%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT005-1 : 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 : n013.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 04:11:38 PM UTC 2026
% Result : Unsatisfiable 0.40s 1.60s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 77)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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_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(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(associative_property1,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(identity2,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
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_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(product_on_codomain,axiom,
product(codomain(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
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(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(ad_defined,hypothesis,
defined(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ad_defined) ).
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(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(prove_domain_of_a_is_d,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
cnf(d_is_identity_map,hypothesis,
identity_map(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_identity_map) ).
cnf(i_0_21,axiom,
( product(X1,X6,X5)
| ~ product(X1,X2,X3)
| ~ product(X3,X4,X5)
| ~ product(X2,X4,X6) ),
category_theory_axiom2,
[final] ).
cnf(i_0_22,axiom,
( product(X6,X2,X5)
| ~ product(X1,X2,X3)
| ~ product(X4,X3,X5)
| ~ product(X4,X1,X6) ),
category_theory_axiom5,
[final] ).
cnf(i_0_23,axiom,
( defined(X1,X5)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ defined(X3,X4) ),
category_theory_axiom1,
[final] ).
cnf(i_0_24,axiom,
( defined(X5,X2)
| ~ product(X1,X2,X3)
| ~ product(X4,X1,X5)
| ~ defined(X4,X3) ),
category_theory_axiom4,
[final] ).
cnf(i_0_25,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined,
[final] ).
cnf(i_0_26,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2,
[final] ).
cnf(i_0_27,axiom,
( defined(X4,X1)
| ~ product(X1,X2,X3)
| ~ defined(X4,X3) ),
category_theory_axiom3,
[final] ).
cnf(i_0_28,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition,
[final] ).
cnf(i_0_29,axiom,
( defined(X1,X2)
| ~ product(X1,X2,X3) ),
associative_property1,
[final] ).
cnf(i_0_30,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
identity2,
[final] ).
cnf(i_0_31,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1,
[final] ).
cnf(i_0_32,axiom,
( defined(X1,X3)
| ~ defined(X1,X2)
| ~ defined(X2,X3)
| ~ identity_map(X2) ),
category_theory_axiom6,
[final] ).
cnf(i_0_33,axiom,
product(codomain(X1),X1,X1),
product_on_codomain,
[final] ).
cnf(i_0_34,axiom,
product(X1,domain(X1),X1),
product_on_domain,
[final] ).
cnf(i_0_35,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x,
[final] ).
cnf(i_0_36,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain,
[final] ).
cnf(i_0_37,hypothesis,
defined(a,d),
ad_defined,
[final] ).
cnf(i_0_38,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map,
[final] ).
cnf(i_0_39,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map,
[final] ).
cnf(i_0_40,negated_conjecture,
domain(a) != d,
prove_domain_of_a_is_d,
[final] ).
cnf(i_0_41,hypothesis,
identity_map(d),
d_is_identity_map,
[final] ).
cnf(i_0_42,axiom,
X1 = X1 ).
cnf(i_0_43,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_44,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_45,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| ~ defined(X1,X3)
| defined(X2,X3) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| ~ defined(X3,X1)
| defined(X3,X2) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| ~ identity_map(X1)
| identity_map(X2) ) ).
cnf(i_0_42_001,axiom,
X1 = X1 ).
cnf(i_0_43_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_44_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_45_004,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_46_005,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_47_006,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_48_007,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_49_008,axiom,
( X1 != X2
| ~ defined(X1,X3)
| defined(X2,X3) ) ).
cnf(i_0_50_009,axiom,
( X1 != X2
| ~ defined(X3,X1)
| defined(X3,X2) ) ).
cnf(i_0_51_010,axiom,
( X1 != X2
| ~ identity_map(X1)
| identity_map(X2) ) ).
cnf(i_0_52,plain,
~ product(codomain(d),d,domain(a)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_25]) ).
cnf(i_0_53,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_54,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_55,plain,
d != domain(a),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_25,i_0_48]) ).
cnf(i_0_56,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_57,plain,
defined(codomain(X1),codomain(X1)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_35,i_0_25,i_0_48,i_0_27]) ).
cnf(i_0_58,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_59,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_60,plain,
product(codomain(d),d,codomain(d)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_35,i_0_58,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30]) ).
cnf(i_0_61,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_62,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_63,plain,
product(d,domain(d),domain(d)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_35,i_0_58,i_0_36,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31]) ).
cnf(i_0_64,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_65,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_66,plain,
~ product(d,domain(d),domain(a)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_34,i_0_35,i_0_58,i_0_36,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21]) ).
cnf(i_0_67,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_68,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_69,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_70,plain,
~ product(codomain(codomain(d)),codomain(d),domain(a)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_34,i_0_35,i_0_58,i_0_36,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22]) ).
cnf(i_0_71,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_72,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_73,plain,
defined(codomain(d),domain(d)),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_34,i_0_35,i_0_58,i_0_61,i_0_36,i_0_64,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22,i_0_32]) ).
