%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP404-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 10:13:52 AM UTC 2026
% Result : Unsatisfiable 12.52s 2.75s
% Output : Refutation 12.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 10 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(X1,multiply(inverse(X1),X1)))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
fof(f5,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),inverse(multiply(X3,multiply(inverse(X3),X3))))) = multiply(X1,inverse(multiply(inverse(X0),inverse(multiply(X2,multiply(inverse(X2),X2)))))),
inference(superposition,[],[f1,f1]) ).
fof(f23,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X2)),multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,multiply(inverse(X2),X2))))))) = X1,
inference(superposition,[],[f1,f5]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X3,
inference(superposition,[],[f1,f5]) ).
fof(f38,plain,
! [X0,X4,X5] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X4)),multiply(X0,X5))),inverse(multiply(X4,multiply(inverse(X4),X4))))) = X5,
inference(superposition,[],[f27,f27]) ).
fof(f72,plain,
! [X2,X0,X1] : inverse(multiply(X2,multiply(inverse(X2),X2))) = multiply(inverse(multiply(X1,X2)),inverse(multiply(X0,inverse(multiply(multiply(X1,X0),multiply(inverse(multiply(X1,X0)),multiply(X1,X0))))))),
inference(superposition,[],[f1,f38]) ).
fof(f98,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X0)) = multiply(inverse(multiply(X3,X2)),multiply(X3,X0)),
inference(superposition,[],[f23,f38]) ).
fof(f132,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,inverse(multiply(X2,multiply(inverse(X2),X2))))),multiply(X1,X3)) = multiply(X0,multiply(inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X0))),X3)),
inference(superposition,[],[f98,f38]) ).
fof(f452,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(X0,multiply(inverse(X0),X0)))) = X2,
inference(superposition,[],[f23,f72]) ).
fof(f518,plain,
! [X2,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(multiply(X2,multiply(inverse(X2),X2))))),multiply(X1,inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(superposition,[],[f132,f452]) ).
fof(f569,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f518,f518]) ).
fof(f764,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(X2,multiply(inverse(X0),X0)))) = X3,
inference(superposition,[],[f452,f569]) ).
fof(f786,plain,
! [X0] : a2 != multiply(multiply(inverse(X0),X0),a2),
inference(superposition,[],[f3,f569]) ).
fof(f792,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),X2)),multiply(inverse(X0),X0))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X1,
inference(superposition,[],[f38,f569]) ).
fof(f947,plain,
! [X2,X3,X0] : multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X2),multiply(inverse(X3),X3)))) = X2,
inference(superposition,[],[f764,f569]) ).
fof(f1050,plain,
! [X2,X0,X1] : multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X0),X0))),
inference(superposition,[],[f947,f569]) ).
fof(f1225,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(X3),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),X1)),X2)),multiply(inverse(X0),X0))),inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(superposition,[],[f38,f1050]) ).
fof(f1243,plain,
! [X3,X1] : multiply(inverse(X1),X1) = inverse(multiply(inverse(X3),X3)),
inference(forward_demodulation,[],[f1225,f792]) ).
fof(f1275,plain,
! [X2,X0,X1] : multiply(inverse(X1),X1) = inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X2),X2))),
inference(superposition,[],[f1243,f1243]) ).
fof(f1385,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(multiply(inverse(X0),X0),multiply(inverse(X2),X3)),
inference(superposition,[],[f98,f1243]) ).
fof(f2800,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X0),X0))))) = X3,
inference(superposition,[],[f23,f1275]) ).
fof(f4498,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(inverse(X4),X4),X0) = multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X3),X3))))),
inference(superposition,[],[f1385,f947]) ).
fof(f4656,plain,
! [X0,X4] : multiply(multiply(inverse(X4),X4),X0) = X0,
inference(forward_demodulation,[],[f4498,f2800]) ).
fof(f4714,plain,
a2 != a2,
inference(superposition,[],[f786,f4656]) ).
fof(f4762,plain,
$false,
inference(trivial_inequality_removal,[],[f4714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP404-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:58:57 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.90/2.56 % (2302900)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.90/2.56 % (2302905)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3787769861:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.90/2.56 % (2302908)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=825465193:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.90/2.56 % (2302906)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3438429750:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.90/2.56 % (2302907)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3917952164:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.90/2.56 % (2302911)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2909784109:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.90/2.56 % (2302910)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=458354185:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.90/2.56 % (2302909)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3112005156:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.90/2.56 % (2302908)Instruction limit reached!
% 11.90/2.56 % (2302908)------------------------------
% 11.90/2.56 % (2302908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.90/2.56 % (2302908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.90/2.56 % (2302908)CaDiCaL version: 2.1.3
% 11.90/2.56 % (2302908)Termination reason: Instruction limit
% 11.90/2.56 % (2302908)Termination phase: Saturation
% 11.90/2.56 % (2302908)Time elapsed: 0.075 s
% 11.90/2.56 % (2302908)Peak memory usage: 89 MB
% 11.90/2.56 % (2302908)Instructions burned: 136 (million)
% 11.90/2.56 % (2302909)Instruction limit reached!
