%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN350+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 : n009.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 09:37:39 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 86 ( 32 ~; 29 |; 17 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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; 0-2 aty)
% Number of variables : 41 ( 4 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_2,conjecture,
! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
file('theBenchmark.p',church_46_18_2) ).
fof(church_46_18_2_neg,negated_conjecture,
~ ! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
inference(assume_negation,[status(cth)],[church_46_18_2]) ).
fof(nnf_1,plain,
? [X] :
! [Y1,Y2] :
? [Z] :
( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,Z) )
| ~ big_f(Y2,Z)
| ~ big_f(X,Z) )
& ( ( ( big_f(Y1,Y2)
| ~ big_f(Y1,Z) )
& big_f(Y2,Z) )
| big_f(X,Z) )
& ( ~ big_f(Z,X)
| big_f(X,Z) )
& ( big_f(Z,X)
| ~ big_f(X,Z) ) ),
inference(fof_nnf,[status(thm)],[church_46_18_2_neg]) ).
fof(sk_church_46_18_2_neg_sk,plain,
! [Y1,Y2] :
( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,sK1(Y1,Y2)) )
| ~ big_f(Y2,sK1(Y1,Y2))
| ~ big_f(sK0,sK1(Y1,Y2)) )
& ( ( ( big_f(Y1,Y2)
| ~ big_f(Y1,sK1(Y1,Y2)) )
& big_f(Y2,sK1(Y1,Y2)) )
| big_f(sK0,sK1(Y1,Y2)) )
& ( ~ big_f(sK1(Y1,Y2),sK0)
| big_f(sK0,sK1(Y1,Y2)) )
& ( big_f(sK1(Y1,Y2),sK0)
| ~ big_f(sK0,sK1(Y1,Y2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Z,sK1(Y1,Y2))],[nnf_1]) ).
fof(sk_church_46_18_2_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_f(VAR_0,VAR_1)
| ~ big_f(VAR_1,sK1(VAR_0,VAR_1))
| ~ big_f(sK0,sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(VAR_0,sK1(VAR_0,VAR_1))
| ~ big_f(VAR_1,sK1(VAR_0,VAR_1))
| ~ big_f(sK0,sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(VAR_0,VAR_1)
| ~ big_f(VAR_0,sK1(VAR_0,VAR_1))
| big_f(sK0,sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(VAR_1,sK1(VAR_0,VAR_1))
| big_f(sK0,sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK1(VAR_0,VAR_1),sK0)
| big_f(sK0,sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_f(sK1(VAR_0,VAR_1),sK0)
| ~ big_f(sK0,sK1(VAR_0,VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_18_2_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_f(sK1(A,B),sK0)
| ~ big_f(sK0,sK1(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_18_2_neg]) ).
cnf(c_4,negated_conjecture,
( big_f(B,sK1(A,B))
| big_f(sK0,sK1(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_18_2_neg]) ).
cnf(c_6,negated_conjecture,
( big_f(A,sK1(A,B))
| ~ big_f(B,sK1(A,B))
| ~ big_f(sK0,sK1(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_18_2_neg]) ).
cnf(c_7,negated_conjecture,
( ~ big_f(A,B)
| ~ big_f(B,sK1(A,B))
| ~ big_f(sK0,sK1(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_18_2_neg]) ).
cnf(c_8,plain,
big_f(sK0,sK1(A,sK0)),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_13,plain,
( big_f(A,sK1(A,sK0))
| ~ big_f(sK0,sK1(A,sK0)) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_9,plain,
big_f(A,sK1(A,sK0)),
inference(resolve,[status(thm)],[c_8,c_13]) ).
cnf(c_14,plain,
( ~ big_f(A,sK0)
| ~ big_f(sK0,sK1(A,sK0)) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_10,plain,
~ big_f(A,sK0),
inference(resolve,[status(thm)],[c_8,c_14]) ).
cnf(c_11,negated_conjecture,
~ big_f(sK0,sK1(A,B)),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_12,plain,
$false,
inference(resolve,[status(thm)],[c_11,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 17:36:59 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 732686 was started by sandbox2 on n009,
% 0.08/0.36 % Sat Sep 26 17:36:59 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 10.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 15.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------