TSTP Solution File: FLD036-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD036-1 : 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 : n005.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 22:27:29 EDT 2023
% Result : Unsatisfiable 23.60s 23.72s
% Output : CNFRefutation 23.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of formulae : 64 ( 19 unt; 12 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 58 ~; 60 |; 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 : 58 ( 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(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(multiply_equals_multiply_4,negated_conjecture,
equalish(multiply(a,c),multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_equals_multiply_4) ).
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(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(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(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(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
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_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(c_not_equal_to_additive_identity_6,negated_conjecture,
~ equalish(c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_equal_to_additive_identity_6) ).
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(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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_not_equal_to_b_5,negated_conjecture,
~ equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_b_5) ).
cnf(c_0_15,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_16,negated_conjecture,
equalish(multiply(a,c),multiply(b,c)),
multiply_equals_multiply_4 ).
cnf(c_0_17,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_18,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_19,negated_conjecture,
( equalish(multiply(multiply(a,c),X1),multiply(multiply(b,c),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,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_17,c_0_18]) ).
cnf(c_0_21,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_22,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_23,negated_conjecture,
( equalish(X1,multiply(multiply(b,c),X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(a,c),X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_24,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X1),X2))
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_26,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_27,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_28,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_29,negated_conjecture,
( equalish(multiply(multiply(c,X1),a),multiply(multiply(b,c),X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_30,plain,
( equalish(multiplicative_identity,multiply(X1,multiplicative_inverse(X1)))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( equalish(X1,multiply(multiply(b,c),X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(c,X2),a)) ),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_32,plain,
( equalish(multiply(multiplicative_identity,X1),multiply(multiply(X2,multiplicative_inverse(X2)),X1))
| equalish(X2,additive_identity)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ equalish(c,additive_identity),
c_not_equal_to_additive_identity_6 ).
cnf(c_0_34,negated_conjecture,
( equalish(multiply(multiplicative_identity,a),multiply(multiply(b,c),multiplicative_inverse(c)))
| ~ defined(multiplicative_inverse(c)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26]),c_0_25])]),c_0_33]) ).
cnf(c_0_35,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_36,negated_conjecture,
equalish(multiply(multiplicative_identity,a),multiply(multiply(b,c),multiplicative_inverse(c))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25])]),c_0_33]) ).
cnf(c_0_37,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_38,negated_conjecture,
( equalish(X1,multiply(multiply(b,c),multiplicative_inverse(c)))
| ~ equalish(X1,multiply(multiplicative_identity,a)) ),
inference(spm,[status(thm)],[c_0_17,c_0_36]) ).
cnf(c_0_39,plain,
( equalish(X1,multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
equalish(a,multiply(multiply(b,c),multiplicative_inverse(c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
equalish(multiply(multiply(b,c),multiplicative_inverse(c)),a),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiply(b,c),multiplicative_inverse(c))) ),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_43,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_44,negated_conjecture,
( equalish(multiply(multiply(c,multiplicative_inverse(c)),b),a)
| ~ defined(multiplicative_inverse(c)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_25]),c_0_43])]) ).
cnf(c_0_45,negated_conjecture,
equalish(multiply(multiply(c,multiplicative_inverse(c)),b),a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_25])]),c_0_33]) ).
cnf(c_0_46,negated_conjecture,
( equalish(X1,a)
| ~ equalish(X1,multiply(multiply(c,multiplicative_inverse(c)),b)) ),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
equalish(multiply(multiplicative_identity,b),a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_32]),c_0_43]),c_0_25])]),c_0_33]) ).
cnf(c_0_48,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,multiply(multiplicative_identity,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_37]) ).
cnf(c_0_49,negated_conjecture,
equalish(a,multiply(multiplicative_identity,b)),
inference(spm,[status(thm)],[c_0_27,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
~ equalish(a,b),
a_not_equal_to_b_5 ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_43])]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD036-1 : 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
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 23:24:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 23.60/23.72 % Version : CSE_E---1.5
% 23.60/23.72 % Problem : theBenchmark.p
% 23.60/23.72 % Proof found
% 23.60/23.72 % SZS status Theorem for theBenchmark.p
% 23.60/23.72 % SZS output start Proof
% See solution above
% 23.70/23.73 % Total time : 23.158000 s
% 23.70/23.73 % SZS output end Proof
% 23.70/23.73 % Total time : 23.162000 s
%------------------------------------------------------------------------------