TSTP Solution File: SET641+3 by leanCoP---2.2

%------------------------------------------------------------------------------
% File     : leanCoP---2.2
% Problem  : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leancop_casc.sh %s %d

% Computer : n029.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 02:55:04 EDT 2022

% Result   : Theorem 5.21s 5.55s
% Output   : Proof 5.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : leancop_casc.sh %s %d
% 0.12/0.33  % Computer : n029.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 08:31:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 5.21/5.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.21/5.56  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.21/5.56  
% 5.21/5.56  %-----------------------------------------------------
% 5.21/5.56  fof(prove_relset_1_3, conjecture, ! [_51262] : (ilf_type(_51262, set_type) => ! [_51280] : (ilf_type(_51280, set_type) => ! [_51298] : (ilf_type(_51298, set_type) => subset(_51262, cross_product(_51280, _51298)) => ilf_type(_51262, relation_type(_51280, _51298))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prove_relset_1_3)).
% 5.21/5.56  fof(p1, axiom, ! [_51631] : (ilf_type(_51631, set_type) => ! [_51649] : (ilf_type(_51649, set_type) => ! [_51667] : (ilf_type(_51667, subset_type(cross_product(_51631, _51649))) => ilf_type(_51667, relation_type(_51631, _51649))) & ! [_51713] : (ilf_type(_51713, relation_type(_51631, _51649)) => ilf_type(_51713, subset_type(cross_product(_51631, _51649)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p1)).
% 5.21/5.56  fof(p4, axiom, ! [_52058] : (ilf_type(_52058, set_type) => ! [_52076] : (ilf_type(_52076, set_type) => ilf_type(cross_product(_52058, _52076), set_type))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p4)).
% 5.21/5.56  fof(p5, axiom, ! [_52270] : (ilf_type(_52270, set_type) => ! [_52288] : (ilf_type(_52288, set_type) => (subset(_52270, _52288) <=> ! [_52316] : (ilf_type(_52316, set_type) => member(_52316, _52270) => member(_52316, _52288))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p5)).
% 5.21/5.56  fof(p7, axiom, ! [_52579] : (ilf_type(_52579, set_type) => ! [_52597] : (ilf_type(_52597, set_type) => (ilf_type(_52597, subset_type(_52579)) <=> ilf_type(_52597, member_type(power_set(_52579)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p7)).
% 5.21/5.56  fof(p10, axiom, ! [_52829] : (ilf_type(_52829, set_type) => ! [_52847] : (ilf_type(_52847, set_type) => (member(_52829, power_set(_52847)) <=> ! [_52879] : (ilf_type(_52879, set_type) => member(_52879, _52829) => member(_52879, _52847))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p10)).
% 5.21/5.56  fof(p11, axiom, ! [_53170] : (ilf_type(_53170, set_type) => ~ empty(power_set(_53170)) & ilf_type(power_set(_53170), set_type)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p11)).
% 5.21/5.56  fof(p12, axiom, ! [_53364] : (ilf_type(_53364, set_type) => ! [_53382] : (~ empty(_53382) & ilf_type(_53382, set_type) => (ilf_type(_53364, member_type(_53382)) <=> member(_53364, _53382)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p12)).
% 5.21/5.56  fof(p18, axiom, ! [_53627] : ilf_type(_53627, set_type), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', p18)).
% 5.21/5.56  
% 5.21/5.56  cnf(1, plain, [-(ilf_type(12 ^ [], set_type))], clausify(prove_relset_1_3)).
% 5.21/5.56  cnf(2, plain, [-(ilf_type(13 ^ [], set_type))], clausify(prove_relset_1_3)).
% 5.21/5.56  cnf(3, plain, [-(ilf_type(14 ^ [], set_type))], clausify(prove_relset_1_3)).
% 5.21/5.56  cnf(4, plain, [-(subset(12 ^ [], cross_product(13 ^ [], 14 ^ [])))], clausify(prove_relset_1_3)).
% 5.21/5.56  cnf(5, plain, [ilf_type(12 ^ [], relation_type(13 ^ [], 14 ^ []))], clausify(prove_relset_1_3)).
