TSTP Solution File: FLD063-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD063-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 : Wed Aug 30 22:27:45 EDT 2023
% Result : Unsatisfiable 76.70s 76.96s
% Output : CNFRefutation 76.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 31
% Syntax : Number of formulae : 154 ( 47 unt; 11 typ; 0 def)
% Number of atoms : 285 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 283 ( 141 ~; 142 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% 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 : 145 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
equalish: ( $i * $i ) > $o ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_identity: $i ).
tff(decl_26,type,
additive_inverse: $i > $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
multiplicative_identity: $i ).
tff(decl_29,type,
multiplicative_inverse: $i > $i ).
tff(decl_30,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_31,type,
a: $i ).
tff(decl_32,type,
b: $i ).
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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
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_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(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_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(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
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(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(less_or_equal_3,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
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(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
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(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(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(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(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(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,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_23,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_24,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_25,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_27,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_28,hypothesis,
( less_or_equal(X1,b)
| less_or_equal(b,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ less_or_equal(a,b),
not_less_or_equal_4 ).
cnf(c_0_30,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_31,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_33,hypothesis,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_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 ).
cnf(c_0_35,hypothesis,
less_or_equal(b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_29]) ).
cnf(c_0_36,plain,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,X2)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,hypothesis,
equalish(additive_identity,add(a,additive_inverse(a))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
( less_or_equal(add(b,X1),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_40,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_41,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_42,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,add(a,additive_inverse(a))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,hypothesis,
( less_or_equal(add(b,additive_inverse(X1)),add(a,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
less_or_equal_3 ).
cnf(c_0_45,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(a,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_46,plain,
( equalish(add(X1,additive_inverse(X2)),add(additive_inverse(X2),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_47,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_42,c_0_43]),c_0_27])]) ).
cnf(c_0_48,negated_conjecture,
( less_or_equal(X1,additive_inverse(a))
| ~ equalish(additive_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_49,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_50,hypothesis,
equalish(add(b,additive_inverse(b)),additive_identity),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_51,hypothesis,
( equalish(add(X1,b),add(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_52,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_53,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_45,c_0_46]),c_0_27])]) ).
cnf(c_0_54,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_55,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(b,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( less_or_equal(add(X1,X2),add(additive_inverse(a),X2))
| ~ defined(X2)
| ~ equalish(additive_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_57,hypothesis,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(b,additive_inverse(b))) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,hypothesis,
( equalish(add(additive_inverse(X1),b),add(b,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_59,plain,
( equalish(additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_60,hypothesis,
( less_or_equal(X1,add(a,additive_inverse(X2)))
| ~ defined(X2)
| ~ equalish(add(b,additive_inverse(X2)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_61,hypothesis,
( less_or_equal(X1,additive_identity)
| ~ less_or_equal(X1,add(additive_inverse(a),a)) ),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( less_or_equal(add(additive_inverse(b),X1),add(additive_inverse(a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_63,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_64,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_65,plain,
equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(spm,[status(thm)],[c_0_32,c_0_54]) ).
cnf(c_0_66,plain,
( less_or_equal(additive_inverse(X1),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_67,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_68,hypothesis,
less_or_equal(add(additive_inverse(a),b),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_23]),c_0_27])]) ).
cnf(c_0_69,negated_conjecture,
( less_or_equal(X1,add(additive_inverse(a),X2))
| ~ defined(X2)
| ~ equalish(add(X3,X2),X1)
| ~ equalish(additive_inverse(b),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_56]) ).
cnf(c_0_70,hypothesis,
equalish(add(additive_inverse(b),b),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_23])]) ).
cnf(c_0_71,hypothesis,
equalish(additive_inverse(b),additive_inverse(b)),
inference(spm,[status(thm)],[c_0_59,c_0_23]) ).
cnf(c_0_72,hypothesis,
less_or_equal(additive_identity,add(a,additive_inverse(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_50]),c_0_23])]) ).
cnf(c_0_73,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_61,c_0_62]),c_0_27])]) ).
cnf(c_0_74,hypothesis,
( equalish(add(X1,a),add(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_75,hypothesis,
( less_or_equal(X1,b)
| ~ equalish(b,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_63]) ).
cnf(c_0_76,hypothesis,
equalish(add(additive_identity,b),b),
inference(spm,[status(thm)],[c_0_64,c_0_23]) ).