cnf(i_0_74,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_75,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_76,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_77,plain,
( X1 != codomain(d)
| ~ product(X1,d,domain(a)) ),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_34,i_0_35,i_0_58,i_0_61,i_0_36,i_0_64,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22,i_0_32,i_0_46]) ).
cnf(i_0_78,plain,
( X1 != d
| ~ product(codomain(d),X1,domain(a)) ),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_34,i_0_35,i_0_58,i_0_61,i_0_36,i_0_64,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22,i_0_32,i_0_46,i_0_47]) ).
cnf(i_0_79,plain,
( identity_map(X1)
| d != X1 ),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_34,i_0_35,i_0_58,i_0_61,i_0_36,i_0_64,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22,i_0_32,i_0_46,i_0_47,i_0_51]) ).
cnf(i_0_80,plain,
( defined(codomain(a),X1)
| ~ product(a,d,X1) ),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_71,i_0_34,i_0_35,i_0_58,i_0_61,i_0_36,i_0_64,i_0_37,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22,i_0_32,i_0_46,i_0_47,i_0_51,i_0_23]) ).
cnf(i_0_81,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_82,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_83,plain,
( defined(X1,X2)
| ~ product(codomain(X2),codomain(X2),X1) ),
inference(scs_inference,[],[i_0_40,i_0_33,i_0_53,i_0_56,i_0_68,i_0_71,i_0_81,i_0_34,i_0_35,i_0_58,i_0_61,i_0_75,i_0_36,i_0_64,i_0_37,i_0_41,i_0_25,i_0_48,i_0_27,i_0_30,i_0_31,i_0_21,i_0_22,i_0_32,i_0_46,i_0_47,i_0_51,i_0_23,i_0_24]) ).
cnf(i_0_84,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_85,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_86,plain,
~ product(codomain(d),d,domain(a)),
inference(equality_inference,[],[77]) ).
cnf(i_0_87,plain,
~ product(codomain(d),d,domain(a)),
inference(equality_inference,[],[78]) ).
cnf(i_0_88,plain,
identity_map(d),
inference(equality_inference,[],[79]) ).
cnf(i_0_89,plain,
defined(d,codomain(d)),
inference(scs_inference,[],[i_0_57,i_0_60,i_0_26]) ).
cnf(i_0_90,plain,
defined(codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_91,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_92,plain,
product(a,d,a),
inference(scs_inference,[],[i_0_37,i_0_57,i_0_60,i_0_41,i_0_26,i_0_30]) ).
cnf(i_0_93,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_94,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(scs_inference,[],[i_0_37,i_0_57,i_0_90,i_0_60,i_0_38,i_0_41,i_0_26,i_0_30,i_0_31]) ).
cnf(i_0_95,plain,
defined(codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_96,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_97,plain,
defined(a,codomain(d)),
inference(scs_inference,[],[i_0_37,i_0_57,i_0_90,i_0_60,i_0_38,i_0_33,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27]) ).
cnf(i_0_98,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_99,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_100,plain,
codomain(d) != domain(a),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_60,i_0_38,i_0_33,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48]) ).
cnf(i_0_101,plain,
~ product(codomain(d),domain(d),domain(a)),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_60,i_0_38,i_0_33,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21]) ).
cnf(i_0_102,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_103,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_104,plain,
~ product(codomain(d),codomain(d),domain(a)),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_60,i_0_38,i_0_33,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22]) ).
cnf(i_0_105,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_106,plain,
( X1 != codomain(d)
| ~ product(codomain(codomain(d)),X1,domain(a)) ),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_70,i_0_60,i_0_38,i_0_33,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22,i_0_47]) ).
cnf(i_0_107,plain,
( identity_map(X1)
| codomain(d) != X1 ),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_70,i_0_60,i_0_38,i_0_33,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22,i_0_47,i_0_51]) ).
cnf(i_0_108,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_109,plain,
( X1 != codomain(codomain(d))
| ~ product(X1,codomain(d),domain(a)) ),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_70,i_0_60,i_0_38,i_0_33,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22,i_0_47,i_0_51,i_0_46]) ).
cnf(i_0_110,plain,
( defined(X1,d)
| ~ product(a,codomain(d),X1) ),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_70,i_0_60,i_0_38,i_0_33,i_0_98,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22,i_0_47,i_0_51,i_0_46,i_0_24]) ).
cnf(i_0_111,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_112,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_113,plain,
( defined(codomain(d),X1)
| ~ product(d,codomain(d),X1) ),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_95,i_0_70,i_0_60,i_0_38,i_0_33,i_0_98,i_0_34,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22,i_0_47,i_0_51,i_0_46,i_0_24,i_0_23]) ).
