%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN068+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 : n008.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 09:36:56 AM UTC 2026
% Result : Theorem 0.13s 20.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 3 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 16 |; 17 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 25 ( 0 sgn 10 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel44_1,axiom,
! [X] :
( big_f(X)
=> ( ? [Y1] :
( ~ big_h(X,Y1)
& big_g(Y1) )
& ? [Y] :
( big_h(X,Y)
& big_g(Y) ) ) ),
file('theBenchmark.p',pel44_1) ).
fof(pel44_2,axiom,
? [X] :
( ! [Y] :
( big_g(Y)
=> big_h(X,Y) )
& big_j(X) ),
file('theBenchmark.p',pel44_2) ).
fof(pel44,conjecture,
? [X] :
( ~ big_f(X)
& big_j(X) ),
file('theBenchmark.p',pel44) ).
fof(pel44_neg,negated_conjecture,
~ ? [X] :
( ~ big_f(X)
& big_j(X) ),
inference(assume_negation,[status(cth)],[pel44]) ).
cnf(c_4,negated_conjecture,
( big_f(A)
| ~ big_j(A) ),
inference(clausify,[status(thm)],[pel44_neg]) ).
fof(nnf_1,plain,
! [X] :
( ( ? [Y1] :
( ~ big_h(X,Y1)
& big_g(Y1) )
& ? [Y] :
( big_h(X,Y)
& big_g(Y) ) )
| ~ big_f(X) ),
inference(fof_nnf,[status(thm)],[pel44_1]) ).
fof(sk_pel44_1_sk,plain,
! [X] :
( ( ~ big_h(X,sK0(X))
& big_g(sK0(X))
& big_h(X,sK2(X))
& big_g(sK2(X)) )
| ~ big_f(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0]),skolemize(Y,sK2(X)),skolemize(Y1,sK0(X))],[nnf_1]) ).
fof(sk_pel44_1,plain,
( ! [VAR_0] :
( ~ big_h(VAR_0,sK0(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0] :
( big_g(sK0(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0] :
( big_h(VAR_0,sK2(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0] :
( big_g(sK2(VAR_0))
| ~ big_f(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel44_1_sk]) ).
cnf(c_5,plain,
( ~ big_h(A,sK0(A))
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel44_1]) ).
cnf(c_6,plain,
( big_g(sK0(A))
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel44_1]) ).
fof(nnf_2,plain,
? [X] :
( ! [Y] :
( big_h(X,Y)
| ~ big_g(Y) )
& big_j(X) ),
inference(fof_nnf,[status(thm)],[pel44_2]) ).
fof(sk_pel44_2,plain,
( ! [Y] :
( big_h(sK1,Y)
| ~ big_g(Y) )
& big_j(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X,sK1)],[nnf_2]) ).
cnf(c_9,plain,
( big_h(sK1,A)
| ~ big_g(A) ),
inference(split_conjunct,[status(thm)],[sk_pel44_2]) ).
cnf(c_10,negated_conjecture,
( big_g(sK0(A))
| ~ big_j(A) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_12,negated_conjecture,
( ~ big_h(A,sK0(A))
| ~ big_j(A) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_13,negated_conjecture,
( ~ big_j(A)
| big_h(sK1,sK0(A)) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_16,negated_conjecture,
( ~ big_j(sK1)
| ~ big_j(sK1) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_17,negated_conjecture,
~ big_j(sK1),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,plain,
big_j(sK1),
inference(split_conjunct,[status(thm)],[sk_pel44_2]) ).
cnf(c_19,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN068+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/20.38 % Computer : n008.cluster.edu
% 0.09/20.38 % Model : x86_64 x86_64
% 0.09/20.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/20.38 % Memory : 8046.5625MB
% 0.09/20.38 % OS : Linux 6.8.0-71-generic
% 0.09/20.38 % CPULimit : 300
% 0.09/20.38 % WCLimit : 300
% 0.09/20.38 % DateTime : Sat Sep 26 17:09:32 UTC 2026
% 0.09/20.38 % CPUTime :
% 0.09/20.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/20.39 % Process 4119275 was started by sandbox on n008,
% 0.09/20.39 % Sat Sep 26 17:09:32 2026
% 0.09/20.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/20.39
% 0.09/20.39 % From the command line: assign(max_seconds, 300).
% 0.13/20.40
% 0.13/20.40 % SZS status Theorem for theBenchmark
% 0.13/20.40
% 0.13/20.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/20.40 % Length of proof is 14.
% 0.13/20.40 % Level of proof is 6.
% 0.13/20.40 % Maximum clause weight is 2.000.
% 0.13/20.40 % Given clauses 0.
% 0.13/20.40
% 0.13/20.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------