%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COM022+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 18:37:01 EDT 2023

% Result   : Theorem 6.97s 7.19s
% Output   : Proof 7.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : COM022+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 29 13:03:43 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 6.97/7.19  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.nEenl2z5Wn/cvc5---1.0.5_21194.p...
% 6.97/7.19  ------- get file name : TPTP file name is COM022+4
% 6.97/7.19  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21194.smt2...
% 6.97/7.19  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.97/7.19  % SZS status Theorem for COM022+4
% 6.97/7.19  % SZS output start Proof for COM022+4
% 6.97/7.19  (
% 6.97/7.19  (let ((_let_1 (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xc))) (let ((_let_2 (tptp.aReductOfIn0 tptp.xc tptp.xa tptp.xR))) (let ((_let_3 (= tptp.xa tptp.xc))) (let ((_let_4 (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xb))) (let ((_let_5 (tptp.aReductOfIn0 tptp.xb tptp.xa tptp.xR))) (let ((_let_6 (= tptp.xa tptp.xb))) (let ((_let_7 (not (=> (=> (and (or _let_5 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aReductOfIn0 W0 tptp.xa tptp.xR) (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xb))) _let_4) (or _let_2 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aReductOfIn0 W0 tptp.xa tptp.xR) (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xc))) _let_1)) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aReductOfIn0 W0 tptp.xa tptp.xR) (or (= W0 tptp.xb) (and (or (tptp.aReductOfIn0 tptp.xb W0 tptp.xR) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (tptp.aReductOfIn0 W1 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W1 tptp.xR tptp.xb)))) (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xb))) (tptp.sdtmndtasgtdt0 W0 tptp.xR tptp.xb) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (tptp.aReductOfIn0 W1 tptp.xa tptp.xR) (or (= W1 tptp.xc) (and (or (tptp.aReductOfIn0 tptp.xc W1 tptp.xR) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (tptp.aReductOfIn0 W2 W1 tptp.xR) (tptp.sdtmndtplgtdt0 W2 tptp.xR tptp.xc)))) (tptp.sdtmndtplgtdt0 W1 tptp.xR tptp.xc))) (tptp.sdtmndtasgtdt0 W1 tptp.xR tptp.xc) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (or (= W0 W2) (and (or (tptp.aReductOfIn0 W2 W0 tptp.xR) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W3 tptp.xR W2)))) (tptp.sdtmndtplgtdt0 W0 tptp.xR W2))) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2) (or (= W1 W2) (and (or (tptp.aReductOfIn0 W2 W1 tptp.xR) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W1 tptp.xR) (tptp.sdtmndtplgtdt0 W3 tptp.xR W2)))) (tptp.sdtmndtplgtdt0 W1 tptp.xR W2))) (tptp.sdtmndtasgtdt0 W1 tptp.xR W2) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (or (= W2 W3) (and (or (tptp.aReductOfIn0 W3 W2 tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 W2 tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 W2 tptp.xR W3))) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3) (not (exists ((W4 $$unsorted)) (tptp.aReductOfIn0 W4 W3 tptp.xR))) (tptp.aNormalFormOfIn0 W3 W2 tptp.xR) (or (= tptp.xb W3) (and (or (tptp.aReductOfIn0 W3 tptp.xb tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 tptp.xb tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR W3))) (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR W3) (or (= tptp.xc W3) (and (or (tptp.aReductOfIn0 W3 tptp.xc tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 tptp.xc tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR W3))) (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR W3)))))))))) (=> (and (or _let_6 (and (or _let_5 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aReductOfIn0 W0 tptp.xa tptp.xR) (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xb)))) _let_4)) (tptp.sdtmndtasgtdt0 tptp.xa tptp.xR tptp.xb) (or _let_3 (and (or _let_2 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aReductOfIn0 W0 tptp.xa tptp.xR) (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xc)))) _let_1)) (tptp.sdtmndtasgtdt0 tptp.xa tptp.xR