%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN319+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 : n004.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 09:37:32 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 89 ( 29 ~; 22 |; 24 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% Number of variables : 42 ( 13 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_2_5,conjecture,
? [X,Y] :
! [Z1,Z2] :
( ( ( big_f(Y)
=> big_g(Z1) )
=> ( ~ big_f(Z1)
& big_g(X) ) )
=> ( ( ( big_g(X)
| big_f(X) )
=> big_h(X) )
=> ( ( big_h(Y)
=> ( ( big_g(Z2)
| big_f(Z2) )
=> big_h(Z2) ) )
& big_h(Z2) ) ) ),
file('theBenchmark.p',church_46_2_5) ).
fof(church_46_2_5_neg,negated_conjecture,
~ ? [X,Y] :
! [Z1,Z2] :
( ( ( big_f(Y)
=> big_g(Z1) )
=> ( ~ big_f(Z1)
& big_g(X) ) )
=> ( ( ( big_g(X)
| big_f(X) )
=> big_h(X) )
=> ( ( big_h(Y)
=> ( ( big_g(Z2)
| big_f(Z2) )
=> big_h(Z2) ) )
& big_h(Z2) ) ) ),
inference(assume_negation,[status(cth)],[church_46_2_5]) ).
fof(nnf_1,plain,
! [X,Y] :
? [Z1,Z2] :
( ( ( ~ big_h(Z2)
& ( big_g(Z2)
| big_f(Z2) )
& big_h(Y) )
| ~ big_h(Z2) )
& ( big_h(X)
| ( ~ big_g(X)
& ~ big_f(X) ) )
& ( ( ~ big_f(Z1)
& big_g(X) )
| ( ~ big_g(Z1)
& big_f(Y) ) ) ),
inference(fof_nnf,[status(thm)],[church_46_2_5_neg]) ).
fof(sk_church_46_2_5_neg_sk,plain,
! [X,Y] :
( ( ( ~ big_h(sK0(X,Y))
& ( big_g(sK0(X,Y))
| big_f(sK0(X,Y)) )
& big_h(Y) )
| ~ big_h(sK0(X,Y)) )
& ( big_h(X)
| ( ~ big_g(X)
& ~ big_f(X) ) )
& ( ( ~ big_f(sK1(X,Y))
& big_g(X) )
| ( ~ big_g(sK1(X,Y))
& big_f(Y) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(Z1,sK1(X,Y)),skolemize(Z2,sK0(X,Y))],[nnf_1]) ).
fof(sk_church_46_2_5_neg,plain,
( ! [VAR_0,VAR_1] : ~ big_h(sK0(VAR_0,VAR_1))
& ! [VAR_0] :
( big_h(VAR_0)
| ~ big_g(VAR_0) )
& ! [VAR_0] :
( big_h(VAR_0)
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK1(VAR_0,VAR_1))
| ~ big_g(sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_0)
| ~ big_g(sK1(VAR_0,VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ big_f(sK1(VAR_1,VAR_0))
| big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_1)
| big_f(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_2_5_neg_sk]) ).
cnf(c_2,negated_conjecture,
~ big_h(sK0(A,B)),
inference(split_conjunct,[status(thm)],[sk_church_46_2_5_neg]) ).
cnf(c_3,negated_conjecture,
( big_h(A)
| ~ big_g(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_2_5_neg]) ).
cnf(c_4,negated_conjecture,
( big_h(A)
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_2_5_neg]) ).
cnf(c_5,negated_conjecture,
~ big_f(sK0(A,B)),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_6,negated_conjecture,
~ big_g(sK0(A,B)),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_9,negated_conjecture,
( ~ big_f(sK1(B,A))
| big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_2_5_neg]) ).
cnf(c_10,negated_conjecture,
( big_g(B)
| big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_2_5_neg]) ).
cnf(c_12,negated_conjecture,
~ big_f(sK1(A,sK0(B,C))),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_14,plain,
big_f(A),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN319+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n004.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sat Sep 26 17:33:08 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.38 % Process 2246918 was started by sandbox on n004,
% 0.13/0.38 % Sat Sep 26 17:33:08 2026
% 0.13/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 11.
% 0.13/0.39 % Level of proof is 4.
% 0.13/0.39 % Maximum clause weight is 6.000.
% 0.13/0.39 % Given clauses 6.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------