TSTP Solution File: SEV254^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV254^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 19:22:01 EDT 2023
% Result : Theorem 36.29s 36.54s
% Output : Proof 36.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV254^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.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 01:55:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 %----Proving TH0
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEV254^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.48 % Domain : Set Theory (Sets of sets)
% 0.20/0.48 % Problem : TPS problem from SETS-OF-SETS-THMS
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_1170 [Bro09]
% 0.20/0.48 % : tps_1171 [Bro09]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.18 v8.1.0, 0.42 v7.5.0, 0.33 v7.3.0, 0.40 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.1, 0.67 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.20/0.48 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.48 % Number of connectives : 71 ( 0 ~; 0 |; 9 &; 46 @)
% 0.20/0.48 % ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 17 ( 17 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.48 % Number of variables : 28 ( 5 ^; 15 !; 8 ?; 28 :)
% 0.20/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(cTHM2C_pme,conjecture,
% 0.20/0.48 ! [K: ( $i > $o ) > $i > $o] :
% 0.20/0.48 ( ( ! [Xx: $i > $o] :
% 0.20/0.48 ( ! [Xx0: $i] :
% 0.20/0.48 ( ( Xx @ Xx0 )
% 0.20/0.48 => ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx1: $i] :
% 0.20/0.48 ( ( S @ Xx1 )
% 0.20/0.48 => ( K @ S @ Xx1 ) )
% 0.20/0.48 & ( S @ Xx0 ) ) )
% 0.20/0.48 => ! [Xx0: $i] :
% 0.20/0.48 ( ( K @ Xx @ Xx0 )
% 0.20/0.48 => ( K
% 0.20/0.48 @ ^ [Xx1: $i] :
% 0.20/0.48 ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx2: $i] :
% 0.20/0.48 ( ( S @ Xx2 )
% 0.20/0.48 => ( K @ S @ Xx2 ) )
% 0.20/0.48 & ( S @ Xx1 ) )
% 0.20/0.48 @ Xx0 ) ) )
% 0.20/0.48 & ( ! [Xx: $i] :
% 0.20/0.48 ( ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx0: $i] :
% 0.20/0.48 ( ( S @ Xx0 )
% 0.20/0.48 => ( K @ S @ Xx0 ) )
% 0.20/0.48 & ( S @ Xx ) )
% 0.20/0.48 => ( K
% 0.20/0.48 @ ^ [Xx0: $i] :
% 0.20/0.48 ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx1: $i] :
% 0.20/0.48 ( ( S @ Xx1 )
% 0.20/0.48 => ( K @ S @ Xx1 ) )
% 0.20/0.48 & ( S @ Xx0 ) )
% 0.20/0.48 @ Xx ) )
% 0.20/0.48 => ! [Xx: $i] :
% 0.20/0.48 ( ( K
% 0.20/0.48 @ ^ [Xx0: $i] :
% 0.20/0.48 ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx1: $i] :
% 0.20/0.48 ( ( S @ Xx1 )
% 0.20/0.48 => ( K @ S @ Xx1 ) )
% 0.20/0.48 & ( S @ Xx0 ) )
% 0.20/0.48 @ Xx )
% 0.20/0.48 => ( K
% 0.20/0.48 @ ( K
% 0.20/0.48 @ ^ [Xx0: $i] :
% 0.20/0.48 ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx1: $i] :
% 0.20/0.48 ( ( S @ Xx1 )
% 0.20/0.48 => ( K @ S @ Xx1 ) )
% 0.20/0.48 & ( S @ Xx0 ) ) )
% 0.20/0.48 @ Xx ) ) ) )
% 0.20/0.48 => ! [Xx: $i] :
% 0.20/0.48 ( ( K
% 0.20/0.48 @ ^ [Xx0: $i] :
% 0.20/0.48 ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx1: $i] :
% 0.20/0.48 ( ( S @ Xx1 )
% 0.20/0.48 => ( K @ S @ Xx1 ) )
% 0.20/0.48 & ( S @ Xx0 ) )
% 0.20/0.48 @ Xx )
% 0.20/0.48 <=> ? [S: $i > $o] :
% 0.20/0.48 ( ! [Xx0: $i] :
% 0.20/0.48 ( ( S @ Xx0 )
% 0.20/0.48 => ( K @ S @ Xx0 ) )
% 0.20/0.48 & ( S @ Xx ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.5VHUJigvED/cvc5---1.0.5_22530.p...
% 0.20/0.48 (declare-sort $$unsorted 0)
% 36.29/36.54 (assert (not (forall ((K (-> (-> $$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) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx0 $$unsorted)) (=> (@ S Xx0) (@ (@ K S) Xx0))) (@ S Xx)))))))))
% 36.29/36.54 (set-info :filename cvc5---1.0.5_22530)
% 36.29/36.54 (check-sat-assuming ( true ))
% 36.29/36.54 ------- get file name : TPTP file name is SEV254^5
% 36.29/36.54 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22530.smt2...
