%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:22:57 PM UTC 2026
% Result : Unsatisfiable 7.73s 1.47s
% Output : CNFRefutation 7.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of clauses : 120 ( 37 unt; 8 nHn; 120 RR)
% Number of literals : 278 ( 0 equ; 155 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 185 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(associativity_addition_1,axiom,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(commutativity_addition,axiom,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
cnf(associativity_addition_2,axiom,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(totality_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_addition) ).
cnf(transitivity_of_order_relation,axiom,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_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(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(c_0_17,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_18,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_1]) ).
cnf(c_0_19,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_17 ).
cnf(c_0_20,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_21,plain,
( ~ sum(X5,X6,X3)
| ~ sum(X4,X6,X2)
| ~ sum(X1,X4,X5)
| sum(X1,X2,X3) ),
c_0_18 ).
cnf(c_0_22,hypothesis,
sum(additive_identity,b,b),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_25,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,b,X2)
| sum(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_addition_2]) ).
cnf(c_0_27,plain,
( ~ sum(X2,X1,X3)
| sum(X1,X2,X3) ),
c_0_23 ).
cnf(c_0_28,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_24 ).
cnf(c_0_29,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_31,plain,
( ~ sum(X4,X6,X3)
| ~ sum(X5,X2,X6)
| ~ sum(X4,X5,X1)
| sum(X1,X2,X3) ),
c_0_26 ).
cnf(c_0_32,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_33,hypothesis,
sum(b,additive_identity,b),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_34,plain,
( ~ defined(X1)
| sum(additive_identity,additive_inverse(X1),additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_35,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(b,X1,b) ),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_36,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),X1,additive_identity) ),
c_0_30 ).
cnf(c_0_37,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_38,hypothesis,
( ~ sum(X3,additive_identity,X1)
| ~ sum(X3,b,X2)
| sum(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_39,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_32 ).
cnf(c_0_40,hypothesis,
( ~ sum(X3,b,X1)
| ~ sum(X3,b,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_41,plain,
( ~ sum(X1,X4,additive_identity)
| ~ sum(X4,additive_inverse(X3),X2)
| ~ defined(X3)
| sum(X1,X2,additive_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_42,hypothesis,
sum(b,additive_inverse(additive_identity),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_43,hypothesis,
( ~ sum(additive_inverse(b),additive_identity,X1)
| sum(X1,b,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_36]),c_0_20])]) ).
cnf(c_0_44,plain,
( ~ defined(X1)
| sum(additive_inverse(X1),additive_identity,additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_45,plain,
( ~ defined(X1)
| ~ defined(X2)
| less_or_equal(X2,additive_inverse(X1))
| less_or_equal(additive_inverse(X1),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_46,hypothesis,
( ~ sum(additive_inverse(b),b,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_20])]) ).
cnf(c_0_47,hypothesis,
( ~ sum(X1,b,additive_identity)
| sum(X1,b,additive_inverse(additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_37])]) ).
cnf(c_0_48,hypothesis,
sum(additive_inverse(b),b,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_20])]) ).
cnf(c_0_49,plain,
( ~ defined(X1)
| ~ defined(X2)
| less_or_equal(additive_inverse(X2),additive_inverse(X1))
| less_or_equal(additive_inverse(X1),additive_inverse(X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_28]) ).
cnf(c_0_50,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_51,hypothesis,
sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_52,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_addition]) ).
cnf(c_0_53,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_54,hypothesis,
( ~ defined(X1)
| less_or_equal(additive_inverse(X1),additive_inverse(a))
| less_or_equal(additive_inverse(a),additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_56,hypothesis,
sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_57,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_addition]) ).
cnf(c_0_58,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X1,X2)) ),
c_0_52 ).
cnf(c_0_59,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_53 ).
cnf(c_0_60,hypothesis,
less_or_equal(additive_inverse(a),additive_inverse(a)),
inference(spm,[status(thm)],[c_0_54,c_0_50]) ).
cnf(c_0_61,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_55 ).
cnf(c_0_62,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_63,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,additive_identity,additive_inverse(additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_37])]) ).
cnf(c_0_64,plain,
( ~ defined(X1)
| less_or_equal(X1,additive_identity)
| less_or_equal(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_65,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
c_0_57 ).
cnf(c_0_66,hypothesis,
( ~ sum(additive_identity,b,X1)
| sum(X1,additive_identity,b) ),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_67,plain,
( ~ defined(X2)
| ~ defined(X1)
| sum(X1,X2,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_58]) ).
