%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 01:15:45 PM UTC 2026
% Result : Unsatisfiable 158.10s 37.33s
% Output : CNFRefutation 158.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 140 ( 22 unt; 0 def)
% Number of atoms : 430 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 579 ( 289 ~; 290 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 270 ( 0 sgn 270 !; 0 ?; 207 :)
% 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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f21,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| sum(additive_identity,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
fof(f23,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
fof(f32,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
fof(f33,negated_conjecture,
sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).
tcf(c_82,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_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_84,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,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_88,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_89,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_90,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_92,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_93,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_95,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( defined(multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_98,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X0,X1)
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1)
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_or_equal(X2,X4)
| ~ less_or_equal(X0,X3)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_109,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,plain,
defined(c),
inference(cnf_transformation,[],[f29]) ).
tcf(c_111,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f30]) ).
tcf(c_112,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f31]) ).
tcf(c_113,negated_conjecture,
product(a,b,c),
inference(cnf_transformation,[],[f32]) ).
tcf(c_114,negated_conjecture,
sum(additive_identity,c,additive_identity),
inference(cnf_transformation,[],[f33]) ).
tcf(c_116,plain,
( product(multiplicative_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_117,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_121,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_130,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_134,plain,
( product(b,a,c)
| ~ product(a,b,c) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_135,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_136,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,c)
| ~ product(a,b,c)
| ~ product(X1,b,X2)
| ~ product(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_161,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_87]) ).
tcf(c_197,plain,
sum(c,additive_identity,additive_identity),
inference(resolution,[status(thm)],[c_86,c_114]) ).
tcf(c_206,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c_91,c_89]) ).
tcf(c_210,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_88]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X5,X2,X3)
| ~ product(X4,X2,X0)
| ~ sum(X4,X1,X5)
| ~ product(X1,X2,multiply(X1,X2))
| ~ sum(X0,multiply(X1,X2),X3) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,X1,X2)
| ~ sum(additive_identity,X0,X2)
| ~ sum(c,X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_82]) ).
tcf(c_286,plain,
( sum(additive_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,a)
| ~ sum(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ sum(c,X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_257]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X4,a,X5)
| ~ product(X1,X3,a)
| ~ product(X2,X3,X5)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_428,plain,
( product(multiplicative_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_466,plain,
( product(multiplicative_identity,b,b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_469,plain,
! [X0: $i] :
( product(X0,b,multiply(X0,b))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_470,plain,
( product(additive_identity,b,multiply(additive_identity,b))
| ~ defined(additive_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_469]) ).
tcf(c_497,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_93]) ).
tcf(c_507,plain,
sum(c,additive_identity,additive_identity),
inference(superposition,[status(thm)],[c_114,c_86]) ).
tcf(c_539,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(superposition,[status(thm)],[c_507,c_320]) ).
tcf(c_540,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_539,c_95,c_117]) ).
tcf(c_583,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,X1,X2)
| ~ sum(additive_identity,X0,X2)
| ~ sum(additive_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_540,c_82]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_inverse(b),X1,X0)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(b,X0,X1)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,multiply(X0,X1))
| ~ product(multiplicative_identity,X1,X1)
| ~ product(X0,multiplicative_identity,X2)
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,multiplicative_identity,X2)
| ~ product(X0,multiplicative_identity,X0)
| ~ sum(X0,X1,X3)
| ~ product(X1,multiplicative_identity,multiply(X1,multiplicative_identity))
| ~ sum(X0,multiply(X1,multiplicative_identity),X2) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_861,plain,
! [X0: $i] :
( sum(additive_identity,additive_identity,X0)
| ~ sum(additive_identity,c,X0) ),
inference(superposition,[status(thm)],[c_114,c_583]) ).
tcf(c_906,plain,
( sum(additive_identity,additive_identity,c)
| ~ defined(c) ),
inference(superposition,[status(thm)],[c_84,c_861]) ).
tcf(c_1021,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X0,additive_identity)
| ~ sum(X0,c,X1) ),
inference(resolution,[status(thm)],[c_105,c_114]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X2,X1)
| ~ defined(X1)
| ~ less_or_equal(X0,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_105,c_84]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X3,X2,X1)
| ~ defined(X1)
| ~ sum(X3,X0,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_82,c_84]) ).
tcf(c_1385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X3,X1,X2)
| ~ defined(X1)
| ~ sum(X0,additive_identity,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_83,c_84]) ).
tcf(c_1431,plain,
( sum(a,additive_identity,a)
| ~ sum(additive_identity,a,a) ),
inference(instantiation,[status(thm)],[c_287]) ).
