%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET789+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 : n018.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 0.17s 0.57s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 13 unt; 6 def)
% Number of atoms : 313 ( 24 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 390 ( 145 ~; 144 |; 76 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 193 ( 173 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,X)
& apply(R,X,Y) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
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(f11,conjecture,
! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> ! [X] :
( greatest(X,R,E)
=> M = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> ! [X] :
( greatest(X,R,E)
=> M = X ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,definition,
! [R,E] :
( sP0_prd(E,R)
<=> ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f15,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) ) ),
inference(formula_renaming,[status(thm)],[f13,f14]) ).
fof(f16,plain,
! [R,E] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ~ sP0_prd(E,R)
| order(R,E) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) )
| ~ order(R,E) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [R,E] :
( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ~ sP0_prd(E,R)
| order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) )
| ~ order(R,E) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [R,E] :
( ( ~ apply(R,sK0_skl(E,R),sK2_skl(E,R))
& apply(R,sK1_skl(E,R),sK2_skl(E,R))
& apply(R,sK0_skl(E,R),sK1_skl(E,R))
& member(sK2_skl(E,R),E)
& member(sK1_skl(E,R),E)
& member(sK0_skl(E,R),E) )
| ~ sP0_prd(E,R)
| order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) )
| ~ order(R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl(E,R)),skolemize(Y,sK1_skl(E,R)),skolemize(Z,sK2_skl(E,R))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( sP0_prd(X1,X0)
| ~ order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,plain,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( apply(R,X,M)
| ~ member(X,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| upper_bound(M,R,E) )
& ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
| ~ upper_bound(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| upper_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
| ~ upper_bound(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [R,E,M] :
( ( ~ apply(R,sK5_skl(M,E,R),M)
& member(sK5_skl(M,E,R),E) )
| upper_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
| ~ upper_bound(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(X,sK5_skl(M,E,R))],[f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( apply(X1,X3,X0)
| ~ member(X3,X2)
| ~ upper_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( member(sK5_skl(X0,X2,X1),X2)
| upper_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ apply(X1,sK5_skl(X0,X2,X1),X0)
| upper_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
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(f55,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ greatest(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( apply(X1,X3,X0)
| ~ member(X3,X2)
| ~ greatest(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f105,plain,
? [R,E,M] :
( ? [X] :
( M != X
& greatest(X,R,E) )
& greatest(M,R,E)
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f106,plain,
( sK15_skl != sK16_skl
& greatest(sK16_skl,sK13_skl,sK14_skl)
& greatest(sK15_skl,sK13_skl,sK14_skl)
& order(sK13_skl,sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(R,sK13_skl),skolemize(E,sK14_skl),skolemize(M,sK15_skl),skolemize(X,sK16_skl)],[f105]) ).
fof(f107,plain,
order(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
greatest(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
greatest(sK16_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
sK15_skl != sK16_skl,
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,definition,
! [R,E,X] :
( sP1_prd(X,E,R)
<=> ( apply(R,X,X)
| ~ member(X,E) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f112,plain,
! [R,E] :
( sP0_prd(E,R)
<=> ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) ) ),
inference(formula_renaming,[status(thm)],[f14,f111]) ).
fof(f113,plain,
! [R,E] :
( ( ? [X,Y] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP1_prd(X,E,R)
| sP0_prd(E,R) )
& ( ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) )
| ~ sP0_prd(E,R) ) ),
inference(NNF_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
( ! [R,E] :
( ? [X,Y] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP1_prd(X,E,R)
| sP0_prd(E,R) )
& ! [R,E] :
( ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) )
| ~ sP0_prd(E,R) ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
( ! [R,E] :
( ( sK18_skl(E,R) != sK19_skl(E,R)
& apply(R,sK19_skl(E,R),sK18_skl(E,R))
& apply(R,sK18_skl(E,R),sK19_skl(E,R))
& member(sK19_skl(E,R),E)
& member(sK18_skl(E,R),E) )
| ~ sP1_prd(sK17_skl(E,R),E,R)
| sP0_prd(E,R) )
& ! [R,E] :
( ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) )
| ~ sP0_prd(E,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(X,sK17_skl(E,R)),skolemize(X,sK18_skl(E,R)),skolemize(Y,sK19_skl(E,R))],[f114]) ).
