%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU235+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 : n013.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 17.49s 3.17s
% Output : CNFRefutation 17.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 15
% Syntax : Number of formulae : 118 ( 46 unt; 0 def)
% Number of atoms : 275 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 278 ( 121 ~; 97 |; 39 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 2 sgn 54 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
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(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
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(t23_ordinal1,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('theBenchmark.p',t23_ordinal1) ).
fof(t24_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_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(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t7_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t32_ordinal1,conjecture,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('theBenchmark.p',t32_ordinal1) ).
fof(t32_ordinal1_neg,negated_conjecture,
~ ! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
inference(assume_negation,[status(cth)],[t32_ordinal1]) ).
cnf(c_51,plain,
( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[d2_ordinal1]) ).
cnf(c_60,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_75,plain,
( subset(B,A)
| ~ in(B,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_60,c_51]) ).
cnf(c_94,plain,
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(nnf_10,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK0(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_10]) ).
cnf(c_95,plain,
element(sK0(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_96,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc12_relat_1]) ).
cnf(c_113,plain,
( ~ subset(A,B)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_117,plain,
( ordinal(B)
| ~ in(B,A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t23_ordinal1]) ).
cnf(c_118,plain,
( in(B,A)
| B = A
| in(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t24_ordinal1]) ).
cnf(c_119,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_121,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_122,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_123,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
fof(nnf_39,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_tarski]) ).
fof(sk_t7_tarski_sk,plain,
! [A,B] :
( ( ! [D] :
( ~ in(D,sK1(A,B))
| ~ in(D,B) )
& in(sK1(A,B),B) )
| ~ in(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1(A,B))],[nnf_39]) ).
fof(sk_t7_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,sK1(VAR_0,VAR_1))
| ~ in(VAR_2,VAR_1)
| ~ in(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK1(VAR_0,VAR_1),VAR_1)
| ~ in(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t7_tarski_sk]) ).
cnf(c_126,plain,
( in(sK1(A,B),B)
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t7_tarski]) ).
cnf(c_127,plain,
( ~ in(C,sK1(A,B))
| ~ in(C,B)
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t7_tarski]) ).
cnf(c_128,plain,
( ~ empty(B)
| B = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t8_boole]) ).
fof(nnf_41,plain,
? [A,B] :
( ! [C] :
( ? [D] :
( ~ ordinal_subset(C,D)
& in(D,A)
& ordinal(D) )
| ~ in(C,A)
| ~ ordinal(C) )
& empty_set != A
& subset(A,B)
& ordinal(B) ),
inference(fof_nnf,[status(thm)],[t32_ordinal1_neg]) ).
fof(sk_t32_ordinal1_neg_sk,plain,
( ! [C] :
( ( ~ ordinal_subset(C,sK4(C))
& in(sK4(C),sK3)
& ordinal(sK4(C)) )
| ~ in(C,sK3)
| ~ ordinal(C) )
& empty_set != sK3
& subset(sK3,sK2)
& ordinal(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(A,sK3),skolemize(B,sK2),skolemize(D,sK4(C))],[nnf_41]) ).
fof(sk_t32_ordinal1_neg,plain,
( ! [VAR_0] :
( ~ ordinal_subset(VAR_0,sK4(VAR_0))
| ~ in(VAR_0,sK3)
| ~ ordinal(VAR_0) )
& ! [VAR_0] :
( in(sK4(VAR_0),sK3)
| ~ in(VAR_0,sK3)
| ~ ordinal(VAR_0) )
& ! [VAR_0] :
( ordinal(sK4(VAR_0))
| ~ in(VAR_0,sK3)
| ~ ordinal(VAR_0) )
& empty_set != sK3
& subset(sK3,sK2)
& ordinal(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_t32_ordinal1_neg_sk]) ).
cnf(c_129,negated_conjecture,
ordinal(sK2),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_130,negated_conjecture,
subset(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_131,negated_conjecture,
empty_set != sK3,
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_132,negated_conjecture,
sK3 != empty_set,
inference(copy,[status(thm)],[c_131]) ).
cnf(c_133,negated_conjecture,
( ordinal(sK4(A))
| ~ in(A,sK3)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_134,negated_conjecture,
( in(sK4(A),sK3)
| ~ in(A,sK3)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_135,negated_conjecture,
( ~ ordinal_subset(A,sK4(A))
| ~ in(A,sK3)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_9905,plain,
( ordinal_subset(A,A)
| ordinal_subset(A,A)
| ~ ordinal(A) ),
inference(factor,[status(thm)],[c_94]) ).
cnf(c_137,plain,
( ordinal_subset(A,A)
| ~ ordinal(A) ),
inference(copy,[status(thm)],[c_9905]) ).
