TSTP Solution File: CAT008-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : CAT008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 18:14:06 EDT 2023
% Result : Unsatisfiable 0.20s 0.72s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 38 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 53 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 9 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
defined: ( $i * $i ) > $o ).
tff(decl_23,type,
compose: ( $i * $i ) > $i ).
tff(decl_24,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
identity_map: $i > $o ).
tff(decl_26,type,
domain: $i > $i ).
tff(decl_27,type,
codomain: $i > $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
b: $i ).
cnf(category_theory_axiom3,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
cnf(ab_defined,hypothesis,
defined(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_defined) ).
cnf(associative_property2,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
cnf(product_on_codomain,axiom,
product(codomain(X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
cnf(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
cnf(composition_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
cnf(identity2,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity2) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
cnf(prove_domain_of_a_equals_codomain_of_b,negated_conjecture,
domain(a) != codomain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_a_equals_codomain_of_b) ).
cnf(c_0_11,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3 ).
cnf(c_0_12,hypothesis,
defined(a,b),
ab_defined ).
cnf(c_0_13,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2 ).
cnf(c_0_14,axiom,
product(X1,domain(X1),X1),
product_on_domain ).
cnf(c_0_15,hypothesis,
( defined(a,X1)
| ~ product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,axiom,
product(codomain(X1),X1,X1),
product_on_codomain ).
cnf(c_0_17,plain,
( defined(domain(X1),X2)
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
defined(a,codomain(b)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1 ).
cnf(c_0_20,hypothesis,
defined(domain(a),codomain(b)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_22,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined ).
cnf(c_0_23,hypothesis,
product(domain(a),codomain(b),codomain(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
identity2 ).
cnf(c_0_25,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map ).
cnf(c_0_26,hypothesis,
( X1 = codomain(b)
| ~ product(domain(a),codomain(b),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
product(domain(a),codomain(b),domain(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
domain(a) != codomain(b),
prove_domain_of_a_equals_codomain_of_b ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : CAT008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 00:29:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.72 % Version : CSE_E---1.5
% 0.20/0.72 % Problem : theBenchmark.p
% 0.20/0.72 % Proof found
% 0.20/0.72 % SZS status Theorem for theBenchmark.p
% 0.20/0.72 % SZS output start Proof
% See solution above
% 0.20/0.73 % Total time : 0.139000 s
% 0.20/0.73 % SZS output end Proof
% 0.20/0.73 % Total time : 0.142000 s
%------------------------------------------------------------------------------