%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU481^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:32:10 AM UTC 2026
% Result : Theorem 6.02s 1.30s
% Output : Refutation 6.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU481^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n020.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:44:05 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 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
% 6.02/1.27 % (1071937)Will run a generic schedule for satisfiability detection.
% 6.02/1.27 % (1071943)% WARNING: option uhcvi not known.
% 6.02/1.27 % (1071943)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=260357957:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.02/1.27 % (1071942)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3249204413_2999 on theBenchmark for (2999ds/0Mi)
% 6.02/1.27 % (1071945)dis+10_1_sil=32000:sp=arity:random_seed=3696992839:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.02/1.27 % (1071944)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4091643265:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.02/1.27 % (1071943)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.27 % Exception at run slice level
% 6.02/1.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (1071943)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.02/1.27
% 6.02/1.27 % (1071946)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=354662612:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.02/1.27 % (1071946)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.27 % (1071947)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3610017121:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.02/1.27 % (1071948)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1153210000:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.02/1.27 % (1071953)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2468271787:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.02/1.27 % Exception at run slice level
% 6.02/1.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.27 % (1071958)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2615763398:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.02/1.27 % (1071945)Instruction limit reached!
% 6.02/1.27 % (1071945)------------------------------
% 6.02/1.27 % (1071945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.27 % (1071945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.27 % (1071945)CaDiCaL version: 2.1.3
% 6.02/1.27 % (1071945)Termination reason: Instruction limit
% 6.02/1.27 % (1071945)Termination phase: Saturation
% 6.02/1.27 % (1071945)Time elapsed: 0.052 s
% 6.02/1.27 % (1071945)Peak memory usage: 12 MB
% 6.02/1.27 % (1071945)Instructions burned: 104 (million)
% 6.02/1.27 % (1071960)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=2313782082:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.02/1.27 % (1071960)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.27 % (1071960)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.02/1.27 % (1071946)Instruction limit reached!
% 6.02/1.27 % (1071946)------------------------------
% 6.02/1.27 % (1071946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.27 % (1071946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.27 % (1071946)CaDiCaL version: 2.1.3
% 6.02/1.27 % (1071946)Termination reason: Instruction limit
% 6.02/1.27 % (1071946)Termination phase: Saturation
% 6.02/1.27 % (1071946)Time elapsed: 0.101 s
% 6.02/1.27 % (1071946)Peak memory usage: 13 MB
% 6.02/1.27 % (1071946)Instructions burned: 117 (million)
% 6.02/1.27 % (1071958)Instruction limit reached!
% 6.02/1.27 % (1071958)------------------------------
% 6.02/1.27 % (1071958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.27 % (1071958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.27 % (1071958)CaDiCaL version: 2.1.3
% 6.02/1.27 % (1071958)Termination reason: Instruction limit
% 6.02/1.27 % (1071958)Termination phase: Saturation
% 6.02/1.27 % (1071958)Time elapsed: 0.069 s
% 6.02/1.27 % (1071958)Peak memory usage: 13 MB
% 6.02/1.27 % (1071958)Instructions burned: 132 (million)
% 6.02/1.27 % (1071947)Instruction limit reached!
% 6.02/1.27 % (1071947)------------------------------
% 6.02/1.27 % (1071947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071947)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071947)Termination reason: Instruction limit
% 6.02/1.29 % (1071947)Termination phase: Saturation
% 6.02/1.29 % (1071947)Time elapsed: 0.114 s
% 6.02/1.29 % (1071947)Peak memory usage: 13 MB
% 6.02/1.29 % (1071947)Instructions burned: 131 (million)
% 6.02/1.29 % (1071962)ott-21_1_sil=16000:fs=off:random_seed=722722434:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.02/1.29 % (1071963)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=151451133:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.02/1.29 % (1071964)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1668429162:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % (1071948)Instruction limit reached!
% 6.02/1.29 % (1071948)------------------------------
% 6.02/1.29 % (1071948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071948)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071948)Termination reason: Instruction limit
% 6.02/1.29 % (1071948)Termination phase: Saturation
% 6.02/1.29 % (1071948)Time elapsed: 0.179 s
% 6.02/1.29 % (1071948)Peak memory usage: 13 MB
% 6.02/1.29 % (1071948)Instructions burned: 160 (million)
% 6.02/1.29 % (1071968)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=828740309:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 6.02/1.29 % (1071969)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=626911824:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % (1071962)Instruction limit reached!
% 6.02/1.29 % (1071962)------------------------------
% 6.02/1.29 % (1071962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071962)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071962)Termination reason: Instruction limit
% 6.02/1.29 % (1071962)Termination phase: Saturation
% 6.02/1.29 % (1071962)Time elapsed: 0.139 s
% 6.02/1.29 % (1071962)Peak memory usage: 12 MB
% 6.02/1.29 % (1071962)Instructions burned: 180 (million)
% 6.02/1.29 % (1071972)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=3886505864: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)
% 6.02/1.29 % (1071972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.29 % (1071973)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=572603791:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 6.02/1.29 % (1071973)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.29 % (1071960)Instruction limit reached!
% 6.02/1.29 % (1071960)------------------------------
% 6.02/1.29 % (1071960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071960)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071960)Termination reason: Instruction limit
% 6.02/1.29 % (1071960)Termination phase: Saturation
% 6.02/1.29 % (1071960)Time elapsed: 0.346 s
% 6.02/1.29 % (1071960)Peak memory usage: 16 MB
% 6.02/1.29 % (1071960)Instructions burned: 684 (million)
% 6.02/1.29 % (1071963)Instruction limit reached!
