%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET800+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 : n010.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 8.63s 1.58s
% Output : CNFRefutation 8.63s
% 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(lower_bound,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('theBenchmark.p',lower_bound) ).
fof(greatest_lower_bound,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( ! [M] :
( ( lower_bound(M,R,X)
& member(M,E) )
=> apply(R,M,A) )
& lower_bound(A,R,X)
& member(A,X) ) ),
file('theBenchmark.p',greatest_lower_bound) ).
fof(thIV12,conjecture,
! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M2,X2,R,E)
& greatest_lower_bound(M1,X1,R,E) )
=> apply(R,M2,M1) ) ) ),
file('theBenchmark.p',thIV12) ).
fof(thIV12_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M2,X2,R,E)
& greatest_lower_bound(M1,X1,R,E) )
=> apply(R,M2,M1) ) ) ),
inference(assume_negation,[status(cth)],[thIV12]) ).
fof(nnf_22,plain,
? [R,E] :
( ? [X1,X2] :
( ? [M1,M2] :
( ~ apply(R,M2,M1)
& greatest_lower_bound(M2,X2,R,E)
& greatest_lower_bound(M1,X1,R,E) )
& subset(X1,X2)
& subset(X2,E)
& subset(X1,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV12_neg]) ).
fof(sk_thIV12_neg,plain,
( ~ apply(sK3,sK5,sK2)
& greatest_lower_bound(sK5,sK1,sK3,sK4)
& greatest_lower_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_thIV12_neg]) ).
cnf(c_33,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset]) ).
cnf(c_378,negated_conjecture,
greatest_lower_bound(sK2,sK0,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_thIV12_neg]) ).
cnf(c_379,negated_conjecture,
greatest_lower_bound(sK5,sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_thIV12_neg]) ).
cnf(c_380,plain,
( lower_bound(A,C,B)
| ~ greatest_lower_bound(A,B,C,D) ),
inference(clausify,[status(thm)],[greatest_lower_bound]) ).
cnf(c_381,plain,
( member(A,B)
| ~ greatest_lower_bound(A,B,C,D) ),
inference(clausify,[status(thm)],[greatest_lower_bound]) ).
cnf(c_383,negated_conjecture,
member(sK2,sK0),
inference(resolve,[status(thm)],[c_381,c_378]) ).
cnf(c_384,negated_conjecture,
lower_bound(sK5,sK3,sK1),
inference(resolve,[status(thm)],[c_380,c_379]) ).
cnf(c_646,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_681,plain,
( apply(B,A,D)
| ~ member(D,C)
| ~ lower_bound(A,B,C) ),
inference(clausify,[status(thm)],[lower_bound]) ).
cnf(c_684,negated_conjecture,
~ apply(sK3,sK5,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV12_neg]) ).
cnf(c_1289,plain,
member(sK2,sK1),
inference(resolve,[status(thm)],[c_646,c_383]) ).
cnf(c_2160,plain,
( apply(sK3,sK5,A)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_681,c_384]) ).
cnf(c_2890,plain,
apply(sK3,sK5,sK2),
inference(resolve,[status(thm)],[c_2160,c_1289]) ).
cnf(c_2889,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_684,c_2890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET800+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.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 : Sat Sep 26 08:17:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2884450 was started by sandbox on n010,
% 0.09/0.35 % Sat Sep 26 08:17:14 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 8.63/1.58
% 8.63/1.58 % given #500 (I,wt=56): 891 -member(f8(A,B),B) | -member(f9(A,B),B) | apply(A,f8(A,B),f9(A,B)) | apply(A,f9(A,B),f8(A,B)) | -apply(A,f11(A,B),f10(A,B)) | member(f4(A,B),B) | f6(A,B) != f5(A,B). [factor(426,c,h)].
% 8.63/1.58
% 8.63/1.58 % SZS status Theorem for theBenchmark
% 8.63/1.58
% 8.63/1.58 % Proof 1 at 0.98 (+ 0.10) seconds.
% 8.63/1.58 % Length of proof is 18.
% 8.63/1.58 % Level of proof is 4.
% 8.63/1.58 % Maximum clause weight is 16.000.
% 8.63/1.58 % Given clauses 706.
% 8.63/1.58
% 8.63/1.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------