%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU239+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:45:33 AM UTC 2026
% Result : Theorem 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 9 unt; 0 def)
% Number of atoms : 127 ( 2 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 137 ( 52 ~; 59 |; 15 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('theBenchmark.p',d1_relat_2) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(l1_wellord1,conjecture,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('theBenchmark.p',l1_wellord1) ).
fof(l1_wellord1_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
inference(assume_negation,[status(cth)],[l1_wellord1]) ).
fof(nnf_35,plain,
? [A] :
( ( ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) )
| ~ reflexive(A) )
& ( ! [X0] :
( in(ordered_pair(X0,X0),A)
| ~ in(X0,relation_field(A)) )
| reflexive(A) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[l1_wellord1_neg]) ).
fof(sk_l1_wellord1_neg_sk,plain,
( ( ( ~ in(ordered_pair(sK2,sK2),sK0)
& in(sK2,relation_field(sK0)) )
| ~ reflexive(sK0) )
& ( ! [X0] :
( in(ordered_pair(X0,X0),sK0)
| ~ in(X0,relation_field(sK0)) )
| reflexive(sK0) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2]),skolemize(A,sK0),skolemize(B,sK2)],[nnf_35]) ).
fof(sk_l1_wellord1_neg,plain,
( ( ~ in(ordered_pair(sK2,sK2),sK0)
| ~ reflexive(sK0) )
& ( in(sK2,relation_field(sK0))
| ~ reflexive(sK0) )
& ! [VAR_0] :
( in(ordered_pair(VAR_0,VAR_0),sK0)
| ~ in(VAR_0,relation_field(sK0))
| reflexive(sK0) )
& relation(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_l1_wellord1_neg_sk]) ).
cnf(c_41,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_l1_wellord1_neg]) ).
cnf(c_46,plain,
( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
cnf(c_47,plain,
( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
fof(nnf_6,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ( ! [X0] :
( in(ordered_pair(X0,X0),A)
| ~ in(X0,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_relat_2]) ).
fof(sk_d1_relat_2_sk,plain,
! [A] :
( ! [B] :
( ( ( ~ in(ordered_pair(sK1(A,B),sK1(A,B)),A)
& in(sK1(A,B),B) )
| is_reflexive_in(A,B) )
& ( ! [X0] :
( in(ordered_pair(X0,X0),A)
| ~ in(X0,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1(A,B))],[nnf_6]) ).
fof(sk_d1_relat_2,plain,
( ! [VAR_0,VAR_1] :
( ~ in(ordered_pair(sK1(VAR_0,VAR_1),sK1(VAR_0,VAR_1)),VAR_0)
| is_reflexive_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK1(VAR_0,VAR_1),VAR_1)
| is_reflexive_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(VAR_2,VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| ~ is_reflexive_in(VAR_0,VAR_1)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_relat_2_sk]) ).
cnf(c_49,plain,
( ~ in(ordered_pair(sK1(A,B),sK1(A,B)),A)
| is_reflexive_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_2]) ).
cnf(c_50,plain,
( in(sK1(A,B),B)
| is_reflexive_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_2]) ).
cnf(c_51,plain,
( in(ordered_pair(C,C),A)
| ~ in(C,B)
| ~ is_reflexive_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_2]) ).
cnf(c_56,negated_conjecture,
( in(ordered_pair(B,B),sK0)
| ~ in(B,A)
| ~ is_reflexive_in(sK0,A) ),
inference(resolve,[status(thm)],[c_51,c_41]) ).
cnf(c_60,negated_conjecture,
( in(sK1(sK0,A),A)
| is_reflexive_in(sK0,A) ),
inference(resolve,[status(thm)],[c_50,c_41]) ).
cnf(c_64,negated_conjecture,
( ~ in(ordered_pair(sK1(sK0,A),sK1(sK0,A)),sK0)
| is_reflexive_in(sK0,A) ),
inference(resolve,[status(thm)],[c_49,c_41]) ).
cnf(c_76,negated_conjecture,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ reflexive(sK0) ),
inference(resolve,[status(thm)],[c_47,c_41]) ).
cnf(c_80,negated_conjecture,
( ~ is_reflexive_in(sK0,relation_field(sK0))
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_46,c_41]) ).
