%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU131+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 : n007.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 02:19:18 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 151 ( 28 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 166 ( 60 ~; 74 |; 24 &)
% ( 6 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 101 ( 93 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f14,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f21,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)],[f20]) ).
fof(f22,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)],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
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) )
& ( ! [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(f28,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)],[f27]) ).
fof(f29,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))],[f28]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f34,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)],[f29]) ).
fof(f35,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)],[f29]) ).
fof(f37,plain,
? [A,B] :
( set_difference(A,B) = empty_set
<~> subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f38,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)],[f37]) ).
fof(f39,plain,
( ( ~ subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) != empty_set )
& ( subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl)],[f38]) ).
fof(f40,plain,
( subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
( ~ subset(sK2_skl,sK3_skl)
| set_difference(sK2_skl,sK3_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f54,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f65,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f75,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f54,f64]) ).
fof(f81,plain,
! [X0] :
( subset(sK2_skl,sK3_skl)
| in(X0,sK3_skl)
| ~ in(X0,sK2_skl)
| in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f40,f65]) ).
fof(f83,plain,
! [X0] :
( subset(sK2_skl,sK3_skl)
| in(X0,sK3_skl)
| ~ in(X0,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f75]) ).
fof(f85,plain,
! [X0] :
( in(X0,sK3_skl)
| ~ in(X0,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f24]) ).
fof(f95,plain,
! [X0] :
( in(sK0_skl(X0,sK2_skl),sK3_skl)
| subset(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f25,f85]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(sK0_skl(X0,empty_set),X1)
| subset(empty_set,X0) ),
inference(resolution,[status(thm)],[f25,f75]) ).
fof(f107,plain,
! [X0] :
( subset(empty_set,X0)
| subset(empty_set,X0) ),
inference(resolution,[status(thm)],[f97,f25]) ).
fof(f109,plain,
! [X0] : subset(empty_set,X0),
inference(duplicate_literals_removal,[status(thm)],[f107]) ).
fof(f110,plain,
! [X0,X1] :
( in(X0,X1)
| ~ in(X0,empty_set) ),
inference(resolution,[status(thm)],[f109,f24]) ).
fof(f111,plain,
! [X0] : ~ in(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f110,f75]) ).
fof(f116,plain,
( subset(sK2_skl,sK3_skl)
| subset(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f95,f26]) ).
fof(f119,plain,
subset(sK2_skl,sK3_skl),
inference(duplicate_literals_removal,[status(thm)],[f116]) ).
fof(f120,plain,
set_difference(sK2_skl,sK3_skl) != empty_set,
inference(backward_subsumption_resolution,[status(thm)],[f41,f119]) ).
fof(f134,plain,
! [X0,X1] :
( in(sK1_skl(X0,X1,sK2_skl),sK3_skl)
| in(sK1_skl(X0,X1,sK2_skl),X0)
| X0 = set_difference(sK2_skl,X1) ),
inference(resolution,[status(thm)],[f34,f85]) ).
fof(f155,plain,
! [X0] :
( in(sK1_skl(X0,sK3_skl,sK2_skl),X0)
| X0 = set_difference(sK2_skl,sK3_skl)
| in(sK1_skl(X0,sK3_skl,sK2_skl),X0)
| X0 = set_difference(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f134,f35]) ).
fof(f158,plain,
! [X0] :
( in(sK1_skl(X0,sK3_skl,sK2_skl),X0)
| X0 = set_difference(sK2_skl,sK3_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f155]) ).
fof(f421,plain,
empty_set = set_difference(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f158,f111]) ).
fof(f429,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f421,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:49:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.46 % Refutation found
% 0.12/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.105107 seconds
% 0.12/0.47 % CPU time: 0.683448 seconds
% 0.12/0.47 % Total memory used: 112.379 MB
% 0.12/0.47 % Net memory used: 110.279 MB
%------------------------------------------------------------------------------