%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU234+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 : n008.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 0.93s 0.56s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 7 unt; 0 def)
% Number of atoms : 190 ( 26 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 199 ( 62 ~; 91 |; 36 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 57 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d3_ordinal1,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('theBenchmark.p',d3_ordinal1) ).
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',d4_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(t31_ordinal1,conjecture,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_ordinal1) ).
fof(t31_ordinal1_neg,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
inference(assume_negation,[status(cth)],[t31_ordinal1]) ).
cnf(c_48,plain,
( ~ epsilon_connected(A)
| ~ epsilon_transitive(A)
| ordinal(A) ),
inference(clausify,[status(thm)],[d4_ordinal1]) ).
fof(nnf_8,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [X0] :
( subset(X0,A)
| ~ in(X0,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(sk_d2_ordinal1_sk,plain,
! [A] :
( ( ( ~ subset(sK0(A),A)
& in(sK0(A),A) )
| epsilon_transitive(A) )
& ( ! [X0] :
( subset(X0,A)
| ~ in(X0,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_8]) ).
fof(sk_d2_ordinal1,plain,
( ! [VAR_0] :
( ~ subset(sK0(VAR_0),VAR_0)
| epsilon_transitive(VAR_0) )
& ! [VAR_0] :
( in(sK0(VAR_0),VAR_0)
| epsilon_transitive(VAR_0) )
& ! [VAR_0,VAR_1] :
( subset(VAR_1,VAR_0)
| ~ in(VAR_1,VAR_0)
| ~ epsilon_transitive(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_ordinal1_sk]) ).
cnf(c_54,plain,
( ~ subset(sK0(A),A)
| epsilon_transitive(A) ),
inference(split_conjunct,[status(thm)],[sk_d2_ordinal1]) ).
cnf(c_55,plain,
( in(sK0(A),A)
| epsilon_transitive(A) ),
inference(split_conjunct,[status(thm)],[sk_d2_ordinal1]) ).
cnf(c_83,plain,
( ~ epsilon_connected(A)
| ordinal(A)
| in(sK0(A),A) ),
inference(resolve,[status(thm)],[c_55,c_48]) ).
cnf(c_84,plain,
( ~ epsilon_connected(A)
| ordinal(A)
| ~ subset(sK0(A),A) ),
inference(resolve,[status(thm)],[c_54,c_48]) ).
fof(nnf_9,plain,
! [A] :
( ( ? [B,C] :
( ~ in(C,B)
& C != B
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ( ! [X0,X1] :
( in(X1,X0)
| X1 = X0
| in(X0,X1)
| ~ in(X1,A)
| ~ in(X0,A) )
| ~ epsilon_connected(A) ) ),
inference(fof_nnf,[status(thm)],[d3_ordinal1]) ).
fof(sk_d3_ordinal1_sk,plain,
! [A] :
( ( ( ~ in(sK2(A),sK1(A))
& sK2(A) != sK1(A)
& ~ in(sK1(A),sK2(A))
& in(sK2(A),A)
& in(sK1(A),A) )
| epsilon_connected(A) )
& ( ! [X0,X1] :
( in(X1,X0)
| X1 = X0
| in(X0,X1)
| ~ in(X1,A)
| ~ in(X0,A) )
| ~ epsilon_connected(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1(A)),skolemize(C,sK2(A))],[nnf_9]) ).
fof(sk_d3_ordinal1,plain,
( ! [VAR_0] :
( ~ in(sK2(VAR_0),sK1(VAR_0))
| epsilon_connected(VAR_0) )
& ! [VAR_0] :
( sK2(VAR_0) != sK1(VAR_0)
| epsilon_connected(VAR_0) )
& ! [VAR_0] :
( ~ in(sK1(VAR_0),sK2(VAR_0))
| epsilon_connected(VAR_0) )
& ! [VAR_0] :
( in(sK2(VAR_0),VAR_0)
| epsilon_connected(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),VAR_0)
| epsilon_connected(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| VAR_2 = VAR_1
| in(VAR_1,VAR_2)
| ~ in(VAR_2,VAR_0)
| ~ in(VAR_1,VAR_0)
| ~ epsilon_connected(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_ordinal1_sk]) ).
cnf(c_94,plain,
( in(sK1(A),A)
| epsilon_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_ordinal1]) ).
cnf(c_95,plain,
( in(sK2(A),A)
| epsilon_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_ordinal1]) ).
cnf(c_96,plain,
( ~ in(sK1(A),sK2(A))
| epsilon_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_ordinal1]) ).
cnf(c_97,plain,
( sK2(A) != sK1(A)
| epsilon_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_ordinal1]) ).
cnf(c_98,plain,
( ~ in(sK2(A),sK1(A))
| epsilon_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_ordinal1]) ).
cnf(c_118,plain,
( in(B,A)
| B = A
| in(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(clausify,[status(thm)],[t24_ordinal1]) ).
fof(nnf_38,plain,
? [A] :
( ~ ordinal(A)
& ! [B] :
( ( subset(B,A)
& ordinal(B) )
| ~ in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1_neg]) ).
fof(sk_t31_ordinal1_neg_sk,plain,
( ~ ordinal(sK3)
& ! [B] :
( ( subset(B,sK3)
& ordinal(B) )
| ~ in(B,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(A,sK3)],[nnf_38]) ).
fof(sk_t31_ordinal1_neg,plain,
( ~ ordinal(sK3)
& ! [VAR_0] :
( subset(VAR_0,sK3)
| ~ in(VAR_0,sK3) )
& ! [VAR_0] :
( ordinal(VAR_0)
| ~ in(VAR_0,sK3) ) ),
inference(cnf_transformation,[status(thm)],[sk_t31_ordinal1_neg_sk]) ).
