%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 10:17:07 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 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 : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23x_2) ).
fof(f21,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p23x) ).
fof(f28,plain,
! [X0] : multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(a,b),multiply(inverse(X0),X0)),
inference(superposition,[],[f21,f3]) ).
fof(f32,plain,
! [X0] : multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(a,b),multiply(X0,inverse(X0))),
inference(superposition,[],[f28,f19]) ).
fof(f47,plain,
! [X0] : multiply(a,least_upper_bound(inverse(a),b)) != least_upper_bound(multiply(X0,inverse(X0)),multiply(a,b)),
inference(superposition,[],[f32,f6]) ).
fof(f223,plain,
multiply(a,least_upper_bound(inverse(a),b)) != multiply(a,least_upper_bound(inverse(a),b)),
inference(superposition,[],[f47,f13]) ).
fof(f230,plain,
$false,
inference(trivial_inequality_removal,[],[f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 27 09:32:20 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.44 Running first-order model finding
% 0.15/0.44 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
% 0.15/0.48 % (2289956)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2289966)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=531786:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (2289966) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2289956-2289966"...
% 0.15/0.48 % (2289966)...printing done.
% 0.15/0.48 % (2289962)% WARNING: option uhcvi not known.
% 0.15/0.48 % (2289966)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2289966)------------------------------
% 0.15/0.48 % (2289966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2289966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2289966)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2289966)Termination reason: Refutation
% 0.15/0.48 % (2289966)Time elapsed: 0.006 s
% 0.15/0.48 % (2289966)Peak memory usage: 11 MB
% 0.15/0.48 % (2289966)Instructions burned: 9 (million)
% 0.15/0.48 % (2289956)Success in time 0.03 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------