%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN073+2 : 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 : n019.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 0.18s 5.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 35 unt; 0 def)
% Number of atoms : 162 ( 69 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 65 ~; 44 |; 49 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 114 ( 7 sgn 56 !; 23 ?)
% 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_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('theBenchmark.p',axiom_1a) ).
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(oneuneqtwo,conjecture,
! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( Y2 != Y1
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
file('theBenchmark.p',oneuneqtwo) ).
fof(oneuneqtwo_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( Y2 != Y1
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
inference(assume_negation,[status(cth)],[oneuneqtwo]) ).
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_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,
? [Y1] :
( ? [Y3] :
( r2(Y3,Y1)
& ? [Y5] :
( r2(Y5,Y3)
& r1(Y5) ) )
& ? [Y2] :
( Y1 = Y2
& ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) ) ) ),
inference(fof_nnf,[status(thm)],[oneuneqtwo_neg]) ).
fof(sk_oneuneqtwo_neg,plain,
( r2(sK7,sK8)
& r2(sK3,sK7)
& r1(sK3)
& sK8 = sK9
& r2(sK2,sK9)
& r1(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK9,sK8,sK3,sK7]),skolemize(Y1,sK8),skolemize(Y2,sK9),skolemize(Y4,sK2),skolemize(Y3,sK7),skolemize(Y5,sK3)],[nnf_12]) ).
cnf(c_21,negated_conjecture,
r1(sK2),
inference(split_conjunct,[status(thm)],[sk_oneuneqtwo_neg]) ).
cnf(c_22,negated_conjecture,
r1(sK3),
inference(split_conjunct,[status(thm)],[sk_oneuneqtwo_neg]) ).
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] :
( ( sK4(X13,X14) = X15
& r3(X13,X14,X15) )
| ( sK4(X13,X14) != X15
& ~ r3(X13,X14,X15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(Y22,sK4(X13,X14))],[nnf_3]) ).
fof(sk_axiom_3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( r3(VAR_0,VAR_1,VAR_2)
| sK4(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK4(VAR_0,VAR_1) = VAR_2
| ~ r3(VAR_0,VAR_1,VAR_2) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_3_sk]) ).
cnf(c_23,plain,
( sK4(A,B) = C
| ~ r3(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_axiom_3]) ).
fof(nnf_5,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y4 = Y5
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(fof_nnf,[status(thm)],[axiom_1a]) ).
fof(sk_axiom_1a,plain,
! [X1,X8] :
( r3(X1,X8,sK5(X1,X8))
& r2(sK5(X1,X8),sK13(X1,X8))
& sK13(X1,X8) = sK12(X1,X8)
& r3(X1,sK11(X1,X8),sK12(X1,X8))
& r2(X8,sK11(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK5]),skolemize(Y4,sK13(X1,X8)),skolemize(Y5,sK12(X1,X8)),skolemize(Y15,sK11(X1,X8)),skolemize(Y7,sK5(X1,X8))],[nnf_5]) ).
cnf(c_26,plain,
r3(A,B,sK5(A,B)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
cnf(c_28,plain,
r3(A,sK1(A),sK6(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_39,negated_conjecture,
sK0 = sK3,
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_40,negated_conjecture,
sK3 = sK0,
inference(copy,[status(thm)],[c_39]) ).
cnf(c_41,negated_conjecture,
( ~ r2(B,A)
| A != sK3 ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_173,negated_conjecture,
( ~ r2(B,A)
| A != sK0 ),
inference(paramod,[status(thm)],[c_40,c_41]) ).
cnf(c_42,negated_conjecture,
( ~ r2(B,A)
| sK0 != A ),
inference(copy,[status(thm)],[c_173]) ).
cnf(c_43,negated_conjecture,
sK0 = sK2,
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_44,negated_conjecture,
sK2 = sK0,
inference(copy,[status(thm)],[c_43]) ).
cnf(c_65,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_66,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_65]) ).
cnf(c_67,negated_conjecture,
r2(sK7,sK8),
inference(split_conjunct,[status(thm)],[sk_oneuneqtwo_neg]) ).
cnf(c_68,negated_conjecture,
r2(sK3,sK7),
inference(split_conjunct,[status(thm)],[sk_oneuneqtwo_neg]) ).