% 6.02/1.29 % (1071963)------------------------------
% 6.02/1.29 % (1071963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071963)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071963)Termination reason: Instruction limit
% 6.02/1.29 % (1071963)Termination phase: Saturation
% 6.02/1.29 % (1071963)Time elapsed: 0.265 s
% 6.02/1.29 % (1071963)Peak memory usage: 13 MB
% 6.02/1.29 % (1071963)Instructions burned: 478 (million)
% 6.02/1.29 % (1071976)fmb+10_1_sil=64000:random_seed=2597589703:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 6.02/1.29 % (1071977)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=620435493:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 6.02/1.29 % (1071976)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % (1071980)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=312664732:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 6.02/1.29 % (1071981)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=992459575:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 6.02/1.29 % (1071981)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % (1071984)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=320737885:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 6.02/1.29 % (1071984)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.02/1.29 % (1071984)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.02/1.29 % (1071968)Instruction limit reached!
% 6.02/1.29 % (1071968)------------------------------
% 6.02/1.29 % (1071968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071968)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071968)Termination reason: Instruction limit
% 6.02/1.29 % (1071968)Termination phase: Saturation
% 6.02/1.29 % (1071968)Time elapsed: 0.578 s
% 6.02/1.29 % (1071968)Peak memory usage: 17 MB
% 6.02/1.29 % (1071968)Instructions burned: 1181 (million)
% 6.02/1.29 % (1071973)Instruction limit reached!
% 6.02/1.29 % (1071973)------------------------------
% 6.02/1.29 % (1071973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.29 % (1071973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.29 % (1071973)CaDiCaL version: 2.1.3
% 6.02/1.29 % (1071973)Termination reason: Instruction limit
% 6.02/1.29 % (1071973)Termination phase: Saturation
% 6.02/1.29 % (1071973)Time elapsed: 0.489 s
% 6.02/1.29 % (1071973)Peak memory usage: 15 MB
% 6.02/1.29 % (1071973)Instructions burned: 880 (million)
% 6.02/1.29 % (1071987)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3436615506:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % (1071988)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1856106563:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 6.02/1.29 % Exception at run slice level
% 6.02/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.29 % (1071990)ott-2_1_sil=16000:newcnf=on:random_seed=3785016506:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 6.02/1.30 % (1071990)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.02/1.30 % (1071992)ott+10_1_sil=32000:tgt=ground:random_seed=4245230820:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 6.02/1.30 % (1071972)Instruction limit reached!
% 6.02/1.30 % (1071972)------------------------------
% 6.02/1.30 % (1071972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.02/1.30 % (1071972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.02/1.30 % (1071972)CaDiCaL version: 2.1.3
% 6.02/1.30 % (1071972)Termination reason: Instruction limit
% 6.02/1.30 % (1071972)Termination phase: Saturation
% 6.02/1.30 % (1071972)Time elapsed: 0.614 s
% 6.02/1.30 % (1071972)Peak memory usage: 15 MB
% 6.02/1.30 % (1071972)Instructions burned: 693 (million)
% 6.02/1.30 % (1071995)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3295770979:i=54282_2990 on theBenchmark for (2990ds/54282Mi)
% 6.02/1.30 % Exception at run slice level
% 6.02/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.02/1.30 % (1071943) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1071937-1071943"...
% 6.02/1.30 % (1071943)...printing done.
% 6.02/1.30 % (1071997)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=4049045335:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 6.02/1.30 % (1071943)Refutation found. Thanks to Tanya!
% 6.02/1.30 % SZS status Theorem for theBenchmark
% 6.02/1.30 % SZS output start Proof for theBenchmark
% 6.02/1.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 6.02/1.30 thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_2, type, inv: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_3, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_4, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_5, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_6, type, refl: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_7, type, irrefl: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_8, type, rc: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_9, type, symm: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_10, type, antisymm: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_11, type, asymm: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_12, type, sc: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_13, type, trans: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_14, type, tc: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_15, type, trc: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_16, type, trsc: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_17, type, po: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_18, type, so: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_19, type, total: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_20, type, term: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_21, type, ind: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_22, type, innf: (($i > $i > $o) > $i > $o)).
% 6.02/1.30 thf(func_def_23, type, nfof: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_24, type, norm: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_25, type, join: (($i > $i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_26, type, lconfl: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_27, type, sconfl: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_28, type, confl: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_29, type, cr: (($i > $i > $o) > $o)).
% 6.02/1.30 thf(func_def_30, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.02/1.30 thf(func_def_31, type, vIMP: ($o > $o > $o)).
% 6.02/1.30 thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
% 6.02/1.30 thf(func_def_33, type, db0: !>[X0: $tType]:(X0)).
% 6.02/1.30 thf(func_def_34, type, db1: !>[X0: $tType]:(X0)).
% 6.02/1.30 thf(func_def_35, type, db2: !>[X0: $tType]:(X0)).
% 6.02/1.30 thf(func_def_36, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.02/1.30 thf(func_def_37, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.02/1.30 thf(func_def_38, type, vNOT: ($o > $o)).
% 6.02/1.30 thf(func_def_39, type, vOR: ($o > $o > $o)).
% 6.02/1.30 thf(func_def_40, type, vAND: ($o > $o > $o)).
% 6.02/1.30 thf(func_def_41, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.02/1.30 thf(func_def_44, type, sK0: ($i > $i > $o)).
