TSTP Solution File: FLD066-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD066-1 : 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 : 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 : Wed Aug 30 22:27:46 EDT 2023
% Result : Unsatisfiable 49.87s 49.95s
% Output : CNFRefutation 49.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 32
% Syntax : Number of formulae : 182 ( 45 unt; 12 typ; 0 def)
% Number of atoms : 372 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 403 ( 201 ~; 202 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 185 ( 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 ).
tff(decl_33,type,
c: $i ).
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_4,negated_conjecture,
less_or_equal(add(a,c),add(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
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(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(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_less_or_equal_5,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
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(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(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_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(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(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(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(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(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(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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(c_0_20,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_21,negated_conjecture,
less_or_equal(add(a,c),add(b,c)),
less_or_equal_4 ).
cnf(c_0_22,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_23,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_24,negated_conjecture,
( equalish(add(b,c),add(a,c))
| ~ less_or_equal(add(b,c),add(a,c)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( less_or_equal(add(X1,X2),add(X3,X2))
| less_or_equal(X3,X1)
| ~ defined(X2)
| ~ defined(X3)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_27,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_28,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_29,negated_conjecture,
~ less_or_equal(a,b),
not_less_or_equal_5 ).
cnf(c_0_30,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_31,negated_conjecture,
equalish(add(b,c),add(a,c)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( equalish(X1,add(a,c))
| ~ equalish(X1,add(b,c)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_34,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_35,negated_conjecture,
equalish(add(c,b),add(a,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]),c_0_26])]) ).
cnf(c_0_36,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_37,negated_conjecture,
equalish(add(a,c),add(b,c)),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
equalish(add(a,c),add(c,b)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( less_or_equal(add(b,c),X1)
| ~ less_or_equal(add(a,c),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_23]) ).
cnf(c_0_41,negated_conjecture,
( less_or_equal(add(c,b),X1)
| ~ less_or_equal(add(a,c),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( less_or_equal(add(b,c),add(a,c))
| ~ defined(add(a,c)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,axiom,
( defined(add(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_addition ).
cnf(c_0_44,negated_conjecture,
less_or_equal(add(c,b),add(b,c)),
inference(spm,[status(thm)],[c_0_41,c_0_21]) ).
cnf(c_0_45,axiom,
( equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_addition ).
cnf(c_0_46,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_36,c_0_33]) ).
cnf(c_0_47,plain,
( less_or_equal(add(X1,X2),add(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_48,axiom,
( equalish(add(X1,additive_inverse(X1)),additive_identity)
| ~ defined(X1) ),
existence_of_inverse_addition ).
cnf(c_0_49,negated_conjecture,
less_or_equal(add(b,c),add(a,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_26]),c_0_27])]) ).
cnf(c_0_50,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_51,negated_conjecture,
( less_or_equal(add(add(c,b),X1),add(add(b,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_52,plain,
( less_or_equal(add(add(X1,X2),X3),X4)
| ~ less_or_equal(add(X1,add(X2,X3)),X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
cnf(c_0_53,plain,
( less_or_equal(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(add(X2,additive_inverse(X2)),X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_55,axiom,
( defined(additive_inverse(X1))
| ~ defined(X1) ),
well_definedness_of_additive_inverse ).
cnf(c_0_56,negated_conjecture,
( less_or_equal(add(add(b,c),X1),add(add(a,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
( less_or_equal(X1,add(add(b,c),X2))
| ~ less_or_equal(X1,add(add(c,b),X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,plain,
( less_or_equal(add(add(X1,X2),X3),add(add(X2,X3),X1))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_43]) ).
cnf(c_0_59,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_60,plain,
( less_or_equal(additive_identity,add(additive_inverse(X1),X1))
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_53]),c_0_55]) ).
cnf(c_0_61,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_62,negated_conjecture,
( less_or_equal(X1,add(add(a,c),X2))
| ~ less_or_equal(X1,add(add(b,c),X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
( less_or_equal(add(add(X1,c),b),add(add(b,c),X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_28]),c_0_26])]) ).
