%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COM023+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 21.02s 21.25s
% Output   : Proof 21.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : COM023+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 12:56:13 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 21.02/21.25  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.di8Jcfza9y/cvc5---1.0.5_15506.p...
% 21.02/21.25  ------- get file name : TPTP file name is COM023+4
% 21.02/21.25  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15506.smt2...
% 21.02/21.25  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 21.02/21.25  --- Run --no-e-matching --full-saturate-quant at 5...
% 21.02/21.25  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.02/21.25  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 21.02/21.25  % SZS status Theorem for COM023+4
% 21.02/21.25  % SZS output start Proof for COM023+4
% 21.02/21.25  (
% 21.02/21.25  (let ((_let_1 (not (or (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (or (= W0 W1) (and (or (tptp.aReductOfIn0 W1 W0 tptp.xR) (exists ((W3 $$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) (and (or (tptp.aReductOfIn0 W2 W0 tptp.xR) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W3 tptp.xR W2)))) (tptp.sdtmndtplgtdt0 W0 tptp.xR W2))) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (or (= W1 W3) (tptp.aReductOfIn0 W3 W1 tptp.xR) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.aReductOfIn0 W4 W1 tptp.xR) (tptp.sdtmndtplgtdt0 W4 tptp.xR W3))) (tptp.sdtmndtplgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (or (= W2 W3) (tptp.aReductOfIn0 W3 W2 tptp.xR) (exists ((W4 $$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.isConfluent0 tptp.xR))))) (let ((_let_2 (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 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 tptp.xR) (tptp.sdtmndtplgtdt0 W3 tptp.xR W2))) (tptp.sdtmndtplgtdt0 W0 tptp.xR W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2))) (exists ((W3 $$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 ((_let_3 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_4 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_5 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (forall ((W3 $$unsorted) (BOUND_VARIABLE_1450 $$unsorted) (BOUND_VARIABLE_1438 $$unsorted)) (or (not (tptp.aElement0 W3)) (and (not (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (or (and (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1438)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1438 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1438 tptp.xR W3)))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3)))) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3)) (and (not (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (or (and (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1450)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1450 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1450 tptp.xR W3)))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3)))) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3)))))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (not _let_10))) (let ((_let_12 (not (tptp.aReductOfIn0 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR)))) (let ((_let_13 (not (tptp.aElement0 tptp.xR)))) (let ((_let_14 (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR)))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (not _let_15))) (let ((_let_17 (and _let_16 _let_14 (or _let_13 _let_12 (not (tptp.sdtmndtplgtdt0 tptp.xR tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) _let_11 _let_9))) (let ((_let_18 (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_19 (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (not _let_19))) (let ((_let_21 (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR)))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (not _let_22))) (let ((_let_24 (and _let_23 _let_21 (or _let_13 _let_12 (not (tptp.sdtmndtplgtdt0 tptp.xR tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) _let_20 _let_18))) (let ((_let_25 (not _let_5))) (let ((_let_26 (not _let_4))) (let ((_let_27 (not _let_3))) (let ((_let_28 (or _let_27 _let_26 _let_25 _let_24 _let_17 _let_7))) (let ((_let_29 (forall ((W3 $$unsorted) (BOUND_VARIABLE_1586 $$unsorted) (BOUND_VARIABLE_1576 $$unsorted)) (or (not (tptp.aElement0 W3)) (and (not (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1576)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1576 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1576 tptp.xR W3))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3))) (and (not (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1586)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1586 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1586 tptp.xR W3))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3))))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or (and _let_14 (or (not (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR)) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) _let_11))) (let ((_let_32 (and _let_16 _let_31))) (let ((_let_33 (or (and _let_21 (or (not (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.xR)) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) _let_20))) (let ((_let_34 (and _let_23 _let_33))) (let ((_let_35 (or _let_27 _let_26 _let_25 _let_34 _let_18 _let_32 _let_9 _let_30))) (let ((_let_36 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (BOUND_VARIABLE_1641 $$unsorted) (BOUND_VARIABLE_1629 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (and (not (= W0 W1)) (or (and (not (tptp.aReductOfIn0 W1 W0 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1629)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1629 W0 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1629 tptp.xR W1)))) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR W1)))) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (and (not (= W0 W2)) (or (and (not (tptp.aReductOfIn0 W2 W0 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1641)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1641 W0 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1641 tptp.xR W2)))) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR W2)))) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1586 $$unsorted) (BOUND_VARIABLE_1576 $$unsorted)) (or (not (tptp.aElement0 W3)) (and (not (= W1 W3)) (not (tptp.aReductOfIn0 W3 W1 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1576)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1576 W1 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1576 tptp.xR W3))) (not (tptp.sdtmndtplgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3))) (and (not (= W2 W3)) (not (tptp.aReductOfIn0 W3 W2 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1586)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1586 W2 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1586 tptp.xR W3))) (not (tptp.sdtmndtplgtdt0 W2 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (or))) (let ((_let_39 (not _let_36))) (let ((_let_40 (_let_39))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_40)) :args _let_40) (REWRITE :args ((=> _let_39 (not (or _let_27 _let_26 _let_25 _let_34 _let_18 _let_32 _let_9 (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1586 $$unsorted) (BOUND_VARIABLE_1576 $$unsorted)) (or (not (tptp.aElement0 W3)) (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 W3)) (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1576)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1576 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1576 tptp.xR W3))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3))) (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 W3)) (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1586)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1586 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1586 tptp.xR W3))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_36))) (REFL :args (_let_37)) :args _let_38)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_37 true _let_36)))) (let ((_let_42 (REFL :args (_let_35)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_3))) :args _let_38)) :args ((or _let_3 _let_35))) _let_41 :args (_let_3 true _let_35)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 2)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_5))) :args _let_38)) :args ((or _let_5 _let_35))) _let_41 :args (_let_5 true _let_35)))) (let ((_let_45 (forall ((W3 $$unsorted) (BOUND_VARIABLE_1299 $$unsorted) (BOUND_VARIABLE_1287 $$unsorted)) (or (not (tptp.aElement0 W3)) (and (not (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (or (and (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1287)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1287 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1287 tptp.xR W3)))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3)))) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR W3)) (and (not (= W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (or (and (not (tptp.aReductOfIn0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1299)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1299 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1299 tptp.xR W3)))) (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3)))) (not (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR W3)))))) (let ((_let_46 (tptp.sdtmndtasgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47))) (let ((_let_47 (not _let_46))) (let ((_let_48 (not (tptp.sdtmndtplgtdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47)))) (let ((_let_49 (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)))) (let ((_let_50 (or (and _let_49 (or (not (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48)) (not (tptp.aReductOfIn0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)) (not (tptp.sdtmndtplgtdt0 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47)))) (let ((_let_58 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 (and _let_57 _let_56) _let_53 (and _let_51 _let_50) _let_47))) (let ((_let_61 (not (tptp.sdtmndtplgtdt0 tptp.xR tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47)))) (let ((_let_62 (not (tptp.aReductOfIn0 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.xR)))) (let ((_let_63 (and _let_57 _let_55 (or _let_13 _let_62 _let_61) _let_54 _let_53))) (let ((_let_64 (not (tptp.aReductOfIn0 tptp.xR SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.xR)))) (let ((_let_65 (and _let_51 _let_49 (or _let_13 _let_64 _let_61) _let_48 _let_47))) (let ((_let_66 (or _let_59 _let_63 _let_65))) (let ((_let_67 (REFL :args (_let_60)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 7)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_38)) :args ((or _let_29 _let_35))) _let_41 :args (_let_29 true _let_35)))) (let ((_let_69 (_let_29))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (not _let_45))) (let ((_let_72 (_let_71))) (let ((_let_73 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (BOUND_VARIABLE_1497 $$unsorted) (BOUND_VARIABLE_1487 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (and (not (= W0 W1)) (not (tptp.aReductOfIn0 W1 W0 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1487)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1487 W0 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1487 tptp.xR W1))) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1))) (and (not (= W0 W2)) (not (tptp.aReductOfIn0 W2 W0 tptp.xR)) (or (not (tptp.aElement0 BOUND_VARIABLE_1497)) (not (tptp.aReductOfIn0 BOUND_VARIABLE_1497 W0 tptp.xR)) (not (tptp.sdtmndtplgtdt0 BOUND_VARIABLE_1497 tptp.xR W2))) (not (tptp.sdtmndtplgtdt0 W0 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2))) (not 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(tptp.aElement0 W2))))) (forall ((W0 $$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 (tptp.sdtmndtplgtdt0 W0 W1 W2) (tptp.sdtmndtplgtdt0 W2 W1 W3)) (tptp.sdtmndtplgtdt0 W0 W1 W3)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2)) (= (tptp.sdtmndtasgtdt0 W0 W1 W2) (or (= W0 W2) (tptp.sdtmndtplgtdt0 W0 W1 W2))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3)) (=> (and (tptp.sdtmndtasgtdt0 W0 W1 W2) (tptp.sdtmndtasgtdt0 W2 W1 W3)) (tptp.sdtmndtasgtdt0 W0 W1 W3)))) (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isLocallyConfluent0 W0) (forall ((W1 $$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_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 21.02/21.25  )
% 21.02/21.25  % SZS output end Proof for COM023+4
% 21.02/21.25  % cvc5---1.0.5 exiting
% 21.02/21.26  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------