TSTP Solution File: ITP020^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : ITP020^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 10:36:00 EDT 2024
% Result : Theorem 3.86s 1.87s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 6 unt; 7 typ; 0 def)
% Number of atoms : 81 ( 5 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 252 ( 9 ~; 3 |; 0 &; 240 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-5 aty)
% Number of variables : 56 ( 0 ^ 34 !; 15 ?; 56 :)
% ( 7 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Epred__set_2EBIJ_type,type,
c_2Epred__set_2EBIJ:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2ECROSS_type,type,
c_2Epred__set_2ECROSS:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( tyop_2Epair_2Eprod @ TB @ TA ) > $o ) ).
thf(c_2Epred__set_2EUNIV_type,type,
c_2Epred__set_2EUNIV:
!>[TA: $tType] : ( TA > $o ) ).
thf(sk1_type,type,
sk1: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
thf(sk3_type,type,
sk3:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > TA > TB ) ).
thf(3,axiom,
? [A: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum] : ( c_2Epred__set_2EBIJ @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ A @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).
thf(7,plain,
? [A: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum] : ( c_2Epred__set_2EBIJ @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ A @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
c_2Epred__set_2EBIJ @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ sk1 @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ),
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ? [C: TB > TA] : ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ A @ B ) )
= ( ? [C: TA > TB] : ( c_2Epred__set_2EBIJ @ TA @ TB @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).
thf(9,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o] :
( ( ? [C: TB > TA] : ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ A @ B ) )
= ( ? [C: TA > TB] : ( c_2Epred__set_2EBIJ @ TA @ TB @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [TA: $tType,TB: $tType,B: TB > $o,A: TA > $o] :
( ( ? [C: TA > TB] : ( c_2Epred__set_2EBIJ @ TA @ TB @ C @ A @ B ) )
= ( ? [C: TB > TA] : ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,TB: $tType,B: TB > $o,A: TA > $o] :
( ( ? [C: TA > TB] : ( c_2Epred__set_2EBIJ @ TA @ TB @ C @ A @ B ) )
= ( ? [C: TB > TA] : ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
! [TA: $tType,TB: $tType,B: TB > $o,A: TA > $o] :
( ? [C: TA > TB] : ( c_2Epred__set_2EBIJ @ TA @ TB @ C @ A @ B )
| ~ ? [C: TB > TA] : ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ B @ A ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(16,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA > $o] :
( ~ ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ B @ A )
| ( c_2Epred__set_2EBIJ @ TA @ TB @ ( sk3 @ TB @ TA @ B @ A ) @ A @ B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(1,conjecture,
? [A: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ A @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
thf(2,negated_conjecture,
~ ? [A: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ A @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ? [A: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] : ( c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ A @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum )] :
~ ( c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ A @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(19,plain,
! [TA: $tType,TB: $tType,D: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ),C: TB > TA,B: TB > $o,A: TA > $o] :
( ~ ( c_2Epred__set_2EBIJ @ TB @ TA @ C @ B @ A )
| ( ( c_2Epred__set_2EBIJ @ TA @ TB @ ( sk3 @ TB @ TA @ B @ A ) @ A @ B )
!= ( c_2Epred__set_2EBIJ @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ D @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,6]) ).
thf(20,plain,
! [A: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum] :
~ ( c_2Epred__set_2EBIJ @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ A @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ),
inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum )),bind(B,$thf( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) )),bind(C,$thf( C )),bind(D,$thf( sk3 @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) )),bind_type(TA,$thf( tyop_2Enum_2Enum )),bind_type(TB,$thf( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ))]]) ).
thf(24,plain,
! [A: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum] :
~ ( c_2Epred__set_2EBIJ @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum @ A @ ( c_2Epred__set_2ECROSS @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ tyop_2Enum_2Enum ) ),
inference(simp,[status(thm)],[20]) ).
thf(25,plain,
$false,
inference(rewrite,[status(thm)],[8,24]) ).
thf(26,plain,
$false,
inference(simp,[status(thm)],[25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP020^3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 22:01:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.03 % [INFO] Parsing done (169ms).
% 1.37/1.04 % [INFO] Running in sequential loop mode.
% 1.98/1.26 % [INFO] nitpick registered as external prover.
% 1.98/1.26 % [INFO] Scanning for conjecture ...
% 1.98/1.32 % [INFO] Found a conjecture and 38 axioms. Running axiom selection ...
% 2.21/1.36 % [INFO] Axiom selection finished. Selected 2 axioms (removed 36 axioms).
% 2.21/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.37 % [INFO] Type checking passed.
% 2.21/1.37 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.86/1.86 % [INFO] Killing All external provers ...
% 3.86/1.87 % Time passed: 1336ms (effective reasoning time: 822ms)
% 3.86/1.87 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.86/1.87 % Axioms used in derivation (2): thm_2Eutil__prob_2ENUM__2D__BIJ, thm_2Epred__set_2EBIJ__SYM
% 3.86/1.87 % No. of inferences in proof: 18
% 3.86/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1336 ms resp. 822 ms w/o parsing
% 3.86/1.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.86/1.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------