%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN328+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 : n013.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 09:37:34 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 4 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 200 ( 68 ~; 78 |; 34 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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; 1-1 aty)
% Number of variables : 47 ( 3 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_12_3,conjecture,
? [X] :
! [Y,Z] :
( ( ( big_f(Y)
=> big_g(Y) )
<=> big_f(X) )
=> ( ( ( big_f(Y)
=> big_h(Y) )
<=> big_g(X) )
=> ( ( ( ( big_f(Y)
=> big_g(Y) )
=> big_h(Y) )
<=> big_h(X) )
=> ( big_h(Z)
& big_g(Z)
& big_f(Z) ) ) ) ),
file('theBenchmark.p',church_46_12_3) ).
fof(church_46_12_3_neg,negated_conjecture,
~ ? [X] :
! [Y,Z] :
( ( ( big_f(Y)
=> big_g(Y) )
<=> big_f(X) )
=> ( ( ( big_f(Y)
=> big_h(Y) )
<=> big_g(X) )
=> ( ( ( ( big_f(Y)
=> big_g(Y) )
=> big_h(Y) )
<=> big_h(X) )
=> ( big_h(Z)
& big_g(Z)
& big_f(Z) ) ) ) ),
inference(assume_negation,[status(cth)],[church_46_12_3]) ).
fof(nnf_1,plain,
! [X] :
? [Y,Z] :
( ( ~ big_h(Z)
| ~ big_g(Z)
| ~ big_f(Z) )
& ( ~ big_h(X)
| big_h(Y)
| ( ~ big_g(Y)
& big_f(Y) ) )
& ( big_h(X)
| ( ~ big_h(Y)
& ( big_g(Y)
| ~ big_f(Y) ) ) )
& ( ~ big_g(X)
| big_h(Y)
| ~ big_f(Y) )
& ( big_g(X)
| ( ~ big_h(Y)
& big_f(Y) ) )
& ( ~ big_f(X)
| big_g(Y)
| ~ big_f(Y) )
& ( big_f(X)
| ( ~ big_g(Y)
& big_f(Y) ) ) ),
inference(fof_nnf,[status(thm)],[church_46_12_3_neg]) ).
fof(sk_church_46_12_3_neg_sk,plain,
! [X] :
( ( ~ big_h(sK1(X))
| ~ big_g(sK1(X))
| ~ big_f(sK1(X)) )
& ( ~ big_h(X)
| big_h(sK0(X))
| ( ~ big_g(sK0(X))
& big_f(sK0(X)) ) )
& ( big_h(X)
| ( ~ big_h(sK0(X))
& ( big_g(sK0(X))
| ~ big_f(sK0(X)) ) ) )
& ( ~ big_g(X)
| big_h(sK0(X))
| ~ big_f(sK0(X)) )
& ( big_g(X)
| ( ~ big_h(sK0(X))
& big_f(sK0(X)) ) )
& ( ~ big_f(X)
| big_g(sK0(X))
| ~ big_f(sK0(X)) )
& ( big_f(X)
| ( ~ big_g(sK0(X))
& big_f(sK0(X)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Y,sK0(X)),skolemize(Z,sK1(X))],[nnf_1]) ).
