%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU271+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 : 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 08:45:39 AM UTC 2026
% Result : Theorem 14.05s 7.41s
% Output : CNFRefutation 14.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 16 unt; 0 def)
% Number of atoms : 214 ( 31 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 223 ( 77 ~; 115 |; 21 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 127 ( 1 sgn 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_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(d4_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
=> C = D ) ) ),
file('theBenchmark.p',d4_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(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)),
file('theBenchmark.p',dt_k1_wellord2) ).
fof(t5_wellord2,conjecture,
! [A] : antisymmetric(inclusion_relation(A)),
file('theBenchmark.p',t5_wellord2) ).
fof(t5_wellord2_neg,negated_conjecture,
~ ! [A] : antisymmetric(inclusion_relation(A)),
inference(assume_negation,[status(cth)],[t5_wellord2]) ).
cnf(c_68,plain,
relation(inclusion_relation(A)),
inference(clausify,[status(thm)],[dt_k1_wellord2]) ).
fof(nnf_12,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( D != C
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
| is_antisymmetric_in(A,B) )
& ( ! [X0,X1] :
( X1 = X0
| ~ in(ordered_pair(X1,X0),A)
| ~ in(ordered_pair(X0,X1),A)
| ~ in(X1,B)
| ~ in(X0,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_2]) ).
fof(sk_d4_relat_2_sk,plain,
! [A] :
( ! [B] :
( ( ( sK0(A,B) != sK1(A,B)
& in(ordered_pair(sK0(A,B),sK1(A,B)),A)
& in(ordered_pair(sK1(A,B),sK0(A,B)),A)
& in(sK0(A,B),B)
& in(sK1(A,B),B) )
| is_antisymmetric_in(A,B) )
& ( ! [X0,X1] :
( X1 = X0
| ~ in(ordered_pair(X1,X0),A)
| ~ in(ordered_pair(X0,X1),A)
| ~ in(X1,B)
| ~ in(X0,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(C,sK1(A,B)),skolemize(D,sK0(A,B))],[nnf_12]) ).
fof(sk_d4_relat_2,plain,
( ! [VAR_0,VAR_1] :
( sK0(VAR_0,VAR_1) != sK1(VAR_0,VAR_1)
| is_antisymmetric_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(ordered_pair(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1)),VAR_0)
| is_antisymmetric_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(ordered_pair(sK1(VAR_0,VAR_1),sK0(VAR_0,VAR_1)),VAR_0)
| is_antisymmetric_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_1)
| is_antisymmetric_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(sK1(VAR_0,VAR_1),VAR_1)
| is_antisymmetric_in(VAR_0,VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_2
| ~ in(ordered_pair(VAR_3,VAR_2),VAR_0)
| ~ in(ordered_pair(VAR_2,VAR_3),VAR_0)
| ~ in(VAR_3,VAR_1)
| ~ in(VAR_2,VAR_1)
| ~ is_antisymmetric_in(VAR_0,VAR_1)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_relat_2_sk]) ).
cnf(c_70,plain,
( sK0(A,B) != sK1(A,B)
| is_antisymmetric_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_relat_2]) ).
cnf(c_71,plain,
( in(ordered_pair(sK0(A,B),sK1(A,B)),A)
| is_antisymmetric_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_relat_2]) ).
cnf(c_72,plain,
( in(ordered_pair(sK1(A,B),sK0(A,B)),A)
| is_antisymmetric_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_relat_2]) ).
cnf(c_73,plain,
( in(sK0(A,B),B)
| is_antisymmetric_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_relat_2]) ).
cnf(c_74,plain,
( in(sK1(A,B),B)
| is_antisymmetric_in(A,B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_relat_2]) ).
cnf(c_81,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_82,plain,
( relation_field(A) = B
| inclusion_relation(B) != A
| ~ relation(A) ),
inference(clausify,[status(thm)],[d1_wellord2]) ).
cnf(c_83,plain,
( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d12_relat_2]) ).
cnf(c_195,plain,
( ~ is_antisymmetric_in(inclusion_relation(A),relation_field(inclusion_relation(A)))
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_68,c_83]) ).
cnf(c_196,plain,
( relation_field(inclusion_relation(B)) = A
| inclusion_relation(A) != inclusion_relation(B) ),
inference(resolve,[status(thm)],[c_68,c_82]) ).
cnf(c_197,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_68,c_81]) ).
cnf(c_204,plain,
( in(sK1(inclusion_relation(A),B),B)
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_68,c_74]) ).
cnf(c_205,plain,
( in(sK0(inclusion_relation(A),B),B)
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_68,c_73]) ).
cnf(c_206,plain,
( in(ordered_pair(sK1(inclusion_relation(A),B),sK0(inclusion_relation(A),B)),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_68,c_72]) ).
