%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG008-3 : 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 : n006.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 1.00s 1.20s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 89 ( 89 unt; 0 def)
% Number of atoms : 89 ( 88 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 : 88 ( 0 sgn 88 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_identity) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/RNG002-0.ax',distribute2) ).
fof(f8,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
fof(f9,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
fof(f18,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/RNG002-0.ax',associative_multiplication) ).
fof(f21,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f22,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
fof(f24,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f25,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f26,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f25]) ).
tcf(c_68,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,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_71,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_73,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(cnf_transformation,[],[f12]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : add(additive_inverse(X0),additive_inverse(X1)) = additive_inverse(add(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_83,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f22]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_85,negated_conjecture,
multiply(a,b) = c,
inference(cnf_transformation,[],[f24]) ).
tcf(c_86,negated_conjecture,
multiply(b,a) != c,
inference(cnf_transformation,[],[f26]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(demodulation,[status(thm)],[c_78,c_77]) ).
tcf(c_259,plain,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference(superposition,[status(thm)],[c_85,c_77]) ).
tcf(c_270,plain,
! [X0: $i] : multiply(X0,additive_inverse(X0)) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_84,c_77]) ).
tcf(c_283,plain,
! [X0: $i] : multiply(additive_inverse(X0),X0) = X0,
inference(superposition,[status(thm)],[c_73,c_270]) ).
tcf(c_293,plain,
! [X0: $i] : add(c,multiply(a,X0)) = multiply(a,add(b,X0)),
inference(superposition,[status(thm)],[c_85,c_70]) ).
tcf(c_296,plain,
! [X0: $i] : add(additive_inverse(c),multiply(a,X0)) = multiply(a,add(additive_inverse(b),X0)),
inference(superposition,[status(thm)],[c_259,c_70]) ).
tcf(c_326,plain,
multiply(a,add(additive_inverse(b),additive_inverse(a))) = add(additive_inverse(c),additive_inverse(a)),
inference(superposition,[status(thm)],[c_270,c_296]) ).
tcf(c_330,plain,
multiply(a,add(additive_inverse(a),additive_inverse(b))) = add(additive_inverse(a),additive_inverse(c)),
inference(theory_normalisation,[status(thm)],[c_326,c_79,c_80]) ).
tcf(c_364,plain,
multiply(a,additive_inverse(add(a,b))) = additive_inverse(add(a,c)),
inference(demodulation,[status(thm)],[c_330,c_76]) ).
tcf(c_366,plain,
multiply(a,additive_inverse(additive_inverse(add(a,b)))) = additive_inverse(additive_inverse(add(a,c))),
inference(superposition,[status(thm)],[c_364,c_77]) ).
tcf(c_395,plain,
multiply(a,add(a,b)) = add(a,c),
inference(demodulation,[status(thm)],[c_366,c_73]) ).
tcf(c_409,plain,
! [X0: $i] : additive_inverse(X0) = X0,
inference(demodulation,[status(thm)],[c_283,c_137,c_270]) ).
tcf(c_413,plain,
! [X0: $i] : add(X0,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_83,c_409]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(superposition,[status(thm)],[c_84,c_71]) ).
tcf(c_435,plain,
! [X0: $i] : add(c,multiply(X0,b)) = multiply(add(a,X0),b),
inference(superposition,[status(thm)],[c_85,c_71]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_413,c_79]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_84,c_81]) ).
tcf(c_500,plain,
! [X0: $i] : multiply(a,multiply(add(a,b),X0)) = multiply(add(a,c),X0),
inference(superposition,[status(thm)],[c_395,c_81]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,X1))) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_81,c_84]) ).
tcf(c_529,plain,
multiply(add(a,b),b) = add(c,b),
inference(superposition,[status(thm)],[c_84,c_435]) ).
tcf(c_537,plain,
multiply(add(a,b),b) = add(b,c),
inference(theory_normalisation,[status(thm)],[c_529,c_79,c_80]) ).
tcf(c_540,plain,
! [X0: $i] : multiply(add(a,b),multiply(b,X0)) = multiply(add(b,c),X0),
inference(superposition,[status(thm)],[c_537,c_81]) ).
tcf(c_577,plain,
multiply(add(a,c),b) = multiply(a,add(b,c)),
inference(superposition,[status(thm)],[c_537,c_500]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i] : add(X0,add(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_486,c_68]) ).
tcf(c_731,plain,
! [X0: $i] : multiply(add(a,c),multiply(b,X0)) = multiply(a,multiply(add(b,c),X0)),
inference(superposition,[status(thm)],[c_540,c_500]) ).
tcf(c_765,plain,
multiply(a,c) = c,
inference(superposition,[status(thm)],[c_85,c_496]) ).
tcf(c_809,plain,
multiply(a,add(b,c)) = add(c,c),
inference(superposition,[status(thm)],[c_765,c_293]) ).
tcf(c_814,plain,
multiply(add(a,c),b) = add(c,c),
inference(demodulation,[status(thm)],[c_577,c_809]) ).
tcf(c_858,plain,
multiply(a,add(b,c)) = additive_identity,
inference(demodulation,[status(thm)],[c_809,c_413]) ).
tcf(c_860,plain,
! [X0: $i] : multiply(a,multiply(add(b,c),X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_858,c_81]) ).
