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (1232939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (1232939)CaDiCaL version: 2.1.3
% 4.25/0.95 % (1232939)Termination reason: Instruction limit
% 4.25/0.95 % (1232939)Termination phase: Property scanning
% 4.25/0.95 % (1232939)Time elapsed: 0.046 s
% 4.25/0.95 % (1232939)Peak memory usage: 12 MB
% 4.25/0.95 % (1232939)Instructions burned: 104 (million)
% 4.25/0.95 % (1232940)Instruction limit reached!
% 4.25/0.95 % (1232940)------------------------------
% 4.25/0.95 % (1232940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (1232940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (1232940)CaDiCaL version: 2.1.3
% 4.25/0.95 % (1232940)Termination reason: Instruction limit
% 4.25/0.95 % (1232940)Termination phase: Property scanning
% 4.25/0.95 % (1232940)Time elapsed: 0.050 s
% 4.25/0.95 % (1232940)Peak memory usage: 12 MB
% 4.25/0.95 % (1232940)Instructions burned: 117 (million)
% 4.25/0.95 % (1232964)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3764883006:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.25/0.95 % (1232942)Instruction limit reached!
% 4.25/0.95 % (1232942)------------------------------
% 4.25/0.95 % (1232942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (1232942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (1232942)CaDiCaL version: 2.1.3
% 4.25/0.95 % (1232942)Termination reason: Instruction limit
% 4.25/0.95 % (1232942)Termination phase: Function definition elimination
% 4.25/0.95 % (1232942)Time elapsed: 0.056 s
% 4.25/0.95 % (1232942)Peak memory usage: 12 MB
% 4.25/0.95 % (1232942)Instructions burned: 131 (million)
% 4.25/0.95 % (1232970)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=432884955:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.25/0.95 % (1232943)Instruction limit reached!
% 4.25/0.95 % (1232943)------------------------------
% 4.25/0.95 % (1232943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.25/0.95 % (1232943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/0.95 % (1232943)CaDiCaL version: 2.1.3
% 4.25/0.95 % (1232943)Termination reason: Instruction limit
% 4.25/0.95 % (1232943)Termination phase: Property scanning
% 4.25/0.95 % (1232943)Time elapsed: 0.066 s
% 4.25/0.95 % (1232943)Peak memory usage: 13 MB
% 4.25/0.95 % (1232943)Instructions burned: 160 (million)
% 4.25/0.95 % (1232973)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=2769236066:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.25/0.95 % (1232937)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.63/1.67 % (1232977)ott-21_1_sil=16000:fs=off:random_seed=128460717:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 8.63/1.67 % (1232985)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1973052719:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.63/1.67 % (1232973)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1232970)Instruction limit reached!
% 8.63/1.67 % (1232970)------------------------------
% 8.63/1.67 % (1232970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1232970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1232970)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1232970)Termination reason: Instruction limit
% 8.63/1.67 % (1232970)Termination phase: Function definition elimination
% 8.63/1.67 % (1232970)Time elapsed: 0.055 s
% 8.63/1.67 % (1232970)Peak memory usage: 12 MB
% 8.63/1.67 % (1232970)Instructions burned: 131 (million)
% 8.63/1.67 % (1233003)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=820959363:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.63/1.67 % (1233004)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2782079322:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 8.63/1.67 % (1232973)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.63/1.67 % (1232977)Instruction limit reached!
% 8.63/1.67 % (1232977)------------------------------
% 8.63/1.67 % (1232977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1232977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1232977)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1232977)Termination reason: Instruction limit
% 8.63/1.67 % (1232977)Termination phase: Saturation
% 8.63/1.67 % (1232977)Time elapsed: 0.076 s
% 8.63/1.67 % (1232977)Peak memory usage: 12 MB
% 8.63/1.67 % (1232977)Instructions burned: 180 (million)
% 8.63/1.67 % (1233016)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2723686359:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 8.63/1.67 % (1232985)Instruction limit reached!
% 8.63/1.67 % (1232985)------------------------------
% 8.63/1.67 % (1232985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1232985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1232985)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1232985)Termination reason: Instruction limit
% 8.63/1.67 % (1232985)Termination phase: Saturation
% 8.63/1.67 % (1232985)Time elapsed: 0.122 s
% 8.63/1.67 % (1232985)Peak memory usage: 16 MB
% 8.63/1.67 % (1232985)Instructions burned: 481 (million)
% 8.63/1.67 % (1233049)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=2096523719: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)
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233049)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.63/1.67 % (1233054)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=936555284:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 8.63/1.67 % (1233054)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233060)fmb+10_1_sil=64000:random_seed=2928807389:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 8.63/1.67 % (1233060)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233062)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3996903424:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 8.63/1.67 % (1232973)Instruction limit reached!
% 8.63/1.67 % (1232973)------------------------------
% 8.63/1.67 % (1232973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1232973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1232973)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1232973)Termination reason: Instruction limit
% 8.63/1.67 % (1232973)Termination phase: Saturation
% 8.63/1.67 % (1232973)Time elapsed: 0.308 s
% 8.63/1.67 % (1232973)Peak memory usage: 18 MB
% 8.63/1.67 % (1232973)Instructions burned: 685 (million)
% 8.63/1.67 % (1233049)Instruction limit reached!
% 8.63/1.67 % (1233049)------------------------------
% 8.63/1.67 % (1233049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1233049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1233049)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1233049)Termination reason: Instruction limit
% 8.63/1.67 % (1233049)Termination phase: Saturation
% 8.63/1.67 % (1233049)Time elapsed: 0.170 s
% 8.63/1.67 % (1233049)Peak memory usage: 18 MB
% 8.63/1.67 % (1233049)Instructions burned: 695 (million)
% 8.63/1.67 % (1233065)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3398188046:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 8.63/1.67 % (1233064)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2056266718:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 8.63/1.67 % (1233065)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233068)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2271176387:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233070)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=650426342:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 8.63/1.67 % (1233068)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.63/1.67 % (1233068)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233072)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3679842735:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 8.63/1.67 % (1233054)Instruction limit reached!
% 8.63/1.67 % (1233054)------------------------------
% 8.63/1.67 % (1233054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1233054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1233054)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1233054)Termination reason: Instruction limit
% 8.63/1.67 % (1233054)Termination phase: Saturation
% 8.63/1.67 % (1233054)Time elapsed: 0.393 s
% 8.63/1.67 % (1233054)Peak memory usage: 21 MB
% 8.63/1.67 % (1233054)Instructions burned: 881 (million)
% 8.63/1.67 % (1233074)ott-2_1_sil=16000:newcnf=on:random_seed=4278453089:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233074)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.63/1.67 % (1233004)Instruction limit reached!
% 8.63/1.67 % (1233004)------------------------------
% 8.63/1.67 % (1233004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1233004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1233004)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1233004)Termination reason: Instruction limit
% 8.63/1.67 % (1233004)Termination phase: Saturation
% 8.63/1.67 % (1233004)Time elapsed: 0.529 s
% 8.63/1.67 % (1233004)Peak memory usage: 22 MB
% 8.63/1.67 % (1233004)Instructions burned: 1181 (million)
% 8.63/1.67 % (1233076)ott+10_1_sil=32000:tgt=ground:random_seed=3037369589:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 8.63/1.67 % (1233077)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=543992697:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 8.63/1.67 % Exception at run slice level
% 8.63/1.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.63/1.67 % (1233080)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1984705272:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 8.63/1.67 % (1233080)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.63/1.67 % (1233074)Instruction limit reached!
% 8.63/1.67 % (1233074)------------------------------
% 8.63/1.67 % (1233074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1233074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1233074)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1233074)Termination reason: Instruction limit
% 8.63/1.67 % (1233074)Termination phase: Saturation
% 8.63/1.67 % (1233074)Time elapsed: 0.391 s
% 8.63/1.67 % (1233074)Peak memory usage: 19 MB
% 8.63/1.67 % (1233074)Instructions burned: 869 (million)
% 8.63/1.67 % (1233082)dis+21_1_sil=32000:sas=cadical:random_seed=3139410274:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 8.63/1.67 % (1233068)Instruction limit reached!
% 8.63/1.67 % (1233068)------------------------------
% 8.63/1.67 % (1233068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.67 % (1233068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.67 % (1233068)CaDiCaL version: 2.1.3
% 8.63/1.67 % (1233068)Termination reason: Instruction limit
% 8.63/1.67 % (1233068)Termination phase: Saturation
% 8.63/1.67 % (1233068)Time elapsed: 0.654 s
% 8.63/1.67 % (1233068)Peak memory usage: 20 MB
% 8.63/1.67 % (1233068)Instructions burned: 1473 (million)
% 8.63/1.67 % (1233084)ott+11_1_sil=16000:gs=on:random_seed=2931425813:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 8.63/1.67 % (1233084)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.63/1.67 % (1233084) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1232915-1233084"...
% 8.63/1.67 % (1233084)...printing done.
% 8.63/1.67 % (1233084)Refutation found. Thanks to Tanya!
% 8.63/1.67 % SZS status Theorem for theBenchmark
% 8.63/1.67 % SZS output start Proof for theBenchmark
% 8.63/1.67 thf(type_def_5, type, term: $tType).
% 8.63/1.67 thf(type_def_6, type, subst: $tType).
% 8.63/1.67 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 8.63/1.67 thf(type_def_8, type, d_term: $tType).
% 8.63/1.67 thf(type_def_9, type, d_subst: $tType).
% 8.63/1.67 thf(func_def_0, type, one: term).
% 8.63/1.67 thf(func_def_1, type, ap: (term > term > term)).
% 8.63/1.67 thf(func_def_2, type, lam: (term > term)).
% 8.63/1.67 thf(func_def_3, type, sub: (term > subst > term)).
% 8.63/1.67 thf(func_def_4, type, id: subst).
% 8.63/1.67 thf(func_def_5, type, sh: subst).
% 8.63/1.67 thf(func_def_6, type, push: (term > subst > subst)).
% 8.63/1.67 thf(func_def_7, type, comp: (subst > subst > subst)).
% 8.63/1.67 thf(func_def_8, type, var: (term > $o)).
% 8.63/1.67 thf(func_def_9, type, pushprop_lem1v2: $o).
% 8.63/1.67 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 8.63/1.67 thf(func_def_11, type, axmap: $o).
% 8.63/1.67 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 8.63/1.67 thf(func_def_13, type, shinj: $o).
% 8.63/1.67 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 8.63/1.67 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 8.63/1.67 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 8.63/1.67 thf(func_def_17, type, induction2lem: $o).
% 8.63/1.67 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 8.63/1.67 thf(func_def_19, type, axvarshift: $o).
% 8.63/1.67 thf(func_def_20, type, hoasapinj2: $o).
% 8.63/1.67 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 8.63/1.67 thf(func_def_22, type, hoasapinj1: $o).
% 8.63/1.67 thf(func_def_23, type, ulamvar1: $o).
% 8.63/1.67 thf(func_def_24, type, induction2lem_lthm: $o).
% 8.63/1.67 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 8.63/1.67 thf(func_def_26, type, apnotvar: $o).
% 8.63/1.67 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 8.63/1.67 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 8.63/1.67 thf(func_def_29, type, hoasinduction_lthm: $o).
% 8.63/1.67 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 8.63/1.67 thf(func_def_31, type, hoaslaminj: $o).
% 8.63/1.67 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 8.63/1.67 thf(func_def_33, type, induction2lem_gthm: $o).
% 8.63/1.67 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 8.63/1.67 thf(func_def_35, type, hoasinduction_lem3: $o).
% 8.63/1.67 thf(func_def_36, type, hoasinduction_lem2: $o).
% 8.63/1.67 thf(func_def_37, type, termmset_lthm: $o).
% 8.63/1.67 thf(func_def_38, type, hoasinduction_lem1: $o).
% 8.63/1.67 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 8.63/1.67 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 8.63/1.67 thf(func_def_41, type, hoasapnotvar: $o).
% 8.63/1.67 thf(func_def_42, type, hoasinduction_lem0: $o).
% 8.63/1.67 thf(func_def_43, type, hoasinduction: $o).
% 8.63/1.67 thf(func_def_44, type, hoasinduction_gthm: $o).
% 8.63/1.67 thf(func_def_45, type, axapp: $o).
% 8.63/1.67 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 8.63/1.67 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 8.63/1.67 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 8.63/1.67 thf(func_def_49, type, ulamvarind: $o).
% 8.63/1.67 thf(func_def_50, type, induction: $o).
% 8.63/1.67 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 8.63/1.67 thf(func_def_52, type, termmset_gthm: $o).
% 8.63/1.67 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 8.63/1.67 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 8.63/1.67 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 8.63/1.67 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 8.63/1.67 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 8.63/1.67 thf(func_def_58, type, pushprop_lem2v2: $o).
% 8.63/1.67 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 8.63/1.67 thf(func_def_60, type, axclos: $o).
% 8.63/1.67 thf(func_def_61, type, axassoc: $o).
% 8.63/1.67 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 8.63/1.67 thf(func_def_63, type, pushprop_lthm: $o).
% 8.63/1.67 thf(func_def_64, type, apinj2: $o).
% 8.63/1.67 thf(func_def_65, type, apinj1: $o).
% 8.63/1.67 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 8.63/1.67 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 8.63/1.67 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 8.63/1.67 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 8.63/1.67 thf(func_def_70, type, axvarcons: $o).
% 8.63/1.67 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 8.63/1.67 thf(func_def_72, type, axscons: $o).
% 8.63/1.67 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 8.63/1.67 thf(func_def_74, type, axidr: $o).
% 8.63/1.67 thf(func_def_75, type, pushprop_lem1: $o).
% 8.63/1.67 thf(func_def_76, type, laminj: $o).
% 8.63/1.67 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 8.63/1.67 thf(func_def_78, type, pushprop_lem0: $o).
% 8.63/1.67 thf(func_def_79, type, pushprop_gthm: $o).
% 8.63/1.67 thf(func_def_80, type, axabs: $o).
% 8.63/1.67 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 8.63/1.67 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 8.63/1.67 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 8.63/1.67 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 8.63/1.67 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 8.63/1.67 thf(func_def_86, type, lamnotap: $o).
% 8.63/1.67 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 8.63/1.67 thf(func_def_88, type, hoaslamnotvar: $o).
% 8.63/1.67 thf(func_def_89, type, axidl: $o).
% 8.63/1.67 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 8.63/1.67 thf(func_def_91, type, induction2_lthm: $o).
% 8.63/1.67 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 8.63/1.67 thf(func_def_93, type, substmonoid_lthm: $o).
% 8.63/1.67 thf(func_def_94, type, pushprop: $o).
% 8.63/1.67 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 8.63/1.67 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 8.63/1.67 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 8.63/1.67 thf(func_def_98, type, substmonoid: $o).
% 8.63/1.67 thf(func_def_99, type, lamnotvar: $o).
% 8.63/1.67 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 8.63/1.67 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 8.63/1.67 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 8.63/1.67 thf(func_def_103, type, induction2_gthm: $o).
% 8.63/1.67 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 8.63/1.67 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_106, type, hoaslamnotap: $o).
% 8.63/1.67 thf(func_def_107, type, substmonoid_gthm: $o).
% 8.63/1.67 thf(func_def_108, type, ulamvarsh: $o).
% 8.63/1.67 thf(func_def_109, type, induction2: $o).
% 8.63/1.67 thf(func_def_110, type, pushprop_lem3v2: $o).
% 8.63/1.67 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 8.63/1.67 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 8.63/1.67 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 8.63/1.67 thf(func_def_114, type, axshiftcons: $o).
% 8.63/1.67 thf(func_def_115, type, termmset: $o).
% 8.63/1.67 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 8.63/1.67 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 8.63/1.67 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 8.63/1.67 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 8.63/1.67 thf(func_def_120, type, axvarid: $o).
% 8.63/1.67 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 8.63/1.67 thf(func_def_122, type, d2term: (d_term > term)).
% 8.63/1.67 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 8.63/1.67 thf(func_def_124, type, d_one: d_term).
% 8.63/1.67 thf(func_def_125, type, d_id: d_subst).
% 8.63/1.67 thf(func_def_127, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 8.63/1.67 thf(func_def_128, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.63/1.67 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)).
% 8.63/1.67 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)).
% 8.63/1.67 thf(func_def_131, type, db2: !>[X0: $tType]:(X0)).
% 8.63/1.67 thf(func_def_132, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.63/1.67 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)).
% 8.63/1.67 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)).
% 8.63/1.67 thf(func_def_137, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.63/1.67 thf(func_def_138, type, sP0: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_139, type, sP1: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_140, type, sP2: $o).
% 8.63/1.67 thf(func_def_141, type, sP3: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_142, type, sP4: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_145, type, sP7: $o).
% 8.63/1.67 thf(func_def_146, type, sP8: $o).
% 8.63/1.67 thf(func_def_147, type, sP9: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_148, type, sP10: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_149, type, sP11: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_150, type, sP12: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_151, type, sP13: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_152, type, sP14: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_153, type, sP15: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_154, type, sP16: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_155, type, sP17: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_156, type, sP18: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_157, type, sP19: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_158, type, sP20: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_159, type, sP21: $o).
% 8.63/1.67 thf(func_def_160, type, sP22: $o).
% 8.63/1.67 thf(func_def_161, type, sP23: $o).
% 8.63/1.67 thf(func_def_162, type, sP24: $o).
% 8.63/1.67 thf(func_def_163, type, sP25: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_164, type, sP26: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_165, type, sP27: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_166, type, sP28: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_168, type, sP30: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_169, type, sP31: $o).
% 8.63/1.67 thf(func_def_170, type, sP32: $o).
% 8.63/1.67 thf(func_def_171, type, sP33: $o).
% 8.63/1.67 thf(func_def_172, type, sP34: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_173, type, sP35: $o).
% 8.63/1.67 thf(func_def_174, type, sP36: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_175, type, sP37: $o).
% 8.63/1.67 thf(func_def_176, type, sP38: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_177, type, sP39: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_179, type, sP41: $o).
% 8.63/1.67 thf(func_def_180, type, sP42: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_182, type, sP44: $o).
% 8.63/1.67 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_185, type, sP47: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_186, type, sP48: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_187, type, sP49: $o).
% 8.63/1.67 thf(func_def_188, type, sP50: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_189, type, sP51: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_190, type, sP52: $o).
% 8.63/1.67 thf(func_def_191, type, sP53: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_192, type, sP54: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_193, type, sP55: $o).
% 8.63/1.67 thf(func_def_194, type, sP56: $o).
% 8.63/1.67 thf(func_def_195, type, sP57: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_196, type, sP58: $o).
% 8.63/1.67 thf(func_def_197, type, sP59: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_198, type, sP60: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_199, type, sP61: $o).
% 8.63/1.67 thf(func_def_200, type, sP62: $o).
% 8.63/1.67 thf(func_def_201, type, sP63: $o).
% 8.63/1.67 thf(func_def_202, type, sP64: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_203, type, sP65: $o).
% 8.63/1.67 thf(func_def_204, type, sP66: $o).
% 8.63/1.67 thf(func_def_205, type, sP67: $o).
% 8.63/1.67 thf(func_def_206, type, sP68: $o).
% 8.63/1.67 thf(func_def_207, type, sP69: $o).
% 8.63/1.67 thf(func_def_208, type, sP70: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_209, type, sP71: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_210, type, sP72: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_211, type, sP73: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_212, type, sP74: $o).
% 8.63/1.67 thf(func_def_213, type, sP75: $o).
% 8.63/1.67 thf(func_def_214, type, sP76: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_215, type, sP77: $o).
% 8.63/1.67 thf(func_def_216, type, sP78: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_217, type, sP79: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_218, type, sP80: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_219, type, sP81: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_220, type, sP82: $o).
% 8.63/1.67 thf(func_def_221, type, sP83: $o).
% 8.63/1.67 thf(func_def_222, type, sP84: $o).
% 8.63/1.67 thf(func_def_223, type, sP85: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_224, type, sP86: $o).
% 8.63/1.67 thf(func_def_225, type, sP87: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_226, type, sP88: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_227, type, sP89: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_228, type, sP90: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_229, type, sP91: $o).
% 8.63/1.67 thf(func_def_230, type, sP92: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_231, type, sP93: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_232, type, sP94: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_233, type, sP95: $o).
% 8.63/1.67 thf(func_def_234, type, sP96: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_235, type, sP97: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_236, type, sP98: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_237, type, sP99: $o).
% 8.63/1.67 thf(func_def_238, type, sP100: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_239, type, sP101: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_240, type, sP102: ((term > $o) > $o)).
% 8.63/1.67 thf(func_def_241, type, sP103: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_242, type, sP104: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_243, type, sP105: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_244, type, sP106: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_245, type, sP107: ((subst > term > subst > $o) > $o)).
% 8.63/1.67 thf(func_def_246, type, sP108: $o).
% 8.63/1.67 thf(func_def_247, type, sP109: $o).
% 8.63/1.67 thf(func_def_248, type, sP110: $o).
% 8.63/1.67 thf(func_def_249, type, sK111: (term > $o)).
% 8.63/1.67 thf(func_def_250, type, sK112: term).
% 8.63/1.67 thf(func_def_251, type, sK113: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_252, type, sK114: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_253, type, sK115: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_254, type, sK116: (term > $o)).
% 8.63/1.67 thf(func_def_255, type, sK117: term).
% 8.63/1.67 thf(func_def_256, type, sK118: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_257, type, sK119: term).
% 8.63/1.67 thf(func_def_258, type, sK120: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_263, type, sK125: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_269, type, sK131: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_270, type, sK132: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_271, type, sK133: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_272, type, sK134: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_273, type, sK135: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_274, type, sK136: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_275, type, sK137: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_276, type, sK138: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_277, type, sK139: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_278, type, sK140: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_279, type, sK141: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_280, type, sK142: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_281, type, sK143: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_282, type, sK144: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_283, type, sK145: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_284, type, sK146: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_285, type, sK147: (term > $o)).
% 8.63/1.67 thf(func_def_286, type, sK148: term).
% 8.63/1.67 thf(func_def_287, type, sK149: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_288, type, sK150: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_289, type, sK151: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_290, type, sK152: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_291, type, sK153: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_293, type, sK155: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_294, type, sK156: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_296, type, sK158: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_297, type, sK159: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_298, type, sK160: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_299, type, sK161: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_300, type, sK162: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_301, type, sK163: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_302, type, sK164: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_303, type, sK165: (term > $o)).
% 8.63/1.67 thf(func_def_304, type, sK166: term).
% 8.63/1.67 thf(func_def_305, type, sK167: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_306, type, sK168: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_307, type, sK169: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_308, type, sK170: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_309, type, sK171: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_311, type, sK173: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_312, type, sK174: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_315, type, sK177: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_316, type, sK178: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_317, type, sK179: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_318, type, sK180: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_319, type, sK181: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_320, type, sK182: (term > $o)).
% 8.63/1.67 thf(func_def_321, type, sK183: term).
% 8.63/1.67 thf(func_def_322, type, sK184: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_323, type, sK185: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_324, type, sK186: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_325, type, sK187: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_326, type, sK188: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_327, type, sK189: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_328, type, sK190: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_329, type, sK191: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_330, type, sK192: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_331, type, sK193: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_332, type, sK194: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_333, type, sK195: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_334, type, sK196: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_335, type, sK197: term).
% 8.63/1.67 thf(func_def_336, type, sK198: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_337, type, sK199: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_338, type, sK200: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_339, type, sK201: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_340, type, sK202: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_342, type, sK204: subst).
% 8.63/1.67 thf(func_def_343, type, sK205: subst).
% 8.63/1.67 thf(func_def_344, type, sK206: subst).
% 8.63/1.67 thf(func_def_345, type, sK207: subst).
% 8.63/1.67 thf(func_def_346, type, sK208: (subst > (term > $o) > term)).
% 8.63/1.67 thf(func_def_347, type, sK209: (term > $o)).
% 8.63/1.67 thf(func_def_348, type, sK210: term).
% 8.63/1.67 thf(func_def_349, type, sK211: subst).
% 8.63/1.67 thf(func_def_350, type, sK212: (term > $o)).
% 8.63/1.67 thf(func_def_351, type, sK213: term).
% 8.63/1.67 thf(func_def_352, type, sK214: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_353, type, sK215: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_354, type, sK216: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_355, type, sK217: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_356, type, sK218: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_357, type, sK219: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_358, type, sK220: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_359, type, sK221: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_360, type, sK222: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_361, type, sK223: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_362, type, sK224: (term > $o)).
% 8.63/1.67 thf(func_def_363, type, sK225: term).
% 8.63/1.67 thf(func_def_364, type, sK226: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_365, type, sK227: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_366, type, sK228: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_367, type, sK229: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_368, type, sK230: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_369, type, sK231: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_370, type, sK232: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_371, type, sK233: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_372, type, sK234: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_373, type, sK235: term).
% 8.63/1.67 thf(func_def_374, type, sK236: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_375, type, sK237: term).
% 8.63/1.67 thf(func_def_376, type, sK238: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_377, type, sK239: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_380, type, sK242: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_381, type, sK243: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_382, type, sK244: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_383, type, sK245: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_385, type, sK247: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_386, type, sK248: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_387, type, sK249: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_388, type, sK250: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_389, type, sK251: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_390, type, sK252: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_391, type, sK253: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_392, type, sK254: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_393, type, sK255: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_394, type, sK256: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_395, type, sK257: term).
% 8.63/1.67 thf(func_def_396, type, sK258: term).
% 8.63/1.67 thf(func_def_397, type, sK259: term).
% 8.63/1.67 thf(func_def_398, type, sK260: subst).
% 8.63/1.67 thf(func_def_399, type, sK261: term).
% 8.63/1.67 thf(func_def_400, type, sK262: subst).
% 8.63/1.67 thf(func_def_401, type, sK263: (subst > term > term)).
% 8.63/1.67 thf(func_def_402, type, sK264: (subst > term > term)).
% 8.63/1.67 thf(func_def_403, type, sK265: subst).
% 8.63/1.67 thf(func_def_404, type, sK266: term).
% 8.63/1.67 thf(func_def_405, type, sK267: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_406, type, sK268: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_407, type, sK269: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_408, type, sK270: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_409, type, sK271: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_410, type, sK272: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_411, type, sK273: term).
% 8.63/1.67 thf(func_def_412, type, sK274: term).
% 8.63/1.67 thf(func_def_413, type, sK275: term).
% 8.63/1.67 thf(func_def_414, type, sK276: term).
% 8.63/1.67 thf(func_def_415, type, sK277: term).
% 8.63/1.67 thf(func_def_416, type, sK278: term).
% 8.63/1.67 thf(func_def_417, type, sK279: term).
% 8.63/1.67 thf(func_def_418, type, sK280: term).
% 8.63/1.67 thf(func_def_419, type, sK281: term).
% 8.63/1.67 thf(func_def_420, type, sK282: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_421, type, sK283: (term > $o)).
% 8.63/1.67 thf(func_def_422, type, sK284: term).
% 8.63/1.67 thf(func_def_423, type, sK285: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_424, type, sK286: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_425, type, sK287: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_426, type, sK288: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_427, type, sK289: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_428, type, sK290: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_429, type, sK291: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_430, type, sK292: term).
% 8.63/1.67 thf(func_def_431, type, sK293: term).
% 8.63/1.67 thf(func_def_432, type, sK294: term).
% 8.63/1.67 thf(func_def_433, type, sK295: term).
% 8.63/1.67 thf(func_def_434, type, sK296: term).
% 8.63/1.67 thf(func_def_435, type, sK297: term).
% 8.63/1.67 thf(func_def_436, type, sK298: term).
% 8.63/1.67 thf(func_def_437, type, sK299: term).
% 8.63/1.67 thf(func_def_438, type, sK300: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_439, type, sK301: (term > $o)).
% 8.63/1.67 thf(func_def_440, type, sK302: term).
% 8.63/1.67 thf(func_def_441, type, sK303: term).
% 8.63/1.67 thf(func_def_442, type, sK304: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_443, type, sK305: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_444, type, sK306: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_445, type, sK307: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_446, type, sK308: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_447, type, sK309: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_449, type, sK311: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_450, type, sK312: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_451, type, sK313: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_452, type, sK314: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_453, type, sK315: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_454, type, sK316: term).
% 8.63/1.67 thf(func_def_455, type, sK317: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_456, type, sK318: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_457, type, sK319: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_458, type, sK320: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_459, type, sK321: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_461, type, sK323: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_462, type, sK324: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_463, type, sK325: term).
% 8.63/1.67 thf(func_def_464, type, sK326: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_465, type, sK327: term).
% 8.63/1.67 thf(func_def_466, type, sK328: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_467, type, sK329: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_468, type, sK330: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_469, type, sK331: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_470, type, sK332: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_471, type, sK333: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_472, type, sK334: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_473, type, sK335: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_474, type, sK336: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_475, type, sK337: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_476, type, sK338: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_477, type, sK339: (term > $o)).
% 8.63/1.67 thf(func_def_478, type, sK340: term).
% 8.63/1.67 thf(func_def_479, type, sK341: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_480, type, sK342: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_481, type, sK343: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_482, type, sK344: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_483, type, sK345: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_484, type, sK346: term).
% 8.63/1.67 thf(func_def_485, type, sK347: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_486, type, sK348: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_487, type, sK349: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_488, type, sK350: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_489, type, sK351: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_490, type, sK352: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_491, type, sK353: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_492, type, sK354: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_493, type, sK355: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_494, type, sK356: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_495, type, sK357: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_496, type, sK358: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_497, type, sK359: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_498, type, sK360: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_499, type, sK361: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_501, type, sK363: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_502, type, sK364: term).
% 8.63/1.67 thf(func_def_503, type, sK365: term).
% 8.63/1.67 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_505, type, sK367: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_509, type, sK371: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_510, type, sK372: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_514, type, sK376: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_515, type, sK377: term).
% 8.63/1.67 thf(func_def_516, type, sK378: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_519, type, sK381: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_520, type, sK382: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_521, type, sK383: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_522, type, sK384: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_523, type, sK385: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_524, type, sK386: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_525, type, sK387: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_526, type, sK388: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_527, type, sK389: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_528, type, sK390: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_530, type, sK392: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_531, type, sK393: term).
% 8.63/1.67 thf(func_def_532, type, sK394: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_533, type, sK395: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_534, type, sK396: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_535, type, sK397: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_536, type, sK398: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_538, type, sK400: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_539, type, sK401: term).
% 8.63/1.67 thf(func_def_540, type, sK402: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_541, type, sK403: (term > (subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_542, type, sK404: (term > (subst > term > term) > term)).
% 8.63/1.67 thf(func_def_543, type, sK405: (term > (subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_544, type, sK406: (term > (subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_545, type, sK407: (term > (subst > term > term) > term)).
% 8.63/1.67 thf(func_def_546, type, sK408: (term > (subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_547, type, sK409: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_548, type, sK410: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_549, type, sK411: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_550, type, sK412: (term > $o)).
% 8.63/1.67 thf(func_def_551, type, sK413: term).
% 8.63/1.67 thf(func_def_552, type, sK414: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_553, type, sK415: ((term > $o) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_554, type, sK416: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_555, type, sK417: (term > $o)).
% 8.63/1.67 thf(func_def_556, type, sK418: term).
% 8.63/1.67 thf(func_def_557, type, sK419: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_558, type, sK420: term).
% 8.63/1.67 thf(func_def_559, type, sK421: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_560, type, sK422: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_561, type, sK423: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_562, type, sK424: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_563, type, sK425: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_564, type, sK426: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_565, type, sK427: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_566, type, sK428: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_567, type, sK429: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_568, type, sK430: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_569, type, sK431: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_570, type, sK432: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_571, type, sK433: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_572, type, sK434: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_573, type, sK435: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_574, type, sK436: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_575, type, sK437: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_576, type, sK438: (term > $o)).
% 8.63/1.67 thf(func_def_577, type, sK439: term).
% 8.63/1.67 thf(func_def_578, type, sK440: (term > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_579, type, sK441: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_580, type, sK442: term).
% 8.63/1.67 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_582, type, sK444: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_584, type, sK446: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_585, type, sK447: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_586, type, sK448: term).
% 8.63/1.67 thf(func_def_587, type, sK449: term).
% 8.63/1.67 thf(func_def_588, type, sK450: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_589, type, sK451: term).
% 8.63/1.67 thf(func_def_590, type, sK452: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_591, type, sK453: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_592, type, sK454: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_593, type, sK455: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_595, type, sK457: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_596, type, sK458: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_597, type, sK459: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_598, type, sK460: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_599, type, sK461: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_600, type, sK462: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_601, type, sK463: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_602, type, sK464: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_603, type, sK465: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_604, type, sK466: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_605, type, sK467: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_606, type, sK468: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_607, type, sK469: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_608, type, sK470: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_609, type, sK471: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_610, type, sK472: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_611, type, sK473: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_612, type, sK474: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_613, type, sK475: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_614, type, sK476: ((subst > term > subst > $o) > subst > term > term)).
% 8.63/1.67 thf(func_def_615, type, sK477: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_616, type, sK478: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_617, type, sK479: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_618, type, sK480: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_619, type, sK481: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_620, type, sK482: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_621, type, sK483: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_622, type, sK484: ((subst > term > subst > $o) > subst)).