cnf(i_0_114,plain,
defined(codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_115,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_116,plain,
( defined(codomain(a),d)
| codomain(d) != a ),
inference(scs_inference,[],[i_0_52,i_0_37,i_0_57,i_0_90,i_0_95,i_0_70,i_0_60,i_0_38,i_0_33,i_0_98,i_0_34,i_0_35,i_0_41,i_0_26,i_0_30,i_0_31,i_0_27,i_0_48,i_0_21,i_0_22,i_0_47,i_0_51,i_0_46,i_0_24,i_0_23,i_0_32]) ).
cnf(i_0_117,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_118,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_119,plain,
~ product(codomain(codomain(d)),codomain(d),domain(a)),
inference(equality_inference,[],[106]) ).
cnf(i_0_120,plain,
identity_map(codomain(d)),
inference(equality_inference,[],[107]) ).
cnf(i_0_121,plain,
~ product(codomain(codomain(d)),codomain(d),domain(a)),
inference(equality_inference,[],[109]) ).
cnf(i_0_122,plain,
defined(d,d),
inference(scs_inference,[],[i_0_37,i_0_92,i_0_26]) ).
cnf(i_0_123,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_124,plain,
product(codomain(d),domain(d),codomain(d)),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_92,i_0_39,i_0_26,i_0_30]) ).
cnf(i_0_125,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_126,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_127,plain,
product(codomain(d),domain(d),domain(d)),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_92,i_0_39,i_0_38,i_0_26,i_0_30,i_0_31]) ).
cnf(i_0_128,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_129,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_130,plain,
domain(d) != domain(a),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_66,i_0_63,i_0_92,i_0_39,i_0_38,i_0_26,i_0_30,i_0_31,i_0_48]) ).
cnf(i_0_131,plain,
defined(codomain(codomain(d)),domain(d)),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32]) ).
cnf(i_0_132,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_133,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_134,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_135,plain,
d != a,
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45]) ).
cnf(i_0_136,plain,
~ product(a,d,d),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25]) ).
cnf(i_0_137,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_138,plain,
defined(codomain(codomain(d)),d),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27]) ).
cnf(i_0_139,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_140,plain,
( X1 != domain(d)
| ~ product(d,X1,domain(a)) ),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47]) ).
cnf(i_0_141,plain,
codomain(d) != a,
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_33,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47,i_0_46]) ).
cnf(i_0_142,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_143,plain,
( identity_map(X1)
| domain(X2) != X1 ),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_125,i_0_33,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47,i_0_46,i_0_51]) ).
cnf(i_0_144,plain,
( ~ product(d,d,X1)
| ~ product(X1,domain(d),domain(a)) ),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_125,i_0_33,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47,i_0_46,i_0_51,i_0_21]) ).
cnf(i_0_145,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_146,plain,
( ~ product(d,d,X1)
| ~ product(a,X1,d) ),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_66,i_0_63,i_0_92,i_0_39,i_0_125,i_0_33,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47,i_0_46,i_0_51,i_0_21,i_0_22]) ).
cnf(i_0_147,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_148,plain,
( defined(X1,domain(d))
| ~ product(d,d,X1) ),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_36,i_0_66,i_0_63,i_0_92,i_0_39,i_0_125,i_0_33,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47,i_0_46,i_0_51,i_0_21,i_0_22,i_0_24]) ).
cnf(i_0_149,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_150,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_151,plain,
( defined(a,X1)
| ~ product(d,d,X1) ),
inference(scs_inference,[],[i_0_37,i_0_73,i_0_35,i_0_36,i_0_66,i_0_63,i_0_92,i_0_39,i_0_125,i_0_33,i_0_38,i_0_128,i_0_26,i_0_30,i_0_31,i_0_48,i_0_32,i_0_45,i_0_25,i_0_27,i_0_47,i_0_46,i_0_51,i_0_21,i_0_22,i_0_24,i_0_23]) ).
cnf(i_0_152,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_153,plain,
~ product(d,domain(d),domain(a)),
inference(equality_inference,[],[140]) ).
cnf(i_0_154,plain,
identity_map(domain(X1)),
inference(equality_inference,[],[143]) ).
cnf(i_0_155,plain,
defined(domain(a),d),
inference(scs_inference,[],[i_0_37,i_0_34,i_0_26]) ).
cnf(i_0_156,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_157,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_158,plain,
product(a,codomain(d),a),
inference(scs_inference,[],[i_0_37,i_0_34,i_0_97,i_0_38,i_0_26,i_0_30]) ).
cnf(i_0_159,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_160,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_161,plain,
~ identity_map(a),
inference(scs_inference,[],[i_0_136,i_0_37,i_0_34,i_0_97,i_0_38,i_0_26,i_0_30,i_0_31]) ).
cnf(i_0_162,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_163,plain,
domain(X1) != a,
inference(scs_inference,[],[i_0_136,i_0_37,i_0_34,i_0_97,i_0_39,i_0_38,i_0_26,i_0_30,i_0_31,i_0_51]) ).
