%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD043-5 : 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 : n012.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 01:15:45 PM UTC 2026
% Result : Unsatisfiable 103.95s 23.75s
% Output : CNFRefutation 103.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 103 ( 13 unt; 0 def)
% Number of atoms : 308 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 409 ( 204 ~; 205 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 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; 0-2 aty)
% Number of variables : 192 ( 0 sgn 192 !; 0 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
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(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(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
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(f16,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
fof(f20,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
~ product(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_2) ).
tcf(c_79,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_83,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_84,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_85,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X5,X1,X6)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( defined(multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_93,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_102,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[],[f26]) ).
tcf(c_103,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_104,negated_conjecture,
~ product(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,plain,
( product(multiplicative_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_109,plain,
( defined(multiply(additive_identity,additive_identity))
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_113,plain,
( product(additive_identity,additive_identity,multiply(additive_identity,additive_identity))
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_117,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_118,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,multiply(X0,X1))
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X1)
| ~ product(multiplicative_identity,X1,X1)
| ~ product(X3,X0,multiplicative_identity)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_123,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_83]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ product(X2,X3,multiplicative_identity)
| ~ product(X1,X3,additive_identity)
| ~ product(X0,X3,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X4,X1,X3)
| ~ sum(X0,multiplicative_identity,X4)
| ~ product(multiplicative_identity,X1,X1)
| ~ sum(X2,X1,X3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,multiply(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c_96,c_86]) ).
tcf(c_193,plain,
( sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X5,X1,X3)
| ~ sum(X4,X0,X5)
| ~ product(X4,X1,X2)
| ~ sum(X2,multiply(X1,X0),X3)
| ~ product(X0,X1,multiply(X1,X0)) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(X1,multiplicative_identity,additive_identity)
| ~ product(X0,multiplicative_identity,additive_identity)
| ~ sum(X0,X1,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_266,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,X0)
| ~ product(multiplicative_identity,multiplicative_identity,X1)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X1,X2)
| ~ sum(X0,multiplicative_identity,X3)
| ~ product(multiplicative_identity,X1,X1)
| ~ sum(multiply(X0,X1),X1,X2)
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X1)
| ~ defined(X1)
| ~ product(X3,X0,multiplicative_identity)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_82,c_84]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X1,X0)
| ~ defined(multiplicative_identity)
| ~ defined(X0)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[c_358,c_84]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X1,X0)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X1)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X1,X0)
| ~ product(multiplicative_identity,X0,X1)
| ~ defined(X0) ),
inference(global_subsumption_just,[status(thm)],[c_401,c_93,c_401]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X1,X0)
| ~ defined(X0)
| ~ product(multiplicative_identity,X0,X1) ),
inference(renaming,[status(thm)],[c_434]) ).
tcf(c_465,plain,
! [X0: $i] :
( product(multiplicative_identity,multiply(X0,multiplicative_identity),X0)
| ~ defined(multiplicative_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c_435,c_182]) ).
tcf(c_525,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_265]) ).
tcf(c_537,plain,
! [X0: $i] :
( product(multiply(multiplicative_identity,multiplicative_identity),X0,X0)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_277]) ).
tcf(c_538,plain,
( product(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity))
| ~ defined(multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_539,plain,
( product(multiply(multiplicative_identity,multiplicative_identity),additive_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_537]) ).
tcf(c_735,plain,
! [X0: $i] :
( product(multiplicative_identity,multiply(X0,multiplicative_identity),X0)
| ~ defined(X0) ),
inference(global_subsumption_just,[status(thm)],[c_465,c_93,c_465]) ).
tcf(c_742,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,multiply(X0,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_896,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,multiply(X0,multiplicative_identity))
| ~ defined(X0)
| ~ defined(multiply(X0,multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_735,c_435]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(multiply(X0,X1),X0,X2)
| ~ sum(X0,multiply(X0,X1),X2) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_1191,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,multiply(X0,X1),multiply(X0,X1))
| ~ defined(multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_1192,plain,
( sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity))
| ~ defined(multiply(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_1191]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,multiply(X0,X1),additive_identity)
| product(multiplicative_inverse(multiply(X0,X1)),multiply(X0,X1),multiplicative_identity)
| ~ defined(multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_1291,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,multiply(X0,multiplicative_identity))
| ~ defined(X0)
| ~ defined(multiply(X0,multiplicative_identity)) ),
inference(resolution,[status(thm)],[c_896,c_86]) ).
tcf(c_1476,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,multiply(X0,multiplicative_identity))
| ~ defined(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1291,c_93,c_742]) ).
tcf(c_1510,plain,
( product(multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[c_1476,c_435]) ).
