%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 08:36:59 AM UTC 2026
% Result : Theorem 6.64s 1.37s
% Output : CNFRefutation 6.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 12 ~; 8 |; 21 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 47 ( 3 sgn 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(upper_bound,axiom,
! [R,E,M] :
( upper_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,X,M) ) ),
file('theBenchmark.p',upper_bound) ).
fof(least_upper_bound,axiom,
! [A,X,R,E] :
( least_upper_bound(A,X,R,E)
<=> ( ! [M] :
( ( upper_bound(M,R,X)
& member(M,E) )
=> apply(R,A,M) )
& upper_bound(A,R,X)
& member(A,X) ) ),
file('theBenchmark.p',least_upper_bound) ).
fof(thIV11,conjecture,
! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( least_upper_bound(M2,X2,R,E)
& least_upper_bound(M1,X1,R,E) )
=> apply(R,M1,M2) ) ) ),
file('theBenchmark.p',thIV11) ).
fof(thIV11_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( least_upper_bound(M2,X2,R,E)
& least_upper_bound(M1,X1,R,E) )
=> apply(R,M1,M2) ) ) ),
inference(assume_negation,[status(cth)],[thIV11]) ).
fof(nnf_22,plain,
? [R,E] :
( ? [X1,X2] :
( ? [M1,M2] :
( ~ apply(R,M1,M2)
& least_upper_bound(M2,X2,R,E)
& least_upper_bound(M1,X1,R,E) )
& subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV11_neg]) ).
fof(sk_thIV11_neg,plain,
( ~ apply(sK3,sK2,sK5)
& least_upper_bound(sK5,sK1,sK3,sK4)
& least_upper_bound(sK2,sK0,sK3,sK4)
& subset(sK0,sK1)
& subset(sK1,sK4)
& subset(sK0,sK4)
& order(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK0,sK1,sK2,sK5]),skolemize(R,sK3),skolemize(E,sK4),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(M1,sK2),skolemize(M2,sK5)],[nnf_22]) ).
cnf(c_29,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV11_neg]) ).
cnf(c_33,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset]) ).
cnf(c_370,plain,
( upper_bound(A,C,B)
| ~ least_upper_bound(A,B,C,D) ),
inference(clausify,[status(thm)],[least_upper_bound]) ).
cnf(c_371,plain,
( member(A,B)
| ~ least_upper_bound(A,B,C,D) ),
inference(clausify,[status(thm)],[least_upper_bound]) ).
cnf(c_374,negated_conjecture,
least_upper_bound(sK2,sK0,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_thIV11_neg]) ).
cnf(c_375,negated_conjecture,
least_upper_bound(sK5,sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_thIV11_neg]) ).
cnf(c_388,negated_conjecture,
upper_bound(sK5,sK3,sK1),
inference(resolve,[status(thm)],[c_375,c_370]) ).
cnf(c_390,negated_conjecture,
member(sK2,sK0),
inference(resolve,[status(thm)],[c_374,c_371]) ).
cnf(c_585,negated_conjecture,
~ apply(sK3,sK2,sK5),
inference(split_conjunct,[status(thm)],[sk_thIV11_neg]) ).
cnf(c_588,plain,
( apply(B,D,A)
| ~ member(D,C)
| ~ upper_bound(A,B,C) ),
inference(clausify,[status(thm)],[upper_bound]) ).
cnf(c_620,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_1222,plain,
( apply(sK3,A,sK5)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_588,c_388]) ).
cnf(c_1507,plain,
member(sK2,sK1),
inference(resolve,[status(thm)],[c_620,c_390]) ).
cnf(c_2189,plain,
apply(sK3,sK2,sK5),
inference(resolve,[status(thm)],[c_1222,c_1507]) ).
cnf(c_2188,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_585,c_2189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:16:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2620775 was started by sandbox on n014,
% 0.12/0.37 % Sat Sep 26 08:16:47 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 6.64/1.37
% 6.64/1.37 % given #500 (I,wt=53): 889 -apply(A,f4(A,B),f4(A,B)) | apply(A,f5(A,B),f6(A,B)) | -apply(A,f7(A,B),f9(A,B)) | -member(f7(A,B),B) | -member(f9(A,B),B) | -apply(A,f9(A,B),f7(A,B)) | f9(A,B) = f7(A,B). [factor(442,c,f)].
% 6.64/1.37
% 6.64/1.37 % SZS status Theorem for theBenchmark
% 6.64/1.37
% 6.64/1.37 % Proof 1 at 0.85 (+ 0.13) seconds.
% 6.64/1.37 % Length of proof is 18.
% 6.64/1.37 % Level of proof is 4.
% 6.64/1.37 % Maximum clause weight is 13.000.
% 6.64/1.37 % Given clauses 722.
% 6.64/1.37
% 6.64/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------