%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG008-4 : 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 02:38:09 PM UTC 2026
% Result : Unsatisfiable 3.24s 1.23s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 90 ( 90 unt; 0 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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; 4 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 89 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
fof(f3,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute2) ).
fof(f8,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
fof(f9,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id2) ).
fof(f12,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute_additive_inverse) ).
fof(f14,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
fof(f15,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
fof(f16,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
fof(f18,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
fof(f19,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_multiplication) ).
fof(f20,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
fof(f21,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f22,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f23,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f22]) ).
tcf(c_66,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_72,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_80,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(cnf_transformation,[],[f20]) ).
tcf(c_81,negated_conjecture,
multiply(a,b) = c,
inference(cnf_transformation,[],[f21]) ).
tcf(c_82,negated_conjecture,
multiply(b,a) != c,
inference(cnf_transformation,[],[f23]) ).
tcf(c_95,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_67,c_77,c_78]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(demodulation,[status(thm)],[c_76,c_75]) ).
tcf(c_210,plain,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference(superposition,[status(thm)],[c_81,c_75]) ).
tcf(c_222,plain,
! [X0: $i] : multiply(X0,additive_inverse(X0)) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_80,c_75]) ).
tcf(c_234,plain,
! [X0: $i] : multiply(additive_inverse(X0),X0) = X0,
inference(superposition,[status(thm)],[c_71,c_222]) ).
tcf(c_244,plain,
! [X0: $i] : multiply(a,add(b,X0)) = add(c,multiply(a,X0)),
inference(superposition,[status(thm)],[c_81,c_68]) ).
tcf(c_247,plain,
! [X0: $i] : multiply(a,add(additive_inverse(b),X0)) = add(additive_inverse(c),multiply(a,X0)),
inference(superposition,[status(thm)],[c_210,c_68]) ).
tcf(c_276,plain,
multiply(a,add(additive_inverse(b),additive_inverse(a))) = add(additive_inverse(c),additive_inverse(a)),
inference(superposition,[status(thm)],[c_222,c_247]) ).
tcf(c_280,plain,
multiply(a,add(additive_inverse(a),additive_inverse(b))) = add(additive_inverse(a),additive_inverse(c)),
inference(theory_normalisation,[status(thm)],[c_276,c_77,c_78]) ).
tcf(c_314,plain,
multiply(a,additive_inverse(add(a,b))) = additive_inverse(add(a,c)),
inference(demodulation,[status(thm)],[c_280,c_74]) ).
tcf(c_316,plain,
multiply(a,additive_inverse(additive_inverse(add(a,b)))) = additive_inverse(additive_inverse(add(a,c))),
inference(superposition,[status(thm)],[c_314,c_75]) ).
tcf(c_345,plain,
multiply(a,add(a,b)) = add(a,c),
inference(demodulation,[status(thm)],[c_316,c_71]) ).
tcf(c_359,plain,
! [X0: $i] : additive_inverse(X0) = X0,
inference(demodulation,[status(thm)],[c_234,c_131,c_222]) ).
tcf(c_362,plain,
! [X0: $i] : add(X0,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_95,c_359]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_80,c_69]) ).
tcf(c_385,plain,
! [X0: $i] : multiply(add(a,X0),b) = add(c,multiply(X0,b)),
inference(superposition,[status(thm)],[c_81,c_69]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_362,c_77]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_80,c_79]) ).
tcf(c_449,plain,
! [X0: $i] : multiply(a,multiply(add(a,b),X0)) = multiply(add(a,c),X0),
inference(superposition,[status(thm)],[c_345,c_79]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,X1))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_478,plain,
multiply(add(a,b),b) = add(c,b),
inference(superposition,[status(thm)],[c_80,c_385]) ).
tcf(c_486,plain,
multiply(add(a,b),b) = add(b,c),
inference(theory_normalisation,[status(thm)],[c_478,c_77,c_78]) ).
tcf(c_489,plain,
! [X0: $i] : multiply(add(a,b),multiply(b,X0)) = multiply(add(b,c),X0),
inference(superposition,[status(thm)],[c_486,c_79]) ).
tcf(c_526,plain,
multiply(add(a,c),b) = multiply(a,add(b,c)),
inference(superposition,[status(thm)],[c_486,c_449]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_435,c_66]) ).
tcf(c_680,plain,
! [X0: $i] : multiply(add(a,c),multiply(b,X0)) = multiply(a,multiply(add(b,c),X0)),
inference(superposition,[status(thm)],[c_489,c_449]) ).
tcf(c_714,plain,
multiply(a,c) = c,
inference(superposition,[status(thm)],[c_81,c_445]) ).
tcf(c_758,plain,
multiply(a,add(b,c)) = add(c,c),
inference(superposition,[status(thm)],[c_714,c_244]) ).
tcf(c_763,plain,
multiply(add(a,c),b) = add(c,c),
inference(demodulation,[status(thm)],[c_526,c_758]) ).
tcf(c_807,plain,
multiply(a,add(b,c)) = additive_identity,
inference(demodulation,[status(thm)],[c_758,c_362]) ).
tcf(c_809,plain,
! [X0: $i] : multiply(a,multiply(add(b,c),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_807,c_79]) ).
tcf(c_818,plain,
! [X0: $i] : multiply(a,multiply(add(b,c),X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_809,c_73]) ).