cnf(c_207,plain,
( in(ordered_pair(sK0(inclusion_relation(A),B),sK1(inclusion_relation(A),B)),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_68,c_71]) ).
cnf(c_208,plain,
( sK0(inclusion_relation(A),B) != sK1(inclusion_relation(A),B)
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(resolve,[status(thm)],[c_68,c_70]) ).
fof(nnf_51,plain,
? [A] : ~ antisymmetric(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t5_wellord2_neg]) ).
fof(sk_t5_wellord2_neg,plain,
~ antisymmetric(inclusion_relation(sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_51]) ).
cnf(c_211,negated_conjecture,
~ antisymmetric(inclusion_relation(sK2)),
inference(split_conjunct,[status(thm)],[sk_t5_wellord2_neg]) ).
cnf(c_234,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_235,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_239,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_7346,plain,
( in(unordered_pair(unordered_pair(sK0(inclusion_relation(A),B),sK1(inclusion_relation(A),B)),singleton(sK0(inclusion_relation(A),B))),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(paramod,[status(thm)],[c_234,c_207]) ).
cnf(c_7347,plain,
( in(unordered_pair(unordered_pair(sK1(inclusion_relation(A),B),sK0(inclusion_relation(A),B)),singleton(sK0(inclusion_relation(A),B))),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(paramod,[status(thm)],[c_239,c_7346]) ).
cnf(c_249,plain,
( in(unordered_pair(singleton(sK0(inclusion_relation(A),B)),unordered_pair(sK1(inclusion_relation(A),B),sK0(inclusion_relation(A),B))),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(paramod,[status(thm)],[c_239,c_7347]) ).
cnf(c_7348,plain,
( in(unordered_pair(unordered_pair(sK1(inclusion_relation(A),B),sK0(inclusion_relation(A),B)),singleton(sK1(inclusion_relation(A),B))),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(paramod,[status(thm)],[c_234,c_206]) ).
cnf(c_250,plain,
( in(unordered_pair(singleton(sK1(inclusion_relation(A),B)),unordered_pair(sK1(inclusion_relation(A),B),sK0(inclusion_relation(A),B))),inclusion_relation(A))
| is_antisymmetric_in(inclusion_relation(A),B) ),
inference(paramod,[status(thm)],[c_239,c_7348]) ).
cnf(c_7349,plain,
( subset(C,D)
| ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),inclusion_relation(B))
| ~ in(D,A)
| ~ in(C,A)
| inclusion_relation(A) != inclusion_relation(B) ),
inference(paramod,[status(thm)],[c_234,c_197]) ).
cnf(c_255,plain,
( subset(C,D)
| ~ in(unordered_pair(singleton(C),unordered_pair(C,D)),inclusion_relation(B))
| ~ in(D,A)
| ~ in(C,A)
| inclusion_relation(A) != inclusion_relation(B) ),
inference(paramod,[status(thm)],[c_239,c_7349]) ).
cnf(c_324,plain,
relation_field(inclusion_relation(A)) = A,
inference(xxres,[status(thm)],[c_196]) ).
cnf(c_331,plain,
( ~ is_antisymmetric_in(inclusion_relation(A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(paramod,[status(thm)],[c_324,c_195]) ).
cnf(c_373,plain,
( subset(A,C)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,C)),inclusion_relation(B))
| ~ in(C,B)
| ~ in(A,B) ),
inference(xxres,[status(thm)],[c_255]) ).
cnf(c_479,plain,
( in(unordered_pair(singleton(sK1(inclusion_relation(A),A)),unordered_pair(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))),inclusion_relation(A))
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_331,c_250]) ).
cnf(c_480,plain,
( in(unordered_pair(singleton(sK0(inclusion_relation(A),A)),unordered_pair(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))),inclusion_relation(A))
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_331,c_249]) ).
cnf(c_481,plain,
( in(sK0(inclusion_relation(A),A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_331,c_205]) ).
cnf(c_482,plain,
( in(sK1(inclusion_relation(A),A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_331,c_204]) ).
cnf(c_1237,plain,
( antisymmetric(inclusion_relation(B))
| subset(A,sK1(inclusion_relation(B),B))
| ~ in(unordered_pair(singleton(A),unordered_pair(A,sK1(inclusion_relation(B),B))),inclusion_relation(B))
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_373,c_482]) ).
cnf(c_3607,plain,
( subset(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))
| ~ in(sK0(inclusion_relation(A),A),A)
| ~ in(sK1(inclusion_relation(A),A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_479,c_373]) ).
cnf(c_7350,plain,
( antisymmetric(inclusion_relation(A))
| subset(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))
| ~ in(sK0(inclusion_relation(A),A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_3607,c_482]) ).
cnf(c_3641,plain,
( subset(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))
| ~ in(sK0(inclusion_relation(A),A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(copy,[status(thm)],[c_7350]) ).