cnf(c_0_68,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ defined(X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_69,hypothesis,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_60])]) ).
cnf(c_0_70,plain,
( ~ sum(X2,additive_identity,X1)
| ~ less_or_equal(X2,additive_identity)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(additive_identity,X1,additive_inverse(additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_63]) ).
cnf(c_0_72,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_64,c_0_37]) ).
cnf(c_0_73,plain,
( ~ sum(X3,additive_inverse(X2),X1)
| ~ defined(X2)
| ~ less_or_equal(X3,additive_identity)
| less_or_equal(X1,additive_inverse(X2)) ),
inference(spm,[status(thm)],[c_0_61,c_0_34]) ).
cnf(c_0_74,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_order_relation]) ).
cnf(c_0_75,plain,
( ~ defined(X1)
| ~ defined(X2)
| sum(additive_identity,add(X1,X2),add(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_65]) ).
cnf(c_0_76,hypothesis,
sum(add(b,additive_identity),additive_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_37]),c_0_20])]) ).
cnf(c_0_77,hypothesis,
sum(additive_inverse(additive_identity),b,b),
inference(spm,[status(thm)],[c_0_27,c_0_42]) ).
cnf(c_0_78,hypothesis,
( ~ sum(additive_identity,additive_identity,X1)
| sum(additive_inverse(a),a,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_50])]) ).
cnf(c_0_79,hypothesis,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_62])]) ).
cnf(c_0_80,hypothesis,
less_or_equal(additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_56]),c_0_72]),c_0_37])]) ).
cnf(c_0_81,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_74 ).
cnf(c_0_82,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
less_or_equal_3 ).
cnf(c_0_83,plain,
( ~ defined(X1)
| sum(X1,additive_inverse(X1),additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_36]) ).
cnf(c_0_84,negated_conjecture,
~ less_or_equal(a,b),
inference(fof_simplification,[status(thm)],[not_less_or_equal_4]) ).
cnf(c_0_85,hypothesis,
( ~ sum(X2,additive_identity,X1)
| ~ less_or_equal(X2,b)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_61,c_0_33]) ).
cnf(c_0_86,plain,
( ~ defined(X1)
| ~ defined(X2)
| sum(add(X1,X2),additive_identity,add(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_75]) ).
cnf(c_0_87,plain,
( ~ sum(X4,add(X2,X3),X1)
| ~ defined(X2)
| ~ defined(X3)
| ~ less_or_equal(X4,additive_identity)
| less_or_equal(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_61,c_0_75]) ).
cnf(c_0_88,hypothesis,
sum(additive_identity,add(b,additive_identity),b),
inference(spm,[status(thm)],[c_0_27,c_0_76]) ).
cnf(c_0_89,hypothesis,
sum(additive_identity,a,a),
inference(spm,[status(thm)],[c_0_19,c_0_50]) ).
cnf(c_0_90,hypothesis,
( ~ sum(X3,b,X2)
| ~ sum(X1,X3,additive_inverse(additive_identity))
| sum(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_77]) ).
cnf(c_0_91,hypothesis,
( ~ sum(additive_identity,additive_identity,X1)
| sum(a,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_78]) ).
cnf(c_0_92,hypothesis,
sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_79]),c_0_80])]) ).
cnf(c_0_93,negated_conjecture,
( ~ less_or_equal(X1,additive_identity)
| less_or_equal(X1,add(b,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_94,plain,
( ~ sum(X2,additive_inverse(X3),X1)
| ~ defined(X3)
| ~ less_or_equal(X2,X3)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_61,c_0_83]) ).
cnf(c_0_95,hypothesis,
( ~ defined(X1)
| less_or_equal(X1,b)
| less_or_equal(b,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_96,negated_conjecture,
~ less_or_equal(a,b),
c_0_84 ).
cnf(c_0_97,hypothesis,
( ~ defined(X1)
| ~ less_or_equal(X1,b)
| less_or_equal(add(X1,additive_identity),b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_58]),c_0_37])]) ).
cnf(c_0_98,plain,
( ~ sum(X4,additive_identity,X1)
| ~ defined(X2)
| ~ defined(X3)
| ~ less_or_equal(X4,add(X2,X3))
| less_or_equal(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_61,c_0_86]) ).
