%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU132+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:19:19 PM UTC 2026
% Result : Theorem 1.22s 0.64s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 153 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 173 ( 70 ~; 70 |; 26 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 115 ( 104 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
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(sK0_skl(B,A),B)
& in(sK0_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,[sK0_skl]),skolemize(C,sK0_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(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(sK0_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)],[f3]) ).
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(sK1_skl(C,B,A),B)
& in(sK1_skl(C,B,A),A) )
| in(sK1_skl(C,B,A),C) )
& ( in(sK1_skl(C,B,A),B)
| ~ in(sK1_skl(C,B,A),A)
| ~ in(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
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(f33,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X0,X2,X1),X2)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f36,plain,
empty(sK2_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(A,sK2_skl)],[f7]) ).
fof(f37,plain,
empty(sK2_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f42,plain,
? [A,B,C] :
( ~ subset(set_difference(A,C),set_difference(B,C))
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f43,plain,
? [A,B] :
( ? [C] : ~ subset(set_difference(A,C),set_difference(B,C))
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( ~ subset(set_difference(sK4_skl,sK6_skl),set_difference(sK5_skl,sK6_skl))
& subset(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f43]) ).
fof(f45,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
~ subset(set_difference(sK4_skl,sK6_skl),set_difference(sK5_skl,sK6_skl)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f51,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f52,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f59,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f80,plain,
in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),set_difference(sK4_skl,sK6_skl)),
inference(resolution,[status(thm)],[f24,f46]) ).
fof(f82,plain,
~ in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),set_difference(sK5_skl,sK6_skl)),
inference(resolution,[status(thm)],[f25,f46]) ).
fof(f84,plain,
~ in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),sK6_skl),
inference(resolution,[status(thm)],[f80,f58]) ).
fof(f88,plain,
( in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),sK6_skl)
| ~ in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),sK5_skl) ),
inference(resolution,[status(thm)],[f82,f59]) ).
fof(f91,plain,
~ in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),sK5_skl),
inference(forward_subsumption_resolution,[status(thm)],[f88,f84]) ).
fof(f135,plain,
! [X0] : ~ in(X0,sK2_skl),
inference(resolution,[status(thm)],[f53,f37]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(X0,X2,X1),X3)
| ~ subset(X3,X2)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_difference(X1,X2) ),
inference(resolution,[status(thm)],[f34,f23]) ).
fof(f384,plain,
! [X0,X1] :
( ~ in(sK1_skl(X0,sK5_skl,X1),sK4_skl)
| in(sK1_skl(X0,sK5_skl,X1),X0)
| X0 = set_difference(X1,sK5_skl) ),
inference(resolution,[status(thm)],[f155,f45]) ).
fof(f624,plain,
! [X0] :
( in(sK1_skl(X0,sK5_skl,sK4_skl),X0)
| X0 = set_difference(sK4_skl,sK5_skl)
| in(sK1_skl(X0,sK5_skl,sK4_skl),X0)
| X0 = set_difference(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f384,f33]) ).
fof(f631,plain,
! [X0] :
( in(sK1_skl(X0,sK5_skl,sK4_skl),X0)
| X0 = set_difference(sK4_skl,sK5_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f624]) ).
fof(f1014,plain,
sK2_skl = set_difference(sK4_skl,sK5_skl),
inference(resolution,[status(thm)],[f631,f135]) ).
fof(f1187,plain,
! [X0] :
( in(X0,sK5_skl)
| ~ in(X0,sK4_skl)
| in(X0,sK2_skl) ),
inference(paramodulation,[status(thm)],[f1014,f59]) ).
fof(f1267,plain,
! [X0] :
( in(X0,sK5_skl)
| ~ in(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1187,f135]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ in(X0,set_difference(sK4_skl,X1))
| in(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f1267,f57]) ).
fof(f1321,plain,
in(sK0_skl(set_difference(sK5_skl,sK6_skl),set_difference(sK4_skl,sK6_skl)),sK5_skl),
inference(resolution,[status(thm)],[f1275,f80]) ).
fof(f1328,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1321,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU132+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:52:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.22/0.64 % Refutation found
% 1.22/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.22/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.22/0.67 % Elapsed time: 0.292075 seconds
% 1.22/0.67 % CPU time: 1.978267 seconds
% 1.22/0.67 % Total memory used: 128.789 MB
% 1.22/0.67 % Net memory used: 124.450 MB
%------------------------------------------------------------------------------