%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO264^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:49:37 AM UTC 2026
% Result : Theorem 6.90s 1.28s
% Output : Refutation 6.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO264^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n011.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:42:16 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 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
% 4.34/0.99 % (324517)Will run a generic schedule for satisfiability detection.
% 4.34/0.99 % (324528)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1574012374:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.34/0.99 % (324523)% WARNING: option uhcvi not known.
% 4.34/0.99 % (324523)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=770488594:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.34/0.99 % (324527)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4246523345:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.34/0.99 % (324522)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2852167317_2999 on theBenchmark for (2999ds/0Mi)
% 4.34/0.99 % (324525)dis+10_1_sil=32000:sp=arity:random_seed=4031134145:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.34/0.99 % (324526)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1760219487:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.34/0.99 % (324524)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3843330545:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.34/0.99 % (324523)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.34/0.99 % (324526)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.34/0.99 % (324523)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.34/0.99 % Exception at run slice level
% 4.34/0.99 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.34/0.99 % (324536)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3431007794:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.34/0.99 % Exception at run slice level
% 4.34/0.99 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.34/0.99 % (324528)Instruction limit reached!
% 4.34/0.99 % (324528)------------------------------
% 4.34/0.99 % (324528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.34/0.99 % (324528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/0.99 % (324528)CaDiCaL version: 2.1.3
% 4.34/0.99 % (324528)Termination reason: Instruction limit
% 4.34/0.99 % (324528)Termination phase: Saturation
% 4.34/0.99 % (324528)Time elapsed: 0.044 s
% 4.34/0.99 % (324528)Peak memory usage: 13 MB
% 4.34/0.99 % (324528)Instructions burned: 159 (million)
% 4.34/0.99 % (324538)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2839512648:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.34/0.99 % (324539)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=2441283148:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.34/0.99 % (324539)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.34/0.99 % (324539)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.34/0.99 % (324525)Instruction limit reached!
% 4.34/0.99 % (324525)------------------------------
% 4.34/0.99 % (324525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.34/0.99 % (324525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/0.99 % (324525)CaDiCaL version: 2.1.3
% 4.34/0.99 % (324525)Termination reason: Instruction limit
% 4.34/0.99 % (324525)Termination phase: Saturation
% 4.34/0.99 % (324525)Time elapsed: 0.054 s
% 4.34/0.99 % (324525)Peak memory usage: 12 MB
% 4.34/0.99 % (324525)Instructions burned: 105 (million)
% 4.34/0.99 % (324526)Instruction limit reached!
% 4.34/0.99 % (324526)------------------------------
% 4.34/0.99 % (324526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.34/0.99 % (324526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/0.99 % (324526)CaDiCaL version: 2.1.3
% 4.34/0.99 % (324526)Termination reason: Instruction limit
% 4.34/0.99 % (324526)Termination phase: Saturation
% 4.34/0.99 % (324526)Time elapsed: 0.057 s
% 4.34/0.99 % (324526)Peak memory usage: 12 MB
% 4.34/0.99 % (324526)Instructions burned: 117 (million)
% 4.34/0.99 % (324527)Instruction limit reached!
% 4.34/0.99 % (324527)------------------------------
% 4.34/0.99 % (324527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.34/0.99 % (324527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324527)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324527)Termination reason: Instruction limit
% 6.90/1.28 % (324527)Termination phase: Saturation
% 6.90/1.28 % (324527)Time elapsed: 0.068 s
% 6.90/1.28 % (324527)Peak memory usage: 12 MB
% 6.90/1.28 % (324527)Instructions burned: 133 (million)
% 6.90/1.28 % (324542)ott-21_1_sil=16000:fs=off:random_seed=369103267:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.90/1.28 % (324543)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3432851534:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 6.90/1.28 % (324544)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3105087364:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324548)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2722077626:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.90/1.28 % (324538)Instruction limit reached!
% 6.90/1.28 % (324538)------------------------------
% 6.90/1.28 % (324538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324538)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324538)Termination reason: Instruction limit
% 6.90/1.28 % (324538)Termination phase: Saturation
% 6.90/1.28 % (324538)Time elapsed: 0.072 s
% 6.90/1.28 % (324538)Peak memory usage: 12 MB
% 6.90/1.28 % (324538)Instructions burned: 133 (million)
% 6.90/1.28 % (324550)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=675550639:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324542)Instruction limit reached!
