%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM390+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 : n004.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 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 96 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 30 ~; 20 |; 16 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 46 ( 1 sgn 22 !; 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(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t21_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t7_ordinal1,axiom,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('theBenchmark.p',t7_ordinal1) ).
fof(t22_ordinal1,conjecture,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
file('theBenchmark.p',t22_ordinal1) ).
fof(t22_ordinal1_neg,negated_conjecture,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
inference(assume_negation,[status(cth)],[t22_ordinal1]) ).
cnf(c_45,plain,
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[t21_ordinal1]) ).
fof(nnf_37,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(A,C)
& in(B,C)
& subset(A,B)
& ordinal(C) )
& ordinal(B) )
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[t22_ordinal1_neg]) ).
fof(sk_t22_ordinal1_neg,plain,
( ~ in(sK1,sK0)
& in(sK2,sK0)
& subset(sK1,sK2)
& ordinal(sK0)
& ordinal(sK2)
& epsilon_transitive(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_37]) ).
cnf(c_47,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t22_ordinal1_neg]) ).
cnf(c_51,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_70,negated_conjecture,
~ in(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t22_ordinal1_neg]) ).
cnf(c_71,negated_conjecture,
in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t22_ordinal1_neg]) ).
cnf(c_72,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t22_ordinal1_neg]) ).
cnf(c_73,negated_conjecture,
epsilon_transitive(sK1),
inference(split_conjunct,[status(thm)],[sk_t22_ordinal1_neg]) ).
cnf(c_75,plain,
( ~ subset(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_ordinal1]) ).
cnf(c_80,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_81,plain,
( subset(A,B)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_83,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
cnf(c_85,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_95,plain,
( B = A
| ~ subset(A,B)
| proper_subset(A,B) ),
inference(clausify,[status(thm)],[d8_xboole_0]) ).
cnf(c_100,plain,
( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[d2_ordinal1]) ).
cnf(c_104,negated_conjecture,
( in(A,sK0)
| ~ proper_subset(A,sK0)
| ~ epsilon_transitive(A) ),
inference(resolve,[status(thm)],[c_45,c_47]) ).
cnf(c_107,negated_conjecture,
epsilon_transitive(sK0),
inference(resolve,[status(thm)],[c_51,c_47]) ).
cnf(c_109,plain,
~ subset(sK0,sK2),
inference(resolve,[status(thm)],[c_75,c_71]) ).
cnf(c_113,plain,
( subset(sK1,A)
| ~ subset(sK2,A) ),
inference(resolve,[status(thm)],[c_83,c_72]) ).
cnf(c_116,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_85,c_80]) ).
cnf(c_162,negated_conjecture,
( subset(sK2,sK0)
| ~ epsilon_transitive(sK0) ),
inference(resolve,[status(thm)],[c_100,c_71]) ).
cnf(c_131,negated_conjecture,
subset(sK2,sK0),
inference(resolve,[status(thm)],[c_107,c_162]) ).
cnf(c_163,negated_conjecture,
( in(sK1,sK0)
| ~ proper_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_104,c_73]) ).
cnf(c_134,negated_conjecture,
~ proper_subset(sK1,sK0),
inference(resolve,[status(thm)],[c_163,c_70]) ).
cnf(c_164,negated_conjecture,
( subset(A,sK2)
| ~ subset(A,sK1) ),
inference(resolve,[status(thm)],[c_83,c_72]) ).
cnf(c_138,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_164,c_109]) ).
cnf(c_153,plain,
subset(sK1,sK0),
inference(resolve,[status(thm)],[c_113,c_131]) ).
cnf(c_156,plain,
~ element(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_81,c_138]) ).
cnf(c_165,plain,
( sK0 = sK1
| proper_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_153,c_95]) ).
cnf(c_159,plain,
sK0 = sK1,
inference(resolve,[status(thm)],[c_134,c_165]) ).
cnf(c_166,plain,
~ element(sK1,powerset(sK1)),
inference(paramod,[status(thm)],[c_159,c_156]) ).
cnf(c_161,plain,
$false,
inference(resolve,[status(thm)],[c_116,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n004.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 02:38:11 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 638020 was started by sandbox2 on n004,
% 0.10/5.37 % Sat Sep 26 02:38:11 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Theorem for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 35.
% 0.14/5.40 % Level of proof is 6.
% 0.14/5.40 % Maximum clause weight is 9.000.
% 0.14/5.40 % Given clauses 63.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------