%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN325+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 : n008.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 09:37:34 AM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 37 ( 11 ~; 8 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 17 ( 1 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_9_2,conjecture,
? [X] :
! [Y] :
( ( ( big_f(X,X)
=> big_f(Y,Y) )
=> ( big_g(X)
& big_f(X,Y) ) )
=> big_g(Y) ),
file('theBenchmark.p',church_46_9_2) ).
fof(church_46_9_2_neg,negated_conjecture,
~ ? [X] :
! [Y] :
( ( ( big_f(X,X)
=> big_f(Y,Y) )
=> ( big_g(X)
& big_f(X,Y) ) )
=> big_g(Y) ),
inference(assume_negation,[status(cth)],[church_46_9_2]) ).
fof(nnf_1,plain,
! [X] :
? [Y] :
( ~ big_g(Y)
& ( ( big_g(X)
& big_f(X,Y) )
| ( ~ big_f(Y,Y)
& big_f(X,X) ) ) ),
inference(fof_nnf,[status(thm)],[church_46_9_2_neg]) ).
fof(sk_church_46_9_2_neg_sk,plain,
! [X] :
( ~ big_g(sK0(X))
& ( ( big_g(X)
& big_f(X,sK0(X)) )
| ( ~ big_f(sK0(X),sK0(X))
& big_f(X,X) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_1]) ).
fof(sk_church_46_9_2_neg,plain,
( ! [VAR_0] : ~ big_g(sK0(VAR_0))
& ! [VAR_0] :
( big_g(VAR_0)
| ~ big_f(sK0(VAR_0),sK0(VAR_0)) )
& ! [VAR_0] :
( big_f(VAR_0,sK0(VAR_0))
| ~ big_f(sK0(VAR_0),sK0(VAR_0)) )
& ! [VAR_0] :
( big_g(VAR_0)
| big_f(VAR_0,VAR_0) )
& ! [VAR_0] :
( big_f(VAR_0,sK0(VAR_0))
| big_f(VAR_0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_9_2_neg_sk]) ).
cnf(c_2,negated_conjecture,
~ big_g(sK0(A)),
inference(split_conjunct,[status(thm)],[sk_church_46_9_2_neg]) ).
cnf(c_3,negated_conjecture,
( big_g(A)
| ~ big_f(sK0(A),sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_9_2_neg]) ).
cnf(c_4,negated_conjecture,
( big_g(A)
| big_f(A,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_9_2_neg]) ).
cnf(c_5,negated_conjecture,
big_f(sK0(A),sK0(A)),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_6,negated_conjecture,
~ big_f(sK0(sK0(A)),sK0(sK0(A))),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN325+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 17:34:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 4158904 was started by sandbox on n008,
% 0.11/0.37 % Sat Sep 26 17:34:55 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 7.
% 0.11/0.38 % Level of proof is 3.
% 0.11/0.38 % Maximum clause weight is 5.000.
% 0.11/0.38 % Given clauses 0.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------