%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 09:43:22 AM UTC 2026
% Result : Theorem 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 43 ( 15 ~; 10 |; 10 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 32 ( 0 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ( ! [X,Y,Z] :
( ( r(Y,Z)
& r(X,Y) )
=> r(X,Z) )
& ! [X,Y] :
( r(X,Y)
=> r(Y,X) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ( ! [X,Y,Z] :
( ( r(Y,Z)
& r(X,Y) )
=> r(X,Z) )
& ! [X,Y] :
( r(X,Y)
=> r(Y,X) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X2,X3,Z] :
( r(X2,Z)
| ~ r(X3,Z)
| ~ r(X2,X3) )
& ! [X0,X1] :
( r(X1,X0)
| ~ r(X0,X1) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
( ~ r(sK0,sK0)
& r(sK0,sK1)
& ! [X2,X3,Z] :
( r(X2,Z)
| ~ r(X3,Z)
| ~ r(X2,X3) )
& ! [X0,X1] :
( r(X1,X0)
| ~ r(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( r(B,A)
| ~ r(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( r(A,C)
| ~ r(B,C)
| ~ r(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
r(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
~ r(sK0,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
r(sK1,sK0),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_10,negated_conjecture,
( r(sK0,A)
| ~ r(sK1,A) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_8,negated_conjecture,
~ r(sK1,sK0),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n016.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 18:54:45 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.34 % Process 1490225 was started by sandbox2 on n016,
% 0.09/0.34 % Sat Sep 26 18:54:45 2026
% 0.09/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.09/0.36
% 0.09/0.36 % SZS status Theorem for theBenchmark
% 0.09/0.36
% 0.09/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.36 % Length of proof is 8.
% 0.09/0.36 % Level of proof is 3.
% 0.09/0.36 % Maximum clause weight is 9.000.
% 0.09/0.36 % Given clauses 4.
% 0.09/0.36
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------