TSTP Solution File: SET047^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 : Thu Aug 31 14:37:08 EDT 2023
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 13:55:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 % File : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% 0.21/0.51 % Domain : Set Theory
% 0.21/0.51 % Problem : TPTP problem SET047+1.p with axiomatized equality
% 0.21/0.51 % Version : [BP13] axioms.
% 0.21/0.51 % English :
% 0.21/0.51
% 0.21/0.51 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.21/0.51 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.21/0.51 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.21/0.51 % Source : [TPTP]
% 0.21/0.51 % Names : SET047+1 [QMLTP]
% 0.21/0.51
% 0.21/0.51 % Status : Theorem
% 0.21/0.51 % Rating : 0.23 v8.1.0
% 0.21/0.51 % Syntax : Number of formulae : 27 ( 10 unt; 15 typ; 10 def)
% 0.21/0.51 % Number of atoms : 37 ( 10 equ; 0 cnn)
% 0.21/0.51 % Maximal formula atoms : 9 ( 3 avg)
% 0.21/0.51 % Number of connectives : 50 ( 1 ~; 1 |; 2 &; 43 @)
% 0.21/0.51 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.51 % Maximal formula depth : 13 ( 3 avg)
% 0.21/0.51 % Number of types : 3 ( 1 usr)
% 0.21/0.51 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.21/0.51 % Number of symbols : 15 ( 14 usr; 1 con; 0-3 aty)
% 0.21/0.51 % Number of variables : 32 ( 28 ^; 2 !; 2 ?; 32 :)
% 0.21/0.51 % SPC : TH0_THM_EQU_NAR
% 0.21/0.51
% 0.21/0.51 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.21/0.51 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.21/0.51 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.21/0.51 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.21/0.51 % $modalities == $modal_system_K].
% 0.21/0.51 %------------------------------------------------------------------------------
% 0.21/0.51 thf(mworld,type,
% 0.21/0.51 mworld: $tType ).
% 0.21/0.51
% 0.21/0.51 thf(mrel_type,type,
% 0.21/0.51 mrel: mworld > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mactual_type,type,
% 0.21/0.51 mactual: mworld ).
% 0.21/0.51
% 0.21/0.51 thf(mlocal_type,type,
% 0.21/0.51 mlocal: ( mworld > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mlocal_def,definition,
% 0.21/0.51 ( mlocal
% 0.21/0.51 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mnot_type,type,
% 0.21/0.51 mnot: ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mand_type,type,
% 0.21/0.51 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mor_type,type,
% 0.21/0.51 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mimplies_type,type,
% 0.21/0.51 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mequiv_type,type,
% 0.21/0.51 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mnot_def,definition,
% 0.21/0.51 ( mnot
% 0.21/0.51 = ( ^ [A: mworld > $o,W: mworld] :
% 0.21/0.51 ~ ( A @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mand_def,definition,
% 0.21/0.51 ( mand
% 0.21/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.51 ( ( A @ W )
% 0.21/0.51 & ( B @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mor_def,definition,
% 0.21/0.51 ( mor
% 0.21/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.51 ( ( A @ W )
% 0.21/0.51 | ( B @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mimplies_def,definition,
% 0.21/0.51 ( mimplies
% 0.21/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.51 ( ( A @ W )
% 0.21/0.51 => ( B @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mequiv_def,definition,
% 0.21/0.51 ( mequiv
% 0.21/0.51 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.21/0.51 ( ( A @ W )
% 0.21/0.51 <=> ( B @ W ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mbox_type,type,
% 0.21/0.51 mbox: ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mbox_def,definition,
% 0.21/0.51 ( mbox
% 0.21/0.51 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.21/0.51 ! [V: mworld] :
% 0.21/0.51 ( ( mrel @ W @ V )
% 0.21/0.51 => ( Phi @ V ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mdia_type,type,
% 0.21/0.51 mdia: ( mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mdia_def,definition,
% 0.21/0.51 ( mdia
% 0.21/0.51 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.21/0.51 ? [V: mworld] :
% 0.21/0.51 ( ( mrel @ W @ V )
% 0.21/0.51 & ( Phi @ V ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mforall_di_type,type,
% 0.21/0.51 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mforall_di_def,definition,
% 0.21/0.51 ( mforall_di
% 0.21/0.51 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.21/0.51 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(mexists_di_type,type,
% 0.21/0.51 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(mexists_di_def,definition,
% 0.21/0.51 ( mexists_di
% 0.21/0.51 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.21/0.51 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(set_equal_decl,type,
% 0.21/0.51 set_equal: $i > $i > mworld > $o ).
