%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC388+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 20:25:15 EDT 2023

% Result   : Theorem 78.99s 79.27s
% Output   : Proof 78.99s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWC388+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n026.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
% 0.22/0.36  % CPULimit   : 300
% 0.22/0.36  % WCLimit    : 300
% 0.22/0.36  % DateTime   : Mon Aug 28 16:34:35 EDT 2023
% 0.22/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 78.99/79.27  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.5oMz9mDlRs/cvc5---1.0.5_23715.p...
% 78.99/79.27  ------- get file name : TPTP file name is SWC388+1
% 78.99/79.27  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23715.smt2...
% 78.99/79.27  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 78.99/79.27  --- Run --no-e-matching --full-saturate-quant at 5...
% 78.99/79.27  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 78.99/79.27  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 78.99/79.27  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 78.99/79.27  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 78.99/79.27  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 78.99/79.27  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 78.99/79.27  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 78.99/79.27  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 78.99/79.27  --- Run --relevant-triggers --full-saturate-quant at 5...
% 78.99/79.27  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 78.99/79.27  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 78.99/79.27  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 78.99/79.27  % SZS status Theorem for SWC388+1
% 78.99/79.27  % SZS output start Proof for SWC388+1
% 78.99/79.27  (
% 78.99/79.27  (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.segmentP X W)) (exists ((Y $$unsorted)) (and (tptp.ssItem Y) (= (tptp.cons Y tptp.nil) U) (tptp.memberP V Y))) (and (not (tptp.singletonP W)) (tptp.neq X tptp.nil)) (and (= tptp.nil V) (= tptp.nil U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_5 (tptp.singletonP tptp.nil))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_11 (tptp.ssList tptp.nil))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_16 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.segmentP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_20 (tptp.singletonP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (not _let_20))) (let ((_let_22 (and _let_21 _let_19))) (let ((_let_23 (not _let_16))) (let ((_let_24 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (and _let_17 _let_24))) (let ((_let_26 (forall ((Y $$unsorted)) (or (not (tptp.ssItem Y)) (not (= (tptp.cons Y tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)))))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29 _let_27 _let_25 _let_23 _let_22))) (let ((_let_33 (forall ((U $$unsorted) (BOUND_VARIABLE_5266 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5266)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssItem Y)) (not (= U (tptp.cons Y tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5266 Y))))) (and (= tptp.nil BOUND_VARIABLE_5266) (= tptp.nil U)) (not (tptp.segmentP BOUND_VARIABLE_5266 U)) (and (not (tptp.singletonP U)) (tptp.neq BOUND_VARIABLE_5266 tptp.nil)))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (or))) (let ((_let_37 (not _let_33))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_35) :args (_let_37)) (REWRITE :args ((=> _let_37 (not (or _let_31 _let_29 (not (forall ((Y $$unsorted)) (or (not (tptp.ssItem Y)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.cons Y tptp.nil))) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y))))) _let_25 _let_23 _let_22))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_33))) (REFL :args (_let_34)) :args _let_36)) _let_35 :args (_let_34 true _let_33)))) (let ((_let_39 (REFL :args (_let_32)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 4)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_16))) :args _let_36)) :args ((or _let_16 _let_32))) _let_38 :args (_let_16 true _let_32)))) (let ((_let_41 (not _let_17))) (let ((_let_42 (= _let_19 _let_41))) (let ((_let_43 (not _let_11))) (let ((_let_44 (or _let_29 _let_43 _let_42))) (let ((_let_45 (forall ((U $$unsorted) (BOUND_VARIABLE_3269 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3269)) (= (tptp.neq U BOUND_VARIABLE_3269) (not (= U BOUND_VARIABLE_3269))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 1)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_36)) :args ((or _let_28 _let_32))) _let_38 :args (_let_28 true _let_32)))) (let ((_let_48 (ASSUME :args (_let_11)))) (let ((_let_49 (not _let_19))) (let ((_let_50 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_51 (not _let_50))) (let ((_let_52 (= _let_20 _let_51))) (let ((_let_53 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 tptp.nil))) (let ((_let_54 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_53))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55))) (let ((_let_59 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_60 (tptp.ssItem _let_59))) (let ((_let_61 (or _let_31 _let_24 _let_60))) (let ((_let_62 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_63 (tptp.cons _let_59 tptp.nil))) (let ((_let_64 (= (tptp.cons _let_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (tptp.app _let_63 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_65 (not _let_60))) (let ((_let_66 (not _let_62))) (let ((_let_67 (or _let_66 _let_65 _let_64))) (let ((_let_68 (forall ((W $$unsorted) (BOUND_VARIABLE_2134 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2134)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app W (tptp.cons (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2134)))))))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_59))) (let ((_let_71 (= _let_70 _let_69))) (let ((_let_72 (or _let_29 _let_65 _let_71))) (let ((_let_73 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 (tptp.hd _let_53)))) (let ((_let_74 (or _let_43 _let_57 _let_73))) (let ((_let_75 (= tptp.nil (tptp.tl _let_53)))) (let ((_let_76 (or _let_43 _let_57 _let_75))) (let ((_let_77 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_63))) (let ((_let_78 (not _let_70))) (let ((_let_79 (not _let_77))) (let ((_let_80 (or _let_65 _let_79 _let_78))) (let ((_let_81 (tptp.app (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_82 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons _let_59 _let_81))))) (let ((_let_83 (not _let_82))) (let ((_let_84 (tptp.ssList _let_81))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_87 (not _let_86))) (let ((_let_88 (or _let_87 _let_85 _let_83))) (let ((_let_89 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_90 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_89))) (let ((_let_91 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_92 (= _let_89 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))))) (let ((_let_93 (or _let_31 _let_52))) (let ((_let_94 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 0)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_36)) :args ((or _let_30 _let_32))) _let_38 :args (_let_30 true _let_32)))) (let ((_let_97 (ASSUME :args (_let_6)))) (let ((_let_98 (not _let_24))) (let ((_let_99 (ASSUME :args (_let_20)))) (let ((_let_100 (ASSUME :args (_let_24)))) (let ((_let_101 (_let_51))) (let ((_let_102 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (REFL :args (_let_58)))) (let ((_let_105 (not _let_90))) (let ((_let_106 (or _let_87 _let_66 _let_105))) (let ((_let_107 (forall ((W $$unsorted) (BOUND_VARIABLE_2299 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2299)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2299))))))) (let ((_let_108 (not _let_106))) (let ((_let_109 (not _let_107))) (let ((_let_110 (= _let_16 _let_109))) (let ((_let_111 (or _let_29 _let_31 _let_110))) (let ((_let_112 (forall ((U $$unsorted) (BOUND_VARIABLE_2324 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2324)) (= (tptp.segmentP U BOUND_VARIABLE_2324) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2299 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2299)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2324) BOUND_VARIABLE_2299))))))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (_let_109))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_114)) :args _let_114)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_107))) (REFL :args (_let_108)) :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_110)) :args ((or _let_23 _let_109 (not _let_110)))) _let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_31 _let_29 _let_110 (not _let_111)))) _let_96 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.segmentP U BOUND_VARIABLE_2324)))) :args (_let_112))) _let_113 :args (_let_111 false _let_112)) :args (_let_110 false _let_30 false _let_28 false _let_111)) :args (_let_109 false _let_16 false _let_110)) :args (_let_108 true _let_107)))) (let ((_let_116 (REFL :args (_let_106)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 1)) (CONG _let_116 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_62))) :args _let_36)) :args ((or _let_62 _let_106))) _let_115 :args (_let_62 true _let_106)))) (let ((_let_118 (forall ((U $$unsorted) (BOUND_VARIABLE_4780 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4780)) (= (tptp.cons BOUND_VARIABLE_4780 U) (tptp.app (tptp.cons BOUND_VARIABLE_4780 tptp.nil) U)))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (forall ((U $$unsorted) (BOUND_VARIABLE_2160 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2160)) (= (tptp.memberP U BOUND_VARIABLE_2160) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2134 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2134)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2160 BOUND_VARIABLE_2134)))))))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (forall ((U $$unsorted) (BOUND_VARIABLE_3498 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3498)) (= BOUND_VARIABLE_3498 (tptp.hd (tptp.cons BOUND_VARIABLE_3498 U))))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_125 (forall ((U $$unsorted) (BOUND_VARIABLE_3528 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3528)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3528 U))))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (and _let_54 _let_73))) (let ((_let_128 (_let_54 _let_73))) (let ((_let_129 (APPLY_UF tptp.cons))) (let ((_let_130 (REFL :args (tptp.nil)))) (let ((_let_131 (APPLY_UF tptp.hd))) (let ((_let_132 (ASSUME :args (_let_54)))) (let ((_let_133 (SYMM _let_132))) (let ((_let_134 (ASSUME :args (_let_73)))) (let ((_let_135 (SYMM (SYMM _let_134)))) (let ((_let_136 (_let_26))) (let ((_let_137 (not _let_71))) (let ((_let_138 (_let_68))) (let ((_let_139 (or _let_66 _let_91))) (let ((_let_140 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_141 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_142 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_66 _let_91 (not _let_139)))) _let_117 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_141 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_140))) _let_141 :args (_let_139 false _let_140)) :args (_let_91 false _let_62 false _let_139)))) (let ((_let_143 (or _let_87 _let_31 _let_66 _let_92))) (let ((_let_144 (forall ((U $$unsorted) (BOUND_VARIABLE_4824 $$unsorted) (BOUND_VARIABLE_4822 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4822)) (not (tptp.ssList BOUND_VARIABLE_4824)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4822) BOUND_VARIABLE_4824) (tptp.app U (tptp.app BOUND_VARIABLE_4822 BOUND_VARIABLE_4824))))))) (let ((_let_145 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 0)) (CONG _let_116 (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_86))) :args _let_36)) :args ((or _let_86 _let_106))) _let_115 :args (_let_86 true _let_106)))) (let ((_let_147 (and _let_90 _let_54 _let_73 _let_75 _let_91 _let_92 _let_64))) (let ((_let_148 (APPLY_UF tptp.app))) (let ((_let_149 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_150 (APPLY_UF tptp.tl))) (let ((_let_151 (SYMM _let_133))) (let ((_let_152 (SYMM _let_151))) (let ((_let_153 (ASSUME :args (_let_75)))) (let ((_let_154 (SYMM _let_153))) (let ((_let_155 (ASSUME :args (_let_91)))) (let ((_let_156 (SYMM _let_155))) (let ((_let_157 (ASSUME :args (_let_64)))) (let ((_let_158 (ASSUME :args (_let_92)))) (let ((_let_159 (ASSUME :args (_let_90)))) (let ((_let_160 (and _let_62 _let_54 _let_75 _let_91))) (let ((_let_161 (ASSUME :args (_let_62)))) (let ((_let_162 (_let_22))) (let ((_let_163 (not _let_42))) (let ((_let_164 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_42)) (CONG (REFL :args (_let_163)) (REFL :args (_let_19)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_17))) :args _let_36)) :args ((or _let_17 _let_19 _let_163))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_162) (CONG (REFL :args _let_162) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) (REFL :args (_let_49)) :args _let_36)) :args ((or _let_20 _let_22 _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_87 _let_85 _let_83 (not _let_88)))) _let_146 (RESOLUTION (CNF_AND_NEG :args (_let_160)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_161 _let_155 _let_153 _let_132) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (CONG (TRANS (CONG _let_151 :args _let_150) _let_154) _let_149 :args _let_148) _let_156) :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_161))) :args (_let_62 _let_91 _let_75 _let_54))) :args (_let_62 _let_54 _let_75 _let_91))) :args (true _let_160)) _let_142 _let_117 (RESOLUTION (CNF_AND_NEG :args (_let_147)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_132 _let_153 _let_155 _let_157 _let_134 _let_158 _let_159) (SCOPE (TRANS (SYMM (SYMM _let_159)) (SYMM (SYMM _let_158)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (TRANS (CONG (TRANS _let_151 (CONG (TRANS _let_135 (CONG _let_152 :args _let_131)) _let_130 :args _let_129)) _let_149 :args _let_148) (SYMM _let_157) (CONG (REFL :args (_let_59)) (TRANS (SYMM _let_156) (CONG (TRANS (SYMM _let_154) (CONG _let_152 :args _let_150)) _let_149 :args _let_148)) :args _let_129)) :args _let_148)) :args (_let_54 _let_75 _let_91 _let_64 _let_73 _let_92 _let_90))) :args (_let_90 _let_54 _let_73 _let_75 _let_91 _let_92 _let_64))) :args (true _let_147)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_31 _let_87 _let_66 _let_92 (not _let_143)))) _let_96 _let_146 _let_117 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app U BOUND_VARIABLE_4822) BOUND_VARIABLE_4824)))) :args (_let_144))) _let_145 :args (_let_143 false _let_144)) :args (_let_92 false _let_30 false _let_86 false _let_62 false _let_143)) _let_142 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_106 2)) (CONG _let_116 (MACRO_SR_PRED_INTRO :args ((= (not _let_105) _let_90))) :args _let_36)) :args ((or _let_90 _let_106))) _let_115 :args (_let_90 true _let_106)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_138) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_81 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_138)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_71)) (CONG (REFL :args (_let_137)) (REFL :args (_let_70)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_36)) :args ((or _let_70 _let_68 _let_137))) (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_65 _let_78 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_136) :args (_let_59 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem Y) false))))) :args _let_136))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 2)) (CONG _let_39 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_36)) :args ((or _let_26 _let_32))) _let_38 :args (_let_26 true _let_32)) :args (_let_80 false _let_26)) (RESOLUTION (CNF_AND_NEG :args (_let_127)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_132 _let_134) (SCOPE (TRANS _let_132 (CONG (TRANS _let_135 (CONG _let_133 :args _let_131)) _let_130 :args _let_129)) :args _let_128)) :args _let_128)) :args (true _let_127)) (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_43 _let_57 _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args _let_124) :args (_let_125))) _let_126 :args (_let_76 false _let_125)) _let_48 (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_43 _let_57 _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_123 :args _let_124) :args (_let_122))) _let_123 :args (_let_74 false _let_122)) _let_48 (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_29 _let_65 _let_71 (not _let_72)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_59 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2160)))) :args (_let_120))) _let_121 :args (_let_72 false _let_120)) _let_47 (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_65 _let_66 _let_64 (not _let_67)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_59 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.cons BOUND_VARIABLE_4780 tptp.nil) U)))) :args (_let_118))) _let_119 :args (_let_67 false _let_118)) _let_117 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_36)) :args ((or _let_54 _let_58))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_36)) :args ((or _let_56 _let_58))) (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_31 _let_24 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_102))) _let_103 :args (_let_61 false _let_102)) _let_96 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_101)) :args _let_101) (REWRITE :args ((=> _let_51 (not (or _let_57 (not (= _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) (REFL :args ((not _let_58))) :args _let_36)) (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_99 _let_100 _let_97) :args (_let_6 _let_24 _let_20)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_97)) (CONG (SYMM (SYMM _let_100)) :args (APPLY_UF tptp.singletonP)) (TRUE_INTRO _let_99))) :args (_let_20 _let_24 _let_6)) :args ((not (and _let_6 _let_24 _let_20)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) (REFL :args (_let_98)) (REFL :args (_let_21)) :args _let_36)) :args ((or _let_5 _let_21 _let_98))) _let_97 (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or _let_21 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_31 _let_52 (not _let_93)))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_94)))) _let_95 :args (_let_93 false _let_94)) :args (_let_52 false _let_30 false _let_93)) :args (_let_21 false _let_86 false _let_84 false _let_91 false _let_62 false _let_82 false _let_92 false _let_91 false _let_90 false _let_88 false _let_68 true _let_70 false _let_80 false _let_77 false _let_75 false _let_76 false _let_11 false _let_73 false _let_74 false _let_11 false _let_71 false _let_72 false _let_28 false _let_64 false _let_67 false _let_62 false _let_54 false _let_56 false _let_60 false _let_61 false _let_30 true _let_58 true _let_24 true _let_5 true _let_50 false _let_52)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_32 5)) _let_38 :args ((not _let_22) true _let_32)) :args (_let_49 true _let_20 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_29 _let_42 (not _let_44)))) _let_48 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3269)))) :args (_let_45)))) _let_46 :args (_let_44 false _let_45)) :args (_let_42 false _let_11 false _let_28 false _let_44)) :args (_let_17 true _let_19 false _let_42)))) (let ((_let_165 (= _let_24 _let_18))) (let ((_let_166 (not _let_18))) (let ((_let_167 (or _let_31 _let_165))) (let ((_let_168 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_169 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_170 (and _let_17 _let_16))) (let ((_let_171 (ASSUME :args (_let_16)))) (let ((_let_172 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_170)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_171 _let_172) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_172)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) :args (APPLY_UF tptp.segmentP)) (TRUE_INTRO _let_171))) :args (_let_16 _let_17))) :args (_let_17 _let_16))) :args (true _let_170)) :args ((or _let_23 _let_41 _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_165)) :args ((or _let_24 _let_166 (not _let_165)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_25)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_32 3)) _let_38 :args ((not _let_25) true _let_32)) _let_164 :args (_let_98 true _let_25 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_167)) :args ((or _let_31 _let_165 (not _let_167)))) _let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_169 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_168)))) _let_169 :args (_let_167 false _let_168)) :args (_let_165 false _let_30 false _let_167)) :args (_let_166 true _let_24 false _let_165)) _let_164 _let_40 :args (false true _let_18 false _let_17 false _let_16)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) _let_15 _let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_10 _let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_3 _let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 78.99/79.28  )
% 78.99/79.28  % SZS output end Proof for SWC388+1
% 78.99/79.28  % cvc5---1.0.5 exiting
% 78.99/79.28  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------