%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU340+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 : n026.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 6.86s 1.43s
% Output : CNFRefutation 6.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 23 unt; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 218 ( 88 ~; 78 |; 27 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 22 sgn 38 !; 4 ?)
% 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(d5_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( transitive_relstr(A)
<=> is_transitive_in(the_InternalRel(A),the_carrier(A)) ) ),
file('theBenchmark.p',d5_orders_2) ).
fof(d8_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('theBenchmark.p',d8_relat_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(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(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(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t26_orders_2,conjecture,
! [A] :
( ( rel_str(A)
& transitive_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ( ( related(A,C,D)
& related(A,B,C) )
=> related(A,B,D) ) ) ) ) ),
file('theBenchmark.p',t26_orders_2) ).
fof(t26_orders_2_neg,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& transitive_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ( ( related(A,C,D)
& related(A,B,C) )
=> related(A,B,D) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t26_orders_2]) ).
cnf(c_46,plain,
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B)
| ~ is_transitive_in(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d8_relat_2]) ).
cnf(c_47,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_54,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] :
( ? [D] :
( ~ related(A,B,D)
& related(A,C,D)
& related(A,B,C)
& element(D,the_carrier(A)) )
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& rel_str(A)
& transitive_relstr(A) ),
inference(fof_nnf,[status(thm)],[t26_orders_2_neg]) ).
fof(sk_t26_orders_2_neg,plain,
( ~ related(sK0,sK1,sK3)
& related(sK0,sK2,sK3)
& related(sK0,sK1,sK2)
& element(sK3,the_carrier(sK0))
& element(sK2,the_carrier(sK0))
& element(sK1,the_carrier(sK0))
& rel_str(sK0)
& transitive_relstr(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_45]) ).
cnf(c_56,negated_conjecture,
rel_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_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_59,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_61,plain,
( is_transitive_in(the_InternalRel(A),the_carrier(A))
| ~ transitive_relstr(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d5_orders_2]) ).
cnf(c_65,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_67,negated_conjecture,
relation_of2_as_subset(the_InternalRel(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_54,c_56]) ).
cnf(c_77,negated_conjecture,
element(the_InternalRel(sK0),powerset(cartesian_product2(the_carrier(sK0),the_carrier(sK0)))),
inference(resolve,[status(thm)],[c_67,c_65]) ).
cnf(c_80,negated_conjecture,
( is_transitive_in(the_InternalRel(sK0),the_carrier(sK0))
| ~ transitive_relstr(sK0) ),
inference(resolve,[status(thm)],[c_61,c_56]) ).
cnf(c_84,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_59,c_56]) ).
cnf(c_86,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_56]) ).
cnf(c_103,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[t106_zfmisc_1]) ).
cnf(c_104,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[t106_zfmisc_1]) ).
cnf(c_107,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_108,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_109,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_111,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_113,negated_conjecture,
transitive_relstr(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_114,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_115,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_116,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_117,negated_conjecture,
related(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_118,negated_conjecture,
related(sK0,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_119,negated_conjecture,
~ related(sK0,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t26_orders_2_neg]) ).
cnf(c_120,plain,
( ~ element(A,powerset(cartesian_product2(F,V6)))
| in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B)
| ~ is_transitive_in(A,B) ),
inference(resolve,[status(thm)],[c_46,c_47]) ).
cnf(c_135,negated_conjecture,
is_transitive_in(the_InternalRel(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_113,c_80]) ).
cnf(c_189,plain,
( in(sK3,the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_116,c_107]) ).
cnf(c_3575,negated_conjecture,
( in(ordered_pair(sK1,sK2),the_InternalRel(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_117,c_84]) ).
cnf(c_3576,negated_conjecture,
( in(ordered_pair(sK1,sK2),the_InternalRel(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_114,c_3575]) ).
cnf(c_190,negated_conjecture,
in(ordered_pair(sK1,sK2),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_115,c_3576]) ).
cnf(c_3577,negated_conjecture,
( in(ordered_pair(sK2,sK3),the_InternalRel(sK0))
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_118,c_84]) ).
cnf(c_3578,negated_conjecture,
( in(ordered_pair(sK2,sK3),the_InternalRel(sK0))
| ~ element(sK3,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_115,c_3577]) ).
cnf(c_191,negated_conjecture,
in(ordered_pair(sK2,sK3),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_116,c_3578]) ).
cnf(c_3579,negated_conjecture,
( ~ in(ordered_pair(sK1,A),the_InternalRel(sK0))
| related(sK0,sK1,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_86,c_114]) ).
