%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU131+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.08s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 5 unt; 0 def)
% Number of atoms : 158 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 182 ( 70 ~; 76 |; 27 &)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 98 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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(f20,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f55,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f69,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f70,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)],[f69]) ).
fof(f71,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)],[f70]) ).
fof(f72,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_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,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0,X1] :
( ~ in(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f85,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)],[f9]) ).
fof(f86,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)],[f85]) ).
fof(f87,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK4_skl(C,B,A),B)
& in(sK4_skl(C,B,A),A) )
| in(sK4_skl(C,B,A),C) )
& ( in(sK4_skl(C,B,A),B)
| ~ in(sK4_skl(C,B,A),A)
| ~ in(sK4_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,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f86]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f109,plain,
? [A,B] :
( set_difference(A,B) = empty_set
<~> subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f110,plain,
? [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) != empty_set )
& ( subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
( ( ~ subset(sK5_skl,sK6_skl)
| set_difference(sK5_skl,sK6_skl) != empty_set )
& ( subset(sK5_skl,sK6_skl)
| set_difference(sK5_skl,sK6_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f110]) ).
fof(f112,plain,
( subset(sK5_skl,sK6_skl)
| set_difference(sK5_skl,sK6_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
( ~ subset(sK5_skl,sK6_skl)
| set_difference(sK5_skl,sK6_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f171,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f178,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f88]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f89]) ).
fof(f180,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f90]) ).
fof(f204,plain,
! [X0] :
( subset(sK5_skl,sK6_skl)
| in(X0,sK6_skl)
| ~ in(X0,sK5_skl)
| in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f112,f180]) ).
fof(f206,plain,
! [X0] :
( subset(sK5_skl,sK6_skl)
| in(X0,sK6_skl)
| ~ in(X0,sK5_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f171]) ).
fof(f207,plain,
! [X0] :
( in(X0,sK6_skl)
| ~ in(X0,sK5_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f73]) ).
fof(f276,plain,
! [X0,X1] :
( ~ in(sK0_skl(set_difference(X0,X1)),X1)
| set_difference(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f59,f179]) ).
fof(f277,plain,
! [X0,X1] :
( in(sK0_skl(set_difference(X0,X1)),X0)
| set_difference(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f59,f178]) ).
fof(f547,plain,
! [X0] :
( in(sK0_skl(set_difference(sK5_skl,X0)),sK6_skl)
| set_difference(sK5_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f277,f207]) ).
fof(f667,plain,
! [X0] :
( in(sK2_skl(X0,sK5_skl),sK6_skl)
| subset(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f74,f207]) ).
fof(f692,plain,
( set_difference(sK5_skl,sK6_skl) = empty_set
| set_difference(sK5_skl,sK6_skl) = empty_set ),
inference(resolution,[status(thm)],[f547,f276]) ).
fof(f698,plain,
set_difference(sK5_skl,sK6_skl) = empty_set,
inference(duplicate_literals_removal,[status(thm)],[f692]) ).
fof(f700,plain,
( ~ subset(sK5_skl,sK6_skl)
| empty_set != empty_set ),
inference(backward_demodulation,[status(thm)],[f698,f113]) ).
fof(f711,plain,
~ subset(sK5_skl,sK6_skl),
inference(trivial_equality_resolution,[status(thm)],[f700]) ).
fof(f837,plain,
( subset(sK5_skl,sK6_skl)
| subset(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f75,f667]) ).
fof(f842,plain,
subset(sK5_skl,sK6_skl),
inference(duplicate_literals_removal,[status(thm)],[f837]) ).
fof(f843,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f842,f711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU131+2 : 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 : n006.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 05:51:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.64 % Refutation found
% 0.08/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.67 % Elapsed time: 0.308597 seconds
% 0.19/0.67 % CPU time: 1.761504 seconds
% 0.19/0.67 % Total memory used: 118.292 MB
% 0.19/0.67 % Net memory used: 115.226 MB
%------------------------------------------------------------------------------