TMTP Model File: CAT020-1.003-Sat
View Problem
- Process Model
%------------------------------------------------------------------------------
% File : E---1.9
% Problem : CAT020-1 : TPTP v6.2.0. Released v2.5.0.
% Transform : none
% Format : tptp:raw
% Command : eprover --auto-schedule --tstp-format -s --proof-object --memory-limit=2048 --cpu-limit=%d %s
% Computer : n124.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-504.16.2.el6.x86_64
% CPULimit : 300s
% DateTime : Mon May 18 09:18:22 EDT 2015
% Result : Satisfiable 0.02s
% Output : Saturation 0.02s
% Verified :
% Statistics : Number of clauses : 85 ( 255 expanded)
% Number of leaves : 18 ( 143 expanded)
% Depth : 7
% Number of atoms : 178 ( 498 expanded)
% Number of equality atoms : 15 ( 29 expanded)
% Maximal clause size : 4 ( 2 average)
% Maximal term depth : 3 ( 1 average)
% Comments :
%------------------------------------------------------------------------------
cnf(c_0_0,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3)).
cnf(c_0_1,axiom,
( product(codomain(X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain)).
cnf(c_0_2,axiom,
( defined(codomain(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x)).
cnf(c_0_3,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2)).
cnf(c_0_4,axiom,
( product(X1,domain(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain)).
cnf(c_0_5,axiom,
( defined(X1,domain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain)).
cnf(c_0_6,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1)).
cnf(c_0_7,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2)).
cnf(c_0_8,axiom,
( identity_map(codomain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map)).
cnf(c_0_9,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(c_0_10,axiom,
( identity_map(domain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map)).
cnf(c_0_11,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(c_0_12,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(c_0_13,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition)).
cnf(c_0_14,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(c_0_15,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(c_0_16,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(c_0_17,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1)).
cnf(c_0_18,plain,
( defined(X1,codomain(X2))
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_0,c_0_1]),
[final]).
cnf(c_0_19,plain,
( defined(codomain(X1),codomain(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_2]),
[final]).
cnf(c_0_20,plain,
( defined(domain(X1),X2)
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]),
[final]).
cnf(c_0_21,plain,
( defined(codomain(X1),codomain(codomain(X1))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19])).
cnf(c_0_22,plain,
( defined(domain(X1),domain(X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_5]),
[final]).
cnf(c_0_23,plain,
( product(X1,domain(X1),domain(X1))
| ~ identity_map(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_5]),
[final]).
cnf(c_0_24,plain,
( product(codomain(X1),X1,codomain(X1))
| ~ identity_map(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_2]),
[final]).
cnf(c_0_25,plain,
( product(codomain(X1),codomain(codomain(X1)),codomain(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_21]),c_0_8])])).
cnf(c_0_26,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,domain(X3))
| ~ product(X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_4]),
[final]).
cnf(c_0_27,plain,
( product(domain(X1),domain(X1),domain(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_22]),c_0_10])]),
[final]).
cnf(c_0_28,plain,
( X1 = X2
| ~ product(X2,domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_4]),
[final]).
cnf(c_0_29,plain,
( product(domain(X1),domain(domain(X1)),domain(domain(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_10])).
cnf(c_0_30,plain,
( product(codomain(X1),domain(codomain(X1)),domain(codomain(X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_8])).
cnf(c_0_31,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,codomain(X3))
| ~ product(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_1]),
[final]).
cnf(c_0_32,plain,
( product(codomain(X1),codomain(X1),codomain(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_19]),c_0_8])]),
[final]).
cnf(c_0_33,plain,
( X1 = X2
| ~ product(codomain(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_1]),
[final]).
cnf(c_0_34,plain,
( product(codomain(domain(X1)),domain(X1),codomain(domain(X1))) ),
inference(spm,[status(thm)],[c_0_24,c_0_10])).
cnf(c_0_35,plain,
( X1 = codomain(X2)
| ~ product(codomain(X2),codomain(codomain(X2)),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_25])).
