%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET804+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 : n020.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 6.63s 1.37s
% Output : CNFRefutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 69 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 63 ( 24 ~; 16 |; 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(least,axiom,
! [R,E,M] :
( least(M,R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,M,X) )
& member(M,E) ) ),
file('theBenchmark.p',least) ).
fof(min,axiom,
! [R,E,M] :
( min(M,R,E)
<=> ( ! [X] :
( ( apply(R,X,M)
& member(X,E) )
=> M = X )
& member(M,E) ) ),
file('theBenchmark.p',min) ).
fof(thIV16,conjecture,
! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
=> ~ ? [M] : least(M,R,E) ) ),
file('theBenchmark.p',thIV16) ).
fof(thIV16_neg,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [M1,M2] :
( ( M1 != M2
& min(M2,R,E)
& min(M1,R,E) )
=> ~ ? [M] : least(M,R,E) ) ),
inference(assume_negation,[status(cth)],[thIV16]) ).
cnf(c_332,plain,
( apply(B,A,D)
| ~ member(D,C)
| ~ least(A,B,C) ),
inference(clausify,[status(thm)],[least]) ).
fof(nnf_11,plain,
? [R,E] :
( ? [M1,M2] :
( ? [M] : least(M,R,E)
& M2 != M1
& min(M2,R,E)
& min(M1,R,E) )
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV16_neg]) ).
fof(sk_thIV16_neg,plain,
( least(sK0,sK1,sK2)
& sK4 != sK3
& min(sK4,sK1,sK2)
& min(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_335,negated_conjecture,
least(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV16_neg]) ).
cnf(c_336,plain,
( member(A,C)
| ~ least(A,B,C) ),
inference(clausify,[status(thm)],[least]) ).
cnf(c_342,plain,
( A = D
| ~ apply(B,D,A)
| ~ member(D,C)
| ~ min(A,B,C) ),
inference(clausify,[status(thm)],[min]) ).
cnf(c_346,negated_conjecture,
min(sK3,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV16_neg]) ).
cnf(c_347,negated_conjecture,
min(sK4,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_thIV16_neg]) ).
cnf(c_348,plain,
( member(A,C)
| ~ min(A,B,C) ),
inference(clausify,[status(thm)],[min]) ).
cnf(c_558,negated_conjecture,
sK4 != sK3,
inference(split_conjunct,[status(thm)],[sk_thIV16_neg]) ).
cnf(c_808,negated_conjecture,
( apply(sK1,sK0,A)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_332,c_335]) ).
cnf(c_809,negated_conjecture,
member(sK0,sK2),
inference(resolve,[status(thm)],[c_336,c_335]) ).
cnf(c_814,negated_conjecture,
( sK3 = A
| ~ apply(sK1,A,sK3)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_342,c_346]) ).
cnf(c_815,negated_conjecture,
( sK4 = A
| ~ apply(sK1,A,sK4)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_342,c_347]) ).
cnf(c_816,negated_conjecture,
member(sK3,sK2),
inference(resolve,[status(thm)],[c_348,c_346]) ).
cnf(c_817,negated_conjecture,
member(sK4,sK2),
inference(resolve,[status(thm)],[c_348,c_347]) ).
cnf(c_1190,plain,
apply(sK1,sK0,sK3),
inference(resolve,[status(thm)],[c_816,c_808]) ).
cnf(c_1274,plain,
apply(sK1,sK0,sK4),
inference(resolve,[status(thm)],[c_817,c_808]) ).
cnf(c_2392,negated_conjecture,
( sK3 = sK0
| ~ member(sK0,sK2) ),
inference(resolve,[status(thm)],[c_1190,c_814]) ).
cnf(c_2393,negated_conjecture,
( sK0 = sK3
| ~ member(sK0,sK2) ),
inference(copy,[status(thm)],[c_2392]) ).
cnf(c_2143,negated_conjecture,
sK0 = sK3,
inference(resolve,[status(thm)],[c_809,c_2393]) ).
cnf(c_2394,negated_conjecture,
( sK4 = sK0
| ~ member(sK0,sK2) ),
inference(resolve,[status(thm)],[c_1274,c_815]) ).
cnf(c_2395,negated_conjecture,
( sK0 = sK4
| ~ member(sK0,sK2) ),
inference(copy,[status(thm)],[c_2394]) ).
cnf(c_2266,negated_conjecture,
sK0 = sK4,
inference(resolve,[status(thm)],[c_809,c_2395]) ).
cnf(c_2396,plain,
sK4 = sK3,
inference(paramod,[status(thm)],[c_2266,c_2143]) ).
cnf(c_2391,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_558,c_2396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n020.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Sat Sep 26 08:18:04 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 1064109 was started by sandbox2 on n020,
% 0.15/0.44 % Sat Sep 26 08:18:04 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.48
% 0.15/0.48 % From the command line: assign(max_seconds, 300).
% 6.63/1.37
% 6.63/1.37 % given #500 (I,wt=56): 868 member(f1(A,B),B) | apply(A,f3(A,B),f2(A,B)) | apply(A,f4(A,B),f5(A,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(494,b,i)].
% 6.63/1.37
% 6.63/1.37 % SZS status Theorem for theBenchmark
% 6.63/1.37
% 6.63/1.37 % Proof 1 at 0.80 (+ 0.07) seconds.
% 6.63/1.37 % Length of proof is 22.
% 6.63/1.37 % Level of proof is 5.
% 6.63/1.37 % Maximum clause weight is 15.000.
% 6.63/1.37 % Given clauses 664.
% 6.63/1.37
% 6.63/1.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------