%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET984+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 : n012.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 0.06s 0.33s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 19 unt; 6 def)
% Number of atoms : 147 ( 82 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 49 ~; 59 |; 12 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 78 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( ( B = D
& A = C )
| B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [A,B] :
( ( ( B != empty_set
& A != empty_set )
| cartesian_product2(A,B) = empty_set )
& ( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
( ! [A,B] :
( ( B != empty_set
& A != empty_set )
| cartesian_product2(A,B) = empty_set )
& ! [A,B] :
( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( X0 != empty_set
| cartesian_product2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( X1 != empty_set
| cartesian_product2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| B = empty_set
| A = empty_set
| cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
? [A,B,C,D] :
( ( ~ subset(B,D)
| ~ subset(A,C) )
& cartesian_product2(A,B) != empty_set
& subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
( ( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK2_skl,sK4_skl) )
& cartesian_product2(sK2_skl,sK3_skl) != empty_set
& subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f33]) ).
fof(f35,plain,
subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
cartesian_product2(sK2_skl,sK3_skl) != empty_set,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ subset(sK3_skl,sK5_skl)
| ~ subset(sK2_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,definition,
( sQ0_spl
<=> subset(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f44,definition,
( sQ1_spl
<=> subset(sK3_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ1_spl
| ~ subset(sK3_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f41,f44]) ).
fof(f48,plain,
! [X0] : cartesian_product2(empty_set,X0) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f49,plain,
! [X0] : cartesian_product2(X0,empty_set) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f92,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X1),
inference(paramodulation,[status(thm)],[f14,f38]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4,X5] :
( X1 = set_intersection2(X3,X5)
| X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)) ),
inference(paramodulation,[status(thm)],[f29,f32]) ).
fof(f124,plain,
set_intersection2(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)) = cartesian_product2(sK2_skl,sK3_skl),
inference(resolution,[status(thm)],[f40,f35]) ).
fof(f126,plain,
! [X0,X1] : set_intersection2(set_intersection2(X0,X1),X1) = set_intersection2(X0,X1),
inference(resolution,[status(thm)],[f92,f40]) ).
fof(f146,plain,
! [X0,X1] : set_intersection2(X0,set_intersection2(X1,X0)) = set_intersection2(X1,X0),
inference(paramodulation,[status(thm)],[f14,f126]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = set_intersection2(X2,X4)
| X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)) ),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f358,plain,
set_intersection2(cartesian_product2(sK4_skl,sK5_skl),cartesian_product2(sK2_skl,sK3_skl)) = set_intersection2(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)),
inference(paramodulation,[status(thm)],[f124,f146]) ).
fof(f381,plain,
set_intersection2(cartesian_product2(sK4_skl,sK5_skl),cartesian_product2(sK2_skl,sK3_skl)) = cartesian_product2(sK2_skl,sK3_skl),
inference(forward_demodulation,[status(thm)],[f124,f358]) ).
fof(f425,definition,
( sQ11_spl
<=> set_intersection2(sK3_skl,sK5_skl) = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( ~ sQ11_spl
| set_intersection2(sK3_skl,sK5_skl) = sK3_skl ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f479,plain,
( sK3_skl = set_intersection2(sK3_skl,sK5_skl)
| sK3_skl = empty_set
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f106,f124]) ).
fof(f506,definition,
( sQ22_spl
<=> sK2_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( ~ sQ22_spl
| sK2_skl = empty_set ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ23_spl
<=> sK3_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ23_spl
| sK3_skl = empty_set ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( sQ11_spl
| sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f479,f506,f509,f425]) ).
fof(f599,plain,
( ~ sQ23_spl
| cartesian_product2(sK2_skl,empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f510,f36]) ).
fof(f600,plain,
( ~ sQ23_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f49,f599]) ).
fof(f601,plain,
( ~ sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f600]) ).
fof(f602,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f642,plain,
( ~ sQ11_spl
| subset(sK3_skl,sK5_skl) ),
inference(paramodulation,[status(thm)],[f426,f92]) ).
fof(f643,plain,
( ~ sQ11_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f46]) ).
fof(f644,plain,
( ~ sQ11_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( ~ sQ22_spl
| cartesian_product2(empty_set,sK3_skl) != empty_set ),
inference(backward_demodulation,[status(thm)],[f507,f36]) ).
fof(f651,plain,
( ~ sQ22_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f48,f646]) ).
fof(f652,plain,
( ~ sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f651]) ).
fof(f653,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f967,definition,
( sQ31_spl
<=> set_intersection2(sK4_skl,sK2_skl) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f968,plain,
( ~ sQ31_spl
| set_intersection2(sK4_skl,sK2_skl) = sK2_skl ),
inference(component_clause,[status(thm)],[f967]) ).
fof(f990,plain,
( sK2_skl = set_intersection2(sK4_skl,sK2_skl)
| sK3_skl = empty_set
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f169,f381]) ).
fof(f1012,plain,
( sQ31_spl
| sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f990,f506,f509,f967]) ).
fof(f1082,plain,
( ~ sQ31_spl
| subset(sK2_skl,sK4_skl) ),
inference(paramodulation,[status(thm)],[f968,f38]) ).
fof(f1087,plain,
( ~ sQ31_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f1082,f41,f967]) ).
fof(f1088,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f512,f602,f644,f653,f1012,f1087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 05:45:53 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.06/0.33 % Refutation found
% 0.06/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.34 % Elapsed time: 0.044463 seconds
% 0.06/0.34 % CPU time: 0.144377 seconds
% 0.06/0.34 % Total memory used: 104.892 MB
% 0.06/0.34 % Net memory used: 104.351 MB
%------------------------------------------------------------------------------