% 8.63/1.67 thf(func_def_623, type, sK485: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_624, type, sK486: ((subst > term > subst > $o) > term)).
% 8.63/1.67 thf(func_def_625, type, sK487: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_626, type, sK488: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_627, type, sK489: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_628, type, sK490: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_629, type, sK491: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_630, type, sK492: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_631, type, sK493: (term > $o)).
% 8.63/1.67 thf(func_def_632, type, sK494: term).
% 8.63/1.67 thf(func_def_633, type, sK495: (term > $o)).
% 8.63/1.67 thf(func_def_634, type, sK496: term).
% 8.63/1.67 thf(func_def_635, type, sK497: subst).
% 8.63/1.67 thf(func_def_636, type, sK498: (subst > (term > $o) > term)).
% 8.63/1.67 thf(func_def_637, type, sK499: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_638, type, sK500: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_639, type, sK501: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_640, type, sK502: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_641, type, sK503: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_642, type, sK504: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_643, type, sK505: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_644, type, sK506: (term > $o)).
% 8.63/1.67 thf(func_def_645, type, sK507: term).
% 8.63/1.67 thf(func_def_646, type, sK508: subst).
% 8.63/1.67 thf(func_def_647, type, sK509: (subst > (term > $o) > term)).
% 8.63/1.67 thf(func_def_648, type, sK510: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_649, type, sK511: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_650, type, sK512: (term > (term > $o) > term)).
% 8.63/1.67 thf(func_def_651, type, sK513: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_652, type, sK514: ((subst > term > subst > $o) > term > $o)).
% 8.63/1.67 thf(func_def_653, type, sK515: term).
% 8.63/1.67 thf(func_def_654, type, sK516: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_655, type, sK517: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_656, type, sK518: term).
% 8.63/1.67 thf(func_def_657, type, sK519: term).
% 8.63/1.67 thf(func_def_658, type, sK520: (term > $o)).
% 8.63/1.67 thf(func_def_659, type, sK521: term).
% 8.63/1.67 thf(func_def_660, type, sK522: subst).
% 8.63/1.67 thf(func_def_661, type, sK523: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_662, type, sK524: (subst > term > (term > $o) > term > $o)).
% 8.63/1.67 thf(func_def_663, type, sK525: term).
% 8.63/1.67 thf(func_def_664, type, sK526: term).
% 8.63/1.67 thf(func_def_665, type, sK527: subst).
% 8.63/1.67 thf(func_def_666, type, sK528: (term > $o)).
% 8.63/1.67 thf(func_def_667, type, sK529: (term > $o)).
% 8.63/1.67 thf(func_def_668, type, sK530: term).
% 8.63/1.67 thf(func_def_669, type, sK531: subst).
% 8.63/1.67 thf(func_def_670, type, sK532: term).
% 8.63/1.67 thf(func_def_671, type, sK533: term).
% 8.63/1.67 thf(func_def_672, type, sK534: subst).
% 8.63/1.67 thf(func_def_673, type, sK535: term).
% 8.63/1.67 thf(func_def_674, type, sK536: subst).
% 8.63/1.67 thf(func_def_675, type, sK537: (subst > term > term)).
% 8.63/1.67 thf(func_def_676, type, sK538: term).
% 8.63/1.67 thf(func_def_677, type, sK539: term).
% 8.63/1.67 thf(func_def_678, type, sK540: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_679, type, sK541: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_680, type, sK542: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_681, type, sK543: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_682, type, sK544: term).
% 8.63/1.67 thf(func_def_683, type, sK545: subst).
% 8.63/1.67 thf(func_def_684, type, sK546: subst).
% 8.63/1.67 thf(func_def_685, type, sK547: term).
% 8.63/1.67 thf(func_def_686, type, sK548: (term > subst > term > term)).
% 8.63/1.67 thf(func_def_687, type, sK549: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_688, type, sK550: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_689, type, sK551: ((subst > term > subst > $o) > term > $o)).
% 8.63/1.67 thf(func_def_690, type, sK552: term).
% 8.63/1.67 thf(func_def_691, type, sK553: subst).
% 8.63/1.67 thf(func_def_692, type, sK554: (term > subst > term > term)).
% 8.63/1.67 thf(func_def_693, type, sK555: term).
% 8.63/1.67 thf(func_def_694, type, sK556: term).
% 8.63/1.67 thf(func_def_695, type, sK557: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_696, type, sK558: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_697, type, sK559: (term > $o)).
% 8.63/1.67 thf(func_def_698, type, sK560: term).
% 8.63/1.67 thf(func_def_699, type, sK561: subst).
% 8.63/1.67 thf(func_def_700, type, sK562: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_701, type, sK563: (subst > term > (term > $o) > term > $o)).
% 8.63/1.67 thf(func_def_702, type, sK564: term).
% 8.63/1.67 thf(func_def_703, type, sK565: term).
% 8.63/1.67 thf(func_def_704, type, sK566: term).
% 8.63/1.67 thf(func_def_705, type, sK567: (term > $o)).
% 8.63/1.67 thf(func_def_706, type, sK568: (term > $o)).
% 8.63/1.67 thf(func_def_707, type, sK569: term).
% 8.63/1.67 thf(func_def_708, type, sK570: subst).
% 8.63/1.67 thf(func_def_709, type, sK571: term).
% 8.63/1.67 thf(func_def_710, type, sK572: subst).
% 8.63/1.67 thf(func_def_711, type, sK573: subst).
% 8.63/1.67 thf(func_def_712, type, sK574: term).
% 8.63/1.67 thf(func_def_713, type, sK575: subst).
% 8.63/1.67 thf(func_def_714, type, sK576: term).
% 8.63/1.67 thf(func_def_715, type, sK577: term).
% 8.63/1.67 thf(func_def_716, type, sK578: term).
% 8.63/1.67 thf(func_def_717, type, sK579: term).
% 8.63/1.67 thf(func_def_718, type, sK580: term).
% 8.63/1.67 thf(func_def_719, type, sK581: term).
% 8.63/1.67 thf(func_def_720, type, sK582: term).
% 8.63/1.67 thf(func_def_721, type, sK583: term).
% 8.63/1.67 thf(func_def_722, type, sK584: term).
% 8.63/1.67 thf(func_def_723, type, sK585: term).
% 8.63/1.67 thf(func_def_724, type, sK586: (term > subst > term > term)).
% 8.63/1.67 thf(func_def_725, type, sK587: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_726, type, sK588: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_727, type, sK589: ((subst > term > subst > $o) > term > $o)).
% 8.63/1.67 thf(func_def_728, type, sK590: (term > $o)).
% 8.63/1.67 thf(func_def_729, type, sK591: (term > $o)).
% 8.63/1.67 thf(func_def_730, type, sK592: term).
% 8.63/1.67 thf(func_def_731, type, sK593: subst).
% 8.63/1.67 thf(func_def_732, type, sK594: (subst > term > (term > $o) > (term > $o) > term)).
% 8.63/1.67 thf(func_def_733, type, sK595: term).
% 8.63/1.67 thf(func_def_734, type, sK596: subst).
% 8.63/1.67 thf(func_def_735, type, sK597: term).
% 8.63/1.67 thf(func_def_736, type, sK598: term).
% 8.63/1.67 thf(func_def_737, type, sK599: (subst > term > term)).
% 8.63/1.67 thf(func_def_738, type, sK600: (subst > term > term)).
% 8.63/1.67 thf(func_def_739, type, sK601: subst).
% 8.63/1.67 thf(func_def_740, type, sK602: term).
% 8.63/1.67 thf(func_def_741, type, sK603: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_742, type, sK604: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_743, type, sK605: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_744, type, sK606: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_745, type, sK607: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_746, type, sK608: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_747, type, sK609: ((subst > term > subst > $o) > term > $o)).
% 8.63/1.67 thf(func_def_748, type, sK610: term).
% 8.63/1.67 thf(func_def_749, type, sK611: (subst > term > subst > $o)).
% 8.63/1.67 thf(func_def_750, type, sK612: ((term > $o) > term)).
% 8.63/1.67 thf(func_def_751, type, sK613: term).
% 8.63/1.67 thf(func_def_752, type, sK614: ((subst > term > term) > term)).
% 8.63/1.67 thf(func_def_753, type, sK615: ((subst > term > term) > subst)).
% 8.63/1.67 thf(func_def_754, type, sK616: (term > subst > term > term)).
% 8.63/1.67 thf(func_def_755, type, sK617: subst).
% 8.63/1.67 thf(func_def_756, type, sK618: term).
% 8.63/1.67 thf(func_def_757, type, sK619: subst).
% 8.63/1.67 thf(func_def_758, type, sK620: term).
% 8.63/1.68 thf(func_def_759, type, sK621: subst).
% 8.63/1.68 thf(func_def_760, type, sK622: term).
% 8.63/1.68 thf(func_def_761, type, sK623: term).
% 8.63/1.68 thf(func_def_762, type, sK624: term).
% 8.63/1.68 thf(func_def_763, type, sK625: term).
% 8.63/1.68 thf(func_def_764, type, sK626: term).
% 8.63/1.68 thf(func_def_765, type, sK627: term).
% 8.63/1.68 thf(func_def_766, type, sK628: term).
% 8.63/1.68 thf(func_def_767, type, sK629: term).
% 8.63/1.68 thf(func_def_768, type, sK630: term).
% 8.63/1.68 thf(func_def_769, type, sK631: ((subst > term > term) > term)).
% 8.63/1.68 thf(func_def_770, type, sK632: ((subst > term > term) > subst)).
% 8.63/1.68 thf(func_def_771, type, sK633: (term > subst > term > term)).
% 8.63/1.68 thf(func_def_772, type, sK634: term).
% 8.63/1.68 thf(func_def_773, type, sK635: term).
% 8.63/1.68 thf(func_def_774, type, sK636: (term > $o)).
% 8.63/1.68 thf(func_def_775, type, sK637: (term > $o)).
% 8.63/1.68 thf(func_def_776, type, sK638: term).
% 8.63/1.68 thf(func_def_777, type, sK639: subst).
% 8.63/1.68 thf(func_def_778, type, sK640: (subst > term > (term > $o) > (term > $o) > term)).
% 8.63/1.68 thf(func_def_779, type, sK641: (subst > d_subst)).
% 8.63/1.68 thf(func_def_780, type, sK642: (term > d_term)).
% 8.63/1.68 thf(func_def_781, type, vNOT: ($o > $o)).
% 8.63/1.68 thf(func_def_782, type, sK643: subst).
% 8.63/1.68 thf(func_def_783, type, db6: !>[X0: $tType]:(X0)).
% 8.63/1.68 thf(func_def_784, type, db5: !>[X0: $tType]:(X0)).
% 8.63/1.68 thf(func_def_785, type, sK644: term).
% 8.63/1.68 thf(func_def_786, type, sK645: (term > $o)).
% 8.63/1.68 thf(func_def_787, type, sK646: ((term > $o) > term)).
% 8.63/1.68 thf(func_def_788, type, sK647: ((term > $o) > subst > term > term > $o)).
% 8.63/1.68 thf(f1,axiom,(
% 8.63/1.68 (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : ((X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) & hoasapnotvar_lthm & (pushprop_lem0_lthm <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (hoasinduction_lem3v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : ((X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X26 : (term > $o),X13 : term,X14 : subst,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & pushprop_lem2v2_gthm & pushprop_lem3v2 & (induction2 <=> ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))) & ulamvarsh & substmonoid_gthm & (hoaslamnotap <=> ! [X18 : (subst > term > term),X46 : term,X47 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem2v2_lthm & induction2_gthm & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & hoasinduction_lem1_gthm & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & lamnotvar & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & hoasinduction_lem2_gthm & hoasinduction_lem3_gthm & pushprop & (substmonoid_lthm <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))))) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13))) => ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))))) & hoaslaminj_gthm & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & hoaslamnotvar & hoasapinj1_gthm & ~lamnotap & hoasinduction_lem1_lthm & hoasapinj2_gthm & hoasinduction_lem2_lthm & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & axabs & pushprop_gthm & (pushprop_lem0 <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) & (laminj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & (pushprop_lem1 <=> ! [X10 : (term > $o),X26 : (term > $o),X13 : term,X14 : subst,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & hoasinduction_lem2v2_gthm & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X18 : (subst > term > term),X31 : (subst > term > term),X32 : subst,X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & (hoasinduction_lem3v2a <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & (hoasapinj2_lthm <=> (! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & (apinj1 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (apinj2 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & pushprop_lthm & (hoasinduction_lem2v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X44 : term,X45 : term] : ((X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~(X11 @ X44) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & axassoc & axclos & hoasinduction_lem3a_gthm & pushprop_lem2v2 & hoasinduction_lem3b_gthm & hoaslamnotvar_gthm & hoaslamnotap_gthm & pushprop_lem1v2_gthm & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & termmset_gthm & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & (induction <=> ! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))) & ulamvarind & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & pushprop_lem3v2_lthm & hoaslamnotvar_lthm & axapp & hoasinduction_gthm & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & hoasapnotvar & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X11 : (term > $o),X13 : term,X14 : subst] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13)))) & hoaslamnotap_lthm & hoasinduction_lem1 & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem3 <=> ! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & induction2lem_gthm & (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X39 : subst,X40 : term,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X36 : subst,X37 : term,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))) & (hoaslaminj <=> ! [X18 : (subst > term > term),X31 : (subst > term > term),X32 : subst,X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))))))) & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => (! [X10 : (subst > term > subst > $o),X27 : term] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & pushprop_lthm_orig & apnotvar & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => ! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))))))) & ~ulamvar1 & (hoasapinj1 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & hoasapnotvar_gthm & (hoasapinj2 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & axvarshift & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (induction2lem <=> ! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))) & hoasinduction_lem1v2_gthm & hoasinduction_lem1v2 & (shinj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & pushprop_lem0_gthm & axmap & pushprop_lem1_gthm & (pushprop_lem1v2 <=> ! [X10 : (term > $o),X11 : (term > $o),X13 : term,X14 : subst] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13))) & ~(var @ (d2term @ d_one)) & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (sh = ((d2subst @ d_id))) & (id = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (one = ((d2term @ d_one))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ! [X5 : d_subst] : (X5 = d_id) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & ! [X1 : d_term] : (X1 = d_one) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1)))),
% 8.63/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 8.63/1.68 thf(f2,conjecture,(
% 8.63/1.68 (pushprop_lem0 = ! [X0 : (term > $o),X1 : term,X2 : subst] : ? [X3 : (term > $o)] : (pushprop_p_and_p_prime @ X1 @ X2 @ X0 @ X3))),
% 8.63/1.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0)).
% 8.63/1.68 thf(f3,negated_conjecture,(
% 8.63/1.68 ~ (pushprop_lem0 = ! [X0 : (term > $o),X1 : term,X2 : subst] : ? [X3 : (term > $o)] : (pushprop_p_and_p_prime @ X1 @ X2 @ X0 @ X3))),
% 8.63/1.68 inference(negated_conjecture,[status(cth)],[f2])).
% 8.63/1.68 thf(f4,plain,(
% 8.63/1.68 (hoasinduction_lthm_3 <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((X3 @ X4) | ~ ! [X5 : term] : ((X3 @ (lam @ X5)) | ~ ! [X6 : term] : ((X3 @ (sub @ X5 @ (push @ X6 @ id))) | ~(X3 @ X6))) | ~ ! [X7 : term,X8 : term] : ((X3 @ (ap @ X7 @ X8)) | ~(X3 @ X8) | ~(X3 @ X7)) | ~ ! [X9 : term] : ((X3 @ X9) | ~(var @ X9))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((X12 @ (lam @ X13)) | ~ ! [X14 : term] : ((X12 @ (sub @ X13 @ (push @ X14 @ id))) | ~(X12 @ X14)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id) | ~ ! [X17 : term] : ((X11 @ id @ (X16 @ id @ X17) @ id) | ~(X11 @ id @ X17 @ id)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((X21 @ id @ X22 @ id) | ~ ! [X23 : (subst > term > term)] : ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id) | ~ ! [X24 : term] : ((X21 @ id @ (X23 @ id @ X24) @ id) | ~(X21 @ id @ X24 @ id)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id) | ~(X21 @ id @ X29 @ id) | ~(X21 @ id @ X28 @ id)) | ~ ! [X30 : term] : ((X21 @ id @ X30 @ id) | ~(var @ (sub @ X30 @ id))) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((X21 @ X31 @ X32 @ (comp @ X34 @ X33)) | ~(X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37) | ~(X21 @ X35 @ X36 @ (comp @ X38 @ X37))))))))) & (axvarid <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & (hoasinduction_lem3v2_lthm <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((X42 @ (lam @ X43)) | ~ ! [X44 : term] : ((X42 @ (sub @ X43 @ (push @ X44 @ id))) | ~(X42 @ X44)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id) | ~ ! [X47 : term] : ((X41 @ id @ (X46 @ id @ X47) @ id) | ~(X41 @ id @ X47 @ id)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((X41 @ X51 @ X52 @ (comp @ X54 @ X53)) | ~(X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57) | ~(X41 @ X55 @ X56 @ (comp @ X58 @ X57)))))) & hoasapnotvar_lthm & (pushprop_lem0_lthm <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & (termmset <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & (axshiftcons <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & (hoasinduction_lem3v2 <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((X68 @ (lam @ X69)) | ~ ! [X70 : term] : ((X68 @ (sub @ X69 @ (push @ X70 @ id))) | ~(X68 @ X70)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id) | ~ ! [X73 : term] : ((X67 @ id @ (X72 @ id @ X73) @ id) | ~(X67 @ id @ X73 @ id)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((X67 @ X77 @ X78 @ (comp @ X80 @ X79)) | ~(X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83) | ~(X67 @ X81 @ X82 @ (comp @ X84 @ X83))))) & (pushprop_lem1_lthm <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((X90 @ (sub @ X91 @ (push @ X93 @ X92))) | ~(X89 @ X91))))) & pushprop_lem2v2_gthm & pushprop_lem3v2 & (induction2 <=> ! [X94 : (term > $o),X95 : term] : ((X94 @ X95) | ~ ! [X96 : term] : ((X94 @ (lam @ X96)) | ~ ! [X97 : term] : ((X94 @ (sub @ X96 @ (push @ X97 @ id))) | ~(X94 @ X97))) | ~ ! [X98 : term,X99 : term] : ((X94 @ (ap @ X98 @ X99)) | ~(X94 @ X99) | ~(X94 @ X98)) | ~ ! [X100 : term] : ((X94 @ X100) | ~(var @ X100)))) & ulamvarsh & substmonoid_gthm & (hoaslamnotap <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem2v2_lthm & induction2_gthm & (hoasinduction_no_psi_cond <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((X107 @ id @ X108 @ id) | ~ ! [X109 : (subst > term > term)] : ((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id) | ~ ! [X110 : term] : ((X107 @ id @ (X109 @ id @ X110) @ id) | ~(X107 @ id @ X110 @ id)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id) | ~(X107 @ id @ X115 @ id) | ~(X107 @ id @ X114 @ id)))) & hoasinduction_lem1_gthm & (hoasinduction_lem3a <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((X116 @ id @ (lam @ X117) @ id) | ~ ! [X118 : term] : ((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id) | ~(X116 @ id @ X118 @ id)) | ~ ! [X119 : (subst > term > term)] : ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id) | ~ ! [X120 : term] : ((X116 @ id @ (X119 @ id @ X120) @ id) | ~(X116 @ id @ X120 @ id)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & lamnotvar & (substmonoid <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & (hoasinduction_lem3b <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & hoasinduction_lem2_gthm & hoasinduction_lem3_gthm & pushprop & (substmonoid_lthm <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & (hoasinduction_lem0_lthm <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & (induction2_lthm <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((X136 @ (sub @ X137 @ X138)) | ~ ! [X139 : term] : ((X136 @ (sub @ X139 @ X138)) | ~(var @ X139)) | ~ ! [X140 : term] : ((X136 @ (lam @ X140)) | ~ ! [X141 : term] : ((X136 @ (sub @ X140 @ (push @ X141 @ id))) | ~(X136 @ X141))) | ~ ! [X142 : term,X143 : term] : ((X136 @ (ap @ X142 @ X143)) | ~(X136 @ X143) | ~(X136 @ X142))) => ! [X144 : (term > $o),X145 : term] : ((X144 @ X145) | ~ ! [X146 : term] : ((X144 @ (lam @ X146)) | ~ ! [X147 : term] : ((X144 @ (sub @ X146 @ (push @ X147 @ id))) | ~(X144 @ X147))) | ~ ! [X148 : term,X149 : term] : ((X144 @ (ap @ X148 @ X149)) | ~(X144 @ X149) | ~(X144 @ X148)) | ~ ! [X150 : term] : ((X144 @ X150) | ~(var @ X150)))))) & hoaslaminj_gthm & (axidl <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & hoaslamnotvar & hoasapinj1_gthm & ~lamnotap & hoasinduction_lem1_lthm & hoasapinj2_gthm & hoasinduction_lem2_lthm & (hoasinduction_lem3v2a_lthm <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((X158 @ (lam @ X159)) | ~ ! [X160 : term] : ((X158 @ (sub @ X159 @ (push @ X160 @ id))) | ~(X158 @ X160)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id) | ~ ! [X163 : term] : ((X157 @ id @ (X162 @ id @ X163) @ id) | ~(X157 @ id @ X163 @ id)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & axabs & pushprop_gthm & (pushprop_lem0 <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & (hoasinduction_lem3_lthm <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id) | ~ ! [X175 : term] : ((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id) | ~(X173 @ id @ X175 @ id)) | ~ ! [X176 : (subst > term > term)] : ((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id) | ~ ! [X177 : term] : ((X173 @ id @ (X176 @ id @ X177) @ id) | ~(X173 @ id @ X177 @ id)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((X181 @ id @ (lam @ X182) @ id) | ~ ! [X183 : term] : ((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id) | ~(X181 @ id @ X183 @ id)) | ~ ! [X184 : (subst > term > term)] : ((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id) | ~ ! [X185 : term] : ((X181 @ id @ (X184 @ id @ X185) @ id) | ~(X181 @ id @ X185 @ id)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((X181 @ X189 @ X190 @ (comp @ X192 @ X191)) | ~(X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195) | ~(X181 @ X193 @ X194 @ (comp @ X196 @ X195))))))) & (laminj <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & (pushprop_lem1 <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((X200 @ (sub @ X201 @ (push @ X203 @ X202))) | ~(X199 @ X201))) & (axidr <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & hoasinduction_lem2v2_gthm & (axscons <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & (axvarcons <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & (hoaslaminj_lthm <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & (hoasapinj1_lthm <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & (hoasinduction_lem3v2a <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((X234 @ (lam @ X235)) | ~ ! [X236 : term] : ((X234 @ (sub @ X235 @ (push @ X236 @ id))) | ~(X234 @ X236)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id) | ~ ! [X239 : term] : ((X233 @ id @ (X238 @ id @ X239) @ id) | ~(X233 @ id @ X239 @ id)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & (hoasapinj2_lthm <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & (apinj1 <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & (apinj2 <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & pushprop_lthm & (hoasinduction_lem2v2 <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((X260 @ (ap @ X261 @ X262)) | ~(X260 @ X262) | ~(X260 @ X261) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id) | ~(X259 @ id @ X265 @ id) | ~(X259 @ id @ X264 @ id)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((X259 @ X266 @ X267 @ (comp @ X269 @ X268)) | ~(X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272) | ~(X259 @ X270 @ X271 @ (comp @ X273 @ X272))))) & axassoc & axclos & hoasinduction_lem3a_gthm & pushprop_lem2v2 & hoasinduction_lem3b_gthm & hoaslamnotvar_gthm & hoaslamnotap_gthm & pushprop_lem1v2_gthm & (hoasinduction_lem3aa <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id) | ~ ! [X276 : term] : ((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id) | ~(X274 @ id @ X276 @ id)) | ~ ! [X277 : (subst > term > term)] : ((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id) | ~ ! [X278 : term] : ((X274 @ id @ (X277 @ id @ X278) @ id) | ~(X274 @ id @ X278 @ id)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & termmset_gthm & (hoasinduction_lem3a_lthm <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id) | ~ ! [X285 : term] : ((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id) | ~(X283 @ id @ X285 @ id)) | ~ ! [X286 : (subst > term > term)] : ((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id) | ~ ! [X287 : term] : ((X283 @ id @ (X286 @ id @ X287) @ id) | ~(X283 @ id @ X287 @ id)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((X291 @ id @ (lam @ X292) @ id) | ~ ! [X293 : term] : ((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id) | ~(X291 @ id @ X293 @ id)) | ~ ! [X294 : (subst > term > term)] : ((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id) | ~ ! [X295 : term] : ((X291 @ id @ (X294 @ id @ X295) @ id) | ~(X291 @ id @ X295 @ id)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & (induction <=> ! [X299 : (term > $o),X300 : term] : ((X299 @ X300) | ~ ! [X301 : term] : ((X299 @ (lam @ X301)) | ~(X299 @ X301)) | ~ ! [X302 : term,X303 : term] : ((X299 @ (ap @ X302 @ X303)) | ~(X299 @ X303) | ~(X299 @ X302)) | ~ ! [X304 : term] : ((X299 @ X304) | ~(var @ X304)))) & ulamvarind & (hoasinduction_lem3b_lthm <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & pushprop_lem3v2_lthm & hoaslamnotvar_lthm & axapp & hoasinduction_gthm & (hoasinduction <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((X307 @ id @ X308 @ id) | ~ ! [X309 : (subst > term > term)] : ((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id) | ~ ! [X310 : term] : ((X307 @ id @ (X309 @ id @ X310) @ id) | ~(X307 @ id @ X310 @ id)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id) | ~(X307 @ id @ X315 @ id) | ~(X307 @ id @ X314 @ id)) | ~ ! [X316 : term] : ((X307 @ id @ X316 @ id) | ~(var @ (sub @ X316 @ id))) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((X307 @ X317 @ X318 @ (comp @ X320 @ X319)) | ~(X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323) | ~(X307 @ X321 @ X322 @ (comp @ X324 @ X323))))) & (hoasinduction_lem0 <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & hoasapnotvar & (pushprop_lem1v2_lthm <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((X331 @ one) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | ~(X330 @ X332)))) & hoaslamnotap_lthm & hoasinduction_lem1 & (termmset_lthm <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & (hoasinduction_lem2 <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((X337 @ id @ (ap @ X338 @ X339) @ id) | ~(X337 @ id @ X339 @ id) | ~(X337 @ id @ X338 @ id) | ~ ! [X340 : term,X341 : term] : ((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id) | ~(X337 @ id @ X341 @ id) | ~(X337 @ id @ X340 @ id)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((X337 @ X342 @ X343 @ (comp @ X345 @ X344)) | ~(X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348) | ~(X337 @ X346 @ X347 @ (comp @ X349 @ X348))))) & (hoasinduction_lem3 <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((X350 @ id @ (lam @ X351) @ id) | ~ ! [X352 : term] : ((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id) | ~(X350 @ id @ X352 @ id)) | ~ ! [X353 : (subst > term > term)] : ((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id) | ~ ! [X354 : term] : ((X350 @ id @ (X353 @ id @ X354) @ id) | ~(X350 @ id @ X354 @ id)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((X350 @ X358 @ X359 @ (comp @ X361 @ X360)) | ~(X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364) | ~(X350 @ X362 @ X363 @ (comp @ X365 @ X364))))) & (hoasinduction_lem3aa_lthm <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id) | ~ ! [X368 : term] : ((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id) | ~(X366 @ id @ X368 @ id)) | ~ ! [X369 : (subst > term > term)] : ((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id) | ~ ! [X370 : term] : ((X366 @ id @ (X369 @ id @ X370) @ id) | ~(X366 @ id @ X370 @ id)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & induction2lem_gthm & (hoasinduction_lem3aaa <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id) | ~ ! [X376 : term] : ((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id) | ~(X374 @ id @ X376 @ id)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (X374 @ id @ (lam @ (X377 @ sh @ one)) @ id) | ~ ! [X385 : term] : ((X374 @ id @ (X377 @ id @ X385) @ id) | ~(X374 @ id @ X385 @ id))))) & (hoaslaminj <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((X399 @ X400) | ~ ! [X401 : term] : ((X399 @ (lam @ X401)) | ~ ! [X402 : term] : ((X399 @ (sub @ X401 @ (push @ X402 @ id))) | ~(X399 @ X402))) | ~ ! [X403 : term,X404 : term] : ((X399 @ (ap @ X403 @ X404)) | ~(X399 @ X404) | ~(X399 @ X403)) | ~ ! [X405 : term] : ((X399 @ X405) | ~(var @ X405))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((X408 @ (lam @ X409)) | ~ ! [X410 : term] : ((X408 @ (sub @ X409 @ (push @ X410 @ id))) | ~(X408 @ X410)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id) | ~ ! [X413 : term] : ((X407 @ id @ (X412 @ id @ X413) @ id) | ~(X407 @ id @ X413 @ id)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((X417 @ id @ X418 @ id) | ~ ! [X419 : (subst > term > term)] : ((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id) | ~ ! [X420 : term] : ((X417 @ id @ (X419 @ id @ X420) @ id) | ~(X417 @ id @ X420 @ id)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id) | ~(X417 @ id @ X425 @ id) | ~(X417 @ id @ X424 @ id)))))))) & (hoasinduction_lthm <=> (! [X426 : (term > $o),X427 : term] : ((X426 @ X427) | ~ ! [X428 : term] : ((X426 @ (lam @ X428)) | ~ ! [X429 : term] : ((X426 @ (sub @ X428 @ (push @ X429 @ id))) | ~(X426 @ X429))) | ~ ! [X430 : term,X431 : term] : ((X426 @ (ap @ X430 @ X431)) | ~(X426 @ X431) | ~(X426 @ X430)) | ~ ! [X432 : term] : ((X426 @ X432) | ~(var @ X432))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((X433 @ id @ (ap @ X434 @ X435) @ id) | ~(X433 @ id @ X435 @ id) | ~(X433 @ id @ X434 @ id) | ~ ! [X436 : term,X437 : term] : ((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id) | ~(X433 @ id @ X437 @ id) | ~(X433 @ id @ X436 @ id)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((X433 @ X438 @ X439 @ (comp @ X441 @ X440)) | ~(X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444) | ~(X433 @ X442 @ X443 @ (comp @ X445 @ X444)))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((X446 @ id @ (lam @ X447) @ id) | ~ ! [X448 : term] : ((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id) | ~(X446 @ id @ X448 @ id)) | ~ ! [X449 : (subst > term > term)] : ((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id) | ~ ! [X450 : term] : ((X446 @ id @ (X449 @ id @ X450) @ id) | ~(X446 @ id @ X450 @ id)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((X446 @ X454 @ X455 @ (comp @ X457 @ X456)) | ~(X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460) | ~(X446 @ X458 @ X459 @ (comp @ X461 @ X460)))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((X462 @ id @ X463 @ id) | ~ ! [X464 : (subst > term > term)] : ((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id) | ~ ! [X465 : term] : ((X462 @ id @ (X464 @ id @ X465) @ id) | ~(X462 @ id @ X465 @ id)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id) | ~(X462 @ id @ X470 @ id) | ~(X462 @ id @ X469 @ id)) | ~ ! [X471 : term] : ((X462 @ id @ X471 @ id) | ~(var @ (sub @ X471 @ id))) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((X462 @ X472 @ X473 @ (comp @ X475 @ X474)) | ~(X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478) | ~(X462 @ X476 @ X477 @ (comp @ X479 @ X478)))))))) & (hoasinduction_lem3v2_f_lthm <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & pushprop_lthm_orig & apnotvar & hoasinduction_lem3v2_gthm & (induction2lem_lthm <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((X489 @ X490) | ~ ! [X491 : term] : ((X489 @ (lam @ X491)) | ~(X489 @ X491)) | ~ ! [X492 : term,X493 : term] : ((X489 @ (ap @ X492 @ X493)) | ~(X489 @ X493) | ~(X489 @ X492)) | ~ ! [X494 : term] : ((X489 @ X494) | ~(var @ X494))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((X495 @ (sub @ X496 @ X497)) | ~ ! [X498 : term] : ((X495 @ (sub @ X498 @ X497)) | ~(var @ X498)) | ~ ! [X499 : term] : ((X495 @ (lam @ X499)) | ~ ! [X500 : term] : ((X495 @ (sub @ X499 @ (push @ X500 @ id))) | ~(X495 @ X500))) | ~ ! [X501 : term,X502 : term] : ((X495 @ (ap @ X501 @ X502)) | ~(X495 @ X502) | ~(X495 @ X501)))))))) & ~ulamvar1 & (hoasapinj1 <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & hoasapnotvar_gthm & (hoasapinj2 <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & axvarshift & (hoasinduction_lem3v2_f <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & (induction2lem <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((X515 @ (sub @ X516 @ X517)) | ~ ! [X518 : term] : ((X515 @ (sub @ X518 @ X517)) | ~(var @ X518)) | ~ ! [X519 : term] : ((X515 @ (lam @ X519)) | ~ ! [X520 : term] : ((X515 @ (sub @ X519 @ (push @ X520 @ id))) | ~(X515 @ X520))) | ~ ! [X521 : term,X522 : term] : ((X515 @ (ap @ X521 @ X522)) | ~(X515 @ X522) | ~(X515 @ X521)))) & hoasinduction_lem1v2_gthm & hoasinduction_lem1v2 & (shinj <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & pushprop_lem0_gthm & axmap & pushprop_lem1_gthm & (pushprop_lem1v2 <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((X526 @ one) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | ~(X525 @ X527))) & ~(var @ (d2term @ d_one)) & (pushprop_p_and_p_prime = (^[X530 : term, X531 : subst, X532 : (term > $o), X533 : (term > $o)] : (! [X534 : term] : (((X533 @ X534)) = ((X532 @ (sub @ X534 @ (push @ X530 @ X531)))))))) & (hoasinduction_p_and_p_prime = (^[X535 : (subst > term > subst > $o), X536 : (term > $o)] : (! [X537 : term] : (((X536 @ X537)) = ((X535 @ id @ X537 @ id)))))) & (hoaslam = (^[X538 : subst, X539 : (subst > term > term)] : ((d2term @ d_one)))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (sh = ((d2subst @ d_id))) & (id = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (one = ((d2term @ d_one))) & ! [X540 : d_subst,X541 : d_subst] : ((((d2subst @ X540)) = ((d2subst @ X541))) => (X540 = X541)) & ! [X542 : d_subst] : (d_id = X542) & ! [X543 : subst] : ? [X544 : d_subst] : (((d2subst @ X544)) = X543) & ! [X545 : d_term,X546 : d_term] : ((((d2term @ X545)) = ((d2term @ X546))) => (X545 = X546)) & ! [X547 : d_term] : (d_one = X547) & ! [X548 : term] : ? [X549 : d_term] : (((d2term @ X549)) = X548)),
% 8.63/1.68 inference(rectify,[],[f1])).