cnf(i_0_164,plain,
a != d,
inference(scs_inference,[],[i_0_136,i_0_37,i_0_34,i_0_97,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48]) ).
cnf(i_0_165,plain,
~ product(a,codomain(d),d),
inference(scs_inference,[],[i_0_136,i_0_37,i_0_34,i_0_60,i_0_97,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48,i_0_22]) ).
cnf(i_0_166,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_167,plain,
defined(a,domain(d)),
inference(scs_inference,[],[i_0_136,i_0_37,i_0_34,i_0_156,i_0_60,i_0_97,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48,i_0_22,i_0_24]) ).
cnf(i_0_168,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_169,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_170,plain,
defined(codomain(d),domain(domain(d))),
inference(scs_inference,[],[i_0_136,i_0_73,i_0_37,i_0_36,i_0_34,i_0_156,i_0_60,i_0_97,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48,i_0_22,i_0_24,i_0_32]) ).
cnf(i_0_171,plain,
defined(X1,domain(X1)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_172,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_173,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_174,plain,
( X1 != d
| ~ product(a,X1,d) ),
inference(scs_inference,[],[i_0_136,i_0_73,i_0_37,i_0_36,i_0_34,i_0_156,i_0_60,i_0_97,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48,i_0_22,i_0_24,i_0_32,i_0_47]) ).
cnf(i_0_175,plain,
( X1 != codomain(d)
| ~ product(X1,codomain(d),domain(a)) ),
inference(scs_inference,[],[i_0_136,i_0_73,i_0_37,i_0_36,i_0_34,i_0_156,i_0_60,i_0_97,i_0_104,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48,i_0_22,i_0_24,i_0_32,i_0_47,i_0_46]) ).
cnf(i_0_176,plain,
( defined(a,X1)
| ~ product(domain(a),d,X1) ),
inference(scs_inference,[],[i_0_136,i_0_73,i_0_37,i_0_36,i_0_34,i_0_156,i_0_168,i_0_60,i_0_97,i_0_104,i_0_39,i_0_38,i_0_92,i_0_26,i_0_30,i_0_31,i_0_51,i_0_48,i_0_22,i_0_24,i_0_32,i_0_47,i_0_46,i_0_23]) ).
cnf(i_0_177,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_178,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_179,plain,
~ product(a,d,d),
inference(equality_inference,[],[174]) ).
cnf(i_0_180,plain,
~ product(codomain(d),codomain(d),domain(a)),
inference(equality_inference,[],[175]) ).
cnf(i_0_181,plain,
defined(domain(a),codomain(d)),
inference(scs_inference,[],[i_0_33,i_0_155,i_0_27]) ).
cnf(i_0_182,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_183,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_184,plain,
product(d,d,d),
inference(scs_inference,[],[i_0_33,i_0_122,i_0_155,i_0_41,i_0_27,i_0_31]) ).
cnf(i_0_185,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_186,plain,
product(d,codomain(d),d),
inference(scs_inference,[],[i_0_33,i_0_122,i_0_89,i_0_155,i_0_38,i_0_41,i_0_27,i_0_31,i_0_30]) ).
cnf(i_0_187,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_188,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_189,plain,
codomain(X1) != a,
inference(scs_inference,[],[i_0_33,i_0_122,i_0_89,i_0_155,i_0_161,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51]) ).
cnf(i_0_190,plain,
~ product(a,domain(d),d),
inference(scs_inference,[],[i_0_33,i_0_124,i_0_122,i_0_89,i_0_165,i_0_155,i_0_158,i_0_161,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21]) ).
cnf(i_0_191,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_192,plain,
~ product(d,codomain(d),domain(a)),
inference(scs_inference,[],[i_0_33,i_0_124,i_0_122,i_0_89,i_0_165,i_0_155,i_0_158,i_0_161,i_0_66,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21,i_0_22]) ).
cnf(i_0_193,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_194,plain,
defined(codomain(domain(a)),d),
inference(scs_inference,[],[i_0_35,i_0_33,i_0_124,i_0_122,i_0_89,i_0_165,i_0_155,i_0_158,i_0_161,i_0_66,i_0_39,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21,i_0_22,i_0_32]) ).
cnf(i_0_195,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_196,plain,
defined(codomain(X1),X1),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_197,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| defined(X3,X2)
| ~ defined(X3,X1) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_198,plain,
~ product(d,d,domain(a)),
inference(scs_inference,[],[i_0_40,i_0_35,i_0_33,i_0_124,i_0_122,i_0_89,i_0_165,i_0_155,i_0_158,i_0_161,i_0_66,i_0_39,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21,i_0_22,i_0_32,i_0_25]) ).
cnf(i_0_199,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_200,plain,
( X1 != domain(d)
| ~ product(codomain(d),X1,domain(a)) ),
inference(scs_inference,[],[i_0_40,i_0_35,i_0_33,i_0_124,i_0_122,i_0_89,i_0_101,i_0_165,i_0_155,i_0_158,i_0_161,i_0_66,i_0_39,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21,i_0_22,i_0_32,i_0_25,i_0_47]) ).