cnf(c_138,plain,
( ~ in(A,sK1(A,B))
| ~ in(A,B) ),
inference(factor,[status(thm)],[c_127]) ).
cnf(c_157,plain,
( in(sK0(A),A)
| empty(A) ),
inference(resolve,[status(thm)],[c_119,c_95]) ).
cnf(c_177,plain,
element(sK3,powerset(sK2)),
inference(resolve,[status(thm)],[c_130,c_121]) ).
cnf(c_9906,plain,
( ~ empty(A)
| A = empty_set ),
inference(resolve,[status(thm)],[c_128,c_96]) ).
cnf(c_179,negated_conjecture,
~ empty(sK3),
inference(resolve,[status(thm)],[c_9906,c_132]) ).
cnf(c_195,plain,
( ~ empty(sK2)
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_177,c_123]) ).
cnf(c_196,plain,
( element(A,sK2)
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_177,c_122]) ).
cnf(c_9907,plain,
( ~ empty(sK2)
| empty(sK3) ),
inference(resolve,[status(thm)],[c_157,c_195]) ).
cnf(c_202,plain,
~ empty(sK2),
inference(resolve,[status(thm)],[c_179,c_9907]) ).
cnf(c_9908,negated_conjecture,
( in(sK4(sK0(sK3)),sK3)
| ~ ordinal(sK0(sK3))
| empty(sK3) ),
inference(resolve,[status(thm)],[c_157,c_134]) ).
cnf(c_205,negated_conjecture,
( in(sK4(sK0(sK3)),sK3)
| ~ ordinal(sK0(sK3)) ),
inference(resolve,[status(thm)],[c_179,c_9908]) ).
cnf(c_9909,plain,
( empty(sK3)
| element(sK0(sK3),sK2) ),
inference(resolve,[status(thm)],[c_196,c_157]) ).
cnf(c_238,plain,
element(sK0(sK3),sK2),
inference(resolve,[status(thm)],[c_179,c_9909]) ).
cnf(c_9910,plain,
( in(sK0(sK3),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_238,c_119]) ).
cnf(c_239,plain,
in(sK0(sK3),sK2),
inference(resolve,[status(thm)],[c_202,c_9910]) ).
cnf(c_9911,plain,
( ordinal(sK0(sK3))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_239,c_117]) ).
cnf(c_242,negated_conjecture,
ordinal(sK0(sK3)),
inference(resolve,[status(thm)],[c_129,c_9911]) ).
cnf(c_249,negated_conjecture,
in(sK4(sK0(sK3)),sK3),
inference(resolve,[status(thm)],[c_242,c_205]) ).
cnf(c_292,plain,
( ~ in(A,sK1(sK4(sK0(sK3)),sK3))
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_249,c_127]) ).
cnf(c_293,plain,
in(sK1(sK4(sK0(sK3)),sK3),sK3),
inference(resolve,[status(thm)],[c_249,c_126]) ).
cnf(c_663,plain,
element(sK1(sK4(sK0(sK3)),sK3),sK2),
inference(resolve,[status(thm)],[c_293,c_196]) ).
cnf(c_664,plain,
( in(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3)
| ~ ordinal(sK1(sK4(sK0(sK3)),sK3)) ),
inference(resolve,[status(thm)],[c_293,c_134]) ).
cnf(c_665,plain,
( ordinal(sK4(sK1(sK4(sK0(sK3)),sK3)))
| ~ ordinal(sK1(sK4(sK0(sK3)),sK3)) ),
inference(resolve,[status(thm)],[c_293,c_133]) ).
cnf(c_667,plain,
in(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK3),
inference(resolve,[status(thm)],[c_293,c_126]) ).
cnf(c_675,plain,
~ in(sK1(sK4(sK0(sK3)),sK3),sK1(sK1(sK4(sK0(sK3)),sK3),sK3)),
inference(resolve,[status(thm)],[c_138,c_293]) ).
cnf(c_9912,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_663,c_119]) ).
cnf(c_852,plain,
in(sK1(sK4(sK0(sK3)),sK3),sK2),
inference(resolve,[status(thm)],[c_202,c_9912]) ).
cnf(c_9913,plain,
( ordinal(sK1(sK4(sK0(sK3)),sK3))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_852,c_117]) ).
cnf(c_945,negated_conjecture,
ordinal(sK1(sK4(sK0(sK3)),sK3)),
inference(resolve,[status(thm)],[c_129,c_9913]) ).
cnf(c_963,plain,
ordinal(sK4(sK1(sK4(sK0(sK3)),sK3))),
inference(resolve,[status(thm)],[c_945,c_665]) ).
cnf(c_964,plain,
in(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),
inference(resolve,[status(thm)],[c_945,c_664]) ).