% 6.90/1.28 % (324542)------------------------------
% 6.90/1.28 % (324542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324542)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324542)Termination reason: Instruction limit
% 6.90/1.28 % (324542)Termination phase: Saturation
% 6.90/1.28 % (324542)Time elapsed: 0.081 s
% 6.90/1.28 % (324542)Peak memory usage: 12 MB
% 6.90/1.28 % (324542)Instructions burned: 183 (million)
% 6.90/1.28 % (324552)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=2714941245:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 6.90/1.28 % (324552)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.28 % (324553)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=443697378:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 6.90/1.28 % (324553)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.28 % (324539)Instruction limit reached!
% 6.90/1.28 % (324539)------------------------------
% 6.90/1.28 % (324539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324539)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324539)Termination reason: Instruction limit
% 6.90/1.28 % (324539)Termination phase: Saturation
% 6.90/1.28 % (324539)Time elapsed: 0.175 s
% 6.90/1.28 % (324539)Peak memory usage: 14 MB
% 6.90/1.28 % (324539)Instructions burned: 687 (million)
% 6.90/1.28 % (324574)fmb+10_1_sil=64000:random_seed=3042450834:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 6.90/1.28 % (324574)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324579)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3222473370:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324585)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4259894833:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324591)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2754334672:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 6.90/1.28 % (324591)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.28 % (324543)Instruction limit reached!
% 6.90/1.28 % (324543)------------------------------
% 6.90/1.28 % (324543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324543)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324543)Termination reason: Instruction limit
% 6.90/1.28 % (324543)Termination phase: Saturation
% 6.90/1.28 % (324543)Time elapsed: 0.236 s
% 6.90/1.28 % (324543)Peak memory usage: 13 MB
% 6.90/1.28 % (324543)Instructions burned: 477 (million)
% 6.90/1.28 % (324619)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3949991139:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 6.90/1.28 % (324619)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.90/1.28 % (324619)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.90/1.28 % (324552)Instruction limit reached!
% 6.90/1.28 % (324552)------------------------------
% 6.90/1.28 % (324552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324552)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324552)Termination reason: Instruction limit
% 6.90/1.28 % (324552)Termination phase: Saturation
% 6.90/1.28 % (324552)Time elapsed: 0.321 s
% 6.90/1.28 % (324552)Peak memory usage: 16 MB
% 6.90/1.28 % (324552)Instructions burned: 694 (million)
% 6.90/1.28 % (324658)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2038687830:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324667)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=996675483:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324673)ott-2_1_sil=16000:newcnf=on:random_seed=4270409684:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 6.90/1.28 % (324673)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.90/1.28 % (324553)Instruction limit reached!
% 6.90/1.28 % (324553)------------------------------
% 6.90/1.28 % (324553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324553)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324553)Termination reason: Instruction limit
% 6.90/1.28 % (324553)Termination phase: Saturation
% 6.90/1.28 % (324553)Time elapsed: 0.450 s
% 6.90/1.28 % (324553)Peak memory usage: 15 MB
% 6.90/1.28 % (324553)Instructions burned: 881 (million)
% 6.90/1.28 % (324693)ott+10_1_sil=32000:tgt=ground:random_seed=1659255012:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.90/1.28 % (324548)Instruction limit reached!
% 6.90/1.28 % (324548)------------------------------
% 6.90/1.28 % (324548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324548)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324548)Termination reason: Instruction limit
% 6.90/1.28 % (324548)Termination phase: Saturation
% 6.90/1.28 % (324548)Time elapsed: 0.572 s
% 6.90/1.28 % (324548)Peak memory usage: 16 MB
% 6.90/1.28 % (324548)Instructions burned: 1181 (million)
% 6.90/1.28 % (324712)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4127176045:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 6.90/1.28 % Exception at run slice level
% 6.90/1.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.90/1.28 % (324716)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2881965949:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 6.90/1.28 % (324716)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.90/1.28 % (324673)Instruction limit reached!
% 6.90/1.28 % (324673)------------------------------
% 6.90/1.28 % (324673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.28 % (324673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.28 % (324673)CaDiCaL version: 2.1.3
% 6.90/1.28 % (324673)Termination reason: Instruction limit
% 6.90/1.28 % (324673)Termination phase: Saturation
% 6.90/1.28 % (324673)Time elapsed: 0.414 s
% 6.90/1.28 % (324673)Peak memory usage: 14 MB
% 6.90/1.28 % (324673)Instructions burned: 871 (million)
% 6.90/1.28 % (324785)dis+21_1_sil=32000:sas=cadical:random_seed=1193137821:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 6.90/1.28 % (324591) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-324517-324591"...
% 6.90/1.28 % (324591)...printing done.
% 6.90/1.28 % (324591)Refutation found. Thanks to Tanya!
% 6.90/1.28 % SZS status Theorem for theBenchmark
% 6.90/1.28 % SZS output start Proof for theBenchmark
% 6.90/1.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 6.90/1.28 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $i > $o)).
