TSTP Solution File: SET159+3 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n015.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 02:51:56 EDT 2022
% Result : Theorem 0.48s 1.39s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET159+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n015.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 : Mon Jul 11 02:22:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/1.40 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/1.40
% 0.48/1.40 %-----------------------------------------------------
% 0.48/1.40 fof(prove_associativity_of_union, conjecture, ! [_24979, _24982, _24985] : union(union(_24979, _24982), _24985) = union(_24979, union(_24982, _24985)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prove_associativity_of_union)).
% 0.48/1.40 fof(union_defn, axiom, ! [_25196, _25199, _25202] : (member(_25202, union(_25196, _25199)) <=> member(_25202, _25196) | member(_25202, _25199)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', union_defn)).
% 0.48/1.40 fof(commutativity_of_union, axiom, ! [_25424, _25427] : union(_25424, _25427) = union(_25427, _25424), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', commutativity_of_union)).
% 0.48/1.40 fof(equal_member_defn, axiom, ! [_25576, _25579] : (_25576 = _25579 <=> ! [_25593] : (member(_25593, _25576) <=> member(_25593, _25579))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', equal_member_defn)).
% 0.48/1.40
% 0.48/1.40 cnf(1, plain, [union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))], clausify(prove_associativity_of_union)).
% 0.48/1.40 cnf(2, plain, [-(_5208 = _5208)], theory(equality)).
% 0.48/1.40 cnf(3, plain, [-(member(_6183, _6314)), member(_6116, _6249), _6116 = _6183, _6249 = _6314], theory(equality)).
% 0.48/1.40 cnf(4, plain, [-(member(_8151, union(_8034, _8093))), member(_8151, _8034)], clausify(union_defn)).
% 0.48/1.40 cnf(5, plain, [-(member(_8151, union(_8034, _8093))), member(_8151, _8093)], clausify(union_defn)).
% 0.48/1.40 cnf(6, plain, [member(_8151, union(_8034, _8093)), -(member(_8151, _8034)), -(member(_8151, _8093))], clausify(union_defn)).
% 0.48/1.40 cnf(7, plain, [-(union(_8943, _8988) = union(_8988, _8943))], clausify(commutativity_of_union)).
% 0.48/1.40 cnf(8, plain, [-(_9878 = _9934), member(2 ^ [_9934, _9878], _9878), member(2 ^ [_9934, _9878], _9934)], clausify(equal_member_defn)).
% 0.48/1.40 cnf(9, plain, [-(_9878 = _9934), -(member(2 ^ [_9934, _9878], _9878)), -(member(2 ^ [_9934, _9878], _9934))], clausify(equal_member_defn)).
% 0.48/1.40
% 0.48/1.40 cnf('1',plain,[union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))],start(1)).
% 0.48/1.40 cnf('1.1',plain,[-(union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ [])), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])))],extension(8,bind([[_9878, _9934], [union(union(3 ^ [], 4 ^ []), 5 ^ []), union(3 ^ [], union(4 ^ [], 5 ^ []))]]))).
% 0.48/1.40 cnf('1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ []))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ []))],extension(4,bind([[_8093, _8151, _8034], [5 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ [])]]))).
% 0.48/1.40 cnf('1.1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ []))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ [])],extension(4,bind([[_8093, _8151, _8034], [4 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ []]]))).
% 0.48/1.40 cnf('1.1.1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ [])), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(4 ^ [], 5 ^ []), 3 ^ [])), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ [])))],extension(6,bind([[_8093, _8151, _8034], [3 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ [])]]))).
% 0.48/1.40 cnf('1.1.1.1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(4 ^ [], 5 ^ []), 3 ^ []))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ []))), 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])] = 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])) = union(union(4 ^ [], 5 ^ []), 3 ^ [])],extension(3,bind([[_6116, _6183, _6249, _6314], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(4 ^ [], 5 ^ []), 3 ^ [])]]))).
% 0.48/1.40 cnf('1.1.1.1.1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])))), -(union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ [])))],extension(9,bind([[_9934, _9878], [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])]]))).
% 0.48/1.40 cnf('1.1.1.1.1.1.1.1',plain,[union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))],extension(1)).
% 0.48/1.40 cnf('1.1.1.1.1.1.1.2',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ []))],reduction('1.1')).
% 0.48/1.40 cnf('1.1.1.1.1.1.2',plain,[-(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])] = 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])])],extension(2,bind([[_5208], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])]]]))).