tcf(c_2065,plain,
( product(multiplicative_inverse(b),c,a)
| ~ product(multiplicative_identity,a,a)
| ~ product(b,a,c)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_642]) ).
tcf(c_2510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X2,X3,c)
| ~ product(X1,b,X3)
| ~ product(X0,b,X2)
| ~ sum(X0,X1,a) ),
inference(resolution,[status(thm)],[c_92,c_113]) ).
tcf(c_2513,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X4,X5,multiply(X2,X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ product(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_92,c_101]) ).
tcf(c_2830,plain,
( less_or_equal(additive_identity,c)
| ~ defined(c)
| ~ less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[c_1022,c_114]) ).
tcf(c_2925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X0,X3,X4)
| ~ product(X2,multiplicative_identity,X4)
| ~ product(X1,multiplicative_identity,X3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_3130,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(X1,b),c)
| ~ defined(b)
| ~ defined(X1)
| ~ product(X0,b,X2)
| ~ sum(X0,X1,a) ),
inference(resolution,[status(thm)],[c_2510,c_101]) ).
tcf(c_3339,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,multiply(X0,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_3340,plain,
( product(additive_identity,multiplicative_identity,multiply(additive_identity,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_3339]) ).
tcf(c_3533,plain,
! [X0: $i,X1: $i] :
( product(X1,b,multiply(X0,b))
| ~ product(multiplicative_identity,b,b)
| ~ product(X0,multiplicative_identity,X1)
| ~ product(X0,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_655]) ).
tcf(c_3699,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ sum(c,X0,X1) ),
inference(resolution,[status(thm)],[c_1127,c_114]) ).
tcf(c_3897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X3,multiply(X2,multiplicative_identity),X5)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X0,X4)
| ~ sum(X0,X1,multiply(X2,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_3898,plain,
( sum(additive_identity,multiply(additive_identity,multiplicative_identity),additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,multiply(additive_identity,multiplicative_identity)) ),
inference(instantiation,[status(thm)],[c_3897]) ).
tcf(c_4146,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X0,X1)
| ~ defined(X0)
| ~ sum(c,X0,X1) ),
inference(resolution,[status(thm)],[c_1385,c_197]) ).
tcf(c_4266,plain,
! [X0: $i] :
( less_or_equal(X0,additive_identity)
| ~ defined(X0)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ sum(c,X0,c) ),
inference(resolution,[status(thm)],[c_3699,c_1021]) ).
tcf(c_5002,plain,
( product(c,multiplicative_inverse(b),a)
| ~ product(multiplicative_inverse(b),c,a) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_5010,plain,
! [X0: $i] :
( product(multiplicative_inverse(b),X0,c)
| ~ product(a,b,c)
| ~ product(c,b,X0)
| ~ product(multiplicative_inverse(b),c,a) ),
inference(instantiation,[status(thm)],[c_159]) ).
tcf(c_5077,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,X0)
| ~ defined(X0)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ sum(c,X0,X1) ),
inference(resolution,[status(thm)],[c_4146,c_1022]) ).
tcf(c_7446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,multiplicative_identity,c)
| ~ product(X1,multiplicative_identity,X1)
| ~ product(X0,multiplicative_identity,X3)
| ~ sum(X3,X1,c)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_497]) ).
tcf(c_7447,plain,
( product(additive_identity,multiplicative_identity,c)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,c) ),
inference(instantiation,[status(thm)],[c_7446]) ).
tcf(c_9267,plain,
! [X0: $i,X1: $i] :
( product(X0,multiplicative_inverse(b),X1)
| ~ product(multiplicative_inverse(b),X0,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_9268,plain,
( product(additive_identity,multiplicative_inverse(b),additive_identity)
| ~ product(multiplicative_inverse(b),additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_9267]) ).
tcf(c_11173,plain,
! [X0: $i] :
( defined(multiply(X0,b))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_11174,plain,
( defined(multiply(additive_identity,b))
| ~ defined(additive_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_11173]) ).
tcf(c_11842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X3,X1,multiply(X2,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X2)
| ~ defined(X1)
| ~ product(X0,multiplicative_identity,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_2513,c_206]) ).
tcf(c_11843,plain,
( sum(additive_identity,additive_identity,multiply(additive_identity,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_11842]) ).
tcf(c_12119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(c,multiplicative_identity,X2)
| ~ product(X3,multiplicative_identity,X0)
| ~ product(X1,multiplicative_identity,X1)
| ~ sum(X3,X1,c)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_497]) ).
tcf(c_12120,plain,
( product(c,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,c) ),
inference(instantiation,[status(thm)],[c_12119]) ).