cnf(c_0_36,plain,
( product(codomain(X1),codomain(codomain(X1)),codomain(codomain(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_21]),c_0_8])])).
cnf(c_0_37,plain,
( product(X1,domain(X1),compose(X1,domain(X1))) ),
inference(spm,[status(thm)],[c_0_13,c_0_5])).
cnf(c_0_38,plain,
( product(X1,domain(X2),X2)
| ~ product(X2,domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]),
[final]).
cnf(c_0_39,plain,
( domain(domain(X1)) = domain(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]),
[final]).
cnf(c_0_40,plain,
( domain(codomain(X1)) = codomain(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_30]),
[final]).
cnf(c_0_41,plain,
( product(codomain(X1),X2,X1)
| ~ product(codomain(X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]),
[final]).
cnf(c_0_42,plain,
( codomain(domain(X1)) = domain(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]),
[final]).
cnf(c_0_43,plain,
( codomain(codomain(X1)) = codomain(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]),
[final]).
cnf(c_0_44,plain,
( defined(X1,domain(X2))
| ~ identity_map(X2)
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_5]),
[final]).
cnf(c_0_45,plain,
( compose(X1,domain(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_37]),
[final]).
cnf(c_0_46,plain,
( X1 = codomain(X2)
| ~ product(codomain(X2),codomain(X2),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_32]),
[final]).
cnf(c_0_47,plain,
( product(codomain(X1),codomain(X1),compose(codomain(X1),codomain(X1))) ),
inference(spm,[status(thm)],[c_0_13,c_0_19])).
cnf(c_0_48,plain,
( product(codomain(X1),X1,compose(codomain(X1),X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_2])).
cnf(c_0_49,plain,
( product(X1,domain(X2),domain(X2))
| ~ product(domain(X2),domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]),
[final]).
cnf(c_0_50,plain,
( product(X1,X2,domain(X3))
| ~ product(X4,domain(X3),X2)
| ~ product(X1,X4,domain(X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_27]),
[final]).
cnf(c_0_51,plain,
( product(X1,X2,domain(X3))
| ~ product(domain(X3),X4,X1)
| ~ product(X4,X2,domain(X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_27]),
[final]).
cnf(c_0_52,plain,
( product(X1,codomain(X2),codomain(X2))
| ~ product(codomain(X2),codomain(X2),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_40]),
[final]).
cnf(c_0_53,plain,
( product(domain(X1),X2,domain(X1))
| ~ product(domain(X1),domain(X1),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]),
[final]).
cnf(c_0_54,plain,
( product(codomain(X1),X2,codomain(X1))
| ~ product(codomain(X1),codomain(X1),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_43]),
[final]).
cnf(c_0_55,plain,
( product(X1,X2,codomain(X3))
| ~ product(X4,codomain(X3),X2)
| ~ product(X1,X4,codomain(X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_32]),
[final]).
cnf(c_0_56,plain,
( product(X1,X2,codomain(X3))
| ~ product(codomain(X3),X4,X1)
| ~ product(X4,X2,codomain(X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_32]),
[final]).
cnf(c_0_57,plain,
( X1 = domain(X2)
| ~ product(domain(X2),domain(X2),X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_27]),
[final]).
cnf(c_0_58,plain,
( product(X1,X2,X3)
| ~ product(X4,domain(X3),X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_4]),
[final]).
cnf(c_0_59,plain,
( product(X1,X2,X3)
| ~ product(codomain(X3),X4,X1)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_1]),
[final]).
cnf(c_0_60,plain,
( defined(X1,X2)
| ~ product(X1,codomain(X2),X3)
| ~ defined(X3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_1]),
[final]).
cnf(c_0_61,plain,
( defined(X1,X2)
| ~ product(domain(X1),X2,X3)
| ~ defined(X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_4]),
[final]).
cnf(c_0_62,plain,
( defined(codomain(X1),domain(X1))
| ~ identity_map(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_2]),
[final]).
cnf(c_0_63,plain,
( defined(X1,X2)
| ~ defined(X1,codomain(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_2]),c_0_8])]),
[final]).
