%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET798+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 : n008.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 10.52s 1.86s
% Output : CNFRefutation 10.52s
% 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(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(thIV10,conjecture,
! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
file('theBenchmark.p',thIV10) ).
fof(thIV10_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X,Y] :
( ( subset(X,Y)
& subset(Y,E)
& subset(X,E) )
=> ! [M] :
( lower_bound(M,R,Y)
=> lower_bound(M,R,X) ) ) ),
inference(assume_negation,[status(cth)],[thIV10]) ).
fof(nnf_22,plain,
? [R,E] :
( ? [X,Y] :
( ? [M] :
( ~ lower_bound(M,R,X)
& lower_bound(M,R,Y) )
& subset(X,Y)
& subset(Y,E)
& subset(X,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV10_neg]) ).
fof(sk_thIV10_neg,plain,
( ~ lower_bound(sK3,sK4,sK0)
& lower_bound(sK3,sK4,sK1)
& subset(sK0,sK1)
& subset(sK1,sK5)
& subset(sK0,sK5)
& order(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK0,sK1,sK3]),skolemize(R,sK4),skolemize(E,sK5),skolemize(X,sK0),skolemize(Y,sK1),skolemize(M,sK3)],[nnf_22]) ).
cnf(c_29,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV10_neg]) ).
cnf(c_33,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset]) ).
cnf(c_638,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_33,c_29]) ).
fof(nnf_15,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ( ! [X0] :
( apply(R,M,X0)
| ~ member(X0,E) )
| ~ lower_bound(M,R,E) ) ),
inference(fof_nnf,[status(thm)],[lower_bound]) ).
fof(sk_lower_bound_sk,plain,
! [R,E,M] :
( ( ( ~ apply(R,M,sK2(R,E,M))
& member(sK2(R,E,M),E) )
| lower_bound(M,R,E) )
& ( ! [X0] :
( apply(R,M,X0)
| ~ member(X0,E) )
| ~ lower_bound(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X,sK2(R,E,M))],[nnf_15]) ).
fof(sk_lower_bound,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ apply(VAR_1,VAR_0,sK2(VAR_1,VAR_2,VAR_0))
| lower_bound(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(sK2(VAR_1,VAR_2,VAR_0),VAR_2)
| lower_bound(VAR_0,VAR_1,VAR_2) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( apply(VAR_1,VAR_0,VAR_3)
| ~ member(VAR_3,VAR_2)
| ~ lower_bound(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_lower_bound_sk]) ).
cnf(c_673,plain,
( apply(B,A,D)
| ~ member(D,C)
| ~ lower_bound(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_lower_bound]) ).
cnf(c_674,plain,
( member(sK2(B,C,A),C)
| lower_bound(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_lower_bound]) ).
cnf(c_675,plain,
( ~ apply(B,A,sK2(B,C,A))
| lower_bound(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_lower_bound]) ).
cnf(c_676,negated_conjecture,
lower_bound(sK3,sK4,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV10_neg]) ).
cnf(c_677,negated_conjecture,
~ lower_bound(sK3,sK4,sK0),
inference(split_conjunct,[status(thm)],[sk_thIV10_neg]) ).
cnf(c_2006,plain,
( apply(sK4,sK3,A)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_676,c_673]) ).
cnf(c_2007,plain,
member(sK2(sK4,sK0,sK3),sK0),
inference(resolve,[status(thm)],[c_677,c_674]) ).
cnf(c_3429,plain,
member(sK2(sK4,sK0,sK3),sK1),
inference(resolve,[status(thm)],[c_2007,c_638]) ).
cnf(c_3578,plain,
apply(sK4,sK3,sK2(sK4,sK0,sK3)),
inference(resolve,[status(thm)],[c_3429,c_2006]) ).
cnf(c_4237,plain,
lower_bound(sK3,sK4,sK0),
inference(resolve,[status(thm)],[c_3578,c_675]) ).
cnf(c_4236,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_677,c_4237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET798+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n008.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:17:24 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3182778 was started by sandbox on n008,
% 0.19/0.45 % Sat Sep 26 08:17:24 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 10.52/1.86
% 10.52/1.86 % given #500 (I,wt=57): 889 -member(f5(A,B),B) | -member(f6(A,B),B) | apply(A,f5(A,B),f6(A,B)) | apply(A,f6(A,B),f5(A,B)) | -apply(A,f11(A,B),f10(A,B)) | -apply(A,f4(A,B),f4(A,B)) | member(f7(A,B),B). [factor(432,c,g)].
% 10.52/1.86
% 10.52/1.86 % SZS status Theorem for theBenchmark
% 10.52/1.86
% 10.52/1.86 % Proof 1 at 1.25 (+ 0.10) seconds.
% 10.52/1.86 % Length of proof is 16.
% 10.52/1.86 % Level of proof is 5.
% 10.52/1.86 % Maximum clause weight is 21.000.
% 10.52/1.86 % Given clauses 708.
% 10.52/1.86
% 10.52/1.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------