%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET793+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 5.47s 1.19s
% Output : Proof 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 253 ( 15 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 293 ( 95 ~; 110 |; 72 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 134 ( 1 sgn 75 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [R,E] :
( total_order(R,E)
<=> ( ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( apply(R,Y,X)
| apply(R,X,Y) ) )
& order(R,E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_order) ).
fof(f1_nnf,plain,
! [R,E] :
( ( ? [X,Y] :
( ~ apply(R,Y,X)
& ~ apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ~ order(R,E)
| total_order(R,E) )
& ( ( ! [X,Y] :
( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [R,E,X,Y] :
( ( ( ~ apply(R,sk7(R,E),sk6(R,E))
& ~ apply(R,sk6(R,E),sk7(R,E))
& member(sk7(R,E),E)
& member(sk6(R,E),E) )
| ~ order(R,E)
| total_order(R,E) )
& ( ( ( apply(R,Y,X)
| apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& order(R,E) )
| ~ total_order(R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f1_nnf]) ).
cnf(c64,plain,
( apply(X0,X3,X2)
| apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ total_order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f10,conjecture,
! [R,E,M] :
( ( max(M,R,E)
& total_order(R,E) )
=> greatest(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV5) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E,M] :
( ( max(M,R,E)
& total_order(R,E) )
=> greatest(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E,M] :
( ~ greatest(M,R,E)
& max(M,R,E)
& total_order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ greatest(sk18,sk16,sk17)
& max(sk18,sk16,sk17)
& total_order(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18])],[f10_nnf]) ).
cnf(c105,plain,
total_order(sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p271,plain,
( apply(sk16,X1,X0)
| apply(sk16,X0,X1)
| ~ member(X1,sk17)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c64,c105]) ).
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(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(p110,plain,
member(sk18,sk17),
inference(resolution,[status(thm)],[c83,c106]) ).
cnf(p273,plain,
( apply(sk16,X0,sk18)
| apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p271,p110]) ).
fof(f2,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_bound) ).
fof(f2_nnf,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| upper_bound(M,R,E) )
& ( ! [X] :
( apply(R,X,M)
| ~ member(X,E) )
| ~ upper_bound(M,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,sk8(R,E,M),M)
& member(sk8(R,E,M),E) )
| upper_bound(M,R,E) )
& ( apply(R,X,M)
| ~ member(X,E)
| ~ upper_bound(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f2_nnf]) ).
cnf(c70,plain,
( member(sk8(X0,X1,X2),X1)
| upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p287,plain,
( upper_bound(X1,X0,sk17)
| apply(sk16,sk8(X0,sk17,X1),sk18)
| apply(sk16,sk18,sk8(X0,sk17,X1)) ),
inference(resolution,[status(thm)],[p273,c70]) ).
cnf(c71,plain,
( ~ apply(X0,sk8(X0,X1,X2),X2)
| upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p298,plain,
( upper_bound(sk18,sk16,sk17)
| upper_bound(sk18,sk16,sk17)
| apply(sk16,sk18,sk8(sk16,sk17,sk18)) ),
inference(resolution,[status(thm)],[p287,c71]) ).
cnf(p299,plain,
( upper_bound(sk18,sk16,sk17)
| apply(sk16,sk18,sk8(sk16,sk17,sk18)) ),
inference(factoring,[status(thm)],[p298]) ).
cnf(c84,plain,
( X2 = X3
| ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ max(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p256,plain,
( sk18 = X0
| ~ apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c84,c106]) ).
cnf(p258,plain,
( upper_bound(X1,X0,sk17)
| sk18 = sk8(X0,sk17,X1)
| ~ apply(sk16,sk18,sk8(X0,sk17,X1)) ),
inference(resolution,[status(thm)],[p256,c70]) ).
cnf(p300,plain,
( upper_bound(sk18,sk16,sk17)
| sk18 = sk8(sk16,sk17,sk18)
| upper_bound(sk18,sk16,sk17) ),
inference(resolution,[status(thm)],[p299,p258]) ).
cnf(p301,plain,
( sk18 = sk8(sk16,sk17,sk18)
| upper_bound(sk18,sk16,sk17) ),
inference(factoring,[status(thm)],[p300]) ).
cnf(p302,plain,
( ~ apply(sk16,sk18,sk18)
| upper_bound(sk18,sk16,sk17)
| upper_bound(sk18,sk16,sk17) ),
inference(superposition,[status(thm)],[p301,c71]) ).
cnf(p304,plain,
( ~ apply(sk16,sk18,sk18)
| upper_bound(sk18,sk16,sk17) ),
inference(factoring,[status(thm)],[p302]) ).
cnf(c63,plain,
( order(X0,X1)
| ~ total_order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p108,plain,
order(sk16,sk17),
inference(resolution,[status(thm)],[c63,c105]) ).
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(c0,plain,
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p109,plain,
( apply(sk16,X0,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p108,c0]) ).
cnf(p112,plain,
apply(sk16,sk18,sk18),
inference(resolution,[status(thm)],[p109,p110]) ).
cnf(p305,plain,
upper_bound(sk18,sk16,sk17),
inference(resolution,[status(thm)],[p304,p112]) ).
cnf(c69,plain,
( apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ upper_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p306,plain,
( apply(sk16,X0,sk18)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p305,c69]) ).
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(c77,plain,
( member(sk10(X0,X1,X2),X1)
| ~ member(X2,X1)
| greatest(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p119,plain,
( member(sk10(X0,sk17,sk18),sk17)
| greatest(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c77,p110]) ).
cnf(p312,plain,
( greatest(sk18,X0,sk17)
| apply(sk16,sk10(X0,sk17,sk18),sk18) ),
inference(resolution,[status(thm)],[p306,p119]) ).
cnf(c78,plain,
( ~ apply(X0,sk10(X0,X1,X2),X2)
| ~ member(X2,X1)
| greatest(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p197,plain,
( ~ apply(X0,sk10(X0,sk17,sk18),sk18)
| greatest(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c78,p110]) ).
cnf(p319,plain,
( greatest(sk18,sk16,sk17)
| greatest(sk18,sk16,sk17) ),
inference(resolution,[status(thm)],[p312,p197]) ).
cnf(p320,plain,
greatest(sk18,sk16,sk17),
inference(factoring,[status(thm)],[p319]) ).
cnf(c107,plain,
~ greatest(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p321,plain,
$false,
inference(resolution,[status(thm)],[p320,c107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET793+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:58:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.47/1.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.47/1.19 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------