TSTP Solution File: SEV238^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV238^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %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 : Thu Aug 31 19:21:58 EDT 2023
% Result : Theorem 40.56s 40.83s
% Output : Proof 40.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV238^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n022.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 : Thu Aug 24 03:32:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 % File : SEV238^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.48 % Domain : Set Theory (Sets of sets)
% 0.21/0.48 % Problem : TPS problem THM2D
% 0.21/0.48 % Version : Especial.
% 0.21/0.48 % English :
% 0.21/0.48
% 0.21/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.48 % Source : [Bro09]
% 0.21/0.48 % Names : tps_0480 [Bro09]
% 0.21/0.48 % : THM2D [TPS]
% 0.21/0.48
% 0.21/0.48 % Status : Theorem
% 0.21/0.48 % Rating : 0.09 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.17 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v4.1.0, 0.67 v4.0.1, 0.33 v4.0.0
% 0.21/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.21/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.48 % Number of connectives : 92 ( 0 ~; 0 |; 12 &; 61 @)
% 0.21/0.48 % ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% 0.21/0.48 % Maximal formula depth : 18 ( 18 avg)
% 0.21/0.48 % Number of types : 2 ( 0 usr)
% 0.21/0.48 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.21/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.48 % Number of variables : 36 ( 8 ^; 18 !; 10 ?; 36 :)
% 0.21/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.48
% 0.21/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.48 % : Polymorphic definitions expanded.
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 thf(cTHM2D_pme,conjecture,
% 0.21/0.48 ! [K: ( $i > $o ) > $i > $o] :
% 0.21/0.48 ( ( ! [Xx: $i > $o] :
% 0.21/0.48 ( ! [Xx0: $i] :
% 0.21/0.48 ( ( Xx @ Xx0 )
% 0.21/0.48 => ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx1: $i] :
% 0.21/0.48 ( ( S @ Xx1 )
% 0.21/0.48 => ( K @ S @ Xx1 ) )
% 0.21/0.48 & ( S @ Xx0 ) ) )
% 0.21/0.48 => ! [Xx0: $i] :
% 0.21/0.48 ( ( K @ Xx @ Xx0 )
% 0.21/0.48 => ( K
% 0.21/0.48 @ ^ [Xx1: $i] :
% 0.21/0.48 ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx2: $i] :
% 0.21/0.48 ( ( S @ Xx2 )
% 0.21/0.48 => ( K @ S @ Xx2 ) )
% 0.21/0.48 & ( S @ Xx1 ) )
% 0.21/0.48 @ Xx0 ) ) )
% 0.21/0.48 & ( ! [Xx: $i] :
% 0.21/0.48 ( ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx0: $i] :
% 0.21/0.48 ( ( S @ Xx0 )
% 0.21/0.48 => ( K @ S @ Xx0 ) )
% 0.21/0.48 & ( S @ Xx ) )
% 0.21/0.48 => ( K
% 0.21/0.48 @ ^ [Xx0: $i] :
% 0.21/0.48 ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx1: $i] :
% 0.21/0.48 ( ( S @ Xx1 )
% 0.21/0.48 => ( K @ S @ Xx1 ) )
% 0.21/0.48 & ( S @ Xx0 ) )
% 0.21/0.48 @ Xx ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( K
% 0.21/0.48 @ ^ [Xx0: $i] :
% 0.21/0.48 ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx1: $i] :
% 0.21/0.48 ( ( S @ Xx1 )
% 0.21/0.48 => ( K @ S @ Xx1 ) )
