TSTP Solution File: CAT003-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : CAT003-1 : 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 : n028.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 18:14:02 EDT 2023
% Result : Unsatisfiable 1.11s 1.17s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 29
% Syntax : Number of formulae : 73 ( 30 unt; 12 typ; 0 def)
% Number of atoms : 117 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 114 ( 58 ~; 56 |; 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 : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 10 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 ).
tff(decl_31,type,
h: $i ).
tff(decl_32,type,
d: $i ).
tff(decl_33,type,
g: $i ).
cnf(associative_property1,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(ga_equals_d,hypothesis,
product(g,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ga_equals_d) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
cnf(associative_property2,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(category_theory_axiom1,axiom,
( defined(X1,X5)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom1) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
cnf(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
cnf(ha_equals_d,hypothesis,
product(h,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_equals_d) ).
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(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(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(mapping_from_x_to_its_domain,axiom,
defined(X1,domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
cnf(category_theory_axiom5,axiom,
( product(X6,X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X3,X5)
| ~ product(X4,X1,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).
cnf(composition_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
cnf(cancellation_for_product,hypothesis,
( X1 = X3
| ~ product(X1,c,X2)
| ~ product(X3,c,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_17,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
associative_property1 ).
cnf(c_0_18,hypothesis,
product(g,a,d),
ga_equals_d ).
cnf(c_0_19,hypothesis,
product(a,b,c),
ab_equals_c ).
cnf(c_0_20,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2 ).
cnf(c_0_21,hypothesis,
defined(g,a),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
( defined(X1,X5)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ defined(X3,X4) ),
category_theory_axiom1 ).
cnf(c_0_23,hypothesis,
defined(a,b),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_24,hypothesis,
( defined(X1,a)
| ~ product(X2,X1,g) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
product(X1,domain(X1),X1),
product_on_domain ).
cnf(c_0_26,hypothesis,
( defined(X1,X2)
| ~ product(X3,b,X2)
| ~ product(X1,X3,a) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1 ).
cnf(c_0_28,hypothesis,
defined(domain(g),a),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_30,hypothesis,
product(h,a,d),
ha_equals_d ).
cnf(c_0_31,hypothesis,
( defined(X1,c)
| ~ product(X1,a,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_32,hypothesis,
product(domain(g),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3 ).
cnf(c_0_34,hypothesis,
defined(h,a),
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
cnf(c_0_35,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6 ).
cnf(c_0_36,hypothesis,
defined(domain(g),c),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,hypothesis,
( defined(h,X1)
| ~ product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,hypothesis,
( defined(X1,c)
| ~ defined(X1,domain(g)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_29])]) ).
cnf(c_0_39,hypothesis,
defined(h,domain(g)),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_40,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition ).
cnf(c_0_41,hypothesis,
defined(h,c),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain ).
cnf(c_0_43,axiom,
( product(X6,X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X3,X5)
| ~ product(X4,X1,X6) ),
category_theory_axiom5 ).
cnf(c_0_44,hypothesis,
product(h,c,compose(h,c)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,hypothesis,
defined(g,c),
inference(spm,[status(thm)],[c_0_38,c_0_42]) ).
cnf(c_0_46,hypothesis,
( product(X1,X2,compose(h,c))
| ~ product(h,X3,X1)
| ~ product(X3,X2,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,hypothesis,
product(g,c,compose(g,c)),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_48,hypothesis,
( product(d,X1,compose(h,c))
| ~ product(a,X1,c) ),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_49,hypothesis,
( product(X1,X2,compose(g,c))
| ~ product(g,X3,X1)
| ~ product(X3,X2,c) ),
inference(spm,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_50,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined ).
cnf(c_0_51,hypothesis,
product(d,b,compose(h,c)),
inference(spm,[status(thm)],[c_0_48,c_0_19]) ).
cnf(c_0_52,hypothesis,
( product(d,X1,compose(g,c))
| ~ product(a,X1,c) ),
inference(spm,[status(thm)],[c_0_49,c_0_18]) ).
cnf(c_0_53,hypothesis,
( X1 = compose(h,c)
| ~ product(d,b,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,hypothesis,
product(d,b,compose(g,c)),
inference(spm,[status(thm)],[c_0_52,c_0_19]) ).
cnf(c_0_55,hypothesis,
( X1 = X3
| ~ product(X1,c,X2)
| ~ product(X3,c,X2) ),
cancellation_for_product ).
cnf(c_0_56,hypothesis,
compose(g,c) = compose(h,c),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,hypothesis,
( X1 = h
| ~ product(X1,c,compose(h,c)) ),
inference(spm,[status(thm)],[c_0_55,c_0_44]) ).
cnf(c_0_58,hypothesis,
product(g,c,compose(h,c)),
inference(rw,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
h != g,
prove_h_equals_g ).
cnf(c_0_60,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : CAT003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n028.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 00:42:37 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.11/1.17 % Version : CSE_E---1.5
% 1.11/1.17 % Problem : theBenchmark.p
% 1.11/1.17 % Proof found
% 1.11/1.17 % SZS status Theorem for theBenchmark.p
% 1.11/1.18 % SZS output start Proof
% See solution above
% 1.11/1.18 % Total time : 0.599000 s
% 1.11/1.18 % SZS output end Proof
% 1.11/1.18 % Total time : 0.602000 s
%------------------------------------------------------------------------------