%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD063-1 : 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 : n020.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 04:18:27 PM UTC 2026
% Result : Unsatisfiable 239.39s 100.26s
% Output : CNFRefutation 241.78s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_111)
% 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/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(associativity_addition,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(less_or_equal_3,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(well_definedness_of_additive_inverse,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/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,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse,
[final] ).
cnf(i_0_53,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality,
[final] ).
cnf(i_0_54,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
less_or_equal_3,
[final] ).
cnf(i_0_55,negated_conjecture,
~ less_or_equal(a,b),
not_less_or_equal_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(b),
b_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(b,b),
inference(scs_inference,[],[i_0_58,i_0_53]) ).
cnf(i_0_64,plain,
less_or_equal(b,a),
inference(scs_inference,[],[i_0_55,i_0_58,i_0_59,i_0_53,i_0_50]) ).
cnf(i_0_73,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_60,i_0_53]) ).
cnf(i_0_80,plain,
equalish(additive_identity,additive_identity),
inference(scs_inference,[],[i_0_61,i_0_53]) ).
cnf(i_0_87,plain,
equalish(a,a),
inference(scs_inference,[],[i_0_59,i_0_53]) ).
cnf(i_0_91,plain,
less_or_equal(multiplicative_identity,multiplicative_identity),
inference(scs_inference,[],[i_0_60,i_0_50]) ).
cnf(i_0_93,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51]) ).
cnf(i_0_95,plain,
defined(additive_inverse(multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57]) ).
cnf(i_0_97,plain,
equalish(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48]) ).
cnf(i_0_99,plain,
equalish(add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49]) ).
cnf(i_0_101,plain,
equalish(add(multiplicative_identity,additive_inverse(multiplicative_identity)),additive_identity),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49,i_0_45]) ).
cnf(i_0_103,plain,
defined(multiply(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49,i_0_45,i_0_46]) ).
cnf(i_0_105,plain,
defined(add(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49,i_0_45,i_0_46,i_0_47]) ).
cnf(i_0_107,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(scs_inference,[],[i_0_56,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49,i_0_45,i_0_46,i_0_47,i_0_52]) ).
cnf(i_0_262,plain,
equalish(multiply(b,multiply(b,b)),multiply(multiply(b,b),b)),
inference(scs_inference,[],[i_0_58,i_0_32]) ).
cnf(i_0_264,plain,
equalish(add(b,add(b,b)),add(add(b,b),b)),
inference(scs_inference,[],[i_0_58,i_0_32,i_0_33]) ).
cnf(i_0_115,plain,
equalish(multiply(a,multiplicative_identity),multiply(a,multiplicative_identity)),
inference(scs_inference,[],[i_0_54,i_0_56,i_0_87,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49,i_0_45,i_0_46,i_0_47,i_0_52,i_0_37,i_0_38,i_0_34,i_0_35]) ).
cnf(i_0_117,plain,
equalish(add(a,multiplicative_identity),add(a,multiplicative_identity)),
inference(scs_inference,[],[i_0_54,i_0_56,i_0_87,i_0_60,i_0_50,i_0_51,i_0_57,i_0_48,i_0_49,i_0_45,i_0_46,i_0_47,i_0_52,i_0_37,i_0_38,i_0_34,i_0_35,i_0_36]) ).
cnf(i_0_132,plain,
equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_97,i_0_51]) ).
cnf(i_0_148,plain,
~ equalish(additive_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_54,i_0_111,i_0_103,i_0_97,i_0_56,i_0_51,i_0_46,i_0_47,i_0_37,i_0_38,i_0_34,i_0_35,i_0_36,i_0_44]) ).
cnf(i_0_175,plain,
equalish(multiplicative_identity,add(additive_identity,multiplicative_identity)),
inference(scs_inference,[],[i_0_99,i_0_51]) ).
cnf(i_0_451,plain,
equalish(multiply(multiply(b,b),b),multiply(b,multiply(b,b))),
inference(scs_inference,[],[i_0_262,i_0_51]) ).
cnf(i_0_504,plain,
equalish(add(add(b,b),b),add(b,add(b,b))),
inference(scs_inference,[],[i_0_264,i_0_51]) ).
cnf(i_0_506,plain,
less_or_equal(add(additive_inverse(b),b),add(additive_inverse(a),b)),
inference(scs_inference,[],[i_0_54,i_0_264,i_0_58,i_0_51,i_0_34]) ).
cnf(c_0_87,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
i_0_51 ).