cnf(c_0_99,hypothesis,
less_or_equal(b,add(b,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_72]),c_0_37]),c_0_20])]) ).
cnf(c_0_100,hypothesis,
sum(a,additive_identity,a),
inference(spm,[status(thm)],[c_0_27,c_0_89]) ).
cnf(c_0_101,hypothesis,
( ~ sum(X1,X3,additive_identity)
| ~ sum(X3,a,X2)
| sum(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_21,c_0_89]) ).
cnf(c_0_102,hypothesis,
( ~ sum(additive_inverse(a),b,X1)
| sum(a,X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_103,negated_conjecture,
( ~ less_or_equal(X1,additive_identity)
| ~ less_or_equal(add(b,additive_inverse(a)),X1)
| sum(additive_identity,add(b,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_93]) ).
cnf(c_0_104,plain,
( ~ defined(X1)
| ~ defined(X2)
| ~ less_or_equal(X1,X2)
| less_or_equal(add(X1,additive_inverse(X2)),additive_identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_58]),c_0_28]) ).
cnf(c_0_105,hypothesis,
less_or_equal(b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_50]),c_0_96]) ).
cnf(c_0_106,hypothesis,
( ~ defined(X2)
| ~ less_or_equal(X2,b)
| ~ less_or_equal(X1,add(X2,additive_identity))
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_81,c_0_97]) ).
cnf(c_0_107,hypothesis,
( ~ sum(b,additive_identity,X1)
| less_or_equal(X1,add(b,additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_37]),c_0_20])]) ).
cnf(c_0_108,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_95,c_0_20]) ).
cnf(c_0_109,hypothesis,
( ~ sum(X3,a,X1)
| ~ sum(X3,a,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_100]) ).
cnf(c_0_110,hypothesis,
( ~ sum(X1,additive_identity,additive_identity)
| sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_101,c_0_89]) ).
cnf(c_0_111,hypothesis,
( ~ defined(additive_inverse(a))
| sum(a,add(b,additive_inverse(a)),b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_67]),c_0_20])]) ).
cnf(c_0_112,negated_conjecture,
sum(additive_identity,add(b,additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_72]),c_0_105]),c_0_50]),c_0_20])]) ).
cnf(c_0_113,hypothesis,
( ~ sum(b,additive_identity,X1)
| less_or_equal(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_20])]) ).
cnf(c_0_114,hypothesis,
( ~ sum(X2,a,X1)
| ~ sum(X2,additive_identity,additive_identity)
| sum(X1,additive_identity,a) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_115,hypothesis,
( ~ defined(additive_inverse(a))
| sum(add(b,additive_inverse(a)),a,b) ),
inference(spm,[status(thm)],[c_0_27,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
sum(add(b,additive_inverse(a)),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_27,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
~ sum(b,additive_identity,a),
inference(spm,[status(thm)],[c_0_96,c_0_113]) ).
cnf(c_0_118,hypothesis,
~ defined(additive_inverse(a)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]),c_0_117]) ).
cnf(c_0_119,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_28]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:49:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.73/1.47 % Version: 3.5.1
% 7.73/1.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.73/1.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.73/1.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.73/1.47 % Starting new_bool_3 with 300s (1) cores
% 7.73/1.47 % Starting new_bool_1 with 300s (1) cores
% 7.73/1.47 % Starting sh5l with 300s (1) cores
% 7.73/1.47 % new_bool_3 with pid 2784422 completed with status 0
% 7.73/1.47 % Result found by new_bool_3
% 7.73/1.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.73/1.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.73/1.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.73/1.47 % Starting new_bool_3 with 300s (1) cores
% 7.73/1.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 7.73/1.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.73/1.47 % Search class: FGUNF-FFMS21-SFFFFFNN
% 7.73/1.47 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 7.73/1.47 % Starting SubtermCWHack with 28s (1) cores
% 7.73/1.47 % SubtermCWHack with pid 2784428 completed with status 0
% 7.73/1.47 % Result found by SubtermCWHack
% 7.73/1.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.73/1.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.73/1.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.73/1.47 % Starting new_bool_3 with 300s (1) cores
% 7.73/1.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 7.73/1.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.73/1.47 % Search class: FGUNF-FFMS21-SFFFFFNN
% 7.73/1.47 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 7.73/1.47 % Starting SubtermCWHack with 28s (1) cores
% 7.73/1.47 % Preprocessing time : 0.001 s
% 7.73/1.47
% 7.73/1.47 % Proof found!
