TSTP Solution File: SWC073+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC073+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 20:23:02 EDT 2023
% Result : Theorem 42.26s 42.81s
% Output : Proof 42.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.13 % Problem : SWC073+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 15:14:37 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 42.26/42.81 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.axZG7Z68iM/cvc5---1.0.5_11228.p...
% 42.26/42.81 ------- get file name : TPTP file name is SWC073+1
% 42.26/42.81 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11228.smt2...
% 42.26/42.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 42.26/42.81 --- Run --no-e-matching --full-saturate-quant at 5...
% 42.26/42.81 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 42.26/42.81 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 42.26/42.81 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 42.26/42.81 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 42.26/42.81 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 42.26/42.81 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 42.26/42.81 % SZS status Theorem for SWC073+1
% 42.26/42.81 % SZS output start Proof for SWC073+1
% 42.26/42.81 (
% 42.26/42.81 (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)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (= tptp.nil V) (= tptp.nil U)) (and (tptp.neq X tptp.nil) (or (not (tptp.neq W tptp.nil)) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (not (= X Z)) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (= (tptp.tl W) X1) (= (tptp.app X1 X2) Z) (exists ((X3 $$unsorted)) (and (tptp.ssItem X3) (= (tptp.cons X3 tptp.nil) X2) (= (tptp.hd W) X3) (tptp.neq tptp.nil W))) (tptp.neq tptp.nil W))))))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_7 (forall ((U $$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 ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (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 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (not _let_15))) (let ((_let_17 (and _let_16 _let_14))) (let ((_let_18 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (tptp.cons _let_18 tptp.nil))) (let ((_let_20 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (tptp.app _let_20 _let_19))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.ssList _let_21))) (let ((_let_25 (tptp.ssList _let_20))) (let ((_let_26 (tptp.ssList _let_19))) (let ((_let_27 (tptp.ssItem _let_18))) (let ((_let_28 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (and _let_28 _let_27 _let_26 _let_25 _let_24 _let_23))) (let ((_let_30 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29))) (let ((_let_33 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_34 (and _let_33 _let_32))) (let ((_let_35 (and _let_14 _let_15))) (let ((_let_36 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_37 _let_35 _let_17 _let_34))) (let ((_let_43 (forall ((U $$unsorted) (BOUND_VARIABLE_5424 $$unsorted)) (let ((_let_1 (tptp.hd U))) (let ((_let_2 (tptp.cons _let_1 tptp.nil))) (let ((_let_3 (tptp.tl U))) (let ((_let_4 (tptp.app _let_3 _let_2))) (let ((_let_5 (= tptp.nil BOUND_VARIABLE_5424))) (let ((_let_6 (= tptp.nil U))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5424)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5424 Y)) (not (tptp.segmentP U Y))))) (and _let_5 _let_6) (and (not _let_6) _let_5) (and (tptp.neq BOUND_VARIABLE_5424 tptp.nil) (or (not (tptp.neq U tptp.nil)) (and (tptp.neq tptp.nil U) (tptp.ssItem _let_1) (tptp.ssList _let_2) (tptp.ssList _let_3) (tptp.ssList _let_4) (not (= _let_4 BOUND_VARIABLE_5424))))))))))))))) (let ((_let_44 (not _let_42))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (or))) (let ((_let_47 (not _let_43))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_45) :args (_let_47)) (REWRITE :args ((=> _let_47 (not (or _let_41 _let_39 _let_37 _let_35 _let_17 (and _let_33 (or _let_31 (and _let_28 _let_27 _let_26 _let_25 _let_24 (not (= _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_43))) (REFL :args (_let_44)) :args _let_46)) _let_45 :args (_let_44 true _let_43)))) (let ((_let_49 (not _let_14))) (let ((_let_50 (= _let_33 _let_49))) (let ((_let_51 (not _let_11))) (let ((_let_52 (or _let_39 _let_51 _let_50))) (let ((_let_53 (forall ((U $$unsorted) (BOUND_VARIABLE_3303 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3303)) (= (tptp.neq U BOUND_VARIABLE_3303) (not (= U BOUND_VARIABLE_3303))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 (REFL :args (_let_42)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_46)) :args ((or _let_38 _let_42))) _let_48 :args (_let_38 true _let_42)))) (let ((_let_58 (ASSUME :args (_let_11)))) (let ((_let_59 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_60 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_61 (not _let_60))) (let ((_let_62 (not _let_59))) (let ((_let_63 (not _let_33))) (let ((_let_64 (or _let_39 _let_63 _let_62 _let_61))) (let ((_let_65 (= _let_16 _let_30))) (let ((_let_66 (= _let_16 _let_28))) (let ((_let_67 (or _let_41 _let_15 _let_27))) (let ((_let_68 (or _let_41 _let_15 _let_25))) (let ((_let_69 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.cons _let_18 _let_20)))) (let ((_let_70 (or _let_41 _let_15 _let_69))) (let ((_let_71 (not _let_27))) (let ((_let_72 (or _let_51 _let_71 _let_26))) (let ((_let_73 (tptp.app tptp.nil _let_20))) (let ((_let_74 (= _let_20 _let_73))) (let ((_let_75 (not _let_25))) (let ((_let_76 (or _let_75 _let_74))) (let ((_let_77 (tptp.segmentP _let_20 _let_20))) (let ((_let_78 (or _let_75 _let_77))) (let ((_let_79 (tptp.neq _let_20 tptp.nil))) (let ((_let_80 (= tptp.nil _let_20))) (let ((_let_81 (not _let_80))) (let ((_let_82 (= _let_81 _let_79))) (let ((_let_83 (or _let_75 _let_51 _let_82))) (let ((_let_84 (tptp.app _let_19 _let_20))) (let ((_let_85 (= _let_84 (tptp.cons _let_18 _let_73)))) (let ((_let_86 (or _let_75 _let_51 _let_71 _let_85))) (let ((_let_87 (not _let_26))) (let ((_let_88 (or _let_75 _let_87 _let_24))) (let ((_let_89 (= _let_19 (tptp.app tptp.nil _let_19)))) (let ((_let_90 (or _let_87 _let_89))) (let ((_let_91 (tptp.segmentP _let_19 _let_19))) (let ((_let_92 (or _let_87 _let_91))) (let ((_let_93 (tptp.segmentP (tptp.app _let_73 _let_19) _let_20))) (let ((_let_94 (not _let_77))) (let ((_let_95 (or _let_75 _let_75 _let_94 _let_51 _let_87 _let_93))) (let ((_let_96 (tptp.segmentP (tptp.app _let_84 tptp.nil) _let_20))) (let ((_let_97 (or _let_75 _let_75 _let_94 _let_87 _let_51 _let_96))) (let ((_let_98 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil)))) (let ((_let_99 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20))) (let ((_let_100 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_101 (not _let_99))) (let ((_let_102 (not _let_100))) (let ((_let_103 (not _let_79))) (let ((_let_104 (or _let_75 _let_103 _let_102 _let_101))) (let ((_let_105 (or _let_39 _let_59))) (let ((_let_106 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (_let_106))) (let ((_let_109 ((not (= (tptp.ssList U) false))))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 2)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_46)) :args ((or _let_36 _let_42))) _let_48 :args (_let_36 true _let_42)))) (let ((_let_111 (_let_36))) (let ((_let_112 ((not (= (tptp.ssList Y) false))))) (let ((_let_113 (ASSUME :args _let_111))) (let ((_let_114 (or _let_41 _let_51 _let_65))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_46)) :args ((or _let_40 _let_42))) _let_48 :args (_let_40 true _let_42)))) (let ((_let_116 (or _let_51 _let_41 _let_66))) (let ((_let_117 (not _let_66))) (let ((_let_118 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))))) (let ((_let_119 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_122 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (forall ((U $$unsorted) (BOUND_VARIABLE_3326 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3326)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3326 U)))))) (let ((_let_127 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_128 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (_let_128))) (let ((_let_131 ((not (= (tptp.ssList U) false))))) (let ((_let_132 (forall ((U $$unsorted) (BOUND_VARIABLE_3626 $$unsorted) (BOUND_VARIABLE_3624 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3624)) (not (tptp.ssItem BOUND_VARIABLE_3626)) (= (tptp.cons BOUND_VARIABLE_3626 (tptp.app BOUND_VARIABLE_3624 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3626 BOUND_VARIABLE_3624) U)))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (forall ((U $$unsorted) (BOUND_VARIABLE_3584 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3584)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3584)))))) (let ((_let_135 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (forall ((U $$unsorted) (BOUND_VARIABLE_4477 $$unsorted) (BOUND_VARIABLE_4475 $$unsorted) (BOUND_VARIABLE_4473 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4473)) (not (tptp.segmentP U BOUND_VARIABLE_4473)) (not (tptp.ssList BOUND_VARIABLE_4477)) (not (tptp.ssList BOUND_VARIABLE_4475)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4477 U) BOUND_VARIABLE_4475) BOUND_VARIABLE_4473))))) (let ((_let_137 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (_let_136))) (let ((_let_139 (not _let_24))) (let ((_let_140 (not _let_28))) (let ((_let_141 (_let_29))) (let ((_let_142 (not _let_69))) (let ((_let_143 (not _let_89))) (let ((_let_144 (not _let_91))) (let ((_let_145 (ASSUME :args (_let_91)))) (let ((_let_146 (APPLY_UF tptp.segmentP))) (let ((_let_147 (APPLY_UF tptp.cons))) (let ((_let_148 (ASSUME :args (_let_80)))) (let ((_let_149 (SYMM _let_148))) (let ((_let_150 (REFL :args 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(ASSUME :args (_let_74)))) (let ((_let_172 (SYMM (SYMM _let_171)))) (let ((_let_173 (ASSUME :args (_let_98)))) (let ((_let_174 (and _let_22 _let_74 _let_93))) (let ((_let_175 (ASSUME :args (_let_93)))) (let ((_let_176 (not _let_50))) (let ((_let_177 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_50)) (CONG (REFL :args (_let_176)) (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_14))) :args _let_46)) :args ((or _let_14 _let_33 _let_176))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_75 _let_101 _let_102 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_111)) _let_110 :args (_let_104 false _let_36)) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_174)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_175 _let_171 _let_160) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_161 (CONG 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$$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$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))))) _let_8 _let_7 _let_6 (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$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_3 (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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (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 $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 42.26/42.82 )
% 42.26/42.82 % SZS output end Proof for SWC073+1
% 42.26/42.82 % cvc5---1.0.5 exiting
% 42.26/42.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------