% 6.02/1.30 thf(func_def_45, type, sK1: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_46, type, sK2: ($i > ($i > $o) > $i > $i > $o)).
% 6.02/1.30 thf(func_def_47, type, sK3: ($i > $o)).
% 6.02/1.30 thf(func_def_49, type, sK5: ($i > $i)).
% 6.02/1.30 thf(func_def_51, type, sK7: ($i > $i)).
% 6.02/1.30 thf(func_def_52, type, sK8: ($i > $i)).
% 6.02/1.30 thf(func_def_53, type, sK9: ($i > $i)).
% 6.02/1.30 thf(func_def_54, type, sK10: ($i > $i)).
% 6.02/1.30 thf(func_def_55, type, sK11: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_56, type, sK12: (($i > $o) > ($i > $i > $o) > ($i > $i) > ($i > $i) > $i)).
% 6.02/1.30 thf(func_def_57, type, sK13: ($i > $i)).
% 6.02/1.30 thf(func_def_58, type, sK14: ($i > $i)).
% 6.02/1.30 thf(func_def_59, type, sK15: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_60, type, sK16: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_61, type, sK17: ($i > $i)).
% 6.02/1.30 thf(func_def_62, type, sK18: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_63, type, sK19: ($i > ($i > $o) > $i)).
% 6.02/1.30 thf(func_def_64, type, sK20: ($i > $i)).
% 6.02/1.30 thf(func_def_65, type, sK21: (($i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_66, type, sK22: ($i > $i)).
% 6.02/1.30 thf(func_def_67, type, sK23: ($i > ($i > $i) > $i)).
% 6.02/1.30 thf(func_def_68, type, sK24: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_69, type, sK25: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_70, type, sK26: ($i > ($i > $i) > $i)).
% 6.02/1.30 thf(func_def_71, type, sK27: ($i > $i)).
% 6.02/1.30 thf(func_def_72, type, sK28: ($i > $i)).
% 6.02/1.30 thf(func_def_73, type, sK29: ($i > $i)).
% 6.02/1.30 thf(func_def_74, type, sK30: ($i > $i)).
% 6.02/1.30 thf(func_def_75, type, sK31: (($i > $i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_76, type, sK32: (($i > $i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_77, type, sK33: (($i > $i > $o) > $i)).
% 6.02/1.30 thf(func_def_78, type, sK34: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_79, type, sK35: ($i > $i)).
% 6.02/1.30 thf(func_def_80, type, sK36: (($i > $i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_81, type, sK37: ($i > $i)).
% 6.02/1.30 thf(func_def_82, type, sK38: ($i > $i)).
% 6.02/1.30 thf(func_def_83, type, sK39: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_84, type, sK40: (($i > $i) > ($i > $o) > $i)).
% 6.02/1.30 thf(func_def_85, type, sK41: (($i > $i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_86, type, sK42: (($i > $o) > $i)).
% 6.02/1.30 thf(func_def_87, type, sK43: ($i > ($i > $i > $o) > $i)).
% 6.02/1.30 thf(func_def_88, type, sK44: ($i > $i)).
% 6.02/1.30 thf(func_def_89, type, sK45: (($i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_90, type, sK46: ($i > ($i > $i) > $i)).
% 6.02/1.30 thf(func_def_91, type, sK47: (($i > $i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_92, type, sK48: (($i > $i > $o) > $i > $i)).
% 6.02/1.30 thf(func_def_93, type, sK49: ($i > $i)).
% 6.02/1.30 thf(func_def_94, type, sK50: ($i > $i)).
% 6.02/1.30 thf(func_def_95, type, sK51: ($i > ($i > $i) > $i)).
% 6.02/1.30 thf(func_def_96, type, sK52: (($i > $o) > $i > $i)).
% 6.02/1.30 thf(f1,axiom,(
% 6.02/1.30 (subrel = (^[X0 : ($i > $i > $o), X1 : ($i > $i > $o)] : (! [X2 : $i,X3 : $i] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 6.02/1.30 file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',subrel)).
% 6.02/1.30 thf(f13,axiom,(
% 6.02/1.30 (trans = (^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i,X3 : $i] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))))),
% 6.02/1.30 file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive)).
% 6.02/1.30 thf(f14,axiom,(
% 6.02/1.30 (tc = (^[X0 : ($i > $i > $o), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))))),
% 6.02/1.30 file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive_closure)).
% 6.02/1.30 thf(f20,axiom,(
% 6.02/1.30 (term = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (? [X2 : $i] : (X1 @ X2) => ? [X2 : $i] : (! [X3 : $i] : ((X1 @ X3) => ~(X0 @ X2 @ X3)) & (X1 @ X2))))))),
% 6.02/1.30 file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',terminating)).
% 6.02/1.30 thf(f21,axiom,(
% 6.02/1.30 (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X2 : $i] : (X1 @ X2)))))),
% 6.02/1.30 file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',satisfying_the_induction_principle)).
% 6.02/1.30 thf(f30,conjecture,(
% 6.02/1.30 ! [X0 : ($i > $i > $o)] : ((ind @ X0) => (term @ X0))),
% 6.02/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction_implies_termination)).
% 6.02/1.30 thf(f31,negated_conjecture,(
% 6.02/1.30 ~ ! [X0 : ($i > $i > $o)] : ((ind @ X0) => (term @ X0))),
% 6.02/1.30 inference(negated_conjecture,[status(cth)],[f30])).
