TSTP Solution File: SWC088+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC088+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 20:23:08 EDT 2023
% Result : Theorem 68.93s 69.20s
% Output : Proof 69.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWC088+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.19/0.37 % Computer : n019.cluster.edu
% 0.19/0.37 % Model : x86_64 x86_64
% 0.19/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.37 % Memory : 8042.1875MB
% 0.19/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.37 % CPULimit : 300
% 0.19/0.37 % WCLimit : 300
% 0.22/0.37 % DateTime : Mon Aug 28 14:54:13 EDT 2023
% 0.22/0.37 % CPUTime :
% 0.22/0.52 %----Proving TF0_NAR, FOF, or CNF
% 68.93/69.20 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.GLbuZHtxRk/cvc5---1.0.5_29346.p...
% 68.93/69.20 ------- get file name : TPTP file name is SWC088+1
% 68.93/69.20 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29346.smt2...
% 68.93/69.20 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 68.93/69.20 --- Run --no-e-matching --full-saturate-quant at 5...
% 68.93/69.20 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 68.93/69.20 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 68.93/69.20 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 68.93/69.20 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 68.93/69.20 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 68.93/69.20 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 68.93/69.20 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 68.93/69.20 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 68.93/69.20 --- Run --relevant-triggers --full-saturate-quant at 5...
% 68.93/69.20 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 68.93/69.20 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 68.93/69.20 % SZS status Theorem for SWC088+1
% 68.93/69.20 % SZS output start Proof for SWC088+1
% 68.93/69.20 (
% 68.93/69.20 (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.neq V tptp.nil)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (and (tptp.ssList X1) (not (= (tptp.app X1 _let_1) W)) (= (tptp.app _let_1 X1) X)))))) (and (not (= tptp.nil W)) (= tptp.nil X)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_4 (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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))) (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 $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_14 (= tptp.nil skv_7))) (let ((_let_15 (= tptp.nil (tptp.app tptp.nil tptp.nil)))) (let ((_let_16 (= skv_7 (tptp.app tptp.nil skv_7)))) (let ((_let_17 (tptp.tl skv_7))) (let ((_let_18 (tptp.hd skv_7))) (let ((_let_19 (tptp.cons _let_18 _let_17))) (let ((_let_20 (= skv_7 _let_19))) (let ((_let_21 (tptp.app skv_6 tptp.nil))) (let ((_let_22 (= skv_6 _let_21))) (let ((_let_23 (tptp.app skv_7 tptp.nil))) (let ((_let_24 (= skv_7 _let_23))) (let ((_let_25 (tptp.app tptp.nil _let_17))) (let ((_let_26 (= _let_17 _let_25))) (let ((_let_27 (tptp.cons _let_18 tptp.nil))) (let ((_let_28 (= skv_6 (tptp.app _let_17 _let_27)))) (let ((_let_29 (= tptp.nil _let_17))) (let ((_let_30 (= tptp.nil skv_6))) (let ((_let_31 (not _let_14))) (let ((_let_32 (tptp.neq skv_7 tptp.nil))) (let ((_let_33 (= _let_32 _let_31))) (let ((_let_34 (not _let_11))) (let ((_let_35 (tptp.ssList skv_7))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34 _let_33))) (let ((_let_38 (forall ((U $$unsorted) (BOUND_VARIABLE_3282 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3282)) (= (tptp.neq U BOUND_VARIABLE_3282) (not (= U BOUND_VARIABLE_3282))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 (ASSUME :args (_let_11)))) (let ((_let_42 (not _let_30))) (let ((_let_43 (forall ((Z $$unsorted) (BOUND_VARIABLE_5246 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5246)) (= (tptp.app BOUND_VARIABLE_5246 _let_1) skv_6) (not (= (tptp.app _let_1 BOUND_VARIABLE_5246) skv_7))))))) (let ((_let_44 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP skv_7 Y)) (not (tptp.segmentP skv_6 Y)))))) (let ((_let_45 (not _let_32))) (let ((_let_46 (tptp.ssList skv_6))) (let ((_let_47 (not _let_46))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((U $$unsorted) (BOUND_VARIABLE_5319 