%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 : Tue Sep 29 10:17:42 AM UTC 2026
% Result : Unsatisfiable 1.79s 0.89s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 33 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
fof(f2,axiom,
! [X2,X0,X1] :
( multiply(X0,X1) != multiply(X2,X1)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax',right_cancellation) ).
fof(f3,axiom,
! [X2,X0,X1] :
( multiply(X0,X1) != multiply(X0,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
fof(f4,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,multiply(X0,commutator(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(commutator(X0,X1),X2) = multiply(X2,commutator(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nilpotency) ).
fof(f6,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( multiply(X0,multiply(X1,X2)) != multiply(multiply(X0,X1),X3)
| X2 = X3 ),
inference(superposition,[],[f3,f1]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( multiply(X0,multiply(X1,X2)) != multiply(X0,multiply(X1,X3))
| X2 = X3 ),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f37,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(multiply(X0,commutator(X0,X1)),X2)),
inference(superposition,[],[f1,f4]) ).
fof(f38,plain,
! [X2,X0,X1] :
( multiply(X0,X1) != multiply(X1,X2)
| multiply(X0,commutator(X0,X1)) = X2 ),
inference(superposition,[],[f3,f4]) ).
fof(f43,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,multiply(commutator(X0,X1),X2))),
inference(forward_demodulation,[],[f37,f1]) ).
fof(f45,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,multiply(commutator(X0,X1),X2))),
inference(forward_demodulation,[],[f43,f1]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,commutator(X2,X3))) = multiply(commutator(X2,X3),multiply(X0,X1)),
inference(superposition,[],[f5,f1]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( multiply(X0,commutator(X1,X2)) != multiply(X3,X0)
| commutator(X1,X2) = X3 ),
inference(superposition,[],[f2,f5]) ).
fof(f52,plain,
! [X2,X3,X0,X1] : multiply(X2,multiply(commutator(X0,X1),X3)) = multiply(multiply(commutator(X0,X1),X2),X3),
inference(superposition,[],[f1,f5]) ).
fof(f58,plain,
! [X2,X3,X0,X1] : multiply(X2,multiply(commutator(X0,X1),X3)) = multiply(commutator(X0,X1),multiply(X2,X3)),
inference(forward_demodulation,[],[f52,f1]) ).
fof(f173,plain,
! [X2,X0,X1] :
( multiply(X0,X1) != multiply(X1,multiply(X0,X2))
| commutator(X0,X1) = X2 ),
inference(superposition,[],[f31,f4]) ).
fof(f225,plain,
! [X0] : multiply(X0,commutator(X0,X0)) = X0,
inference(equality_resolution,[],[f38]) ).
fof(f280,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(commutator(X0,X0),X1)),
inference(superposition,[],[f1,f225]) ).
fof(f283,plain,
! [X0,X1] :
( multiply(X0,X1) != X0
| commutator(X0,X0) = X1 ),
inference(superposition,[],[f3,f225]) ).
fof(f287,plain,
! [X2,X0,X1] :
( multiply(X1,X0) != multiply(X1,multiply(X0,X2))
| commutator(X0,X0) = X2 ),
inference(superposition,[],[f31,f225]) ).
fof(f520,plain,
! [X0] : multiply(commutator(X0,X0),X0) = multiply(X0,commutator(commutator(X0,X0),X0)),
inference(superposition,[],[f4,f280]) ).
fof(f538,plain,
! [X0] : multiply(X0,commutator(X0,X0)) = multiply(X0,commutator(commutator(X0,X0),X0)),
inference(forward_demodulation,[],[f520,f5]) ).
fof(f547,plain,
! [X0] : multiply(X0,commutator(commutator(X0,X0),X0)) = X0,
inference(forward_demodulation,[],[f538,f225]) ).
fof(f561,plain,
! [X0] :
( X0 != X0
| commutator(X0,X0) = commutator(commutator(X0,X0),X0) ),
inference(superposition,[],[f283,f547]) ).
fof(f565,plain,
! [X0] : commutator(X0,X0) = commutator(commutator(X0,X0),X0),
inference(trivial_inequality_removal,[],[f561]) ).
fof(f736,plain,
! [X0,X1] :
( multiply(X1,X0) != X0
| commutator(X0,X0) = X1 ),
inference(superposition,[],[f50,f225]) ).
fof(f1134,plain,
! [X0,X1] : multiply(X0,multiply(commutator(commutator(X0,X0),X0),X1)) = multiply(commutator(X0,X0),multiply(X0,X1)),
inference(superposition,[],[f280,f45]) ).
fof(f1160,plain,
! [X0,X1] : multiply(X0,multiply(commutator(X0,X0),X1)) = multiply(commutator(X0,X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f1134,f565]) ).
fof(f1174,plain,
! [X0,X1] : multiply(X0,X1) = multiply(commutator(X0,X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f1160,f280]) ).
fof(f1220,plain,
! [X0,X1] :
( multiply(X0,X1) != multiply(X0,X1)
| commutator(X0,X0) = commutator(multiply(X0,X1),multiply(X0,X1)) ),
inference(superposition,[],[f736,f1174]) ).