tcf(c_1103,plain,
multiply(add(a,c),b) = additive_identity,
inference(demodulation,[status(thm)],[c_763,c_362]) ).
tcf(c_1106,plain,
! [X0: $i] : multiply(add(a,c),multiply(b,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_1103,c_79]) ).
tcf(c_1115,plain,
! [X0: $i] : multiply(add(a,c),multiply(b,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1106,c_73,c_680]) ).
tcf(c_2487,plain,
multiply(b,add(a,c)) = multiply(b,additive_identity),
inference(superposition,[status(thm)],[c_1115,c_450]) ).
tcf(c_2488,plain,
multiply(add(b,c),a) = multiply(add(b,c),additive_identity),
inference(superposition,[status(thm)],[c_818,c_450]) ).
tcf(c_2670,plain,
multiply(b,add(a,c)) = additive_identity,
inference(demodulation,[status(thm)],[c_2487,c_72]) ).
tcf(c_2679,plain,
! [X0: $i] : multiply(b,add(X0,add(a,c))) = add(multiply(b,X0),additive_identity),
inference(superposition,[status(thm)],[c_2670,c_68]) ).
tcf(c_2693,plain,
! [X0: $i] : multiply(b,add(X0,add(a,c))) = add(additive_identity,multiply(b,X0)),
inference(theory_normalisation,[status(thm)],[c_2679,c_77,c_78]) ).
tcf(c_2757,plain,
multiply(add(b,c),a) = additive_identity,
inference(demodulation,[status(thm)],[c_2488,c_72]) ).
tcf(c_2763,plain,
! [X0: $i] : multiply(add(b,c),multiply(a,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_2757,c_79]) ).
tcf(c_2774,plain,
! [X0: $i] : multiply(add(b,c),multiply(a,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_2763,c_73]) ).
tcf(c_2796,plain,
multiply(add(b,c),c) = additive_identity,
inference(superposition,[status(thm)],[c_714,c_2774]) ).
tcf(c_3092,plain,
! [X0: $i] : multiply(b,add(X0,add(a,c))) = multiply(b,X0),
inference(demodulation,[status(thm)],[c_2693,c_66]) ).
tcf(c_3100,plain,
multiply(b,a) = multiply(b,c),
inference(superposition,[status(thm)],[c_571,c_3092]) ).
tcf(c_3226,plain,
multiply(add(c,b),c) = add(c,multiply(b,a)),
inference(superposition,[status(thm)],[c_3100,c_384]) ).
tcf(c_3234,plain,
multiply(add(b,c),c) = add(c,multiply(b,a)),
inference(theory_normalisation,[status(thm)],[c_3226,c_77,c_78]) ).
tcf(c_3235,plain,
add(c,multiply(b,a)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_3234,c_2796]) ).
tcf(c_3294,plain,
multiply(b,a) = add(c,additive_identity),
inference(superposition,[status(thm)],[c_3235,c_571]) ).
tcf(c_3301,plain,
multiply(b,a) = add(additive_identity,c),
inference(theory_normalisation,[status(thm)],[c_3294,c_77,c_78]) ).
tcf(c_3311,plain,
multiply(b,a) = c,
inference(demodulation,[status(thm)],[c_3301,c_66]) ).
tcf(c_3312,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3311,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 07:43:44 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running UEQ theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.46 % Proving...
% 3.24/1.23 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.24/1.23 % SZS status Started for theBenchmark.p
% 3.24/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 3.24/1.23
% 3.24/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.24/1.23
% 3.24/1.23 % ------ iProver source info
% 3.24/1.23
% 3.24/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.24/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.24/1.23 % git: non_committed_changes: false
% 3.24/1.23
% 3.24/1.23 % ------ Parsing...% successful
% 3.24/1.23
% 3.24/1.23
% 3.24/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.24/1.23
% 3.24/1.23 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.24/1.23
% 3.24/1.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.24/1.23
% 3.24/1.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.24/1.23 % ------ Proving...
% 3.24/1.23 % ------ Problem Properties
% 3.24/1.23
% 3.24/1.23 %
% 3.24/1.23 % clauses 17
% 3.24/1.23 % conjectures 2
% 3.24/1.23 % EPR 0
% 3.24/1.23 % Horn 17
% 3.24/1.23 % unary 17
% 3.24/1.23 % binary 0
% 3.24/1.23 % lits 17
% 3.24/1.23 % lits eq 17
% 3.24/1.23 % fd_pure 0
% 3.24/1.23 % fd_pseudo 0
% 3.24/1.23 % fd_cond 0
% 3.24/1.23 % fd_pseudo_cond 0
% 3.24/1.23 % AC symbols 1
% 3.24/1.23
% 3.24/1.23 % ------ Input Options Time Limit: Unbounded
% 3.24/1.23
% 3.24/1.23
% 3.24/1.23 % ------
% 3.24/1.23 % Current options:
% 3.24/1.23 % ------
% 3.24/1.23
% 3.24/1.23
% 3.24/1.23 %
% 3.24/1.23
% 3.24/1.23 % ------ Proving...
% 3.24/1.23 %
% 3.24/1.23
% 3.24/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 3.24/1.23
% 3.24/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.24/1.24
% 3.24/1.24
%------------------------------------------------------------------------------