TSTP Solution File: SET587+3 by leanCoP---2.2
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- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n005.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 02:54:25 EDT 2022
% Result : Theorem 0.45s 1.40s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n005.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 : Sat Jul 9 18:26:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.45/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/1.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/1.41
% 0.45/1.41 %-----------------------------------------------------
% 0.45/1.41 fof(prove_difference_empty_set, conjecture, ! [_26444, _26447] : (difference(_26444, _26447) = empty_set <=> subset(_26444, _26447)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prove_difference_empty_set)).
% 0.45/1.41 fof(member_equal, axiom, ! [_26687, _26690] : (! [_26698] : (member(_26698, _26687) <=> member(_26698, _26690)) => _26687 = _26690), file('/export/starexec/sandbox/benchmark/theBenchmark.p', member_equal)).
% 0.45/1.41 fof(difference_defn, axiom, ! [_26887, _26890, _26893] : (member(_26893, difference(_26887, _26890)) <=> member(_26893, _26887) & ~ member(_26893, _26890)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', difference_defn)).
% 0.45/1.41 fof(empty_set_defn, axiom, ! [_27119] : ~ member(_27119, empty_set), file('/export/starexec/sandbox/benchmark/theBenchmark.p', empty_set_defn)).
% 0.45/1.41 fof(subset_defn, axiom, ! [_27233, _27236] : (subset(_27233, _27236) <=> ! [_27254] : (member(_27254, _27233) => member(_27254, _27236))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset_defn)).
% 0.45/1.41 fof(equal_member_defn, axiom, ! [_27467, _27470] : (_27467 = _27470 <=> ! [_27484] : (member(_27484, _27467) <=> member(_27484, _27470))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', equal_member_defn)).
% 0.45/1.41
% 0.45/1.41 cnf(1, plain, [-(8 ^ []), difference(5 ^ [], 6 ^ []) = empty_set], clausify(prove_difference_empty_set)).
% 0.45/1.41 cnf(2, plain, [-(8 ^ []), -(subset(5 ^ [], 6 ^ []))], clausify(prove_difference_empty_set)).
% 0.45/1.41 cnf(3, plain, [-(7 ^ []), subset(5 ^ [], 6 ^ [])], clausify(prove_difference_empty_set)).
% 0.45/1.41 cnf(4, plain, [-(7 ^ []), -(difference(5 ^ [], 6 ^ []) = empty_set)], clausify(prove_difference_empty_set)).
% 0.45/1.41 cnf(5, plain, [7 ^ [], 8 ^ []], clausify(prove_difference_empty_set)).
% 0.45/1.41 cnf(6, plain, [-(_5848 = _5848)], theory(equality)).
% 0.45/1.41 cnf(7, plain, [_6001 = _6046, -(_6046 = _6001)], theory(equality)).
% 0.45/1.41 cnf(8, plain, [-(subset(_7766, _7897)), subset(_7699, _7832), _7699 = _7766, _7832 = _7897], theory(equality)).
% 0.45/1.41 cnf(9, plain, [-(_9018 = _9074), -(member(1 ^ [_9074, _9018], _9018)), -(member(1 ^ [_9074, _9018], _9074))], clausify(member_equal)).
% 0.45/1.41 cnf(10, plain, [member(_9600, difference(_9479, _9540)), -(member(_9600, _9479))], clausify(difference_defn)).
% 0.45/1.41 cnf(11, plain, [member(_9600, difference(_9479, _9540)), member(_9600, _9540)], clausify(difference_defn)).
% 0.45/1.41 cnf(12, plain, [-(member(_9600, difference(_9479, _9540))), member(_9600, _9479), -(member(_9600, _9540))], clausify(difference_defn)).
% 0.45/1.41 cnf(13, plain, [member(_10014, empty_set)], clausify(empty_set_defn)).
% 0.45/1.41 cnf(14, plain, [-(subset(_10206, _10262)), -(member(2 ^ [_10262, _10206], _10206))], clausify(subset_defn)).
% 0.45/1.41 cnf(15, plain, [-(subset(_10206, _10262)), member(2 ^ [_10262, _10206], _10262)], clausify(subset_defn)).