% 7.73/1.47 % SZS status Unsatisfiable
% 7.73/1.47 % SZS output start CNFRefutation
% See solution above
% 7.73/1.47 % Parsed axioms : 30
% 7.73/1.47 % Removed by relevancy pruning/SinE : 7
% 7.73/1.47 % Initial clauses : 23
% 7.73/1.47 % Removed in clause preprocessing : 0
% 7.73/1.47 % Initial clauses in saturation : 23
% 7.73/1.47 % Processed clauses : 14719
% 7.73/1.47 % ...of these trivial : 60
% 7.73/1.47 % ...subsumed : 11326
% 7.73/1.47 % ...remaining for further processing : 3333
% 7.73/1.47 % Other redundant clauses eliminated : 0
% 7.73/1.47 % Clauses deleted for lack of memory : 0
% 7.73/1.47 % Backward-subsumed : 521
% 7.73/1.47 % Backward-rewritten : 1
% 7.73/1.47 % Generated clauses : 111712
% 7.73/1.47 % ...of the previous two non-redundant : 88191
% 7.73/1.47 % ...aggressively subsumed : 0
% 7.73/1.47 % Contextual simplify-reflections : 55
% 7.73/1.47 % Paramodulations : 111712
% 7.73/1.47 % Factorizations : 0
% 7.73/1.47 % NegExts : 0
% 7.73/1.47 % Equation resolutions : 0
% 7.73/1.47 % Disequality decompositions : 0
% 7.73/1.47 % Total rewrite steps : 64913
% 7.73/1.47 % ...of those cached : 64804
% 7.73/1.47 % Propositional unsat checks : 0
% 7.73/1.47 % Propositional check models : 0
% 7.73/1.47 % Propositional check unsatisfiable : 0
% 7.73/1.47 % Propositional clauses : 0
% 7.73/1.47 % Propositional clauses after purity: 0
% 7.73/1.47 % Propositional unsat core size : 0
% 7.73/1.47 % Propositional preprocessing time : 0.000
% 7.73/1.47 % Propositional encoding time : 0.000
% 7.73/1.47 % Propositional solver time : 0.000
% 7.73/1.47 % Success case prop preproc time : 0.000
% 7.73/1.47 % Success case prop encoding time : 0.000
% 7.73/1.47 % Success case prop solver time : 0.000
% 7.73/1.47 % Current number of processed clauses : 2811
% 7.73/1.47 % Positive orientable unit clauses : 125
% 7.73/1.47 % Positive unorientable unit clauses: 0
% 7.73/1.47 % Negative unit clauses : 67
% 7.73/1.47 % Non-unit-clauses : 2619
% 7.73/1.47 % Current number of unprocessed clauses: 73312
% 7.73/1.47 % ...number of literals in the above : 283097
% 7.73/1.47 % Current number of archived formulas : 0
% 7.73/1.47 % Current number of archived clauses : 522
% 7.73/1.47 % Clause-clause subsumption calls (NU) : 798166
% 7.73/1.47 % Rec. Clause-clause subsumption calls : 559855
% 7.73/1.47 % Non-unit clause-clause subsumptions : 9629
% 7.73/1.47 % Unit Clause-clause subsumption calls : 36791
% 7.73/1.47 % Rewrite failures with RHS unbound : 0
% 7.73/1.47 % BW rewrite match attempts : 194
% 7.73/1.47 % BW rewrite match successes : 1
% 7.73/1.47 % Condensation attempts : 0
% 7.73/1.47 % Condensation successes : 0
% 7.73/1.47 % Termbank termtop insertions : 1787046
% 7.73/1.47 % Search garbage collected termcells : 135
% 7.73/1.47
% 7.73/1.47 % -------------------------------------------------
% 7.73/1.47 % User time : 0.995 s
% 7.73/1.47 % System time : 0.031 s
% 7.73/1.47 % Total time : 1.026 s
% 7.73/1.47 % Maximum resident set size: 3660 pages
% 7.73/1.47
% 7.73/1.47 % -------------------------------------------------
% 7.73/1.47 % User time : 0.995 s
% 7.73/1.47 % System time : 0.037 s
% 7.73/1.47 % Total time : 1.032 s
% 7.73/1.47 % Maximum resident set size: 4864 pages
% 7.73/1.47 % E exiting
%------------------------------------------------------------------------------