%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET624^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:23:44 AM UTC 2026
% Result : Theorem 1.06s 0.46s
% Output : Refutation 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:37:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.06/0.46 % (3369686)Will run a generic schedule for satisfiability detection.
% 1.06/0.46 % (3369692)% WARNING: option uhcvi not known.
% 1.06/0.46 % (3369691)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=431503982_2999 on theBenchmark for (2999ds/0Mi)
% 1.06/0.46 % (3369695)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3736391024:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.06/0.46 % (3369692)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=27209304:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.06/0.46 % (3369693)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2089112057:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.06/0.46 % (3369694)dis+10_1_sil=32000:sp=arity:random_seed=1428300907:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.06/0.46 % (3369695)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.06/0.46 % (3369692)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.06/0.46 % Exception at run slice level
% 1.06/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.06/0.46 % (3369692)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.06/0.46 % (3369696)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3134503703:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.06/0.46 % (3369697)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3795031289:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.06/0.46 % (3369703)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1400838630:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.06/0.46 % Exception at run slice level
% 1.06/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.06/0.46 % (3369707)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1190818760:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.06/0.46 % (3369694)Instruction limit reached!
% 1.06/0.46 % (3369694)------------------------------
% 1.06/0.46 % (3369694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.46 % (3369694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.46 % (3369694)CaDiCaL version: 2.1.3
% 1.06/0.46 % (3369694)Termination reason: Instruction limit
% 1.06/0.46 % (3369694)Termination phase: Saturation
% 1.06/0.46 % (3369694)Time elapsed: 0.055 s
% 1.06/0.46 % (3369694)Peak memory usage: 12 MB
% 1.06/0.46 % (3369694)Instructions burned: 104 (million)
% 1.06/0.46 % (3369695)Instruction limit reached!
% 1.06/0.46 % (3369695)------------------------------
% 1.06/0.46 % (3369695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.46 % (3369695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.46 % (3369695)CaDiCaL version: 2.1.3
% 1.06/0.46 % (3369695)Termination reason: Instruction limit
% 1.06/0.46 % (3369695)Termination phase: Saturation
% 1.06/0.46 % (3369695)Time elapsed: 0.056 s
% 1.06/0.46 % (3369695)Peak memory usage: 12 MB
% 1.06/0.46 % (3369695)Instructions burned: 116 (million)
% 1.06/0.46 % (3369709)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=2367768392:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.06/0.46 % (3369710)ott-21_1_sil=16000:fs=off:random_seed=1011809182:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.06/0.46 % (3369709)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.06/0.46 % (3369696)Instruction limit reached!
% 1.06/0.46 % (3369696)------------------------------
% 1.06/0.46 % (3369696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.46 % (3369696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.46 % (3369696)CaDiCaL version: 2.1.3
% 1.06/0.46 % (3369696)Termination reason: Instruction limit
% 1.06/0.46 % (3369696)Termination phase: Saturation
% 1.06/0.46 % (3369696)Time elapsed: 0.067 s
% 1.06/0.46 % (3369696)Peak memory usage: 13 MB
% 1.06/0.46 % (3369696)Instructions burned: 131 (million)
% 1.06/0.46 % (3369709)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.06/0.46 % (3369713)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=308689709:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.06/0.46 % (3369707)Instruction limit reached!
% 1.06/0.46 % (3369707)------------------------------
% 1.06/0.46 % (3369707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.46 % (3369707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.46 % (3369707)CaDiCaL version: 2.1.3
% 1.06/0.46 % (3369707)Termination reason: Instruction limit
% 1.06/0.46 % (3369707)Termination phase: Saturation
% 1.06/0.46 % (3369707)Time elapsed: 0.071 s
% 1.06/0.46 % (3369707)Peak memory usage: 12 MB
% 1.06/0.46 % (3369707)Instructions burned: 132 (million)
% 1.06/0.46 % (3369697)Instruction limit reached!
