%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD041-3 : 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 : n005.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 29.76s 5.33s
% Output : CNFRefutation 29.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 16 unt; 0 def)
% Number of atoms : 289 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 391 ( 196 ~; 195 |; 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 181 ( 0 sgn 181 !; 0 ?; 136 :)
% 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(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(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,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
fof(f31,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
tcf(c_80,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_82,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_85,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_86,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_87,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_90,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_91,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_93,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( defined(multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_96,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_106,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_107,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_108,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_109,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f30]) ).
tcf(c_110,negated_conjecture,
product(a,b,additive_identity),
inference(cnf_transformation,[],[f31]) ).
tcf(c_112,plain,
( product(multiplicative_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_113,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_124,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_128,plain,
( product(b,a,additive_identity)
| ~ product(a,b,additive_identity) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_129,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_130,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_129]) ).
tcf(c_145,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_85]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X2,X4,multiply(X0,X1))
| ~ product(X3,X1,X4)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,multiply(X0,X1)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(additive_identity,a,additive_identity)
| ~ product(X2,X3,additive_identity)
| ~ product(X1,X3,a)
| ~ product(X0,X3,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_172,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_91]) ).
tcf(c_267,plain,
( sum(additive_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,a)
| ~ sum(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_375,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[c_89,c_87]) ).
tcf(c_615,plain,
( product(multiplicative_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_642,plain,
! [X0: $i] :
( product(X0,b,multiply(X0,b))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_643,plain,
( product(additive_identity,b,multiply(additive_identity,b))
| ~ defined(additive_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_642]) ).
tcf(c_677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X3,X2)
| ~ product(X2,multiplicative_identity,X2)
| ~ product(X1,multiplicative_identity,X3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,multiplicative_identity,X3)
| ~ product(X1,multiplicative_identity,X1)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_789,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_145]) ).
tcf(c_866,plain,
! [X0: $i,X1: $i] :
( product(X1,additive_identity,multiply(X0,b))
| ~ product(a,b,additive_identity)
| ~ product(X1,a,X0)
| ~ product(X0,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_1169,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_172]) ).
tcf(c_1286,plain,
( product(b,additive_identity,multiply(additive_identity,b))
| ~ product(b,a,additive_identity)
| ~ product(a,b,additive_identity)
| ~ product(additive_identity,b,multiply(additive_identity,b)) ),
inference(instantiation,[status(thm)],[c_866]) ).
tcf(c_1363,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_80,c_82]) ).
tcf(c_1839,plain,
( sum(a,additive_identity,a)
| ~ sum(additive_identity,a,a) ),
inference(instantiation,[status(thm)],[c_268]) ).
tcf(c_1958,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X2,X3,additive_identity)
| ~ product(X1,b,X3)
| ~ product(X0,b,X2)
| ~ sum(X0,X1,a) ),
inference(resolution,[status(thm)],[c_90,c_110]) ).
tcf(c_1963,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_90,c_99]) ).
tcf(c_2773,plain,
! [X0: $i,X1: $i] :
( sum(X1,additive_identity,additive_identity)
| ~ sum(X0,a,a)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[c_1958,c_110]) ).
tcf(c_2779,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(X1,b),additive_identity)
| ~ defined(b)
| ~ defined(X1)
| ~ product(X0,b,X2)
| ~ sum(X0,X1,a) ),
inference(resolution,[status(thm)],[c_1958,c_99]) ).
tcf(c_2855,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ sum(a,a,a) ),
inference(resolution,[status(thm)],[c_2773,c_110]) ).
tcf(c_2921,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_2855,c_93,c_113]) ).
tcf(c_2990,plain,
( product(multiplicative_inverse(b),additive_identity,a)
| ~ product(multiplicative_identity,a,a)
| ~ product(b,a,additive_identity)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_789]) ).
tcf(c_2992,plain,
! [X0: $i] :
( product(multiplicative_inverse(b),multiply(X0,b),X0)
| ~ product(multiplicative_identity,X0,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(b,X0,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_789]) ).
tcf(c_2994,plain,
( product(multiplicative_inverse(b),multiply(additive_identity,b),additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(b,additive_identity,multiply(additive_identity,b)) ),
inference(instantiation,[status(thm)],[c_2992]) ).
tcf(c_3493,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[c_1363,c_2921]) ).
tcf(c_4019,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,multiply(X0,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_4020,plain,
( product(additive_identity,multiplicative_identity,multiply(additive_identity,multiplicative_identity))
| ~ defined(multiplicative_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_4019]) ).
tcf(c_4054,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,a,additive_identity)
| ~ product(X2,multiplicative_identity,additive_identity)
| ~ product(X1,multiplicative_identity,a)
| ~ product(X0,multiplicative_identity,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_4056,plain,
( sum(additive_identity,a,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,a)
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_4054]) ).
tcf(c_4501,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_80]) ).
tcf(c_4502,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_4501]) ).
tcf(c_6709,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,a)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(b),additive_identity,a)
| ~ product(multiplicative_inverse(b),additive_identity,X0) ),
inference(instantiation,[status(thm)],[c_679]) ).
