%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN081+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 : n020.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 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 74 ( 22 ~; 15 |; 37 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 86 ( 24 sgn 12 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
file('theBenchmark.p',axiom_2a) ).
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(xplusyidthree,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& id(Y3,Y4) )
& r3(Y1,Y2,Y3) ),
file('theBenchmark.p',xplusyidthree) ).
fof(xplusyidthree_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( r2(Y7,Y6)
& r1(Y7) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& id(Y3,Y4) )
& r3(Y1,Y2,Y3) ),
inference(assume_negation,[status(cth)],[xplusyidthree]) ).
fof(nnf_13,plain,
! [X2,X9] :
? [Y2] :
( ? [Y6] :
( r4(X2,X9,Y6)
& r3(Y6,X2,Y2) )
& ? [Y3] :
( ? [Y14] :
( r4(X2,Y14,Y3)
& r2(X9,Y14) )
& id(Y3,Y2) ) ),
inference(fof_nnf,[status(thm)],[axiom_2a]) ).
fof(sk_axiom_2a,plain,
! [X2,X9] :
( r4(X2,X9,sK6(X2,X9))
& r3(sK6(X2,X9),X2,sK5(X2,X9))
& r4(X2,sK0(X2,X9),sK4(X2,X9))
& r2(X9,sK0(X2,X9))
& id(sK4(X2,X9),sK5(X2,X9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK0,sK6]),skolemize(Y2,sK5(X2,X9)),skolemize(Y3,sK4(X2,X9)),skolemize(Y14,sK0(X2,X9)),skolemize(Y6,sK6(X2,X9))],[nnf_13]) ).
cnf(c_45,plain,
r2(A,sK0(B,A)),
inference(split_conjunct,[status(thm)],[sk_axiom_2a]) ).
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,sK2(X4),sK1(X4))
& r1(sK2(X4))
& id(sK1(X4),X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(Y9,sK1(X4)),skolemize(Y16,sK2(X4))],[nnf_15]) ).
cnf(c_50,plain,
id(sK1(A),A),
inference(split_conjunct,[status(thm)],[sk_axiom_4a]) ).
cnf(c_52,plain,
r3(A,sK2(A),sK1(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(sK3(X5))
& id(sK8(X5),sK3(X5))
& r4(X5,sK7(X5),sK8(X5))
& r1(sK7(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK3]),skolemize(Y8,sK8(X5)),skolemize(Y17,sK7(X5)),skolemize(Y18,sK3(X5))],[nnf_16]) ).
cnf(c_56,plain,
r1(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_axiom_5a]) ).
cnf(c_62,negated_conjecture,
( ~ r2(V6,F)
| ~ r1(V6)
| ~ r2(F,E)
| ~ r2(E,D)
| ~ id(C,D)
| ~ r3(A,B,C) ),
inference(clausify,[status(thm)],[xplusyidthree_neg]) ).
cnf(c_206,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| ~ r2(D,C)
| ~ r3(A,B,sK1(C)) ),
inference(resolve,[status(thm)],[c_62,c_50]) ).
cnf(c_207,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ r2(E,D)
| ~ r3(A,B,sK1(sK0(C,D))) ),
inference(resolve,[status(thm)],[c_206,c_45]) ).
cnf(c_208,negated_conjecture,
( ~ r2(F,E)
| ~ r1(F)
| ~ r3(A,B,sK1(sK0(C,sK0(D,E)))) ),
inference(resolve,[status(thm)],[c_207,c_45]) ).
cnf(c_209,negated_conjecture,
( ~ r2(sK3(F),E)
| ~ r3(A,B,sK1(sK0(C,sK0(D,E)))) ),
inference(resolve,[status(thm)],[c_208,c_56]) ).
cnf(c_204,negated_conjecture,
~ r3(A,B,sK1(sK0(C,sK0(D,sK0(E,sK3(F)))))),
inference(resolve,[status(thm)],[c_209,c_45]) ).
cnf(c_205,plain,
$false,
inference(resolve,[status(thm)],[c_204,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN081+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n020.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 04:32:49 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 619052 was started by sandbox2 on n020,
% 0.18/0.44 % Sat Sep 26 04:32:49 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.48 % Length of proof is 11.
% 0.18/0.48 % Level of proof is 3.
% 0.18/0.48 % Maximum clause weight is 46.000.
% 0.18/0.48 % Given clauses 43.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------