%------------------------------------------------------------------------------
% File     : leanCoP---2.2
% Problem  : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leancop_casc.sh %s %d

% Computer : n024.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  : 600s
% DateTime : Tue Jul 19 02:55:14 EDT 2022

% Result   : Theorem 191.36s 184.96s
% Output   : Proof 191.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : leancop_casc.sh %s %d
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 17:13:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 191.36/184.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 191.40/184.97  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 191.40/184.97  
% 191.40/184.97  %-----------------------------------------------------
% 191.40/184.97  fof(p24, axiom, ! [_64085] : ilf_type(_64085, set_type), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p24)).
% 191.40/184.97  fof(p6, axiom, ! [_64198] : (ilf_type(_64198, set_type) => ! [_64216] : (ilf_type(_64216, set_type) => (ilf_type(_64216, identity_relation_of_type(_64198)) <=> ilf_type(_64216, relation_type(_64198, _64198))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p6)).
% 191.40/184.97  fof(p14, axiom, ! [_64444] : (ilf_type(_64444, set_type) => ! [_64462] : (ilf_type(_64462, set_type) => (subset(_64444, _64462) <=> ! [_64490] : (ilf_type(_64490, set_type) => member(_64490, _64444) => member(_64490, _64462))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p14)).
% 191.40/184.97  fof(p1, axiom, ! [_64754] : (ilf_type(_64754, set_type) => ! [_64772] : (ilf_type(_64772, set_type) => ! [_64790] : (ilf_type(_64790, subset_type(cross_product(_64754, _64772))) => ilf_type(_64790, relation_type(_64754, _64772))) & ! [_64836] : (ilf_type(_64836, relation_type(_64754, _64772)) => ilf_type(_64836, subset_type(cross_product(_64754, _64772)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p1)).
% 191.40/184.97  fof(p16, axiom, ! [_65178] : (ilf_type(_65178, set_type) => ! [_65196] : (ilf_type(_65196, set_type) => (member(_65178, power_set(_65196)) <=> ! [_65228] : (ilf_type(_65228, set_type) => member(_65228, _65178) => member(_65228, _65196))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p16)).
% 191.40/184.97  fof(p3, axiom, ! [_65495] : (ilf_type(_65495, set_type) => subset(identity_relation_of(_65495), cross_product(_65495, _65495))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p3)).
% 191.40/184.97  fof(p12, axiom, ! [_65672] : (ilf_type(_65672, set_type) => ! [_65690] : (ilf_type(_65690, set_type) => (ilf_type(_65690, subset_type(_65672)) <=> ilf_type(_65690, member_type(power_set(_65672)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p12)).
% 191.40/184.97  fof(p17, axiom, ! [_65926] : (ilf_type(_65926, set_type) => ~ empty(power_set(_65926)) & ilf_type(power_set(_65926), set_type)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p17)).
% 191.40/184.97  fof(p18, axiom, ! [_66109] : (ilf_type(_66109, set_type) => ! [_66127] : (~ empty(_66127) & ilf_type(_66127, set_type) => (ilf_type(_66109, member_type(_66127)) <=> member(_66109, _66127)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p18)).
% 191.40/184.97  fof(prove_relset_1_29, conjecture, ! [_66389] : (ilf_type(_66389, set_type) => ilf_type(identity_relation_of(_66389), identity_relation_of_type(_66389))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prove_relset_1_29)).
% 191.40/184.97  
% 191.40/184.97  cnf(1, plain, [-(ilf_type(_33391, set_type))], clausify(p24)).
% 191.40/184.97  cnf(2, plain, [ilf_type(_24940, set_type), ilf_type(_25061, set_type), -(ilf_type(_25061, identity_relation_of_type(_24940))), ilf_type(_25061, relation_type(_24940, _24940))], clausify(p6)).
% 191.40/184.97  cnf(3, plain, [ilf_type(_28098, set_type), ilf_type(_28231, set_type), subset(_28098, _28231), ilf_type(_28416, set_type), member(_28416, _28098), -(member(_28416, _28231))], clausify(p14)).
% 191.40/184.97  cnf(4, plain, [ilf_type(_22061, set_type), ilf_type(_22215, set_type), ilf_type(_22372, subset_type(cross_product(_22061, _22215))), -(ilf_type(_22372, relation_type(_22061, _22215)))], clausify(p1)).
