%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET803+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 7.15s 1.39s
% Output : CNFRefutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 67 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 24 ~; 15 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 40 ( 2 sgn 16 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(greatest,axiom,
! [R,E,M] :
( greatest(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,M) )
& member(M,E) ) ),
file('theBenchmark.p',greatest) ).
fof(max,axiom,
! [R,E,M] :
( max(M,R,E)
<=> ( ! [X] :
( ( apply(R,M,X)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('theBenchmark.p',max) ).
fof(thIV15,conjecture,
! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& max(M2,R,E)
& max(M1,R,E) )
=> ~ ? [M] : greatest(M,R,E) ) ),
file('theBenchmark.p',thIV15) ).
fof(thIV15_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& max(M2,R,E)
& max(M1,R,E) )
=> ~ ? [M] : greatest(M,R,E) ) ),
inference(assume_negation,[status(cth)],[thIV15]) ).
cnf(c_329,plain,
( apply(B,D,A)
| ~ member(D,C)
| ~ greatest(A,B,C) ),
inference(clausify,[status(thm)],[greatest]) ).
cnf(c_330,plain,
( member(A,C)
| ~ greatest(A,B,C) ),
inference(clausify,[status(thm)],[greatest]) ).
fof(nnf_11,plain,
? [R,E] :
( ? [M1,M2] :
( ? [M] : greatest(M,R,E)
& M2 != M1
& max(M2,R,E)
& max(M1,R,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV15_neg]) ).
fof(sk_thIV15_neg,plain,
( greatest(sK0,sK1,sK2)
& sK4 != sK3
& max(sK4,sK1,sK2)
& max(sK3,sK1,sK2)
& order(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK0]),skolemize(R,sK1),skolemize(E,sK2),skolemize(M1,sK3),skolemize(M2,sK4),skolemize(M,sK0)],[nnf_11]) ).
cnf(c_332,negated_conjecture,
greatest(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV15_neg]) ).
cnf(c_338,plain,
( A = D
| ~ apply(B,A,D)
| ~ member(D,C)
| ~ max(A,B,C) ),
inference(clausify,[status(thm)],[max]) ).
cnf(c_339,plain,
( member(A,C)
| ~ max(A,B,C) ),
inference(clausify,[status(thm)],[max]) ).
cnf(c_342,negated_conjecture,
max(sK3,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV15_neg]) ).
cnf(c_343,negated_conjecture,
max(sK4,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV15_neg]) ).
cnf(c_369,negated_conjecture,
member(sK4,sK2),
inference(resolve,[status(thm)],[c_343,c_339]) ).
cnf(c_370,negated_conjecture,
( sK4 = A
| ~ apply(sK1,sK4,A)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_343,c_338]) ).
cnf(c_371,negated_conjecture,
member(sK3,sK2),
inference(resolve,[status(thm)],[c_342,c_339]) ).
cnf(c_372,negated_conjecture,
( sK3 = A
| ~ apply(sK1,sK3,A)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_342,c_338]) ).
cnf(c_377,negated_conjecture,
member(sK0,sK2),
inference(resolve,[status(thm)],[c_332,c_330]) ).
cnf(c_378,negated_conjecture,
( apply(sK1,A,sK0)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_332,c_329]) ).
cnf(c_564,negated_conjecture,
sK4 != sK3,
inference(split_conjunct,[status(thm)],[sk_thIV15_neg]) ).
cnf(c_1057,negated_conjecture,
( sK4 = sK3
| ~ apply(sK1,sK4,sK3) ),
inference(resolve,[status(thm)],[c_371,c_370]) ).
cnf(c_1026,negated_conjecture,
~ apply(sK1,sK4,sK3),
inference(resolve,[status(thm)],[c_564,c_1057]) ).
cnf(c_1058,negated_conjecture,
( sK3 = sK0
| ~ apply(sK1,sK3,sK0) ),
inference(resolve,[status(thm)],[c_377,c_372]) ).
cnf(c_1048,negated_conjecture,
( sK0 = sK3
| ~ apply(sK1,sK3,sK0) ),
inference(copy,[status(thm)],[c_1058]) ).
cnf(c_1053,plain,
apply(sK1,sK3,sK0),
inference(resolve,[status(thm)],[c_378,c_371]) ).
cnf(c_1054,plain,
apply(sK1,sK4,sK0),
inference(resolve,[status(thm)],[c_378,c_369]) ).
cnf(c_1055,negated_conjecture,
sK0 = sK3,
inference(resolve,[status(thm)],[c_1053,c_1048]) ).
cnf(c_1059,plain,
apply(sK1,sK4,sK3),
inference(paramod,[status(thm)],[c_1055,c_1054]) ).
cnf(c_1056,plain,
$false,
inference(resolve,[status(thm)],[c_1026,c_1059]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET803+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 08:16:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 16248 was started by sandbox2 on n011,
% 0.11/0.37 % Sat Sep 26 08:16:59 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 7.15/1.39
% 7.15/1.39 % SZS status Theorem for theBenchmark
% 7.15/1.39
% 7.15/1.39 % Proof 1 at 0.92 (+ 0.04) seconds.
% 7.15/1.39 % Length of proof is 23.
% 7.15/1.39 % Level of proof is 5.
% 7.15/1.39 % Maximum clause weight is 15.000.
% 7.15/1.39 % Given clauses 11.
% 7.15/1.39
% 7.15/1.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------