%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU268+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 08:45:38 AM UTC 2026
% Result : Theorem 50.98s 17.80s
% Output : CNFRefutation 50.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 108 ( 14 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 116 ( 48 ~; 51 |; 8 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 76 ( 3 sgn 28 !; 2 ?)
% 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(d1_wellord2,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('theBenchmark.p',d1_wellord2) ).
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(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)),
file('theBenchmark.p',dt_k1_wellord2) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_wellord2,conjecture,
! [A] : reflexive(inclusion_relation(A)),
file('theBenchmark.p',t2_wellord2) ).
fof(t2_wellord2_neg,negated_conjecture,
~ ! [A] : reflexive(inclusion_relation(A)),
inference(assume_negation,[status(cth)],[t2_wellord2]) ).
cnf(c_67,plain,
relation(inclusion_relation(A)),
inference(clausify,[status(thm)],[dt_k1_wellord2]) ).
cnf(c_68,plain,
( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_relat_2]) ).
cnf(c_75,plain,
( ~ subset(C,D)
| in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B)
| inclusion_relation(B) != A
| ~ relation(A) ),
inference(clausify,[status(thm)],[d1_wellord2]) ).
cnf(c_77,plain,
( relation_field(A) = B
| inclusion_relation(B) != A
| ~ relation(A) ),
inference(clausify,[status(thm)],[d1_wellord2]) ).
fof(nnf_9,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(sK0(A,B),sK0(A,B)),A)
& in(sK0(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,[sK0]),skolemize(C,sK0(A,B))],[nnf_9]) ).
fof(sk_d1_relat_2,plain,
( ! [VAR_0,VAR_1] :
( ~ in(ordered_pair(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1)),VAR_0)
| is_reflexive_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK0(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_78,plain,
( ~ in(ordered_pair(sK0(A,B),sK0(A,B)),A)
| is_reflexive_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_2]) ).
cnf(c_79,plain,
( in(sK0(A,B),B)
| is_reflexive_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d1_relat_2]) ).
cnf(c_173,plain,
( in(sK0(inclusion_relation(A),B),B)
| is_reflexive_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_67,c_79]) ).
cnf(c_174,plain,
( ~ in(ordered_pair(sK0(inclusion_relation(A),B),sK0(inclusion_relation(A),B)),inclusion_relation(A))
| is_reflexive_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_67,c_78]) ).
cnf(c_175,plain,
( relation_field(inclusion_relation(B)) = A
| inclusion_relation(A) != inclusion_relation(B) ),
inference(resolve,[status(thm)],[c_67,c_77]) ).
cnf(c_177,plain,
( ~ subset(C,D)
| in(ordered_pair(C,D),inclusion_relation(B))
| ~ in(D,A)
| ~ in(C,A)
| inclusion_relation(A) != inclusion_relation(B) ),
inference(resolve,[status(thm)],[c_67,c_75]) ).
cnf(c_185,plain,
( ~ is_reflexive_in(inclusion_relation(A),relation_field(inclusion_relation(A)))
| reflexive(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_67,c_68]) ).
fof(nnf_50,plain,
? [A] : ~ reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t2_wellord2_neg]) ).
fof(sk_t2_wellord2_neg,plain,
~ reflexive(inclusion_relation(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_50]) ).
cnf(c_186,negated_conjecture,
~ reflexive(inclusion_relation(sK1)),
inference(split_conjunct,[status(thm)],[sk_t2_wellord2_neg]) ).
cnf(c_197,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_209,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_19674,plain,
( ~ subset(C,C)
| in(ordered_pair(C,C),inclusion_relation(B))
| ~ in(C,A)
| inclusion_relation(A) != inclusion_relation(B) ),
inference(factor,[status(thm)],[c_177]) ).
cnf(c_19675,plain,
( ~ subset(C,C)
| in(unordered_pair(unordered_pair(C,C),singleton(C)),inclusion_relation(B))
| ~ in(C,A)
| inclusion_relation(A) != inclusion_relation(B) ),
inference(paramod,[status(thm)],[c_209,c_19674]) ).
cnf(c_219,plain,
( in(unordered_pair(unordered_pair(C,C),singleton(C)),inclusion_relation(B))
| ~ in(C,A)
| inclusion_relation(A) != inclusion_relation(B) ),
inference(resolve,[status(thm)],[c_197,c_19675]) ).