% 6.02/1.30 thf(f32,plain,(
% 6.02/1.30 (subrel = (^[X0 : ($i > $i > $o), X1 : ($i > $i > $o)] : (! [X2 : $i,X3 : $i] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 6.02/1.30 inference(rectify,[],[f1])).
% 6.02/1.30 thf(f33,plain,(
% 6.02/1.30 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 6.02/1.30 inference(fool_elimination,[],[f32])).
% 6.02/1.30 thf(f54,plain,(
% 6.02/1.30 (trans = (^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i,X3 : $i] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))))),
% 6.02/1.30 inference(rectify,[],[f13])).
% 6.02/1.30 thf(f55,plain,(
% 6.02/1.30 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 6.02/1.30 inference(fool_elimination,[],[f54])).
% 6.02/1.30 thf(f56,plain,(
% 6.02/1.30 (tc = (^[X0 : ($i > $i > $o), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))))),
% 6.02/1.30 inference(rectify,[],[f14])).
% 6.02/1.30 thf(f57,plain,(
% 6.02/1.30 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 6.02/1.30 inference(fool_elimination,[],[f56])).
% 6.02/1.30 thf(f66,plain,(
% 6.02/1.30 (term = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (? [X2 : $i] : (X1 @ X2) => ? [X3 : $i] : (! [X4 : $i] : ((X1 @ X4) => ~(X0 @ X3 @ X4)) & (X1 @ X3))))))),
% 6.02/1.30 inference(rectify,[],[f20])).
% 6.02/1.30 thf(f67,plain,(
% 6.02/1.30 (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (~ (Y0 @ Y2 @ Y3)))))))))))))),
% 6.02/1.30 inference(fool_elimination,[],[f66])).
% 6.02/1.30 thf(f68,plain,(
% 6.02/1.30 (ind = (^[X0 : ($i > $i > $o)] : (! [X1 : ($i > $o)] : (! [X2 : $i] : (! [X3 : $i] : ((tc @ X0 @ X2 @ X3) => (X1 @ X3)) => (X1 @ X2)) => ! [X4 : $i] : (X1 @ X4)))))),
% 6.02/1.30 inference(rectify,[],[f21])).
% 6.02/1.30 thf(f69,plain,(
% 6.02/1.30 (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 6.02/1.30 inference(fool_elimination,[],[f68])).
% 6.02/1.30 thf(f86,plain,(
% 6.02/1.30 ~ ! [X0 : ($i > $i > $o)] : ((ind @ X0) => (term @ X0))),
% 6.02/1.30 inference(rectify,[],[f31])).
% 6.02/1.30 thf(f87,plain,(
% 6.02/1.30 ~ ! [X0 : ($i > $i > $o)] : ((((ind @ X0)) = $true) => (((term @ X0)) = $true))),
% 6.02/1.30 inference(fool_elimination,[],[f86])).
% 6.02/1.30 thf(f88,plain,(
% 6.02/1.30 ? [X0 : ($i > $i > $o)] : ((((term @ X0)) != $true) & (((ind @ X0)) = $true))),
% 6.02/1.30 inference(ennf_transformation,[],[f87])).
% 6.02/1.30 thf(f89,plain,(
% 6.02/1.30 ($true != ((term @ sK0))) & ($true = ((ind @ sK0)))),
% 6.02/1.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88])).
% 6.02/1.30 thf(f90,plain,(
% 6.02/1.30 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 6.02/1.30 inference(cnf_transformation,[],[f33])).
% 6.02/1.30 thf(f102,plain,(
% 6.02/1.30 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 6.02/1.30 inference(cnf_transformation,[],[f55])).
% 6.02/1.30 thf(f103,plain,(
% 6.02/1.30 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 6.02/1.30 inference(cnf_transformation,[],[f57])).
% 6.02/1.30 thf(f109,plain,(
% 6.02/1.30 (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (~ (Y0 @ Y2 @ Y3)))))))))))))),
% 6.02/1.30 inference(cnf_transformation,[],[f67])).
% 6.02/1.30 thf(f110,plain,(
% 6.02/1.30 (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((tc @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 6.02/1.30 inference(cnf_transformation,[],[f69])).
% 6.02/1.30 thf(f119,plain,(
% 6.02/1.30 ($true = ((ind @ sK0)))),
% 6.02/1.30 inference(cnf_transformation,[],[f89])).
% 6.02/1.30 thf(f120,plain,(
% 6.02/1.30 ($true != ((term @ sK0)))),
% 6.02/1.30 inference(cnf_transformation,[],[f89])).
% 6.02/1.30 thf(f122,definition,(
% 6.02/1.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.02/1.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 6.02/1.30 thf(f125,plain,(
% 6.02/1.30 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 6.02/1.30 inference(definition_unfolding,[],[f103,f102,f90])).
% 6.02/1.30 thf(f130,plain,(
% 6.02/1.30 (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: ((((^[Y8 : $i > $i > $o]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y8 @ Y11 @ Y10) & (Y8 @ Y10 @ Y9)) => (Y8 @ Y11 @ Y9))))))))) @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((Y8 @ Y11 @ Y10) => (Y9 @ Y11 @ Y10))))))))) @ Y4 @ Y7)) => (Y7 @ Y5 @ Y6))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 6.02/1.30 inference(definition_unfolding,[],[f110,f125])).
% 6.02/1.30 thf(f138,plain,(
% 6.02/1.30 ($true != (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (~ (Y0 @ Y2 @ Y3)))))))))))) @ sK0)))),
% 6.02/1.30 inference(definition_unfolding,[],[f120,f109])).
