TSTP Solution File: SEU159+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU159+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 20:41:16 EDT 2024
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f13,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(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)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| ~ in(X3,X0)
| X3 = X1
| X3 = X2 ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X2 ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f22,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f23,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)],[f22]) ).
fof(f24,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)],[f23]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f35,plain,
? [A,B,C] :
( subset(unordered_pair(A,B),C)
<~> ( in(A,C)
& in(B,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f36,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)],[f35]) ).
fof(f37,plain,
( ( subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| ( in(sk0_4,sk0_6)
& in(sk0_5,sk0_6) ) )
& ( ~ subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| ~ in(sk0_4,sk0_6)
| ~ in(sk0_5,sk0_6) ) ),
inference(skolemization,[status(esa)],[f36]) ).
fof(f38,plain,
( subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| in(sk0_4,sk0_6) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
( subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| in(sk0_5,sk0_6) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f40,plain,
( ~ subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| ~ in(sk0_4,sk0_6)
| ~ in(sk0_5,sk0_6) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f41,plain,
( spl0_0
<=> subset(unordered_pair(sk0_4,sk0_5),sk0_6) ),
introduced(split_symbol_definition) ).
fof(f42,plain,
( subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( ~ subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| spl0_0 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( spl0_1
<=> in(sk0_4,sk0_6) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( ~ in(sk0_4,sk0_6)
| spl0_1 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f38,f41,f44]) ).
fof(f48,plain,
( spl0_2
<=> in(sk0_5,sk0_6) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f39,f41,f48]) ).
fof(f52,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f40,f41,f44,f48]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(destructive_equality_resolution,[status(esa)],[f16]) ).
fof(f54,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f17]) ).
fof(f55,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f68,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)],[f27,f53]) ).
fof(f71,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)],[f12,f68]) ).
fof(f363,plain,
! [X0] :
( ~ in(X0,unordered_pair(sk0_4,sk0_5))
| in(X0,sk0_6)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f42,f26]) ).
fof(f366,plain,
( in(sk0_5,sk0_6)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f363,f55]) ).
fof(f367,plain,
( in(sk0_4,sk0_6)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f363,f54]) ).
fof(f368,plain,
( $false
| spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f46]) ).
fof(f369,plain,
( spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f376,plain,
( spl0_3
<=> sk0_1(sk0_6,unordered_pair(sk0_5,sk0_4)) = sk0_5 ),
introduced(split_symbol_definition) ).
fof(f377,plain,
( sk0_1(sk0_6,unordered_pair(sk0_5,sk0_4)) = sk0_5
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f379,plain,
( spl0_4
<=> sk0_1(sk0_6,unordered_pair(sk0_5,sk0_4)) = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f380,plain,
( sk0_1(sk0_6,unordered_pair(sk0_5,sk0_4)) = sk0_4
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( sk0_1(sk0_6,unordered_pair(sk0_5,sk0_4)) = sk0_5
| sk0_1(sk0_6,unordered_pair(sk0_5,sk0_4)) = sk0_4
| spl0_0 ),
inference(resolution,[status(thm)],[f43,f71]) ).
fof(f383,plain,
( spl0_3
| spl0_4
| spl0_0 ),
inference(split_clause,[status(thm)],[f382,f376,f379,f41]) ).
fof(f394,plain,
( spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f366,f48,f41]) ).
fof(f395,plain,
( sk0_1(sk0_6,unordered_pair(sk0_4,sk0_5)) = sk0_5
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f12,f377]) ).
fof(f407,plain,
( subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| ~ in(sk0_5,sk0_6)
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f395,f28]) ).
fof(f408,plain,
( spl0_0
| ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f407,f41,f48,f376]) ).
fof(f419,plain,
( sk0_1(sk0_6,unordered_pair(sk0_4,sk0_5)) = sk0_4
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f12,f380]) ).
fof(f433,plain,
( subset(unordered_pair(sk0_4,sk0_5),sk0_6)
| ~ in(sk0_4,sk0_6)
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f419,f28]) ).
fof(f434,plain,
( spl0_0
| ~ spl0_1
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f433,f41,f44,f379]) ).
fof(f439,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f51,f52,f369,f383,f394,f408,f434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU159+3 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 19:39:47 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 0.14/0.36 % Refutation found
% 0.14/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.37 % Elapsed time: 0.026101 seconds
% 0.14/0.37 % CPU time: 0.078984 seconds
% 0.14/0.37 % Total memory used: 15.744 MB
% 0.14/0.37 % Net memory used: 15.700 MB
%------------------------------------------------------------------------------