%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD020-1 : 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 : n026.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 04:18:14 PM UTC 2026
% Result : Unsatisfiable 271.80s 100.27s
% Output : CNFRefutation 272.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 31
% Syntax : Number of clauses : 179 ( 75 unt; 9 nHn; 179 RR)
% Number of literals : 370 ( 0 equ; 193 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 197 ( 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(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(add_equals_a_3,negated_conjecture,
equalish(add(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_a_3) ).
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(m_not_equal_to_additive_identity_4,negated_conjecture,
~ equalish(m,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_not_equal_to_additive_identity_4) ).
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(m_is_defined,hypothesis,
defined(m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_defined) ).
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_31,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_32,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication,
[final] ).
cnf(i_0_33,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition,
[final] ).
cnf(i_0_34,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_35,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication,
[final] ).
cnf(i_0_36,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition,
[final] ).
cnf(i_0_37,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication,
[final] ).
cnf(i_0_38,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition,
[final] ).
cnf(i_0_39,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_40,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication,
[final] ).
cnf(i_0_41,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation,
[final] ).
cnf(i_0_42,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation,
[final] ).
cnf(i_0_43,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation,
[final] ).
cnf(i_0_44,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality,
[final] ).
cnf(i_0_45,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition,
[final] ).
cnf(i_0_46,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication,
[final] ).
cnf(i_0_47,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition,
[final] ).
cnf(i_0_48,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication,
[final] ).
cnf(i_0_49,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition,
[final] ).
cnf(i_0_50,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation,
[final] ).
cnf(i_0_51,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality,
[final] ).
cnf(i_0_52,negated_conjecture,
equalish(add(m,a),a),
add_equals_a_3,
[final] ).
cnf(i_0_53,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse,
[final] ).
cnf(i_0_54,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality,
[final] ).
cnf(i_0_55,negated_conjecture,
~ equalish(m,additive_identity),
m_not_equal_to_additive_identity_4,
[final] ).
cnf(i_0_56,axiom,
~ equalish(additive_identity,multiplicative_identity),
different_identities,
[final] ).
cnf(i_0_57,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse,
[final] ).
cnf(i_0_58,hypothesis,
defined(m),
m_is_defined,
[final] ).
cnf(i_0_59,hypothesis,
defined(a),
a_is_defined,
[final] ).
cnf(i_0_60,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity,
[final] ).
cnf(i_0_61,axiom,
defined(additive_identity),
well_definedness_of_additive_identity,
[final] ).
cnf(i_0_62,plain,
equalish(a,add(m,a)),
inference(scs_inference,[],[i_0_52,i_0_51]) ).
cnf(i_0_64,plain,
equalish(m,m),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_51,i_0_54]) ).
cnf(i_0_66,plain,
equalish(a,a),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_51,i_0_54,i_0_44]) ).
cnf(i_0_70,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_60,i_0_54]) ).
cnf(i_0_76,plain,
equalish(additive_identity,additive_identity),
inference(scs_inference,[],[i_0_61,i_0_54]) ).
cnf(i_0_91,plain,
defined(additive_inverse(a)),
inference(scs_inference,[],[i_0_59,i_0_57]) ).
cnf(i_0_93,plain,
equalish(multiply(multiplicative_identity,a),a),
inference(scs_inference,[],[i_0_59,i_0_57,i_0_48]) ).
cnf(i_0_95,plain,
equalish(add(additive_identity,a),a),
inference(scs_inference,[],[i_0_59,i_0_57,i_0_48,i_0_49]) ).
cnf(i_0_97,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(scs_inference,[],[i_0_59,i_0_57,i_0_48,i_0_49,i_0_45]) ).
cnf(i_0_99,plain,
~ equalish(additive_identity,m),
inference(scs_inference,[],[i_0_55,i_0_59,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51]) ).
cnf(i_0_101,plain,
defined(multiply(a,a)),
inference(scs_inference,[],[i_0_55,i_0_59,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46]) ).
cnf(i_0_103,plain,
defined(add(a,a)),
inference(scs_inference,[],[i_0_55,i_0_59,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47]) ).
cnf(i_0_105,plain,
defined(multiplicative_inverse(m)),
inference(scs_inference,[],[i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53]) ).
cnf(i_0_107,plain,
equalish(multiply(a,a),multiply(a,a)),
inference(scs_inference,[],[i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37]) ).
cnf(i_0_109,plain,
equalish(add(a,a),add(a,a)),
inference(scs_inference,[],[i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38]) ).
cnf(i_0_111,plain,
equalish(multiply(add(m,a),a),multiply(a,a)),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35]) ).
cnf(i_0_113,plain,
equalish(add(add(m,a),a),add(a,a)),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36]) ).