cnf(c_225,plain,
( ~ in(unordered_pair(unordered_pair(sK0(inclusion_relation(A),B),sK0(inclusion_relation(A),B)),singleton(sK0(inclusion_relation(A),B))),inclusion_relation(A))
| is_reflexive_in(inclusion_relation(A),B) ),
inference(paramod,[status(thm)],[c_209,c_174]) ).
cnf(c_282,plain,
relation_field(inclusion_relation(A)) = A,
inference(xxres,[status(thm)],[c_175]) ).
cnf(c_285,plain,
( ~ is_reflexive_in(inclusion_relation(A),A)
| reflexive(inclusion_relation(A)) ),
inference(paramod,[status(thm)],[c_282,c_185]) ).
cnf(c_329,plain,
( in(unordered_pair(unordered_pair(A,A),singleton(A)),inclusion_relation(B))
| ~ in(A,B) ),
inference(xxres,[status(thm)],[c_219]) ).
cnf(c_721,plain,
( in(sK0(inclusion_relation(A),A),A)
| reflexive(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_285,c_173]) ).
cnf(c_1243,plain,
( in(unordered_pair(unordered_pair(sK0(inclusion_relation(A),A),sK0(inclusion_relation(A),A)),singleton(sK0(inclusion_relation(A),A))),inclusion_relation(A))
| reflexive(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_721,c_329]) ).
cnf(c_19668,plain,
( is_reflexive_in(inclusion_relation(A),A)
| reflexive(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_1243,c_225]) ).
cnf(c_19676,plain,
( reflexive(inclusion_relation(A))
| reflexive(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_19668,c_285]) ).
cnf(c_19672,plain,
reflexive(inclusion_relation(A)),
inference(copy,[status(thm)],[c_19676]) ).
cnf(c_19673,plain,
$false,
inference(resolve,[status(thm)],[c_19672,c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU268+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.38 % Computer : n017.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Sat Sep 26 08:57:43 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/10.39 % Process 324490 was started by sandbox2 on n017,
% 0.12/10.39 % Sat Sep 26 08:57:43 2026
% 0.12/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/10.40
% 0.16/10.40 % From the command line: assign(max_seconds, 300).
% 50.98/17.80
% 50.98/17.80 % given #500 (T,wt=34): 2125 reflexive(inclusion_relation(f1(empty_set,powerset(empty_set)))) | -empty(A) | relation_dom(inclusion_relation(powerset(empty_set))) = A. [resolve(1931,b,187,c)].
% 50.98/17.80
% 50.98/17.80 % given #1000 (A,wt=57): 682 inclusion_relation(relation_field(empty_set)) = empty_set | inclusion_relation(relation_field(empty_set)) != c7 | in(unordered_pair(unordered_pair(f3(relation_field(empty_set),empty_set),f3(relation_field(empty_set),empty_set)),singleton(f3(relation_field(empty_set),empty_set))),c7). [resolve(280,b,214,b)].
% 50.98/17.80
% 50.98/17.80 % given #1500 (T,wt=41): 7833 f4(powerset(f1(empty_set,powerset(empty_set)))) = f1(empty_set,powerset(empty_set)) | empty(relation_rng(inclusion_relation(powerset(empty_set)))). [resolve(2975,a,748,b)].
% 50.98/17.80
% 50.98/17.80 % given #2000 (A,wt=61): 1105 reflexive(c9) | inclusion_relation(relation_field(c9)) != c1 | -in(A,relation_field(c9)) | -in(unordered_pair(unordered_pair(A,f1(empty_set,relation_field(c9))),singleton(f1(empty_set,relation_field(c9)))),c1) | subset(f1(empty_set,relation_field(c9)),A). [resolve(718,b,339,b)].
% 50.98/17.80
% 50.98/17.80 % SZS status Theorem for theBenchmark
% 50.98/17.80
% 50.98/17.80 % Proof 1 at 5.89 (+ 1.29) seconds.
% 50.98/17.80 % Length of proof is 31.
% 50.98/17.80 % Level of proof is 9.
% 50.98/17.80 % Maximum clause weight is 52.000.
% 50.98/17.80 % Given clauses 2388.
% 50.98/17.80
% 50.98/17.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------