cnf(c_0_77,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_65]) ).
cnf(c_0_78,plain,
( equalish(add(additive_identity,additive_inverse(X1)),additive_inverse(X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_39]) ).
cnf(c_0_79,plain,
less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_66,c_0_22]) ).
cnf(c_0_80,hypothesis,
( equalish(additive_identity,add(additive_inverse(a),b))
| ~ less_or_equal(additive_identity,add(additive_inverse(a),b)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_81,negated_conjecture,
less_or_equal(additive_identity,add(additive_inverse(a),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_23]),c_0_71])]) ).
cnf(c_0_82,hypothesis,
( less_or_equal(X1,add(a,additive_inverse(b)))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_83,negated_conjecture,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(additive_inverse(b),a),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_84,hypothesis,
( equalish(add(additive_inverse(X1),a),add(a,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_39]) ).
cnf(c_0_85,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,X2)
| ~ equalish(b,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_75]) ).
cnf(c_0_86,hypothesis,
equalish(b,add(additive_identity,b)),
inference(spm,[status(thm)],[c_0_32,c_0_76]) ).
cnf(c_0_87,plain,
less_or_equal(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_22])]) ).
cnf(c_0_88,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ equalish(additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_79]) ).
cnf(c_0_89,hypothesis,
equalish(additive_identity,add(additive_inverse(a),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_90,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_identity,additive_inverse(additive_identity))) ),
inference(spm,[status(thm)],[c_0_49,c_0_54]) ).
cnf(c_0_91,plain,
( equalish(additive_inverse(X1),add(additive_identity,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_78]) ).
cnf(c_0_92,hypothesis,
( equalish(add(a,additive_inverse(b)),X1)
| ~ less_or_equal(add(a,additive_inverse(b)),X1)
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_67,c_0_82]) ).
cnf(c_0_93,negated_conjecture,
( less_or_equal(X1,add(additive_inverse(a),b))
| ~ less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_81]) ).
cnf(c_0_94,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_83,c_0_84]),c_0_23])]) ).
cnf(c_0_95,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_96,plain,
( less_or_equal(add(additive_inverse(additive_identity),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_87]) ).
cnf(c_0_97,plain,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ equalish(additive_inverse(additive_identity),X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_88]) ).
cnf(c_0_98,hypothesis,
( equalish(X1,add(additive_inverse(a),b))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_49,c_0_89]) ).
cnf(c_0_99,plain,
equalish(additive_inverse(additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_22])]) ).
cnf(c_0_100,hypothesis,
equalish(add(a,additive_inverse(b)),add(additive_inverse(a),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_68]),c_0_94])]) ).
cnf(c_0_101,hypothesis,
less_or_equal(add(additive_inverse(additive_identity),b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_23])]) ).
cnf(c_0_102,hypothesis,
( less_or_equal(X1,additive_inverse(additive_identity))
| ~ equalish(add(additive_inverse(a),b),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).
cnf(c_0_103,hypothesis,
equalish(add(additive_inverse(a),b),add(a,additive_inverse(b))),
inference(spm,[status(thm)],[c_0_32,c_0_100]) ).
cnf(c_0_104,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(additive_inverse(additive_identity),b)) ),
inference(spm,[status(thm)],[c_0_30,c_0_101]) ).
cnf(c_0_105,plain,
( less_or_equal(add(X1,X2),add(additive_inverse(additive_identity),X2))
| ~ defined(X2)
| ~ equalish(additive_inverse(additive_identity),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_88]) ).
cnf(c_0_106,hypothesis,
( less_or_equal(X1,add(a,additive_inverse(b)))
| ~ less_or_equal(X2,additive_identity)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_82]) ).
cnf(c_0_107,hypothesis,
less_or_equal(add(a,additive_inverse(b)),additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,hypothesis,
( less_or_equal(add(X1,b),b)
| ~ equalish(additive_inverse(additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_23])]) ).
cnf(c_0_109,hypothesis,
( less_or_equal(X1,add(a,additive_inverse(b)))
| ~ equalish(add(b,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_47]) ).
cnf(c_0_110,hypothesis,
equalish(add(a,additive_inverse(b)),additive_inverse(additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_107]),c_0_87])]) ).
cnf(c_0_111,negated_conjecture,
equalish(add(additive_inverse(a),b),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_81]),c_0_68])]) ).