% 11.90/2.56 % (2302909)------------------------------
% 11.90/2.56 % (2302909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.90/2.56 % (2302909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.90/2.56 % (2302909)CaDiCaL version: 2.1.3
% 11.90/2.56 % (2302909)Termination reason: Instruction limit
% 11.90/2.56 % (2302909)Termination phase: Saturation
% 11.90/2.56 % (2302909)Time elapsed: 0.101 s
% 11.90/2.56 % (2302909)Peak memory usage: 89 MB
% 11.90/2.56 % (2302909)Instructions burned: 181 (million)
% 11.90/2.56 % (2302910)Instruction limit reached!
% 11.90/2.56 % (2302910)------------------------------
% 11.90/2.56 % (2302910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.90/2.56 % (2302910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.90/2.56 % (2302910)CaDiCaL version: 2.1.3
% 11.90/2.56 % (2302910)Termination reason: Instruction limit
% 11.90/2.56 % (2302910)Termination phase: Saturation
% 11.90/2.56 % (2302910)Time elapsed: 0.151 s
% 11.90/2.56 % (2302910)Peak memory usage: 90 MB
% 11.90/2.56 % (2302910)Instructions burned: 258 (million)
% 11.90/2.56 % (2302919)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3289631879:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 11.90/2.56 % (2302920)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1856984732:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 11.90/2.56 % (2302921)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=417500199:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 11.90/2.56 % (2302921)Instruction limit reached!
% 11.90/2.56 % (2302921)------------------------------
% 11.90/2.56 % (2302921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.90/2.56 % (2302921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.90/2.56 % (2302921)CaDiCaL version: 2.1.3
% 11.90/2.56 % (2302921)Termination reason: Instruction limit
% 11.90/2.56 % (2302921)Termination phase: Saturation
% 11.90/2.56 % (2302921)Time elapsed: 0.132 s
% 12.52/2.75 % (2302921)Peak memory usage: 90 MB
% 12.52/2.75 % (2302921)Instructions burned: 216 (million)
% 12.52/2.75 % (2302925)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1056681989:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 12.52/2.75 % (2302911)Instruction limit reached!
% 12.52/2.75 % (2302911)------------------------------
% 12.52/2.75 % (2302911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.75 % (2302911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.75 % (2302911)CaDiCaL version: 2.1.3
% 12.52/2.75 % (2302911)Termination reason: Instruction limit
% 12.52/2.75 % (2302911)Termination phase: Saturation
% 12.52/2.75 % (2302911)Time elapsed: 0.598 s
% 12.52/2.75 % (2302911)Peak memory usage: 95 MB
% 12.52/2.75 % (2302911)Instructions burned: 1188 (million)
% 12.52/2.75 % (2302925)Instruction limit reached!
% 12.52/2.75 % (2302925)------------------------------
% 12.52/2.75 % (2302925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.75 % (2302925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.75 % (2302925)CaDiCaL version: 2.1.3
% 12.52/2.75 % (2302925)Termination reason: Instruction limit
% 12.52/2.75 % (2302925)Termination phase: Saturation
% 12.52/2.75 % (2302925)Time elapsed: 0.179 s
% 12.52/2.75 % (2302925)Peak memory usage: 91 MB
% 12.52/2.75 % (2302925)Instructions burned: 318 (million)
% 12.52/2.75 % (2302927)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2062394928:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 12.52/2.75 % (2302928)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2981462535:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 12.52/2.75 % (2302906)First to succeed.
% 12.52/2.75 % (2302906)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2302900"
% 12.52/2.75 % (2302919)Instruction limit reached!
% 12.52/2.75 % (2302919)------------------------------
% 12.52/2.75 % (2302919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.75 % (2302919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.75 % (2302919)CaDiCaL version: 2.1.3
% 12.52/2.75 % (2302919)Termination reason: Instruction limit
% 12.52/2.75 % (2302919)Termination phase: Saturation
% 12.52/2.75 % (2302919)Time elapsed: 1.242 s
% 12.52/2.75 % (2302919)Peak memory usage: 139 MB
% 12.52/2.75 % (2302919)Instructions burned: 2052 (million)
% 12.52/2.75 % (2302906)Refutation found. Thanks to Tanya!
% 12.52/2.75 % SZS status Unsatisfiable for theBenchmark
% 12.52/2.75 % SZS output start Proof for theBenchmark
% See solution above
% 12.52/2.75 % (2302906)------------------------------
% 12.52/2.75 % (2302906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.75 % (2302906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.75 % (2302906)CaDiCaL version: 2.1.3
% 12.52/2.75 % (2302906)Termination reason: Refutation
% 12.52/2.75 % (2302906)Time elapsed: 1.287 s
% 12.52/2.75 % (2302906)Peak memory usage: 140 MB
% 12.52/2.75 % (2302906)Instructions burned: 2163 (million)
% 12.52/2.75 % (2302906)------------------------------
% 12.52/2.75 % (2302906)------------------------------
% 12.52/2.75 % (2302900)Success in time 1.688 s
% 12.52/2.75 % Vampire exiting
%------------------------------------------------------------------------------