TSTP Solution File: SEU248+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU248+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 20:41:42 EDT 2024
% Result : Theorem 38.45s 5.14s
% Output : CNFRefutation 38.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 4 unt; 0 def)
% Number of atoms : 199 ( 19 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 255 ( 100 ~; 103 |; 35 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 153 ( 135 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(E,A)
& in(ordered_pair(D,E),B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f46,plain,
! [A,B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(E,A)
& in(ordered_pair(D,E),B) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f47,plain,
! [A,B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_rng_restriction(A,B)
| ! [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ( in(E,A)
& in(ordered_pair(D,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),B) ) ) )
& ( C = relation_rng_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),B) )
& ( in(ordered_pair(D,E),C)
| ( in(E,A)
& in(ordered_pair(D,E),B) ) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ! [A] :
( C != relation_rng_restriction(A,B)
| ( ! [D,E] :
( ~ in(ordered_pair(D,E),C)
| ( in(E,A)
& in(ordered_pair(D,E),B) ) )
& ! [D,E] :
( in(ordered_pair(D,E),C)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),B) ) ) )
& ! [A] :
( C = relation_rng_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),B) )
& ( in(ordered_pair(D,E),C)
| ( in(E,A)
& in(ordered_pair(D,E),B) ) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ! [A] :
( C != relation_rng_restriction(A,B)
| ( ! [D,E] :
( ~ in(ordered_pair(D,E),C)
| ( in(E,A)
& in(ordered_pair(D,E),B) ) )
& ! [D,E] :
( in(ordered_pair(D,E),C)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),B) ) ) )
& ! [A] :
( C = relation_rng_restriction(A,B)
| ( ( ~ in(ordered_pair(sk0_0(A,C,B),sk0_1(A,C,B)),C)
| ~ in(sk0_1(A,C,B),A)
| ~ in(ordered_pair(sk0_0(A,C,B),sk0_1(A,C,B)),B) )
& ( in(ordered_pair(sk0_0(A,C,B),sk0_1(A,C,B)),C)
| ( in(sk0_1(A,C,B),A)
& in(ordered_pair(sk0_0(A,C,B),sk0_1(A,C,B)),B) ) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(X0)
| ~ relation(X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ in(ordered_pair(X3,X4),X1)
| in(ordered_pair(X3,X4),X0) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f56,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f57,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)],[f56]) ).
fof(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_2(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_2(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f63,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f64,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_dom(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f63]) ).
fof(f65,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f64]) ).
fof(f66,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_3(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_4(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_4(B,A),D),A) )
& ( in(sk0_4(B,A),B)
| in(ordered_pair(sk0_4(B,A),sk0_5(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,sk0_3(X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f72,plain,
! [A,B] :
( ~ relation(B)
| relation(relation_rng_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f73,plain,
! [B] :
( ~ relation(B)
| ! [A] : relation(relation_rng_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[status(esa)],[f73]) ).
fof(f83,plain,
? [A,B] :
( relation(B)
& ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f84,plain,
? [B] :
( relation(B)
& ? [A] : ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
inference(miniscoping,[status(esa)],[f83]) ).
fof(f85,plain,
( relation(sk0_7)
& ~ subset(relation_dom(relation_rng_restriction(sk0_8,sk0_7)),relation_dom(sk0_7)) ),
inference(skolemization,[status(esa)],[f84]) ).
fof(f86,plain,
relation(sk0_7),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f87,plain,
~ subset(relation_dom(relation_rng_restriction(sk0_8,sk0_7)),relation_dom(sk0_7)),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| in(ordered_pair(X2,X3),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f130,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,sk0_3(X1,relation_dom(X0),X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f67]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f68]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))
| in(ordered_pair(X1,X2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f74]) ).
fof(f1131,plain,
! [X0,X1,X2] :
( ~ relation(relation_rng_restriction(X0,X1))
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ relation(X1)
| in(ordered_pair(X2,sk0_3(X2,relation_dom(relation_rng_restriction(X0,X1)),relation_rng_restriction(X0,X1))),X1) ),
inference(resolution,[status(thm)],[f130,f133]) ).
fof(f1132,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(ordered_pair(X0,sk0_3(X0,relation_dom(relation_rng_restriction(X1,X2)),relation_rng_restriction(X1,X2))),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1131,f74]) ).
fof(f1481,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(resolution,[status(thm)],[f1132,f131]) ).
fof(f1482,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(duplicate_literals_removal,[status(esa)],[f1481]) ).
fof(f1521,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(sk0_2(X1,relation_dom(relation_rng_restriction(X2,X0))),relation_dom(X0))
| subset(relation_dom(relation_rng_restriction(X2,X0)),X1) ),
inference(resolution,[status(thm)],[f1482,f61]) ).
fof(f4760,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0))
| subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0)) ),
inference(resolution,[status(thm)],[f1521,f62]) ).
fof(f4761,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f4760]) ).
fof(f4783,plain,
~ relation(sk0_7),
inference(resolution,[status(thm)],[f4761,f87]) ).
fof(f4784,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4783,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU248+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n022.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 19:41:58 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.6.0
% 38.45/5.14 % Refutation found
% 38.45/5.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 38.45/5.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 39.03/5.25 % Elapsed time: 4.977010 seconds
% 39.03/5.25 % CPU time: 39.155869 seconds
% 39.03/5.25 % Total memory used: 373.721 MB
% 39.03/5.25 % Net memory used: 364.336 MB
%------------------------------------------------------------------------------