%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU236+3 : 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 : 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 08:45:32 AM UTC 2026
% Result : Theorem 34.82s 4.85s
% Output : CNFRefutation 34.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 81 ( 25 unt; 0 def)
% Number of atoms : 191 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 181 ( 71 ~; 73 |; 19 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 2 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_xboole_1,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t33_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t33_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
inference(assume_negation,[status(cth)],[t33_ordinal1]) ).
fof(nnf_51,plain,
? [A] :
( ? [B] :
( ( ~ ordinal_subset(succ(A),B)
| ~ in(A,B) )
& ( ordinal_subset(succ(A),B)
| in(A,B) )
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[t33_ordinal1_neg]) ).
fof(sk_t33_ordinal1_neg,plain,
( ( ~ ordinal_subset(succ(sK0),sK1)
| ~ in(sK0,sK1) )
& ( ordinal_subset(succ(sK0),sK1)
| in(sK0,sK1) )
& ordinal(sK1)
& ordinal(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_51]) ).
cnf(c_72,negated_conjecture,
( ~ ordinal_subset(succ(sK0),sK1)
| ~ in(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_73,negated_conjecture,
( ordinal_subset(succ(sK0),sK1)
| in(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_74,negated_conjecture,
ordinal(sK1),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_75,negated_conjecture,
ordinal(sK0),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_76,plain,
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t8_xboole_1]) ).
cnf(c_78,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_84,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_85,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
cnf(c_87,plain,
in(A,succ(A)),
inference(clausify,[status(thm)],[t10_ordinal1]) ).
cnf(c_90,plain,
( ~ subset(A,B)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_91,plain,
( subset(A,B)
| ~ ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_114,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_118,plain,
( ordinal(succ(A))
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[fc3_ordinal1]) ).
fof(nnf_13,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK2(A,B),B)
& in(sK2(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_13]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK2(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_127,plain,
( ~ in(sK2(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_128,plain,
( in(sK2(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_129,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_133,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_134,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_135,plain,
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[connectedness_r1_ordinal1]) ).
cnf(c_141,plain,
( ~ in(B,A)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_163,plain,
( ordinal(set_union2(A,singleton(A)))
| ~ ordinal(A) ),
inference(paramod,[status(thm)],[c_134,c_118]) ).
cnf(c_164,plain,
in(A,set_union2(A,singleton(A))),
inference(paramod,[status(thm)],[c_134,c_87]) ).
cnf(c_165,negated_conjecture,
( ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
| in(sK0,sK1) ),
inference(paramod,[status(thm)],[c_134,c_73]) ).
cnf(c_166,negated_conjecture,
( ~ ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
| ~ in(sK0,sK1) ),
inference(paramod,[status(thm)],[c_134,c_72]) ).
cnf(c_167,plain,
~ in(A,A),
inference(factor,[status(thm)],[c_141]) ).
cnf(c_174,plain,
( ~ subset(A,sK1)
| ordinal_subset(A,sK1)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_90,c_74]) ).
cnf(c_175,plain,
( subset(sK0,A)
| ~ ordinal_subset(sK0,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_91,c_75]) ).
cnf(c_176,plain,
( subset(sK1,A)
| ~ ordinal_subset(sK1,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_91,c_74]) ).
cnf(c_14193,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_114]) ).
cnf(c_14194,plain,
( A = B
| ~ in(A,set_union2(singleton(B),singleton(B))) ),
inference(resolve,[status(thm)],[c_133,c_14193]) ).
cnf(c_242,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(paramod,[status(thm)],[c_114,c_14194]) ).
cnf(c_248,plain,
( ordinal_subset(A,sK0)
| ordinal_subset(sK0,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_135,c_75]) ).
cnf(c_285,plain,
ordinal(set_union2(sK0,singleton(sK0))),
inference(resolve,[status(thm)],[c_163,c_75]) ).
cnf(c_293,plain,
( in(A,B)
| ~ subset(set_union2(A,singleton(A)),B) ),
inference(resolve,[status(thm)],[c_164,c_129]) ).
cnf(c_14195,negated_conjecture,
( subset(set_union2(sK0,singleton(sK0)),sK1)
| ~ ordinal(sK1)
| ~ ordinal(set_union2(sK0,singleton(sK0)))
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_165,c_91]) ).
cnf(c_14196,negated_conjecture,
( subset(set_union2(sK0,singleton(sK0)),sK1)
| ~ ordinal(sK1)
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_285,c_14195]) ).
cnf(c_298,negated_conjecture,
( subset(set_union2(sK0,singleton(sK0)),sK1)
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_74,c_14196]) ).
cnf(c_407,plain,
( subset(sK0,sK1)
| ~ ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_175,c_74]) ).
cnf(c_424,plain,
( subset(sK1,sK0)
| ~ ordinal_subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_176,c_75]) ).