% 0.21/0.48 & ( S @ Xx0 ) )
% 0.21/0.48 @ Xx )
% 0.21/0.48 => ( K
% 0.21/0.48 @ ( K
% 0.21/0.48 @ ^ [Xx0: $i] :
% 0.21/0.48 ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx1: $i] :
% 0.21/0.48 ( ( S @ Xx1 )
% 0.21/0.48 => ( K @ S @ Xx1 ) )
% 0.21/0.48 & ( S @ Xx0 ) ) )
% 0.21/0.48 @ Xx ) ) ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( K
% 0.21/0.48 @ ^ [Xx0: $i] :
% 0.21/0.48 ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx1: $i] :
% 0.21/0.48 ( ( S @ Xx1 )
% 0.21/0.48 => ( K @ S @ Xx1 ) )
% 0.21/0.48 & ( S @ Xx0 ) )
% 0.21/0.48 @ Xx )
% 0.21/0.48 <=> ( ! [Xx0: $i] :
% 0.21/0.48 ( ( K
% 0.21/0.48 @ ^ [Xx1: $i] :
% 0.21/0.48 ? [S: $i > $o] :
% 0.21/0.48 ( ! [Xx2: $i] :
% 0.21/0.48 ( ( S @ Xx2 )
% 0.21/0.48 => ( K @ S @ Xx2 ) )
% 0.21/0.48 & ( S @ Xx1 ) )
% 0.21/0.48 @ Xx0 )
% 0.21/0.48 => ( K
% 40.56/40.83 @ ( K
% 40.56/40.83 @ ^ [Xx1: $i] :
% 40.56/40.83 ? [S: $i > $o] :
% 40.56/40.83 ( ! [Xx2: $i] :
% 40.56/40.83 ( ( S @ Xx2 )
% 40.56/40.83 => ( K @ S @ Xx2 ) )
% 40.56/40.83 & ( S @ Xx1 ) ) )
% 40.56/40.83 @ Xx0 ) )
% 40.56/40.83 & ( K
% 40.56/40.83 @ ^ [Xx0: $i] :
% 40.56/40.83 ? [S: $i > $o] :
% 40.56/40.83 ( ! [Xx1: $i] :
% 40.56/40.83 ( ( S @ Xx1 )
% 40.56/40.83 => ( K @ S @ Xx1 ) )
% 40.56/40.83 & ( S @ Xx0 ) )
% 40.56/40.83 @ Xx ) ) ) ) ).
% 40.56/40.83
% 40.56/40.83 %------------------------------------------------------------------------------
% 40.56/40.83 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7ftSJUbjKc/cvc5---1.0.5_26331.p...
% 40.56/40.83 (declare-sort $$unsorted 0)
% 40.56/40.83 (assert (not (forall ((K (-> (-> $$unsorted Bool) $$unsorted Bool))) (=> (and (forall ((Xx (-> $$unsorted Bool))) (=> (forall ((Xx0 $$unsorted)) (=> (@ Xx Xx0) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) (forall ((Xx0 $$unsorted)) (=> (@ (@ K Xx) Xx0) (@ (@ K (lambda ((Xx1 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx2 $$unsorted)) (=> (@ S Xx2) (@ (@ K S) Xx2))) (@ S Xx1))))) Xx0))))) (=> (forall ((Xx $$unsorted)) (=> (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx0 $$unsorted)) (=> (@ S Xx0) (@ (@ K S) Xx0))) (@ S Xx))) (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx))) (forall ((Xx $$unsorted)) (=> (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx) (@ (@ K (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0)))))) Xx))))) (forall ((Xx $$unsorted)) (= (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx) (and (forall ((Xx0 $$unsorted)) (=> (@ (@ K (lambda ((Xx1 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx2 $$unsorted)) (=> (@ S Xx2) (@ (@ K S) Xx2))) (@ S Xx1))))) Xx0) (@ (@ K (@ K (lambda ((Xx1 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx2 $$unsorted)) (=> (@ S Xx2) (@ (@ K S) Xx2))) (@ S Xx1)))))) Xx0))) (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx))))))))
% 40.56/40.83 (set-info :filename cvc5---1.0.5_26331)
% 40.56/40.83 (check-sat-assuming ( true ))
% 40.56/40.83 ------- get file name : TPTP file name is SEV238^5
% 40.56/40.83 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26331.smt2...
% 40.56/40.83 --- Run --ho-elim --full-saturate-quant at 10...
