%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN936+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 09:43:24 AM UTC 2026
% Result : Theorem 0.25s 5.70s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 46 ( 17 ~; 15 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 16 ( 4 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X] :
( c
=> p(X) )
<=> ( c
=> ! [X] : p(X) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ! [X] :
( c
=> p(X) )
<=> ( c
=> ! [X] : p(X) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ( ( ? [X] : ~ p(X)
& c )
| ? [X2] :
( ~ p(X2)
& c ) )
& ( ! [X1] : p(X1)
| ~ c
| ! [X0] :
( p(X0)
| ~ c ) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ( ( ~ p(sK1)
& c )
| ( ~ p(sK0)
& c ) )
& ( ! [X1] : p(X1)
| ~ c
| ! [X0] :
( p(X0)
| ~ c ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X,sK1)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ( ~ p(sK1)
| ~ p(sK0) )
& c
& ! [VAR_0,VAR_1] :
( p(VAR_1)
| p(VAR_0)
| ~ c ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( p(B)
| p(A)
| ~ c ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
c,
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( ~ p(sK1)
| ~ p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,plain,
( p(A)
| ~ c ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_5,negated_conjecture,
p(A),
inference(resolve,[status(thm)],[c_3,c_7]) ).
cnf(c_8,negated_conjecture,
~ p(sK1),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_6,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN936+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.67 % Computer : n001.cluster.edu
% 0.19/5.67 % Model : x86_64 x86_64
% 0.19/5.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.67 % Memory : 8046.5625MB
% 0.19/5.67 % OS : Linux 6.8.0-71-generic
% 0.19/5.67 % CPULimit : 300
% 0.19/5.67 % WCLimit : 300
% 0.19/5.67 % DateTime : Sat Sep 26 18:56:49 UTC 2026
% 0.19/5.68 % CPUTime :
% 0.19/5.68 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.68 % Process 2456516 was started by sandbox2 on n001,
% 0.19/5.68 % Sat Sep 26 18:56:49 2026
% 0.19/5.68 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.69
% 0.19/5.69 % From the command line: assign(max_seconds, 300).
% 0.25/5.70
% 0.25/5.70 % SZS status Theorem for theBenchmark
% 0.25/5.70
% 0.25/5.70 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.25/5.70 % Length of proof is 6.
% 0.25/5.70 % Level of proof is 3.
% 0.25/5.70 % Maximum clause weight is 5.000.
% 0.25/5.70 % Given clauses 0.
% 0.25/5.70
% 0.25/5.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------