%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN371+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 : n002.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 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 23 ( 8 ~; 3 |; 6 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 21 ( 0 sgn 14 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2122,conjecture,
( ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) )
=> ? [U] :
! [V] :
( big_r(U,U)
=> big_r(V,V) ) ),
file('theBenchmark.p',x2122) ).
fof(x2122_neg,negated_conjecture,
~ ( ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) )
=> ? [U] :
! [V] :
( big_r(U,U)
=> big_r(V,V) ) ),
inference(assume_negation,[status(cth)],[x2122]) ).
fof(nnf_1,plain,
( ! [U] :
? [V] :
( ~ big_r(V,V)
& big_r(U,U) )
& ( ! [Y] : big_r(Y,Y)
| ! [X] : ~ big_r(X,X) ) ),
inference(fof_nnf,[status(thm)],[x2122_neg]) ).
fof(sk_x2122_neg_sk,plain,
( ! [U] :
( ~ big_r(sK0(U),sK0(U))
& big_r(U,U) )
& ( ! [Y] : big_r(Y,Y)
| ! [X] : ~ big_r(X,X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(V,sK0(U))],[nnf_1]) ).
fof(sk_x2122_neg,plain,
( ! [VAR_0] : ~ big_r(sK0(VAR_0),sK0(VAR_0))
& ! [VAR_0] : big_r(VAR_0,VAR_0)
& ! [VAR_0,VAR_1] :
( big_r(VAR_1,VAR_1)
| ~ big_r(VAR_0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2122_neg_sk]) ).
cnf(c_3,negated_conjecture,
big_r(A,A),
inference(split_conjunct,[status(thm)],[sk_x2122_neg]) ).
cnf(c_4,negated_conjecture,
~ big_r(sK0(A),sK0(A)),
inference(split_conjunct,[status(thm)],[sk_x2122_neg]) ).
cnf(c_5,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN371+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:41:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2315676 was started by sandbox on n002,
% 0.09/0.36 % Sat Sep 26 17:41:53 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 4.
% 0.09/0.38 % Level of proof is 2.
% 0.09/0.38 % Maximum clause weight is 5.000.
% 0.09/0.38 % Given clauses 0.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------