TSTP Solution File: ALG002-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 16:00:02 EDT 2023
% Result : Unsatisfiable 0.16s 0.59s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 39 ( 9 unt; 7 typ; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 35 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 45 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiplicative_identity: $i ).
tff(decl_23,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
additive_identity: $i ).
tff(decl_25,type,
additive_inverse: $i > $i ).
tff(decl_26,type,
multiplicative_inverse: $i > $i ).
tff(decl_27,type,
greater_than_0: $i > $o ).
tff(decl_28,type,
a: $i ).
cnf(product_and_greater_than_0,axiom,
( greater_than_0(X3)
| ~ product(X1,X2,X3)
| ~ greater_than_0(X1)
| ~ greater_than_0(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
cnf(product_to_inverse,axiom,
( product(X1,additive_inverse(X2),additive_inverse(X3))
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
cnf(square_to_0,axiom,
( product(X3,X3,additive_identity)
| ~ product(X1,X2,X3)
| ~ product(X1,X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
cnf(product_and_inverse,axiom,
( greater_than_0(X1)
| product(X1,X1,additive_identity)
| greater_than_0(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
cnf(commutativity_of_product,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_product) ).
cnf(inverse_and_identity,axiom,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| product(X1,X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
cnf(right_identity,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(inverse_greater_than_0,axiom,
( ~ greater_than_0(X1)
| ~ greater_than_0(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_greater_than_0) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
cnf(greater_than_0_square,axiom,
( ~ greater_than_0(X1)
| ~ product(X1,X1,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
cnf(c_0_12,axiom,
( greater_than_0(X3)
| ~ product(X1,X2,X3)
| ~ greater_than_0(X1)
| ~ greater_than_0(X2) ),
product_and_greater_than_0 ).
cnf(c_0_13,axiom,
( product(X1,additive_inverse(X2),additive_inverse(X3))
| ~ product(X1,X2,X3) ),
product_to_inverse ).
cnf(c_0_14,axiom,
( product(X3,X3,additive_identity)
| ~ product(X1,X2,X3)
| ~ product(X1,X1,additive_identity) ),
square_to_0 ).
cnf(c_0_15,axiom,
( greater_than_0(X1)
| product(X1,X1,additive_identity)
| greater_than_0(additive_inverse(X1)) ),
product_and_inverse ).
cnf(c_0_16,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_product ).
cnf(c_0_17,axiom,
( product(X1,multiplicative_inverse(X1),multiplicative_identity)
| product(X1,X1,additive_identity) ),
inverse_and_identity ).
cnf(c_0_18,plain,
( greater_than_0(additive_inverse(X1))
| ~ greater_than_0(additive_inverse(X2))
| ~ greater_than_0(X3)
| ~ product(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,axiom,
product(X1,multiplicative_identity,X1),
right_identity ).
cnf(c_0_20,axiom,
( ~ greater_than_0(X1)
| ~ greater_than_0(additive_inverse(X1)) ),
inverse_greater_than_0 ).
cnf(c_0_21,plain,
( greater_than_0(additive_inverse(X1))
| greater_than_0(X1)
| product(X2,X2,additive_identity)
| ~ product(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( product(multiplicative_inverse(X1),X1,multiplicative_identity)
| product(X1,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
not_abelian ).
cnf(c_0_24,axiom,
( ~ greater_than_0(X1)
| ~ product(X1,X1,additive_identity) ),
greater_than_0_square ).
cnf(c_0_25,plain,
( ~ greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_26,plain,
( greater_than_0(additive_inverse(multiplicative_inverse(X1)))
| greater_than_0(multiplicative_inverse(X1))
| product(X1,X1,additive_identity) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( ~ greater_than_0(additive_inverse(multiplicative_inverse(X1)))
| ~ greater_than_0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
prove_a_inverse_greater_than_0 ).
cnf(c_0_29,plain,
( greater_than_0(multiplicative_inverse(X1))
| ~ greater_than_0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_27]) ).
cnf(c_0_30,hypothesis,
greater_than_0(a),
a_greater_than_0 ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : ALG002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n005.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 28 03:58:53 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.55 start to proof: theBenchmark
% 0.16/0.59 % Version : CSE_E---1.5
% 0.16/0.59 % Problem : theBenchmark.p
% 0.16/0.59 % Proof found
% 0.16/0.59 % SZS status Theorem for theBenchmark.p
% 0.16/0.59 % SZS output start Proof
% See solution above
% 0.16/0.60 % Total time : 0.034000 s
% 0.16/0.60 % SZS output end Proof
% 0.16/0.60 % Total time : 0.036000 s
%------------------------------------------------------------------------------