cnf(c_0_64,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(add(additive_identity,X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_59]) ).
cnf(c_0_65,plain,
( less_or_equal(add(additive_identity,X1),add(add(additive_inverse(X2),X2),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( equalish(add(add(c,b),X1),add(add(a,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_35]) ).
cnf(c_0_67,negated_conjecture,
( less_or_equal(add(add(X1,b),c),add(add(a,c),X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_58]),c_0_26]),c_0_28])]) ).
cnf(c_0_68,negated_conjecture,
( less_or_equal(X1,add(add(b,c),X2))
| ~ less_or_equal(X1,add(add(X2,c),b))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_63]) ).
cnf(c_0_69,plain,
( less_or_equal(X1,add(add(additive_inverse(X2),X2),X1))
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( less_or_equal(add(add(a,c),X1),X2)
| ~ less_or_equal(add(add(c,b),X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_66]) ).
cnf(c_0_71,plain,
( less_or_equal(add(add(X1,X2),X3),add(X1,add(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_47]),c_0_43]) ).
cnf(c_0_72,negated_conjecture,
( less_or_equal(X1,add(add(a,c),X2))
| ~ less_or_equal(X1,add(add(X2,b),c))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( equalish(add(add(a,c),X1),add(add(b,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_37]) ).
cnf(c_0_74,negated_conjecture,
( equalish(add(add(b,c),X1),add(add(a,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_31]) ).
cnf(c_0_75,negated_conjecture,
( less_or_equal(b,add(add(b,c),additive_inverse(c)))
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_28]),c_0_26])]) ).
cnf(c_0_76,negated_conjecture,
( less_or_equal(add(add(a,c),X1),add(c,add(b,X1)))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_28]),c_0_26])]) ).
cnf(c_0_77,negated_conjecture,
( less_or_equal(c,add(add(a,c),additive_inverse(b)))
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_69]),c_0_26]),c_0_28])]) ).
cnf(c_0_78,negated_conjecture,
( less_or_equal(add(add(b,c),X1),X2)
| ~ less_or_equal(add(add(a,c),X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_73]) ).
cnf(c_0_79,negated_conjecture,
( less_or_equal(add(add(a,c),X1),X2)
| ~ less_or_equal(add(add(b,c),X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
less_or_equal(b,add(add(b,c),additive_inverse(c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_55]),c_0_26])]) ).
cnf(c_0_81,plain,
( equalish(X1,add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_59]) ).
cnf(c_0_82,plain,
( equalish(additive_identity,add(X1,additive_inverse(X1)))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_83,negated_conjecture,
( less_or_equal(X1,add(c,add(b,X2)))
| ~ less_or_equal(X1,add(add(a,c),X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
less_or_equal(c,add(add(a,c),additive_inverse(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_55]),c_0_28])]) ).
cnf(c_0_85,negated_conjecture,
( less_or_equal(add(add(b,c),X1),add(a,add(c,X1)))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_71]),c_0_26]),c_0_27])]) ).
cnf(c_0_86,negated_conjecture,
( less_or_equal(add(add(a,c),X1),add(b,add(c,X1)))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_71]),c_0_26]),c_0_28])]) ).
cnf(c_0_87,negated_conjecture,
( less_or_equal(b,add(add(a,c),additive_inverse(c)))
| ~ defined(additive_inverse(c)) ),
inference(spm,[status(thm)],[c_0_62,c_0_80]) ).
cnf(c_0_88,plain,
( less_or_equal(add(additive_identity,X1),X2)
| ~ less_or_equal(X1,X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_81]) ).
cnf(c_0_89,plain,
( less_or_equal(add(X1,additive_inverse(X1)),X2)
| ~ less_or_equal(additive_identity,X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_82]) ).
