%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : FLD068-1 : 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 : n031.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 04:18:29 PM UTC 2026
% Result : Unsatisfiable 39.00s 23.40s
% Output : CNFRefutation 39.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of clauses : 96 ( 31 unt; 3 nHn; 96 RR)
% Number of literals : 194 ( 0 equ; 97 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; 4 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
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(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(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_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_less_or_equal_4,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_4) ).
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(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_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(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(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(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(less_or_equal_3,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
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(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(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(c_0_20,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_21,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_20]) ).
cnf(c_0_22,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_23,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_24,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_26,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_27,hypothesis,
( less_or_equal(X1,b)
| ~ equalish(b,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_29,hypothesis,
equalish(multiply(multiplicative_identity,b),b),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_30,hypothesis,
equalish(add(additive_identity,b),b),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_31,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_32,hypothesis,
( less_or_equal(X1,b)
| less_or_equal(b,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_33,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_34,negated_conjecture,
~ less_or_equal(a,b),
not_less_or_equal_4 ).
cnf(c_0_35,hypothesis,
( less_or_equal(X1,b)
| ~ equalish(b,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_36,hypothesis,
equalish(b,multiply(multiplicative_identity,b)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_38,hypothesis,
equalish(b,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_39,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_40,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_41,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_42,hypothesis,
less_or_equal(b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_43,hypothesis,
( less_or_equal(X1,b)
| ~ equalish(multiply(multiplicative_identity,b),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,hypothesis,
( equalish(X1,add(additive_identity,b))
| ~ equalish(X1,b) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_46,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
cnf(c_0_47,hypothesis,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,hypothesis,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_29])]) ).
cnf(c_0_49,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,X2)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_45]) ).
cnf(c_0_50,hypothesis,
equalish(additive_identity,add(a,additive_inverse(a))),
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_51,axiom,
( less_or_equal(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ less_or_equal(X1,X3) ),
compatibility_of_order_relation_and_addition ).
cnf(c_0_52,hypothesis,
less_or_equal(add(additive_identity,b),a),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,hypothesis,
( less_or_equal(add(add(additive_identity,b),X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,hypothesis,
( less_or_equal(add(add(additive_identity,b),additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_57,hypothesis,
less_or_equal(add(add(additive_identity,b),additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_33])]) ).
cnf(c_0_58,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_59,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(add(additive_identity,b),additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_57]) ).
cnf(c_0_60,hypothesis,
( equalish(add(add(additive_identity,b),X1),add(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_30]) ).
cnf(c_0_61,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_62,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
less_or_equal_3 ).
cnf(c_0_63,hypothesis,
( less_or_equal(add(b,additive_inverse(a)),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( equalish(add(b,additive_inverse(a)),additive_identity)
| ~ less_or_equal(add(b,additive_inverse(a)),additive_identity) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,hypothesis,
less_or_equal(add(b,additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_56]),c_0_33])]) ).
cnf(c_0_66,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_67,negated_conjecture,
equalish(add(b,additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_68,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_37,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( equalish(add(add(b,additive_inverse(a)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_67]) ).
cnf(c_0_70,hypothesis,
equalish(add(add(b,additive_inverse(a)),a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_33])]) ).
cnf(c_0_71,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,X2)
| ~ equalish(b,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_72,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(add(b,additive_inverse(a)),a)) ),
inference(spm,[status(thm)],[c_0_37,c_0_70]) ).
cnf(c_0_73,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_74,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_71,c_0_38]) ).
cnf(c_0_75,hypothesis,
( less_or_equal(add(add(b,additive_inverse(a)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_65]) ).
cnf(c_0_76,hypothesis,
( equalish(add(b,add(additive_inverse(a),a)),a)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_33]),c_0_22])]) ).
cnf(c_0_77,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_78,hypothesis,
less_or_equal(add(add(b,additive_inverse(a)),b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_22])]) ).
cnf(c_0_79,negated_conjecture,
( less_or_equal(X1,add(b,additive_inverse(a)))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_62]) ).
cnf(c_0_80,hypothesis,
equalish(add(b,add(additive_inverse(a),a)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_56]),c_0_33])]) ).
cnf(c_0_81,hypothesis,
( equalish(add(X1,b),add(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_22]) ).
cnf(c_0_82,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_83,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(add(b,additive_inverse(a)),b)) ),
inference(spm,[status(thm)],[c_0_41,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( less_or_equal(add(X1,X2),add(add(b,additive_inverse(a)),X2))
| ~ less_or_equal(X1,additive_identity)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_79]) ).
cnf(c_0_85,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(b,add(additive_inverse(a),a))) ),
inference(spm,[status(thm)],[c_0_37,c_0_80]) ).
cnf(c_0_86,hypothesis,
( equalish(add(add(X1,X2),b),add(b,add(X1,X2)))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_87,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_88,negated_conjecture,
( less_or_equal(add(X1,b),b)
| ~ less_or_equal(X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_22])]) ).
cnf(c_0_89,hypothesis,
( equalish(add(add(additive_inverse(a),a),b),a)
| ~ defined(additive_inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_33])]) ).
cnf(c_0_90,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(a,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_50]) ).
cnf(c_0_91,plain,
( equalish(add(X1,additive_inverse(X2)),add(additive_inverse(X2),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_56]) ).
cnf(c_0_92,negated_conjecture,
( less_or_equal(X1,b)
| ~ less_or_equal(X2,additive_identity)
| ~ equalish(add(X2,b),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_88]) ).
cnf(c_0_93,hypothesis,
equalish(add(add(additive_inverse(a),a),b),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_56]),c_0_33])]) ).
cnf(c_0_94,hypothesis,
less_or_equal(add(additive_inverse(a),a),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_33])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD068-1 : 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
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:32:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 39.00/23.40 % Version : CSE_E---1.7
% 39.00/23.40 % Problem : theBenchmark.p
% 39.00/23.40 % SZS status Unsatisfiable for theBenchmark.p
% 39.00/23.40 % SZS output start CNFRefutation
% See solution above
% 39.10/23.54 % Total time : 17.402s
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