%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET789+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 : n003.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 08:36:58 AM UTC 2026
% Result : Theorem 3.87s 1.05s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 78 ( 14 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 79 ( 28 ~; 23 |; 16 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 39 ( 1 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(order,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,X)
& apply(R,X,Y) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('theBenchmark.p',order) ).
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(thIV1,conjecture,
! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> ! [X] :
( greatest(X,R,E)
=> M = X ) ),
file('theBenchmark.p',thIV1) ).
fof(thIV1_neg,negated_conjecture,
~ ! [R,E,M] :
( ( greatest(M,R,E)
& order(R,E) )
=> ! [X] :
( greatest(X,R,E)
=> M = X ) ),
inference(assume_negation,[status(cth)],[thIV1]) ).
cnf(c_14,plain,
( D = C
| ~ apply(A,D,C)
| ~ apply(A,C,D)
| ~ member(D,B)
| ~ member(C,B)
| ~ order(A,B) ),
inference(clausify,[status(thm)],[order]) ).
fof(nnf_11,plain,
? [R,E,M] :
( ? [X] :
( M != X
& greatest(X,R,E) )
& greatest(M,R,E)
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV1_neg]) ).
fof(sk_thIV1_neg,plain,
( sK2 != sK3
& greatest(sK3,sK0,sK1)
& greatest(sK2,sK0,sK1)
& order(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(R,sK0),skolemize(E,sK1),skolemize(M,sK2),skolemize(X,sK3)],[nnf_11]) ).
cnf(c_80,negated_conjecture,
order(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV1_neg]) ).
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]) ).
cnf(c_332,negated_conjecture,
greatest(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV1_neg]) ).
cnf(c_333,negated_conjecture,
greatest(sK3,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV1_neg]) ).
cnf(c_372,negated_conjecture,
member(sK3,sK1),
inference(resolve,[status(thm)],[c_333,c_330]) ).
cnf(c_373,negated_conjecture,
( apply(sK0,A,sK3)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_333,c_329]) ).
cnf(c_374,negated_conjecture,
member(sK2,sK1),
inference(resolve,[status(thm)],[c_332,c_330]) ).
cnf(c_375,negated_conjecture,
( apply(sK0,A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_332,c_329]) ).
cnf(c_379,negated_conjecture,
( B = A
| ~ apply(sK0,B,A)
| ~ apply(sK0,A,B)
| ~ member(B,sK1)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_80,c_14]) ).
cnf(c_561,negated_conjecture,
sK2 != sK3,
inference(split_conjunct,[status(thm)],[sk_thIV1_neg]) ).
cnf(c_562,negated_conjecture,
sK3 != sK2,
inference(copy,[status(thm)],[c_561]) ).
cnf(c_1031,plain,
apply(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_374,c_373]) ).
cnf(c_1041,plain,
apply(sK0,sK3,sK2),
inference(resolve,[status(thm)],[c_375,c_372]) ).
cnf(c_2485,negated_conjecture,
( sK2 = sK3
| ~ apply(sK0,sK3,sK2)
| ~ member(sK2,sK1)
| ~ member(sK3,sK1) ),
inference(resolve,[status(thm)],[c_1031,c_379]) ).
cnf(c_2486,negated_conjecture,
( sK3 = sK2
| ~ apply(sK0,sK3,sK2)
| ~ member(sK2,sK1)
| ~ member(sK3,sK1) ),
inference(copy,[status(thm)],[c_2485]) ).
cnf(c_2487,negated_conjecture,
( sK3 = sK2
| ~ apply(sK0,sK3,sK2)
| ~ member(sK2,sK1) ),
inference(resolve,[status(thm)],[c_372,c_2486]) ).
cnf(c_2488,negated_conjecture,
( sK3 = sK2
| ~ apply(sK0,sK3,sK2) ),
inference(resolve,[status(thm)],[c_374,c_2487]) ).
cnf(c_2489,negated_conjecture,
sK3 = sK2,
inference(resolve,[status(thm)],[c_1041,c_2488]) ).
cnf(c_2484,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_562,c_2489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET789+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 : n003.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 08:17:53 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.15/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.36 % Process 2418651 was started by sandbox2 on n003,
% 0.15/0.36 % Sat Sep 26 08:17:53 2026
% 0.15/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 3.87/1.05
% 3.87/1.05 % given #500 (I,wt=53): 868 member(f1(A,B),B) | apply(A,f3(A,B),f2(A,B)) | member(f6(A,B),B) | -member(f3(A,B),B) | -member(C,B) | -member(f2(A,B),B) | -apply(A,f3(A,B),C) | -apply(A,C,f2(A,B)). [factor(500,b,i)].
% 3.87/1.05
% 3.87/1.05 % SZS status Theorem for theBenchmark
% 3.87/1.05
% 3.87/1.05 % Proof 1 at 0.60 (+ 0.05) seconds.
% 3.87/1.05 % Length of proof is 19.
% 3.87/1.05 % Level of proof is 4.
% 3.87/1.05 % Maximum clause weight is 22.000.
% 3.87/1.05 % Given clauses 658.
% 3.87/1.05
% 3.87/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------