TSTP Solution File: SEU182+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 12:36:09 EDT 2023
% Result : Theorem 219.28s 27.97s
% Output : CNFRefutation 219.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 12 unt; 0 def)
% Number of atoms : 263 ( 23 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 317 ( 123 ~; 130 |; 39 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-5 aty)
% Number of variables : 165 (; 142 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f34,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f41,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)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f43,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f47,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)],[f4]) ).
fof(f48,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)],[f47]) ).
fof(f49,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)],[f48]) ).
fof(f50,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_1(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_2(B,A),D),A) )
& ( in(sk0_2(B,A),B)
| in(ordered_pair(sk0_2(B,A),sk0_3(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,sk0_1(X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,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)],[f50]) ).
fof(f56,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f57,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_composition(A,B)
| ! [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) ) ) )
& ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_composition(A,B)
| ( ! [D,E] :
( ~ in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) )
& ! [D,E] :
( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) ) ) )
& ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f57]) ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_composition(A,B)
| ( ! [D,E] :
( ~ in(ordered_pair(D,E),C)
| ( in(ordered_pair(D,sk0_4(E,D,C,B,A)),A)
& in(ordered_pair(sk0_4(E,D,C,B,A),E),B) ) )
& ! [D,E] :
( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) ) ) )
& ( C = relation_composition(A,B)
| ( ( ~ in(ordered_pair(sk0_5(C,B,A),sk0_6(C,B,A)),C)
| ! [F] :
( ~ in(ordered_pair(sk0_5(C,B,A),F),A)
| ~ in(ordered_pair(F,sk0_6(C,B,A)),B) ) )
& ( in(ordered_pair(sk0_5(C,B,A),sk0_6(C,B,A)),C)
| ( in(ordered_pair(sk0_5(C,B,A),sk0_7(C,B,A)),A)
& in(ordered_pair(sk0_7(C,B,A),sk0_6(C,B,A)),B) ) ) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_composition(X0,X1)
| ~ in(ordered_pair(X3,X4),X2)
| in(ordered_pair(X3,sk0_4(X4,X3,X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f66,plain,
! [A,B] :
( ~ relation(A)
| ~ relation(B)
| relation(relation_composition(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f67,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f75,plain,
( empty(sk0_9)
& relation(sk0_9) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f76,plain,
empty(sk0_9),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f77,plain,
relation(sk0_9),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f99,plain,
? [A] :
( relation(A)
& ? [B] :
( relation(B)
& ~ subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f100,plain,
( relation(sk0_14)
& relation(sk0_15)
& ~ subset(relation_dom(relation_composition(sk0_14,sk0_15)),relation_dom(sk0_14)) ),
inference(skolemization,[status(esa)],[f99]) ).
fof(f101,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f102,plain,
relation(sk0_15),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f103,plain,
~ subset(relation_dom(relation_composition(sk0_14,sk0_15)),relation_dom(sk0_14)),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f110,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f111,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f110]) ).
fof(f118,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,sk0_1(X1,relation_dom(X0),X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f52]) ).
fof(f120,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(X2,sk0_4(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f60]) ).
fof(f2800,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(X2,sk0_4(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f67]) ).
fof(f2857,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X0)
| in(X2,relation_dom(X0)) ),
inference(resolution,[status(thm)],[f2800,f119]) ).
fof(f2858,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(X2,relation_dom(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f2857]) ).
fof(f2972,plain,
sk0_9 = empty_set,
inference(resolution,[status(thm)],[f76,f111]) ).
fof(f2998,plain,
( spl0_7
<=> relation(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f3000,plain,
( ~ relation(sk0_14)
| spl0_7 ),
inference(component_clause,[status(thm)],[f2998]) ).
fof(f3001,plain,
( spl0_8
<=> relation(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f3003,plain,
( ~ relation(sk0_15)
| spl0_8 ),
inference(component_clause,[status(thm)],[f3001]) ).
fof(f3579,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ relation(X1)
| in(X2,relation_dom(X0))
| ~ relation(relation_composition(X0,X1))
| ~ in(X2,relation_dom(relation_composition(X0,X1))) ),
inference(resolution,[status(thm)],[f2858,f118]) ).
fof(f3580,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ relation(X1)
| in(X2,relation_dom(X0))
| ~ in(X2,relation_dom(relation_composition(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3579,f67]) ).
fof(f4197,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f3003,f102]) ).
fof(f4198,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f4197]) ).
fof(f4199,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f3000,f101]) ).
fof(f4200,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f4199]) ).
fof(f5435,plain,
( spl0_60
<=> relation(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f5437,plain,
( ~ relation(sk0_9)
| spl0_60 ),
inference(component_clause,[status(thm)],[f5435]) ).
fof(f5495,plain,
( $false
| spl0_60 ),
inference(forward_subsumption_resolution,[status(thm)],[f5437,f77]) ).
fof(f5496,plain,
spl0_60,
inference(contradiction_clause,[status(thm)],[f5495]) ).
fof(f8056,plain,
relation(empty_set),
inference(backward_demodulation,[status(thm)],[f2972,f77]) ).
fof(f8105,plain,
( spl0_136
<=> relation(empty_set) ),
introduced(split_symbol_definition) ).
fof(f8107,plain,
( ~ relation(empty_set)
| spl0_136 ),
inference(component_clause,[status(thm)],[f8105]) ).
fof(f8185,plain,
( $false
| spl0_136 ),
inference(forward_subsumption_resolution,[status(thm)],[f8107,f8056]) ).
fof(f8186,plain,
spl0_136,
inference(contradiction_clause,[status(thm)],[f8185]) ).
fof(f9423,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ relation(X1)
| in(sk0_0(X2,relation_dom(relation_composition(X0,X1))),relation_dom(X0))
| subset(relation_dom(relation_composition(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f3580,f45]) ).
fof(f9860,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
inference(resolution,[status(thm)],[f9423,f46]) ).
fof(f9861,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f9860]) ).
fof(f9883,plain,
( ~ relation(sk0_14)
| ~ relation(sk0_15) ),
inference(resolution,[status(thm)],[f9861,f103]) ).
fof(f9884,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f9883,f2998,f3001]) ).
fof(f9890,plain,
$false,
inference(sat_refutation,[status(thm)],[f4198,f4200,f5496,f8186,f9884]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SEU182+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n015.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 09:26:34 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 219.28/27.97 % Refutation found
% 219.28/27.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 219.28/27.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 220.88/28.65 % Elapsed time: 28.325805 seconds
% 220.88/28.65 % CPU time: 220.894889 seconds
% 220.88/28.65 % Memory used: 786.657 MB
%------------------------------------------------------------------------------