TSTP Solution File: FLD027-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD027-3 : 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 : n025.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 22:27:25 EDT 2023
% Result : Unsatisfiable 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 67 ( 27 unt; 12 typ; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 48 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 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 ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
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(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
cnf(not_sum_4,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_4) ).
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(product_5,negated_conjecture,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
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(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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(not_product_6,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_6) ).
cnf(c_0_13,axiom,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_14,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_15,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
not_sum_3 ).
cnf(c_0_16,axiom,
( product(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ product(X5,X2,X6)
| ~ product(X4,X6,X3) ),
associativity_multiplication_2 ).
cnf(c_0_17,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_19,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
not_sum_4 ).
cnf(c_0_20,axiom,
( defined(multiplicative_inverse(X1))
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_21,hypothesis,
( product(X1,a,X2)
| ~ product(X3,multiplicative_inverse(a),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
product_5 ).
cnf(c_0_23,hypothesis,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_19]) ).
cnf(c_0_24,axiom,
( product(multiplicative_identity,X1,X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_25,hypothesis,
defined(multiplicative_inverse(b)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_19]) ).
cnf(c_0_26,axiom,
( product(X1,X2,X3)
| ~ product(X2,X1,X3) ),
commutativity_multiplication ).
cnf(c_0_27,negated_conjecture,
( product(multiplicative_inverse(b),a,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,hypothesis,
( product(X1,b,X2)
| ~ product(X3,multiplicative_inverse(b),X1)
| ~ product(X3,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_29,hypothesis,
product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ product(X4,X6,X2)
| ~ product(X5,X6,X3) ),
associativity_multiplication_1 ).
cnf(c_0_31,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_32,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( product(a,multiplicative_inverse(b),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_35,hypothesis,
( product(multiplicative_inverse(b),b,X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,hypothesis,
( product(X1,X2,multiplicative_identity)
| ~ product(X3,multiplicative_inverse(a),X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,hypothesis,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_38,hypothesis,
( product(X1,b,X2)
| ~ product(a,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_39,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_40,hypothesis,
( product(b,multiplicative_inverse(b),X1)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_41,hypothesis,
product(multiplicative_identity,b,b),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_42,hypothesis,
( product(X1,multiplicative_inverse(a),multiplicative_identity)
| ~ product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,hypothesis,
( product(X1,b,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_45,hypothesis,
( product(X1,b,X2)
| ~ product(b,multiplicative_identity,X2)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_46,hypothesis,
product(b,multiplicative_identity,b),
inference(spm,[status(thm)],[c_0_26,c_0_41]) ).
cnf(c_0_47,hypothesis,
( product(multiplicative_identity,a,X1)
| ~ product(X2,multiplicative_identity,a)
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_42]) ).
cnf(c_0_48,hypothesis,
( product(b,X1,a)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_49,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_50,hypothesis,
( product(X1,b,b)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,hypothesis,
( product(multiplicative_identity,a,X1)
| ~ product(b,multiplicative_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_52,hypothesis,
( product(b,X1,b)
| ~ product(multiplicative_identity,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
~ product(multiplicative_identity,a,b),
not_product_6 ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_49])]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD027-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n025.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 : Mon Aug 28 00:26:54 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.69 % Version : CSE_E---1.5
% 0.20/0.69 % Problem : theBenchmark.p
% 0.20/0.69 % Proof found
% 0.20/0.69 % SZS status Theorem for theBenchmark.p
% 0.20/0.69 % SZS output start Proof
% See solution above
% 0.20/0.70 % Total time : 0.113000 s
% 0.20/0.70 % SZS output end Proof
% 0.20/0.70 % Total time : 0.115000 s
%------------------------------------------------------------------------------