TSTP Solution File: SEV260^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV260^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 19:22:02 EDT 2023
% Result : Theorem 47.48s 47.73s
% Output : Proof 47.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV260^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n002.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 : Thu Aug 24 03:17:31 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 % File : SEV260^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.50 % Domain : Set Theory (Sets of sets)
% 0.22/0.50 % Problem : TPS problem CLOSED-THM1
% 0.22/0.50 % Version : Especial.
% 0.22/0.50 % English : The inverse image of a closed set under a continuous function is
% 0.22/0.50 % closed.
% 0.22/0.50
% 0.22/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.50 % Source : [Bro09]
% 0.22/0.50 % Names : tps_0474 [Bro09]
% 0.22/0.50 % : CLOSED-THM1 [TPS]
% 0.22/0.50
% 0.22/0.50 % Status : Theorem
% 0.22/0.50 % Rating : 0.54 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.22/0.50 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.22/0.50 % Number of atoms : 16 ( 12 equ; 0 cnn)
% 0.22/0.50 % Maximal formula atoms : 12 ( 16 avg)
% 0.22/0.50 % Number of connectives : 73 ( 4 ~; 0 |; 18 &; 34 @)
% 0.22/0.50 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.22/0.50 % Maximal formula depth : 20 ( 20 avg)
% 0.22/0.50 % Number of types : 3 ( 2 usr)
% 0.22/0.50 % Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% 0.22/0.50 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.22/0.50 % Number of variables : 39 ( 12 ^; 25 !; 2 ?; 39 :)
% 0.22/0.50 % SPC : TH0_THM_EQU_NAR
% 0.22/0.50
% 0.22/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.50 % : Polymorphic definitions expanded.
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 thf(a_type,type,
% 0.22/0.50 a: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(b_type,type,
% 0.22/0.50 b: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(cCLOSED_THM1_pme,conjecture,
% 0.22/0.50 ! [T: ( a > $o ) > $o,S: ( b > $o ) > $o,Xf: a > b] :
% 0.22/0.50 ( ( ! [R: a > $o] :
% 0.22/0.50 ( ( R
% 0.22/0.50 = ( ^ [Xx: a] : $false ) )
% 0.22/0.50 => ( T @ R ) )
% 0.22/0.50 & ! [R: a > $o] :
% 0.22/0.50 ( ( R
% 0.22/0.50 = ( ^ [Xx: a] : ~ $false ) )
% 0.22/0.50 => ( T @ R ) )
% 0.22/0.50 & ! [K: ( a > $o ) > $o,R: a > $o] :
% 0.22/0.50 ( ( ! [Xx: a > $o] :
% 0.22/0.50 ( ( K @ Xx )
% 0.22/0.50 => ( T @ Xx ) )
% 0.22/0.50 & ( R
% 0.22/0.50 = ( ^ [Xx: a] :
% 0.22/0.50 ? [S0: a > $o] :
% 0.22/0.50 ( ( K @ S0 )
% 0.22/0.50 & ( S0 @ Xx ) ) ) ) )
% 0.22/0.50 => ( T @ R ) )
% 0.22/0.50 & ! [Y: a > $o,Z: a > $o,S0: a > $o] :
% 0.22/0.50 ( ( ( T @ Y )
% 0.22/0.50 & ( T @ Z )
% 0.22/0.50 & ( S0
% 0.22/0.50 = ( ^ [Xx: a] :
% 0.22/0.50 ( ( Y @ Xx )
% 0.22/0.50 & ( Z @ Xx ) ) ) ) )
% 0.22/0.50 => ( T @ S0 ) )
% 0.22/0.50 & ! [R: b > $o] :
% 0.22/0.50 ( ( R
% 0.22/0.50 = ( ^ [Xx: b] : $false ) )
% 0.22/0.50 => ( S @ R ) )
% 0.22/0.50 & ! [R: b > $o] :
% 0.22/0.50 ( ( R
% 0.22/0.50 = ( ^ [Xx: b] : ~ $false ) )
% 0.22/0.50 => ( S @ R ) )
% 0.22/0.50 & ! [K: ( b > $o ) > $o,R: b > $o] :
% 0.22/0.50 ( ( ! [Xx: b > $o] :
% 0.22/0.50 ( ( K @ Xx )