fof(f1221,plain,
! [X0,X1] : commutator(X0,X0) = commutator(multiply(X0,X1),multiply(X0,X1)),
inference(trivial_inequality_removal,[],[f1220]) ).
fof(f1295,plain,
! [X0,X1] : multiply(X1,X0) = multiply(commutator(X0,X0),multiply(X1,X0)),
inference(superposition,[],[f46,f225]) ).
fof(f1360,plain,
! [X2,X0,X1] : multiply(X0,commutator(X1,X2)) = multiply(X0,multiply(commutator(X0,commutator(X1,X2)),commutator(X1,X2))),
inference(superposition,[],[f4,f46]) ).
fof(f1383,plain,
! [X2,X0,X1] : multiply(X0,commutator(X1,X2)) = multiply(X0,multiply(commutator(X1,X2),commutator(X0,commutator(X1,X2)))),
inference(forward_demodulation,[],[f1360,f5]) ).
fof(f1462,plain,
! [X0,X1] :
( multiply(X0,X1) != multiply(X0,X1)
| commutator(multiply(X0,X1),multiply(X0,X1)) = commutator(X1,X1) ),
inference(superposition,[],[f736,f1295]) ).
fof(f1463,plain,
! [X0,X1] : commutator(multiply(X0,X1),multiply(X0,X1)) = commutator(X1,X1),
inference(trivial_inequality_removal,[],[f1462]) ).
fof(f1570,plain,
! [X0,X1] : commutator(X0,X0) = commutator(X1,X1),
inference(superposition,[],[f1221,f1463]) ).
fof(f1729,plain,
! [X2,X0,X1] : multiply(commutator(X0,X1),X2) = multiply(commutator(X0,X1),multiply(X2,commutator(commutator(X0,X1),X2))),
inference(superposition,[],[f58,f4]) ).
fof(f9388,plain,
! [X2,X0,X1] :
( multiply(X0,commutator(X1,X2)) != multiply(commutator(X1,X2),X0)
| commutator(X0,commutator(X1,X2)) = commutator(commutator(X1,X2),X0) ),
inference(superposition,[],[f173,f1383]) ).
fof(f9444,plain,
! [X2,X0,X1] : commutator(X0,commutator(X1,X2)) = commutator(commutator(X1,X2),X0),
inference(forward_subsumption_resolution,[],[f9388,f5]) ).
fof(f9531,plain,
commutator(a,commutator(b,c)) != commutator(c,commutator(a,b)),
inference(backward_demodulation,[],[f6,f9444]) ).
fof(f10026,plain,
! [X2,X0,X1] :
( multiply(commutator(X0,X1),X2) != multiply(commutator(X0,X1),X2)
| commutator(commutator(X0,X1),X2) = commutator(X2,X2) ),
inference(superposition,[],[f287,f1729]) ).
fof(f10057,plain,
! [X2,X0,X1] : commutator(commutator(X0,X1),X2) = commutator(X2,X2),
inference(trivial_inequality_removal,[],[f10026]) ).
fof(f10138,plain,
! [X2,X0,X1] : commutator(X0,commutator(X1,X2)) = commutator(X0,X0),
inference(superposition,[],[f10057,f9444]) ).
fof(f10267,plain,
commutator(c,commutator(a,b)) != commutator(a,a),
inference(backward_demodulation,[],[f9531,f10138]) ).
fof(f10421,plain,
commutator(a,a) != commutator(c,c),
inference(forward_demodulation,[],[f10267,f10138]) ).
fof(f10423,plain,
$false,
inference(forward_subsumption_resolution,[],[f10421,f1570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n017.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:57:35 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 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
% 1.79/0.88 % (2302468)Will run a generic schedule for satisfiability detection.
% 1.79/0.88 % (2302473)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4046912066_2999 on theBenchmark for (2999ds/0Mi)
% 1.79/0.88 % TRYING [1]
% 1.79/0.88 % TRYING [2]
% 1.79/0.88 % TRYING [3]
% 1.79/0.88 % TRYING [4]
% 1.79/0.88 % (2302474)% WARNING: option uhcvi not known.
% 1.79/0.88 % (2302474)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2471314986:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.79/0.88 % (2302475)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3604628196:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.79/0.88 % (2302476)dis+10_1_sil=32000:sp=arity:random_seed=1219151917:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.79/0.88 % (2302477)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3070901706:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.79/0.88 % (2302478)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=177961821:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.79/0.88 % (2302479)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2934180601:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.79/0.88 % TRYING [5]
% 1.79/0.88 % TRYING [6]
% 1.79/0.88 % (2302476)Instruction limit reached!
% 1.79/0.88 % (2302476)------------------------------
% 1.79/0.88 % (2302476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2302476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2302476)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2302476)Termination reason: Instruction limit
% 1.79/0.88 % (2302476)Termination phase: Saturation
% 1.79/0.88 % (2302476)Time elapsed: 0.060 s
% 1.79/0.88 % (2302476)Peak memory usage: 12 MB
% 1.79/0.88 % (2302476)Instructions burned: 103 (million)
% 1.79/0.88 % (2302477)Instruction limit reached!
