%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET803+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 : Fri Sep 25 02:43:58 PM UTC 2026
% Result : Theorem 5.19s 1.43s
% Output : Proof 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 102 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 110 ( 41 ~; 32 |; 29 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 58 ( 2 sgn 32 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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',max) ).
fof(f6_nnf,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)],[f6]) ).
fof(f6_sk,plain,
! [M,R,E,X] :
( ( ( M != sk12(R,E,M)
& apply(R,M,sk12(R,E,M))
& member(sk12(R,E,M),E) )
| ~ member(M,E)
| max(M,R,E) )
& ( ( ( M = X
| ~ apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ max(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f6_nnf]) ).
cnf(c84,plain,
( X2 = X3
| ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ max(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f10,conjecture,
! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& max(M2,R,E)
& max(M1,R,E) )
=> ~ ? [M] : greatest(M,R,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV15) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& max(M2,R,E)
& max(M1,R,E) )
=> ~ ? [M] : greatest(M,R,E) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E] :
( ? [M1,M2] :
( ? [M] : greatest(M,R,E)
& M1 != M2
& max(M2,R,E)
& max(M1,R,E) )
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( greatest(sk20,sk16,sk17)
& sk18 != sk19
& max(sk19,sk16,sk17)
& max(sk18,sk16,sk17)
& order(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18,sk19,sk20])],[f10_nnf]) ).
cnf(c107,plain,
max(sk19,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p1427,plain,
( sk19 = X0
| ~ apply(sk16,sk19,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c84,c107]) ).
cnf(c83,plain,
( member(X2,X1)
| ~ max(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c106,plain,
max(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p117,plain,
member(sk18,sk17),
inference(resolution,[status(thm)],[c83,c106]) ).
cnf(p2001,plain,
( sk19 = sk18
| ~ apply(sk16,sk19,sk18) ),
inference(resolution,[status(thm)],[p1427,p117]) ).
cnf(p1426,plain,
( sk18 = X0
| ~ apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c84,c106]) ).
fof(f4,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',greatest) ).
fof(f4_nnf,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)],[f4]) ).
fof(f4_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,sk10(R,E,M),M)
& member(sk10(R,E,M),E) )
| ~ member(M,E)
| greatest(M,R,E) )
& ( ( ( apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ greatest(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f4_nnf]) ).
cnf(c75,plain,
( member(X2,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c109,plain,
greatest(sk20,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p111,plain,
member(sk20,sk17),
inference(resolution,[status(thm)],[c75,c109]) ).
cnf(p1673,plain,
( sk18 = sk20
| ~ apply(sk16,sk18,sk20) ),
inference(resolution,[status(thm)],[p1426,p111]) ).
cnf(c76,plain,
( apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p921,plain,
( apply(sk16,X0,sk20)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c76,c109]) ).
cnf(p923,plain,
apply(sk16,sk18,sk20),
inference(resolution,[status(thm)],[p921,p117]) ).
cnf(p1694,plain,
sk18 = sk20,
inference(resolution,[status(thm)],[p1673,p923]) ).
cnf(p118,plain,
member(sk19,sk17),
inference(resolution,[status(thm)],[c83,c107]) ).
cnf(p924,plain,
apply(sk16,sk19,sk20),
inference(resolution,[status(thm)],[p921,p118]) ).
cnf(p1781,plain,
apply(sk16,sk19,sk18),
inference(superposition,[status(thm)],[p1694,p924]) ).
cnf(p2019,plain,
sk19 = sk18,
inference(resolution,[status(thm)],[p2001,p1781]) ).
cnf(c108,plain,
sk18 != sk19,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p2020,plain,
sk18 != sk18,
inference(demodulation,[status(thm)],[p2019,c108]) ).
cnf(p2036,plain,
$false,
inference(equality_resolution,[status(thm)],[p2020]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET803+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.66 % Computer : n007.cluster.edu
% 0.19/0.66 % Model : x86_64 x86_64
% 0.19/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.66 % Memory : 8046.5625MB
% 0.19/0.66 % OS : Linux 6.8.0-71-generic
% 0.19/0.66 % CPULimit : 300
% 0.19/0.66 % WCLimit : 300
% 0.19/0.66 % DateTime : Thu Sep 24 11:58:10 UTC 2026
% 0.19/0.67 % CPUTime :
% 0.19/0.67 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.19/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.19/1.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------