%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD040-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 01:15:44 PM UTC 2026
% Result : Unsatisfiable 24.38s 4.47s
% Output : CNFRefutation 24.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 69 ( 12 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 238 ( 117 ~; 121 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 120 ( 0 sgn 120 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sum(X5,X6,X2)
| ~ product(X4,X1,X6)
| ~ product(X3,X1,X5)
| ~ sum(X3,X4,X0)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
fof(f29,negated_conjecture,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_3) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_80,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_81,plain,
! [X0: $i] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_85,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_86,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X4,X5,X6)
| ~ product(X2,X3,X6)
| ~ product(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X2,X6,X5)
| ~ product(X1,X6,X4)
| ~ product(X0,X6,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_91,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_95,plain,
! [X0: $i] :
( defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_104,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,negated_conjecture,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,plain,
( product(multiplicative_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_109,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_117,plain,
( defined(multiplicative_inverse(a))
| sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_118,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_119,plain,
( sum(additive_identity,a,additive_identity)
| ~ sum(a,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(X2,X4,X1)
| ~ product(multiplicative_identity,X1,X1)
| ~ sum(X0,X3,multiplicative_identity)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_130,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_131,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_130]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X1,X2)
| ~ product(multiplicative_identity,X1,X1)
| ~ product(X0,multiplicative_identity,X3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X2,X3,multiplicative_identity)
| ~ product(X1,a,X3)
| ~ product(X0,a,X2)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(X0,X1,multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(a,additive_identity,additive_identity)
| ~ sum(a,X0,X2)
| ~ sum(X2,X1,additive_identity)
| ~ sum(X0,X1,additive_identity) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_238,plain,
( sum(additive_inverse(a),a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X2,multiplicative_identity,X4)
| ~ product(X1,multiplicative_identity,X1)
| ~ product(X0,multiplicative_identity,X3)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_340,plain,
! [X0: $i] :
( product(X0,a,multiplicative_identity)
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ product(multiplicative_inverse(a),multiplicative_identity,X0) ),
inference(instantiation,[status(thm)],[c_138]) ).
tcf(c_341,plain,
( product(additive_identity,a,multiplicative_identity)
| ~ product(multiplicative_identity,a,a)
| ~ product(multiplicative_inverse(a),multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,X1)
| ~ sum(X0,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X1,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_756,plain,
! [X0: $i] :
( sum(X0,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_812,plain,
( product(multiplicative_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i] :
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X0,a,X1)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(X0,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_1640,plain,
! [X0: $i] :
( sum(X0,X0,X0)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_349]) ).
tcf(c_1995,plain,
sum(multiplicative_inverse(a),additive_identity,additive_identity),
inference(superposition,[status(thm)],[c_106,c_82]) ).
tcf(c_2064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(additive_identity,X2,X3)
| ~ defined(X0)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_80,c_78]) ).
tcf(c_2069,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(multiplicative_inverse(a),X1,X2)
| ~ sum(additive_identity,X0,X2)
| ~ sum(additive_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_1995,c_78]) ).
tcf(c_2089,plain,
! [X0: $i] :
( sum(multiplicative_inverse(a),additive_identity,X0)
| ~ sum(additive_identity,multiplicative_inverse(a),X0) ),
inference(superposition,[status(thm)],[c_106,c_2069]) ).
tcf(c_2104,plain,
! [X0: $i] :
( sum(additive_identity,additive_identity,X0)
| ~ defined(additive_identity)
| ~ sum(additive_identity,multiplicative_inverse(a),X0) ),
inference(superposition,[status(thm)],[c_106,c_2064]) ).
tcf(c_2115,plain,
( sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(superposition,[status(thm)],[c_80,c_2089]) ).
tcf(c_2119,plain,
! [X0: $i] :
( sum(additive_identity,additive_identity,X0)
| ~ sum(additive_identity,multiplicative_inverse(a),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2104,c_91,c_2104]) ).
tcf(c_2122,plain,
( sum(additive_identity,additive_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a)) ),
inference(superposition,[status(thm)],[c_80,c_2119]) ).
