%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN088+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:19:25 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 18 ~; 11 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 17 ( 3 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(zerounidone,conjecture,
! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ~ r1(Y3) )
| ! [Y2] :
( ~ r1(Y2)
| ~ id(Y2,Y1) ) ),
file('theBenchmark.p',zerounidone) ).
fof(zerounidone_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ~ r1(Y3) )
| ! [Y2] :
( ~ r1(Y2)
| ~ id(Y2,Y1) ) ),
inference(assume_negation,[status(cth)],[zerounidone]) ).
cnf(c_61,plain,
( ~ r2(C,B)
| ~ r1(A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_19,plain,
? [Y1] :
( ? [Y3] :
( r2(Y3,Y1)
& r1(Y3) )
& ? [Y2] :
( r1(Y2)
& id(Y2,Y1) ) ),
inference(fof_nnf,[status(thm)],[zerounidone_neg]) ).
fof(sk_zerounidone_neg,plain,
( r2(sK2,sK1)
& r1(sK2)
& r1(sK0)
& id(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(Y1,sK1),skolemize(Y2,sK0),skolemize(Y3,sK2)],[nnf_19]) ).
cnf(c_62,negated_conjecture,
id(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_zerounidone_neg]) ).
cnf(c_63,negated_conjecture,
r1(sK0),
inference(split_conjunct,[status(thm)],[sk_zerounidone_neg]) ).
cnf(c_65,negated_conjecture,
r2(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_zerounidone_neg]) ).
cnf(c_209,negated_conjecture,
( ~ r2(A,sK1)
| ~ r1(sK0) ),
inference(resolve,[status(thm)],[c_61,c_62]) ).
cnf(c_207,negated_conjecture,
~ r2(A,sK1),
inference(resolve,[status(thm)],[c_209,c_63]) ).
cnf(c_208,plain,
$false,
inference(resolve,[status(thm)],[c_207,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN088+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n020.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 04:33:34 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 620954 was started by sandbox2 on n020,
% 0.16/0.42 % Sat Sep 26 04:33:34 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % 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 0.01 (+ 0.01) seconds.
% 0.16/0.46 % Length of proof is 8.
% 0.16/0.46 % Level of proof is 3.
% 0.16/0.46 % Maximum clause weight is 8.000.
% 0.16/0.46 % Given clauses 44.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------