cnf(i_0_201,plain,
( codomain(domain(a)) != codomain(d)
| domain(a) != domain(d) ),
inference(scs_inference,[],[i_0_40,i_0_35,i_0_33,i_0_182,i_0_124,i_0_122,i_0_89,i_0_101,i_0_165,i_0_155,i_0_158,i_0_161,i_0_66,i_0_39,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21,i_0_22,i_0_32,i_0_25,i_0_47,i_0_46]) ).
cnf(i_0_202,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_203,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_204,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_205,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_206,plain,
( domain(a) != domain(d)
| defined(codomain(codomain(d)),X1)
| ~ product(codomain(codomain(d)),d,X1) ),
inference(scs_inference,[],[i_0_40,i_0_94,i_0_35,i_0_33,i_0_182,i_0_202,i_0_124,i_0_122,i_0_89,i_0_138,i_0_101,i_0_165,i_0_155,i_0_158,i_0_161,i_0_66,i_0_39,i_0_38,i_0_187,i_0_41,i_0_27,i_0_31,i_0_30,i_0_51,i_0_21,i_0_22,i_0_32,i_0_25,i_0_47,i_0_46,i_0_23]) ).
cnf(i_0_207,plain,
~ product(codomain(d),domain(d),domain(a)),
inference(equality_inference,[],[200]) ).
cnf(i_0_208,plain,
defined(codomain(domain(a)),codomain(d)),
inference(scs_inference,[],[i_0_33,i_0_194,i_0_27]) ).
cnf(i_0_209,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_210,plain,
( ~ defined(X1,X2)
| defined(X1,X3)
| ~ product(X3,X4,X2) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_211,plain,
product(d,codomain(d),codomain(d)),
inference(scs_inference,[],[i_0_89,i_0_33,i_0_194,i_0_41,i_0_27,i_0_31]) ).
cnf(i_0_212,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_213,plain,
product(a,domain(d),a),
inference(scs_inference,[],[i_0_89,i_0_33,i_0_167,i_0_194,i_0_39,i_0_41,i_0_27,i_0_31,i_0_30]) ).
cnf(i_0_214,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_215,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_216,plain,
( X1 != d
| ~ product(d,X1,domain(a)) ),
inference(scs_inference,[],[i_0_198,i_0_89,i_0_33,i_0_167,i_0_194,i_0_39,i_0_41,i_0_27,i_0_31,i_0_30,i_0_47]) ).
cnf(i_0_217,plain,
( X1 != d
| ~ product(X1,d,domain(a)) ),
inference(scs_inference,[],[i_0_198,i_0_89,i_0_33,i_0_167,i_0_194,i_0_39,i_0_41,i_0_27,i_0_31,i_0_30,i_0_47,i_0_46]) ).
cnf(i_0_218,plain,
( defined(X1,domain(d))
| ~ product(codomain(codomain(d)),d,X1) ),
inference(scs_inference,[],[i_0_198,i_0_89,i_0_63,i_0_33,i_0_131,i_0_167,i_0_194,i_0_39,i_0_41,i_0_27,i_0_31,i_0_30,i_0_47,i_0_46,i_0_24]) ).
cnf(i_0_219,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_220,plain,
( ~ product(domain(d),d,X1)
| ~ product(codomain(d),X1,domain(a)) ),
inference(scs_inference,[],[i_0_52,i_0_198,i_0_89,i_0_63,i_0_33,i_0_131,i_0_167,i_0_124,i_0_194,i_0_39,i_0_41,i_0_27,i_0_31,i_0_30,i_0_47,i_0_46,i_0_24,i_0_22]) ).
cnf(i_0_221,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_222,plain,
( defined(codomain(codomain(d)),X1)
| ~ product(codomain(codomain(d)),domain(d),X1) ),
inference(scs_inference,[],[i_0_52,i_0_198,i_0_94,i_0_89,i_0_63,i_0_33,i_0_131,i_0_167,i_0_124,i_0_194,i_0_39,i_0_41,i_0_27,i_0_31,i_0_30,i_0_47,i_0_46,i_0_24,i_0_22,i_0_23]) ).
cnf(i_0_223,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_224,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_225,plain,
~ product(d,d,domain(a)),
inference(equality_inference,[],[216]) ).
cnf(i_0_226,plain,
~ product(d,d,domain(a)),
inference(equality_inference,[],[217]) ).
cnf(i_0_227,plain,
defined(domain(domain(a)),d),
inference(scs_inference,[],[i_0_155,i_0_34,i_0_26]) ).
cnf(i_0_228,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_229,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_230,plain,
product(codomain(codomain(d)),d,d),
inference(scs_inference,[],[i_0_138,i_0_155,i_0_34,i_0_38,i_0_26,i_0_31]) ).
