%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN066+2 : 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 : n013.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 6.18s 16.32s
% Output : CNFRefutation 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 75 ( 13 unt; 0 def)
% Number of atoms : 199 ( 111 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 197 ( 73 ~; 87 |; 37 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 130 ( 11 sgn 43 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('theBenchmark.p',axiom_1) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('theBenchmark.p',axiom_2) ).
fof(axiom_3a,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('theBenchmark.p',axiom_3a) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('theBenchmark.p',axiom_4a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(nonzerononetwoexist,conjecture,
? [Y1] :
( ! [Y5] :
( Y1 != Y5
| ~ r1(Y5) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ! [Y4] :
( ~ r2(Y4,Y3)
| ~ r1(Y4) ) ) ) ),
file('theBenchmark.p',nonzerononetwoexist) ).
fof(nonzerononetwoexist_neg,negated_conjecture,
~ ? [Y1] :
( ! [Y5] :
( Y1 != Y5
| ~ r1(Y5) )
& ! [Y2] :
( Y1 != Y2
| ! [Y3] :
( ~ r2(Y3,Y2)
| ! [Y4] :
( ~ r2(Y4,Y3)
| ~ r1(Y4) ) ) ) ),
inference(assume_negation,[status(cth)],[nonzerononetwoexist]) ).
fof(nnf_1,plain,
? [Y24] :
! [X19] :
( ( Y24 = X19
& r1(X19) )
| ( Y24 != X19
& ~ r1(X19) ) ),
inference(fof_nnf,[status(thm)],[axiom_1]) ).
fof(sk_axiom_1_sk,plain,
! [X19] :
( ( sK0 = X19
& r1(X19) )
| ( sK0 != X19
& ~ r1(X19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y24,sK0)],[nnf_1]) ).
fof(sk_axiom_1,plain,
( ! [VAR_0] :
( r1(VAR_0)
| sK0 != VAR_0 )
& ! [VAR_0] :
( sK0 = VAR_0
| ~ r1(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_1_sk]) ).
cnf(c_29,plain,
( sK0 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_30,plain,
( r1(A)
| sK0 != A ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
fof(nnf_2,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( Y21 = X12
& r2(X11,X12) )
| ( Y21 != X12
& ~ r2(X11,X12) ) ),
inference(fof_nnf,[status(thm)],[axiom_2]) ).
fof(sk_axiom_2_sk,plain,
! [X11,X12] :
( ( sK1(X11) = X12
& r2(X11,X12) )
| ( sK1(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y21,sK1(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK1(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK1(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_31,plain,
( sK1(A) = B
| ~ r2(A,B) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_32,plain,
( r2(A,B)
| sK1(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_40,plain,
( D = A
| ~ r2(D,C)
| C != B
| ~ r2(A,B) ),
inference(clausify,[status(thm)],[axiom_3a]) ).
fof(nnf_8,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(fof_nnf,[status(thm)],[axiom_4a]) ).
fof(sk_axiom_4a,plain,
! [X4] :
( sK2(X4) = X4
& r3(X4,sK7(X4),sK2(X4))
& r1(sK7(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK2]),skolemize(Y9,sK2(X4)),skolemize(Y16,sK7(X4))],[nnf_8]) ).
cnf(c_42,plain,
sK2(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_53,plain,
( ~ r2(C,B)
| B != A
| ~ r1(A) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_12,plain,
! [Y1] :
( ? [Y5] :
( Y1 = Y5
& r1(Y5) )
| ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& ? [Y4] :
( r2(Y4,Y3)
& r1(Y4) ) ) ) ),
inference(fof_nnf,[status(thm)],[nonzerononetwoexist_neg]) ).
fof(sk_nonzerononetwoexist_neg_sk,plain,
! [Y1] :
( ( Y1 = sK5(Y1)
& r1(sK5(Y1)) )
| ( Y1 = sK6(Y1)
& r2(sK4(Y1),sK6(Y1))
& r2(sK3(Y1),sK4(Y1))
& r1(sK3(Y1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK6,sK5]),skolemize(Y2,sK6(Y1)),skolemize(Y3,sK4(Y1)),skolemize(Y4,sK3(Y1)),skolemize(Y5,sK5(Y1))],[nnf_12]) ).
fof(sk_nonzerononetwoexist_neg,plain,
( ! [VAR_0] :
( VAR_0 = sK5(VAR_0)
| VAR_0 = sK6(VAR_0) )
& ! [VAR_0] :
( r1(sK5(VAR_0))
| VAR_0 = sK6(VAR_0) )
& ! [VAR_0] :
( VAR_0 = sK5(VAR_0)
| r2(sK4(VAR_0),sK6(VAR_0)) )
& ! [VAR_0] :
( r1(sK5(VAR_0))
| r2(sK4(VAR_0),sK6(VAR_0)) )
& ! [VAR_0] :
( VAR_0 = sK5(VAR_0)
| r2(sK3(VAR_0),sK4(VAR_0)) )
& ! [VAR_0] :
( r1(sK5(VAR_0))
| r2(sK3(VAR_0),sK4(VAR_0)) )
& ! [VAR_0] :
( VAR_0 = sK5(VAR_0)
| r1(sK3(VAR_0)) )
& ! [VAR_0] :
( r1(sK5(VAR_0))
| r1(sK3(VAR_0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_nonzerononetwoexist_neg_sk]) ).
