TSTP Solution File: CAT018-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : CAT018-1 : 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 : n016.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 18:14:12 EDT 2023
% Result : Unsatisfiable 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 36 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 6 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 ).
tff(decl_30,type,
c: $i ).
cnf(category_theory_axiom3,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
cnf(closure_of_composition,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
cnf(assume_bc_exists,hypothesis,
defined(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
cnf(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
cnf(assume_ab_exists,hypothesis,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
cnf(category_theory_axiom6,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
cnf(prove_a_bc_exists,negated_conjecture,
~ defined(a,compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
cnf(c_0_9,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3 ).
cnf(c_0_10,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x ).
cnf(c_0_11,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition ).
cnf(c_0_12,hypothesis,
defined(b,c),
assume_bc_exists ).
cnf(c_0_13,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1 ).
cnf(c_0_14,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map ).
cnf(c_0_15,plain,
( defined(codomain(X1),X2)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,hypothesis,
product(b,c,compose(b,c)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
defined(a,b),
assume_ab_exists ).
cnf(c_0_18,plain,
( product(codomain(X1),X2,X2)
| ~ defined(codomain(X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,hypothesis,
defined(codomain(compose(b,c)),b),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6 ).
cnf(c_0_21,hypothesis,
( defined(a,X1)
| ~ product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_22,hypothesis,
product(codomain(compose(b,c)),b,b),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( defined(X1,X2)
| ~ defined(X1,codomain(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_10]),c_0_14])]) ).
cnf(c_0_24,hypothesis,
defined(a,codomain(compose(b,c))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ defined(a,compose(b,c)),
prove_a_bc_exists ).
cnf(c_0_26,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : CAT018-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n016.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 00:42:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.015000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.020000 s
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