%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU361+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 : n001.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 02:20:17 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 11 unt; 10 def)
% Number of atoms : 267 ( 25 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 324 ( 128 ~; 124 |; 45 &)
% ( 10 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 10 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 61 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( rel_str(A)
=> bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( rel_str(A)
=> element(bottom_of_relstr(A),the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) )
=> ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [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/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,plain,
! [A] :
( bottom_of_relstr(A) = join_on_relstr(A,empty_set)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( bottom_of_relstr(X0) = join_on_relstr(X0,empty_set)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [A] :
( element(bottom_of_relstr(A),the_carrier(A))
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f40,plain,
! [X0] :
( element(bottom_of_relstr(X0),the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f66,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f67,definition,
! [A,B,C,D] :
( sP0_prd(D,C,B,A)
<=> ( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f68,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ? [D] : sP0_prd(D,C,B,A)
| ~ relstr_set_smaller(A,C,B) )
& ( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(formula_renaming,[status(thm)],[f66,f67]) ).
fof(f69,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| ? [D] : sP0_prd(D,C,B,A)
| ~ relstr_set_smaller(A,C,B) )
& ! [C] :
( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
| sP0_prd(sK7_skl(C,B,A),C,B,A)
| ~ relstr_set_smaller(A,C,B) )
& ! [C] :
( ( ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(D,sK7_skl(C,B,A))],[f69]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( related(X0,X1,X3)
| ~ relstr_set_smaller(X0,X2,X3)
| ~ element(X3,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,X2)
| X1 != join_on_relstr(X0,X2)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f75,plain,
! [A] :
( ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) )
| ~ rel_str(A)
| ~ lower_bounded_relstr(A)
| ~ antisymmetric_relstr(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f76,plain,
! [X0] :
( ex_sup_of_relstr_set(X0,empty_set)
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,plain,
? [A] :
( ? [B] :
( ~ related(A,bottom_of_relstr(A),B)
& element(B,the_carrier(A)) )
& rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f79,plain,
( ~ related(sK8_skl,bottom_of_relstr(sK8_skl),sK9_skl)
& element(sK9_skl,the_carrier(sK8_skl))
& rel_str(sK8_skl)
& lower_bounded_relstr(sK8_skl)
& antisymmetric_relstr(sK8_skl)
& ~ empty_carrier(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f78]) ).
fof(f80,plain,
~ empty_carrier(sK8_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
antisymmetric_relstr(sK8_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
lower_bounded_relstr(sK8_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
rel_str(sK8_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f84,plain,
element(sK9_skl,the_carrier(sK8_skl)),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f85,plain,
~ related(sK8_skl,bottom_of_relstr(sK8_skl),sK9_skl),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f88,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)],[f27]) ).
fof(f89,plain,
! [X0,X1] :
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f103,plain,
( ex_sup_of_relstr_set(sK8_skl,empty_set)
| ~ rel_str(sK8_skl)
| ~ antisymmetric_relstr(sK8_skl)
| empty_carrier(sK8_skl) ),
inference(resolution,[status(thm)],[f76,f82]) ).
fof(f105,definition,
( sQ0_spl
<=> empty_carrier(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ0_spl
| empty_carrier(sK8_skl) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ1_spl
<=> antisymmetric_relstr(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ1_spl
| ~ antisymmetric_relstr(sK8_skl) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ2_spl
<=> rel_str(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ2_spl
| ~ rel_str(sK8_skl) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
( sQ3_spl
<=> ex_sup_of_relstr_set(sK8_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ3_spl
| ex_sup_of_relstr_set(sK8_skl,empty_set) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f103,f105,f108,f111,f114]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sQ3_spl
| related(sK8_skl,X0,X1)
| ~ relstr_set_smaller(sK8_skl,empty_set,X1)
| ~ element(X1,the_carrier(sK8_skl))
| X0 != join_on_relstr(sK8_skl,empty_set)
| ~ element(X0,the_carrier(sK8_skl))
| ~ rel_str(sK8_skl)
| ~ antisymmetric_relstr(sK8_skl) ),
inference(resolution,[status(thm)],[f115,f72]) ).