cnf(c_0_64,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X6,X5,X2)
| ~ product(X1,X6,X4) ),
c_0_12,
[final]).
cnf(c_0_65,plain,
( product(X1,X2,X3)
| ~ product(X4,X5,X3)
| ~ product(X4,X6,X1)
| ~ product(X6,X2,X5) ),
c_0_9,
[final]).
cnf(c_0_66,plain,
( defined(X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X1,X3,X5)
| ~ defined(X5,X4) ),
c_0_15,
[final]).
cnf(c_0_67,plain,
( defined(X1,X2)
| ~ product(X3,X4,X1)
| ~ product(X4,X2,X5)
| ~ defined(X3,X5) ),
c_0_16,
[final]).
cnf(c_0_68,plain,
( defined(X1,X2)
| ~ identity_map(X3)
| ~ defined(X3,X2)
| ~ defined(X1,X3) ),
c_0_14,
[final]).
cnf(c_0_69,plain,
( defined(X1,X2)
| ~ product(X3,X1,X4)
| ~ defined(X4,X2) ),
c_0_3,
[final]).
cnf(c_0_70,plain,
( defined(X1,X2)
| ~ product(X2,X3,X4)
| ~ defined(X1,X4) ),
c_0_0,
[final]).
cnf(c_0_71,plain,
( X1 = X2
| ~ product(X3,X4,X2)
| ~ product(X3,X4,X1) ),
c_0_11,
[final]).
cnf(c_0_72,plain,
( product(X1,X2,X1)
| ~ identity_map(X2)
| ~ defined(X1,X2) ),
c_0_7,
[final]).
cnf(c_0_73,plain,
( product(X1,X2,X2)
| ~ identity_map(X1)
| ~ defined(X1,X2) ),
c_0_6,
[final]).
cnf(c_0_74,plain,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
c_0_17,
[final]).
cnf(c_0_75,plain,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
c_0_13,
[final]).
cnf(c_0_76,plain,
( compose(domain(X1),domain(X1)) = domain(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_39]),
[final]).
cnf(c_0_77,plain,
( compose(codomain(X1),codomain(X1)) = codomain(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]),
[final]).
cnf(c_0_78,plain,
( compose(codomain(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_48]),
[final]).
cnf(c_0_79,plain,
( product(codomain(X1),X1,X1) ),
c_0_1,
[final]).
cnf(c_0_80,plain,
( product(X1,domain(X1),X1) ),
c_0_4,
[final]).
cnf(c_0_81,plain,
( defined(codomain(X1),X1) ),
c_0_2,
[final]).
cnf(c_0_82,plain,
( defined(X1,domain(X1)) ),
c_0_5,
[final]).
cnf(c_0_83,plain,
( identity_map(codomain(X1)) ),
c_0_8,
[final]).
cnf(c_0_84,plain,
( identity_map(domain(X1)) ),
c_0_10,
[final]).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT020-1 : TPTP v6.2.0. Released v2.5.0.
% 0.00/0.03 % Command : eprover --auto-schedule --tstp-format -s --proof-object --memory-limit=2048 --cpu-limit=%d %s
% 0.02/1.07 % Computer : n124.star.cs.uiowa.edu
% 0.02/1.07 % Model : x86_64 x86_64
% 0.02/1.07 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/1.07 % Memory : 32286.75MB
% 0.02/1.07 % OS : Linux 2.6.32-504.16.2.el6.x86_64
% 0.02/1.07 % CPULimit : 300
% 0.02/1.07 % DateTime : Sun May 17 11:41:32 CDT 2015
% 0.02/1.07 % CPUTime :
% 0.02/1.07 # No SInE strategy applied
% 0.02/1.07 # Trying AutoSched0 for 151 seconds
% 0.02/1.10 # AutoSched0-Mode selected heuristic H_____102_C18_F1_PI_AE_Q4_CS_SP_S1S
% 0.02/1.10 # and selection function SelectComplexAHP.