fof(f117,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ apply(X1,X3,X2)
| ~ apply(X1,X2,X3)
| ~ member(X3,X0)
| ~ member(X2,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f128,plain,
sP0_prd(sK14_skl,sK13_skl),
inference(resolution,[status(thm)],[f19,f107]) ).
fof(f129,plain,
member(sK16_skl,sK14_skl),
inference(resolution,[status(thm)],[f55,f109]) ).
fof(f130,plain,
member(sK15_skl,sK14_skl),
inference(resolution,[status(thm)],[f55,f108]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( ~ member(sK5_skl(X0,X2,X1),X3)
| ~ greatest(X0,X1,X3)
| upper_bound(X0,X1,X2) ),
inference(resolution,[status(thm)],[f43,f56]) ).
fof(f133,plain,
! [X0,X1,X2] :
( upper_bound(X0,X1,X2)
| ~ greatest(X0,X1,X2)
| upper_bound(X0,X1,X2) ),
inference(resolution,[status(thm)],[f132,f42]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ greatest(X0,X1,X2)
| upper_bound(X0,X1,X2) ),
inference(duplicate_literals_removal,[status(thm)],[f133]) ).
fof(f135,plain,
upper_bound(sK16_skl,sK13_skl,sK14_skl),
inference(resolution,[status(thm)],[f134,f109]) ).
fof(f136,plain,
upper_bound(sK15_skl,sK13_skl,sK14_skl),
inference(resolution,[status(thm)],[f134,f108]) ).
fof(f137,plain,
! [X0] :
( apply(sK13_skl,X0,sK16_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f135,f41]) ).
fof(f141,plain,
! [X0] :
( apply(sK13_skl,X0,sK15_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f136,f41]) ).
fof(f254,definition,
( sQ13_spl
<=> member(sK15_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ13_spl
| ~ member(sK15_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f258,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f130]) ).
fof(f259,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f264,definition,
( sQ15_spl
<=> member(sK16_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( sQ15_spl
| ~ member(sK16_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f268,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f129]) ).
fof(f269,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f454,plain,
! [X0,X1] :
( X0 = X1
| ~ apply(sK13_skl,X1,X0)
| ~ apply(sK13_skl,X0,X1)
| ~ member(X1,sK14_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f117,f128]) ).
fof(f509,definition,
( sQ36_spl
<=> sK16_skl = sK15_skl ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ36_spl
| sK16_skl = sK15_skl ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f516,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f110]) ).
fof(f517,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f581,plain,
! [X0] :
( ~ member(X0,sK14_skl)
| sK15_skl = X0
| ~ apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl)
| ~ member(sK15_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f454,f141]) ).
fof(f593,definition,
! [X0] :
( sQ41_spl
<=> ( ~ member(X0,sK14_skl)
| sK15_skl = X0
| ~ apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f594,plain,
! [X0] :
( ~ sQ41_spl
| ~ member(X0,sK14_skl)
| sK15_skl = X0
| ~ apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( sQ41_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f581,f254,f593]) ).
fof(f605,plain,
! [X0] :
( ~ sQ41_spl
| sK15_skl = X0
| ~ apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f594]) ).
fof(f611,plain,
( ~ sQ41_spl
| ~ member(sK15_skl,sK14_skl)
| sK15_skl = sK16_skl
| ~ member(sK16_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f605,f137]) ).
fof(f618,plain,
( ~ sQ41_spl
| ~ sQ13_spl
| sQ36_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f611,f264,f509,f254,f593]) ).
fof(f624,plain,
$false,
inference(sat_refutation,[status(thm)],[f259,f269,f517,f596,f618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET789+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 % Computer : n018.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Mon Sep 21 05:39:59 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.48 % Drodi V4.1.1
% 0.17/0.57 % Refutation found
% 0.17/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.62 % Elapsed time: 0.139274 seconds
% 0.23/0.62 % CPU time: 0.651035 seconds
% 0.23/0.62 % Total memory used: 86.790 MB
% 0.23/0.62 % Net memory used: 85.988 MB
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