% 6.90/1.28 thf(func_def_7, type, sK4: ($i > $o)).
% 6.90/1.28 thf(func_def_8, type, sK5: (($i > $o) > $i)).
% 6.90/1.28 thf(func_def_9, type, vNOT: ($o > $o)).
% 6.90/1.28 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.90/1.28 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 6.90/1.28 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.90/1.28 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 6.90/1.28 thf(func_def_15, type, sK7: ($i > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_16, type, sK8: ($i > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_17, type, sK9: ($i > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_18, type, db2: !>[X0: $tType]:(X0)).
% 6.90/1.28 thf(func_def_19, type, sK10: ($i > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_20, type, sK11: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_21, type, sK12: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_22, type, sK13: ($i > $i)).
% 6.90/1.28 thf(func_def_23, type, sK14: ($i > $i)).
% 6.90/1.28 thf(func_def_24, type, sK15: (($i > $o) > $i)).
% 6.90/1.28 thf(func_def_25, type, sK16: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_26, type, sK17: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_27, type, sK18: (($i > $o) > $i)).
% 6.90/1.28 thf(func_def_28, type, sK19: (($i > $o) > $i)).
% 6.90/1.28 thf(func_def_30, type, sK21: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_31, type, sK22: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_32, type, sK23: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_33, type, sK24: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_34, type, sK25: (($i > $o) > $i)).
% 6.90/1.28 thf(func_def_35, type, sK26: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_36, type, sK27: (($i > $o) > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_37, type, sK28: (($i > $o) > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_38, type, sK29: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_39, type, sK30: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_40, type, sK31: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_41, type, sK32: (($i > $i > $o) > ($i > $i) > ($i > $i > $i) > $i)).
% 6.90/1.28 thf(func_def_42, type, sK33: (($i > $i > $i) > ($i > $i) > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_43, type, sK34: (($i > $i > $o) > ($i > $i) > ($i > $i > $i) > $i)).
% 6.90/1.28 thf(func_def_44, type, sK35: (($i > $i > $i) > ($i > $i) > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_45, type, sK36: (($i > $i > $i) > ($i > $i) > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_46, type, sK37: (($i > $i > $o) > ($i > $i) > ($i > $i > $i) > $i)).
% 6.90/1.28 thf(func_def_47, type, sK38: ($i > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_48, type, sK39: ($i > ($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_49, type, sK40: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_50, type, sK41: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_51, type, sK42: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_52, type, sK43: (($i > $o) > $i)).
% 6.90/1.28 thf(func_def_53, type, sK44: (($i > $i > $o) > $i)).
% 6.90/1.28 thf(func_def_54, type, sK45: (($i > $o) > $i)).
% 6.90/1.28 thf(f1,conjecture,(
% 6.90/1.28 ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & (~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X1) | (X3 @ X1)) & ((X5 @ X0) | (X4 @ X0)))),
% 6.90/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM125C)).
% 6.90/1.28 thf(f2,negated_conjecture,(
% 6.90/1.28 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & (~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X1) | (X3 @ X1)) & ((X5 @ X0) | (X4 @ X0)))),
% 6.90/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 6.90/1.28 thf(f3,plain,(
% 6.90/1.28 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((X5 @ X6) <=> ~(X3 @ X6)) & (~(X3 @ X2) | (X4 @ X2)) & ((X5 @ X1) | (X3 @ X1)) & ((X5 @ X0) | (X4 @ X0)))),
% 6.90/1.28 inference(rectify,[],[f2])).
% 6.90/1.28 thf(f4,plain,(
% 6.90/1.28 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((((X5 @ X6)) = $true) <=> ~ (((X3 @ X6)) = $true)) & (~ (((X3 @ X2)) = $true) | (((X4 @ X2)) = $true)) & ((((X5 @ X1)) = $true) | (((X3 @ X1)) = $true)) & ((((X5 @ X0)) = $true) | (((X4 @ X0)) = $true)))),
% 6.90/1.28 inference(fool_elimination,[],[f3])).
% 6.90/1.28 thf(f5,plain,(
% 6.90/1.28 ~ ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (! [X6 : $i] : ((((X5 @ X6)) = $true) <=> (((X3 @ X6)) != $true)) & ((((X3 @ X2)) != $true) | (((X4 @ X2)) = $true)) & ((((X5 @ X1)) = $true) | (((X3 @ X1)) = $true)) & ((((X5 @ X0)) = $true) | (((X4 @ X0)) = $true)))),
% 6.90/1.28 inference(flattening,[],[f4])).