% 0.02/1.10 #
% 0.02/1.10
% 0.02/1.10 # No proof found!
% 0.02/1.10 # SZS status Satisfiable
% 0.02/1.10 # SZS output start Saturation.
% 0.02/1.10 cnf(c_0_0,axiom,(defined(X4,X1)|~product(X1,X2,X3)|~defined(X4,X3)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', category_theory_axiom3)).
% 0.02/1.10 cnf(c_0_1,axiom,(product(codomain(X1),X1,X1)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', product_on_codomain)).
% 0.02/1.10 cnf(c_0_2,axiom,(defined(codomain(X1),X1)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', mapping_from_codomain_of_x_to_x)).
% 0.02/1.10 cnf(c_0_3,axiom,(defined(X2,X4)|~product(X1,X2,X3)|~defined(X3,X4)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', associative_property2)).
% 0.02/1.10 cnf(c_0_4,axiom,(product(X1,domain(X1),X1)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', product_on_domain)).
% 0.02/1.10 cnf(c_0_5,axiom,(defined(X1,domain(X1))), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', mapping_from_x_to_its_domain)).
% 0.02/1.10 cnf(c_0_6,axiom,(product(X1,X2,X2)|~defined(X1,X2)|~identity_map(X1)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', identity1)).
% 0.02/1.10 cnf(c_0_7,axiom,(product(X1,X2,X1)|~defined(X1,X2)|~identity_map(X2)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', identity2)).
% 0.02/1.10 cnf(c_0_8,axiom,(identity_map(codomain(X1))), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', codomain_is_an_identity_map)).
% 0.02/1.10 cnf(c_0_9,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)).
% 0.02/1.10 cnf(c_0_10,axiom,(identity_map(domain(X1))), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', domain_is_an_identity_map)).
% 0.02/1.10 cnf(c_0_11,axiom,(X3=X4|~product(X1,X2,X3)|~product(X1,X2,X4)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', composition_is_well_defined)).
% 0.02/1.10 cnf(c_0_12,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)).
% 0.02/1.10 cnf(c_0_13,axiom,(product(X1,X2,compose(X1,X2))|~defined(X1,X2)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', closure_of_composition)).
% 0.02/1.10 cnf(c_0_14,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)).
% 0.02/1.10 cnf(c_0_15,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)).
% 0.02/1.10 cnf(c_0_16,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)).
% 0.02/1.10 cnf(c_0_17,axiom,(defined(X1,X2)|~product(X1,X2,X3)), file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax', associative_property1)).
% 0.02/1.10 cnf(c_0_18,plain,(defined(X1,codomain(X2))|~defined(X1,X2)), inference(spm,[status(thm)],[c_0_0, c_0_1]), ['final']).
% 0.02/1.10 cnf(c_0_19,plain,(defined(codomain(X1),codomain(X1))), inference(spm,[status(thm)],[c_0_18, c_0_2]), ['final']).
% 0.02/1.10 cnf(c_0_20,plain,(defined(domain(X1),X2)|~defined(X1,X2)), inference(spm,[status(thm)],[c_0_3, c_0_4]), ['final']).
% 0.02/1.10 cnf(c_0_21,plain,(defined(codomain(X1),codomain(codomain(X1)))), inference(spm,[status(thm)],[c_0_18, c_0_19])).
% 0.02/1.10 cnf(c_0_22,plain,(defined(domain(X1),domain(X1))), inference(spm,[status(thm)],[c_0_20, c_0_5]), ['final']).
% 0.02/1.10 cnf(c_0_23,plain,(product(X1,domain(X1),domain(X1))|~identity_map(X1)), inference(spm,[status(thm)],[c_0_6, c_0_5]), ['final']).
% 0.02/1.10 cnf(c_0_24,plain,(product(codomain(X1),X1,codomain(X1))|~identity_map(X1)), inference(spm,[status(thm)],[c_0_7, c_0_2]), ['final']).
% 0.02/1.10 cnf(c_0_25,plain,(product(codomain(X1),codomain(codomain(X1)),codomain(X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7, c_0_21]), c_0_8])])).
