%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN062+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 : n016.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 0.13s 5.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 18 unt; 0 def)
% Number of atoms : 137 ( 72 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 68 ~; 49 |; 34 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 11 sgn 52 !; 18 ?)
% 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_3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('theBenchmark.p',axiom_3) ).
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(infiniteNumbers,conjecture,
! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( Y3 = Y2
& r3(X1,Y1,Y3) )
& ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) ) ),
file('theBenchmark.p',infiniteNumbers) ).
fof(infiniteNumbers_neg,negated_conjecture,
~ ! [X1] :
? [Y2,Y1] :
( ? [Y3] :
( Y3 = Y2
& r3(X1,Y1,Y3) )
& ! [Y4] :
( Y1 != Y4
| ~ r1(Y4) ) ),
inference(assume_negation,[status(cth)],[infiniteNumbers]) ).
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_13,plain,
( r1(A)
| sK0 != A ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
cnf(c_14,plain,
( sK0 = A
| ~ r1(A) ),
inference(split_conjunct,[status(thm)],[sk_axiom_1]) ).
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] :
( sK6(X4) = X4
& r3(X4,sK1(X4),sK6(X4))
& r1(sK1(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK6]),skolemize(Y9,sK6(X4)),skolemize(Y16,sK1(X4))],[nnf_8]) ).
cnf(c_15,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_20,plain,
( ~ r2(C,B)
| B != A
| ~ r1(A) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_12,plain,
? [X1] :
! [Y2,Y1] :
( ! [Y3] :
( Y2 != Y3
| ~ r3(X1,Y1,Y3) )
| ? [Y4] :
( Y1 = Y4
& r1(Y4) ) ),
inference(fof_nnf,[status(thm)],[infiniteNumbers_neg]) ).
fof(sk_infiniteNumbers_neg_sk,plain,
! [Y2,Y1] :
( ! [Y3] :
( Y2 != Y3
| ~ r3(sK3,Y1,Y3) )
| ( Y1 = sK2(Y2,Y1)
& r1(sK2(Y2,Y1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X1,sK3),skolemize(Y4,sK2(Y2,Y1))],[nnf_12]) ).
fof(sk_infiniteNumbers_neg,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( VAR_1 != VAR_2
| ~ r3(sK3,VAR_0,VAR_2)
| VAR_0 = sK2(VAR_1,VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_0 != VAR_2
| ~ r3(sK3,VAR_1,VAR_2)
| r1(sK2(VAR_0,VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_infiniteNumbers_neg_sk]) ).
cnf(c_21,negated_conjecture,
( A != C
| ~ r3(sK3,B,C)
| r1(sK2(A,B)) ),
inference(split_conjunct,[status(thm)],[sk_infiniteNumbers_neg]) ).
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] :
( ( sK4(X11) = X12
& r2(X11,X12) )
| ( sK4(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(Y21,sK4(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK4(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK4(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_33,plain,
( r2(A,B)
| sK4(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
fof(nnf_3,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( Y22 = X15
& r3(X13,X14,X15) )
| ( Y22 != X15
& ~ r3(X13,X14,X15) ) ),
inference(fof_nnf,[status(thm)],[axiom_3]) ).
fof(sk_axiom_3_sk,plain,
! [X13,X14,X15] :
( ( sK5(X13,X14) = X15
& r3(X13,X14,X15) )
| ( sK5(X13,X14) != X15
& ~ r3(X13,X14,X15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y22,sK5(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r3(VAR_0,VAR_1,VAR_2)
| sK5(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK5(VAR_0,VAR_1) = VAR_2
| ~ r3(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_34,plain,
( sK5(A,B) = C
| ~ r3(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_35,plain,
( r3(A,B,C)
| sK5(A,B) != C ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
cnf(c_48,plain,
r3(A,sK1(A),sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_49,plain,
sK6(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_56,negated_conjecture,
( B != C
| ~ r3(sK3,A,C)
| A = sK2(B,A) ),
inference(split_conjunct,[status(thm)],[sk_infiniteNumbers_neg]) ).
cnf(c_57,negated_conjecture,
( A != C
| ~ r3(sK3,B,C)
| sK2(A,B) = B ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_58,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_59,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_58]) ).
cnf(c_76,plain,
( sK0 != B
| ~ r2(C,A)
| A != B ),
inference(resolve,[status(thm)],[c_20,c_13]) ).
cnf(c_79,negated_conjecture,
( sK0 = sK2(C,A)
| C != B
| ~ r3(sK3,A,B) ),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_80,negated_conjecture,
( sK2(C,A) = sK0
| C != B
| ~ r3(sK3,A,B) ),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_166,plain,
r3(A,sK0,sK6(A)),
inference(paramod,[status(thm)],[c_59,c_48]) ).
cnf(c_82,plain,
r3(A,sK0,A),
inference(paramod,[status(thm)],[c_49,c_166]) ).
cnf(c_167,plain,
( ~ r2(B,sK0)
| sK0 != A ),
inference(factor,[status(thm)],[c_76]) ).
cnf(c_84,plain,
~ r2(A,sK0),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_86,plain,
r3(A,B,sK5(A,B)),
inference(xxres,[status(thm)],[c_35]) ).
cnf(c_127,plain,
sK5(A,sK0) = A,
inference(resolve,[status(thm)],[c_82,c_34]) ).
cnf(c_135,plain,
sK4(A) != sK0,
inference(resolve,[status(thm)],[c_33,c_84]) ).
cnf(c_168,negated_conjecture,
( sK2(A,B) = sK0
| A != sK5(sK3,B) ),
inference(resolve,[status(thm)],[c_80,c_86]) ).
cnf(c_169,negated_conjecture,
sK2(sK5(sK5(sK3,A),sK0),A) = sK0,
inference(resolve,[status(thm)],[c_168,c_127]) ).
cnf(c_157,negated_conjecture,
sK2(sK5(sK3,A),A) = sK0,
inference(paramod,[status(thm)],[c_127,c_169]) ).
cnf(c_170,negated_conjecture,
( A != sK5(sK3,B)
| sK2(A,B) = B ),
inference(resolve,[status(thm)],[c_57,c_86]) ).
cnf(c_171,negated_conjecture,
sK2(sK5(sK5(sK3,A),sK0),A) = A,
inference(resolve,[status(thm)],[c_170,c_127]) ).
cnf(c_172,negated_conjecture,
sK2(sK5(sK3,A),A) = A,
inference(paramod,[status(thm)],[c_127,c_171]) ).
cnf(c_164,negated_conjecture,
sK0 = A,
inference(paramod,[status(thm)],[c_157,c_172]) ).
cnf(c_173,plain,
sK0 != sK4(A),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_165,plain,
$false,
inference(resolve,[status(thm)],[c_164,c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n016.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 04:33:52 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 4182344 was started by sandbox on n016,
% 0.10/5.37 % Sat Sep 26 04:33:52 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/5.42
% 0.13/5.42 % SZS status Theorem for theBenchmark
% 0.13/5.42
% 0.13/5.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/5.42 % Length of proof is 31.
% 0.13/5.42 % Level of proof is 8.
% 0.13/5.42 % Maximum clause weight is 22.000.
% 0.13/5.42 % Given clauses 41.
% 0.13/5.42
% 0.13/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------