%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD040-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:18:20 PM UTC 2026
% Result : Unsatisfiable 34.75s 21.01s
% Output : CNFRefutation 34.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 24
% Syntax : Number of clauses : 142 ( 55 unt; 6 nHn; 142 RR)
% Number of literals : 289 ( 0 equ; 146 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(a_not_equal_to_additive_identity_2,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_2) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(multiplicative_inverse_equals_additive_identity_3,negated_conjecture,
equalish(multiplicative_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse_equals_additive_identity_3) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(distributivity,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',distributivity) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( less_or_equal(additive_identity,multiply(X1,X2))
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(antisymmetry_of_order_relation,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(c_0_24,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_25,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_26,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_2 ).
cnf(c_0_27,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_28,negated_conjecture,
equalish(multiplicative_inverse(a),additive_identity),
multiplicative_inverse_equals_additive_identity_3 ).
cnf(c_0_29,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_30,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,hypothesis,
equalish(add(additive_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_34,hypothesis,
equalish(add(additive_identity,multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,hypothesis,
equalish(additive_identity,add(additive_identity,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,hypothesis,
( equalish(X1,add(additive_identity,multiplicative_inverse(a)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_37,hypothesis,
( equalish(add(additive_identity,multiplicative_inverse(a)),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_38,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,add(additive_identity,multiplicative_inverse(a)))
| ~ equalish(X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_39,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_40,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_41,hypothesis,
( equalish(X1,X2)
| ~ equalish(X2,additive_identity)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_42,plain,
equalish(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_44,hypothesis,
( equalish(X1,multiply(multiplicative_identity,additive_identity))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_46,hypothesis,
( equalish(multiply(multiplicative_identity,additive_identity),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_47,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_48,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_49,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_50,hypothesis,
equalish(multiply(multiplicative_identity,additive_identity),multiplicative_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_51,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_25]),c_0_26]) ).
cnf(c_0_52,hypothesis,
( equalish(multiply(X1,a),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_53,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_54,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_55,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_56,hypothesis,
equalish(multiply(multiplicative_inverse(a),a),multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_52,c_0_30]) ).
cnf(c_0_57,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiplicative_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_58,hypothesis,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_59,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_33,c_0_51]) ).
cnf(c_0_60,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_61,hypothesis,
equalish(multiply(multiplicative_inverse(a),a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
equalish(additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_63,negated_conjecture,
equalish(multiply(multiply(a,multiplicative_inverse(a)),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40])]) ).
cnf(c_0_64,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_65,hypothesis,
equalish(a,a),
inference(spm,[status(thm)],[c_0_60,c_0_25]) ).
cnf(c_0_66,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiplicative_inverse(a),a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( equalish(multiply(additive_identity,X1),multiply(multiplicative_inverse(a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_63]) ).
cnf(c_0_69,hypothesis,
( equalish(multiply(X1,X2),multiply(multiply(a,multiplicative_inverse(a)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_54,c_0_64]) ).
cnf(c_0_70,hypothesis,
( equalish(multiply(a,X1),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
equalish(multiply(additive_identity,a),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_25])]) ).
cnf(c_0_72,hypothesis,
equalish(multiply(additive_identity,a),multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_52,c_0_40]) ).
cnf(c_0_73,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_74,hypothesis,
( equalish(multiply(X1,additive_identity),additive_identity)
| ~ equalish(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_40])]) ).
cnf(c_0_75,hypothesis,
equalish(multiply(a,additive_identity),multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_70,c_0_40]) ).
cnf(c_0_76,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_77,hypothesis,
equalish(multiply(a,additive_identity),multiply(additive_identity,a)),
inference(spm,[status(thm)],[c_0_33,c_0_72]) ).
cnf(c_0_78,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_79,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_60,c_0_73]) ).
cnf(c_0_80,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_81,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(X2,additive_identity))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_74]) ).
cnf(c_0_82,hypothesis,
( equalish(multiply(multiply(a,additive_identity),X1),multiply(multiply(a,additive_identity),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_75]) ).
cnf(c_0_83,hypothesis,
equalish(multiply(a,additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,plain,
( equalish(add(multiplicative_identity,X1),add(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
equalish(add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_73]) ).
cnf(c_0_86,plain,
( equalish(add(X1,additive_identity),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_40]) ).
cnf(c_0_87,hypothesis,
equalish(multiply(multiply(a,additive_identity),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_40])]) ).
cnf(c_0_88,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_89,plain,
equalish(add(multiplicative_identity,additive_identity),add(multiplicative_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_84,c_0_40]) ).
cnf(c_0_90,plain,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,add(additive_identity,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_85]) ).
cnf(c_0_91,plain,
equalish(add(multiplicative_identity,additive_identity),add(additive_identity,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_86,c_0_73]) ).
cnf(c_0_92,negated_conjecture,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_62]) ).
cnf(c_0_93,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiply(a,additive_identity),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_87]) ).
cnf(c_0_94,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_88]) ).
cnf(c_0_95,plain,
( equalish(multiply(add(multiplicative_identity,additive_identity),X1),multiply(add(multiplicative_identity,additive_identity),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_89]) ).
cnf(c_0_96,plain,
equalish(add(multiplicative_identity,additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
distributivity ).
cnf(c_0_98,negated_conjecture,
( equalish(multiplicative_inverse(a),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_33,c_0_92]) ).