% 1.06/0.46 % (3369697)------------------------------
% 1.06/0.46 % (3369697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.46 % (3369697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.46 % (3369697)CaDiCaL version: 2.1.3
% 1.06/0.46 % (3369697)Termination reason: Instruction limit
% 1.06/0.46 % (3369697)Termination phase: Saturation
% 1.06/0.46 % (3369697)Time elapsed: 0.113 s
% 1.06/0.46 % (3369697)Peak memory usage: 12 MB
% 1.06/0.46 % (3369697)Instructions burned: 160 (million)
% 1.06/0.46 % (3369715)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=953634450:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.06/0.46 % Exception at run slice level
% 1.06/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.06/0.46 % (3369716)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=517177123:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.06/0.46 % (3369718)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2974404951:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.06/0.46 % Exception at run slice level
% 1.06/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.06/0.46 % (3369710)Instruction limit reached!
% 1.06/0.46 % (3369710)------------------------------
% 1.06/0.46 % (3369710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.46 % (3369710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.46 % (3369710)CaDiCaL version: 2.1.3
% 1.06/0.46 % (3369710)Termination reason: Instruction limit
% 1.06/0.46 % (3369710)Termination phase: Saturation
% 1.06/0.46 % (3369710)Time elapsed: 0.082 s
% 1.06/0.46 % (3369710)Peak memory usage: 12 MB
% 1.06/0.46 % (3369710)Instructions burned: 181 (million)
% 1.06/0.46 % (3369721)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=2160840094: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)
% 1.06/0.46 % (3369721)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.06/0.46 % (3369722)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1262814526:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.06/0.46 % (3369722)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.06/0.46 % (3369713) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3369686-3369713"...
% 1.06/0.46 % (3369713)...printing done.
% 1.06/0.46 % (3369713)Refutation found. Thanks to Tanya!
% 1.06/0.46 % SZS status Theorem for theBenchmark
% 1.06/0.46 % SZS output start Proof for theBenchmark
% 1.06/0.46 thf(type_def_5, type, a: $tType).
% 1.06/0.46 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.06/0.46 thf(func_def_3, type, sP0: ((a > $o) > (a > $o) > (a > $o) > $o)).
% 1.06/0.46 thf(func_def_4, type, sK1: ((a > $o) > (a > $o) > a)).
% 1.06/0.46 thf(func_def_5, type, sK2: ((a > $o) > (a > $o) > a)).
% 1.06/0.46 thf(func_def_6, type, sK3: (a > $o)).
% 1.06/0.46 thf(func_def_7, type, sK4: (a > $o)).
% 1.06/0.46 thf(func_def_8, type, sK5: (a > $o)).
% 1.06/0.46 thf(func_def_9, type, sK6: a).
% 1.06/0.46 thf(func_def_10, type, vNOT: ($o > $o)).
% 1.06/0.46 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 1.06/0.46 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.06/0.46 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 1.06/0.46 thf(func_def_15, type, sK8: (a > (a > a > a) > a)).
% 1.06/0.46 thf(func_def_16, type, sK9: (a > (a > a > $o) > a)).
% 1.06/0.46 thf(func_def_17, type, sK10: (a > (a > a > $o) > a)).
% 1.06/0.46 thf(func_def_18, type, sK11: (a > (a > a > a) > a)).
% 1.06/0.46 thf(func_def_19, type, sK12: ((a > a > $o) > a > a)).
% 1.06/0.46 thf(func_def_20, type, db2: !>[X0: $tType]:(X0)).
% 1.06/0.46 thf(func_def_21, type, sK13: (a > (a > a > $o) > a)).
% 1.06/0.46 thf(func_def_22, type, sK14: (a > a)).
% 1.06/0.46 thf(func_def_23, type, sK15: (a > a)).
% 1.06/0.46 thf(f1,conjecture,(
% 1.06/0.46 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : (((X2 @ X3) | (X1 @ X3)) & (X0 @ X3)) <=> (? [X3 : a] : ((X2 @ X3) & (X0 @ X3)) | ? [X3 : a] : ((X1 @ X3) & (X0 @ X3))))),
% 1.06/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_100_pme)).
% 1.06/0.46 thf(f2,negated_conjecture,(
% 1.06/0.46 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : (((X2 @ X3) | (X1 @ X3)) & (X0 @ X3)) <=> (? [X3 : a] : ((X2 @ X3) & (X0 @ X3)) | ? [X3 : a] : ((X1 @ X3) & (X0 @ X3))))),
% 1.06/0.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.06/0.46 thf(f3,plain,(
% 1.06/0.46 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : (((X2 @ X3) | (X1 @ X3)) & (X0 @ X3)) <=> (? [X4 : a] : ((X2 @ X4) & (X0 @ X4)) | ? [X5 : a] : ((X1 @ X5) & (X0 @ X5))))),
% 1.06/0.46 inference(rectify,[],[f2])).