% 0.22/0.50 => ( S @ Xx ) )
% 0.22/0.50 & ( R
% 0.22/0.50 = ( ^ [Xx: b] :
% 0.22/0.50 ? [S0: b > $o] :
% 0.22/0.50 ( ( K @ S0 )
% 0.22/0.50 & ( S0 @ Xx ) ) ) ) )
% 0.22/0.50 => ( S @ R ) )
% 0.22/0.50 & ! [Y: b > $o,Z: b > $o,S0: b > $o] :
% 0.22/0.50 ( ( ( S @ Y )
% 0.22/0.50 & ( S @ Z )
% 0.22/0.50 & ( S0
% 0.22/0.50 = ( ^ [Xx: b] :
% 0.22/0.50 ( ( Y @ Xx )
% 0.22/0.50 & ( Z @ Xx ) ) ) ) )
% 0.22/0.50 => ( S @ S0 ) )
% 0.22/0.50 & ! [X: b > $o] :
% 0.22/0.50 ( ( S @ X )
% 0.22/0.50 => ! [Y: a > $o] :
% 0.22/0.50 ( ( Y
% 0.22/0.50 = ( ^ [Xb: a] : ( X @ ( Xf @ Xb ) ) ) )
% 0.22/0.50 => ( T @ Y ) ) ) )
% 0.22/0.50 => ! [X: b > $o] :
% 0.22/0.50 ( ! [R: b > $o] :
% 0.22/0.50 ( ( R
% 0.22/0.50 = ( ^ [Xx: b] :
% 0.22/0.50 ~ ( X @ Xx ) ) )
% 0.22/0.50 => ( S @ R ) )
% 0.22/0.50 => ! [Y: a > $o] :
% 0.22/0.50 ( ( Y
% 0.22/0.50 = ( ^ [Xb: a] : ( X @ ( Xf @ Xb ) ) ) )
% 47.48/47.73 => ! [R: a > $o] :
% 47.48/47.73 ( ( R
% 47.48/47.73 = ( ^ [Xx: a] :
% 47.48/47.73 ~ ( Y @ Xx ) ) )
% 47.48/47.73 => ( T @ R ) ) ) ) ) ).
% 47.48/47.73
% 47.48/47.73 %------------------------------------------------------------------------------
% 47.48/47.73 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.1t8YJ6pYgo/cvc5---1.0.5_17826.p...
% 47.48/47.73 (declare-sort $$unsorted 0)
% 47.48/47.73 (declare-sort tptp.a 0)
% 47.48/47.73 (declare-sort tptp.b 0)
% 47.48/47.73 (assert (not (forall ((T (-> (-> tptp.a Bool) Bool)) (S (-> (-> tptp.b Bool) Bool)) (Xf (-> tptp.a tptp.b))) (=> (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) (@ T R))) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) (@ T R))) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) (@ T Xx))) (= R (lambda ((Xx tptp.a)) (exists ((S0 (-> tptp.a Bool))) (and (@ K S0) (@ S0 Xx)))))) (@ T R))) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S0 (-> tptp.a Bool))) (=> (and (@ T Y) (@ T Z) (= S0 (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) (@ T S0))) (forall ((R (-> tptp.b Bool))) (=> (= R (lambda ((Xx tptp.b)) false)) (@ S R))) (forall ((R (-> tptp.b Bool))) (=> (= R (lambda ((Xx tptp.b)) (not false))) (@ S R))) (forall ((K (-> (-> tptp.b Bool) Bool)) (R (-> tptp.b Bool))) (=> (and (forall ((Xx (-> tptp.b Bool))) (=> (@ K Xx) (@ S Xx))) (= R (lambda ((Xx tptp.b)) (exists ((S0 (-> tptp.b Bool))) (and (@ K S0) (@ S0 Xx)))))) (@ S R))) (forall ((Y (-> tptp.b Bool)) (Z (-> tptp.b Bool)) (S0 (-> tptp.b Bool))) (=> (and (@ S Y) (@ S Z) (= S0 (lambda ((Xx tptp.b)) (and (@ Y Xx) (@ Z Xx))))) (@ S S0))) (forall ((X (-> tptp.b Bool))) (=> (@ S X) (forall ((Y (-> tptp.a Bool))) (=> (= Y (lambda ((Xb tptp.a)) (@ X (@ Xf Xb)))) (@ T Y)))))) (forall ((X (-> tptp.b Bool))) (=> (forall ((R (-> tptp.b Bool))) (=> (= R (lambda ((Xx tptp.b)) (not (@ X Xx)))) (@ S R))) (forall ((Y (-> tptp.a Bool))) (=> (= Y (lambda ((Xb tptp.a)) (@ X (@ Xf Xb)))) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not (@ Y Xx)))) (@ T R)))))))))))
% 47.48/47.73 (set-info :filename cvc5---1.0.5_17826)
% 47.48/47.73 (check-sat-assuming ( true ))
% 47.48/47.73 ------- get file name : TPTP file name is SEV260^5
% 47.48/47.73 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17826.smt2...
