TSTP Solution File: FLD033-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD033-1 : 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 : n009.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 22:27:28 EDT 2023
% Result : Unsatisfiable 0.53s 0.76s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 81 ( 29 unt; 11 typ; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 132 ( 67 ~; 65 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 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,
m: $i ).
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(m_is_defined,hypothesis,
defined(m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_defined) ).
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(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(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(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(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
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_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(reflexivity_of_equality,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',reflexivity_of_equality) ).
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(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(multiply_equals_a_4,negated_conjecture,
equalish(multiply(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_a_4) ).
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(m_not_equal_to_multiplicative_identity_5,negated_conjecture,
~ equalish(m,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_not_equal_to_multiplicative_identity_5) ).
cnf(c_0_16,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_17,hypothesis,
defined(m),
m_is_defined ).
cnf(c_0_18,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_19,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_20,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_3 ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_22,hypothesis,
equalish(multiply(multiplicative_identity,m),m),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_24,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_25,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_26,hypothesis,
( equalish(X1,m)
| ~ equalish(X1,multiply(multiplicative_identity,m)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,hypothesis,
( equalish(multiply(multiply(a,multiplicative_inverse(a)),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_29,hypothesis,
equalish(multiply(multiply(a,multiplicative_inverse(a)),m),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17])]) ).
cnf(c_0_30,hypothesis,
( equalish(X1,multiply(a,multiplicative_inverse(a)))
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_31,hypothesis,
( equalish(X1,m)
| ~ equalish(X1,multiply(multiply(a,multiplicative_inverse(a)),m)) ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_32,hypothesis,
( equalish(multiply(X1,X2),multiply(multiply(a,multiplicative_inverse(a)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_33,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_34,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_35,hypothesis,
( equalish(multiply(X1,m),m)
| ~ equalish(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17])]) ).
cnf(c_0_36,plain,
( equalish(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,axiom,
( equalish(X1,X1)
| ~ defined(X1) ),
reflexivity_of_equality ).
cnf(c_0_38,hypothesis,
( equalish(X1,m)
| ~ equalish(X1,multiply(X2,m))
| ~ equalish(X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_39,hypothesis,
equalish(multiply(m,multiplicative_identity),multiply(multiplicative_identity,m)),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_40,plain,
equalish(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_41,hypothesis,
equalish(multiply(m,multiplicative_identity),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_42,hypothesis,
equalish(m,multiply(m,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_43,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_44,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_45,negated_conjecture,
equalish(multiply(m,a),a),
multiply_equals_a_4 ).
cnf(c_0_46,hypothesis,
( equalish(X1,multiply(m,multiplicative_identity))
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_21,c_0_42]) ).
cnf(c_0_47,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),X1)
| ~ equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_48,plain,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X2,X3),X1))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_49,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_19]),c_0_20]) ).
cnf(c_0_50,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_51,negated_conjecture,
( equalish(multiply(multiply(m,a),X1),multiply(a,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_52,hypothesis,
( equalish(multiply(m,multiplicative_identity),X1)
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_53,hypothesis,
( equalish(multiply(X1,m),multiply(m,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_54,hypothesis,
( equalish(multiply(a,multiplicative_inverse(a)),m)
| ~ equalish(multiply(multiplicative_identity,m),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_55,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_56,hypothesis,
equalish(multiply(m,multiply(a,multiplicative_inverse(a))),m),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_48]),c_0_17]),c_0_49]),c_0_19])]) ).
cnf(c_0_57,hypothesis,
equalish(multiply(multiply(m,a),multiplicative_inverse(a)),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_49])]) ).
cnf(c_0_58,hypothesis,
( equalish(X1,X2)
| ~ equalish(X1,multiply(m,multiplicative_identity))
| ~ equalish(X2,m) ),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_59,hypothesis,
equalish(multiply(multiplicative_identity,m),multiply(m,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_53,c_0_34]) ).
cnf(c_0_60,hypothesis,
( equalish(m,multiply(a,multiplicative_inverse(a)))
| ~ equalish(multiply(multiplicative_identity,m),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
~ equalish(m,multiplicative_identity),
m_not_equal_to_multiplicative_identity_5 ).
cnf(c_0_62,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_21,c_0_55]) ).
cnf(c_0_63,hypothesis,
equalish(m,multiply(m,multiply(a,multiplicative_inverse(a)))),
inference(spm,[status(thm)],[c_0_25,c_0_56]) ).
cnf(c_0_64,hypothesis,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiply(m,a),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_21,c_0_57]) ).
cnf(c_0_65,hypothesis,
( equalish(multiply(multiplicative_identity,m),X1)
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,hypothesis,
~ equalish(multiply(multiplicative_identity,m),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_60]),c_0_61]) ).
cnf(c_0_67,hypothesis,
equalish(m,multiply(multiply(m,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_62,c_0_63]),c_0_49]),c_0_19]),c_0_17])]) ).
cnf(c_0_68,hypothesis,
~ equalish(multiply(multiply(m,a),multiplicative_inverse(a)),m),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_69,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : FLD033-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 00:12:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.50/0.57 start to proof: theBenchmark
% 0.53/0.76 % Version : CSE_E---1.5
% 0.53/0.76 % Problem : theBenchmark.p
% 0.53/0.76 % Proof found
% 0.53/0.76 % SZS status Theorem for theBenchmark.p
% 0.53/0.76 % SZS output start Proof
% See solution above
% 0.53/0.77 % Total time : 0.185000 s
% 0.53/0.77 % SZS output end Proof
% 0.53/0.77 % Total time : 0.188000 s
%------------------------------------------------------------------------------