%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN361+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.10s 0.37s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 37 ( 15 ~; 6 |; 10 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 3 sgn 18 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2112,conjecture,
( ( ! [X,Y] :
( big_p(X,Y)
=> ~ big_q(X,Y) )
& ! [X] :
( big_s(X)
=> ? [Y] : big_q(Y,X) )
& ? [V] :
! [X] : big_p(X,V) )
=> ? [U] : ~ big_s(U) ),
file('theBenchmark.p',x2112) ).
fof(x2112_neg,negated_conjecture,
~ ( ( ! [X,Y] :
( big_p(X,Y)
=> ~ big_q(X,Y) )
& ! [X] :
( big_s(X)
=> ? [Y] : big_q(Y,X) )
& ? [V] :
! [X] : big_p(X,V) )
=> ? [U] : ~ big_s(U) ),
inference(assume_negation,[status(cth)],[x2112]) ).
fof(nnf_1,plain,
( ! [U] : big_s(U)
& ! [X,Y] :
( ~ big_q(X,Y)
| ~ big_p(X,Y) )
& ! [X1] :
( ? [X2] : big_q(X2,X1)
| ~ big_s(X1) )
& ? [V] :
! [X0] : big_p(X0,V) ),
inference(fof_nnf,[status(thm)],[x2112_neg]) ).
fof(sk_x2112_neg,plain,
( ! [U] : big_s(U)
& ! [X,Y] :
( ~ big_q(X,Y)
| ~ big_p(X,Y) )
& ! [X1] :
( big_q(sK1(X1),X1)
| ~ big_s(X1) )
& ! [X0] : big_p(X0,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(V,sK0),skolemize(X2,sK1(X1))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( ~ big_q(A,B)
| ~ big_p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2112_neg]) ).
cnf(c_3,negated_conjecture,
big_p(A,sK0),
inference(split_conjunct,[status(thm)],[sk_x2112_neg]) ).
cnf(c_4,negated_conjecture,
( big_q(sK1(A),A)
| ~ big_s(A) ),
inference(split_conjunct,[status(thm)],[sk_x2112_neg]) ).
cnf(c_5,negated_conjecture,
big_s(A),
inference(split_conjunct,[status(thm)],[sk_x2112_neg]) ).
cnf(c_6,negated_conjecture,
~ big_q(A,sK0),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
big_q(sK1(A),A),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_8,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN361+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 17:41:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 398892 was started by sandbox2 on n015,
% 0.10/0.36 % Sat Sep 26 17:41:28 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.10/0.37
% 0.10/0.37 % SZS status Theorem for theBenchmark
% 0.10/0.37
% 0.10/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.37 % Length of proof is 8.
% 0.10/0.37 % Level of proof is 3.
% 0.10/0.37 % Maximum clause weight is 0.000.
% 0.10/0.37 % Given clauses 0.
% 0.10/0.37
% 0.10/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------