%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT001-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 : Tue May 5 04:11:36 PM UTC 2026
% Result : Unsatisfiable 3.87s 3.10s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 62 ( 29 unt; 0 nHn; 56 RR)
% Number of literals : 120 ( 10 equ; 60 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 100 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associative_property1,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(bg_equals_d,hypothesis,
product(b,g,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_equals_d) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
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_axiom4,axiom,
( defined(X5,X2)
| ~ product(X1,X2,X3)
| ~ product(X4,X1,X5)
| ~ defined(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).
cnf(product_on_codomain,axiom,
product(codomain(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
cnf(bh_equals_d,hypothesis,
product(b,h,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_d) ).
cnf(identity2,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
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(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_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(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(category_theory_axiom2,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).
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(c,X1,X2)
| ~ product(c,X3,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(b,g,d),
bg_equals_d ).
cnf(c_0_19,hypothesis,
product(a,b,c),
ab_equals_c ).
cnf(c_0_20,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3 ).
cnf(c_0_21,hypothesis,
defined(b,g),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
( defined(X5,X2)
| ~ product(X1,X2,X3)
| ~ product(X4,X1,X5)
| ~ defined(X4,X3) ),
category_theory_axiom4 ).
cnf(c_0_23,hypothesis,
defined(a,b),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_24,hypothesis,
( defined(b,X1)
| ~ product(X1,X2,g) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
product(codomain(X1),X1,X1),
product_on_codomain ).
cnf(c_0_26,hypothesis,
product(b,h,d),
bh_equals_d ).
cnf(c_0_27,hypothesis,
( defined(X1,X2)
| ~ product(a,X3,X1)
| ~ product(X3,X2,b) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
identity2 ).
cnf(c_0_29,hypothesis,
defined(b,codomain(g)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map ).
cnf(c_0_31,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2 ).
cnf(c_0_32,hypothesis,
defined(b,h),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_33,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6 ).
cnf(c_0_34,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x ).
cnf(c_0_35,hypothesis,
( defined(c,X1)
| ~ product(b,X1,b) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_36,hypothesis,
product(b,codomain(g),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_37,hypothesis,
( defined(X1,h)
| ~ product(X2,X1,b) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( defined(X1,X2)
| ~ defined(X1,codomain(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30])]) ).
cnf(c_0_39,hypothesis,
defined(c,codomain(g)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,hypothesis,
defined(codomain(g),h),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_41,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition ).
cnf(c_0_42,hypothesis,
defined(c,g),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,hypothesis,
( defined(X1,h)
| ~ defined(X1,codomain(g)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_30])]) ).
cnf(c_0_44,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
category_theory_axiom2 ).
cnf(c_0_45,hypothesis,
product(c,g,compose(c,g)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,hypothesis,
defined(c,h),
inference(spm,[status(thm)],[c_0_43,c_0_39]) ).
cnf(c_0_47,hypothesis,
( product(X1,X2,compose(c,g))
| ~ product(X3,g,X2)
| ~ product(X1,X3,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,hypothesis,
product(c,h,compose(c,h)),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_49,hypothesis,
( product(X1,d,compose(c,g))
| ~ product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_50,hypothesis,
( product(X1,X2,compose(c,h))
| ~ product(X3,h,X2)
| ~ product(X1,X3,c) ),
inference(spm,[status(thm)],[c_0_44,c_0_48]) ).
cnf(c_0_51,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined ).
cnf(c_0_52,hypothesis,
product(a,d,compose(c,g)),
inference(spm,[status(thm)],[c_0_49,c_0_19]) ).
cnf(c_0_53,hypothesis,
( product(X1,d,compose(c,h))
| ~ product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_54,hypothesis,
( X1 = X3
| ~ product(c,X1,X2)
| ~ product(c,X3,X2) ),
cancellation_for_product ).
cnf(c_0_55,hypothesis,
( X1 = compose(c,g)
| ~ product(a,d,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,hypothesis,
product(a,d,compose(c,h)),
inference(spm,[status(thm)],[c_0_53,c_0_19]) ).
cnf(c_0_57,hypothesis,
( X1 = g
| ~ product(c,X1,compose(c,g)) ),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_58,hypothesis,
compose(c,g) = compose(c,h),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,hypothesis,
( X1 = g
| ~ product(c,X1,compose(c,h)) ),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_60,negated_conjecture,
h != g,
prove_h_equals_g ).
cnf(c_0_61,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_48]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT001-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:46:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.87/3.10 % Version : CSE_E---1.7
% 3.87/3.10 % Problem : theBenchmark.p
% 3.87/3.10 % SZS status Unsatisfiable for theBenchmark.p
% 3.87/3.10 % SZS output start CNFRefutation
% See solution above
% 3.87/3.11 % Total time : 2.368s
%------------------------------------------------------------------------------