% 0.45/1.41 cnf(16, plain, [subset(_10206, _10262), member(_10376, _10206), -(member(_10376, _10262))], clausify(subset_defn)).
% 0.45/1.41 cnf(17, plain, [_11063 = _11119, member(_11233, _11063), -(member(_11233, _11119))], clausify(equal_member_defn)).
% 0.45/1.41 cnf(18, plain, [_11063 = _11119, -(member(_11233, _11063)), member(_11233, _11119)], clausify(equal_member_defn)).
% 0.45/1.41
% 0.45/1.41 cnf('1',plain,[member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ [])), member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 6 ^ [])],start(11,bind([[_9479, _9600, _9540], [5 ^ [], 1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 6 ^ []]]))).
% 0.45/1.41 cnf('1.1',plain,[-(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ []))), -(difference(5 ^ [], 6 ^ []) = empty_set), -(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set))],extension(9,bind([[_9018, _9074], [difference(5 ^ [], 6 ^ []), empty_set]]))).
% 0.45/1.41 cnf('1.1.1',plain,[difference(5 ^ [], 6 ^ []) = empty_set, member(2 ^ [6 ^ [], 5 ^ []], difference(5 ^ [], 6 ^ [])), -(member(2 ^ [6 ^ [], 5 ^ []], empty_set))],extension(17,bind([[_11063, _11233, _11119], [difference(5 ^ [], 6 ^ []), 2 ^ [6 ^ [], 5 ^ []], empty_set]]))).
% 0.45/1.41 cnf('1.1.1.1',plain,[-(member(2 ^ [6 ^ [], 5 ^ []], difference(5 ^ [], 6 ^ []))), member(2 ^ [6 ^ [], 5 ^ []], 5 ^ []), -(member(2 ^ [6 ^ [], 5 ^ []], 6 ^ []))],extension(12,bind([[_9479, _9600, _9540], [5 ^ [], 2 ^ [6 ^ [], 5 ^ []], 6 ^ []]]))).
% 0.45/1.41 cnf('1.1.1.1.1',plain,[-(member(2 ^ [6 ^ [], 5 ^ []], 5 ^ [])), -(subset(5 ^ [], 6 ^ []))],extension(14,bind([[_10206, _10262], [5 ^ [], 6 ^ []]]))).
% 0.45/1.41 cnf('1.1.1.1.1.1',plain,[subset(5 ^ [], 6 ^ []), -(7 ^ [])],extension(3)).
% 0.45/1.41 cnf('1.1.1.1.1.1.1',plain,[7 ^ [], 8 ^ []],extension(5)).
% 0.45/1.41 cnf('1.1.1.1.1.1.1.1',plain,[-(8 ^ []), difference(5 ^ [], 6 ^ []) = empty_set],extension(1)).
% 0.45/1.41 cnf('1.1.1.1.1.1.1.1.1',plain,[-(difference(5 ^ [], 6 ^ []) = empty_set)],reduction('1.1')).
% 0.45/1.41 cnf('1.1.1.1.2',plain,[member(2 ^ [6 ^ [], 5 ^ []], 6 ^ []), -(subset(5 ^ [], 6 ^ []))],extension(15,bind([[_10206, _10262], [5 ^ [], 6 ^ []]]))).
% 0.45/1.41 cnf('1.1.1.1.2.1',plain,[subset(5 ^ [], 6 ^ []), -(7 ^ [])],extension(3)).
% 0.45/1.41 cnf('1.1.1.1.2.1.1',plain,[7 ^ [], 8 ^ []],extension(5)).
% 0.45/1.41 cnf('1.1.1.1.2.1.1.1',plain,[-(8 ^ []), difference(5 ^ [], 6 ^ []) = empty_set],extension(1)).
% 0.45/1.41 cnf('1.1.1.1.2.1.1.1.1',plain,[-(difference(5 ^ [], 6 ^ []) = empty_set)],reduction('1.1')).
% 0.45/1.41 cnf('1.1.1.2',plain,[member(2 ^ [6 ^ [], 5 ^ []], empty_set)],extension(13,bind([[_10014], [2 ^ [6 ^ [], 5 ^ []]]]))).
% 0.45/1.41 cnf('1.1.2',plain,[member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set)],extension(13,bind([[_10014], [1 ^ [empty_set, difference(5 ^ [], 6 ^ [])]]]))).