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5319)) (not (tptp.neq BOUND_VARIABLE_5319 tptp.nil)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5319 Y)) (not (tptp.segmentP U Y))))) (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5246 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5246)) (= U (tptp.app BOUND_VARIABLE_5246 _let_1)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5246) BOUND_VARIABLE_5319)))))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5319))))) (not (or _let_47 _let_36 _let_45 (not _let_44) (not _let_43) (and _let_42 _let_14)))))))))) (let ((_let_49 (NOT_NOT_ELIM (NOT_OR_ELIM _let_48 :args (1))))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or _let_45 _let_31 (not _let_33)))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_48 :args (2))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_34 _let_33 (not _let_37)))) _let_49 _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (skv_7 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_40))) _let_39 :args (_let_37 false _let_38)) :args (_let_33 false _let_35 false _let_11 false _let_37)) :args (_let_31 false _let_32 false _let_33)))) (let ((_let_51 (or _let_34 _let_15))) (let ((_let_52 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 ((not (= (tptp.ssList U) false))))) (let ((_let_56 (or _let_36 _let_16))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_36 _let_16 (not _let_56)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_56 false _let_52)) :args (_let_16 false _let_35 false _let_56)))) (let ((_let_58 (or _let_36 _let_14 _let_20))) (let ((_let_59 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_36 _let_14 _let_20 (not _let_58)))) _let_49 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_20 false _let_35 true _let_14 false _let_58)))) (let ((_let_62 (or _let_47 _let_22))) (let ((_let_63 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((not (= (tptp.ssList U) false))))) (let ((_let_67 (NOT_NOT_ELIM (NOT_OR_ELIM _let_48 :args (0))))) (let ((_let_68 (or _let_36 _let_24))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_36 _let_24 (not _let_68)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_68 false _let_63)) :args (_let_24 false _let_35 false _let_68)))) (let ((_let_70 (tptp.ssList _let_17))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_26))) (let ((_let_73 (or _let_36 _let_14 _let_70))) (let ((_let_74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_36 _let_14 _let_70 (not _let_73)))) _let_49 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tl U)))) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_70 false _let_35 true _let_14 false _let_73)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_71 _let_26 (not _let_72)))) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_54)) _let_53 :args (_let_72 false _let_52)) :args (_let_26 false _let_70 false _let_72)))) (let ((_let_78 (tptp.app _let_27 _let_17))) (let ((_let_79 (= skv_7 _let_78))) (let ((_let_80 (not _let_79))) (let ((_let_81 (tptp.ssItem _let_18))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_71 _let_28 _let_80))) (let ((_let_84 (NOT_NOT_ELIM (NOT_OR_ELIM _let_48 :args (4))))) (let ((_let_85 (_let_43))) (let ((_let_86 (ASSUME :args _let_85))) (let ((_let_87 (= _let_19 _let_78))) (let ((_let_88 (or _let_71 _let_82 _let_87))) (let ((_let_89 (forall ((U $$unsorted) (BOUND_VARIABLE_4793 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4793)) (= (tptp.cons BOUND_VARIABLE_4793 U) (tptp.app (tptp.cons BOUND_VARIABLE_4793 tptp.nil) U)))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (or _let_36 _let_14 _let_81))) (let ((_let_92 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_36 _let_14 _let_81 (not _let_91)))) _let_49 _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_81 false _let_35 true _let_14 false _let_91)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_82 _let_71 _let_87 (not _let_88)))) _let_94 _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (_let_17 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4793 U)))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_87 false _let_81 false _let_70 false _let_88)))) (let ((_let_96 (and _let_20 _let_87))) (let ((_let_97 (ASSUME :args (_let_87)))) (let ((_let_98 (ASSUME :args (_let_20)))) (let ((_let_99 (SYMM _let_98))) (let ((_let_100 (SYMM _let_99))) (let ((_let_101 (TRANS _let_100 (SYMM (SYMM _let_97))))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_82 _let_71 _let_28 _let_80 (not _let_83)))) _let_94 _let_76 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_96)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_97 _let_98) (SCOPE _let_101 :args (_let_87 _let_20))) :args (_let_20 _let_87))) :args (true _let_96)) _let_61 _let_95 :args (_let_79 false _let_20 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_86 :args (_let_18 _let_17 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.cons Z tptp.nil) BOUND_VARIABLE_5246)))) :args _let_85))) _let_84 :args (_let_83 false _let_43)) :args (_let_28 false _let_81 false _let_70 false _let_79 false _let_83)))) (let ((_let_103 (tptp.neq _let_17 tptp.nil))) (let ((_let_104 (not _let_29))) (let ((_let_105 (= _let_104 _let_103))) (let ((_let_106 (or _let_71 _let_34 _let_105))) (let ((_let_107 (tptp.segmentP skv_6 _let_17))) (let ((_let_108 (not _let_107))) (let ((_let_109 (tptp.segmentP skv_7 _let_17))) (let ((_let_110 (not _let_109))) (let ((_let_111 (not _let_103))) (let ((_let_112 (or _let_71 _let_111 _let_110 _let_108))) (let ((_let_113 (NOT_NOT_ELIM (NOT_OR_ELIM _let_48 :args (3))))) (let ((_let_114 (_let_44))) (let ((_let_115 ((not (= (tptp.ssList Y) false))))) (let ((_let_116 (ASSUME :args _let_114))) (let ((_let_117 (tptp.segmentP (tptp.app _let_25 _let_27) _let_17))) (let ((_let_118 (tptp.ssList _let_27))) (let ((_let_119 (not _let_118))) (let ((_let_120 (tptp.segmentP _let_17 _let_17))) (let ((_let_121 (not _let_120))) (let ((_let_122 (or _let_71 _let_71 _let_121 _let_34 _let_119 _let_117))) (let ((_let_123 (forall ((U $$unsorted) (BOUND_VARIABLE_4456 $$unsorted) (BOUND_VARIABLE_4454 $$unsorted) (BOUND_VARIABLE_4452 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4452)) (not (tptp.segmentP U BOUND_VARIABLE_4452)) (not (tptp.ssList BOUND_VARIABLE_4456)) (not (tptp.ssList BOUND_VARIABLE_4454)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4456 U) BOUND_VARIABLE_4454) BOUND_VARIABLE_4452))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (_let_123))) (let ((_let_126 (or _let_71 _let_120))) (let ((_let_127 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_128 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_129 (_let_127))) (let ((_let_130 ((not (= (tptp.ssList U) false))))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_71 _let_120 (not _let_126)))) _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_128 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_130)) :args _let_129)) _let_128 :args (_let_126 false _let_127)) :args (_let_120 false _let_70 false _let_126)))) (let ((_let_132 (or _let_34 _let_82 _let_118))) (let ((_let_133 (forall ((U $$unsorted) (BOUND_VARIABLE_3305 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3305)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3305 U)))))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_132)) :args ((or _let_34 _let_82 _let_118 (not _let_132)))) _let_41 _let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (tptp.nil _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3305 U)))) :args (_let_133))) _let_134 :args (_let_132 false 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(forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$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_13 _let_12 _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 $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) _let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$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_8 (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)))) (not (tptp.singletonP tptp.nil)) (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_7 _let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$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)))))) _let_5 (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_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) _let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 69.01/69.21 )
% 69.01/69.21 % SZS output end Proof for SWC088+1
% 69.01/69.21 % cvc5---1.0.5 exiting
% 69.01/69.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------