TSTP Solution File: SET950+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:35:36 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 5 unt; 0 def)
% Number of atoms : 155 ( 23 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 188 ( 75 ~; 65 |; 39 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-5 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 162 (; 138 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
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(f10,conjecture,
! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
<=> ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ),
introduced(predicate_definition,[f3]) ).
fof(f16,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] : pd0_0(F,E,D,B,A) ) ),
inference(formula_renaming,[status(thm)],[f3,f15]) ).
fof(f17,plain,
! [A,B,C] :
( ( C != cartesian_product2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f19,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| pd0_0(sk0_1(D,C,B,A),sk0_0(D,C,B,A),D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ! [E,F] : ~ pd0_0(F,E,sk0_2(C,B,A),B,A) )
& ( in(sk0_2(C,B,A),C)
| pd0_0(sk0_4(C,B,A),sk0_3(C,B,A),sk0_2(C,B,A),B,A) ) ) ) ),
inference(skolemization,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| pd0_0(sk0_1(X3,X0,X2,X1),sk0_0(X3,X0,X2,X1),X3,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f24,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f25,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)],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_5(B,A),A)
& ~ in(sk0_5(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f39,plain,
? [A,B,C,D] :
( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
( ~ in(E,B)
| ~ in(F,C)
| D != ordered_pair(E,F) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f40,plain,
? [B,C,D] :
( ? [A] :
( subset(A,cartesian_product2(B,C))
& in(D,A) )
& ! [E,F] :
( ~ in(E,B)
| ~ in(F,C)
| D != ordered_pair(E,F) ) ),
inference(miniscoping,[status(esa)],[f39]) ).
fof(f41,plain,
( subset(sk0_11,cartesian_product2(sk0_8,sk0_9))
& in(sk0_10,sk0_11)
& ! [E,F] :
( ~ in(E,sk0_8)
| ~ in(F,sk0_9)
| sk0_10 != ordered_pair(E,F) ) ),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
subset(sk0_11,cartesian_product2(sk0_8,sk0_9)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
in(sk0_10,sk0_11),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X0,sk0_8)
| ~ in(X1,sk0_9)
| sk0_10 != ordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f45,plain,
! [A,B,D,E,F] :
( ( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f46,plain,
( ! [A,B,D,E,F] :
( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| in(X1,X4) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| in(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| X2 = ordered_pair(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| pd0_0(sk0_1(X0,cartesian_product2(X1,X2),X2,X1),sk0_0(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f20]) ).
fof(f55,plain,
! [X0] :
( ~ in(X0,sk0_11)
| in(X0,cartesian_product2(sk0_8,sk0_9)) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| X0 = ordered_pair(sk0_0(X0,cartesian_product2(X1,X2),X2,X1),sk0_1(X0,cartesian_product2(X1,X2),X2,X1)) ),
inference(resolution,[status(thm)],[f51,f49]) ).
fof(f69,plain,
! [X0,X1,X2] :
( in(sk0_0(X0,cartesian_product2(X1,X2),X2,X1),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f47,f51]) ).
fof(f78,plain,
! [X0,X1,X2] :
( in(sk0_1(X0,cartesian_product2(X1,X2),X2,X1),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f48,f51]) ).
fof(f125,plain,
! [X0,X1] :
( ~ in(sk0_10,cartesian_product2(X0,X1))
| ~ in(sk0_0(sk0_10,cartesian_product2(X0,X1),X1,X0),sk0_8)
| ~ in(sk0_1(sk0_10,cartesian_product2(X0,X1),X1,X0),sk0_9) ),
inference(resolution,[status(thm)],[f64,f44]) ).
fof(f151,plain,
! [X0] :
( ~ in(sk0_10,cartesian_product2(X0,sk0_9))
| ~ in(sk0_0(sk0_10,cartesian_product2(X0,sk0_9),sk0_9,X0),sk0_8)
| ~ in(sk0_10,cartesian_product2(X0,sk0_9)) ),
inference(resolution,[status(thm)],[f125,f78]) ).
fof(f152,plain,
! [X0] :
( ~ in(sk0_10,cartesian_product2(X0,sk0_9))
| ~ in(sk0_0(sk0_10,cartesian_product2(X0,sk0_9),sk0_9,X0),sk0_8) ),
inference(duplicate_literals_removal,[status(esa)],[f151]) ).
fof(f153,plain,
( spl0_4
<=> in(sk0_10,cartesian_product2(sk0_8,sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f155,plain,
( ~ in(sk0_10,cartesian_product2(sk0_8,sk0_9))
| spl0_4 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ in(sk0_10,cartesian_product2(sk0_8,sk0_9))
| ~ in(sk0_10,cartesian_product2(sk0_8,sk0_9)) ),
inference(resolution,[status(thm)],[f152,f69]) ).
fof(f157,plain,
~ spl0_4,
inference(split_clause,[status(thm)],[f156,f153]) ).
fof(f158,plain,
( ~ in(sk0_10,sk0_11)
| spl0_4 ),
inference(resolution,[status(thm)],[f155,f55]) ).
fof(f159,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f43]) ).
fof(f160,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f161,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:15:53 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.015359 seconds
% 0.14/0.53 % CPU time: 0.014480 seconds
% 0.14/0.53 % Memory used: 3.768 MB
%------------------------------------------------------------------------------