% 8.63/1.68 thf(f5,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | ~ (((X3 @ X6)) = $true))) | ~ ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | ~ (((X3 @ X8)) = $true) | ~ (((X3 @ X7)) = $true)) | ~ ! [X9 : term] : ((((X3 @ X9)) = $true) | ~ (((var @ X9)) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) = $true) | ~ ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | ~ (((X12 @ X14)) = $true)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) = $true) | ~ (((X11 @ id @ X17 @ id)) = $true)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | ~ (((X21 @ id @ X29 @ id)) = $true) | ~ (((X21 @ id @ X28 @ id)) = $true)) | ~ ! [X30 : term] : ((((X21 @ id @ X30 @ id)) = $true) | ~ (((var @ (sub @ X30 @ id))) = $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) = $true) | ~ (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) = $true) | ~ (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true)))))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ~ ! [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) = $true) | ~ (((X42 @ X44)) = $true)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | ~ (((X41 @ id @ X47 @ id)) = $true)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) = $true) | ~ (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) = $true) | ~ (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ~ ! [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) = $true) | ~ (((X68 @ X70)) = $true)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | ~ (((X67 @ id @ X73 @ id)) = $true)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) = $true) | ~ (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) = $true) | ~ (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | ~ (((X89 @ X91)) = $true))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X96 : term] : ((((X94 @ (lam @ X96))) = $true) | ~ ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | ~ (((X94 @ X97)) = $true))) | ~ ! [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) = $true) | ~ (((X94 @ X99)) = $true) | ~ (((X94 @ X98)) = $true)) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | ~ (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ~ ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ~ ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | ~ (((X107 @ id @ X110 @ id)) = $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) = $true) | ~ (((X107 @ id @ X115 @ id)) = $true) | ~ (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ~ ! [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) = $true) | ~ (((X116 @ id @ X118 @ id)) = $true)) | ~ ! [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) = $true) | ~ ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | ~ (((X116 @ id @ X120 @ id)) = $true)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) = $true) | ~ ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | ~ (((var @ X139)) = $true)) | ~ ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ~ ! [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ~ (((X136 @ X141)) = $true))) | ~ ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | ~ (((X136 @ X143)) = $true) | ~ (((X136 @ X142)) = $true))) => ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ~ ! [X146 : term] : ((((X144 @ (lam @ X146))) = $true) | ~ ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | ~ (((X144 @ X147)) = $true))) | ~ ! [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) = $true) | ~ (((X144 @ X149)) = $true) | ~ (((X144 @ X148)) = $true)) | ~ ! [X150 : term] : ((((X144 @ X150)) = $true) | ~ (((var @ X150)) = $true)))))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ~ (lamnotap = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) = $true) | ~ (((X158 @ X160)) = $true)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) = $true) | ~ ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | ~ (((X157 @ id @ X163 @ id)) = $true)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | ~ (((X173 @ id @ X175 @ id)) = $true)) | ~ ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) = $true) | ~ (((X173 @ id @ X177 @ id)) = $true)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ~ ! [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) = $true) | ~ (((X181 @ id @ X183 @ id)) = $true)) | ~ ! [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) = $true) | ~ ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | ~ (((X181 @ id @ X185 @ id)) = $true)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) = $true) | ~ (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) = $true) | ~ (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true)))))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | ~ (((X199 @ X201)) = $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | ~ (((X234 @ X236)) = $true)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | ~ (((X233 @ id @ X239 @ id)) = $true)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | ~ (((X260 @ X262)) = $true) | ~ (((X260 @ X261)) = $true) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) = $true) | ~ (((X259 @ id @ X265 @ id)) = $true) | ~ (((X259 @ id @ X264 @ id)) = $true)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) = $true) | ~ (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) = $true) | ~ (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) = $true) | ~ (((X274 @ id @ X276 @ id)) = $true)) | ~ ! [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | ~ (((X274 @ id @ X278 @ id)) = $true)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | ~ (((X283 @ id @ X285 @ id)) = $true)) | ~ ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ~ ! [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) = $true) | ~ (((X283 @ id @ X287 @ id)) = $true)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ~ ! [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) = $true) | ~ (((X291 @ id @ X293 @ id)) = $true)) | ~ ! [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | ~ (((X291 @ id @ X295 @ id)) = $true)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ~ ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | ~ (((X299 @ X301)) = $true)) | ~ ! [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) = $true) | ~ (((X299 @ X303)) = $true) | ~ (((X299 @ X302)) = $true)) | ~ ! [X304 : term] : ((((X299 @ X304)) = $true) | ~ (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ~ ! [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) = $true) | ~ ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | ~ (((X307 @ id @ X310 @ id)) = $true)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) = $true) | ~ (((X307 @ id @ X315 @ id)) = $true) | ~ (((X307 @ id @ X314 @ id)) = $true)) | ~ ! [X316 : term] : ((((X307 @ id @ X316 @ id)) = $true) | ~ (((var @ (sub @ X316 @ id))) = $true)) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) = $true) | ~ (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) = $true) | ~ (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | ~ (((X330 @ X332)) = $true)))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | ~ (((X337 @ id @ X339 @ id)) = $true) | ~ (((X337 @ id @ X338 @ id)) = $true) | ~ ! [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) = $true) | ~ (((X337 @ id @ X341 @ id)) = $true) | ~ (((X337 @ id @ X340 @ id)) = $true)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) = $true) | ~ (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) = $true) | ~ (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ~ ! [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) = $true) | ~ (((X350 @ id @ X352 @ id)) = $true)) | ~ ! [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | ~ (((X350 @ id @ X354 @ id)) = $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) = $true) | ~ (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) = $true) | ~ (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) = $true) | ~ (((X366 @ id @ X368 @ id)) = $true)) | ~ ! [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | ~ (((X366 @ id @ X370 @ id)) = $true)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) = $true) | ~ (((X374 @ id @ X376 @ id)) = $true)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | ~ (((X374 @ id @ X385 @ id)) = $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) = $true) | ~ ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ~ ! [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) = $true) | ~ (((X399 @ X402)) = $true))) | ~ ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | ~ (((X399 @ X404)) = $true) | ~ (((X399 @ X403)) = $true)) | ~ ! [X405 : term] : ((((X399 @ X405)) = $true) | ~ (((var @ X405)) = $true))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | ~ (((X408 @ X410)) = $true)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) = $true) | ~ (((X407 @ id @ X413 @ id)) = $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ~ ! [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | ~ (((X417 @ id @ X420 @ id)) = $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) = $true) | ~ (((X417 @ id @ X425 @ id)) = $true) | ~ (((X417 @ id @ X424 @ id)) = $true)))))))) & ((hoasinduction_lthm = $true) <=> (! [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) = $true) | ~ ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ~ ! [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) = $true) | ~ (((X426 @ X429)) = $true))) | ~ ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | ~ (((X426 @ X431)) = $true) | ~ (((X426 @ X430)) = $true)) | ~ ! [X432 : term] : ((((X426 @ X432)) = $true) | ~ (((var @ X432)) = $true))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) = $true) | ~ (((X433 @ id @ X435 @ id)) = $true) | ~ (((X433 @ id @ X434 @ id)) = $true) | ~ ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | ~ (((X433 @ id @ X437 @ id)) = $true) | ~ (((X433 @ id @ X436 @ id)) = $true)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | ~ (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) = $true)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | ~ (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) = $true))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) = $true) | ~ ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | ~ (((X446 @ id @ X448 @ id)) = $true)) | ~ ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) = $true) | ~ (((X446 @ id @ X450 @ id)) = $true)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | ~ (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) = $true)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | ~ (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) = $true))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ~ ! [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | ~ (((X462 @ id @ X465 @ id)) = $true)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) = $true) | ~ (((X462 @ id @ X470 @ id)) = $true) | ~ (((X462 @ id @ X469 @ id)) = $true)) | ~ ! [X471 : term] : ((((X462 @ id @ X471 @ id)) = $true) | ~ (((var @ (sub @ X471 @ id))) = $true)) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) = $true) | ~ (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) = $true) | ~ (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) = $true) | ~ ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | ~ (((X489 @ X491)) = $true)) | ~ ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | ~ (((X489 @ X493)) = $true) | ~ (((X489 @ X492)) = $true)) | ~ ! [X494 : term] : ((((X489 @ X494)) = $true) | ~ (((var @ X494)) = $true))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ~ ! [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) = $true) | ~ (((var @ X498)) = $true)) | ~ ! [X499 : term] : ((((X495 @ (lam @ X499))) = $true) | ~ ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | ~ (((X495 @ X500)) = $true))) | ~ ! [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) = $true) | ~ (((X495 @ X502)) = $true) | ~ (((X495 @ X501)) = $true)))))))) & ~ (ulamvar1 = $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ~ ! [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) = $true) | ~ (((var @ X518)) = $true)) | ~ ! [X519 : term] : ((((X515 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | ~ (((X515 @ X520)) = $true))) | ~ ! [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) = $true) | ~ (((X515 @ X522)) = $true) | ~ (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | ~ (((X525 @ X527)) = $true))) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X540 : d_subst,X541 : d_subst] : ((((d2subst @ X540)) = ((d2subst @ X541))) => (X540 = X541)) & ! [X542 : d_subst] : (d_id = X542) & ! [X543 : subst] : ? [X544 : d_subst] : (((d2subst @ X544)) = X543) & ! [X545 : d_term,X546 : d_term] : ((((d2term @ X545)) = ((d2term @ X546))) => (X545 = X546)) & ! [X547 : d_term] : (d_one = X547) & ! [X548 : term] : ? [X549 : d_term] : (((d2term @ X549)) = X548)),
% 8.63/1.68 inference(fool_elimination,[],[f4])).
% 8.63/1.68 thf(f6,plain,(
% 8.63/1.68 ~ (pushprop_lem0 = ! [X0 : (term > $o),X1 : term,X2 : subst] : ? [X3 : (term > $o)] : (pushprop_p_and_p_prime @ X1 @ X2 @ X0 @ X3))),
% 8.63/1.68 inference(rectify,[],[f3])).
% 8.63/1.68 thf(f7,plain,(
% 8.63/1.68 ~ (pushprop_lem0 = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (?? @ (term > $o) @ (^[Y3 : term > $o]: (pushprop_p_and_p_prime @ Y1 @ Y0 @ Y2 @ Y3)))))))))))),
% 8.63/1.68 inference(fool_elimination,[],[f6])).
% 8.63/1.68 thf(f8,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | ~ (((X3 @ X6)) = $true))) | ~ ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | ~ (((X3 @ X8)) = $true) | ~ (((X3 @ X7)) = $true)) | ~ ! [X9 : term] : ((((X3 @ X9)) = $true) | ~ (((var @ X9)) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) = $true) | ~ ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | ~ (((X12 @ X14)) = $true)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) = $true) | ~ (((X11 @ id @ X17 @ id)) = $true)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | ~ (((X21 @ id @ X29 @ id)) = $true) | ~ (((X21 @ id @ X28 @ id)) = $true)) | ~ ! [X30 : term] : ((((X21 @ id @ X30 @ id)) = $true) | ~ (((var @ (sub @ X30 @ id))) = $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) = $true) | ~ (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) = $true) | ~ (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true)))))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ~ ! [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) = $true) | ~ (((X42 @ X44)) = $true)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | ~ (((X41 @ id @ X47 @ id)) = $true)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) = $true) | ~ (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) = $true) | ~ (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ~ ! [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) = $true) | ~ (((X68 @ X70)) = $true)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | ~ (((X67 @ id @ X73 @ id)) = $true)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) = $true) | ~ (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) = $true) | ~ (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | ~ (((X89 @ X91)) = $true))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X96 : term] : ((((X94 @ (lam @ X96))) = $true) | ~ ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | ~ (((X94 @ X97)) = $true))) | ~ ! [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) = $true) | ~ (((X94 @ X99)) = $true) | ~ (((X94 @ X98)) = $true)) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | ~ (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ~ ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ~ ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | ~ (((X107 @ id @ X110 @ id)) = $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) = $true) | ~ (((X107 @ id @ X115 @ id)) = $true) | ~ (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ~ ! [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) = $true) | ~ (((X116 @ id @ X118 @ id)) = $true)) | ~ ! [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) = $true) | ~ ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | ~ (((X116 @ id @ X120 @ id)) = $true)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) = $true) | ~ ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | ~ (((var @ X139)) = $true)) | ~ ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ~ ! [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | ~ (((X136 @ X141)) = $true))) | ~ ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | ~ (((X136 @ X143)) = $true) | ~ (((X136 @ X142)) = $true))) => ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ~ ! [X146 : term] : ((((X144 @ (lam @ X146))) = $true) | ~ ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | ~ (((X144 @ X147)) = $true))) | ~ ! [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) = $true) | ~ (((X144 @ X149)) = $true) | ~ (((X144 @ X148)) = $true)) | ~ ! [X150 : term] : ((((X144 @ X150)) = $true) | ~ (((var @ X150)) = $true)))))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & ~ (lamnotap = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) = $true) | ~ (((X158 @ X160)) = $true)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) = $true) | ~ ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | ~ (((X157 @ id @ X163 @ id)) = $true)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | ~ (((X173 @ id @ X175 @ id)) = $true)) | ~ ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) = $true) | ~ (((X173 @ id @ X177 @ id)) = $true)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ~ ! [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) = $true) | ~ (((X181 @ id @ X183 @ id)) = $true)) | ~ ! [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) = $true) | ~ ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | ~ (((X181 @ id @ X185 @ id)) = $true)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) = $true) | ~ (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) = $true) | ~ (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true)))))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | ~ (((X199 @ X201)) = $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | ~ (((X234 @ X236)) = $true)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | ~ (((X233 @ id @ X239 @ id)) = $true)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | ~ (((X260 @ X262)) = $true) | ~ (((X260 @ X261)) = $true) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) = $true) | ~ (((X259 @ id @ X265 @ id)) = $true) | ~ (((X259 @ id @ X264 @ id)) = $true)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) = $true) | ~ (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) = $true) | ~ (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) = $true) | ~ (((X274 @ id @ X276 @ id)) = $true)) | ~ ! [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | ~ (((X274 @ id @ X278 @ id)) = $true)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | ~ (((X283 @ id @ X285 @ id)) = $true)) | ~ ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ~ ! [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) = $true) | ~ (((X283 @ id @ X287 @ id)) = $true)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ~ ! [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) = $true) | ~ (((X291 @ id @ X293 @ id)) = $true)) | ~ ! [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | ~ (((X291 @ id @ X295 @ id)) = $true)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ~ ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | ~ (((X299 @ X301)) = $true)) | ~ ! [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) = $true) | ~ (((X299 @ X303)) = $true) | ~ (((X299 @ X302)) = $true)) | ~ ! [X304 : term] : ((((X299 @ X304)) = $true) | ~ (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ~ ! [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) = $true) | ~ ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | ~ (((X307 @ id @ X310 @ id)) = $true)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) = $true) | ~ (((X307 @ id @ X315 @ id)) = $true) | ~ (((X307 @ id @ X314 @ id)) = $true)) | ~ ! [X316 : term] : ((((X307 @ id @ X316 @ id)) = $true) | ~ (((var @ (sub @ X316 @ id))) = $true)) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) = $true) | ~ (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) = $true) | ~ (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | ~ (((X330 @ X332)) = $true)))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | ~ (((X337 @ id @ X339 @ id)) = $true) | ~ (((X337 @ id @ X338 @ id)) = $true) | ~ ! [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) = $true) | ~ (((X337 @ id @ X341 @ id)) = $true) | ~ (((X337 @ id @ X340 @ id)) = $true)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) = $true) | ~ (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) = $true) | ~ (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ~ ! [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) = $true) | ~ (((X350 @ id @ X352 @ id)) = $true)) | ~ ! [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | ~ (((X350 @ id @ X354 @ id)) = $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) = $true) | ~ (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) = $true) | ~ (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) = $true) | ~ (((X366 @ id @ X368 @ id)) = $true)) | ~ ! [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | ~ (((X366 @ id @ X370 @ id)) = $true)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) = $true) | ~ (((X374 @ id @ X376 @ id)) = $true)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | ~ (((X374 @ id @ X385 @ id)) = $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) = $true) | ~ ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ~ ! [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) = $true) | ~ (((X399 @ X402)) = $true))) | ~ ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | ~ (((X399 @ X404)) = $true) | ~ (((X399 @ X403)) = $true)) | ~ ! [X405 : term] : ((((X399 @ X405)) = $true) | ~ (((var @ X405)) = $true))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | ~ (((X408 @ X410)) = $true)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) = $true) | ~ (((X407 @ id @ X413 @ id)) = $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ~ ! [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | ~ (((X417 @ id @ X420 @ id)) = $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) = $true) | ~ (((X417 @ id @ X425 @ id)) = $true) | ~ (((X417 @ id @ X424 @ id)) = $true)))))))) & ((hoasinduction_lthm = $true) <=> (! [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) = $true) | ~ ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ~ ! [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) = $true) | ~ (((X426 @ X429)) = $true))) | ~ ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | ~ (((X426 @ X431)) = $true) | ~ (((X426 @ X430)) = $true)) | ~ ! [X432 : term] : ((((X426 @ X432)) = $true) | ~ (((var @ X432)) = $true))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) = $true) | ~ (((X433 @ id @ X435 @ id)) = $true) | ~ (((X433 @ id @ X434 @ id)) = $true) | ~ ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | ~ (((X433 @ id @ X437 @ id)) = $true) | ~ (((X433 @ id @ X436 @ id)) = $true)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | ~ (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) = $true)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | ~ (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) = $true))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) = $true) | ~ ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | ~ (((X446 @ id @ X448 @ id)) = $true)) | ~ ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) = $true) | ~ (((X446 @ id @ X450 @ id)) = $true)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | ~ (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) = $true)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | ~ (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) = $true))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ~ ! [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | ~ (((X462 @ id @ X465 @ id)) = $true)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) = $true) | ~ (((X462 @ id @ X470 @ id)) = $true) | ~ (((X462 @ id @ X469 @ id)) = $true)) | ~ ! [X471 : term] : ((((X462 @ id @ X471 @ id)) = $true) | ~ (((var @ (sub @ X471 @ id))) = $true)) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) = $true) | ~ (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) = $true) | ~ (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) = $true) | ~ ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | ~ (((X489 @ X491)) = $true)) | ~ ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | ~ (((X489 @ X493)) = $true) | ~ (((X489 @ X492)) = $true)) | ~ ! [X494 : term] : ((((X489 @ X494)) = $true) | ~ (((var @ X494)) = $true))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ~ ! [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) = $true) | ~ (((var @ X498)) = $true)) | ~ ! [X499 : term] : ((((X495 @ (lam @ X499))) = $true) | ~ ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | ~ (((X495 @ X500)) = $true))) | ~ ! [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) = $true) | ~ (((X495 @ X502)) = $true) | ~ (((X495 @ X501)) = $true)))))))) & ~ (ulamvar1 = $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ~ ! [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) = $true) | ~ (((var @ X518)) = $true)) | ~ ! [X519 : term] : ((((X515 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | ~ (((X515 @ X520)) = $true))) | ~ ! [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) = $true) | ~ (((X515 @ X522)) = $true) | ~ (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | ~ (((X525 @ X527)) = $true))) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((((d2subst @ X530)) = ((d2subst @ X531))) => (X530 = X531)) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((((d2term @ X535)) = ((d2term @ X536))) => (X535 = X536)) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(rectify,[],[f5])).
% 8.63/1.68 thf(f9,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) = $true) | ~ ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | (((X3 @ X6)) != $true))) | ~ ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)) | ~ ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) = $true) | ~ ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) | ~ ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) = $true) | (((X11 @ id @ X17 @ id)) != $true)) | ~ ! [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) = ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ~ ! [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | (((X21 @ id @ X29 @ id)) != $true) | (((X21 @ id @ X28 @ id)) != $true)) | ~ ! [X30 : term] : ((((X21 @ id @ X30 @ id)) = $true) | (((var @ (sub @ X30 @ id))) != $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) = $true) | (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) != $true)) | ~ ! [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) = $true) | (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) != $true)))))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X40 : term] : (((sub @ X40 @ id)) = X40) => ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ~ ! [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) = $true) | (((X42 @ X44)) != $true)) | ~ ! [X45 : term] : (((X42 @ X45)) = ((X41 @ id @ X45 @ id))) | ~ ! [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) | ~ ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ~ ! [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) = $true) | (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) != $true)) | ~ ! [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) = $true) | (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) != $true))))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ~ ! [X62 : (term > $o)] : ~ ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ~ ! [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) = $true) | (((X68 @ X70)) != $true)) | ~ ! [X71 : term] : (((X68 @ X71)) = ((X67 @ id @ X71 @ id))) | ~ ! [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ~ ! [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) = $true) | (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) != $true)) | ~ ! [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) = $true) | (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) != $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85) => (! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) => ! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ~ ! [X96 : term] : ((((X94 @ (lam @ X96))) = $true) | ~ ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ~ ! [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) = $true) | (((X94 @ X99)) != $true) | (((X94 @ X98)) != $true)) | ~ ! [X100 : term] : ((((X94 @ X100)) = $true) | (((var @ X100)) != $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ~ ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ~ ! [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) = $true) | ~ ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) | ~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ~ ! [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) = $true) | (((X107 @ id @ X115 @ id)) != $true) | (((X107 @ id @ X114 @ id)) != $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ~ ! [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) = $true) | (((X116 @ id @ X118 @ id)) != $true)) | ~ ! [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) = $true) | ~ ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) | ~ ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ~ ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X128 : subst] : (((comp @ id @ X128)) = X128) => (! [X129 : subst] : (((comp @ X129 @ id)) = X129) => (! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ~ ! [X133 : (term > $o)] : ~ ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X135 : term] : (((sub @ X135 @ id)) = X135) => (! [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) = $true) | ~ ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) | ~ ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ~ ! [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) = $true) | (((X136 @ X141)) != $true))) | ~ ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true))) => ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ~ ! [X146 : term] : ((((X144 @ (lam @ X146))) = $true) | ~ ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ~ ! [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) = $true) | (((X144 @ X149)) != $true) | (((X144 @ X148)) != $true)) | ~ ! [X150 : term] : ((((X144 @ X150)) = $true) | (((var @ X150)) != $true)))))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X152 : term] : ~ ! [X153 : (subst > term > term)] : ~ ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))) => (! [X156 : term] : (((sub @ X156 @ id)) = X156) => ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ~ ! [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) = $true) | (((X158 @ X160)) != $true)) | ~ ! [X161 : term] : (((X158 @ X161)) = ((X157 @ id @ X161 @ id))) | ~ ! [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) = $true) | ~ ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) | ~ ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ~ ! [X170 : (term > $o)] : ~ ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X172 : term] : (((sub @ X172 @ id)) = X172) => (! [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) | ~ ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) = $true) | (((X173 @ id @ X177 @ id)) != $true)) | ~ ! [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) = ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) => ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ~ ! [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) = $true) | (((X181 @ id @ X183 @ id)) != $true)) | ~ ! [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) = $true) | ~ ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) | ~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ~ ! [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) = $true) | (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) != $true)) | ~ ! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) = $true) | (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) != $true)))))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) = X208) => (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) => (! [X212 : term,X213 : term] : ((X212 = X213) | (((lam @ X212)) != ((lam @ X213)))) => ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ~ ! [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) = ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ~ ! [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) = ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X224 : term] : (((sub @ X224 @ id)) = X224) => (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 = X226) | (((ap @ X225 @ X227)) != ((ap @ X226 @ X228)))) => ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) = $true) | (((X234 @ X236)) != $true)) | ~ ! [X237 : term] : (((X234 @ X237)) = ((X233 @ id @ X237 @ id))) | ~ ! [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) | ~ ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 = X246) | (((ap @ X243 @ X245)) != ((ap @ X244 @ X246)))) => ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ~ ! [X263 : term] : (((X260 @ X263)) = ((X259 @ id @ X263 @ id))) | ~ ! [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) = $true) | (((X259 @ id @ X265 @ id)) != $true) | (((X259 @ id @ X264 @ id)) != $true)) | ~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) = $true) | (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) != $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) = $true) | (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) != $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) = $true) | (((X274 @ id @ X276 @ id)) != $true)) | ~ ! [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) = $true) | ~ ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) | ~ ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X282 : term] : (((sub @ X282 @ id)) = X282) => (! [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) | ~ ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ~ ! [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) = $true) | (((X283 @ id @ X287 @ id)) != $true)) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) = ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) => ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ~ ! [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) = $true) | (((X291 @ id @ X293 @ id)) != $true)) | ~ ! [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) = $true) | ~ ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) | ~ ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ~ ! [X301 : term] : ((((X299 @ (lam @ X301))) = $true) | (((X299 @ X301)) != $true)) | ~ ! [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) = $true) | (((X299 @ X303)) != $true) | (((X299 @ X302)) != $true)) | ~ ! [X304 : term] : ((((X299 @ X304)) = $true) | (((var @ X304)) != $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ~ ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ~ ! [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) = $true) | ~ ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) | ~ ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ~ ! [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) = $true) | (((X307 @ id @ X315 @ id)) != $true) | (((X307 @ id @ X314 @ id)) != $true)) | ~ ! [X316 : term] : ((((X307 @ id @ X316 @ id)) = $true) | (((var @ (sub @ X316 @ id))) != $true)) | ~ ! [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) = $true) | (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) != $true)) | ~ ! [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) = $true) | (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) != $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328) => ! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ~ ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X335 : term] : (((sub @ X335 @ id)) = X335) => ! [X336 : term] : (((sub @ X336 @ id)) = X336))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ~ ! [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) = $true) | (((X337 @ id @ X341 @ id)) != $true) | (((X337 @ id @ X340 @ id)) != $true)) | ~ ! [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) = $true) | (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) != $true)) | ~ ! [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) = $true) | (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) != $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ~ ! [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) = $true) | (((X350 @ id @ X352 @ id)) != $true)) | ~ ! [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ~ ! [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) = $true) | (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) != $true)) | ~ ! [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) = $true) | (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) != $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) = $true) | (((X366 @ id @ X368 @ id)) != $true)) | ~ ! [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) | ~ ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) = $true) | (((X374 @ id @ X376 @ id)) != $true)) | ~ ! [X377 : (subst > term > term),X378 : term] : (~ ! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) | ~ ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) | (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ~ ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X396 : (subst > term > subst > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))) => (! [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) = $true) | ~ ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ~ ! [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) = $true) | (((X399 @ X402)) != $true))) | ~ ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)) | ~ ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true))) => (! [X406 : term] : (((sub @ X406 @ id)) = X406) => (! [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) = $true) | ~ ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) | ~ ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) | ~ ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) = $true) | (((X407 @ id @ X413 @ id)) != $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) = ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) => ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ~ ! [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ~ ! [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) = $true) | (((X417 @ id @ X425 @ id)) != $true) | (((X417 @ id @ X424 @ id)) != $true)))))))) & ((hoasinduction_lthm = $true) <=> (! [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) = $true) | ~ ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ~ ! [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) = $true) | (((X426 @ X429)) != $true))) | ~ ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)) | ~ ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true))) => (! [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) = $true) | (((X433 @ id @ X435 @ id)) != $true) | (((X433 @ id @ X434 @ id)) != $true) | ~ ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)) | ~ ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) | ~ ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true))) => (! [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) = $true) | ~ ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) | ~ ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) = $true) | (((X446 @ id @ X450 @ id)) != $true)) | ~ ! [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) = ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) | ~ ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) | ~ ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true))) => ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ~ ! [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) = $true) | ~ ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) | ~ ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ~ ! [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) = $true) | (((X462 @ id @ X470 @ id)) != $true) | (((X462 @ id @ X469 @ id)) != $true)) | ~ ! [X471 : term] : ((((X462 @ id @ X471 @ id)) = $true) | (((var @ (sub @ X471 @ id))) != $true)) | ~ ! [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) = $true) | (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) != $true)) | ~ ! [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) = $true) | (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) != $true))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ~ ! [X481 : (subst > term > term)] : ~ ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484) => (! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) => (! [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) = $true) | ~ ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) | ~ ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)) | ~ ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true))) => ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ~ ! [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) = $true) | (((var @ X498)) != $true)) | ~ ! [X499 : term] : ((((X495 @ (lam @ X499))) = $true) | ~ ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ~ ! [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) = $true) | (((X495 @ X502)) != $true) | (((X495 @ X501)) != $true)))))))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ~ ! [X512 : (subst > term > term)] : ~ ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ~ ! [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) = $true) | (((var @ X518)) != $true)) | ~ ! [X519 : term] : ((((X515 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ~ ! [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) = $true) | (((X515 @ X522)) != $true) | (((X515 @ X521)) != $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ~ ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((((d2subst @ X530)) = ((d2subst @ X531))) => (X530 = X531)) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((((d2term @ X535)) = ((d2term @ X536))) => (X535 = X536)) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(flattening,[],[f8])).
% 8.63/1.68 thf(f10,plain,(
% 8.63/1.68 (pushprop_lem0 != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (?? @ (term > $o) @ (^[Y3 : term > $o]: (pushprop_p_and_p_prime @ Y1 @ Y0 @ Y2 @ Y3)))))))))))),
% 8.63/1.68 inference(flattening,[],[f7])).
