%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:11:05 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 4 unt; 2 def)
% Number of atoms : 59 ( 13 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 24 ~; 19 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 38 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ ! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [A,B] :
( A != B
=> disjoint(singleton(A),singleton(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(C,D)
& ~ disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( disjoint(cartesian_product2(X2,X0),cartesian_product2(X3,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
? [A,B,C,D] :
( ( ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
| ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) )
& A != B ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
? [A,B] :
( ( ? [C,D] : ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
| ? [C,D] : ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) )
& A != B ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ( ~ disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl)))
| ~ disjoint(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK5_skl)) )
& sK2_skl != sK3_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl),skolemize(C,sK6_skl),skolemize(D,sK7_skl)],[f18]) ).
fof(f20,plain,
sK2_skl != sK3_skl,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( ~ disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl)))
| ~ disjoint(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK5_skl)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [A,B] :
( disjoint(singleton(A),singleton(B))
| A = B ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1] :
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,definition,
( sQ0_spl
<=> disjoint(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f26,plain,
( sQ0_spl
| ~ disjoint(cartesian_product2(singleton(sK2_skl),sK4_skl),cartesian_product2(singleton(sK3_skl),sK5_skl)) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,definition,
( sQ1_spl
<=> disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( sQ1_spl
| ~ disjoint(cartesian_product2(sK6_skl,singleton(sK2_skl)),cartesian_product2(sK7_skl,singleton(sK3_skl))) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f24,f27]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
| X0 = X1 ),
inference(resolution,[status(thm)],[f23,f15]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| disjoint(cartesian_product2(X0,singleton(X1)),cartesian_product2(X2,singleton(X3))) ),
inference(resolution,[status(thm)],[f16,f23]) ).
fof(f34,plain,
( sQ0_spl
| sK2_skl = sK3_skl ),
inference(resolution,[status(thm)],[f31,f26]) ).
fof(f38,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f20]) ).
fof(f39,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f43,plain,
( sQ1_spl
| sK2_skl = sK3_skl ),
inference(resolution,[status(thm)],[f29,f33]) ).
fof(f44,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f20]) ).
fof(f45,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f44]) ).
fof(f46,plain,
$false,
inference(sat_refutation,[status(thm)],[f30,f39,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n013.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:45:21 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.59 % Elapsed time: 0.137287 seconds
% 0.23/0.59 % CPU time: 0.099556 seconds
% 0.23/0.59 % Total memory used: 2.512 MB
% 0.23/0.59 % Net memory used: 2.510 MB
%------------------------------------------------------------------------------