fof(sk_church_46_12_3_neg,plain,
( ! [VAR_0] :
( ~ big_h(sK1(VAR_0))
| ~ big_g(sK1(VAR_0))
| ~ big_f(sK1(VAR_0)) )
& ! [VAR_0] :
( ~ big_h(VAR_0)
| big_h(sK0(VAR_0))
| ~ big_g(sK0(VAR_0)) )
& ! [VAR_0] :
( ~ big_h(VAR_0)
| big_h(sK0(VAR_0))
| big_f(sK0(VAR_0)) )
& ! [VAR_0] :
( big_h(VAR_0)
| ~ big_h(sK0(VAR_0)) )
& ! [VAR_0] :
( big_h(VAR_0)
| big_g(sK0(VAR_0))
| ~ big_f(sK0(VAR_0)) )
& ! [VAR_0] :
( ~ big_g(VAR_0)
| big_h(sK0(VAR_0))
| ~ big_f(sK0(VAR_0)) )
& ! [VAR_0] :
( big_g(VAR_0)
| ~ big_h(sK0(VAR_0)) )
& ! [VAR_0] :
( big_g(VAR_0)
| big_f(sK0(VAR_0)) )
& ! [VAR_0] :
( ~ big_f(VAR_0)
| big_g(sK0(VAR_0))
| ~ big_f(sK0(VAR_0)) )
& ! [VAR_0] :
( big_f(VAR_0)
| ~ big_g(sK0(VAR_0)) )
& ! [VAR_0] :
( big_f(VAR_0)
| big_f(sK0(VAR_0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_12_3_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ big_f(A)
| big_g(sK0(A))
| ~ big_f(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_3,negated_conjecture,
( big_f(A)
| ~ big_g(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_5,negated_conjecture,
( big_g(A)
| ~ big_h(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_g(A)
| big_h(sK0(A))
| ~ big_f(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_7,negated_conjecture,
( big_h(A)
| big_g(sK0(A))
| ~ big_f(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_9,negated_conjecture,
( ~ big_h(sK1(A))
| ~ big_g(sK1(A))
| ~ big_f(sK1(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_11,negated_conjecture,
( ~ big_h(sK0(sK1(A)))
| ~ big_h(sK1(A))
| ~ big_f(sK1(A)) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_15,negated_conjecture,
( big_f(A)
| big_h(A)
| ~ big_f(sK0(A)) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_17,negated_conjecture,
( ~ big_f(A)
| ~ big_f(sK0(A))
| big_h(sK0(sK0(A)))
| ~ big_f(sK0(sK0(A))) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_18,negated_conjecture,
( big_f(A)
| ~ big_h(sK0(sK0(A))) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_21,negated_conjecture,
( big_h(A)
| ~ big_h(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_22,negated_conjecture,
( big_f(A)
| big_f(sK0(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_3_neg]) ).
cnf(c_71,negated_conjecture,
( big_f(A)
| big_h(A)
| big_f(A) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_26,negated_conjecture,
( big_h(A)
| big_f(A) ),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,negated_conjecture,
( ~ big_f(A)
| ~ big_f(sK0(A))
| big_h(sK0(sK0(A)))
| big_h(sK0(sK0(A))) ),
inference(resolve,[status(thm)],[c_26,c_17]) ).
cnf(c_33,negated_conjecture,
( ~ big_f(A)
| ~ big_f(sK0(A))
| big_h(sK0(sK0(A))) ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_35,plain,
( big_h(A)
| big_f(sK0(A)) ),
inference(resolve,[status(thm)],[c_26,c_21]) ).
cnf(c_46,plain,
( big_h(A)
| ~ big_f(A)
| big_h(sK0(sK0(A))) ),
inference(resolve,[status(thm)],[c_33,c_35]) ).
cnf(c_73,plain,
( big_h(A)
| big_h(A)
| big_h(sK0(sK0(A))) ),
inference(resolve,[status(thm)],[c_46,c_26]) ).
cnf(c_52,plain,
( big_h(A)
| big_h(sK0(sK0(A))) ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_59,plain,
( big_h(sK0(A))
| big_h(A) ),
inference(resolve,[status(thm)],[c_52,c_21]) ).
cnf(c_74,negated_conjecture,
( big_h(A)
| big_h(A) ),
inference(resolve,[status(thm)],[c_59,c_21]) ).
cnf(c_66,negated_conjecture,
big_h(A),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_69,negated_conjecture,
big_f(A),
inference(resolve,[status(thm)],[c_66,c_18]) ).
cnf(c_75,negated_conjecture,
( ~ big_h(sK0(sK1(A)))
| ~ big_h(sK1(A)) ),
inference(resolve,[status(thm)],[c_69,c_11]) ).
cnf(c_76,negated_conjecture,
~ big_h(sK0(sK1(A))),
inference(resolve,[status(thm)],[c_66,c_75]) ).
cnf(c_70,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN328+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n013.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 17:34:08 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3251196 was started by sandbox2 on n013,
% 0.17/0.44 % Sat Sep 26 17:34:08 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 22.
% 0.17/0.46 % Level of proof is 10.
% 0.17/0.46 % Maximum clause weight is 28.000.
% 0.17/0.46 % Given clauses 26.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------