cnf(c_978,plain,
ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK1(sK4(sK0(sK3)),sK3)),
inference(resolve,[status(thm)],[c_945,c_137]) ).
cnf(c_979,plain,
( in(sK1(sK4(sK0(sK3)),sK3),A)
| sK1(sK4(sK0(sK3)),sK3) = A
| in(A,sK1(sK4(sK0(sK3)),sK3))
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_945,c_118]) ).
cnf(c_9914,negated_conjecture,
( ~ ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3)))
| ~ in(sK1(sK4(sK0(sK3)),sK3),sK3) ),
inference(resolve,[status(thm)],[c_135,c_945]) ).
cnf(c_982,negated_conjecture,
~ ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3))),
inference(resolve,[status(thm)],[c_9914,c_293]) ).
cnf(c_9915,plain,
( ~ subset(sK1(sK4(sK0(sK3)),sK3),A)
| ordinal_subset(sK1(sK4(sK0(sK3)),sK3),A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_113,c_945]) ).
cnf(c_9916,plain,
( ~ subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3)))
| ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3))) ),
inference(resolve,[status(thm)],[c_9915,c_963]) ).
cnf(c_1153,plain,
~ subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3))),
inference(resolve,[status(thm)],[c_9916,c_982]) ).
cnf(c_9917,plain,
( subset(A,sK4(sK1(sK4(sK0(sK3)),sK3)))
| ~ in(A,sK4(sK1(sK4(sK0(sK3)),sK3))) ),
inference(resolve,[status(thm)],[c_75,c_963]) ).
cnf(c_1284,plain,
~ in(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3))),
inference(resolve,[status(thm)],[c_9917,c_1153]) ).
cnf(c_1616,plain,
in(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK3),
inference(resolve,[status(thm)],[c_964,c_126]) ).
cnf(c_1625,plain,
~ in(sK4(sK1(sK4(sK0(sK3)),sK3)),sK1(sK4(sK0(sK3)),sK3)),
inference(resolve,[status(thm)],[c_292,c_964]) ).
cnf(c_2418,plain,
element(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK2),
inference(resolve,[status(thm)],[c_667,c_196]) ).
cnf(c_2436,plain,
~ in(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK1(sK4(sK0(sK3)),sK3)),
inference(resolve,[status(thm)],[c_292,c_667]) ).
cnf(c_9918,plain,
( in(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_2418,c_119]) ).
cnf(c_3386,plain,
in(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK2),
inference(resolve,[status(thm)],[c_202,c_9918]) ).
cnf(c_9919,plain,
( ordinal(sK1(sK1(sK4(sK0(sK3)),sK3),sK3))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_3386,c_117]) ).
cnf(c_3894,negated_conjecture,
ordinal(sK1(sK1(sK4(sK0(sK3)),sK3),sK3)),
inference(resolve,[status(thm)],[c_129,c_9919]) ).
cnf(c_5244,plain,
element(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK2),
inference(resolve,[status(thm)],[c_1616,c_196]) ).
cnf(c_9920,plain,
( in(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_5244,c_119]) ).
cnf(c_6917,plain,
in(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK2),
inference(resolve,[status(thm)],[c_202,c_9920]) ).
cnf(c_9921,plain,
( ordinal(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_6917,c_117]) ).
cnf(c_7974,negated_conjecture,
ordinal(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3)),
inference(resolve,[status(thm)],[c_129,c_9921]) ).
cnf(c_9922,negated_conjecture,
( ~ ordinal_subset(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK4(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3)))
| ~ in(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK3) ),
inference(resolve,[status(thm)],[c_135,c_7974]) ).
cnf(c_8051,negated_conjecture,
~ ordinal_subset(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3),sK4(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3))),
inference(resolve,[status(thm)],[c_9922,c_1616]) ).
cnf(c_9923,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK1(sK1(sK4(sK0(sK3)),sK3),sK3))
| sK1(sK4(sK0(sK3)),sK3) = sK1(sK1(sK4(sK0(sK3)),sK3),sK3)
| in(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK1(sK4(sK0(sK3)),sK3)) ),
inference(resolve,[status(thm)],[c_979,c_3894]) ).
cnf(c_9924,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK1(sK1(sK4(sK0(sK3)),sK3),sK3))
| sK1(sK1(sK4(sK0(sK3)),sK3),sK3) = sK1(sK4(sK0(sK3)),sK3)
| in(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK1(sK4(sK0(sK3)),sK3)) ),
inference(copy,[status(thm)],[c_9923]) ).