% 8.63/1.68 thf(f11,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) <=> ((((! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ? [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ X28 @ id)) = $true)) | ? [X30 : term] : ((((X21 @ id @ X30 @ id)) != $true) & (((var @ (sub @ X30 @ id))) = $true)) | ? [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) != $true) & (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ? [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) != $true) & (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true))) | ? [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) != $true) & ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) & ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true)) | ? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) != ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20))))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) != $true) & ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ? [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) != $true) & (((X3 @ X6)) = $true))) & ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)) & ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true)))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ? [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) != $true) & (((X42 @ X44)) = $true)) | ? [X45 : term] : (((X42 @ X45)) != ((X41 @ id @ X45 @ id))) | ? [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) != $true) & ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) & ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ? [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) != $true) & (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ? [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) != $true) & (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))) | ? [X40 : term] : (((sub @ X40 @ id)) != X40))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ? [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) != $true) & (((X68 @ X70)) = $true)) | ? [X71 : term] : (((X68 @ X71)) != ((X67 @ id @ X71 @ id))) | ? [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) != $true) & ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) & ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ? [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) != $true) & (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) != $true) & (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> ((! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88)) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ? [X96 : term] : ((((X94 @ (lam @ X96))) != $true) & ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ? [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) != $true) & (((X94 @ X99)) = $true) & (((X94 @ X98)) = $true)) | ? [X100 : term] : ((((X94 @ X100)) != $true) & (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ? [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) != $true) & (((X107 @ id @ X115 @ id)) = $true) & (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ? [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) != $true) & (((X116 @ id @ X118 @ id)) = $true)) | ? [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) != $true) & ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) & ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129)) | ? [X128 : subst] : (((comp @ id @ X128)) != X128))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> ((! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ? [X146 : term] : ((((X144 @ (lam @ X146))) != $true) & ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ? [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) != $true) & (((X144 @ X149)) = $true) & (((X144 @ X148)) = $true)) | ? [X150 : term] : ((((X144 @ X150)) != $true) & (((var @ X150)) = $true))) | ? [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) != $true) & ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) & ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ? [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) != $true) & (((X136 @ X141)) = $true))) & ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true)))) | ? [X135 : term] : (((sub @ X135 @ id)) != X135))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ? [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) != $true) & (((X158 @ X160)) = $true)) | ? [X161 : term] : (((X158 @ X161)) != ((X157 @ id @ X161 @ id))) | ? [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) != $true) & ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166)))))) | ? [X156 : term] : (((sub @ X156 @ id)) != X156)) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ? [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) != $true) & (((X181 @ id @ X183 @ id)) = $true)) | ? [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) != $true) & ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) & ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ? [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) != $true) & (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ? [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) != $true) & (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true))) | ? [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) != $true) & ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) & ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) != $true) & (((X173 @ id @ X177 @ id)) = $true)) | ? [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) != ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180))))))) | ? [X172 : term] : (((sub @ X172 @ id)) != X172))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (((! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))) | ? [X212 : term,X213 : term] : ((X212 != X213) & (((lam @ X212)) = ((lam @ X213))))) | ? [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) != X211)) | ? [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) != X208))) & ((hoasapinj1_lthm = $true) <=> ((! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228))))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ? [X263 : term] : (((X260 @ X263)) != ((X259 @ id @ X263 @ id))) | ? [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) != $true) & (((X259 @ id @ X265 @ id)) = $true) & (((X259 @ id @ X264 @ id)) = $true)) | ? [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) != $true) & (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ? [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) != $true) & (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ? [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) != $true) & (((X274 @ id @ X276 @ id)) = $true)) | ? [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true) & ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) & ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ? [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) != $true) & (((X291 @ id @ X293 @ id)) = $true)) | ? [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) & ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298)))))) | ? [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) != $true) & ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) & ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ? [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) != $true) & (((X283 @ id @ X287 @ id)) = $true)) | ? [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) != ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))))))) | ? [X282 : term] : (((sub @ X282 @ id)) != X282))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ? [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) != $true) & (((X299 @ X303)) = $true) & (((X299 @ X302)) = $true)) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ? [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) != $true) & ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) & ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ? [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) != $true) & (((X307 @ id @ X315 @ id)) = $true) & (((X307 @ id @ X314 @ id)) = $true)) | ? [X316 : term] : ((((X307 @ id @ X316 @ id)) != $true) & (((var @ (sub @ X316 @ id))) = $true)) | ? [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) != $true) & (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ? [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) != $true) & (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ? [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) != $true) & (((X337 @ id @ X341 @ id)) = $true) & (((X337 @ id @ X340 @ id)) = $true)) | ? [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) != $true) & (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ? [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) != $true) & (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ? [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) != $true) & (((X350 @ id @ X352 @ id)) = $true)) | ? [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true) & ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) & ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ? [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) != $true) & (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ? [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) != $true) & (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) != $true) & (((X366 @ id @ X368 @ id)) = $true)) | ? [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) & ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ? [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) != $true) & (((X374 @ id @ X376 @ id)) = $true)) | ? [X377 : (subst > term > term),X378 : term] : (! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) & ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) & (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true) & ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ? [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) != $true) & ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) & ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ? [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) != $true) & (((X417 @ id @ X425 @ id)) = $true) & (((X417 @ id @ X424 @ id)) = $true))) | ? [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) != $true) & ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) & ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) & ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ? [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) != $true) & (((X407 @ id @ X413 @ id)) = $true)) | ? [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) != ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416))))))) | ? [X406 : term] : (((sub @ X406 @ id)) != X406)) | ? [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) != $true) & ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ? [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) != $true) & (((X399 @ X402)) = $true))) & ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)) & ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true)))) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))))) & ((hoasinduction_lthm = $true) <=> (((! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ? [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) != $true) & ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ? [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) != $true) & (((X462 @ id @ X470 @ id)) = $true) & (((X462 @ id @ X469 @ id)) = $true)) | ? [X471 : term] : ((((X462 @ id @ X471 @ id)) != $true) & (((var @ (sub @ X471 @ id))) = $true)) | ? [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) != $true) & (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ? [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) != $true) & (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))) | ? [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) != $true) & ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) & ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ? [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) != $true) & (((X446 @ id @ X450 @ id)) = $true)) | ? [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) != ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) & ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) & ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true)))) | ? [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) != $true) & (((X433 @ id @ X435 @ id)) = $true) & (((X433 @ id @ X434 @ id)) = $true) & ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)) & ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) & ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true)))) | ? [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) != $true) & ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ? [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) != $true) & (((X426 @ X429)) = $true))) & ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)) & ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ? [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) != $true) & (((var @ X498)) = $true)) | ? [X499 : term] : ((((X495 @ (lam @ X499))) != $true) & ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ? [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) != $true) & (((X495 @ X502)) = $true) & (((X495 @ X501)) = $true))) | ? [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) != $true) & ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) & ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)) & ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true)))) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488)) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487)) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ? [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) != $true) & (((var @ X518)) = $true)) | ? [X519 : term] : ((((X515 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ? [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) != $true) & (((X515 @ X522)) = $true) & (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(ennf_transformation,[],[f9])).
% 8.63/1.68 thf(f12,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) <=> (! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))) | ? [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ X28 @ id)) = $true)) | ? [X30 : term] : ((((X21 @ id @ X30 @ id)) != $true) & (((var @ (sub @ X30 @ id))) = $true)) | ? [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) != $true) & (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)) | ? [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) != $true) & (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true))) | ? [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) != $true) & ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) & ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true)) | ? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) != ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20)))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) != $true) & ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ? [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) != $true) & (((X3 @ X6)) = $true))) & ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)) & ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ? [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) != $true) & (((X42 @ X44)) = $true)) | ? [X45 : term] : (((X42 @ X45)) != ((X41 @ id @ X45 @ id))) | ? [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) != $true) & ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) & ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))) | ? [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) != $true) & (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)) | ? [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) != $true) & (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true))) | ? [X40 : term] : (((sub @ X40 @ id)) != X40))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ? [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) != $true) & (((X68 @ X70)) = $true)) | ? [X71 : term] : (((X68 @ X71)) != ((X67 @ id @ X71 @ id))) | ? [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) != $true) & ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) & ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))) | ? [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) != $true) & (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)) | ? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) != $true) & (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ? [X96 : term] : ((((X94 @ (lam @ X96))) != $true) & ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))) | ? [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) != $true) & (((X94 @ X99)) = $true) & (((X94 @ X98)) = $true)) | ? [X100 : term] : ((((X94 @ X100)) != $true) & (((var @ X100)) = $true)))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))) | ? [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) != $true) & (((X107 @ id @ X115 @ id)) = $true) & (((X107 @ id @ X114 @ id)) = $true)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ? [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) != $true) & (((X116 @ id @ X118 @ id)) = $true)) | ? [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) != $true) & ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) & ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129) | ? [X128 : subst] : (((comp @ id @ X128)) != X128))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ? [X146 : term] : ((((X144 @ (lam @ X146))) != $true) & ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))) | ? [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) != $true) & (((X144 @ X149)) = $true) & (((X144 @ X148)) = $true)) | ? [X150 : term] : ((((X144 @ X150)) != $true) & (((var @ X150)) = $true))) | ? [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) != $true) & ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) & ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ? [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) != $true) & (((X136 @ X141)) = $true))) & ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true))) | ? [X135 : term] : (((sub @ X135 @ id)) != X135))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ? [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) != $true) & (((X158 @ X160)) = $true)) | ? [X161 : term] : (((X158 @ X161)) != ((X157 @ id @ X161 @ id))) | ? [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) != $true) & ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166)))))) | ? [X156 : term] : (((sub @ X156 @ id)) != X156) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ? [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) != $true) & (((X181 @ id @ X183 @ id)) = $true)) | ? [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) != $true) & ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) & ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))) | ? [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) != $true) & (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)) | ? [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) != $true) & (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true))) | ? [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) != $true) & ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) & ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) != $true) & (((X173 @ id @ X177 @ id)) = $true)) | ? [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) != ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180)))))) | ? [X172 : term] : (((sub @ X172 @ id)) != X172))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> (! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223))))) | ? [X212 : term,X213 : term] : ((X212 != X213) & (((lam @ X212)) = ((lam @ X213)))) | ? [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) != X211) | ? [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) != X208))) & ((hoasapinj1_lthm = $true) <=> (! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232)))) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228)))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224))) & ((hoasinduction_lem3v2a = $true) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))) & ((hoasapinj2_lthm = $true) <=> (! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250)))) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))))) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ? [X263 : term] : (((X260 @ X263)) != ((X259 @ id @ X263 @ id))) | ? [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) != $true) & (((X259 @ id @ X265 @ id)) = $true) & (((X259 @ id @ X264 @ id)) = $true)) | ? [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) != $true) & (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ? [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) != $true) & (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ? [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) != $true) & (((X274 @ id @ X276 @ id)) = $true)) | ? [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true) & ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) & ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ? [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) != $true) & (((X291 @ id @ X293 @ id)) = $true)) | ? [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) & ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298)))))) | ? [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) != $true) & ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) & ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ? [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) != $true) & (((X283 @ id @ X287 @ id)) = $true)) | ? [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) != ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290)))))) | ? [X282 : term] : (((sub @ X282 @ id)) != X282))) & ((induction = $true) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ? [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) != $true) & (((X299 @ X303)) = $true) & (((X299 @ X302)) = $true)) | ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true)))) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ? [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) != $true) & ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) & ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))) | ? [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) != $true) & (((X307 @ id @ X315 @ id)) = $true) & (((X307 @ id @ X314 @ id)) = $true)) | ? [X316 : term] : ((((X307 @ id @ X316 @ id)) != $true) & (((var @ (sub @ X316 @ id))) = $true)) | ? [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) != $true) & (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)) | ? [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) != $true) & (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335))) & ((hoasinduction_lem2 = $true) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ? [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) != $true) & (((X337 @ id @ X341 @ id)) = $true) & (((X337 @ id @ X340 @ id)) = $true)) | ? [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) != $true) & (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ? [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) != $true) & (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))) & ((hoasinduction_lem3 = $true) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ? [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) != $true) & (((X350 @ id @ X352 @ id)) = $true)) | ? [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true) & ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) & ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))) | ? [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) != $true) & (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)) | ? [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) != $true) & (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) != $true) & (((X366 @ id @ X368 @ id)) = $true)) | ? [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) & ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ? [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) != $true) & (((X374 @ id @ X376 @ id)) = $true)) | ? [X377 : (subst > term > term),X378 : term] : (! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) & ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) & (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true) & ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ? [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) != $true) & ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) & ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))) | ? [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) != $true) & (((X417 @ id @ X425 @ id)) = $true) & (((X417 @ id @ X424 @ id)) = $true))) | ? [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) != $true) & ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) & ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) & ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ? [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) != $true) & (((X407 @ id @ X413 @ id)) = $true)) | ? [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) != ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416)))))) | ? [X406 : term] : (((sub @ X406 @ id)) != X406) | ? [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) != $true) & ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ? [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) != $true) & (((X399 @ X402)) = $true))) & ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)) & ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true))) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))))) & ((hoasinduction_lthm = $true) <=> (! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ? [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) != $true) & ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))) | ? [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) != $true) & (((X462 @ id @ X470 @ id)) = $true) & (((X462 @ id @ X469 @ id)) = $true)) | ? [X471 : term] : ((((X462 @ id @ X471 @ id)) != $true) & (((var @ (sub @ X471 @ id))) = $true)) | ? [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) != $true) & (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ? [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) != $true) & (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true))) | ? [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) != $true) & ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) & ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ? [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) != $true) & (((X446 @ id @ X450 @ id)) = $true)) | ? [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) != ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))) & ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)) & ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true))) | ? [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) != $true) & (((X433 @ id @ X435 @ id)) = $true) & (((X433 @ id @ X434 @ id)) = $true) & ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)) & ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) & ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true))) | ? [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) != $true) & ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ? [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) != $true) & (((X426 @ X429)) = $true))) & ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)) & ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ? [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) != $true) & (((var @ X498)) = $true)) | ? [X499 : term] : ((((X495 @ (lam @ X499))) != $true) & ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))) | ? [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) != $true) & (((X495 @ X502)) = $true) & (((X495 @ X501)) = $true))) | ? [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) != $true) & ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) & ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)) & ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true))) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ? [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) != $true) & (((var @ X518)) = $true)) | ? [X519 : term] : ((((X515 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))) | ? [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) != $true) & (((X515 @ X522)) = $true) & (((X515 @ X521)) = $true)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(flattening,[],[f11])).
% 8.63/1.68 thf(f13,definition,(
% 8.63/1.68 ! [X515 : (term > $o)] : (($true = ((sP0 @ X515))) <=> ? [X519 : term] : ((((X515 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X515 @ (sub @ X519 @ (push @ X520 @ id)))) = $true) | (((X515 @ X520)) != $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f14,definition,(
% 8.63/1.68 ! [X515 : (term > $o)] : (($true = ((sP1 @ X515))) <=> ? [X521 : term,X522 : term] : ((((X515 @ (ap @ X521 @ X522))) != $true) & (((X515 @ X522)) = $true) & (((X515 @ X521)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f15,definition,(
% 8.63/1.68 ($true = sP2) <=> ! [X515 : (term > $o),X516 : term,X517 : subst] : ((((X515 @ (sub @ X516 @ X517))) = $true) | ? [X518 : term] : ((((X515 @ (sub @ X518 @ X517))) != $true) & (((var @ X518)) = $true)) | ($true = ((sP0 @ X515))) | ($true = ((sP1 @ X515))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f16,definition,(
% 8.63/1.68 ! [X489 : (term > $o)] : (($true = ((sP3 @ X489))) <=> ! [X492 : term,X493 : term] : ((((X489 @ (ap @ X492 @ X493))) = $true) | (((X489 @ X493)) != $true) | (((X489 @ X492)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f17,definition,(
% 8.63/1.68 ! [X489 : (term > $o)] : (($true = ((sP4 @ X489))) <=> ! [X494 : term] : ((((X489 @ X494)) = $true) | (((var @ X494)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f18,definition,(
% 8.63/1.68 ! [X495 : (term > $o)] : (($true = ((sP5 @ X495))) <=> ? [X499 : term] : ((((X495 @ (lam @ X499))) != $true) & ! [X500 : term] : ((((X495 @ (sub @ X499 @ (push @ X500 @ id)))) = $true) | (((X495 @ X500)) != $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f19,definition,(
% 8.63/1.68 ! [X495 : (term > $o)] : (($true = ((sP6 @ X495))) <=> ? [X501 : term,X502 : term] : ((((X495 @ (ap @ X501 @ X502))) != $true) & (((X495 @ X502)) = $true) & (((X495 @ X501)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f20,definition,(
% 8.63/1.68 ($true = sP7) <=> ! [X495 : (term > $o),X496 : term,X497 : subst] : ((((X495 @ (sub @ X496 @ X497))) = $true) | ? [X498 : term] : ((((X495 @ (sub @ X498 @ X497))) != $true) & (((var @ X498)) = $true)) | ($true = ((sP5 @ X495))) | ($true = ((sP6 @ X495))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f21,definition,(
% 8.63/1.68 ($true = sP8) <=> ? [X489 : (term > $o),X490 : term] : ((((X489 @ X490)) != $true) & ! [X491 : term] : ((((X489 @ (lam @ X491))) = $true) | (((X489 @ X491)) != $true)) & ($true = ((sP3 @ X489))) & ($true = ((sP4 @ X489))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f22,definition,(
% 8.63/1.68 ! [X426 : (term > $o)] : (($true = ((sP9 @ X426))) <=> ! [X430 : term,X431 : term] : ((((X426 @ (ap @ X430 @ X431))) = $true) | (((X426 @ X431)) != $true) | (((X426 @ X430)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f23,definition,(
% 8.63/1.68 ! [X426 : (term > $o)] : (($true = ((sP10 @ X426))) <=> ! [X432 : term] : ((((X426 @ X432)) = $true) | (((var @ X432)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f24,definition,(
% 8.63/1.68 ! [X426 : (term > $o)] : (($true = ((sP11 @ X426))) <=> ! [X428 : term] : ((((X426 @ (lam @ X428))) = $true) | ? [X429 : term] : ((((X426 @ (sub @ X428 @ (push @ X429 @ id)))) != $true) & (((X426 @ X429)) = $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f25,definition,(
% 8.63/1.68 ! [X433 : (subst > term > subst > $o)] : (($true = ((sP12 @ X433))) <=> ! [X436 : term,X437 : term] : ((((X433 @ id @ (ap @ (sub @ X436 @ id) @ X437) @ id)) = $true) | (((X433 @ id @ X437 @ id)) != $true) | (((X433 @ id @ X436 @ id)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f26,definition,(
% 8.63/1.68 ! [X433 : (subst > term > subst > $o)] : (($true = ((sP13 @ X433))) <=> ! [X442 : subst,X443 : term,X444 : subst,X445 : subst] : ((((X433 @ (comp @ X442 @ X445) @ (sub @ X443 @ X445) @ X444)) = $true) | (((X433 @ X442 @ X443 @ (comp @ X445 @ X444))) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f27,definition,(
% 8.63/1.68 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP14 @ X446))) <=> ! [X449 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X449 @ sh @ one)) @ id)) = $true) | ? [X450 : term] : ((((X446 @ id @ (X449 @ id @ X450) @ id)) != $true) & (((X446 @ id @ X450 @ id)) = $true)) | ? [X451 : subst,X452 : term,X453 : subst] : (((sub @ (X449 @ X451 @ X452) @ X453)) != ((X449 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f28,definition,(
% 8.63/1.68 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP15 @ X446))) <=> ! [X458 : subst,X459 : term,X460 : subst,X461 : subst] : ((((X446 @ (comp @ X458 @ X461) @ (sub @ X459 @ X461) @ X460)) = $true) | (((X446 @ X458 @ X459 @ (comp @ X461 @ X460))) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f29,definition,(
% 8.63/1.68 ! [X446 : (subst > term > subst > $o)] : (($true = ((sP16 @ X446))) <=> ! [X454 : subst,X455 : term,X456 : subst,X457 : subst] : ((((X446 @ X454 @ X455 @ (comp @ X457 @ X456))) = $true) | (((X446 @ (comp @ X454 @ X457) @ (sub @ X455 @ X457) @ X456)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f30,definition,(
% 8.63/1.68 ! [X462 : (subst > term > subst > $o)] : (($true = ((sP17 @ X462))) <=> ? [X464 : (subst > term > term)] : ((((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id)) != $true) & ! [X465 : term] : ((((X462 @ id @ (X464 @ id @ X465) @ id)) = $true) | (((X462 @ id @ X465 @ id)) != $true)) & ! [X466 : subst,X467 : term,X468 : subst] : (((sub @ (X464 @ X466 @ X467) @ X468)) = ((X464 @ (comp @ X466 @ X468) @ (sub @ X467 @ X468))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f31,definition,(
% 8.63/1.68 ! [X462 : (subst > term > subst > $o)] : (($true = ((sP18 @ X462))) <=> ? [X469 : term,X470 : term] : ((((X462 @ id @ (ap @ (sub @ X469 @ id) @ X470) @ id)) != $true) & (((X462 @ id @ X470 @ id)) = $true) & (((X462 @ id @ X469 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f32,definition,(
% 8.63/1.68 ! [X462 : (subst > term > subst > $o)] : (($true = ((sP19 @ X462))) <=> ? [X476 : subst,X477 : term,X478 : subst,X479 : subst] : ((((X462 @ (comp @ X476 @ X479) @ (sub @ X477 @ X479) @ X478)) != $true) & (((X462 @ X476 @ X477 @ (comp @ X479 @ X478))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f33,definition,(
% 8.63/1.68 ! [X462 : (subst > term > subst > $o)] : (($true = ((sP20 @ X462))) <=> ? [X472 : subst,X473 : term,X474 : subst,X475 : subst] : ((((X462 @ X472 @ X473 @ (comp @ X475 @ X474))) != $true) & (((X462 @ (comp @ X472 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f34,definition,(
% 8.63/1.68 ($true = sP21) <=> ! [X462 : (subst > term > subst > $o),X463 : term] : ((((X462 @ id @ X463 @ id)) = $true) | ($true = ((sP17 @ X462))) | ($true = ((sP18 @ X462))) | ? [X471 : term] : ((((X462 @ id @ X471 @ id)) != $true) & (((var @ (sub @ X471 @ id))) = $true)) | ($true = ((sP20 @ X462))) | ($true = ((sP19 @ X462))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f35,definition,(
% 8.63/1.68 ($true = sP22) <=> ? [X433 : (subst > term > subst > $o),X434 : term,X435 : term] : ((((X433 @ id @ (ap @ X434 @ X435) @ id)) != $true) & (((X433 @ id @ X435 @ id)) = $true) & (((X433 @ id @ X434 @ id)) = $true) & ($true = ((sP12 @ X433))) & ! [X438 : subst,X439 : term,X440 : subst,X441 : subst] : ((((X433 @ X438 @ X439 @ (comp @ X441 @ X440))) = $true) | (((X433 @ (comp @ X438 @ X441) @ (sub @ X439 @ X441) @ X440)) != $true)) & ($true = ((sP13 @ X433))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f36,definition,(
% 8.63/1.68 ($true = sP23) <=> ? [X446 : (subst > term > subst > $o),X447 : term] : ((((X446 @ id @ (lam @ X447) @ id)) != $true) & ! [X448 : term] : ((((X446 @ id @ (sub @ X447 @ (push @ X448 @ id)) @ id)) = $true) | (((X446 @ id @ X448 @ id)) != $true)) & ($true = ((sP14 @ X446))) & ($true = ((sP16 @ X446))) & ($true = ((sP15 @ X446))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f37,definition,(
% 8.63/1.68 ($true = sP24) <=> ? [X426 : (term > $o),X427 : term] : ((((X426 @ X427)) != $true) & ($true = ((sP11 @ X426))) & ($true = ((sP9 @ X426))) & ($true = ((sP10 @ X426))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f38,definition,(
% 8.63/1.68 ! [X399 : (term > $o)] : (($true = ((sP25 @ X399))) <=> ! [X403 : term,X404 : term] : ((((X399 @ (ap @ X403 @ X404))) = $true) | (((X399 @ X404)) != $true) | (((X399 @ X403)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f39,definition,(
% 8.63/1.68 ! [X399 : (term > $o)] : (($true = ((sP26 @ X399))) <=> ! [X405 : term] : ((((X399 @ X405)) = $true) | (((var @ X405)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f40,definition,(
% 8.63/1.68 ! [X399 : (term > $o)] : (($true = ((sP27 @ X399))) <=> ! [X401 : term] : ((((X399 @ (lam @ X401))) = $true) | ? [X402 : term] : ((((X399 @ (sub @ X401 @ (push @ X402 @ id)))) != $true) & (((X399 @ X402)) = $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f41,definition,(
% 8.63/1.68 ! [X407 : (subst > term > subst > $o)] : (($true = ((sP28 @ X407))) <=> ! [X412 : (subst > term > term)] : ((((X407 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ? [X413 : term] : ((((X407 @ id @ (X412 @ id @ X413) @ id)) != $true) & (((X407 @ id @ X413 @ id)) = $true)) | ? [X414 : subst,X415 : term,X416 : subst] : (((sub @ (X412 @ X414 @ X415) @ X416)) != ((X412 @ (comp @ X414 @ X416) @ (sub @ X415 @ X416))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f42,definition,(
% 8.63/1.68 ! [X417 : (subst > term > subst > $o)] : (($true = ((sP29 @ X417))) <=> ? [X419 : (subst > term > term)] : ((((X417 @ id @ (lam @ (X419 @ sh @ one)) @ id)) != $true) & ! [X420 : term] : ((((X417 @ id @ (X419 @ id @ X420) @ id)) = $true) | (((X417 @ id @ X420 @ id)) != $true)) & ! [X421 : subst,X422 : term,X423 : subst] : (((sub @ (X419 @ X421 @ X422) @ X423)) = ((X419 @ (comp @ X421 @ X423) @ (sub @ X422 @ X423))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f43,definition,(
% 8.63/1.68 ! [X417 : (subst > term > subst > $o)] : (($true = ((sP30 @ X417))) <=> ? [X424 : term,X425 : term] : ((((X417 @ id @ (ap @ (sub @ X424 @ id) @ X425) @ id)) != $true) & (((X417 @ id @ X425 @ id)) = $true) & (((X417 @ id @ X424 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f44,definition,(
% 8.63/1.68 ($true = sP31) <=> ! [X417 : (subst > term > subst > $o),X418 : term] : ((((X417 @ id @ X418 @ id)) = $true) | ($true = ((sP29 @ X417))) | ($true = ((sP30 @ X417))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f45,definition,(
% 8.63/1.68 ($true = sP32) <=> ? [X407 : (subst > term > subst > $o),X408 : (term > $o),X409 : term] : ((((X408 @ (lam @ X409))) != $true) & ! [X410 : term] : ((((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true) | (((X408 @ X410)) != $true)) & ! [X411 : term] : (((X408 @ X411)) = ((X407 @ id @ X411 @ id))) & ($true = ((sP28 @ X407))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f46,definition,(
% 8.63/1.68 ($true = sP33) <=> ? [X399 : (term > $o),X400 : term] : ((((X399 @ X400)) != $true) & ($true = ((sP27 @ X399))) & ($true = ((sP25 @ X399))) & ($true = ((sP26 @ X399))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f47,definition,(
% 8.63/1.68 ! [X374 : (subst > term > subst > $o)] : (($true = ((sP34 @ X374))) <=> ? [X377 : (subst > term > term),X378 : term] : (! [X379 : subst,X380 : term,X381 : subst] : (((X377 @ (comp @ X379 @ X381) @ (sub @ X380 @ X381))) = ((sub @ X378 @ (push @ (sub @ X380 @ X381) @ (comp @ X379 @ X381))))) & ! [X382 : subst,X383 : term,X384 : subst] : (((sub @ (X377 @ X382 @ X383) @ X384)) = ((sub @ (sub @ X378 @ (push @ X383 @ X382)) @ X384))) & (((X374 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true) & ! [X385 : term] : ((((X374 @ id @ (X377 @ id @ X385) @ id)) = $true) | (((X374 @ id @ X385 @ id)) != $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f48,definition,(
% 8.63/1.68 ($true = sP35) <=> ! [X374 : (subst > term > subst > $o),X375 : term] : ((((X374 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id)) = $true) | ? [X376 : term] : ((((X374 @ id @ (sub @ X375 @ (push @ X376 @ id)) @ id)) != $true) & (((X374 @ id @ X376 @ id)) = $true)) | ($true = ((sP34 @ X374))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f49,definition,(
% 8.63/1.68 ! [X366 : (subst > term > subst > $o)] : (($true = ((sP36 @ X366))) <=> ? [X369 : (subst > term > term)] : ((((X366 @ id @ (lam @ (X369 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X366 @ id @ (X369 @ id @ X370) @ id)) = $true) | (((X366 @ id @ X370 @ id)) != $true)) & ! [X371 : subst,X372 : term,X373 : subst] : (((sub @ (X369 @ X371 @ X372) @ X373)) = ((X369 @ (comp @ X371 @ X373) @ (sub @ X372 @ X373))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f50,definition,(
% 8.63/1.68 ($true = sP37) <=> ! [X366 : (subst > term > subst > $o),X367 : term] : ((((X366 @ id @ (lam @ (sub @ X367 @ (push @ one @ sh))) @ id)) = $true) | ? [X368 : term] : ((((X366 @ id @ (sub @ X367 @ (push @ X368 @ id)) @ id)) != $true) & (((X366 @ id @ X368 @ id)) = $true)) | ($true = ((sP36 @ X366))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f51,definition,(
% 8.63/1.68 ! [X350 : (subst > term > subst > $o)] : (($true = ((sP38 @ X350))) <=> ? [X353 : (subst > term > term)] : ((((X350 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true) & ! [X354 : term] : ((((X350 @ id @ (X353 @ id @ X354) @ id)) = $true) | (((X350 @ id @ X354 @ id)) != $true)) & ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X353 @ X355 @ X356) @ X357)) = ((X353 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f52,definition,(
