%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN960+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 : n014.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 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 23 ( 10 ~; 8 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 30 ( 6 sgn 12 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ? [X,Y] : a(X,Y)
<=> ? [Y,X] : a(X,Y) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ? [X,Y] : a(X,Y)
<=> ? [Y,X] : a(X,Y) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ( ! [Y,X] : ~ a(X,Y)
| ! [X4,X5] : ~ a(X4,X5) )
& ( ? [X2,X3] : a(X3,X2)
| ? [X0,X1] : a(X0,X1) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ( ! [Y,X] : ~ a(X,Y)
| ! [X4,X5] : ~ a(X4,X5) )
& ( a(sK2,sK3)
| a(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK3),skolemize(X3,sK2)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ a(VAR_2,VAR_3)
| ~ a(VAR_0,VAR_1) )
& ( a(sK2,sK3)
| a(sK0,sK1) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( a(sK2,sK3)
| a(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( ~ a(C,D)
| ~ a(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,plain,
~ a(A,B),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_6,negated_conjecture,
a(sK2,sK3),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_5,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN960+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n014.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 18:52:02 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3869936 was started by sandbox on n014,
% 0.18/0.44 % Sat Sep 26 18:52:02 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.45
% 0.18/0.45 % SZS status Theorem for theBenchmark
% 0.18/0.45
% 0.18/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.45 % Length of proof is 5.
% 0.18/0.45 % Level of proof is 3.
% 0.18/0.45 % Maximum clause weight is 6.000.
% 0.18/0.45 % Given clauses 0.
% 0.18/0.45
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------