TSTP Solution File: FLD026-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD026-1 : 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 : n003.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 22:27:24 EDT 2023
% Result : Unsatisfiable 4.15s 4.27s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 27
% Syntax : Number of formulae : 92 ( 37 unt; 11 typ; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 146 ( 72 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 71 ( 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(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(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(a_equals_b_4,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b_4) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(multiplicative_inverses_not_equal,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_not_equal) ).
cnf(c_0_16,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_17,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_18,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_19,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
equalish(a,b),
a_equals_b_4 ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_22,plain,
equalish(additive_identity,add(additive_identity,additive_identity)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
equalish(b,a),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_24,plain,
( equalish(X1,add(additive_identity,additive_identity))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_26,plain,
( equalish(add(additive_identity,additive_identity),X1)
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_27,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_28,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_29,negated_conjecture,
( equalish(add(additive_identity,additive_identity),a)
| ~ equalish(b,additive_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_31,hypothesis,
( defined(multiplicative_inverse(b))
| equalish(b,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
( equalish(a,add(additive_identity,additive_identity))
| ~ equalish(b,additive_identity) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_3 ).
cnf(c_0_35,hypothesis,
( equalish(multiply(multiplicative_identity,multiplicative_inverse(b)),multiplicative_inverse(b))
| equalish(b,additive_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
~ equalish(b,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_38,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_39,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(b)),multiplicative_inverse(b)),
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_41,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]) ).
cnf(c_0_42,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_43,hypothesis,
( equalish(X1,multiplicative_inverse(b))
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_44,hypothesis,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,hypothesis,
defined(multiplicative_inverse(b)),
inference(sr,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_46,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_47,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_48,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,X3)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
cnf(c_0_49,hypothesis,
equalish(multiply(multiply(a,multiplicative_inverse(a)),multiplicative_inverse(b)),multiplicative_inverse(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_50,hypothesis,
( equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity)
| equalish(b,additive_identity) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_51,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
( equalish(X1,multiply(X2,multiply(X3,X4)))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_53,hypothesis,
equalish(multiplicative_inverse(b),multiply(multiply(a,multiplicative_inverse(a)),multiplicative_inverse(b))),
inference(spm,[status(thm)],[c_0_18,c_0_49]) ).
cnf(c_0_54,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_34]) ).
cnf(c_0_55,hypothesis,
equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity),
inference(sr,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_56,negated_conjecture,
( equalish(multiply(a,X1),multiply(b,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_57,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_18,c_0_41]) ).
cnf(c_0_58,plain,
( equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(X4,multiply(X2,X3))) ),
inference(spm,[status(thm)],[c_0_21,c_0_51]) ).
cnf(c_0_59,hypothesis,
equalish(multiplicative_inverse(b),multiply(a,multiply(multiplicative_inverse(a),multiplicative_inverse(b)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45]),c_0_54]),c_0_38])]) ).
cnf(c_0_60,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(b,multiplicative_inverse(b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_61,hypothesis,
equalish(multiply(a,multiplicative_inverse(b)),multiply(b,multiplicative_inverse(b))),
inference(spm,[status(thm)],[c_0_56,c_0_45]) ).
cnf(c_0_62,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_57]) ).
cnf(c_0_63,hypothesis,
equalish(multiplicative_inverse(b),multiply(multiply(multiplicative_inverse(a),multiplicative_inverse(b)),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_38]),c_0_45]),c_0_54])]) ).
cnf(c_0_64,hypothesis,
equalish(multiply(a,multiplicative_inverse(b)),multiplicative_identity),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,hypothesis,
( equalish(multiply(X1,a),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_38]) ).
cnf(c_0_66,hypothesis,
( equalish(multiply(X1,X2),multiply(multiply(a,multiplicative_inverse(a)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_40,c_0_62]) ).
cnf(c_0_67,hypothesis,
equalish(multiplicative_inverse(b),multiply(multiplicative_inverse(a),multiply(multiplicative_inverse(b),a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_63]),c_0_38]),c_0_45]),c_0_54])]) ).
cnf(c_0_68,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(b))) ),
inference(spm,[status(thm)],[c_0_21,c_0_64]) ).
cnf(c_0_69,hypothesis,
equalish(multiply(multiplicative_inverse(b),a),multiply(a,multiplicative_inverse(b))),
inference(spm,[status(thm)],[c_0_65,c_0_45]) ).
cnf(c_0_70,hypothesis,
( equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(X3,X2))
| ~ equalish(X3,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_66]) ).
cnf(c_0_71,hypothesis,
equalish(multiplicative_inverse(b),multiply(multiply(multiplicative_inverse(b),a),multiplicative_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_67]),c_0_54]),c_0_38]),c_0_45])]) ).
cnf(c_0_72,hypothesis,
equalish(multiply(multiplicative_inverse(b),a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,hypothesis,
equalish(multiply(multiplicative_identity,multiplicative_inverse(a)),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_74,hypothesis,
( equalish(X1,multiply(multiplicative_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_75,hypothesis,
equalish(multiplicative_inverse(b),multiply(multiply(a,multiplicative_inverse(a)),multiplicative_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_54]),c_0_72])]) ).
cnf(c_0_76,hypothesis,
( equalish(X1,multiplicative_inverse(a))
| ~ equalish(X1,multiply(multiplicative_identity,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_73]) ).
cnf(c_0_77,hypothesis,
equalish(multiplicative_inverse(b),multiply(multiplicative_identity,multiplicative_inverse(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_54])]) ).
cnf(c_0_78,hypothesis,
equalish(multiplicative_inverse(b),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
~ equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
multiplicative_inverses_not_equal ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_78]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : FLD026-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 23:31:10 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.60 start to proof: theBenchmark
% 4.15/4.27 % Version : CSE_E---1.5
% 4.15/4.27 % Problem : theBenchmark.p
% 4.15/4.27 % Proof found
% 4.15/4.27 % SZS status Theorem for theBenchmark.p
% 4.15/4.27 % SZS output start Proof
% See solution above
% 4.15/4.28 % Total time : 3.658000 s
% 4.15/4.28 % SZS output end Proof
% 4.15/4.28 % Total time : 3.662000 s
%------------------------------------------------------------------------------