%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU339+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 : n003.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 08:45:51 AM UTC 2026
% Result : Theorem 1.68s 0.67s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 35 unt; 0 def)
% Number of atoms : 224 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 230 ( 95 ~; 87 |; 23 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 124 ( 17 sgn 42 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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(d6_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( antisymmetric_relstr(A)
<=> is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) ) ),
file('theBenchmark.p',d6_orders_2) ).
fof(d9_orders_2,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('theBenchmark.p',d9_orders_2) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( rel_str(A)
=> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ),
file('theBenchmark.p',dt_u1_orders_2) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t106_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t25_orders_2,conjecture,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,C,B)
& related(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t25_orders_2) ).
fof(t25_orders_2_neg,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,C,B)
& related(A,B,C) )
=> B = C ) ) ) ),
inference(assume_negation,[status(cth)],[t25_orders_2]) ).
cnf(c_46,plain,
( 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)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_relat_2]) ).
cnf(c_47,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_53,plain,
( relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_u1_orders_2]) ).
fof(nnf_45,plain,
? [A] :
( ? [B] :
( ? [C] :
( C != B
& related(A,C,B)
& related(A,B,C)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[t25_orders_2_neg]) ).
fof(sk_t25_orders_2_neg,plain,
( sK2 != sK1
& related(sK0,sK2,sK1)
& related(sK0,sK1,sK2)
& element(sK2,the_carrier(sK0))
& element(sK1,the_carrier(sK0))
& rel_str(sK0)
& antisymmetric_relstr(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_45]) ).
cnf(c_55,negated_conjecture,
rel_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_58,plain,
( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d9_orders_2]) ).
cnf(c_60,plain,
( is_antisymmetric_in(the_InternalRel(A),the_carrier(A))
| ~ antisymmetric_relstr(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d6_orders_2]) ).
cnf(c_64,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_66,negated_conjecture,
relation_of2_as_subset(the_InternalRel(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_53,c_55]) ).
cnf(c_73,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_74,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_75,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_74,c_73]) ).
cnf(c_76,negated_conjecture,
element(the_InternalRel(sK0),powerset(cartesian_product2(the_carrier(sK0),the_carrier(sK0)))),
inference(resolve,[status(thm)],[c_66,c_64]) ).
cnf(c_79,negated_conjecture,
( is_antisymmetric_in(the_InternalRel(sK0),the_carrier(sK0))
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_60,c_55]) ).
cnf(c_83,negated_conjecture,
( in(ordered_pair(A,B),the_InternalRel(sK0))
| ~ related(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_58,c_55]) ).
cnf(c_88,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_89,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_90,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_88,c_89]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_93,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_105,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[t106_zfmisc_1]) ).
cnf(c_106,plain,
( in(B,D)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_90,c_105]) ).
cnf(c_110,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_111,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_112,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_113,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_116,negated_conjecture,
antisymmetric_relstr(sK0),
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_117,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_118,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_119,negated_conjecture,
related(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_120,negated_conjecture,
related(sK0,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_121,negated_conjecture,
sK2 != sK1,
inference(split_conjunct,[status(thm)],[sk_t25_orders_2_neg]) ).
cnf(c_122,plain,
( ~ element(A,powerset(cartesian_product2(E,F)))
| 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) ),
inference(resolve,[status(thm)],[c_46,c_47]) ).
cnf(c_3816,plain,
( ~ element(A,powerset(cartesian_product2(E,F)))
| D = C
| ~ in(ordered_pair(D,C),A)
| ~ in(unordered_pair(singleton(C),unordered_pair(C,D)),A)
| ~ in(D,B)
| ~ in(C,B)
| ~ is_antisymmetric_in(A,B) ),
inference(paramod,[status(thm)],[c_90,c_122]) ).
cnf(c_123,plain,
( ~ element(A,powerset(cartesian_product2(E,F)))
| D = C
| ~ in(unordered_pair(singleton(D),unordered_pair(D,C)),A)
| ~ in(unordered_pair(singleton(C),unordered_pair(C,D)),A)
| ~ in(D,B)
| ~ in(C,B)
| ~ is_antisymmetric_in(A,B) ),
inference(paramod,[status(thm)],[c_90,c_3816]) ).
cnf(c_140,negated_conjecture,
( in(unordered_pair(singleton(A),unordered_pair(A,B)),the_InternalRel(sK0))
| ~ related(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0)) ),
inference(paramod,[status(thm)],[c_90,c_83]) ).
cnf(c_143,negated_conjecture,
is_antisymmetric_in(the_InternalRel(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_116,c_79]) ).
cnf(c_176,plain,
( element(A,cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| ~ in(A,the_InternalRel(sK0)) ),
inference(resolve,[status(thm)],[c_111,c_76]) ).
cnf(c_3817,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_112,c_75]) ).
cnf(c_193,plain,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_3817,c_93]) ).
cnf(c_198,plain,
( in(sK1,the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_117,c_110]) ).
cnf(c_199,plain,
( in(sK2,the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_118,c_110]) ).
cnf(c_204,plain,
( C = B
| ~ in(unordered_pair(singleton(C),unordered_pair(C,B)),the_InternalRel(sK0))
| ~ in(unordered_pair(singleton(B),unordered_pair(B,C)),the_InternalRel(sK0))
| ~ in(C,A)
| ~ in(B,A)
| ~ is_antisymmetric_in(the_InternalRel(sK0),A) ),
inference(resolve,[status(thm)],[c_123,c_76]) ).
