%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU145+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 02:19:22 PM UTC 2026
% Result : Theorem 23.15s 3.40s
% Output : CNFRefutation 23.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 5 unt; 0 def)
% Number of atoms : 161 ( 32 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 190 ( 67 ~; 77 |; 37 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 96 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK2_skl(C,B,A),B)
& in(sK2_skl(C,B,A),A) )
| in(sK2_skl(C,B,A),C) )
& ( in(sK2_skl(C,B,A),B)
| ~ in(sK2_skl(C,B,A),A)
| ~ in(sK2_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f27]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f35,plain,
? [A,B,C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
? [A,B] :
( ? [C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A) )
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
( ~ subset(sK3_skl,set_difference(sK4_skl,singleton(sK5_skl)))
& ~ in(sK5_skl,sK3_skl)
& subset(sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f36]) ).
fof(f38,plain,
subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
~ in(sK5_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
~ subset(sK3_skl,set_difference(sK4_skl,singleton(sK5_skl))),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f44,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0] :
( in(X0,sK4_skl)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f23,f38]) ).
fof(f51,plain,
! [X0] :
( in(sK1_skl(X0,sK3_skl),sK4_skl)
| subset(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f24,f46]) ).
fof(f59,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(equality_resolution,[status(thm)],[f31]) ).
fof(f79,plain,
! [X0,X1,X2] :
( in(sK1_skl(set_difference(X1,X2),X0),X2)
| ~ in(sK1_skl(set_difference(X1,X2),X0),X1)
| subset(X0,set_difference(X1,X2)) ),
inference(resolution,[status(thm)],[f25,f59]) ).
fof(f240,plain,
! [X0] :
( subset(sK3_skl,set_difference(sK4_skl,X0))
| in(sK1_skl(set_difference(sK4_skl,X0),sK3_skl),X0)
| subset(sK3_skl,set_difference(sK4_skl,X0)) ),
inference(resolution,[status(thm)],[f79,f51]) ).
fof(f245,plain,
! [X0] :
( in(sK1_skl(set_difference(sK4_skl,X0),sK3_skl),X0)
| subset(sK3_skl,set_difference(sK4_skl,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f240]) ).
fof(f338,plain,
! [X0] :
( sK1_skl(set_difference(sK4_skl,singleton(X0)),sK3_skl) = X0
| subset(sK3_skl,set_difference(sK4_skl,singleton(X0))) ),
inference(resolution,[status(thm)],[f245,f44]) ).
fof(f5238,plain,
! [X0] :
( subset(sK3_skl,set_difference(sK4_skl,singleton(X0)))
| in(X0,sK3_skl)
| subset(sK3_skl,set_difference(sK4_skl,singleton(X0))) ),
inference(paramodulation,[status(thm)],[f338,f24]) ).
fof(f5252,plain,
! [X0] :
( in(X0,sK3_skl)
| subset(sK3_skl,set_difference(sK4_skl,singleton(X0))) ),
inference(duplicate_literals_removal,[status(thm)],[f5238]) ).
fof(f8242,plain,
in(sK5_skl,sK3_skl),
inference(resolution,[status(thm)],[f5252,f40]) ).
fof(f8244,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8242,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU145+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:52:19 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 23.15/3.40 % Refutation found
% 23.15/3.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.15/3.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.37/3.45 % Elapsed time: 3.090475 seconds
% 15.37/3.45 % CPU time: 23.913949 seconds
% 15.37/3.45 % Total memory used: 274.073 MB
% 15.37/3.45 % Net memory used: 240.787 MB
%------------------------------------------------------------------------------