fof(f120,definition,
! [X0,X1] :
( sQ4_spl
<=> ( related(sK8_skl,X0,X1)
| ~ relstr_set_smaller(sK8_skl,empty_set,X1)
| ~ element(X1,the_carrier(sK8_skl))
| X0 != join_on_relstr(sK8_skl,empty_set)
| ~ element(X0,the_carrier(sK8_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f121,plain,
! [X0,X1] :
( ~ sQ4_spl
| related(sK8_skl,X0,X1)
| ~ relstr_set_smaller(sK8_skl,empty_set,X1)
| ~ element(X1,the_carrier(sK8_skl))
| X0 != join_on_relstr(sK8_skl,empty_set)
| ~ element(X0,the_carrier(sK8_skl)) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( ~ sQ3_spl
| sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f119,f108,f111,f120,f114]) ).
fof(f124,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f83]) ).
fof(f125,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f126,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f81]) ).
fof(f127,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f128,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f80]) ).
fof(f129,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f128]) ).
fof(f162,definition,
( sQ9_spl
<=> element(sK9_skl,the_carrier(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ9_spl
| ~ element(sK9_skl,the_carrier(sK8_skl)) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f168,definition,
( sQ11_spl
<=> element(bottom_of_relstr(sK8_skl),the_carrier(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ11_spl
| ~ element(bottom_of_relstr(sK8_skl),the_carrier(sK8_skl)) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ12_spl
<=> bottom_of_relstr(sK8_skl) = join_on_relstr(sK8_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ12_spl
| bottom_of_relstr(sK8_skl) = join_on_relstr(sK8_skl,empty_set) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f173,plain,
( sQ12_spl
| bottom_of_relstr(sK8_skl) != join_on_relstr(sK8_skl,empty_set) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f175,plain,
( sQ12_spl
| ~ rel_str(sK8_skl) ),
inference(resolution,[status(thm)],[f173,f35]) ).
fof(f176,plain,
( sQ12_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f175,f111,f171]) ).
fof(f177,plain,
( sQ11_spl
| ~ rel_str(sK8_skl) ),
inference(resolution,[status(thm)],[f170,f40]) ).
fof(f178,plain,
( sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f177,f111,f168]) ).
fof(f179,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f84]) ).
fof(f180,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f199,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ12_spl
| related(sK8_skl,X0,X1)
| ~ relstr_set_smaller(sK8_skl,empty_set,X1)
| ~ element(X1,the_carrier(sK8_skl))
| X0 != bottom_of_relstr(sK8_skl)
| ~ element(X0,the_carrier(sK8_skl)) ),
inference(backward_demodulation,[status(thm)],[f172,f121]) ).
fof(f200,plain,
( ~ sQ12_spl
| bottom_of_relstr(sK8_skl) = bottom_of_relstr(sK8_skl)
| ~ rel_str(sK8_skl) ),
inference(paramodulation,[status(thm)],[f172,f35]) ).
fof(f204,definition,
( sQ15_spl
<=> bottom_of_relstr(sK8_skl) = bottom_of_relstr(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ12_spl
| sQ15_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f200,f111,f204,f171]) ).
fof(f215,plain,
! [X0] :
( relstr_set_smaller(sK8_skl,empty_set,X0)
| ~ element(X0,the_carrier(sK8_skl)) ),
inference(resolution,[status(thm)],[f89,f83]) ).
fof(f228,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ12_spl
| related(sK8_skl,X0,X1)
| ~ element(X1,the_carrier(sK8_skl))
| X0 != bottom_of_relstr(sK8_skl)
| ~ element(X0,the_carrier(sK8_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f215]) ).
fof(f229,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ element(sK9_skl,the_carrier(sK8_skl))
| bottom_of_relstr(sK8_skl) != bottom_of_relstr(sK8_skl)
| ~ element(bottom_of_relstr(sK8_skl),the_carrier(sK8_skl)) ),
inference(resolution,[status(thm)],[f228,f85]) ).
fof(f231,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f229,f168,f204,f162,f171,f120]) ).
fof(f233,plain,
$false,
inference(sat_refutation,[status(thm)],[f117,f123,f125,f127,f129,f176,f178,f180,f207,f231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU361+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 06:21:13 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.50 % Elapsed time: 0.052758 seconds
% 0.22/0.50 % CPU time: 0.141105 seconds
% 0.22/0.50 % Total memory used: 28.580 MB
% 0.22/0.50 % Net memory used: 28.523 MB
%------------------------------------------------------------------------------