%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET790+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 : 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 08:36:58 AM UTC 2026
% Result : Theorem 6.51s 1.24s
% Output : CNFRefutation 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 74 ( 13 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 73 ( 25 ~; 20 |; 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(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(thIV2,conjecture,
! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
file('theBenchmark.p',thIV2) ).
fof(thIV2_neg,negated_conjecture,
~ ! [R,E,M] :
( ( least(M,R,E)
& order(R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
inference(assume_negation,[status(cth)],[thIV2]) ).
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
& least(X,R,E) )
& least(M,R,E)
& order(R,E) ),
inference(fof_nnf,[status(thm)],[thIV2_neg]) ).
fof(sk_thIV2_neg,plain,
( sK2 != sK3
& least(sK3,sK0,sK1)
& least(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_thIV2_neg]) ).
cnf(c_332,plain,
( apply(B,A,D)
| ~ member(D,C)
| ~ least(A,B,C) ),
inference(clausify,[status(thm)],[least]) ).
cnf(c_335,negated_conjecture,
least(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV2_neg]) ).
cnf(c_336,negated_conjecture,
least(sK3,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIV2_neg]) ).
cnf(c_337,plain,
( member(A,C)
| ~ least(A,B,C) ),
inference(clausify,[status(thm)],[least]) ).
cnf(c_375,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_557,negated_conjecture,
sK2 != sK3,
inference(split_conjunct,[status(thm)],[sk_thIV2_neg]) ).
cnf(c_558,negated_conjecture,
sK3 != sK2,
inference(copy,[status(thm)],[c_557]) ).
cnf(c_808,negated_conjecture,
( apply(sK0,sK2,A)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_332,c_335]) ).
cnf(c_809,negated_conjecture,
( apply(sK0,sK3,A)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_332,c_336]) ).
cnf(c_810,negated_conjecture,
member(sK2,sK1),
inference(resolve,[status(thm)],[c_337,c_335]) ).
cnf(c_811,negated_conjecture,
member(sK3,sK1),
inference(resolve,[status(thm)],[c_337,c_336]) ).
cnf(c_1023,plain,
apply(sK0,sK3,sK2),
inference(resolve,[status(thm)],[c_810,c_809]) ).
cnf(c_1650,plain,
apply(sK0,sK2,sK3),
inference(resolve,[status(thm)],[c_811,c_808]) ).
cnf(c_2482,negated_conjecture,
( sK3 = sK2
| ~ apply(sK0,sK2,sK3)
| ~ member(sK3,sK1)
| ~ member(sK2,sK1) ),
inference(resolve,[status(thm)],[c_1023,c_375]) ).
cnf(c_2483,negated_conjecture,
( sK3 = sK2
| ~ apply(sK0,sK2,sK3)
| ~ member(sK3,sK1) ),
inference(resolve,[status(thm)],[c_810,c_2482]) ).
cnf(c_2484,negated_conjecture,
( sK3 = sK2
| ~ apply(sK0,sK2,sK3) ),
inference(resolve,[status(thm)],[c_811,c_2483]) ).
cnf(c_2485,negated_conjecture,
sK3 = sK2,
inference(resolve,[status(thm)],[c_1650,c_2484]) ).
cnf(c_2481,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_558,c_2485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:17:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1062462 was started by sandbox on n020,
% 0.09/0.36 % Sat Sep 26 08:17:03 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 6.51/1.24
% 6.51/1.24 % 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(496,b,i)].
% 6.51/1.24
% 6.51/1.24 % SZS status Theorem for theBenchmark
% 6.51/1.24
% 6.51/1.24 % Proof 1 at 0.75 (+ 0.04) seconds.
% 6.51/1.24 % Length of proof is 19.
% 6.51/1.24 % Level of proof is 4.
% 6.51/1.24 % Maximum clause weight is 22.000.
% 6.51/1.24 % Given clauses 655.
% 6.51/1.24
% 6.51/1.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------