%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET797+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 : n026.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 11.75s 1.98s
% Output : CNFRefutation 11.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 68 ( 20 ~; 18 |; 20 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 35 !; 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(thIV9,conjecture,
! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( upper_bound(M,R,Y)
=> upper_bound(M,R,X) ) ) ),
file('theBenchmark.p',thIV9) ).
fof(thIV9_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( upper_bound(M,R,Y)
=> upper_bound(M,R,X) ) ) ),
inference(assume_negation,[status(cth)],[thIV9]) ).
fof(nnf_22,plain,
? [R,E] :
( ? [X,Y] :
( ? [M] :
( ~ upper_bound(M,R,X)
& upper_bound(M,R,Y) )
& subset(X,Y)
& subset(Y,E)
& subset(X,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV9_neg]) ).
fof(sk_thIV9_neg,plain,
( ~ upper_bound(sK2,sK3,sK0)
& upper_bound(sK2,sK3,sK1)
& subset(sK0,sK1)
& subset(sK1,sK5)
& subset(sK0,sK5)
& order(sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK5,sK0,sK1,sK2]),skolemize(R,sK3),skolemize(E,sK5),skolemize(X,sK0),skolemize(Y,sK1),skolemize(M,sK2)],[nnf_22]) ).
cnf(c_29,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV9_neg]) ).
cnf(c_33,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset]) ).
cnf(c_577,negated_conjecture,
~ upper_bound(sK2,sK3,sK0),
inference(split_conjunct,[status(thm)],[sk_thIV9_neg]) ).
cnf(c_578,negated_conjecture,
upper_bound(sK2,sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV9_neg]) ).
fof(nnf_14,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,X,M)
& member(X,E) )
| upper_bound(M,R,E) )
& ( ! [X0] :
( apply(R,X0,M)
| ~ member(X0,E) )
| ~ upper_bound(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[upper_bound]) ).
fof(sk_upper_bound_sk,plain,
! [R,E,M] :
( ( ( ~ apply(R,sK4(R,E,M),M)
& member(sK4(R,E,M),E) )
| upper_bound(M,R,E) )
& ( ! [X0] :
( apply(R,X0,M)
| ~ member(X0,E) )
| ~ upper_bound(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X,sK4(R,E,M))],[nnf_14]) ).
fof(sk_upper_bound,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ apply(VAR_1,sK4(VAR_1,VAR_2,VAR_0),VAR_0)
| upper_bound(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(sK4(VAR_1,VAR_2,VAR_0),VAR_2)
| upper_bound(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( apply(VAR_1,VAR_3,VAR_0)
| ~ member(VAR_3,VAR_2)
| ~ upper_bound(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_upper_bound_sk]) ).
cnf(c_579,plain,
( ~ apply(B,sK4(B,C,A),A)
| upper_bound(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_upper_bound]) ).
cnf(c_580,plain,
( member(sK4(B,C,A),C)
| upper_bound(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_upper_bound]) ).
cnf(c_581,plain,
( apply(B,D,A)
| ~ member(D,C)
| ~ upper_bound(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_upper_bound]) ).
cnf(c_613,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
cnf(c_1075,plain,
member(sK4(sK3,sK0,sK2),sK0),
inference(resolve,[status(thm)],[c_580,c_577]) ).
cnf(c_1077,plain,
( apply(sK3,A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_581,c_578]) ).
cnf(c_1648,plain,
member(sK4(sK3,sK0,sK2),sK1),
inference(resolve,[status(thm)],[c_1075,c_613]) ).
cnf(c_2187,plain,
apply(sK3,sK4(sK3,sK0,sK2),sK2),
inference(resolve,[status(thm)],[c_1648,c_1077]) ).
cnf(c_2385,plain,
upper_bound(sK2,sK3,sK0),
inference(resolve,[status(thm)],[c_2187,c_579]) ).
cnf(c_2384,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_577,c_2385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET797+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:19:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 528506 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 08:19:10 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 11.75/1.98
% 11.75/1.98 % given #500 (I,wt=59): 887 -apply(A,f4(A,B),f4(A,B)) | apply(A,f5(A,B),f6(A,B)) | apply(A,f8(A,B),f9(A,B)) | -member(f8(A,B),B) | -member(C,B) | -member(f9(A,B),B) | -apply(A,f8(A,B),C) | -apply(A,C,f9(A,B)). [factor(438,c,i)].
% 11.75/1.98
% 11.75/1.98 % SZS status Theorem for theBenchmark
% 11.75/1.98
% 11.75/1.98 % Proof 1 at 1.39 (+ 0.13) seconds.
% 11.75/1.98 % Length of proof is 16.
% 11.75/1.98 % Level of proof is 5.
% 11.75/1.98 % Maximum clause weight is 21.000.
% 11.75/1.98 % Given clauses 703.
% 11.75/1.98
% 11.75/1.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------