TSTP Solution File: SET027^3 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET027^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 10:48:48 EDT 2024
% Result : Theorem 3.81s 2.10s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 44 ( 17 unt; 13 typ; 5 def)
% Number of atoms : 95 ( 14 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 230 ( 18 ~; 7 |; 2 &; 192 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 21 ^ 29 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mand_type,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_type,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] : ( A @ C @ B ) ) ) ).
thf(member_type,type,
member: $i > $i > mworld > $o ).
thf(subset_type,type,
subset: $i > $i > mworld > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(12,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B @ mactual )
= ( ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ C ) ) @ ( subset @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ C ) ) @ ( subset @ A @ C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B @ mactual )
& ( subset @ B @ C @ mactual ) )
=> ( subset @ A @ C @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
subset @ sk1 @ sk2 @ mactual,
inference(cnf,[status(esa)],[6]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) )
| ( ( subset @ A @ B @ mactual )
!= ( subset @ sk1 @ sk2 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[14,9]) ).
thf(29,plain,
! [A: $i] :
( ( member @ A @ sk1 @ mactual )
=> ( member @ A @ sk2 @ mactual ) ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(52,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 @ mactual )
| ( member @ A @ sk2 @ mactual ) ),
inference(cnf,[status(esa)],[29]) ).
thf(8,plain,
subset @ sk2 @ sk3 @ mactual,
inference(cnf,[status(esa)],[6]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) )
| ( ( subset @ A @ B @ mactual )
!= ( subset @ sk2 @ sk3 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(39,plain,
! [A: $i] :
( ( member @ A @ sk2 @ mactual )
=> ( member @ A @ sk3 @ mactual ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(47,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 @ mactual )
| ( member @ A @ sk3 @ mactual ) ),
inference(cnf,[status(esa)],[39]) ).
thf(7,plain,
~ ( subset @ sk1 @ sk3 @ mactual ),
inference(cnf,[status(esa)],[6]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ! [C: $i] :
( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) )
| ( ( subset @ A @ B @ mactual )
!= ( subset @ sk1 @ sk3 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[14,7]) ).
thf(33,plain,
~ ! [A: $i] :
( ( member @ A @ sk1 @ mactual )
=> ( member @ A @ sk3 @ mactual ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(42,plain,
~ ( member @ sk5 @ sk3 @ mactual ),
inference(cnf,[status(esa)],[33]) ).
thf(58,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 @ mactual )
| ( ( member @ A @ sk3 @ mactual )
!= ( member @ sk5 @ sk3 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[47,42]) ).
thf(59,plain,
~ ( member @ sk5 @ sk2 @ mactual ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( sk5 ))]]) ).
thf(98,plain,
! [A: $i] :
( ~ ( member @ A @ sk1 @ mactual )
| ( ( member @ A @ sk2 @ mactual )
!= ( member @ sk5 @ sk2 @ mactual ) ) ),
inference(paramod_ordered,[status(thm)],[52,59]) ).
thf(99,plain,
~ ( member @ sk5 @ sk1 @ mactual ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( sk5 ))]]) ).
thf(43,plain,
member @ sk5 @ sk1 @ mactual,
inference(cnf,[status(esa)],[33]) ).
thf(108,plain,
~ $true,
inference(rewrite,[status(thm)],[99,43]) ).
thf(109,plain,
$false,
inference(simp,[status(thm)],[108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET027^3 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n004.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 20:44:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.07 % [INFO] Parsing done (167ms).
% 1.38/1.08 % [INFO] Running in sequential loop mode.
% 1.91/1.39 % [INFO] nitpick registered as external prover.
% 1.91/1.40 % [INFO] Scanning for conjecture ...
% 2.06/1.47 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 2.06/1.49 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.06/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.50 % [INFO] Type checking passed.
% 2.06/1.50 % [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 ...
% 3.81/2.10 % [INFO] Killing All external provers ...
% 3.81/2.10 % Time passed: 1547ms (effective reasoning time: 1011ms)
% 3.81/2.10 % 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)>
% 3.81/2.10 % Axioms used in derivation (1): subset_defn
% 3.81/2.10 % No. of inferences in proof: 26
% 3.81/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1547 ms resp. 1011 ms w/o parsing
% 3.86/2.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------