%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN359+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 : n004.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 09:37:42 AM UTC 2026
% Result : Theorem 0.09s 15.39s
% 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 : 39 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 42 ( 15 ~; 9 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 4 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2110,conjecture,
( ( ! [X,Y] :
( big_q(X,Y)
=> big_q(X,X) )
& ! [Y] :
( big_r(Y)
=> ? [Z] : big_q(Y,Z) )
& ? [X] : big_r(X) )
=> ? [X,Y] :
( big_r(Y)
& big_q(X,Y) ) ),
file('theBenchmark.p',x2110) ).
fof(x2110_neg,negated_conjecture,
~ ( ( ! [X,Y] :
( big_q(X,Y)
=> big_q(X,X) )
& ! [Y] :
( big_r(Y)
=> ? [Z] : big_q(Y,Z) )
& ? [X] : big_r(X) )
=> ? [X,Y] :
( big_r(Y)
& big_q(X,Y) ) ),
inference(assume_negation,[status(cth)],[x2110]) ).
fof(nnf_1,plain,
( ! [X,Y] :
( ~ big_r(Y)
| ~ big_q(X,Y) )
& ! [X2,X3] :
( big_q(X2,X2)
| ~ big_q(X2,X3) )
& ! [X1] :
( ? [Z] : big_q(X1,Z)
| ~ big_r(X1) )
& ? [X0] : big_r(X0) ),
inference(fof_nnf,[status(thm)],[x2110_neg]) ).
fof(sk_x2110_neg,plain,
( ! [X,Y] :
( ~ big_r(Y)
| ~ big_q(X,Y) )
& ! [X2,X3] :
( big_q(X2,X2)
| ~ big_q(X2,X3) )
& ! [X1] :
( big_q(X1,sK0(X1))
| ~ big_r(X1) )
& big_r(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(Z,sK0(X1))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( big_q(A,sK0(A))
| ~ big_r(A) ),
inference(split_conjunct,[status(thm)],[sk_x2110_neg]) ).
cnf(c_3,negated_conjecture,
big_r(sK1),
inference(split_conjunct,[status(thm)],[sk_x2110_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_r(B)
| ~ big_q(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2110_neg]) ).
cnf(c_5,negated_conjecture,
~ big_q(A,sK1),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_6,negated_conjecture,
big_q(sK1,sK0(sK1)),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
( big_q(A,A)
| ~ big_q(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2110_neg]) ).
cnf(c_8,plain,
~ big_q(sK1,A),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN359+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/15.37 % Computer : n004.cluster.edu
% 0.09/15.37 % Model : x86_64 x86_64
% 0.09/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.37 % Memory : 8046.5625MB
% 0.09/15.37 % OS : Linux 6.8.0-71-generic
% 0.09/15.37 % CPULimit : 300
% 0.09/15.37 % WCLimit : 300
% 0.09/15.37 % DateTime : Sat Sep 26 17:37:53 UTC 2026
% 0.09/15.38 % CPUTime :
% 0.09/15.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/15.38 % Process 2255812 was started by sandbox on n004,
% 0.09/15.38 % Sat Sep 26 17:37:53 2026
% 0.09/15.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/15.38
% 0.09/15.38 % From the command line: assign(max_seconds, 300).
% 0.09/15.39
% 0.09/15.39 % SZS status Theorem for theBenchmark
% 0.09/15.39
% 0.09/15.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/15.39 % Length of proof is 9.
% 0.09/15.39 % Level of proof is 4.
% 0.09/15.39 % Maximum clause weight is 6.000.
% 0.09/15.39 % Given clauses 3.
% 0.09/15.39
% 0.09/15.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------