% 1.06/0.46 thf(f4,plain,(
% 1.06/0.46 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : (((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)) & (((X0 @ X3)) = $true)) <=> (? [X4 : a] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) = $true)) | ? [X5 : a] : ((((X1 @ X5)) = $true) & (((X0 @ X5)) = $true))))),
% 1.06/0.46 inference(fool_elimination,[],[f3])).
% 1.06/0.46 thf(f5,plain,(
% 1.06/0.46 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : (((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)) & (((X0 @ X3)) = $true)) <~> (? [X4 : a] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) = $true)) | ? [X5 : a] : ((((X1 @ X5)) = $true) & (((X0 @ X5)) = $true))))),
% 1.06/0.46 inference(ennf_transformation,[],[f4])).
% 1.06/0.46 thf(f6,definition,(
% 1.06/0.46 ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true = ((sP0 @ X1 @ X0 @ X2))) <=> (? [X4 : a] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) = $true)) | ? [X5 : a] : ((((X1 @ X5)) = $true) & (((X0 @ X5)) = $true))))),
% 1.06/0.46 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.06/0.46 thf(f7,plain,(
% 1.06/0.46 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (? [X3 : a] : (((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)) & (((X0 @ X3)) = $true)) <~> ($true = ((sP0 @ X1 @ X0 @ X2))))),
% 1.06/0.47 inference(definition_folding,[],[f5,f6])).
% 1.06/0.47 thf(f8,plain,(
% 1.06/0.47 ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : ((($true = ((sP0 @ X1 @ X0 @ X2))) | (! [X4 : a] : ((((X2 @ X4)) != $true) | (((X0 @ X4)) != $true)) & ! [X5 : a] : ((((X1 @ X5)) != $true) | (((X0 @ X5)) != $true)))) & ((? [X4 : a] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) = $true)) | ? [X5 : a] : ((((X1 @ X5)) = $true) & (((X0 @ X5)) = $true))) | ($true != ((sP0 @ X1 @ X0 @ X2)))))),
% 1.06/0.47 inference(nnf_transformation,[],[f6])).
% 1.06/0.47 thf(f9,plain,(
% 1.06/0.47 ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : ((($true = ((sP0 @ X1 @ X0 @ X2))) | (! [X4 : a] : ((((X2 @ X4)) != $true) | (((X0 @ X4)) != $true)) & ! [X5 : a] : ((((X1 @ X5)) != $true) | (((X0 @ X5)) != $true)))) & (? [X4 : a] : ((((X2 @ X4)) = $true) & (((X0 @ X4)) = $true)) | ? [X5 : a] : ((((X1 @ X5)) = $true) & (((X0 @ X5)) = $true)) | ($true != ((sP0 @ X1 @ X0 @ X2)))))),
% 1.06/0.47 inference(flattening,[],[f8])).
% 1.06/0.47 thf(f10,plain,(
% 1.06/0.47 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | (! [X3 : a] : ((((X0 @ X3)) != $true) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X2 @ X4)) != $true) | ($true != ((X1 @ X4)))))) & (? [X5 : a] : ((((X0 @ X5)) = $true) & (((X1 @ X5)) = $true)) | ? [X6 : a] : (($true = ((X2 @ X6))) & ($true = ((X1 @ X6)))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 1.06/0.47 inference(rectify,[],[f9])).
% 1.06/0.47 thf(f11,plain,(
% 1.06/0.47 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | (! [X3 : a] : ((((X0 @ X3)) != $true) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X2 @ X4)) != $true) | ($true != ((X1 @ X4)))))) & ((($true = ((X0 @ (sK1 @ X1 @ X0)))) & ($true = ((X1 @ (sK1 @ X1 @ X0))))) | (($true = ((X2 @ (sK2 @ X2 @ X1)))) & ($true = ((X1 @ (sK2 @ X2 @ X1))))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 1.06/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X6,sK2 @ X2 @ X1),skolemize(X6,sK2 @ X2 @ X1)],[f10])).