cnf(i_0_115,plain,
equalish(multiply(m,multiplicative_inverse(m)),multiplicative_identity),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36,i_0_40]) ).
cnf(i_0_117,plain,
less_or_equal(a,a),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36,i_0_40,i_0_50]) ).
cnf(i_0_119,plain,
equalish(multiply(a,multiply(a,a)),multiply(multiply(a,a),a)),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36,i_0_40,i_0_50,i_0_32]) ).
cnf(i_0_121,plain,
equalish(add(a,add(a,a)),add(add(a,a),a)),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36,i_0_40,i_0_50,i_0_32,i_0_33]) ).
cnf(i_0_123,plain,
equalish(add(multiply(a,a),multiply(a,a)),multiply(add(a,a),a)),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36,i_0_40,i_0_50,i_0_32,i_0_33,i_0_31]) ).
cnf(i_0_127,plain,
less_or_equal(add(a,a),add(a,a)),
inference(scs_inference,[],[i_0_52,i_0_55,i_0_59,i_0_58,i_0_57,i_0_48,i_0_49,i_0_45,i_0_51,i_0_46,i_0_47,i_0_53,i_0_37,i_0_38,i_0_35,i_0_36,i_0_40,i_0_50,i_0_32,i_0_33,i_0_31,i_0_43,i_0_34]) ).
cnf(i_0_548,plain,
defined(additive_inverse(m)),
inference(scs_inference,[],[i_0_58,i_0_57]) ).
cnf(i_0_550,plain,
equalish(multiply(multiplicative_identity,m),m),
inference(scs_inference,[],[i_0_58,i_0_57,i_0_48]) ).
cnf(i_0_552,plain,
equalish(add(additive_identity,m),m),
inference(scs_inference,[],[i_0_58,i_0_57,i_0_48,i_0_49]) ).
cnf(i_0_554,plain,
equalish(multiply(add(m,a),additive_inverse(m)),multiply(a,additive_inverse(m))),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_57,i_0_48,i_0_49,i_0_35]) ).
cnf(i_0_556,plain,
equalish(add(add(m,a),additive_inverse(m)),add(a,additive_inverse(m))),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_57,i_0_48,i_0_49,i_0_35,i_0_36]) ).
cnf(i_0_560,plain,
equalish(add(additive_inverse(m),additive_inverse(m)),add(additive_inverse(m),additive_inverse(m))),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_57,i_0_48,i_0_49,i_0_35,i_0_36,i_0_37,i_0_38]) ).
cnf(i_0_562,plain,
defined(multiply(m,m)),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_57,i_0_48,i_0_49,i_0_35,i_0_36,i_0_37,i_0_38,i_0_46]) ).
cnf(i_0_564,plain,
defined(add(m,m)),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_57,i_0_48,i_0_49,i_0_35,i_0_36,i_0_37,i_0_38,i_0_46,i_0_47]) ).
cnf(i_0_570,plain,
equalish(add(additive_inverse(m),additive_inverse(additive_inverse(m))),additive_identity),
inference(scs_inference,[],[i_0_52,i_0_58,i_0_57,i_0_48,i_0_49,i_0_35,i_0_36,i_0_37,i_0_38,i_0_46,i_0_47,i_0_32,i_0_33,i_0_45]) ).
cnf(i_0_773,plain,
defined(additive_inverse(multiplicative_identity)),
inference(scs_inference,[],[i_0_60,i_0_57]) ).
cnf(i_0_775,plain,
equalish(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_60,i_0_57,i_0_48]) ).
cnf(i_0_777,plain,
equalish(add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_60,i_0_57,i_0_48,i_0_49]) ).
cnf(c_0_574,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
i_0_44 ).
cnf(c_0_575,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
i_0_45 ).
cnf(c_0_576,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
i_0_51 ).
cnf(c_0_577,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
i_0_49 ).
cnf(c_0_578,plain,
( equalish(X1,additive_identity)
| ~ defined(X2)
| ~ equalish(X1,add(X2,additive_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_574,c_0_575]) ).
cnf(c_0_579,plain,
( equalish(X1,add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_576,c_0_577]) ).
cnf(c_0_580,axiom,
defined(additive_identity),
i_0_61 ).
cnf(c_0_581,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
i_0_50 ).
cnf(c_0_582,hypothesis,
defined(m),
i_0_58 ).
cnf(c_0_583,plain,
equalish(add(additive_identity,m),m),
i_0_552 ).
cnf(c_0_584,plain,
( equalish(additive_inverse(additive_identity),additive_identity)
| ~ defined(additive_inverse(additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_578,c_0_579]),c_0_580])]) ).
cnf(c_0_585,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
i_0_57 ).
cnf(c_0_586,hypothesis,
( less_or_equal(X1,m)
| less_or_equal(m,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_581,c_0_582]) ).
