%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN318+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 : n002.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 09:37:32 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 36 ( 13 ~; 7 |; 6 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 18 ( 6 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_2_4,conjecture,
? [Y] :
( ! [X] :
( big_f(X)
=> ( big_f(Y)
=> big_g(X) ) )
=> ( p
=> ! [X] :
( big_f(X)
=> big_g(Y) ) ) ),
file('theBenchmark.p',church_46_2_4) ).
fof(church_46_2_4_neg,negated_conjecture,
~ ? [Y] :
( ! [X] :
( big_f(X)
=> ( big_f(Y)
=> big_g(X) ) )
=> ( p
=> ! [X] :
( big_f(X)
=> big_g(Y) ) ) ),
inference(assume_negation,[status(cth)],[church_46_2_4]) ).
fof(nnf_1,plain,
! [Y] :
( ? [X] :
( ~ big_g(Y)
& big_f(X) )
& p
& ! [X0] :
( big_g(X0)
| ~ big_f(Y)
| ~ big_f(X0) ) ),
inference(fof_nnf,[status(thm)],[church_46_2_4_neg]) ).
fof(sk_church_46_2_4_neg,plain,
! [Y] :
( ~ big_g(Y)
& big_f(sK0(Y))
& p
& ! [X0] :
( big_g(X0)
| ~ big_f(Y)
| ~ big_f(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(Y))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
~ big_g(A),
inference(split_conjunct,[status(thm)],[sk_church_46_2_4_neg]) ).
cnf(c_3,negated_conjecture,
( big_g(A)
| ~ big_f(B)
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_2_4_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_f(B)
| ~ big_f(A) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_5,negated_conjecture,
big_f(sK0(A)),
inference(split_conjunct,[status(thm)],[sk_church_46_2_4_neg]) ).
cnf(c_7,plain,
~ big_f(A),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN318+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:36:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2300433 was started by sandbox on n002,
% 0.10/0.38 % Sat Sep 26 17:36:06 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 7.
% 0.10/0.39 % Level of proof is 4.
% 0.10/0.39 % Maximum clause weight is 4.000.
% 0.10/0.39 % Given clauses 2.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------