tptp.xc)) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (= tptp.xb W0) (tptp.aReductOfIn0 W0 tptp.xb tptp.xR) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (tptp.aReductOfIn0 W1 tptp.xb tptp.xR) (tptp.sdtmndtplgtdt0 W1 tptp.xR W0))) (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR W0) (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR W0)) (or (= tptp.xc W0) (tptp.aReductOfIn0 W0 tptp.xc tptp.xR) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (tptp.aReductOfIn0 W1 tptp.xc tptp.xR) (tptp.sdtmndtplgtdt0 W1 tptp.xR W0))) (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR W0) (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR W0))))))))) (let ((_let_8 (tptp.aElement0 tptp.xc))) (let ((_let_9 (tptp.aElement0 tptp.xb))) (let ((_let_10 (tptp.aElement0 tptp.xa))) (let ((_let_11 (and _let_10 _let_9 _let_8))) (let ((_let_12 (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR tptp.xc))) (let ((_let_13 (not _let_12))) (let ((_let_14 (not (tptp.aReductOfIn0 tptp.xc tptp.xb tptp.xR)))) (let ((_let_15 (not _let_8))) (let ((_let_16 (not (= tptp.xb tptp.xc)))) (let ((_let_17 (and _let_16 _let_14 (or _let_15 _let_14 (not (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR tptp.xc))) _let_13 (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR tptp.xc))))) (let ((_let_18 (or _let_15 _let_17))) (let ((_let_19 (2))) (let ((_let_20 (ASSUME :args (_let_11)))) (let ((_let_21 (not _let_17))) (let ((_let_22 (and (or _let_5 (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aReductOfIn0 W0 tptp.xa tptp.xR)) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xb)))))) _let_4))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_5 (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aReductOfIn0 W0 tptp.xa tptp.xR)) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xb))))) _let_4))) (let ((_let_25 (not _let_4))) (let ((_let_26 (or _let_2 (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aReductOfIn0 W0 tptp.xa tptp.xR)) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xc))))) _let_1))) (let ((_let_27 (and _let_24 _let_26))) (let ((_let_28 (and (or _let_2 (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aReductOfIn0 W0 tptp.xa tptp.xR)) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xc)))))) _let_1))) (let ((_let_29 (not (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xa)))) (let ((_let_30 (not (tptp.aReductOfIn0 tptp.xa tptp.xc tptp.xR)))) (let ((_let_31 (not _let_10))) (let ((_let_32 (not _let_3))) (let ((_let_33 (and _let_32 _let_30 (or _let_31 _let_30 _let_29) (not (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR tptp.xa)) (not (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR tptp.xa))))) (let ((_let_34 (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR tptp.xb))) (let ((_let_35 (not (tptp.aReductOfIn0 tptp.xa tptp.xb tptp.xR)))) (let ((_let_36 (not _let_6))) (let ((_let_37 (and _let_36 _let_35 (or _let_31 _let_35 _let_29) (not (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR tptp.xa)) (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR tptp.xa))))) (let ((_let_38 (or _let_31 _let_37 _let_33))) (let ((_let_39 (not _let_34))) (let ((_let_40 (not (tptp.aReductOfIn0 tptp.xb tptp.xc tptp.xR)))) (let ((_let_41 (not _let_9))) (let ((_let_42 (and _let_16 _let_40 (or _let_41 _let_40 (not (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR tptp.xb))) _let_39 (not (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR tptp.xb))))) (let ((_let_43 (or _let_41 _let_42))) (let ((_let_44 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2387 $$unsorted) (BOUND_VARIABLE_2377 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (= tptp.xb W0)) (not (tptp.aReductOfIn0 W0 tptp.xb tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2377)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2377 tptp.xb tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2377 tptp.xR W0))) (not (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR W0)) (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR W0))) (and (not (= tptp.xc W0)) (not (tptp.aReductOfIn0 W0 tptp.xc tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2387)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2387 