% 1.06/0.47 thf(f12,plain,(
% 1.06/0.47 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true != ((sP0 @ X1 @ X0 @ X2))) | ! [X3 : a] : (((((X2 @ X3)) != $true) & (((X1 @ X3)) != $true)) | (((X0 @ X3)) != $true))) & (($true = ((sP0 @ X1 @ X0 @ X2))) | ? [X3 : a] : (((((X2 @ X3)) = $true) | (((X1 @ X3)) = $true)) & (((X0 @ X3)) = $true))))),
% 1.06/0.47 inference(nnf_transformation,[],[f7])).
% 1.06/0.47 thf(f13,plain,(
% 1.06/0.47 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((($true != ((sP0 @ X1 @ X0 @ X2))) | ! [X3 : a] : (((((X2 @ X3)) != $true) & (((X1 @ X3)) != $true)) | (((X0 @ X3)) != $true))) & (($true = ((sP0 @ X1 @ X0 @ X2))) | ? [X4 : a] : (((((X2 @ X4)) = $true) | ($true = ((X1 @ X4)))) & (((X0 @ X4)) = $true))))),
% 1.06/0.47 inference(rectify,[],[f12])).
% 1.06/0.47 thf(f14,plain,(
% 1.06/0.47 (($true != ((sP0 @ sK4 @ sK3 @ sK5))) | ! [X3 : a] : ((($true != ((sK5 @ X3))) & ($true != ((sK4 @ X3)))) | ($true != ((sK3 @ X3))))) & (($true = ((sP0 @ sK4 @ sK3 @ sK5))) | ((($true = ((sK5 @ sK6))) | ($true = ((sK4 @ sK6)))) & ($true = ((sK3 @ sK6)))))),
% 1.06/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X4,sK6)],[f13])).
% 1.06/0.47 thf(f15,plain,(
% 1.06/0.47 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X1 @ (sK2 @ X2 @ X1)))) | ($true = ((X1 @ (sK1 @ X1 @ X0))))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f11])).
% 1.06/0.47 thf(f16,plain,(
% 1.06/0.47 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X2 @ (sK2 @ X2 @ X1)))) | ($true = ((X1 @ (sK1 @ X1 @ X0))))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f11])).
% 1.06/0.47 thf(f17,plain,(
% 1.06/0.47 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X1 @ (sK2 @ X2 @ X1)))) | ($true = ((X0 @ (sK1 @ X1 @ X0))))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f11])).
% 1.06/0.47 thf(f18,plain,(
% 1.06/0.47 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | ($true = ((X2 @ (sK2 @ X2 @ X1)))) | ($true = ((X0 @ (sK1 @ X1 @ X0))))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f11])).
% 1.06/0.47 thf(f19,plain,(
% 1.06/0.47 ( ! [X2 : (a > $o),X0 : (a > $o),X1 : (a > $o),X4 : a] : (($true != ((X1 @ X4))) | (((X2 @ X4)) != $true) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f11])).
% 1.06/0.47 thf(f20,plain,(
% 1.06/0.47 ( ! [X2 : (a > $o),X3 : a,X0 : (a > $o),X1 : (a > $o)] : ((((X1 @ X3)) != $true) | (((X0 @ X3)) != $true) | ($true = ((sP0 @ X2 @ X1 @ X0)))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f11])).
% 1.06/0.47 thf(f21,plain,(
% 1.06/0.47 ($true = ((sP0 @ sK4 @ sK3 @ sK5))) | ($true = ((sK3 @ sK6)))),
% 1.06/0.47 inference(cnf_transformation,[],[f14])).
% 1.06/0.47 thf(f22,plain,(
% 1.06/0.47 ($true = ((sP0 @ sK4 @ sK3 @ sK5))) | ($true = ((sK5 @ sK6))) | ($true = ((sK4 @ sK6)))),
% 1.06/0.47 inference(cnf_transformation,[],[f14])).
% 1.06/0.47 thf(f23,plain,(
% 1.06/0.47 ( ! [X3 : a] : (($true != ((sP0 @ sK4 @ sK3 @ sK5))) | ($true != ((sK4 @ X3))) | ($true != ((sK3 @ X3)))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f14])).
% 1.06/0.47 thf(f24,plain,(
% 1.06/0.47 ( ! [X3 : a] : (($true != ((sP0 @ sK4 @ sK3 @ sK5))) | ($true != ((sK5 @ X3))) | ($true != ((sK3 @ X3)))) )),
% 1.06/0.47 inference(cnf_transformation,[],[f14])).
