TSTP Solution File: FLD040-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD040-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:27:31 EDT 2023
% Result : Unsatisfiable 4.70s 4.88s
% Output : CNFRefutation 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 35
% Syntax : Number of formulae : 153 ( 54 unt; 10 typ; 0 def)
% Number of atoms : 294 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 301 ( 150 ~; 151 |; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 154 ( 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 ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(a_not_equal_to_additive_identity_2,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_2) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(multiplicative_inverse_equals_additive_identity_3,negated_conjecture,
equalish(multiplicative_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse_equals_additive_identity_3) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(distributivity,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',distributivity) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(totality_of_order_relation,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(transitivity_of_order_relation,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_order_relation) ).
cnf(compatibility_of_order_relation_and_multiplication,axiom,
( less_or_equal(additive_identity,multiply(X1,X2))
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
cnf(antisymmetry_of_order_relation,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(c_0_25,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_26,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_27,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_2 ).
cnf(c_0_28,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_29,negated_conjecture,
equalish(multiplicative_inverse(a),additive_identity),
multiplicative_inverse_equals_additive_identity_3 ).
cnf(c_0_30,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_31,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiplicative_inverse(a)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
equalish(add(additive_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_35,hypothesis,
equalish(add(additive_identity,multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
equalish(additive_identity,add(additive_identity,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,hypothesis,
( equalish(X1,add(additive_identity,multiplicative_inverse(a)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_38,hypothesis,
( equalish(add(additive_identity,multiplicative_inverse(a)),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_39,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,add(additive_identity,multiplicative_inverse(a)))
| ~ equalish(X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_40,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_41,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_42,hypothesis,
( equalish(X1,X2)
| ~ equalish(X2,additive_identity)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_43,plain,
equalish(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_45,hypothesis,
( equalish(X1,multiply(multiplicative_identity,additive_identity))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_28,c_0_44]) ).
cnf(c_0_47,hypothesis,
( equalish(multiply(multiplicative_identity,additive_identity),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_45]) ).
cnf(c_0_48,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_49,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_50,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_51,hypothesis,
equalish(multiply(multiplicative_identity,additive_identity),multiplicative_inverse(a)),
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,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_26]),c_0_27]) ).
cnf(c_0_53,hypothesis,
( equalish(multiply(X1,a),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_54,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_28,c_0_51]) ).
cnf(c_0_55,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_56,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_28,c_0_52]) ).
cnf(c_0_57,hypothesis,
equalish(multiply(multiplicative_inverse(a),a),multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_53,c_0_31]) ).
cnf(c_0_58,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiplicative_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_32,c_0_54]) ).
cnf(c_0_59,hypothesis,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_60,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
cnf(c_0_61,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_62,hypothesis,
equalish(multiply(multiplicative_inverse(a),a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
equalish(additive_identity,multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_64,negated_conjecture,
equalish(multiply(multiply(a,multiplicative_inverse(a)),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_41])]) ).
cnf(c_0_65,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_60]) ).
cnf(c_0_66,hypothesis,
equalish(a,a),
inference(spm,[status(thm)],[c_0_61,c_0_26]) ).
cnf(c_0_67,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiplicative_inverse(a),a)) ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( equalish(multiply(additive_identity,X1),multiply(multiplicative_inverse(a),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),additive_identity)) ),
inference(spm,[status(thm)],[c_0_28,c_0_64]) ).
cnf(c_0_70,hypothesis,
( equalish(multiply(X1,X2),multiply(multiply(a,multiplicative_inverse(a)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_55,c_0_65]) ).
cnf(c_0_71,hypothesis,
( equalish(multiply(a,X1),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_66]) ).
cnf(c_0_72,negated_conjecture,
equalish(multiply(additive_identity,a),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_26])]) ).
cnf(c_0_73,hypothesis,
equalish(multiply(additive_identity,a),multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_53,c_0_41]) ).
cnf(c_0_74,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_75,negated_conjecture,
( equalish(multiply(X1,additive_identity),additive_identity)
| ~ equalish(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_41])]) ).
cnf(c_0_76,hypothesis,
equalish(multiply(a,additive_identity),multiply(a,additive_identity)),
inference(spm,[status(thm)],[c_0_71,c_0_41]) ).