tcf(c_12564,plain,
! [X0: $i] :
( product(multiplicative_inverse(b),multiply(X0,b),c)
| ~ product(a,b,c)
| ~ product(multiplicative_inverse(b),c,a)
| ~ product(c,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_5010]) ).
tcf(c_12565,plain,
! [X0: $i] :
( product(c,b,multiply(X0,b))
| ~ product(multiplicative_identity,b,b)
| ~ product(X0,multiplicative_identity,c)
| ~ product(X0,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_3533]) ).
tcf(c_12566,plain,
( product(multiplicative_inverse(b),multiply(additive_identity,b),c)
| ~ product(a,b,c)
| ~ product(multiplicative_inverse(b),c,a)
| ~ product(c,b,multiply(additive_identity,b)) ),
inference(instantiation,[status(thm)],[c_12564]) ).
tcf(c_12567,plain,
( product(c,b,multiply(additive_identity,b))
| ~ product(multiplicative_identity,b,b)
| ~ product(additive_identity,multiplicative_identity,c)
| ~ product(additive_identity,b,multiply(additive_identity,b)) ),
inference(instantiation,[status(thm)],[c_12565]) ).
tcf(c_14706,plain,
! [X0: $i] :
( less_or_equal(X0,additive_identity)
| ~ defined(X0)
| ~ sum(c,X0,c) ),
inference(global_subsumption_just,[status(thm)],[c_4266,c_95,c_121,c_4266]) ).
tcf(c_18560,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X1,a,X3)
| ~ sum(X0,c,X2)
| ~ product(c,multiplicative_inverse(b),a)
| ~ product(X2,multiplicative_inverse(b),X3)
| ~ product(X0,multiplicative_inverse(b),X1) ),
inference(instantiation,[status(thm)],[c_357]) ).
tcf(c_18561,plain,
( sum(additive_identity,a,additive_identity)
| ~ sum(additive_identity,c,additive_identity)
| ~ product(additive_identity,multiplicative_inverse(b),additive_identity)
| ~ product(c,multiplicative_inverse(b),a) ),
inference(instantiation,[status(thm)],[c_18560]) ).
tcf(c_26788,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(multiply(X3,b),multiplicative_identity,X2)
| ~ product(X0,multiplicative_identity,X0)
| ~ product(X1,multiplicative_identity,multiply(X1,multiplicative_identity))
| ~ sum(X0,X1,multiply(X3,b))
| ~ sum(X0,multiply(X1,multiplicative_identity),X2) ),
inference(instantiation,[status(thm)],[c_848]) ).
tcf(c_26789,plain,
( product(multiply(additive_identity,b),multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,multiply(additive_identity,multiplicative_identity))
| ~ sum(additive_identity,additive_identity,multiply(additive_identity,b))
| ~ sum(additive_identity,multiply(additive_identity,multiplicative_identity),additive_identity) ),
inference(instantiation,[status(thm)],[c_26788]) ).
tcf(c_78125,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_inverse(b),X1,X2)
| ~ product(c,multiplicative_identity,X2)
| ~ product(multiply(X0,b),multiplicative_identity,X1)
| ~ product(multiplicative_inverse(b),multiply(X0,b),c) ),
inference(instantiation,[status(thm)],[c_2925]) ).
tcf(c_78126,plain,
( product(multiplicative_inverse(b),additive_identity,additive_identity)
| ~ product(c,multiplicative_identity,additive_identity)
| ~ product(multiply(additive_identity,b),multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(b),multiply(additive_identity,b),c) ),
inference(instantiation,[status(thm)],[c_78125]) ).
tcf(c_109458,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(X1,b),c)
| ~ sum(X0,X1,a)
| ~ product(X0,b,X2)
| ~ defined(X1) ),
inference(global_subsumption_just,[status(thm)],[c_3130,c_109,c_3130]) ).
tcf(c_109459,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(X1,b),c)
| ~ defined(X1)
| ~ product(X0,b,X2)
| ~ sum(X0,X1,a) ),
inference(renaming,[status(thm)],[c_109458]) ).
tcf(c_179267,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,multiply(X0,b))
| ~ less_or_equal(X1,multiply(X0,b))
| ~ less_or_equal(multiply(X0,b),X1) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_179268,plain,
( sum(additive_identity,additive_identity,multiply(additive_identity,b))
| ~ less_or_equal(additive_identity,multiply(additive_identity,b))
| ~ less_or_equal(multiply(additive_identity,b),additive_identity) ),
inference(instantiation,[status(thm)],[c_179267]) ).
tcf(c_340051,plain,
! [X0: $i] :
( sum(c,multiply(X0,b),c)
| ~ defined(X0)
| ~ sum(a,X0,a) ),
inference(resolution,[status(thm)],[c_109459,c_113]) ).