cnf(c_0_90,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_91,negated_conjecture,
( less_or_equal(c,add(c,add(b,additive_inverse(b))))
| ~ defined(additive_inverse(b)) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_92,negated_conjecture,
( less_or_equal(X1,add(a,add(c,X2)))
| ~ less_or_equal(X1,add(add(b,c),X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( less_or_equal(X1,add(b,add(c,X2)))
| ~ less_or_equal(X1,add(add(a,c),X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
less_or_equal(b,add(add(a,c),additive_inverse(c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_55]),c_0_26])]) ).
cnf(c_0_95,plain,
( less_or_equal(add(additive_identity,X1),X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_40]) ).
cnf(c_0_96,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_89,c_0_40]),c_0_90])]) ).
cnf(c_0_97,plain,
( less_or_equal(X1,add(X2,X3))
| ~ less_or_equal(X1,add(X3,X2))
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_98,negated_conjecture,
less_or_equal(c,add(c,add(b,additive_inverse(b)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_55]),c_0_28])]) ).
cnf(c_0_99,negated_conjecture,
( less_or_equal(b,add(a,add(c,additive_inverse(c))))
| ~ defined(additive_inverse(c)) ),
inference(spm,[status(thm)],[c_0_92,c_0_80]) ).
cnf(c_0_100,negated_conjecture,
( less_or_equal(b,add(b,add(c,additive_inverse(c))))
| ~ defined(additive_inverse(c)) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,add(additive_identity,X2))
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_95]) ).
cnf(c_0_102,plain,
( less_or_equal(add(add(X1,additive_inverse(X1)),X2),add(additive_identity,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
( less_or_equal(c,add(add(b,additive_inverse(b)),c))
| ~ defined(add(b,additive_inverse(b))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_26])]) ).
cnf(c_0_104,negated_conjecture,
less_or_equal(b,add(a,add(c,additive_inverse(c)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_55]),c_0_26])]) ).
cnf(c_0_105,negated_conjecture,
less_or_equal(b,add(b,add(c,additive_inverse(c)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_55]),c_0_26])]) ).
cnf(c_0_106,plain,
( less_or_equal(add(add(X1,additive_inverse(X1)),X2),X2)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( less_or_equal(c,add(add(b,additive_inverse(b)),c))
| ~ defined(additive_inverse(b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_43]),c_0_28])]) ).
cnf(c_0_108,negated_conjecture,
( less_or_equal(b,add(add(c,additive_inverse(c)),a))
| ~ defined(add(c,additive_inverse(c))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_104]),c_0_27])]) ).
cnf(c_0_109,negated_conjecture,
( less_or_equal(b,add(add(c,additive_inverse(c)),b))
| ~ defined(add(c,additive_inverse(c))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_105]),c_0_28])]) ).
cnf(c_0_110,plain,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,add(add(X3,additive_inverse(X3)),X2))
| ~ defined(X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_106]) ).
cnf(c_0_111,negated_conjecture,
less_or_equal(c,add(add(b,additive_inverse(b)),c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_55]),c_0_28])]) ).
cnf(c_0_112,negated_conjecture,
( less_or_equal(b,add(add(c,additive_inverse(c)),a))
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_43]),c_0_26])]) ).
cnf(c_0_113,negated_conjecture,
( less_or_equal(b,add(add(c,additive_inverse(c)),b))
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_43]),c_0_26])]) ).
cnf(c_0_114,negated_conjecture,
less_or_equal(c,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_26]),c_0_28])]) ).
cnf(c_0_115,negated_conjecture,
less_or_equal(b,add(add(c,additive_inverse(c)),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_55]),c_0_26])]) ).
cnf(c_0_116,negated_conjecture,
less_or_equal(b,add(add(c,additive_inverse(c)),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_55]),c_0_26])]) ).
cnf(c_0_117,negated_conjecture,
equalish(c,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_114]),c_0_114])]) ).
cnf(c_0_118,negated_conjecture,
less_or_equal(b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_115]),c_0_27]),c_0_26])]) ).
cnf(c_0_119,negated_conjecture,
less_or_equal(b,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_116]),c_0_28]),c_0_26])]) ).
cnf(c_0_120,plain,
( equalish(X1,add(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_121,negated_conjecture,
( equalish(add(c,X1),add(c,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_117]) ).
