%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET794+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 7.23s 1.45s
% Output : Proof 7.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 255 ( 17 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 295 ( 95 ~; 112 |; 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 : 138 ( 1 sgn 75 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(c89,plain,
( X2 = X3
| ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f10,conjecture,
! [R,E,M] :
( ( min(M,R,E)
& total_order(R,E) )
=> least(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV6) ).
fof(f10_neg,negated_conjecture,
~ ! [R,E,M] :
( ( min(M,R,E)
& total_order(R,E) )
=> least(M,R,E) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [R,E,M] :
( ~ least(M,R,E)
& min(M,R,E)
& total_order(R,E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ least(sk18,sk16,sk17)
& min(sk18,sk16,sk17)
& total_order(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18])],[f10_nnf]) ).
cnf(c106,plain,
min(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p1539,plain,
( sk18 = X0
| ~ apply(sk16,X0,sk18)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c89,c106]) ).
fof(f3,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).
fof(f3_nnf,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [M,R,E,X] :
( ( ( ~ apply(R,M,sk9(R,E,M))
& member(sk9(R,E,M),E) )
| lower_bound(M,R,E) )
& ( apply(R,M,X)
| ~ member(X,E)
| ~ lower_bound(M,R,E) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f3_nnf]) ).
cnf(c73,plain,
( member(sk9(X0,X1,X2),X1)
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p1547,plain,
( lower_bound(X1,X0,sk17)
| sk18 = sk9(X0,sk17,X1)
| ~ apply(sk16,sk9(X0,sk17,X1),sk18) ),
inference(resolution,[status(thm)],[p1539,c73]) ).
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]) ).
cnf(c105,plain,
total_order(sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p502,plain,
( apply(sk16,X1,X0)
| apply(sk16,X0,X1)
| ~ member(X1,sk17)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[c64,c105]) ).
cnf(c88,plain,
( member(X2,X1)
| ~ min(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p111,plain,
member(sk18,sk17),
inference(resolution,[status(thm)],[c88,c106]) ).
cnf(p503,plain,
( apply(sk16,X0,sk18)
| apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p502,p111]) ).
cnf(p722,plain,
( apply(sk16,sk9(X1,sk17,X0),sk18)
| apply(sk16,sk18,sk9(X1,sk17,X0))
| lower_bound(X0,X1,sk17) ),
inference(resolution,[status(thm)],[c73,p503]) ).
cnf(p1561,plain,
( apply(sk16,sk18,sk9(X0,sk17,X1))
| lower_bound(X1,X0,sk17)
| lower_bound(X1,X0,sk17)
| sk18 = sk9(X0,sk17,X1) ),
inference(resolution,[status(thm)],[p1547,p722]) ).
cnf(p2118,plain,
( apply(sk16,sk18,sk9(X0,sk17,X1))
| lower_bound(X1,X0,sk17)
| sk18 = sk9(X0,sk17,X1) ),
inference(factoring,[status(thm)],[p1561]) ).
cnf(c74,plain,
( ~ apply(X0,X2,sk9(X0,X1,X2))
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p2119,plain,
( lower_bound(sk18,sk16,sk17)
| lower_bound(sk18,sk16,sk17)
| sk18 = sk9(sk16,sk17,sk18) ),
inference(resolution,[status(thm)],[p2118,c74]) ).
cnf(p2120,plain,
( lower_bound(sk18,sk16,sk17)
| sk18 = sk9(sk16,sk17,sk18) ),
inference(factoring,[status(thm)],[p2119]) ).
cnf(p2123,plain,
( ~ apply(sk16,sk18,sk18)
| lower_bound(sk18,sk16,sk17)
| lower_bound(sk18,sk16,sk17) ),
inference(superposition,[status(thm)],[p2120,c74]) ).
cnf(p2128,plain,
( ~ apply(sk16,sk18,sk18)
| lower_bound(sk18,sk16,sk17) ),
inference(factoring,[status(thm)],[p2123]) ).
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)],[p111,p109]) ).
cnf(p2129,plain,
lower_bound(sk18,sk16,sk17),
inference(resolution,[status(thm)],[p2128,p112]) ).
cnf(c72,plain,
( apply(X0,X2,X3)
| ~ member(X3,X1)
| ~ lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p2130,plain,
( apply(sk16,sk18,X0)
| ~ member(X0,sk17) ),
inference(resolution,[status(thm)],[p2129,c72]) ).
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(c81,plain,
( member(sk11(X0,X1,X2),X1)
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p903,plain,
( member(sk11(X0,sk17,sk18),sk17)
| least(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c81,p111]) ).
cnf(p2170,plain,
( least(sk18,X0,sk17)
| apply(sk16,sk18,sk11(X0,sk17,sk18)) ),
inference(resolution,[status(thm)],[p2130,p903]) ).
cnf(c82,plain,
( ~ apply(X0,X2,sk11(X0,X1,X2))
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p1018,plain,
( ~ apply(X0,sk18,sk11(X0,sk17,sk18))
| least(sk18,X0,sk17) ),
inference(resolution,[status(thm)],[c82,p111]) ).
cnf(p2217,plain,
( least(sk18,sk16,sk17)
| least(sk18,sk16,sk17) ),
inference(resolution,[status(thm)],[p2170,p1018]) ).
cnf(p2218,plain,
least(sk18,sk16,sk17),
inference(factoring,[status(thm)],[p2217]) ).
cnf(c107,plain,
~ least(sk18,sk16,sk17),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p2219,plain,
$false,
inference(resolution,[status(thm)],[p2218,c107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n019.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 11:58:34 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.23/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.23/1.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------