%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN067+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 08:19:20 AM UTC 2026
% Result : Theorem 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 20 ~; 12 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 43 ( 7 sgn 16 !; 11 ?)
% 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_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
file('theBenchmark.p',axiom_1a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(nonzerosexistid,conjecture,
? [Y1] :
! [Y2] :
( ~ r1(Y2)
| ~ id(Y1,Y2) ),
file('theBenchmark.p',nonzerosexistid) ).
fof(nonzerosexistid_neg,negated_conjecture,
~ ? [Y1] :
! [Y2] :
( ~ r1(Y2)
| ~ id(Y1,Y2) ),
inference(assume_negation,[status(cth)],[nonzerosexistid]) ).
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_12,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) )
& id(Y5,Y4) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(sk_axiom_1a,plain,
! [X1,X8] :
( r3(X1,X8,sK4(X1,X8))
& r2(sK4(X1,X8),sK3(X1,X8))
& r3(X1,sK0(X1,X8),sK2(X1,X8))
& r2(X8,sK0(X1,X8))
& id(sK2(X1,X8),sK3(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK4]),skolemize(Y4,sK3(X1,X8)),skolemize(Y5,sK2(X1,X8)),skolemize(Y15,sK0(X1,X8)),skolemize(Y7,sK4(X1,X8))],[nnf_12]) ).
cnf(c_40,plain,
r2(A,sK0(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_61,plain,
( ~ r2(C,B)
| ~ r1(A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_19,plain,
! [Y1] :
? [Y2] :
( r1(Y2)
& id(Y1,Y2) ),
inference(fof_nnf,[status(thm)],[nonzerosexistid_neg]) ).
fof(sk_nonzerosexistid_neg,plain,
! [Y1] :
( r1(sK1(Y1))
& id(Y1,sK1(Y1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y2,sK1(Y1))],[nnf_19]) ).
cnf(c_62,negated_conjecture,
id(A,sK1(A)),
inference(split_conjunct,[status(thm)],[sk_nonzerosexistid_neg]) ).
cnf(c_63,negated_conjecture,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_nonzerosexistid_neg]) ).
cnf(c_199,plain,
( ~ r2(B,A)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_61,c_28]) ).
cnf(c_193,plain,
~ r1(sK0(A,B)),
inference(resolve,[status(thm)],[c_199,c_40]) ).
cnf(c_200,negated_conjecture,
( r1(A)
| ~ r1(sK1(A)) ),
inference(resolve,[status(thm)],[c_62,c_32]) ).
cnf(c_197,negated_conjecture,
r1(A),
inference(resolve,[status(thm)],[c_63,c_200]) ).
cnf(c_198,plain,
$false,
inference(resolve,[status(thm)],[c_197,c_193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN067+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 04:29:58 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 819564 was started by sandbox2 on n004,
% 0.10/5.38 % Sat Sep 26 04:29:58 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.41
% 0.14/5.41 % SZS status Theorem for theBenchmark
% 0.14/5.41
% 0.14/5.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/5.41 % Length of proof is 14.
% 0.14/5.41 % Level of proof is 3.
% 0.14/5.41 % Maximum clause weight is 8.000.
% 0.14/5.41 % Given clauses 43.
% 0.14/5.41
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------