%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n015.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 10:18:00 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.46s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 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 : 10 ( 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 : 41 ( 41 !; 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(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(f14,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(X0,inverse(multiply(X3,multiply(X2,inverse(X2))))))))) = X3,
inference(superposition,[],[f3,f9]) ).
fof(f19,plain,
! [X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X3)))))) = X3,
inference(forward_demodulation,[],[f14,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(f57,plain,
! [X2,X0,X1] : multiply(X1,X2) = multiply(X1,multiply(multiply(X0,X2),inverse(X0))),
inference(superposition,[],[f19,f1]) ).
fof(f77,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[],[f57,f36]) ).
fof(f123,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(X2,multiply(multiply(X0,inverse(X0)),X1)),
inference(superposition,[],[f57,f77]) ).
fof(f173,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X1,inverse(X0)))) = X0,
inference(superposition,[],[f123,f1]) ).
fof(f240,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(superposition,[],[f1,f173]) ).
fof(f242,plain,
! [X0,X1] : multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(forward_demodulation,[],[f240,f77]) ).
fof(f266,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f12,f242]) ).
fof(f327,plain,
multiply(a,b) != multiply(a,b),
inference(superposition,[],[f2,f266]) ).
fof(f357,plain,
$false,
inference(trivial_inequality_removal,[],[f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP516-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:09:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.46 % (1428570)Will run a generic schedule for satisfiability detection.
% 0.09/0.46 % (1428580)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2573565730_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.46 % TRYING [1]
% 0.09/0.46 % TRYING [2]
% 0.09/0.46 % TRYING [3]
% 0.09/0.46 % TRYING [4]
% 0.09/0.46 % (1428582)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2201904454:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.46 % (1428583)dis+10_1_sil=32000:sp=arity:random_seed=3790519403:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.46 % (1428584)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=414655298:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.46 % (1428585)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3103150974:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.46 % (1428581)% WARNING: option uhcvi not known.
% 0.09/0.46 % (1428586)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3896858975:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.46 % (1428581)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=362121444:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.46 % (1428582) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1428570-1428582"...
% 0.09/0.46 % (1428582)...printing done.
% 0.09/0.46 % (1428582)Refutation found. Thanks to Tanya!
% 0.09/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.46 % (1428582)------------------------------
% 0.09/0.46 % (1428582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.46 % (1428582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.46 % (1428582)CaDiCaL version: 2.1.3
% 0.09/0.46 % (1428582)Termination reason: Refutation
% 0.09/0.46 % (1428582)Time elapsed: 0.012 s
% 0.09/0.46 % (1428582)Peak memory usage: 11 MB
% 0.09/0.46 % (1428582)Instructions burned: 19 (million)
% 0.09/0.46 % (1428570)Success in time 0.048 s
% 0.09/0.46 % Vampire exiting
%------------------------------------------------------------------------------