tcf(c_1605,plain,
product(multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(global_subsumption_just,[status(thm)],[c_1510,c_93,c_1510]) ).
tcf(c_1619,plain,
product(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[c_1605,c_86]) ).
tcf(c_2073,plain,
! [X0: $i] :
( product(multiplicative_identity,multiplicative_identity,X0)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_428]) ).
tcf(c_2074,plain,
( product(multiplicative_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_2073]) ).
tcf(c_2211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X4,X2,X3)
| ~ defined(X2)
| ~ defined(X1)
| ~ product(X0,X1,X4)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c_83,c_96]) ).
tcf(c_2520,plain,
! [X0: $i,X1: $i] :
( product(multiply(multiplicative_identity,multiplicative_identity),X1,X0)
| ~ defined(X0)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[c_1619,c_358]) ).
tcf(c_5690,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X0,X1)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(additive_identity,X0,multiply(additive_identity,X0))
| ~ sum(multiply(additive_identity,X0),X0,X1) ),
inference(instantiation,[status(thm)],[c_295]) ).
tcf(c_7248,plain,
( product(additive_identity,a,additive_identity)
| ~ product(a,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_11780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(multiply(X0,X1),X0,multiply(X2,X3))
| ~ sum(X0,multiply(X0,X1),multiply(X2,X3)) ),
inference(instantiation,[status(thm)],[c_1103]) ).
tcf(c_11781,plain,
( sum(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,additive_identity))
| ~ sum(additive_identity,multiply(additive_identity,additive_identity),multiply(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_11780]) ).
tcf(c_12340,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X0)
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X0)
| ~ product(multiply(multiplicative_identity,multiplicative_identity),X1,X3)
| ~ product(multiplicative_identity,X0,multiply(X1,X2)) ),
inference(resolution,[status(thm)],[c_2211,c_2520]) ).
tcf(c_12341,plain,
( product(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity)
| ~ product(multiplicative_identity,additive_identity,multiply(additive_identity,additive_identity))
| ~ product(multiply(multiplicative_identity,multiplicative_identity),additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_12340]) ).
tcf(c_26387,plain,
( product(additive_identity,a,multiply(additive_identity,a))
| ~ defined(additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_28465,plain,
( sum(additive_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_33697,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X0,multiply(X1,X2))
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(additive_identity,X0,multiply(additive_identity,X0))
| ~ sum(multiply(additive_identity,X0),X0,multiply(X1,X2)) ),
inference(instantiation,[status(thm)],[c_5690]) ).
tcf(c_33698,plain,
( product(multiplicative_identity,additive_identity,multiply(additive_identity,additive_identity))
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(additive_identity,additive_identity,multiply(additive_identity,additive_identity))
| ~ sum(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,additive_identity)) ),
inference(instantiation,[status(thm)],[c_33697]) ).
tcf(c_47863,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,additive_identity,additive_identity)
| ~ sum(X2,X0,a)
| ~ product(X2,additive_identity,X1)
| ~ sum(X1,multiply(additive_identity,X0),additive_identity)
| ~ product(X0,additive_identity,multiply(additive_identity,X0)) ),
inference(instantiation,[status(thm)],[c_223]) ).
tcf(c_55227,plain,
! [X0: $i] :
( sum(additive_identity,multiply(X0,a),additive_identity)
| product(multiplicative_inverse(multiply(X0,a)),multiply(X0,a),multiplicative_identity)
| ~ defined(multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_1200]) ).
tcf(c_55230,plain,
( sum(additive_identity,multiply(additive_identity,a),additive_identity)
| product(multiplicative_inverse(multiply(additive_identity,a)),multiply(additive_identity,a),multiplicative_identity)
| ~ defined(multiply(additive_identity,a)) ),
inference(instantiation,[status(thm)],[c_55227]) ).
tcf(c_56499,plain,
! [X0: $i] :
( product(a,X0,multiply(X0,a))
| ~ product(X0,a,multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_56501,plain,
( product(a,additive_identity,multiply(additive_identity,a))
| ~ product(additive_identity,a,multiply(additive_identity,a)) ),
inference(instantiation,[status(thm)],[c_56499]) ).
tcf(c_59540,plain,
! [X0: $i] :
( product(a,additive_identity,additive_identity)
| ~ sum(additive_identity,a,a)
| ~ product(additive_identity,additive_identity,X0)
| ~ product(a,additive_identity,multiply(additive_identity,a))
| ~ sum(X0,multiply(additive_identity,a),additive_identity) ),
inference(instantiation,[status(thm)],[c_47863]) ).