% 6.02/1.30 thf(f139,plain,(
% 6.02/1.30 ($true = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: ((((^[Y8 : $i > $i > $o]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y8 @ Y11 @ Y10) & (Y8 @ Y10 @ Y9)) => (Y8 @ Y11 @ Y9))))))))) @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((Y8 @ Y11 @ Y10) => (Y9 @ Y11 @ Y10))))))))) @ Y4 @ Y7)) => (Y7 @ Y5 @ Y6))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2))))))) @ sK0)))),
% 6.02/1.30 inference(definition_unfolding,[],[f119,f130])).
% 6.02/1.30 thf(f140,plain,(
% 6.02/1.30 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))))))),
% 6.02/1.30 inference(beta-eta_normalization,[],[f139])).
% 6.02/1.30 thf(f141,plain,(
% 6.02/1.30 ( ! [X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2)))) => (Y0 @ Y2)))) => (Y0 @ Y1)))) => (!! @ $i @ Y0))) @ X1)))) )),
% 6.02/1.30 inference(pi_proxy_clausification,[],[f140])).
% 6.02/1.30 thf(f142,plain,(
% 6.02/1.30 ( ! [X1 : ($i > $o)] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK0 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))) => (X1 @ Y1)))) => (X1 @ Y0)))) => (!! @ $i @ X1))))) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f141])).
% 6.02/1.30 thf(f143,plain,(
% 6.02/1.30 ( ! [X1 : ($i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK0 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))) => (X1 @ Y1)))) => (X1 @ Y0)))))) | ($true = ((!! @ $i @ X1)))) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f142])).
% 6.02/1.30 thf(f144,plain,(
% 6.02/1.30 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK0 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))) => (X1 @ Y1)))) => (X1 @ Y0))) @ (sK1 @ X1)))) | ($true = ((!! @ $i @ X1)))) )),
% 6.02/1.30 inference(sigma_proxy_clausification,[],[f143])).
% 6.02/1.30 thf(f145,plain,(
% 6.02/1.30 ( ! [X2 : $i,X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK0 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))) => (X1 @ Y1)))) => (X1 @ Y0))) @ (sK1 @ X1)))) | (((X1 @ X2)) = $true)) )),
% 6.02/1.30 inference(pi_proxy_clausification,[],[f144])).
% 6.02/1.30 thf(f146,plain,(
% 6.02/1.30 ( ! [X2 : $i,X1 : ($i > $o)] : (($false = (((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ (sK1 @ X1) @ Y0)))) => (X1 @ Y0)))) => (X1 @ (sK1 @ X1))))) | (((X1 @ X2)) = $true)) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f145])).
% 6.02/1.30 thf(f147,plain,(
% 6.02/1.30 ( ! [X2 : $i,X1 : ($i > $o)] : (($false = ((X1 @ (sK1 @ X1)))) | (((X1 @ X2)) = $true)) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f146])).
% 6.02/1.30 thf(f148,plain,(
% 6.02/1.30 ( ! [X2 : $i,X1 : ($i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ (sK1 @ X1) @ Y0)))) => (X1 @ Y0)))))) | (((X1 @ X2)) = $true)) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f146])).
% 6.02/1.30 thf(f149,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($true = (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ (sK1 @ X1) @ Y0)))) => (X1 @ Y0))) @ X3))) | (((X1 @ X2)) = $true)) )),
% 6.02/1.30 inference(pi_proxy_clausification,[],[f148])).
% 6.02/1.30 thf(f150,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($true = (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ (sK1 @ X1) @ X3)))) => (X1 @ X3)))) | (((X1 @ X2)) = $true)) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f149])).
% 6.02/1.30 thf(f151,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ (sK1 @ X1) @ X3)))))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f150])).
% 6.02/1.30 thf(f152,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($false = (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ (sK1 @ X1) @ X3))) @ (sK2 @ X3 @ X1)))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(sigma_proxy_clausification,[],[f151])).
% 6.02/1.30 thf(f153,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($false = ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ X3 @ X1 @ Y2 @ Y1) & (sK2 @ X3 @ X1 @ Y1 @ Y0)) => (sK2 @ X3 @ X1 @ Y2 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (sK2 @ X3 @ X1 @ Y1 @ Y0))))))) => (sK2 @ X3 @ X1 @ (sK1 @ X1) @ X3)))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f152])).
% 6.02/1.30 thf(f154,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($false = ((sK2 @ X3 @ X1 @ (sK1 @ X1) @ X3))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f153])).
% 6.02/1.30 thf(f155,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ X3 @ X1 @ Y2 @ Y1) & (sK2 @ X3 @ X1 @ Y1 @ Y0)) => (sK2 @ X3 @ X1 @ Y2 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (sK2 @ X3 @ X1 @ Y1 @ Y0))))))))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f153])).
% 6.02/1.30 thf(f156,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (sK2 @ X3 @ X1 @ Y1 @ Y0)))))))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(and_proxy_clausification,[],[f155])).
% 6.02/1.30 thf(f166,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (sK2 @ X3 @ X1 @ Y1 @ Y0))))) @ X4))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(pi_proxy_clausification,[],[f156])).
% 6.02/1.30 thf(f167,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o),X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X4) => (sK2 @ X3 @ X1 @ Y0 @ X4)))))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f166])).