% 8.63/1.68 ! [X350 : (subst > term > subst > $o)] : (($true = ((sP39 @ X350))) <=> ? [X362 : subst,X363 : term,X364 : subst,X365 : subst] : ((((X350 @ (comp @ X362 @ X365) @ (sub @ X363 @ X365) @ X364)) != $true) & (((X350 @ X362 @ X363 @ (comp @ X365 @ X364))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f53,definition,(
% 8.63/1.68 ! [X350 : (subst > term > subst > $o)] : (($true = ((sP40 @ X350))) <=> ? [X358 : subst,X359 : term,X360 : subst,X361 : subst] : ((((X350 @ X358 @ X359 @ (comp @ X361 @ X360))) != $true) & (((X350 @ (comp @ X358 @ X361) @ (sub @ X359 @ X361) @ X360)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f54,definition,(
% 8.63/1.68 ($true = sP41) <=> ! [X350 : (subst > term > subst > $o),X351 : term] : ((((X350 @ id @ (lam @ X351) @ id)) = $true) | ? [X352 : term] : ((((X350 @ id @ (sub @ X351 @ (push @ X352 @ id)) @ id)) != $true) & (((X350 @ id @ X352 @ id)) = $true)) | ($true = ((sP38 @ X350))) | ($true = ((sP40 @ X350))) | ($true = ((sP39 @ X350))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f55,definition,(
% 8.63/1.68 ! [X337 : (subst > term > subst > $o)] : (($true = ((sP42 @ X337))) <=> ? [X340 : term,X341 : term] : ((((X337 @ id @ (ap @ (sub @ X340 @ id) @ X341) @ id)) != $true) & (((X337 @ id @ X341 @ id)) = $true) & (((X337 @ id @ X340 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f56,definition,(
% 8.63/1.68 ! [X337 : (subst > term > subst > $o)] : (($true = ((sP43 @ X337))) <=> ? [X346 : subst,X347 : term,X348 : subst,X349 : subst] : ((((X337 @ (comp @ X346 @ X349) @ (sub @ X347 @ X349) @ X348)) != $true) & (((X337 @ X346 @ X347 @ (comp @ X349 @ X348))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f57,definition,(
% 8.63/1.68 ($true = sP44) <=> ! [X337 : (subst > term > subst > $o),X338 : term,X339 : term] : ((((X337 @ id @ (ap @ X338 @ X339) @ id)) = $true) | (((X337 @ id @ X339 @ id)) != $true) | (((X337 @ id @ X338 @ id)) != $true) | ($true = ((sP42 @ X337))) | ? [X342 : subst,X343 : term,X344 : subst,X345 : subst] : ((((X337 @ X342 @ X343 @ (comp @ X345 @ X344))) != $true) & (((X337 @ (comp @ X342 @ X345) @ (sub @ X343 @ X345) @ X344)) = $true)) | ($true = ((sP43 @ X337))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f58,definition,(
% 8.63/1.68 ! [X307 : (subst > term > subst > $o)] : (($true = ((sP45 @ X307))) <=> ? [X309 : (subst > term > term)] : ((((X307 @ id @ (lam @ (X309 @ sh @ one)) @ id)) != $true) & ! [X310 : term] : ((((X307 @ id @ (X309 @ id @ X310) @ id)) = $true) | (((X307 @ id @ X310 @ id)) != $true)) & ! [X311 : subst,X312 : term,X313 : subst] : (((sub @ (X309 @ X311 @ X312) @ X313)) = ((X309 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f59,definition,(
% 8.63/1.68 ! [X307 : (subst > term > subst > $o)] : (($true = ((sP46 @ X307))) <=> ? [X314 : term,X315 : term] : ((((X307 @ id @ (ap @ (sub @ X314 @ id) @ X315) @ id)) != $true) & (((X307 @ id @ X315 @ id)) = $true) & (((X307 @ id @ X314 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f60,definition,(
% 8.63/1.68 ! [X307 : (subst > term > subst > $o)] : (($true = ((sP47 @ X307))) <=> ? [X321 : subst,X322 : term,X323 : subst,X324 : subst] : ((((X307 @ (comp @ X321 @ X324) @ (sub @ X322 @ X324) @ X323)) != $true) & (((X307 @ X321 @ X322 @ (comp @ X324 @ X323))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f61,definition,(
% 8.63/1.68 ! [X307 : (subst > term > subst > $o)] : (($true = ((sP48 @ X307))) <=> ? [X317 : subst,X318 : term,X319 : subst,X320 : subst] : ((((X307 @ X317 @ X318 @ (comp @ X320 @ X319))) != $true) & (((X307 @ (comp @ X317 @ X320) @ (sub @ X318 @ X320) @ X319)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f62,definition,(
% 8.63/1.68 ($true = sP49) <=> ! [X307 : (subst > term > subst > $o),X308 : term] : ((((X307 @ id @ X308 @ id)) = $true) | ($true = ((sP45 @ X307))) | ($true = ((sP46 @ X307))) | ? [X316 : term] : ((((X307 @ id @ X316 @ id)) != $true) & (((var @ (sub @ X316 @ id))) = $true)) | ($true = ((sP48 @ X307))) | ($true = ((sP47 @ X307))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f63,definition,(
% 8.63/1.68 ! [X299 : (term > $o)] : (($true = ((sP50 @ X299))) <=> ? [X302 : term,X303 : term] : ((((X299 @ (ap @ X302 @ X303))) != $true) & (((X299 @ X303)) = $true) & (((X299 @ X302)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f64,definition,(
% 8.63/1.68 ! [X299 : (term > $o)] : (($true = ((sP51 @ X299))) <=> ? [X304 : term] : ((((X299 @ X304)) != $true) & (((var @ X304)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f65,definition,(
% 8.63/1.68 ($true = sP52) <=> ! [X299 : (term > $o),X300 : term] : ((((X299 @ X300)) = $true) | ? [X301 : term] : ((((X299 @ (lam @ X301))) != $true) & (((X299 @ X301)) = $true)) | ($true = ((sP50 @ X299))) | ($true = ((sP51 @ X299))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f66,definition,(
% 8.63/1.68 ! [X283 : (subst > term > subst > $o)] : (($true = ((sP53 @ X283))) <=> ! [X286 : (subst > term > term)] : ((((X283 @ id @ (lam @ (X286 @ sh @ one)) @ id)) = $true) | ? [X287 : term] : ((((X283 @ id @ (X286 @ id @ X287) @ id)) != $true) & (((X283 @ id @ X287 @ id)) = $true)) | ? [X288 : subst,X289 : term,X290 : subst] : (((sub @ (X286 @ X288 @ X289) @ X290)) != ((X286 @ (comp @ X288 @ X290) @ (sub @ X289 @ X290))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f67,definition,(
% 8.63/1.68 ! [X291 : (subst > term > subst > $o)] : (($true = ((sP54 @ X291))) <=> ? [X294 : (subst > term > term)] : ((((X291 @ id @ (lam @ (X294 @ sh @ one)) @ id)) != $true) & ! [X295 : term] : ((((X291 @ id @ (X294 @ id @ X295) @ id)) = $true) | (((X291 @ id @ X295 @ id)) != $true)) & ! [X296 : subst,X297 : term,X298 : subst] : (((sub @ (X294 @ X296 @ X297) @ X298)) = ((X294 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f68,definition,(
% 8.63/1.68 ($true = sP55) <=> ! [X291 : (subst > term > subst > $o),X292 : term] : ((((X291 @ id @ (lam @ X292) @ id)) = $true) | ? [X293 : term] : ((((X291 @ id @ (sub @ X292 @ (push @ X293 @ id)) @ id)) != $true) & (((X291 @ id @ X293 @ id)) = $true)) | ($true = ((sP54 @ X291))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f69,definition,(
% 8.63/1.68 ($true = sP56) <=> ? [X283 : (subst > term > subst > $o),X284 : term] : ((((X283 @ id @ (lam @ (sub @ X284 @ (push @ one @ sh))) @ id)) != $true) & ! [X285 : term] : ((((X283 @ id @ (sub @ X284 @ (push @ X285 @ id)) @ id)) = $true) | (((X283 @ id @ X285 @ id)) != $true)) & ($true = ((sP53 @ X283))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f70,definition,(
% 8.63/1.68 ! [X274 : (subst > term > subst > $o)] : (($true = ((sP57 @ X274))) <=> ? [X277 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X277 @ sh @ one)) @ id)) != $true) & ! [X278 : term] : ((((X274 @ id @ (X277 @ id @ X278) @ id)) = $true) | (((X274 @ id @ X278 @ id)) != $true)) & ! [X279 : subst,X280 : term,X281 : subst] : (((sub @ (X277 @ X279 @ X280) @ X281)) = ((X277 @ (comp @ X279 @ X281) @ (sub @ X280 @ X281))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f71,definition,(
% 8.63/1.68 ($true = sP58) <=> ! [X274 : (subst > term > subst > $o),X275 : term] : ((((X274 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id)) = $true) | ? [X276 : term] : ((((X274 @ id @ (sub @ X275 @ (push @ X276 @ id)) @ id)) != $true) & (((X274 @ id @ X276 @ id)) = $true)) | ($true = ((sP57 @ X274))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f72,definition,(
% 8.63/1.68 ! [X259 : (subst > term > subst > $o)] : (($true = ((sP59 @ X259))) <=> ? [X264 : term,X265 : term] : ((((X259 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id)) != $true) & (((X259 @ id @ X265 @ id)) = $true) & (((X259 @ id @ X264 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f73,definition,(
% 8.63/1.68 ! [X259 : (subst > term > subst > $o)] : (($true = ((sP60 @ X259))) <=> ? [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X259 @ (comp @ X270 @ X273) @ (sub @ X271 @ X273) @ X272)) != $true) & (((X259 @ X270 @ X271 @ (comp @ X273 @ X272))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f74,definition,(
% 8.63/1.68 ($true = sP61) <=> ! [X259 : (subst > term > subst > $o),X260 : (term > $o),X261 : term,X262 : term] : ((((X260 @ (ap @ X261 @ X262))) = $true) | (((X260 @ X262)) != $true) | (((X260 @ X261)) != $true) | ? [X263 : term] : (((X260 @ X263)) != ((X259 @ id @ X263 @ id))) | ($true = ((sP59 @ X259))) | ? [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X259 @ X266 @ X267 @ (comp @ X269 @ X268))) != $true) & (((X259 @ (comp @ X266 @ X269) @ (sub @ X267 @ X269) @ X268)) = $true)) | ($true = ((sP60 @ X259))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f75,definition,(
% 8.63/1.68 ($true = sP62) <=> ! [X247 : term,X248 : term,X249 : term,X250 : term] : ((X249 = X250) | (((ap @ (sub @ X247 @ id) @ X249)) != ((ap @ (sub @ X248 @ id) @ X250))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f76,definition,(
% 8.63/1.68 ($true = sP63) <=> (($true = sP62) | ? [X243 : term,X244 : term,X245 : term,X246 : term] : ((X245 != X246) & (((ap @ X243 @ X245)) = ((ap @ X244 @ X246)))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f77,definition,(
% 8.63/1.68 ! [X233 : (subst > term > subst > $o)] : (($true = ((sP64 @ X233))) <=> ? [X238 : (subst > term > term)] : ((((X233 @ id @ (lam @ (X238 @ sh @ one)) @ id)) != $true) & ! [X239 : term] : ((((X233 @ id @ (X238 @ id @ X239) @ id)) = $true) | (((X233 @ id @ X239 @ id)) != $true)) & ! [X240 : subst,X241 : term,X242 : subst] : (((sub @ (X238 @ X240 @ X241) @ X242)) = ((X238 @ (comp @ X240 @ X242) @ (sub @ X241 @ X242))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f78,definition,(
% 8.63/1.68 ($true = sP65) <=> ! [X233 : (subst > term > subst > $o),X234 : (term > $o),X235 : term] : ((((X234 @ (lam @ X235))) = $true) | ? [X236 : term] : ((((X234 @ (sub @ X235 @ (push @ X236 @ id)))) != $true) & (((X234 @ X236)) = $true)) | ? [X237 : term] : (((X234 @ X237)) != ((X233 @ id @ X237 @ id))) | ($true = ((sP64 @ X233))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f79,definition,(
% 8.63/1.68 ($true = sP66) <=> ! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X230) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X230 @ id) @ X232))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f80,definition,(
% 8.63/1.68 ($true = sP67) <=> (($true = sP66) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X226) & (((ap @ X225 @ X227)) = ((ap @ X226 @ X228)))) | ? [X224 : term] : (((sub @ X224 @ id)) != X224))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f81,definition,(
% 8.63/1.68 ($true = sP68) <=> ! [X214 : (subst > term > term),X215 : (subst > term > term),X216 : subst,X217 : term] : ((((X214 @ X216 @ X217)) = ((X215 @ X216 @ X217))) | (((lam @ (X214 @ sh @ one))) != ((lam @ (X215 @ sh @ one)))) | ? [X218 : subst,X219 : term,X220 : subst] : (((sub @ (X215 @ X218 @ X219) @ X220)) != ((X215 @ (comp @ X218 @ X220) @ (sub @ X219 @ X220)))) | ? [X221 : subst,X222 : term,X223 : subst] : (((sub @ (X214 @ X221 @ X222) @ X223)) != ((X214 @ (comp @ X221 @ X223) @ (sub @ X222 @ X223)))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f82,definition,(
% 8.63/1.68 ($true = sP69) <=> (($true = sP68) | ? [X212 : term,X213 : term] : ((X212 != X213) & (((lam @ X212)) = ((lam @ X213)))) | ? [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) != X211) | ? [X208 : term,X209 : subst] : (((sub @ one @ (push @ X208 @ X209))) != X208))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f83,definition,(
% 8.63/1.68 ! [X173 : (subst > term > subst > $o)] : (($true = ((sP70 @ X173))) <=> ! [X176 : (subst > term > term)] : ((((X173 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : ((((X173 @ id @ (X176 @ id @ X177) @ id)) != $true) & (((X173 @ id @ X177 @ id)) = $true)) | ? [X178 : subst,X179 : term,X180 : subst] : (((sub @ (X176 @ X178 @ X179) @ X180)) != ((X176 @ (comp @ X178 @ X180) @ (sub @ X179 @ X180))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f84,definition,(
% 8.63/1.68 ! [X181 : (subst > term > subst > $o)] : (($true = ((sP71 @ X181))) <=> ? [X184 : (subst > term > term)] : ((((X181 @ id @ (lam @ (X184 @ sh @ one)) @ id)) != $true) & ! [X185 : term] : ((((X181 @ id @ (X184 @ id @ X185) @ id)) = $true) | (((X181 @ id @ X185 @ id)) != $true)) & ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X184 @ X186 @ X187) @ X188)) = ((X184 @ (comp @ X186 @ X188) @ (sub @ X187 @ X188))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f85,definition,(
% 8.63/1.68 ! [X181 : (subst > term > subst > $o)] : (($true = ((sP72 @ X181))) <=> ? [X193 : subst,X194 : term,X195 : subst,X196 : subst] : ((((X181 @ (comp @ X193 @ X196) @ (sub @ X194 @ X196) @ X195)) != $true) & (((X181 @ X193 @ X194 @ (comp @ X196 @ X195))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f86,definition,(
% 8.63/1.68 ! [X181 : (subst > term > subst > $o)] : (($true = ((sP73 @ X181))) <=> ? [X189 : subst,X190 : term,X191 : subst,X192 : subst] : ((((X181 @ X189 @ X190 @ (comp @ X192 @ X191))) != $true) & (((X181 @ (comp @ X189 @ X192) @ (sub @ X190 @ X192) @ X191)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f87,definition,(
% 8.63/1.68 ($true = sP74) <=> ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ (lam @ X182) @ id)) = $true) | ? [X183 : term] : ((((X181 @ id @ (sub @ X182 @ (push @ X183 @ id)) @ id)) != $true) & (((X181 @ id @ X183 @ id)) = $true)) | ($true = ((sP71 @ X181))) | ($true = ((sP73 @ X181))) | ($true = ((sP72 @ X181))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f88,definition,(
% 8.63/1.68 ($true = sP75) <=> ? [X173 : (subst > term > subst > $o),X174 : term] : ((((X173 @ id @ (lam @ (sub @ X174 @ (push @ one @ sh))) @ id)) != $true) & ! [X175 : term] : ((((X173 @ id @ (sub @ X174 @ (push @ X175 @ id)) @ id)) = $true) | (((X173 @ id @ X175 @ id)) != $true)) & ($true = ((sP70 @ X173))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f89,definition,(
% 8.63/1.68 ! [X157 : (subst > term > subst > $o)] : (($true = ((sP76 @ X157))) <=> ? [X162 : (subst > term > term)] : ((((X157 @ id @ (lam @ (X162 @ sh @ one)) @ id)) != $true) & ! [X163 : term] : ((((X157 @ id @ (X162 @ id @ X163) @ id)) = $true) | (((X157 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X165 : term,X166 : subst] : (((sub @ (X162 @ X164 @ X165) @ X166)) = ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f90,definition,(
% 8.63/1.68 ($true = sP77) <=> ! [X157 : (subst > term > subst > $o),X158 : (term > $o),X159 : term] : ((((X158 @ (lam @ X159))) = $true) | ? [X160 : term] : ((((X158 @ (sub @ X159 @ (push @ X160 @ id)))) != $true) & (((X158 @ X160)) = $true)) | ? [X161 : term] : (((X158 @ X161)) != ((X157 @ id @ X161 @ id))) | ($true = ((sP76 @ X157))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f91,definition,(
% 8.63/1.68 ! [X136 : (term > $o)] : (($true = ((sP78 @ X136))) <=> ! [X142 : term,X143 : term] : ((((X136 @ (ap @ X142 @ X143))) = $true) | (((X136 @ X143)) != $true) | (((X136 @ X142)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f92,definition,(
% 8.63/1.68 ! [X136 : (term > $o)] : (($true = ((sP79 @ X136))) <=> ! [X140 : term] : ((((X136 @ (lam @ X140))) = $true) | ? [X141 : term] : ((((X136 @ (sub @ X140 @ (push @ X141 @ id)))) != $true) & (((X136 @ X141)) = $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f93,definition,(
% 8.63/1.68 ! [X144 : (term > $o)] : (($true = ((sP80 @ X144))) <=> ? [X146 : term] : ((((X144 @ (lam @ X146))) != $true) & ! [X147 : term] : ((((X144 @ (sub @ X146 @ (push @ X147 @ id)))) = $true) | (((X144 @ X147)) != $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f94,definition,(
% 8.63/1.68 ! [X144 : (term > $o)] : (($true = ((sP81 @ X144))) <=> ? [X148 : term,X149 : term] : ((((X144 @ (ap @ X148 @ X149))) != $true) & (((X144 @ X149)) = $true) & (((X144 @ X148)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f95,definition,(
% 8.63/1.68 ($true = sP82) <=> ! [X144 : (term > $o),X145 : term] : ((((X144 @ X145)) = $true) | ($true = ((sP80 @ X144))) | ($true = ((sP81 @ X144))) | ? [X150 : term] : ((((X144 @ X150)) != $true) & (((var @ X150)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f96,definition,(
% 8.63/1.68 ($true = sP83) <=> ? [X136 : (term > $o),X137 : term,X138 : subst] : ((((X136 @ (sub @ X137 @ X138))) != $true) & ! [X139 : term] : ((((X136 @ (sub @ X139 @ X138))) = $true) | (((var @ X139)) != $true)) & ($true = ((sP79 @ X136))) & ($true = ((sP78 @ X136))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f97,definition,(
% 8.63/1.68 ($true = sP84) <=> ((! [X130 : subst] : (((comp @ X130 @ id)) = X130) & ! [X131 : subst] : (((comp @ id @ X131)) = X131)) | ? [X129 : subst] : (((comp @ X129 @ id)) != X129) | ? [X128 : subst] : (((comp @ id @ X128)) != X128))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f98,definition,(
% 8.63/1.68 ! [X116 : (subst > term > subst > $o)] : (($true = ((sP85 @ X116))) <=> ? [X119 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)) != $true) & ! [X120 : term] : ((((X116 @ id @ (X119 @ id @ X120) @ id)) = $true) | (((X116 @ id @ X120 @ id)) != $true)) & ! [X121 : subst,X122 : term,X123 : subst] : (((sub @ (X119 @ X121 @ X122) @ X123)) = ((X119 @ (comp @ X121 @ X123) @ (sub @ X122 @ X123))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f99,definition,(
% 8.63/1.68 ($true = sP86) <=> ! [X116 : (subst > term > subst > $o),X117 : term] : ((((X116 @ id @ (lam @ X117) @ id)) = $true) | ? [X118 : term] : ((((X116 @ id @ (sub @ X117 @ (push @ X118 @ id)) @ id)) != $true) & (((X116 @ id @ X118 @ id)) = $true)) | ($true = ((sP85 @ X116))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f100,definition,(
% 8.63/1.68 ! [X107 : (subst > term > subst > $o)] : (($true = ((sP87 @ X107))) <=> ? [X109 : (subst > term > term)] : ((((X107 @ id @ (lam @ (X109 @ sh @ one)) @ id)) != $true) & ! [X110 : term] : ((((X107 @ id @ (X109 @ id @ X110) @ id)) = $true) | (((X107 @ id @ X110 @ id)) != $true)) & ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X109 @ X111 @ X112) @ X113)) = ((X109 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f101,definition,(
% 8.63/1.68 ! [X107 : (subst > term > subst > $o)] : (($true = ((sP88 @ X107))) <=> ? [X114 : term,X115 : term] : ((((X107 @ id @ (ap @ (sub @ X114 @ id) @ X115) @ id)) != $true) & (((X107 @ id @ X115 @ id)) = $true) & (((X107 @ id @ X114 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f102,definition,(
% 8.63/1.68 ! [X94 : (term > $o)] : (($true = ((sP89 @ X94))) <=> ? [X96 : term] : ((((X94 @ (lam @ X96))) != $true) & ! [X97 : term] : ((((X94 @ (sub @ X96 @ (push @ X97 @ id)))) = $true) | (((X94 @ X97)) != $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f103,definition,(
% 8.63/1.68 ! [X94 : (term > $o)] : (($true = ((sP90 @ X94))) <=> ? [X98 : term,X99 : term] : ((((X94 @ (ap @ X98 @ X99))) != $true) & (((X94 @ X99)) = $true) & (((X94 @ X98)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f104,definition,(
% 8.63/1.68 ($true = sP91) <=> ! [X94 : (term > $o),X95 : term] : ((((X94 @ X95)) = $true) | ($true = ((sP89 @ X94))) | ($true = ((sP90 @ X94))) | ? [X100 : term] : ((((X94 @ X100)) != $true) & (((var @ X100)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f105,definition,(
% 8.63/1.68 ! [X67 : (subst > term > subst > $o)] : (($true = ((sP92 @ X67))) <=> ? [X72 : (subst > term > term)] : ((((X67 @ id @ (lam @ (X72 @ sh @ one)) @ id)) != $true) & ! [X73 : term] : ((((X67 @ id @ (X72 @ id @ X73) @ id)) = $true) | (((X67 @ id @ X73 @ id)) != $true)) & ! [X74 : subst,X75 : term,X76 : subst] : (((sub @ (X72 @ X74 @ X75) @ X76)) = ((X72 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f106,definition,(
% 8.63/1.68 ! [X67 : (subst > term > subst > $o)] : (($true = ((sP93 @ X67))) <=> ? [X81 : subst,X82 : term,X83 : subst,X84 : subst] : ((((X67 @ (comp @ X81 @ X84) @ (sub @ X82 @ X84) @ X83)) != $true) & (((X67 @ X81 @ X82 @ (comp @ X84 @ X83))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f107,definition,(
% 8.63/1.68 ! [X67 : (subst > term > subst > $o)] : (($true = ((sP94 @ X67))) <=> ? [X77 : subst,X78 : term,X79 : subst,X80 : subst] : ((((X67 @ X77 @ X78 @ (comp @ X80 @ X79))) != $true) & (((X67 @ (comp @ X77 @ X80) @ (sub @ X78 @ X80) @ X79)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f108,definition,(
% 8.63/1.68 ($true = sP95) <=> ! [X67 : (subst > term > subst > $o),X68 : (term > $o),X69 : term] : ((((X68 @ (lam @ X69))) = $true) | ? [X70 : term] : ((((X68 @ (sub @ X69 @ (push @ X70 @ id)))) != $true) & (((X68 @ X70)) = $true)) | ? [X71 : term] : (((X68 @ X71)) != ((X67 @ id @ X71 @ id))) | ($true = ((sP92 @ X67))) | ($true = ((sP94 @ X67))) | ($true = ((sP93 @ X67))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f109,definition,(
% 8.63/1.68 ! [X41 : (subst > term > subst > $o)] : (($true = ((sP96 @ X41))) <=> ? [X46 : (subst > term > term)] : ((((X41 @ id @ (lam @ (X46 @ sh @ one)) @ id)) != $true) & ! [X47 : term] : ((((X41 @ id @ (X46 @ id @ X47) @ id)) = $true) | (((X41 @ id @ X47 @ id)) != $true)) & ! [X48 : subst,X49 : term,X50 : subst] : (((sub @ (X46 @ X48 @ X49) @ X50)) = ((X46 @ (comp @ X48 @ X50) @ (sub @ X49 @ X50))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f110,definition,(
% 8.63/1.68 ! [X41 : (subst > term > subst > $o)] : (($true = ((sP97 @ X41))) <=> ? [X55 : subst,X56 : term,X57 : subst,X58 : subst] : ((((X41 @ (comp @ X55 @ X58) @ (sub @ X56 @ X58) @ X57)) != $true) & (((X41 @ X55 @ X56 @ (comp @ X58 @ X57))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f111,definition,(
% 8.63/1.68 ! [X41 : (subst > term > subst > $o)] : (($true = ((sP98 @ X41))) <=> ? [X51 : subst,X52 : term,X53 : subst,X54 : subst] : ((((X41 @ X51 @ X52 @ (comp @ X54 @ X53))) != $true) & (((X41 @ (comp @ X51 @ X54) @ (sub @ X52 @ X54) @ X53)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f112,definition,(
% 8.63/1.68 ($true = sP99) <=> ! [X41 : (subst > term > subst > $o),X42 : (term > $o),X43 : term] : ((((X42 @ (lam @ X43))) = $true) | ? [X44 : term] : ((((X42 @ (sub @ X43 @ (push @ X44 @ id)))) != $true) & (((X42 @ X44)) = $true)) | ? [X45 : term] : (((X42 @ X45)) != ((X41 @ id @ X45 @ id))) | ($true = ((sP96 @ X41))) | ($true = ((sP98 @ X41))) | ($true = ((sP97 @ X41))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f113,definition,(
% 8.63/1.68 ! [X3 : (term > $o)] : (($true = ((sP100 @ X3))) <=> ! [X7 : term,X8 : term] : ((((X3 @ (ap @ X7 @ X8))) = $true) | (((X3 @ X8)) != $true) | (((X3 @ X7)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f114,definition,(
% 8.63/1.68 ! [X3 : (term > $o)] : (($true = ((sP101 @ X3))) <=> ! [X9 : term] : ((((X3 @ X9)) = $true) | (((var @ X9)) != $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f115,definition,(
% 8.63/1.68 ! [X3 : (term > $o)] : (($true = ((sP102 @ X3))) <=> ! [X5 : term] : ((((X3 @ (lam @ X5))) = $true) | ? [X6 : term] : ((((X3 @ (sub @ X5 @ (push @ X6 @ id)))) != $true) & (((X3 @ X6)) = $true))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f116,definition,(
% 8.63/1.68 ! [X11 : (subst > term > subst > $o)] : (($true = ((sP103 @ X11))) <=> ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X17 : term] : ((((X11 @ id @ (X16 @ id @ X17) @ id)) != $true) & (((X11 @ id @ X17 @ id)) = $true)) | ? [X18 : subst,X19 : term,X20 : subst] : (((sub @ (X16 @ X18 @ X19) @ X20)) != ((X16 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f117,definition,(
% 8.63/1.68 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP104 @ X21))) <=> ? [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X23 @ X25 @ X26) @ X27)) = ((X23 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f118,definition,(
% 8.63/1.68 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP105 @ X21))) <=> ? [X28 : term,X29 : term] : ((((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ X28 @ id)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f119,definition,(
% 8.63/1.68 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP106 @ X21))) <=> ? [X35 : subst,X36 : term,X37 : subst,X38 : subst] : ((((X21 @ (comp @ X35 @ X38) @ (sub @ X36 @ X38) @ X37)) != $true) & (((X21 @ X35 @ X36 @ (comp @ X38 @ X37))) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f120,definition,(
% 8.63/1.68 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP107 @ X21))) <=> ? [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X21 @ X31 @ X32 @ (comp @ X34 @ X33))) != $true) & (((X21 @ (comp @ X31 @ X34) @ (sub @ X32 @ X34) @ X33)) = $true)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f121,definition,(
% 8.63/1.68 ($true = sP108) <=> ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ($true = ((sP104 @ X21))) | ($true = ((sP105 @ X21))) | ? [X30 : term] : ((((X21 @ id @ X30 @ id)) != $true) & (((var @ (sub @ X30 @ id))) = $true)) | ($true = ((sP107 @ X21))) | ($true = ((sP106 @ X21))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f122,definition,(
% 8.63/1.68 ($true = sP109) <=> ? [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : ((((X12 @ (lam @ X13))) != $true) & ! [X14 : term] : ((((X12 @ (sub @ X13 @ (push @ X14 @ id)))) = $true) | (((X12 @ X14)) != $true)) & ! [X15 : term] : (((X12 @ X15)) = ((X11 @ id @ X15 @ id))) & ($true = ((sP103 @ X11))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f123,definition,(
% 8.63/1.68 ($true = sP110) <=> ? [X3 : (term > $o),X4 : term] : ((((X3 @ X4)) != $true) & ($true = ((sP102 @ X3))) & ($true = ((sP100 @ X3))) & ($true = ((sP101 @ X3))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 8.63/1.68 thf(f124,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) <=> (($true = sP108) | ($true = sP109) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ($true = sP110) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))))) & ((axvarid = $true) <=> ! [X39 : term] : (((sub @ X39 @ id)) = X39)) & ((hoasinduction_lem3v2_lthm = $true) <=> (($true = sP99) | ? [X40 : term] : (((sub @ X40 @ id)) != X40))) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & ((termmset = $true) <=> ! [X64 : term] : (((sub @ X64 @ id)) = X64)) & ((axshiftcons = $true) <=> ! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66)) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP95)) & ((pushprop_lem1_lthm = $true) <=> (! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) <=> ($true = sP91)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ($true = ((sP87 @ X107))) | ($true = ((sP88 @ X107))))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP86)) & (lamnotvar = $true) & ((substmonoid = $true) <=> (! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125))) & ((hoasinduction_lem3b = $true) <=> ! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh))))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> ($true = sP84)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id)))) & ((induction2_lthm = $true) <=> (($true = sP82) | ($true = sP83) | ? [X135 : term] : (((sub @ X135 @ id)) != X135))) & (hoaslaminj_gthm = $true) & ((axidl = $true) <=> ! [X151 : subst] : (((comp @ id @ X151)) = X151)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (($true = sP77) | ? [X156 : term] : (((sub @ X156 @ id)) != X156) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))))) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & ((hoasinduction_lem3_lthm = $true) <=> (($true = sP74) | ($true = sP75) | ? [X172 : term] : (((sub @ X172 @ id)) != X172))) & ((laminj = $true) <=> ! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198))))) & ((pushprop_lem1 = $true) <=> ! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true))) & ((axidr = $true) <=> ! [X204 : subst] : (((comp @ X204 @ id)) = X204)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) <=> ! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205)) & ((axvarcons = $true) <=> ! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206)) & ((hoaslaminj_lthm = $true) <=> ($true = sP69)) & ((hoasapinj1_lthm = $true) <=> ($true = sP67)) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP65)) & ((hoasapinj2_lthm = $true) <=> ($true = sP63)) & ((apinj1 = $true) <=> ! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254))))) & ((apinj2 = $true) <=> ! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258))))) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP61)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ($true = sP58)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (($true = sP55) | ($true = sP56) | ? [X282 : term] : (((sub @ X282 @ id)) != X282))) & ((induction = $true) <=> ($true = sP52)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh))))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) <=> ($true = sP49)) & ((hoasinduction_lem0 = $true) <=> ! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id)))) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) <=> (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335))) & ((hoasinduction_lem2 = $true) <=> ($true = sP44)) & ((hoasinduction_lem3 = $true) <=> ($true = sP41)) & ((hoasinduction_lem3aa_lthm = $true) <=> ($true = sP37)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP35)) & ((hoaslaminj = $true) <=> ! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (($true = sP31) | ($true = sP32) | ? [X406 : term] : (((sub @ X406 @ id)) != X406) | ($true = sP33) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))))) & ((hoasinduction_lthm = $true) <=> (($true = sP21) | ($true = sP23) | ($true = sP22) | ($true = sP24))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482)))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) <=> (($true = sP7) | ($true = sP8) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484))) & (ulamvar1 != $true) & ((hoasapinj1 = $true) <=> ! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510))))) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513)))) & ((induction2lem = $true) <=> ($true = sP2)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) <=> ! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh))))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(definition_folding,[],[f12,f123,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,f72,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])).
% 8.63/1.68 thf(f462,plain,(
% 8.63/1.68 (((hoasinduction_lthm_3 = $true) | (($true != sP108) & ($true != sP109) & ! [X10 : term] : (((sub @ X10 @ id)) = X10) & ($true != sP110) & ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))))) & ((($true = sP108) | ($true = sP109) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ($true = sP110) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id)))) | (hoasinduction_lthm_3 != $true))) & (((axvarid = $true) | ? [X39 : term] : (((sub @ X39 @ id)) != X39)) & (! [X39 : term] : (((sub @ X39 @ id)) = X39) | (axvarid != $true))) & (((hoasinduction_lem3v2_lthm = $true) | (($true != sP99) & ! [X40 : term] : (((sub @ X40 @ id)) = X40))) & ((($true = sP99) | ? [X40 : term] : (((sub @ X40 @ id)) != X40)) | (hoasinduction_lem3v2_lthm != $true))) & (hoasapnotvar_lthm = $true) & (((pushprop_lem0_lthm = $true) | ? [X59 : (term > $o),X60 : term,X61 : subst] : ! [X62 : (term > $o)] : ? [X63 : term] : (((X62 @ X63)) != ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & (! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61))))) | (pushprop_lem0_lthm != $true))) & (((termmset = $true) | ? [X64 : term] : (((sub @ X64 @ id)) != X64)) & (! [X64 : term] : (((sub @ X64 @ id)) = X64) | (termmset != $true))) & (((axshiftcons = $true) | ? [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) != X66)) & (! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66) | (axshiftcons != $true))) & (((hoasinduction_lem3v2 = $true) | ($true != sP95)) & (($true = sP95) | (hoasinduction_lem3v2 != $true))) & (((pushprop_lem1_lthm = $true) | (? [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) != $true) & (((X89 @ X91)) = $true)) & ! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) & ! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85))) & ((! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85)) | (pushprop_lem1_lthm != $true))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & (((induction2 = $true) | ($true != sP91)) & (($true = sP91) | (induction2 != $true))) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & (((hoaslamnotap = $true) | ? [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) = ((ap @ (sub @ X102 @ id) @ X103))) & ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))))) | (hoaslamnotap != $true))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) != $true) & ($true != ((sP87 @ X107))) & ($true != ((sP88 @ X107))))) & (! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ($true = ((sP87 @ X107))) | ($true = ((sP88 @ X107)))) | (hoasinduction_no_psi_cond != $true))) & (hoasinduction_lem1_gthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP86)) & (($true = sP86) | (hoasinduction_lem3a != $true))) & (lamnotvar = $true) & (((substmonoid = $true) | (? [X124 : subst] : (((comp @ X124 @ id)) != X124) | ? [X125 : subst] : (((comp @ id @ X125)) != X125))) & ((! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125)) | (substmonoid != $true))) & (((hoasinduction_lem3b = $true) | ? [X126 : term] : ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & (((substmonoid_lthm = $true) | ($true != sP84)) & (($true = sP84) | (substmonoid_lthm != $true))) & (((hoasinduction_lem0_lthm = $true) | ? [X132 : (subst > term > subst > $o)] : ! [X133 : (term > $o)] : ? [X134 : term] : (((X133 @ X134)) != ((X132 @ id @ X134 @ id)))) & (! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((induction2_lthm = $true) | (($true != sP82) & ($true != sP83) & ! [X135 : term] : (((sub @ X135 @ id)) = X135))) & ((($true = sP82) | ($true = sP83) | ? [X135 : term] : (((sub @ X135 @ id)) != X135)) | (induction2_lthm != $true))) & (hoaslaminj_gthm = $true) & (((axidl = $true) | ? [X151 : subst] : (((comp @ id @ X151)) != X151)) & (! [X151 : subst] : (((comp @ id @ X151)) = X151) | (axidl != $true))) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (((hoasinduction_lem3v2a_lthm = $true) | (($true != sP77) & ! [X156 : term] : (((sub @ X156 @ id)) = X156) & ! [X152 : term] : ? [X153 : (subst > term > term)] : ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))))) & ((($true = sP77) | ? [X156 : term] : (((sub @ X156 @ id)) != X156) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154)))) | (hoasinduction_lem3v2a_lthm != $true))) & (axabs = $true) & (pushprop_gthm = $true) & (((pushprop_lem0 = $true) | ? [X167 : (term > $o),X168 : term,X169 : subst] : ! [X170 : (term > $o)] : ? [X171 : term] : (((X170 @ X171)) != ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & (! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169))))) | (pushprop_lem0 != $true))) & (((hoasinduction_lem3_lthm = $true) | (($true != sP74) & ($true != sP75) & ! [X172 : term] : (((sub @ X172 @ id)) = X172))) & ((($true = sP74) | ($true = sP75) | ? [X172 : term] : (((sub @ X172 @ id)) != X172)) | (hoasinduction_lem3_lthm != $true))) & (((laminj = $true) | ? [X197 : term,X198 : term] : ((X197 != X198) & (((lam @ X197)) = ((lam @ X198))))) & (! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198)))) | (laminj != $true))) & (((pushprop_lem1 = $true) | ? [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) != $true) & (((X199 @ X201)) = $true))) & (! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true)) | (pushprop_lem1 != $true))) & (((axidr = $true) | ? [X204 : subst] : (((comp @ X204 @ id)) != X204)) & (! [X204 : subst] : (((comp @ X204 @ id)) = X204) | (axidr != $true))) & (hoasinduction_lem2v2_gthm = $true) & (((axscons = $true) | ? [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) != X205)) & (! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205) | (axscons != $true))) & (((axvarcons = $true) | ? [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) != X206)) & (! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206) | (axvarcons != $true))) & (((hoaslaminj_lthm = $true) | ($true != sP69)) & (($true = sP69) | (hoaslaminj_lthm != $true))) & (((hoasapinj1_lthm = $true) | ($true != sP67)) & (($true = sP67) | (hoasapinj1_lthm != $true))) & (((hoasinduction_lem3v2a = $true) | ($true != sP65)) & (($true = sP65) | (hoasinduction_lem3v2a != $true))) & (((hoasapinj2_lthm = $true) | ($true != sP63)) & (($true = sP63) | (hoasapinj2_lthm != $true))) & (((apinj1 = $true) | ? [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 != X252) & (((ap @ X251 @ X253)) = ((ap @ X252 @ X254))))) & (! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254)))) | (apinj1 != $true))) & (((apinj2 = $true) | ? [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 != X258) & (((ap @ X255 @ X257)) = ((ap @ X256 @ X258))))) & (! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258)))) | (apinj2 != $true))) & (pushprop_lthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP61)) & (($true = sP61) | (hoasinduction_lem2v2 != $true))) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true))) & (termmset_gthm = $true) & (((hoasinduction_lem3a_lthm = $true) | (($true != sP55) & ($true != sP56) & ! [X282 : term] : (((sub @ X282 @ id)) = X282))) & ((($true = sP55) | ($true = sP56) | ? [X282 : term] : (((sub @ X282 @ id)) != X282)) | (hoasinduction_lem3a_lthm != $true))) & (((induction = $true) | ($true != sP52)) & (($true = sP52) | (induction != $true))) & (ulamvarind = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X305 : term] : ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true))) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & (((hoasinduction = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction != $true))) & (((hoasinduction_lem0 = $true) | ? [X325 : (subst > term > subst > $o)] : ! [X326 : (term > $o)] : ? [X327 : term] : (((X326 @ X327)) != ((X325 @ id @ X327 @ id)))) & (! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id))) | (hoasinduction_lem0 != $true))) & (hoasapnotvar = $true) & (((pushprop_lem1v2_lthm = $true) | (? [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) != $true) & ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) & (((X330 @ X332)) = $true)) & ! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328))) & ((! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328)) | (pushprop_lem1v2_lthm != $true))) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & (((termmset_lthm = $true) | (? [X336 : term] : (((sub @ X336 @ id)) != X336) & ! [X335 : term] : (((sub @ X335 @ id)) = X335))) & ((! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335)) | (termmset_lthm != $true))) & (((hoasinduction_lem2 = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_lem2 != $true))) & (((hoasinduction_lem3 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem3 != $true))) & (((hoasinduction_lem3aa_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3aa_lthm != $true))) & (induction2lem_gthm = $true) & (((hoasinduction_lem3aaa = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3aaa != $true))) & (((hoaslaminj = $true) | ? [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) != ((X387 @ X388 @ X389))) & (((lam @ (X386 @ sh @ one))) = ((lam @ (X387 @ sh @ one)))) & ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) & ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & (! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395))))) | (hoaslaminj != $true))) & (((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP31) & ($true != sP32) & ! [X406 : term] : (((sub @ X406 @ id)) = X406) & ($true != sP33) & ! [X396 : (subst > term > subst > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))))) & ((($true = sP31) | ($true = sP32) | ? [X406 : term] : (((sub @ X406 @ id)) != X406) | ($true = sP33) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id)))) | (hoasinduction_no_psi_cond_lthm != $true))) & (((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP23) & ($true != sP22) & ($true != sP24))) & ((($true = sP21) | ($true = sP23) | ($true = sP22) | ($true = sP24)) | (hoasinduction_lthm != $true))) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X480 : term] : ! [X481 : (subst > term > term)] : ? [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) != ((X481 @ X483 @ X482)))) & (! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482))) | (hoasinduction_lem3v2_f_lthm != $true))) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (((induction2lem_lthm = $true) | (($true != sP7) & ($true != sP8) & ! [X488 : subst] : (((comp @ X488 @ id)) = X488) & ! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) & ! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484))) & ((($true = sP7) | ($true = sP8) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484)) | (induction2lem_lthm != $true))) & (ulamvar1 != $true) & (((hoasapinj1 = $true) | ? [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 != X504) & (((ap @ (sub @ X503 @ id) @ X505)) = ((ap @ (sub @ X504 @ id) @ X506))))) & (! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506)))) | (hoasapinj1 != $true))) & (hoasapnotvar_gthm = $true) & (((hoasapinj2 = $true) | ? [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 != X510) & (((ap @ (sub @ X507 @ id) @ X509)) = ((ap @ (sub @ X508 @ id) @ X510))))) & (! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510)))) | (hoasapinj2 != $true))) & (axvarshift = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X511 : term] : ! [X512 : (subst > term > term)] : ? [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) != ((X512 @ X514 @ X513)))) & (! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513))) | (hoasinduction_lem3v2_f != $true))) & (((induction2lem = $true) | ($true != sP2)) & (($true = sP2) | (induction2lem != $true))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((shinj = $true) | ? [X523 : term,X524 : term] : ((X523 != X524) & (((sub @ X523 @ sh)) = ((sub @ X524 @ sh))))) & (! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh)))) | (shinj != $true))) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & (((pushprop_lem1v2 = $true) | ? [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) != $true) & ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) & (((X525 @ X527)) = $true))) & (! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true)) | (pushprop_lem1v2 != $true))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(nnf_transformation,[],[f124])).
