%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU136+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 : n011.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 02:19:20 PM UTC 2026
% Result : Theorem 79.47s 12.71s
% Output : CNFRefutation 79.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 158 ( 27 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 197 ( 77 ~; 85 |; 31 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 110 ( 104 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f19,conjecture,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f33,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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f34,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_union2(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_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [A,B,C] :
( ( ( in(sK0_skl(C,B,A),B)
| in(sK0_skl(C,B,A),A)
| in(sK0_skl(C,B,A),C) )
& ( ( ~ in(sK0_skl(C,B,A),B)
& ~ in(sK0_skl(C,B,A),A) )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_union2(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_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f49,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)],[f6]) ).
fof(f50,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)],[f49]) ).
fof(f51,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))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0,X1,X2] :
( in(sK2_skl(X0,X2,X1),X2)
| ~ in(sK2_skl(X0,X2,X1),X1)
| ~ in(sK2_skl(X0,X2,X1),X0)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f56,plain,
! [X0,X1,X2] :
( in(sK2_skl(X0,X2,X1),X1)
| in(sK2_skl(X0,X2,X1),X0)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(X0,X2,X1),X2)
| in(sK2_skl(X0,X2,X1),X0)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f75,plain,
? [A,B] : set_difference(set_union2(A,B),B) != set_difference(A,B),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f76,plain,
set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl) != set_difference(sK5_skl,sK6_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f75]) ).
fof(f77,plain,
set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl) != set_difference(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f89,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f92,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f94,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_difference(set_union2(X1,X2),X3)) ),
inference(resolution,[status(thm)],[f92,f89]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,X1)
| in(X0,X3)
| in(X0,set_difference(set_union2(X1,X2),X3)) ),
inference(resolution,[status(thm)],[f94,f90]) ).
fof(f261,plain,
( in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK6_skl)
| ~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK5_skl)
| ~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl)) ),
inference(resolution,[status(thm)],[f55,f77]) ).
fof(f266,plain,
( in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK6_skl)
| ~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f261,f110]) ).
fof(f270,plain,
( in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK5_skl)
| in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl)) ),
inference(resolution,[status(thm)],[f56,f77]) ).
fof(f291,plain,
( ~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK6_skl)
| in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl)) ),
inference(resolution,[status(thm)],[f57,f77]) ).
fof(f298,plain,
~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f266,f299]) ).
fof(f299,plain,
~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK6_skl),
inference(forward_subsumption_resolution,[status(thm)],[f291,f93]) ).
fof(f304,plain,
in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK5_skl),
inference(backward_subsumption_resolution,[status(thm)],[f270,f298]) ).
fof(f544,plain,
( ~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK5_skl)
| in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f298,f115]) ).
fof(f562,plain,
~ in(sK2_skl(set_difference(set_union2(sK5_skl,sK6_skl),sK6_skl),sK6_skl,sK5_skl),sK5_skl),
inference(forward_subsumption_resolution,[status(thm)],[f544,f299]) ).
fof(f563,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f304,f562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU136+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:52:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 79.47/12.71 % Refutation found
% 79.47/12.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 79.47/12.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 79.47/12.76 % Elapsed time: 12.393750 seconds
% 79.47/12.76 % CPU time: 98.138347 seconds
% 79.47/12.76 % Total memory used: 473.506 MB
% 79.47/12.76 % Net memory used: 406.903 MB
%------------------------------------------------------------------------------