%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:50 PM UTC 2026
% Result : Theorem 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 11 unt; 4 def)
% Number of atoms : 157 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 63 ~; 66 |; 20 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(X,Y)
& member(Y,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : equal_set(sum(singleton(A)),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : equal_set(sum(singleton(A)),A),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
( ! [X,A] :
( X != A
| member(X,singleton(A)) )
& ! [X,A] :
( X = A
| ~ member(X,singleton(A)) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f55,plain,
! [X,A] :
( ( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
( ! [X,A] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ! [X,A] :
( ? [Y] :
( member(X,Y)
& member(Y,A) )
| ~ member(X,sum(A)) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
( ! [X,A] :
( ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) )
| member(X,sum(A)) )
& ! [X,A] :
( ( member(X,sK1_skl(A,X))
& member(sK1_skl(A,X),A) )
| ~ member(X,sum(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(A,X))],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( member(X0,sK1_skl(X1,X0))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f68,plain,
? [A] : ~ equal_set(sum(singleton(A)),A),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ equal_set(sum(singleton(sK3_skl)),sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f68]) ).
fof(f70,plain,
~ equal_set(sum(singleton(sK3_skl)),sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0] : member(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f74,plain,
( ~ subset(sK3_skl,sum(singleton(sK3_skl)))
| ~ subset(sum(singleton(sK3_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f25,f70]) ).
fof(f75,definition,
( sQ0_spl
<=> subset(sum(singleton(sK3_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ0_spl
| ~ subset(sum(singleton(sK3_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ1_spl
<=> subset(sK3_skl,sum(singleton(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ1_spl
| ~ subset(sK3_skl,sum(singleton(sK3_skl))) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f74,f75,f78]) ).
fof(f91,plain,
( sQ0_spl
| member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sum(singleton(sK3_skl))) ),
inference(resolution,[status(thm)],[f19,f77]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(sum(X1),X0),X2)
| ~ member(X2,X1)
| subset(X0,sum(X1)) ),
inference(resolution,[status(thm)],[f20,f60]) ).
fof(f109,plain,
( sQ0_spl
| member(sK1_skl(singleton(sK3_skl),sK0_skl(sK3_skl,sum(singleton(sK3_skl)))),singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f91,f58]) ).
fof(f110,plain,
( sQ0_spl
| sK1_skl(singleton(sK3_skl),sK0_skl(sK3_skl,sum(singleton(sK3_skl)))) = sK3_skl ),
inference(resolution,[status(thm)],[f109,f48]) ).
fof(f128,definition,
( sQ3_spl
<=> member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ3_spl
| member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK3_skl) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f130,plain,
( sQ3_spl
| ~ member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK3_skl) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f132,plain,
( sQ1_spl
| member(sK0_skl(sum(singleton(sK3_skl)),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f80,f19]) ).
fof(f152,plain,
! [X0] :
( sQ1_spl
| ~ member(sK0_skl(sum(singleton(sK3_skl)),sK3_skl),X0)
| ~ member(X0,singleton(sK3_skl)) ),
inference(resolution,[status(thm)],[f94,f80]) ).
fof(f239,plain,
( sQ1_spl
| ~ member(sK0_skl(sum(singleton(sK3_skl)),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f152,f71]) ).
fof(f241,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f132]) ).
fof(f242,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f241]) ).
fof(f411,plain,
( sQ0_spl
| member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK1_skl(singleton(sK3_skl),sK0_skl(sK3_skl,sum(singleton(sK3_skl))))) ),
inference(resolution,[status(thm)],[f91,f59]) ).
fof(f468,definition,
! [X0] :
( sQ9_spl
<=> member(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f469,plain,
! [X0] :
( ~ sQ9_spl
| member(X0,empty_set) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f475,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f40]) ).
fof(f476,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f530,plain,
( ~ sQ3_spl
| subset(sum(singleton(sK3_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f129,f20]) ).
fof(f537,plain,
( ~ sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f77]) ).
fof(f538,plain,
( ~ sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f673,plain,
( sQ0_spl
| member(sK0_skl(sK3_skl,sum(singleton(sK3_skl))),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f110,f411]) ).
fof(f674,plain,
( sQ0_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f673,f130]) ).
fof(f675,plain,
( sQ0_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f674]) ).
fof(f676,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f242,f476,f538,f675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n002.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:12:47 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.54 % Elapsed time: 0.105355 seconds
% 0.17/0.54 % CPU time: 0.522673 seconds
% 0.17/0.54 % Total memory used: 86.871 MB
% 0.17/0.54 % Net memory used: 86.189 MB
%------------------------------------------------------------------------------