% 6.90/1.28 thf(f6,plain,(
% 6.90/1.28 ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ X6)) = $true) <~> (((X3 @ X6)) != $true)) | ((((X3 @ X2)) = $true) & (((X4 @ X2)) != $true)) | ((((X5 @ X1)) != $true) & (((X3 @ X1)) != $true)) | ((((X5 @ X0)) != $true) & (((X4 @ X0)) != $true)))),
% 6.90/1.28 inference(ennf_transformation,[],[f5])).
% 6.90/1.28 thf(f7,definition,(
% 6.90/1.28 ! [X0 : $i,X5 : ($i > $o),X4 : ($i > $o)] : (((((X5 @ X0)) != $true) & (((X4 @ X0)) != $true)) | ~ ($true = ((sP0 @ X4 @ X5 @ X0))))),
% 6.90/1.28 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.90/1.28 thf(f8,plain,(
% 6.90/1.28 ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ X6)) = $true) <~> (((X3 @ X6)) != $true)) | ((((X3 @ X2)) = $true) & (((X4 @ X2)) != $true)) | ((((X5 @ X1)) != $true) & (((X3 @ X1)) != $true)) | ($true = ((sP0 @ X4 @ X5 @ X0))))),
% 6.90/1.28 inference(definition_folding,[],[f6,f7])).
% 6.90/1.28 thf(f9,plain,(
% 6.90/1.28 ! [X0 : $i,X5 : ($i > $o),X4 : ($i > $o)] : (((((X5 @ X0)) != $true) & (((X4 @ X0)) != $true)) | ($true != ((sP0 @ X4 @ X5 @ X0))))),
% 6.90/1.28 inference(nnf_transformation,[],[f7])).
% 6.90/1.28 thf(f10,plain,(
% 6.90/1.28 ! [X0 : $i,X1 : ($i > $o),X2 : ($i > $o)] : ((($true != ((X1 @ X0))) & ($true != ((X2 @ X0)))) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
% 6.90/1.28 inference(rectify,[],[f9])).
% 6.90/1.28 thf(f11,plain,(
% 6.90/1.28 ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : (((((X3 @ X6)) = $true) | (((X5 @ X6)) != $true)) & ((((X3 @ X6)) != $true) | (((X5 @ X6)) = $true))) | ((((X3 @ X2)) = $true) & (((X4 @ X2)) != $true)) | ((((X5 @ X1)) != $true) & (((X3 @ X1)) != $true)) | ($true = ((sP0 @ X4 @ X5 @ X0))))),
% 6.90/1.28 inference(nnf_transformation,[],[f8])).
% 6.90/1.28 thf(f12,plain,(
% 6.90/1.28 ! [X4 : ($i > $o),X5 : ($i > $o)] : (((($true = ((sK4 @ (sK5 @ X5)))) | ($true != ((X5 @ (sK5 @ X5))))) & (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((X5 @ (sK5 @ X5)))))) | (($true = ((sK4 @ sK3))) & ($true != ((X4 @ sK3)))) | (($true != ((X5 @ sK2))) & ($true != ((sK4 @ sK2)))) | ($true = ((sP0 @ X4 @ X5 @ sK1))))),
% 6.90/1.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4),skolemize(X6,sK5 @ X5)],[f11])).
% 6.90/1.28 thf(f13,plain,(
% 6.90/1.28 ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : (($true != ((X2 @ X0))) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 6.90/1.28 inference(cnf_transformation,[],[f10])).
% 6.90/1.28 thf(f15,plain,(
% 6.90/1.28 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true != ((sK4 @ sK2))) | ($true = ((sP0 @ X4 @ X5 @ sK1)))) )),
% 6.90/1.28 inference(cnf_transformation,[],[f12])).
% 6.90/1.28 thf(f16,plain,(
% 6.90/1.28 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true = ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true != ((X5 @ sK2))) | ($true = ((sP0 @ X4 @ X5 @ sK1)))) )),
% 6.90/1.28 inference(cnf_transformation,[],[f12])).
% 6.90/1.28 thf(f19,plain,(
% 6.90/1.28 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true = ((sK4 @ (sK5 @ X5)))) | ($true != ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true != ((sK4 @ sK2))) | ($true = ((sP0 @ X4 @ X5 @ sK1)))) )),
% 6.90/1.28 inference(cnf_transformation,[],[f12])).
% 6.90/1.28 thf(f20,plain,(
% 6.90/1.28 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((X5 @ sK2))) | ($true != ((X5 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ X5)))) | ($true = ((sP0 @ X4 @ X5 @ sK1)))) )),
% 6.90/1.28 inference(cnf_transformation,[],[f12])).