% 5.21/5.56  cnf(6, plain, [ilf_type(_19928, set_type), ilf_type(_20082, set_type), ilf_type(_20239, subset_type(cross_product(_19928, _20082))), -(ilf_type(_20239, relation_type(_19928, _20082)))], clausify(p1)).
% 5.21/5.56  cnf(7, plain, [ilf_type(_22718, set_type), ilf_type(_22831, set_type), -(ilf_type(cross_product(_22718, _22831), set_type))], clausify(p4)).
% 5.21/5.56  cnf(8, plain, [ilf_type(_23151, set_type), ilf_type(_23284, set_type), subset(_23151, _23284), ilf_type(_23469, set_type), member(_23469, _23151), -(member(_23469, _23284))], clausify(p5)).
% 5.21/5.56  cnf(9, plain, [ilf_type(_24303, set_type), ilf_type(_24425, set_type), -(ilf_type(_24425, subset_type(_24303))), ilf_type(_24425, member_type(power_set(_24303)))], clausify(p7)).
% 5.21/5.56  cnf(10, plain, [ilf_type(_25418, set_type), ilf_type(_25553, set_type), -(member(_25418, power_set(_25553))), -(ilf_type(6 ^ [_25553, _25418], set_type))], clausify(p10)).
% 5.21/5.56  cnf(11, plain, [ilf_type(_25418, set_type), ilf_type(_25553, set_type), -(member(_25418, power_set(_25553))), -(member(6 ^ [_25553, _25418], _25418))], clausify(p10)).
% 5.21/5.56  cnf(12, plain, [ilf_type(_25418, set_type), ilf_type(_25553, set_type), -(member(_25418, power_set(_25553))), member(6 ^ [_25553, _25418], _25553)], clausify(p10)).
% 5.21/5.56  cnf(13, plain, [ilf_type(_26157, set_type), empty(power_set(_26157))], clausify(p11)).
% 5.21/5.56  cnf(14, plain, [ilf_type(_26157, set_type), -(ilf_type(power_set(_26157), set_type))], clausify(p11)).
% 5.21/5.56  cnf(15, plain, [ilf_type(_26523, set_type), ilf_type(_26648, set_type), -(empty(_26648)), -(ilf_type(_26523, member_type(_26648))), member(_26523, _26648)], clausify(p12)).
% 5.21/5.56  cnf(16, plain, [-(ilf_type(_29738, set_type))], clausify(p18)).
% 5.21/5.56  
% 5.21/5.56  cnf('1',plain,[ilf_type(12 ^ [], relation_type(13 ^ [], 14 ^ []))],start(5)).
% 5.21/5.56  cnf('1.1',plain,[-(ilf_type(12 ^ [], relation_type(13 ^ [], 14 ^ []))), ilf_type(13 ^ [], set_type), ilf_type(14 ^ [], set_type), ilf_type(12 ^ [], subset_type(cross_product(13 ^ [], 14 ^ [])))],extension(6,bind([[_20239, _19928, _20082], [12 ^ [], 13 ^ [], 14 ^ []]]))).
% 5.21/5.56  cnf('1.1.1',plain,[-(ilf_type(13 ^ [], set_type))],extension(2)).
% 5.21/5.56  cnf('1.1.2',plain,[-(ilf_type(14 ^ [], set_type))],extension(3)).
% 5.21/5.56  cnf('1.1.3',plain,[-(ilf_type(12 ^ [], subset_type(cross_product(13 ^ [], 14 ^ [])))), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type), ilf_type(12 ^ [], set_type), ilf_type(12 ^ [], member_type(power_set(cross_product(13 ^ [], 14 ^ []))))],extension(9,bind([[_24425, _24303], [12 ^ [], cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.1',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type)), ilf_type(13 ^ [], set_type), ilf_type(14 ^ [], set_type)],extension(7,bind([[_22718, _22831], [13 ^ [], 14 ^ []]]))).
% 5.21/5.56  cnf('1.1.3.1.1',plain,[-(ilf_type(13 ^ [], set_type))],extension(2)).
% 5.21/5.56  cnf('1.1.3.1.2',plain,[-(ilf_type(14 ^ [], set_type))],extension(3)).