cnf(c_0_587,plain,
( equalish(X1,m)
| ~ equalish(X1,add(additive_identity,m)) ),
inference(spm,[status(thm)],[c_0_574,c_0_583]) ).
cnf(c_0_588,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_38 ).
cnf(c_0_589,plain,
( less_or_equal(X1,additive_identity)
| less_or_equal(additive_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_581,c_0_580]) ).
cnf(c_0_590,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_584,c_0_585]),c_0_580])]) ).
cnf(c_0_591,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
i_0_42 ).
cnf(c_0_592,hypothesis,
less_or_equal(m,m),
inference(spm,[status(thm)],[c_0_586,c_0_582]) ).
cnf(c_0_593,plain,
equalish(add(m,additive_identity),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_587,c_0_588]),c_0_580]),c_0_582])]) ).
cnf(c_0_594,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_589,c_0_580]) ).
cnf(c_0_595,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_576,c_0_590]) ).
cnf(c_0_596,hypothesis,
( less_or_equal(X1,m)
| ~ equalish(m,X1) ),
inference(spm,[status(thm)],[c_0_591,c_0_592]) ).
cnf(c_0_597,plain,
equalish(m,add(m,additive_identity)),
inference(spm,[status(thm)],[c_0_576,c_0_593]) ).
cnf(c_0_598,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_591,c_0_594]) ).
cnf(c_0_599,plain,
( equalish(X1,additive_inverse(additive_identity))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_574,c_0_595]) ).
cnf(c_0_600,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_574,c_0_588]) ).
cnf(c_0_601,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_47 ).
cnf(c_0_602,hypothesis,
( less_or_equal(X1,m)
| ~ equalish(m,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_591,c_0_596]) ).
cnf(c_0_603,plain,
( equalish(X1,add(m,additive_identity))
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_574,c_0_597]) ).
cnf(c_0_604,plain,
equalish(m,m),
i_0_64 ).
cnf(c_0_605,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_591,c_0_598]) ).
cnf(c_0_606,plain,
( equalish(X1,m)
| ~ equalish(X1,add(m,additive_identity)) ),
inference(spm,[status(thm)],[c_0_574,c_0_593]) ).
cnf(c_0_607,plain,
( equalish(additive_inverse(additive_identity),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_576,c_0_599]) ).
cnf(c_0_608,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
i_0_36 ).
cnf(c_0_609,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
i_0_33 ).
cnf(c_0_610,plain,
( equalish(add(additive_identity,add(X1,X2)),add(X2,X1))
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_600,c_0_577]),c_0_601]) ).
cnf(c_0_611,plain,
( equalish(X1,additive_inverse(additive_identity))
| ~ equalish(X2,additive_identity)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_574,c_0_599]) ).
cnf(c_0_612,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
i_0_43 ).
cnf(c_0_613,plain,
( less_or_equal(X1,m)
| ~ equalish(add(m,additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_602,c_0_603]),c_0_604])]) ).
cnf(c_0_614,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_605,c_0_595]) ).
cnf(c_0_615,plain,
( equalish(additive_inverse(additive_identity),m)
| ~ equalish(add(m,additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_606,c_0_607]) ).
cnf(c_0_616,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X3)
| ~ equalish(X1,add(X4,X3))
| ~ equalish(X4,X2) ),
inference(spm,[status(thm)],[c_0_574,c_0_608]) ).
cnf(c_0_617,plain,
( equalish(X1,add(add(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,add(X2,add(X3,X4))) ),
inference(spm,[status(thm)],[c_0_574,c_0_609]) ).
cnf(c_0_618,plain,
equalish(add(additive_identity,add(additive_identity,m)),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_606,c_0_610]),c_0_582]),c_0_580])]) ).
cnf(c_0_619,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
i_0_97 ).
cnf(c_0_620,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_574,c_0_590]) ).
cnf(c_0_621,plain,
( equalish(X1,additive_inverse(additive_identity))
| ~ equalish(X1,add(additive_identity,additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_611,c_0_577]),c_0_580])]) ).
cnf(c_0_622,plain,
( equalish(m,X1)
| ~ less_or_equal(m,X1)
| ~ equalish(add(m,additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_612,c_0_613]) ).
cnf(c_0_623,plain,
( less_or_equal(m,additive_identity)
| ~ equalish(add(m,additive_identity),additive_identity) ),
inference(spm,[status(thm)],[c_0_614,c_0_615]) ).
cnf(c_0_624,negated_conjecture,
~ equalish(m,additive_identity),
i_0_55 ).
cnf(c_0_625,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X3)
| ~ defined(X4)
| ~ defined(X5)
| ~ equalish(X1,add(X5,add(X4,X3)))
| ~ equalish(add(X5,X4),X2) ),
inference(spm,[status(thm)],[c_0_616,c_0_617]) ).
