TSTP Solution File: SET352+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET352+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 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 : 300s
% DateTime : Tue Apr 30 20:39:35 EDT 2024
% Result : Theorem 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 9 unt; 0 def)
% Number of atoms : 239 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 247 ( 95 ~; 109 |; 28 &)
% ( 14 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 128 ( 121 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = A
| X = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] : equal_set(sum(unordered_pair(A,B)),union(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : equal_set(sum(unordered_pair(A,B)),union(A,B)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f26,plain,
! [X,A] :
( ( ~ member(X,power_set(A))
| subset(X,A) )
& ( member(X,power_set(A))
| ~ subset(X,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
( ! [X,A] :
( ~ member(X,power_set(A))
| subset(X,A) )
& ! [X,A] :
( member(X,power_set(A))
| ~ subset(X,A) ) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f35,plain,
! [X,A,B] :
( ( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ! [X,A,B] :
( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f50,plain,
! [X,A,B] :
( ( ~ member(X,unordered_pair(A,B))
| X = A
| X = B )
& ( member(X,unordered_pair(A,B))
| ( X != A
& X != B ) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f51,plain,
( ! [X,A,B] :
( ~ member(X,unordered_pair(A,B))
| X = A
| X = B )
& ! [X,A,B] :
( member(X,unordered_pair(A,B))
| ( X != A
& X != B ) ) ),
inference(miniscoping,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f54,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f55,plain,
! [X,A] :
( ( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f56,plain,
( ! [X,A] :
( ~ member(X,sum(A))
| ? [Y] :
( member(Y,A)
& member(X,Y) ) )
& ! [X,A] :
( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(miniscoping,[status(esa)],[f55]) ).
fof(f57,plain,
( ! [X,A] :
( ~ member(X,sum(A))
| ( member(sk0_1(A,X),A)
& member(X,sk0_1(A,X)) ) )
& ! [X,A] :
( member(X,sum(A))
| ! [Y] :
( ~ member(Y,A)
| ~ member(X,Y) ) ) ),
inference(skolemization,[status(esa)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(X0,sk0_1(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2] :
( member(X0,sum(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f68,plain,
? [A,B] : ~ equal_set(sum(unordered_pair(A,B)),union(A,B)),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f72,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f53]) ).
fof(f73,plain,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(esa)],[f54]) ).
fof(f108,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| equal_set(X1,X0)
| ~ subset(X1,X0) ),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f137,plain,
( spl0_0
<=> member(union(sk0_3,sk0_4),power_set(sum(unordered_pair(sk0_3,sk0_4)))) ),
introduced(split_symbol_definition) ).
fof(f139,plain,
( ~ member(union(sk0_3,sk0_4),power_set(sum(unordered_pair(sk0_3,sk0_4))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( spl0_1
<=> subset(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f142,plain,
( ~ subset(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4))
| spl0_1 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ member(union(sk0_3,sk0_4),power_set(sum(unordered_pair(sk0_3,sk0_4))))
| ~ subset(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)) ),
inference(resolution,[status(thm)],[f108,f70]) ).
fof(f144,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f143,f137,f140]) ).
fof(f146,plain,
( ~ subset(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))
| spl0_0 ),
inference(resolution,[status(thm)],[f139,f29]) ).
fof(f150,plain,
( ~ member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),sum(unordered_pair(sk0_3,sk0_4)))
| spl0_0 ),
inference(resolution,[status(thm)],[f146,f20]) ).
fof(f151,plain,
( member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),union(sk0_3,sk0_4))
| spl0_0 ),
inference(resolution,[status(thm)],[f146,f19]) ).
fof(f153,plain,
! [X0] :
( ~ member(X0,unordered_pair(sk0_3,sk0_4))
| ~ member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f150,f60]) ).
fof(f166,plain,
( ~ member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f153,f73]) ).
fof(f167,plain,
( ~ member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f153,f72]) ).
fof(f173,plain,
! [X0] :
( ~ member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),union(X0,sk0_4))
| member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f166,f37]) ).
fof(f194,plain,
( member(sk0_0(sum(unordered_pair(sk0_3,sk0_4)),union(sk0_3,sk0_4)),sk0_3)
| spl0_0 ),
inference(resolution,[status(thm)],[f173,f151]) ).
fof(f195,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f167]) ).
fof(f196,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( ~ member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),union(sk0_3,sk0_4))
| spl0_1 ),
inference(resolution,[status(thm)],[f142,f20]) ).
fof(f198,plain,
( member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sum(unordered_pair(sk0_3,sk0_4)))
| spl0_1 ),
inference(resolution,[status(thm)],[f142,f19]) ).
fof(f204,plain,
( ~ member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f197,f39]) ).
fof(f205,plain,
( ~ member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_3)
| spl0_1 ),
inference(resolution,[status(thm)],[f197,f38]) ).
fof(f209,plain,
( member(sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))),unordered_pair(sk0_3,sk0_4))
| spl0_1 ),
inference(resolution,[status(thm)],[f198,f58]) ).
fof(f227,plain,
( spl0_6
<=> sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))) = sk0_3 ),
introduced(split_symbol_definition) ).
fof(f228,plain,
( sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))) = sk0_3
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,plain,
( spl0_7
<=> sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))) = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f231,plain,
( sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))) = sk0_4
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))) = sk0_3
| sk0_1(unordered_pair(sk0_3,sk0_4),sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4)))) = sk0_4
| spl0_1 ),
inference(resolution,[status(thm)],[f209,f52]) ).
fof(f234,plain,
( spl0_6
| spl0_7
| spl0_1 ),
inference(split_clause,[status(thm)],[f233,f227,f230,f140]) ).
fof(f236,plain,
( spl0_8
<=> member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sum(unordered_pair(sk0_3,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f238,plain,
( ~ member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sum(unordered_pair(sk0_3,sk0_4)))
| spl0_8 ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( spl0_9
<=> member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f240,plain,
( member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_3)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( ~ member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sum(unordered_pair(sk0_3,sk0_4)))
| member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_3)
| ~ spl0_6 ),
inference(paramodulation,[status(thm)],[f228,f59]) ).
fof(f243,plain,
( ~ spl0_8
| spl0_9
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f242,f236,f239,f227]) ).
fof(f244,plain,
( $false
| spl0_1
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f198]) ).
fof(f245,plain,
( spl0_1
| spl0_8 ),
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( $false
| spl0_1
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f205]) ).
fof(f247,plain,
( spl0_1
| ~ spl0_9 ),
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( spl0_10
<=> member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f249,plain,
( member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_4)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( ~ member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sum(unordered_pair(sk0_3,sk0_4)))
| member(sk0_0(union(sk0_3,sk0_4),sum(unordered_pair(sk0_3,sk0_4))),sk0_4)
| ~ spl0_7 ),
inference(paramodulation,[status(thm)],[f231,f59]) ).
fof(f252,plain,
( ~ spl0_8
| spl0_10
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f251,f236,f248,f230]) ).
fof(f253,plain,
( $false
| spl0_1
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f204]) ).
fof(f254,plain,
( spl0_1
| ~ spl0_10 ),
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f255,plain,
$false,
inference(sat_refutation,[status(thm)],[f144,f196,f234,f243,f245,f247,f252,f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET352+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 21:23:26 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.6.0
% 0.16/0.44 % Refutation found
% 0.16/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.44 % Elapsed time: 0.117693 seconds
% 0.16/0.44 % CPU time: 0.833719 seconds
% 0.16/0.44 % Total memory used: 62.614 MB
% 0.16/0.44 % Net memory used: 62.070 MB
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