cnf(c_9925,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK1(sK1(sK4(sK0(sK3)),sK3),sK3))
| sK1(sK1(sK4(sK0(sK3)),sK3),sK3) = sK1(sK4(sK0(sK3)),sK3) ),
inference(resolve,[status(thm)],[c_2436,c_9924]) ).
cnf(c_9865,plain,
sK1(sK1(sK4(sK0(sK3)),sK3),sK3) = sK1(sK4(sK0(sK3)),sK3),
inference(resolve,[status(thm)],[c_675,c_9925]) ).
cnf(c_9926,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3)))
| sK1(sK4(sK0(sK3)),sK3) = sK4(sK1(sK4(sK0(sK3)),sK3))
| in(sK4(sK1(sK4(sK0(sK3)),sK3)),sK1(sK4(sK0(sK3)),sK3)) ),
inference(resolve,[status(thm)],[c_979,c_963]) ).
cnf(c_9927,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3)))
| sK4(sK1(sK4(sK0(sK3)),sK3)) = sK1(sK4(sK0(sK3)),sK3)
| in(sK4(sK1(sK4(sK0(sK3)),sK3)),sK1(sK4(sK0(sK3)),sK3)) ),
inference(copy,[status(thm)],[c_9926]) ).
cnf(c_9928,plain,
( in(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3)))
| sK4(sK1(sK4(sK0(sK3)),sK3)) = sK1(sK4(sK0(sK3)),sK3) ),
inference(resolve,[status(thm)],[c_1625,c_9927]) ).
cnf(c_9899,plain,
sK4(sK1(sK4(sK0(sK3)),sK3)) = sK1(sK4(sK0(sK3)),sK3),
inference(resolve,[status(thm)],[c_1284,c_9928]) ).
cnf(c_9929,negated_conjecture,
~ ordinal_subset(sK1(sK1(sK4(sK0(sK3)),sK3),sK3),sK4(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3))),
inference(paramod,[status(thm)],[c_9899,c_8051]) ).
cnf(c_9930,negated_conjecture,
~ ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK1(sK4(sK0(sK3)),sK3)),sK3))),
inference(paramod,[status(thm)],[c_9865,c_9929]) ).
cnf(c_9931,negated_conjecture,
~ ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK1(sK4(sK0(sK3)),sK3),sK3))),
inference(paramod,[status(thm)],[c_9899,c_9930]) ).
cnf(c_9932,negated_conjecture,
~ ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK4(sK1(sK4(sK0(sK3)),sK3))),
inference(paramod,[status(thm)],[c_9865,c_9931]) ).
cnf(c_9933,negated_conjecture,
~ ordinal_subset(sK1(sK4(sK0(sK3)),sK3),sK1(sK4(sK0(sK3)),sK3)),
inference(paramod,[status(thm)],[c_9899,c_9932]) ).
cnf(c_9904,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_978,c_9933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU235+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n013.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sat Sep 26 08:56:06 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.57 % Process 2382135 was started by sandbox2 on n013,
% 0.11/0.57 % Sat Sep 26 08:56:06 2026
% 0.11/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.58
% 0.11/0.58 % From the command line: assign(max_seconds, 300).
% 17.49/3.17
% 17.49/3.17 % given #500 (F,wt=6): 1231 -in(c7,f3(f2(c7),c7)). [ur(438,a,107,a)].
% 17.49/3.17
% 17.49/3.17 % given #1000 (A,wt=14): 485 -in(f2(f3(f4(f2(c14)),c14)),c14) | empty(f3(f4(f2(c14)),c14)). [resolve(292,b,157,b)].
% 17.49/3.17
% 17.49/3.17 % given #1500 (T,wt=9): 4593 ordinal_subset(f4(f3(f4(f4(f2(c14))),c14)),c15). [resolve(4325,a,113,d),unit_del(a,1875),unit_del(b,129)].
% 17.49/3.17
% 17.49/3.17 % given #2000 (F,wt=16): 3058 -in(f4(f4(f3(f2(c14),c14))),f3(f4(f4(f4(f4(f4(f2(c14)))))),c14)). [ur(127,a,1437,a,b,828,a)].
% 17.49/3.17
% 17.49/3.17 % given #2500 (T,wt=11): 1238 f2(c15) = empty_set | in(f3(empty_set,f2(c15)),f2(c15)). [resolve(460,a,126,a)].
% 17.49/3.17
% 17.49/3.17 % SZS status Theorem for theBenchmark
% 17.49/3.17
% 17.49/3.17 % Proof 1 at 2.14 (+ 0.40) seconds.
% 17.49/3.17 % Length of proof is 80.
% 17.49/3.17 % Level of proof is 18.
% 17.49/3.17 % Maximum clause weight is 23.000.
% 17.49/3.17 % Given clauses 2638.
% 17.49/3.17
% 17.49/3.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------