%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP512-1 : 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 : 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 10:14:45 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.35s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 29 unt; 1 def)
% Number of atoms : 35 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,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(f4,definition,
( spl0_1
<=> multiply(a,b) = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f6,plain,
( multiply(a,b) != multiply(b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f4]) ).
fof(f7,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2,f4]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,X3),inverse(multiply(multiply(multiply(X1,X0),X2),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(multiply(multiply(X1,X0),X2),X3),inverse(multiply(X1,X2))),inverse(X0)) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f17,plain,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(X3,multiply(X1,X2)),inverse(multiply(X3,X0))))))) = X2,
inference(superposition,[],[f1,f9]) ).
fof(f32,plain,
! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,inverse(multiply(multiply(X0,X1),X2))))) = X2,
inference(superposition,[],[f9,f8]) ).
fof(f42,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X3,multiply(X1,X2)),inverse(multiply(X3,X0)))) = inverse(multiply(X1,multiply(X2,inverse(X0)))),
inference(superposition,[],[f32,f9]) ).
fof(f44,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,multiply(X1,X2))))) = X2,
inference(superposition,[],[f32,f8]) ).
fof(f52,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(X1,inverse(multiply(X1,multiply(X2,inverse(X0))))))) = X2,
inference(backward_demodulation,[],[f17,f42]) ).
fof(f88,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3)))) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(superposition,[],[f8,f10]) ).
fof(f101,plain,
! [X2,X0] : inverse(X2) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(forward_demodulation,[],[f88,f1]) ).
fof(f110,plain,
! [X3,X0] : multiply(multiply(X3,X0),inverse(X3)) = X0,
inference(superposition,[],[f101,f44]) ).
fof(f111,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X0),X2))),
inference(superposition,[],[f101,f1]) ).
fof(f133,plain,
! [X2,X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(multiply(X1,inverse(X0)),multiply(inverse(X1),X2))))) = X2,
inference(superposition,[],[f44,f101]) ).
fof(f176,plain,
! [X2,X1] : inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(backward_demodulation,[],[f9,f111]) ).
fof(f178,plain,
! [X2,X1] : inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(backward_demodulation,[],[f133,f111]) ).
fof(f230,plain,
! [X2,X0] : multiply(X0,multiply(X2,inverse(X0))) = X2,
inference(backward_demodulation,[],[f52,f176]) ).
fof(f321,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f110,f110]) ).
fof(f334,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f176,f321]) ).
fof(f338,plain,
! [X2,X1] : multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(backward_demodulation,[],[f178,f334]) ).
fof(f359,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,inverse(inverse(X1))),
inference(superposition,[],[f338,f230]) ).
fof(f364,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f359,f334]) ).
fof(f365,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f6,f364]) ).
fof(f366,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f365]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f7]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f366]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f367,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP512-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:06:32 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.74/1.35 % (723520)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.74/1.35 % (723530)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3787714818:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.74/1.35 % (723530)First to succeed.
% 2.74/1.35 % (723530)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-723520"
% 2.74/1.35 % (723526)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=1087183539:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.74/1.35 % (723529)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3093876035:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.74/1.35 % (723525)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=2950886739:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.74/1.35 % (723527)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1836663253:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.74/1.35 % (723528)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2702170719:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.74/1.35 % (723531)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=772394041:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.74/1.35 % (723528)Also succeeded, but the first one will report.
% 2.74/1.35 % (723531)Also succeeded, but the first one will report.
% 2.74/1.35 % (723529)Instruction limit reached!
% 2.74/1.35 % (723529)------------------------------
% 2.74/1.35 % (723529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.35 % (723529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.35 % (723529)CaDiCaL version: 2.1.3
% 2.74/1.35 % (723529)Termination reason: Instruction limit
% 2.74/1.35 % (723529)Termination phase: Saturation
% 2.74/1.35 % (723529)Time elapsed: 0.104 s
% 2.74/1.35 % (723529)Peak memory usage: 89 MB
% 2.74/1.35 % (723529)Instructions burned: 181 (million)
% 2.74/1.35 % (723530)Refutation found. Thanks to Tanya!
% 2.74/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.35 % (723530)------------------------------
% 2.74/1.35 % (723530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.35 % (723530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.35 % (723530)CaDiCaL version: 2.1.3
% 2.74/1.35 % (723530)Termination reason: Refutation
% 2.74/1.35 % (723530)Time elapsed: 0.016 s
% 2.74/1.35 % (723530)Peak memory usage: 89 MB
% 2.74/1.35 % (723530)Instructions burned: 43 (million)
% 2.74/1.35 % (723530)------------------------------
% 2.74/1.35 % (723530)------------------------------
% 2.74/1.35 % (723520)Success in time 0.303 s
% 2.74/1.35 % Vampire exiting
%------------------------------------------------------------------------------