TSTP Solution File: ALG272^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG272^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 : Wed Aug 30 16:09:09 EDT 2023
% Result : Theorem 15.86s 16.03s
% Output : Proof 15.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ALG272^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.15/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n016.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 : Mon Aug 28 03:08:29 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 % File : ALG272^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.22/0.52 % Domain : General Algebra
% 0.22/0.52 % Problem : TPS problem EQUIV-01-02
% 0.22/0.52 % Version : Especial.
% 0.22/0.52 % English :
% 0.22/0.52
% 0.22/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.52 % Source : [Bro09]
% 0.22/0.52 % Names : tps_0531 [Bro09]
% 0.22/0.52 % : EQUIV-01-02 [TPS]
% 0.22/0.52
% 0.22/0.52 % Status : Theorem
% 0.22/0.52 % Rating : 0.46 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.22/0.52 % Syntax : Number of formulae : 16 ( 7 unt; 8 typ; 7 def)
% 0.22/0.52 % Number of atoms : 29 ( 14 equ; 0 cnn)
% 0.22/0.52 % Maximal formula atoms : 2 ( 3 avg)
% 0.22/0.52 % Number of connectives : 41 ( 0 ~; 0 |; 6 &; 34 @)
% 0.22/0.52 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.22/0.52 % Maximal formula depth : 6 ( 2 avg)
% 0.22/0.52 % Number of types : 2 ( 1 usr)
% 0.22/0.52 % Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% 0.22/0.52 % Number of symbols : 8 ( 7 usr; 0 con; 1-2 aty)
% 0.22/0.52 % Number of variables : 24 ( 13 ^; 9 !; 2 ?; 24 :)
% 0.22/0.52 % SPC : TH0_THM_EQU_NAR
% 0.22/0.52
% 0.22/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.52 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.22/0.52 % : v5.3.0 - Fixed tType to $tType from last bugfixes.
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 thf(g_type,type,
% 0.22/0.52 g: $tType ).
% 0.22/0.52
% 0.22/0.52 thf(cGROUP1_type,type,
% 0.22/0.52 cGROUP1: ( g > g > g ) > g > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGROUP2_type,type,
% 0.22/0.52 cGROUP2: ( g > g > g ) > g > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_ASSOC_type,type,
% 0.22/0.52 cGRP_ASSOC: ( g > g > g ) > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_INVERSE_type,type,
% 0.22/0.52 cGRP_INVERSE: ( g > g > g ) > g > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_LEFT_INVERSE_type,type,
% 0.22/0.52 cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_LEFT_UNIT_type,type,
% 0.22/0.52 cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_UNIT_type,type,
% 0.22/0.52 cGRP_UNIT: ( g > g > g ) > g > $o ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_ASSOC_def,definition,
% 0.22/0.52 ( cGRP_ASSOC
% 0.22/0.52 = ( ^ [Xf: g > g > g] :
% 0.22/0.52 ! [Xa: g,Xb: g,Xc: g] :
% 0.22/0.52 ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
% 0.22/0.52 = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_INVERSE_def,definition,
% 0.22/0.52 ( cGRP_INVERSE
% 0.22/0.52 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ! [Xa: g] :
% 0.22/0.52 ? [Xb: g] :
% 0.22/0.52 ( ( ( Xf @ Xa @ Xb )
% 0.22/0.52 = Xe )
% 0.22/0.52 & ( ( Xf @ Xb @ Xa )
% 0.22/0.52 = Xe ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_LEFT_INVERSE_def,definition,
% 0.22/0.52 ( cGRP_LEFT_INVERSE
% 0.22/0.52 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ! [Xa: g] :
% 0.22/0.52 ? [Xb: g] :
% 0.22/0.52 ( ( Xf @ Xb @ Xa )
% 0.22/0.52 = Xe ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_LEFT_UNIT_def,definition,
% 0.22/0.52 ( cGRP_LEFT_UNIT
% 0.22/0.52 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ! [Xa: g] :
% 0.22/0.52 ( ( Xf @ Xe @ Xa )
% 0.22/0.52 = Xa ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cGRP_UNIT_def,definition,
% 0.22/0.52 ( cGRP_UNIT
% 0.22/0.52 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ! [Xa: g] :
% 0.22/0.52 ( ( ( Xf @ Xe @ Xa )
% 0.22/0.52 = Xa )
% 0.22/0.52 & ( ( Xf @ Xa @ Xe )
% 0.22/0.52 = Xa ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cGROUP1_def,definition,
% 0.22/0.52 ( cGROUP1
% 0.22/0.52 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ( ( cGRP_ASSOC @ Xf )
% 0.22/0.52 & ( cGRP_UNIT @ Xf @ Xe )
% 0.22/0.52 & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cGROUP2_def,definition,
% 0.22/0.52 ( cGROUP2
% 0.22/0.52 = ( ^ [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ( ( cGRP_ASSOC @ Xf )
% 0.22/0.52 & ( cGRP_LEFT_UNIT @ Xf @ Xe )
% 0.22/0.52 & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ) ).
