%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN370+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 09:37:43 AM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 13 ( 4 ~; 5 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 15 ( 1 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2121,conjecture,
? [V] :
! [Y] :
? [Z] :
( ( big_p(V,Y,f(Y))
| big_p(a,Y,h(Y)) )
=> big_p(V,Y,Z) ),
file('theBenchmark.p',x2121) ).
fof(x2121_neg,negated_conjecture,
~ ? [V] :
! [Y] :
? [Z] :
( ( big_p(V,Y,f(Y))
| big_p(a,Y,h(Y)) )
=> big_p(V,Y,Z) ),
inference(assume_negation,[status(cth)],[x2121]) ).
fof(nnf_1,plain,
! [V] :
? [Y] :
! [Z] :
( ~ big_p(V,Y,Z)
& ( big_p(V,Y,f(Y))
| big_p(a,Y,h(Y)) ) ),
inference(fof_nnf,[status(thm)],[x2121_neg]) ).
fof(sk_x2121_neg,plain,
! [V,Z] :
( ~ big_p(V,sK0(V),Z)
& ( big_p(V,sK0(V),f(sK0(V)))
| big_p(a,sK0(V),h(sK0(V))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(V))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( big_p(A,sK0(A),f(sK0(A)))
| big_p(a,sK0(A),h(sK0(A))) ),
inference(split_conjunct,[status(thm)],[sk_x2121_neg]) ).
cnf(c_3,negated_conjecture,
~ big_p(A,sK0(A),B),
inference(split_conjunct,[status(thm)],[sk_x2121_neg]) ).
cnf(c_4,negated_conjecture,
big_p(a,sK0(A),h(sK0(A))),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_5,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN370+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n004.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 17:38:23 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 2257307 was started by sandbox on n004,
% 0.18/0.46 % Sat Sep 26 17:38:23 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.48 % Length of proof is 5.
% 0.18/0.48 % Level of proof is 3.
% 0.18/0.48 % Maximum clause weight is 14.000.
% 0.18/0.48 % Given clauses 0.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------