% 0.48/1.40 cnf('1.1.1.1.1.1.3',plain,[-(union(3 ^ [], union(4 ^ [], 5 ^ [])) = union(union(4 ^ [], 5 ^ []), 3 ^ []))],extension(7,bind([[_8988, _8943], [union(4 ^ [], 5 ^ []), 3 ^ []]]))).
% 0.48/1.40 cnf('1.1.1.1.1.2',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ [])), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 4 ^ [])), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 5 ^ []))],extension(6,bind([[_8034, _8151, _8093], [4 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 5 ^ []]]))).
% 0.48/1.40 cnf('1.1.1.1.1.2.1',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 4 ^ []), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ [])))],extension(5,bind([[_8151, _8034, _8093], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ [], 4 ^ []]]))).
% 0.48/1.40 cnf('1.1.1.1.1.2.1.1',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ []))],reduction('1.1.1')).
% 0.48/1.40 cnf('1.1.1.1.1.2.2',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 5 ^ []), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ [])))],extension(5,bind([[_8151, _8034, _8093], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ []), 5 ^ []]]))).
% 0.48/1.40 cnf('1.1.1.1.1.2.2.1',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ []))],reduction('1.1')).
% 0.48/1.40 cnf('1.1.2',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ []))],extension(5,bind([[_8034, _8151, _8093], [3 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ [])]]))).
% 0.48/1.40 cnf('1.1.2.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ []))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 5 ^ [])],extension(5,bind([[_8034, _8151, _8093], [4 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 5 ^ []]]))).
% 0.48/1.40 cnf('1.1.2.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 5 ^ [])), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(5 ^ [], union(3 ^ [], 4 ^ []))), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ [])))],extension(6,bind([[_8034, _8151, _8093], [5 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ [])]]))).
% 0.48/1.40 cnf('1.1.2.1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(5 ^ [], union(3 ^ [], 4 ^ [])))), member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ [])), 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])] = 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(5 ^ [], union(3 ^ [], 4 ^ []))],extension(3,bind([[_6116, _6183, _6249, _6314], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ []), union(5 ^ [], union(3 ^ [], 4 ^ []))]]))).
% 0.48/1.40 cnf('1.1.2.1.1.1.1',plain,[-(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(union(3 ^ [], 4 ^ []), 5 ^ []))), -(union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ []))))],extension(9,bind([[_9878, _9934], [union(union(3 ^ [], 4 ^ []), 5 ^ []), union(3 ^ [], union(4 ^ [], 5 ^ []))]]))).
% 0.48/1.40 cnf('1.1.2.1.1.1.1.1',plain,[union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(3 ^ [], union(4 ^ [], 5 ^ []))],extension(1)).
% 0.48/1.40 cnf('1.1.2.1.1.1.1.2',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])))],reduction('1.1')).
% 0.48/1.40 cnf('1.1.2.1.1.1.2',plain,[-(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])] = 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])])],extension(2,bind([[_5208], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])]]]))).
% 0.48/1.40 cnf('1.1.2.1.1.1.3',plain,[-(union(union(3 ^ [], 4 ^ []), 5 ^ []) = union(5 ^ [], union(3 ^ [], 4 ^ [])))],extension(7,bind([[_8988, _8943], [5 ^ [], union(3 ^ [], 4 ^ [])]]))).
% 0.48/1.40 cnf('1.1.2.1.1.2',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], 4 ^ [])), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ [])), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 4 ^ []))],extension(6,bind([[_8034, _8151, _8093], [3 ^ [], 2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 4 ^ []]]))).
% 0.48/1.40 cnf('1.1.2.1.1.2.1',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ []), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ []))))],extension(4,bind([[_8151, _8034, _8093], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 3 ^ [], union(4 ^ [], 5 ^ [])]]))).
% 0.48/1.40 cnf('1.1.2.1.1.2.1.1',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(3 ^ [], union(4 ^ [], 5 ^ [])))],reduction('1.1')).
% 0.48/1.40 cnf('1.1.2.1.1.2.2',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 4 ^ []), -(member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ [])))],extension(4,bind([[_8151, _8034, _8093], [2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], 4 ^ [], 5 ^ []]]))).
% 0.48/1.40 cnf('1.1.2.1.1.2.2.1',plain,[member(2 ^ [union(3 ^ [], union(4 ^ [], 5 ^ [])), union(union(3 ^ [], 4 ^ []), 5 ^ [])], union(4 ^ [], 5 ^ []))],reduction('1.1.2')).
% 0.48/1.40 %-----------------------------------------------------
% 0.48/1.41
% 0.48/1.41 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------