%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP516-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 10:14:46 AM UTC 2026
% Result : Unsatisfiable 3.44s 1.35s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 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 : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f3,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(multiply(X0,X3),inverse(multiply(X2,X3))))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f4,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X2,multiply(multiply(X0,X3),inverse(multiply(X1,X3)))),inverse(X0))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(superposition,[],[f3,f1]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[],[f3,f9]) ).
fof(f21,plain,
! [X2,X0,X1] : multiply(multiply(X2,X1),multiply(X0,inverse(multiply(X0,X1)))) = X2,
inference(superposition,[],[f3,f12]) ).
fof(f36,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(multiply(X0,X1),multiply(X2,inverse(X0))),
inference(superposition,[],[f3,f21]) ).
fof(f72,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(X2,multiply(multiply(X0,X1),inverse(X0))),
inference(superposition,[],[f4,f12]) ).
fof(f97,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[],[f72,f36]) ).
fof(f148,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(X2,multiply(multiply(X0,inverse(X0)),X1)),
inference(superposition,[],[f72,f97]) ).
fof(f209,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = X0,
inference(superposition,[],[f148,f9]) ).
fof(f334,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X1)),X0) = X0,
inference(superposition,[],[f12,f209]) ).
fof(f404,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(multiply(multiply(X1,inverse(X1)),X2),X0),
inference(superposition,[],[f97,f334]) ).
fof(f433,plain,
! [X2,X0] : multiply(X0,X2) = multiply(X2,X0),
inference(forward_demodulation,[],[f404,f334]) ).
fof(f619,plain,
multiply(a,b) != multiply(a,b),
inference(superposition,[],[f2,f433]) ).
fof(f656,plain,
$false,
inference(trivial_inequality_removal,[],[f619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP516-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.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 10:06:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 3.44/1.35 % (569178)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.44/1.35 % (569244)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=2657152171:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.44/1.35 % (569250)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3156419163:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.44/1.35 % (569248)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1297713204:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.44/1.35 % (569246)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2337256147:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.44/1.35 % (569245)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=3062525982:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.44/1.35 % (569247)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1692789729:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.44/1.35 % (569249)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=233121788:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.44/1.35 % (569250)First to succeed.
% 3.44/1.35 % (569250)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-569178"
% 3.44/1.35 % (569249)Also succeeded, but the first one will report.
% 3.44/1.35 % (569247)Instruction limit reached!
% 3.44/1.35 % (569247)------------------------------
% 3.44/1.35 % (569247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.35 % (569247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.35 % (569247)CaDiCaL version: 2.1.3
% 3.44/1.35 % (569247)Termination reason: Instruction limit
% 3.44/1.35 % (569247)Termination phase: Saturation
% 3.44/1.35 % (569247)Time elapsed: 0.081 s
% 3.44/1.35 % (569247)Peak memory usage: 89 MB
% 3.44/1.35 % (569247)Instructions burned: 136 (million)
% 3.44/1.35 % (569248)Instruction limit reached!
% 3.44/1.35 % (569248)------------------------------
% 3.44/1.35 % (569248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.35 % (569248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.35 % (569248)CaDiCaL version: 2.1.3
% 3.44/1.35 % (569248)Termination reason: Instruction limit
% 3.44/1.35 % (569248)Termination phase: Saturation
% 3.44/1.35 % (569248)Time elapsed: 0.102 s
% 3.44/1.35 % (569248)Peak memory usage: 89 MB
% 3.44/1.35 % (569248)Instructions burned: 182 (million)
% 3.44/1.35 % (569258)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1154478492:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.44/1.35 % (569259)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2806604786:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.44/1.35 % (569250)Refutation found. Thanks to Tanya!
% 3.44/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.44/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.35 % (569250)------------------------------
% 3.44/1.35 % (569250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.35 % (569250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.35 % (569250)CaDiCaL version: 2.1.3
% 3.44/1.35 % (569250)Termination reason: Refutation
% 3.44/1.35 % (569250)Time elapsed: 0.018 s
% 3.44/1.35 % (569250)Peak memory usage: 88 MB
% 3.44/1.35 % (569250)Instructions burned: 29 (million)
% 3.44/1.35 % (569250)------------------------------
% 3.44/1.35 % (569250)------------------------------
% 3.44/1.35 % (569178)Success in time 0.408 s
% 3.44/1.35 % Vampire exiting
%------------------------------------------------------------------------------