cnf(i_0_231,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_232,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_233,plain,
product(codomain(d),domain(domain(d)),codomain(d)),
inference(scs_inference,[],[i_0_138,i_0_170,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30]) ).
cnf(i_0_234,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_235,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_236,plain,
~ product(a,domain(domain(d)),d),
inference(scs_inference,[],[i_0_165,i_0_158,i_0_138,i_0_170,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21]) ).
cnf(i_0_237,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_238,plain,
~ product(codomain(codomain(d)),d,domain(a)),
inference(scs_inference,[],[i_0_198,i_0_184,i_0_165,i_0_158,i_0_138,i_0_170,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21,i_0_22]) ).
cnf(i_0_239,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_240,plain,
( X1 != d
| ~ product(a,domain(domain(d)),X1) ),
inference(scs_inference,[],[i_0_198,i_0_184,i_0_165,i_0_158,i_0_138,i_0_170,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21,i_0_22,i_0_48]) ).
cnf(i_0_241,plain,
( X1 != codomain(d)
| ~ product(a,X1,d) ),
inference(scs_inference,[],[i_0_198,i_0_184,i_0_165,i_0_158,i_0_138,i_0_170,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21,i_0_22,i_0_48,i_0_47]) ).
cnf(i_0_242,plain,
( X1 != codomain(d)
| ~ product(X1,domain(d),domain(a)) ),
inference(scs_inference,[],[i_0_198,i_0_184,i_0_165,i_0_158,i_0_138,i_0_170,i_0_101,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21,i_0_22,i_0_48,i_0_47,i_0_46]) ).
cnf(i_0_243,plain,
( defined(X1,d)
| ~ product(domain(a),d,X1) ),
inference(scs_inference,[],[i_0_198,i_0_184,i_0_165,i_0_158,i_0_138,i_0_170,i_0_101,i_0_155,i_0_34,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21,i_0_22,i_0_48,i_0_47,i_0_46,i_0_24]) ).
cnf(i_0_244,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_245,plain,
( defined(domain(a),X1)
| ~ product(domain(domain(a)),d,X1) ),
inference(scs_inference,[],[i_0_198,i_0_184,i_0_165,i_0_158,i_0_138,i_0_170,i_0_101,i_0_155,i_0_34,i_0_228,i_0_38,i_0_39,i_0_26,i_0_31,i_0_30,i_0_21,i_0_22,i_0_48,i_0_47,i_0_46,i_0_24,i_0_23]) ).
cnf(i_0_246,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_247,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_248,plain,
~ product(a,domain(domain(d)),d),
inference(equality_inference,[],[240]) ).
cnf(i_0_249,plain,
~ product(a,codomain(d),d),
inference(equality_inference,[],[241]) ).
cnf(i_0_250,plain,
~ product(codomain(d),domain(d),domain(a)),
inference(equality_inference,[],[242]) ).
cnf(i_0_251,plain,
defined(domain(domain(a)),codomain(d)),
inference(scs_inference,[],[i_0_181,i_0_34,i_0_26]) ).
cnf(i_0_252,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_253,plain,
( ~ defined(X1,X2)
| defined(X3,X2)
| ~ product(X4,X3,X1) ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_254,plain,
product(codomain(codomain(d)),domain(d),domain(d)),
inference(scs_inference,[],[i_0_131,i_0_181,i_0_34,i_0_38,i_0_26,i_0_31]) ).
cnf(i_0_255,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_256,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_257,plain,
product(domain(a),d,domain(a)),
inference(scs_inference,[],[i_0_131,i_0_155,i_0_181,i_0_34,i_0_41,i_0_38,i_0_26,i_0_31,i_0_30]) ).
cnf(i_0_258,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_259,plain,
domain(a) != codomain(d),
inference(scs_inference,[],[i_0_52,i_0_131,i_0_155,i_0_181,i_0_34,i_0_41,i_0_38,i_0_26,i_0_31,i_0_30,i_0_46]) ).
cnf(i_0_260,plain,
~ product(codomain(d),codomain(codomain(d)),domain(a)),
inference(scs_inference,[],[i_0_52,i_0_131,i_0_155,i_0_181,i_0_34,i_0_41,i_0_38,i_0_230,i_0_26,i_0_31,i_0_30,i_0_46,i_0_21]) ).
cnf(i_0_261,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_262,plain,
~ product(codomain(d),domain(domain(d)),domain(a)),
inference(scs_inference,[],[i_0_52,i_0_131,i_0_155,i_0_181,i_0_34,i_0_41,i_0_38,i_0_233,i_0_230,i_0_26,i_0_31,i_0_30,i_0_46,i_0_21,i_0_25]) ).
