TSTP Solution File: FLD025-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD025-3 : 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 : n008.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 22:27:23 EDT 2023
% Result : Unsatisfiable 0.60s 0.79s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 79 ( 36 unt; 14 typ; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 116 ( 59 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 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 : 79 ( 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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(commutativity_multiplication,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_5,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5) ).
cnf(associativity_multiplication_2,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(totality_of_multiplication,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).
cnf(product_6,negated_conjecture,
product(multiplicative_identity,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(not_product_7,negated_conjecture,
~ product(d,b,multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_7) ).
cnf(c_0_14,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_15,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_16,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,multiplicative_identity)
| ~ product(X4,X3,X2)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_18,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_19,negated_conjecture,
product(multiplicative_identity,a,b),
product_5 ).
cnf(c_0_20,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_21,plain,
( product(multiplicative_identity,X1,X2)
| ~ product(multiplicative_identity,X2,X1)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17])]) ).
cnf(c_0_22,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_23,negated_conjecture,
product(a,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( product(X1,a,X2)
| ~ product(X3,b,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
product(multiplicative_identity,b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( product(X1,X2,b)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( product(X1,a,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
( product(X1,X2,multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
totality_of_multiplication ).
cnf(c_0_29,negated_conjecture,
( product(X1,b,b)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17])]) ).
cnf(c_0_31,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),b,b),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,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_20,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
product(b,multiply(multiplicative_identity,multiplicative_identity),b),
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( product(X1,multiplicative_identity,b)
| ~ product(b,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17])]) ).
cnf(c_0_35,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_36,negated_conjecture,
product(multiply(b,multiplicative_identity),multiplicative_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_17]),c_0_35])]) ).
cnf(c_0_37,negated_conjecture,
product(multiplicative_identity,multiply(b,multiplicative_identity),b),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( product(multiplicative_identity,b,multiply(b,multiplicative_identity))
| ~ defined(multiply(b,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_39,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_40,plain,
( product(X1,X2,X3)
| ~ product(X4,multiplicative_identity,X1)
| ~ product(X4,X2,X3)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_41,negated_conjecture,
product(b,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_42,negated_conjecture,
product(multiplicative_identity,b,multiply(b,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_17]),c_0_35])]) ).
cnf(c_0_43,negated_conjecture,
( product(a,X1,X2)
| ~ product(b,X1,X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
product(b,multiplicative_identity,multiply(b,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
product(a,multiplicative_identity,multiply(b,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17])]) ).
cnf(c_0_46,negated_conjecture,
product(multiplicative_identity,a,multiply(b,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_47,negated_conjecture,
product(multiplicative_identity,multiply(b,multiplicative_identity),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_46]),c_0_22])]) ).
cnf(c_0_48,negated_conjecture,
( product(X1,multiplicative_identity,a)
| ~ product(multiplicative_identity,b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_17]),c_0_35])]) ).
cnf(c_0_49,negated_conjecture,
product(multiplicative_identity,c,d),
product_6 ).
cnf(c_0_50,negated_conjecture,
product(multiply(multiplicative_identity,b),multiplicative_identity,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_35]),c_0_17])]) ).
cnf(c_0_51,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,d,X2)
| ~ product(X3,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_49]) ).
cnf(c_0_52,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_53,negated_conjecture,
product(multiplicative_identity,multiply(multiplicative_identity,b),a),
inference(spm,[status(thm)],[c_0_18,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( product(X1,c,d)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_15]),c_0_52])]) ).
cnf(c_0_55,negated_conjecture,
( product(X1,b,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_35]),c_0_17])]) ).
cnf(c_0_56,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3)
| ~ defined(X4)
| ~ defined(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_57,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),c,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_17])]) ).
cnf(c_0_58,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_59,negated_conjecture,
product(multiply(multiplicative_identity,multiplicative_identity),b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_28]),c_0_17])]) ).
cnf(c_0_60,negated_conjecture,
( product(X1,d,multiply(X2,c))
| ~ product(X1,multiply(multiplicative_identity,multiplicative_identity),X2)
| ~ defined(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_61,negated_conjecture,
product(b,multiply(multiplicative_identity,multiplicative_identity),a),
inference(spm,[status(thm)],[c_0_18,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
product(b,d,multiply(a,c)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_22])]) ).
cnf(c_0_63,negated_conjecture,
~ product(d,b,multiply(a,c)),
not_product_7 ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD025-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 00:37:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 0.60/0.79 % Version : CSE_E---1.5
% 0.60/0.79 % Problem : theBenchmark.p
% 0.60/0.79 % Proof found
% 0.60/0.79 % SZS status Theorem for theBenchmark.p
% 0.60/0.79 % SZS output start Proof
% See solution above
% 0.60/0.80 % Total time : 0.189000 s
% 0.60/0.80 % SZS output end Proof
% 0.60/0.80 % Total time : 0.192000 s
%------------------------------------------------------------------------------