%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN057+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 : n020.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 09:36:53 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 24 ~; 12 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn 5 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel27_1,axiom,
? [X] :
( ~ big_g(X)
& big_f(X) ),
file('theBenchmark.p',pel27_1) ).
fof(pel27_2,axiom,
! [X] :
( big_f(X)
=> big_h(X) ),
file('theBenchmark.p',pel27_2) ).
fof(pel27_3,axiom,
! [X] :
( ( big_i(X)
& big_j(X) )
=> big_f(X) ),
file('theBenchmark.p',pel27_3) ).
fof(pel27_4,axiom,
( ? [X] :
( ~ big_g(X)
& big_h(X) )
=> ! [X1] :
( big_i(X1)
=> ~ big_h(X1) ) ),
file('theBenchmark.p',pel27_4) ).
fof(pel27,conjecture,
! [X] :
( big_j(X)
=> ~ big_i(X) ),
file('theBenchmark.p',pel27) ).
fof(pel27_neg,negated_conjecture,
~ ! [X] :
( big_j(X)
=> ~ big_i(X) ),
inference(assume_negation,[status(cth)],[pel27]) ).
cnf(c_6,plain,
( big_h(A)
| ~ big_f(A) ),
inference(clausify,[status(thm)],[pel27_2]) ).
fof(nnf_1,plain,
? [X] :
( ~ big_g(X)
& big_f(X) ),
inference(fof_nnf,[status(thm)],[pel27_1]) ).
fof(sk_pel27_1,plain,
( ~ big_g(sK0)
& big_f(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_1]) ).
cnf(c_7,plain,
big_f(sK0),
inference(split_conjunct,[status(thm)],[sk_pel27_1]) ).
cnf(c_8,plain,
( big_f(A)
| ~ big_i(A)
| ~ big_j(A) ),
inference(clausify,[status(thm)],[pel27_3]) ).
cnf(c_9,plain,
~ big_g(sK0),
inference(split_conjunct,[status(thm)],[sk_pel27_1]) ).
cnf(c_10,plain,
( ~ big_h(B)
| ~ big_i(B)
| big_g(A)
| ~ big_h(A) ),
inference(clausify,[status(thm)],[pel27_4]) ).
cnf(c_11,plain,
( big_h(A)
| ~ big_i(A)
| ~ big_j(A) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
fof(nnf_5,plain,
? [X] :
( big_i(X)
& big_j(X) ),
inference(fof_nnf,[status(thm)],[pel27_neg]) ).
fof(sk_pel27_neg,plain,
( big_i(sK1)
& big_j(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X,sK1)],[nnf_5]) ).
cnf(c_12,negated_conjecture,
big_j(sK1),
inference(split_conjunct,[status(thm)],[sk_pel27_neg]) ).
cnf(c_13,negated_conjecture,
big_i(sK1),
inference(split_conjunct,[status(thm)],[sk_pel27_neg]) ).
cnf(c_14,negated_conjecture,
( big_h(sK1)
| ~ big_i(sK1) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_15,plain,
( ~ big_h(A)
| ~ big_i(A)
| ~ big_h(sK0) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_16,negated_conjecture,
( ~ big_h(sK1)
| ~ big_h(sK0) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_17,negated_conjecture,
big_h(sK1),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_18,plain,
big_h(sK0),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_20,negated_conjecture,
~ big_h(sK1),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_19,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN057+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 17:08:19 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2086347 was started by sandbox on n020,
% 0.17/0.44 % Sat Sep 26 17:08:19 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 19.
% 0.17/0.46 % Level of proof is 5.
% 0.17/0.46 % Maximum clause weight is 4.000.
% 0.17/0.46 % Given clauses 0.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------