% 0.22/0.52
% 0.22/0.52 thf(cEQUIV_01_02,conjecture,
% 0.22/0.52 ! [Xf: g > g > g,Xe: g] :
% 0.22/0.52 ( ( cGROUP1 @ Xf @ Xe )
% 0.22/0.52 <=> ( cGROUP2 @ Xf @ Xe ) ) ).
% 0.22/0.52
% 0.22/0.52 %------------------------------------------------------------------------------
% 0.22/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.wnKGIqRG2i/cvc5---1.0.5_5171.p...
% 0.22/0.52 (declare-sort $$unsorted 0)
% 0.22/0.52 (declare-sort tptp.g 0)
% 15.86/16.03 (declare-fun tptp.cGROUP1 ((-> tptp.g tptp.g tptp.g) tptp.g) Bool)
% 15.86/16.03 (declare-fun tptp.cGROUP2 ((-> tptp.g tptp.g tptp.g) tptp.g) Bool)
% 15.86/16.03 (declare-fun tptp.cGRP_ASSOC ((-> tptp.g tptp.g tptp.g)) Bool)
% 15.86/16.03 (declare-fun tptp.cGRP_INVERSE ((-> tptp.g tptp.g tptp.g) tptp.g) Bool)
% 15.86/16.03 (declare-fun tptp.cGRP_LEFT_INVERSE ((-> tptp.g tptp.g tptp.g) tptp.g) Bool)
% 15.86/16.03 (declare-fun tptp.cGRP_LEFT_UNIT ((-> tptp.g tptp.g tptp.g) tptp.g) Bool)
% 15.86/16.03 (declare-fun tptp.cGRP_UNIT ((-> tptp.g tptp.g tptp.g) tptp.g) Bool)
% 15.86/16.03 (assert (= tptp.cGRP_ASSOC (lambda ((Xf (-> tptp.g tptp.g tptp.g))) (forall ((Xa tptp.g) (Xb tptp.g) (Xc tptp.g)) (let ((_let_1 (@ Xf Xa))) (= (@ (@ Xf (@ _let_1 Xb)) Xc) (@ _let_1 (@ (@ Xf Xb) Xc))))))))
% 15.86/16.03 (assert (= tptp.cGRP_INVERSE (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (exists ((Xb tptp.g)) (and (= (@ (@ Xf Xa) Xb) Xe) (= (@ (@ Xf Xb) Xa) Xe)))))))
% 15.86/16.03 (assert (= tptp.cGRP_LEFT_INVERSE (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (exists ((Xb tptp.g)) (= (@ (@ Xf Xb) Xa) Xe))))))
% 15.86/16.03 (assert (= tptp.cGRP_LEFT_UNIT (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (= (@ (@ Xf Xe) Xa) Xa)))))
% 15.86/16.03 (assert (= tptp.cGRP_UNIT (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (and (= (@ (@ Xf Xe) Xa) Xa) (= (@ (@ Xf Xa) Xe) Xa))))))
% 15.86/16.03 (assert (= tptp.cGROUP1 (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (and (@ tptp.cGRP_ASSOC Xf) (@ (@ tptp.cGRP_UNIT Xf) Xe) (@ (@ tptp.cGRP_INVERSE Xf) Xe)))))
% 15.86/16.03 (assert (= tptp.cGROUP2 (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (and (@ tptp.cGRP_ASSOC Xf) (@ (@ tptp.cGRP_LEFT_UNIT Xf) Xe) (@ (@ tptp.cGRP_LEFT_INVERSE Xf) Xe)))))
% 15.86/16.03 (assert (not (forall ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (= (@ (@ tptp.cGROUP1 Xf) Xe) (@ (@ tptp.cGROUP2 Xf) Xe)))))
% 15.86/16.03 (set-info :filename cvc5---1.0.5_5171)
% 15.86/16.03 (check-sat-assuming ( true ))
% 15.86/16.03 ------- get file name : TPTP file name is ALG272^5
% 15.86/16.03 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5171.smt2...