cnf(c_7351,plain,
( antisymmetric(inclusion_relation(A))
| subset(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_3641,c_481]) ).
cnf(c_3645,plain,
( subset(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))
| antisymmetric(inclusion_relation(A)) ),
inference(copy,[status(thm)],[c_7351]) ).
cnf(c_7352,plain,
( ~ subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A))
| sK1(inclusion_relation(A),A) = sK0(inclusion_relation(A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_3645,c_235]) ).
cnf(c_3661,plain,
( ~ subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A))
| sK0(inclusion_relation(A),A) = sK1(inclusion_relation(A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(copy,[status(thm)],[c_7352]) ).
cnf(c_7353,plain,
( antisymmetric(inclusion_relation(A))
| antisymmetric(inclusion_relation(A))
| subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A))
| ~ in(unordered_pair(singleton(sK0(inclusion_relation(A),A)),unordered_pair(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A))),inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_1237,c_481]) ).
cnf(c_7354,plain,
( antisymmetric(inclusion_relation(A))
| antisymmetric(inclusion_relation(A))
| subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A))
| ~ in(unordered_pair(singleton(sK0(inclusion_relation(A),A)),unordered_pair(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))),inclusion_relation(A)) ),
inference(paramod,[status(thm)],[c_239,c_7353]) ).
cnf(c_4714,plain,
( antisymmetric(inclusion_relation(A))
| subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A))
| ~ in(unordered_pair(singleton(sK0(inclusion_relation(A),A)),unordered_pair(sK1(inclusion_relation(A),A),sK0(inclusion_relation(A),A))),inclusion_relation(A)) ),
inference(copy,[status(thm)],[c_7354]) ).
cnf(c_7355,plain,
( antisymmetric(inclusion_relation(A))
| antisymmetric(inclusion_relation(A))
| subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A)) ),
inference(resolve,[status(thm)],[c_4714,c_480]) ).
cnf(c_7314,plain,
( antisymmetric(inclusion_relation(A))
| subset(sK0(inclusion_relation(A),A),sK1(inclusion_relation(A),A)) ),
inference(copy,[status(thm)],[c_7355]) ).
cnf(c_7356,plain,
( sK0(inclusion_relation(A),A) = sK1(inclusion_relation(A),A)
| antisymmetric(inclusion_relation(A))
| antisymmetric(inclusion_relation(A)) ),
inference(resolve,[status(thm)],[c_7314,c_3661]) ).
cnf(c_7315,plain,
( sK0(inclusion_relation(A),A) = sK1(inclusion_relation(A),A)
| antisymmetric(inclusion_relation(A)) ),
inference(copy,[status(thm)],[c_7356]) ).
cnf(c_7340,plain,
sK0(inclusion_relation(sK2),sK2) = sK1(inclusion_relation(sK2),sK2),
inference(resolve,[status(thm)],[c_7315,c_211]) ).
cnf(c_7343,plain,
is_antisymmetric_in(inclusion_relation(sK2),sK2),
inference(resolve,[status(thm)],[c_7340,c_208]) ).
cnf(c_7357,plain,
antisymmetric(inclusion_relation(sK2)),
inference(resolve,[status(thm)],[c_7343,c_331]) ).
cnf(c_7345,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_211,c_7357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU271+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n008.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 09:03:14 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 3261880 was started by sandbox2 on n008,
% 0.08/5.37 % Sat Sep 26 09:03:14 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 14.05/7.41
% 14.05/7.41 % given #500 (A,wt=73): 403 inclusion_relation(relation_field(c9)) = c9 | -is_antisymmetric_in(c7,relation_field(c9)) | -in(A,relation_field(c9)) | -in(unordered_pair(singleton(A),unordered_pair(A,f1(relation_field(c9),c9))),c7) | -in(unordered_pair(singleton(f1(relation_field(c9),c9)),unordered_pair(f1(relation_field(c9),c9),A)),c7) | f1(relation_field(c9),c9) = A. [resolve(300,b,286,c)].
% 14.05/7.41
% 14.05/7.41 % given #1000 (T,wt=53): 612 inclusion_relation(A) != inclusion_relation(B) | -in(f5(powerset(C)),A) | -in(C,A) | in(unordered_pair(singleton(f5(powerset(C))),unordered_pair(C,f5(powerset(C)))),inclusion_relation(B)). [resolve(360,a,254,e),rewrite([239(13)])].
% 14.05/7.41
% 14.05/7.41 % SZS status Theorem for theBenchmark
% 14.05/7.41
% 14.05/7.41 % Proof 1 at 1.62 (+ 0.37) seconds.
% 14.05/7.41 % Length of proof is 50.
% 14.05/7.41 % Level of proof is 13.
% 14.05/7.41 % Maximum clause weight is 57.000.
% 14.05/7.41 % Given clauses 1454.
% 14.05/7.41
% 14.05/7.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
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