% 1.06/0.47 thf(f26,definition,(
% 1.06/0.47 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.06/0.47 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.06/0.47 thf(f28,definition,(
% 1.06/0.47 spl7_1 <=> ($true = ((sK3 @ sK6)))),
% 1.06/0.47 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 1.06/0.47 thf(f30,plain,(
% 1.06/0.47 ($true = ((sK3 @ sK6))) | ~spl7_1),
% 1.06/0.47 inference(avatar_component_clause,[],[f28])).
% 1.06/0.47 thf(f32,definition,(
% 1.06/0.47 spl7_2 <=> ($true = ((sP0 @ sK4 @ sK3 @ sK5)))),
% 1.06/0.47 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 1.06/0.47 thf(f33,plain,(
% 1.06/0.47 ($true != ((sP0 @ sK4 @ sK3 @ sK5))) | spl7_2),
% 1.06/0.47 inference(avatar_component_clause,[],[f32])).
% 1.06/0.47 thf(f34,plain,(
% 1.06/0.47 ($true = ((sP0 @ sK4 @ sK3 @ sK5))) | ~spl7_2),
% 1.06/0.47 inference(avatar_component_clause,[],[f32])).
% 1.06/0.47 thf(f35,plain,(
% 1.06/0.47 spl7_1 | spl7_2),
% 1.06/0.47 inference(avatar_split_clause,[],[f21,f32,f28])).
% 1.06/0.47 thf(f36,plain,(
% 1.06/0.47 ( ! [X3 : a] : (($true != ((sK4 @ X3))) | ($true != ((sK3 @ X3)))) ) | ~spl7_2),
% 1.06/0.47 inference(forward_subsumption_resolution,[],[f23,f34])).
% 1.06/0.47 thf(f52,plain,(
% 1.06/0.47 ( ! [X0 : a] : (($true != $true) | ($true != ((sK3 @ X0))) | ($false = ((sK4 @ X0)))) ) | ~spl7_2),
% 1.06/0.47 inference(constrained_superposition,[],[f36,f26])).
% 1.06/0.47 thf(f56,plain,(
% 1.06/0.47 ( ! [X0 : a] : (($true != ((sK3 @ X0))) | ($false = ((sK4 @ X0)))) ) | ~spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f52])).
% 1.06/0.47 thf(f511,plain,(
% 1.06/0.47 ( ! [X3 : a] : (($true != ((sK4 @ X3))) | ($true != ((sK3 @ X3)))) )),
% 1.06/0.47 inference(forward_subsumption_resolution,[],[f23,f19])).
% 1.06/0.47 thf(f515,plain,(
% 1.06/0.47 ( ! [X3 : a] : (($true != ((sK5 @ X3))) | ($true != ((sK3 @ X3)))) )),
% 1.06/0.47 inference(forward_subsumption_resolution,[],[f24,f20])).
% 1.06/0.47 thf(f519,plain,(
% 1.06/0.47 ( ! [X0 : a] : (($true != $true) | ($true != ((sK3 @ X0))) | ($false = ((sK5 @ X0)))) )),
% 1.06/0.47 inference(constrained_superposition,[],[f515,f26])).
% 1.06/0.47 thf(f520,plain,(
% 1.06/0.47 ( ! [X0 : a] : (($true != ((sK3 @ X0))) | ($false = ((sK5 @ X0)))) )),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f519])).
% 1.06/0.47 thf(f531,plain,(
% 1.06/0.47 ($true != $true) | ($true = ((sK3 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(constrained_superposition,[],[f15,f34])).
% 1.06/0.47 thf(f532,plain,(
% 1.06/0.47 ($true = ((sK3 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f531])).
% 1.06/0.47 thf(f538,definition,(
% 1.06/0.47 spl7_22 <=> ($true = ((sK3 @ (sK1 @ sK3 @ sK5))))),
% 1.06/0.47 introduced(definition,[new_symbols(definition,[spl7_22])],[avatar_definition])).
% 1.06/0.47 thf(f539,plain,(
% 1.06/0.47 ($true != ((sK3 @ (sK1 @ sK3 @ sK5)))) | spl7_22),
% 1.06/0.47 inference(avatar_component_clause,[],[f538])).