% 15.86/16.03 --- Run --ho-elim --full-saturate-quant at 10...
% 15.86/16.03 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 15.86/16.03 % SZS status Theorem for ALG272^5
% 15.86/16.03 % SZS output start Proof for ALG272^5
% 15.86/16.03 (
% 15.86/16.03 (let ((_let_1 (not (forall ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (= (@ (@ tptp.cGROUP1 Xf) Xe) (@ (@ tptp.cGROUP2 Xf) Xe)))))) (let ((_let_2 (= tptp.cGROUP2 (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (and (@ tptp.cGRP_ASSOC Xf) (@ (@ tptp.cGRP_LEFT_UNIT Xf) Xe) (@ (@ tptp.cGRP_LEFT_INVERSE Xf) Xe)))))) (let ((_let_3 (= tptp.cGROUP1 (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (and (@ tptp.cGRP_ASSOC Xf) (@ (@ tptp.cGRP_UNIT Xf) Xe) (@ (@ tptp.cGRP_INVERSE Xf) Xe)))))) (let ((_let_4 (= tptp.cGRP_UNIT (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (and (= (@ (@ Xf Xe) Xa) Xa) (= (@ (@ Xf Xa) Xe) Xa))))))) (let ((_let_5 (= tptp.cGRP_LEFT_UNIT (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (= (@ (@ Xf Xe) Xa) Xa)))))) (let ((_let_6 (= tptp.cGRP_LEFT_INVERSE (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (exists ((Xb tptp.g)) (= (@ (@ Xf Xb) Xa) Xe))))))) (let ((_let_7 (= tptp.cGRP_INVERSE (lambda ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (forall ((Xa tptp.g)) (exists ((Xb tptp.g)) (and (= (@ (@ Xf Xa) Xb) Xe) (= (@ (@ Xf Xb) Xa) Xe)))))))) (let ((_let_8 (= tptp.cGRP_ASSOC (lambda ((Xf (-> tptp.g tptp.g tptp.g))) (forall ((Xa tptp.g) (Xb tptp.g) (Xc tptp.g)) (let ((_let_1 (@ Xf Xa))) (= (@ (@ Xf (@ _let_1 Xb)) Xc) (@ _let_1 (@ (@ Xf Xb) Xc))))))))) (let ((_let_9 (forall ((Xa tptp.g)) (= Xa (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) Xa))))) (let ((_let_10 (forall ((Xa tptp.g)) (not (forall ((Xb tptp.g)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) Xa)))))))) (let ((_let_11 (forall ((Xa tptp.g) (Xb tptp.g) (Xc tptp.g)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xa))) (= (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) Xc)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_3 _let_1 Xb)) Xc)))))) (let ((_let_12 (and _let_11 _let_9 _let_10))) (let ((_let_13 (forall ((BOUND_VARIABLE_733 tptp.g)) (= BOUND_VARIABLE_733 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) BOUND_VARIABLE_733))))) (let ((_let_14 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (ho_3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169 _let_15))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596 (ho_3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596)))) (let ((_let_18 (forall ((BOUND_VARIABLE_739 tptp.g)) (= BOUND_VARIABLE_739 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 BOUND_VARIABLE_739) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_19 (forall ((Xa tptp.g)) (not (forall ((Xb tptp.g)) (or (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xa) Xb))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) Xa))))))))) (let ((_let_20 (and _let_11 _let_19 _let_13 _let_18))) (let ((_let_21 (= _let_20 _let_12))) (let ((_let_22 (forall ((Xb tptp.g)) (or (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169) Xb))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169))))))) (let ((_let_23 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596))) (let ((_let_24 (ho_3 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169))) (let ((_let_25 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24))) (let ((_let_26 (not _let_25))) (let ((_let_27 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596))) (let ((_let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_27))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_26))) (let ((_let_31 (ho_3 _let_23 _let_27))) (let ((_let_32 (= _let_31 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_24) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596)))) (let ((_let_33 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4216))) (let ((_let_34 (ho_3 _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596))) (let ((_let_35 (= (ho_3 _let_33 _let_31) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_34) _let_27)))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_34))) (let ((_let_37 (= (ho_3 _let_14 _let_27) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596)))) (let ((_let_38 (not _let_13))) (let ((_let_39 (ALPHA_EQUIV :args (_let_13 (= BOUND_VARIABLE_733 Xa))))) (let ((_let_40 (_let_13))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596 QUANTIFIERS_INST_ENUM))) (let ((_let_43 (forall ((Xb tptp.g)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_44 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) _let_45))) (let ((_let_47 (forall ((Xb tptp.g)) (or (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xb))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_48 (not _let_12))) (let ((_let_49 (or))) (let ((_let_50 (_let_43))) (let ((_let_51 (not _let_10))) (let ((_let_52 (_let_51))) (let ((_let_53 (forall ((BOUND_VARIABLE_969 |u_(-> tptp.g tptp.g tptp.g)|) (Xe tptp.g)) (let ((_let_1 (forall ((Xa tptp.g) (Xb tptp.g) (Xc tptp.g)) (let ((_let_1 (ho_2 BOUND_VARIABLE_969 Xa))) (= (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_969 Xb) Xc)) (ho_3 (ho_2 BOUND_VARIABLE_969 (ho_3 _let_1 Xb)) Xc)))))) (= (and _let_1 (forall ((Xa tptp.g)) (not (forall ((Xb tptp.g)) (or (not (= Xe (ho_3 (ho_2 BOUND_VARIABLE_969 Xa) Xb))) (not (= Xe (ho_3 (ho_2 BOUND_VARIABLE_969 Xb) Xa))))))) (forall ((BOUND_VARIABLE_733 tptp.g)) (= BOUND_VARIABLE_733 (ho_3 (ho_2 BOUND_VARIABLE_969 Xe) BOUND_VARIABLE_733))) (forall ((BOUND_VARIABLE_739 tptp.g)) (= BOUND_VARIABLE_739 (ho_3 (ho_2 BOUND_VARIABLE_969 BOUND_VARIABLE_739) Xe)))) (and _let_1 (forall ((Xa tptp.g)) (= Xa (ho_3 (ho_2 BOUND_VARIABLE_969 Xe) Xa))) (forall ((Xa tptp.g)) (not (forall ((Xb tptp.g)) (not (= Xe (ho_3 (ho_2 BOUND_VARIABLE_969 Xb) Xa)))))))))))) (let ((_let_54 (not _let_21))) (let ((_let_55 (not _let_53))) (let ((_let_56 (ASSUME :args (_let_8)))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_58 _let_57 _let_56) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_61 _let_60 _let_59 _let_58 _let_57 _let_56) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xf (-> tptp.g tptp.g tptp.g)) (Xe tptp.g)) (let ((_let_1 (forall ((Xa tptp.g) (Xb tptp.g) (Xc tptp.g)) (let ((_let_1 (@ Xf Xa))) (= (@ (@ Xf (@ _let_1 Xb)) Xc) (@ _let_1 (@ (@ Xf Xb) Xc))))))) (= (and _let_1 (forall ((Xa tptp.g)) (= Xa (@ (@ Xf Xe) Xa))) (forall ((Xa tptp.g)) (not (forall ((Xb tptp.g)) (not (= Xe (@ (@ Xf Xb) Xa))))))) (and _let_1 (forall ((Xa tptp.g)) (not (forall ((Xb tptp.g)) (or (not (= Xe (@ (@ Xf Xa) Xb))) (not (= Xe (@ (@ Xf Xb) Xa))))))) (forall ((BOUND_VARIABLE_733 tptp.g)) (= BOUND_VARIABLE_733 (@ (@ Xf Xe) BOUND_VARIABLE_733))) (forall ((BOUND_VARIABLE_739 tptp.g)) (= BOUND_VARIABLE_739 (@ (@ Xf BOUND_VARIABLE_739) Xe)))))))) _let_55))))))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_53))) (REFL :args (_let_54)) :args _let_49)) _let_62 :args (_let_54 true _let_53)))) (let ((_let_64 (_let_21))) (let ((_let_65 (REORDERING (CNF_EQUIV_NEG1 :args _let_64) :args ((or _let_20 _let_12 _let_21))))) (let ((_let_66 (not _let_20))) (let ((_let_67 (_let_19))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (not _let_47))) (let ((_let_70 (_let_69))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_70)) :args _let_70)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_47))) (REFL :args ((not _let_46))) :args _let_49)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_ENUM)) :args _let_67)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_49)) :args ((or _let_44 _let_46))) (REORDERING (CNF_AND_POS :args (_let_20 1)) :args ((or _let_19 _let_66))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_50) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_50)) _let_65 _let_63 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_52)) :args _let_52) (REWRITE :args ((=> _let_51 (not (not _let_43))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_10))) (REFL :args _let_50) :args _let_49)) (REORDERING (CNF_AND_POS :args (_let_12 2)) :args ((or _let_10 _let_48))) :args (_let_10 true _let_47 false _let_46 false _let_19 true _let_44 false _let_20 true _let_21 false _let_43 true _let_12)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST _let_65 _let_63 (REORDERING (CNF_AND_POS :args (_let_12 