tcf(c_340724,plain,
! [X0: $i] :
( less_or_equal(multiply(X0,b),additive_identity)
| ~ defined(X0)
| ~ sum(a,X0,a)
| ~ defined(multiply(X0,b)) ),
inference(resolution,[status(thm)],[c_340051,c_14706]) ).
tcf(c_340727,plain,
( less_or_equal(multiply(additive_identity,b),additive_identity)
| ~ defined(additive_identity)
| ~ sum(a,additive_identity,a)
| ~ defined(multiply(additive_identity,b)) ),
inference(instantiation,[status(thm)],[c_340724]) ).
tcf(c_469635,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,X0)
| ~ defined(X0)
| ~ sum(c,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_5077,c_95,c_121,c_5077]) ).
tcf(c_469768,plain,
! [X0: $i] :
( less_or_equal(c,multiply(X0,b))
| ~ defined(X0)
| ~ sum(a,X0,a)
| ~ defined(multiply(X0,b)) ),
inference(resolution,[status(thm)],[c_469635,c_340051]) ).
tcf(c_474453,plain,
! [X0: $i] :
( less_or_equal(c,multiply(X0,b))
| ~ defined(X0)
| ~ sum(a,X0,a) ),
inference(global_subsumption_just,[status(thm)],[c_469768,c_109,c_11173,c_469768]) ).
tcf(c_474474,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,multiply(X0,b))
| ~ defined(X0)
| ~ less_or_equal(X1,c)
| ~ sum(a,X0,a) ),
inference(resolution,[status(thm)],[c_474453,c_103]) ).
tcf(c_474475,plain,
( less_or_equal(additive_identity,multiply(additive_identity,b))
| ~ defined(additive_identity)
| ~ less_or_equal(additive_identity,c)
| ~ sum(a,additive_identity,a) ),
inference(instantiation,[status(thm)],[c_474474]) ).
tcf(c_474476,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_474475,c_340727,c_179268,c_78126,c_26789,c_18561,c_12567,c_12566,c_12120,c_11843,c_11174,c_9268,c_7447,c_5002,c_3898,c_3340,c_2830,c_2065,c_1431,c_906,c_470,c_466,c_428,c_286,c_136,c_134,c_130,c_121,c_117,c_116,c_111,c_112,c_113,c_114,c_95,c_98,c_108,c_109,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 10:49:21 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.50
% 0.16/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.50
% 0.16/0.50 % Detected problem language: tptp
% 0.24/0.51 % Proving...
% 158.10/37.33 % SZS status Started for theBenchmark.p
% 158.10/37.33 % SZS status Unsatisfiable for theBenchmark.p
% 158.10/37.33
% 158.10/37.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 158.10/37.33
% 158.10/37.33 % ------ iProver source info
% 158.10/37.33
% 158.10/37.33 % git: date: 2026-07-19 20:42:38 +0200
% 158.10/37.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 158.10/37.33 % git: non_committed_changes: false
% 158.10/37.33
% 158.10/37.33 % ------ Parsing...% successful
% 158.10/37.33
% 158.10/37.33
% 158.10/37.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 158.10/37.33
% 158.10/37.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 158.10/37.33
% 158.10/37.33 % ------ Preprocessing...
% 158.10/37.33 % ------ Proving...
% 158.10/37.33 % ------ Problem Properties
% 158.10/37.33
% 158.10/37.33 %
% 158.10/37.33 % clauses 33
% 158.10/37.33 % conjectures 4
% 158.10/37.33 % EPR 25
% 158.10/37.33 % Horn 30
% 158.10/37.33 % unary 10
% 158.10/37.33 % binary 6
% 158.10/37.33 % lits 84
% 158.10/37.33 % lits eq 0
% 158.10/37.33 % fd_pure 0
% 158.10/37.33 % fd_pseudo 0
% 158.10/37.33 % fd_cond 0
% 158.10/37.33 % fd_pseudo_cond 0
% 158.10/37.33 % AC symbols 0
% 158.10/37.33
% 158.10/37.33 % ------ Input Options Time Limit: Unbounded
% 158.10/37.33
% 158.10/37.33
% 158.10/37.33 % ------
% 158.10/37.33 % Current options:
% 158.10/37.33 % ------
% 158.10/37.33
% 158.10/37.33
% 158.10/37.33 %
% 158.10/37.33
% 158.10/37.33 % ------ Proving...
% 158.10/37.33 %
% 158.10/37.33
% 158.10/37.33 % SZS status Unsatisfiable for theBenchmark.p
% 158.10/37.33
% 158.10/37.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 158.10/37.33
% 158.10/37.33
%------------------------------------------------------------------------------