TSTP Solution File: SET044^23 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 14:37:06 EDT 2023
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 11:21:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : SET044^23 : TPTP v8.1.2. Released v8.1.0.
% 0.20/0.49 % Domain : Set Theory
% 0.20/0.49 % Problem : TPTP problem SET044+1.p with axiomatized equality
% 0.20/0.49 % Version : [BP13] axioms.
% 0.20/0.49 % English :
% 0.20/0.49
% 0.20/0.49 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.49 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.49 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.49 % Source : [TPTP]
% 0.20/0.49 % Names : SET044+1 [QMLTP]
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % Rating : 0.23 v8.1.0
% 0.20/0.49 % Syntax : Number of formulae : 30 ( 12 unt; 15 typ; 10 def)
% 0.20/0.49 % Number of atoms : 47 ( 10 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 15 ( 3 avg)
% 0.20/0.49 % Number of connectives : 75 ( 1 ~; 1 |; 5 &; 62 @)
% 0.20/0.49 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 14 ( 3 avg)
% 0.20/0.49 % Number of types : 3 ( 1 usr)
% 0.20/0.49 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 15 ( 14 usr; 1 con; 0-3 aty)
% 0.20/0.49 % Number of variables : 41 ( 28 ^; 10 !; 3 ?; 41 :)
% 0.20/0.49 % SPC : TH0_THM_EQU_NAR
% 0.20/0.49
% 0.20/0.49 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.49 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.49 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.49 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.20/0.49 % $modalities == $modal_system_S5].
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 thf(mworld,type,
% 0.20/0.49 mworld: $tType ).
% 0.20/0.49
% 0.20/0.49 thf(mrel_type,type,
% 0.20/0.49 mrel: mworld > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mactual_type,type,
% 0.20/0.49 mactual: mworld ).
% 0.20/0.49
% 0.20/0.49 thf(mlocal_type,type,
% 0.20/0.49 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mlocal_def,definition,
% 0.20/0.49 ( mlocal
% 0.20/0.49 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mnot_type,type,
% 0.20/0.49 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mand_type,type,
% 0.20/0.49 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mor_type,type,
% 0.20/0.49 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mimplies_type,type,
% 0.20/0.49 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mequiv_type,type,
% 0.20/0.49 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mnot_def,definition,
% 0.20/0.49 ( mnot
% 0.20/0.49 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.49 ~ ( A @ W ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mand_def,definition,
% 0.20/0.49 ( mand
% 0.20/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.49 ( ( A @ W )
% 0.20/0.49 & ( B @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mor_def,definition,
% 0.20/0.49 ( mor
% 0.20/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.49 ( ( A @ W )
% 0.20/0.49 | ( B @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mimplies_def,definition,
% 0.20/0.49 ( mimplies
% 0.20/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.49 ( ( A @ W )
% 0.20/0.49 => ( B @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mequiv_def,definition,
% 0.20/0.49 ( mequiv
% 0.20/0.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.49 ( ( A @ W )
% 0.20/0.49 <=> ( B @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mbox_type,type,
% 0.20/0.49 mbox: ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mbox_def,definition,
% 0.20/0.49 ( mbox
% 0.20/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.49 ! [V: mworld] :
% 0.20/0.49 ( ( mrel @ W @ V )
% 0.20/0.49 => ( Phi @ V ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mdia_type,type,
% 0.20/0.49 mdia: ( mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mdia_def,definition,
% 0.20/0.49 ( mdia
% 0.20/0.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.20/0.49 ? [V: mworld] :
% 0.20/0.49 ( ( mrel @ W @ V )
% 0.20/0.49 & ( Phi @ V ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mrel_reflexive,axiom,
% 0.20/0.49 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.20/0.49
% 0.20/0.49 thf(mrel_euclidean,axiom,
% 0.20/0.49 ! [W: mworld,V: mworld,U: mworld] :
% 0.20/0.49 ( ( ( mrel @ W @ U )
% 0.20/0.49 & ( mrel @ W @ V ) )
% 0.20/0.49 => ( mrel @ U @ V ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(eiw_di_type,type,
% 0.20/0.49 eiw_di: $i > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(eiw_di_nonempty,axiom,
% 0.20/0.49 ! [W: mworld] :
% 0.20/0.49 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.20/0.49
% 0.20/0.49 thf(eiw_di_decr,axiom,
% 0.20/0.49 ! [W: mworld,V: mworld,X: $i] :
% 0.20/0.49 ( ( ( eiw_di @ X @ W )
% 0.20/0.49 & ( mrel @ V @ W ) )
% 0.20/0.49 => ( eiw_di @ X @ V ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mforall_di_type,type,
% 0.20/0.49 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mforall_di_def,definition,
% 0.20/0.49 ( mforall_di
% 0.20/0.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.49 ! [X: $i] :
% 0.20/0.49 ( ( eiw_di @ X @ W )
% 0.20/0.49 => ( A @ X @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(mexists_di_type,type,
% 0.20/0.49 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mexists_di_def,definition,
% 0.20/0.49 ( mexists_di
% 0.20/0.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.20/0.49 ? [X: $i] :
% 0.20/0.49 ( ( eiw_di @ X @ W )
% 0.20/0.49 & ( A @ X @ W ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 thf(element_decl,type,
% 0.20/0.49 element: $i > $i > mworld > $o ).