cnf(c_0_88,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
i_0_45 ).
cnf(c_0_89,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
i_0_48 ).
cnf(c_0_90,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
i_0_42 ).
cnf(c_0_91,plain,
( equalish(additive_identity,add(X1,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_92,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
i_0_50 ).
cnf(c_0_93,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
i_0_44 ).
cnf(c_0_94,plain,
( equalish(X1,multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_89]) ).
cnf(c_0_95,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_38 ).
cnf(c_0_96,plain,
( less_or_equal(add(X1,additive_inverse(X1)),X2)
| ~ less_or_equal(additive_identity,X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_92]) ).
cnf(c_0_98,axiom,
defined(additive_identity),
i_0_61 ).
cnf(c_0_99,plain,
( equalish(X1,multiply(multiplicative_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
equalish(b,b),
i_0_62 ).
cnf(c_0_101,hypothesis,
defined(b),
i_0_58 ).
cnf(c_0_102,plain,
( less_or_equal(add(X1,X2),X3)
| ~ less_or_equal(add(X2,X1),X3)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_95]) ).
cnf(c_0_103,plain,
( less_or_equal(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]) ).
cnf(c_0_104,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
i_0_57 ).
cnf(c_0_105,plain,
equalish(b,multiply(multiplicative_identity,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101])]) ).
cnf(c_0_106,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
i_0_41 ).
cnf(c_0_107,plain,
( less_or_equal(add(additive_inverse(X1),X1),additive_identity)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_108,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
i_0_34 ).
cnf(c_0_109,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
i_0_54 ).
cnf(c_0_110,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
i_0_49 ).
cnf(c_0_111,plain,
( less_or_equal(multiply(multiplicative_identity,b),X1)
| ~ less_or_equal(b,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_105]) ).
cnf(c_0_112,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,add(additive_inverse(X2),X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( less_or_equal(add(additive_inverse(b),X1),add(additive_inverse(a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,hypothesis,
defined(a),
i_0_59 ).
cnf(c_0_115,plain,
( equalish(X1,add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_110]) ).
cnf(c_0_116,plain,
less_or_equal(b,a),
i_0_64 ).
cnf(c_0_117,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(multiply(multiplicative_identity,X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_89]) ).
cnf(c_0_118,plain,
less_or_equal(multiply(multiplicative_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_97]),c_0_101])]) ).
cnf(c_0_119,negated_conjecture,
less_or_equal(add(additive_inverse(b),a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114])]) ).
cnf(c_0_120,plain,
( equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_115]) ).
cnf(c_0_121,plain,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(add(X2,additive_inverse(X2)),X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_88]) ).
cnf(c_0_122,plain,
( less_or_equal(add(b,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_116]) ).
cnf(c_0_123,plain,
( less_or_equal(add(additive_identity,X1),X2)
| ~ less_or_equal(X1,X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_115]) ).
cnf(c_0_124,plain,
less_or_equal(b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_101])]) ).
cnf(c_0_125,negated_conjecture,
( less_or_equal(add(a,additive_inverse(b)),additive_identity)
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_119]),c_0_114])]) ).
cnf(c_0_126,plain,
equalish(b,add(additive_identity,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_100]),c_0_101])]) ).
cnf(c_0_127,plain,
( less_or_equal(additive_identity,add(a,additive_inverse(b)))
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_101])]) ).
cnf(c_0_128,plain,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_101])]) ).
cnf(c_0_129,negated_conjecture,
less_or_equal(add(a,additive_inverse(b)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_104]),c_0_101])]) ).
cnf(c_0_130,plain,
equalish(add(additive_identity,b),b),
inference(spm,[status(thm)],[c_0_87,c_0_126]) ).
cnf(c_0_131,plain,
less_or_equal(additive_identity,add(a,additive_inverse(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_104]),c_0_101])]) ).
cnf(c_0_132,plain,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_106,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( less_or_equal(add(add(a,additive_inverse(b)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_129]) ).
cnf(c_0_134,plain,
( less_or_equal(b,X1)
| ~ less_or_equal(add(additive_identity,b),X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_130]) ).
cnf(c_0_135,plain,
( less_or_equal(add(additive_identity,X1),add(add(a,additive_inverse(b)),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_131]) ).
cnf(c_0_136,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
i_0_43 ).
cnf(c_0_137,plain,
less_or_equal(add(add(a,additive_inverse(b)),b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_101])]) ).
