%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU235+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:45:31 AM UTC 2026
% Result : Theorem 21.21s 3.51s
% Output : CNFRefutation 21.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 46 unt; 0 def)
% Number of atoms : 263 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 265 ( 117 ~; 91 |; 35 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 3 sgn 53 !; 6 ?)
% 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(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_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(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_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(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
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(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_52,plain,
( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[d2_ordinal1]) ).
cnf(c_61,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
fof(nnf_43,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,sK1(C))
& in(sK1(C),sK0)
& ordinal(sK1(C)) )
| ~ in(C,sK0)
| ~ ordinal(C) )
& empty_set != sK0
& subset(sK0,sK2)
& ordinal(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(A,sK0),skolemize(B,sK2),skolemize(D,sK1(C))],[nnf_43]) ).
fof(sk_t32_ordinal1_neg,plain,
( ! [VAR_0] :
( ~ ordinal_subset(VAR_0,sK1(VAR_0))
| ~ in(VAR_0,sK0)
| ~ ordinal(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),sK0)
| ~ in(VAR_0,sK0)
| ~ ordinal(VAR_0) )
& ! [VAR_0] :
( ordinal(sK1(VAR_0))
| ~ in(VAR_0,sK0)
| ~ ordinal(VAR_0) )
& empty_set != sK0
& subset(sK0,sK2)
& ordinal(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_t32_ordinal1_neg_sk]) ).
cnf(c_75,negated_conjecture,
( ~ ordinal_subset(A,sK1(A))
| ~ in(A,sK0)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_76,negated_conjecture,
( in(sK1(A),sK0)
| ~ in(A,sK0)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_77,negated_conjecture,
( ordinal(sK1(A))
| ~ in(A,sK0)
| ~ ordinal(A) ),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_78,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_79,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_78]) ).
cnf(c_80,negated_conjecture,
subset(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
cnf(c_81,negated_conjecture,
ordinal(sK2),
inference(split_conjunct,[status(thm)],[sk_t32_ordinal1_neg]) ).
fof(nnf_41,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,sK3(A,B))
| ~ in(D,B) )
& in(sK3(A,B),B) )
| ~ in(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(C,sK3(A,B))],[nnf_41]) ).
fof(sk_t7_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(VAR_2,sK3(VAR_0,VAR_1))
| ~ in(VAR_2,VAR_1)
| ~ in(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK3(VAR_0,VAR_1),VAR_1)
| ~ in(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t7_tarski_sk]) ).
cnf(c_83,plain,
( ~ in(C,sK3(A,B))
| ~ in(C,B)
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t7_tarski]) ).
cnf(c_84,plain,
( in(sK3(A,B),B)
| ~ in(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t7_tarski]) ).
cnf(c_86,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_87,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_88,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_89,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_91,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_92,plain,
( in(B,A)
| B = A
| in(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t24_ordinal1]) ).
cnf(c_93,plain,
( ordinal(B)
| ~ in(B,A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t23_ordinal1]) ).
cnf(c_96,plain,
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[reflexivity_r1_ordinal1]) ).
cnf(c_97,plain,
( ~ subset(A,B)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(nnf_13,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK4(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(B,sK4(A))],[nnf_13]) ).
cnf(c_115,plain,
element(sK4(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_133,plain,
( subset(B,A)
| ~ in(B,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_61,c_52]) ).
cnf(c_134,plain,
( ~ in(A,sK3(A,B))
| ~ in(A,B) ),
inference(factor,[status(thm)],[c_83]) ).
cnf(c_135,plain,
( ordinal_subset(A,A)
| ~ ordinal(A) ),
inference(factor,[status(thm)],[c_96]) ).
cnf(c_9879,negated_conjecture,
empty_set != sK0,
inference(copy,[status(thm)],[c_79]) ).
cnf(c_137,negated_conjecture,
~ empty(sK0),
inference(resolve,[status(thm)],[c_86,c_9879]) ).
cnf(c_138,plain,
element(sK0,powerset(sK2)),
inference(resolve,[status(thm)],[c_89,c_80]) ).
cnf(c_151,plain,
( in(sK4(A),A)
| empty(A) ),
inference(resolve,[status(thm)],[c_115,c_91]) ).
cnf(c_173,plain,
( element(A,sK2)
| ~ in(A,sK0) ),
inference(resolve,[status(thm)],[c_138,c_88]) ).