cnf(c_3818,negated_conjecture,
( in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK1)),the_InternalRel(sK0))
| ~ element(sK1,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_140,c_120]) ).
cnf(c_3819,negated_conjecture,
( in(unordered_pair(singleton(sK2),unordered_pair(sK1,sK2)),the_InternalRel(sK0))
| ~ element(sK1,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(paramod,[status(thm)],[c_88,c_3818]) ).
cnf(c_3820,negated_conjecture,
( in(unordered_pair(singleton(sK2),unordered_pair(sK1,sK2)),the_InternalRel(sK0))
| ~ element(sK1,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_118,c_3819]) ).
cnf(c_275,negated_conjecture,
in(unordered_pair(singleton(sK2),unordered_pair(sK1,sK2)),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_117,c_3820]) ).
cnf(c_3821,negated_conjecture,
( in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),the_InternalRel(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_140,c_119]) ).
cnf(c_3822,negated_conjecture,
( in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),the_InternalRel(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_117,c_3821]) ).
cnf(c_276,negated_conjecture,
in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_118,c_3822]) ).
cnf(c_290,plain,
~ in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,empty_set)),
inference(resolve,[status(thm)],[c_106,c_193]) ).
cnf(c_3823,plain,
( ~ empty(A)
| ~ element(the_InternalRel(sK0),powerset(A)) ),
inference(resolve,[status(thm)],[c_112,c_275]) ).
cnf(c_1867,negated_conjecture,
~ empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_3823,c_76]) ).
cnf(c_1881,plain,
element(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_276,c_176]) ).
cnf(c_3824,plain,
( sK2 = sK1
| ~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK1)),the_InternalRel(sK0))
| ~ in(sK2,A)
| ~ in(sK1,A)
| ~ is_antisymmetric_in(the_InternalRel(sK0),A) ),
inference(resolve,[status(thm)],[c_204,c_276]) ).
cnf(c_3825,plain,
( sK2 = sK1
| ~ in(unordered_pair(singleton(sK2),unordered_pair(sK1,sK2)),the_InternalRel(sK0))
| ~ in(sK2,A)
| ~ in(sK1,A)
| ~ is_antisymmetric_in(the_InternalRel(sK0),A) ),
inference(paramod,[status(thm)],[c_88,c_3824]) ).
cnf(c_3826,plain,
( sK2 = sK1
| ~ in(sK2,A)
| ~ in(sK1,A)
| ~ is_antisymmetric_in(the_InternalRel(sK0),A) ),
inference(resolve,[status(thm)],[c_275,c_3825]) ).
cnf(c_3333,negated_conjecture,
( ~ in(sK2,A)
| ~ in(sK1,A)
| ~ is_antisymmetric_in(the_InternalRel(sK0),A) ),
inference(resolve,[status(thm)],[c_121,c_3826]) ).
cnf(c_3827,plain,
( empty(the_carrier(sK0))
| ~ in(sK2,the_carrier(sK0))
| ~ is_antisymmetric_in(the_InternalRel(sK0),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3333,c_198]) ).
cnf(c_3337,negated_conjecture,
( empty(the_carrier(sK0))
| ~ in(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_143,c_3827]) ).
cnf(c_3828,plain,
( empty(the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3337,c_199]) ).
cnf(c_3345,plain,
empty(the_carrier(sK0)),
inference(copy,[status(thm)],[c_3828]) ).
cnf(c_3829,plain,
empty_set = the_carrier(sK0),
inference(resolve,[status(thm)],[c_3345,c_113]) ).
cnf(c_3355,plain,
the_carrier(sK0) = empty_set,
inference(copy,[status(thm)],[c_3829]) ).
cnf(c_3830,plain,
element(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),cartesian_product2(empty_set,the_carrier(sK0))),
inference(paramod,[status(thm)],[c_3355,c_1881]) ).
cnf(c_3470,plain,
element(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),cartesian_product2(empty_set,empty_set)),
inference(paramod,[status(thm)],[c_3355,c_3830]) ).
cnf(c_3831,negated_conjecture,
~ empty(cartesian_product2(empty_set,the_carrier(sK0))),
inference(paramod,[status(thm)],[c_3355,c_1867]) ).
cnf(c_3480,negated_conjecture,
~ empty(cartesian_product2(empty_set,empty_set)),
inference(paramod,[status(thm)],[c_3355,c_3831]) ).
cnf(c_3832,plain,
( in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),cartesian_product2(empty_set,empty_set))
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(resolve,[status(thm)],[c_3470,c_110]) ).
cnf(c_3833,plain,
in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK2)),cartesian_product2(empty_set,empty_set)),
inference(resolve,[status(thm)],[c_3480,c_3832]) ).
cnf(c_3815,plain,
$false,
inference(resolve,[status(thm)],[c_290,c_3833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 09:17:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 2540601 was started by sandbox on n003,
% 0.07/0.36 % Sat Sep 26 09:17:09 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.37
% 0.07/0.37 % From the command line: assign(max_seconds, 300).
% 1.68/0.67
% 1.68/0.67 % SZS status Theorem for theBenchmark
% 1.68/0.67
% 1.68/0.67 % Proof 1 at 0.16 (+ 0.06) seconds.
% 1.68/0.67 % Length of proof is 67.
% 1.68/0.67 % Level of proof is 10.
% 1.68/0.67 % Maximum clause weight is 53.000.
% 1.68/0.67 % Given clauses 317.
% 1.68/0.67
% 1.68/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
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