cnf(c_0_77,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_28,c_0_72]) ).
cnf(c_0_78,hypothesis,
equalish(multiply(a,additive_identity),multiply(additive_identity,a)),
inference(spm,[status(thm)],[c_0_34,c_0_73]) ).
cnf(c_0_79,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_80,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_61,c_0_74]) ).
cnf(c_0_81,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_82,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(X2,additive_identity))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_83,hypothesis,
( equalish(multiply(multiply(a,additive_identity),X1),multiply(multiply(a,additive_identity),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_76]) ).
cnf(c_0_84,hypothesis,
equalish(multiply(a,additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
( equalish(add(multiplicative_identity,X1),add(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,plain,
equalish(add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_74]) ).
cnf(c_0_87,plain,
( equalish(add(X1,additive_identity),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_41]) ).
cnf(c_0_88,negated_conjecture,
equalish(multiply(multiply(a,additive_identity),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_41])]) ).
cnf(c_0_89,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_90,plain,
equalish(add(multiplicative_identity,additive_identity),add(multiplicative_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_85,c_0_41]) ).
cnf(c_0_91,plain,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,add(additive_identity,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_28,c_0_86]) ).
cnf(c_0_92,plain,
equalish(add(multiplicative_identity,additive_identity),add(additive_identity,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_87,c_0_74]) ).
cnf(c_0_93,negated_conjecture,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_63]) ).
cnf(c_0_94,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiply(a,additive_identity),additive_identity)) ),
inference(spm,[status(thm)],[c_0_28,c_0_88]) ).
cnf(c_0_95,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_89]) ).
cnf(c_0_96,plain,
( equalish(multiply(add(multiplicative_identity,additive_identity),X1),multiply(add(multiplicative_identity,additive_identity),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_90]) ).
cnf(c_0_97,plain,
equalish(add(multiplicative_identity,additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
distributivity ).
cnf(c_0_99,negated_conjecture,
( equalish(multiplicative_inverse(a),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_93]) ).
cnf(c_0_100,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_101,negated_conjecture,
equalish(multiply(additive_identity,multiply(a,additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_41]),c_0_26])]) ).
cnf(c_0_102,negated_conjecture,
equalish(multiply(add(multiplicative_identity,additive_identity),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_96]),c_0_97]),c_0_41])]) ).
cnf(c_0_103,plain,
( equalish(X1,multiply(add(X2,X3),X4))
| ~ defined(X3)
| ~ defined(X4)
| ~ defined(X2)
| ~ equalish(X1,add(multiply(X2,X4),multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_28,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( equalish(add(multiplicative_inverse(a),X1),add(X2,X1))
| ~ defined(X1)
| ~ equalish(X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_79,c_0_99]) ).
cnf(c_0_105,plain,
( equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_28,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
equalish(additive_identity,multiply(additive_identity,multiply(a,additive_identity))),
inference(spm,[status(thm)],[c_0_34,c_0_101]) ).
cnf(c_0_107,axiom,
( less_or_equal(X1,X2)
| less_or_equal(X2,X1)
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_order_relation ).
cnf(c_0_108,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(add(multiplicative_identity,additive_identity),additive_identity)) ),
inference(spm,[status(thm)],[c_0_28,c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( equalish(add(multiplicative_inverse(a),multiply(X1,X2)),multiply(add(X3,X1),X2))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(multiply(X3,X2),additive_identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_89]) ).
cnf(c_0_110,negated_conjecture,
equalish(additive_identity,multiply(multiply(additive_identity,a),additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_41]),c_0_26])]) ).
cnf(c_0_111,plain,
( less_or_equal(X1,X1)
| ~ defined(X1) ),
inference(ef,[status(thm)],[c_0_107]) ).
cnf(c_0_112,negated_conjecture,
( equalish(add(multiplicative_inverse(a),X1),add(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_29]) ).
cnf(c_0_113,negated_conjecture,
equalish(add(multiplicative_inverse(a),multiply(additive_identity,additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_41]),c_0_74]),c_0_43])]) ).
cnf(c_0_114,negated_conjecture,
equalish(multiply(multiply(additive_identity,a),additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_110]) ).
cnf(c_0_115,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X3,X2)
| ~ equalish(X3,X1) ),
compatibility_of_equality_and_order_relation ).