cnf(c_69,negated_conjecture,
r2(sK0,sK7),
inference(paramod,[status(thm)],[c_40,c_68]) ).
cnf(c_70,negated_conjecture,
sK8 = sK9,
inference(split_conjunct,[status(thm)],[sk_oneuneqtwo_neg]) ).
cnf(c_71,negated_conjecture,
sK9 = sK8,
inference(copy,[status(thm)],[c_70]) ).
cnf(c_72,negated_conjecture,
r2(sK2,sK9),
inference(split_conjunct,[status(thm)],[sk_oneuneqtwo_neg]) ).
cnf(c_174,negated_conjecture,
r2(sK0,sK9),
inference(paramod,[status(thm)],[c_44,c_72]) ).
cnf(c_73,negated_conjecture,
r2(sK0,sK8),
inference(paramod,[status(thm)],[c_71,c_174]) ).
cnf(c_80,plain,
sK6(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_81,plain,
( D = A
| ~ r2(D,C)
| C != B
| ~ r2(A,B) ),
inference(clausify,[status(thm)],[axiom_3a]) ).
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] :
( ( sK10(X11) = X12
& r2(X11,X12) )
| ( sK10(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(Y21,sK10(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK10(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK10(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_89,plain,
( sK10(A) = B
| ~ r2(A,B) ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_92,plain,
sK4(A,B) = sK5(A,B),
inference(resolve,[status(thm)],[c_23,c_26]) ).
cnf(c_95,plain,
sK4(A,sK1(A)) = sK6(A),
inference(resolve,[status(thm)],[c_23,c_28]) ).
cnf(c_175,plain,
sK4(A,sK0) = sK6(A),
inference(paramod,[status(thm)],[c_66,c_95]) ).
cnf(c_176,plain,
sK5(A,sK0) = sK6(A),
inference(paramod,[status(thm)],[c_92,c_175]) ).
cnf(c_96,plain,
sK5(A,sK0) = A,
inference(paramod,[status(thm)],[c_80,c_176]) ).
cnf(c_177,negated_conjecture,
sK0 != sK8,
inference(resolve,[status(thm)],[c_67,c_42]) ).
cnf(c_112,negated_conjecture,
sK8 != sK0,
inference(copy,[status(thm)],[c_177]) ).
cnf(c_145,plain,
sK10(sK0) = sK8,
inference(resolve,[status(thm)],[c_89,c_73]) ).
cnf(c_178,negated_conjecture,
sK10(sK0) = sK7,
inference(resolve,[status(thm)],[c_89,c_69]) ).
cnf(c_179,negated_conjecture,
sK8 = sK7,
inference(paramod,[status(thm)],[c_145,c_178]) ).
cnf(c_146,negated_conjecture,
sK7 = sK8,
inference(copy,[status(thm)],[c_179]) ).
cnf(c_150,negated_conjecture,
r2(sK8,sK8),
inference(paramod,[status(thm)],[c_146,c_67]) ).
cnf(c_180,negated_conjecture,
( B = sK0
| ~ r2(B,A)
| A != sK8 ),
inference(resolve,[status(thm)],[c_81,c_73]) ).
cnf(c_181,negated_conjecture,
( A = sK0
| ~ r2(A,sK5(sK8,sK0)) ),
inference(resolve,[status(thm)],[c_180,c_96]) ).
cnf(c_182,negated_conjecture,
~ r2(sK8,sK5(sK8,sK0)),
inference(resolve,[status(thm)],[c_181,c_112]) ).
cnf(c_183,negated_conjecture,
~ r2(sK8,sK8),
inference(paramod,[status(thm)],[c_96,c_182]) ).
cnf(c_172,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_150,c_183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN073+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n019.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 04:30:57 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.40 % Process 408831 was started by sandbox2 on n019,
% 0.11/5.40 % Sat Sep 26 04:30:57 2026
% 0.11/5.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.41
% 0.18/5.41 % From the command line: assign(max_seconds, 300).
% 0.18/5.44
% 0.18/5.44 % SZS status Theorem for theBenchmark
% 0.18/5.44
% 0.18/5.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/5.44 % Length of proof is 42.
% 0.18/5.44 % Level of proof is 8.
% 0.18/5.44 % Maximum clause weight is 12.000.
% 0.18/5.44 % Given clauses 37.
% 0.18/5.44
% 0.18/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------