% 8.63/1.68 thf(f463,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) | (($true != sP108) & ($true != sP109) & ! [X10 : term] : (((sub @ X10 @ id)) = X10) & ($true != sP110) & ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))))) & (($true = sP108) | ($true = sP109) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ($true = sP110) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | (hoasinduction_lthm_3 != $true)) & ((axvarid = $true) | ? [X39 : term] : (((sub @ X39 @ id)) != X39)) & (! [X39 : term] : (((sub @ X39 @ id)) = X39) | (axvarid != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP99) & ! [X40 : term] : (((sub @ X40 @ id)) = X40))) & (($true = sP99) | ? [X40 : term] : (((sub @ X40 @ id)) != X40) | (hoasinduction_lem3v2_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X59 : (term > $o),X60 : term,X61 : subst] : ! [X62 : (term > $o)] : ? [X63 : term] : (((X62 @ X63)) != ((X59 @ (sub @ X63 @ (push @ X60 @ X61)))))) & (! [X59 : (term > $o),X60 : term,X61 : subst] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X59 @ (sub @ X63 @ (push @ X60 @ X61))))) | (pushprop_lem0_lthm != $true)) & ((termmset = $true) | ? [X64 : term] : (((sub @ X64 @ id)) != X64)) & (! [X64 : term] : (((sub @ X64 @ id)) = X64) | (termmset != $true)) & ((axshiftcons = $true) | ? [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) != X66)) & (! [X65 : term,X66 : subst] : (((comp @ sh @ (push @ X65 @ X66))) = X66) | (axshiftcons != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP95)) & (($true = sP95) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1_lthm = $true) | (? [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) != $true) & (((X89 @ X91)) = $true)) & ! [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) = X88) & ! [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) = X85))) & (! [X89 : (term > $o),X90 : (term > $o),X91 : term,X92 : subst,X93 : term] : ((((X90 @ (sub @ X91 @ (push @ X93 @ X92)))) = $true) | (((X89 @ X91)) != $true)) | ? [X87 : term,X88 : subst] : (((comp @ sh @ (push @ X87 @ X88))) != X88) | ? [X85 : term,X86 : subst] : (((sub @ one @ (push @ X85 @ X86))) != X85) | (pushprop_lem1_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) | ($true != sP91)) & (($true = sP91) | (induction2 != $true)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) | ? [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) = ((ap @ (sub @ X102 @ id) @ X103))) & ! [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) = ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106)))))) & (! [X101 : (subst > term > term),X102 : term,X103 : term] : ((((lam @ (X101 @ sh @ one))) != ((ap @ (sub @ X102 @ id) @ X103))) | ? [X104 : subst,X105 : term,X106 : subst] : (((sub @ (X101 @ X104 @ X105) @ X106)) != ((X101 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))))) | (hoaslamnotap != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) != $true) & ($true != ((sP87 @ X107))) & ($true != ((sP88 @ X107))))) & (! [X107 : (subst > term > subst > $o),X108 : term] : ((((X107 @ id @ X108 @ id)) = $true) | ($true = ((sP87 @ X107))) | ($true = ((sP88 @ X107)))) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP86)) & (($true = sP86) | (hoasinduction_lem3a != $true)) & (lamnotvar = $true) & ((substmonoid = $true) | ? [X124 : subst] : (((comp @ X124 @ id)) != X124) | ? [X125 : subst] : (((comp @ id @ X125)) != X125)) & ((! [X124 : subst] : (((comp @ X124 @ id)) = X124) & ! [X125 : subst] : (((comp @ id @ X125)) = X125)) | (substmonoid != $true)) & ((hoasinduction_lem3b = $true) | ? [X126 : term] : ! [X127 : (subst > term > term)] : (((X127 @ sh @ one)) != ((sub @ X126 @ (push @ one @ sh))))) & (! [X126 : term] : ? [X127 : (subst > term > term)] : (((X127 @ sh @ one)) = ((sub @ X126 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) | ($true != sP84)) & (($true = sP84) | (substmonoid_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X132 : (subst > term > subst > $o)] : ! [X133 : (term > $o)] : ? [X134 : term] : (((X133 @ X134)) != ((X132 @ id @ X134 @ id)))) & (! [X132 : (subst > term > subst > $o)] : ? [X133 : (term > $o)] : ! [X134 : term] : (((X133 @ X134)) = ((X132 @ id @ X134 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP82) & ($true != sP83) & ! [X135 : term] : (((sub @ X135 @ id)) = X135))) & (($true = sP82) | ($true = sP83) | ? [X135 : term] : (((sub @ X135 @ id)) != X135) | (induction2_lthm != $true)) & (hoaslaminj_gthm = $true) & ((axidl = $true) | ? [X151 : subst] : (((comp @ id @ X151)) != X151)) & (! [X151 : subst] : (((comp @ id @ X151)) = X151) | (axidl != $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP77) & ! [X156 : term] : (((sub @ X156 @ id)) = X156) & ! [X152 : term] : ? [X153 : (subst > term > term)] : ! [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) = ((X153 @ X155 @ X154))))) & (($true = sP77) | ? [X156 : term] : (((sub @ X156 @ id)) != X156) | ? [X152 : term] : ! [X153 : (subst > term > term)] : ? [X154 : term,X155 : subst] : (((sub @ X152 @ (push @ X154 @ X155))) != ((X153 @ X155 @ X154))) | (hoasinduction_lem3v2a_lthm != $true)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) | ? [X167 : (term > $o),X168 : term,X169 : subst] : ! [X170 : (term > $o)] : ? [X171 : term] : (((X170 @ X171)) != ((X167 @ (sub @ X171 @ (push @ X168 @ X169)))))) & (! [X167 : (term > $o),X168 : term,X169 : subst] : ? [X170 : (term > $o)] : ! [X171 : term] : (((X170 @ X171)) = ((X167 @ (sub @ X171 @ (push @ X168 @ X169))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP74) & ($true != sP75) & ! [X172 : term] : (((sub @ X172 @ id)) = X172))) & (($true = sP74) | ($true = sP75) | ? [X172 : term] : (((sub @ X172 @ id)) != X172) | (hoasinduction_lem3_lthm != $true)) & ((laminj = $true) | ? [X197 : term,X198 : term] : ((X197 != X198) & (((lam @ X197)) = ((lam @ X198))))) & (! [X197 : term,X198 : term] : ((X197 = X198) | (((lam @ X197)) != ((lam @ X198)))) | (laminj != $true)) & ((pushprop_lem1 = $true) | ? [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) != $true) & (((X199 @ X201)) = $true))) & (! [X199 : (term > $o),X200 : (term > $o),X201 : term,X202 : subst,X203 : term] : ((((X200 @ (sub @ X201 @ (push @ X203 @ X202)))) = $true) | (((X199 @ X201)) != $true)) | (pushprop_lem1 != $true)) & ((axidr = $true) | ? [X204 : subst] : (((comp @ X204 @ id)) != X204)) & (! [X204 : subst] : (((comp @ X204 @ id)) = X204) | (axidr != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) | ? [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) != X205)) & (! [X205 : subst] : (((push @ (sub @ one @ X205) @ (comp @ sh @ X205))) = X205) | (axscons != $true)) & ((axvarcons = $true) | ? [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) != X206)) & (! [X206 : term,X207 : subst] : (((sub @ one @ (push @ X206 @ X207))) = X206) | (axvarcons != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP69)) & (($true = sP69) | (hoaslaminj_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP67)) & (($true = sP67) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP65)) & (($true = sP65) | (hoasinduction_lem3v2a != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP63)) & (($true = sP63) | (hoasapinj2_lthm != $true)) & ((apinj1 = $true) | ? [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 != X252) & (((ap @ X251 @ X253)) = ((ap @ X252 @ X254))))) & (! [X251 : term,X252 : term,X253 : term,X254 : term] : ((X251 = X252) | (((ap @ X251 @ X253)) != ((ap @ X252 @ X254)))) | (apinj1 != $true)) & ((apinj2 = $true) | ? [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 != X258) & (((ap @ X255 @ X257)) = ((ap @ X256 @ X258))))) & (! [X255 : term,X256 : term,X257 : term,X258 : term] : ((X257 = X258) | (((ap @ X255 @ X257)) != ((ap @ X256 @ X258)))) | (apinj2 != $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP61)) & (($true = sP61) | (hoasinduction_lem2v2 != $true)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP55) & ($true != sP56) & ! [X282 : term] : (((sub @ X282 @ id)) = X282))) & (($true = sP55) | ($true = sP56) | ? [X282 : term] : (((sub @ X282 @ id)) != X282) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ($true != sP52)) & (($true = sP52) | (induction != $true)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X305 : term] : ! [X306 : (subst > term > term)] : (((X306 @ sh @ one)) != ((sub @ X305 @ (push @ one @ sh))))) & (! [X305 : term] : ? [X306 : (subst > term > term)] : (((X306 @ sh @ one)) = ((sub @ X305 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction != $true)) & ((hoasinduction_lem0 = $true) | ? [X325 : (subst > term > subst > $o)] : ! [X326 : (term > $o)] : ? [X327 : term] : (((X326 @ X327)) != ((X325 @ id @ X327 @ id)))) & (! [X325 : (subst > term > subst > $o)] : ? [X326 : (term > $o)] : ! [X327 : term] : (((X326 @ X327)) = ((X325 @ id @ X327 @ id))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) != $true) & ! [X334 : term] : (((X331 @ X334)) = ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) & (((X330 @ X332)) = $true)) & ! [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) = X328))) & (! [X330 : (term > $o),X331 : (term > $o),X332 : term,X333 : subst] : ((((X331 @ one)) = $true) | ? [X334 : term] : (((X331 @ X334)) != ((X330 @ (sub @ X334 @ (push @ X332 @ X333))))) | (((X330 @ X332)) != $true)) | ? [X328 : term,X329 : subst] : (((sub @ one @ (push @ X328 @ X329))) != X328) | (pushprop_lem1v2_lthm != $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) | (? [X336 : term] : (((sub @ X336 @ id)) != X336) & ! [X335 : term] : (((sub @ X335 @ id)) = X335))) & (! [X336 : term] : (((sub @ X336 @ id)) = X336) | ? [X335 : term] : (((sub @ X335 @ id)) != X335) | (termmset_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3aaa != $true)) & ((hoaslaminj = $true) | ? [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) != ((X387 @ X388 @ X389))) & (((lam @ (X386 @ sh @ one))) = ((lam @ (X387 @ sh @ one)))) & ! [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) = ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) & ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) = ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395)))))) & (! [X386 : (subst > term > term),X387 : (subst > term > term),X388 : subst,X389 : term] : ((((X386 @ X388 @ X389)) = ((X387 @ X388 @ X389))) | (((lam @ (X386 @ sh @ one))) != ((lam @ (X387 @ sh @ one)))) | ? [X390 : subst,X391 : term,X392 : subst] : (((sub @ (X387 @ X390 @ X391) @ X392)) != ((X387 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392)))) | ? [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X386 @ X393 @ X394) @ X395)) != ((X386 @ (comp @ X393 @ X395) @ (sub @ X394 @ X395))))) | (hoaslaminj != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP31) & ($true != sP32) & ! [X406 : term] : (((sub @ X406 @ id)) = X406) & ($true != sP33) & ! [X396 : (subst > term > subst > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X397 @ X398)) = ((X396 @ id @ X398 @ id))))) & (($true = sP31) | ($true = sP32) | ? [X406 : term] : (((sub @ X406 @ id)) != X406) | ($true = sP33) | ? [X396 : (subst > term > subst > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X397 @ X398)) != ((X396 @ id @ X398 @ id))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP23) & ($true != sP22) & ($true != sP24))) & (($true = sP21) | ($true = sP23) | ($true = sP22) | ($true = sP24) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X480 : term] : ! [X481 : (subst > term > term)] : ? [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) != ((X481 @ X483 @ X482)))) & (! [X480 : term] : ? [X481 : (subst > term > term)] : ! [X482 : term,X483 : subst] : (((sub @ X480 @ (push @ X482 @ X483))) = ((X481 @ X483 @ X482))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) | (($true != sP7) & ($true != sP8) & ! [X488 : subst] : (((comp @ X488 @ id)) = X488) & ! [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) = X487) & ! [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) = X484))) & (($true = sP7) | ($true = sP8) | ? [X488 : subst] : (((comp @ X488 @ id)) != X488) | ? [X486 : term,X487 : subst] : (((comp @ sh @ (push @ X486 @ X487))) != X487) | ? [X484 : term,X485 : subst] : (((sub @ one @ (push @ X484 @ X485))) != X484) | (induction2lem_lthm != $true)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) | ? [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 != X504) & (((ap @ (sub @ X503 @ id) @ X505)) = ((ap @ (sub @ X504 @ id) @ X506))))) & (! [X503 : term,X504 : term,X505 : term,X506 : term] : ((X503 = X504) | (((ap @ (sub @ X503 @ id) @ X505)) != ((ap @ (sub @ X504 @ id) @ X506)))) | (hoasapinj1 != $true)) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) | ? [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 != X510) & (((ap @ (sub @ X507 @ id) @ X509)) = ((ap @ (sub @ X508 @ id) @ X510))))) & (! [X507 : term,X508 : term,X509 : term,X510 : term] : ((X509 = X510) | (((ap @ (sub @ X507 @ id) @ X509)) != ((ap @ (sub @ X508 @ id) @ X510)))) | (hoasapinj2 != $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X511 : term] : ! [X512 : (subst > term > term)] : ? [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) != ((X512 @ X514 @ X513)))) & (! [X511 : term] : ? [X512 : (subst > term > term)] : ! [X513 : term,X514 : subst] : (((sub @ X511 @ (push @ X513 @ X514))) = ((X512 @ X514 @ X513))) | (hoasinduction_lem3v2_f != $true)) & ((induction2lem = $true) | ($true != sP2)) & (($true = sP2) | (induction2lem != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) | ? [X523 : term,X524 : term] : ((X523 != X524) & (((sub @ X523 @ sh)) = ((sub @ X524 @ sh))))) & (! [X523 : term,X524 : term] : ((X523 = X524) | (((sub @ X523 @ sh)) != ((sub @ X524 @ sh)))) | (shinj != $true)) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) != $true) & ! [X529 : term] : (((X526 @ X529)) = ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) & (((X525 @ X527)) = $true))) & (! [X525 : (term > $o),X526 : (term > $o),X527 : term,X528 : subst] : ((((X526 @ one)) = $true) | ? [X529 : term] : (((X526 @ X529)) != ((X525 @ (sub @ X529 @ (push @ X527 @ X528))))) | (((X525 @ X527)) != $true)) | (pushprop_lem1v2 != $true)) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X530 : d_subst,X531 : d_subst] : ((X530 = X531) | (((d2subst @ X530)) != ((d2subst @ X531)))) & ! [X532 : d_subst] : (d_id = X532) & ! [X533 : subst] : ? [X534 : d_subst] : (((d2subst @ X534)) = X533) & ! [X535 : d_term,X536 : d_term] : ((X535 = X536) | (((d2term @ X535)) != ((d2term @ X536)))) & ! [X537 : d_term] : (d_one = X537) & ! [X538 : term] : ? [X539 : d_term] : (((d2term @ X539)) = X538)),
% 8.63/1.68 inference(flattening,[],[f462])).
% 8.63/1.68 thf(f464,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) | (($true != sP108) & ($true != sP109) & ! [X0 : term] : (((sub @ X0 @ id)) = X0) & ($true != sP110) & ! [X1 : (subst > term > subst > $o)] : ? [X2 : (term > $o)] : ! [X3 : term] : (((X2 @ X3)) = ((X1 @ id @ X3 @ id))))) & (($true = sP108) | ($true = sP109) | ? [X4 : term] : (((sub @ X4 @ id)) != X4) | ($true = sP110) | ? [X5 : (subst > term > subst > $o)] : ! [X6 : (term > $o)] : ? [X7 : term] : (((X6 @ X7)) != ((X5 @ id @ X7 @ id))) | (hoasinduction_lthm_3 != $true)) & ((axvarid = $true) | ? [X8 : term] : (((sub @ X8 @ id)) != X8)) & (! [X9 : term] : (((sub @ X9 @ id)) = X9) | (axvarid != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP99) & ! [X10 : term] : (((sub @ X10 @ id)) = X10))) & (($true = sP99) | ? [X11 : term] : (((sub @ X11 @ id)) != X11) | (hoasinduction_lem3v2_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X12 : (term > $o),X13 : term,X14 : subst] : ! [X15 : (term > $o)] : ? [X16 : term] : (((X15 @ X16)) != ((X12 @ (sub @ X16 @ (push @ X13 @ X14)))))) & (! [X17 : (term > $o),X18 : term,X19 : subst] : ? [X20 : (term > $o)] : ! [X21 : term] : (((X20 @ X21)) = ((X17 @ (sub @ X21 @ (push @ X18 @ X19))))) | (pushprop_lem0_lthm != $true)) & ((termmset = $true) | ? [X22 : term] : (((sub @ X22 @ id)) != X22)) & (! [X23 : term] : (((sub @ X23 @ id)) = X23) | (termmset != $true)) & ((axshiftcons = $true) | ? [X24 : term,X25 : subst] : (((comp @ sh @ (push @ X24 @ X25))) != X25)) & (! [X26 : term,X27 : subst] : (((comp @ sh @ (push @ X26 @ X27))) = X27) | (axshiftcons != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP95)) & (($true = sP95) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1_lthm = $true) | (? [X28 : (term > $o),X29 : (term > $o),X30 : term,X31 : subst,X32 : term] : (($true != ((X29 @ (sub @ X30 @ (push @ X32 @ X31))))) & ($true = ((X28 @ X30)))) & ! [X33 : term,X34 : subst] : (((comp @ sh @ (push @ X33 @ X34))) = X34) & ! [X35 : term,X36 : subst] : (((sub @ one @ (push @ X35 @ X36))) = X35))) & (! [X37 : (term > $o),X38 : (term > $o),X39 : term,X40 : subst,X41 : term] : (($true = ((X38 @ (sub @ X39 @ (push @ X41 @ X40))))) | ($true != ((X37 @ X39)))) | ? [X42 : term,X43 : subst] : (((comp @ sh @ (push @ X42 @ X43))) != X43) | ? [X44 : term,X45 : subst] : (((sub @ one @ (push @ X44 @ X45))) != X44) | (pushprop_lem1_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) | ($true != sP91)) & (($true = sP91) | (induction2 != $true)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) | ? [X46 : (subst > term > term),X47 : term,X48 : term] : ((((lam @ (X46 @ sh @ one))) = ((ap @ (sub @ X47 @ id) @ X48))) & ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ (X46 @ X49 @ X50) @ X51)) = ((X46 @ (comp @ X49 @ X51) @ (sub @ X50 @ X51)))))) & (! [X52 : (subst > term > term),X53 : term,X54 : term] : ((((lam @ (X52 @ sh @ one))) != ((ap @ (sub @ X53 @ id) @ X54))) | ? [X55 : subst,X56 : term,X57 : subst] : (((sub @ (X52 @ X55 @ X56) @ X57)) != ((X52 @ (comp @ X55 @ X57) @ (sub @ X56 @ X57))))) | (hoaslamnotap != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X58 : (subst > term > subst > $o),X59 : term] : (($true != ((X58 @ id @ X59 @ id))) & ($true != ((sP87 @ X58))) & ($true != ((sP88 @ X58))))) & (! [X60 : (subst > term > subst > $o),X61 : term] : (($true = ((X60 @ id @ X61 @ id))) | ($true = ((sP87 @ X60))) | ($true = ((sP88 @ X60)))) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP86)) & (($true = sP86) | (hoasinduction_lem3a != $true)) & (lamnotvar = $true) & ((substmonoid = $true) | ? [X62 : subst] : (((comp @ X62 @ id)) != X62) | ? [X63 : subst] : (((comp @ id @ X63)) != X63)) & ((! [X64 : subst] : (((comp @ X64 @ id)) = X64) & ! [X65 : subst] : (((comp @ id @ X65)) = X65)) | (substmonoid != $true)) & ((hoasinduction_lem3b = $true) | ? [X66 : term] : ! [X67 : (subst > term > term)] : (((X67 @ sh @ one)) != ((sub @ X66 @ (push @ one @ sh))))) & (! [X68 : term] : ? [X69 : (subst > term > term)] : (((X69 @ sh @ one)) = ((sub @ X68 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) | ($true != sP84)) & (($true = sP84) | (substmonoid_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X70 : (subst > term > subst > $o)] : ! [X71 : (term > $o)] : ? [X72 : term] : (((X71 @ X72)) != ((X70 @ id @ X72 @ id)))) & (! [X73 : (subst > term > subst > $o)] : ? [X74 : (term > $o)] : ! [X75 : term] : (((X74 @ X75)) = ((X73 @ id @ X75 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP82) & ($true != sP83) & ! [X76 : term] : (((sub @ X76 @ id)) = X76))) & (($true = sP82) | ($true = sP83) | ? [X77 : term] : (((sub @ X77 @ id)) != X77) | (induction2_lthm != $true)) & (hoaslaminj_gthm = $true) & ((axidl = $true) | ? [X78 : subst] : (((comp @ id @ X78)) != X78)) & (! [X79 : subst] : (((comp @ id @ X79)) = X79) | (axidl != $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP77) & ! [X80 : term] : (((sub @ X80 @ id)) = X80) & ! [X81 : term] : ? [X82 : (subst > term > term)] : ! [X83 : term,X84 : subst] : (((sub @ X81 @ (push @ X83 @ X84))) = ((X82 @ X84 @ X83))))) & (($true = sP77) | ? [X85 : term] : (((sub @ X85 @ id)) != X85) | ? [X86 : term] : ! [X87 : (subst > term > term)] : ? [X88 : term,X89 : subst] : (((sub @ X86 @ (push @ X88 @ X89))) != ((X87 @ X89 @ X88))) | (hoasinduction_lem3v2a_lthm != $true)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) | ? [X90 : (term > $o),X91 : term,X92 : subst] : ! [X93 : (term > $o)] : ? [X94 : term] : (((X93 @ X94)) != ((X90 @ (sub @ X94 @ (push @ X91 @ X92)))))) & (! [X95 : (term > $o),X96 : term,X97 : subst] : ? [X98 : (term > $o)] : ! [X99 : term] : (((X98 @ X99)) = ((X95 @ (sub @ X99 @ (push @ X96 @ X97))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP74) & ($true != sP75) & ! [X100 : term] : (((sub @ X100 @ id)) = X100))) & (($true = sP74) | ($true = sP75) | ? [X101 : term] : (((sub @ X101 @ id)) != X101) | (hoasinduction_lem3_lthm != $true)) & ((laminj = $true) | ? [X102 : term,X103 : term] : ((X102 != X103) & (((lam @ X102)) = ((lam @ X103))))) & (! [X104 : term,X105 : term] : ((X104 = X105) | (((lam @ X104)) != ((lam @ X105)))) | (laminj != $true)) & ((pushprop_lem1 = $true) | ? [X106 : (term > $o),X107 : (term > $o),X108 : term,X109 : subst,X110 : term] : (($true != ((X107 @ (sub @ X108 @ (push @ X110 @ X109))))) & ($true = ((X106 @ X108))))) & (! [X111 : (term > $o),X112 : (term > $o),X113 : term,X114 : subst,X115 : term] : (($true = ((X112 @ (sub @ X113 @ (push @ X115 @ X114))))) | ($true != ((X111 @ X113)))) | (pushprop_lem1 != $true)) & ((axidr = $true) | ? [X116 : subst] : (((comp @ X116 @ id)) != X116)) & (! [X117 : subst] : (((comp @ X117 @ id)) = X117) | (axidr != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) | ? [X118 : subst] : (((push @ (sub @ one @ X118) @ (comp @ sh @ X118))) != X118)) & (! [X119 : subst] : (((push @ (sub @ one @ X119) @ (comp @ sh @ X119))) = X119) | (axscons != $true)) & ((axvarcons = $true) | ? [X120 : term,X121 : subst] : (((sub @ one @ (push @ X120 @ X121))) != X120)) & (! [X122 : term,X123 : subst] : (((sub @ one @ (push @ X122 @ X123))) = X122) | (axvarcons != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP69)) & (($true = sP69) | (hoaslaminj_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP67)) & (($true = sP67) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP65)) & (($true = sP65) | (hoasinduction_lem3v2a != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP63)) & (($true = sP63) | (hoasapinj2_lthm != $true)) & ((apinj1 = $true) | ? [X124 : term,X125 : term,X126 : term,X127 : term] : ((X124 != X125) & (((ap @ X124 @ X126)) = ((ap @ X125 @ X127))))) & (! [X128 : term,X129 : term,X130 : term,X131 : term] : ((X128 = X129) | (((ap @ X128 @ X130)) != ((ap @ X129 @ X131)))) | (apinj1 != $true)) & ((apinj2 = $true) | ? [X132 : term,X133 : term,X134 : term,X135 : term] : ((X134 != X135) & (((ap @ X132 @ X134)) = ((ap @ X133 @ X135))))) & (! [X136 : term,X137 : term,X138 : term,X139 : term] : ((X138 = X139) | (((ap @ X136 @ X138)) != ((ap @ X137 @ X139)))) | (apinj2 != $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP61)) & (($true = sP61) | (hoasinduction_lem2v2 != $true)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP55) & ($true != sP56) & ! [X140 : term] : (((sub @ X140 @ id)) = X140))) & (($true = sP55) | ($true = sP56) | ? [X141 : term] : (((sub @ X141 @ id)) != X141) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ($true != sP52)) & (($true = sP52) | (induction != $true)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X142 : term] : ! [X143 : (subst > term > term)] : (((X143 @ sh @ one)) != ((sub @ X142 @ (push @ one @ sh))))) & (! [X144 : term] : ? [X145 : (subst > term > term)] : (((X145 @ sh @ one)) = ((sub @ X144 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction != $true)) & ((hoasinduction_lem0 = $true) | ? [X146 : (subst > term > subst > $o)] : ! [X147 : (term > $o)] : ? [X148 : term] : (((X147 @ X148)) != ((X146 @ id @ X148 @ id)))) & (! [X149 : (subst > term > subst > $o)] : ? [X150 : (term > $o)] : ! [X151 : term] : (((X150 @ X151)) = ((X149 @ id @ X151 @ id))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) | (? [X152 : (term > $o),X153 : (term > $o),X154 : term,X155 : subst] : (($true != ((X153 @ one))) & ! [X156 : term] : (((X153 @ X156)) = ((X152 @ (sub @ X156 @ (push @ X154 @ X155))))) & ($true = ((X152 @ X154)))) & ! [X157 : term,X158 : subst] : (((sub @ one @ (push @ X157 @ X158))) = X157))) & (! [X159 : (term > $o),X160 : (term > $o),X161 : term,X162 : subst] : (($true = ((X160 @ one))) | ? [X163 : term] : (((X160 @ X163)) != ((X159 @ (sub @ X163 @ (push @ X161 @ X162))))) | ($true != ((X159 @ X161)))) | ? [X164 : term,X165 : subst] : (((sub @ one @ (push @ X164 @ X165))) != X164) | (pushprop_lem1v2_lthm != $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) | (? [X166 : term] : (((sub @ X166 @ id)) != X166) & ! [X167 : term] : (((sub @ X167 @ id)) = X167))) & (! [X168 : term] : (((sub @ X168 @ id)) = X168) | ? [X169 : term] : (((sub @ X169 @ id)) != X169) | (termmset_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3aaa != $true)) & ((hoaslaminj = $true) | ? [X170 : (subst > term > term),X171 : (subst > term > term),X172 : subst,X173 : term] : ((((X170 @ X172 @ X173)) != ((X171 @ X172 @ X173))) & (((lam @ (X170 @ sh @ one))) = ((lam @ (X171 @ sh @ one)))) & ! [X174 : subst,X175 : term,X176 : subst] : (((sub @ (X171 @ X174 @ X175) @ X176)) = ((X171 @ (comp @ X174 @ X176) @ (sub @ X175 @ X176)))) & ! [X177 : subst,X178 : term,X179 : subst] : (((sub @ (X170 @ X177 @ X178) @ X179)) = ((X170 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179)))))) & (! [X180 : (subst > term > term),X181 : (subst > term > term),X182 : subst,X183 : term] : ((((X180 @ X182 @ X183)) = ((X181 @ X182 @ X183))) | (((lam @ (X180 @ sh @ one))) != ((lam @ (X181 @ sh @ one)))) | ? [X184 : subst,X185 : term,X186 : subst] : (((sub @ (X181 @ X184 @ X185) @ X186)) != ((X181 @ (comp @ X184 @ X186) @ (sub @ X185 @ X186)))) | ? [X187 : subst,X188 : term,X189 : subst] : (((sub @ (X180 @ X187 @ X188) @ X189)) != ((X180 @ (comp @ X187 @ X189) @ (sub @ X188 @ X189))))) | (hoaslaminj != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP31) & ($true != sP32) & ! [X190 : term] : (((sub @ X190 @ id)) = X190) & ($true != sP33) & ! [X191 : (subst > term > subst > $o)] : ? [X192 : (term > $o)] : ! [X193 : term] : (((X192 @ X193)) = ((X191 @ id @ X193 @ id))))) & (($true = sP31) | ($true = sP32) | ? [X194 : term] : (((sub @ X194 @ id)) != X194) | ($true = sP33) | ? [X195 : (subst > term > subst > $o)] : ! [X196 : (term > $o)] : ? [X197 : term] : (((X196 @ X197)) != ((X195 @ id @ X197 @ id))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP23) & ($true != sP22) & ($true != sP24))) & (($true = sP21) | ($true = sP23) | ($true = sP22) | ($true = sP24) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X198 : term] : ! [X199 : (subst > term > term)] : ? [X200 : term,X201 : subst] : (((sub @ X198 @ (push @ X200 @ X201))) != ((X199 @ X201 @ X200)))) & (! [X202 : term] : ? [X203 : (subst > term > term)] : ! [X204 : term,X205 : subst] : (((sub @ X202 @ (push @ X204 @ X205))) = ((X203 @ X205 @ X204))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) | (($true != sP7) & ($true != sP8) & ! [X206 : subst] : (((comp @ X206 @ id)) = X206) & ! [X207 : term,X208 : subst] : (((comp @ sh @ (push @ X207 @ X208))) = X208) & ! [X209 : term,X210 : subst] : (((sub @ one @ (push @ X209 @ X210))) = X209))) & (($true = sP7) | ($true = sP8) | ? [X211 : subst] : (((comp @ X211 @ id)) != X211) | ? [X212 : term,X213 : subst] : (((comp @ sh @ (push @ X212 @ X213))) != X213) | ? [X214 : term,X215 : subst] : (((sub @ one @ (push @ X214 @ X215))) != X214) | (induction2lem_lthm != $true)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) | ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 != X217) & (((ap @ (sub @ X216 @ id) @ X218)) = ((ap @ (sub @ X217 @ id) @ X219))))) & (! [X220 : term,X221 : term,X222 : term,X223 : term] : ((X220 = X221) | (((ap @ (sub @ X220 @ id) @ X222)) != ((ap @ (sub @ X221 @ id) @ X223)))) | (hoasapinj1 != $true)) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) | ? [X224 : term,X225 : term,X226 : term,X227 : term] : ((X226 != X227) & (((ap @ (sub @ X224 @ id) @ X226)) = ((ap @ (sub @ X225 @ id) @ X227))))) & (! [X228 : term,X229 : term,X230 : term,X231 : term] : ((X230 = X231) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X228 @ id) @ X230)))) | (hoasapinj2 != $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X232 : term] : ! [X233 : (subst > term > term)] : ? [X234 : term,X235 : subst] : (((sub @ X232 @ (push @ X234 @ X235))) != ((X233 @ X235 @ X234)))) & (! [X236 : term] : ? [X237 : (subst > term > term)] : ! [X238 : term,X239 : subst] : (((sub @ X236 @ (push @ X238 @ X239))) = ((X237 @ X239 @ X238))) | (hoasinduction_lem3v2_f != $true)) & ((induction2lem = $true) | ($true != sP2)) & (($true = sP2) | (induction2lem != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) | ? [X240 : term,X241 : term] : ((X240 != X241) & (((sub @ X240 @ sh)) = ((sub @ X241 @ sh))))) & (! [X242 : term,X243 : term] : ((X242 = X243) | (((sub @ X242 @ sh)) != ((sub @ X243 @ sh)))) | (shinj != $true)) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) | ? [X244 : (term > $o),X245 : (term > $o),X246 : term,X247 : subst] : (($true != ((X245 @ one))) & ! [X248 : term] : (((X245 @ X248)) = ((X244 @ (sub @ X248 @ (push @ X246 @ X247))))) & ($true = ((X244 @ X246))))) & (! [X249 : (term > $o),X250 : (term > $o),X251 : term,X252 : subst] : (($true = ((X250 @ one))) | ? [X253 : term] : (((X250 @ X253)) != ((X249 @ (sub @ X253 @ (push @ X251 @ X252))))) | ($true != ((X249 @ X251)))) | (pushprop_lem1v2 != $true)) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X254 : d_subst,X255 : d_subst] : ((X254 = X255) | (((d2subst @ X254)) != ((d2subst @ X255)))) & ! [X256 : d_subst] : (d_id = X256) & ! [X257 : subst] : ? [X258 : d_subst] : (((d2subst @ X258)) = X257) & ! [X259 : d_term,X260 : d_term] : ((X259 = X260) | (((d2term @ X259)) != ((d2term @ X260)))) & ! [X261 : d_term] : (d_one = X261) & ! [X262 : term] : ? [X263 : d_term] : (((d2term @ X263)) = X262)),
% 8.63/1.68 inference(rectify,[],[f463])).
