%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN333+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 : n015.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 09:37:35 AM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 68 ( 28 ~; 20 |; 16 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 33 ( 4 sgn 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_5,conjecture,
? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( ( ( big_g(X,Y)
& big_f(X,Y) )
=> ( big_g(Z,Z)
& big_g(X,Z) ) )
& big_f(Z,Z)
& big_f(Y,Z) ) ),
file('theBenchmark.p',church_46_14_5) ).
fof(church_46_14_5_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( ( ( big_g(X,Y)
& big_f(X,Y) )
=> ( big_g(Z,Z)
& big_g(X,Z) ) )
& big_f(Z,Z)
& big_f(Y,Z) ) ),
inference(assume_negation,[status(cth)],[church_46_14_5]) ).
fof(nnf_1,plain,
! [X,Y] :
? [Z] :
( ( ( ( ~ big_g(Z,Z)
| ~ big_g(X,Z) )
& big_g(X,Y)
& big_f(X,Y) )
| ~ big_f(Z,Z)
| ~ big_f(Y,Z) )
& big_f(X,Y) ),
inference(fof_nnf,[status(thm)],[church_46_14_5_neg]) ).
fof(sk_church_46_14_5_neg_sk,plain,
! [X,Y] :
( ( ( ( ~ big_g(sK0(X,Y),sK0(X,Y))
| ~ big_g(X,sK0(X,Y)) )
& big_g(X,Y)
& big_f(X,Y) )
| ~ big_f(sK0(X,Y),sK0(X,Y))
| ~ big_f(Y,sK0(X,Y)) )
& big_f(X,Y) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_church_46_14_5_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_g(sK0(VAR_1,VAR_0),sK0(VAR_1,VAR_0))
| ~ big_g(VAR_1,sK0(VAR_1,VAR_0))
| ~ big_f(sK0(VAR_1,VAR_0),sK0(VAR_1,VAR_0))
| ~ big_f(VAR_0,sK0(VAR_1,VAR_0)) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_1,VAR_0)
| ~ big_f(sK0(VAR_1,VAR_0),sK0(VAR_1,VAR_0))
| ~ big_f(VAR_0,sK0(VAR_1,VAR_0)) )
& ! [VAR_0,VAR_1] : big_f(VAR_0,VAR_1) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_14_5_neg_sk]) ).
cnf(c_2,negated_conjecture,
big_f(A,B),
inference(split_conjunct,[status(thm)],[sk_church_46_14_5_neg]) ).
cnf(c_3,negated_conjecture,
( big_g(B,A)
| ~ big_f(sK0(B,A),sK0(B,A))
| ~ big_f(A,sK0(B,A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_5_neg]) ).
cnf(c_7,negated_conjecture,
( big_g(A,B)
| ~ big_f(sK0(A,B),sK0(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_4,negated_conjecture,
big_g(A,B),
inference(resolve,[status(thm)],[c_2,c_7]) ).
cnf(c_5,negated_conjecture,
( ~ big_g(sK0(B,A),sK0(B,A))
| ~ big_g(B,sK0(B,A))
| ~ big_f(sK0(B,A),sK0(B,A))
| ~ big_f(A,sK0(B,A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_5_neg]) ).
cnf(c_8,negated_conjecture,
( ~ big_g(sK0(A,B),sK0(A,B))
| ~ big_g(A,sK0(A,B))
| ~ big_f(sK0(A,B),sK0(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_5]) ).
cnf(c_9,negated_conjecture,
( ~ big_g(sK0(A,B),sK0(A,B))
| ~ big_g(A,sK0(A,B)) ),
inference(resolve,[status(thm)],[c_2,c_8]) ).
cnf(c_10,negated_conjecture,
~ big_g(sK0(A,B),sK0(A,B)),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_6,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_4,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN333+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 17:38:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 392109 was started by sandbox on n015,
% 0.08/0.36 % Sat Sep 26 17:38:44 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 6.
% 0.08/0.37 % Level of proof is 3.
% 0.08/0.37 % Maximum clause weight is 3.000.
% 0.08/0.37 % Given clauses 0.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------