% 6.90/1.28 thf(f24,definition,(
% 6.90/1.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.90/1.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 6.90/1.28 thf(f33,definition,(
% 6.90/1.28 spl6_1 <=> ($true = ((sK4 @ sK2)))),
% 6.90/1.28 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 6.90/1.28 thf(f34,plain,(
% 6.90/1.28 ($true = ((sK4 @ sK2))) | ~spl6_1),
% 6.90/1.28 inference(avatar_component_clause,[],[f33])).
% 6.90/1.28 thf(f35,plain,(
% 6.90/1.29 ($true != ((sK4 @ sK2))) | spl6_1),
% 6.90/1.29 inference(avatar_component_clause,[],[f33])).
% 6.90/1.29 thf(f37,definition,(
% 6.90/1.29 spl6_2 <=> ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true = ((sP0 @ X4 @ X5 @ sK1))) | ($true = ((X5 @ (sK5 @ X5)))))),
% 6.90/1.29 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 6.90/1.29 thf(f38,plain,(
% 6.90/1.29 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((sK4 @ (sK5 @ X5)))) | ($true != ((X4 @ sK3))) | ($true = ((sP0 @ X4 @ X5 @ sK1))) | ($true = ((X5 @ (sK5 @ X5))))) ) | ~spl6_2),
% 6.90/1.29 inference(avatar_component_clause,[],[f37])).
% 6.90/1.29 thf(f39,plain,(
% 6.90/1.29 ~spl6_1 | spl6_2),
% 6.90/1.29 inference(avatar_split_clause,[],[f15,f37,f33])).
% 6.90/1.29 thf(f46,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != $true) | ($true = ((X0 @ (sK5 @ X0)))) | ($true != ((X1 @ sK3))) | ($true != ((X0 @ sK2))) | ($true = ((sP0 @ X1 @ X0 @ sK1))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 6.90/1.29 inference(constrained_superposition,[],[f16,f24])).
% 6.90/1.29 thf(f47,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != ((X1 @ sK3))) | ($true = ((X0 @ (sK5 @ X0)))) | ($true != ((X0 @ sK2))) | ($true = ((sP0 @ X1 @ X0 @ sK1))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f46])).
% 6.90/1.29 thf(f58,plain,(
% 6.90/1.29 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X6 @ Y0))) @ sK2))) | ($true != (((^[Y0 : $i]: (~ (X6 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK1)))) )),
% 6.90/1.29 inference(primitive_instantiation,[],[f20])).
% 6.90/1.29 thf(f74,plain,(
% 6.90/1.29 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true != ((~ (X6 @ sK2)))) | ($true != ((~ (X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK1)))) )),
% 6.90/1.29 inference(beta-eta_normalization,[],[f58])).
% 6.90/1.29 thf(f75,plain,(
% 6.90/1.29 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true = ((X6 @ sK2))) | ($true != ((~ (X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0)))))))) | ($true != ((X4 @ sK3))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK1)))) )),
% 6.90/1.29 inference(not_proxy_clausification,[],[f74])).
% 6.90/1.29 thf(f76,plain,(
% 6.90/1.29 ( ! [X6 : ($i > $o),X4 : ($i > $o)] : (($true != ((X4 @ sK3))) | ($true = ((X6 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((X6 @ sK2))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X6 @ Y0))))))) | ($true = ((sP0 @ X4 @ (^[Y0 : $i]: (~ (X6 @ Y0))) @ sK1)))) )),
% 6.90/1.29 inference(not_proxy_clausification,[],[f75])).
% 6.90/1.29 thf(f109,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((sP0 @ (^[Y0 : $i]: ($true)) @ X0 @ X1)))) )),
% 6.90/1.29 inference(equality_resolution,[],[f13])).
% 6.90/1.29 thf(f254,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true != ((X0 @ sK2))) | ($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ X0 @ sK1))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 6.90/1.29 inference(equality_resolution,[],[f47])).
% 6.90/1.29 thf(f413,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ sK2))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (X0 @ Y0))) @ sK1)))) )),
% 6.90/1.29 inference(equality_resolution,[],[f76])).
% 6.90/1.29 thf(f2705,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK2))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) )),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f254,f109])).
% 6.90/1.29 thf(f2711,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ sK2)))) )),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f413,f109])).
% 6.90/1.29 thf(f2757,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X1 @ Y0))) @ sK2))) | ($true = (((^[Y0 : $i]: (~ (X1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) )),
% 6.90/1.29 inference(primitive_instantiation,[],[f2705])).
% 6.90/1.29 thf(f2794,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($true != ((~ (X1 @ sK2)))) | ($true = ((~ (X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) )),
% 6.90/1.29 inference(beta-eta_normalization,[],[f2757])).
% 6.90/1.29 thf(f2795,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ sK2))) | ($true = ((~ (X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) )),
% 6.90/1.29 inference(not_proxy_clausification,[],[f2794])).