cnf(i_0_263,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_264,plain,
( X1 != domain(a)
| ~ product(codomain(d),codomain(codomain(d)),X1) ),
inference(scs_inference,[],[i_0_52,i_0_131,i_0_155,i_0_181,i_0_34,i_0_41,i_0_38,i_0_233,i_0_230,i_0_26,i_0_31,i_0_30,i_0_46,i_0_21,i_0_25,i_0_48]) ).
cnf(i_0_265,plain,
( X1 != a
| ~ product(codomain(d),codomain(codomain(d)),domain(X1)) ),
inference(scs_inference,[],[i_0_52,i_0_131,i_0_155,i_0_181,i_0_34,i_0_41,i_0_38,i_0_233,i_0_230,i_0_26,i_0_31,i_0_30,i_0_46,i_0_21,i_0_25,i_0_48,i_0_45]) ).
cnf(i_0_266,plain,
( ~ product(codomain(codomain(d)),d,X1)
| defined(codomain(codomain(d)),X1)
| domain(a) != domain(d) ),
inference(rename_variables,[],[i_0_206]) ).
cnf(i_0_267,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_268,plain,
defined(codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_269,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_270,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_272,plain,
~ product(codomain(d),codomain(codomain(d)),domain(a)),
inference(equality_inference,[],[264]) ).
cnf(i_0_273,plain,
~ product(codomain(d),codomain(codomain(d)),domain(a)),
inference(equality_inference,[],[265]) ).
cnf(i_0_274,plain,
~ product(domain(a),d,domain(d)),
inference(scs_inference,[],[i_0_130,i_0_257,i_0_25]) ).
cnf(i_0_275,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_276,plain,
product(domain(a),d,d),
inference(scs_inference,[],[i_0_130,i_0_155,i_0_257,i_0_39,i_0_25,i_0_31]) ).
cnf(i_0_277,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_278,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_279,plain,
product(domain(a),codomain(d),domain(a)),
inference(scs_inference,[],[i_0_130,i_0_155,i_0_181,i_0_38,i_0_257,i_0_39,i_0_25,i_0_31,i_0_30]) ).
cnf(i_0_280,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_281,plain,
( ~ defined(X1,X2)
| ~ identity_map(X2)
| product(X1,X2,X1) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_282,plain,
domain(a) != domain(d),
inference(scs_inference,[],[i_0_130,i_0_155,i_0_181,i_0_38,i_0_257,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48]) ).
cnf(i_0_283,plain,
domain(a) != codomain(codomain(d)),
inference(scs_inference,[],[i_0_130,i_0_155,i_0_181,i_0_70,i_0_38,i_0_257,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48,i_0_46]) ).
cnf(i_0_284,plain,
~ product(a,codomain(codomain(d)),d),
inference(scs_inference,[],[i_0_130,i_0_155,i_0_181,i_0_190,i_0_70,i_0_34,i_0_38,i_0_257,i_0_254,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48,i_0_46,i_0_21]) ).
cnf(i_0_285,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_286,plain,
( ~ product(X1,X2,X3)
| product(X4,X3,X5)
| ~ product(X4,X1,X6)
| ~ product(X6,X2,X5) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_287,plain,
~ product(codomain(a),a,d),
inference(scs_inference,[],[i_0_136,i_0_130,i_0_92,i_0_155,i_0_181,i_0_33,i_0_190,i_0_70,i_0_34,i_0_38,i_0_257,i_0_254,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48,i_0_46,i_0_21,i_0_22]) ).
cnf(i_0_288,plain,
product(codomain(X1),X1,X1),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_289,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_290,plain,
( X1 != domain(domain(d))
| ~ product(codomain(d),X1,domain(a)) ),
inference(scs_inference,[],[i_0_136,i_0_262,i_0_130,i_0_92,i_0_155,i_0_181,i_0_33,i_0_190,i_0_70,i_0_34,i_0_38,i_0_257,i_0_254,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48,i_0_46,i_0_21,i_0_22,i_0_47]) ).
cnf(i_0_291,plain,
( defined(X1,d)
| ~ product(codomain(domain(a)),d,X1) ),
inference(scs_inference,[],[i_0_136,i_0_262,i_0_130,i_0_184,i_0_92,i_0_155,i_0_194,i_0_181,i_0_33,i_0_190,i_0_70,i_0_34,i_0_38,i_0_257,i_0_254,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48,i_0_46,i_0_21,i_0_22,i_0_47,i_0_24]) ).
cnf(i_0_292,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_293,plain,
( defined(codomain(domain(a)),X1)
| ~ product(codomain(domain(a)),d,X1) ),
inference(scs_inference,[],[i_0_136,i_0_262,i_0_130,i_0_94,i_0_184,i_0_92,i_0_155,i_0_194,i_0_181,i_0_33,i_0_190,i_0_70,i_0_34,i_0_38,i_0_257,i_0_254,i_0_39,i_0_25,i_0_31,i_0_30,i_0_48,i_0_46,i_0_21,i_0_22,i_0_47,i_0_24,i_0_23]) ).