cnf(c_127,negated_conjecture,
( ordinal(A)
| ~ in(A,sK3) ),
inference(split_conjunct,[status(thm)],[sk_t31_ordinal1_neg]) ).
cnf(c_128,negated_conjecture,
( subset(A,sK3)
| ~ in(A,sK3) ),
inference(split_conjunct,[status(thm)],[sk_t31_ordinal1_neg]) ).
cnf(c_129,negated_conjecture,
~ ordinal(sK3),
inference(split_conjunct,[status(thm)],[sk_t31_ordinal1_neg]) ).
cnf(c_178,plain,
( epsilon_connected(sK3)
| ordinal(sK2(sK3)) ),
inference(resolve,[status(thm)],[c_127,c_95]) ).
cnf(c_179,plain,
( epsilon_connected(sK3)
| ordinal(sK1(sK3)) ),
inference(resolve,[status(thm)],[c_127,c_94]) ).
cnf(c_527,plain,
( epsilon_connected(sK3)
| in(A,sK2(sK3))
| A = sK2(sK3)
| in(sK2(sK3),A)
| ~ ordinal(A) ),
inference(resolve,[status(thm)],[c_118,c_178]) ).
cnf(c_528,plain,
( epsilon_connected(sK3)
| epsilon_connected(sK3)
| in(sK1(sK3),sK2(sK3))
| sK1(sK3) = sK2(sK3)
| in(sK2(sK3),sK1(sK3)) ),
inference(resolve,[status(thm)],[c_527,c_179]) ).
cnf(c_529,plain,
( epsilon_connected(sK3)
| epsilon_connected(sK3)
| in(sK1(sK3),sK2(sK3))
| sK2(sK3) = sK1(sK3)
| in(sK2(sK3),sK1(sK3)) ),
inference(copy,[status(thm)],[c_528]) ).
cnf(c_220,plain,
( epsilon_connected(sK3)
| in(sK1(sK3),sK2(sK3))
| sK2(sK3) = sK1(sK3)
| in(sK2(sK3),sK1(sK3)) ),
inference(copy,[status(thm)],[c_529]) ).
cnf(c_530,plain,
( epsilon_connected(sK3)
| epsilon_connected(sK3)
| in(sK1(sK3),sK2(sK3))
| sK2(sK3) = sK1(sK3) ),
inference(resolve,[status(thm)],[c_220,c_98]) ).
cnf(c_427,plain,
( epsilon_connected(sK3)
| in(sK1(sK3),sK2(sK3))
| sK2(sK3) = sK1(sK3) ),
inference(copy,[status(thm)],[c_530]) ).
cnf(c_531,plain,
( epsilon_connected(sK3)
| epsilon_connected(sK3)
| sK2(sK3) = sK1(sK3) ),
inference(resolve,[status(thm)],[c_427,c_96]) ).
cnf(c_502,plain,
( epsilon_connected(sK3)
| sK2(sK3) = sK1(sK3) ),
inference(copy,[status(thm)],[c_531]) ).
cnf(c_532,plain,
( ordinal(sK3)
| in(sK0(sK3),sK3)
| sK2(sK3) = sK1(sK3) ),
inference(resolve,[status(thm)],[c_502,c_83]) ).
cnf(c_503,negated_conjecture,
( in(sK0(sK3),sK3)
| sK2(sK3) = sK1(sK3) ),
inference(resolve,[status(thm)],[c_129,c_532]) ).
cnf(c_504,plain,
( subset(sK0(sK3),sK3)
| sK2(sK3) = sK1(sK3) ),
inference(resolve,[status(thm)],[c_503,c_128]) ).
cnf(c_533,plain,
( sK2(sK3) = sK1(sK3)
| ~ epsilon_connected(sK3)
| ordinal(sK3) ),
inference(resolve,[status(thm)],[c_84,c_504]) ).
cnf(c_534,plain,
( sK2(sK3) = sK1(sK3)
| sK2(sK3) = sK1(sK3)
| ordinal(sK3) ),
inference(resolve,[status(thm)],[c_533,c_502]) ).
cnf(c_535,plain,
( sK2(sK3) = sK1(sK3)
| ordinal(sK3) ),
inference(copy,[status(thm)],[c_534]) ).
cnf(c_521,negated_conjecture,
sK2(sK3) = sK1(sK3),
inference(resolve,[status(thm)],[c_129,c_535]) ).
cnf(c_522,plain,
epsilon_connected(sK3),
inference(resolve,[status(thm)],[c_521,c_97]) ).
cnf(c_536,plain,
( ordinal(sK3)
| in(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_522,c_83]) ).
cnf(c_524,negated_conjecture,
in(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_129,c_536]) ).
cnf(c_537,negated_conjecture,
( ~ epsilon_connected(sK3)
| ~ subset(sK0(sK3),sK3) ),
inference(resolve,[status(thm)],[c_84,c_129]) ).
cnf(c_525,negated_conjecture,
~ subset(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_537,c_522]) ).
cnf(c_538,negated_conjecture,
subset(sK0(sK3),sK3),
inference(resolve,[status(thm)],[c_524,c_128]) ).
cnf(c_526,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_525,c_538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU234+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 : n008.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 08:57:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3254070 was started by sandbox2 on n008,
% 0.11/0.37 % Sat Sep 26 08:57:09 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 0.93/0.56
% 0.93/0.56 % SZS status Theorem for theBenchmark
% 0.93/0.56
% 0.93/0.56 % Proof 1 at 0.08 (+ 0.04) seconds.
% 0.93/0.56 % Length of proof is 31.
% 0.93/0.56 % Level of proof is 11.
% 0.93/0.56 % Maximum clause weight is 27.000.
% 0.93/0.56 % Given clauses 213.
% 0.93/0.56
% 0.93/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------