% 6.90/1.29 thf(f2796,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($false = ((X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($true = ((X1 @ sK2)))) )),
% 6.90/1.29 inference(not_proxy_clausification,[],[f2795])).
% 6.90/1.29 thf(f5408,definition,(
% 6.90/1.29 spl6_14 <=> ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))),
% 6.90/1.29 introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition])).
% 6.90/1.29 thf(f5410,plain,(
% 6.90/1.29 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_14),
% 6.90/1.29 inference(avatar_component_clause,[],[f5408])).
% 6.90/1.29 thf(f6817,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != $true) | ($true != ((X1 @ sK3))) | ($true = ((sP0 @ X1 @ X0 @ sK1))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 6.90/1.29 inference(constrained_superposition,[],[f38,f24])).
% 6.90/1.29 thf(f6871,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : (($true != ((X1 @ sK3))) | ($true = ((sP0 @ X1 @ X0 @ sK1))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f6817])).
% 6.90/1.29 thf(f6939,plain,(
% 6.90/1.29 ( ! [X4 : ($i > $o),X5 : ($i > $o)] : (($true != ((X4 @ sK3))) | ($true != ((X5 @ (sK5 @ X5)))) | ($true = ((sK4 @ (sK5 @ X5)))) | ($true = ((sP0 @ X4 @ X5 @ sK1)))) ) | ~spl6_1),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f19,f34])).
% 6.90/1.29 thf(f6992,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ X0)))) | ($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ X0 @ sK1)))) ) | ~spl6_1),
% 6.90/1.29 inference(equality_resolution,[],[f6939])).
% 6.90/1.29 thf(f7064,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_1),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f6992,f109])).
% 6.90/1.29 thf(f7074,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X1 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) ) | ~spl6_1),
% 6.90/1.29 inference(primitive_instantiation,[],[f7064])).
% 6.90/1.29 thf(f7189,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($true != ((~ (X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) ) | ~spl6_1),
% 6.90/1.29 inference(beta-eta_normalization,[],[f7074])).
% 6.90/1.29 thf(f7190,plain,(
% 6.90/1.29 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0))))))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X1 @ Y0)))))))) ) | ~spl6_1),
% 6.90/1.29 inference(not_proxy_clausification,[],[f7189])).
% 6.90/1.29 thf(f7847,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ X0 @ sK1))) | ($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 6.90/1.29 inference(equality_resolution,[],[f6871])).
% 6.90/1.29 thf(f7925,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($false = ((sK4 @ (sK5 @ X0))))) ) | ~spl6_2),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f7847,f109])).
% 6.90/1.29 thf(f8900,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = $false) | ($true = ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0)) ) | (~spl6_1 | ~spl6_2)),
% 6.90/1.29 inference(constrained_superposition,[],[f7925,f7190])).
% 6.90/1.29 thf(f9275,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0)) ) | (~spl6_1 | ~spl6_2)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f8900])).
% 6.90/1.29 thf(f9276,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0)) ) | (~spl6_1 | ~spl6_2)),
% 6.90/1.29 inference(beta-eta_normalization,[],[f9275])).
% 6.90/1.29 thf(f10075,definition,(
% 6.90/1.29 spl6_21 <=> ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK5 @ X0)))) | ((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0))),
% 6.90/1.29 introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition])).
% 6.90/1.29 thf(f10076,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (((^[Y0 : $i]: (~ (sK4 @ Y0))) != X0) | ($true = ((X0 @ (sK5 @ X0))))) ) | ~spl6_21),
% 6.90/1.29 inference(avatar_component_clause,[],[f10075])).
% 6.90/1.29 thf(f10077,plain,(
% 6.90/1.29 spl6_14 | spl6_21 | ~spl6_1 | ~spl6_2),
% 6.90/1.29 inference(avatar_split_clause,[],[f9276,f37,f33,f10075,f5408])).
% 6.90/1.29 thf(f10148,plain,(
% 6.90/1.29 ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_21),
% 6.90/1.29 inference(equality_resolution,[],[f10076])).
% 6.90/1.29 thf(f10149,plain,(
% 6.90/1.29 ($true = ((~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) | ~spl6_21),
% 6.90/1.29 inference(beta-eta_normalization,[],[f10148])).
% 6.90/1.29 thf(f10150,plain,(
% 6.90/1.29 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_21),
% 6.90/1.29 inference(not_proxy_clausification,[],[f10149])).
% 6.90/1.29 thf(f10160,plain,(
% 6.90/1.29 ($true = $false) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | (~spl6_1 | ~spl6_21)),
% 6.90/1.29 inference(constrained_superposition,[],[f10150,f7190])).
