%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN327+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 : n014.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 62 ( 24 ~; 14 |; 16 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 19 ( 1 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_12_2,conjecture,
! [X] :
? [Y] :
! [Z] :
( big_f(Y,X)
=> ( ( big_f(X,Y)
=> ( ~ big_f(X,Z)
=> ( big_f(Z,Y)
& big_f(Y,X) ) ) )
& ( big_f(X,Z)
=> big_f(X,Y) ) ) ),
file('theBenchmark.p',church_46_12_2) ).
fof(church_46_12_2_neg,negated_conjecture,
~ ! [X] :
? [Y] :
! [Z] :
( big_f(Y,X)
=> ( ( big_f(X,Y)
=> ( ~ big_f(X,Z)
=> ( big_f(Z,Y)
& big_f(Y,X) ) ) )
& ( big_f(X,Z)
=> big_f(X,Y) ) ) ),
inference(assume_negation,[status(cth)],[church_46_12_2]) ).
fof(nnf_1,plain,
? [X] :
! [Y] :
? [Z] :
( ( ( ( ~ big_f(Z,Y)
| ~ big_f(Y,X) )
& ~ big_f(X,Z)
& big_f(X,Y) )
| ( ~ big_f(X,Y)
& big_f(X,Z) ) )
& big_f(Y,X) ),
inference(fof_nnf,[status(thm)],[church_46_12_2_neg]) ).
fof(sk_church_46_12_2_neg_sk,plain,
! [Y] :
( ( ( ( ~ big_f(sK1(Y),Y)
| ~ big_f(Y,sK0) )
& ~ big_f(sK0,sK1(Y))
& big_f(sK0,Y) )
| ( ~ big_f(sK0,Y)
& big_f(sK0,sK1(Y)) ) )
& big_f(Y,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Z,sK1(Y))],[nnf_1]) ).
fof(sk_church_46_12_2_neg,plain,
( ! [VAR_0] :
( ~ big_f(sK1(VAR_0),VAR_0)
| ~ big_f(VAR_0,sK0)
| ~ big_f(sK0,VAR_0) )
& ! [VAR_0] :
( ~ big_f(sK0,sK1(VAR_0))
| ~ big_f(sK0,VAR_0) )
& ! [VAR_0] :
( ~ big_f(sK1(VAR_0),VAR_0)
| ~ big_f(VAR_0,sK0)
| big_f(sK0,sK1(VAR_0)) )
& ! [VAR_0] :
( big_f(sK0,VAR_0)
| big_f(sK0,sK1(VAR_0)) )
& ! [VAR_0] : big_f(VAR_0,sK0) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_12_2_neg_sk]) ).
cnf(c_2,negated_conjecture,
big_f(A,sK0),
inference(split_conjunct,[status(thm)],[sk_church_46_12_2_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_f(sK1(A),A)
| ~ big_f(A,sK0)
| big_f(sK0,sK1(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_2_neg]) ).
cnf(c_5,negated_conjecture,
( ~ big_f(sK1(A),A)
| big_f(sK0,sK1(A)) ),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_6,negated_conjecture,
( ~ big_f(sK0,sK1(A))
| ~ big_f(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_2_neg]) ).
cnf(c_9,plain,
big_f(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_11,negated_conjecture,
~ big_f(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_10,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_9,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN327+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:34:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3729179 was started by sandbox2 on n014,
% 0.08/0.36 % Sat Sep 26 17:34:17 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 7.
% 0.13/0.37 % Level of proof is 4.
% 0.13/0.37 % Maximum clause weight is 8.000.
% 0.13/0.37 % Given clauses 4.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------