%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:11:03 PM UTC 2026
% Result : Theorem 0.15s 0.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 8 unt; 6 def)
% Number of atoms : 160 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 73 ~; 72 |; 16 &)
% ( 9 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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(f10,conjecture,
! [A,B] :
( cartesian_product2(A,B) = cartesian_product2(B,A)
=> ( A = B
| B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B] :
( cartesian_product2(A,B) = cartesian_product2(B,A)
=> ( A = B
| B = empty_set
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f20,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f24,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)],[f7]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,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)],[f25]) ).
fof(f33,plain,
? [A,B] :
( A != B
& B != empty_set
& A != empty_set
& cartesian_product2(A,B) = cartesian_product2(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
( sK3_skl != sK4_skl
& sK4_skl != empty_set
& sK3_skl != empty_set
& cartesian_product2(sK3_skl,sK4_skl) = cartesian_product2(sK4_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f33]) ).
fof(f35,plain,
cartesian_product2(sK3_skl,sK4_skl) = cartesian_product2(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
sK3_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
sK4_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
sK3_skl != sK4_skl,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK5_skl(B,A),B)
| ~ in(sK5_skl(B,A),A) )
& ( in(sK5_skl(B,A),B)
| in(sK5_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(C,sK5_skl(B,A))],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( X1 = X0
| in(sK5_skl(X0,X1),X0)
| in(sK5_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( X1 = X0
| ~ in(sK5_skl(X0,X1),X0)
| ~ in(sK5_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( in(X0,sK4_skl)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f35,f26]) ).
fof(f46,plain,
! [X0,X1] :
( in(X1,sK3_skl)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f35,f27]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(X1,sK4_skl)
| ~ in(X0,sK3_skl)
| in(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f45,f28]) ).
fof(f59,definition,
! [X0] :
( sQ2_spl
<=> ( ~ in(X0,sK3_skl)
| in(X0,sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,sK3_skl)
| in(X0,sK4_skl) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,definition,
! [X1] :
( sQ3_spl
<=> ~ in(X1,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f63,plain,
! [X0] :
( ~ sQ3_spl
| ~ in(X0,sK4_skl) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f58,f59,f62]) ).
fof(f85,plain,
! [X0,X1] :
( in(X1,sK3_skl)
| ~ in(X1,sK4_skl)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f28,f46]) ).
fof(f89,definition,
! [X0] :
( sQ4_spl
<=> ~ in(X0,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f90,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,definition,
! [X1] :
( sQ5_spl
<=> ( in(X1,sK3_skl)
| ~ in(X1,sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f93,plain,
! [X0] :
( ~ sQ5_spl
| in(X0,sK3_skl)
| ~ in(X0,sK4_skl) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f85,f89,f92]) ).
fof(f109,plain,
( ~ sQ3_spl
| sK4_skl = empty_set ),
inference(resolution,[status(thm)],[f20,f63]) ).
fof(f110,plain,
( ~ sQ4_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f20,f90]) ).
fof(f113,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f37]) ).
fof(f114,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f36]) ).
fof(f116,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f115]) ).
fof(f121,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK5_skl(X0,sK4_skl),sK3_skl)
| sK4_skl = X0
| ~ in(sK5_skl(X0,sK4_skl),X0) ),
inference(resolution,[status(thm)],[f43,f60]) ).
fof(f124,plain,
! [X0] :
( ~ sQ5_spl
| sK4_skl = X0
| in(sK5_skl(X0,sK4_skl),X0)
| in(sK5_skl(X0,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f93,f42]) ).
fof(f230,definition,
( sQ14_spl
<=> sK4_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( ~ sQ14_spl
| sK4_skl = sK3_skl ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f236,definition,
( sQ16_spl
<=> in(sK5_skl(sK3_skl,sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( ~ sQ16_spl
| in(sK5_skl(sK3_skl,sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( sQ16_spl
| ~ in(sK5_skl(sK3_skl,sK4_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f270,plain,
( ~ sQ5_spl
| sQ16_spl
| sK4_skl = sK3_skl
| in(sK5_skl(sK3_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f238,f124]) ).
fof(f272,plain,
( ~ sQ5_spl
| sQ14_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f270,f236,f230,f92]) ).
fof(f274,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f38]) ).
fof(f275,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f296,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| sK4_skl = sK3_skl
| ~ in(sK5_skl(sK3_skl,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f237,f121]) ).
fof(f298,plain,
( ~ sQ2_spl
| sQ14_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f296,f236,f230,f59]) ).
fof(f299,plain,
$false,
inference(sat_refutation,[status(thm)],[f65,f95,f114,f116,f272,f275,f298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n001.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 21 05:51:13 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.15/0.49 % Refutation found
% 0.15/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.52 % Elapsed time: 0.078074 seconds
% 0.15/0.52 % CPU time: 0.268838 seconds
% 0.15/0.52 % Total memory used: 93.984 MB
% 0.15/0.52 % Net memory used: 93.621 MB
%------------------------------------------------------------------------------