cnf(c_57,negated_conjecture,
( r1(sK5(A))
| r2(sK3(A),sK4(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerononetwoexist_neg]) ).
cnf(c_58,negated_conjecture,
( A = sK5(A)
| r2(sK3(A),sK4(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerononetwoexist_neg]) ).
cnf(c_59,negated_conjecture,
( sK5(A) = A
| r2(sK3(A),sK4(A)) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_60,negated_conjecture,
( r1(sK5(A))
| r2(sK4(A),sK6(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerononetwoexist_neg]) ).
cnf(c_61,negated_conjecture,
( A = sK5(A)
| r2(sK4(A),sK6(A)) ),
inference(split_conjunct,[status(thm)],[sk_nonzerononetwoexist_neg]) ).
cnf(c_62,negated_conjecture,
( sK5(A) = A
| r2(sK4(A),sK6(A)) ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_63,negated_conjecture,
( r1(sK5(A))
| A = sK6(A) ),
inference(split_conjunct,[status(thm)],[sk_nonzerononetwoexist_neg]) ).
cnf(c_64,negated_conjecture,
( r1(sK5(A))
| sK6(A) = A ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_65,negated_conjecture,
( A = sK5(A)
| A = sK6(A) ),
inference(split_conjunct,[status(thm)],[sk_nonzerononetwoexist_neg]) ).
cnf(c_1943,negated_conjecture,
( A = sK5(A)
| sK6(A) = A ),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_66,negated_conjecture,
( sK5(A) = A
| sK6(A) = A ),
inference(copy,[status(thm)],[c_1943]) ).
cnf(c_81,plain,
r1(sK0),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_82,plain,
r2(A,sK1(A)),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_122,plain,
( sK1(sK3(A)) = sK4(A)
| r1(sK5(A)) ),
inference(resolve,[status(thm)],[c_57,c_31]) ).
cnf(c_1944,plain,
( ~ r2(B,A)
| A != sK0 ),
inference(resolve,[status(thm)],[c_81,c_53]) ).
cnf(c_141,plain,
( ~ r2(B,A)
| sK0 != A ),
inference(copy,[status(thm)],[c_1944]) ).
cnf(c_1945,plain,
( ~ r2(B,A)
| A != sK0 ),
inference(resolve,[status(thm)],[c_53,c_81]) ).
cnf(c_1946,plain,
~ r2(A,sK2(sK0)),
inference(resolve,[status(thm)],[c_1945,c_42]) ).
cnf(c_142,plain,
~ r2(A,sK0),
inference(paramod,[status(thm)],[c_42,c_1946]) ).
cnf(c_143,plain,
sK1(A) != sK0,
inference(resolve,[status(thm)],[c_32,c_142]) ).
cnf(c_1947,negated_conjecture,
( sK5(A) = A
| sK0 != sK4(A) ),
inference(resolve,[status(thm)],[c_141,c_59]) ).
cnf(c_157,negated_conjecture,
( sK5(A) = A
| sK4(A) != sK0 ),
inference(copy,[status(thm)],[c_1947]) ).
cnf(c_162,plain,
( sK1(B) != A
| ~ r1(A) ),
inference(resolve,[status(thm)],[c_82,c_53]) ).
cnf(c_163,plain,
( C = A
| sK1(C) != B
| ~ r2(A,B) ),
inference(resolve,[status(thm)],[c_82,c_40]) ).
cnf(c_1948,negated_conjecture,
( sK6(B) = B
| sK1(A) != sK5(B) ),
inference(resolve,[status(thm)],[c_162,c_64]) ).
cnf(c_181,negated_conjecture,
( sK6(A) = A
| sK5(A) != sK1(B) ),
inference(copy,[status(thm)],[c_1948]) ).
cnf(c_1949,negated_conjecture,
( sK6(sK1(A)) = sK1(A)
| sK6(sK1(A)) = sK1(A) ),
inference(resolve,[status(thm)],[c_181,c_66]) ).
cnf(c_300,negated_conjecture,
sK6(sK1(A)) = sK1(A),
inference(copy,[status(thm)],[c_1949]) ).
cnf(c_1950,negated_conjecture,
( sK5(B) = B
| A = sK4(B)
| sK1(A) != sK6(B) ),
inference(resolve,[status(thm)],[c_163,c_62]) ).
cnf(c_1951,negated_conjecture,
( sK5(B) = B
| A = sK4(B)
| sK6(B) != sK1(A) ),
inference(copy,[status(thm)],[c_1950]) ).
