%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG026-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 02:38:14 PM UTC 2026
% Result : Unsatisfiable 2.68s 1.18s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 14 ( 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).
fof(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/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,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_teichmuller_identity) ).
fof(f31,plain,
additive_identity != add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
additive_identity != add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))),
inference(definition_unfolding,[],[f31,f18,f18,f18,f18,f18]) ).
tcf(c_72,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(cnf_transformation,[],[f6]) ).
tcf(c_76,plain,
! [X0: $i] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_77,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
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(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))) != additive_identity,
inference(cnf_transformation,[],[f32]) ).
tcf(c_110,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_76,c_82,c_81]) ).
tcf(c_111,negated_conjecture,
add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(additive_inverse(multiply(multiply(a,b),multiply(c,d))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d))))))))) != additive_identity,
inference(theory_normalisation,[status(thm)],[c_92,c_82,c_81]) ).
tcf(c_157,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),add(additive_inverse(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(add(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),multiply(a,multiply(b,c))),d)))),additive_identity))) != additive_identity,
inference(ac_demodulation,[status(thm)],[c_111,c_110,c_80,c_82,c_81]) ).
tcf(c_158,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(add(multiply(multiply(a,b),c),additive_identity),d)))))) != additive_identity,
inference(ac_demodulation,[status(thm)],[c_157,c_73,c_110,c_82,c_81]) ).
tcf(c_159,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),multiply(multiply(multiply(a,b),c),d)))))) != additive_identity,
inference(ac_demodulation,[status(thm)],[c_158,c_73,c_82,c_81]) ).
tcf(c_160,plain,
add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(add(multiply(multiply(multiply(a,b),c),d),add(additive_inverse(multiply(a,multiply(multiply(b,c),d))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))))))) != additive_identity,
inference(theory_normalisation,[status(thm)],[c_159,c_82,c_81]) ).
tcf(c_161,plain,
add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(multiply(a,b),c),d),multiply(a,add(multiply(multiply(b,c),additive_inverse(d)),add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d)))))))))) != additive_identity,
inference(demodulation,[status(thm)],[c_160,c_87,c_79]) ).
tcf(c_162,plain,
add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(multiply(a,b),c),d),multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),add(additive_inverse(d),d)))))))) != additive_identity,
inference(ac_demodulation,[status(thm)],[c_161,c_79,c_82,c_81]) ).
tcf(c_163,plain,
add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(multiply(a,b),c),d),multiply(a,add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_identity))))))) != additive_identity,
inference(ac_demodulation,[status(thm)],[c_162,c_110,c_82,c_81]) ).
tcf(c_164,plain,
add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(multiply(a,b),c),d),multiply(a,add(multiply(multiply(b,c),additive_identity),multiply(b,multiply(c,additive_inverse(d))))))))) != additive_identity,
inference(theory_normalisation,[status(thm)],[c_163,c_82,c_81]) ).
tcf(c_165,plain,
add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(multiply(a,b),c),d),multiply(a,multiply(b,multiply(c,additive_inverse(d)))))))) != additive_identity,
inference(demodulation,[status(thm)],[c_164,c_72,c_75]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_82,c_77]) ).
tcf(c_320,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_165,c_319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG026-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 07:49:33 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running UEQ theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 2.68/1.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.68/1.18 % SZS status Started for theBenchmark.p
% 2.68/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.68/1.18
% 2.68/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.68/1.18
% 2.68/1.18 % ------ iProver source info
% 2.68/1.18
% 2.68/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.68/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.68/1.18 % git: non_committed_changes: false
% 2.68/1.18
% 2.68/1.18 % ------ Parsing...% successful
% 2.68/1.18
% 2.68/1.18
% 2.68/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.68/1.18
% 2.68/1.18 % ------ Preprocessing... sup_sim: 7 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.68/1.18
% 2.68/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.68/1.18
% 2.68/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.68/1.18 % ------ Proving...
% 2.68/1.18 % ------ Problem Properties
% 2.68/1.18
% 2.68/1.18 %
% 2.68/1.18 % clauses 17
% 2.68/1.18 % conjectures 0
% 2.68/1.18 % EPR 0
% 2.68/1.18 % Horn 17
% 2.68/1.18 % unary 17
% 2.68/1.18 % binary 0
% 2.68/1.18 % lits 17
% 2.68/1.18 % lits eq 17
% 2.68/1.18 % fd_pure 0
% 2.68/1.18 % fd_pseudo 0
% 2.68/1.18 % fd_cond 0
% 2.68/1.18 % fd_pseudo_cond 0
% 2.68/1.18 % AC symbols 1
% 2.68/1.18
% 2.68/1.18 % ------ Input Options Time Limit: Unbounded
% 2.68/1.18
% 2.68/1.18
% 2.68/1.18 % ------
% 2.68/1.18 % Current options:
% 2.68/1.18 % ------
% 2.68/1.18
% 2.68/1.18
% 2.68/1.18 %
% 2.68/1.18
% 2.68/1.18 % ------ Proving...
% 2.68/1.18 %
% 2.68/1.18
% 2.68/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.68/1.18
% 2.68/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.68/1.18
% 2.68/1.18
%------------------------------------------------------------------------------