% 6.90/1.29 thf(f10231,plain,(
% 6.90/1.29 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | (~spl6_1 | ~spl6_21)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f10160])).
% 6.90/1.29 thf(f10232,plain,(
% 6.90/1.29 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (~spl6_1 | ~spl6_21)),
% 6.90/1.29 inference(beta-eta_normalization,[],[f10231])).
% 6.90/1.29 thf(f10241,plain,(
% 6.90/1.29 ($true = $false) | (~spl6_1 | ~spl6_21)),
% 6.90/1.29 inference(forward_demodulation,[],[f10232,f10150])).
% 6.90/1.29 thf(f10242,plain,(
% 6.90/1.29 $false | (~spl6_1 | ~spl6_21)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f10241])).
% 6.90/1.29 thf(f10243,plain,(
% 6.90/1.29 ~spl6_1 | ~spl6_21),
% 6.90/1.29 inference(avatar_contradiction_clause,[],[f10242])).
% 6.90/1.29 thf(f16094,definition,(
% 6.90/1.29 spl6_27 <=> ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))),
% 6.90/1.29 introduced(definition,[new_symbols(definition,[spl6_27])],[avatar_definition])).
% 6.90/1.29 thf(f16095,plain,(
% 6.90/1.29 ($false != ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | spl6_27),
% 6.90/1.29 inference(avatar_component_clause,[],[f16094])).
% 6.90/1.29 thf(f16096,plain,(
% 6.90/1.29 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ~spl6_27),
% 6.90/1.29 inference(avatar_component_clause,[],[f16094])).
% 6.90/1.29 thf(f16126,plain,(
% 6.90/1.29 ($true = $false) | ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ~spl6_27),
% 6.90/1.29 inference(constrained_superposition,[],[f2711,f16096])).
% 6.90/1.29 thf(f16152,plain,(
% 6.90/1.29 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ~spl6_27),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f16126])).
% 6.90/1.29 thf(f16153,plain,(
% 6.90/1.29 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true = ((sK4 @ sK2))) | ~spl6_27),
% 6.90/1.29 inference(beta-eta_normalization,[],[f16152])).
% 6.90/1.29 thf(f16196,plain,(
% 6.90/1.29 ($true = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (spl6_1 | ~spl6_27)),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f16153,f35])).
% 6.90/1.29 thf(f16198,plain,(
% 6.90/1.29 ($true = $false) | (spl6_1 | ~spl6_27)),
% 6.90/1.29 inference(forward_demodulation,[],[f16196,f16096])).
% 6.90/1.29 thf(f16199,plain,(
% 6.90/1.29 $false | (spl6_1 | ~spl6_27)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f16198])).
% 6.90/1.29 thf(f16200,plain,(
% 6.90/1.29 spl6_1 | ~spl6_27),
% 6.90/1.29 inference(avatar_contradiction_clause,[],[f16199])).
% 6.90/1.29 thf(f16213,plain,(
% 6.90/1.29 ($false != $false) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | spl6_27),
% 6.90/1.29 inference(constrained_superposition,[],[f16095,f2796])).
% 6.90/1.29 thf(f16246,plain,(
% 6.90/1.29 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK4 @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : $i]: (sK4 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | spl6_27),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f16213])).
% 6.90/1.29 thf(f16247,plain,(
% 6.90/1.29 ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true = ((sK4 @ sK2))) | spl6_27),
% 6.90/1.29 inference(beta-eta_normalization,[],[f16246])).
% 6.90/1.29 thf(f16255,plain,(
% 6.90/1.29 ($true = ((sK4 @ sK2))) | spl6_27),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f16247,f16095])).
% 6.90/1.29 thf(f16256,plain,(
% 6.90/1.29 $false | (spl6_1 | spl6_27)),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f16255,f35])).
% 6.90/1.29 thf(f16257,plain,(
% 6.90/1.29 spl6_1 | spl6_27),
% 6.90/1.29 inference(avatar_contradiction_clause,[],[f16256])).
% 6.90/1.29 thf(f17860,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != $true) | ($true != ((X0 @ sK3))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) ) | (~spl6_2 | ~spl6_14)),
% 6.90/1.29 inference(constrained_superposition,[],[f38,f5410])).
% 6.90/1.29 thf(f17955,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK3))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) ) | (~spl6_2 | ~spl6_14)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f17860])).
% 6.90/1.29 thf(f17956,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK3))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | ($true = ((~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))))) ) | (~spl6_2 | ~spl6_14)),
% 6.90/1.29 inference(beta-eta_normalization,[],[f17955])).
