%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU362+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 : n014.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 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 22 unt; 9 def)
% Number of atoms : 274 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 293 ( 111 ~; 113 |; 32 &)
% ( 14 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 10 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 102 ( 96 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( rel_str(B)
=> ( subrelstr(B,A)
<=> ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> rel_str(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( related(B,E,F)
& F = D
& E = C )
=> related(A,C,D) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( related(B,E,F)
& F = D
& E = C )
=> related(A,C,D) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f53,plain,
! [A] :
( ! [B] :
( ( subrelstr(B,A)
<=> ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) ) )
| ~ rel_str(B) )
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [A] :
( ! [B] :
( ( ( ~ subset(the_InternalRel(B),the_InternalRel(A))
| ~ subset(the_carrier(B),the_carrier(A))
| subrelstr(B,A) )
& ( ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) )
| ~ subrelstr(B,A) ) )
| ~ rel_str(B) )
| ~ rel_str(A) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f59,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ in(ordered_pair(B,C),the_InternalRel(A))
| related(A,B,C) )
& ( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
! [A] :
( ! [B] :
( rel_str(B)
| ~ subrelstr(B,A) )
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f65,plain,
! [X0,X1] :
( rel_str(X1)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f111,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f112,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f114,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f116,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f118,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f121,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ related(A,C,D)
& related(B,E,F)
& F = D
& E = C
& element(F,the_carrier(B)) )
& element(E,the_carrier(B)) )
& element(D,the_carrier(A)) )
& element(C,the_carrier(A)) )
& subrelstr(B,A) )
& rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f124,plain,
( ~ related(sK11_skl,sK13_skl,sK14_skl)
& related(sK12_skl,sK15_skl,sK16_skl)
& sK16_skl = sK14_skl
& sK15_skl = sK13_skl
& element(sK16_skl,the_carrier(sK12_skl))
& element(sK15_skl,the_carrier(sK12_skl))
& element(sK14_skl,the_carrier(sK11_skl))
& element(sK13_skl,the_carrier(sK11_skl))
& subrelstr(sK12_skl,sK11_skl)
& rel_str(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(D,sK14_skl),skolemize(E,sK15_skl),skolemize(F,sK16_skl)],[f123]) ).
fof(f125,plain,
rel_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
subrelstr(sK12_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
element(sK13_skl,the_carrier(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
element(sK14_skl,the_carrier(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f129,plain,
element(sK15_skl,the_carrier(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f130,plain,
element(sK16_skl,the_carrier(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f131,plain,
sK15_skl = sK13_skl,
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f132,plain,
sK16_skl = sK14_skl,
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f133,plain,
related(sK12_skl,sK15_skl,sK16_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f134,plain,
~ related(sK11_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f143,plain,
element(sK13_skl,the_carrier(sK12_skl)),
inference(forward_demodulation,[status(thm)],[f131,f129]) ).
fof(f144,plain,
element(sK14_skl,the_carrier(sK12_skl)),
inference(forward_demodulation,[status(thm)],[f132,f130]) ).
fof(f145,plain,
! [X0,X1] :
( subset(the_InternalRel(X1),the_InternalRel(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f65]) ).
fof(f147,plain,
related(sK12_skl,sK13_skl,sK16_skl),
inference(forward_demodulation,[status(thm)],[f131,f133]) ).
fof(f148,plain,
related(sK12_skl,sK13_skl,sK14_skl),
inference(forward_demodulation,[status(thm)],[f132,f147]) ).
fof(f149,plain,
( in(ordered_pair(sK13_skl,sK14_skl),the_InternalRel(sK12_skl))
| ~ element(sK14_skl,the_carrier(sK12_skl))
| ~ element(sK13_skl,the_carrier(sK12_skl))
| ~ rel_str(sK12_skl) ),
inference(resolution,[status(thm)],[f148,f60]) ).
fof(f150,definition,
( sQ0_spl
<=> rel_str(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ0_spl
| ~ rel_str(sK12_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> element(sK13_skl,the_carrier(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ1_spl
| ~ element(sK13_skl,the_carrier(sK12_skl)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ2_spl
<=> element(sK14_skl,the_carrier(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( sQ2_spl
| ~ element(sK14_skl,the_carrier(sK12_skl)) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ3_spl
<=> in(ordered_pair(sK13_skl,sK14_skl),the_InternalRel(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ3_spl
| in(ordered_pair(sK13_skl,sK14_skl),the_InternalRel(sK12_skl)) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f149,f150,f153,f156,f159]) ).
