%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT020-1 : TPTP v9.2.1. Released v2.5.0.
% 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 04:11:44 PM UTC 2026
% Result : Satisfiable 1.28s 1.73s
% Output : Saturation 1.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(product_on_codomain,axiom,
product(codomain(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
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(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
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(identity2,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
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(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
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(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(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(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(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(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_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(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(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(associative_property1,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(c_0_18,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3,
[final] ).
cnf(c_0_19,axiom,
product(codomain(X1),X1,X1),
product_on_codomain,
[final] ).
cnf(c_0_20,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2,
[final] ).
cnf(c_0_21,axiom,
product(X1,domain(X1),X1),
product_on_domain,
[final] ).
cnf(c_0_22,plain,
( defined(X1,codomain(X2))
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]),
[final] ).
cnf(c_0_23,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x,
[final] ).
cnf(c_0_24,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
identity2,
[final] ).
cnf(c_0_25,plain,
( defined(domain(X1),X2)
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]),
[final] ).
cnf(c_0_26,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain,
[final] ).
cnf(c_0_27,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1,
[final] ).
cnf(c_0_28,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
category_theory_axiom2,
[final] ).
cnf(c_0_29,plain,
defined(codomain(X1),codomain(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]),
[final] ).
cnf(c_0_30,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map,
[final] ).
cnf(c_0_31,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined,
[final] ).
cnf(c_0_32,plain,
( product(codomain(X1),X1,codomain(X1))
| ~ identity_map(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]),
[final] ).
cnf(c_0_33,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map,
[final] ).
cnf(c_0_34,axiom,
( product(X6,X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X3,X5)
| ~ product(X4,X1,X6) ),
category_theory_axiom5,
[final] ).
cnf(c_0_35,plain,
defined(domain(X1),domain(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]),
[final] ).
cnf(c_0_36,plain,
( product(X1,domain(X1),domain(X1))
| ~ identity_map(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]),
[final] ).
cnf(c_0_37,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition,
[final] ).
cnf(c_0_38,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,codomain(X3))
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]),
[final] ).
cnf(c_0_39,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_30])]),
[final] ).
cnf(c_0_40,plain,
( X1 = X2
| ~ product(codomain(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]),
[final] ).
cnf(c_0_41,plain,
product(codomain(domain(X1)),domain(X1),codomain(domain(X1))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,domain(X3))
| ~ product(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_21]),
[final] ).
cnf(c_0_43,plain,
product(domain(X1),domain(X1),domain(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_35]),c_0_33])]),
[final] ).
cnf(c_0_44,plain,
( X1 = X2
| ~ product(X2,domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]),
[final] ).
cnf(c_0_45,plain,
product(domain(X1),domain(domain(X1)),domain(domain(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_46,plain,
product(codomain(X1),domain(codomain(X1)),domain(codomain(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_47,plain,
product(codomain(codomain(X1)),codomain(X1),codomain(codomain(X1))),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_48,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6,
[final] ).
cnf(c_0_49,plain,
product(X1,domain(X1),compose(X1,domain(X1))),
inference(spm,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_50,plain,
( product(codomain(X1),X2,X1)
| ~ product(codomain(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]),
[final] ).
cnf(c_0_51,plain,
codomain(domain(X1)) = domain(X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]),
[final] ).
cnf(c_0_52,plain,
( product(X1,domain(X2),X2)
| ~ product(X2,domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]),
[final] ).
cnf(c_0_53,plain,
domain(domain(X1)) = domain(X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]),
[final] ).
cnf(c_0_54,plain,
domain(codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_44,c_0_46]),
[final] ).
cnf(c_0_55,plain,
codomain(codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_40,c_0_47]),
[final] ).
cnf(c_0_56,axiom,
( defined(X1,X5)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ defined(X3,X4) ),
category_theory_axiom1,
[final] ).
cnf(c_0_57,axiom,
( defined(X5,X2)
| ~ product(X1,X2,X3)
| ~ product(X4,X1,X5)
| ~ defined(X4,X3) ),
category_theory_axiom4,
[final] ).
cnf(c_0_58,plain,
( defined(X1,domain(X2))
| ~ identity_map(X2)
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_26]),
[final] ).
cnf(c_0_59,plain,
compose(X1,domain(X1)) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_49]),
[final] ).
cnf(c_0_60,plain,
( X1 = codomain(X2)
| ~ product(codomain(X2),codomain(X2),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_39]),
[final] ).
cnf(c_0_61,plain,
product(codomain(X1),codomain(X1),compose(codomain(X1),codomain(X1))),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_62,plain,
product(codomain(X1),X1,compose(codomain(X1),X1)),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_63,plain,
( product(X1,X2,domain(X3))
| ~ product(X4,domain(X3),X2)
| ~ product(X1,X4,domain(X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_43]),
[final] ).
cnf(c_0_64,plain,
( product(X1,X2,domain(X3))
| ~ product(domain(X3),X4,X1)
| ~ product(X4,X2,domain(X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_43]),
[final] ).
cnf(c_0_65,plain,
( product(X1,X2,codomain(X3))
| ~ product(X4,codomain(X3),X2)
| ~ product(X1,X4,codomain(X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_39]),
[final] ).
cnf(c_0_66,plain,
( product(X1,X2,codomain(X3))
| ~ product(codomain(X3),X4,X1)
| ~ product(X4,X2,codomain(X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_39]),
[final] ).
cnf(c_0_67,plain,
( product(domain(X1),X2,domain(X1))
| ~ product(domain(X1),domain(X1),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]),
[final] ).
cnf(c_0_68,plain,
( product(X1,domain(X2),domain(X2))
| ~ product(domain(X2),domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]),
[final] ).
cnf(c_0_69,plain,
( product(X1,codomain(X2),codomain(X2))
| ~ product(codomain(X2),codomain(X2),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_54]),
[final] ).
cnf(c_0_70,plain,
( product(codomain(X1),X2,codomain(X1))
| ~ product(codomain(X1),codomain(X1),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_55]),
[final] ).
cnf(c_0_71,plain,
( X1 = domain(X2)
| ~ product(domain(X2),domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_43]),
[final] ).
cnf(c_0_72,plain,
( product(X1,X2,X3)
| ~ product(X4,domain(X3),X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_21]),
[final] ).
cnf(c_0_73,plain,
( product(X1,X2,X3)
| ~ product(codomain(X3),X4,X1)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]),
[final] ).
cnf(c_0_74,plain,
( defined(X1,X2)
| ~ product(X1,codomain(X2),X3)
| ~ defined(X3,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_19]),
[final] ).
cnf(c_0_75,plain,
( defined(X1,X2)
| ~ product(domain(X1),X2,X3)
| ~ defined(X1,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_21]),
[final] ).
cnf(c_0_76,plain,
( defined(codomain(X1),domain(X1))
| ~ identity_map(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_23]),
[final] ).
cnf(c_0_77,plain,
( defined(X1,X2)
| ~ defined(X1,codomain(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_30])]),
[final] ).
cnf(c_0_78,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
associative_property1,
[final] ).
cnf(c_0_79,plain,
compose(domain(X1),domain(X1)) = domain(X1),
inference(spm,[status(thm)],[c_0_59,c_0_53]),
[final] ).
cnf(c_0_80,plain,
compose(codomain(X1),codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_60,c_0_61]),
[final] ).
cnf(c_0_81,plain,
compose(codomain(X1),X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_62]),
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT020-1 : TPTP v9.2.1. Released v2.5.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n007.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:47:38 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Satisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start Saturation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------