TSTP Solution File: SEU183+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU183+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : Tue Apr 30 20:41:23 EDT 2024
% Result : Theorem 2.95s 0.79s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 219 ( 19 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 288 ( 114 ~; 117 |; 37 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-5 aty)
% Number of variables : 159 ( 137 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
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_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f48,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_rng(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(sk0_1(C,B,A),C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] : ~ in(ordered_pair(D,sk0_2(B,A)),A) )
& ( in(sk0_2(B,A),B)
| in(ordered_pair(sk0_3(B,A),sk0_2(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| ~ in(X2,X1)
| in(ordered_pair(sk0_1(X2,X1,X0),X2),X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| in(X2,X1)
| ~ in(ordered_pair(X3,X2),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(f61,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(sk0_4(X4,X3,X2,X1,X0),X4),X1) ),
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(f99,plain,
? [A] :
( relation(A)
& ? [B] :
( relation(B)
& ~ subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f100,plain,
( relation(sk0_14)
& relation(sk0_15)
& ~ subset(relation_rng(relation_composition(sk0_14,sk0_15)),relation_rng(sk0_15)) ),
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_rng(relation_composition(sk0_14,sk0_15)),relation_rng(sk0_15)),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f118,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| in(ordered_pair(sk0_1(X1,relation_rng(X0),X0),X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_rng(X0))
| ~ in(ordered_pair(X2,X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f52]) ).
fof(f122,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(sk0_4(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
inference(destructive_equality_resolution,[status(esa)],[f61]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(sk0_4(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f122,f67]) ).
fof(f128,plain,
! [X0,X1] :
( in(X0,relation_rng(sk0_15))
| ~ in(ordered_pair(X1,X0),sk0_15) ),
inference(resolution,[status(thm)],[f119,f102]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_rng(relation_composition(X1,X2)))
| in(ordered_pair(sk0_1(X0,relation_rng(relation_composition(X1,X2)),relation_composition(X1,X2)),X0),relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(resolution,[status(thm)],[f118,f67]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_rng(relation_composition(X1,X2)))
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sk0_4(X0,sk0_1(X0,relation_rng(relation_composition(X1,X2)),relation_composition(X1,X2)),relation_composition(X1,X2),X2,X1),X0),X2) ),
inference(resolution,[status(thm)],[f168,f125]) ).
fof(f240,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_rng(relation_composition(X1,X2)))
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sk0_4(X0,sk0_1(X0,relation_rng(relation_composition(X1,X2)),relation_composition(X1,X2)),relation_composition(X1,X2),X2,X1),X0),X2) ),
inference(duplicate_literals_removal,[status(esa)],[f239]) ).
fof(f421,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(relation_composition(X1,sk0_15)))
| ~ relation(X1)
| in(ordered_pair(sk0_4(X0,sk0_1(X0,relation_rng(relation_composition(X1,sk0_15)),relation_composition(X1,sk0_15)),relation_composition(X1,sk0_15),sk0_15,X1),X0),sk0_15) ),
inference(resolution,[status(thm)],[f240,f102]) ).
fof(f572,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(relation_composition(X1,sk0_15)))
| ~ relation(X1)
| in(X0,relation_rng(sk0_15)) ),
inference(resolution,[status(thm)],[f421,f128]) ).
fof(f609,plain,
! [X0,X1] :
( ~ in(sk0_0(relation_rng(sk0_15),X0),relation_rng(relation_composition(X1,sk0_15)))
| ~ relation(X1)
| subset(X0,relation_rng(sk0_15)) ),
inference(resolution,[status(thm)],[f572,f46]) ).
fof(f640,plain,
! [X0] :
( ~ relation(X0)
| subset(relation_rng(relation_composition(X0,sk0_15)),relation_rng(sk0_15))
| subset(relation_rng(relation_composition(X0,sk0_15)),relation_rng(sk0_15)) ),
inference(resolution,[status(thm)],[f609,f45]) ).
fof(f641,plain,
! [X0] :
( ~ relation(X0)
| subset(relation_rng(relation_composition(X0,sk0_15)),relation_rng(sk0_15)) ),
inference(duplicate_literals_removal,[status(esa)],[f640]) ).
fof(f642,plain,
~ relation(sk0_14),
inference(resolution,[status(thm)],[f641,f103]) ).
fof(f643,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f642,f101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU183+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 19:52:43 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 2.95/0.79 % Refutation found
% 2.95/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.95/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.46/0.81 % Elapsed time: 0.458387 seconds
% 3.46/0.81 % CPU time: 3.512090 seconds
% 3.46/0.81 % Total memory used: 103.160 MB
% 3.46/0.81 % Net memory used: 101.650 MB
%------------------------------------------------------------------------------