%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN076+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 : n011.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 08:19:22 AM UTC 2026
% Result : Theorem 16.30s 2.57s
% Output : CNFRefutation 16.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 126 ( 45 ~; 33 |; 48 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 111 ( 24 sgn 19 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
file('theBenchmark.p',axiom_1) ).
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_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(thereexistsanevennumberid,conjecture,
? [Y1,Y2,Y3] :
( ? [Y5] :
( r3(Y2,Y3,Y5)
& id(Y5,Y1) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& id(Y4,Y1) ) ),
file('theBenchmark.p',thereexistsanevennumberid) ).
fof(thereexistsanevennumberid_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y5] :
( r3(Y2,Y3,Y5)
& id(Y5,Y1) )
& ? [Y4] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r4(Y6,Y2,Y4) )
& id(Y4,Y1) ) ),
inference(assume_negation,[status(cth)],[thereexistsanevennumberid]) ).
fof(nnf_1,plain,
? [Y24] :
! [X19] :
( ( ~ id(X19,Y24)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,Y24) ) ),
inference(fof_nnf,[status(thm)],[axiom_1]) ).
fof(sk_axiom_1_sk,plain,
! [X19] :
( ( ~ id(X19,sK0)
& ~ r1(X19) )
| ( r1(X19)
& id(X19,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y24,sK0)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( ~ id(VAR_0,sK0)
| r1(VAR_0) )
& ! [VAR_0] :
( ~ r1(VAR_0)
| id(VAR_0,sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_20,plain,
( ~ r1(A)
| id(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
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,sK9(X1,X8))
& r2(sK9(X1,X8),sK8(X1,X8))
& r3(X1,sK1(X1,X8),sK7(X1,X8))
& r2(X8,sK1(X1,X8))
& id(sK7(X1,X8),sK8(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK1,sK9]),skolemize(Y4,sK8(X1,X8)),skolemize(Y5,sK7(X1,X8)),skolemize(Y15,sK1(X1,X8)),skolemize(Y7,sK9(X1,X8))],[nnf_12]) ).
cnf(c_40,plain,
r2(A,sK1(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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,sK3(X4),sK2(X4))
& r1(sK3(X4))
& id(sK2(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(Y9,sK2(X4)),skolemize(Y16,sK3(X4))],[nnf_15]) ).
cnf(c_50,plain,
id(sK2(A),A),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_52,plain,
r3(A,sK3(A),sK2(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(sK6(X5))
& id(sK5(X5),sK6(X5))
& r4(X5,sK4(X5),sK5(X5))
& r1(sK4(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(Y8,sK5(X5)),skolemize(Y17,sK4(X5)),skolemize(Y18,sK6(X5))],[nnf_16]) ).
cnf(c_53,plain,
r1(sK4(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_54,plain,
r4(A,sK4(A),sK5(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_55,plain,
id(sK5(A),sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_56,plain,
r1(sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r3(D,V7,V6)
| ~ id(V6,B)
| ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,C)
| ~ r4(C,D,A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[thereexistsanevennumberid_neg]) ).
cnf(c_132,plain,
( r1(sK2(A))
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_50,c_32]) ).
cnf(c_10132,plain,
( r1(sK5(A))
| ~ r1(sK6(A)) ),
inference(resolve,[status(thm)],[c_55,c_32]) ).
cnf(c_149,plain,
r1(sK5(A)),
inference(resolve,[status(thm)],[c_56,c_10132]) ).
cnf(c_1625,plain,
id(sK5(A),sK0),
inference(resolve,[status(thm)],[c_149,c_20]) ).
cnf(c_8046,plain,
r1(sK2(sK6(A))),
inference(resolve,[status(thm)],[c_132,c_56]) ).
cnf(c_8047,plain,
r1(sK2(sK4(A))),
inference(resolve,[status(thm)],[c_132,c_53]) ).
cnf(c_10133,negated_conjecture,
( ~ r3(B,V6,F)
| ~ id(F,sK0)
| ~ r2(E,D)
| ~ r1(E)
| ~ r2(D,A)
| ~ r4(A,B,sK5(C)) ),
inference(resolve,[status(thm)],[c_62,c_1625]) ).
cnf(c_10134,negated_conjecture,
( ~ r3(sK4(B),E,D)
| ~ id(D,sK0)
| ~ r2(C,A)
| ~ r1(C)
| ~ r2(A,B) ),
inference(resolve,[status(thm)],[c_10133,c_54]) ).
cnf(c_10135,negated_conjecture,
( ~ r3(sK4(sK1(D,B)),E,C)
| ~ id(C,sK0)
| ~ r2(A,B)
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_10134,c_40]) ).
cnf(c_10136,negated_conjecture,
( ~ r3(sK4(sK1(D,B)),E,C)
| ~ id(C,sK0)
| ~ r2(sK2(sK6(A)),B) ),
inference(resolve,[status(thm)],[c_10135,c_8046]) ).
cnf(c_10137,negated_conjecture,
( ~ r3(sK4(sK1(B,sK1(C,sK2(sK6(D))))),E,A)
| ~ id(A,sK0) ),
inference(resolve,[status(thm)],[c_10136,c_40]) ).
cnf(c_9976,negated_conjecture,
~ id(sK2(sK4(sK1(A,sK1(B,sK2(sK6(C)))))),sK0),
inference(resolve,[status(thm)],[c_10137,c_52]) ).
cnf(c_10130,plain,
id(sK2(sK4(A)),sK0),
inference(resolve,[status(thm)],[c_8047,c_20]) ).
cnf(c_10131,plain,
$false,
inference(resolve,[status(thm)],[c_10130,c_9976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN076+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n011.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 04:30:29 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 3774733 was started by sandbox2 on n011,
% 0.19/0.44 % Sat Sep 26 04:30:29 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 16.30/2.57
% 16.30/2.57 % SZS status Theorem for theBenchmark
% 16.30/2.57
% 16.30/2.57 % Proof 1 at 1.56 (+ 0.52) seconds.
% 16.30/2.57 % Length of proof is 24.
% 16.30/2.57 % Level of proof is 5.
% 16.30/2.57 % Maximum clause weight is 22.000.
% 16.30/2.57 % Given clauses 107.
% 16.30/2.57
% 16.30/2.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------