%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN360+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 : n017.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 25 ( 9 ~; 4 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 35 ( 4 sgn 22 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2111,conjecture,
( ( ! [Z] :
? [Y] : big_p(Z,Y)
& ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Y] : big_q(X,Y) ) )
=> ! [Y,X] : big_q(X,Y) ),
file('theBenchmark.p',x2111) ).
fof(x2111_neg,negated_conjecture,
~ ( ( ! [Z] :
? [Y] : big_p(Z,Y)
& ! [X] :
( ? [Y] : big_p(X,Y)
=> ! [Y] : big_q(X,Y) ) )
=> ! [Y,X] : big_q(X,Y) ),
inference(assume_negation,[status(cth)],[x2111]) ).
fof(nnf_1,plain,
( ? [Y,X] : ~ big_q(X,Y)
& ! [Z] :
? [X3] : big_p(Z,X3)
& ! [X0] :
( ! [X2] : big_q(X0,X2)
| ! [X1] : ~ big_p(X0,X1) ) ),
inference(fof_nnf,[status(thm)],[x2111_neg]) ).
fof(sk_x2111_neg_sk,plain,
( ~ big_q(sK1,sK2)
& ! [Z] : big_p(Z,sK0(Z))
& ! [X0] :
( ! [X2] : big_q(X0,X2)
| ! [X1] : ~ big_p(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(Z)),skolemize(Y,sK2),skolemize(X,sK1)],[nnf_1]) ).
fof(sk_x2111_neg,plain,
( ~ big_q(sK1,sK2)
& ! [VAR_0] : big_p(VAR_0,sK0(VAR_0))
& ! [VAR_0,VAR_1,VAR_2] :
( big_q(VAR_0,VAR_2)
| ~ big_p(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2111_neg_sk]) ).
cnf(c_2,negated_conjecture,
big_p(A,sK0(A)),
inference(split_conjunct,[status(thm)],[sk_x2111_neg]) ).
cnf(c_3,negated_conjecture,
( big_q(A,C)
| ~ big_p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2111_neg]) ).
cnf(c_4,negated_conjecture,
~ big_q(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_x2111_neg]) ).
cnf(c_5,negated_conjecture,
big_q(A,B),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_6,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN360+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 17:33:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1273148 was started by sandbox on n017,
% 0.11/0.37 % Sat Sep 26 17:33:49 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 6.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 0.000.
% 0.14/0.39 % Given clauses 0.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------