cnf(c_647,plain,
( ordinal_subset(sK1,sK0)
| ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_248,c_74]) ).
cnf(c_648,plain,
( subset(sK1,sK0)
| ordinal_subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_647,c_424]) ).
cnf(c_649,plain,
( subset(sK0,sK1)
| subset(sK1,sK0) ),
inference(resolve,[status(thm)],[c_648,c_407]) ).
cnf(c_652,plain,
( in(A,sK0)
| ~ in(A,sK1)
| subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_649,c_129]) ).
cnf(c_2457,plain,
( ~ subset(set_union2(sK0,singleton(sK0)),sK1)
| ordinal_subset(set_union2(sK0,singleton(sK0)),sK1) ),
inference(resolve,[status(thm)],[c_285,c_174]) ).
cnf(c_14197,plain,
( in(sK0,sK1)
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_298,c_293]) ).
cnf(c_2964,plain,
in(sK0,sK1),
inference(copy,[status(thm)],[c_14197]) ).
cnf(c_2965,negated_conjecture,
~ ordinal_subset(set_union2(sK0,singleton(sK0)),sK1),
inference(resolve,[status(thm)],[c_2964,c_166]) ).
cnf(c_2967,negated_conjecture,
~ subset(set_union2(sK0,singleton(sK0)),sK1),
inference(resolve,[status(thm)],[c_2965,c_2457]) ).
cnf(c_14198,plain,
( in(sK0,sK0)
| subset(sK0,sK1) ),
inference(resolve,[status(thm)],[c_2964,c_652]) ).
cnf(c_2988,plain,
subset(sK0,sK1),
inference(resolve,[status(thm)],[c_167,c_14198]) ).
cnf(c_2996,plain,
element(sK0,sK1),
inference(resolve,[status(thm)],[c_2964,c_85]) ).
cnf(c_2999,plain,
~ empty(sK1),
inference(resolve,[status(thm)],[c_2964,c_78]) ).
cnf(c_14199,plain,
( subset(set_union2(sK0,A),sK1)
| ~ subset(A,sK1) ),
inference(resolve,[status(thm)],[c_76,c_2988]) ).
cnf(c_3095,plain,
~ subset(singleton(sK0),sK1),
inference(resolve,[status(thm)],[c_14199,c_2967]) ).
cnf(c_3168,plain,
in(sK2(singleton(sK0),sK1),singleton(sK0)),
inference(resolve,[status(thm)],[c_3095,c_128]) ).
cnf(c_3170,plain,
~ in(sK2(singleton(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_127,c_3095]) ).
cnf(c_14200,plain,
( in(A,sK1)
| ~ element(A,sK1) ),
inference(resolve,[status(thm)],[c_84,c_2999]) ).
cnf(c_3786,plain,
~ element(sK2(singleton(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_14200,c_3170]) ).
cnf(c_14139,plain,
sK2(singleton(sK0),sK1) = sK0,
inference(resolve,[status(thm)],[c_3168,c_242]) ).
cnf(c_14201,plain,
~ element(sK0,sK1),
inference(paramod,[status(thm)],[c_14139,c_3786]) ).
cnf(c_14192,plain,
$false,
inference(resolve,[status(thm)],[c_2996,c_14201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU236+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:56:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2962041 was started by sandbox2 on n010,
% 0.11/0.38 % Sat Sep 26 08:56:45 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 34.82/4.85
% 34.82/4.85 % given #500 (F,wt=21): 1334 -in(singleton(c10),singleton(powerset(empty_set))). [ur(242,b,1129,a(flip))].
% 34.82/4.85
% 34.82/4.85 % given #1000 (W,wt=18): 3029 in(f4(c15),c10) | element(c10,powerset(c15)). [back_unit_del(2122),unit_del(a,2999)].
% 34.82/4.85
% 34.82/4.85 % given #1500 (F,wt=23): 3696 -in(set_union2(c15,singleton(c15)),f4(powerset(c14))). [ur(129,a,225,a,c,3094,a)].
% 34.82/4.85
% 34.82/4.85 % given #2000 (T,wt=21): 3852 subset(set_union2(c10,c14),c15) | c14 = empty_set | in(empty_set,c10). [resolve(3089,a,3564,b)].
% 34.82/4.85
% 34.82/4.85 % given #2500 (F,wt=24): 11168 -subset(set_union2(A,c10),f3(set_union2(c10,A),empty_set)). [para(136(a,1),5223(a,1))].
% 34.82/4.85
% 34.82/4.85 % SZS status Theorem for theBenchmark
% 34.82/4.85
% 34.82/4.85 % Proof 1 at 3.32 (+ 1.09) seconds.
% 34.82/4.85 % Length of proof is 66.
% 34.82/4.85 % Level of proof is 11.
% 34.82/4.85 % Maximum clause weight is 27.000.
% 34.82/4.85 % Given clauses 2606.
% 34.82/4.85
% 34.82/4.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------