%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN381+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 09:37:45 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 50 ( 16 ~; 15 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 39 ( 4 sgn 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2133,conjecture,
( ( ! [W,Z] :
( big_q(W,Z)
=> ( big_q(Z,Z)
| big_q(Z,W) ) )
& ! [V] :
? [U] : big_q(U,V)
& ! [X] :
( ? [Y] : big_q(X,Y)
=> big_p(X) ) )
=> ! [Z] : big_p(Z) ),
file('theBenchmark.p',x2133) ).
fof(x2133_neg,negated_conjecture,
~ ( ( ! [W,Z] :
( big_q(W,Z)
=> ( big_q(Z,Z)
| big_q(Z,W) ) )
& ! [V] :
? [U] : big_q(U,V)
& ! [X] :
( ? [Y] : big_q(X,Y)
=> big_p(X) ) )
=> ! [Z] : big_p(Z) ),
inference(assume_negation,[status(cth)],[x2133]) ).
fof(nnf_1,plain,
( ? [Z] : ~ big_p(Z)
& ! [W,X0] :
( big_q(X0,X0)
| big_q(X0,W)
| ~ big_q(W,X0) )
& ! [V] :
? [U] : big_q(U,V)
& ! [X] :
( big_p(X)
| ! [Y] : ~ big_q(X,Y) ) ),
inference(fof_nnf,[status(thm)],[x2133_neg]) ).
fof(sk_x2133_neg_sk,plain,
( ~ big_p(sK0)
& ! [W,X0] :
( big_q(X0,X0)
| big_q(X0,W)
| ~ big_q(W,X0) )
& ! [V] : big_q(sK1(V),V)
& ! [X] :
( big_p(X)
| ! [Y] : ~ big_q(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(U,sK1(V)),skolemize(Z,sK0)],[nnf_1]) ).
fof(sk_x2133_neg,plain,
( ~ big_p(sK0)
& ! [VAR_0,VAR_1] :
( big_q(VAR_1,VAR_1)
| big_q(VAR_1,VAR_0)
| ~ big_q(VAR_0,VAR_1) )
& ! [VAR_0] : big_q(sK1(VAR_0),VAR_0)
& ! [VAR_0,VAR_1] :
( big_p(VAR_0)
| ~ big_q(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2133_neg_sk]) ).
cnf(c_2,negated_conjecture,
~ big_p(sK0),
inference(split_conjunct,[status(thm)],[sk_x2133_neg]) ).
cnf(c_3,negated_conjecture,
( big_p(A)
| ~ big_q(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2133_neg]) ).
cnf(c_4,negated_conjecture,
~ big_q(sK0,A),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_5,negated_conjecture,
( big_q(B,B)
| big_q(B,A)
| ~ big_q(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2133_neg]) ).
cnf(c_6,negated_conjecture,
big_q(sK1(A),A),
inference(split_conjunct,[status(thm)],[sk_x2133_neg]) ).
cnf(c_9,negated_conjecture,
( big_q(sK0,sK0)
| ~ big_q(A,sK0) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,negated_conjecture,
~ big_q(A,sK0),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN381+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 17:42:07 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2316817 was started by sandbox on n002,
% 0.17/0.44 % Sat Sep 26 17:42:07 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 8.
% 0.17/0.45 % Level of proof is 4.
% 0.17/0.45 % Maximum clause weight is 9.000.
% 0.17/0.45 % Given clauses 2.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------