%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD007-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:18:10 PM UTC 2026
% Result : Unsatisfiable 169.86s 93.03s
% Output : CNFRefutation 171.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 29
% Syntax : Number of clauses : 117 ( 38 unt; 6 nHn; 117 RR)
% Number of literals : 258 ( 0 equ; 143 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(associativity_addition,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
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/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_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/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(antisymmetry_of_order_relation,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(existence_of_inverse_addition,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(well_definedness_of_addition,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(additive_inverse_not_equal_to_a_2,negated_conjecture,
~ equalish(additive_inverse(additive_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_not_equal_to_a_2) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(i_0_29,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
distributivity,
[final] ).
cnf(i_0_30,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication,
[final] ).
cnf(i_0_31,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition,
[final] ).
cnf(i_0_32,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
compatibility_of_order_relation_and_addition,
[final] ).
cnf(i_0_33,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication,
[final] ).
cnf(i_0_34,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition,
[final] ).
cnf(i_0_35,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication,
[final] ).
cnf(i_0_36,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition,
[final] ).
cnf(i_0_37,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,
[final] ).
cnf(i_0_38,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication,
[final] ).
cnf(i_0_39,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation,
[final] ).
cnf(i_0_40,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation,
[final] ).
cnf(i_0_41,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation,
[final] ).
cnf(i_0_42,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality,
[final] ).
cnf(i_0_43,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition,
[final] ).
cnf(i_0_44,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication,
[final] ).
cnf(i_0_45,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition,
[final] ).
cnf(i_0_46,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication,
[final] ).
cnf(i_0_47,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition,
[final] ).
cnf(i_0_48,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation,
[final] ).
cnf(i_0_49,negated_conjecture,
~ equalish(additive_inverse(additive_inverse(a)),a),
additive_inverse_not_equal_to_a_2,
[final] ).
cnf(i_0_50,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality,
[final] ).
cnf(i_0_51,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse,
[final] ).
cnf(i_0_52,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality,
[final] ).
cnf(i_0_53,axiom,
~ equalish(additive_identity,multiplicative_identity),
different_identities,
[final] ).
cnf(i_0_54,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse,
[final] ).
cnf(i_0_55,hypothesis,
defined(a),
a_is_defined,
[final] ).
cnf(i_0_56,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity,
[final] ).
cnf(i_0_57,axiom,
defined(additive_identity),
well_definedness_of_additive_identity,
[final] ).
cnf(i_0_58,plain,
equalish(a,a),
inference(scs_inference,[],[i_0_55,i_0_52]) ).
cnf(i_0_62,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_56,i_0_52]) ).
cnf(i_0_66,plain,
equalish(additive_identity,additive_identity),
inference(scs_inference,[],[i_0_57,i_0_52]) ).
cnf(i_0_70,plain,
~ equalish(a,additive_inverse(additive_inverse(a))),
inference(scs_inference,[],[i_0_49,i_0_50]) ).
cnf(i_0_72,plain,
defined(additive_inverse(a)),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54]) ).
cnf(i_0_74,plain,
equalish(multiply(multiplicative_identity,a),a),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46]) ).
cnf(i_0_76,plain,
equalish(add(additive_identity,a),a),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46,i_0_47]) ).
cnf(i_0_78,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46,i_0_47,i_0_43]) ).
cnf(i_0_80,plain,
defined(multiply(a,a)),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46,i_0_47,i_0_43,i_0_44]) ).
cnf(i_0_82,plain,
defined(add(a,a)),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46,i_0_47,i_0_43,i_0_44,i_0_45]) ).
cnf(i_0_84,plain,
equalish(multiply(a,a),multiply(a,a)),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46,i_0_47,i_0_43,i_0_44,i_0_45,i_0_35]) ).
cnf(i_0_86,plain,
equalish(add(a,a),add(a,a)),
inference(scs_inference,[],[i_0_49,i_0_55,i_0_50,i_0_54,i_0_46,i_0_47,i_0_43,i_0_44,i_0_45,i_0_35,i_0_36]) ).
cnf(i_0_104,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(scs_inference,[],[i_0_53,i_0_50]) ).
cnf(i_0_451,plain,
defined(additive_inverse(multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_54]) ).
cnf(i_0_453,plain,
equalish(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_56,i_0_54,i_0_46]) ).
cnf(i_0_455,plain,
equalish(add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_56,i_0_54,i_0_46,i_0_47]) ).
cnf(i_0_461,plain,
defined(multiply(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_54,i_0_46,i_0_47,i_0_35,i_0_36,i_0_44]) ).