% 6.02/1.30 thf(f168,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((sK0 @ Y0 @ X4) => (sK2 @ X3 @ X1 @ Y0 @ X4))) @ X5))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(pi_proxy_clausification,[],[f167])).
% 6.02/1.30 thf(f169,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = (((sK0 @ X5 @ X4) => (sK2 @ X3 @ X1 @ X5 @ X4)))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true)) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f168])).
% 6.02/1.30 thf(f170,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X1 : ($i > $o),X4 : $i,X5 : $i] : (($true = ((sK2 @ X3 @ X1 @ X5 @ X4))) | (((X1 @ X2)) = $true) | (((X1 @ X3)) = $true) | ($false = ((sK0 @ X5 @ X4)))) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f169])).
% 6.02/1.30 thf(f171,plain,(
% 6.02/1.30 ($true != ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (~ (sK0 @ Y1 @ Y2)))))))))))))),
% 6.02/1.30 inference(beta-eta_normalization,[],[f138])).
% 6.02/1.30 thf(f172,plain,(
% 6.02/1.30 ($false = (((^[Y0 : $i > $o]: ((?? @ $i @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (~ (sK0 @ Y1 @ Y2)))))))))) @ sK3)))),
% 6.02/1.30 inference(sigma_proxy_clausification,[],[f171])).
% 6.02/1.30 thf(f173,plain,(
% 6.02/1.30 ($false = (((?? @ $i @ sK3) => (?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) => (~ (sK0 @ Y0 @ Y1)))))))))))),
% 6.02/1.30 inference(beta-eta_normalization,[],[f172])).
% 6.02/1.30 thf(f174,plain,(
% 6.02/1.30 ($false = ((?? @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) => (~ (sK0 @ Y0 @ Y1))))))))))),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f173])).
% 6.02/1.30 thf(f175,plain,(
% 6.02/1.30 ($true = ((?? @ $i @ sK3)))),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f173])).
% 6.02/1.30 thf(f176,plain,(
% 6.02/1.30 ($true = ((sK3 @ sK4)))),
% 6.02/1.30 inference(sigma_proxy_clausification,[],[f175])).
% 6.02/1.30 thf(f177,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK3 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) => (~ (sK0 @ Y0 @ Y1))))))) @ X1)))) )),
% 6.02/1.30 inference(pi_proxy_clausification,[],[f174])).
% 6.02/1.30 thf(f178,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($false = (((sK3 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (~ (sK0 @ X1 @ Y0))))))))) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f177])).
% 6.02/1.30 thf(f179,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) => (~ (sK0 @ X1 @ Y0))))))) | ($false = ((sK3 @ X1)))) )),
% 6.02/1.30 inference(and_proxy_clausification,[],[f178])).
% 6.02/1.30 thf(f180,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK3 @ Y0) => (~ (sK0 @ X1 @ Y0)))) @ (sK5 @ X1)))) | ($false = ((sK3 @ X1)))) )),
% 6.02/1.30 inference(sigma_proxy_clausification,[],[f179])).
% 6.02/1.30 thf(f181,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($false = (((sK3 @ (sK5 @ X1)) => (~ (sK0 @ X1 @ (sK5 @ X1)))))) | ($false = ((sK3 @ X1)))) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f180])).
% 6.02/1.30 thf(f182,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($false = ((~ (sK0 @ X1 @ (sK5 @ X1))))) | ($false = ((sK3 @ X1)))) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f181])).
% 6.02/1.30 thf(f183,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($true = ((sK3 @ (sK5 @ X1)))) | ($false = ((sK3 @ X1)))) )),
% 6.02/1.30 inference(imp_proxy_clausification,[],[f181])).
% 6.02/1.30 thf(f184,plain,(
% 6.02/1.30 ( ! [X1 : $i] : (($true = ((sK0 @ X1 @ (sK5 @ X1)))) | ($false = ((sK3 @ X1)))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f182])).
% 6.02/1.30 thf(f198,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : ($i > $o)] : (($false = (((^[Y0 : $i]: (~ (X3 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X3 @ Y0))))))) | ($true = (((^[Y0 : $i]: (~ (X3 @ Y0))) @ X2)))) )),
% 6.02/1.30 inference(primitive_instantiation,[],[f147])).
% 6.02/1.30 thf(f239,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : ($i > $o)] : (($false = ((~ (X3 @ (sK1 @ (^[Y0 : $i]: (~ (X3 @ Y0)))))))) | ($true = ((~ (X3 @ X2))))) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f198])).
% 6.02/1.30 thf(f240,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : ($i > $o)] : (($true = ((X3 @ (sK1 @ (^[Y0 : $i]: (~ (X3 @ Y0))))))) | ($true = ((~ (X3 @ X2))))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f239])).
% 6.02/1.30 thf(f241,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : ($i > $o)] : (($true = ((X3 @ (sK1 @ (^[Y0 : $i]: (~ (X3 @ Y0))))))) | ($false = ((X3 @ X2)))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f240])).
% 6.02/1.30 thf(f377,plain,(
% 6.02/1.30 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ X1))) | ($false = ((X0 @ X1))) | ($false != ((X0 @ (sK1 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))))) )),
% 6.02/1.30 inference(equality_factoring,[],[f241])).
% 6.02/1.30 thf(f474,plain,(
% 6.02/1.30 ( ! [X0 : ($i > $o),X1 : $i] : (($false != ((X0 @ (sK1 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($false = ((X0 @ X1)))) )),
% 6.02/1.30 inference(forward_subsumption_resolution,[],[f377,f122])).