% 8.63/1.68 thf(f465,plain,(
% 8.63/1.68 ((hoasinduction_lthm_3 = $true) | (($true != sP108) & ($true != sP109) & ! [X0 : term] : (((sub @ X0 @ id)) = X0) & ($true != sP110) & ! [X1 : (subst > term > subst > $o)] : ! [X3 : term] : (((X1 @ id @ X3 @ id)) = ((sK514 @ X1 @ X3))))) & (($true = sP108) | ($true = sP109) | (sK515 != ((sub @ sK515 @ id))) | ($true = sP110) | ! [X6 : (term > $o)] : (((X6 @ (sK517 @ X6))) != ((sK516 @ id @ (sK517 @ X6) @ id))) | (hoasinduction_lthm_3 != $true)) & ((axvarid = $true) | (sK518 != ((sub @ sK518 @ id)))) & (! [X9 : term] : (((sub @ X9 @ id)) = X9) | (axvarid != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP99) & ! [X10 : term] : (((sub @ X10 @ id)) = X10))) & (($true = sP99) | (sK519 != ((sub @ sK519 @ id))) | (hoasinduction_lem3v2_lthm != $true)) & (hoasapnotvar_lthm = $true) & ((pushprop_lem0_lthm = $true) | ! [X15 : (term > $o)] : (((X15 @ (sK523 @ X15))) != ((sK520 @ (sub @ (sK523 @ X15) @ (push @ sK521 @ sK522)))))) & (! [X17 : (term > $o),X18 : term,X19 : subst] : ! [X21 : term] : (((X17 @ (sub @ X21 @ (push @ X18 @ X19)))) = ((sK524 @ X19 @ X18 @ X17 @ X21))) | (pushprop_lem0_lthm != $true)) & ((termmset = $true) | (sK525 != ((sub @ sK525 @ id)))) & (! [X23 : term] : (((sub @ X23 @ id)) = X23) | (termmset != $true)) & ((axshiftcons = $true) | (sK527 != ((comp @ sh @ (push @ sK526 @ sK527))))) & (! [X26 : term,X27 : subst] : (((comp @ sh @ (push @ X26 @ X27))) = X27) | (axshiftcons != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP95)) & (($true = sP95) | (hoasinduction_lem3v2 != $true)) & ((pushprop_lem1_lthm = $true) | ((($true != ((sK529 @ (sub @ sK530 @ (push @ sK532 @ sK531))))) & ($true = ((sK528 @ sK530)))) & ! [X33 : term,X34 : subst] : (((comp @ sh @ (push @ X33 @ X34))) = X34) & ! [X35 : term,X36 : subst] : (((sub @ one @ (push @ X35 @ X36))) = X35))) & (! [X37 : (term > $o),X38 : (term > $o),X39 : term,X40 : subst,X41 : term] : (($true = ((X38 @ (sub @ X39 @ (push @ X41 @ X40))))) | ($true != ((X37 @ X39)))) | (sK534 != ((comp @ sh @ (push @ sK533 @ sK534)))) | (sK535 != ((sub @ one @ (push @ sK535 @ sK536)))) | (pushprop_lem1_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2 = $true) | ($true != sP91)) & (($true = sP91) | (induction2 != $true)) & (ulamvarsh = $true) & (substmonoid_gthm = $true) & ((hoaslamnotap = $true) | ((((lam @ (sK537 @ sh @ one))) = ((ap @ (sub @ sK538 @ id) @ sK539))) & ! [X49 : subst,X50 : term,X51 : subst] : (((sub @ (sK537 @ X49 @ X50) @ X51)) = ((sK537 @ (comp @ X49 @ X51) @ (sub @ X50 @ X51)))))) & (! [X52 : (subst > term > term),X53 : term,X54 : term] : ((((lam @ (X52 @ sh @ one))) != ((ap @ (sub @ X53 @ id) @ X54))) | (((sub @ (X52 @ (sK540 @ X52) @ (sK541 @ X52)) @ (sK542 @ X52))) != ((X52 @ (comp @ (sK540 @ X52) @ (sK542 @ X52)) @ (sub @ (sK541 @ X52) @ (sK542 @ X52)))))) | (hoaslamnotap != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) | (($true != ((sK543 @ id @ sK544 @ id))) & ($true != ((sP87 @ sK543))) & ($true != ((sP88 @ sK543))))) & (! [X60 : (subst > term > subst > $o),X61 : term] : (($true = ((X60 @ id @ X61 @ id))) | ($true = ((sP87 @ X60))) | ($true = ((sP88 @ X60)))) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP86)) & (($true = sP86) | (hoasinduction_lem3a != $true)) & (lamnotvar = $true) & ((substmonoid = $true) | (sK545 != ((comp @ sK545 @ id))) | (sK546 != ((comp @ id @ sK546)))) & ((! [X64 : subst] : (((comp @ X64 @ id)) = X64) & ! [X65 : subst] : (((comp @ id @ X65)) = X65)) | (substmonoid != $true)) & ((hoasinduction_lem3b = $true) | ! [X67 : (subst > term > term)] : (((X67 @ sh @ one)) != ((sub @ sK547 @ (push @ one @ sh))))) & (! [X68 : term] : (((sub @ X68 @ (push @ one @ sh))) = ((sK548 @ X68 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop = $true) & ((substmonoid_lthm = $true) | ($true != sP84)) & (($true = sP84) | (substmonoid_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X71 : (term > $o)] : (((X71 @ (sK550 @ X71))) != ((sK549 @ id @ (sK550 @ X71) @ id)))) & (! [X73 : (subst > term > subst > $o)] : ! [X75 : term] : (((X73 @ id @ X75 @ id)) = ((sK551 @ X73 @ X75))) | (hoasinduction_lem0_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP82) & ($true != sP83) & ! [X76 : term] : (((sub @ X76 @ id)) = X76))) & (($true = sP82) | ($true = sP83) | (sK552 != ((sub @ sK552 @ id))) | (induction2_lthm != $true)) & (hoaslaminj_gthm = $true) & ((axidl = $true) | (sK553 != ((comp @ id @ sK553)))) & (! [X79 : subst] : (((comp @ id @ X79)) = X79) | (axidl != $true)) & (hoaslamnotvar = $true) & (hoasapinj1_gthm = $true) & (lamnotap != $true) & (hoasinduction_lem1_lthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP77) & ! [X80 : term] : (((sub @ X80 @ id)) = X80) & ! [X81 : term] : ! [X83 : term,X84 : subst] : (((sub @ X81 @ (push @ X83 @ X84))) = ((sK554 @ X81 @ X84 @ X83))))) & (($true = sP77) | (sK555 != ((sub @ sK555 @ id))) | ! [X87 : (subst > term > term)] : (((sub @ sK556 @ (push @ (sK557 @ X87) @ (sK558 @ X87)))) != ((X87 @ (sK558 @ X87) @ (sK557 @ X87)))) | (hoasinduction_lem3v2a_lthm != $true)) & (axabs = $true) & (pushprop_gthm = $true) & ((pushprop_lem0 = $true) | ! [X93 : (term > $o)] : (((X93 @ (sK562 @ X93))) != ((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))))) & (! [X95 : (term > $o),X96 : term,X97 : subst] : ! [X99 : term] : (((X95 @ (sub @ X99 @ (push @ X96 @ X97)))) = ((sK563 @ X97 @ X96 @ X95 @ X99))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP74) & ($true != sP75) & ! [X100 : term] : (((sub @ X100 @ id)) = X100))) & (($true = sP74) | ($true = sP75) | (sK564 != ((sub @ sK564 @ id))) | (hoasinduction_lem3_lthm != $true)) & ((laminj = $true) | ((sK565 != sK566) & (((lam @ sK565)) = ((lam @ sK566))))) & (! [X104 : term,X105 : term] : ((X104 = X105) | (((lam @ X104)) != ((lam @ X105)))) | (laminj != $true)) & ((pushprop_lem1 = $true) | (($true != ((sK568 @ (sub @ sK569 @ (push @ sK571 @ sK570))))) & ($true = ((sK567 @ sK569))))) & (! [X111 : (term > $o),X112 : (term > $o),X113 : term,X114 : subst,X115 : term] : (($true = ((X112 @ (sub @ X113 @ (push @ X115 @ X114))))) | ($true != ((X111 @ X113)))) | (pushprop_lem1 != $true)) & ((axidr = $true) | (sK572 != ((comp @ sK572 @ id)))) & (! [X117 : subst] : (((comp @ X117 @ id)) = X117) | (axidr != $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axscons = $true) | (sK573 != ((push @ (sub @ one @ sK573) @ (comp @ sh @ sK573))))) & (! [X119 : subst] : (((push @ (sub @ one @ X119) @ (comp @ sh @ X119))) = X119) | (axscons != $true)) & ((axvarcons = $true) | (sK574 != ((sub @ one @ (push @ sK574 @ sK575))))) & (! [X122 : term,X123 : subst] : (((sub @ one @ (push @ X122 @ X123))) = X122) | (axvarcons != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP69)) & (($true = sP69) | (hoaslaminj_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP67)) & (($true = sP67) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP65)) & (($true = sP65) | (hoasinduction_lem3v2a != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP63)) & (($true = sP63) | (hoasapinj2_lthm != $true)) & ((apinj1 = $true) | ((sK576 != sK577) & (((ap @ sK576 @ sK578)) = ((ap @ sK577 @ sK579))))) & (! [X128 : term,X129 : term,X130 : term,X131 : term] : ((X128 = X129) | (((ap @ X128 @ X130)) != ((ap @ X129 @ X131)))) | (apinj1 != $true)) & ((apinj2 = $true) | ((sK582 != sK583) & (((ap @ sK580 @ sK582)) = ((ap @ sK581 @ sK583))))) & (! [X136 : term,X137 : term,X138 : term,X139 : term] : ((X138 = X139) | (((ap @ X136 @ X138)) != ((ap @ X137 @ X139)))) | (apinj2 != $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP61)) & (($true = sP61) | (hoasinduction_lem2v2 != $true)) & (axassoc = $true) & (axclos = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2 = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & (termmset_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP55) & ($true != sP56) & ! [X140 : term] : (((sub @ X140 @ id)) = X140))) & (($true = sP55) | ($true = sP56) | (sK584 != ((sub @ sK584 @ id))) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ($true != sP52)) & (($true = sP52) | (induction != $true)) & (ulamvarind = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X143 : (subst > term > term)] : (((X143 @ sh @ one)) != ((sub @ sK585 @ (push @ one @ sh))))) & (! [X144 : term] : (((sub @ X144 @ (push @ one @ sh))) = ((sK586 @ X144 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_lthm = $true) & (axapp = $true) & (hoasinduction_gthm = $true) & ((hoasinduction = $true) | ($true != sP49)) & (($true = sP49) | (hoasinduction != $true)) & ((hoasinduction_lem0 = $true) | ! [X147 : (term > $o)] : (((X147 @ (sK588 @ X147))) != ((sK587 @ id @ (sK588 @ X147) @ id)))) & (! [X149 : (subst > term > subst > $o)] : ! [X151 : term] : (((X149 @ id @ X151 @ id)) = ((sK589 @ X149 @ X151))) | (hoasinduction_lem0 != $true)) & (hoasapnotvar = $true) & ((pushprop_lem1v2_lthm = $true) | ((($true != ((sK591 @ one))) & ! [X156 : term] : (((sK591 @ X156)) = ((sK590 @ (sub @ X156 @ (push @ sK592 @ sK593))))) & ($true = ((sK590 @ sK592)))) & ! [X157 : term,X158 : subst] : (((sub @ one @ (push @ X157 @ X158))) = X157))) & (! [X159 : (term > $o),X160 : (term > $o),X161 : term,X162 : subst] : (($true = ((X160 @ one))) | (((X160 @ (sK594 @ X162 @ X161 @ X160 @ X159))) != ((X159 @ (sub @ (sK594 @ X162 @ X161 @ X160 @ X159) @ (push @ X161 @ X162))))) | ($true != ((X159 @ X161)))) | (sK595 != ((sub @ one @ (push @ sK595 @ sK596)))) | (pushprop_lem1v2_lthm != $true)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem1 = $true) & ((termmset_lthm = $true) | ((sK597 != ((sub @ sK597 @ id))) & ! [X167 : term] : (((sub @ X167 @ id)) = X167))) & (! [X168 : term] : (((sub @ X168 @ id)) = X168) | (sK598 != ((sub @ sK598 @ id))) | (termmset_lthm != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP44)) & (($true = sP44) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3aa_lthm != $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP35)) & (($true = sP35) | (hoasinduction_lem3aaa != $true)) & ((hoaslaminj = $true) | ((((sK599 @ sK601 @ sK602)) != ((sK600 @ sK601 @ sK602))) & (((lam @ (sK599 @ sh @ one))) = ((lam @ (sK600 @ sh @ one)))) & ! [X174 : subst,X175 : term,X176 : subst] : (((sub @ (sK600 @ X174 @ X175) @ X176)) = ((sK600 @ (comp @ X174 @ X176) @ (sub @ X175 @ X176)))) & ! [X177 : subst,X178 : term,X179 : subst] : (((sub @ (sK599 @ X177 @ X178) @ X179)) = ((sK599 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179)))))) & (! [X180 : (subst > term > term),X181 : (subst > term > term),X182 : subst,X183 : term] : ((((X180 @ X182 @ X183)) = ((X181 @ X182 @ X183))) | (((lam @ (X180 @ sh @ one))) != ((lam @ (X181 @ sh @ one)))) | (((sub @ (X181 @ (sK603 @ X181) @ (sK604 @ X181)) @ (sK605 @ X181))) != ((X181 @ (comp @ (sK603 @ X181) @ (sK605 @ X181)) @ (sub @ (sK604 @ X181) @ (sK605 @ X181))))) | (((sub @ (X180 @ (sK606 @ X180) @ (sK607 @ X180)) @ (sK608 @ X180))) != ((X180 @ (comp @ (sK606 @ X180) @ (sK608 @ X180)) @ (sub @ (sK607 @ X180) @ (sK608 @ X180)))))) | (hoaslaminj != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP31) & ($true != sP32) & ! [X190 : term] : (((sub @ X190 @ id)) = X190) & ($true != sP33) & ! [X191 : (subst > term > subst > $o)] : ! [X193 : term] : (((X191 @ id @ X193 @ id)) = ((sK609 @ X191 @ X193))))) & (($true = sP31) | ($true = sP32) | (sK610 != ((sub @ sK610 @ id))) | ($true = sP33) | ! [X196 : (term > $o)] : (((X196 @ (sK612 @ X196))) != ((sK611 @ id @ (sK612 @ X196) @ id))) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP21) & ($true != sP23) & ($true != sP22) & ($true != sP24))) & (($true = sP21) | ($true = sP23) | ($true = sP22) | ($true = sP24) | (hoasinduction_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X199 : (subst > term > term)] : (((sub @ sK613 @ (push @ (sK614 @ X199) @ (sK615 @ X199)))) != ((X199 @ (sK615 @ X199) @ (sK614 @ X199))))) & (! [X202 : term] : ! [X204 : term,X205 : subst] : (((sub @ X202 @ (push @ X204 @ X205))) = ((sK616 @ X202 @ X205 @ X204))) | (hoasinduction_lem3v2_f_lthm != $true)) & (pushprop_lthm_orig = $true) & (apnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ((induction2lem_lthm = $true) | (($true != sP7) & ($true != sP8) & ! [X206 : subst] : (((comp @ X206 @ id)) = X206) & ! [X207 : term,X208 : subst] : (((comp @ sh @ (push @ X207 @ X208))) = X208) & ! [X209 : term,X210 : subst] : (((sub @ one @ (push @ X209 @ X210))) = X209))) & (($true = sP7) | ($true = sP8) | (sK617 != ((comp @ sK617 @ id))) | (sK619 != ((comp @ sh @ (push @ sK618 @ sK619)))) | (sK620 != ((sub @ one @ (push @ sK620 @ sK621)))) | (induction2lem_lthm != $true)) & (ulamvar1 != $true) & ((hoasapinj1 = $true) | ((sK622 != sK623) & (((ap @ (sub @ sK622 @ id) @ sK624)) = ((ap @ (sub @ sK623 @ id) @ sK625))))) & (! [X220 : term,X221 : term,X222 : term,X223 : term] : ((X220 = X221) | (((ap @ (sub @ X220 @ id) @ X222)) != ((ap @ (sub @ X221 @ id) @ X223)))) | (hoasapinj1 != $true)) & (hoasapnotvar_gthm = $true) & ((hoasapinj2 = $true) | ((sK628 != sK629) & (((ap @ (sub @ sK626 @ id) @ sK628)) = ((ap @ (sub @ sK627 @ id) @ sK629))))) & (! [X228 : term,X229 : term,X230 : term,X231 : term] : ((X230 = X231) | (((ap @ (sub @ X229 @ id) @ X231)) != ((ap @ (sub @ X228 @ id) @ X230)))) | (hoasapinj2 != $true)) & (axvarshift = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X233 : (subst > term > term)] : (((sub @ sK630 @ (push @ (sK631 @ X233) @ (sK632 @ X233)))) != ((X233 @ (sK632 @ X233) @ (sK631 @ X233))))) & (! [X236 : term] : ! [X238 : term,X239 : subst] : (((sub @ X236 @ (push @ X238 @ X239))) = ((sK633 @ X236 @ X239 @ X238))) | (hoasinduction_lem3v2_f != $true)) & ((induction2lem = $true) | ($true != sP2)) & (($true = sP2) | (induction2lem != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((shinj = $true) | ((sK634 != sK635) & (((sub @ sK634 @ sh)) = ((sub @ sK635 @ sh))))) & (! [X242 : term,X243 : term] : ((X242 = X243) | (((sub @ X242 @ sh)) != ((sub @ X243 @ sh)))) | (shinj != $true)) & (pushprop_lem0_gthm = $true) & (axmap = $true) & (pushprop_lem1_gthm = $true) & ((pushprop_lem1v2 = $true) | (($true != ((sK637 @ one))) & ! [X248 : term] : (((sK637 @ X248)) = ((sK636 @ (sub @ X248 @ (push @ sK638 @ sK639))))) & ($true = ((sK636 @ sK638))))) & (! [X249 : (term > $o),X250 : (term > $o),X251 : term,X252 : subst] : (($true = ((X250 @ one))) | (((X250 @ (sK640 @ X252 @ X251 @ X250 @ X249))) != ((X249 @ (sub @ (sK640 @ X252 @ X251 @ X250 @ X249) @ (push @ X251 @ X252))))) | ($true != ((X249 @ X251)))) | (pushprop_lem1v2 != $true)) & (((var @ (d2term @ d_one))) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2subst @ d_id)) = sh) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ! [X254 : d_subst,X255 : d_subst] : ((X254 = X255) | (((d2subst @ X254)) != ((d2subst @ X255)))) & ! [X256 : d_subst] : (d_id = X256) & ! [X257 : subst] : (((d2subst @ (sK641 @ X257))) = X257) & ! [X259 : d_term,X260 : d_term] : ((X259 = X260) | (((d2term @ X259)) != ((d2term @ X260)))) & ! [X261 : d_term] : (d_one = X261) & ! [X262 : term] : (((d2term @ (sK642 @ X262))) = X262)),
% 8.63/1.68 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK515,sK516,vAPP,sK518,sK519,sK520,sK521,sK522,vAPP,vAPP,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,vAPP,vAPP,vAPP,sK543,sK544,sK545,sK546,sK547,vAPP,sK549,vAPP,vAPP,sK552,sK553,vAPP,sK555,sK556,vAPP,vAPP,sK559,sK560,sK561,vAPP,vAPP,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,vAPP,sK587,vAPP,vAPP,sK590,sK591,sK592,sK593,vAPP,sK595,sK596,sK597,sK598,sK599,sK600,sK601,sK602,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK610,sK611,vAPP,sK613,vAPP,vAPP,vAPP,sK617,sK618,sK619,sK620,sK621,sK622,sK623,sK624,sK625,sK626,sK627,sK628,sK629,sK630,vAPP,vAPP,vAPP,sK634,sK635,sK636,sK637,sK638,sK639,vAPP,vAPP,vAPP]),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK515),skolemize(X5,sK516),skolemize(X4,sK114 @ X1 @ X0),skolemize(X8,sK518),skolemize(X11,sK519),skolemize(X12,sK520),skolemize(X13,sK521),skolemize(X14,sK522),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X22,sK525),skolemize(X24,sK526),skolemize(X25,sK527),skolemize(X28,sK528),skolemize(X29,sK529),skolemize(X30,sK530),skolemize(X31,sK531),skolemize(X32,sK532),skolemize(X42,sK533),skolemize(X43,sK534),skolemize(X44,sK535),skolemize(X45,sK536),skolemize(X46,sK537),skolemize(X47,sK538),skolemize(X48,sK539),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X58,sK543),skolemize(X59,sK544),skolemize(X62,sK545),skolemize(X63,sK546),skolemize(X66,sK547),skolemize(X4,sK114 @ X1 @ X0),skolemize(X70,sK549),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X77,sK552),skolemize(X78,sK553),skolemize(X4,sK114 @ X1 @ X0),skolemize(X85,sK555),skolemize(X86,sK556),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X90,sK559),skolemize(X91,sK560),skolemize(X92,sK561),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X101,sK564),skolemize(X102,sK565),skolemize(X103,sK566),skolemize(X106,sK567),skolemize(X107,sK568),skolemize(X108,sK569),skolemize(X109,sK570),skolemize(X110,sK571),skolemize(X116,sK572),skolemize(X118,sK573),skolemize(X120,sK574),skolemize(X121,sK575),skolemize(X124,sK576),skolemize(X125,sK577),skolemize(X126,sK578),skolemize(X127,sK579),skolemize(X132,sK580),skolemize(X133,sK581),skolemize(X134,sK582),skolemize(X135,sK583),skolemize(X141,sK584),skolemize(X142,sK585),skolemize(X4,sK114 @ X1 @ X0),skolemize(X146,sK587),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X152,sK590),skolemize(X153,sK591),skolemize(X154,sK592),skolemize(X155,sK593),skolemize(X4,sK114 @ X1 @ X0),skolemize(X164,sK595),skolemize(X165,sK596),skolemize(X166,sK597),skolemize(X169,sK598),skolemize(X170,sK599),skolemize(X171,sK600),skolemize(X172,sK601),skolemize(X173,sK602),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X194,sK610),skolemize(X195,sK611),skolemize(X4,sK114 @ X1 @ X0),skolemize(X198,sK613),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X211,sK617),skolemize(X212,sK618),skolemize(X213,sK619),skolemize(X214,sK620),skolemize(X215,sK621),skolemize(X216,sK622),skolemize(X217,sK623),skolemize(X218,sK624),skolemize(X219,sK625),skolemize(X224,sK626),skolemize(X225,sK627),skolemize(X226,sK628),skolemize(X227,sK629),skolemize(X232,sK630),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X240,sK634),skolemize(X241,sK635),skolemize(X244,sK636),skolemize(X245,sK637),skolemize(X246,sK638),skolemize(X247,sK639),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0),skolemize(X4,sK114 @ X1 @ X0)],[f464])).
% 8.63/1.68 thf(f985,plain,(
% 8.63/1.68 ( ! [X262 : term] : ((((d2term @ (sK642 @ X262))) = X262)) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f986,plain,(
% 8.63/1.68 ( ! [X261 : d_term] : ((d_one = X261)) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f988,plain,(
% 8.63/1.68 ( ! [X257 : subst] : ((((d2subst @ (sK641 @ X257))) = X257)) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f989,plain,(
% 8.63/1.68 ( ! [X256 : d_subst] : ((d_id = X256)) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f991,plain,(
% 8.63/1.68 (one = ((d2term @ d_one)))),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f995,plain,(
% 8.63/1.68 (((d2subst @ d_id)) = id)),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1002,plain,(
% 8.63/1.68 (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))))))))))))))),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1018,plain,(
% 8.63/1.68 ( ! [X238 : term,X239 : subst,X236 : term] : ((((sub @ X236 @ (push @ X238 @ X239))) = ((sK633 @ X236 @ X239 @ X238))) | (hoasinduction_lem3v2_f != $true)) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1019,plain,(
% 8.63/1.68 ( ! [X233 : (subst > term > term)] : ((hoasinduction_lem3v2_f = $true) | (((sub @ sK630 @ (push @ (sK631 @ X233) @ (sK632 @ X233)))) != ((X233 @ (sK632 @ X233) @ (sK631 @ X233))))) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1038,plain,(
% 8.63/1.68 ( ! [X205 : subst,X202 : term,X204 : term] : ((((sub @ X202 @ (push @ X204 @ X205))) = ((sK616 @ X202 @ X205 @ X204))) | (hoasinduction_lem3v2_f_lthm != $true)) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1039,plain,(
% 8.63/1.68 ( ! [X199 : (subst > term > term)] : ((hoasinduction_lem3v2_f_lthm = $true) | (((sub @ sK613 @ (push @ (sK614 @ X199) @ (sK615 @ X199)))) != ((X199 @ (sK615 @ X199) @ (sK614 @ X199))))) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1139,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : ((pushprop_lem0 = $true) | (((X93 @ (sK562 @ X93))) != ((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))))) )),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1181,plain,(
% 8.63/1.68 (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true)),
% 8.63/1.68 inference(cnf_transformation,[],[f465])).
% 8.63/1.68 thf(f1216,plain,(
% 8.63/1.68 (pushprop_lem0 != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (?? @ (term > $o) @ (^[Y3 : term > $o]: (pushprop_p_and_p_prime @ Y1 @ Y0 @ Y2 @ Y3)))))))))))),
% 8.63/1.68 inference(cnf_transformation,[],[f10])).
% 8.63/1.68 thf(f1219,plain,(
% 8.63/1.68 (pushprop_lem0 != ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (?? @ (term > $o) @ (^[Y3 : term > $o]: ((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y1 @ Y0 @ Y2 @ Y3)))))))))))),
% 8.63/1.68 inference(definition_unfolding,[],[f1216,f1002])).
% 8.63/1.68 thf(f1221,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (?? @ (term > $o) @ (^[Y3 : term > $o]: ((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y1 @ Y0 @ Y2 @ Y3)))))))))))),
% 8.63/1.68 inference(xor_proxy_clausification,[],[f1219])).
% 8.63/1.68 thf(f1222,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (?? @ (term > $o) @ (^[Y3 : term > $o]: ((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y1 @ Y0 @ Y2 @ Y3)))))))) @ sK643)))),
% 8.63/1.68 inference(sigma_proxy_clausification,[],[f1221])).
% 8.63/1.68 thf(f1223,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = ((!! @ term @ (^[Y0 : term]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (?? @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y2 @ Y3) = (Y1 @ (sub @ Y3 @ (push @ Y0 @ sK643))))))))))))))),
% 8.63/1.68 inference(beta-eta_normalization,[],[f1222])).
% 8.63/1.68 thf(f1224,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = (((^[Y0 : term]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (?? @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y2 @ Y3) = (Y1 @ (sub @ Y3 @ (push @ Y0 @ sK643))))))))))) @ sK644)))),
% 8.63/1.68 inference(sigma_proxy_clausification,[],[f1223])).
% 8.63/1.68 thf(f1225,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (sub @ Y2 @ (push @ sK644 @ sK643))))))))))))),
% 8.63/1.68 inference(beta-eta_normalization,[],[f1224])).