cnf(c_0_626,plain,
equalish(m,add(additive_identity,add(additive_identity,m))),
inference(spm,[status(thm)],[c_0_576,c_0_618]) ).
cnf(c_0_627,plain,
equalish(additive_identity,add(a,additive_inverse(a))),
inference(spm,[status(thm)],[c_0_576,c_0_619]) ).
cnf(c_0_628,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_620,c_0_621]) ).
cnf(c_0_629,plain,
( equalish(add(X1,additive_identity),m)
| ~ equalish(X1,m) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_606,c_0_608]),c_0_580])]) ).
cnf(c_0_630,plain,
( equalish(add(m,additive_identity),X1)
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_576,c_0_603]) ).
cnf(c_0_631,plain,
~ equalish(add(m,additive_identity),additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_622,c_0_623]),c_0_624]) ).
cnf(c_0_632,plain,
( equalish(add(add(X1,X2),X3),add(X1,add(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_576,c_0_609]) ).
cnf(c_0_633,plain,
( equalish(m,add(X1,m))
| ~ equalish(add(additive_identity,additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_625,c_0_626]),c_0_582]),c_0_580])]) ).
cnf(c_0_634,plain,
( equalish(X1,add(a,additive_inverse(a)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_574,c_0_627]) ).
cnf(c_0_635,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_628,c_0_588]),c_0_580])]) ).
cnf(c_0_636,plain,
( equalish(X1,m)
| ~ equalish(X1,add(X2,additive_identity))
| ~ equalish(X2,m) ),
inference(spm,[status(thm)],[c_0_574,c_0_629]) ).
cnf(c_0_637,plain,
~ equalish(additive_inverse(additive_identity),m),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_620,c_0_630]),c_0_631]) ).
cnf(c_0_638,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_574,c_0_577]) ).
cnf(c_0_639,plain,
( equalish(X1,add(X2,add(X3,X4)))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,add(add(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_574,c_0_632]) ).
cnf(c_0_640,plain,
equalish(m,add(add(a,additive_inverse(a)),m)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_633,c_0_634]),c_0_635])]) ).
cnf(c_0_641,plain,
defined(additive_inverse(a)),
i_0_91 ).
cnf(c_0_642,hypothesis,
defined(a),
i_0_59 ).
cnf(c_0_643,plain,
( ~ equalish(add(X1,additive_identity),additive_identity)
| ~ equalish(X1,m) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_636,c_0_607]),c_0_637]) ).
cnf(c_0_644,plain,
( equalish(add(X1,X2),X2)
| ~ defined(X2)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_638,c_0_608]) ).
cnf(c_0_645,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_574,c_0_619]) ).
cnf(c_0_646,plain,
( equalish(X1,add(X2,add(X3,X4)))
| ~ defined(X2)
| ~ defined(X4)
| ~ defined(X3)
| ~ equalish(X1,add(X3,add(X4,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_600,c_0_617]),c_0_601]) ).
cnf(c_0_647,plain,
equalish(m,add(a,add(additive_inverse(a),m))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_639,c_0_640]),c_0_582]),c_0_641]),c_0_642])]) ).
cnf(c_0_648,plain,
( ~ equalish(X1,m)
| ~ equalish(X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_643,c_0_644]),c_0_580])]) ).
cnf(c_0_649,plain,
( equalish(add(X1,additive_inverse(a)),additive_identity)
| ~ equalish(X1,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_645,c_0_608]),c_0_641])]) ).
cnf(c_0_650,plain,
( equalish(add(add(X1,X2),X3),X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| ~ equalish(X4,add(X1,add(X2,X3))) ),
inference(spm,[status(thm)],[c_0_576,c_0_617]) ).
cnf(c_0_651,plain,
equalish(m,add(m,add(a,additive_inverse(a)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_646,c_0_647]),c_0_582]),c_0_641]),c_0_642])]) ).
cnf(c_0_652,plain,
( ~ equalish(add(X1,additive_inverse(a)),m)
| ~ equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_648,c_0_649]) ).
cnf(c_0_653,plain,
equalish(add(add(m,a),additive_inverse(a)),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_650,c_0_651]),c_0_641]),c_0_642]),c_0_582])]) ).
cnf(c_0_654,negated_conjecture,
equalish(add(m,a),a),
i_0_52 ).
cnf(c_0_655,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_652,c_0_653]),c_0_654])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : FLD020-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n026.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 17:27:08 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 271.80/100.27 % Version : CSE_E---1.7
% 271.80/100.27 % Problem : theBenchmark.p
% 271.80/100.27 % SZS status Unsatisfiable for theBenchmark.p
% 271.80/100.27 % SZS output start CNFRefutation
% See solution above
% 272.99/101.49 % Total time : 97.708s
%------------------------------------------------------------------------------