% 0.21/0.51
% 0.21/0.51 thf(element_decl,type,
% 0.21/0.54 element: $i > $i > mworld > $o ).
% 0.21/0.54
% 0.21/0.54 thf(pel43_1,axiom,
% 0.21/0.54 ( mlocal
% 0.21/0.54 @ ( mforall_di
% 0.21/0.54 @ ^ [X: $i] :
% 0.21/0.54 ( mforall_di
% 0.21/0.54 @ ^ [Y: $i] :
% 0.21/0.54 ( mequiv @ ( set_equal @ X @ Y )
% 0.21/0.54 @ ( mforall_di
% 0.21/0.54 @ ^ [Z: $i] : ( mequiv @ ( element @ Z @ X ) @ ( element @ Z @ Y ) ) ) ) ) ) ) ).
% 0.21/0.54
% 0.21/0.54 thf(pel43,conjecture,
% 0.21/0.54 ( mlocal
% 0.21/0.54 @ ( mforall_di
% 0.21/0.54 @ ^ [X: $i] :
% 0.21/0.54 ( mforall_di
% 0.21/0.54 @ ^ [Y: $i] : ( mequiv @ ( set_equal @ X @ Y ) @ ( set_equal @ Y @ X ) ) ) ) ) ).
% 0.21/0.54
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.cBOPc8i4vb/cvc5---1.0.5_22115.p...
% 0.21/0.54 (declare-sort $$unsorted 0)
% 0.21/0.54 (declare-sort tptp.mworld 0)
% 0.21/0.54 (declare-fun tptp.mrel (tptp.mworld tptp.mworld) Bool)
% 0.21/0.54 (declare-fun tptp.mactual () tptp.mworld)
% 0.21/0.54 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.21/0.54 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.21/0.54 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.21/0.54 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.21/0.54 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.21/0.54 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.21/0.54 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.21/0.54 (declare-fun tptp.mbox ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (assert (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.21/0.54 (declare-fun tptp.mdia ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (assert (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.21/0.54 (declare-fun tptp.mforall_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (assert (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))))
% 0.21/0.54 (declare-fun tptp.mexists_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.21/0.54 (assert (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))))
% 0.21/0.54 (declare-fun tptp.set_equal ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.21/0.54 (declare-fun tptp.element ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.21/0.54 (assert (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.element Z))) (@ (@ (@ tptp.mequiv (@ _let_1 X)) (@ _let_1 Y)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))
% 0.21/0.54 (assert (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))))
% 0.21/0.54 (set-info :filename cvc5---1.0.5_22115)
% 0.21/0.54 (check-sat-assuming ( true ))
% 0.21/0.54 ------- get file name : TPTP file name is SET047^1
% 0.21/0.54 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22115.smt2...
% 0.21/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for SET047^1
% 0.21/0.54 % SZS output start Proof for SET047^1
% 0.21/0.54 (
% 0.21/0.54 (let ((_let_1 (not (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ (@ tptp.set_equal Y) X)) __flatten_var_0))) __flatten_var_0))))))) (let ((_let_2 (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ A X) W)))))) (let ((_let_3 (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (@ (@ A X) W)))))) (let ((_let_4 (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_5 (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))) (let ((_let_6 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))) (let ((_let_7 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_8 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))) (let ((_let_9 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))) (let ((_let_10 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))) (let ((_let_11 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) (SCOPE (SCOPE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_3)) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_6)) (ASSUME :args (_let_7)) (ASSUME :args (_let_8)) (ASSUME :args (_let_9)) (ASSUME :args (_let_10)) (ASSUME :args (_let_11))) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 (@ tptp.mlocal (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ (@ tptp.mequiv (@ (@ tptp.set_equal X) Y)) (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.element Z))) (@ (@ (@ tptp.mequiv (@ _let_1 X)) (@ _let_1 Y)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))) _let_1 true))))))))))))))
% 0.21/0.54 )
% 0.21/0.54 % SZS output end Proof for SET047^1
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------