% 191.40/184.97  cnf(5, plain, [ilf_type(_29071, set_type), ilf_type(_29206, set_type), -(member(_29071, power_set(_29206))), -(member(6 ^ [_29206, _29071], _29071))], clausify(p16)).
% 191.40/184.97  cnf(6, plain, [ilf_type(_23563, set_type), -(subset(identity_relation_of(_23563), cross_product(_23563, _23563)))], clausify(p3)).
% 191.40/184.97  cnf(7, plain, [ilf_type(_27237, set_type), ilf_type(_27359, set_type), -(ilf_type(_27359, subset_type(_27237))), ilf_type(_27359, member_type(power_set(_27237)))], clausify(p12)).
% 191.40/184.97  cnf(8, plain, [ilf_type(_29810, set_type), empty(power_set(_29810))], clausify(p17)).
% 191.40/184.97  cnf(9, plain, [ilf_type(_30176, set_type), ilf_type(_30301, set_type), -(empty(_30301)), -(ilf_type(_30176, member_type(_30301))), member(_30176, _30301)], clausify(p18)).
% 191.40/184.97  cnf(10, plain, [ilf_type(_29071, set_type), ilf_type(_29206, set_type), -(member(_29071, power_set(_29206))), member(6 ^ [_29206, _29071], _29206)], clausify(p16)).
% 191.40/184.97  cnf(11, plain, [ilf_type(identity_relation_of(12 ^ []), identity_relation_of_type(12 ^ []))], clausify(prove_relset_1_29)).
% 191.40/184.97  
% 191.40/184.97  cnf('1',plain,[ilf_type(cross_product(12 ^ [], 12 ^ []), set_type), empty(power_set(cross_product(12 ^ [], 12 ^ [])))],start(8,bind([[_29810], [cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.1',plain,[-(ilf_type(cross_product(12 ^ [], 12 ^ []), set_type))],extension(1,bind([[_33391], [cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2',plain,[-(empty(power_set(cross_product(12 ^ [], 12 ^ [])))), ilf_type(identity_relation_of(12 ^ []), set_type), ilf_type(power_set(cross_product(12 ^ [], 12 ^ [])), set_type), -(ilf_type(identity_relation_of(12 ^ []), member_type(power_set(cross_product(12 ^ [], 12 ^ []))))), member(identity_relation_of(12 ^ []), power_set(cross_product(12 ^ [], 12 ^ [])))],extension(9,bind([[_30176, _30301], [identity_relation_of(12 ^ []), power_set(cross_product(12 ^ [], 12 ^ []))]]))).
% 191.40/184.97  cnf('1.2.1',plain,[-(ilf_type(identity_relation_of(12 ^ []), set_type))],extension(1,bind([[_33391], [identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.2',plain,[-(ilf_type(power_set(cross_product(12 ^ [], 12 ^ [])), set_type))],extension(1,bind([[_33391], [power_set(cross_product(12 ^ [], 12 ^ []))]]))).
% 191.40/184.97  cnf('1.2.3',plain,[ilf_type(identity_relation_of(12 ^ []), member_type(power_set(cross_product(12 ^ [], 12 ^ [])))), ilf_type(cross_product(12 ^ [], 12 ^ []), set_type), ilf_type(identity_relation_of(12 ^ []), set_type), -(ilf_type(identity_relation_of(12 ^ []), subset_type(cross_product(12 ^ [], 12 ^ []))))],extension(7,bind([[_27359, _27237], [identity_relation_of(12 ^ []), cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.3.1',plain,[-(ilf_type(cross_product(12 ^ [], 12 ^ []), set_type))],extension(1,bind([[_33391], [cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.3.2',plain,[-(ilf_type(identity_relation_of(12 ^ []), set_type))],extension(1,bind([[_33391], [identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.3.3',plain,[ilf_type(identity_relation_of(12 ^ []), subset_type(cross_product(12 ^ [], 12 ^ []))), ilf_type(12 ^ [], set_type), ilf_type(12 ^ [], set_type), -(ilf_type(identity_relation_of(12 ^ []), relation_type(12 ^ [], 12 ^ [])))],extension(4,bind([[_22372, _22061, _22215], [identity_relation_of(12 ^ []), 12 ^ [], 12 ^ []]]))).
% 191.40/184.97  cnf('1.2.3.3.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1,bind([[_33391], [12 ^ []]]))).