cnf(c_0_99,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_100,hypothesis,
equalish(multiply(additive_identity,multiply(a,additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_40]),c_0_25])]) ).
cnf(c_0_101,hypothesis,
equalish(multiply(add(multiplicative_identity,additive_identity),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_95]),c_0_96]),c_0_40])]) ).
cnf(c_0_102,plain,
( equalish(X1,multiply(add(X2,X3),X4))
| ~ defined(X3)
| ~ defined(X4)
| ~ defined(X2)
| ~ equalish(X1,add(multiply(X2,X4),multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_27,c_0_97]) ).
cnf(c_0_103,negated_conjecture,
( equalish(add(multiplicative_inverse(a),X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_78,c_0_98]) ).
cnf(c_0_104,plain,
( equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_27,c_0_99]) ).
cnf(c_0_105,hypothesis,
equalish(additive_identity,multiply(additive_identity,multiply(a,additive_identity))),
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_106,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_107,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(add(multiplicative_identity,additive_identity),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_101]) ).
cnf(c_0_108,negated_conjecture,
( equalish(add(multiplicative_inverse(a),multiply(X1,X2)),multiply(add(X3,X1),X2))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(multiply(X3,X2),additive_identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_88]) ).
cnf(c_0_109,hypothesis,
equalish(additive_identity,multiply(multiply(additive_identity,a),additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_40]),c_0_25])]) ).
cnf(c_0_110,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_106]) ).
cnf(c_0_111,negated_conjecture,
( equalish(add(multiplicative_inverse(a),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_28]) ).
cnf(c_0_112,hypothesis,
equalish(add(multiplicative_inverse(a),multiply(additive_identity,additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_40]),c_0_73]),c_0_42])]) ).
cnf(c_0_113,hypothesis,
equalish(multiply(multiply(additive_identity,a),additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_33,c_0_109]) ).
cnf(c_0_114,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_115,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_110,c_0_40]) ).
cnf(c_0_116,negated_conjecture,
( equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,add(multiplicative_inverse(a),X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_111]) ).
cnf(c_0_117,hypothesis,
equalish(additive_identity,add(multiplicative_inverse(a),multiply(additive_identity,additive_identity))),
inference(spm,[status(thm)],[c_0_33,c_0_112]) ).
cnf(c_0_118,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiply(additive_identity,a),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_113]) ).
cnf(c_0_119,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( equalish(additive_identity,add(additive_identity,multiply(additive_identity,additive_identity)))
| ~ defined(multiply(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,plain,
( equalish(add(additive_identity,multiply(X1,X2)),multiply(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_88]) ).
cnf(c_0_122,negated_conjecture,
( equalish(multiply(X1,X2),multiply(multiplicative_inverse(a),X2))
| ~ defined(X2)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_54,c_0_92]) ).
cnf(c_0_123,hypothesis,
equalish(multiply(additive_identity,multiply(additive_identity,a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_94]),c_0_40]),c_0_25])]) ).
cnf(c_0_124,axiom,
( less_or_equal(additive_identity,multiply(X1,X2))
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2) ),
compatibility_of_order_relation_and_multiplication ).
cnf(c_0_125,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_119]) ).
cnf(c_0_126,negated_conjecture,
equalish(additive_identity,add(additive_identity,multiply(additive_identity,additive_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_88]),c_0_40])]) ).
cnf(c_0_127,plain,
( equalish(add(additive_identity,multiply(X1,additive_identity)),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_40]) ).
cnf(c_0_128,negated_conjecture,
( equalish(multiply(X1,a),multiplicative_identity)
| ~ equalish(X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_122]),c_0_25])]) ).
cnf(c_0_129,hypothesis,
equalish(additive_identity,multiply(additive_identity,multiply(additive_identity,a))),
inference(spm,[status(thm)],[c_0_33,c_0_123]) ).
cnf(c_0_130,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_131,plain,
( less_or_equal(X1,multiply(X2,X3))
| ~ less_or_equal(additive_identity,X3)
| ~ less_or_equal(additive_identity,X2)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(additive_identity,multiply(additive_identity,additive_identity)),X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_133,plain,
equalish(add(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_127,c_0_40]) ).
cnf(c_0_134,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(X2,a))
| ~ equalish(X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_128]) ).
cnf(c_0_135,hypothesis,
equalish(additive_identity,multiply(multiply(additive_identity,additive_identity),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_129]),c_0_25]),c_0_40])]) ).
cnf(c_0_136,axiom,
~ equalish(additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_137,plain,
( equalish(multiply(X1,X2),X3)
| ~ less_or_equal(multiply(X1,X2),X3)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X1)
| ~ equalish(additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
less_or_equal(multiply(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_139,plain,
equalish(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_140,negated_conjecture,
~ equalish(multiply(additive_identity,additive_identity),additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]) ).
cnf(c_0_141,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_115]),c_0_139])]),c_0_140]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD040-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:28:50 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 34.75/21.01 % Version : CSE_E---1.7
% 34.75/21.01 % Problem : theBenchmark.p
% 34.75/21.01 % SZS status Unsatisfiable for theBenchmark.p
% 34.75/21.01 % SZS output start CNFRefutation
% See solution above
% 34.97/21.16 % Total time : 15.395s
%------------------------------------------------------------------------------