%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:09:31 PM UTC 2026
% Result : Theorem 120.86s 21.12s
% Output : CNFRefutation 120.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 102 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 117 ( 57 ~; 44 |; 13 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f19,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
( ! [B,C] :
( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [B,C] :
( ( ( member(sK1_skl(C,B),C)
| member(sK1_skl(C,B),B) )
& ( ~ member(sK1_skl(C,B),C)
| ~ member(sK1_skl(C,B),B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| ~ member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X1)
| member(sK1_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f35,plain,
? [B,C,D] : union(union(B,C),D) != union(B,union(C,D)),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
union(union(sK2_skl,sK3_skl),sK4_skl) != union(sK2_skl,union(sK3_skl,sK4_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f35]) ).
fof(f37,plain,
union(union(sK2_skl,sK3_skl),sK4_skl) != union(sK2_skl,union(sK3_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
union(union(sK2_skl,sK3_skl),sK4_skl) != union(union(sK3_skl,sK4_skl),sK2_skl),
inference(backward_demodulation,[status(thm)],[f19,f37]) ).
fof(f53,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK3_skl,sK4_skl),sK2_skl))
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK2_skl,sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f33,f41]) ).
fof(f65,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK2_skl)
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK2_skl,sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f53,f13]) ).
fof(f66,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK3_skl,sK4_skl))
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK2_skl,sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f53,f12]) ).
fof(f84,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK2_skl,sK3_skl))
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK2_skl) ),
inference(resolution,[status(thm)],[f65,f12]) ).
fof(f91,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f84,f12]) ).
fof(f95,plain,
! [X0] :
( member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),X0)
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(X0,sK2_skl)) ),
inference(resolution,[status(thm)],[f91,f11]) ).
fof(f97,plain,
! [X0] :
( member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),X0)
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK2_skl,X0)) ),
inference(resolution,[status(thm)],[f91,f11]) ).
fof(f99,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK4_skl)
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f66,f13]) ).
fof(f100,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK2_skl,sK3_skl))
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f66,f12]) ).
fof(f107,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK4_skl),
inference(forward_subsumption_resolution,[status(thm)],[f99,f13]) ).
fof(f111,plain,
! [X0] :
( member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),X0)
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f107,f11]) ).
fof(f546,plain,
( ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK3_skl)
| ~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f100,f12]) ).
fof(f556,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f546,f13]) ).
fof(f3929,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK3_skl,sK2_skl)),
inference(resolution,[status(thm)],[f95,f556]) ).
fof(f4013,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK2_skl,sK3_skl)),
inference(forward_demodulation,[status(thm)],[f19,f3929]) ).
fof(f4184,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f111,f556]) ).
fof(f4192,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK2_skl,sK3_skl),sK4_skl)),
inference(resolution,[status(thm)],[f111,f4013]) ).
fof(f4391,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(sK2_skl,union(sK3_skl,sK4_skl))),
inference(resolution,[status(thm)],[f4184,f97]) ).
fof(f4410,plain,
~ member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK3_skl,sK4_skl),sK2_skl)),
inference(forward_demodulation,[status(thm)],[f19,f4391]) ).
fof(f5685,plain,
( member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK3_skl,sK4_skl),sK2_skl))
| union(union(sK2_skl,sK3_skl),sK4_skl) = union(union(sK3_skl,sK4_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f4192,f34]) ).
fof(f5696,plain,
member(sK1_skl(union(union(sK3_skl,sK4_skl),sK2_skl),union(union(sK2_skl,sK3_skl),sK4_skl)),union(union(sK3_skl,sK4_skl),sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f5685,f41]) ).
fof(f7151,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5696,f4410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n016.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Mon Sep 21 05:02:14 UTC 2026
% 0.12/5.37 % CPUTime :
% 0.12/5.38 % Drodi V4.1.1
% 120.86/21.12 % Refutation found
% 120.86/21.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 120.86/21.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 110.87/22.34 % Elapsed time: 16.746446 seconds
% 110.87/22.34 % CPU time: 120.948474 seconds
% 110.87/22.34 % Total memory used: 451.340 MB
% 110.87/22.34 % Net memory used: 413.502 MB
%------------------------------------------------------------------------------