% 1.79/0.88 % (2302477)------------------------------
% 1.79/0.88 % (2302477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.88 % (2302477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.88 % (2302477)CaDiCaL version: 2.1.3
% 1.79/0.88 % (2302477)Termination reason: Instruction limit
% 1.79/0.89 % (2302477)Termination phase: Saturation
% 1.79/0.89 % (2302477)Time elapsed: 0.071 s
% 1.79/0.89 % (2302477)Peak memory usage: 12 MB
% 1.79/0.89 % (2302477)Instructions burned: 116 (million)
% 1.79/0.89 % (2302487)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=234564408:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.79/0.89 % TRYING [1]
% 1.79/0.89 % TRYING [2]
% 1.79/0.89 % TRYING [3]
% 1.79/0.89 % (2302478)Instruction limit reached!
% 1.79/0.89 % (2302478)------------------------------
% 1.79/0.89 % (2302478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.89 % (2302478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.89 % (2302478)CaDiCaL version: 2.1.3
% 1.79/0.89 % (2302478)Termination reason: Instruction limit
% 1.79/0.89 % (2302478)Termination phase: Saturation
% 1.79/0.89 % (2302478)Time elapsed: 0.083 s
% 1.79/0.89 % (2302478)Peak memory usage: 12 MB
% 1.79/0.89 % (2302478)Instructions burned: 131 (million)
% 1.79/0.89 % TRYING [4]
% 1.79/0.89 % (2302488)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=455930902:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.79/0.89 % (2302479)Instruction limit reached!
% 1.79/0.89 % (2302479)------------------------------
% 1.79/0.89 % (2302479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.89 % (2302479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.89 % (2302479)CaDiCaL version: 2.1.3
% 1.79/0.89 % (2302479)Termination reason: Instruction limit
% 1.79/0.89 % (2302479)Termination phase: Saturation
% 1.79/0.89 % (2302479)Time elapsed: 0.099 s
% 1.79/0.89 % (2302479)Peak memory usage: 12 MB
% 1.79/0.89 % (2302479)Instructions burned: 159 (million)
% 1.79/0.89 % TRYING [5]
% 1.79/0.89 % (2302490)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=2245380955:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.79/0.89 % (2302492)ott-21_1_sil=16000:fs=off:random_seed=427379281:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.79/0.89 % TRYING [6]
% 1.79/0.89 % (2302488)Instruction limit reached!
% 1.79/0.89 % (2302488)------------------------------
% 1.79/0.89 % (2302488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.89 % (2302488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.89 % (2302488)CaDiCaL version: 2.1.3
% 1.79/0.89 % (2302488)Termination reason: Instruction limit
% 1.79/0.89 % (2302488)Termination phase: Saturation
% 1.79/0.89 % (2302488)Time elapsed: 0.085 s
% 1.79/0.89 % (2302488)Peak memory usage: 12 MB
% 1.79/0.89 % (2302488)Instructions burned: 131 (million)
% 1.79/0.89 % (2302495)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4029704270:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.79/0.89 % (2302492)Instruction limit reached!
% 1.79/0.89 % (2302492)------------------------------
% 1.79/0.89 % (2302492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.89 % (2302492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.89 % (2302492)CaDiCaL version: 2.1.3
% 1.79/0.89 % (2302492)Termination reason: Instruction limit
% 1.79/0.89 % (2302492)Termination phase: Saturation
% 1.79/0.89 % (2302492)Time elapsed: 0.088 s
% 1.79/0.89 % (2302492)Peak memory usage: 11 MB
% 1.79/0.89 % (2302492)Instructions burned: 180 (million)
% 1.79/0.89 % TRYING [7]
% 1.79/0.89 % (2302497)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=579836768:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.79/0.89 % TRYING [1]
% 1.79/0.89 % TRYING [2]
% 1.79/0.89 % TRYING [3]
% 1.79/0.89 % TRYING [4]
% 1.79/0.89 % TRYING [5]
% 1.79/0.89 % TRYING [6]
% 1.79/0.89 % (2302495) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2302468-2302495"...
% 1.79/0.89 % (2302495)...printing done.
% 1.79/0.89 % (2302495)Refutation found. Thanks to Tanya!
% 1.79/0.89 % SZS status Unsatisfiable for theBenchmark
% 1.79/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 1.79/0.89 % (2302495)------------------------------
% 1.79/0.89 % (2302495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.79/0.89 % (2302495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.79/0.89 % (2302495)CaDiCaL version: 2.1.3
% 1.79/0.89 % (2302495)Termination reason: Refutation
% 1.79/0.89 % (2302495)Time elapsed: 0.206 s
% 1.79/0.89 % (2302495)Peak memory usage: 14 MB
% 1.79/0.89 % (2302495)Instructions burned: 371 (million)
% 1.79/0.89 % (2302468)Success in time 0.449 s
% 1.79/0.89 % Vampire exiting
%------------------------------------------------------------------------------