tcf(c_6710,plain,
( product(additive_identity,multiplicative_identity,a)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(b),additive_identity,additive_identity)
| ~ product(multiplicative_inverse(b),additive_identity,a) ),
inference(instantiation,[status(thm)],[c_6709]) ).
tcf(c_14465,plain,
! [X0: $i] :
( defined(multiply(X0,b))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_14466,plain,
( defined(multiply(additive_identity,b))
| ~ defined(additive_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_14465]) ).
tcf(c_15036,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_1963,c_375]) ).
tcf(c_15037,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_15036]) ).
tcf(c_35038,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_1169]) ).
tcf(c_35039,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_35038]) ).
tcf(c_41314,plain,
! [X0: $i] :
( product(multiplicative_inverse(b),X0,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiply(additive_identity,b),multiplicative_identity,X0)
| ~ product(multiplicative_inverse(b),multiply(additive_identity,b),additive_identity) ),
inference(instantiation,[status(thm)],[c_677]) ).
tcf(c_41317,plain,
( product(multiplicative_inverse(b),additive_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiply(additive_identity,b),multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(b),multiply(additive_identity,b),additive_identity) ),
inference(instantiation,[status(thm)],[c_41314]) ).
tcf(c_44882,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(X1,b),additive_identity)
| ~ sum(X0,X1,a)
| ~ product(X0,b,X2)
| ~ defined(X1) ),
inference(global_subsumption_just,[status(thm)],[c_2779,c_107,c_2779]) ).
tcf(c_44883,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,multiply(X1,b),additive_identity)
| ~ defined(X1)
| ~ product(X0,b,X2)
| ~ sum(X0,X1,a) ),
inference(renaming,[status(thm)],[c_44882]) ).
tcf(c_44900,plain,
! [X0: $i] :
( sum(additive_identity,multiply(X0,b),additive_identity)
| ~ defined(X0)
| ~ sum(a,X0,a) ),
inference(resolution,[status(thm)],[c_44883,c_110]) ).
tcf(c_45201,plain,
! [X0: $i] :
( sum(additive_identity,additive_identity,multiply(X0,b))
| ~ defined(X0)
| ~ sum(a,X0,a)
| ~ defined(multiply(X0,b)) ),
inference(resolution,[status(thm)],[c_44900,c_3493]) ).
tcf(c_45206,plain,
( sum(additive_identity,additive_identity,multiply(additive_identity,b))
| ~ defined(additive_identity)
| ~ sum(a,additive_identity,a)
| ~ defined(multiply(additive_identity,b)) ),
inference(instantiation,[status(thm)],[c_45201]) ).
tcf(c_45207,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_45206,c_41317,c_35039,c_15037,c_14466,c_6710,c_4502,c_4056,c_4020,c_2994,c_2990,c_1839,c_1286,c_643,c_615,c_267,c_130,c_128,c_124,c_113,c_112,c_108,c_109,c_110,c_93,c_96,c_106,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD041-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 10:49:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 29.76/5.33 % SZS status Started for theBenchmark.p
% 29.76/5.33 % SZS status Unsatisfiable for theBenchmark.p
% 29.76/5.33
% 29.76/5.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.76/5.33
% 29.76/5.33 % ------ iProver source info
% 29.76/5.33
% 29.76/5.33 % git: date: 2026-07-19 20:42:38 +0200
% 29.76/5.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.76/5.33 % git: non_committed_changes: false
% 29.76/5.33
% 29.76/5.33 % ------ Parsing...% successful
% 29.76/5.33
% 29.76/5.33
% 29.76/5.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.76/5.33
% 29.76/5.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 29.76/5.33
% 29.76/5.33 % ------ Preprocessing...
% 29.76/5.33 % ------ Proving...
% 29.76/5.33 % ------ Problem Properties
% 29.76/5.33
% 29.76/5.33 %
% 29.76/5.33 % clauses 31
% 29.76/5.33 % conjectures 4
% 29.76/5.33 % EPR 23
% 29.76/5.33 % Horn 28
% 29.76/5.33 % unary 8
% 29.76/5.33 % binary 6
% 29.76/5.33 % lits 82
% 29.76/5.33 % lits eq 0
% 29.76/5.33 % fd_pure 0
% 29.76/5.33 % fd_pseudo 0
% 29.76/5.33 % fd_cond 0
% 29.76/5.33 % fd_pseudo_cond 0
% 29.76/5.33 % AC symbols 0
% 29.76/5.33
% 29.76/5.33 % ------ Input Options Time Limit: Unbounded
% 29.76/5.33
% 29.76/5.33
% 29.76/5.33 % ------
% 29.76/5.33 % Current options:
% 29.76/5.33 % ------
% 29.76/5.33
% 29.76/5.33
% 29.76/5.33 %
% 29.76/5.33
% 29.76/5.33 % ------ Proving...
% 29.76/5.33 %
% 29.76/5.33
% 29.76/5.33 % SZS status Unsatisfiable for theBenchmark.p
% 29.76/5.33
% 29.76/5.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.76/5.34
% 29.76/5.34
%------------------------------------------------------------------------------