%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:19:30 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 6 unt; 2 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 60 ( 24 ~; 20 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f60,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f261,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f262,plain,
! [A,B] :
( ( ! [C] : subset(cartesian_product2(C,A),cartesian_product2(C,B))
& ! [C] : subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f261]) ).
fof(f263,plain,
! [X0,X1,X2] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f262]) ).
fof(f264,plain,
! [X0,X1,X2] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f262]) ).
fof(f265,plain,
? [A,B,C,D] :
( ~ subset(cartesian_product2(A,C),cartesian_product2(B,D))
& subset(C,D)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f266,plain,
( ~ subset(cartesian_product2(sK18_skl,sK20_skl),cartesian_product2(sK19_skl,sK21_skl))
& subset(sK20_skl,sK21_skl)
& subset(sK18_skl,sK19_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(A,sK18_skl),skolemize(B,sK19_skl),skolemize(C,sK20_skl),skolemize(D,sK21_skl)],[f265]) ).
fof(f267,plain,
subset(sK18_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f268,plain,
subset(sK20_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,plain,
~ subset(cartesian_product2(sK18_skl,sK20_skl),cartesian_product2(sK19_skl,sK21_skl)),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f276,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f277,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f276]) ).
fof(f278,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( subset(X2,cartesian_product2(X1,X3))
| ~ subset(X2,cartesian_product2(X0,X3))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f263,f278]) ).
fof(f464,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f432,f264]) ).
fof(f474,plain,
( ~ subset(sK20_skl,sK21_skl)
| ~ subset(sK18_skl,sK19_skl) ),
inference(resolution,[status(thm)],[f464,f269]) ).
fof(f479,definition,
( sQ4_spl
<=> subset(sK18_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( sQ4_spl
| ~ subset(sK18_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ5_spl
<=> subset(sK20_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ5_spl
| ~ subset(sK20_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f474,f479,f482]) ).
fof(f486,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f267]) ).
fof(f487,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f488,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f268]) ).
fof(f489,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f490,plain,
$false,
inference(sat_refutation,[status(thm)],[f485,f487,f489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+2 : 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 : n004.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 05:54:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.043902 seconds
% 0.13/0.40 % CPU time: 0.107086 seconds
% 0.13/0.40 % Total memory used: 20.377 MB
% 0.13/0.40 % Net memory used: 20.333 MB
%------------------------------------------------------------------------------