%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET804+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 : n004.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 02:10:39 PM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 133 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 149 ( 53 ~; 44 |; 42 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 93 ( 77 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
=> ~ ? [M] : least(M,R,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
=> ~ ? [M] : least(M,R,E) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
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(f80,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| ~ min(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f105,plain,
? [R,E] :
( ? [M1,M2] :
( ? [M] : least(M,R,E)
& M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f106,plain,
? [R,E] :
( ? [M] : least(M,R,E)
& ? [M1,M2] :
( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
& order(R,E) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
( least(sK17_skl,sK13_skl,sK14_skl)
& sK15_skl != sK16_skl
& min(sK16_skl,sK13_skl,sK14_skl)
& min(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,sK17_skl]),skolemize(R,sK13_skl),skolemize(E,sK14_skl),skolemize(M1,sK15_skl),skolemize(M2,sK16_skl),skolemize(M,sK17_skl)],[f106]) ).
fof(f109,plain,
min(sK15_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
min(sK16_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
sK15_skl != sK16_skl,
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
least(sK17_skl,sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f131,plain,
member(sK15_skl,sK14_skl),
inference(resolution,[status(thm)],[f80,f109]) ).
fof(f132,plain,
member(sK16_skl,sK14_skl),
inference(resolution,[status(thm)],[f110,f80]) ).
fof(f138,plain,
! [X0] :
( apply(sK13_skl,sK17_skl,X0)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f112,f64]) ).
fof(f139,plain,
member(sK17_skl,sK14_skl),
inference(resolution,[status(thm)],[f112,f63]) ).
fof(f140,plain,
apply(sK13_skl,sK17_skl,sK16_skl),
inference(resolution,[status(thm)],[f138,f132]) ).
fof(f141,plain,
apply(sK13_skl,sK17_skl,sK15_skl),
inference(resolution,[status(thm)],[f138,f131]) ).
fof(f144,plain,
! [X0] :
( sK16_skl = X0
| ~ apply(sK13_skl,X0,sK16_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f81,f110]) ).
fof(f145,plain,
! [X0] :
( sK15_skl = X0
| ~ apply(sK13_skl,X0,sK15_skl)
| ~ member(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f81,f109]) ).
fof(f146,plain,
( sK16_skl = sK17_skl
| ~ member(sK17_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f144,f140]) ).
fof(f147,plain,
sK16_skl = sK17_skl,
inference(forward_subsumption_resolution,[status(thm)],[f146,f139]) ).
fof(f148,plain,
( sK15_skl = sK17_skl
| ~ member(sK17_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f141,f145]) ).
fof(f150,plain,
sK15_skl = sK17_skl,
inference(forward_subsumption_resolution,[status(thm)],[f148,f139]) ).
fof(f156,plain,
sK15_skl = sK16_skl,
inference(forward_demodulation,[status(thm)],[f147,f150]) ).
fof(f157,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f156,f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.40 % Computer : n004.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Mon Sep 21 05:38:55 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.42 % Drodi V4.1.1
% 0.14/5.45 % Refutation found
% 0.14/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/5.51 % Elapsed time: 0.094767 seconds
% 0.18/5.51 % CPU time: 0.103892 seconds
% 0.18/5.51 % Total memory used: 5.225 MB
% 0.18/5.51 % Net memory used: 5.215 MB
%------------------------------------------------------------------------------