%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN323+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 : n017.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 09:37:33 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 28 ( 12 ~; 6 |; 0 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 20 ( 0 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_4_2,conjecture,
? [Y] :
( ! [X] :
( ( big_f(X,Y)
=> big_f(Y,X) )
=> big_g(X,Y) )
=> ~ ! [X] :
( ( big_f(X,Y)
=> big_f(Y,X) )
=> ~ big_g(X,Y) ) ),
file('theBenchmark.p',church_46_4_2) ).
fof(church_46_4_2_neg,negated_conjecture,
~ ? [Y] :
( ! [X] :
( ( big_f(X,Y)
=> big_f(Y,X) )
=> big_g(X,Y) )
=> ~ ! [X] :
( ( big_f(X,Y)
=> big_f(Y,X) )
=> ~ big_g(X,Y) ) ),
inference(assume_negation,[status(cth)],[church_46_4_2]) ).
cnf(c_2,negated_conjecture,
( big_g(B,A)
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[church_46_4_2_neg]) ).
cnf(c_3,negated_conjecture,
( big_g(A,B)
| big_f(A,B) ),
inference(clausify,[status(thm)],[church_46_4_2_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_g(A,B)
| big_f(A,B) ),
inference(clausify,[status(thm)],[church_46_4_2_neg]) ).
cnf(c_5,negated_conjecture,
( ~ big_g(B,A)
| ~ big_f(A,B) ),
inference(clausify,[status(thm)],[church_46_4_2_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_g(B,A)
| ~ big_g(A,B) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_8,negated_conjecture,
( big_g(B,A)
| big_g(A,B) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_9,plain,
~ big_g(A,A),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_11,plain,
big_g(A,A),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_10,plain,
$false,
inference(resolve,[status(thm)],[c_9,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN323+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 17:29:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1266597 was started by sandbox2 on n017,
% 0.10/0.37 % Sat Sep 26 17:29:49 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 9.
% 0.10/0.38 % Level of proof is 4.
% 0.10/0.38 % Maximum clause weight is 6.000.
% 0.10/0.38 % Given clauses 0.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------