% 1.06/0.47 thf(f540,plain,(
% 1.06/0.47 ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_22),
% 1.06/0.47 inference(avatar_component_clause,[],[f538])).
% 1.06/0.47 thf(f542,definition,(
% 1.06/0.47 spl7_23 <=> ($true = ((sK3 @ (sK2 @ sK4 @ sK3))))),
% 1.06/0.47 introduced(definition,[new_symbols(definition,[spl7_23])],[avatar_definition])).
% 1.06/0.47 thf(f544,plain,(
% 1.06/0.47 ($true = ((sK3 @ (sK2 @ sK4 @ sK3)))) | ~spl7_23),
% 1.06/0.47 inference(avatar_component_clause,[],[f542])).
% 1.06/0.47 thf(f545,plain,(
% 1.06/0.47 spl7_22 | spl7_23 | ~spl7_2),
% 1.06/0.47 inference(avatar_split_clause,[],[f532,f32,f542,f538])).
% 1.06/0.47 thf(f756,plain,(
% 1.06/0.47 ($true != $true) | ($true = ((sK4 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(constrained_superposition,[],[f16,f34])).
% 1.06/0.47 thf(f759,plain,(
% 1.06/0.47 ($true = ((sK4 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f756])).
% 1.06/0.47 thf(f957,plain,(
% 1.06/0.47 ($true != $true) | ($true = ((sK3 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(constrained_superposition,[],[f17,f34])).
% 1.06/0.47 thf(f962,plain,(
% 1.06/0.47 ($true = ((sK3 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f957])).
% 1.06/0.47 thf(f1297,plain,(
% 1.06/0.47 ($true != $true) | ($true = ((sK4 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(constrained_superposition,[],[f18,f34])).
% 1.06/0.47 thf(f1303,plain,(
% 1.06/0.47 ($true = ((sK4 @ (sK2 @ sK4 @ sK3)))) | ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1297])).
% 1.06/0.47 thf(f1324,plain,(
% 1.06/0.47 ($true != $true) | ($false = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_22),
% 1.06/0.47 inference(constrained_superposition,[],[f520,f540])).
% 1.06/0.47 thf(f1327,plain,(
% 1.06/0.47 ($false = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_22),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1324])).
% 1.06/0.47 thf(f1544,definition,(
% 1.06/0.47 spl7_38 <=> ($true = ((sK5 @ (sK1 @ sK3 @ sK5))))),
% 1.06/0.47 introduced(definition,[new_symbols(definition,[spl7_38])],[avatar_definition])).
% 1.06/0.47 thf(f1546,plain,(
% 1.06/0.47 ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | ~spl7_38),
% 1.06/0.47 inference(avatar_component_clause,[],[f1544])).
% 1.06/0.47 thf(f1547,plain,(
% 1.06/0.47 spl7_38 | spl7_23 | ~spl7_2),
% 1.06/0.47 inference(avatar_split_clause,[],[f962,f32,f542,f1544])).
% 1.06/0.47 thf(f1554,plain,(
% 1.06/0.47 ($true != $true) | ($true != ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_38),
% 1.06/0.47 inference(constrained_superposition,[],[f515,f1546])).
% 1.06/0.47 thf(f1555,plain,(
% 1.06/0.47 ($true != ((sK3 @ (sK1 @ sK3 @ sK5)))) | ~spl7_38),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1554])).
% 1.06/0.47 thf(f1566,plain,(
% 1.06/0.47 $false | (~spl7_22 | ~spl7_38)),
% 1.06/0.47 inference(forward_subsumption_resolution,[],[f1555,f540])).
% 1.06/0.47 thf(f1567,plain,(
% 1.06/0.47 ~spl7_22 | ~spl7_38),
% 1.06/0.47 inference(avatar_contradiction_clause,[],[f1566])).
% 1.06/0.47 thf(f1575,plain,(
% 1.06/0.47 ($true != $true) | ($false = ((sK3 @ (sK1 @ sK3 @ sK5)))) | spl7_22),
% 1.06/0.47 inference(constrained_superposition,[],[f539,f26])).
% 1.06/0.47 thf(f1576,plain,(
% 1.06/0.47 ($false = ((sK3 @ (sK1 @ sK3 @ sK5)))) | spl7_22),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1575])).
