%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 9 unt; 6 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 214 ( 86 ~; 81 |; 25 &)
% ( 10 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,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(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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(f21,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)],[f20]) ).
fof(f22,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,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)],[f3]) ).
fof(f29,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)],[f28]) ).
fof(f30,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)],[f29]) ).
fof(f31,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ~ related(A,C,sK0_skl(B,C,A))
& in(sK0_skl(B,C,A),B)
& element(sK0_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,[sK0_skl]),skolemize(D,sK0_skl(B,C,A))],[f30]) ).
fof(f34,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,X1,X0),X2)
| relstr_element_smaller(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,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)],[f4]) ).
fof(f37,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)],[f36]) ).
fof(f38,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)],[f37]) ).
fof(f39,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ~ related(A,sK1_skl(B,C,A),C)
& in(sK1_skl(B,C,A),B)
& element(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(B,C,A))],[f38]) ).
fof(f42,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,X1,X0),X2)
| relstr_set_smaller(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f52,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f66,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)],[f21]) ).
fof(f67,plain,
( ( ~ relstr_element_smaller(sK8_skl,empty_set,sK9_skl)
| ~ relstr_set_smaller(sK8_skl,empty_set,sK9_skl) )
& element(sK9_skl,the_carrier(sK8_skl))
& rel_str(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f66]) ).
fof(f68,plain,
rel_str(sK8_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
element(sK9_skl,the_carrier(sK8_skl)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
( ~ relstr_element_smaller(sK8_skl,empty_set,sK9_skl)
| ~ relstr_set_smaller(sK8_skl,empty_set,sK9_skl) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f72,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,definition,
( sQ0_spl
<=> relstr_set_smaller(sK8_skl,empty_set,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ0_spl
| ~ relstr_set_smaller(sK8_skl,empty_set,sK9_skl) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ1_spl
<=> relstr_element_smaller(sK8_skl,empty_set,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( sQ1_spl
| ~ relstr_element_smaller(sK8_skl,empty_set,sK9_skl) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f77,f80]) ).
fof(f125,plain,
( sQ0_spl
| in(sK1_skl(empty_set,sK9_skl,sK8_skl),empty_set)
| ~ element(sK9_skl,the_carrier(sK8_skl))
| ~ rel_str(sK8_skl) ),
inference(resolution,[status(thm)],[f42,f79]) ).
fof(f126,definition,
( sQ6_spl
<=> rel_str(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ6_spl
| ~ rel_str(sK8_skl) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ7_spl
<=> element(sK9_skl,the_carrier(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ7_spl
| ~ element(sK9_skl,the_carrier(sK8_skl)) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ8_spl
<=> in(sK1_skl(empty_set,sK9_skl,sK8_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ8_spl
| in(sK1_skl(empty_set,sK9_skl,sK8_skl),empty_set) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( sQ0_spl
| sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f125,f126,f129,f132,f77]) ).
fof(f136,plain,
( sQ1_spl
| in(sK0_skl(empty_set,sK9_skl,sK8_skl),empty_set)
| ~ element(sK9_skl,the_carrier(sK8_skl))
| ~ rel_str(sK8_skl) ),
inference(resolution,[status(thm)],[f82,f34]) ).
fof(f138,definition,
( sQ9_spl
<=> in(sK0_skl(empty_set,sK9_skl,sK8_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ9_spl
| in(sK0_skl(empty_set,sK9_skl,sK8_skl),empty_set) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( sQ1_spl
| sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f136,f126,f129,f138,f80]) ).
fof(f146,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f69]) ).
fof(f147,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f148,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f68]) ).
fof(f149,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ sQ8_spl
| ~ empty(empty_set) ),
inference(resolution,[status(thm)],[f133,f73]) ).
fof(f154,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f52]) ).
fof(f155,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( ~ sQ9_spl
| ~ empty(empty_set) ),
inference(resolution,[status(thm)],[f139,f73]) ).
fof(f160,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f52]) ).
fof(f161,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f162,plain,
$false,
inference(sat_refutation,[status(thm)],[f83,f135,f141,f147,f149,f155,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n004.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 06:14:36 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.060305 seconds
% 0.12/0.41 % CPU time: 0.158573 seconds
% 0.12/0.41 % Total memory used: 81.046 MB
% 0.12/0.41 % Net memory used: 80.805 MB
%------------------------------------------------------------------------------