cnf(c_0_112,hypothesis,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(X2,b))
| ~ equalish(additive_inverse(additive_identity),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_108]) ).
cnf(c_0_113,hypothesis,
( less_or_equal(add(X1,X2),add(add(a,additive_inverse(b)),X2))
| ~ defined(X2)
| ~ equalish(add(b,additive_inverse(a)),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_109]) ).
cnf(c_0_114,hypothesis,
equalish(additive_inverse(additive_identity),add(a,additive_inverse(b))),
inference(spm,[status(thm)],[c_0_32,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
equalish(additive_identity,add(a,additive_inverse(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_94]),c_0_72])]) ).
cnf(c_0_116,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_inverse(a),b)) ),
inference(spm,[status(thm)],[c_0_49,c_0_111]) ).
cnf(c_0_117,hypothesis,
( less_or_equal(add(X1,b),b)
| ~ equalish(add(b,additive_inverse(a)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_23])]) ).
cnf(c_0_118,negated_conjecture,
( equalish(X1,add(a,additive_inverse(b)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_49,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
equalish(add(b,additive_inverse(a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_46]),c_0_23]),c_0_27])]) ).
cnf(c_0_120,negated_conjecture,
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_117,c_0_118]),c_0_119])]) ).
cnf(c_0_121,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_122,negated_conjecture,
( less_or_equal(X1,b)
| ~ equalish(add(add(a,additive_inverse(b)),b),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_120]) ).
cnf(c_0_123,plain,
( equalish(add(add(X1,X2),X3),add(X1,add(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_121]) ).
cnf(c_0_124,negated_conjecture,
( less_or_equal(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_122,c_0_123]),c_0_23]),c_0_27])]) ).
cnf(c_0_125,negated_conjecture,
( less_or_equal(X1,b)
| ~ defined(additive_inverse(b))
| ~ equalish(add(a,add(additive_inverse(b),b)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_124]) ).
cnf(c_0_126,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_127,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_64,c_0_27]) ).
cnf(c_0_128,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_129,negated_conjecture,
( less_or_equal(X1,b)
| ~ equalish(add(a,add(additive_inverse(b),b)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_39]),c_0_23])]) ).
cnf(c_0_130,plain,
( equalish(add(X1,add(X2,X3)),add(add(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_126]) ).
cnf(c_0_131,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_49,c_0_127]) ).
cnf(c_0_132,hypothesis,
( equalish(add(add(b,additive_inverse(b)),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_50]) ).
cnf(c_0_133,hypothesis,
equalish(additive_identity,add(b,additive_inverse(b))),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_134,negated_conjecture,
( less_or_equal(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_129,c_0_130]),c_0_27]),c_0_23])]) ).
cnf(c_0_135,hypothesis,
equalish(add(add(b,additive_inverse(b)),a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_27])]) ).
cnf(c_0_136,hypothesis,
( equalish(X1,add(b,additive_inverse(b)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_49,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( less_or_equal(X1,b)
| ~ defined(additive_inverse(b))
| ~ equalish(add(add(additive_inverse(b),b),a),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_134]) ).
cnf(c_0_138,hypothesis,
( equalish(X1,a)
| ~ equalish(X1,add(add(b,additive_inverse(b)),a)) ),
inference(spm,[status(thm)],[c_0_49,c_0_135]) ).
cnf(c_0_139,hypothesis,
( equalish(add(X1,X2),add(add(b,additive_inverse(b)),X2))
| ~ defined(X2)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_128,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
( less_or_equal(X1,b)
| ~ equalish(add(add(additive_inverse(b),b),a),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_39]),c_0_23])]) ).
cnf(c_0_141,hypothesis,
( equalish(add(X1,a),a)
| ~ equalish(X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_27])]) ).
cnf(c_0_142,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_70])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : FLD063-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 00:09:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.49/0.57 start to proof: theBenchmark
% 76.70/76.96 % Version : CSE_E---1.5
% 76.70/76.96 % Problem : theBenchmark.p
% 76.70/76.96 % Proof found
% 76.70/76.96 % SZS status Theorem for theBenchmark.p
% 76.70/76.96 % SZS output start Proof
% See solution above
% 76.70/76.97 % Total time : 76.213000 s
% 76.70/76.97 % SZS output end Proof
% 76.70/76.97 % Total time : 76.219000 s
%------------------------------------------------------------------------------