0)) :args ((or _let_11 _let_48))) (REORDERING (CNF_AND_POS :args (_let_20 0)) :args ((or _let_11 _let_66))) :args (_let_11 true _let_21 true _let_12 true _let_20)))) (let ((_let_73 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (let ((_let_74 (ho_3 _let_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_166))) (let ((_let_75 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_166) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (let ((_let_76 (= (ho_3 _let_73 _let_75) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_74) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)))) (let ((_let_77 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 (ho_3 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)))) (let ((_let_78 (forall ((Xb tptp.g)) (or (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) Xb))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))))))) (let ((_let_79 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 (ho_3 _let_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_80 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_75))) (let ((_let_81 (not _let_80))) (let ((_let_82 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_74))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_81))) (let ((_let_85 (not _let_19))) (let ((_let_86 (_let_11))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_ENUM))) (let ((_let_89 (not _let_18))) (let ((_let_90 (_let_89))) (let ((_let_91 (not _let_78))) (let ((_let_92 (_let_91))) (let ((_let_93 (REFL :args (_let_84)))) (let ((_let_94 (and _let_77 _let_82 _let_80 _let_76))) (let ((_let_95 (APPLY_UF ho_3))) (let ((_let_96 (ASSUME :args (_let_80)))) (let ((_let_97 (ASSUME :args (_let_76)))) (let ((_let_98 (APPLY_UF ho_2))) (let ((_let_99 (ASSUME :args (_let_82)))) (let ((_let_100 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_101 (ASSUME :args (_let_77)))) (let ((_let_102 (_let_22))) (let ((_let_103 (_let_85))) (let ((_let_104 (forall ((Xb tptp.g)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169)))))) (let ((_let_105 (not _let_104))) (let ((_let_106 (_let_10))) (let ((_let_107 (ASSUME :args _let_106))) (let ((_let_108 (_let_25))) (let ((_let_109 (_let_105))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_109)) :args _let_109) (REWRITE :args ((=> _let_105 (not _let_26)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_105) _let_104))) (REFL :args _let_108) :args _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169 QUANTIFIERS_INST_ENUM)) :args _let_106)) _let_71 :args (_let_105 false _let_10)) :args (_let_25 true _let_104)))) (let ((_let_111 (forall ((Xb tptp.g)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xb) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596)))))) (let ((_let_112 (not _let_111))) (let ((_let_113 (_let_36))) (let ((_let_114 (not _let_36))) (let ((_let_115 (_let_112))) (let ((_let_116 (and _let_16 _let_25 _let_17 _let_36 _let_32 _let_35 _let_37))) (let ((_let_117 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596)))) (let ((_let_118 (ASSUME :args (_let_16)))) (let ((_let_119 (ASSUME :args (_let_37)))) (let ((_let_120 (ASSUME :args _let_113))) (let ((_let_121 (ASSUME :args (_let_35)))) (let ((_let_122 (ASSUME :args (_let_32)))) (let ((_let_123 (ASSUME :args _let_108))) (let ((_let_124 (ASSUME :args (_let_17)))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_116)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_118 _let_119 _let_120 _let_121 _let_122 _let_123 _let_124) (SCOPE (TRANS _let_120 (CONG (REFL :args (_let_33)) (TRANS (SYMM (SYMM _let_124)) (CONG (CONG _let_100 (SYMM (SYMM _let_123)) :args _let_98) _let_117 :args _let_95) (SYMM _let_122)) :args _let_95) (SYMM (SYMM _let_121)) (CONG (CONG _let_100 (SYMM _let_120) :args _let_98) (REFL :args (_let_27)) :args _let_95) (SYMM (SYMM _let_119)) (CONG (CONG _let_100 (SYMM _let_118) :args _let_98) _let_117 :args _let_95)) :args (_let_16 _let_37 _let_36 _let_35 _let_32 _let_25 _let_17))) :args (_let_16 _let_25 _let_17 _let_36 _let_32 _let_35 _let_37))) :args (true _let_116)) :args ((or (not _let_16) _let_26 (not _let_17) _let_28 _let_114 (not _let_32) (not _let_35) (not _let_37)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_86)) _let_72 :args (_let_37 false _let_11)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_115)) :args _let_115) (REWRITE :args ((=> _let_112 (not _let_114)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_112) _let_111))) (REFL :args _let_113) :args _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args _let_42) :args _let_106)) _let_71 :args (_let_112 false _let_10)) :args (_let_36 true _let_111)) _let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4216 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596 _let_27 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_86)) _let_72 :args (_let_35 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_596 QUANTIFIERS_INST_ENUM)) :args _let_86)) _let_72 :args (_let_32 false _let_11)) (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_26 _let_29 (not _let_30)))) _let_110 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_102) :args _let_42) :args _let_102)) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_103)) :args _let_103) (REWRITE :args ((=> _let_85 (not (not _let_22))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_19))) (REFL :args _let_102) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_94)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_97 _let_96 _let_101) (SCOPE (TRANS (SYMM (SYMM _let_101)) (CONG (CONG _let_100 (SYMM (SYMM _let_99)) :args _let_98) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)) :args _let_95) (SYMM _let_97) (CONG (REFL :args (_let_73)) (SYMM _let_96) :args _let_95)) :args (_let_82 _let_76 _let_80 _let_77))) :args (_let_77 _let_82 _let_80 _let_76))) :args (true _let_94)) :args ((or _let_79 (not _let_77) _let_83 _let_81 (not _let_76)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 1)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_80))) :args _let_49)) :args ((or _let_80 _let_84))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_84 0)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_82))) :args _let_49)) :args ((or _let_82 _let_84))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_92)) :args _let_92)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_78))) (REFL :args ((not _let_84))) :args _let_49)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_90)) :args _let_90)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_18))) (REFL :args ((not _let_79))) :args _let_49)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args _let_88) :args _let_67)) (CNF_AND_NEG :args (_let_20)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args _let_88) :args _let_40)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_166 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_86)) :args ((or _let_20 (not _let_11) _let_85 _let_38) false _let_80 false _let_82 true _let_84 true _let_79 true _let_78 true _let_18 false _let_77 false _let_76)) _let_72 (CNF_EQUIV_NEG2 :args _let_64) _let_63 (CNF_AND_NEG :args (_let_12)) _let_72 _let_71 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args _let_42) :args _let_40)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_169 QUANTIFIERS_INST_CBQI_PROP)) :args _let_40)) (REORDERING (EQUIV_ELIM1 _let_39) :args ((or _let_9 _let_38))) :args (_let_38 false _let_37 false _let_36 false _let_25 false _let_35 false _let_32 true _let_28 false _let_25 false _let_30 false _let_22 true _let_19 false _let_11 true _let_20 true _let_21 false _let_12 false _let_11 false _let_10 false _let_17 false _let_16 false _let_9)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_12 1)) :args ((or _let_9 _let_48))) (MACRO_RESOLUTION_TRUST _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_20 2)) :args ((or _let_13 _let_66))) _let_125 :args (_let_66 true _let_13)) _let_63 :args (_let_12 true _let_20 true _let_21)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_39) _let_125 :args ((not _let_9) true _let_13)) :args (false false _let_12 true _let_9)) :args (_let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.86/16.04 )
% 15.86/16.04 % SZS output end Proof for ALG272^5
% 15.86/16.04 % cvc5---1.0.5 exiting
% 15.86/16.04 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------