%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN321+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 : n005.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 0.14s 5.80s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 57 ( 20 ~; 18 |; 9 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 53 ( 10 sgn 28 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_3_2,conjecture,
? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
file('theBenchmark.p',church_46_3_2) ).
fof(church_46_3_2_neg,negated_conjecture,
~ ? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
inference(assume_negation,[status(cth)],[church_46_3_2]) ).
fof(nnf_1,plain,
! [X,Y] :
( ( ? [Z] : ~ big_g(X,Z)
| ~ big_f(X,Y) )
& ( ! [X3] : big_g(X,X3)
| big_f(X,Y) )
& ! [X2] :
( big_f(X2,Y)
| ~ big_g(X2,X2) )
& ( ! [X1] : big_g(X,X1)
| ! [X0] : ~ big_f(X,X0) ) ),
inference(fof_nnf,[status(thm)],[church_46_3_2_neg]) ).
fof(sk_church_46_3_2_neg_sk,plain,
! [X,Y] :
( ( ~ big_g(X,sK0(X,Y))
| ~ big_f(X,Y) )
& ( ! [X3] : big_g(X,X3)
| big_f(X,Y) )
& ! [X2] :
( big_f(X2,Y)
| ~ big_g(X2,X2) )
& ( ! [X1] : big_g(X,X1)
| ! [X0] : ~ big_f(X,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_church_46_3_2_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_g(VAR_0,sK0(VAR_0,VAR_1))
| ~ big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_g(VAR_0,VAR_2)
| big_f(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_f(VAR_0,VAR_1)
| ~ big_g(VAR_0,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_g(VAR_0,VAR_2)
| ~ big_f(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_3_2_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_f(A,B)
| ~ big_g(A,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_3_2_neg]) ).
cnf(c_3,negated_conjecture,
( big_g(A,C)
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_3_2_neg]) ).
cnf(c_4,negated_conjecture,
( big_g(A,C)
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_3_2_neg]) ).
cnf(c_5,negated_conjecture,
( ~ big_g(A,sK0(A,B))
| ~ big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_3_2_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_g(A,A)
| ~ big_g(A,sK0(A,B)) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_7,negated_conjecture,
( big_g(A,C)
| big_g(A,B) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_9,plain,
big_g(A,B),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_11,negated_conjecture,
~ big_g(A,A),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_10,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_9,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN321+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.78 % Computer : n005.cluster.edu
% 0.11/5.78 % Model : x86_64 x86_64
% 0.11/5.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.78 % Memory : 8046.5625MB
% 0.11/5.78 % OS : Linux 6.8.0-71-generic
% 0.11/5.78 % CPULimit : 300
% 0.11/5.78 % WCLimit : 300
% 0.11/5.78 % DateTime : Sat Sep 26 17:33:22 UTC 2026
% 0.11/5.78 % CPUTime :
% 0.11/5.79 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.79 % Process 2657782 was started by sandbox2 on n005,
% 0.11/5.79 % Sat Sep 26 17:33:22 2026
% 0.11/5.79 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.79
% 0.11/5.79 % From the command line: assign(max_seconds, 300).
% 0.14/5.80
% 0.14/5.80 % SZS status Theorem for theBenchmark
% 0.14/5.80
% 0.14/5.80 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.80 % Length of proof is 9.
% 0.14/5.80 % Level of proof is 4.
% 0.14/5.80 % Maximum clause weight is 8.000.
% 0.14/5.80 % Given clauses 0.
% 0.14/5.80
% 0.14/5.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------