% 36.29/36.54 --- Run --ho-elim --full-saturate-quant at 10...
% 36.29/36.54 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 36.29/36.54 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 36.29/36.54 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 36.29/36.54 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 36.29/36.54 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 36.29/36.54 % SZS status Theorem for SEV254^5
% 36.29/36.54 % SZS output start Proof for SEV254^5
% 36.29/36.54 (
% 36.29/36.54 (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 $$unsorted)) (=> (@ S Xx1) (@ (@ K S) Xx1))) (@ S Xx0))))) Xx) (exists ((S (-> $$unsorted Bool))) (and (forall ((Xx0 $$unsorted)) (=> (@ S Xx0) (@ (@ K S) Xx0))) (@ S Xx)))))))))) (let ((_let_2 (= lambdaF_7 lambdaF_38))) (let ((_let_3 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_4 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_5 (lambdaF_38 k_55))) (let ((_let_6 (lambdaF_7 k_55))) (let ((_let_7 (= _let_6 _let_5))) (let ((_let_8 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S k_55)))))) (let ((_let_9 (not _let_8))) (let ((_let_10 (= _let_6 _let_9))) (let ((_let_11 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S k_55)))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (= _let_5 _let_12))) (let ((_let_14 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S k_55)))))) (let ((_let_15 (not _let_6))) (let ((_let_16 (_let_7))) (let ((_let_17 (forall ((Xx0 $$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_7 Xx0))))) (let ((_let_18 ((forall ((Xx0 $$unsorted)) (= (lambdaF_7 Xx0) (@ (lambda ((Xx0 $$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_19 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_18) (REWRITE :args _let_18)))) (let ((_let_20 (_let_17))) (let ((_let_21 ((lambdaF_7 Xx0)))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (k_55 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20))) _let_19 :args (_let_10 false _let_17)))) (let ((_let_23 (not _let_10))) (let ((_let_24 (_let_10))) (let ((_let_25 (forall ((Xx1 $$unsorted)) (= (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S Xx1))))) (lambdaF_38 Xx1))))) (let ((_let_26 ((forall ((Xx1 $$unsorted)) (= (lambdaF_38 Xx1) (@ (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)))))) Xx1)))))) (let ((_let_27 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_26) (REWRITE :args _let_26)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_27 :args (k_55 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_38 Xx1)))) :args (_let_25)))) _let_27 :args (_let_13 false _let_25)))) (let ((_let_29 (not _let_13))) (let ((_let_30 (or))) (let ((_let_31 (_let_13))) (let ((_let_32 (= S S))) (let ((_let_33 (= Xx1 Xx1))) (let ((_let_34 (ALPHA_EQUIV :args (_let_14 _let_33 _let_32)))) (let ((_let_35 (ALPHA_EQUIV :args (_let_14 (= Xx1 Xx2) (= S S))))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (THEORY_LEMMA :args ((or _let_2 (not _let_7)) THEORY_UF)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 _let_35) (EQUIV_ELIM2 _let_34) (REORDERING (CNF_EQUIV_POS1 :args _let_31) :args ((or (not _let_5) _let_12 _let_29))) _let_28 (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_24) (CONG (REFL :args (_let_23)) (REFL :args (_let_6)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_30)) :args ((or _let_6 _let_8 _let_23))) _let_22 (REORDERING (CNF_EQUIV_NEG1 :args _let_16) :args ((or _let_6 _let_5 _let_7))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_35) (EQUIV_ELIM1 _let_34) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_31) (CONG (REFL :args (_let_29)) (REFL :args (_let_5)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_30)) :args ((or _let_5 _let_11 _let_29))) _let_28 (REORDERING (CNF_EQUIV_POS1 :args _let_24) :args ((or _let_15 _let_9 _let_23))) _let_22 (CNF_EQUIV_NEG2 :args _let_16) :args ((or _let_7 _let_15) true _let_14 false _let_11 false _let_13 true _let_8 false _let_10 true _let_5)) :args (_let_7 false _let_14 true _let_11 false _let_13 false _let_8 false _let_10 false _let_5 true _let_6)) :args (_let_2 false _let_7)))) (let ((_let_37 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_38 (not _let_37))) (let ((_let_39 (forall ((Xx0 $$unsorted)) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx0)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) Xx0))))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_3 _let_40 _let_38))) (let ((_let_42 (not _let_3))) (let ((_let_43 (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 $$unsorted)) (or (not (@ S Xx1)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx1)))) (not (@ S Xx0)))))))) Xx))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (and _let_41 _let_44))) (let ((_let_46 (not _let_41))) (let ((_let_47 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_48 (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx0 $$unsorted)) (or (not (@ S Xx0)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx0)))) (not (@ S SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_49 (not _let_48))) (let ((_let_50 (= _let_49 _let_47))) (let ((_let_51 (forall ((Xx (-> $$unsorted Bool)) (BOUND_VARIABLE_775 $$unsorted)) (or (not (forall ((Xx0 $$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_775)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 S) Xx2)))) (not (@ S Xx1))))))) BOUND_VARIABLE_775))))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_45 _let_50))) (let ((_let_54 (forall ((K (-> (-> $$unsorted Bool) $$unsorted Bool)) (BOUND_VARIABLE_933 $$unsorted) (BOUND_VARIABLE_919 (-> $$unsorted Bool)) (BOUND_VARIABLE_917 $$unsorted)) (or (not (forall ((Xx (-> $$unsorted Bool)) (BOUND_VARIABLE_775 $$unsorted)) (or (not (forall ((Xx0 $$unsorted)) (or (not (@ Xx Xx0)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) Xx1)))) (not (@ S Xx0)))))))) (not (@ (@ K Xx) BOUND_VARIABLE_775)) (@ (@ K (lambda ((Xx1 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx2 $$unsorted)) (or (not (@ S Xx2)) (@ (@ K S) Xx2)))) (not (@ S Xx1))))))) BOUND_VARIABLE_775)))) (and (or (@ (@ K (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) Xx1)))) (not (@ S Xx0))))))) BOUND_VARIABLE_917) (not (forall ((Xx0 $$unsorted)) (or (not (@ BOUND_VARIABLE_919 Xx0)) (@ (@ K BOUND_VARIABLE_919) Xx0)))) (not (@ BOUND_VARIABLE_919 BOUND_VARIABLE_917))) (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) Xx1)))) (not (@ S Xx0))))))) Xx)) (@ (@ K (@ K (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) Xx1)))) (not (@ S Xx0)))))))) Xx))))) (= (@ (@ K (lambda ((Xx0 $$unsorted)) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx1 $$unsorted)) (or (not (@ S Xx1)) (@ (@ K S) Xx1)))) (not (@ S Xx0))))))) BOUND_VARIABLE_933) (not (forall ((S (-> $$unsorted Bool))) (or (not (forall ((Xx0 $$unsorted)) (or (not (@ S Xx0)) (@ (@ K S) Xx0)))) (not (@ S BOUND_VARIABLE_933)))))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (forall ((u (-> $$unsorted Bool)) (e Bool) (i $$unsorted)) (not (forall ((v (-> $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_57 (forall ((u (-> (-> $$unsorted Bool) $$unsorted 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_let_263)) :args (true _let_262)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_3))) _let_170 (REFL :args (_let_261)) :args _let_30)) :args ((or _let_3 _let_261 _let_169))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_242)) :args ((or _let_4 _let_239 _let_241 (not _let_242)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_259)) :args ((or _let_38 _let_238 (not _let_259)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 2)) (CONG _let_252 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_30)) :args ((or _let_37 _let_41))) _let_237 :args (_let_37 true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_260) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_ENUM)) :args _let_260) (CONG (REFL :args _let_260) (CONG _let_67 _let_243 :args _let_30) :args _let_60))) _let_253 :args (_let_259 false _let_39)) :args (_let_238 false _let_37 false _let_259)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_244)) :args _let_244) (CONG _let_245 (CONG (CONG _let_257 (REFL :args (_let_247)) :args _let_30) :args _let_61) :args _let_60))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_241) _let_240))) (REFL :args ((not _let_250))) :args _let_30)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_258) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING)) :args _let_258) (CONG (REFL :args _let_258) (CONG (REFL :args (_let_254)) _let_257 :args _let_30) :args _let_60))) (REORDERING (CNF_OR_POS :args (_let_255)) :args ((or _let_249 _let_254 (not _let_255)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_250 1)) (CONG _let_256 (MACRO_SR_PRED_INTRO :args ((= (not _let_247) _let_246))) :args _let_30)) :args ((or _let_246 _let_250))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_250 0)) (CONG _let_256 (MACRO_SR_PRED_INTRO :args ((= (not _let_249) _let_248))) :args _let_30)) :args ((or _let_248 _let_250))) :args ((or _let_250 _let_254) true _let_255 false _let_246 false _let_248)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_39 (= Xx0 Xx1)))) _let_253 :args (_let_251 false _let_39)) :args (_let_250 false _let_251)) :args (_let_240 false _let_250)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_191 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_190)) :args _let_188) (CONG _let_189 (CONG _let_245 (CONG _let_243 :args _let_61) (TRANS (CONG _let_185 _let_68 :args _let_64) (THEORY_PREPROCESS :args ((= (@ _let_184 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_4)))) :args _let_30) :args _let_60))) _let_183 :args (_let_242 false _let_51)) :args (_let_4 false _let_238 false _let_240 false _let_242)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 0)) _let_237 :args (_let_42 true _let_41)) _let_36 :args (false false _let_4 true _let_3 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 36.29/36.54 )
% 36.29/36.54 % SZS output end Proof for SEV254^5
% 36.29/36.54 % cvc5---1.0.5 exiting
% 36.29/36.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------