%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:16:54 AM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 62 ( 20 ~; 13 |; 15 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 36 ( 1 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t19_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(A,B)
& in(C,A) )
=> in(C,B) ) ) ) ),
file('theBenchmark.p',t19_ordinal1) ).
fof(t19_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( epsilon_transitive(C)
=> ( ( in(A,B)
& in(C,A) )
=> in(C,B) ) ) ) ),
inference(assume_negation,[status(cth)],[t19_ordinal1]) ).
fof(nnf_31,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,B)
& in(A,B)
& in(C,A)
& epsilon_transitive(C) )
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[t19_ordinal1_neg]) ).
fof(sk_t19_ordinal1_neg,plain,
( ~ in(sK1,sK0)
& in(sK2,sK0)
& in(sK1,sK2)
& epsilon_transitive(sK1)
& ordinal(sK0)
& ordinal(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(A,sK2),skolemize(B,sK0),skolemize(C,sK1)],[nnf_31]) ).
cnf(c_43,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_ordinal1_neg]) ).
cnf(c_44,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_45,plain,
( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[d2_ordinal1]) ).
cnf(c_48,negated_conjecture,
epsilon_transitive(sK0),
inference(resolve,[status(thm)],[c_44,c_43]) ).
cnf(c_75,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_77,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_78,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_81,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_83,negated_conjecture,
in(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t19_ordinal1_neg]) ).
cnf(c_84,negated_conjecture,
in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t19_ordinal1_neg]) ).
cnf(c_85,negated_conjecture,
~ in(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t19_ordinal1_neg]) ).
cnf(c_88,negated_conjecture,
( subset(A,sK0)
| ~ in(A,sK0) ),
inference(resolve,[status(thm)],[c_45,c_48]) ).
cnf(c_119,plain,
~ empty(sK0),
inference(resolve,[status(thm)],[c_84,c_81]) ).
cnf(c_127,plain,
subset(sK2,sK0),
inference(resolve,[status(thm)],[c_88,c_84]) ).
cnf(c_158,plain,
( in(A,sK0)
| ~ element(A,sK0) ),
inference(resolve,[status(thm)],[c_75,c_119]) ).
cnf(c_139,negated_conjecture,
~ element(sK1,sK0),
inference(resolve,[status(thm)],[c_158,c_85]) ).
cnf(c_147,plain,
element(sK2,powerset(sK0)),
inference(resolve,[status(thm)],[c_127,c_77]) ).
cnf(c_159,negated_conjecture,
( element(sK1,A)
| ~ element(sK2,powerset(A)) ),
inference(resolve,[status(thm)],[c_78,c_83]) ).
cnf(c_160,negated_conjecture,
~ element(sK2,powerset(sK0)),
inference(resolve,[status(thm)],[c_159,c_139]) ).
cnf(c_157,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_147,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 02:38:48 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 437846 was started by sandbox on n020,
% 0.18/0.45 % Sat Sep 26 02:38:48 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % 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 0.00 (+ 0.00) seconds.
% 0.18/0.48 % Length of proof is 24.
% 0.18/0.48 % Level of proof is 6.
% 0.18/0.48 % Maximum clause weight is 20.000.
% 0.18/0.48 % Given clauses 58.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------