%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN731+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 19 ( 1 sgn 8 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2150,conjecture,
? [W] :
( ! [X] :
? [Y] : p(W,X,Y)
=> ? [Z] : p(Z,Z,W) ),
file('theBenchmark.p',x2150) ).
fof(x2150_neg,negated_conjecture,
~ ? [W] :
( ! [X] :
? [Y] : p(W,X,Y)
=> ? [Z] : p(Z,Z,W) ),
inference(assume_negation,[status(cth)],[x2150]) ).
fof(nnf_1,plain,
! [W] :
( ! [Z] : ~ p(Z,Z,W)
& ! [X] :
? [Y] : p(W,X,Y) ),
inference(fof_nnf,[status(thm)],[x2150_neg]) ).
fof(sk_x2150_neg,plain,
! [W] :
( ! [Z] : ~ p(Z,Z,W)
& ! [X] : p(W,X,sK0(W,X)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(W,X))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
~ p(A,A,B),
inference(split_conjunct,[status(thm)],[sk_x2150_neg]) ).
cnf(c_3,negated_conjecture,
p(A,B,sK0(A,B)),
inference(split_conjunct,[status(thm)],[sk_x2150_neg]) ).
cnf(c_4,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN731+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 18:23:39 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 81966 was started by sandbox2 on n008,
% 0.11/0.36 % Sat Sep 26 18:23:39 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 4.
% 0.11/0.38 % Level of proof is 2.
% 0.11/0.38 % Maximum clause weight is 0.000.
% 0.11/0.38 % Given clauses 0.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------