%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG020-7 : 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 : n015.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 02:38:12 PM UTC 2026
% Result : Unsatisfiable 2.38s 11.21s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
fof(f18,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/Axioms/RNG003-0.ax',associator) ).
fof(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
fof(f25,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_linearised_form2) ).
fof(f31,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))),
inference(definition_unfolding,[],[f30,f18,f18,f18]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_92,negated_conjecture,
add(add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(cnf_transformation,[],[f31]) ).
tcf(c_111,negated_conjecture,
add(multiply(multiply(x,u),y),add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(u,y))),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(theory_normalisation,[status(thm)],[c_92,c_82,c_81]) ).
tcf(c_157,plain,
add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),multiply(add(multiply(x,u),multiply(x,v)),y))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(ac_demodulation,[status(thm)],[c_111,c_80,c_82,c_81]) ).
tcf(c_158,plain,
add(additive_inverse(multiply(x,multiply(u,y))),add(additive_inverse(multiply(x,multiply(v,y))),multiply(multiply(x,add(u,v)),y))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(ac_demodulation,[status(thm)],[c_157,c_79,c_82,c_81]) ).
tcf(c_159,plain,
add(multiply(x,multiply(u,additive_inverse(y))),add(multiply(x,multiply(v,additive_inverse(y))),multiply(multiply(x,add(u,v)),y))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,multiply(add(u,v),additive_inverse(y)))),
inference(demodulation,[status(thm)],[c_158,c_87]) ).
tcf(c_160,plain,
add(multiply(multiply(x,add(u,v)),y),multiply(x,add(multiply(u,additive_inverse(y)),multiply(v,additive_inverse(y))))) != add(multiply(multiply(x,add(u,v)),y),multiply(x,multiply(add(u,v),additive_inverse(y)))),
inference(ac_demodulation,[status(thm)],[c_159,c_79,c_82,c_81]) ).
tcf(c_161,plain,
$false,
inference(ac_demodulation,[status(thm)],[c_160,c_80,c_82,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG020-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.40 % Computer : n015.cluster.edu
% 0.13/10.40 % Model : x86_64 x86_64
% 0.13/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.40 % Memory : 8046.5625MB
% 0.13/10.40 % OS : Linux 6.8.0-71-generic
% 0.13/10.40 % CPULimit : 300
% 0.13/10.40 % WCLimit : 300
% 0.13/10.40 % DateTime : Thu Sep 24 07:50:22 UTC 2026
% 0.13/10.40 % CPUTime :
% 0.13/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.44 Running UEQ theorem proving
% 0.13/10.44 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
% 0.13/10.45
% 0.13/10.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.45
% 0.13/10.45 % Detected problem language: tptp
% 0.13/10.46 % Proving...
% 2.38/11.21 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.38/11.21 % SZS status Started for theBenchmark.p
% 2.38/11.21 % SZS status Unsatisfiable for theBenchmark.p
% 2.38/11.21
% 2.38/11.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.38/11.21
% 2.38/11.21 % ------ iProver source info
% 2.38/11.21
% 2.38/11.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.38/11.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.38/11.21 % git: non_committed_changes: false
% 2.38/11.21
% 2.38/11.21 % ------ Parsing...% successful
% 2.38/11.21
% 2.38/11.21
% 2.38/11.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.38/11.21
% 2.38/11.21 % ------ Preprocessing...%
% 2.38/11.21
% 2.38/11.21 % SZS status Unsatisfiable for theBenchmark.p
% 2.38/11.21
% 2.38/11.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.38/11.21
% 2.38/11.21
%------------------------------------------------------------------------------