%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG011-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 : Fri Sep 25 02:38:11 PM UTC 2026
% Result : Unsatisfiable 0.50s 1.40s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 11 ( 0 sgn 11 !; 0 ?; 2 :)
% 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]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : 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))))) = additive_identity,
inference(cnf_transformation,[],[f31]) ).
tcf(c_90,negated_conjecture,
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))))) != additive_identity,
inference(cnf_transformation,[],[f32]) ).
tcf(c_144,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_90,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG011-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.43 % Computer : n026.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Thu Sep 24 07:47:54 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.49 Running UEQ theorem proving
% 0.15/0.49 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.51
% 0.20/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.20/0.51
% 0.20/0.51 % Detected problem language: tptp
% 0.20/0.52 % Proving...
% 0.50/1.40 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 0.50/1.40 % SZS status Started for theBenchmark.p
% 0.50/1.40 % SZS status Unsatisfiable for theBenchmark.p
% 0.50/1.40
% 0.50/1.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.50/1.40
% 0.50/1.40 % ------ iProver source info
% 0.50/1.40
% 0.50/1.40 % git: date: 2026-07-19 20:42:38 +0200
% 0.50/1.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.50/1.40 % git: non_committed_changes: false
% 0.50/1.40
% 0.50/1.40 % ------ Parsing...% successful
% 0.50/1.40
% 0.50/1.40
% 0.50/1.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.50/1.40
% 0.50/1.40 % ------ Preprocessing...%
% 0.50/1.40
% 0.50/1.40 % SZS status Unsatisfiable for theBenchmark.p
% 0.50/1.40
% 0.50/1.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.50/1.40
% 0.50/1.40
%------------------------------------------------------------------------------