%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP409-1 : 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 : n006.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 2.07s 1.39s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 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 : 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 : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X2,inverse(multiply(X0,X3)))),multiply(X2,inverse(X3))) = multiply(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(superposition,[],[f1,f1]) ).
fof(f74,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[],[f3,f3]) ).
fof(f75,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X1,inverse(multiply(multiply(X0,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X1,inverse(X2))) = X0,
inference(superposition,[],[f3,f1]) ).
fof(f143,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(X0))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(superposition,[],[f74,f75]) ).
fof(f204,plain,
! [X2,X0,X1,X5] : multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X0))) = multiply(inverse(multiply(X5,inverse(X2))),multiply(X5,inverse(X0))),
inference(superposition,[],[f143,f1]) ).
fof(f263,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X2)))),multiply(X4,inverse(X3))) = multiply(inverse(X0),multiply(multiply(inverse(multiply(X1,inverse(multiply(X0,X2)))),multiply(X1,inverse(X2))),inverse(X3))),
inference(superposition,[],[f204,f1]) ).
fof(f556,plain,
! [X2,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))),
inference(superposition,[],[f263,f1]) ).
fof(f721,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f556,f1]) ).
fof(f951,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f721]) ).
fof(f1002,plain,
$false,
inference(forward_subsumption_resolution,[],[f951,f721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:03:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.07/1.39 % (2749515)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.07/1.39 % (2749524)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1340277049:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.07/1.39 % (2749526)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1590977708:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.07/1.39 % (2749525)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3464096405:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.07/1.39 % (2749523)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2320953514:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.07/1.39 % (2749522)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4260830975:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.07/1.39 % (2749521)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=4146064638:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.07/1.39 % (2749520)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=500370567:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.07/1.39 % (2749524)Instruction limit reached!
% 2.07/1.39 % (2749524)------------------------------
% 2.07/1.39 % (2749524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/1.39 % (2749524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/1.39 % (2749524)CaDiCaL version: 2.1.3
% 2.07/1.39 % (2749524)Termination reason: Instruction limit
% 2.07/1.39 % (2749524)Termination phase: Saturation
% 2.07/1.39 % (2749524)Time elapsed: 0.055 s
% 2.07/1.39 % (2749524)Peak memory usage: 88 MB
% 2.07/1.39 % (2749524)Instructions burned: 190 (million)
% 2.07/1.39 % (2749526)First to succeed.
% 2.07/1.39 % (2749526)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2749515"
% 2.07/1.39 % (2749523)Instruction limit reached!
% 2.07/1.39 % (2749523)------------------------------
% 2.07/1.39 % (2749523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/1.39 % (2749523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/1.39 % (2749523)CaDiCaL version: 2.1.3
% 2.07/1.39 % (2749523)Termination reason: Instruction limit
% 2.07/1.39 % (2749523)Termination phase: Saturation
% 2.07/1.39 % (2749523)Time elapsed: 0.076 s
% 2.07/1.39 % (2749523)Peak memory usage: 88 MB
% 2.07/1.39 % (2749523)Instructions burned: 136 (million)
% 2.07/1.39 % (2749534)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=433235185:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.07/1.39 % (2749525)Also succeeded, but the first one will report.
% 2.07/1.39 % (2749535)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3614222529:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 2.07/1.39 % (2749526)Refutation found. Thanks to Tanya!
% 2.07/1.39 % SZS status Unsatisfiable for theBenchmark
% 2.07/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.07/1.39 % (2749526)------------------------------
% 2.07/1.39 % (2749526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/1.39 % (2749526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/1.39 % (2749526)CaDiCaL version: 2.1.3
% 2.07/1.39 % (2749526)Termination reason: Refutation
% 2.07/1.39 % (2749526)Time elapsed: 0.051 s
% 2.07/1.39 % (2749526)Peak memory usage: 88 MB
% 2.07/1.39 % (2749526)Instructions burned: 92 (million)
% 2.07/1.39 % (2749526)------------------------------
% 2.07/1.39 % (2749526)------------------------------
% 2.07/1.39 % (2749515)Success in time 0.454 s
% 2.07/1.39 % Vampire exiting
%------------------------------------------------------------------------------