%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:11:04 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 5 unt; 0 def)
% Number of atoms : 143 ( 16 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 176 ( 75 ~; 72 |; 24 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 102 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B,C] :
~ ( ~ subset(B,C)
& ( subset(cartesian_product2(A,B),cartesian_product2(A,C))
| subset(cartesian_product2(B,A),cartesian_product2(C,A)) )
& A != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ subset(B,C)
& ( subset(cartesian_product2(A,B),cartesian_product2(A,C))
| subset(cartesian_product2(B,A),cartesian_product2(C,A)) )
& A != empty_set ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f18,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f22,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f32,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f33,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)],[f32]) ).
fof(f34,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)],[f33]) ).
fof(f35,plain,
( ! [A,B] :
( ( ~ in(sK6_skl(B,A),B)
& in(sK6_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,[sK6_skl]),skolemize(C,sK6_skl(B,A))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( in(sK6_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(sK6_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f42,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f53,plain,
? [A,B,C] :
( ~ subset(B,C)
& ( subset(cartesian_product2(A,B),cartesian_product2(A,C))
| subset(cartesian_product2(B,A),cartesian_product2(C,A)) )
& A != empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
? [B,C] :
( ~ subset(B,C)
& ? [A] :
( ( subset(cartesian_product2(A,B),cartesian_product2(A,C))
| subset(cartesian_product2(B,A),cartesian_product2(C,A)) )
& A != empty_set ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
( ~ subset(sK9_skl,sK10_skl)
& ( subset(cartesian_product2(sK11_skl,sK9_skl),cartesian_product2(sK11_skl,sK10_skl))
| subset(cartesian_product2(sK9_skl,sK11_skl),cartesian_product2(sK10_skl,sK11_skl)) )
& sK11_skl != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(B,sK9_skl),skolemize(C,sK10_skl),skolemize(A,sK11_skl)],[f54]) ).
fof(f56,plain,
sK11_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
( subset(cartesian_product2(sK11_skl,sK9_skl),cartesian_product2(sK11_skl,sK10_skl))
| subset(cartesian_product2(sK9_skl,sK11_skl),cartesian_product2(sK10_skl,sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
~ subset(sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f69,plain,
! [X0] :
( subset(cartesian_product2(sK11_skl,sK9_skl),cartesian_product2(sK11_skl,sK10_skl))
| in(X0,cartesian_product2(sK10_skl,sK11_skl))
| ~ in(X0,cartesian_product2(sK9_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f36,f57]) ).
fof(f71,plain,
! [X0,X1] :
( in(X1,cartesian_product2(sK11_skl,sK10_skl))
| ~ in(X1,cartesian_product2(sK11_skl,sK9_skl))
| in(X0,cartesian_product2(sK10_skl,sK11_skl))
| ~ in(X0,cartesian_product2(sK9_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f69,f36]) ).
fof(f112,plain,
! [X0,X1,X2] :
( in(X2,cartesian_product2(sK11_skl,sK10_skl))
| ~ in(X2,cartesian_product2(sK11_skl,sK9_skl))
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK9_skl,sK11_skl))
| in(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f44,f71]) ).
fof(f138,plain,
! [X0,X1,X2] :
( in(X2,cartesian_product2(sK11_skl,sK10_skl))
| ~ in(X2,cartesian_product2(sK11_skl,sK9_skl))
| in(X0,sK10_skl)
| ~ in(X1,sK11_skl)
| ~ in(X0,sK9_skl) ),
inference(resolution,[status(thm)],[f46,f112]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( in(X3,sK10_skl)
| ~ in(ordered_pair(X2,X3),cartesian_product2(sK11_skl,sK9_skl))
| in(X0,sK10_skl)
| ~ in(X1,sK11_skl)
| ~ in(X0,sK9_skl) ),
inference(resolution,[status(thm)],[f138,f45]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,sK9_skl)
| ~ in(X3,sK11_skl)
| in(X2,sK10_skl)
| in(X0,sK10_skl)
| ~ in(X1,sK11_skl)
| ~ in(X0,sK9_skl) ),
inference(resolution,[status(thm)],[f146,f46]) ).
fof(f152,plain,
! [X0,X1,X2] :
( subset(X0,sK10_skl)
| ~ in(sK6_skl(sK10_skl,X0),sK9_skl)
| ~ in(X2,sK11_skl)
| ~ in(X1,sK11_skl)
| ~ in(sK6_skl(sK10_skl,X0),sK9_skl) ),
inference(resolution,[status(thm)],[f151,f38]) ).
fof(f164,plain,
! [X0,X1,X2] :
( subset(X0,sK10_skl)
| ~ in(X2,sK11_skl)
| ~ in(X1,sK11_skl)
| ~ in(sK6_skl(sK10_skl,X0),sK9_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f152]) ).
fof(f185,plain,
! [X0,X1] :
( subset(sK9_skl,sK10_skl)
| subset(sK9_skl,sK10_skl)
| ~ in(X1,sK11_skl)
| ~ in(X0,sK11_skl) ),
inference(resolution,[status(thm)],[f164,f37]) ).
fof(f186,plain,
! [X0,X1] :
( subset(sK9_skl,sK10_skl)
| ~ in(X1,sK11_skl)
| ~ in(X0,sK11_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f185]) ).
fof(f187,plain,
! [X0,X1] :
( ~ in(X1,sK11_skl)
| ~ in(X0,sK11_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f58]) ).
fof(f189,plain,
! [X0] :
( sK11_skl = empty_set
| ~ in(X0,sK11_skl) ),
inference(resolution,[status(thm)],[f187,f22]) ).
fof(f190,plain,
! [X0] : ~ in(X0,sK11_skl),
inference(forward_subsumption_resolution,[status(thm)],[f189,f56]) ).
fof(f192,plain,
sK11_skl = empty_set,
inference(resolution,[status(thm)],[f190,f22]) ).
fof(f193,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f192,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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 05:46:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.046081 seconds
% 0.13/0.41 % CPU time: 0.148478 seconds
% 0.13/0.41 % Total memory used: 68.085 MB
% 0.13/0.41 % Net memory used: 67.729 MB
%------------------------------------------------------------------------------