TSTP Solution File: FLD049-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD049-3 : 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 : n018.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 22:27:36 EDT 2023
% Result : Unsatisfiable 1.03s 1.10s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 60 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 56 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
additive_identity: $i ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
multiplicative_inverse: $i > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
multiply: ( $i * $i ) > $i ).
tff(decl_31,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
b: $i ).
tff(decl_34,type,
c: $i ).
tff(decl_35,type,
d: $i ).
cnf(associativity_multiplication_1,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(product_7,negated_conjecture,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_5,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
cnf(not_sum_6,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).
cnf(not_product_8,negated_conjecture,
~ product(a,d,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_8) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(c_0_16,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_17,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_18,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_19,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_20,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
product(a,multiplicative_inverse(b),multiply(c,multiplicative_inverse(d))),
product_7 ).
cnf(c_0_23,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_24,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_25,plain,
( product(X1,X2,X3)
| sum(additive_identity,X1,additive_identity)
| ~ product(multiplicative_inverse(X1),X3,X2)
| ~ defined(X3)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
product(multiplicative_inverse(b),a,multiply(c,multiplicative_inverse(d))),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
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,
~ sum(additive_identity,b,additive_identity),
not_sum_5 ).
cnf(c_0_30,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1)
| ~ defined(X2)
| ~ defined(X5) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
product(b,multiply(c,multiplicative_inverse(d)),a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_32,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_33,negated_conjecture,
( product(X1,multiplicative_inverse(d),a)
| ~ product(b,c,X1)
| ~ defined(multiplicative_inverse(d)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_34,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_35,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_36,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
not_sum_6 ).
cnf(c_0_37,plain,
( product(X1,X2,X3)
| sum(additive_identity,X2,additive_identity)
| ~ product(X4,multiplicative_inverse(X2),X1)
| ~ product(X4,multiplicative_identity,X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_38,plain,
( product(X1,multiplicative_identity,X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_39,negated_conjecture,
( product(X1,multiplicative_inverse(d),a)
| ~ product(b,c,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]) ).
cnf(c_0_40,plain,
( product(X1,X2,X3)
| sum(additive_identity,X2,additive_identity)
| ~ product(X3,multiplicative_inverse(X2),X1)
| ~ defined(X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
product(multiply(b,c),multiplicative_inverse(d),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_32]),c_0_28])]) ).
cnf(c_0_42,negated_conjecture,
~ product(a,d,multiply(b,c)),
not_product_8 ).
cnf(c_0_43,negated_conjecture,
~ defined(multiply(b,c)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_35])]),c_0_42]),c_0_36]) ).
cnf(c_0_44,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD049-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n018.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 00:38:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 1.03/1.10 % Version : CSE_E---1.5
% 1.03/1.10 % Problem : theBenchmark.p
% 1.03/1.10 % Proof found
% 1.03/1.10 % SZS status Theorem for theBenchmark.p
% 1.03/1.10 % SZS output start Proof
% See solution above
% 1.03/1.10 % Total time : 0.532000 s
% 1.03/1.10 % SZS output end Proof
% 1.03/1.10 % Total time : 0.535000 s
%------------------------------------------------------------------------------