% 0.45/1.41 cnf('1.2',plain,[-(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 6 ^ [])), subset(empty_set, 6 ^ []), member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set)],extension(16,bind([[_10262, _10376, _10206], [6 ^ [], 1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set]]))).
% 0.45/1.41 cnf('1.2.1',plain,[-(subset(empty_set, 6 ^ [])), subset(empty_set, 6 ^ []), empty_set = empty_set, 6 ^ [] = 6 ^ []],extension(8,bind([[_7699, _7766, _7832, _7897], [empty_set, empty_set, 6 ^ [], 6 ^ []]]))).
% 0.45/1.41 cnf('1.2.1.1',plain,[-(subset(empty_set, 6 ^ [])), -(member(2 ^ [6 ^ [], empty_set], empty_set))],extension(14,bind([[_10262, _10206], [6 ^ [], empty_set]]))).
% 0.45/1.41 cnf('1.2.1.1.1',plain,[member(2 ^ [6 ^ [], empty_set], empty_set)],extension(13,bind([[_10014], [2 ^ [6 ^ [], empty_set]]]))).
% 0.45/1.41 cnf('1.2.1.2',plain,[-(empty_set = empty_set)],extension(6,bind([[_5848], [empty_set]]))).
% 0.45/1.41 cnf('1.2.1.3',plain,[-(6 ^ [] = 6 ^ [])],extension(6,bind([[_5848], [6 ^ []]]))).
% 0.45/1.41 cnf('1.2.2',plain,[-(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set)), -(difference(5 ^ [], 6 ^ []) = empty_set), -(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ [])))],extension(9,bind([[_9074, _9018], [empty_set, difference(5 ^ [], 6 ^ [])]]))).
% 0.45/1.41 cnf('1.2.2.1',plain,[difference(5 ^ [], 6 ^ []) = empty_set, -(empty_set = difference(5 ^ [], 6 ^ []))],extension(7,bind([[_6046, _6001], [empty_set, difference(5 ^ [], 6 ^ [])]]))).
% 0.45/1.41 cnf('1.2.2.1.1',plain,[empty_set = difference(5 ^ [], 6 ^ []), -(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set)), member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ []))],extension(18,bind([[_11063, _11233, _11119], [empty_set, 1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ [])]]))).
% 0.45/1.41 cnf('1.2.2.1.1.1',plain,[member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], empty_set)],extension(13,bind([[_10014], [1 ^ [empty_set, difference(5 ^ [], 6 ^ [])]]]))).
% 0.45/1.41 cnf('1.2.2.1.1.2',plain,[-(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ [])))],lemmata('1')).
% 0.45/1.41 cnf('1.2.2.2',plain,[member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], difference(5 ^ [], 6 ^ [])), -(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 5 ^ []))],extension(10,bind([[_9540, _9600, _9479], [6 ^ [], 1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 5 ^ []]]))).
% 0.45/1.41 cnf('1.2.2.2.1',plain,[member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 5 ^ []), subset(5 ^ [], 6 ^ []), -(member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 6 ^ []))],extension(16,bind([[_10206, _10376, _10262], [5 ^ [], 1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 6 ^ []]]))).
% 0.45/1.41 cnf('1.2.2.2.1.1',plain,[-(subset(5 ^ [], 6 ^ [])), -(8 ^ [])],extension(2)).
% 0.45/1.41 cnf('1.2.2.2.1.1.1',plain,[8 ^ [], 7 ^ []],extension(5)).
% 0.45/1.41 cnf('1.2.2.2.1.1.1.1',plain,[-(7 ^ []), -(difference(5 ^ [], 6 ^ []) = empty_set)],extension(4)).
% 0.45/1.41 cnf('1.2.2.2.1.1.1.1.1',plain,[difference(5 ^ [], 6 ^ []) = empty_set],lemmata('1.2.2')).
% 0.45/1.41 cnf('1.2.2.2.1.2',plain,[member(1 ^ [empty_set, difference(5 ^ [], 6 ^ [])], 6 ^ [])],reduction('1')).
% 0.45/1.41 %-----------------------------------------------------
% 0.45/1.42
% 0.45/1.42 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------