% 40.56/40.83 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 40.56/40.83 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 40.56/40.83 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 40.56/40.83 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 40.56/40.83 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 40.56/40.83 % SZS status Theorem for SEV238^5
% 40.56/40.83 % SZS output start Proof for SEV238^5
% 40.56/40.83 (
% 40.56/40.83 (let ((_let_1 (not (forall ((K (-> (-> $$unsorted Bool) $$unsorted Bool))) (=> (and (forall ((Xx (-> $$unsorted Bool))) (=> (forall ((Xx0 $$unsorted)) (=> (@ Xx Xx0) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) (forall ((Xx0 $$unsorted)) (=> (@ (@ K Xx) Xx0) (@ (@ K (lambda ((Xx1 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx2 $$unsorted)) (=> (@ S Xx2) (@ (@ K S) Xx2))) (@ S Xx1))))) Xx0))))) (=> (forall ((Xx $$unsorted)) (=> (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx0 $$unsorted)) (=> (@ S Xx0) (@ (@ K S) Xx0))) (@ S Xx))) (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx))) (forall ((Xx $$unsorted)) (=> (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx) (@ (@ K (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0)))))) Xx))))) (forall ((Xx $$unsorted)) (= (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx) (and (forall ((Xx0 $$unsorted)) (=> (@ (@ K (lambda ((Xx1 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx2 $$unsorted)) (=> (@ S Xx2) (@ (@ K S) Xx2))) (@ S Xx1))))) Xx0) (@ (@ K (@ K (lambda ((Xx1 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx2 $$unsorted)) (=> (@ S Xx2) (@ (@ K S) Xx2))) (@ S Xx1)))))) Xx0))) (@ (@ K (lambda ((Xx0 $$unsorted)) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx1 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx))))))))) (let ((_let_2 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S k_12)))))) (let ((_let_3 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S k_12)))))) (let ((_let_4 (not _let_2))) (let ((_let_5 (lambdaF_8 k_12))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (forall ((Xx0 $$unsorted)) (= (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0))))) (lambdaF_8 Xx0))))) (let ((_let_8 ((forall ((Xx0 $$unsorted)) (= (lambdaF_8 Xx0) (@ (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0)))))) Xx0)))))) (let ((_let_9 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_8) (REWRITE :args _let_8)))) (let ((_let_10 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_9 :args (k_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_8 Xx0)))) :args (_let_7)))) _let_9 :args (_let_6 false _let_7)))) (let ((_let_11 (lambdaF_7 k_12))) (let ((_let_12 (= _let_11 _let_5))) (let ((_let_13 (= lambdaF_7 lambdaF_8))) (let ((_let_14 (not _let_12))) (let ((_let_15 (= lambdaF_6 lambdaF_8))) (let ((_let_16 (= lambdaF_6 lambdaF_7))) (let ((_let_17 (not _let_13))) (let ((_let_18 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (= lambdaF_6 lambdaF_26))) (let ((_let_20 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (not _let_15))) (let ((_let_22 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (forall ((Xx0 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx0)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0))))))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_18))) (let ((_let_27 (forall ((Xx (-> $$unsorted Bool)) (BOUND_VARIABLE_820 $$unsorted)) (or (not (forall ((Xx0 $$unsorted)) (or (not (@ Xx Xx0)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0)))))))) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx) BOUND_VARIABLE_820)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S Xx1))))))) BOUND_VARIABLE_820))))) (let ((_let_28 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (forall ((Xx0 $$unsorted)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S Xx1))))))) Xx0)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S Xx1)))))))) Xx0))))) (let ((_let_31 (and _let_30 _let_29))) (let ((_let_32 (= _let_31 _let_28))) (let ((_let_33 (forall ((Xx $$unsorted)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0))))))) Xx)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0)))))))) Xx))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (not _let_35))) (let ((_let_37 (forall ((Xx0 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx0)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) Xx0))))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_20 _let_38 _let_36))) (let ((_let_40 (and _let_39 _let_34))) (let ((_let_41 (not _let_27))) (let ((_let_42 (or _let_41 _let_40 _let_32))) (let ((_let_43 (forall ((K (-> (-> $$unsorted Bool) $$unsorted Bool)) (BOUND_VARIABLE_1020 $$unsorted) (BOUND_VARIABLE_1006 (-> $$unsorted Bool)) (BOUND_VARIABLE_1004 $$unsorted)) (or (not (forall ((Xx (-> $$unsorted Bool)) (BOUND_VARIABLE_820 $$unsorted)) (or (not (forall ((Xx0 $$unsorted)) (or (not (@ Xx Xx0)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) Xx1)))) (not (@ S Xx0)))))))) (not (@ (@ K Xx) BOUND_VARIABLE_820)) (@ (@ K (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ K S) Xx2)))) (not (@ S Xx1))))))) BOUND_VARIABLE_820)))) (and (or (@ (@ K (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) Xx1)))) (not (@ S Xx0))))))) BOUND_VARIABLE_1004) (not (forall ((Xx0 $$unsorted)) (or (not (@ BOUND_VARIABLE_1006 Xx0)) (@ (@ K BOUND_VARIABLE_1006) Xx0)))) (not (@ BOUND_VARIABLE_1006 BOUND_VARIABLE_1004))) (not (forall ((Xx $$unsorted)) (or (not (@ (@ K (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) 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_let_16))) :args (_let_16 _let_21))) :args (true _let_154)) (CONG _let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_15))) (REFL :args (_let_17)) :args _let_49)) _let_108 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (ASSUME :args (_let_18)))) (CONG (TRANS (SYMM _let_151) (SYMM (SYMM (ASSUME :args (_let_15))))) _let_58 :args _let_118) (FALSE_INTRO (ASSUME :args (_let_152))))) :args (_let_152 _let_15 _let_19 _let_18))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_152) _let_20))) (REFL :args _let_153) (REFL :args ((not _let_19))) (REFL :args ((not _let_18))) :args _let_49)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 0)) _let_123 :args (_let_152 true _let_39)) _let_151 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_18 _let_23 _let_25 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_36 _let_22 (not _let_128)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_124 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_49)) :args ((or _let_35 _let_39))) _let_123 :args (_let_35 true _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_129) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx0) false))))) :args _let_129) (CONG (REFL :args _let_129) (CONG _let_57 _let_61 :args _let_49) :args _let_50))) _let_125 :args (_let_128 false _let_37)) :args (_let_22 false _let_35 false _let_128)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_62)) :args _let_62) (CONG _let_63 (CONG (CONG _let_126 (REFL :args (_let_66)) :args _let_49) :args _let_51) :args _let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) (REFL :args ((not _let_69))) :args _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_127) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING)) :args _let_127) (CONG (REFL :args _let_127) (CONG (REFL :args (_let_71)) _let_126 :args _let_49) :args _let_50))) (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_68 _let_71 (not _let_72)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_37 (= Xx0 Xx1)))) _let_125 :args (_let_70 false _let_37)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_49)) :args ((or _let_65 _let_69))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_49)) :args ((or _let_67 _let_69))) :args (_let_69 true _let_72 false _let_70 false _let_65 false _let_67)) :args (_let_24 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_64) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx) BOUND_VARIABLE_820) false))))) :args _let_64) (CONG (REFL :args _let_64) (CONG _let_63 (CONG _let_61 :args _let_51) (TRANS (CONG (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S Xx1)))))) lambdaF_26))) :args _let_54) _let_58 :args _let_54) (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_26) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_18)))) :args _let_49) :args _let_50))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_27))) :args _let_49)) :args ((or _let_27 _let_42))) _let_60 :args (_let_27 true _let_42)) :args (_let_26 false _let_27)) :args (_let_18 false _let_22 false _let_24 false _let_26)) :args (_let_21 true _let_20 false _let_19 false _let_18)) :args (_let_17 false _let_16 true _let_15)) :args (_let_14 true _let_13)))) (let ((_let_157 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S k_12)))))) (let ((_let_158 (not _let_157))) (let ((_let_159 (= _let_11 _let_158))) (let ((_let_160 (not _let_11))) (let ((_let_161 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_99 :args (k_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_101)) :args _let_100))) _let_99 :args (_let_159 false _let_97)))) (let ((_let_162 (not _let_159))) (let ((_let_163 (_let_159))) (let ((_let_164 (_let_12))) (let ((_let_165 (ALPHA_EQUIV :args (_let_3 _let_106 _let_105)))) (let ((_let_166 (not _let_6))) (let ((_let_167 (_let_6))) (let ((_let_168 (ALPHA_EQUIV :args (_let_3 (= Xx1 Xx1) (= S S))))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_168) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_167) (CONG (REFL :args (_let_166)) (REFL :args (_let_5)) (MACRO_SR_PRED_INTRO :args ((= (not _let_4) _let_2))) :args _let_49)) :args ((or _let_5 _let_2 _let_166))) _let_10 (EQUIV_ELIM1 _let_165) (CNF_EQUIV_NEG2 :args _let_164) _let_156 (REORDERING (CNF_EQUIV_POS1 :args _let_163) :args ((or _let_160 _let_158 _let_162))) _let_161 :args (_let_160 false _let_2 false _let_6 true _let_3 true _let_5 true _let_12 true _let_157 false _let_159)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 _let_168) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_165) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_163) (CONG (REFL :args (_let_162)) (REFL :args (_let_11)) (MACRO_SR_PRED_INTRO :args ((= (not _let_158) _let_157))) :args _let_49)) :args ((or _let_11 _let_157 _let_162))) _let_169 _let_161 :args (_let_157 true _let_11 false _let_159)) :args (_let_3 false _let_157)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_167) :args ((or (not _let_5) _let_4 _let_166))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_164) :args ((or _let_11 _let_5 _let_12))) _let_169 _let_156 :args (_let_5 true _let_11 true _let_12)) _let_10 :args (_let_4 false _let_5 false _let_6)) :args (false false _let_3 true _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 40.56/40.84 )
% 40.56/40.84 % SZS output end Proof for SEV238^5
% 40.56/40.84 % cvc5---1.0.5 exiting
% 40.56/40.84 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------