cnf(i_0_294,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_295,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_296,plain,
~ product(codomain(d),domain(domain(d)),domain(a)),
inference(equality_inference,[],[290]) ).
cnf(i_0_297,plain,
~ product(codomain(codomain(d)),domain(d),domain(a)),
inference(scs_inference,[],[i_0_282,i_0_254,i_0_25]) ).
cnf(i_0_298,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_299,plain,
product(domain(a),codomain(d),codomain(d)),
inference(scs_inference,[],[i_0_282,i_0_181,i_0_254,i_0_39,i_0_25,i_0_31]) ).
cnf(i_0_300,plain,
identity_map(domain(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_301,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_302,plain,
~ product(a,domain(a),d),
inference(scs_inference,[],[i_0_136,i_0_282,i_0_181,i_0_34,i_0_257,i_0_254,i_0_39,i_0_25,i_0_31,i_0_22]) ).
cnf(i_0_303,plain,
product(X1,domain(X1),X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_304,plain,
( ~ product(X1,X2,X3)
| product(X3,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X1,X6,X5) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_305,plain,
( X1 != d
| ~ product(a,codomain(codomain(d)),X1) ),
inference(scs_inference,[],[i_0_136,i_0_282,i_0_181,i_0_34,i_0_257,i_0_254,i_0_284,i_0_39,i_0_25,i_0_31,i_0_22,i_0_48]) ).
cnf(i_0_306,plain,
( X1 != d
| ~ product(domain(a),X1,domain(d)) ),
inference(scs_inference,[],[i_0_136,i_0_274,i_0_282,i_0_181,i_0_34,i_0_257,i_0_254,i_0_284,i_0_39,i_0_25,i_0_31,i_0_22,i_0_48,i_0_47]) ).
cnf(i_0_307,plain,
( X1 != domain(a)
| ~ product(X1,d,domain(d)) ),
inference(scs_inference,[],[i_0_136,i_0_274,i_0_282,i_0_181,i_0_34,i_0_257,i_0_254,i_0_284,i_0_39,i_0_25,i_0_31,i_0_22,i_0_48,i_0_47,i_0_46]) ).
cnf(i_0_308,plain,
( defined(X1,codomain(d))
| ~ product(codomain(domain(a)),codomain(d),X1) ),
inference(scs_inference,[],[i_0_136,i_0_274,i_0_282,i_0_94,i_0_181,i_0_208,i_0_34,i_0_257,i_0_254,i_0_284,i_0_39,i_0_25,i_0_31,i_0_22,i_0_48,i_0_47,i_0_46,i_0_24]) ).
cnf(i_0_309,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_310,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_311,plain,
( defined(codomain(domain(a)),X1)
| ~ product(codomain(domain(a)),codomain(d),X1) ),
inference(scs_inference,[],[i_0_136,i_0_274,i_0_282,i_0_94,i_0_309,i_0_181,i_0_208,i_0_34,i_0_257,i_0_254,i_0_284,i_0_39,i_0_25,i_0_31,i_0_22,i_0_48,i_0_47,i_0_46,i_0_24,i_0_23]) ).
cnf(i_0_312,plain,
product(codomain(X1),codomain(X1),codomain(X1)),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_313,plain,
( ~ defined(X1,X2)
| defined(X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X5,X2,X4) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_314,plain,
~ product(a,codomain(codomain(d)),d),
inference(equality_inference,[],[305]) ).
cnf(i_0_315,plain,
~ product(domain(a),d,domain(d)),
inference(equality_inference,[],[306]) ).
cnf(i_0_316,plain,
~ product(domain(a),d,domain(d)),
inference(equality_inference,[],[307]) ).
cnf(i_0_317,plain,
~ product(domain(a),codomain(d),domain(d)),
inference(scs_inference,[],[i_0_130,i_0_279,i_0_25]) ).
cnf(i_0_318,plain,
( ~ product(X1,X2,X3)
| X4 = X3
| ~ product(X1,X2,X4) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_319,plain,
product(codomain(domain(a)),d,d),
inference(scs_inference,[],[i_0_130,i_0_194,i_0_279,i_0_38,i_0_25,i_0_31]) ).
cnf(i_0_320,plain,
identity_map(codomain(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_321,plain,
( ~ defined(X1,X2)
| ~ identity_map(X1)
| product(X1,X2,X2) ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_322,plain,
$false,
inference(scs_inference,[],[i_0_198,i_0_130,i_0_184,i_0_194,i_0_257,i_0_279,i_0_276,i_0_38,i_0_25,i_0_31,i_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT005-1 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:46:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.40/1.60 % Version : CSE_E---1.7
% 0.40/1.60 % Problem : theBenchmark.p
% 0.40/1.60 % SZS status Unsatisfiable for theBenchmark.p
% 0.40/1.60 % SZS output start CNFRefutation
% See solution above
% 0.94/2.16 % Total time : 1.270s
%------------------------------------------------------------------------------