% 47.48/47.73 --- Run --ho-elim --full-saturate-quant at 10...
% 47.48/47.73 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 47.48/47.73 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 47.48/47.73 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 47.48/47.73 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 47.48/47.73 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 47.48/47.73 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 47.48/47.73 % SZS status Theorem for SEV260^5
% 47.48/47.73 % SZS output start Proof for SEV260^5
% 47.48/47.73 (
% 47.48/47.73 (let ((_let_1 (not (forall ((T (-> (-> tptp.a Bool) Bool)) (S (-> (-> tptp.b Bool) Bool)) (Xf (-> tptp.a tptp.b))) (=> (and (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) false)) (@ T R))) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not false))) (@ T R))) (forall ((K (-> (-> tptp.a Bool) Bool)) (R (-> tptp.a Bool))) (=> (and (forall ((Xx (-> tptp.a Bool))) (=> (@ K Xx) (@ T Xx))) (= R (lambda ((Xx tptp.a)) (exists ((S0 (-> tptp.a Bool))) (and (@ K S0) (@ S0 Xx)))))) (@ T R))) (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool)) (S0 (-> tptp.a Bool))) (=> (and (@ T Y) (@ T Z) (= S0 (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))) (@ T S0))) (forall ((R (-> tptp.b Bool))) (=> (= R (lambda ((Xx tptp.b)) false)) (@ S R))) (forall ((R (-> tptp.b Bool))) (=> (= R (lambda ((Xx tptp.b)) (not false))) (@ S R))) (forall ((K (-> (-> tptp.b Bool) Bool)) (R (-> tptp.b Bool))) (=> (and (forall ((Xx (-> tptp.b Bool))) (=> (@ K Xx) (@ S Xx))) (= R (lambda ((Xx tptp.b)) (exists ((S0 (-> tptp.b Bool))) (and (@ K S0) (@ S0 Xx)))))) (@ S R))) (forall ((Y (-> tptp.b Bool)) (Z (-> tptp.b Bool)) (S0 (-> tptp.b Bool))) (=> (and (@ S Y) (@ S Z) (= S0 (lambda ((Xx tptp.b)) (and (@ Y Xx) (@ Z Xx))))) (@ S S0))) (forall ((X (-> tptp.b Bool))) (=> (@ S X) (forall ((Y (-> tptp.a Bool))) (=> (= Y (lambda ((Xb tptp.a)) (@ X (@ Xf Xb)))) (@ T Y)))))) (forall ((X (-> tptp.b Bool))) (=> (forall ((R (-> tptp.b Bool))) (=> (= R (lambda ((Xx tptp.b)) (not (@ X Xx)))) (@ S R))) (forall ((Y (-> tptp.a Bool))) (=> (= Y (lambda ((Xb tptp.a)) (@ X (@ Xf Xb)))) (forall ((R (-> tptp.a Bool))) (=> (= R (lambda ((Xx tptp.a)) (not (@ Y Xx)))) (@ T R)))))))))))) (let ((_let_2 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 k_914))) (let ((_let_3 (lambdaF_7 _let_2))) (let ((_let_4 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_2))) (let ((_let_5 (not _let_4))) (let ((_let_6 (= _let_5 _let_3))) (let ((_let_7 (forall ((Xx tptp.b)) (= (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx)) (lambdaF_7 Xx))))) (let ((_let_8 ((forall ((Xx tptp.b)) (= (lambdaF_7 Xx) (@ (lambda ((Xx tptp.b)) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))) Xx)))))) (let ((_let_9 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_8) (REWRITE :args _let_8)))) (let ((_let_10 (=>))) (let ((_let_11 (=))) (let ((_let_12 (not))) (let ((_let_13 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_2) _let_4))))) (let ((_let_14 (REFL :args (_let_3)))) (let ((_let_15 (_let_7))) (let ((_let_16 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_9 :args (_let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_15)) (CONG (REFL :args _let_15) (TRANS (CONG _let_14 (CONG _let_13 :args _let_12) :args _let_11) (REWRITE :args ((= _let_3 _let_5)))) :args _let_10))) _let_9 :args (_let_6 false _let_7)))) (let ((_let_17 (lambdaF_6 k_914))) (let ((_let_18 (= _let_17 _let_5))) (let ((_let_19 (forall ((Xx tptp.a)) (= (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx))) (lambdaF_6 Xx))))) (let ((_let_20 ((forall ((Xx tptp.a)) (= (lambdaF_6 Xx) (@ (lambda ((Xx tptp.a)) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)))) Xx)))))) (let ((_let_21 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_20) (REWRITE :args _let_20)))) (let ((_let_22 (@))) (let ((_let_23 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 k_914) _let_2))))) (let ((_let_24 (REFL :args (_let_17)))) (let ((_let_25 (_let_19))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_21 :args (k_914 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_6 Xx)))) :args _let_25)) (CONG (REFL :args _let_25) (CONG _let_24 (CONG (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_23 :args _let_22) _let_13) :args _let_12) :args _let_11) :args _let_10))) _let_21 :args (_let_18 false _let_19)))) (let ((_let_27 (lambdaF_909 k_914))) (let ((_let_28 (= _let_17 _let_27))) (let ((_let_29 (= _let_27 _let_3))) (let ((_let_30 (not _let_17))) (let ((_let_31 (= lambdaF_6 lambdaF_909))) (let ((_let_32 (not _let_28))) (let ((_let_33 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_6))) (let ((_let_34 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_909))) (let ((_let_35 (not _let_31))) (let ((_let_36 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 lambdaF_7))) (let ((_let_37 (not _let_36))) (let ((_let_38 (forall ((X (-> tptp.b Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xb tptp.a)) (@ X (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb)))))))) (let ((_let_39 (not _let_38))) (let ((_let_40 (not (forall ((Y (-> tptp.b Bool)) (Z (-> tptp.b Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y)) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Z)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (lambda ((Xx tptp.b)) (and (@ Y Xx) (@ Z Xx))))))))) (let ((_let_41 (not (forall ((K (-> (-> tptp.b Bool) Bool))) (or (not (forall ((Xx (-> tptp.b Bool))) (or (not (@ K Xx)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx)))) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (lambda ((Xx tptp.b)) (not (forall ((S0 (-> tptp.b Bool))) (or (not (@ K S0)) (not (@ S0 Xx)))))))))))) (let ((_let_42 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 lambdaF_8))) (let ((_let_43 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 lambdaF_9))) (let ((_let_44 (not (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y)) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Z)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))))))) (let ((_let_45 (not (forall ((K (-> (-> tptp.a Bool) Bool))) (or (not (forall ((Xx (-> tptp.a Bool))) (or (not (@ K Xx)) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx)))) (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx tptp.a)) (not (forall ((S0 (-> tptp.a Bool))) (or (not (@ K S0)) (not (@ S0 Xx)))))))))))) (let ((_let_46 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_10))) (let ((_let_47 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_11))) (let ((_let_48 (or (not _let_47) (not _let_46) _let_45 _let_44 (not _let_43) (not _let_42) _let_41 _let_40 _let_39 _let_37 _let_33))) (let ((_let_49 (not _let_33))) (let ((_let_50 (forall ((T (-> (-> tptp.a Bool) Bool)) (S (-> (-> tptp.b Bool) Bool)) (Xf (-> tptp.a tptp.b)) (BOUND_VARIABLE_974 (-> tptp.b Bool))) (or (not (@ T (lambda ((BOUND_VARIABLE_1307 tptp.a)) false))) (not (@ T (lambda ((BOUND_VARIABLE_1285 tptp.a)) true))) (not (forall ((K (-> (-> tptp.a Bool) Bool))) (or (not (forall ((Xx (-> tptp.a Bool))) (or (not (@ K Xx)) (@ T Xx)))) (@ T (lambda ((Xx tptp.a)) (not (forall ((S0 (-> tptp.a Bool))) (or (not (@ K S0)) (not (@ S0 Xx)))))))))) (not (forall ((Y (-> tptp.a