%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN732+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 09:39:14 AM UTC 2026
% Result : Theorem 0.02s 0.38s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 31 ( 11 ~; 5 |; 9 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 32 ( 2 sgn 21 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x3411,conjecture,
( ! [Y] :
( ! [X] : p(X,Y)
=> ! [U] : q(U,Y) )
=> ? [Z] :
( ? [V] : p(V,Z)
=> ? [W] :
( q(W,Z)
| p(Z,W) ) ) ),
file('theBenchmark.p',x3411) ).
fof(x3411_neg,negated_conjecture,
~ ( ! [Y] :
( ! [X] : p(X,Y)
=> ! [U] : q(U,Y) )
=> ? [Z] :
( ? [V] : p(V,Z)
=> ? [W] :
( q(W,Z)
| p(Z,W) ) ) ),
inference(assume_negation,[status(cth)],[x3411]) ).
fof(nnf_1,plain,
( ! [Z] :
( ! [W] :
( ~ q(W,Z)
& ~ p(Z,W) )
& ? [V] : p(V,Z) )
& ! [Y] :
( ! [U] : q(U,Y)
| ? [X] : ~ p(X,Y) ) ),
inference(fof_nnf,[status(thm)],[x3411_neg]) ).
fof(sk_x3411_neg_sk,plain,
( ! [Z] :
( ! [W] :
( ~ q(W,Z)
& ~ p(Z,W) )
& p(sK0(Z),Z) )
& ! [Y] :
( ! [U] : q(U,Y)
| ~ p(sK1(Y),Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK1(Y)),skolemize(V,sK0(Z))],[nnf_1]) ).
fof(sk_x3411_neg,plain,
( ! [VAR_0,VAR_1] : ~ q(VAR_0,VAR_1)
& ! [VAR_0,VAR_1] : ~ p(VAR_0,VAR_1)
& ! [VAR_0] : p(sK0(VAR_0),VAR_0)
& ! [VAR_0,VAR_1] :
( q(VAR_1,VAR_0)
| ~ p(sK1(VAR_0),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_x3411_neg_sk]) ).
cnf(c_2,negated_conjecture,
p(sK0(A),A),
inference(split_conjunct,[status(thm)],[sk_x3411_neg]) ).
cnf(c_4,negated_conjecture,
~ p(A,B),
inference(split_conjunct,[status(thm)],[sk_x3411_neg]) ).
cnf(c_5,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN732+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 18:24:51 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 1107328 was started by sandbox on n018,
% 0.02/0.36 % Sat Sep 26 18:24:51 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.36
% 0.02/0.36 % From the command line: assign(max_seconds, 300).
% 0.02/0.38
% 0.02/0.38 % SZS status Theorem for theBenchmark
% 0.02/0.38
% 0.02/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.38 % Length of proof is 4.
% 0.02/0.38 % Level of proof is 2.
% 0.02/0.38 % Maximum clause weight is 0.000.
% 0.02/0.38 % Given clauses 0.
% 0.02/0.38
% 0.02/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------