cnf(c_3580,negated_conjecture,
( ~ in(ordered_pair(sK1,sK3),the_InternalRel(sK0))
| related(sK0,sK1,sK3) ),
inference(resolve,[status(thm)],[c_3579,c_116]) ).
cnf(c_192,negated_conjecture,
~ in(ordered_pair(sK1,sK3),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_3580,c_119]) ).
cnf(c_516,plain,
( element(ordered_pair(sK1,sK2),A)
| ~ element(the_InternalRel(sK0),powerset(A)) ),
inference(resolve,[status(thm)],[c_190,c_108]) ).
cnf(c_3581,plain,
( ~ empty(A)
| ~ element(the_InternalRel(sK0),powerset(A)) ),
inference(resolve,[status(thm)],[c_109,c_190]) ).
cnf(c_524,negated_conjecture,
~ empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_3581,c_77]) ).
cnf(c_1423,plain,
element(ordered_pair(sK1,sK2),cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_516,c_77]) ).
cnf(c_3582,plain,
( in(ordered_pair(sK1,sK2),cartesian_product2(the_carrier(sK0),the_carrier(sK0)))
| empty(cartesian_product2(the_carrier(sK0),the_carrier(sK0))) ),
inference(resolve,[status(thm)],[c_1423,c_107]) ).
cnf(c_3344,plain,
in(ordered_pair(sK1,sK2),cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_524,c_3582]) ).
cnf(c_3450,plain,
in(sK2,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_3344,c_104]) ).
cnf(c_3451,plain,
in(sK1,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_3344,c_103]) ).
cnf(c_3457,plain,
~ empty(the_carrier(sK0)),
inference(resolve,[status(thm)],[c_3450,c_111]) ).
cnf(c_3478,plain,
in(sK3,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_3457,c_189]) ).
cnf(c_3583,negated_conjecture,
( ~ element(the_InternalRel(sK0),powerset(cartesian_product2(D,E)))
| in(ordered_pair(A,C),the_InternalRel(sK0))
| ~ in(ordered_pair(B,C),the_InternalRel(sK0))
| ~ in(ordered_pair(A,B),the_InternalRel(sK0))
| ~ in(C,the_carrier(sK0))
| ~ in(B,the_carrier(sK0))
| ~ in(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_120,c_135]) ).
cnf(c_3584,negated_conjecture,
( ~ element(the_InternalRel(sK0),powerset(cartesian_product2(C,D)))
| in(ordered_pair(sK1,B),the_InternalRel(sK0))
| ~ in(ordered_pair(A,B),the_InternalRel(sK0))
| ~ in(ordered_pair(sK1,A),the_InternalRel(sK0))
| ~ in(B,the_carrier(sK0))
| ~ in(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3583,c_3451]) ).
cnf(c_3585,negated_conjecture,
( ~ element(the_InternalRel(sK0),powerset(cartesian_product2(B,C)))
| in(ordered_pair(sK1,A),the_InternalRel(sK0))
| ~ in(ordered_pair(sK2,A),the_InternalRel(sK0))
| ~ in(ordered_pair(sK1,sK2),the_InternalRel(sK0))
| ~ in(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3584,c_3450]) ).
cnf(c_3586,negated_conjecture,
( ~ element(the_InternalRel(sK0),powerset(cartesian_product2(B,C)))
| in(ordered_pair(sK1,A),the_InternalRel(sK0))
| ~ in(ordered_pair(sK2,A),the_InternalRel(sK0))
| ~ in(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3585,c_190]) ).
cnf(c_3587,negated_conjecture,
( ~ element(the_InternalRel(sK0),powerset(cartesian_product2(A,B)))
| in(ordered_pair(sK1,sK3),the_InternalRel(sK0))
| ~ in(sK3,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3586,c_191]) ).
cnf(c_3588,negated_conjecture,
( ~ element(the_InternalRel(sK0),powerset(cartesian_product2(A,B)))
| ~ in(sK3,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_3587,c_192]) ).
cnf(c_3589,negated_conjecture,
~ in(sK3,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_3588,c_77]) ).
cnf(c_3574,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_3478,c_3589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU340+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 09:18:11 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 642124 was started by sandbox on n026,
% 0.11/0.39 % Sat Sep 26 09:18:11 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 6.86/1.43
% 6.86/1.43 % SZS status Theorem for theBenchmark
% 6.86/1.43
% 6.86/1.43 % Proof 1 at 0.85 (+ 0.15) seconds.
% 6.86/1.43 % Length of proof is 53.
% 6.86/1.43 % Level of proof is 10.
% 6.86/1.43 % Maximum clause weight is 48.000.
% 6.86/1.43 % Given clauses 308.
% 6.86/1.43
% 6.86/1.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------