% 191.40/184.97  cnf('1.2.3.3.2',plain,[-(ilf_type(12 ^ [], set_type))],extension(1,bind([[_33391], [12 ^ []]]))).
% 191.40/184.97  cnf('1.2.3.3.3',plain,[ilf_type(identity_relation_of(12 ^ []), relation_type(12 ^ [], 12 ^ [])), ilf_type(12 ^ [], set_type), ilf_type(identity_relation_of(12 ^ []), set_type), -(ilf_type(identity_relation_of(12 ^ []), identity_relation_of_type(12 ^ [])))],extension(2,bind([[_25061, _24940], [identity_relation_of(12 ^ []), 12 ^ []]]))).
% 191.40/184.97  cnf('1.2.3.3.3.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1,bind([[_33391], [12 ^ []]]))).
% 191.40/184.97  cnf('1.2.3.3.3.2',plain,[-(ilf_type(identity_relation_of(12 ^ []), set_type))],extension(1,bind([[_33391], [identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.3.3.3.3',plain,[ilf_type(identity_relation_of(12 ^ []), identity_relation_of_type(12 ^ []))],extension(11)).
% 191.40/184.97  cnf('1.2.4',plain,[-(member(identity_relation_of(12 ^ []), power_set(cross_product(12 ^ [], 12 ^ [])))), ilf_type(identity_relation_of(12 ^ []), set_type), ilf_type(cross_product(12 ^ [], 12 ^ []), set_type), -(member(6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], identity_relation_of(12 ^ [])))],extension(5,bind([[_29206, _29071], [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.1',plain,[-(ilf_type(identity_relation_of(12 ^ []), set_type))],extension(1,bind([[_33391], [identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.2',plain,[-(ilf_type(cross_product(12 ^ [], 12 ^ []), set_type))],extension(1,bind([[_33391], [cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3',plain,[member(6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], identity_relation_of(12 ^ [])), ilf_type(identity_relation_of(12 ^ []), set_type), ilf_type(cross_product(12 ^ [], 12 ^ []), set_type), subset(identity_relation_of(12 ^ []), cross_product(12 ^ [], 12 ^ [])), ilf_type(6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], set_type), -(member(6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], cross_product(12 ^ [], 12 ^ [])))],extension(3,bind([[_28098, _28416, _28231], [identity_relation_of(12 ^ []), 6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3.1',plain,[-(ilf_type(identity_relation_of(12 ^ []), set_type))],extension(1,bind([[_33391], [identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3.2',plain,[-(ilf_type(cross_product(12 ^ [], 12 ^ []), set_type))],extension(1,bind([[_33391], [cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3.3',plain,[-(subset(identity_relation_of(12 ^ []), cross_product(12 ^ [], 12 ^ []))), ilf_type(12 ^ [], set_type)],extension(6,bind([[_23563], [12 ^ []]]))).
% 191.40/184.97  cnf('1.2.4.3.3.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1,bind([[_33391], [12 ^ []]]))).
% 191.40/184.97  cnf('1.2.4.3.4',plain,[-(ilf_type(6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], set_type))],extension(1,bind([[_33391], [6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])]]]))).
% 191.40/184.97  cnf('1.2.4.3.5',plain,[member(6 ^ [cross_product(12 ^ [], 12 ^ []), identity_relation_of(12 ^ [])], cross_product(12 ^ [], 12 ^ [])), ilf_type(identity_relation_of(12 ^ []), set_type), ilf_type(cross_product(12 ^ [], 12 ^ []), set_type), -(member(identity_relation_of(12 ^ []), power_set(cross_product(12 ^ [], 12 ^ []))))],extension(10,bind([[_29071, _29206], [identity_relation_of(12 ^ []), cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3.5.1',plain,[-(ilf_type(identity_relation_of(12 ^ []), set_type))],extension(1,bind([[_33391], [identity_relation_of(12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3.5.2',plain,[-(ilf_type(cross_product(12 ^ [], 12 ^ []), set_type))],extension(1,bind([[_33391], [cross_product(12 ^ [], 12 ^ [])]]))).
% 191.40/184.97  cnf('1.2.4.3.5.3',plain,[member(identity_relation_of(12 ^ []), power_set(cross_product(12 ^ [], 12 ^ [])))],reduction('1.2')).
% 191.40/184.97  %-----------------------------------------------------
% 191.40/184.98  
% 191.40/184.98  % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------