%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN081+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 : 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 08:19:23 AM UTC 2026
% Result : Theorem 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 123 ( 38 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 132 ( 48 ~; 33 |; 51 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 113 ( 20 sgn 27 !; 36 ?)
% 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_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_4a,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('theBenchmark.p',axiom_4a) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('theBenchmark.p',axiom_5a) ).
fof(xplusyeqthree,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& Y3 = Y4 )
& r3(Y1,Y2,Y3) ),
file('theBenchmark.p',xplusyeqthree) ).
fof(xplusyeqthree_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& Y3 = Y4 )
& r3(Y1,Y2,Y3) ),
inference(assume_negation,[status(cth)],[xplusyeqthree]) ).
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_9,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y18 = Y8
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(fof_nnf,[status(thm)],[axiom_5a]) ).
fof(sk_axiom_5a,plain,
! [X5] :
( sK1(X5) = sK7(X5)
& r1(sK1(X5))
& r4(X5,sK6(X5),sK7(X5))
& r1(sK6(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK1]),skolemize(Y8,sK7(X5)),skolemize(Y17,sK6(X5)),skolemize(Y18,sK1(X5))],[nnf_9]) ).
cnf(c_17,plain,
r1(sK1(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_21,negated_conjecture,
( ~ r2(V6,F)
| ~ r1(V6)
| ~ r2(F,E)
| ~ r2(E,D)
| C != D
| ~ r3(A,B,C) ),
inference(clausify,[status(thm)],[xplusyeqthree_neg]) ).
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] :
( sK3(X4) = X4
& r3(X4,sK2(X4),sK3(X4))
& r1(sK2(X4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(Y9,sK3(X4)),skolemize(Y16,sK2(X4))],[nnf_8]) ).
cnf(c_22,plain,
r3(A,sK2(A),sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_25,negated_conjecture,
( ~ r2(sK1(V6),F)
| ~ r2(F,E)
| ~ r2(E,D)
| C != D
| ~ r3(A,B,C) ),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_59,plain,
sK0 = sK1(A),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_60,plain,
sK1(A) = sK0,
inference(copy,[status(thm)],[c_59]) ).
cnf(c_71,plain,
sK3(A) = A,
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
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,sK10(X1,X8))
& r2(sK10(X1,X8),sK9(X1,X8))
& sK9(X1,X8) = sK8(X1,X8)
& r3(X1,sK4(X1,X8),sK8(X1,X8))
& r2(X8,sK4(X1,X8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK8,sK9,sK10]),skolemize(Y4,sK9(X1,X8)),skolemize(Y5,sK8(X1,X8)),skolemize(Y15,sK4(X1,X8)),skolemize(Y7,sK10(X1,X8))],[nnf_5]) ).
cnf(c_78,plain,
r2(A,sK4(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_1a]) ).
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] :
( ( sK5(X11) = X12
& r2(X11,X12) )
| ( sK5(X11) != X12
& ~ r2(X11,X12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(Y21,sK5(X11))],[nnf_2]) ).
fof(sk_axiom_2,plain,
( ! [VAR_0,VAR_1] :
( r2(VAR_0,VAR_1)
| sK5(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1] :
( sK5(VAR_0) = VAR_1
| ~ r2(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_2_sk]) ).
cnf(c_79,plain,
( r2(A,B)
| sK5(A) != B ),
inference(split_conjunct,[status(thm)],[sk_axiom_2]) ).
cnf(c_85,negated_conjecture,
( ~ r2(sK1(E),D)
| ~ r2(D,C)
| ~ r2(C,B)
| sK3(A) != B ),
inference(resolve,[status(thm)],[c_22,c_25]) ).
cnf(c_206,negated_conjecture,
( ~ r2(sK1(E),D)
| ~ r2(D,C)
| ~ r2(C,B)
| A != B ),
inference(paramod,[status(thm)],[c_71,c_85]) ).
cnf(c_207,negated_conjecture,
( ~ r2(sK0,D)
| ~ r2(D,C)
| ~ r2(C,B)
| A != B ),
inference(paramod,[status(thm)],[c_60,c_206]) ).
cnf(c_86,negated_conjecture,
( ~ r2(sK0,C)
| ~ r2(C,A)
| ~ r2(A,B) ),
inference(copy,[status(thm)],[c_207]) ).
cnf(c_208,plain,
A = sK3(A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_209,plain,
r2(A,sK3(sK5(A))),
inference(resolve,[status(thm)],[c_79,c_208]) ).
cnf(c_172,plain,
r2(A,sK5(A)),
inference(paramod,[status(thm)],[c_71,c_209]) ).
cnf(c_210,negated_conjecture,
( ~ r2(sK0,B)
| ~ r2(sK4(A,B),C) ),
inference(resolve,[status(thm)],[c_86,c_78]) ).
cnf(c_204,negated_conjecture,
~ r2(sK4(A,sK4(B,sK0)),C),
inference(resolve,[status(thm)],[c_210,c_78]) ).
cnf(c_205,plain,
$false,
inference(resolve,[status(thm)],[c_204,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.65 % Computer : n002.cluster.edu
% 0.20/0.65 % Model : x86_64 x86_64
% 0.20/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.65 % Memory : 8046.5625MB
% 0.20/0.65 % OS : Linux 6.8.0-71-generic
% 0.20/0.65 % CPULimit : 300
% 0.20/0.65 % WCLimit : 300
% 0.20/0.65 % DateTime : Sat Sep 26 04:34:36 UTC 2026
% 0.20/0.66 % CPUTime :
% 0.20/0.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.66 % Process 833614 was started by sandbox2 on n002,
% 0.20/0.66 % Sat Sep 26 04:34:36 2026
% 0.20/0.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.67
% 0.20/0.67 % From the command line: assign(max_seconds, 300).
% 0.20/0.69
% 0.20/0.69 % SZS status Theorem for theBenchmark
% 0.20/0.69
% 0.20/0.69 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.20/0.69 % Length of proof is 21.
% 0.20/0.69 % Level of proof is 6.
% 0.20/0.69 % Maximum clause weight is 27.000.
% 0.20/0.69 % Given clauses 21.
% 0.20/0.69
% 0.20/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------