%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN331+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 : n016.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 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 46 ( 11 ~; 13 |; 12 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 22 ( 3 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_3,conjecture,
? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Z,Z)
| big_f(Y,X) )
=> ( big_f(Z,Y)
| big_f(Z,X) ) ) ) ) ),
file('theBenchmark.p',church_46_14_3) ).
fof(church_46_14_3_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Z,Z)
| big_f(Y,X) )
=> ( big_f(Z,Y)
| big_f(Z,X) ) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_14_3]) ).
fof(nnf_1,plain,
! [X,Y] :
? [Z] :
( ~ big_f(Z,Y)
& ~ big_f(Z,X)
& ( big_f(Z,Z)
| big_f(Y,X) )
& ( ~ big_f(Z,Z)
| big_f(X,Y) )
& ( big_f(Z,Z)
| ~ big_f(X,Y) )
& big_f(Y,Z)
& big_f(X,Z) ),
inference(fof_nnf,[status(thm)],[church_46_14_3_neg]) ).
fof(sk_church_46_14_3_neg,plain,
! [X,Y] :
( ~ big_f(sK0(X,Y),Y)
& ~ big_f(sK0(X,Y),X)
& ( big_f(sK0(X,Y),sK0(X,Y))
| big_f(Y,X) )
& ( ~ big_f(sK0(X,Y),sK0(X,Y))
| big_f(X,Y) )
& ( big_f(sK0(X,Y),sK0(X,Y))
| ~ big_f(X,Y) )
& big_f(Y,sK0(X,Y))
& big_f(X,sK0(X,Y)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
cnf(c_5,negated_conjecture,
( ~ big_f(sK0(A,B),sK0(A,B))
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_3_neg]) ).
cnf(c_6,negated_conjecture,
( big_f(sK0(B,A),sK0(B,A))
| big_f(A,B) ),
inference(split_conjunct,[status(thm)],[sk_church_46_14_3_neg]) ).
cnf(c_8,negated_conjecture,
~ big_f(sK0(A,B),B),
inference(split_conjunct,[status(thm)],[sk_church_46_14_3_neg]) ).
cnf(c_11,plain,
( big_f(B,A)
| big_f(A,B) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_12,plain,
big_f(A,A),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_13,negated_conjecture,
big_f(A,B),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN331+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 : n016.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 17:39:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1394136 was started by sandbox on n016,
% 0.09/0.36 % Sat Sep 26 17:39:47 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 8.
% 0.09/0.38 % Level of proof is 5.
% 0.09/0.38 % Maximum clause weight is 10.000.
% 0.09/0.38 % Given clauses 5.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------