% 5.21/5.56  cnf('1.1.3.2',plain,[-(ilf_type(12 ^ [], set_type))],extension(1)).
% 5.21/5.56  cnf('1.1.3.3',plain,[-(ilf_type(12 ^ [], member_type(power_set(cross_product(13 ^ [], 14 ^ []))))), ilf_type(12 ^ [], set_type), ilf_type(power_set(cross_product(13 ^ [], 14 ^ [])), set_type), -(empty(power_set(cross_product(13 ^ [], 14 ^ [])))), member(12 ^ [], power_set(cross_product(13 ^ [], 14 ^ [])))],extension(15,bind([[_26523, _26648], [12 ^ [], power_set(cross_product(13 ^ [], 14 ^ []))]]))).
% 5.21/5.56  cnf('1.1.3.3.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1)).
% 5.21/5.56  cnf('1.1.3.3.2',plain,[-(ilf_type(power_set(cross_product(13 ^ [], 14 ^ [])), set_type)), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type)],extension(14,bind([[_26157], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.2.1',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type))],extension(16,bind([[_29738], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.3',plain,[empty(power_set(cross_product(13 ^ [], 14 ^ []))), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type)],extension(13,bind([[_26157], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.3.1',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type))],extension(16,bind([[_29738], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4',plain,[-(member(12 ^ [], power_set(cross_product(13 ^ [], 14 ^ [])))), ilf_type(12 ^ [], set_type), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type), member(6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], cross_product(13 ^ [], 14 ^ []))],extension(12,bind([[_25418, _25553], [12 ^ [], cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1)).
% 5.21/5.56  cnf('1.1.3.3.4.2',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type))],extension(16,bind([[_29738], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3',plain,[-(member(6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], cross_product(13 ^ [], 14 ^ []))), ilf_type(12 ^ [], set_type), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type), subset(12 ^ [], cross_product(13 ^ [], 14 ^ [])), ilf_type(6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], set_type), member(6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], 12 ^ [])],extension(8,bind([[_23284, _23469, _23151], [cross_product(13 ^ [], 14 ^ []), 6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], 12 ^ []]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1)).
% 5.21/5.56  cnf('1.1.3.3.4.3.2',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type))],extension(16,bind([[_29738], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3.3',plain,[-(subset(12 ^ [], cross_product(13 ^ [], 14 ^ [])))],extension(4)).
% 5.21/5.56  cnf('1.1.3.3.4.3.4',plain,[-(ilf_type(6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], set_type)), ilf_type(12 ^ [], set_type), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type), -(member(12 ^ [], power_set(cross_product(13 ^ [], 14 ^ []))))],extension(10,bind([[_25418, _25553], [12 ^ [], cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3.4.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1)).
% 5.21/5.56  cnf('1.1.3.3.4.3.4.2',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type))],extension(16,bind([[_29738], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3.4.3',plain,[member(12 ^ [], power_set(cross_product(13 ^ [], 14 ^ [])))],reduction('1.1.3.3')).
% 5.21/5.56  cnf('1.1.3.3.4.3.5',plain,[-(member(6 ^ [cross_product(13 ^ [], 14 ^ []), 12 ^ []], 12 ^ [])), ilf_type(12 ^ [], set_type), ilf_type(cross_product(13 ^ [], 14 ^ []), set_type), -(member(12 ^ [], power_set(cross_product(13 ^ [], 14 ^ []))))],extension(11,bind([[_25418, _25553], [12 ^ [], cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3.5.1',plain,[-(ilf_type(12 ^ [], set_type))],extension(1)).
% 5.21/5.56  cnf('1.1.3.3.4.3.5.2',plain,[-(ilf_type(cross_product(13 ^ [], 14 ^ []), set_type))],extension(16,bind([[_29738], [cross_product(13 ^ [], 14 ^ [])]]))).
% 5.21/5.56  cnf('1.1.3.3.4.3.5.3',plain,[member(12 ^ [], power_set(cross_product(13 ^ [], 14 ^ [])))],reduction('1.1.3.3')).
% 5.21/5.56  %-----------------------------------------------------
% 5.21/5.57  
% 5.21/5.57  % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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