%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET792+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 : n006.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 5.27s 1.12s
% Output : Proof 5.27s
% 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 : 93 ( 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] :
( ( least(M,R,E)
& order(R,E) )
=> min(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV4) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> min(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E,M] :
( ~ min(M,R,E)
& least(M,R,E)
& order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ min(sk18,sk16,sk17)
& least(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(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(p109,plain,
member(sk18,sk17),
inference(resolution,[status(thm)],[c79,c106]) ).
cnf(p397,plain,
( sk18 = X0
| ~ apply(sk16,X0,sk18)
| ~ apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p110,p109]) ).
fof(f7,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( ( apply(R,X,M)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',min) ).
fof(f7_nnf,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)],[f7]) ).
fof(f7_sk,plain,
! [M,R,E,X] :
( ( ( M != sk13(R,E,M)
& apply(R,sk13(R,E,M),M)
& member(sk13(R,E,M),E) )
| ~ member(M,E)
| min(M,R,E) )
& ( ( ( M = X
| ~ apply(R,X,M)
| ~ member(X,E) )
& member(M,E) )
| ~ min(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f7_nnf]) ).
cnf(c90,plain,
( member(sk13(X0,X1,X2),X1)
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p194,plain,
( member(sk13(X0,sk17,sk18),sk17)
| min(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c90,p109]) ).
cnf(p433,plain,
( min(sk18,X0,sk17)
| sk18 = sk13(X0,sk17,sk18)
| ~ apply(sk16,sk13(X0,sk17,sk18),sk18)
| ~ apply(sk16,sk18,sk13(X0,sk17,sk18)) ),
inference(resolution,[status(thm)],[p397,p194]) ).
cnf(c80,plain,
( apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p122,plain,
( apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c80,c106]) ).
cnf(p215,plain,
( apply(sk16,sk18,sk13(X0,sk17,sk18))
| min(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[p194,p122]) ).
cnf(p1523,plain,
( min(sk18,X0,sk17)
| min(sk18,X0,sk17)
| sk18 = sk13(X0,sk17,sk18)
| ~ apply(sk16,sk13(X0,sk17,sk18),sk18) ),
inference(resolution,[status(thm)],[p433,p215]) ).
cnf(p1524,plain,
( min(sk18,X0,sk17)
| sk18 = sk13(X0,sk17,sk18)
| ~ apply(sk16,sk13(X0,sk17,sk18),sk18) ),
inference(factoring,[status(thm)],[p1523]) ).
cnf(c91,plain,
( apply(X0,sk13(X0,X1,X2),X2)
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p283,plain,
( apply(X0,sk13(X0,sk17,sk18),sk18)
| min(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c91,p109]) ).
cnf(p1525,plain,
( min(sk18,sk16,sk17)
| min(sk18,sk16,sk17)
| sk18 = sk13(sk16,sk17,sk18) ),
inference(resolution,[status(thm)],[p1524,p283]) ).
cnf(p1550,plain,
( min(sk18,sk16,sk17)
| sk18 = sk13(sk16,sk17,sk18) ),
inference(factoring,[status(thm)],[p1525]) ).
cnf(c92,plain,
( X2 != sk13(X0,X1,X2)
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p221,plain,
( sk18 != sk13(X0,sk17,sk18)
| min(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c92,p109]) ).
cnf(p1551,plain,
( min(sk18,sk16,sk17)
| min(sk18,sk16,sk17) ),
inference(resolution,[status(thm)],[p1550,p221]) ).
cnf(p1552,plain,
min(sk18,sk16,sk17),
inference(factoring,[status(thm)],[p1551]) ).
cnf(c107,plain,
~ min(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p1553,plain,
$false,
inference(resolution,[status(thm)],[p1552,c107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 11:58:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.27/1.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.27/1.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------