%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:16:55 AM UTC 2026
% Result : Theorem 0.04s 0.32s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 5 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 30 ~; 24 |; 9 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 39 ( 3 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e2_43__ordinal1,axiom,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
file('theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
fof(t37_ordinal1,axiom,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('theBenchmark.p',t37_ordinal1) ).
fof(t38_ordinal1,conjecture,
! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
file('theBenchmark.p',t38_ordinal1) ).
fof(t38_ordinal1_neg,negated_conjecture,
~ ! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
inference(assume_negation,[status(cth)],[t38_ordinal1]) ).
fof(nnf_32,plain,
? [A] :
! [B] :
( in(B,A)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t38_ordinal1_neg]) ).
fof(sk_t38_ordinal1_neg,plain,
! [B] :
( in(B,sK0)
| ~ ordinal(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_32]) ).
cnf(c_67,negated_conjecture,
( in(A,sK0)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t38_ordinal1_neg]) ).
fof(nnf_28,plain,
! [A] :
? [B] :
( ( ~ ordinal(B)
| ~ in(B,A) )
& ( ordinal(B)
| in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t37_ordinal1]) ).
fof(sk_t37_ordinal1,plain,
! [A] :
( ( ~ ordinal(sK1(A))
| ~ in(sK1(A),A) )
& ( ordinal(sK1(A))
| in(sK1(A),A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(B,sK1(A))],[nnf_28]) ).
cnf(c_71,plain,
( ~ ordinal(sK1(A))
| ~ in(sK1(A),A) ),
inference(split_conjunct,[status(thm)],[sk_t37_ordinal1]) ).
cnf(c_72,plain,
( ordinal(sK1(A))
| in(sK1(A),A) ),
inference(split_conjunct,[status(thm)],[sk_t37_ordinal1]) ).
fof(nnf_25,plain,
! [A] :
? [B] :
! [C] :
( ( ~ ordinal(C)
| ~ in(C,A)
| in(C,B) )
& ( ( ordinal(C)
& in(C,A) )
| ~ in(C,B) ) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e2_43__ordinal1]) ).
fof(sk_s1_xboole_0__e2_43__ordinal1_sk,plain,
! [A,C] :
( ( ~ ordinal(C)
| ~ in(C,A)
| in(C,sK2(A)) )
& ( ( ordinal(C)
& in(C,A) )
| ~ in(C,sK2(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(B,sK2(A))],[nnf_25]) ).
fof(sk_s1_xboole_0__e2_43__ordinal1,plain,
( ! [VAR_0,VAR_1] :
( ~ ordinal(VAR_0)
| ~ in(VAR_0,VAR_1)
| in(VAR_0,sK2(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ordinal(VAR_0)
| ~ in(VAR_0,sK2(VAR_1)) )
& ! [VAR_0,VAR_1] :
( in(VAR_0,VAR_1)
| ~ in(VAR_0,sK2(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_s1_xboole_0__e2_43__ordinal1_sk]) ).
cnf(c_73,plain,
( ~ ordinal(A)
| ~ in(A,B)
| in(A,sK2(B)) ),
inference(split_conjunct,[status(thm)],[sk_s1_xboole_0__e2_43__ordinal1]) ).
cnf(c_74,plain,
( ordinal(A)
| ~ in(A,sK2(B)) ),
inference(split_conjunct,[status(thm)],[sk_s1_xboole_0__e2_43__ordinal1]) ).
cnf(c_143,plain,
( ordinal(sK1(sK2(A)))
| ordinal(sK1(sK2(A))) ),
inference(resolve,[status(thm)],[c_74,c_72]) ).
cnf(c_103,plain,
ordinal(sK1(sK2(A))),
inference(copy,[status(thm)],[c_143]) ).
cnf(c_135,plain,
in(sK1(sK2(A)),sK0),
inference(resolve,[status(thm)],[c_103,c_67]) ).
cnf(c_136,plain,
~ in(sK1(sK2(A)),sK2(A)),
inference(resolve,[status(thm)],[c_71,c_103]) ).
cnf(c_144,plain,
( ~ ordinal(sK1(sK2(A)))
| ~ in(sK1(sK2(A)),A) ),
inference(resolve,[status(thm)],[c_73,c_136]) ).
cnf(c_141,plain,
~ in(sK1(sK2(A)),A),
inference(resolve,[status(thm)],[c_144,c_103]) ).
cnf(c_142,plain,
$false,
inference(resolve,[status(thm)],[c_141,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 26 02:38:50 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 3710768 was started by sandbox2 on n012,
% 0.04/0.30 % Sat Sep 26 02:38:50 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 0.04/0.32
% 0.04/0.32 % SZS status Theorem for theBenchmark
% 0.04/0.32
% 0.04/0.32 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.04/0.32 % Length of proof is 13.
% 0.04/0.32 % Level of proof is 5.
% 0.04/0.32 % Maximum clause weight is 9.000.
% 0.04/0.32 % Given clauses 54.
% 0.04/0.32
% 0.04/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------