%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN089+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 18 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 26 ( 2 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_5,axiom,
! [X20] : id(X20,X20),
file('theBenchmark.p',axiom_5) ).
fof(axiom_8,axiom,
! [X26,X27] :
( ( r1(X27)
& r1(X26) )
| ( ~ r1(X27)
& ~ r1(X26) )
| ~ id(X26,X27) ),
file('theBenchmark.p',axiom_8) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(zerounidtwo,conjecture,
! [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| ~ id(Y4,Y1) )
| ! [Y2] :
( ~ r2(Y2,Y1)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
file('theBenchmark.p',zerounidtwo) ).
fof(zerounidtwo_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y4] :
( ~ r1(Y4)
| ~ id(Y4,Y1) )
| ! [Y2] :
( ~ r2(Y2,Y1)
| ! [Y3] :
( ~ r2(Y3,Y2)
| ~ r1(Y3) ) ) ),
inference(assume_negation,[status(cth)],[zerounidtwo]) ).
cnf(c_28,plain,
id(A,A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_31,plain,
( r1(B)
| ~ r1(A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
cnf(c_61,plain,
( ~ r2(C,B)
| ~ r1(A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_19,plain,
? [Y1] :
( ? [Y4] :
( r1(Y4)
& id(Y4,Y1) )
& ? [Y2] :
( r2(Y2,Y1)
& ? [Y3] :
( r2(Y3,Y2)
& r1(Y3) ) ) ),
inference(fof_nnf,[status(thm)],[zerounidtwo_neg]) ).
fof(sk_zerounidtwo_neg,plain,
( r1(sK2)
& id(sK2,sK1)
& r2(sK0,sK1)
& r2(sK3,sK0)
& r1(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0,sK1,sK2]),skolemize(Y1,sK1),skolemize(Y2,sK0),skolemize(Y3,sK3),skolemize(Y4,sK2)],[nnf_19]) ).
cnf(c_64,negated_conjecture,
r2(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_zerounidtwo_neg]) ).
cnf(c_65,negated_conjecture,
id(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_zerounidtwo_neg]) ).
cnf(c_66,negated_conjecture,
r1(sK2),
inference(split_conjunct,[status(thm)],[sk_zerounidtwo_neg]) ).
cnf(c_230,plain,
( ~ r2(B,A)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_61,c_28]) ).
cnf(c_228,negated_conjecture,
~ r1(sK1),
inference(resolve,[status(thm)],[c_230,c_64]) ).
cnf(c_231,negated_conjecture,
( r1(sK1)
| ~ r1(sK2) ),
inference(resolve,[status(thm)],[c_65,c_31]) ).
cnf(c_232,negated_conjecture,
r1(sK1),
inference(resolve,[status(thm)],[c_66,c_231]) ).
cnf(c_229,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_228,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN089+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 04:38:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 919124 was started by sandbox on n001,
% 0.08/0.36 % Sat Sep 26 04:38:26 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39
% 0.08/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.39 % Length of proof is 12.
% 0.08/0.39 % Level of proof is 3.
% 0.08/0.39 % Maximum clause weight is 13.000.
% 0.08/0.39 % Given clauses 46.
% 0.08/0.39
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------