fof(f169,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f144]) ).
fof(f170,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f171,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f143]) ).
fof(f172,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
! [X0] :
( sQ0_spl
| ~ subrelstr(sK12_skl,X0)
| ~ rel_str(X0) ),
inference(resolution,[status(thm)],[f152,f65]) ).
fof(f174,plain,
( sQ0_spl
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f173,f126]) ).
fof(f176,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f125]) ).
fof(f177,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f176]) ).
fof(f188,plain,
! [X0,X1,X2] :
( related(X2,X0,X1)
| ~ element(X1,the_carrier(X2))
| ~ element(X0,the_carrier(X2))
| ~ rel_str(X2)
| empty(the_InternalRel(X2))
| ~ element(ordered_pair(X0,X1),the_InternalRel(X2)) ),
inference(resolution,[status(thm)],[f112,f61]) ).
fof(f217,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,powerset(the_InternalRel(X0)))
| ~ in(ordered_pair(X1,X2),X3)
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| empty(the_InternalRel(X0)) ),
inference(resolution,[status(thm)],[f188,f119]) ).
fof(f219,plain,
! [X0,X1,X2,X3] :
( ~ element(X3,powerset(the_InternalRel(X0)))
| ~ in(ordered_pair(X1,X2),X3)
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f122]) ).
fof(f293,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(the_InternalRel(sK12_skl),powerset(the_InternalRel(X0)))
| related(X0,sK13_skl,sK14_skl)
| ~ element(sK14_skl,the_carrier(X0))
| ~ element(sK13_skl,the_carrier(X0))
| ~ rel_str(X0) ),
inference(resolution,[status(thm)],[f219,f160]) ).
fof(f299,plain,
( ~ sQ3_spl
| ~ element(the_InternalRel(sK12_skl),powerset(the_InternalRel(sK11_skl)))
| ~ element(sK14_skl,the_carrier(sK11_skl))
| ~ element(sK13_skl,the_carrier(sK11_skl))
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f293,f134]) ).
fof(f301,definition,
( sQ19_spl
<=> rel_str(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ19_spl
| ~ rel_str(sK11_skl) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ20_spl
<=> element(sK13_skl,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ20_spl
| ~ element(sK13_skl,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ21_spl
<=> element(sK14_skl,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ21_spl
| ~ element(sK14_skl,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,definition,
( sQ22_spl
<=> element(the_InternalRel(sK12_skl),powerset(the_InternalRel(sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ22_spl
| ~ element(the_InternalRel(sK12_skl),powerset(the_InternalRel(sK11_skl))) ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,plain,
( ~ sQ3_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f299,f301,f304,f307,f310,f159]) ).
fof(f315,plain,
( sQ22_spl
| ~ subset(the_InternalRel(sK12_skl),the_InternalRel(sK11_skl)) ),
inference(resolution,[status(thm)],[f312,f116]) ).
fof(f318,plain,
( sQ22_spl
| ~ subrelstr(sK12_skl,sK11_skl)
| ~ rel_str(sK11_skl) ),
inference(resolution,[status(thm)],[f315,f145]) ).
fof(f320,definition,
( sQ23_spl
<=> subrelstr(sK12_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ23_spl
| ~ subrelstr(sK12_skl,sK11_skl) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( sQ22_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f318,f301,f320,f310]) ).
fof(f324,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f125]) ).
fof(f325,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f126]) ).
fof(f327,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f127]) ).
fof(f329,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f128]) ).
fof(f331,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f330]) ).
fof(f332,plain,
$false,
inference(sat_refutation,[status(thm)],[f162,f170,f172,f177,f313,f323,f325,f327,f329,f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n014.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Mon Sep 21 06:15:19 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.53 % Elapsed time: 0.086789 seconds
% 0.25/0.53 % CPU time: 0.254346 seconds
% 0.25/0.53 % Total memory used: 104.745 MB
% 0.25/0.53 % Net memory used: 104.575 MB
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