%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN957+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:43:27 AM UTC 2026
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 22 ( 12 ~; 6 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 9 ( 0 sgn 4 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
~ ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ~ ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [Y] :
! [X] :
( ( a(X,X)
| a(X,Y) )
& ( ~ a(X,X)
| ~ a(X,Y) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
! [X] :
( ( a(X,X)
| a(X,sK0) )
& ( ~ a(X,X)
| ~ a(X,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( ~ a(A,A)
| ~ a(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( a(A,A)
| a(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,plain,
~ a(sK0,sK0),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_6,plain,
a(sK0,sK0),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_5,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN957+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n013.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 18:51:21 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 3393804 was started by sandbox on n013,
% 0.20/0.45 % Sat Sep 26 18:51:21 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.20/0.47
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47
% 0.20/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.47 % Length of proof is 5.
% 0.20/0.47 % Level of proof is 3.
% 0.20/0.47 % Maximum clause weight is 6.000.
% 0.20/0.47 % Given clauses 0.
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------