cnf(i_0_463,plain,
defined(add(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_54,i_0_46,i_0_47,i_0_35,i_0_36,i_0_44,i_0_45]) ).
cnf(i_0_688,plain,
defined(additive_inverse(additive_identity)),
inference(scs_inference,[],[i_0_57,i_0_54]) ).
cnf(i_0_690,plain,
equalish(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(scs_inference,[],[i_0_57,i_0_54,i_0_46]) ).
cnf(c_0_93,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
i_0_42 ).
cnf(c_0_94,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
i_0_78 ).
cnf(c_0_95,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_96,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_36 ).
cnf(c_0_97,hypothesis,
defined(a),
i_0_55 ).
cnf(c_0_98,plain,
defined(additive_inverse(a)),
i_0_72 ).
cnf(c_0_99,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
i_0_47 ).
cnf(c_0_100,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
i_0_34 ).
cnf(c_0_101,plain,
equalish(add(additive_inverse(a),a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98])]) ).
cnf(c_0_102,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_99]) ).
cnf(c_0_103,plain,
( equalish(add(add(additive_inverse(a),a),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_104,plain,
( equalish(add(add(additive_inverse(a),a),X1),X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_105,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(add(additive_inverse(a),a),X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_104]) ).
cnf(c_0_106,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
i_0_31 ).
cnf(c_0_107,plain,
( equalish(add(additive_inverse(a),add(a,X1)),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_97]),c_0_98])]) ).
cnf(c_0_108,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_inverse(a),add(a,X2))) ),
inference(spm,[status(thm)],[c_0_93,c_0_107]) ).
cnf(c_0_109,plain,
( equalish(add(add(a,X1),additive_inverse(a)),X1)
| ~ defined(add(a,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_96]),c_0_98])]) ).
cnf(c_0_110,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_45 ).
cnf(c_0_111,plain,
( equalish(add(add(a,X1),additive_inverse(a)),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_97])]) ).
cnf(c_0_112,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(add(a,X2),additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_93,c_0_111]) ).
cnf(c_0_113,plain,
( equalish(add(add(X1,X2),X3),add(add(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_96]) ).
cnf(c_0_114,plain,
equalish(add(additive_identity,a),a),
i_0_76 ).
cnf(c_0_115,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
i_0_43 ).
cnf(c_0_116,plain,
( equalish(add(add(X1,a),additive_inverse(a)),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_98]),c_0_97])]) ).
cnf(c_0_117,plain,
( equalish(X1,a)
| ~ equalish(X1,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_93,c_0_114]) ).
cnf(c_0_118,plain,
( equalish(add(add(X1,additive_inverse(X1)),X2),add(additive_identity,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_115]) ).
cnf(c_0_119,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(add(X2,a),additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_93,c_0_116]) ).
cnf(c_0_120,plain,
( equalish(add(add(X1,additive_inverse(X1)),a),a)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_97])]) ).
cnf(c_0_121,plain,
( equalish(add(additive_inverse(a),add(X1,a)),X1)
| ~ defined(add(X1,a))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_96]),c_0_98])]) ).
cnf(c_0_122,plain,
( equalish(X1,a)
| ~ defined(X2)
| ~ equalish(X1,add(add(X2,additive_inverse(X2)),a)) ),
inference(spm,[status(thm)],[c_0_93,c_0_120]) ).
cnf(c_0_123,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
i_0_54 ).
cnf(c_0_124,plain,
( equalish(add(additive_inverse(a),add(X1,a)),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_110]),c_0_97])]) ).
cnf(c_0_125,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
i_0_50 ).
cnf(c_0_126,plain,
( equalish(add(X1,add(additive_inverse(X1),a)),a)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_106]),c_0_97])]),c_0_123]) ).
cnf(c_0_127,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_inverse(a),add(X2,a))) ),
inference(spm,[status(thm)],[c_0_93,c_0_124]) ).
cnf(c_0_128,plain,
( equalish(a,add(X1,add(additive_inverse(X1),a)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_129,plain,
~ equalish(a,additive_inverse(additive_inverse(a))),
i_0_70 ).
cnf(c_0_130,plain,
~ defined(additive_inverse(additive_inverse(a))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_98])]),c_0_129]) ).
cnf(c_0_131,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_123]),c_0_98])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD007-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.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 17:26:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 169.86/93.03 % Version : CSE_E---1.7
% 169.86/93.03 % Problem : theBenchmark.p
% 169.86/93.03 % SZS status Unsatisfiable for theBenchmark.p
% 169.86/93.03 % SZS output start CNFRefutation
% See solution above
% 171.97/95.12 % Total time : 91.905s
%------------------------------------------------------------------------------