%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG026-6 : 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 : n003.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 3.85s 1.26s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 76 ( 0 sgn 76 !; 0 ?; 53 :)
% 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(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
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(f20,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(f21,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,[],[f20]) ).
fof(f22,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,[],[f21,f18,f18,f18,f18,f18]) ).
tcf(c_65,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,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_73,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_74,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,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,[],[f22]) ).
tcf(c_89,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_69,c_75,c_74]) ).
tcf(c_90,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_78,c_75,c_74]) ).
tcf(c_117,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_90,c_89,c_73,c_75,c_74]) ).
tcf(c_118,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_117,c_66,c_89,c_75,c_74]) ).
tcf(c_119,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_118,c_66,c_75,c_74]) ).
tcf(c_120,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_119,c_75,c_74]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_75,c_74]) ).
tcf(c_220,plain,
additive_inverse(additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_70,c_65]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_70,c_215]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_75,c_70]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(demodulation,[status(thm)],[c_230,c_66]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_71,c_273]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(theory_normalisation,[status(thm)],[c_283,c_75,c_74]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = add(X1,additive_identity),
inference(superposition,[status(thm)],[c_249,c_294]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(additive_inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_355,c_66]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,additive_inverse(X1)))) = X1,
inference(superposition,[status(thm)],[c_74,c_526]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_71,c_526]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(superposition,[status(thm)],[c_71,c_531]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i] : additive_inverse(add(X0,additive_inverse(X1))) = add(X1,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_539,c_294]) ).
tcf(c_698,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),additive_inverse(multiply(X0,add(X1,X2)))) = additive_inverse(multiply(X0,X2)),
inference(superposition,[status(thm)],[c_72,c_592]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,additive_inverse(add(X0,X2)))) = add(X1,additive_inverse(X2)),
inference(superposition,[status(thm)],[c_592,c_215]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i] : additive_inverse(add(additive_inverse(X0),X1)) = add(X0,additive_inverse(X1)),
inference(superposition,[status(thm)],[c_592,c_294]) ).
tcf(c_726,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(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(demodulation,[status(thm)],[c_120,c_713]) ).
tcf(c_753,plain,
add(additive_inverse(multiply(a,multiply(b,multiply(c,d)))),additive_inverse(multiply(a,additive_inverse(multiply(b,multiply(c,d)))))) != additive_identity,
inference(demodulation,[status(thm)],[c_726,c_698,c_717]) ).
tcf(c_762,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X1,X0)),
inference(superposition,[status(thm)],[c_71,c_641]) ).
tcf(c_784,plain,
additive_inverse(add(multiply(a,additive_inverse(multiply(b,multiply(c,d)))),multiply(a,multiply(b,multiply(c,d))))) != additive_identity,
inference(demodulation,[status(thm)],[c_753,c_762]) ).
tcf(c_785,plain,
additive_inverse(add(multiply(a,multiply(b,multiply(c,d))),multiply(a,additive_inverse(multiply(b,multiply(c,d)))))) != additive_identity,
inference(theory_normalisation,[status(thm)],[c_784,c_75,c_74]) ).
tcf(c_786,plain,
$false,
inference(ground_joinability,[status(thm)],[c_785,c_68,c_70,c_72,c_220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG026-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 % Computer : n003.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Thu Sep 24 07:50:52 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.46 Running UEQ theorem proving
% 0.18/0.46 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
% 0.18/0.48
% 0.18/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.48
% 0.18/0.48 % Detected problem language: tptp
% 0.18/0.49 % Proving...
% 3.85/1.26 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.85/1.26 % SZS status Started for theBenchmark.p
% 3.85/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 3.85/1.26
% 3.85/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.85/1.26
% 3.85/1.26 % ------ iProver source info
% 3.85/1.26
% 3.85/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.85/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.85/1.26 % git: non_committed_changes: false
% 3.85/1.26
% 3.85/1.26 % ------ Parsing...% successful
% 3.85/1.26
% 3.85/1.26
% 3.85/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.85/1.26
% 3.85/1.26 % ------ Preprocessing... sup_sim: 1 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 %
% 3.85/1.26
% 3.85/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.85/1.26
% 3.85/1.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.85/1.26 % ------ Proving...
% 3.85/1.26 % ------ Problem Properties
% 3.85/1.26
% 3.85/1.26 %
% 3.85/1.26 % clauses 13
% 3.85/1.26 % conjectures 0
% 3.85/1.26 % EPR 0
% 3.85/1.26 % Horn 13
% 3.85/1.26 % unary 13
% 3.85/1.26 % binary 0
% 3.85/1.26 % lits 13
% 3.85/1.26 % lits eq 13
% 3.85/1.26 % fd_pure 0
% 3.85/1.26 % fd_pseudo 0
% 3.85/1.26 % fd_cond 0
% 3.85/1.26 % fd_pseudo_cond 0
% 3.85/1.26 % AC symbols 1
% 3.85/1.26
% 3.85/1.26 % ------ Input Options Time Limit: Unbounded
% 3.85/1.26
% 3.85/1.26
% 3.85/1.26 % ------
% 3.85/1.26 % Current options:
% 3.85/1.26 % ------
% 3.85/1.26
% 3.85/1.26
% 3.85/1.26 %
% 3.85/1.26
% 3.85/1.26 % ------ Proving...
% 3.85/1.26 %
% 3.85/1.26
% 3.85/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 3.85/1.26
% 3.85/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.26
% 3.85/1.26
%------------------------------------------------------------------------------