%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN062+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 : 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 09:36:55 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 44 ( 18 ~; 13 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 10 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel32_1,axiom,
! [X] :
( ( ( big_h(X)
| big_g(X) )
& big_f(X) )
=> big_i(X) ),
file('theBenchmark.p',pel32_1) ).
fof(pel32_2,axiom,
! [X] :
( ( big_h(X)
& big_i(X) )
=> big_j(X) ),
file('theBenchmark.p',pel32_2) ).
fof(pel32_3,axiom,
! [X] :
( big_k(X)
=> big_h(X) ),
file('theBenchmark.p',pel32_3) ).
fof(pel32,conjecture,
! [X] :
( ( big_k(X)
& big_f(X) )
=> big_j(X) ),
file('theBenchmark.p',pel32) ).
fof(pel32_neg,negated_conjecture,
~ ! [X] :
( ( big_k(X)
& big_f(X) )
=> big_j(X) ),
inference(assume_negation,[status(cth)],[pel32]) ).
fof(nnf_4,plain,
? [X] :
( ~ big_j(X)
& big_k(X)
& big_f(X) ),
inference(fof_nnf,[status(thm)],[pel32_neg]) ).
fof(sk_pel32_neg,plain,
( ~ big_j(sK0)
& big_k(sK0)
& big_f(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_4]) ).
cnf(c_5,negated_conjecture,
big_f(sK0),
inference(split_conjunct,[status(thm)],[sk_pel32_neg]) ).
cnf(c_6,plain,
( big_i(A)
| ~ big_h(A)
| ~ big_f(A) ),
inference(clausify,[status(thm)],[pel32_1]) ).
cnf(c_8,plain,
( big_h(A)
| ~ big_k(A) ),
inference(clausify,[status(thm)],[pel32_3]) ).
cnf(c_9,plain,
( big_j(A)
| ~ big_h(A)
| ~ big_i(A) ),
inference(clausify,[status(thm)],[pel32_2]) ).
cnf(c_10,negated_conjecture,
( big_i(sK0)
| ~ big_h(sK0) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_11,plain,
( big_j(A)
| ~ big_i(A)
| ~ big_k(A) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_12,negated_conjecture,
( ~ big_k(sK0)
| big_i(sK0) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_13,negated_conjecture,
~ big_j(sK0),
inference(split_conjunct,[status(thm)],[sk_pel32_neg]) ).
cnf(c_14,negated_conjecture,
( ~ big_k(sK0)
| big_j(sK0)
| ~ big_k(sK0) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_15,negated_conjecture,
( ~ big_k(sK0)
| ~ big_k(sK0) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_16,negated_conjecture,
~ big_k(sK0),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,negated_conjecture,
big_k(sK0),
inference(split_conjunct,[status(thm)],[sk_pel32_neg]) ).
cnf(c_18,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_16,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN062+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 : n009.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:08:00 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 682160 was started by sandbox2 on n009,
% 0.08/0.35 % Sat Sep 26 17:08:00 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 17.
% 0.12/0.37 % Level of proof is 7.
% 0.12/0.37 % Maximum clause weight is 2.000.
% 0.12/0.37 % Given clauses 0.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------