%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN069+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 : n015.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 09:36:57 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 124 ( 44 ~; 48 |; 28 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 50 ( 9 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel45_1,axiom,
! [X] :
( ( ! [Y] :
( ( big_h(X,Y)
& big_g(Y) )
=> big_j(X,Y) )
& big_f(X) )
=> ! [Y1] :
( big_k(Y1)
& big_h(X,Y1)
& big_g(Y1) ) ),
file('theBenchmark.p',pel45_1) ).
fof(pel45_2,axiom,
~ ? [Y] :
( big_k(Y)
& big_l(Y) ),
file('theBenchmark.p',pel45_2) ).
fof(pel45_3,axiom,
? [X] :
( ! [Y1] :
( ( big_h(X,Y1)
& big_g(Y1) )
=> big_j(X,Y1) )
& ! [Y] :
( big_h(X,Y)
=> big_l(Y) )
& big_f(X) ),
file('theBenchmark.p',pel45_3) ).
fof(nnf_3,plain,
? [X] :
( ! [Y1] :
( big_j(X,Y1)
| ~ big_h(X,Y1)
| ~ big_g(Y1) )
& ! [Y] :
( big_l(Y)
| ~ big_h(X,Y) )
& big_f(X) ),
inference(fof_nnf,[status(thm)],[pel45_3]) ).
fof(sk_pel45_3,plain,
( ! [Y1] :
( big_j(sK0,Y1)
| ~ big_h(sK0,Y1)
| ~ big_g(Y1) )
& ! [Y] :
( big_l(Y)
| ~ big_h(sK0,Y) )
& big_f(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_3]) ).
cnf(c_5,plain,
big_f(sK0),
inference(split_conjunct,[status(thm)],[sk_pel45_3]) ).
fof(nnf_1,plain,
! [X] :
( ! [Y1] :
( big_k(Y1)
& big_h(X,Y1)
& big_g(Y1) )
| ? [Y] :
( ~ big_j(X,Y)
& big_h(X,Y)
& big_g(Y) )
| ~ big_f(X) ),
inference(fof_nnf,[status(thm)],[pel45_1]) ).
fof(sk_pel45_1_sk,plain,
! [X] :
( ! [Y1] :
( big_k(Y1)
& big_h(X,Y1)
& big_g(Y1) )
| ( ~ big_j(X,sK1(X))
& big_h(X,sK1(X))
& big_g(sK1(X)) )
| ~ big_f(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1(X))],[nnf_1]) ).
fof(sk_pel45_1,plain,
( ! [VAR_0,VAR_1] :
( big_k(VAR_1)
| ~ big_j(VAR_0,sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_h(VAR_0,VAR_1)
| ~ big_j(VAR_0,sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_1)
| ~ big_j(VAR_0,sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_k(VAR_1)
| big_h(VAR_0,sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_h(VAR_0,VAR_1)
| big_h(VAR_0,sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_1)
| big_h(VAR_0,sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_k(VAR_1)
| big_g(sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_h(VAR_0,VAR_1)
| big_g(sK1(VAR_0))
| ~ big_f(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_g(VAR_1)
| big_g(sK1(VAR_0))
| ~ big_f(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel45_1_sk]) ).
cnf(c_6,plain,
( big_k(B)
| ~ big_j(A,sK1(A))
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel45_1]) ).
cnf(c_10,plain,
( big_h(A,B)
| big_h(A,sK1(A))
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel45_1]) ).
cnf(c_14,plain,
( big_g(B)
| big_g(sK1(A))
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel45_1]) ).
cnf(c_17,plain,
( big_j(sK0,A)
| ~ big_h(sK0,A)
| ~ big_g(A) ),
inference(split_conjunct,[status(thm)],[sk_pel45_3]) ).
cnf(c_18,plain,
( big_k(A)
| ~ big_j(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_21,plain,
( ~ big_k(A)
| ~ big_l(A) ),
inference(clausify,[status(thm)],[pel45_2]) ).
cnf(c_22,plain,
( big_k(A)
| ~ big_h(sK0,sK1(sK0))
| ~ big_g(sK1(sK0)) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_25,plain,
( big_l(A)
| ~ big_h(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_pel45_3]) ).
cnf(c_26,plain,
( ~ big_h(sK0,sK1(sK0))
| ~ big_g(sK1(sK0))
| ~ big_l(A) ),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_27,plain,
( ~ big_h(sK0,sK1(sK0))
| ~ big_g(sK1(sK0))
| ~ big_h(sK0,A) ),
inference(resolve,[status(thm)],[c_25,c_26]) ).
cnf(c_30,plain,
( big_h(sK0,A)
| big_h(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_32,plain,
( big_g(A)
| big_g(sK1(sK0)) ),
inference(resolve,[status(thm)],[c_5,c_14]) ).
cnf(c_35,plain,
( ~ big_g(sK1(sK0))
| ~ big_h(sK0,sK1(sK0)) ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_36,plain,
big_h(sK0,sK1(sK0)),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_37,plain,
big_g(sK1(sK0)),
inference(factor,[status(thm)],[c_32]) ).
cnf(c_39,plain,
~ big_g(sK1(sK0)),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n015.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 17:12:29 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 357564 was started by sandbox2 on n015,
% 0.16/0.44 % Sat Sep 26 17:12:29 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 20.
% 0.16/0.46 % Level of proof is 7.
% 0.16/0.46 % Maximum clause weight is 10.000.
% 0.16/0.46 % Given clauses 0.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------