%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN356+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:37:41 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 34 ( 13 ~; 7 |; 8 &)
% ( 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 : 20 ( 7 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2107,conjecture,
( ( ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& ! [X,Y] :
( big_r(X,Y)
=> ( big_q(X,Y)
& big_r(Y,X) ) )
& big_r(a,b) )
=> ( big_q(b,b)
& big_q(a,a) ) ),
file('theBenchmark.p',x2107) ).
fof(x2107_neg,negated_conjecture,
~ ( ( ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& ! [X,Y] :
( big_r(X,Y)
=> ( big_q(X,Y)
& big_r(Y,X) ) )
& big_r(a,b) )
=> ( big_q(b,b)
& big_q(a,a) ) ),
inference(assume_negation,[status(cth)],[x2107]) ).
cnf(c_2,negated_conjecture,
big_r(a,b),
inference(clausify,[status(thm)],[x2107_neg]) ).
cnf(c_3,negated_conjecture,
( big_r(B,A)
| ~ big_r(A,B) ),
inference(clausify,[status(thm)],[x2107_neg]) ).
cnf(c_4,negated_conjecture,
( big_q(A,B)
| ~ big_r(A,B) ),
inference(clausify,[status(thm)],[x2107_neg]) ).
cnf(c_5,negated_conjecture,
( big_q(A,A)
| ~ big_q(A,B) ),
inference(clausify,[status(thm)],[x2107_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_q(b,b)
| ~ big_q(a,a) ),
inference(clausify,[status(thm)],[x2107_neg]) ).
cnf(c_7,negated_conjecture,
big_r(b,a),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_9,plain,
( ~ big_q(a,A)
| ~ big_q(b,b) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_13,negated_conjecture,
big_q(b,a),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_14,plain,
( ~ big_q(b,B)
| ~ big_q(a,A) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_17,plain,
( ~ big_r(a,B)
| ~ big_q(b,A) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_21,plain,
~ big_q(b,A),
inference(resolve,[status(thm)],[c_17,c_2]) ).
cnf(c_22,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN356+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 17:38:27 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 4169764 was started by sandbox on n008,
% 0.10/0.37 % Sat Sep 26 17:38:27 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 13.
% 0.10/0.38 % Level of proof is 6.
% 0.10/0.38 % Maximum clause weight is 6.000.
% 0.10/0.38 % Given clauses 9.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------