TSTP Solution File: SET579^3 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET579^3 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 21 03:02:57 EDT 2024
% Result : Theorem 3.12s 1.76s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 51 ( 14 unt; 13 typ; 6 def)
% Number of atoms : 180 ( 11 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 362 ( 5 ~; 0 |; 9 &; 337 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 97 ( 55 ^ 40 !; 2 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_type,type,
mrel: mworld > mworld > $o ).
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(mnot_type,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
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(qmltpeq_type,type,
qmltpeq: $i > $i > mworld > $o ).
thf(member_type,type,
member: $i > $i > mworld > $o ).
thf(subset_type,type,
subset: $i > $i > mworld > $o ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(52,plain,
! [A: $i] : ( subset @ A @ A @ mactual ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [A: mworld] :
? [B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_serial) ).
thf(21,plain,
! [A: mworld] :
? [B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(41,plain,
! [A: $i,B: $i,C: $i] :
( ( ( qmltpeq @ A @ B @ mactual )
& ( subset @ C @ A @ mactual ) )
=> ( subset @ C @ B @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ C ) ) @ ( qmltpeq @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( qmltpeq @ A @ B @ mactual )
& ( qmltpeq @ B @ C @ mactual ) )
=> ( qmltpeq @ A @ C @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,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(49,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)],[15]) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( ( qmltpeq @ A @ B @ mactual )
& ( subset @ A @ C @ mactual ) )
=> ( subset @ B @ C @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_1) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( ( qmltpeq @ A @ B @ mactual )
& ( member @ A @ C @ mactual ) )
=> ( member @ B @ C @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ C @ ( difference @ A @ B ) ) @ ( mand @ ( member @ C @ A ) @ ( mnot @ ( member @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( difference @ A @ B ) @ mactual )
= ( ( member @ C @ A @ mactual )
& ~ ( member @ C @ B @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(23,plain,
! [A: $i] : ( qmltpeq @ A @ A @ mactual ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_substitution_2) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( ( qmltpeq @ A @ B @ mactual )
& ( member @ C @ A @ mactual ) )
=> ( member @ C @ B @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ B @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( qmltpeq @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( qmltpeq @ A @ B @ mactual )
= ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_substitution_1) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_substitution_2) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mimplies
@ ( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ A ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) )
@ ( qmltpeq @ A @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th20) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] :
( mimplies
@ ( mforall_di
@ ^ [D: $i] : ( mequiv @ ( member @ D @ A ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) )
@ ( qmltpeq @ A @ ( difference @ B @ C ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( member @ D @ A @ mactual )
= ( ( member @ D @ B @ mactual )
& ~ ( member @ D @ C @ mactual ) ) )
=> ( qmltpeq @ A @ ( difference @ B @ C ) @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(54,plain,
$false,
inference(cvc4,[status(thm)],[52,21,41,27,49,39,35,43,23,37,25,46,29,32,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET579^3 : TPTP v8.2.0. Released v8.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 13:24:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.00 % [INFO] Parsing done (130ms).
% 1.20/1.01 % [INFO] Running in sequential loop mode.
% 1.77/1.21 % [INFO] eprover registered as external prover.
% 1.77/1.21 % [INFO] cvc4 registered as external prover.
% 1.77/1.22 % [INFO] Scanning for conjecture ...
% 1.88/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.08/1.31 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.08/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.34 % [INFO] Type checking passed.
% 2.08/1.34 % [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 ...
% 3.12/1.75 % External prover 'cvc4' found a proof!
% 3.12/1.75 % [INFO] Killing All external provers ...
% 3.12/1.76 % Time passed: 1224ms (effective reasoning time: 741ms)
% 3.12/1.76 % 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)>
% 3.12/1.76 % Axioms used in derivation (14): member_substitution_1, reflexivity_of_subset, subset_substitution_2, difference_substitution_2, subset_substitution_1, difference_substitution_1, member_substitution_2, symmetry, reflexivity, difference_defn, equal_defn, mrel_serial, transitivity, subset_defn
% 3.12/1.76 % No. of inferences in proof: 32
% 3.12/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1224 ms resp. 741 ms w/o parsing
% 3.53/1.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/1.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------