% 6.02/1.30 thf(f478,definition,(
% 6.02/1.30 spl6_1 <=> ! [X0 : $i] : (sK4 != X0)),
% 6.02/1.30 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 6.02/1.30 thf(f479,plain,(
% 6.02/1.30 ( ! [X0 : $i] : ((sK4 != X0)) ) | ~spl6_1),
% 6.02/1.30 inference(avatar_component_clause,[],[f478])).
% 6.02/1.30 thf(f491,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X4 : ($i > $o)] : (($false = ((sK2 @ X3 @ (^[Y0 : $i]: (~ (X4 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))) @ X3))) | ($true = (((^[Y0 : $i]: (~ (X4 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: (~ (X4 @ Y0))) @ X3)))) )),
% 6.02/1.30 inference(primitive_instantiation,[],[f154])).
% 6.02/1.30 thf(f596,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X4 : ($i > $o)] : (($false = ((sK2 @ X3 @ (^[Y0 : $i]: (~ (X4 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))) @ X3))) | ($true = ((~ (X4 @ X2)))) | ($true = ((~ (X4 @ X3))))) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f491])).
% 6.02/1.30 thf(f597,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X4 : ($i > $o)] : (($false = ((sK2 @ X3 @ (^[Y0 : $i]: (~ (X4 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))) @ X3))) | ($false = ((X4 @ X2))) | ($true = ((~ (X4 @ X3))))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f596])).
% 6.02/1.30 thf(f598,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X4 : ($i > $o)] : (($false = ((sK2 @ X3 @ (^[Y0 : $i]: (~ (X4 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X4 @ Y0)))) @ X3))) | ($false = ((X4 @ X2))) | ($false = ((X4 @ X3)))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f597])).
% 6.02/1.30 thf(f655,plain,(
% 6.02/1.30 $false | ~spl6_1),
% 6.02/1.30 inference(equality_resolution,[],[f479])).
% 6.02/1.30 thf(f656,plain,(
% 6.02/1.30 ~spl6_1),
% 6.02/1.30 inference(avatar_contradiction_clause,[],[f655])).
% 6.02/1.30 thf(f1501,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = $false) | ($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ X0))) | ($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X1 @ Y0)))) @ X0))) | (((X1 @ X3)) = $false) | ($false = ((X1 @ X0)))) )),
% 6.02/1.30 inference(constrained_superposition,[],[f170,f598])).
% 6.02/1.30 thf(f1618,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ X0))) | ($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X1 @ Y0)))) @ X0))) | (((X1 @ X3)) = $false) | ($false = ((X1 @ X0)))) )),
% 6.02/1.30 inference(trivial_inequality_removal,[],[f1501])).
% 6.02/1.30 thf(f1619,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($true = ((~ (X1 @ X2)))) | ($true = ((~ (X1 @ X0)))) | ($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X1 @ Y0)))) @ X0))) | (((X1 @ X3)) = $false) | ($false = ((X1 @ X0)))) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f1618])).
% 6.02/1.30 thf(f1620,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : ((((X1 @ X2)) = $false) | ($true = ((~ (X1 @ X0)))) | ($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X1 @ Y0)))) @ X0))) | (((X1 @ X3)) = $false) | ($false = ((X1 @ X0)))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f1619])).
% 6.02/1.30 thf(f1621,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : ((((X1 @ X2)) = $false) | ($false = ((X1 @ X0))) | ($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X1 @ Y0)))) @ X0))) | (((X1 @ X3)) = $false) | ($false = ((X1 @ X0)))) )),
% 6.02/1.30 inference(not_proxy_clausification,[],[f1620])).
% 6.02/1.30 thf(f1622,plain,(
% 6.02/1.30 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : ($i > $o)] : (($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (X1 @ Y0)))) @ X0))) | (((X1 @ X3)) = $false) | (((X1 @ X2)) = $false) | ($false = ((X1 @ X0)))) )),
% 6.02/1.30 inference(duplicate_literal_removal,[],[f1621])).
% 6.02/1.30 thf(f6215,plain,(
% 6.02/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0)))) @ X1))) | ($false = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X2))) | ($false = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1))) | (sK4 != X0)) )),
% 6.02/1.30 inference(constrained_superposition,[],[f1622,f176])).
% 6.02/1.30 thf(f6987,plain,(
% 6.02/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK3 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0)))) @ X1))) | ($false = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X2))) | ($false = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1))) | (sK4 != X0)) )),
% 6.02/1.30 inference(trivial_inequality_removal,[],[f6215])).
% 6.02/1.30 thf(f6988,plain,(
% 6.02/1.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))) @ X1))) | ($false = ((sK3 @ X2))) | ($false = ((sK3 @ X1))) | (sK4 != X0)) )),
% 6.02/1.30 inference(beta-eta_normalization,[],[f6987])).
% 6.02/1.30 thf(f7089,definition,(
% 6.02/1.30 spl6_43 <=> ! [X2 : $i] : ($false = ((sK3 @ X2)))),
% 6.02/1.30 introduced(definition,[new_symbols(definition,[spl6_43])],[avatar_definition])).
% 6.02/1.30 thf(f7090,plain,(
% 6.02/1.30 ( ! [X2 : $i] : (($false = ((sK3 @ X2)))) ) | ~spl6_43),
% 6.02/1.30 inference(avatar_component_clause,[],[f7089])).
