%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP554-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 10:18:05 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f4,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2)),
inference(definition_unfolding,[],[f4,f2,f2]) ).
fof(f6,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,inverse(divide(X0,divide(X1,X2)))),inverse(divide(X3,X0))),X2) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f14,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X0))) = X2,
inference(superposition,[],[f6,f1]) ).
fof(f19,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(superposition,[],[f14,f14]) ).
fof(f27,plain,
! [X0,X1] : inverse(divide(X1,X0)) = divide(inverse(X1),inverse(X0)),
inference(superposition,[],[f14,f19]) ).
fof(f37,plain,
! [X0,X1] : inverse(divide(X0,divide(X1,inverse(X0)))) = X1,
inference(superposition,[],[f14,f27]) ).
fof(f63,plain,
! [X0,X1] : divide(divide(X0,X0),inverse(X1)) = X1,
inference(superposition,[],[f1,f37]) ).
fof(f73,plain,
a2 != a2,
inference(superposition,[],[f5,f63]) ).
fof(f84,plain,
$false,
inference(trivial_inequality_removal,[],[f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP554-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:07:39 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.46 % (1000900)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (1000920)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1567873205:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (1000920) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1000900-1000920"...
% 0.12/0.46 % (1000920)...printing done.
% 0.12/0.46 % (1000920)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (1000920)------------------------------
% 0.12/0.46 % (1000920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (1000920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (1000920)CaDiCaL version: 2.1.3
% 0.12/0.46 % (1000920)Termination reason: Refutation
% 0.12/0.46 % (1000920)Time elapsed: 0.003 s
% 0.12/0.46 % (1000920)Peak memory usage: 11 MB
% 0.12/0.46 % (1000920)Instructions burned: 6 (million)
% 0.12/0.46 % (1000900)Success in time 0.032 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------