% 0.02/1.10 cnf(c_0_26,plain,(product(X1,X2,X3)|~product(X4,X2,domain(X3))|~product(X3,X4,X1)), inference(spm,[status(thm)],[c_0_9, c_0_4]), ['final']).
% 0.02/1.10 cnf(c_0_27,plain,(product(domain(X1),domain(X1),domain(X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6, c_0_22]), c_0_10])]), ['final']).
% 0.02/1.10 cnf(c_0_28,plain,(X1=X2|~product(X2,domain(X2),X1)), inference(spm,[status(thm)],[c_0_11, c_0_4]), ['final']).
% 0.02/1.10 cnf(c_0_29,plain,(product(domain(X1),domain(domain(X1)),domain(domain(X1)))), inference(spm,[status(thm)],[c_0_23, c_0_10])).
% 0.02/1.10 cnf(c_0_30,plain,(product(codomain(X1),domain(codomain(X1)),domain(codomain(X1)))), inference(spm,[status(thm)],[c_0_23, c_0_8])).
% 0.02/1.10 cnf(c_0_31,plain,(product(X1,X2,X3)|~product(X1,X4,codomain(X3))|~product(X4,X3,X2)), inference(spm,[status(thm)],[c_0_12, c_0_1]), ['final']).
% 0.02/1.10 cnf(c_0_32,plain,(product(codomain(X1),codomain(X1),codomain(X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6, c_0_19]), c_0_8])]), ['final']).
% 0.02/1.10 cnf(c_0_33,plain,(X1=X2|~product(codomain(X2),X2,X1)), inference(spm,[status(thm)],[c_0_11, c_0_1]), ['final']).
% 0.02/1.10 cnf(c_0_34,plain,(product(codomain(domain(X1)),domain(X1),codomain(domain(X1)))), inference(spm,[status(thm)],[c_0_24, c_0_10])).
% 0.02/1.10 cnf(c_0_35,plain,(X1=codomain(X2)|~product(codomain(X2),codomain(codomain(X2)),X1)), inference(spm,[status(thm)],[c_0_11, c_0_25])).
% 0.02/1.10 cnf(c_0_36,plain,(product(codomain(X1),codomain(codomain(X1)),codomain(codomain(X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6, c_0_21]), c_0_8])])).
% 0.02/1.10 cnf(c_0_37,plain,(product(X1,domain(X1),compose(X1,domain(X1)))), inference(spm,[status(thm)],[c_0_13, c_0_5])).
% 0.02/1.10 cnf(c_0_38,plain,(product(X1,domain(X2),X2)|~product(X2,domain(X2),X1)), inference(spm,[status(thm)],[c_0_26, c_0_27]), ['final']).
% 0.02/1.10 cnf(c_0_39,plain,(domain(domain(X1))=domain(X1)), inference(spm,[status(thm)],[c_0_28, c_0_29]), ['final']).
% 0.02/1.10 cnf(c_0_40,plain,(domain(codomain(X1))=codomain(X1)), inference(spm,[status(thm)],[c_0_28, c_0_30]), ['final']).
% 0.02/1.10 cnf(c_0_41,plain,(product(codomain(X1),X2,X1)|~product(codomain(X1),X1,X2)), inference(spm,[status(thm)],[c_0_31, c_0_32]), ['final']).
% 0.02/1.10 cnf(c_0_42,plain,(codomain(domain(X1))=domain(X1)), inference(spm,[status(thm)],[c_0_33, c_0_34]), ['final']).
% 0.02/1.10 cnf(c_0_43,plain,(codomain(codomain(X1))=codomain(X1)), inference(spm,[status(thm)],[c_0_35, c_0_36]), ['final']).
% 0.02/1.10 cnf(c_0_44,plain,(defined(X1,domain(X2))|~identity_map(X2)|~defined(X1,X2)), inference(spm,[status(thm)],[c_0_14, c_0_5]), ['final']).