cnf(c_423,negated_conjecture,
( sK5(A) = A
| sK4(A) = B
| sK6(A) != sK1(B) ),
inference(copy,[status(thm)],[c_1951]) ).
cnf(c_1952,negated_conjecture,
( r1(sK5(B))
| A = sK4(B)
| sK1(A) != sK6(B) ),
inference(resolve,[status(thm)],[c_163,c_60]) ).
cnf(c_1953,negated_conjecture,
( r1(sK5(B))
| A = sK4(B)
| sK6(B) != sK1(A) ),
inference(copy,[status(thm)],[c_1952]) ).
cnf(c_424,negated_conjecture,
( r1(sK5(A))
| sK4(A) = B
| sK6(A) != sK1(B) ),
inference(copy,[status(thm)],[c_1953]) ).
cnf(c_1954,plain,
( sK0 = sK5(A)
| sK1(sK3(A)) = sK4(A) ),
inference(resolve,[status(thm)],[c_122,c_29]) ).
cnf(c_534,plain,
( sK5(A) = sK0
| sK1(sK3(A)) = sK4(A) ),
inference(copy,[status(thm)],[c_1954]) ).
cnf(c_551,plain,
( r1(sK5(sK1(A)))
| sK4(sK1(A)) = A ),
inference(resolve,[status(thm)],[c_424,c_300]) ).
cnf(c_602,plain,
( sK5(sK1(A)) = sK1(A)
| sK4(sK1(A)) = A ),
inference(resolve,[status(thm)],[c_423,c_300]) ).
cnf(c_1348,plain,
( r2(sK3(A),sK4(A))
| sK5(A) = sK0 ),
inference(resolve,[status(thm)],[c_534,c_32]) ).
cnf(c_1955,plain,
( sK0 != sK4(A)
| sK5(A) = sK0 ),
inference(resolve,[status(thm)],[c_1348,c_141]) ).
cnf(c_1375,plain,
( sK4(A) != sK0
| sK5(A) = sK0 ),
inference(copy,[status(thm)],[c_1955]) ).
cnf(c_1956,plain,
( A != sK1(B)
| ~ r1(A) ),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_1896,plain,
( ~ r1(sK5(sK1(A)))
| sK4(sK1(A)) = A ),
inference(resolve,[status(thm)],[c_602,c_1956]) ).
cnf(c_1957,plain,
( sK4(sK1(A)) = A
| sK4(sK1(A)) = A ),
inference(resolve,[status(thm)],[c_1896,c_551]) ).
cnf(c_1928,plain,
sK4(sK1(A)) = A,
inference(copy,[status(thm)],[c_1957]) ).
cnf(c_1932,plain,
sK5(sK1(sK0)) = sK0,
inference(resolve,[status(thm)],[c_1928,c_1375]) ).
cnf(c_1958,plain,
sK5(sK1(sK0)) = sK1(sK0),
inference(resolve,[status(thm)],[c_1928,c_157]) ).
cnf(c_1959,plain,
sK0 = sK1(sK0),
inference(paramod,[status(thm)],[c_1932,c_1958]) ).
cnf(c_1960,plain,
sK1(sK0) = sK0,
inference(copy,[status(thm)],[c_1959]) ).
cnf(c_1942,plain,
$false,
inference(resolve,[status(thm)],[c_143,c_1960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN066+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/15.41 % Computer : n013.cluster.edu
% 0.12/15.41 % Model : x86_64 x86_64
% 0.12/15.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.41 % Memory : 8046.5625MB
% 0.12/15.41 % OS : Linux 6.8.0-71-generic
% 0.12/15.41 % CPULimit : 300
% 0.12/15.41 % WCLimit : 300
% 0.12/15.41 % DateTime : Sat Sep 26 04:29:52 UTC 2026
% 0.12/15.42 % CPUTime :
% 0.12/15.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/15.42 % Process 1929034 was started by sandbox on n013,
% 0.12/15.42 % Sat Sep 26 04:29:52 2026
% 0.12/15.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/15.43
% 0.12/15.43 % From the command line: assign(max_seconds, 300).
% 6.18/16.32
% 6.18/16.32 % given #500 (F,wt=38): 1255 -r2(c1,f11(f1(f11(f1(A),f1(B))),f7(C,f1(D)))). [para(208(a,1),826(a,2,2))].
% 6.18/16.32
% 6.18/16.32 % SZS status Theorem for theBenchmark
% 6.18/16.32
% 6.18/16.32 % Proof 1 at 0.60 (+ 0.26) seconds.
% 6.18/16.32 % Length of proof is 45.
% 6.18/16.32 % Level of proof is 10.
% 6.18/16.32 % Maximum clause weight is 26.000.
% 6.18/16.32 % Given clauses 582.
% 6.18/16.32
% 6.18/16.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------