% 0.20/0.49
% 0.20/0.49 thf(pel40,conjecture,
% 0.20/0.49 ( mlocal
% 0.20/0.49 @ ( mimplies
% 0.20/0.49 @ ( mexists_di
% 0.20/0.49 @ ^ [Y: $i] :
% 0.20/0.49 ( mforall_di
% 0.20/0.49 @ ^ [X: $i] : ( mequiv @ ( element @ X @ Y ) @ ( element @ X @ X ) ) ) )
% 0.20/0.49 @ ( mnot
% 0.20/0.49 @ ( mforall_di
% 0.20/0.49 @ ^ [X1: $i] :
% 0.20/0.49 ( mexists_di
% 0.20/0.49 @ ^ [Y1: $i] :
% 0.20/0.49 ( mforall_di
% 0.20/0.49 @ ^ [Z: $i] : ( mequiv @ ( element @ Z @ Y1 ) @ ( mnot @ ( element @ Z @ X1 ) ) ) ) ) ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.I9PV6NRurc/cvc5---1.0.5_13435.p...
% 0.20/0.49 (declare-sort $$unsorted 0)
% 0.20/0.49 (declare-sort tptp.mworld 0)
% 0.20/0.49 (declare-fun tptp.mrel (tptp.mworld tptp.mworld) Bool)
% 0.20/0.49 (declare-fun tptp.mactual () tptp.mworld)
% 0.20/0.49 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.20/0.49 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.20/0.49 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.20/0.49 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.20/0.49 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.20/0.49 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.20/0.49 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.20/0.49 (declare-fun tptp.mbox ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (assert (= tptp.mbox (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.20/0.49 (declare-fun tptp.mdia ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (assert (= tptp.mdia (lambda ((Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ tptp.mrel W) V) (@ Phi V))))))
% 0.20/0.49 (assert (forall ((W tptp.mworld)) (@ (@ tptp.mrel W) W)))
% 0.20/0.49 (assert (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel W))) (=> (and (@ _let_1 U) (@ _let_1 V)) (@ (@ tptp.mrel U) V)))))
% 0.20/0.49 (declare-fun tptp.eiw_di ($$unsorted tptp.mworld) Bool)
% 0.20/0.49 (assert (forall ((W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ tptp.eiw_di X) W))))
% 0.20/0.49 (assert (forall ((W tptp.mworld) (V tptp.mworld) (X $$unsorted)) (let ((_let_1 (@ tptp.eiw_di X))) (=> (and (@ _let_1 W) (@ (@ tptp.mrel V) W)) (@ _let_1 V)))))
% 0.20/0.49 (declare-fun tptp.mforall_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (assert (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (=> (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))
% 0.20/0.49 (declare-fun tptp.mexists_di ((-> $$unsorted tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.49 (assert (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (and (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))
% 0.20/0.49 (declare-fun tptp.element ($$unsorted $$unsorted tptp.mworld) Bool)
% 0.20/0.49 (assert (not (@ tptp.mlocal (@ (@ tptp.mimplies (@ tptp.mexists_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.element X))) (@ (@ (@ tptp.mequiv (@ _let_1 Y)) (@ _let_1 X)) __flatten_var_0)))) __flatten_var_0)))) (@ tptp.mnot (@ tptp.mforall_di (lambda ((X1 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mexists_di (lambda ((Y1 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.element Z))) (@ (@ (@ tptp.mequiv (@ _let_1 Y1)) (@ tptp.mnot (@ _let_1 X1))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))))))))
% 0.20/0.53 (set-info :filename cvc5---1.0.5_13435)
% 0.20/0.53 (check-sat-assuming ( true ))
% 0.20/0.53 ------- get file name : TPTP file name is SET044^23
% 0.20/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13435.smt2...