% 0.02/1.10 cnf(c_0_45,plain,(compose(X1,domain(X1))=X1), inference(spm,[status(thm)],[c_0_28, c_0_37]), ['final']).
% 0.02/1.10 cnf(c_0_46,plain,(X1=codomain(X2)|~product(codomain(X2),codomain(X2),X1)), inference(spm,[status(thm)],[c_0_11, c_0_32]), ['final']).
% 0.02/1.10 cnf(c_0_47,plain,(product(codomain(X1),codomain(X1),compose(codomain(X1),codomain(X1)))), inference(spm,[status(thm)],[c_0_13, c_0_19])).
% 0.02/1.10 cnf(c_0_48,plain,(product(codomain(X1),X1,compose(codomain(X1),X1))), inference(spm,[status(thm)],[c_0_13, c_0_2])).
% 0.02/1.10 cnf(c_0_49,plain,(product(X1,domain(X2),domain(X2))|~product(domain(X2),domain(X2),X1)), inference(spm,[status(thm)],[c_0_38, c_0_39]), ['final']).
% 0.02/1.10 cnf(c_0_50,plain,(product(X1,X2,domain(X3))|~product(X4,domain(X3),X2)|~product(X1,X4,domain(X3))), inference(spm,[status(thm)],[c_0_12, c_0_27]), ['final']).
% 0.02/1.10 cnf(c_0_51,plain,(product(X1,X2,domain(X3))|~product(domain(X3),X4,X1)|~product(X4,X2,domain(X3))), inference(spm,[status(thm)],[c_0_9, c_0_27]), ['final']).
% 0.02/1.10 cnf(c_0_52,plain,(product(X1,codomain(X2),codomain(X2))|~product(codomain(X2),codomain(X2),X1)), inference(spm,[status(thm)],[c_0_38, c_0_40]), ['final']).
% 0.02/1.10 cnf(c_0_53,plain,(product(domain(X1),X2,domain(X1))|~product(domain(X1),domain(X1),X2)), inference(spm,[status(thm)],[c_0_41, c_0_42]), ['final']).
% 0.02/1.10 cnf(c_0_54,plain,(product(codomain(X1),X2,codomain(X1))|~product(codomain(X1),codomain(X1),X2)), inference(spm,[status(thm)],[c_0_41, c_0_43]), ['final']).
% 0.02/1.10 cnf(c_0_55,plain,(product(X1,X2,codomain(X3))|~product(X4,codomain(X3),X2)|~product(X1,X4,codomain(X3))), inference(spm,[status(thm)],[c_0_12, c_0_32]), ['final']).
% 0.02/1.10 cnf(c_0_56,plain,(product(X1,X2,codomain(X3))|~product(codomain(X3),X4,X1)|~product(X4,X2,codomain(X3))), inference(spm,[status(thm)],[c_0_9, c_0_32]), ['final']).
% 0.02/1.10 cnf(c_0_57,plain,(X1=domain(X2)|~product(domain(X2),domain(X2),X1)), inference(spm,[status(thm)],[c_0_11, c_0_27]), ['final']).
% 0.02/1.10 cnf(c_0_58,plain,(product(X1,X2,X3)|~product(X4,domain(X3),X2)|~product(X1,X4,X3)), inference(spm,[status(thm)],[c_0_12, c_0_4]), ['final']).
% 0.02/1.10 cnf(c_0_59,plain,(product(X1,X2,X3)|~product(codomain(X3),X4,X1)|~product(X4,X2,X3)), inference(spm,[status(thm)],[c_0_9, c_0_1]), ['final']).
% 0.02/1.10 cnf(c_0_60,plain,(defined(X1,X2)|~product(X1,codomain(X2),X3)|~defined(X3,X2)), inference(spm,[status(thm)],[c_0_15, c_0_1]), ['final']).
% 0.02/1.10 cnf(c_0_61,plain,(defined(X1,X2)|~product(domain(X1),X2,X3)|~defined(X1,X3)), inference(spm,[status(thm)],[c_0_16, c_0_4]), ['final']).