% 6.02/1.30 thf(f7092,definition,(
% 6.02/1.30 spl6_44 <=> ! [X1 : $i] : (($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))) @ X1))) | ($false = ((sK3 @ X1))))),
% 6.02/1.30 introduced(definition,[new_symbols(definition,[spl6_44])],[avatar_definition])).
% 6.84/1.30 thf(f7093,plain,(
% 6.84/1.30 ( ! [X1 : $i] : (($false = ((sK0 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))) @ X1))) | ($false = ((sK3 @ X1)))) ) | ~spl6_44),
% 6.84/1.30 inference(avatar_component_clause,[],[f7092])).
% 6.84/1.30 thf(f7111,plain,(
% 6.84/1.30 spl6_1 | spl6_43 | spl6_44),
% 6.84/1.30 inference(avatar_split_clause,[],[f6988,f7092,f7089,f478])).
% 6.84/1.30 thf(f7112,plain,(
% 6.84/1.30 ($true = $false) | ~spl6_43),
% 6.84/1.30 inference(constrained_superposition,[],[f7090,f176])).
% 6.84/1.30 thf(f7227,plain,(
% 6.84/1.30 $false | ~spl6_43),
% 6.84/1.30 inference(trivial_inequality_removal,[],[f7112])).
% 6.84/1.30 thf(f7228,plain,(
% 6.84/1.30 ~spl6_43),
% 6.84/1.30 inference(avatar_contradiction_clause,[],[f7227])).
% 6.84/1.30 thf(f11772,plain,(
% 6.84/1.30 ($true = $false) | ($false = ((sK3 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) | ($false = ((sK3 @ (sK5 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))))) | ~spl6_44),
% 6.84/1.30 inference(constrained_superposition,[],[f184,f7093])).
% 6.84/1.30 thf(f11782,plain,(
% 6.84/1.30 ($false = ((sK3 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) | ($false = ((sK3 @ (sK5 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))))) | ~spl6_44),
% 6.84/1.30 inference(trivial_inequality_removal,[],[f11772])).
% 6.84/1.30 thf(f11911,plain,(
% 6.84/1.30 ($false = ((sK3 @ (sK5 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0)))))))) | ~spl6_44),
% 6.84/1.30 inference(forward_subsumption_resolution,[],[f11782,f474])).
% 6.84/1.30 thf(f11961,plain,(
% 6.84/1.30 ($true = $false) | ($false = ((sK3 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) | ~spl6_44),
% 6.84/1.30 inference(constrained_superposition,[],[f183,f11911])).
% 6.84/1.30 thf(f12085,plain,(
% 6.84/1.30 ($false = ((sK3 @ (sK1 @ (^[Y0 : $i]: (~ (sK3 @ Y0))))))) | ~spl6_44),
% 6.84/1.30 inference(trivial_inequality_removal,[],[f11961])).
% 6.84/1.30 thf(f12717,plain,(
% 6.84/1.30 ( ! [X0 : $i] : (($true = $false) | ($false = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0)))) ) | ~spl6_44),
% 6.84/1.30 inference(constrained_superposition,[],[f241,f12085])).
% 6.84/1.30 thf(f12815,plain,(
% 6.84/1.30 ( ! [X0 : $i] : (($false = (((^[Y0 : $i]: (sK3 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X0)))) ) | ~spl6_44),
% 6.84/1.30 inference(trivial_inequality_removal,[],[f12717])).
% 6.84/1.30 thf(f12816,plain,(
% 6.84/1.30 ( ! [X0 : $i] : (($false = ((sK3 @ X0)))) ) | ~spl6_44),
% 6.84/1.30 inference(beta-eta_normalization,[],[f12815])).
% 6.84/1.30 thf(f12902,plain,(
% 6.84/1.30 spl6_43 | ~spl6_44),
% 6.84/1.30 inference(avatar_split_clause,[],[f12816,f7092,f7089])).
% 6.84/1.30 cnf(s4, plain, ~spl6_1, inference(sat_conversion,[],[f656])).
% 6.84/1.30 cnf(s107, plain, spl6_1 | spl6_43 | spl6_44, inference(sat_conversion,[],[f7111])).
% 6.84/1.30 cnf(s111, plain, ~spl6_43, inference(sat_conversion,[],[f7228])).
% 6.84/1.30 cnf(s280, plain, spl6_43 | ~spl6_44, inference(sat_conversion,[],[f12902])).
% 6.84/1.30 cnf(s295, plain, ~spl6_44, inference(rat,[],[s280,s111])).
% 6.84/1.30 cnf(s297, plain, spl6_1, inference(rat,[],[s107,s295,s111])).
% 6.84/1.30 cnf(s333, plain, $false, inference(rat,[],[s4,s297])).
% 6.84/1.30 thf(f12912,plain,(
% 6.84/1.30 $false),
% 6.84/1.30 inference(avatar_sat_refutation,[],[s333])).
% 6.84/1.30 % SZS output end Proof for theBenchmark
% 6.84/1.30 % (1071943)------------------------------
% 6.84/1.30 % (1071943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.84/1.30 % (1071943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.84/1.30 % (1071943)CaDiCaL version: 2.1.3
% 6.84/1.30 % (1071943)Termination reason: Refutation
% 6.84/1.30 % (1071943)Time elapsed: 0.989 s
% 6.84/1.30 % (1071943)Peak memory usage: 18 MB
% 6.84/1.30 % (1071943)Instructions burned: 2189 (million)
% 6.84/1.30 % (1071937)Success in time 1.025 s
% 6.84/1.30 % Vampire exiting
%------------------------------------------------------------------------------