%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN069+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 : n004.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 08:19:21 AM UTC 2026
% Result : Theorem 0.23s 0.92s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 13 ~; 8 |; 27 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 44 ( 5 sgn 12 !; 18 ?)
% 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_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
file('theBenchmark.p',axiom_2a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(oneidone,conjecture,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& id(Y1,Y1) ),
file('theBenchmark.p',oneidone) ).
fof(oneidone_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& id(Y1,Y1) ),
inference(assume_negation,[status(cth)],[oneidone]) ).
cnf(c_28,plain,
id(A,A),
inference(clausify,[status(thm)],[axiom_5]) ).
cnf(c_32,plain,
( r1(A)
| ~ r1(B)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_8]) ).
fof(nnf_13,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(sk_axiom_2a,plain,
! [X2,X9] :
( r4(X2,X9,sK5(X2,X9))
& r3(sK5(X2,X9),X2,sK4(X2,X9))
& r4(X2,sK0(X2,X9),sK3(X2,X9))
& r2(X9,sK0(X2,X9))
& id(sK3(X2,X9),sK4(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK0,sK5]),skolemize(Y2,sK4(X2,X9)),skolemize(Y3,sK3(X2,X9)),skolemize(Y14,sK0(X2,X9)),skolemize(Y6,sK5(X2,X9))],[nnf_13]) ).
cnf(c_45,plain,
r2(A,sK0(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
fof(nnf_16,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( r1(Y18)
& id(Y8,Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(sk_axiom_5a,plain,
! [X5] :
( r1(sK2(X5))
& id(sK1(X5),sK2(X5))
& r4(X5,sK6(X5),sK1(X5))
& r1(sK6(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK1,sK2]),skolemize(Y8,sK1(X5)),skolemize(Y17,sK6(X5)),skolemize(Y18,sK2(X5))],[nnf_16]) ).
cnf(c_55,plain,
id(sK1(A),sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_56,plain,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r2(B,A)
| ~ r1(B)
| ~ id(A,A) ),
inference(clausify,[status(thm)],[oneidone_neg]) ).
cnf(c_63,negated_conjecture,
( ~ r2(A,B)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_28,c_62]) ).
cnf(c_201,plain,
( r1(sK1(A))
| ~ r1(sK2(A)) ),
inference(resolve,[status(thm)],[c_55,c_32]) ).
cnf(c_147,plain,
r1(sK1(A)),
inference(resolve,[status(thm)],[c_56,c_201]) ).
cnf(c_199,plain,
~ r1(A),
inference(resolve,[status(thm)],[c_63,c_45]) ).
cnf(c_200,plain,
$false,
inference(resolve,[status(thm)],[c_199,c_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN069+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.86 % Computer : n004.cluster.edu
% 0.18/0.86 % Model : x86_64 x86_64
% 0.18/0.86 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.86 % Memory : 8046.5625MB
% 0.18/0.86 % OS : Linux 6.8.0-71-generic
% 0.18/0.86 % CPULimit : 300
% 0.18/0.86 % WCLimit : 300
% 0.18/0.86 % DateTime : Sat Sep 26 04:29:38 UTC 2026
% 0.18/0.87 % CPUTime :
% 0.18/0.87 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.87 % Process 819007 was started by sandbox2 on n004,
% 0.18/0.87 % Sat Sep 26 04:29:38 2026
% 0.18/0.87 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.88
% 0.18/0.88 % From the command line: assign(max_seconds, 300).
% 0.23/0.92
% 0.23/0.92 % SZS status Theorem for theBenchmark
% 0.23/0.92
% 0.23/0.92 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.23/0.92 % Length of proof is 15.
% 0.23/0.92 % Level of proof is 4.
% 0.23/0.92 % Maximum clause weight is 15.000.
% 0.23/0.92 % Given clauses 43.
% 0.23/0.92
% 0.23/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------