tcf(c_2160,plain,
sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a)),
inference(global_subsumption_just,[status(thm)],[c_2115,c_104,c_105,c_117,c_2115]) ).
tcf(c_2165,plain,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(superposition,[status(thm)],[c_2160,c_82]) ).
tcf(c_3626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(multiplicative_inverse(a),multiplicative_identity,X3)
| ~ product(X1,multiplicative_identity,X1)
| ~ product(X0,multiplicative_identity,X2)
| ~ sum(X2,X1,X3)
| ~ sum(X0,X1,multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_260]) ).
tcf(c_3627,plain,
( product(multiplicative_inverse(a),multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_3626]) ).
tcf(c_4092,plain,
( sum(a,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity) ),
inference(instantiation,[status(thm)],[c_756]) ).
tcf(c_13007,plain,
! [X0: $i] :
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(X0,a,multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(X0,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_1287]) ).
tcf(c_13008,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(additive_identity,a,multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_13007]) ).
tcf(c_15453,plain,
! [X0: $i] :
( sum(a,additive_identity,additive_identity)
| ~ sum(a,a,a)
| ~ sum(a,X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_16564,plain,
( sum(a,a,a)
| ~ product(multiplicative_identity,a,a)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_1640]) ).
tcf(c_25215,plain,
( sum(a,additive_identity,additive_identity)
| ~ sum(a,a,a)
| ~ sum(a,additive_inverse(a),additive_identity) ),
inference(instantiation,[status(thm)],[c_15453]) ).
tcf(c_25216,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_25215,c_16564,c_13008,c_4092,c_3627,c_2165,c_2122,c_812,c_341,c_238,c_131,c_119,c_118,c_117,c_109,c_108,c_105,c_91,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD040-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.44 % Computer : n004.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 10:47:52 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.53
% 0.25/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.53
% 0.25/0.53 % Detected problem language: tptp
% 0.25/0.55 % Proving...
% 24.38/4.47 % SZS status Started for theBenchmark.p
% 24.38/4.47 % SZS status Unsatisfiable for theBenchmark.p
% 24.38/4.47
% 24.38/4.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 24.38/4.47
% 24.38/4.47 % ------ iProver source info
% 24.38/4.47
% 24.38/4.47 % git: date: 2026-07-19 20:42:38 +0200
% 24.38/4.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 24.38/4.47 % git: non_committed_changes: false
% 24.38/4.47
% 24.38/4.47 % ------ Parsing...% successful
% 24.38/4.47
% 24.38/4.47
% 24.38/4.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 24.38/4.47
% 24.38/4.47 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 24.38/4.47
% 24.38/4.47 % ------ Preprocessing...
% 24.38/4.47 % ------ Proving...
% 24.38/4.47 % ------ Problem Properties
% 24.38/4.47
% 24.38/4.47 %
% 24.38/4.47 % clauses 29
% 24.38/4.47 % conjectures 3
% 24.38/4.47 % EPR 20
% 24.38/4.47 % Horn 26
% 24.38/4.47 % unary 6
% 24.38/4.47 % binary 6
% 24.38/4.47 % lits 80
% 24.38/4.47 % lits eq 0
% 24.38/4.47 % fd_pure 0
% 24.38/4.47 % fd_pseudo 0
% 24.38/4.47 % fd_cond 0
% 24.38/4.47 % fd_pseudo_cond 0
% 24.38/4.47 % AC symbols 0
% 24.38/4.47
% 24.38/4.47 % ------ Input Options Time Limit: Unbounded
% 24.38/4.47
% 24.38/4.47
% 24.38/4.47 % ------
% 24.38/4.47 % Current options:
% 24.38/4.47 % ------
% 24.38/4.47
% 24.38/4.47
% 24.38/4.47 %
% 24.38/4.47
% 24.38/4.47 % ------ Proving...
% 24.38/4.47 %
% 24.38/4.47
% 24.38/4.47 % SZS status Unsatisfiable for theBenchmark.p
% 24.38/4.47
% 24.38/4.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.38/4.47
% 24.38/4.47
%------------------------------------------------------------------------------