cnf(c_87,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_101,negated_conjecture,
( in(ordered_pair(A,A),sK0)
| ~ in(A,relation_field(sK0))
| reflexive(sK0) ),
inference(split_conjunct,[status(thm)],[sk_l1_wellord1_neg]) ).
cnf(c_102,negated_conjecture,
( in(unordered_pair(unordered_pair(A,A),singleton(A)),sK0)
| ~ in(A,relation_field(sK0))
| reflexive(sK0) ),
inference(paramod,[status(thm)],[c_87,c_101]) ).
cnf(c_103,negated_conjecture,
( in(sK2,relation_field(sK0))
| ~ reflexive(sK0) ),
inference(split_conjunct,[status(thm)],[sk_l1_wellord1_neg]) ).
cnf(c_104,negated_conjecture,
( ~ in(ordered_pair(sK2,sK2),sK0)
| ~ reflexive(sK0) ),
inference(split_conjunct,[status(thm)],[sk_l1_wellord1_neg]) ).
cnf(c_105,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK2,sK2),singleton(sK2)),sK0)
| ~ reflexive(sK0) ),
inference(paramod,[status(thm)],[c_87,c_104]) ).
cnf(c_110,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK1(sK0,A),sK1(sK0,A)),singleton(sK1(sK0,A))),sK0)
| is_reflexive_in(sK0,A) ),
inference(paramod,[status(thm)],[c_87,c_64]) ).
cnf(c_114,negated_conjecture,
( in(unordered_pair(unordered_pair(B,B),singleton(B)),sK0)
| ~ in(B,A)
| ~ is_reflexive_in(sK0,A) ),
inference(paramod,[status(thm)],[c_87,c_56]) ).
cnf(c_115,plain,
( in(sK1(sK0,relation_field(sK0)),relation_field(sK0))
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_80,c_60]) ).
cnf(c_398,negated_conjecture,
( in(unordered_pair(unordered_pair(sK1(sK0,relation_field(sK0)),sK1(sK0,relation_field(sK0))),singleton(sK1(sK0,relation_field(sK0)))),sK0)
| reflexive(sK0)
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_115,c_102]) ).
cnf(c_152,negated_conjecture,
( in(unordered_pair(unordered_pair(sK1(sK0,relation_field(sK0)),sK1(sK0,relation_field(sK0))),singleton(sK1(sK0,relation_field(sK0)))),sK0)
| reflexive(sK0) ),
inference(copy,[status(thm)],[c_398]) ).
cnf(c_347,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_152,c_110]) ).
cnf(c_399,negated_conjecture,
( reflexive(sK0)
| reflexive(sK0) ),
inference(resolve,[status(thm)],[c_347,c_80]) ).
cnf(c_366,negated_conjecture,
reflexive(sK0),
inference(copy,[status(thm)],[c_399]) ).
cnf(c_367,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK2,sK2),singleton(sK2)),sK0),
inference(resolve,[status(thm)],[c_366,c_105]) ).
cnf(c_368,negated_conjecture,
in(sK2,relation_field(sK0)),
inference(resolve,[status(thm)],[c_366,c_103]) ).
cnf(c_369,negated_conjecture,
is_reflexive_in(sK0,relation_field(sK0)),
inference(resolve,[status(thm)],[c_366,c_76]) ).
cnf(c_389,plain,
( in(unordered_pair(unordered_pair(A,A),singleton(A)),sK0)
| ~ in(A,relation_field(sK0)) ),
inference(resolve,[status(thm)],[c_369,c_114]) ).
cnf(c_400,negated_conjecture,
in(unordered_pair(unordered_pair(sK2,sK2),singleton(sK2)),sK0),
inference(resolve,[status(thm)],[c_389,c_368]) ).
cnf(c_397,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_367,c_400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU239+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 08:56:49 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 204175 was started by sandbox on n012,
% 0.03/0.31 % Sat Sep 26 08:56:49 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.31
% 0.03/0.31 % From the command line: assign(max_seconds, 300).
% 0.09/0.36
% 0.09/0.36 % SZS status Theorem for theBenchmark
% 0.09/0.36
% 0.09/0.36 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.09/0.36 % Length of proof is 32.
% 0.09/0.36 % Level of proof is 9.
% 0.09/0.36 % Maximum clause weight is 19.000.
% 0.09/0.36 % Given clauses 151.
% 0.09/0.36
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------