%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 13 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [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(f5,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(f6,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)],[f5]) ).
fof(f7,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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)],[f4]) ).
fof(f15,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)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,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)],[f6]) ).
fof(f19,plain,
( ~ subset(cartesian_product2(sK2_skl,sK4_skl),cartesian_product2(sK3_skl,sK5_skl))
& subset(sK4_skl,sK5_skl)
& subset(sK2_skl,sK3_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)],[f18]) ).
fof(f20,plain,
subset(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
~ subset(cartesian_product2(sK2_skl,sK4_skl),cartesian_product2(sK3_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0] :
( ~ subset(X0,cartesian_product2(sK3_skl,sK5_skl))
| ~ subset(cartesian_product2(sK2_skl,sK4_skl),X0) ),
inference(resolution,[status(thm)],[f25,f22]) ).
fof(f27,plain,
! [X0] :
( ~ subset(sK4_skl,X0)
| ~ subset(cartesian_product2(sK2_skl,X0),cartesian_product2(sK3_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f26,f17]) ).
fof(f31,plain,
( ~ subset(sK2_skl,sK3_skl)
| ~ subset(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f27,f16]) ).
fof(f33,plain,
~ subset(sK2_skl,sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f31,f21]) ).
fof(f34,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f33,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 05:55:45 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.49 % Elapsed time: 0.051221 seconds
% 0.18/0.49 % CPU time: 0.139456 seconds
% 0.18/0.49 % Total memory used: 31.168 MB
% 0.18/0.49 % Net memory used: 30.907 MB
%------------------------------------------------------------------------------