%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN721+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 : n017.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 09:39:12 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 29 ( 11 ~; 6 |; 6 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 29 ( 11 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lx1,conjecture,
( ( ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) )
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& r(a,b) )
=> ? [W] :
( q(W,a)
& r(b,W) ) ),
file('theBenchmark.p',lx1) ).
fof(lx1_neg,negated_conjecture,
~ ( ( ! [U,V] :
( q(U,V)
=> ! [Z] : r(Z,V) )
& ! [X] :
( ? [Y] : r(X,Y)
=> q(X,X) )
& r(a,b) )
=> ? [W] :
( q(W,a)
& r(b,W) ) ),
inference(assume_negation,[status(cth)],[lx1]) ).
cnf(c_2,negated_conjecture,
( q(A,A)
| ~ r(A,B) ),
inference(clausify,[status(thm)],[lx1_neg]) ).
cnf(c_3,negated_conjecture,
r(a,b),
inference(clausify,[status(thm)],[lx1_neg]) ).
cnf(c_4,negated_conjecture,
( r(C,B)
| ~ q(A,B) ),
inference(clausify,[status(thm)],[lx1_neg]) ).
cnf(c_5,negated_conjecture,
( ~ q(A,a)
| ~ r(b,A) ),
inference(clausify,[status(thm)],[lx1_neg]) ).
cnf(c_6,negated_conjecture,
( ~ q(B,A)
| ~ q(A,a) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,negated_conjecture,
( q(C,C)
| ~ q(A,B) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_8,negated_conjecture,
q(a,a),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_9,plain,
( ~ q(C,a)
| ~ q(A,B) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_10,negated_conjecture,
q(A,A),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_11,plain,
~ q(A,B),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_12,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN721+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 18:17:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1365551 was started by sandbox on n017,
% 0.10/0.37 % Sat Sep 26 18:17:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 12.
% 0.10/0.38 % Level of proof is 5.
% 0.10/0.38 % Maximum clause weight is 6.000.
% 0.10/0.38 % Given clauses 5.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------