% 1.06/0.47 thf(f1582,plain,(
% 1.06/0.47 ($true != $true) | ($false = ((sK4 @ (sK2 @ sK4 @ sK3)))) | (~spl7_2 | ~spl7_23)),
% 1.06/0.47 inference(constrained_superposition,[],[f56,f544])).
% 1.06/0.47 thf(f1583,plain,(
% 1.06/0.47 ($false = ((sK4 @ (sK2 @ sK4 @ sK3)))) | (~spl7_2 | ~spl7_23)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1582])).
% 1.06/0.47 thf(f1628,plain,(
% 1.06/0.47 ($true = $false) | ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | (~spl7_2 | ~spl7_23)),
% 1.06/0.47 inference(forward_demodulation,[],[f759,f1583])).
% 1.06/0.47 thf(f1629,plain,(
% 1.06/0.47 ($true = ((sK3 @ (sK1 @ sK3 @ sK5)))) | (~spl7_2 | ~spl7_23)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1628])).
% 1.06/0.47 thf(f1630,plain,(
% 1.06/0.47 ($true = $false) | (~spl7_2 | spl7_22 | ~spl7_23)),
% 1.06/0.47 inference(forward_demodulation,[],[f1629,f1576])).
% 1.06/0.47 thf(f1631,plain,(
% 1.06/0.47 $false | (~spl7_2 | spl7_22 | ~spl7_23)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1630])).
% 1.06/0.47 thf(f1632,plain,(
% 1.06/0.47 ~spl7_2 | spl7_22 | ~spl7_23),
% 1.06/0.47 inference(avatar_contradiction_clause,[],[f1631])).
% 1.06/0.47 thf(f1678,plain,(
% 1.06/0.47 ($true = $false) | ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | (~spl7_2 | ~spl7_23)),
% 1.06/0.47 inference(forward_demodulation,[],[f1303,f1583])).
% 1.06/0.47 thf(f1679,plain,(
% 1.06/0.47 ($true = ((sK5 @ (sK1 @ sK3 @ sK5)))) | (~spl7_2 | ~spl7_23)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1678])).
% 1.06/0.47 thf(f1680,plain,(
% 1.06/0.47 ($true = $false) | (~spl7_2 | ~spl7_22 | ~spl7_23)),
% 1.06/0.47 inference(forward_demodulation,[],[f1679,f1327])).
% 1.06/0.47 thf(f1681,plain,(
% 1.06/0.47 $false | (~spl7_2 | ~spl7_22 | ~spl7_23)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1680])).
% 1.06/0.47 thf(f1682,plain,(
% 1.06/0.47 ~spl7_2 | ~spl7_22 | ~spl7_23),
% 1.06/0.47 inference(avatar_contradiction_clause,[],[f1681])).
% 1.06/0.47 thf(f1683,plain,(
% 1.06/0.47 ($true != $true) | (((sK5 @ sK6)) = $false) | ~spl7_1),
% 1.06/0.47 inference(constrained_superposition,[],[f520,f30])).
% 1.06/0.47 thf(f1696,plain,(
% 1.06/0.47 (((sK5 @ sK6)) = $false) | ~spl7_1),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1683])).
% 1.06/0.47 thf(f1697,plain,(
% 1.06/0.47 ( ! [X0 : a] : (($true != $true) | ($true != ((sK3 @ X0))) | ($false = ((sK4 @ X0)))) )),
% 1.06/0.47 inference(constrained_superposition,[],[f511,f26])).
% 1.06/0.47 thf(f1698,plain,(
% 1.06/0.47 ( ! [X0 : a] : (($true != ((sK3 @ X0))) | ($false = ((sK4 @ X0)))) )),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1697])).
% 1.06/0.47 thf(f1712,plain,(
% 1.06/0.47 ($true != $true) | (((sK4 @ sK6)) = $false) | ~spl7_1),
% 1.06/0.47 inference(constrained_superposition,[],[f1698,f30])).
% 1.06/0.47 thf(f1715,plain,(
% 1.06/0.47 (((sK4 @ sK6)) = $false) | ~spl7_1),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1712])).
% 1.06/0.47 thf(f1734,plain,(
% 1.06/0.47 ($true != $true) | (((sP0 @ sK4 @ sK3 @ sK5)) = $false) | spl7_2),
% 1.06/0.47 inference(constrained_superposition,[],[f33,f26])).