cnf(c_0_122,plain,
( equalish(add(add(X1,X2),X3),add(X1,add(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_123,negated_conjecture,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_50,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_119]),c_0_28])]) ).
cnf(c_0_125,negated_conjecture,
( equalish(add(c,X1),add(X1,c))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_26])]) ).
cnf(c_0_126,plain,
( less_or_equal(add(X1,add(X2,X3)),X4)
| ~ less_or_equal(add(add(X1,X2),X3),X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( less_or_equal(add(add(X1,additive_inverse(X1)),b),a)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_106]),c_0_28])]) ).
cnf(c_0_128,negated_conjecture,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_50,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( less_or_equal(add(X1,c),X2)
| ~ less_or_equal(add(c,X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_125]) ).
cnf(c_0_130,negated_conjecture,
( less_or_equal(add(X1,add(additive_inverse(X1),b)),a)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_28])]),c_0_55]) ).
cnf(c_0_131,negated_conjecture,
( less_or_equal(add(add(X1,additive_inverse(X1)),b),b)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_102]),c_0_28])]) ).
cnf(c_0_132,negated_conjecture,
( less_or_equal(add(add(additive_inverse(c),b),c),a)
| ~ defined(add(additive_inverse(c),b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_26])]) ).
cnf(c_0_133,negated_conjecture,
( less_or_equal(add(X1,add(additive_inverse(X1),b)),b)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_131]),c_0_28])]),c_0_55]) ).
cnf(c_0_134,plain,
( equalish(add(add(X1,X2),X3),add(add(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_33]) ).
cnf(c_0_135,negated_conjecture,
( less_or_equal(add(add(additive_inverse(c),b),c),a)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_43]),c_0_28])]) ).
cnf(c_0_136,negated_conjecture,
( less_or_equal(add(add(additive_inverse(c),b),c),b)
| ~ defined(add(additive_inverse(c),b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_133]),c_0_26])]) ).
cnf(c_0_137,plain,
( less_or_equal(add(add(X1,X2),X3),X4)
| ~ less_or_equal(add(add(X2,X1),X3),X4)
| ~ defined(X3)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_134]) ).
cnf(c_0_138,negated_conjecture,
less_or_equal(add(add(additive_inverse(c),b),c),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_55]),c_0_26])]) ).
cnf(c_0_139,negated_conjecture,
( less_or_equal(add(add(additive_inverse(c),b),c),b)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_43]),c_0_28])]) ).
cnf(c_0_140,negated_conjecture,
( less_or_equal(add(add(b,additive_inverse(c)),c),a)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_26]),c_0_28])]) ).
cnf(c_0_141,negated_conjecture,
less_or_equal(add(add(additive_inverse(c),b),c),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_55]),c_0_26])]) ).
cnf(c_0_142,negated_conjecture,
less_or_equal(add(add(b,additive_inverse(c)),c),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_55]),c_0_26])]) ).
cnf(c_0_143,negated_conjecture,
( less_or_equal(add(add(b,additive_inverse(c)),c),b)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_141]),c_0_26]),c_0_28])]) ).
cnf(c_0_144,negated_conjecture,
equalish(add(c,b),add(c,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_35]),c_0_26]),c_0_27])]) ).
cnf(c_0_145,negated_conjecture,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(add(b,additive_inverse(c)),c)) ),
inference(spm,[status(thm)],[c_0_50,c_0_142]) ).
cnf(c_0_146,negated_conjecture,
less_or_equal(add(add(b,additive_inverse(c)),c),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_55]),c_0_26])]) ).
cnf(c_0_147,negated_conjecture,
( equalish(add(add(c,b),X1),add(add(c,a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_144]) ).
cnf(c_0_148,negated_conjecture,
( less_or_equal(add(add(c,b),additive_inverse(c)),a)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_58]),c_0_28]),c_0_26])]) ).
cnf(c_0_149,negated_conjecture,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(add(b,additive_inverse(c)),c)) ),
inference(spm,[status(thm)],[c_0_50,c_0_146]) ).
