%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG011-5 : TPTP v9.3.1. Released v1.0.0.
% 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 12:35:43 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.55s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
fof(f27,axiom,
! [X0,X1] : multiply(multiply(associator(X0,X0,X1),X0),associator(X0,X0,X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',middle_associator) ).
fof(f28,plain,
! [X0,X1] : additive_identity = multiply(multiply(associator(X0,X0,X1),X0),associator(X0,X0,X1)),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality) ).
fof(f30,plain,
additive_identity != multiply(multiply(associator(a,a,b),a),associator(a,a,b)),
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
! [X0,X1] : additive_identity = multiply(multiply(add(multiply(multiply(X0,X0),X1),additive_inverse(multiply(X0,multiply(X0,X1)))),X0),add(multiply(multiply(X0,X0),X1),additive_inverse(multiply(X0,multiply(X0,X1))))),
inference(definition_unfolding,[],[f28,f25,f25]) ).
fof(f32,plain,
additive_identity != multiply(multiply(add(multiply(multiply(a,a),b),additive_inverse(multiply(a,multiply(a,b)))),a),add(multiply(multiply(a,a),b),additive_inverse(multiply(a,multiply(a,b))))),
inference(definition_unfolding,[],[f30,f25,f25]) ).
fof(f360,plain,
additive_identity != additive_identity,
inference(superposition,[],[f32,f31]) ).
fof(f366,plain,
$false,
inference(trivial_inequality_removal,[],[f360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG011-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 % Computer : n014.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 22:58:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.48 Running first-order model finding
% 0.16/0.49 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
% 0.26/0.55 % (1270128)Will run a generic schedule for satisfiability detection.
% 0.26/0.55 % (1270136)dis+10_1_sil=32000:sp=arity:random_seed=714423636:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.55 % (1270136) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1270128-1270136"...
% 0.26/0.55 % (1270134)% WARNING: option uhcvi not known.
% 0.26/0.55 % (1270136)...printing done.
% 0.26/0.55 % (1270136)Refutation found. Thanks to Tanya!
% 0.26/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.26/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.55 % (1270136)------------------------------
% 0.26/0.55 % (1270136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.55 % (1270136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.55 % (1270136)CaDiCaL version: 2.1.3
% 0.26/0.55 % (1270136)Termination reason: Refutation
% 0.26/0.55 % (1270136)Time elapsed: 0.008 s
% 0.26/0.55 % (1270136)Peak memory usage: 11 MB
% 0.26/0.55 % (1270136)Instructions burned: 13 (million)
% 0.26/0.55 % (1270128)Success in time 0.047 s
% 0.26/0.55 % Vampire exiting
%------------------------------------------------------------------------------