% 1.06/0.47 thf(f1735,plain,(
% 1.06/0.47 (((sP0 @ sK4 @ sK3 @ sK5)) = $false) | spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1734])).
% 1.06/0.47 thf(f1784,plain,(
% 1.06/0.47 ($true = $false) | ($true = ((sK5 @ sK6))) | ($true = ((sK4 @ sK6))) | spl7_2),
% 1.06/0.47 inference(forward_demodulation,[],[f22,f1735])).
% 1.06/0.47 thf(f1785,plain,(
% 1.06/0.47 ($true = ((sK5 @ sK6))) | ($true = ((sK4 @ sK6))) | spl7_2),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1784])).
% 1.06/0.47 thf(f1786,plain,(
% 1.06/0.47 ($true = $false) | ($true = ((sK4 @ sK6))) | (~spl7_1 | spl7_2)),
% 1.06/0.47 inference(forward_demodulation,[],[f1785,f1696])).
% 1.06/0.47 thf(f1787,plain,(
% 1.06/0.47 ($true = ((sK4 @ sK6))) | (~spl7_1 | spl7_2)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1786])).
% 1.06/0.47 thf(f1803,plain,(
% 1.06/0.47 ($true = $false) | (~spl7_1 | spl7_2)),
% 1.06/0.47 inference(backward_demodulation,[],[f1787,f1715])).
% 1.06/0.47 thf(f1814,plain,(
% 1.06/0.47 $false | (~spl7_1 | spl7_2)),
% 1.06/0.47 inference(trivial_inequality_removal,[],[f1803])).
% 1.06/0.47 thf(f1815,plain,(
% 1.06/0.47 ~spl7_1 | spl7_2),
% 1.06/0.47 inference(avatar_contradiction_clause,[],[f1814])).
% 1.06/0.47 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f35])).
% 1.06/0.47 cnf(s34, plain, ~spl7_2 | spl7_22 | spl7_23, inference(sat_conversion,[],[f545])).
% 1.06/0.47 cnf(s77, plain, ~spl7_2 | spl7_23 | spl7_38, inference(sat_conversion,[],[f1547])).
% 1.06/0.47 cnf(s78, plain, ~spl7_22 | ~spl7_38, inference(sat_conversion,[],[f1567])).
% 1.06/0.47 cnf(s80, plain, ~spl7_2 | spl7_22 | ~spl7_23, inference(sat_conversion,[],[f1632])).
% 1.06/0.47 cnf(s81, plain, ~spl7_2 | ~spl7_22 | ~spl7_23, inference(sat_conversion,[],[f1682])).
% 1.06/0.47 cnf(s85, plain, ~spl7_1 | spl7_2, inference(sat_conversion,[],[f1815])).
% 1.06/0.47 cnf(s87, plain, spl7_22 | ~spl7_2, inference(rat,[],[s34,s80])).
% 1.06/0.47 cnf(s88, plain, ~spl7_22 | ~spl7_2, inference(rat,[],[s77,s78,s81])).
% 1.06/0.47 cnf(s89, plain, ~spl7_2, inference(rat,[],[s88,s87])).
% 1.06/0.47 cnf(s90, plain, ~spl7_1, inference(rat,[],[s85,s89])).
% 1.06/0.47 cnf(s92, plain, $false, inference(rat,[],[s1,s89,s90])).
% 1.06/0.47 thf(f1816,plain,(
% 1.06/0.47 $false),
% 1.06/0.47 inference(avatar_sat_refutation,[],[s92])).
% 1.06/0.47 % SZS output end Proof for theBenchmark
% 1.06/0.47 % (3369713)------------------------------
% 1.06/0.47 % (3369713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.06/0.47 % (3369713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.06/0.47 % (3369713)CaDiCaL version: 2.1.3
% 1.06/0.47 % (3369713)Termination reason: Refutation
% 1.06/0.47 % (3369713)Time elapsed: 0.103 s
% 1.06/0.47 % (3369713)Peak memory usage: 13 MB
% 1.06/0.47 % (3369713)Instructions burned: 187 (million)
% 1.06/0.47 % (3369686)Success in time 0.23 s
% 1.06/0.47 % Vampire exiting
%------------------------------------------------------------------------------