TSTP Solution File: SET703+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET703+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 12:35:04 EDT 2023
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 104 ( 14 unt; 0 def)
% Number of atoms : 260 ( 29 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 253 ( 97 ~; 114 |; 21 &)
% ( 20 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 106 (; 102 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,A)
| member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = A
| X = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B] : equal_set(union(singleton(A),singleton(B)),unordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : equal_set(union(singleton(A),singleton(B)),unordered_pair(A,B)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ equal_set(A,B)
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( equal_set(A,B)
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f35,plain,
! [X,A,B] :
( ( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ~ member(X,union(A,B))
| member(X,A)
| member(X,B) )
& ! [X,A,B] :
( member(X,union(A,B))
| ( ~ member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f46,plain,
! [X,A] :
( ( ~ member(X,singleton(A))
| X = A )
& ( member(X,singleton(A))
| X != A ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( ~ member(X,singleton(A))
| X = A )
& ! [X,A] :
( member(X,singleton(A))
| X != A ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X,A,B] :
( ( ~ member(X,unordered_pair(A,B))
| X = A
| X = B )
& ( member(X,unordered_pair(A,B))
| ( X != A
& X != B ) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f51,plain,
( ! [X,A,B] :
( ~ member(X,unordered_pair(A,B))
| X = A
| X = B )
& ! [X,A,B] :
( member(X,unordered_pair(A,B))
| ( X != A
& X != B ) ) ),
inference(miniscoping,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f54,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f68,plain,
? [A,B] : ~ equal_set(union(singleton(A),singleton(B)),unordered_pair(A,B)),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
~ equal_set(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
~ equal_set(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f49]) ).
fof(f72,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f53]) ).
fof(f73,plain,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(esa)],[f54]) ).
fof(f76,plain,
! [X0,X1] :
( member(sk0_0(X0,X1),X1)
| equal_set(X0,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f77,plain,
! [X0,X1] :
( member(sk0_0(X0,X1),X1)
| equal_set(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(resolution,[status(thm)],[f76,f19]) ).
fof(f78,plain,
( spl0_0
<=> member(sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)),unordered_pair(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( member(sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( spl0_1
<=> member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),union(singleton(sk0_3),singleton(sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f82,plain,
( member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),union(singleton(sk0_3),singleton(sk0_4)))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( member(sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)),unordered_pair(sk0_3,sk0_4))
| member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),union(singleton(sk0_3),singleton(sk0_4))) ),
inference(resolution,[status(thm)],[f77,f70]) ).
fof(f85,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f84,f78,f81]) ).
fof(f88,plain,
( spl0_2
<=> sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) = sk0_3 ),
introduced(split_symbol_definition) ).
fof(f89,plain,
( sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) = sk0_3
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( spl0_3
<=> sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) = sk0_4 ),
introduced(split_symbol_definition) ).
fof(f92,plain,
( sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) = sk0_4
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) = sk0_3
| sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) = sk0_4
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f79,f52]) ).
fof(f95,plain,
( spl0_2
| spl0_3
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f94,f88,f91,f78]) ).
fof(f96,plain,
( spl0_4
<=> member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),singleton(sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f97,plain,
( member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),singleton(sk0_3))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( spl0_5
<=> member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),singleton(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f100,plain,
( member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),singleton(sk0_4))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),singleton(sk0_3))
| member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),singleton(sk0_4))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f82,f37]) ).
fof(f103,plain,
( spl0_4
| spl0_5
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f102,f96,f99,f81]) ).
fof(f105,plain,
( sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))) = sk0_4
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f100,f48]) ).
fof(f109,plain,
( spl0_6
<=> subset(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f112,plain,
( spl0_7
<=> member(sk0_4,unordered_pair(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f114,plain,
( ~ member(sk0_4,unordered_pair(sk0_3,sk0_4))
| spl0_7 ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( subset(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ member(sk0_4,unordered_pair(sk0_3,sk0_4))
| ~ spl0_5 ),
inference(paramodulation,[status(thm)],[f105,f20]) ).