% 6.90/1.29 thf(f17957,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK3))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | ($false = ((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))))) ) | (~spl6_2 | ~spl6_14)),
% 6.90/1.29 inference(not_proxy_clausification,[],[f17956])).
% 6.90/1.29 thf(f17982,plain,(
% 6.90/1.29 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK3))) | ($true = ((sP0 @ X0 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1)))) ) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f17957,f16095])).
% 6.90/1.29 thf(f21451,plain,(
% 6.90/1.29 ($true != (((^[Y0 : $i]: ($true)) @ sK3))) | ($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 6.90/1.29 inference(primitive_instantiation,[],[f17982])).
% 6.90/1.29 thf(f21686,plain,(
% 6.90/1.29 ($true != $true) | ($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 6.90/1.29 inference(beta-eta_normalization,[],[f21451])).
% 6.90/1.29 thf(f21687,plain,(
% 6.90/1.29 ($true = ((sP0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK1))) | (~spl6_2 | ~spl6_14 | spl6_27)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f21686])).
% 6.90/1.29 thf(f21705,plain,(
% 6.90/1.29 $false | (~spl6_2 | ~spl6_14 | spl6_27)),
% 6.90/1.29 inference(forward_subsumption_resolution,[],[f21687,f109])).
% 6.90/1.29 thf(f21706,plain,(
% 6.90/1.29 ~spl6_2 | ~spl6_14 | spl6_27),
% 6.90/1.29 inference(avatar_contradiction_clause,[],[f21705])).
% 6.90/1.29 thf(f21711,plain,(
% 6.90/1.29 ($true = $false) | (~spl6_14 | ~spl6_27)),
% 6.90/1.29 inference(constrained_superposition,[],[f16096,f5410])).
% 6.90/1.29 thf(f21837,plain,(
% 6.90/1.29 $false | (~spl6_14 | ~spl6_27)),
% 6.90/1.29 inference(trivial_inequality_removal,[],[f21711])).
% 6.90/1.29 thf(f21838,plain,(
% 6.90/1.29 ~spl6_14 | ~spl6_27),
% 6.90/1.29 inference(avatar_contradiction_clause,[],[f21837])).
% 6.90/1.29 cnf(s1, plain, ~spl6_1 | spl6_2, inference(sat_conversion,[],[f39])).
% 6.90/1.29 cnf(s15, plain, ~spl6_1 | ~spl6_2 | spl6_14 | spl6_21, inference(sat_conversion,[],[f10077])).
% 6.90/1.29 cnf(s17, plain, ~spl6_1 | ~spl6_21, inference(sat_conversion,[],[f10243])).
% 6.90/1.29 cnf(s22, plain, spl6_1 | ~spl6_27, inference(sat_conversion,[],[f16200])).
% 6.90/1.29 cnf(s24, plain, spl6_1 | spl6_27, inference(sat_conversion,[],[f16257])).
% 6.90/1.29 cnf(s36, plain, ~spl6_2 | ~spl6_14 | spl6_27, inference(sat_conversion,[],[f21706])).
% 6.90/1.29 cnf(s38, plain, ~spl6_14 | ~spl6_27, inference(sat_conversion,[],[f21838])).
% 6.90/1.29 cnf(s43, plain, spl6_1, inference(rat,[],[s22,s24])).
% 6.90/1.29 cnf(s45, plain, ~spl6_21, inference(rat,[],[s17,s43])).
% 6.90/1.29 cnf(s46, plain, spl6_2, inference(rat,[],[s1,s43])).
% 6.90/1.29 cnf(s47, plain, spl6_14, inference(rat,[],[s15,s45,s43,s46])).
% 6.90/1.29 cnf(s48, plain, ~spl6_27, inference(rat,[],[s38,s47])).
% 6.90/1.29 cnf(s49, plain, $false, inference(rat,[],[s36,s46,s48,s47])).
% 6.90/1.29 thf(f21840,plain,(
% 6.90/1.29 $false),
% 6.90/1.29 inference(avatar_sat_refutation,[],[s49])).
% 6.90/1.29 % SZS output end Proof for theBenchmark
% 6.90/1.29 % (324591)------------------------------
% 6.90/1.29 % (324591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.90/1.29 % (324591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.90/1.29 % (324591)CaDiCaL version: 2.1.3
% 6.90/1.29 % (324591)Termination reason: Refutation
% 6.90/1.29 % (324591)Time elapsed: 0.757 s
% 6.90/1.29 % (324591)Peak memory usage: 18 MB
% 6.90/1.29 % (324591)Instructions burned: 3169 (million)
% 6.90/1.29 % (324517)Success in time 1.066 s
% 6.90/1.29 % Vampire exiting
%------------------------------------------------------------------------------