cnf(c_0_116,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_111,c_0_41]) ).
cnf(c_0_117,negated_conjecture,
( equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,add(multiplicative_inverse(a),X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
equalish(additive_identity,add(multiplicative_inverse(a),multiply(additive_identity,additive_identity))),
inference(spm,[status(thm)],[c_0_34,c_0_113]) ).
cnf(c_0_119,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiply(additive_identity,a),additive_identity)) ),
inference(spm,[status(thm)],[c_0_28,c_0_114]) ).
cnf(c_0_120,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
( equalish(additive_identity,add(additive_identity,multiply(additive_identity,additive_identity)))
| ~ defined(multiply(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_122,plain,
( equalish(add(additive_identity,multiply(X1,X2)),multiply(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_89]) ).
cnf(c_0_123,negated_conjecture,
( equalish(multiply(X1,X2),multiply(multiplicative_inverse(a),X2))
| ~ defined(X2)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_55,c_0_93]) ).
cnf(c_0_124,negated_conjecture,
equalish(multiply(additive_identity,multiply(additive_identity,a)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_95]),c_0_41]),c_0_26])]) ).
cnf(c_0_125,axiom,
( less_or_equal(X1,X2)
| ~ less_or_equal(X1,X3)
| ~ less_or_equal(X3,X2) ),
transitivity_of_order_relation ).
cnf(c_0_126,axiom,
( less_or_equal(additive_identity,multiply(X1,X2))
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X2) ),
compatibility_of_order_relation_and_multiplication ).
cnf(c_0_127,plain,
( less_or_equal(X1,additive_identity)
| ~ equalish(additive_identity,X2)
| ~ equalish(X2,X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_120]) ).
cnf(c_0_128,negated_conjecture,
equalish(additive_identity,add(additive_identity,multiply(additive_identity,additive_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_89]),c_0_41])]) ).
cnf(c_0_129,plain,
( equalish(add(additive_identity,multiply(X1,additive_identity)),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_41]) ).
cnf(c_0_130,negated_conjecture,
( equalish(multiply(X1,a),multiplicative_identity)
| ~ equalish(X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_123]),c_0_26])]) ).
cnf(c_0_131,negated_conjecture,
equalish(additive_identity,multiply(additive_identity,multiply(additive_identity,a))),
inference(spm,[status(thm)],[c_0_34,c_0_124]) ).
cnf(c_0_132,axiom,
( equalish(X1,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X2,X1) ),
antisymmetry_of_order_relation ).
cnf(c_0_133,plain,
( less_or_equal(X1,multiply(X2,X3))
| ~ less_or_equal(X1,additive_identity)
| ~ less_or_equal(additive_identity,X3)
| ~ less_or_equal(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_134,negated_conjecture,
( less_or_equal(X1,additive_identity)
| ~ equalish(add(additive_identity,multiply(additive_identity,additive_identity)),X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_135,plain,
equalish(add(additive_identity,multiply(additive_identity,additive_identity)),multiply(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_129,c_0_41]) ).
cnf(c_0_136,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(X2,a))
| ~ equalish(X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_28,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
equalish(additive_identity,multiply(multiply(additive_identity,additive_identity),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_131]),c_0_26]),c_0_41])]) ).
cnf(c_0_138,axiom,
~ equalish(additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_139,plain,
( equalish(multiply(X1,X2),X3)
| ~ less_or_equal(multiply(X1,X2),X3)
| ~ less_or_equal(X3,additive_identity)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_140,negated_conjecture,
less_or_equal(multiply(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_141,negated_conjecture,
~ equalish(multiply(additive_identity,additive_identity),additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_116])]),c_0_141]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD040-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Mon Aug 28 00:06:44 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 4.70/4.88 % Version : CSE_E---1.5
% 4.70/4.88 % Problem : theBenchmark.p
% 4.70/4.88 % Proof found
% 4.70/4.88 % SZS status Theorem for theBenchmark.p
% 4.70/4.88 % SZS output start Proof
% See solution above
% 4.70/4.89 % Total time : 4.303000 s
% 4.70/4.89 % SZS output end Proof
% 4.70/4.89 % Total time : 4.307000 s
%------------------------------------------------------------------------------