tcf(c_869,plain,
! [X0: $i] : multiply(a,multiply(add(b,c),X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_860,c_75]) ).
tcf(c_1154,plain,
multiply(add(a,c),b) = additive_identity,
inference(demodulation,[status(thm)],[c_814,c_413]) ).
tcf(c_1157,plain,
! [X0: $i] : multiply(add(a,c),multiply(b,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_1154,c_81]) ).
tcf(c_1166,plain,
! [X0: $i] : multiply(add(a,c),multiply(b,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1157,c_75,c_731]) ).
tcf(c_2538,plain,
multiply(b,add(a,c)) = multiply(b,additive_identity),
inference(superposition,[status(thm)],[c_1166,c_501]) ).
tcf(c_2539,plain,
multiply(add(b,c),additive_identity) = multiply(add(b,c),a),
inference(superposition,[status(thm)],[c_869,c_501]) ).
tcf(c_2721,plain,
multiply(b,add(a,c)) = additive_identity,
inference(demodulation,[status(thm)],[c_2538,c_74]) ).
tcf(c_2729,plain,
! [X0: $i] : multiply(b,add(X0,add(a,c))) = add(multiply(b,X0),additive_identity),
inference(superposition,[status(thm)],[c_2721,c_70]) ).
tcf(c_2744,plain,
! [X0: $i] : multiply(b,add(X0,add(a,c))) = add(additive_identity,multiply(b,X0)),
inference(theory_normalisation,[status(thm)],[c_2729,c_79,c_80]) ).
tcf(c_2808,plain,
multiply(add(b,c),a) = additive_identity,
inference(demodulation,[status(thm)],[c_2539,c_74]) ).
tcf(c_2813,plain,
! [X0: $i] : multiply(add(b,c),multiply(a,X0)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_2808,c_81]) ).
tcf(c_2826,plain,
! [X0: $i] : multiply(add(b,c),multiply(a,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_2813,c_75]) ).
tcf(c_2847,plain,
multiply(add(b,c),c) = additive_identity,
inference(superposition,[status(thm)],[c_765,c_2826]) ).
tcf(c_3143,plain,
! [X0: $i] : multiply(b,add(X0,add(a,c))) = multiply(b,X0),
inference(demodulation,[status(thm)],[c_2744,c_68]) ).
tcf(c_3151,plain,
multiply(b,a) = multiply(b,c),
inference(superposition,[status(thm)],[c_621,c_3143]) ).
tcf(c_3277,plain,
add(c,multiply(b,a)) = multiply(add(c,b),c),
inference(superposition,[status(thm)],[c_3151,c_434]) ).
tcf(c_3285,plain,
add(c,multiply(b,a)) = multiply(add(b,c),c),
inference(theory_normalisation,[status(thm)],[c_3277,c_79,c_80]) ).
tcf(c_3286,plain,
add(c,multiply(b,a)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_3285,c_2847]) ).
tcf(c_3345,plain,
add(c,additive_identity) = multiply(b,a),
inference(superposition,[status(thm)],[c_3286,c_621]) ).
tcf(c_3352,plain,
add(additive_identity,c) = multiply(b,a),
inference(theory_normalisation,[status(thm)],[c_3345,c_79,c_80]) ).
tcf(c_3362,plain,
multiply(b,a) = c,
inference(demodulation,[status(thm)],[c_3352,c_68]) ).
tcf(c_3363,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3362,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 07:43:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running UEQ theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.00/1.20 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.00/1.20 % SZS status Started for theBenchmark.p
% 1.00/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.00/1.20
% 1.00/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.00/1.20
% 1.00/1.20 % ------ iProver source info
% 1.00/1.20
% 1.00/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.00/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.00/1.20 % git: non_committed_changes: false
% 1.00/1.20
% 1.00/1.20 % ------ Parsing...% successful
% 1.00/1.20
% 1.00/1.20
% 1.00/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.00/1.20
% 1.00/1.20 % ------ 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 %
% 1.00/1.20
% 1.00/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.00/1.20
% 1.00/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.00/1.20 % ------ Proving...
% 1.00/1.20 % ------ Problem Properties
% 1.00/1.20
% 1.00/1.20 %
% 1.00/1.20 % clauses 18
% 1.00/1.20 % conjectures 2
% 1.00/1.20 % EPR 0
% 1.00/1.20 % Horn 18
% 1.00/1.20 % unary 18
% 1.00/1.20 % binary 0
% 1.00/1.20 % lits 18
% 1.00/1.20 % lits eq 18
% 1.00/1.20 % fd_pure 0
% 1.00/1.20 % fd_pseudo 0
% 1.00/1.20 % fd_cond 0
% 1.00/1.20 % fd_pseudo_cond 0
% 1.00/1.20 % AC symbols 1
% 1.00/1.20
% 1.00/1.20 % ------ Input Options Time Limit: Unbounded
% 1.00/1.20
% 1.00/1.20
% 1.00/1.20 % ------
% 1.00/1.20 % Current options:
% 1.00/1.20 % ------
% 1.00/1.20
% 1.00/1.20
% 1.00/1.20 %
% 1.00/1.20
% 1.00/1.20 % ------ Proving...
% 1.00/1.20 %
% 1.00/1.20
% 1.00/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.00/1.20
% 1.00/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.00/1.20
% 1.00/1.20
%------------------------------------------------------------------------------