%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:11:06 PM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 80 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 21 ~; 32 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 37 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) )
=> subset(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) )
=> subset(B,D) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,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)],[f5]) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,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)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( subset(X0,X2)
| cartesian_product2(X0,X1) = empty_set
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( subset(X1,X3)
| cartesian_product2(X0,X1) = empty_set
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
? [A] :
( ? [B,C,D] :
( ~ subset(B,D)
& ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) ) )
& ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
? [A] :
( ? [B,D] :
( ~ subset(B,D)
& ( ? [C] : subset(cartesian_product2(B,A),cartesian_product2(D,C))
| ? [C] : subset(cartesian_product2(A,B),cartesian_product2(C,D)) ) )
& ~ empty(A) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( ~ subset(sK3_skl,sK4_skl)
& ( subset(cartesian_product2(sK3_skl,sK2_skl),cartesian_product2(sK4_skl,sK6_skl))
| subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl)) )
& ~ empty(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(D,sK4_skl),skolemize(C,sK5_skl),skolemize(C,sK6_skl)],[f26]) ).
fof(f28,plain,
~ empty(sK2_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( subset(cartesian_product2(sK3_skl,sK2_skl),cartesian_product2(sK4_skl,sK6_skl))
| subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
~ subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
( subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl))
| subset(sK3_skl,sK4_skl)
| cartesian_product2(sK3_skl,sK2_skl) = empty_set ),
inference(resolution,[status(thm)],[f23,f29]) ).
fof(f36,plain,
( subset(cartesian_product2(sK2_skl,sK3_skl),cartesian_product2(sK5_skl,sK4_skl))
| cartesian_product2(sK3_skl,sK2_skl) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f30]) ).
fof(f39,plain,
( subset(sK3_skl,sK4_skl)
| cartesian_product2(sK2_skl,sK3_skl) = empty_set
| cartesian_product2(sK3_skl,sK2_skl) = empty_set ),
inference(resolution,[status(thm)],[f36,f24]) ).
fof(f41,plain,
( cartesian_product2(sK2_skl,sK3_skl) = empty_set
| cartesian_product2(sK3_skl,sK2_skl) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f30]) ).
fof(f60,plain,
( sK2_skl = empty_set
| sK3_skl = empty_set
| cartesian_product2(sK2_skl,sK3_skl) = empty_set ),
inference(resolution,[status(thm)],[f41,f19]) ).
fof(f69,plain,
( sK2_skl = empty_set
| sK3_skl = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f19]) ).
fof(f76,plain,
! [X0] :
( sK2_skl = empty_set
| subset(sK3_skl,X0) ),
inference(paramodulation,[status(thm)],[f69,f31]) ).
fof(f89,plain,
sK2_skl = empty_set,
inference(resolution,[status(thm)],[f76,f30]) ).
fof(f106,plain,
empty(sK2_skl),
inference(backward_demodulation,[status(thm)],[f89,f10]) ).
fof(f114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f106,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:45:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.051844 seconds
% 0.15/0.43 % CPU time: 0.150745 seconds
% 0.15/0.43 % Total memory used: 80.448 MB
% 0.15/0.43 % Net memory used: 79.995 MB
%------------------------------------------------------------------------------