%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET793+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:10:37 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 6 unt; 8 def)
% Number of atoms : 268 ( 18 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 324 ( 124 ~; 131 |; 50 &)
% ( 14 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 9 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 110 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( apply(R,Y,X)
| apply(R,X,Y) ) )
& order(R,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [R,E,M] :
( greatest(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,M) )
& member(M,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [R,E,M] :
( max(M,R,E)
<=> ( ! [X] :
( ( apply(R,M,X)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [R,E,M] :
( ( max(M,R,E)
& total_order(R,E) )
=> greatest(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E,M] :
( ( max(M,R,E)
& total_order(R,E) )
=> greatest(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f27,plain,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [R,E] :
( ( ? [X,Y] :
( ~ apply(R,Y,X)
& ~ apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ~ order(R,E)
| total_order(R,E) )
& ( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [R,E] :
( ? [X,Y] :
( ~ apply(R,Y,X)
& ~ apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ~ order(R,E)
| total_order(R,E) )
& ! [R,E] :
( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [R,E] :
( ( ~ apply(R,sK4_skl(E,R),sK3_skl(E,R))
& ~ apply(R,sK3_skl(E,R),sK4_skl(E,R))
& member(sK4_skl(E,R),E)
& member(sK3_skl(E,R),E) )
| ~ order(R,E)
| total_order(R,E) )
& ! [R,E] :
( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(X,sK3_skl(E,R)),skolemize(Y,sK4_skl(E,R))],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3,X2)
| apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ total_order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f51,plain,
! [R,E,M] :
( greatest(M,R,E)
<=> ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
& member(M,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| greatest(M,R,E) )
& ( ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| greatest(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
( ! [R,E,M] :
( ( ~ apply(R,sK7_skl(M,E,R),M)
& member(sK7_skl(M,E,R),E) )
| ~ member(M,E)
| greatest(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(X,sK7_skl(M,E,R))],[f53]) ).
fof(f57,plain,
! [X0,X1,X2] :
( member(sK7_skl(X0,X2,X1),X2)
| ~ member(X0,X2)
| greatest(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ apply(X1,sK7_skl(X0,X2,X1),X0)
| ~ member(X0,X2)
| greatest(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f67,plain,
! [R,E,M] :
( max(M,R,E)
<=> ( ! [X] :
( M = X
| ~ apply(R,M,X)
| ~ member(X,E) )
& member(M,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f68,plain,
! [R,E,M] :
( ( ? [X] :
( M != X
& apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| max(M,R,E) )
& ( ( ! [X] :
( M = X
| ~ apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
( ! [R,E,M] :
( ? [X] :
( M != X
& apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| max(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( M = X
| ~ apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f70,plain,
( ! [R,E,M] :
( ( M != sK9_skl(M,E,R)
& apply(R,M,sK9_skl(M,E,R))
& member(sK9_skl(M,E,R),E) )
| ~ member(M,E)
| max(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( M = X
| ~ apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X,sK9_skl(M,E,R))],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ max(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ max(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f105,plain,
? [R,E,M] :
( ~ greatest(M,R,E)
& max(M,R,E)
& total_order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f106,plain,
( ~ greatest(sK15_skl,sK13_skl,sK14_skl)
& max(sK15_skl,sK13_skl,sK14_skl)
& total_order(sK13_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(R,sK13_skl),skolemize(E,sK14_skl),skolemize(M,sK15_skl)],[f105]) ).
fof(f107,plain,
total_order(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
max(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
~ greatest(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f127,plain,
! [X0] :
( sK15_skl = X0
| ~ apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f72,f108]) ).
fof(f129,plain,
! [X0,X1] :
( apply(sK13_skl,X0,sK15_skl)
| ~ member(sK15_skl,X1)
| ~ member(X0,X1)
| ~ total_order(sK13_skl,X1)
| sK15_skl = X0
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f127,f32]) ).
fof(f131,plain,
! [X0] :
( apply(sK13_skl,X0,sK15_skl)
| ~ member(sK15_skl,sK14_skl)
| ~ member(X0,sK14_skl)
| sK15_skl = X0
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f129,f107]) ).
fof(f132,definition,
! [X0] :
( sQ0_spl
<=> ( apply(sK13_skl,X0,sK15_skl)
| ~ member(X0,sK14_skl)
| sK15_skl = X0
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f133,plain,
! [X0] :
( ~ sQ0_spl
| apply(sK13_skl,X0,sK15_skl)
| ~ member(X0,sK14_skl)
| sK15_skl = X0
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,definition,
( sQ1_spl
<=> member(sK15_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ1_spl
| ~ member(sK15_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f131,f132,f135]) ).