Bool)) (Z (-> tptp.a Bool))) (or (not (@ T Y)) (not (@ T Z)) (@ T (lambda ((Xx tptp.a)) (and (@ Y Xx) (@ Z Xx))))))) (not (@ S (lambda ((BOUND_VARIABLE_1261 tptp.b)) false))) (not (@ S (lambda ((BOUND_VARIABLE_1239 tptp.b)) true))) (not (forall ((K (-> (-> tptp.b Bool) Bool))) (or (not (forall ((Xx (-> tptp.b Bool))) (or (not (@ K Xx)) (@ S Xx)))) (@ S (lambda ((Xx tptp.b)) (not (forall ((S0 (-> tptp.b Bool))) (or (not (@ K S0)) (not (@ S0 Xx)))))))))) (not (forall ((Y (-> tptp.b Bool)) (Z (-> tptp.b Bool))) (or (not (@ S Y)) (not (@ S Z)) (@ S (lambda ((Xx tptp.b)) (and (@ Y Xx) (@ Z Xx))))))) (not (forall ((X (-> tptp.b Bool))) (or (not (@ S X)) (@ T (lambda ((Xb tptp.a)) (@ X (@ Xf Xb))))))) (not (@ S (lambda ((Xx tptp.b)) (not (@ BOUND_VARIABLE_974 Xx))))) (@ T (lambda ((Xx tptp.a)) (not (@ BOUND_VARIABLE_974 (@ Xf Xx))))))))) (let ((_let_51 (not _let_48))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_50))) (let ((_let_55 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_56 (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 lambdaF_7) _let_36))))) (let ((_let_57 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_58 (_let_54))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_52) :args _let_58) (CONG (REFL :args _let_58) (CONG (CONG (CONG (TRANS (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_1307 tptp.a)) false) lambdaF_11))) :args _let_22) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_11) _let_47)))) :args _let_12) (CONG (TRANS (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_1285 tptp.a)) true) lambdaF_10))) :args _let_22) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_10) _let_46)))) :args _let_12) (REFL :args (_let_45)) (REFL :args (_let_44)) (CONG (TRANS (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_1261 tptp.b)) false) lambdaF_9))) :args _let_22) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 lambdaF_9) _let_43)))) :args _let_12) (CONG (TRANS (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (lambda ((BOUND_VARIABLE_1239 tptp.b)) true) lambdaF_8))) :args _let_22) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 lambdaF_8) _let_42)))) :args _let_12) (REFL :args (_let_41)) (REFL :args (_let_40)) (REFL :args (_let_39)) (CONG (TRANS (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xx tptp.b)) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))) lambdaF_7))) :args _let_22) _let_56) :args _let_12) (TRANS (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xx tptp.a)) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)))) lambdaF_6))) :args _let_22) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_6) _let_33)))) :args _let_53) :args _let_12) :args _let_10))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_50))) (REFL :args (_let_51)) :args _let_53)) _let_52 :args (_let_51 true _let_50)))) (let ((_let_60 (or _let_37 _let_34))) (let ((_let_61 (REFL :args (_let_48)))) (let ((_let_62 (_let_38))) (let ((_let_63 (ASSUME :args (_let_49)))) (let ((_let_64 (ASSUME :args (_let_31)))) (let ((_let_65 (ASSUME :args (_let_34)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (THEORY_LEMMA :args ((or _let_31 _let_32) THEORY_UF)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_63 _let_64 _let_65) :args (_let_49 _let_34 _let_31)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_65)) (CONG (SYMM _let_64) :args (APPLY_UF SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (FALSE_INTRO _let_63))) :args (_let_49 _let_31 _let_34)) :args ((not (and _let_49 _let_34 _let_31)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_33))) (REFL :args ((not _let_34))) (REFL :args (_let_35)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_37 _let_34 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 9)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_53)) :args ((or _let_36 _let_48))) _let_59 :args (_let_36 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args (lambdaF_7 QUANTIFIERS_INST_ENUM)) :args _let_62) (CONG (REFL :args _let_62) (CONG (CONG _let_56 :args _let_12) (TRANS (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xb tptp.a)) (@ lambdaF_7 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb))) lambdaF_909))) :args _let_22) (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_909) _let_34)))) :args _let_53) :args _let_10))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 8)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_53)) :args ((or _let_38 _let_48))) _let_59 :args (_let_38 true _let_48)) :args (_let_60 false _let_38)) :args (_let_34 false _let_36 false _let_60)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 10)) _let_59 :args (_let_49 true _let_48)) :args (_let_35 false _let_34 true _let_33)) :args (_let_32 true _let_31)))) (let ((_let_67 (_let_28))) (let ((_let_68 (not _let_18))) (let ((_let_69 (_let_18))) (let ((_let_70 (forall ((Xb tptp.a)) (= (@ lambdaF_7 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb)) (lambdaF_909 Xb))))) (let ((_let_71 ((forall ((Xb tptp.a)) (= (lambdaF_909 Xb) (@ (lambda ((Xb tptp.a)) (@ lambdaF_7 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb))) Xb)))))) (let ((_let_72 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_71) (REWRITE :args _let_71)))) (let ((_let_73 (_let_70))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (k_914 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_909 Xb)))) :args _let_73)) (CONG (REFL :args _let_73) (CONG (REFL :args (_let_27)) (TRANS (CONG (REFL :args (lambdaF_7)) _let_23 :args _let_22) (THEORY_PREPROCESS :args ((= (@ lambdaF_7 _let_2) _let_3)))) :args _let_11) :args _let_10))) _let_72 :args (_let_29 false _let_70)))) (let ((_let_75 (not _let_29))) (let ((_let_76 (not _let_3))) (let ((_let_77 (_let_29))) (let ((_let_78 (not _let_6))) (let ((_let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))))) (let ((_let_80 (_let_6))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args _let_80) (CONG (REFL :args (_let_78)) _let_79 _let_14 :args _let_53)) :args ((or _let_4 _let_3 _let_78))) _let_16 (REORDERING (CNF_EQUIV_POS2 :args _let_77) :args ((or _let_27 _let_76 _let_75))) _let_74 (REORDERING (CNF_EQUIV_POS1 :args _let_69) :args ((or _let_30 _let_5 _let_68))) _let_26 (CNF_EQUIV_NEG2 :args _let_67) _let_66 :args (_let_30 false _let_6 true _let_3 false _let_29 true _let_4 false _let_18 true _let_27 true _let_28)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_80) :args ((or _let_5 _let_76 _let_78))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_77) :args ((or (not _let_27) _let_3 _let_75))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_67) :args ((or _let_17 _let_27 _let_28))) _let_81 _let_66 :args (_let_27 true _let_17 true _let_28)) _let_74 :args (_let_3 false _let_27 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_69) (CONG (REFL :args (_let_68)) _let_24 _let_79 :args _let_53)) :args ((or _let_17 _let_4 _let_68))) _let_81 _let_26 :args (_let_4 true _let_17 false _let_18)) _let_16 :args (false false _let_3 false _let_4 false _let_6)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 47.48/47.74 )
% 47.48/47.74 % SZS output end Proof for SEV260^5
% 47.48/47.74 % cvc5---1.0.5 exiting
% 47.61/47.74 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------