%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET790+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 : n026.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 4.36s 1.18s
% Output : Proof 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 145 ( 16 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 176 ( 60 ~; 56 |; 48 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 1 sgn 41 !; 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] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV2) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E,M] :
( ? [X] :
( M != X
& least(X,R,E) )
& least(M,R,E)
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( sk18 != sk19
& least(sk19,sk16,sk17)
& least(sk18,sk16,sk17)
& order(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18,sk19])],[f10_nnf]) ).
cnf(c105,plain,
order(sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p112,plain,
( X0 = X1
| ~ apply(sk16,X1,X0)
| ~ apply(sk16,X0,X1)
| ~ member(X1,sk17)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c1,c105]) ).
fof(f5,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
fof(f5_nnf,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)],[f5]) ).
fof(f5_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,M,sk11(R,E,M))
& member(sk11(R,E,M),E) )
| ~ member(M,E)
| least(M,R,E) )
& ( ( ( apply(R,M,X)
| ~ member(X,E) )
& member(M,E) )
| ~ least(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f5_nnf]) ).
cnf(c79,plain,
( member(X2,X1)
| ~ least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(c106,plain,
least(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p110,plain,
member(sk18,sk17),
inference(resolution,[status(thm)],[c79,c106]) ).
cnf(p489,plain,
( sk18 = X0
| ~ apply(sk16,X0,sk18)
| ~ apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p112,p110]) ).
cnf(c107,plain,
least(sk19,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p111,plain,
member(sk19,sk17),
inference(resolution,[status(thm)],[c79,c107]) ).
cnf(p517,plain,
( sk18 = sk19
| ~ apply(sk16,sk19,sk18)
| ~ apply(sk16,sk18,sk19) ),
inference(resolution,[status(thm)],[p489,p111]) ).
cnf(c80,plain,
( apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p125,plain,
( apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c80,c106]) ).
cnf(p127,plain,
apply(sk16,sk18,sk19),
inference(resolution,[status(thm)],[p125,p111]) ).
cnf(p544,plain,
( sk18 = sk19
| ~ apply(sk16,sk19,sk18) ),
inference(resolution,[status(thm)],[p517,p127]) ).
cnf(p126,plain,
( apply(sk16,sk19,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c80,c107]) ).
cnf(p135,plain,
apply(sk16,sk19,sk18),
inference(resolution,[status(thm)],[p126,p110]) ).
cnf(p545,plain,
sk18 = sk19,
inference(resolution,[status(thm)],[p544,p135]) ).
cnf(c108,plain,
sk18 != sk19,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p546,plain,
$false,
inference(resolution,[status(thm)],[p545,c108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.40 % Computer : n026.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Thu Sep 24 12:01:09 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.36/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------