%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP415-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 10:13:57 AM UTC 2026
% Result : Unsatisfiable 7.28s 2.00s
% Output : Refutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 16 ( 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 : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f4,plain,
! [X2,X3,X0,X1,X4] : multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X0)))),inverse(multiply(inverse(X3),X3))))) = inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X0))),inverse(multiply(inverse(X1),X1)))))),
inference(superposition,[],[f1,f1]) ).
fof(f22,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X0))))),inverse(multiply(inverse(X1),X1))))) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f43,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(inverse(X0))))),inverse(multiply(inverse(X2),X2))) = inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),X0)),inverse(multiply(inverse(X1),X1)))))),
inference(superposition,[],[f1,f22]) ).
fof(f106,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X0))))))),inverse(multiply(inverse(X2),X2))) = X0,
inference(superposition,[],[f43,f1]) ).
fof(f109,plain,
! [X2,X0,X1] : multiply(X1,inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))))))) = X2,
inference(superposition,[],[f22,f43]) ).
fof(f177,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),X3) = inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(inverse(multiply(X3,inverse(X0))))))),X1)),X0)),inverse(multiply(inverse(X1),X1)))))),
inference(superposition,[],[f1,f106]) ).
fof(f203,plain,
! [X2,X3,X0,X1] : multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X0),inverse(multiply(inverse(X2),X2)))))))) = inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),inverse(multiply(inverse(X3),X3))))))),
inference(superposition,[],[f109,f109]) ).
fof(f1887,plain,
! [X0,X1] : multiply(inverse(X1),X1) = inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))))),
inference(superposition,[],[f177,f106]) ).
fof(f4589,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(inverse(X1),X1))))))))) = X2,
inference(superposition,[],[f109,f203]) ).
fof(f5496,plain,
! [X2,X0,X1] : multiply(inverse(X2),X2) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X0)))),multiply(X1,inverse(multiply(inverse(X0),X0)))),
inference(superposition,[],[f4589,f1887]) ).
fof(f6960,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f5496,f106]) ).
fof(f7696,plain,
! [X0] : multiply(inverse(X0),X0) != multiply(inverse(a1),a1),
inference(superposition,[],[f2,f6960]) ).
fof(f7796,plain,
$false,
inference(forward_subsumption_resolution,[],[f7696,f6960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP415-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 10:04:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.28/2.00 % (716894)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.28/2.00 % (716900)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=1530588313:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.28/2.00 % (716902)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1426516767:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.28/2.00 % (716903)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2452059324:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.28/2.00 % (716901)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=1705833602:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.28/2.00 % (716904)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3700809296:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.28/2.00 % (716905)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4233866302:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.28/2.00 % (716906)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3599279406:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.28/2.00 % (716903)Instruction limit reached!
% 7.28/2.00 % (716903)------------------------------
% 7.28/2.00 % (716903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/2.00 % (716903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/2.00 % (716903)CaDiCaL version: 2.1.3
% 7.28/2.00 % (716903)Termination reason: Instruction limit
% 7.28/2.00 % (716903)Termination phase: Saturation
% 7.28/2.00 % (716903)Time elapsed: 0.071 s
% 7.28/2.00 % (716903)Peak memory usage: 89 MB
% 7.28/2.00 % (716903)Instructions burned: 137 (million)
% 7.28/2.00 % (716904)Instruction limit reached!
% 7.28/2.00 % (716904)------------------------------
% 7.28/2.00 % (716904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/2.00 % (716904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/2.00 % (716904)CaDiCaL version: 2.1.3
% 7.28/2.00 % (716904)Termination reason: Instruction limit
% 7.28/2.00 % (716904)Termination phase: Saturation
% 7.28/2.00 % (716904)Time elapsed: 0.091 s
% 7.28/2.00 % (716904)Peak memory usage: 89 MB
% 7.28/2.00 % (716904)Instructions burned: 182 (million)
% 7.28/2.00 % (716905)Instruction limit reached!
% 7.28/2.00 % (716905)------------------------------
% 7.28/2.00 % (716905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/2.00 % (716905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/2.00 % (716905)CaDiCaL version: 2.1.3
% 7.28/2.00 % (716905)Termination reason: Instruction limit
% 7.28/2.00 % (716905)Termination phase: Saturation
% 7.28/2.00 % (716905)Time elapsed: 0.145 s
% 7.28/2.00 % (716905)Peak memory usage: 91 MB
% 7.28/2.00 % (716905)Instructions burned: 258 (million)
% 7.28/2.00 % (716914)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1997105392:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 7.28/2.00 % (716915)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3800002308:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 7.28/2.00 % (716916)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1651946185:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 7.28/2.00 % (716916)Instruction limit reached!
% 7.28/2.00 % (716916)------------------------------
% 7.28/2.00 % (716916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/2.00 % (716916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/2.00 % (716916)CaDiCaL version: 2.1.3
% 7.28/2.00 % (716916)Termination reason: Instruction limit
% 7.28/2.00 % (716916)Termination phase: Saturation
% 7.28/2.00 % (716916)Time elapsed: 0.135 s
% 7.28/2.00 % (716916)Peak memory usage: 91 MB
% 7.28/2.00 % (716916)Instructions burned: 216 (million)
% 7.28/2.00 % (716920)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=45973900: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)
% 7.28/2.00 % (716906)First to succeed.
% 7.28/2.00 % (716906)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-716894"
% 7.28/2.00 % (716920)Instruction limit reached!
% 7.28/2.00 % (716920)------------------------------
% 7.28/2.00 % (716920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/2.00 % (716920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/2.00 % (716920)CaDiCaL version: 2.1.3
% 7.28/2.00 % (716920)Termination reason: Instruction limit
% 7.28/2.00 % (716920)Termination phase: Saturation
% 7.28/2.00 % (716920)Time elapsed: 0.152 s
% 7.28/2.00 % (716920)Peak memory usage: 92 MB
% 7.28/2.00 % (716920)Instructions burned: 319 (million)
% 7.28/2.00 % (716906)Refutation found. Thanks to Tanya!
% 7.28/2.00 % SZS status Unsatisfiable for theBenchmark
% 7.28/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 7.28/2.00 % (716906)------------------------------
% 7.28/2.00 % (716906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.28/2.00 % (716906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.28/2.00 % (716906)CaDiCaL version: 2.1.3
% 7.28/2.00 % (716906)Termination reason: Refutation
% 7.28/2.00 % (716906)Time elapsed: 0.552 s
% 7.28/2.00 % (716906)Peak memory usage: 94 MB
% 7.28/2.00 % (716906)Instructions burned: 1146 (million)
% 7.28/2.00 % (716906)------------------------------
% 7.28/2.00 % (716906)------------------------------
% 7.28/2.00 % (716894)Success in time 0.953 s
% 7.28/2.00 % Vampire exiting
%------------------------------------------------------------------------------