%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 09:37:43 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 45 ( 15 ~; 10 |; 12 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 28 ( 4 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2117,conjecture,
( ( ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) )
=> ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) ) ),
file('theBenchmark.p',x2117) ).
fof(x2117_neg,negated_conjecture,
~ ( ( ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) )
=> ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) ) ),
inference(assume_negation,[status(cth)],[x2117]) ).
fof(nnf_1,plain,
( ? [Y] : ~ big_r(Y,Y)
& ? [X] : big_r(X,X)
& ! [W,Z] :
( ( ~ big_r(Z,W)
| big_r(W,W) )
& ( big_r(Z,W)
| ~ big_r(W,W) ) )
& ! [U,V] :
( ( ~ big_r(U,V)
| big_r(U,U) )
& ( big_r(U,V)
| ~ big_r(U,U) ) ) ),
inference(fof_nnf,[status(thm)],[x2117_neg]) ).
fof(sk_x2117_neg,plain,
( ~ big_r(sK1,sK1)
& big_r(sK0,sK0)
& ! [W,Z] :
( ( ~ big_r(Z,W)
| big_r(W,W) )
& ( big_r(Z,W)
| ~ big_r(W,W) ) )
& ! [U,V] :
( ( ~ big_r(U,V)
| big_r(U,U) )
& ( big_r(U,V)
| ~ big_r(U,U) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( big_r(A,B)
| ~ big_r(A,A) ),
inference(split_conjunct,[status(thm)],[sk_x2117_neg]) ).
cnf(c_5,negated_conjecture,
( ~ big_r(B,A)
| big_r(A,A) ),
inference(split_conjunct,[status(thm)],[sk_x2117_neg]) ).
cnf(c_6,negated_conjecture,
big_r(sK0,sK0),
inference(split_conjunct,[status(thm)],[sk_x2117_neg]) ).
cnf(c_7,negated_conjecture,
~ big_r(sK1,sK1),
inference(split_conjunct,[status(thm)],[sk_x2117_neg]) ).
cnf(c_9,negated_conjecture,
big_r(sK0,A),
inference(resolve,[status(thm)],[c_2,c_6]) ).
cnf(c_10,plain,
~ big_r(A,sK1),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n015.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 17:41:59 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 400521 was started by sandbox2 on n015,
% 0.19/0.46 % Sat Sep 26 17:41:59 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 8.
% 0.19/0.48 % Level of proof is 3.
% 0.19/0.48 % Maximum clause weight is 6.000.
% 0.19/0.48 % Given clauses 6.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------