%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% 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 09:37:50 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 50 ( 21 ~; 14 |; 11 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 2 sgn 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish256,conjecture,
( ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) )
=> ~ ? [V] :
! [U] : f(U,V) ),
file('theBenchmark.p',kalish256) ).
fof(kalish256_neg,negated_conjecture,
~ ( ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) )
=> ~ ? [V] :
! [U] : f(U,V) ),
inference(assume_negation,[status(cth)],[kalish256]) ).
fof(nnf_1,plain,
( ? [V] :
! [U] : f(U,V)
& ! [Z] :
? [Y] :
! [X] :
( ( f(X,X)
| ~ f(X,Z)
| f(X,Y) )
& ( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,Y) ) ) ),
inference(fof_nnf,[status(thm)],[kalish256_neg]) ).
fof(sk_kalish256_neg_sk,plain,
( ! [U] : f(U,sK1)
& ! [Z,X] :
( ( f(X,X)
| ~ f(X,Z)
| f(X,sK0(Z)) )
& ( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,sK0(Z)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Y,sK0(Z)),skolemize(V,sK1)],[nnf_1]) ).
fof(sk_kalish256_neg,plain,
( ! [VAR_0] : f(VAR_0,sK1)
& ! [VAR_0,VAR_1] :
( f(VAR_0,VAR_0)
| ~ f(VAR_0,VAR_1)
| f(VAR_0,sK0(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ f(VAR_0,VAR_0)
| ~ f(VAR_0,sK0(VAR_1)) )
& ! [VAR_0,VAR_1] :
( f(VAR_0,VAR_1)
| ~ f(VAR_0,sK0(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_kalish256_neg_sk]) ).
cnf(c_3,negated_conjecture,
( ~ f(A,A)
| ~ f(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_kalish256_neg]) ).
cnf(c_4,negated_conjecture,
( f(A,A)
| ~ f(A,B)
| f(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_kalish256_neg]) ).
cnf(c_5,negated_conjecture,
f(A,sK1),
inference(split_conjunct,[status(thm)],[sk_kalish256_neg]) ).
cnf(c_6,plain,
~ f(sK0(A),sK0(A)),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_9,plain,
( ~ f(sK0(A),A)
| f(sK0(A),sK0(A)) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_7,plain,
~ f(sK0(A),A),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:42:18 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 2148012 was started by sandbox on n020,
% 0.09/0.36 % Sat Sep 26 17:42:18 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 7.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 10.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------