%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUN073+1 : 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 : n010.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 0.20s 15.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 32 ~; 24 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 33 ( 2 sgn 17 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_3a,axiom,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
file('theBenchmark.p',axiom_3a) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('theBenchmark.p',axiom_7a) ).
fof(oneunidtwo,conjecture,
! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( ~ id(Y2,Y1)
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
file('theBenchmark.p',oneunidtwo) ).
fof(oneunidtwo_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( ~ id(Y2,Y1)
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
inference(assume_negation,[status(cth)],[oneunidtwo]) ).
cnf(c_49,plain,
( id(C,D)
| ~ r2(D,B)
| ~ r2(C,A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_3a]) ).
cnf(c_61,plain,
( ~ r2(C,B)
| ~ r1(A)
| ~ id(A,B) ),
inference(clausify,[status(thm)],[axiom_7a]) ).
fof(nnf_19,plain,
? [Y1] :
( ? [Y3] :
( r2(Y3,Y1)
& ? [Y5] :
( r2(Y5,Y3)
& r1(Y5) ) )
& ? [Y2] :
( id(Y2,Y1)
& ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) ) ) ),
inference(fof_nnf,[status(thm)],[oneunidtwo_neg]) ).
fof(sk_oneunidtwo_neg,plain,
( r2(sK4,sK2)
& r2(sK3,sK4)
& r1(sK3)
& id(sK1,sK2)
& r2(sK0,sK1)
& r1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(Y1,sK2),skolemize(Y2,sK1),skolemize(Y4,sK0),skolemize(Y3,sK4),skolemize(Y5,sK3)],[nnf_19]) ).
cnf(c_62,negated_conjecture,
r1(sK0),
inference(split_conjunct,[status(thm)],[sk_oneunidtwo_neg]) ).
cnf(c_63,negated_conjecture,
r2(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_oneunidtwo_neg]) ).
cnf(c_64,negated_conjecture,
id(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_oneunidtwo_neg]) ).
cnf(c_66,negated_conjecture,
r2(sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_oneunidtwo_neg]) ).
cnf(c_67,negated_conjecture,
r2(sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_oneunidtwo_neg]) ).
cnf(c_463,negated_conjecture,
( ~ r2(B,A)
| ~ id(sK0,A) ),
inference(resolve,[status(thm)],[c_61,c_62]) ).
cnf(c_235,negated_conjecture,
~ id(sK0,sK4),
inference(resolve,[status(thm)],[c_463,c_66]) ).
cnf(c_464,negated_conjecture,
( id(sK0,B)
| ~ r2(B,A)
| ~ id(sK1,A) ),
inference(resolve,[status(thm)],[c_49,c_63]) ).
cnf(c_465,negated_conjecture,
( id(sK0,sK4)
| ~ id(sK1,sK2) ),
inference(resolve,[status(thm)],[c_464,c_67]) ).
cnf(c_466,negated_conjecture,
~ id(sK1,sK2),
inference(resolve,[status(thm)],[c_465,c_235]) ).
cnf(c_462,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_64,c_466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/15.43 % Computer : n010.cluster.edu
% 0.17/15.43 % Model : x86_64 x86_64
% 0.17/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.43 % Memory : 8046.5625MB
% 0.17/15.43 % OS : Linux 6.8.0-71-generic
% 0.17/15.43 % CPULimit : 300
% 0.17/15.43 % WCLimit : 300
% 0.17/15.43 % DateTime : Sat Sep 26 04:31:31 UTC 2026
% 0.17/15.44 % CPUTime :
% 0.17/15.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/15.44 % Process 2488031 was started by sandbox on n010,
% 0.17/15.44 % Sat Sep 26 04:31:31 2026
% 0.17/15.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/15.45
% 0.17/15.45 % From the command line: assign(max_seconds, 300).
% 0.20/15.54
% 0.20/15.54 % SZS status Theorem for theBenchmark
% 0.20/15.54
% 0.20/15.54 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.20/15.54 % Length of proof is 12.
% 0.20/15.54 % Level of proof is 3.
% 0.20/15.54 % Maximum clause weight is 17.000.
% 0.20/15.54 % Given clauses 85.
% 0.20/15.54
% 0.20/15.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------