%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU368+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:20:19 PM UTC 2026
% Result : Theorem 104.23s 13.65s
% Output : CNFRefutation 36.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 17 unt; 0 def)
% Number of atoms : 92 ( 49 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 82 ( 35 ~; 26 |; 16 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 72 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,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/sandbox/benchmark/theBenchmark.p') ).
fof(f211,axiom,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f360,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/sandbox/benchmark/theBenchmark.p') ).
fof(f433,axiom,
! [A] : inclusion_order(A) = inclusion_relation(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f448,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f561,conjecture,
! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f562,negated_conjecture,
~ ! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
inference(negated_conjecture,[status(cth)],[f561]) ).
fof(f723,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)],[f1]) ).
fof(f724,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f723]) ).
fof(f1224,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f1740,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)],[f196]) ).
fof(f1745,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f1740]) ).
fof(f1770,plain,
( ! [A] : rel_str(incl_POSet(A))
& ! [A] : strict_rel_str(incl_POSet(A)) ),
inference(miniscoping,[status(thm)],[f211]) ).
fof(f1771,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f1770]) ).
fof(f1772,plain,
! [X0] : rel_str(incl_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f1770]) ).
fof(f2223,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)],[f360]) ).
fof(f2224,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)],[f2223]) ).
fof(f2225,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)],[f2223]) ).
fof(f2522,plain,
! [X0] : inclusion_order(X0) = inclusion_relation(X0),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f2550,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)],[f448]) ).
fof(f2551,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)],[f2550]) ).
fof(f2552,plain,
! [X0,X1,X2] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2551]) ).
fof(f3293,plain,
? [A] :
( the_InternalRel(incl_POSet(A)) != inclusion_order(A)
| the_carrier(incl_POSet(A)) != A ),
inference(pre_NNF_transformation,[status(thm)],[f562]) ).
fof(f3294,plain,
( ? [A] : the_InternalRel(incl_POSet(A)) != inclusion_order(A)
| ? [A] : the_carrier(incl_POSet(A)) != A ),
inference(miniscoping,[status(thm)],[f3293]) ).
fof(f3295,plain,
( the_InternalRel(incl_POSet(sK400_skl)) != inclusion_order(sK400_skl)
| the_carrier(incl_POSet(sK399_skl)) != sK399_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK399_skl,sK400_skl]),skolemize(A,sK399_skl),skolemize(A,sK400_skl)],[f3294]) ).
fof(f3296,plain,
( the_InternalRel(incl_POSet(sK400_skl)) != inclusion_order(sK400_skl)
| the_carrier(incl_POSet(sK399_skl)) != sK399_skl ),
inference(cnf_transformation,[status(thm)],[f3295]) ).
fof(f4574,plain,
! [X0] : relation_of2_as_subset(inclusion_relation(X0),X0,X0),
inference(backward_demodulation,[status(thm)],[f2522,f1745]) ).
fof(f4579,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_relation(X0)),
inference(backward_demodulation,[status(thm)],[f2522,f1224]) ).
fof(f4686,plain,
( the_InternalRel(incl_POSet(sK400_skl)) != inclusion_relation(sK400_skl)
| the_carrier(incl_POSet(sK399_skl)) != sK399_skl ),
inference(forward_demodulation,[status(thm)],[f2522,f3296]) ).
fof(f4905,plain,
! [X0] :
( incl_POSet(X0) = rel_str_of(the_carrier(incl_POSet(X0)),the_InternalRel(incl_POSet(X0)))
| ~ rel_str(incl_POSet(X0)) ),
inference(resolution,[status(thm)],[f1771,f724]) ).
fof(f4906,plain,
! [X0] : incl_POSet(X0) = rel_str_of(the_carrier(incl_POSet(X0)),the_InternalRel(incl_POSet(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f4905,f1772]) ).
fof(f9905,plain,
! [X0] : relation_of2(inclusion_relation(X0),X0,X0),
inference(resolution,[status(thm)],[f2552,f4574]) ).
fof(f25776,plain,
! [X0,X1,X2] :
( X0 = X1
| rel_str_of(X0,inclusion_relation(X0)) != rel_str_of(X1,X2) ),
inference(resolution,[status(thm)],[f2224,f9905]) ).
fof(f25785,plain,
! [X0,X1,X2] :
( X0 = X1
| incl_POSet(X0) != rel_str_of(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f4579,f25776]) ).
fof(f25788,plain,
! [X0,X1,X2] :
( inclusion_relation(X0) = X2
| rel_str_of(X0,inclusion_relation(X0)) != rel_str_of(X1,X2) ),
inference(resolution,[status(thm)],[f2225,f9905]) ).
fof(f25797,plain,
! [X0,X1,X2] :
( inclusion_relation(X0) = X2
| incl_POSet(X0) != rel_str_of(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f4579,f25788]) ).
fof(f25798,plain,
! [X0] : X0 = the_carrier(incl_POSet(X0)),
inference(resolution,[status(thm)],[f25785,f4906]) ).
fof(f25802,plain,
( the_InternalRel(incl_POSet(sK400_skl)) != inclusion_relation(sK400_skl)
| sK399_skl != sK399_skl ),
inference(backward_demodulation,[status(thm)],[f25798,f4686]) ).
fof(f25861,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,the_InternalRel(incl_POSet(X0))),
inference(backward_demodulation,[status(thm)],[f25798,f4906]) ).
fof(f25863,plain,
the_InternalRel(incl_POSet(sK400_skl)) != inclusion_relation(sK400_skl),
inference(trivial_equality_resolution,[status(thm)],[f25802]) ).
fof(f26404,plain,
! [X0] : inclusion_relation(X0) = the_InternalRel(incl_POSet(X0)),
inference(resolution,[status(thm)],[f25797,f25861]) ).
fof(f26408,plain,
inclusion_relation(sK400_skl) != inclusion_relation(sK400_skl),
inference(backward_demodulation,[status(thm)],[f26404,f25863]) ).
fof(f26419,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f26408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU368+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 06:18:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.21/0.48 % Drodi V4.1.1
% 104.23/13.65 % Refutation found
% 104.23/13.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 104.23/13.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 23.59/14.93 % Elapsed time: 14.331451 seconds
% 23.59/14.93 % CPU time: 97.348304 seconds
% 23.59/14.93 % Total memory used: 610.344 MB
% 23.59/14.93 % Net memory used: 576.089 MB
%------------------------------------------------------------------------------