% 0.02/1.10 cnf(c_0_62,plain,(defined(codomain(X1),domain(X1))|~identity_map(X1)), inference(spm,[status(thm)],[c_0_44, c_0_2]), ['final']).
% 0.02/1.10 cnf(c_0_63,plain,(defined(X1,X2)|~defined(X1,codomain(X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14, c_0_2]), c_0_8])]), ['final']).
% 0.02/1.10 cnf(c_0_64,plain,(product(X1,X2,X3)|~product(X4,X5,X3)|~product(X6,X5,X2)|~product(X1,X6,X4)), c_0_12, ['final']).
% 0.02/1.10 cnf(c_0_65,plain,(product(X1,X2,X3)|~product(X4,X5,X3)|~product(X4,X6,X1)|~product(X6,X2,X5)), c_0_9, ['final']).
% 0.02/1.10 cnf(c_0_66,plain,(defined(X1,X2)|~product(X3,X4,X2)|~product(X1,X3,X5)|~defined(X5,X4)), c_0_15, ['final']).
% 0.02/1.10 cnf(c_0_67,plain,(defined(X1,X2)|~product(X3,X4,X1)|~product(X4,X2,X5)|~defined(X3,X5)), c_0_16, ['final']).
% 0.02/1.10 cnf(c_0_68,plain,(defined(X1,X2)|~identity_map(X3)|~defined(X3,X2)|~defined(X1,X3)), c_0_14, ['final']).
% 0.02/1.10 cnf(c_0_69,plain,(defined(X1,X2)|~product(X3,X1,X4)|~defined(X4,X2)), c_0_3, ['final']).
% 0.02/1.10 cnf(c_0_70,plain,(defined(X1,X2)|~product(X2,X3,X4)|~defined(X1,X4)), c_0_0, ['final']).
% 0.02/1.10 cnf(c_0_71,plain,(X1=X2|~product(X3,X4,X2)|~product(X3,X4,X1)), c_0_11, ['final']).
% 0.02/1.10 cnf(c_0_72,plain,(product(X1,X2,X1)|~identity_map(X2)|~defined(X1,X2)), c_0_7, ['final']).
% 0.02/1.10 cnf(c_0_73,plain,(product(X1,X2,X2)|~identity_map(X1)|~defined(X1,X2)), c_0_6, ['final']).
% 0.02/1.10 cnf(c_0_74,plain,(defined(X1,X2)|~product(X1,X2,X3)), c_0_17, ['final']).
% 0.02/1.10 cnf(c_0_75,plain,(product(X1,X2,compose(X1,X2))|~defined(X1,X2)), c_0_13, ['final']).
% 0.02/1.10 cnf(c_0_76,plain,(compose(domain(X1),domain(X1))=domain(X1)), inference(spm,[status(thm)],[c_0_45, c_0_39]), ['final']).
% 0.02/1.10 cnf(c_0_77,plain,(compose(codomain(X1),codomain(X1))=codomain(X1)), inference(spm,[status(thm)],[c_0_46, c_0_47]), ['final']).
% 0.02/1.10 cnf(c_0_78,plain,(compose(codomain(X1),X1)=X1), inference(spm,[status(thm)],[c_0_33, c_0_48]), ['final']).
% 0.02/1.10 cnf(c_0_79,plain,(product(codomain(X1),X1,X1)), c_0_1, ['final']).
% 0.02/1.10 cnf(c_0_80,plain,(product(X1,domain(X1),X1)), c_0_4, ['final']).
% 0.02/1.10 cnf(c_0_81,plain,(defined(codomain(X1),X1)), c_0_2, ['final']).
% 0.02/1.10 cnf(c_0_82,plain,(defined(X1,domain(X1))), c_0_5, ['final']).
% 0.02/1.10 cnf(c_0_83,plain,(identity_map(codomain(X1))), c_0_8, ['final']).
% 0.02/1.10 cnf(c_0_84,plain,(identity_map(domain(X1))), c_0_10, ['final']).
% 0.02/1.10 # SZS output end Saturation.
%------------------------------------------------------------------------------