cnf(c_174,plain,
( ~ empty(sK2)
| ~ in(A,sK0) ),
inference(resolve,[status(thm)],[c_138,c_87]) ).
cnf(c_9880,plain,
( ~ empty(sK2)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_151,c_174]) ).
cnf(c_183,plain,
~ empty(sK2),
inference(resolve,[status(thm)],[c_137,c_9880]) ).
cnf(c_9881,negated_conjecture,
( in(sK1(sK4(sK0)),sK0)
| ~ ordinal(sK4(sK0))
| empty(sK0) ),
inference(resolve,[status(thm)],[c_151,c_76]) ).
cnf(c_196,negated_conjecture,
( in(sK1(sK4(sK0)),sK0)
| ~ ordinal(sK4(sK0)) ),
inference(resolve,[status(thm)],[c_137,c_9881]) ).
cnf(c_9882,plain,
( empty(sK0)
| element(sK4(sK0),sK2) ),
inference(resolve,[status(thm)],[c_173,c_151]) ).
cnf(c_211,plain,
element(sK4(sK0),sK2),
inference(resolve,[status(thm)],[c_137,c_9882]) ).
cnf(c_9883,plain,
( in(sK4(sK0),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_211,c_91]) ).
cnf(c_212,plain,
in(sK4(sK0),sK2),
inference(resolve,[status(thm)],[c_183,c_9883]) ).
cnf(c_9884,plain,
( ordinal(sK4(sK0))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_212,c_93]) ).
cnf(c_215,negated_conjecture,
ordinal(sK4(sK0)),
inference(resolve,[status(thm)],[c_81,c_9884]) ).
cnf(c_220,negated_conjecture,
in(sK1(sK4(sK0)),sK0),
inference(resolve,[status(thm)],[c_215,c_196]) ).
cnf(c_249,plain,
in(sK3(sK1(sK4(sK0)),sK0),sK0),
inference(resolve,[status(thm)],[c_220,c_84]) ).
cnf(c_250,plain,
( ~ in(A,sK3(sK1(sK4(sK0)),sK0))
| ~ in(A,sK0) ),
inference(resolve,[status(thm)],[c_220,c_83]) ).
cnf(c_636,plain,
element(sK3(sK1(sK4(sK0)),sK0),sK2),
inference(resolve,[status(thm)],[c_249,c_173]) ).
cnf(c_642,plain,
in(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK0),
inference(resolve,[status(thm)],[c_249,c_84]) ).
cnf(c_644,plain,
( ordinal(sK1(sK3(sK1(sK4(sK0)),sK0)))
| ~ ordinal(sK3(sK1(sK4(sK0)),sK0)) ),
inference(resolve,[status(thm)],[c_249,c_77]) ).
cnf(c_645,plain,
( in(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0)
| ~ ordinal(sK3(sK1(sK4(sK0)),sK0)) ),
inference(resolve,[status(thm)],[c_249,c_76]) ).
cnf(c_648,plain,
~ in(sK3(sK1(sK4(sK0)),sK0),sK3(sK3(sK1(sK4(sK0)),sK0),sK0)),
inference(resolve,[status(thm)],[c_134,c_249]) ).
cnf(c_9885,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_636,c_91]) ).
cnf(c_839,plain,
in(sK3(sK1(sK4(sK0)),sK0),sK2),
inference(resolve,[status(thm)],[c_183,c_9885]) ).
cnf(c_9886,plain,
( ordinal(sK3(sK1(sK4(sK0)),sK0))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_839,c_93]) ).
cnf(c_914,negated_conjecture,
ordinal(sK3(sK1(sK4(sK0)),sK0)),
inference(resolve,[status(thm)],[c_81,c_9886]) ).
cnf(c_931,plain,
in(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),
inference(resolve,[status(thm)],[c_914,c_645]) ).
cnf(c_932,plain,
ordinal(sK1(sK3(sK1(sK4(sK0)),sK0))),
inference(resolve,[status(thm)],[c_914,c_644]) ).
cnf(c_946,plain,
ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK3(sK1(sK4(sK0)),sK0)),
inference(resolve,[status(thm)],[c_914,c_135]) ).
cnf(c_949,plain,
( in(sK3(sK1(sK4(sK0)),sK0),A)
| sK3(sK1(sK4(sK0)),sK0) = A
| in(A,sK3(sK1(sK4(sK0)),sK0))
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_914,c_92]) ).