tcf(c_59541,plain,
( product(a,additive_identity,additive_identity)
| ~ sum(additive_identity,a,a)
| ~ product(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,multiply(additive_identity,a),additive_identity)
| ~ product(a,additive_identity,multiply(additive_identity,a)) ),
inference(instantiation,[status(thm)],[c_59540]) ).
tcf(c_72224,plain,
! [X0: $i] :
( defined(multiply(X0,a))
| ~ defined(a)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_72225,plain,
( defined(multiply(additive_identity,a))
| ~ defined(additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_72224]) ).
tcf(c_280435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X2,X3,multiplicative_identity)
| ~ product(X0,X4,multiplicative_identity)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_280894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X4,X5,multiply(X2,a))
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,multiply(X2,a)) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_281849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,X3,multiplicative_identity)
| ~ product(X1,X3,multiply(X0,a))
| ~ product(multiplicative_inverse(multiply(X0,a)),X1,X2)
| ~ product(multiplicative_inverse(multiply(X0,a)),multiply(X0,a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_280435]) ).
tcf(c_282425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,multiply(X0,a))
| ~ product(a,X1,X3)
| ~ product(X1,X2,X0)
| ~ product(a,X0,multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_280894]) ).
tcf(c_288674,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiply(X1,a),X2,multiply(X0,a))
| ~ product(X1,X2,X0)
| ~ product(a,X1,multiply(X1,a))
| ~ product(a,X0,multiply(X0,a)) ),
inference(instantiation,[status(thm)],[c_282425]) ).
tcf(c_288675,plain,
( product(multiply(additive_identity,a),additive_identity,multiply(additive_identity,a))
| ~ product(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(additive_identity,a)) ),
inference(instantiation,[status(thm)],[c_288674]) ).
tcf(c_462223,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X1,multiplicative_identity)
| ~ product(multiply(X0,a),X1,multiply(X0,a))
| ~ product(multiplicative_inverse(multiply(X0,a)),multiply(X0,a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_281849]) ).
tcf(c_462224,plain,
( product(multiplicative_identity,additive_identity,multiplicative_identity)
| ~ product(multiply(additive_identity,a),additive_identity,multiply(additive_identity,a))
| ~ product(multiplicative_inverse(multiply(additive_identity,a)),multiply(additive_identity,a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_462223]) ).
tcf(c_462225,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_462224,c_288675,c_72225,c_59541,c_56501,c_55230,c_33698,c_28465,c_26387,c_12341,c_11781,c_7248,c_2074,c_1192,c_538,c_539,c_525,c_266,c_193,c_118,c_113,c_109,c_106,c_102,c_104,c_90,c_93,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD043-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 10:49:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 103.95/23.75 % SZS status Started for theBenchmark.p
% 103.95/23.75 % SZS status Unsatisfiable for theBenchmark.p
% 103.95/23.75
% 103.95/23.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 103.95/23.75
% 103.95/23.75 % ------ iProver source info
% 103.95/23.75
% 103.95/23.75 % git: date: 2026-07-19 20:42:38 +0200
% 103.95/23.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 103.95/23.75 % git: non_committed_changes: false
% 103.95/23.75
% 103.95/23.75 % ------ Parsing...% successful
% 103.95/23.75
% 103.95/23.75
% 103.95/23.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 103.95/23.75
% 103.95/23.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 103.95/23.75
% 103.95/23.75 % ------ Preprocessing...
% 103.95/23.75 % ------ Proving...
% 103.95/23.75 % ------ Problem Properties
% 103.95/23.75
% 103.95/23.75 %
% 103.95/23.75 % clauses 28
% 103.95/23.75 % conjectures 1
% 103.95/23.75 % EPR 20
% 103.95/23.75 % Horn 25
% 103.95/23.75 % unary 5
% 103.95/23.75 % binary 6
% 103.95/23.75 % lits 79
% 103.95/23.75 % lits eq 0
% 103.95/23.75 % fd_pure 0
% 103.95/23.75 % fd_pseudo 0
% 103.95/23.75 % fd_cond 0
% 103.95/23.75 % fd_pseudo_cond 0
% 103.95/23.75 % AC symbols 0
% 103.95/23.75
% 103.95/23.75 % ------ Input Options Time Limit: Unbounded
% 103.95/23.75
% 103.95/23.75
% 103.95/23.75 % ------
% 103.95/23.75 % Current options:
% 103.95/23.75 % ------
% 103.95/23.75
% 103.95/23.75
% 103.95/23.75 %
% 103.95/23.75
% 103.95/23.75 % ------ Proving...
% 103.95/23.75 %
% 103.95/23.75
% 103.95/23.75 % SZS status Unsatisfiable for theBenchmark.p
% 103.95/23.75
% 103.95/23.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 103.95/23.75
% 103.95/23.75
%------------------------------------------------------------------------------