TSTP Solution File: SEU159+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:36:03 EDT 2023
% Result : Theorem 0.11s 0.28s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 5 unt; 0 def)
% Number of atoms : 192 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 210 ( 76 ~; 93 |; 28 &)
% ( 11 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 96 (; 86 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f12,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)],[f3]) ).
fof(f13,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)],[f12]) ).
fof(f14,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_0(C,B,A),C)
| ( sk0_0(C,B,A) != A
& sk0_0(C,B,A) != B ) )
& ( in(sk0_0(C,B,A),C)
| sk0_0(C,B,A) = A
| sk0_0(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| ~ in(X3,X0)
| X3 = X1
| X3 = X2 ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X2 ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f21,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f22,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)],[f21]) ).
fof(f23,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)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_1(B,A),A)
& ~ in(sk0_1(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f30,plain,
? [A,B,C] :
( subset(unordered_pair(A,B),C)
<~> ( in(A,C)
& in(B,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
? [A,B,C] :
( ( subset(unordered_pair(A,B),C)
| ( in(A,C)
& in(B,C) ) )
& ( ~ subset(unordered_pair(A,B),C)
| ~ in(A,C)
| ~ in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( ( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ( in(sk0_2,sk0_4)
& in(sk0_3,sk0_4) ) )
& ( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4) ) ),
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| in(sk0_2,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| in(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,plain,
( spl0_0
<=> subset(unordered_pair(sk0_2,sk0_3),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f37,plain,
( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( ~ subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| spl0_0 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( spl0_1
<=> in(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f41,plain,
( ~ in(sk0_2,sk0_4)
| spl0_1 ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f33,f36,f39]) ).
fof(f43,plain,
( spl0_2
<=> in(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f34,f36,f43]) ).
fof(f47,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f35,f36,f39,f43]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(destructive_equality_resolution,[status(esa)],[f15]) ).
fof(f49,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f16]) ).
fof(f50,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(esa)],[f17]) ).
fof(f63,plain,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
| sk0_1(X2,unordered_pair(X0,X1)) = X0
| sk0_1(X2,unordered_pair(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[f26,f48]) ).
fof(f66,plain,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
| sk0_1(X2,unordered_pair(X1,X0)) = X1
| sk0_1(X2,unordered_pair(X1,X0)) = X0 ),
inference(paramodulation,[status(thm)],[f11,f63]) ).
fof(f365,plain,
! [X0] :
( ~ in(X0,unordered_pair(sk0_2,sk0_3))
| in(X0,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f37,f25]) ).
fof(f368,plain,
( in(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f365,f50]) ).
fof(f369,plain,
( in(sk0_2,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f365,f49]) ).
fof(f370,plain,
( $false
| spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f41]) ).
fof(f371,plain,
( spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f378,plain,
( spl0_3
<=> sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_3 ),
introduced(split_symbol_definition) ).
fof(f379,plain,
( sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_3
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( spl0_4
<=> sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f382,plain,
( sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_2
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,plain,
( sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_3
| sk0_1(sk0_4,unordered_pair(sk0_3,sk0_2)) = sk0_2
| spl0_0 ),
inference(resolution,[status(thm)],[f38,f66]) ).
fof(f385,plain,
( spl0_3
| spl0_4
| spl0_0 ),
inference(split_clause,[status(thm)],[f384,f378,f381,f36]) ).
fof(f396,plain,
( spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f368,f43,f36]) ).
fof(f397,plain,
( sk0_1(sk0_4,unordered_pair(sk0_2,sk0_3)) = sk0_3
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f11,f379]) ).
fof(f409,plain,
( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ in(sk0_3,sk0_4)
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f397,f27]) ).
fof(f410,plain,
( spl0_0
| ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f409,f36,f43,f378]) ).
fof(f421,plain,
( sk0_1(sk0_4,unordered_pair(sk0_2,sk0_3)) = sk0_2
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f11,f382]) ).
fof(f435,plain,
( subset(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ in(sk0_2,sk0_4)
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f421,f27]) ).
fof(f436,plain,
( spl0_0
| ~ spl0_1
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f435,f36,f39,f381]) ).
fof(f441,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f46,f47,f371,f385,f396,f410,f436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU159+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Tue May 30 09:09:30 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.11/0.27 % Drodi V3.5.1
% 0.11/0.28 % Refutation found
% 0.11/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.50 % Elapsed time: 0.016246 seconds
% 0.11/0.50 % CPU time: 0.070747 seconds
% 0.11/0.50 % Memory used: 15.087 MB
%------------------------------------------------------------------------------