cnf(c_0_138,plain,
less_or_equal(b,add(add(a,additive_inverse(b)),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_101])]) ).
cnf(c_0_139,plain,
equalish(b,add(add(a,additive_inverse(b)),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138])]) ).
cnf(c_0_140,plain,
equalish(add(add(a,additive_inverse(b)),b),b),
inference(spm,[status(thm)],[c_0_87,c_0_139]) ).
cnf(c_0_141,plain,
( equalish(X1,b)
| ~ equalish(X1,add(add(a,additive_inverse(b)),b)) ),
inference(spm,[status(thm)],[c_0_93,c_0_140]) ).
cnf(c_0_142,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
i_0_33 ).
cnf(c_0_143,plain,
( equalish(add(a,add(additive_inverse(b),b)),b)
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_101]),c_0_114])]) ).
cnf(c_0_144,plain,
equalish(add(a,add(additive_inverse(b),b)),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_104]),c_0_101])]) ).
cnf(c_0_145,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_95]) ).
cnf(c_0_146,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
i_0_47 ).
cnf(c_0_147,plain,
( equalish(X1,b)
| ~ equalish(X1,add(a,add(additive_inverse(b),b))) ),
inference(spm,[status(thm)],[c_0_93,c_0_144]) ).
cnf(c_0_148,plain,
( equalish(add(X1,add(X2,X3)),add(X3,add(X1,X2)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_142]),c_0_146]) ).
cnf(c_0_149,plain,
( equalish(add(additive_inverse(b),add(b,a)),b)
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_114]),c_0_101])]) ).
cnf(c_0_150,plain,
equalish(add(additive_inverse(b),add(b,a)),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_104]),c_0_101])]) ).
cnf(c_0_151,plain,
( equalish(X1,b)
| ~ equalish(X1,add(additive_inverse(b),add(b,a))) ),
inference(spm,[status(thm)],[c_0_93,c_0_150]) ).
cnf(c_0_152,plain,
( equalish(add(add(X1,X2),X3),add(X1,add(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_142]) ).
cnf(c_0_153,plain,
( equalish(add(add(additive_inverse(b),b),a),b)
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_114]),c_0_101])]) ).
cnf(c_0_154,plain,
equalish(add(add(additive_inverse(b),b),a),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_104]),c_0_101])]) ).
cnf(c_0_155,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
i_0_36 ).
cnf(c_0_156,plain,
( equalish(X1,b)
| ~ equalish(X1,add(add(additive_inverse(b),b),a)) ),
inference(spm,[status(thm)],[c_0_93,c_0_154]) ).
cnf(c_0_157,plain,
( equalish(add(add(X1,X2),X3),add(add(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_95]) ).
cnf(c_0_158,plain,
( equalish(add(add(b,additive_inverse(b)),a),b)
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_114]),c_0_101])]) ).
cnf(c_0_159,plain,
equalish(add(add(b,additive_inverse(b)),a),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_104]),c_0_101])]) ).
cnf(c_0_160,plain,
( equalish(X1,b)
| ~ equalish(X1,add(add(b,additive_inverse(b)),a)) ),
inference(spm,[status(thm)],[c_0_93,c_0_159]) ).
cnf(c_0_161,plain,
( equalish(add(additive_identity,X1),add(add(X2,additive_inverse(X2)),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_155,c_0_91]) ).
cnf(c_0_162,plain,
equalish(add(additive_identity,a),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_114]),c_0_101])]) ).
cnf(c_0_163,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_110]) ).
cnf(c_0_164,plain,
equalish(b,add(additive_identity,a)),
inference(spm,[status(thm)],[c_0_87,c_0_162]) ).
cnf(c_0_165,plain,
equalish(b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_114])]) ).
cnf(c_0_166,plain,
( less_or_equal(a,X1)
| ~ less_or_equal(b,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_165]) ).
cnf(c_0_167,negated_conjecture,
~ less_or_equal(a,b),
i_0_55 ).
cnf(c_0_168,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_97]),c_0_101])]),c_0_167]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD063-1 : 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
% 0.13/0.32 % Computer : n020.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 17:31:05 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 239.39/100.26 % Version : CSE_E---1.7
% 239.39/100.26 % Problem : theBenchmark.p
% 239.39/100.26 % SZS status Unsatisfiable for theBenchmark.p
% 239.39/100.26 % SZS output start CNFRefutation
% See solution above
% 241.78/102.60 % Total time : 90.487s
%------------------------------------------------------------------------------