% 8.63/1.68 thf(f1226,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = (((^[Y0 : term > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ (sub @ Y2 @ (push @ sK644 @ sK643))))))))) @ sK645)))),
% 8.63/1.68 inference(sigma_proxy_clausification,[],[f1225])).
% 8.63/1.68 thf(f1227,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ($false = ((?? @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (sK645 @ (sub @ Y1 @ (push @ sK644 @ sK643))))))))))),
% 8.63/1.68 inference(beta-eta_normalization,[],[f1226])).
% 8.63/1.68 thf(f1228,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = (((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((Y0 @ Y1) = (sK645 @ (sub @ Y1 @ (push @ sK644 @ sK643))))))) @ X1)))) )),
% 8.63/1.68 inference(pi_proxy_clausification,[],[f1227])).
% 8.63/1.68 thf(f1229,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((X1 @ Y0) = (sK645 @ (sub @ Y0 @ (push @ sK644 @ sK643))))))))) )),
% 8.63/1.68 inference(beta-eta_normalization,[],[f1228])).
% 8.63/1.68 thf(f1230,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = (((^[Y0 : term]: ((X1 @ Y0) = (sK645 @ (sub @ Y0 @ (push @ sK644 @ sK643))))) @ (sK646 @ X1))))) )),
% 8.63/1.68 inference(sigma_proxy_clausification,[],[f1229])).
% 8.63/1.68 thf(f1231,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = (((X1 @ (sK646 @ X1)) = (sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643))))))) )),
% 8.63/1.68 inference(beta-eta_normalization,[],[f1230])).
% 8.63/1.68 thf(f1232,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | (((X1 @ (sK646 @ X1))) != ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643)))))) )),
% 8.63/1.68 inference(equality_proxy_clausification,[],[f1231])).
% 8.63/1.68 thf(f1233,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($true = ((X1 @ (sK646 @ X1)))) | ($true = ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643)))))) )),
% 8.63/1.68 inference(xor_proxy_clausification,[],[f1232])).
% 8.63/1.68 thf(f1234,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = ((X1 @ (sK646 @ X1)))) | ($false = ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643)))))) )),
% 8.63/1.68 inference(xor_proxy_clausification,[],[f1232])).
% 8.63/1.68 thf(f1266,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : ((pushprop_lem0 = $true) | ($true = ((X93 @ (sK562 @ X93)))) | ($true = ((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))))) )),
% 8.63/1.68 inference(xor_proxy_clausification,[],[f1139])).
% 8.63/1.68 thf(f1267,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : ((pushprop_lem0 = $true) | (((X93 @ (sK562 @ X93))) = $false) | (((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))) = $false)) )),
% 8.63/1.68 inference(xor_proxy_clausification,[],[f1139])).
% 8.63/1.68 thf(f1323,definition,(
% 8.63/1.68 spl648_1 <=> ! [X1 : (term > $o)] : (($false = ((X1 @ (sK646 @ X1)))) | ($false = ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_1])],[avatar_definition])).
% 8.63/1.68 thf(f1324,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : (($false = ((X1 @ (sK646 @ X1)))) | ($false = ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643)))))) ) | ~spl648_1),
% 8.63/1.68 inference(avatar_component_clause,[],[f1323])).
% 8.63/1.68 thf(f1326,definition,(
% 8.63/1.68 spl648_2 <=> (pushprop_lem0 = $false)),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_2])],[avatar_definition])).
% 8.63/1.68 thf(f1328,plain,(
% 8.63/1.68 (pushprop_lem0 = $false) | ~spl648_2),
% 8.63/1.68 inference(avatar_component_clause,[],[f1326])).
% 8.63/1.68 thf(f1329,plain,(
% 8.63/1.68 spl648_1 | spl648_2),
% 8.63/1.68 inference(avatar_split_clause,[],[f1234,f1326,f1323])).
% 8.63/1.68 thf(f1331,definition,(
% 8.63/1.68 spl648_3 <=> ! [X1 : (term > $o)] : (($true = ((X1 @ (sK646 @ X1)))) | ($true = ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_3])],[avatar_definition])).
% 8.63/1.68 thf(f1332,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : (($true = ((X1 @ (sK646 @ X1)))) | ($true = ((sK645 @ (sub @ (sK646 @ X1) @ (push @ sK644 @ sK643)))))) ) | ~spl648_3),
% 8.63/1.68 inference(avatar_component_clause,[],[f1331])).
% 8.63/1.68 thf(f1333,plain,(
% 8.63/1.68 spl648_3 | spl648_2),
% 8.63/1.68 inference(avatar_split_clause,[],[f1233,f1326,f1331])).
% 8.63/1.68 thf(f1338,definition,(
% 8.63/1.68 spl648_5 <=> (pushprop_lem0 = $true)),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_5])],[avatar_definition])).
% 8.63/1.68 thf(f1340,plain,(
% 8.63/1.68 (pushprop_lem0 = $true) | ~spl648_5),
% 8.63/1.68 inference(avatar_component_clause,[],[f1338])).
% 8.63/1.68 thf(f1413,definition,(
% 8.63/1.68 spl648_20 <=> (hoasinduction_lem3v2_f = $true)),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_20])],[avatar_definition])).
% 8.63/1.68 thf(f1417,definition,(
% 8.63/1.68 spl648_21 <=> ! [X236 : term,X238 : term,X239 : subst] : (((sub @ X236 @ (push @ X238 @ X239))) = ((sK633 @ X236 @ X239 @ X238)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_21])],[avatar_definition])).
% 8.63/1.68 thf(f1418,plain,(
% 8.63/1.68 ( ! [X238 : term,X239 : subst,X236 : term] : ((((sub @ X236 @ (push @ X238 @ X239))) = ((sK633 @ X236 @ X239 @ X238)))) ) | ~spl648_21),
% 8.63/1.68 inference(avatar_component_clause,[],[f1417])).
% 8.63/1.68 thf(f1419,plain,(
% 8.63/1.68 ~spl648_20 | spl648_21),
% 8.63/1.68 inference(avatar_split_clause,[],[f1018,f1417,f1413])).
% 8.63/1.68 thf(f1421,definition,(
% 8.63/1.68 spl648_22 <=> ! [X233 : (subst > term > term)] : (((sub @ sK630 @ (push @ (sK631 @ X233) @ (sK632 @ X233)))) != ((X233 @ (sK632 @ X233) @ (sK631 @ X233))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_22])],[avatar_definition])).
% 8.63/1.68 thf(f1422,plain,(
% 8.63/1.68 ( ! [X233 : (subst > term > term)] : ((((sub @ sK630 @ (push @ (sK631 @ X233) @ (sK632 @ X233)))) != ((X233 @ (sK632 @ X233) @ (sK631 @ X233))))) ) | ~spl648_22),
% 8.63/1.68 inference(avatar_component_clause,[],[f1421])).
% 8.63/1.68 thf(f1423,plain,(
% 8.63/1.68 spl648_22 | spl648_20),
% 8.63/1.68 inference(avatar_split_clause,[],[f1019,f1413,f1421])).
% 8.63/1.68 thf(f1500,definition,(
% 8.63/1.68 spl648_40 <=> (hoasinduction_lem3v2_f_lthm = $true)),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_40])],[avatar_definition])).
% 8.63/1.68 thf(f1504,definition,(
% 8.63/1.68 spl648_41 <=> ! [X205 : subst,X204 : term,X202 : term] : (((sub @ X202 @ (push @ X204 @ X205))) = ((sK616 @ X202 @ X205 @ X204)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_41])],[avatar_definition])).
% 8.63/1.68 thf(f1505,plain,(
% 8.63/1.68 ( ! [X205 : subst,X202 : term,X204 : term] : ((((sub @ X202 @ (push @ X204 @ X205))) = ((sK616 @ X202 @ X205 @ X204)))) ) | ~spl648_41),
% 8.63/1.68 inference(avatar_component_clause,[],[f1504])).
% 8.63/1.68 thf(f1506,plain,(
% 8.63/1.68 ~spl648_40 | spl648_41),
% 8.63/1.68 inference(avatar_split_clause,[],[f1038,f1504,f1500])).
% 8.63/1.68 thf(f1508,definition,(
% 8.63/1.68 spl648_42 <=> ! [X199 : (subst > term > term)] : (((sub @ sK613 @ (push @ (sK614 @ X199) @ (sK615 @ X199)))) != ((X199 @ (sK615 @ X199) @ (sK614 @ X199))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_42])],[avatar_definition])).
% 8.63/1.68 thf(f1509,plain,(
% 8.63/1.68 ( ! [X199 : (subst > term > term)] : ((((sub @ sK613 @ (push @ (sK614 @ X199) @ (sK615 @ X199)))) != ((X199 @ (sK615 @ X199) @ (sK614 @ X199))))) ) | ~spl648_42),
% 8.63/1.68 inference(avatar_component_clause,[],[f1508])).
% 8.63/1.68 thf(f1510,plain,(
% 8.63/1.68 spl648_42 | spl648_40),
% 8.63/1.68 inference(avatar_split_clause,[],[f1039,f1500,f1508])).
% 8.63/1.68 thf(f1961,definition,(
% 8.63/1.68 spl648_140 <=> ! [X93 : (term > $o)] : ((((X93 @ (sK562 @ X93))) = $false) | (((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))) = $false))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_140])],[avatar_definition])).
% 8.63/1.68 thf(f1962,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : ((((X93 @ (sK562 @ X93))) = $false) | (((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))) = $false)) ) | ~spl648_140),
% 8.63/1.68 inference(avatar_component_clause,[],[f1961])).
% 8.63/1.68 thf(f1963,plain,(
% 8.63/1.68 spl648_140 | spl648_5),
% 8.63/1.68 inference(avatar_split_clause,[],[f1267,f1338,f1961])).
% 8.63/1.68 thf(f1965,definition,(
% 8.63/1.68 spl648_141 <=> ! [X93 : (term > $o)] : (($true = ((X93 @ (sK562 @ X93)))) | ($true = ((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561))))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_141])],[avatar_definition])).
% 8.63/1.68 thf(f1966,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((X93 @ (sK562 @ X93)))) | ($true = ((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))))) ) | ~spl648_141),
% 8.63/1.68 inference(avatar_component_clause,[],[f1965])).
% 8.63/1.68 thf(f1967,plain,(
% 8.63/1.68 spl648_141 | spl648_5),
% 8.63/1.68 inference(avatar_split_clause,[],[f1266,f1338,f1965])).
% 8.63/1.68 thf(f2113,plain,(
% 8.63/1.68 ($true != ((hoasvar @ id @ (d2term @ d_one) @ id)))),
% 8.63/1.68 inference(forward_demodulation,[],[f1181,f995])).
% 8.63/1.68 thf(f3428,plain,(
% 8.63/1.68 ($true != ((hoasvar @ id @ one @ id)))),
% 8.63/1.68 inference(forward_demodulation,[],[f2113,f991])).
% 8.63/1.68 thf(f3429,plain,(
% 8.63/1.68 ($true = $false) | (~spl648_2 | ~spl648_5)),
% 8.63/1.68 inference(forward_demodulation,[],[f1340,f1328])).
% 8.63/1.68 thf(f3430,plain,(
% 8.63/1.68 $false | (~spl648_2 | ~spl648_5)),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f3429])).
% 8.63/1.68 thf(f3431,plain,(
% 8.63/1.68 ~spl648_2 | ~spl648_5),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f3430])).
% 8.63/1.68 thf(f3526,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((sK559 @ (sK633 @ (sK562 @ X93) @ sK561 @ sK560)))) | ($true = ((X93 @ (sK562 @ X93))))) ) | (~spl648_21 | ~spl648_141)),
% 8.63/1.68 inference(forward_demodulation,[],[f1966,f1418])).
% 8.63/1.68 thf(f3530,plain,(
% 8.63/1.68 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 8.63/1.68 inference(constrained_superposition,[],[f991,f986])).
% 8.63/1.68 thf(f3531,plain,(
% 8.63/1.68 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )),
% 8.63/1.68 inference(constrained_superposition,[],[f995,f989])).
% 8.63/1.68 thf(f3532,plain,(
% 8.63/1.68 ( ! [X0 : term] : ((((d2term @ d_one)) = X0)) )),
% 8.63/1.68 inference(constrained_superposition,[],[f985,f986])).
% 8.63/1.68 thf(f3533,plain,(
% 8.63/1.68 ( ! [X0 : term] : ((one = X0)) )),
% 8.63/1.68 inference(forward_demodulation,[],[f3532,f3530])).
% 8.63/1.68 thf(f3534,plain,(
% 8.63/1.68 ( ! [X0 : subst] : ((((d2subst @ d_id)) = X0)) )),
% 8.63/1.68 inference(constrained_superposition,[],[f988,f989])).
% 8.63/1.68 thf(f3535,plain,(
% 8.63/1.68 ( ! [X0 : subst] : ((id = X0)) )),
% 8.63/1.68 inference(forward_demodulation,[],[f3534,f3531])).
% 8.63/1.68 thf(f3552,plain,(
% 8.63/1.68 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 8.63/1.68 inference(constrained_superposition,[],[f3533,f3533])).
% 8.63/1.68 thf(f3878,plain,(
% 8.63/1.68 ( ! [X233 : (subst > term > term)] : ((one != ((sub @ sK630 @ (push @ (sK631 @ X233) @ (sK632 @ X233)))))) ) | ~spl648_22),
% 8.63/1.68 inference(forward_demodulation,[],[f1422,f3533])).
% 8.63/1.68 thf(f3913,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($false = ((X93 @ one))) | (((sK559 @ (sub @ (sK562 @ X93) @ (push @ sK560 @ sK561)))) = $false)) ) | ~spl648_140),
% 8.63/1.68 inference(forward_demodulation,[],[f1962,f3533])).
% 8.63/1.68 thf(f3951,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($false = ((sK559 @ (sK616 @ (sK562 @ X93) @ sK561 @ sK560)))) | ($false = ((X93 @ one)))) ) | (~spl648_41 | ~spl648_140)),
% 8.63/1.68 inference(forward_demodulation,[],[f3913,f1505])).
% 8.63/1.68 thf(f3966,definition,(
% 8.63/1.68 spl648_463 <=> ! [X112 : (term > $o)] : ($true = ((X112 @ one)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_463])],[avatar_definition])).
% 8.63/1.68 thf(f3967,plain,(
% 8.63/1.68 ( ! [X112 : (term > $o)] : (($true = ((X112 @ one)))) ) | ~spl648_463),
% 8.63/1.68 inference(avatar_component_clause,[],[f3966])).
% 8.63/1.68 thf(f4025,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($false = ((sK559 @ one))) | ($false = ((X93 @ one)))) ) | (~spl648_41 | ~spl648_140)),
% 8.63/1.68 inference(forward_demodulation,[],[f3951,f3533])).
% 8.63/1.68 thf(f4032,definition,(
% 8.63/1.68 spl648_474 <=> ! [X93 : (term > $o)] : ($false = ((X93 @ one)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_474])],[avatar_definition])).
% 8.63/1.68 thf(f4033,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($false = ((X93 @ one)))) ) | ~spl648_474),
% 8.63/1.68 inference(avatar_component_clause,[],[f4032])).
% 8.63/1.68 thf(f4035,definition,(
% 8.63/1.68 spl648_475 <=> ($false = ((sK559 @ one)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_475])],[avatar_definition])).
% 8.63/1.68 thf(f4037,plain,(
% 8.63/1.68 ($false = ((sK559 @ one))) | ~spl648_475),
% 8.63/1.68 inference(avatar_component_clause,[],[f4035])).
% 8.63/1.68 thf(f4048,plain,(
% 8.63/1.68 ( ! [X199 : (subst > term > term)] : ((one != ((sub @ sK613 @ (push @ (sK614 @ X199) @ (sK615 @ X199)))))) ) | ~spl648_42),
% 8.63/1.68 inference(forward_demodulation,[],[f1509,f3533])).
% 8.63/1.68 thf(f4063,plain,(
% 8.63/1.68 (one != one) | ~spl648_22),
% 8.63/1.68 inference(forward_demodulation,[],[f3878,f3533])).
% 8.63/1.68 thf(f4064,plain,(
% 8.63/1.68 $false | ~spl648_22),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4063])).
% 8.63/1.68 thf(f4065,plain,(
% 8.63/1.68 ~spl648_22),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f4064])).
% 8.63/1.68 thf(f4076,plain,(
% 8.63/1.68 (one != one) | ~spl648_42),
% 8.63/1.68 inference(forward_demodulation,[],[f4048,f3533])).
% 8.63/1.68 thf(f4077,plain,(
% 8.63/1.68 $false | ~spl648_42),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4076])).
% 8.63/1.68 thf(f4078,plain,(
% 8.63/1.68 ~spl648_42),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f4077])).
% 8.63/1.68 thf(f4140,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((sK559 @ one))) | ($true = ((X93 @ (sK562 @ X93))))) ) | (~spl648_21 | ~spl648_141)),
% 8.63/1.68 inference(forward_demodulation,[],[f3526,f3533])).
% 8.63/1.68 thf(f4142,plain,(
% 8.63/1.68 spl648_474 | spl648_475 | ~spl648_41 | ~spl648_140),
% 8.63/1.68 inference(avatar_split_clause,[],[f4025,f1961,f1504,f4035,f4032])).
% 8.63/1.68 thf(f4217,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst),X1 : (term > term)] : (($true != $true) | (one != ((X1 @ one))) | (id != ((X0 @ one)))) ) | ~spl648_463),
% 8.63/1.68 inference(constrained_superposition,[],[f3428,f3967])).
% 8.63/1.68 thf(f4233,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst),X1 : (term > term)] : ((one != ((X1 @ one))) | (id != ((X0 @ one)))) ) | ~spl648_463),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4217])).
% 8.63/1.68 thf(f4259,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst)] : ((one != one) | (id != ((X0 @ one)))) ) | ~spl648_463),
% 8.63/1.68 inference(forward_demodulation,[],[f4233,f3533])).
% 8.63/1.68 thf(f4260,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst)] : ((id != ((X0 @ one)))) ) | ~spl648_463),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4259])).
% 8.63/1.68 thf(f4273,plain,(
% 8.63/1.68 (id != id) | ~spl648_463),
% 8.63/1.68 inference(forward_demodulation,[],[f4260,f3535])).
% 8.63/1.68 thf(f4274,plain,(
% 8.63/1.68 $false | ~spl648_463),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4273])).
% 8.63/1.68 thf(f4275,plain,(
% 8.63/1.68 ~spl648_463),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f4274])).
% 8.63/1.68 thf(f4295,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = $false) | ($true = ((X93 @ (sK562 @ X93))))) ) | (~spl648_21 | ~spl648_141 | ~spl648_474)),
% 8.63/1.68 inference(forward_demodulation,[],[f4140,f4033])).
% 8.63/1.68 thf(f4296,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((X93 @ (sK562 @ X93))))) ) | (~spl648_21 | ~spl648_141 | ~spl648_474)),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4295])).
% 8.63/1.68 thf(f4322,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((X93 @ one)))) ) | (~spl648_21 | ~spl648_141 | ~spl648_474)),
% 8.63/1.68 inference(forward_demodulation,[],[f4296,f3533])).
% 8.63/1.68 thf(f4333,plain,(
% 8.63/1.68 ($true = $false) | (~spl648_21 | ~spl648_141 | ~spl648_474)),
% 8.63/1.68 inference(forward_demodulation,[],[f4322,f4033])).
% 8.63/1.68 thf(f4334,plain,(
% 8.63/1.68 $false | (~spl648_21 | ~spl648_141 | ~spl648_474)),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4333])).
% 8.63/1.68 thf(f4335,plain,(
% 8.63/1.68 ~spl648_21 | ~spl648_141 | ~spl648_474),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f4334])).
% 8.63/1.68 thf(f4379,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = $false) | ($true = ((X93 @ (sK562 @ X93))))) ) | (~spl648_21 | ~spl648_141 | ~spl648_475)),
% 8.63/1.68 inference(forward_demodulation,[],[f4140,f4037])).
% 8.63/1.68 thf(f4380,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((X93 @ (sK562 @ X93))))) ) | (~spl648_21 | ~spl648_141 | ~spl648_475)),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4379])).
% 8.63/1.68 thf(f4394,plain,(
% 8.63/1.68 ( ! [X93 : (term > $o)] : (($true = ((X93 @ one)))) ) | (~spl648_21 | ~spl648_141 | ~spl648_475)),
% 8.63/1.68 inference(forward_demodulation,[],[f4380,f3533])).
% 8.63/1.68 thf(f4411,plain,(
% 8.63/1.68 spl648_463 | ~spl648_21 | ~spl648_141 | ~spl648_475),
% 8.63/1.68 inference(avatar_split_clause,[],[f4394,f4035,f1965,f1417,f3966])).
% 8.63/1.68 thf(f4426,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : (($false = ((sK645 @ one))) | ($false = ((X1 @ (sK646 @ X1))))) ) | ~spl648_1),
% 8.63/1.68 inference(forward_demodulation,[],[f1324,f3533])).
% 8.63/1.68 thf(f4427,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : (($true = ((sK645 @ one))) | ($true = ((X1 @ (sK646 @ X1))))) ) | ~spl648_3),
% 8.63/1.68 inference(forward_demodulation,[],[f1332,f3533])).
% 8.63/1.68 thf(f4431,definition,(
% 8.63/1.68 spl648_483 <=> ! [X1 : (term > $o)] : ($false = ((X1 @ (sK646 @ X1))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_483])],[avatar_definition])).
% 8.63/1.68 thf(f4432,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : (($false = ((X1 @ (sK646 @ X1))))) ) | ~spl648_483),
% 8.63/1.68 inference(avatar_component_clause,[],[f4431])).
% 8.63/1.68 thf(f4434,definition,(
% 8.63/1.68 spl648_484 <=> ($false = ((sK645 @ one)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_484])],[avatar_definition])).
% 8.63/1.68 thf(f4436,plain,(
% 8.63/1.68 ($false = ((sK645 @ one))) | ~spl648_484),
% 8.63/1.68 inference(avatar_component_clause,[],[f4434])).
% 8.63/1.68 thf(f4437,plain,(
% 8.63/1.68 spl648_483 | spl648_484 | ~spl648_1),
% 8.63/1.68 inference(avatar_split_clause,[],[f4426,f1323,f4434,f4431])).
% 8.63/1.68 thf(f4439,definition,(
% 8.63/1.68 spl648_485 <=> ! [X1 : (term > $o)] : ($true = ((X1 @ (sK646 @ X1))))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_485])],[avatar_definition])).
% 8.63/1.68 thf(f4440,plain,(
% 8.63/1.68 ( ! [X1 : (term > $o)] : (($true = ((X1 @ (sK646 @ X1))))) ) | ~spl648_485),
% 8.63/1.68 inference(avatar_component_clause,[],[f4439])).
% 8.63/1.68 thf(f4442,definition,(
% 8.63/1.68 spl648_486 <=> ($true = ((sK645 @ one)))),
% 8.63/1.68 introduced(definition,[new_symbols(definition,[spl648_486])],[avatar_definition])).
% 8.63/1.68 thf(f4444,plain,(
% 8.63/1.68 ($true = ((sK645 @ one))) | ~spl648_486),
% 8.63/1.68 inference(avatar_component_clause,[],[f4442])).
% 8.63/1.68 thf(f4445,plain,(
% 8.63/1.68 spl648_485 | spl648_486 | ~spl648_3),
% 8.63/1.68 inference(avatar_split_clause,[],[f4427,f1331,f4442,f4439])).
% 8.63/1.68 thf(f4478,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst),X1 : (term > term)] : (($true != $true) | (one != ((X1 @ (sK646 @ (^[Y0 : term]: (hoasvar @ (X0 @ Y0) @ (X1 @ Y0) @ id)))))) | (id != ((X0 @ (sK646 @ (^[Y0 : term]: (hoasvar @ (X0 @ Y0) @ (X1 @ Y0) @ id))))))) ) | ~spl648_485),
% 8.63/1.68 inference(constrained_superposition,[],[f3428,f4440])).
% 8.63/1.68 thf(f4494,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst),X1 : (term > term)] : ((one != ((X1 @ (sK646 @ (^[Y0 : term]: (hoasvar @ (X0 @ Y0) @ (X1 @ Y0) @ id)))))) | (id != ((X0 @ (sK646 @ (^[Y0 : term]: (hoasvar @ (X0 @ Y0) @ (X1 @ Y0) @ id))))))) ) | ~spl648_485),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4478])).
% 8.63/1.68 thf(f4530,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst),X1 : (term > term)] : ((one != one) | (id != ((X0 @ (sK646 @ (^[Y0 : term]: (hoasvar @ (X0 @ Y0) @ (X1 @ Y0) @ id))))))) ) | ~spl648_485),
% 8.63/1.68 inference(forward_demodulation,[],[f4494,f3533])).
% 8.63/1.68 thf(f4531,plain,(
% 8.63/1.68 ( ! [X0 : (term > subst),X1 : (term > term)] : ((id != ((X0 @ (sK646 @ (^[Y0 : term]: (hoasvar @ (X0 @ Y0) @ (X1 @ Y0) @ id))))))) ) | ~spl648_485),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4530])).
% 8.63/1.68 thf(f4539,plain,(
% 8.63/1.68 (id != id) | ~spl648_485),
% 8.63/1.68 inference(forward_demodulation,[],[f4531,f3535])).
% 8.63/1.68 thf(f4540,plain,(
% 8.63/1.68 $false | ~spl648_485),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4539])).
% 8.63/1.68 thf(f4541,plain,(
% 8.63/1.68 ~spl648_485),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f4540])).
% 8.63/1.68 thf(f4553,plain,(
% 8.63/1.68 ($true = $false) | (~spl648_484 | ~spl648_486)),
% 8.63/1.68 inference(forward_demodulation,[],[f4444,f4436])).
% 8.63/1.68 thf(f4554,plain,(
% 8.63/1.68 $false | (~spl648_484 | ~spl648_486)),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f4553])).
% 8.63/1.68 thf(f4555,plain,(
% 8.63/1.68 ~spl648_484 | ~spl648_486),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f4554])).
% 8.63/1.68 thf(f4604,plain,(
% 8.63/1.68 ( ! [X2 : (term > $o)] : (($false = (((^[Y0 : term]: (~ (X2 @ Y0))) @ (sK646 @ (^[Y0 : term]: (~ (X2 @ Y0)))))))) ) | ~spl648_483),
% 8.63/1.68 inference(primitive_instantiation,[],[f4432])).
% 8.63/1.68 thf(f4606,plain,(
% 8.63/1.68 ( ! [X0 : term,X1 : (term > $o)] : (($false = ((X1 @ X0)))) ) | ~spl648_483),
% 8.63/1.68 inference(constrained_superposition,[],[f4432,f3552])).
% 8.63/1.68 thf(f5181,plain,(
% 8.63/1.68 ( ! [X2 : (term > $o)] : (($false = ((~ (X2 @ (sK646 @ (^[Y0 : term]: (~ (X2 @ Y0))))))))) ) | ~spl648_483),
% 8.63/1.68 inference(beta-eta_normalization,[],[f4604])).
% 8.63/1.68 thf(f5182,plain,(
% 8.63/1.68 ( ! [X2 : (term > $o)] : (($true = ((X2 @ (sK646 @ (^[Y0 : term]: (~ (X2 @ Y0)))))))) ) | ~spl648_483),
% 8.63/1.68 inference(not_proxy_clausification,[],[f5181])).
% 8.63/1.68 thf(f5188,plain,(
% 8.63/1.68 ($true = $false) | ~spl648_483),
% 8.63/1.68 inference(forward_demodulation,[],[f5182,f4606])).
% 8.63/1.68 thf(f5189,plain,(
% 8.63/1.68 $false | ~spl648_483),
% 8.63/1.68 inference(trivial_inequality_removal,[],[f5188])).
% 8.63/1.68 thf(f5190,plain,(
% 8.63/1.68 ~spl648_483),
% 8.63/1.68 inference(avatar_contradiction_clause,[],[f5189])).
% 8.63/1.68 cnf(s2, plain, spl648_1 | spl648_2, inference(sat_conversion,[],[f1329])).
% 8.63/1.68 cnf(s4, plain, spl648_2 | spl648_3, inference(sat_conversion,[],[f1333])).
% 8.63/1.68 cnf(s40, plain, ~spl648_20 | spl648_21, inference(sat_conversion,[],[f1419])).
% 8.63/1.68 cnf(s42, plain, spl648_20 | spl648_22, inference(sat_conversion,[],[f1423])).
% 8.63/1.68 cnf(s69, plain, ~spl648_40 | spl648_41, inference(sat_conversion,[],[f1506])).
% 8.63/1.68 cnf(s71, plain, spl648_40 | spl648_42, inference(sat_conversion,[],[f1510])).
% 8.63/1.68 cnf(s245, plain, spl648_5 | spl648_140, inference(sat_conversion,[],[f1963])).
% 8.63/1.68 cnf(s247, plain, spl648_5 | spl648_141, inference(sat_conversion,[],[f1967])).
% 8.63/1.68 cnf(s1179, plain, ~spl648_2 | ~spl648_5, inference(sat_conversion,[],[f3431])).
% 8.63/1.68 cnf(s1557, plain, ~spl648_22, inference(sat_conversion,[],[f4065])).
% 8.63/1.68 cnf(s1558, plain, ~spl648_42, inference(sat_conversion,[],[f4078])).
% 8.63/1.68 cnf(s1598, plain, ~spl648_41 | ~spl648_140 | spl648_474 | spl648_475, inference(sat_conversion,[],[f4142])).
% 8.63/1.68 cnf(s1631, plain, ~spl648_463, inference(sat_conversion,[],[f4275])).
% 8.63/1.68 cnf(s1637, plain, ~spl648_21 | ~spl648_141 | ~spl648_474, inference(sat_conversion,[],[f4335])).
% 8.63/1.68 cnf(s1650, plain, ~spl648_21 | ~spl648_141 | spl648_463 | ~spl648_475, inference(sat_conversion,[],[f4411])).
% 8.63/1.68 cnf(s1664, plain, ~spl648_1 | spl648_483 | spl648_484, inference(sat_conversion,[],[f4437])).
% 8.63/1.68 cnf(s1666, plain, ~spl648_3 | spl648_485 | spl648_486, inference(sat_conversion,[],[f4445])).
% 8.63/1.68 cnf(s1696, plain, ~spl648_485, inference(sat_conversion,[],[f4541])).
% 8.63/1.68 cnf(s1702, plain, ~spl648_484 | ~spl648_486, inference(sat_conversion,[],[f4555])).
% 8.63/1.68 cnf(s1898, plain, ~spl648_483, inference(sat_conversion,[],[f5190])).
% 8.63/1.68 cnf(s1899, plain, ~spl648_3 | spl648_486, inference(rat,[],[s1666,s1696])).
% 8.63/1.68 cnf(s1900, plain, ~spl648_1 | spl648_484, inference(rat,[],[s1664,s1898])).
% 8.63/1.68 cnf(s1933, plain, spl648_40, inference(rat,[],[s71,s1558])).
% 8.63/1.68 cnf(s1934, plain, spl648_41, inference(rat,[],[s69,s1933])).
% 8.63/1.68 cnf(s1935, plain, spl648_20, inference(rat,[],[s42,s1557])).
% 8.63/1.68 cnf(s1936, plain, spl648_21, inference(rat,[],[s40,s1935])).
% 8.63/1.68 cnf(s1937, plain, spl648_5, inference(rat,[],[s1598,s1637,s1650,s245,s247,s1934,s1936,s1631])).
% 8.63/1.68 cnf(s1938, plain, ~spl648_2, inference(rat,[],[s1179,s1937])).
% 8.63/1.68 cnf(s1941, plain, spl648_3, inference(rat,[],[s4,s1938])).
% 8.63/1.68 cnf(s1942, plain, spl648_1, inference(rat,[],[s2,s1938])).
% 8.63/1.68 cnf(s1943, plain, spl648_486, inference(rat,[],[s1899,s1941])).
% 8.63/1.68 cnf(s1944, plain, spl648_484, inference(rat,[],[s1900,s1942])).
% 8.63/1.68 cnf(s1945, plain, $false, inference(rat,[],[s1702,s1943,s1944])).
% 8.63/1.68 thf(f5191,plain,(
% 8.63/1.68 $false),
% 8.63/1.68 inference(avatar_sat_refutation,[],[s1945])).
% 8.63/1.68 % SZS output end Proof for theBenchmark
% 8.63/1.68 % (1233084)------------------------------
% 8.63/1.68 % (1233084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.63/1.68 % (1233084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.63/1.68 % (1233084)CaDiCaL version: 2.1.3
% 8.63/1.68 % (1233084)Termination reason: Refutation
% 8.63/1.68 % (1233084)Time elapsed: 0.270 s
% 8.63/1.68 % (1233084)Peak memory usage: 18 MB
% 8.63/1.68 % (1233084)Instructions burned: 575 (million)
% 8.63/1.68 % (1232915)Success in time 1.454 s
% 8.63/1.68 % Vampire exiting
%------------------------------------------------------------------------------