%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN346+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 : n002.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 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 33 ( 12 ~; 7 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 5 sgn 12 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_17_2,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z1,Z2] :
( big_f(X2,Z1)
=> ( big_f(Y1,Z2)
=> ( ( big_f(Y2,Z2)
& big_f(X2,Z2) )
| ( big_f(Y2,Z1)
& big_f(Y1,Z1) ) ) ) ),
file('theBenchmark.p',church_46_17_2) ).
fof(church_46_17_2_neg,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z1,Z2] :
( big_f(X2,Z1)
=> ( big_f(Y1,Z2)
=> ( ( big_f(Y2,Z2)
& big_f(X2,Z2) )
| ( big_f(Y2,Z1)
& big_f(Y1,Z1) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_17_2]) ).
fof(nnf_1,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z1,Z2] :
( ( ~ big_f(Y2,Z2)
| ~ big_f(X2,Z2) )
& ( ~ big_f(Y2,Z1)
| ~ big_f(Y1,Z1) )
& big_f(Y1,Z2)
& big_f(X2,Z1) ),
inference(fof_nnf,[status(thm)],[church_46_17_2_neg]) ).
fof(sk_church_46_17_2_neg,plain,
! [Y1,Y2] :
( ( ~ big_f(Y2,sK2(Y1,Y2))
| ~ big_f(sK0,sK2(Y1,Y2)) )
& ( ~ big_f(Y2,sK1(Y1,Y2))
| ~ big_f(Y1,sK1(Y1,Y2)) )
& big_f(Y1,sK2(Y1,Y2))
& big_f(sK0,sK1(Y1,Y2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK3),skolemize(X2,sK0),skolemize(Z1,sK1(Y1,Y2)),skolemize(Z2,sK2(Y1,Y2))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
big_f(sK0,sK1(A,B)),
inference(split_conjunct,[status(thm)],[sk_church_46_17_2_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_f(B,sK1(A,B))
| ~ big_f(A,sK1(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_17_2_neg]) ).
cnf(c_6,plain,
~ big_f(A,sK1(sK0,A)),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_7,plain,
$false,
inference(resolve,[status(thm)],[c_6,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN346+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n002.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 17:39:05 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2307296 was started by sandbox2 on n002,
% 0.18/0.43 % Sat Sep 26 17:39:05 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.45
% 0.18/0.45 % SZS status Theorem for theBenchmark
% 0.18/0.45
% 0.18/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.45 % Length of proof is 5.
% 0.18/0.45 % Level of proof is 3.
% 0.18/0.45 % Maximum clause weight is 10.000.
% 0.18/0.45 % Given clauses 3.
% 0.18/0.45
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------