cnf(c_9887,negated_conjecture,
( ~ ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0)))
| ~ in(sK3(sK1(sK4(sK0)),sK0),sK0) ),
inference(resolve,[status(thm)],[c_75,c_914]) ).
cnf(c_950,negated_conjecture,
~ ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0))),
inference(resolve,[status(thm)],[c_9887,c_249]) ).
cnf(c_9888,plain,
( ~ subset(sK3(sK1(sK4(sK0)),sK0),A)
| ordinal_subset(sK3(sK1(sK4(sK0)),sK0),A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_97,c_914]) ).
cnf(c_9889,plain,
( ~ subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0)))
| ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0))) ),
inference(resolve,[status(thm)],[c_9888,c_932]) ).
cnf(c_1094,plain,
~ subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0))),
inference(resolve,[status(thm)],[c_9889,c_950]) ).
cnf(c_9890,plain,
( subset(A,sK1(sK3(sK1(sK4(sK0)),sK0)))
| ~ in(A,sK1(sK3(sK1(sK4(sK0)),sK0))) ),
inference(resolve,[status(thm)],[c_133,c_932]) ).
cnf(c_1250,plain,
~ in(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0))),
inference(resolve,[status(thm)],[c_9890,c_1094]) ).
cnf(c_1559,plain,
in(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK0),
inference(resolve,[status(thm)],[c_931,c_84]) ).
cnf(c_1567,plain,
~ in(sK1(sK3(sK1(sK4(sK0)),sK0)),sK3(sK1(sK4(sK0)),sK0)),
inference(resolve,[status(thm)],[c_250,c_931]) ).
cnf(c_2159,plain,
element(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK2),
inference(resolve,[status(thm)],[c_642,c_173]) ).
cnf(c_2176,plain,
~ in(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK3(sK1(sK4(sK0)),sK0)),
inference(resolve,[status(thm)],[c_250,c_642]) ).
cnf(c_9891,plain,
( in(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_2159,c_91]) ).
cnf(c_3101,plain,
in(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK2),
inference(resolve,[status(thm)],[c_183,c_9891]) ).
cnf(c_9892,plain,
( ordinal(sK3(sK3(sK1(sK4(sK0)),sK0),sK0))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_3101,c_93]) ).
cnf(c_3659,negated_conjecture,
ordinal(sK3(sK3(sK1(sK4(sK0)),sK0),sK0)),
inference(resolve,[status(thm)],[c_81,c_9892]) ).
cnf(c_5148,plain,
element(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK2),
inference(resolve,[status(thm)],[c_1559,c_173]) ).
cnf(c_9893,plain,
( in(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK2)
| empty(sK2) ),
inference(resolve,[status(thm)],[c_5148,c_91]) ).
cnf(c_6846,plain,
in(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK2),
inference(resolve,[status(thm)],[c_183,c_9893]) ).
cnf(c_9894,plain,
( ordinal(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0))
| ~ ordinal(sK2) ),
inference(resolve,[status(thm)],[c_6846,c_93]) ).
cnf(c_7920,negated_conjecture,
ordinal(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0)),
inference(resolve,[status(thm)],[c_81,c_9894]) ).
cnf(c_9895,negated_conjecture,
( ~ ordinal_subset(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK1(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0)))
| ~ in(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK0) ),
inference(resolve,[status(thm)],[c_75,c_7920]) ).
cnf(c_7998,negated_conjecture,
~ ordinal_subset(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0),sK1(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0))),
inference(resolve,[status(thm)],[c_9895,c_1559]) ).
cnf(c_9896,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK3(sK3(sK1(sK4(sK0)),sK0),sK0))
| sK3(sK1(sK4(sK0)),sK0) = sK3(sK3(sK1(sK4(sK0)),sK0),sK0)
| in(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK3(sK1(sK4(sK0)),sK0)) ),
inference(resolve,[status(thm)],[c_949,c_3659]) ).
cnf(c_9897,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK3(sK3(sK1(sK4(sK0)),sK0),sK0))
| sK3(sK3(sK1(sK4(sK0)),sK0),sK0) = sK3(sK1(sK4(sK0)),sK0)
| in(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK3(sK1(sK4(sK0)),sK0)) ),
inference(copy,[status(thm)],[c_9896]) ).
cnf(c_9898,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK3(sK3(sK1(sK4(sK0)),sK0),sK0))
| sK3(sK3(sK1(sK4(sK0)),sK0),sK0) = sK3(sK1(sK4(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_2176,c_9897]) ).
