%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:20:18 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 105 ( 43 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 104 ( 44 ~; 36 |; 18 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 76 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A] :
( relation_of2_as_subset(inclusion_order(A),A,A)
& v1_partfun1(inclusion_order(A),A,A)
& transitive(inclusion_order(A))
& antisymmetric(inclusion_order(A))
& reflexive(inclusion_order(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f133,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D) )
| ~ relation_of2(B,A,A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| rel_str_of(X1,X0) != rel_str_of(X2,X3)
| ~ relation_of2(X0,X1,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| rel_str_of(X1,X0) != rel_str_of(X2,X3)
| ~ relation_of2(X0,X1,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f137,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f144,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f145,plain,
( ! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ! [A,B,C] :
( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1,X2] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f148,plain,
! [A,B] :
( ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f149,plain,
! [X0,X1] :
( strict_rel_str(rel_str_of(X1,X0))
| ~ relation_of2(X0,X1,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1] :
( rel_str(rel_str_of(X1,X0))
| ~ relation_of2(X0,X1,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f166,plain,
( ! [A] : relation_of2_as_subset(inclusion_order(A),A,A)
& ! [A] : v1_partfun1(inclusion_order(A),A,A)
& ! [A] : transitive(inclusion_order(A))
& ! [A] : antisymmetric(inclusion_order(A))
& ! [A] : reflexive(inclusion_order(A)) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f171,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f172,plain,
( ! [A] : rel_str(incl_POSet(A))
& ! [A] : strict_rel_str(incl_POSet(A)) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f173,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
! [X0] : rel_str(incl_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f182,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f183,plain,
? [A] :
( the_InternalRel(incl_POSet(A)) != inclusion_order(A)
| the_carrier(incl_POSet(A)) != A ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f184,plain,
( ? [A] : the_InternalRel(incl_POSet(A)) != inclusion_order(A)
| ? [A] : the_carrier(incl_POSet(A)) != A ),
inference(miniscoping,[status(thm)],[f183]) ).
fof(f185,plain,
( the_InternalRel(incl_POSet(sK14_skl)) != inclusion_order(sK14_skl)
| the_carrier(incl_POSet(sK13_skl)) != sK13_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(A,sK14_skl)],[f184]) ).
fof(f186,plain,
( the_InternalRel(incl_POSet(sK14_skl)) != inclusion_order(sK14_skl)
| the_carrier(incl_POSet(sK13_skl)) != sK13_skl ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f213,plain,
! [X0] : relation_of2(inclusion_order(X0),X0,X0),
inference(resolution,[status(thm)],[f146,f171]) ).
fof(f254,plain,
! [X0,X1] :
( ~ strict_rel_str(rel_str_of(X1,X0))
| ~ rel_str(rel_str_of(X1,X0))
| X1 = the_carrier(rel_str_of(X1,X0))
| ~ relation_of2(X0,X1,X1) ),
inference(resolution,[status(thm)],[f134,f137]) ).
fof(f259,plain,
! [X0,X1] :
( ~ strict_rel_str(rel_str_of(X1,X0))
| X1 = the_carrier(rel_str_of(X1,X0))
| ~ relation_of2(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f150]) ).
fof(f263,plain,
! [X0,X1,X2] :
( inclusion_order(X0) = X2
| incl_POSet(X0) != rel_str_of(X1,X2)
| ~ relation_of2(inclusion_order(X0),X0,X0) ),
inference(paramodulation,[status(thm)],[f182,f135]) ).
fof(f267,plain,
! [X0,X1,X2] :
( inclusion_order(X0) = X2
| incl_POSet(X0) != rel_str_of(X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f213]) ).
fof(f278,plain,
! [X0] :
( ~ strict_rel_str(incl_POSet(X0))
| ~ rel_str(incl_POSet(X0))
| inclusion_order(X0) = the_InternalRel(incl_POSet(X0)) ),
inference(resolution,[status(thm)],[f267,f137]) ).
fof(f280,plain,
! [X0] :
( ~ strict_rel_str(incl_POSet(X0))
| inclusion_order(X0) = the_InternalRel(incl_POSet(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f174]) ).
fof(f281,plain,
! [X0,X1] :
( X1 = the_carrier(rel_str_of(X1,X0))
| ~ relation_of2(X0,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f149]) ).
fof(f282,plain,
! [X0] :
( X0 = the_carrier(incl_POSet(X0))
| ~ relation_of2(inclusion_order(X0),X0,X0) ),
inference(paramodulation,[status(thm)],[f182,f281]) ).
fof(f283,plain,
! [X0] : X0 = the_carrier(incl_POSet(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f282,f213]) ).
fof(f284,plain,
( the_InternalRel(incl_POSet(sK14_skl)) != inclusion_order(sK14_skl)
| sK13_skl != sK13_skl ),
inference(backward_demodulation,[status(thm)],[f283,f186]) ).
fof(f288,plain,
the_InternalRel(incl_POSet(sK14_skl)) != inclusion_order(sK14_skl),
inference(trivial_equality_resolution,[status(thm)],[f284]) ).
fof(f290,plain,
inclusion_order(sK14_skl) != inclusion_order(sK14_skl),
inference(backward_demodulation,[status(thm)],[f291,f288]) ).
fof(f291,plain,
! [X0] : inclusion_order(X0) = the_InternalRel(incl_POSet(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f280,f173]) ).
fof(f293,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 06:16:06 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.35 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.047827 seconds
% 0.12/0.40 % CPU time: 0.128324 seconds
% 0.12/0.40 % Total memory used: 104.753 MB
% 0.12/0.40 % Net memory used: 104.680 MB
%------------------------------------------------------------------------------