TSTP Solution File: SET884+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 : Wed May 31 12:35:27 EDT 2023
% Result : Theorem 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 163 ( 82 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 198 ( 77 ~; 72 |; 40 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 100 (; 88 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
~ ( subset(singleton(A),unordered_pair(B,C))
& A != B
& A != C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
~ ( subset(singleton(A),unordered_pair(B,C))
& A != B
& A != C ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f15,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f21,plain,
! [A,B,C] :
( ( C != unordered_pair(A,B)
| ! [D] :
( ( ~ in(D,C)
| D = A
| D = B )
& ( in(D,C)
| ( D != A
& D != B ) ) ) )
& ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f22,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( sk0_1(C,B,A) != A
& sk0_1(C,B,A) != B ) )
& ( in(sk0_1(C,B,A),C)
| sk0_1(C,B,A) = A
| sk0_1(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| ~ in(X3,X0)
| X3 = X1
| X3 = X2 ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f30,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f31,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_2(B,A),A)
& ~ in(sk0_2(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f43,plain,
? [A,B,C] :
( subset(singleton(A),unordered_pair(B,C))
& A != B
& A != C ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
? [A,C] :
( ? [B] :
( subset(singleton(A),unordered_pair(B,C))
& A != B )
& A != C ),
inference(miniscoping,[status(esa)],[f43]) ).
fof(f45,plain,
( subset(singleton(sk0_5),unordered_pair(sk0_7,sk0_6))
& sk0_5 != sk0_7
& sk0_5 != sk0_6 ),
inference(skolemization,[status(esa)],[f44]) ).
fof(f46,plain,
subset(singleton(sk0_5),unordered_pair(sk0_7,sk0_6)),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
sk0_5 != sk0_7,
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f48,plain,
sk0_5 != sk0_6,
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f50,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(destructive_equality_resolution,[status(esa)],[f24]) ).
fof(f62,plain,
! [X0] :
( ~ in(X0,singleton(sk0_5))
| in(X0,unordered_pair(sk0_7,sk0_6)) ),
inference(resolution,[status(thm)],[f34,f46]) ).
fof(f63,plain,
! [X0] :
( ~ in(X0,singleton(sk0_5))
| in(X0,unordered_pair(sk0_6,sk0_7)) ),
inference(forward_demodulation,[status(thm)],[f13,f62]) ).
fof(f65,plain,
! [X0] :
( ~ in(X0,singleton(sk0_5))
| X0 = sk0_6
| X0 = sk0_7 ),
inference(resolution,[status(thm)],[f63,f51]) ).
fof(f66,plain,
( spl0_0
<=> sk0_5 = sk0_6 ),
introduced(split_symbol_definition) ).
fof(f67,plain,
( sk0_5 = sk0_6
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( spl0_1
<=> sk0_5 = sk0_7 ),
introduced(split_symbol_definition) ).
fof(f70,plain,
( sk0_5 = sk0_7
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sk0_5 = sk0_6
| sk0_5 = sk0_7 ),
inference(resolution,[status(thm)],[f65,f50]) ).
fof(f73,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f72,f66,f69]) ).
fof(f74,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f48]) ).
fof(f75,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f74]) ).
fof(f76,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f47]) ).
fof(f77,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f78,plain,
$false,
inference(sat_refutation,[status(thm)],[f73,f75,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:20:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.35 % Refutation found
% 0.19/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37 % Elapsed time: 0.023722 seconds
% 0.19/0.37 % CPU time: 0.031469 seconds
% 0.19/0.37 % Memory used: 14.323 MB
%------------------------------------------------------------------------------