%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN326+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 : n007.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 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 61 ( 13 ~; 14 |; 18 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 24 ( 0 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_12_1,conjecture,
? [X] :
! [Y,Z] :
( ( ( big_f(Y,Z)
=> ( big_g(Y)
=> big_h(X) ) )
=> big_f(X,X) )
=> ( ( ( big_f(Z,X)
=> big_g(X) )
=> big_h(Z) )
=> ( big_f(X,Y)
=> big_f(Z,Z) ) ) ),
file('theBenchmark.p',church_46_12_1) ).
fof(church_46_12_1_neg,negated_conjecture,
~ ? [X] :
! [Y,Z] :
( ( ( big_f(Y,Z)
=> ( big_g(Y)
=> big_h(X) ) )
=> big_f(X,X) )
=> ( ( ( big_f(Z,X)
=> big_g(X) )
=> big_h(Z) )
=> ( big_f(X,Y)
=> big_f(Z,Z) ) ) ),
inference(assume_negation,[status(cth)],[church_46_12_1]) ).
fof(nnf_1,plain,
! [X] :
? [Y,Z] :
( ~ big_f(Z,Z)
& big_f(X,Y)
& ( big_h(Z)
| ( ~ big_g(X)
& big_f(Z,X) ) )
& ( big_f(X,X)
| ( ~ big_h(X)
& big_g(Y)
& big_f(Y,Z) ) ) ),
inference(fof_nnf,[status(thm)],[church_46_12_1_neg]) ).
fof(sk_church_46_12_1_neg_sk,plain,
! [X] :
( ~ big_f(sK0(X),sK0(X))
& big_f(X,sK1(X))
& ( big_h(sK0(X))
| ( ~ big_g(X)
& big_f(sK0(X),X) ) )
& ( big_f(X,X)
| ( ~ big_h(X)
& big_g(sK1(X))
& big_f(sK1(X),sK0(X)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(Y,sK1(X)),skolemize(Z,sK0(X))],[nnf_1]) ).
fof(sk_church_46_12_1_neg,plain,
( ! [VAR_0] : ~ big_f(sK0(VAR_0),sK0(VAR_0))
& ! [VAR_0] : big_f(VAR_0,sK1(VAR_0))
& ! [VAR_0] :
( big_h(sK0(VAR_0))
| ~ big_g(VAR_0) )
& ! [VAR_0] :
( big_h(sK0(VAR_0))
| big_f(sK0(VAR_0),VAR_0) )
& ! [VAR_0] :
( big_f(VAR_0,VAR_0)
| ~ big_h(VAR_0) )
& ! [VAR_0] :
( big_f(VAR_0,VAR_0)
| big_g(sK1(VAR_0)) )
& ! [VAR_0] :
( big_f(VAR_0,VAR_0)
| big_f(sK1(VAR_0),sK0(VAR_0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_church_46_12_1_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_h(sK0(A))
| ~ big_g(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_1_neg]) ).
cnf(c_3,negated_conjecture,
( big_f(A,A)
| big_g(sK1(A)) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_1_neg]) ).
cnf(c_4,negated_conjecture,
( big_f(A,A)
| ~ big_h(A) ),
inference(split_conjunct,[status(thm)],[sk_church_46_12_1_neg]) ).
cnf(c_6,negated_conjecture,
( big_f(A,A)
| big_h(sK0(sK1(A))) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
( big_f(A,A)
| big_f(sK0(sK1(A)),sK0(sK1(A))) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_11,negated_conjecture,
~ big_f(sK0(A),sK0(A)),
inference(split_conjunct,[status(thm)],[sk_church_46_12_1_neg]) ).
cnf(c_13,negated_conjecture,
big_f(A,A),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_14,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN326+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n007.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 17:32:24 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 80861 was started by sandbox on n007,
% 0.17/0.44 % Sat Sep 26 17:32:24 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 9.
% 0.17/0.45 % Level of proof is 5.
% 0.17/0.45 % Maximum clause weight is 25.000.
% 0.17/0.45 % Given clauses 0.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------