%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN921+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 : 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 09:43:22 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 20 ( 7 ~; 3 |; 4 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 11 ( 3 sgn 4 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
! [X] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(sK0(X)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
p(A),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( q(A)
| ~ p(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
~ q(A),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
q(A),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_6,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN921+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 18:55:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2453906 was started by sandbox on n001,
% 0.11/0.37 % Sat Sep 26 18:55:59 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 6.
% 0.11/0.39 % Level of proof is 3.
% 0.11/0.39 % Maximum clause weight is 0.000.
% 0.11/0.39 % Given clauses 0.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------