tptp.xc tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2387 tptp.xR W0))) (not (tptp.sdtmndtplgtdt0 tptp.xc tptp.xR W0)) (not (tptp.sdtmndtasgtdt0 tptp.xc tptp.xR W0))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (NOT_IMPLIES_ELIM2 _let_45))) (let ((_let_47 (NOT_NOT_ELIM (NOT_IMPLIES_ELIM2 _let_46)))) (let ((_let_48 (_let_44))) (let ((_let_49 ((not (= (tptp.aElement0 W0) false)) (tptp.aElement0 BOUND_VARIABLE_2377) (tptp.aElement0 BOUND_VARIABLE_2387)))) (let ((_let_50 (ASSUME :args _let_48))) (let ((_let_51 (or))) (let ((_let_52 (ASSUME :args (_let_39)))) (let ((_let_53 (APPLY_UF tptp.sdtmndtplgtdt0))) (let ((_let_54 (REFL :args (tptp.xR)))) (let ((_let_55 (ASSUME :args (_let_3)))) (let ((_let_56 (ASSUME :args (_let_4)))) (let ((_let_57 (0))) (let ((_let_58 (REORDERING (CNF_AND_POS :args (_let_22 1)) :args ((or _let_4 _let_23))))) (let ((_let_59 (NOT_IMPLIES_ELIM1 _let_46))) (let ((_let_60 (AND_ELIM _let_59 :args _let_57))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_28 1)) :args ((or _let_1 (not _let_28)))) (MACRO_RESOLUTION_TRUST (AND_ELIM _let_59 :args _let_19) (MACRO_RESOLUTION_TRUST _let_60 (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_36 (not _let_37)))) _let_58 (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_31 _let_37 _let_33 (not _let_38)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xa tptp.xa tptp.xa QUANTIFIERS_INST_E_MATCHING _let_49)) :args _let_48))) _let_47 :args (_let_38 false _let_44)) (AND_ELIM _let_20 :args _let_57) (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_52 _let_55 _let_56) :args (_let_4 _let_3 _let_39)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_56)) (CONG (SYMM (SYMM _let_55)) _let_54 (REFL :args (tptp.xb)) :args _let_53) (FALSE_INTRO _let_52))) :args (_let_39 _let_3 _let_4)) :args ((not (and _let_4 _let_3 _let_39)) SB_LITERAL))) (CONG (REFL :args (_let_25)) (REFL :args (_let_32)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_34))) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_42 3)) :args ((or _let_39 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_41 _let_42 (not _let_43)))) (AND_ELIM _let_20 :args (1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.xb tptp.xb tptp.xa QUANTIFIERS_INST_E_MATCHING _let_49)) :args _let_48))) _let_47 :args (_let_43 false _let_44)) :args (_let_42 false _let_9 false _let_43)) :args (_let_39 false _let_42)) (REORDERING (CNF_AND_POS :args (_let_33 0)) :args ((or _let_32 (not _let_33)))) :args (_let_32 true _let_6 true _let_22 false _let_37 false _let_38 false _let_10 true _let_4 true _let_34 true _let_33)) :args (_let_28 true _let_3)) :args (_let_1 false _let_28)))) (let ((_let_62 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2176 $$unsorted) (BOUND_VARIABLE_2172 $$unsorted) (BOUND_VARIABLE_2170 $$unsorted) (BOUND_VARIABLE_2168 $$unsorted) (BOUND_VARIABLE_2166 $$unsorted) (BOUND_VARIABLE_2164 $$unsorted) (BOUND_VARIABLE_2162 $$unsorted) (BOUND_VARIABLE_2160 $$unsorted) (BOUND_VARIABLE_2174 $$unsorted) (BOUND_VARIABLE_2148 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aReductOfIn0 W0 tptp.xa tptp.xR)) (and (not (= tptp.xb W0)) (or (and (not (tptp.aReductOfIn0 tptp.xb W0 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2148)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2148 W0 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2148 tptp.xR tptp.xb)))) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR tptp.xb)))) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR tptp.xb)) (not (tptp.aElement0 BOUND_VARIABLE_2160)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2160 tptp.xa tptp.xR)) (and (not (= tptp.xc BOUND_VARIABLE_2160)) (or (and (not (tptp.aReductOfIn0 tptp.xc BOUND_VARIABLE_2160 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2176)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2176 BOUND_VARIABLE_2160 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2176 tptp.xR tptp.xc)))) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2160 tptp.xR tptp.xc)))) (not (tptp.sdtmndtasgtdt0 BOUND_VARIABLE_2160 tptp.xR tptp.xc)) (not (tptp.aElement0 BOUND_VARIABLE_2174)) (and (not (= W0 BOUND_VARIABLE_2174)) (or (and (not (tptp.aReductOfIn0 BOUND_VARIABLE_2174 W0 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2162)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2162 W0 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2162 tptp.xR BOUND_VARIABLE_2174)))) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR BOUND_VARIABLE_2174)))) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR BOUND_VARIABLE_2174)) (and (not (= BOUND_VARIABLE_2160 BOUND_VARIABLE_2174)) (or (and (not (tptp.aReductOfIn0 BOUND_VARIABLE_2174 BOUND_VARIABLE_2160 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2166)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2166 BOUND_VARIABLE_2160 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2166 tptp.xR BOUND_VARIABLE_2174)))) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2160 tptp.xR BOUND_VARIABLE_2174)))) (not (tptp.sdtmndtasgtdt0 BOUND_VARIABLE_2160 tptp.xR BOUND_VARIABLE_2174)) (not (tptp.aElement0 BOUND_VARIABLE_2168)) (and (not (= BOUND_VARIABLE_2168 BOUND_VARIABLE_2174)) (or (and (not (tptp.aReductOfIn0 BOUND_VARIABLE_2168 BOUND_VARIABLE_2174 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2172)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2172 BOUND_VARIABLE_2174 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2172 tptp.xR BOUND_VARIABLE_2168)))) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2174 tptp.xR BOUND_VARIABLE_2168)))) (not (tptp.sdtmndtasgtdt0 BOUND_VARIABLE_2174 tptp.xR BOUND_VARIABLE_2168)) (not (forall ((W4 $$unsorted)) (not (tptp.aReductOfIn0 W4 BOUND_VARIABLE_2168 tptp.xR)))) (not (tptp.aNormalFormOfIn0 BOUND_VARIABLE_2168 BOUND_VARIABLE_2174 tptp.xR)) (and (not (= tptp.xb BOUND_VARIABLE_2168)) (or (and (not (tptp.aReductOfIn0 BOUND_VARIABLE_2168 tptp.xb tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2170)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2170 tptp.xb tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2170 tptp.xR BOUND_VARIABLE_2168)))) (not (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR BOUND_VARIABLE_2168)))) (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR BOUND_VARIABLE_2168)) (and (not (= tptp.xc BOUND_VARIABLE_2168)) (or (and (not (tptp.aReductOfIn0 BOUND_VARIABLE_2168 tptp.xc tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_2164)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_2164 tptp.xc tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_2164 tptp.xR BOUND_VARIABLE_2168)))) 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(or (and (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.xR)) (or (not (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.xR)) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((W4 $$unsorted)) (not (tptp.aReductOfIn0 W4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.xR)))) (not (tptp.aNormalFormOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.xR)) (and _let_73 (or (and _let_72 (or (not (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xb tptp.xR)) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) _let_71)) _let_70 (and _let_68 (or (and _let_67 (or (not (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xc tptp.xR)) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) _let_66)) _let_65))) (let ((_let_77 (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_78 (and _let_73 _let_72 (or _let_75 _let_72 _let_77) _let_71 _let_70))) (let ((_let_79 (and _let_68 _let_67 (or _let_75 _let_67 _let_77) _let_66 _let_65))) (let ((_let_80 (or _let_75 _let_78 _let_79))) (let ((_let_81 (REFL :args (_let_76)))) (let ((_let_82 (not _let_62))) (let ((_let_83 (_let_82))) (let ((_let_84 (and _let_1 _let_6))) (let ((_let_85 (_let_1 _let_6))) (let ((_let_86 (ASSUME :args (_let_1)))) (let ((_let_87 (ASSUME :args 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(CNF_OR_NEG :args (_let_76 19)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_69))) :args _let_51)) :args ((or _let_69 _let_76))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 13)) (CONG _let_81 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_74))) :args _let_51)) :args ((or _let_74 _let_76))) :args (_let_76 false _let_80 true _let_79 true _let_78 false _let_64 false _let_69 false _let_74)) :args (_let_62 false _let_76)) :args (_let_63 false _let_62)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 2)) _let_61 :args (_let_26 false _let_1)) :args ((not _let_24) true _let_27 false _let_26)) :args (_let_25 true _let_24)) :args (_let_23 true _let_4)) :args (_let_6 true _let_22)) :args (_let_12 false _let_1 false _let_6)) :args (_let_21 false _let_12)) (AND_ELIM _let_20 :args _let_19) :args (false false _let_18 true _let_17 false _let_8)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) true)) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aReductOfIn0 W2 W0 W1) (tptp.aElement0 W2))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2)) (=> (tptp.sdtmndtplgtdt0 W0 W1 W2) true))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2)) (= (tptp.sdtmndtplgtdt0 W0 W1 W2) (or (tptp.aReductOfIn0 W2 W0 W1) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 W1) (tptp.sdtmndtplgtdt0 W3 W1 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3)) (=> (and 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$$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isLocallyConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.aReductOfIn0 W2 W1 W0) (tptp.aReductOfIn0 W3 W1 W0)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isTerminating0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2)) (=> (tptp.sdtmndtplgtdt0 W1 W0 W2) (tptp.iLess0 W2 W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1)) (forall ((W2 $$unsorted)) (= (tptp.aNormalFormOfIn0 W2 W0 W1) (and (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 W1 W2) (not (exists ((W3 $$unsorted)) (tptp.aReductOfIn0 W3 W2 W1)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aRewritingSystem0 W0) (tptp.isTerminating0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (exists ((W2 $$unsorted)) (tptp.aNormalFormOfIn0 W2 W1 W0)))))) (tptp.aRewritingSystem0 tptp.xR) (and (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aReductOfIn0 W1 W0 tptp.xR) (tptp.aReductOfIn0 W2 W0 tptp.xR)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (or (= W1 W3) (and (or (tptp.aReductOfIn0 W3 W1 tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 W1 tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 W1 tptp.xR W3))) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (or (= W2 W3) (and (or (tptp.aReductOfIn0 W3 W2 tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 W2 tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 W2 tptp.xR W3))) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))) (tptp.isLocallyConfluent0 tptp.xR) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (or (tptp.aReductOfIn0 W1 W0 tptp.xR) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (tptp.aReductOfIn0 W2 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W2 tptp.xR W1))) (tptp.sdtmndtplgtdt0 W0 tptp.xR W1)) (tptp.iLess0 W1 W0)))) (tptp.isTerminating0 tptp.xR)) _let_11 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (or (= W0 W1) (tptp.aReductOfIn0 W1 W0 tptp.xR) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W3 tptp.xR W1))) (tptp.sdtmndtplgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (or (= W0 W2) (tptp.aReductOfIn0 W2 W0 tptp.xR) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W3 tptp.xR W2))) (tptp.sdtmndtplgtdt0 W0 tptp.xR W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2))) (=> (tptp.iLess0 W0 tptp.xa) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (or (= W1 W3) (and (or (tptp.aReductOfIn0 W3 W1 tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 W1 tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 W1 tptp.xR W3))) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (or (= W2 W3) (and (or (tptp.aReductOfIn0 W3 W2 tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 W2 tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3)))) (tptp.sdtmndtplgtdt0 W2 tptp.xR W3))) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 7.05/7.24  )
% 7.05/7.24  % SZS output end Proof for COM022+4
% 7.05/7.24  % cvc5---1.0.5 exiting
% 7.12/7.25  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------