%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN070+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 : n002.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 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 89 ( 29 ~; 21 |; 39 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 74 ( 7 sgn 12 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
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_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
file('theBenchmark.p',axiom_4a) ).
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(onepluszeroidone,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
file('theBenchmark.p',onepluszeroidone) ).
fof(onepluszeroidone_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& id(Y1,Y3) )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
inference(assume_negation,[status(cth)],[onepluszeroidone]) ).
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,sK6(X2,X9))
& r3(sK6(X2,X9),X2,sK5(X2,X9))
& r4(X2,sK0(X2,X9),sK4(X2,X9))
& r2(X9,sK0(X2,X9))
& id(sK4(X2,X9),sK5(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK0,sK6]),skolemize(Y2,sK5(X2,X9)),skolemize(Y3,sK4(X2,X9)),skolemize(Y14,sK0(X2,X9)),skolemize(Y6,sK6(X2,X9))],[nnf_13]) ).
cnf(c_45,plain,
r2(A,sK0(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
fof(nnf_15,plain,
! [X4] :
? [Y9] :
( ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) )
& id(Y9,X4) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(sk_axiom_4a,plain,
! [X4] :
( r3(X4,sK2(X4),sK1(X4))
& r1(sK2(X4))
& id(sK1(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(Y9,sK1(X4)),skolemize(Y16,sK2(X4))],[nnf_15]) ).
cnf(c_50,plain,
id(sK1(A),A),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_51,plain,
r1(sK2(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_52,plain,
r3(A,sK2(A),sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
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(sK3(X5))
& id(sK8(X5),sK3(X5))
& r4(X5,sK7(X5),sK8(X5))
& r1(sK7(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK3]),skolemize(Y8,sK8(X5)),skolemize(Y17,sK7(X5)),skolemize(Y18,sK3(X5))],[nnf_16]) ).
cnf(c_56,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ id(C,E)
| ~ r2(D,B)
| ~ r1(D)
| ~ r3(B,A,C)
| ~ r1(A) ),
inference(clausify,[status(thm)],[onepluszeroidone_neg]) ).
cnf(c_206,negated_conjecture,
( ~ r2(D,C)
| ~ r1(D)
| ~ id(sK1(A),C)
| ~ r2(B,A)
| ~ r1(B)
| ~ r1(sK2(A)) ),
inference(resolve,[status(thm)],[c_62,c_52]) ).
cnf(c_207,negated_conjecture,
( ~ r2(D,C)
| ~ r1(D)
| ~ id(sK1(A),C)
| ~ r2(sK3(B),A)
| ~ r1(sK2(A)) ),
inference(resolve,[status(thm)],[c_206,c_56]) ).
cnf(c_208,negated_conjecture,
( ~ r2(D,C)
| ~ r1(D)
| ~ id(sK1(sK0(A,sK3(B))),C)
| ~ r1(sK2(sK0(A,sK3(B)))) ),
inference(resolve,[status(thm)],[c_207,c_45]) ).
cnf(c_209,negated_conjecture,
( ~ r2(C,sK0(A,sK3(B)))
| ~ r1(C)
| ~ r1(sK2(sK0(A,sK3(B)))) ),
inference(resolve,[status(thm)],[c_208,c_50]) ).
cnf(c_210,negated_conjecture,
( ~ r2(sK3(C),sK0(A,sK3(B)))
| ~ r1(sK2(sK0(A,sK3(B)))) ),
inference(resolve,[status(thm)],[c_209,c_56]) ).
cnf(c_211,negated_conjecture,
~ r1(sK2(sK0(A,sK3(B)))),
inference(resolve,[status(thm)],[c_210,c_45]) ).
cnf(c_205,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_51,c_211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN070+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n002.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 04:32:27 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 830260 was started by sandbox on n002,
% 0.10/5.38 % Sat Sep 26 04:32:27 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/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 0.02 (+ 0.00) seconds.
% 0.14/5.41 % Length of proof is 11.
% 0.14/5.41 % Level of proof is 2.
% 0.14/5.41 % Maximum clause weight is 19.000.
% 0.14/5.41 % Given clauses 43.
% 0.14/5.41
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------