cnf(c_0_150,negated_conjecture,
( less_or_equal(add(add(c,a),X1),X2)
| ~ less_or_equal(add(add(c,b),X1),X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_147]) ).
cnf(c_0_151,negated_conjecture,
less_or_equal(add(add(c,b),additive_inverse(c)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_55]),c_0_26])]) ).
cnf(c_0_152,negated_conjecture,
( less_or_equal(add(add(c,b),additive_inverse(c)),b)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_58]),c_0_28]),c_0_26])]) ).
cnf(c_0_153,negated_conjecture,
( less_or_equal(add(add(c,a),additive_inverse(c)),a)
| ~ defined(additive_inverse(c)) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_154,negated_conjecture,
less_or_equal(add(add(c,b),additive_inverse(c)),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_55]),c_0_26])]) ).
cnf(c_0_155,negated_conjecture,
less_or_equal(add(add(c,a),additive_inverse(c)),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_55]),c_0_26])]) ).
cnf(c_0_156,negated_conjecture,
( less_or_equal(add(add(c,a),additive_inverse(c)),b)
| ~ defined(additive_inverse(c)) ),
inference(spm,[status(thm)],[c_0_150,c_0_154]) ).
cnf(c_0_157,negated_conjecture,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(add(c,a),additive_inverse(c))) ),
inference(spm,[status(thm)],[c_0_50,c_0_155]) ).
cnf(c_0_158,negated_conjecture,
less_or_equal(add(add(c,a),additive_inverse(c)),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_55]),c_0_26])]) ).
cnf(c_0_159,negated_conjecture,
( less_or_equal(add(add(additive_inverse(c),c),a),a)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_58]),c_0_27]),c_0_26])]) ).
cnf(c_0_160,negated_conjecture,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(add(c,a),additive_inverse(c))) ),
inference(spm,[status(thm)],[c_0_50,c_0_158]) ).
cnf(c_0_161,negated_conjecture,
less_or_equal(add(add(additive_inverse(c),c),a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_55]),c_0_26])]) ).
cnf(c_0_162,negated_conjecture,
( less_or_equal(add(add(additive_inverse(c),c),a),b)
| ~ defined(additive_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_58]),c_0_27]),c_0_26])]) ).
cnf(c_0_163,negated_conjecture,
( less_or_equal(X1,a)
| ~ less_or_equal(X1,add(add(additive_inverse(c),c),a)) ),
inference(spm,[status(thm)],[c_0_50,c_0_161]) ).
cnf(c_0_164,negated_conjecture,
less_or_equal(add(add(additive_inverse(c),c),a),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_55]),c_0_26])]) ).
cnf(c_0_165,plain,
( less_or_equal(X1,add(add(additive_inverse(X2),X2),X3))
| ~ less_or_equal(X1,X3)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_69]) ).
cnf(c_0_166,negated_conjecture,
less_or_equal(a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_69]),c_0_27]),c_0_26])]) ).
cnf(c_0_167,negated_conjecture,
( less_or_equal(X1,b)
| ~ less_or_equal(X1,add(add(additive_inverse(c),c),a)) ),
inference(spm,[status(thm)],[c_0_50,c_0_164]) ).
cnf(c_0_168,negated_conjecture,
( less_or_equal(a,add(add(additive_inverse(X1),X1),a))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_27])]) ).
cnf(c_0_169,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_26])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : FLD066-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 23:58:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.55 start to proof: theBenchmark
% 49.87/49.95 % Version : CSE_E---1.5
% 49.87/49.95 % Problem : theBenchmark.p
% 49.87/49.95 % Proof found
% 49.87/49.95 % SZS status Theorem for theBenchmark.p
% 49.87/49.95 % SZS output start Proof
% See solution above
% 49.87/49.97 % Total time : 49.382000 s
% 49.87/49.97 % SZS output end Proof
% 49.87/49.97 % Total time : 49.387000 s
%------------------------------------------------------------------------------