cnf(c_9840,plain,
sK3(sK3(sK1(sK4(sK0)),sK0),sK0) = sK3(sK1(sK4(sK0)),sK0),
inference(resolve,[status(thm)],[c_648,c_9898]) ).
cnf(c_9899,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0)))
| sK3(sK1(sK4(sK0)),sK0) = sK1(sK3(sK1(sK4(sK0)),sK0))
| in(sK1(sK3(sK1(sK4(sK0)),sK0)),sK3(sK1(sK4(sK0)),sK0)) ),
inference(resolve,[status(thm)],[c_949,c_932]) ).
cnf(c_9900,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0)))
| sK1(sK3(sK1(sK4(sK0)),sK0)) = sK3(sK1(sK4(sK0)),sK0)
| in(sK1(sK3(sK1(sK4(sK0)),sK0)),sK3(sK1(sK4(sK0)),sK0)) ),
inference(copy,[status(thm)],[c_9899]) ).
cnf(c_9901,plain,
( in(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0)))
| sK1(sK3(sK1(sK4(sK0)),sK0)) = sK3(sK1(sK4(sK0)),sK0) ),
inference(resolve,[status(thm)],[c_1567,c_9900]) ).
cnf(c_9873,plain,
sK1(sK3(sK1(sK4(sK0)),sK0)) = sK3(sK1(sK4(sK0)),sK0),
inference(resolve,[status(thm)],[c_1250,c_9901]) ).
cnf(c_9902,negated_conjecture,
~ ordinal_subset(sK3(sK3(sK1(sK4(sK0)),sK0),sK0),sK1(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0))),
inference(paramod,[status(thm)],[c_9873,c_7998]) ).
cnf(c_9903,negated_conjecture,
~ ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK3(sK1(sK4(sK0)),sK0)),sK0))),
inference(paramod,[status(thm)],[c_9840,c_9902]) ).
cnf(c_9904,negated_conjecture,
~ ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK3(sK1(sK4(sK0)),sK0),sK0))),
inference(paramod,[status(thm)],[c_9873,c_9903]) ).
cnf(c_9905,negated_conjecture,
~ ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK1(sK3(sK1(sK4(sK0)),sK0))),
inference(paramod,[status(thm)],[c_9840,c_9904]) ).
cnf(c_9906,negated_conjecture,
~ ordinal_subset(sK3(sK1(sK4(sK0)),sK0),sK3(sK1(sK4(sK0)),sK0)),
inference(paramod,[status(thm)],[c_9873,c_9905]) ).
cnf(c_9878,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_946,c_9906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU235+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 08:56:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 3914013 was started by sandbox2 on n009,
% 0.11/0.39 % Sat Sep 26 08:56:15 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 21.21/3.51
% 21.21/3.51 % given #500 (T,wt=8): 458 ordinal_subset(c14,f2(c10)) | ordinal_subset(f2(c10),c14). [resolve(449,a,159,a)].
% 21.21/3.51
% 21.21/3.51 % given #1000 (F,wt=15): 1397 -in(f4(f4(f4(f4(f2(c13))))),f3(f4(f4(f4(f4(f2(c13))))),c13)). [ur(134,a,714,a)].
% 21.21/3.51
% 21.21/3.51 % given #1500 (T,wt=9): 4467 in(empty_set,c10) | in(f3(f2(c10),c10),c14). [resolve(4261,b,91,a),unit_del(b,183)].
% 21.21/3.51
% 21.21/3.51 % given #2000 (F,wt=16): 2794 -in(f4(f4(f4(f4(f2(c13))))),f3(f4(f4(f3(f4(f2(c13)),c13))),c13)). [ur(83,a,1562,a,b,714,a)].
% 21.21/3.51
% 21.21/3.51 % given #2500 (T,wt=10): 8351 subset(f4(f3(f4(f4(f4(f2(c13)))),c13)),c14). [resolve(7375,a,133,b),unit_del(a,81)].
% 21.21/3.51
% 21.21/3.51 % SZS status Theorem for theBenchmark
% 21.21/3.51
% 21.21/3.51 % Proof 1 at 2.51 (+ 0.55) seconds.
% 21.21/3.51 % Length of proof is 78.
% 21.21/3.51 % Level of proof is 18.
% 21.21/3.51 % Maximum clause weight is 23.000.
% 21.21/3.51 % Given clauses 2718.
% 21.21/3.51
% 21.21/3.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------