fof(f139,plain,
! [X0] :
( ~ sQ0_spl
| apply(sK13_skl,X0,sK15_skl)
| sK15_skl = X0
| ~ member(X0,sK14_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f133]) ).
fof(f147,plain,
! [X0] :
( sQ1_spl
| ~ max(sK15_skl,X0,sK14_skl) ),
inference(resolution,[status(thm)],[f137,f71]) ).
fof(f156,plain,
( sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f108,f147]) ).
fof(f157,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f265,plain,
( ~ apply(sK13_skl,sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK15_skl)
| ~ member(sK15_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f58,f109]) ).
fof(f267,definition,
( sQ14_spl
<=> apply(sK13_skl,sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ14_spl
| ~ apply(sK13_skl,sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK15_skl) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( ~ sQ14_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f265,f135,f267]) ).
fof(f276,plain,
( ~ sQ0_spl
| sQ14_spl
| sK15_skl = sK7_skl(sK15_skl,sK14_skl,sK13_skl)
| ~ member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f269,f139]) ).
fof(f278,plain,
! [X0] :
( sQ14_spl
| apply(sK13_skl,sK15_skl,sK7_skl(sK15_skl,sK14_skl,sK13_skl))
| ~ member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),X0)
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ),
inference(resolution,[status(thm)],[f269,f32]) ).
fof(f282,definition,
( sQ16_spl
<=> member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ16_spl
| ~ member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f294,definition,
( sQ19_spl
<=> sK15_skl = sK7_skl(sK15_skl,sK14_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ19_spl
| sK15_skl = sK7_skl(sK15_skl,sK14_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( ~ sQ0_spl
| sQ14_spl
| sQ19_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f276,f282,f294,f267,f132]) ).
fof(f298,definition,
! [X0] :
( sQ20_spl
<=> ( ~ member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),X0)
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f299,plain,
! [X0] :
( ~ sQ20_spl
| ~ member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),X0)
| ~ member(sK15_skl,X0)
| ~ total_order(sK13_skl,X0) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,definition,
( sQ21_spl
<=> apply(sK13_skl,sK15_skl,sK7_skl(sK15_skl,sK14_skl,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ21_spl
| apply(sK13_skl,sK15_skl,sK7_skl(sK15_skl,sK14_skl,sK13_skl)) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( sQ14_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f278,f298,f301,f267]) ).
fof(f306,plain,
( ~ sQ20_spl
| ~ member(sK7_skl(sK15_skl,sK14_skl,sK13_skl),sK14_skl)
| ~ member(sK15_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f299,f107]) ).
fof(f307,plain,
( ~ sQ20_spl
| ~ sQ16_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f306,f135,f282,f298]) ).
fof(f308,plain,
( sQ16_spl
| ~ member(sK15_skl,sK14_skl)
| greatest(sK15_skl,sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f284,f57]) ).
fof(f316,definition,
( sQ22_spl
<=> greatest(sK15_skl,sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( ~ sQ22_spl
| greatest(sK15_skl,sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,plain,
( sQ16_spl
| ~ sQ1_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f308,f316,f135,f282]) ).
fof(f320,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f317,f109]) ).
fof(f321,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( sQ14_spl
| ~ sQ19_spl
| ~ apply(sK13_skl,sK15_skl,sK15_skl) ),
inference(backward_demodulation,[status(thm)],[f295,f269]) ).
fof(f359,plain,
( ~ sQ21_spl
| ~ sQ19_spl
| apply(sK13_skl,sK15_skl,sK15_skl) ),
inference(forward_demodulation,[status(thm)],[f295,f302]) ).
fof(f360,plain,
( ~ sQ21_spl
| ~ sQ19_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f323]) ).
fof(f361,plain,
( ~ sQ21_spl
| ~ sQ19_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
$false,
inference(sat_refutation,[status(thm)],[f138,f157,f270,f297,f304,f307,f319,f321,f361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET793+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 05:33:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.066929 seconds
% 0.09/0.43 % CPU time: 0.218442 seconds
% 0.09/0.43 % Total memory used: 83.914 MB
% 0.09/0.43 % Net memory used: 83.685 MB
%------------------------------------------------------------------------------