%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU236+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 : n017.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 29.38s 4.70s
% Output : CNFRefutation 29.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 150 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 145 ( 54 ~; 56 |; 18 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_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(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
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(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(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]) ).
cnf(c_65,plain,
( subset(B,A)
| ~ in(B,A)
| ~ epsilon_transitive(A) ),
inference(clausify,[status(thm)],[d2_ordinal1]) ).
cnf(c_75,plain,
( epsilon_transitive(A)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[cc1_ordinal1]) ).
cnf(c_76,plain,
( subset(B,A)
| ~ in(B,A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_75,c_65]) ).
cnf(c_100,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_101,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
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(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_13]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(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_105,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_106,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_107,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_120,plain,
( ordinal(succ(A))
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[fc3_ordinal1]) ).
cnf(c_121,plain,
( ordinal(set_union2(A,singleton(A)))
| ~ ordinal(A) ),
inference(paramod,[status(thm)],[c_100,c_120]) ).
cnf(c_145,plain,
( subset(A,B)
| ~ ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_146,plain,
( ~ subset(A,B)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[redefinition_r1_ordinal1]) ).
cnf(c_149,plain,
in(A,succ(A)),
inference(clausify,[status(thm)],[t10_ordinal1]) ).
cnf(c_150,plain,
in(A,set_union2(A,singleton(A))),
inference(paramod,[status(thm)],[c_100,c_149]) ).
cnf(c_161,plain,
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t8_xboole_1]) ).
fof(nnf_56,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(sK1),sK2)
| ~ in(sK1,sK2) )
& ( ordinal_subset(succ(sK1),sK2)
| in(sK1,sK2) )
& ordinal(sK2)
& ordinal(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_56]) ).
cnf(c_162,negated_conjecture,
ordinal(sK1),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_163,negated_conjecture,
ordinal(sK2),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_164,negated_conjecture,
( ordinal_subset(succ(sK1),sK2)
| in(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_165,negated_conjecture,
( ordinal_subset(set_union2(sK1,singleton(sK1)),sK2)
| in(sK1,sK2) ),
inference(paramod,[status(thm)],[c_100,c_164]) ).
cnf(c_166,negated_conjecture,
( ~ ordinal_subset(succ(sK1),sK2)
| ~ in(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t33_ordinal1_neg]) ).
cnf(c_167,negated_conjecture,
( ~ ordinal_subset(set_union2(sK1,singleton(sK1)),sK2)
| ~ in(sK1,sK2) ),
inference(paramod,[status(thm)],[c_100,c_166]) ).
cnf(c_172,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_101]) ).
cnf(c_327,plain,
( in(A,B)
| ~ subset(set_union2(A,singleton(A)),B) ),
inference(resolve,[status(thm)],[c_150,c_105]) ).
cnf(c_395,plain,
ordinal(set_union2(sK1,singleton(sK1))),
inference(resolve,[status(thm)],[c_162,c_121]) ).
cnf(c_402,plain,
( ~ subset(A,sK2)
| ordinal_subset(A,sK2)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_163,c_146]) ).
cnf(c_13586,negated_conjecture,
( subset(sK1,sK2)
| ~ ordinal(sK2)
| ordinal_subset(set_union2(sK1,singleton(sK1)),sK2) ),
inference(resolve,[status(thm)],[c_165,c_76]) ).
cnf(c_422,negated_conjecture,
( subset(sK1,sK2)
| ordinal_subset(set_union2(sK1,singleton(sK1)),sK2) ),
inference(resolve,[status(thm)],[c_163,c_13586]) ).
cnf(c_13587,negated_conjecture,
( subset(set_union2(sK1,singleton(sK1)),sK2)
| ~ ordinal(sK2)
| ~ ordinal(set_union2(sK1,singleton(sK1)))
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_165,c_145]) ).
cnf(c_13588,negated_conjecture,
( subset(set_union2(sK1,singleton(sK1)),sK2)
| ~ ordinal(sK2)
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_395,c_13587]) ).
cnf(c_423,negated_conjecture,
( subset(set_union2(sK1,singleton(sK1)),sK2)
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_163,c_13588]) ).
cnf(c_453,plain,
( subset(singleton(A),B)
| sK0(singleton(A),B) = A ),
inference(resolve,[status(thm)],[c_172,c_106]) ).
cnf(c_4887,plain,
( ~ subset(set_union2(sK1,singleton(sK1)),sK2)
| ordinal_subset(set_union2(sK1,singleton(sK1)),sK2) ),
inference(resolve,[status(thm)],[c_395,c_402]) ).
cnf(c_13589,plain,
( in(sK1,sK2)
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_423,c_327]) ).
cnf(c_8854,plain,
in(sK1,sK2),
inference(copy,[status(thm)],[c_13589]) ).
cnf(c_8879,negated_conjecture,
~ ordinal_subset(set_union2(sK1,singleton(sK1)),sK2),
inference(resolve,[status(thm)],[c_8854,c_167]) ).
cnf(c_8948,negated_conjecture,
~ subset(set_union2(sK1,singleton(sK1)),sK2),
inference(resolve,[status(thm)],[c_8879,c_4887]) ).
cnf(c_8959,negated_conjecture,
subset(sK1,sK2),
inference(resolve,[status(thm)],[c_8879,c_422]) ).
cnf(c_13590,plain,
( subset(set_union2(sK1,A),sK2)
| ~ subset(A,sK2) ),
inference(resolve,[status(thm)],[c_161,c_8959]) ).
cnf(c_13549,plain,
~ subset(singleton(sK1),sK2),
inference(resolve,[status(thm)],[c_13590,c_8948]) ).
cnf(c_13582,plain,
sK0(singleton(sK1),sK2) = sK1,
inference(resolve,[status(thm)],[c_13549,c_453]) ).
cnf(c_13591,plain,
~ in(sK0(singleton(sK1),sK2),sK2),
inference(resolve,[status(thm)],[c_107,c_13549]) ).
cnf(c_13592,plain,
~ in(sK1,sK2),
inference(paramod,[status(thm)],[c_13582,c_13591]) ).
cnf(c_13585,plain,
$false,
inference(resolve,[status(thm)],[c_8854,c_13592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU236+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:52:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 317090 was started by sandbox2 on n017,
% 0.17/0.44 % Sat Sep 26 08:52:03 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 29.38/4.70
% 29.38/4.70 % given #500 (F,wt=12): 3159 -in(c10,f3(c10,f4(c10))). [ur(221,a,2944,a)].
% 29.38/4.70
% 29.38/4.70 % SZS status Theorem for theBenchmark
% 29.38/4.70
% 29.38/4.70 % Proof 1 at 2.76 (+ 1.05) seconds.
% 29.38/4.70 % Length of proof is 46.
% 29.38/4.70 % Level of proof is 10.
% 29.38/4.70 % Maximum clause weight is 18.000.
% 29.38/4.70 % Given clauses 794.
% 29.38/4.70
% 29.38/4.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------