%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 10:17:01 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p01b_1) ).
fof(f18,plain,
a = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p01b) ).
fof(f20,plain,
multiply(inverse(c),multiply(a,c)) != greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),
inference(reorient_equations,[],[f19]) ).
fof(f161,plain,
multiply(inverse(c),multiply(a,c)) != multiply(inverse(c),greatest_lower_bound(multiply(a,c),multiply(b,c))),
inference(superposition,[],[f20,f14]) ).
fof(f170,plain,
multiply(inverse(c),multiply(a,c)) != multiply(inverse(c),multiply(greatest_lower_bound(a,b),c)),
inference(forward_demodulation,[],[f161,f16]) ).
fof(f177,plain,
multiply(inverse(c),multiply(a,c)) != multiply(inverse(c),multiply(a,c)),
inference(forward_demodulation,[],[f170,f18]) ).
fof(f178,plain,
$false,
inference(trivial_inequality_removal,[],[f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:34:46 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43 % (546992)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (547002)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2597901632:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.43 % (547002) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-546992-547002"...
% 0.11/0.43 % (546998)% WARNING: option uhcvi not known.
% 0.11/0.43 % (547002)...printing done.
% 0.11/0.43 % (547002)Refutation found. Thanks to Tanya!
% 0.11/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.43 % (547002)------------------------------
% 0.11/0.43 % (547002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (547002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (547002)CaDiCaL version: 2.1.3
% 0.11/0.43 % (547002)Termination reason: Refutation
% 0.11/0.43 % (547002)Time elapsed: 0.003 s
% 0.11/0.43 % (547002)Peak memory usage: 11 MB
% 0.11/0.43 % (547002)Instructions burned: 8 (million)
% 0.11/0.43 % (546992)Success in time 0.027 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------