%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN336+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 : n018.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 09:37:36 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 20 ( 4 ~; 0 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 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 : 17 ( 2 sgn 8 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_15_1,conjecture,
! [X] :
? [Y1,Y2] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y1,Z)
=> ( big_f(Y2,Z)
=> ( big_f(Y1,X)
=> big_f(Z,Y2) ) ) ) ),
file('theBenchmark.p',church_46_15_1) ).
fof(church_46_15_1_neg,negated_conjecture,
~ ! [X] :
? [Y1,Y2] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y1,Z)
=> ( big_f(Y2,Z)
=> ( big_f(Y1,X)
=> big_f(Z,Y2) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_15_1]) ).
fof(nnf_1,plain,
? [X] :
! [Y1,Y2] :
? [Z] :
( ~ big_f(Z,Y2)
& big_f(Y1,X)
& big_f(Y2,Z)
& big_f(Y1,Z)
& big_f(X,Z) ),
inference(fof_nnf,[status(thm)],[church_46_15_1_neg]) ).
fof(sk_church_46_15_1_neg,plain,
! [Y1,Y2] :
( ~ big_f(sK0(Y1,Y2),Y2)
& big_f(Y1,sK1)
& big_f(Y2,sK0(Y1,Y2))
& big_f(Y1,sK0(Y1,Y2))
& big_f(sK1,sK0(Y1,Y2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK1),skolemize(Z,sK0(Y1,Y2))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
~ big_f(sK0(A,B),B),
inference(split_conjunct,[status(thm)],[sk_church_46_15_1_neg]) ).
cnf(c_3,negated_conjecture,
big_f(A,sK1),
inference(split_conjunct,[status(thm)],[sk_church_46_15_1_neg]) ).
cnf(c_7,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN336+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 17:37:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1004444 was started by sandbox2 on n018,
% 0.09/0.37 % Sat Sep 26 17:37:37 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 4.
% 0.09/0.39 % Level of proof is 2.
% 0.09/0.39 % Maximum clause weight is 0.000.
% 0.09/0.39 % Given clauses 0.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------