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for SET044^23
% 0.20/0.53 % SZS output start Proof for SET044^23
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (@ tptp.mlocal (@ (@ tptp.mimplies (@ tptp.mexists_di (lambda ((Y $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((X $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.element X))) (@ (@ (@ tptp.mequiv (@ _let_1 Y)) (@ _let_1 X)) __flatten_var_0)))) __flatten_var_0)))) (@ tptp.mnot (@ tptp.mforall_di (lambda ((X1 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mexists_di (lambda ((Y1 $$unsorted) (__flatten_var_0 tptp.mworld)) (@ (@ tptp.mforall_di (lambda ((Z $$unsorted) (__flatten_var_0 tptp.mworld)) (let ((_let_1 (@ tptp.element Z))) (@ (@ (@ tptp.mequiv (@ _let_1 Y1)) (@ tptp.mnot (@ _let_1 X1))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0))))))))) (let ((_let_2 (= tptp.mexists_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (exists ((X $$unsorted)) (and (@ (@ tptp.eiw_di X) W) (@ (@ A X) W))))))) (let ((_let_3 (= tptp.mforall_di (lambda ((A (-> $$unsorted tptp.mworld Bool)) (W tptp.mworld)) (forall ((X $$unsorted)) (=> (@ (@ tptp.eiw_di X) W) (@ (@ 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))))) (let ((_let_12 (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) tptp.mactual))) (let ((_let_13 (forall ((X $$unsorted)) (not (ho_4 (ho_6 k_5 X) tptp.mactual))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (or _let_14 (not (forall ((X $$unsorted)) (let ((_let_1 (ho_8 k_7 X))) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (= (ho_4 (ho_6 _let_1 X) tptp.mactual) (ho_4 (ho_6 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) tptp.mactual))))))))) (let ((_let_16 (forall ((X $$unsorted)) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (not (forall ((X $$unsorted)) (let ((_let_1 (ho_8 k_7 X))) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (= (ho_4 (ho_6 _let_1 X) tptp.mactual) (ho_4 (ho_6 _let_1 X) tptp.mactual)))))))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (not (forall ((BOUND_VARIABLE_1118 $$unsorted)) (let ((_let_1 (ho_8 k_7 BOUND_VARIABLE_1118))) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_1118) tptp.mactual)) (= (not (ho_4 (ho_6 _let_1 BOUND_VARIABLE_1118) tptp.mactual)) (ho_4 (ho_6 _let_1 X) tptp.mactual)))))))))) (let ((_let_19 (not _let_18))) (let ((_let_20 (not _let_16))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (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)) (PREPROCESS :args ((= (not (=> (not (forall ((X $$unsorted)) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (not (forall ((X $$unsorted)) (let ((_let_1 (@ tptp.element X))) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (= (@ (@ _let_1 X) tptp.mactual) (@ (@ _let_1 X) tptp.mactual))))))))) (not (or (not (forall ((X $$unsorted)) (or (not (@ (@ tptp.eiw_di X) tptp.mactual)) (not (forall ((BOUND_VARIABLE_1118 $$unsorted)) (let ((_let_1 (@ tptp.element BOUND_VARIABLE_1118))) (or (not (@ (@ tptp.eiw_di BOUND_VARIABLE_1118) tptp.mactual)) (= (@ (@ _let_1 X) tptp.mactual) (not (@ (@ _let_1 BOUND_VARIABLE_1118) tptp.mactual)))))))))) (forall ((X $$unsorted)) (not (@ (@ tptp.eiw_di X) tptp.mactual))))))) (not (=> _let_20 (not (or _let_19 _let_13))))))))))) (let ((_let_22 (or))) (let ((_let_23 (_let_20))) (let ((_let_24 (forall ((BOUND_VARIABLE_1118 $$unsorted)) (let ((_let_1 (ho_8 k_7 BOUND_VARIABLE_1118))) (or (not (ho_4 (ho_6 k_5 BOUND_VARIABLE_1118) tptp.mactual)) (= (not (ho_4 (ho_6 _let_1 BOUND_VARIABLE_1118) tptp.mactual)) (ho_4 (ho_6 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) tptp.mactual))))))) (let ((_let_25 (or (not (ho_4 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) tptp.mactual)) (not _let_24)))) (let ((_let_26 (_let_24))) (let ((_let_27 (_let_19))) (let ((_let_28 (_let_13))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (NOT_NOT_ELIM (NOT_IMPLIES_ELIM2 _let_21)) :args ((or _let_13 _let_19))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_27)) :args _let_27)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) (REFL :args ((not _let_25))) :args _let_22)) (REORDERING (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 BOUND_VARIABLE_1118)))) :args _let_26))) :args (_let_25)) :args (_let_18 false _let_25)) :args (_let_13 false _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG (REFL :args (_let_15)) (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_12))) :args _let_22)) :args ((or _let_12 _let_15))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_23)) :args _let_23) (REWRITE :args ((=> _let_20 (not (or _let_14 (not (forall ((X $$unsorted)) (let ((_let_1 (ho_8 k_7 X))) (or (not (ho_4 (ho_6 k_5 X) tptp.mactual)) (= (ho_4 (ho_6 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) tptp.mactual) (ho_4 (ho_6 _let_1 X) tptp.mactual))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_16))) (REFL :args (_let_17)) :args _let_22)) (NOT_IMPLIES_ELIM1 _let_21) :args (_let_17 true _let_16)) :args (_let_12 true _let_15)) :args (false false _let_13 false _let_12)) :args (_let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 (forall ((W tptp.mworld)) (@ (@ tptp.mrel W) W)) (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel W))) (=> (and (@ _let_1 U) (@ _let_1 V)) (@ (@ tptp.mrel U) V)))) (forall ((W tptp.mworld)) (exists ((X $$unsorted)) (@ (@ tptp.eiw_di X) W))) (forall ((W tptp.mworld) (V tptp.mworld) (X $$unsorted)) (let ((_let_1 (@ tptp.eiw_di X))) (=> (and (@ _let_1 W) (@ (@ tptp.mrel V) W)) (@ _let_1 V)))) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))
% 0.20/0.54 )
% 0.20/0.54 % SZS output end Proof for SET044^23
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------