fof(f116,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f115,f109,f112,f99]) ).
fof(f117,plain,
( spl0_8
<=> subset(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f118,plain,
( subset(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4)))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( ~ subset(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4)))
| spl0_8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( spl0_9
<=> member(sk0_3,union(singleton(sk0_3),singleton(sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f122,plain,
( ~ member(sk0_3,union(singleton(sk0_3),singleton(sk0_4)))
| spl0_9 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( subset(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4)))
| ~ member(sk0_3,union(singleton(sk0_3),singleton(sk0_4)))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f89,f20]) ).
fof(f124,plain,
( spl0_8
| ~ spl0_9
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f123,f117,f120,f88]) ).
fof(f125,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f73]) ).
fof(f126,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f125]) ).
fof(f129,plain,
( ~ member(sk0_3,singleton(sk0_3))
| spl0_9 ),
inference(resolution,[status(thm)],[f122,f38]) ).
fof(f130,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f71]) ).
fof(f131,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f160,plain,
( sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))) = sk0_3
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f97,f48]) ).
fof(f162,plain,
( spl0_12
<=> member(sk0_4,union(singleton(sk0_3),singleton(sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f164,plain,
( ~ member(sk0_4,union(singleton(sk0_3),singleton(sk0_4)))
| spl0_12 ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( subset(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4)))
| ~ member(sk0_4,union(singleton(sk0_3),singleton(sk0_4)))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f92,f20]) ).
fof(f166,plain,
( spl0_8
| ~ spl0_12
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f165,f117,f162,f91]) ).
fof(f170,plain,
( ~ member(sk0_4,singleton(sk0_4))
| spl0_12 ),
inference(resolution,[status(thm)],[f164,f39]) ).
fof(f171,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f71]) ).
fof(f172,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f203,plain,
( spl0_15
<=> equal_set(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f204,plain,
( equal_set(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4)))
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( member(sk0_0(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4))),union(singleton(sk0_3),singleton(sk0_4)))
| equal_set(unordered_pair(sk0_3,sk0_4),union(singleton(sk0_3),singleton(sk0_4)))
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f118,f76]) ).
fof(f207,plain,
( spl0_1
| spl0_15
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f206,f81,f203,f117]) ).
fof(f210,plain,
( spl0_16
<=> equal_set(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f211,plain,
( equal_set(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( equal_set(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ subset(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f118,f25]) ).
fof(f214,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f213,f210,f109,f117]) ).
fof(f215,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f70]) ).
fof(f216,plain,
~ spl0_16,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f225,plain,
( subset(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f204,f24]) ).
fof(f226,plain,
( spl0_6
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f225,f109,f203]) ).
fof(f228,plain,
( member(sk0_0(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4)),unordered_pair(sk0_3,sk0_4))
| spl0_8 ),
inference(resolution,[status(thm)],[f119,f19]) ).
fof(f229,plain,
( spl0_0
| spl0_8 ),
inference(split_clause,[status(thm)],[f228,f78,f117]) ).
fof(f239,plain,
( spl0_17
<=> member(sk0_3,unordered_pair(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f241,plain,
( ~ member(sk0_3,unordered_pair(sk0_3,sk0_4))
| spl0_17 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( subset(union(singleton(sk0_3),singleton(sk0_4)),unordered_pair(sk0_3,sk0_4))
| ~ member(sk0_3,unordered_pair(sk0_3,sk0_4))
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f160,f20]) ).
fof(f243,plain,
( spl0_6
| ~ spl0_17
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f242,f109,f239,f96]) ).
fof(f244,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f72]) ).
fof(f245,plain,
spl0_17,
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f95,f103,f116,f124,f126,f131,f166,f172,f207,f214,f216,f226,f229,f243,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET703+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n026.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 10:37:28 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.129619 seconds
% 0.14/0.43 % CPU time: 0.467613 seconds
% 0.14/0.43 % Memory used: 33.581 MB
%------------------------------------------------------------------------------