%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.05s 0.39s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 7 unt; 2 def)
% Number of atoms : 334 ( 26 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 434 ( 161 ~; 162 |; 89 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 231 ( 210 !; 21 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( ( apply(R,X,M)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> min(M,R,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> min(M,R,E) ),
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(f44,plain,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( apply(R,M,X)
| ~ member(X,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ! [R,E,M] :
( ( ~ apply(R,M,sK6_skl(M,E,R))
& member(sK6_skl(M,E,R),E) )
| lower_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(X,sK6_skl(M,E,R))],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( member(sK6_skl(X0,X2,X1),X2)
| lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ apply(X1,X0,sK6_skl(X0,X2,X1))
| lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f59,plain,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| least(M,R,E) )
& ( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| ~ member(M,E)
| least(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [R,E,M] :
( ( ~ apply(R,M,sK8_skl(M,E,R))
& member(sK8_skl(M,E,R),E) )
| ~ member(M,E)
| least(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(X,sK8_skl(M,E,R))],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f76,plain,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f77,plain,
! [R,E,M] :
( ( ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| min(M,R,E) )
& ( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [R,E,M] :
( ? [X] :
( M != X
& apply(R,X,M)
& member(X,E) )
| ~ member(M,E)
| min(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [R,E,M] :
( ( M != sK10_skl(M,E,R)
& apply(R,sK10_skl(M,E,R),M)
& member(sK10_skl(M,E,R),E) )
| ~ member(M,E)
| min(M,R,E) )
& ! [R,E,M] :
( ( ! [X] :
( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(X,sK10_skl(M,E,R))],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( member(sK10_skl(X0,X2,X1),X2)
| ~ member(X0,X2)
| min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( apply(X1,sK10_skl(X0,X2,X1),X0)
| ~ member(X0,X2)
| min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f84,plain,
! [X0,X1,X2] :
( X0 != sK10_skl(X0,X2,X1)
| ~ member(X0,X2)
| min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f105,plain,
? [R,E,M] :
( ~ min(M,R,E)
& least(M,R,E)
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f106,plain,
( ~ min(sK15_skl,sK13_skl,sK14_skl)
& least(sK15_skl,sK13_skl,sK14_skl)
& 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,
order(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
least(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
~ min(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,definition,
! [R,E,X] :
( sP1_prd(X,E,R)
<=> ( apply(R,X,X)
| ~ member(X,E) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f111,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,f110]) ).
fof(f112,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)],[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) )
& ! [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)],[f112]) ).
fof(f114,plain,
( ! [R,E] :
( ( sK17_skl(E,R) != sK18_skl(E,R)
& apply(R,sK18_skl(E,R),sK17_skl(E,R))
& apply(R,sK17_skl(E,R),sK18_skl(E,R))
& member(sK18_skl(E,R),E)
& member(sK17_skl(E,R),E) )
| ~ sP1_prd(sK16_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,[sK16_skl,sK17_skl,sK18_skl]),skolemize(X,sK16_skl(E,R)),skolemize(X,sK17_skl(E,R)),skolemize(Y,sK18_skl(E,R))],[f113]) ).
fof(f116,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)],[f114]) ).
fof(f127,plain,
member(sK15_skl,sK14_skl),
inference(resolution,[status(thm)],[f63,f108]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( ~ member(sK6_skl(X0,X2,X1),X3)
| ~ least(X0,X1,X3)
| lower_bound(X0,X1,X2) ),
inference(resolution,[status(thm)],[f50,f64]) ).
fof(f159,plain,
! [X0,X1,X2] :
( lower_bound(X0,X1,X2)
| ~ least(X0,X1,X2)
| lower_bound(X0,X1,X2) ),
inference(resolution,[status(thm)],[f140,f49]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ least(X0,X1,X2)
| lower_bound(X0,X1,X2) ),
inference(duplicate_literals_removal,[status(thm)],[f159]) ).
fof(f161,plain,
lower_bound(sK15_skl,sK13_skl,sK14_skl),
inference(resolution,[status(thm)],[f160,f108]) ).
fof(f162,plain,
! [X0] :
( apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f161,f48]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( ~ order(X3,X1)
| X0 = X2
| ~ apply(X3,X2,X0)
| ~ apply(X3,X0,X2)
| ~ member(X2,X1)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f116,f19]) ).
fof(f279,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)],[f278,f107]) ).
fof(f280,plain,
! [X0] :
( ~ member(X0,sK14_skl)
| X0 = sK15_skl
| ~ apply(sK13_skl,X0,sK15_skl)
| ~ member(sK15_skl,sK14_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f279,f162]) ).
fof(f290,plain,
! [X0] :
( X0 = sK15_skl
| ~ apply(sK13_skl,X0,sK15_skl)
| ~ member(sK15_skl,sK14_skl)
| ~ member(X0,sK14_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f280]) ).
fof(f291,plain,
! [X0] :
( X0 = sK15_skl
| ~ apply(sK13_skl,X0,sK15_skl)
| ~ member(X0,sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f127]) ).
fof(f297,plain,
! [X0] :
( ~ member(sK15_skl,X0)
| min(sK15_skl,sK13_skl,X0)
| sK10_skl(sK15_skl,X0,sK13_skl) = sK15_skl
| ~ member(sK10_skl(sK15_skl,X0,sK13_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f291,f83]) ).
fof(f301,plain,
! [X0] :
( ~ member(sK15_skl,X0)
| min(sK15_skl,sK13_skl,X0)
| ~ member(sK10_skl(sK15_skl,X0,sK13_skl),sK14_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f297,f84]) ).
fof(f313,plain,
( ~ member(sK15_skl,sK14_skl)
| min(sK15_skl,sK13_skl,sK14_skl)
| ~ member(sK15_skl,sK14_skl)
| min(sK15_skl,sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f301,f82]) ).
fof(f314,plain,
( ~ member(sK15_skl,sK14_skl)
| min(sK15_skl,sK13_skl,sK14_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f313]) ).
fof(f315,plain,
~ member(sK15_skl,sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f314,f109]) ).
fof(f316,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f315,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 21 05:38:21 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 % Drodi V4.1.1
% 0.05/0.39 % Refutation found
% 0.05/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.05/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.100421 seconds
% 0.11/0.40 % CPU time: 0.627352 seconds
% 0.11/0.40 % Total memory used: 92.919 MB
% 0.11/0.40 % Net memory used: 91.631 MB
%------------------------------------------------------------------------------