%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET791+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 : n019.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 02:43:57 PM UTC 2026
% Result : Theorem 2.34s 1.16s
% Output : Proof 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 6 unt; 0 def)
% Number of atoms : 190 ( 20 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 227 ( 75 ~; 84 |; 56 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 1 sgn 51 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,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',order) ).
fof(f0_nnf,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) )
| ? [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) )
| 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) ) )
| ~ order(R,E) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [R,E,X,Y,Z] :
( ( ( ~ apply(R,sk3(R,E),sk5(R,E))
& apply(R,sk4(R,E),sk5(R,E))
& apply(R,sk3(R,E),sk4(R,E))
& member(sk5(R,E),E)
& member(sk4(R,E),E)
& member(sk3(R,E),E) )
| ( sk1(R,E) != sk2(R,E)
& apply(R,sk2(R,E),sk1(R,E))
& apply(R,sk1(R,E),sk2(R,E))
& member(sk2(R,E),E)
& member(sk1(R,E),E) )
| ( ~ apply(R,sk0(R,E),sk0(R,E))
& member(sk0(R,E),E) )
| order(R,E) )
& ( ( ( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ( apply(R,X,X)
| ~ member(X,E) ) )
| ~ order(R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5])],[f0_nnf]) ).
cnf(c1,plain,
( X2 = X3
| ~ apply(X0,X3,X2)
| ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f10,conjecture,
! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> max(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV3) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> max(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E,M] :
( ~ max(M,R,E)
& greatest(M,R,E)
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ max(sk18,sk16,sk17)
& greatest(sk18,sk16,sk17)
& order(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18])],[f10_nnf]) ).
cnf(c105,plain,
order(sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p110,plain,
( X0 = X1
| ~ apply(sk16,X1,X0)
| ~ apply(sk16,X0,X1)
| ~ member(X1,sk17)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c1,c105]) ).
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(c106,plain,
greatest(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p109,plain,
member(sk18,sk17),
inference(resolution,[status(thm)],[c75,c106]) ).
cnf(p397,plain,
( sk18 = X0
| ~ apply(sk16,X0,sk18)
| ~ apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p110,p109]) ).
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(c85,plain,
( member(sk12(X0,X1,X2),X1)
| ~ member(X2,X1)
| max(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p160,plain,
( member(sk12(X0,sk17,sk18),sk17)
| max(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c85,p109]) ).
cnf(p430,plain,
( max(sk18,X0,sk17)
| sk18 = sk12(X0,sk17,sk18)
| ~ apply(sk16,sk12(X0,sk17,sk18),sk18)
| ~ apply(sk16,sk18,sk12(X0,sk17,sk18)) ),
inference(resolution,[status(thm)],[p397,p160]) ).
cnf(c86,plain,
( apply(X0,X2,sk12(X0,X1,X2))
| ~ member(X2,X1)
| max(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p268,plain,
( apply(X0,sk18,sk12(X0,sk17,sk18))
| max(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c86,p109]) ).
cnf(p1643,plain,
( max(sk18,sk16,sk17)
| max(sk18,sk16,sk17)
| sk18 = sk12(sk16,sk17,sk18)
| ~ apply(sk16,sk12(sk16,sk17,sk18),sk18) ),
inference(resolution,[status(thm)],[p430,p268]) ).
cnf(p1644,plain,
( max(sk18,sk16,sk17)
| sk18 = sk12(sk16,sk17,sk18)
| ~ apply(sk16,sk12(sk16,sk17,sk18),sk18) ),
inference(factoring,[status(thm)],[p1643]) ).
cnf(c76,plain,
( apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p122,plain,
( apply(sk16,X0,sk18)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c76,c106]) ).
cnf(p172,plain,
( apply(sk16,sk12(X0,sk17,sk18),sk18)
| max(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[p160,p122]) ).
cnf(p1672,plain,
( max(sk18,sk16,sk17)
| max(sk18,sk16,sk17)
| sk18 = sk12(sk16,sk17,sk18) ),
inference(resolution,[status(thm)],[p1644,p172]) ).
cnf(p1673,plain,
( max(sk18,sk16,sk17)
| sk18 = sk12(sk16,sk17,sk18) ),
inference(factoring,[status(thm)],[p1672]) ).
cnf(c87,plain,
( X2 != sk12(X0,X1,X2)
| ~ member(X2,X1)
| max(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p181,plain,
( sk18 != sk12(X0,sk17,sk18)
| max(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c87,p109]) ).
cnf(p1674,plain,
( max(sk18,sk16,sk17)
| max(sk18,sk16,sk17) ),
inference(resolution,[status(thm)],[p1673,p181]) ).
cnf(p1675,plain,
max(sk18,sk16,sk17),
inference(factoring,[status(thm)],[p1674]) ).
cnf(c107,plain,
~ max(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p1703,plain,
$false,
inference(resolution,[status(thm)],[p1675,c107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET791+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:58:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.34/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/1.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------