%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU141+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 02:19:21 PM UTC 2026
% Result : Theorem 7.46s 1.44s
% Output : CNFRefutation 7.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 7 unt; 0 def)
% Number of atoms : 257 ( 38 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 305 ( 117 ~; 125 |; 51 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 194 ( 181 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_intersection2(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(f16,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f29,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f35,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)],[f34]) ).
fof(f36,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)],[f35]) ).
fof(f37,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))],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,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_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f42,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_intersection2(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_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,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_intersection2(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_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
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) )
& ( ! [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(f51,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)],[f50]) ).
fof(f52,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))],[f51]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f72,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f73,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f78,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( in(sK5_skl(B,A),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(C,sK5_skl(B,A))],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( in(sK5_skl(X1,X0),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f87,plain,
? [A,B] :
( disjoint(A,B)
<~> set_difference(A,B) = A ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f88,plain,
? [A,B] :
( ( set_difference(A,B) != A
| ~ disjoint(A,B) )
& ( set_difference(A,B) = A
| disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
( ( set_difference(sK6_skl,sK7_skl) != sK6_skl
| ~ disjoint(sK6_skl,sK7_skl) )
& ( set_difference(sK6_skl,sK7_skl) = sK6_skl
| disjoint(sK6_skl,sK7_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f88]) ).
fof(f90,plain,
( set_difference(sK6_skl,sK7_skl) = sK6_skl
| disjoint(sK6_skl,sK7_skl) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( set_difference(sK6_skl,sK7_skl) != sK6_skl
| ~ disjoint(sK6_skl,sK7_skl) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f97,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f44]) ).
fof(f98,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f45]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f100,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f102,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f55]) ).
fof(f107,plain,
! [X0] :
( disjoint(sK6_skl,sK7_skl)
| ~ in(X0,sK7_skl)
| ~ in(X0,sK6_skl) ),
inference(paramodulation,[status(thm)],[f90,f101]) ).
fof(f231,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,set_difference(X0,X1)),X0)
| subset(set_difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[f39,f100]) ).
fof(f245,plain,
! [X0,X1,X2] :
( in(sK0_skl(set_difference(X1,X2),X0),X2)
| ~ in(sK0_skl(set_difference(X1,X2),X0),X1)
| subset(X0,set_difference(X1,X2)) ),
inference(resolution,[status(thm)],[f40,f102]) ).
fof(f315,plain,
! [X0,X1] :
( subset(set_difference(X0,X1),X0)
| subset(set_difference(X0,X1),X0) ),
inference(resolution,[status(thm)],[f231,f40]) ).
fof(f332,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f315]) ).
fof(f364,plain,
! [X0,X1] :
( ~ subset(X0,set_difference(X0,X1))
| X0 = set_difference(X0,X1) ),
inference(resolution,[status(thm)],[f332,f33]) ).
fof(f414,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f99,f81]) ).
fof(f500,plain,
! [X0,X1] :
( subset(X0,set_difference(X0,X1))
| in(sK0_skl(set_difference(X0,X1),X0),X1)
| subset(X0,set_difference(X0,X1)) ),
inference(resolution,[status(thm)],[f245,f39]) ).
fof(f508,plain,
! [X0,X1] :
( in(sK0_skl(set_difference(X0,X1),X0),X1)
| subset(X0,set_difference(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f500]) ).
fof(f514,plain,
! [X0] :
( ~ in(X0,sK7_skl)
| ~ in(X0,sK6_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f107,f414]) ).
fof(f522,plain,
! [X0] :
( subset(sK6_skl,X0)
| ~ in(sK0_skl(X0,sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f514,f39]) ).
fof(f743,plain,
! [X0,X1] :
( in(sK5_skl(X1,X0),X1)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f80,f98]) ).
fof(f744,plain,
! [X0,X1] :
( in(sK5_skl(X1,X0),X0)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f80,f97]) ).
fof(f774,plain,
! [X0] :
( ~ in(sK5_skl(sK6_skl,X0),sK7_skl)
| disjoint(X0,sK6_skl) ),
inference(resolution,[status(thm)],[f743,f514]) ).
fof(f1303,plain,
( disjoint(sK7_skl,sK6_skl)
| disjoint(sK7_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f744,f774]) ).
fof(f1317,plain,
disjoint(sK7_skl,sK6_skl),
inference(duplicate_literals_removal,[status(thm)],[f1303]) ).
fof(f1318,plain,
disjoint(sK6_skl,sK7_skl),
inference(resolution,[status(thm)],[f1317,f73]) ).
fof(f1319,plain,
set_difference(sK6_skl,sK7_skl) != sK6_skl,
inference(backward_subsumption_resolution,[status(thm)],[f91,f1318]) ).
fof(f6295,plain,
( subset(sK6_skl,set_difference(sK6_skl,sK7_skl))
| subset(sK6_skl,set_difference(sK6_skl,sK7_skl)) ),
inference(resolution,[status(thm)],[f508,f522]) ).
fof(f6326,plain,
subset(sK6_skl,set_difference(sK6_skl,sK7_skl)),
inference(duplicate_literals_removal,[status(thm)],[f6295]) ).
fof(f6335,plain,
sK6_skl = set_difference(sK6_skl,sK7_skl),
inference(resolution,[status(thm)],[f6326,f364]) ).
fof(f6344,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6335,f1319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU141+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.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 05:52:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 7.46/1.44 % Refutation found
% 7.46/1.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.46/1.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.46/1.46 % Elapsed time: 1.084176 seconds
% 7.46/1.46 % CPU time: 8.350356 seconds
% 7.46/1.46 % Total memory used: 189.526 MB
% 7.46/1.46 % Net memory used: 176.058 MB
%------------------------------------------------------------------------------