%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:10:23 PM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 139 ( 23 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 148 ( 55 ~; 51 |; 17 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( range_of(B) = empty_set
| domain_of(B) = empty_set )
=> B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> D = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> D = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f38,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [B] :
( B = empty_set
| ( range_of(B) != empty_set
& domain_of(B) != empty_set )
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
! [X0] :
( X0 = empty_set
| domain_of(X0) != empty_set
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
! [X0,X1,X2] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f49,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f72,plain,
! [B] :
( ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f73,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f133,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f134,plain,
! [X0,X1,X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f144,plain,
? [B] :
( ? [C] :
( ? [D] :
( D != empty_set
& ilf_type(D,relation_type(empty_set,C))
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f145,plain,
( sK14_skl != empty_set
& ilf_type(sK14_skl,relation_type(empty_set,sK13_skl))
& ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl))
& ilf_type(sK13_skl,set_type)
& ilf_type(sK12_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(D,sK14_skl)],[f144]) ).
fof(f148,plain,
ilf_type(sK14_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,plain,
ilf_type(sK14_skl,relation_type(empty_set,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f150,plain,
sK14_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f151,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f76]) ).
fof(f157,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f143]) ).
fof(f161,plain,
! [X0,X1,X2] :
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f143]) ).
fof(f162,plain,
( subset(domain_of(sK14_skl),empty_set)
| ~ ilf_type(sK13_skl,set_type) ),
inference(resolution,[status(thm)],[f161,f149]) ).
fof(f164,plain,
subset(domain_of(sK14_skl),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f162,f143]) ).
fof(f166,plain,
domain_of(sK14_skl) = empty_set,
inference(resolution,[status(thm)],[f164,f157]) ).
fof(f171,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f143]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f143]) ).
fof(f197,plain,
( ilf_type(sK14_skl,subset_type(cross_product(sK12_skl,sK13_skl)))
| ~ ilf_type(sK13_skl,set_type) ),
inference(resolution,[status(thm)],[f195,f148]) ).
fof(f199,plain,
ilf_type(sK14_skl,subset_type(cross_product(sK12_skl,sK13_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f197,f143]) ).
fof(f236,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f143]) ).
fof(f239,plain,
( relation_like(sK14_skl)
| ~ ilf_type(sK13_skl,set_type) ),
inference(resolution,[status(thm)],[f236,f199]) ).
fof(f243,plain,
relation_like(sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f239,f143]) ).
fof(f245,plain,
ilf_type(sK14_skl,binary_relation_type),
inference(resolution,[status(thm)],[f243,f171]) ).
fof(f250,plain,
( sK14_skl = empty_set
| domain_of(sK14_skl) != empty_set ),
inference(resolution,[status(thm)],[f245,f40]) ).
fof(f252,plain,
( sK14_skl = empty_set
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f166,f250]) ).
fof(f253,plain,
sK14_skl = empty_set,
inference(trivial_equality_resolution,[status(thm)],[f252]) ).
fof(f254,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f253,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n002.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 05:34:33 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Drodi V4.1.1
% 0.17/0.45 % Refutation found
% 0.17/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.49 % Elapsed time: 0.053705 seconds
% 0.17/0.49 % CPU time: 0.156092 seconds
% 0.17/0.49 % Total memory used: 49.478 MB
% 0.17/0.49 % Net memory used: 49.414 MB
%------------------------------------------------------------------------------