%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET790+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 : 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 02:10:37 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 11 unt; 2 def)
% Number of atoms : 234 ( 18 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 303 ( 111 ~; 104 |; 70 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 142 ( 124 !; 18 ?)
% 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(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(f11,conjecture,
! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(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(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(f105,plain,
? [R,E,M] :
( ? [X] :
( M != X
& least(X,R,E) )
& least(M,R,E)
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f106,plain,
( sK15_skl != sK16_skl
& least(sK16_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,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,
least(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
least(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(sK15_skl,sK14_skl),
inference(resolution,[status(thm)],[f63,f108]) ).
fof(f130,plain,
! [X0] :
( apply(sK13_skl,sK15_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f64,f108]) ).
fof(f131,plain,
! [X0] :
( apply(sK13_skl,sK16_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f109,f64]) ).
fof(f132,plain,
member(sK16_skl,sK14_skl),
inference(resolution,[status(thm)],[f109,f63]) ).
fof(f138,plain,
apply(sK13_skl,sK15_skl,sK16_skl),
inference(resolution,[status(thm)],[f130,f132]) ).
fof(f141,plain,
apply(sK13_skl,sK16_skl,sK15_skl),
inference(resolution,[status(thm)],[f131,f129]) ).
fof(f430,plain,
! [X0] :
( sK15_skl = sK16_skl
| ~ apply(sK13_skl,sK15_skl,sK16_skl)
| ~ member(sK16_skl,X0)
| ~ member(sK15_skl,X0)
| ~ sP0_prd(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f117,f141]) ).
fof(f448,plain,
! [X0] :
( sK15_skl = sK16_skl
| ~ member(sK16_skl,X0)
| ~ member(sK15_skl,X0)
| ~ sP0_prd(X0,sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f138]) ).
fof(f472,plain,
! [X0] :
( ~ member(sK16_skl,X0)
| ~ member(sK15_skl,X0)
| ~ sP0_prd(X0,sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f448,f110]) ).
fof(f473,plain,
( ~ member(sK16_skl,sK14_skl)
| ~ sP0_prd(sK14_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f472,f129]) ).
fof(f475,plain,
~ member(sK16_skl,sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f473,f128]) ).
fof(f481,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f475,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:43:58 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.063639 seconds
% 0.12/0.41 % CPU time: 0.207033 seconds
% 0.12/0.41 % Total memory used: 84.143 MB
% 0.12/0.41 % Net memory used: 83.871 MB
%------------------------------------------------------------------------------