%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN730+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 09:39:14 AM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% 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(thm75,conjecture,
? [V] :
! [J] :
? [Q] :
( ( p(V,J,k(J))
| p(a,J,h(J)) )
=> p(V,J,Q) ),
file('theBenchmark.p',thm75) ).
fof(thm75_neg,negated_conjecture,
~ ? [V] :
! [J] :
? [Q] :
( ( p(V,J,k(J))
| p(a,J,h(J)) )
=> p(V,J,Q) ),
inference(assume_negation,[status(cth)],[thm75]) ).
fof(nnf_1,plain,
! [V] :
? [J] :
! [Q] :
( ~ p(V,J,Q)
& ( p(V,J,k(J))
| p(a,J,h(J)) ) ),
inference(fof_nnf,[status(thm)],[thm75_neg]) ).
fof(sk_thm75_neg,plain,
! [V,Q] :
( ~ p(V,sK0(V),Q)
& ( p(V,sK0(V),k(sK0(V)))
| p(a,sK0(V),h(sK0(V))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(J,sK0(V))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( p(A,sK0(A),k(sK0(A)))
| p(a,sK0(A),h(sK0(A))) ),
inference(split_conjunct,[status(thm)],[sk_thm75_neg]) ).
cnf(c_3,negated_conjecture,
~ p(A,sK0(A),B),
inference(split_conjunct,[status(thm)],[sk_thm75_neg]) ).
cnf(c_4,negated_conjecture,
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
% 0.00/0.03 % Problem : SYN730+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 18:22:29 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 839804 was started by sandbox2 on n009,
% 0.12/0.37 % Sat Sep 26 18:22:29 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 5.
% 0.12/0.39 % Level of proof is 3.
% 0.12/0.39 % Maximum clause weight is 14.000.
% 0.12/0.39 % Given clauses 0.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------