%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU355+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 : n013.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 02:20:16 PM UTC 2026
% Result : Theorem 7.33s 1.41s
% Output : CNFRefutation 7.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 150 ( 12 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 195 ( 79 ~; 72 |; 27 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f89,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f643,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f644,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f643]) ).
fof(f1117,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f1118,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f1117]) ).
fof(f1119,plain,
( ! [A] :
( in(sK48_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48_skl]),skolemize(B,sK48_skl(A))],[f1118]) ).
fof(f1120,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f1119]) ).
fof(f1470,plain,
! [A] :
( ! [B,C] :
( ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f145]) ).
fof(f1471,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(NNF_transformation,[status(thm)],[f1470]) ).
fof(f1472,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ! [B] :
( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(miniscoping,[status(thm)],[f1471]) ).
fof(f1473,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ~ related(A,C,sK102_skl(B,C,A))
& in(sK102_skl(B,C,A),B)
& element(sK102_skl(B,C,A),the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ! [B] :
( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102_skl]),skolemize(D,sK102_skl(B,C,A))],[f1472]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( in(sK102_skl(X2,X1,X0),X2)
| relstr_element_smaller(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f1473]) ).
fof(f1525,plain,
! [A] :
( ! [B,C] :
( ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f153]) ).
fof(f1526,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,D,C)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ( ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(NNF_transformation,[status(thm)],[f1525]) ).
fof(f1527,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ? [D] :
( ~ related(A,D,C)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ! [B] :
( ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(miniscoping,[status(thm)],[f1526]) ).
fof(f1528,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ~ related(A,sK113_skl(B,C,A),C)
& in(sK113_skl(B,C,A),B)
& element(sK113_skl(B,C,A),the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ! [B] :
( ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113_skl]),skolemize(D,sK113_skl(B,C,A))],[f1527]) ).
fof(f1531,plain,
! [X0,X1,X2] :
( in(sK113_skl(X2,X1,X0),X2)
| relstr_set_smaller(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f1528]) ).
fof(f3422,plain,
? [A] :
( ? [B] :
( ( ~ relstr_element_smaller(A,empty_set,B)
| ~ relstr_set_smaller(A,empty_set,B) )
& element(B,the_carrier(A)) )
& rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f644]) ).
fof(f3423,plain,
( ( ~ relstr_element_smaller(sK386_skl,empty_set,sK387_skl)
| ~ relstr_set_smaller(sK386_skl,empty_set,sK387_skl) )
& element(sK387_skl,the_carrier(sK386_skl))
& rel_str(sK386_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK386_skl,sK387_skl]),skolemize(A,sK386_skl),skolemize(B,sK387_skl)],[f3422]) ).
fof(f3424,plain,
rel_str(sK386_skl),
inference(cnf_transformation,[status(thm)],[f3423]) ).
fof(f3425,plain,
element(sK387_skl,the_carrier(sK386_skl)),
inference(cnf_transformation,[status(thm)],[f3423]) ).
fof(f3426,plain,
( ~ relstr_element_smaller(sK386_skl,empty_set,sK387_skl)
| ~ relstr_set_smaller(sK386_skl,empty_set,sK387_skl) ),
inference(cnf_transformation,[status(thm)],[f3423]) ).
fof(f4321,plain,
! [X0,X1] :
( in(sK102_skl(X1,X0,sK386_skl),X1)
| relstr_element_smaller(sK386_skl,X1,X0)
| ~ element(X0,the_carrier(sK386_skl)) ),
inference(resolution,[status(thm)],[f1476,f3424]) ).
fof(f4323,plain,
! [X0,X1] :
( in(sK113_skl(X1,X0,sK386_skl),X1)
| relstr_set_smaller(sK386_skl,X1,X0)
| ~ element(X0,the_carrier(sK386_skl)) ),
inference(resolution,[status(thm)],[f1531,f3424]) ).
fof(f4369,plain,
! [X0,X1] :
( X1 != empty_set
| relstr_element_smaller(sK386_skl,X1,X0)
| ~ element(X0,the_carrier(sK386_skl)) ),
inference(resolution,[status(thm)],[f4321,f1120]) ).
fof(f4373,plain,
! [X0,X1] :
( X1 != empty_set
| relstr_set_smaller(sK386_skl,X1,X0)
| ~ element(X0,the_carrier(sK386_skl)) ),
inference(resolution,[status(thm)],[f4323,f1120]) ).
fof(f4705,plain,
( ~ relstr_element_smaller(sK386_skl,empty_set,sK387_skl)
| empty_set != empty_set
| ~ element(sK387_skl,the_carrier(sK386_skl)) ),
inference(resolution,[status(thm)],[f4373,f3426]) ).
fof(f4706,plain,
( ~ relstr_element_smaller(sK386_skl,empty_set,sK387_skl)
| ~ element(sK387_skl,the_carrier(sK386_skl)) ),
inference(trivial_equality_resolution,[status(thm)],[f4705]) ).
fof(f4707,plain,
~ relstr_element_smaller(sK386_skl,empty_set,sK387_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4706,f3425]) ).
fof(f5354,plain,
( empty_set != empty_set
| ~ element(sK387_skl,the_carrier(sK386_skl)) ),
inference(resolution,[status(thm)],[f4707,f4369]) ).
fof(f5355,plain,
~ element(sK387_skl,the_carrier(sK386_skl)),
inference(trivial_equality_resolution,[status(thm)],[f5354]) ).
fof(f5356,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5355,f3425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:14:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.45 % Drodi V4.1.1
% 7.33/1.41 % Refutation found
% 7.33/1.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.33/1.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.33/1.46 % Elapsed time: 1.088176 seconds
% 7.33/1.46 % CPU time: 7.761396 seconds
% 7.33/1.46 % Total memory used: 275.159 MB
% 7.33/1.46 % Net memory used: 265.973 MB
%------------------------------------------------------------------------------