TSTP Solution File: SWC315+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC315+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 20:24:42 EDT 2023
% Result : Theorem 13.78s 13.97s
% Output : Proof 13.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWC315+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n001.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Aug 28 18:08:50 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 13.78/13.97 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.fXtG1TFji0/cvc5---1.0.5_4126.p...
% 13.78/13.97 ------- get file name : TPTP file name is SWC315+1
% 13.78/13.97 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4126.smt2...
% 13.78/13.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 13.78/13.97 --- Run --no-e-matching --full-saturate-quant at 5...
% 13.78/13.97 % SZS status Theorem for SWC315+1
% 13.78/13.97 % SZS output start Proof for SWC315+1
% 13.78/13.97 (
% 13.78/13.97 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssList Z)) (not (= (tptp.app _let_1 Z) V)) (= (tptp.app Z _let_1) U)))))) (or (not (= tptp.nil V)) (= tptp.nil U))) (and (forall ((X1 $$unsorted)) (=> (tptp.ssItem X1) (forall ((X2 $$unsorted)) (let ((_let_1 (tptp.cons X1 tptp.nil))) (or (not (tptp.ssList X2)) (not (= (tptp.app _let_1 X2) X)) (not (= (tptp.app X2 _let_1) W))))))) (tptp.neq X tptp.nil))))))))))))) (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 $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))))) (let ((_let_4 (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 ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_12 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_13 (tptp.app _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_13))) (let ((_let_15 (tptp.hd _let_12))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_15))) (let ((_let_17 (tptp.tl _let_12))) (let ((_let_18 (= tptp.nil _let_17))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_20 (= (tptp.tl _let_13) (tptp.app _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_21 (= _let_15 (tptp.hd _let_13)))) (let ((_let_22 (= tptp.nil _let_13))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_12)))) (let ((_let_24 (not _let_14))) (let ((_let_25 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_24 _let_23))) (let ((_let_30 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30))) (let ((_let_34 (and _let_29 _let_33))) (let ((_let_35 (not _let_30))) (let ((_let_36 (and _let_35 _let_31))) (let ((_let_37 (or))) (let ((_let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))))) (let ((_let_39 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG (REFL :args (_let_33)) _let_38 :args _let_37)) :args ((or _let_31 _let_33))))) (let ((_let_40 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_41 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil))) (let ((_let_42 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_41)))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.app _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_45 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_44))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_46 _let_43))) (let ((_let_52 (and _let_51 _let_40))) (let ((_let_53 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_54 _let_34 _let_36 _let_52))) (let ((_let_56 (forall ((U $$unsorted) (BOUND_VARIABLE_5479 $$unsorted) (BOUND_VARIABLE_5477 $$unsorted) (BOUND_VARIABLE_5475 $$unsorted) (BOUND_VARIABLE_5473 $$unsorted) (BOUND_VARIABLE_5471 $$unsorted)) (let ((_let_1 (tptp.cons BOUND_VARIABLE_5475 tptp.nil))) (let ((_let_2 (= tptp.nil BOUND_VARIABLE_5471))) (let ((_let_3 (= tptp.nil U))) (let ((_let_4 (tptp.cons BOUND_VARIABLE_5479 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5471)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5479)) (not (tptp.ssList BOUND_VARIABLE_5477)) (not (= BOUND_VARIABLE_5471 (tptp.app _let_4 BOUND_VARIABLE_5477))) (= U (tptp.app BOUND_VARIABLE_5477 _let_4))) (or (not _let_2) _let_3)) (and (not _let_3) _let_2) (and (or (not (tptp.ssItem BOUND_VARIABLE_5475)) (not (tptp.ssList BOUND_VARIABLE_5473)) (not (= BOUND_VARIABLE_5471 (tptp.app _let_1 BOUND_VARIABLE_5473))) (not (= U (tptp.app BOUND_VARIABLE_5473 _let_1)))) (tptp.neq BOUND_VARIABLE_5471 tptp.nil)))))))))) (let ((_let_57 (not _let_55))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (not _let_56))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_58) :args (_let_59))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_56))) (REFL :args (_let_57)) :args _let_37)) _let_58 :args (_let_57 true _let_56)))) (let ((_let_61 (REFL :args (_let_32)))) (let ((_let_62 (_let_36))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_55 2)) _let_60 :args ((not _let_34) true _let_55)))) (let ((_let_64 (CNF_AND_NEG :args (_let_34)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_62) (CONG (REFL :args _let_62) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_30))) _let_61 :args _let_37)) :args ((or _let_32 _let_30 _let_36))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_55 3)) _let_60 :args ((not _let_36) true _let_55)) (CNF_OR_NEG :args (_let_33 1)) _let_39 :args (_let_33 true _let_36 true _let_30 false _let_31)) :args ((not _let_29) true _let_34 false _let_33)))) (let ((_let_66 (REFL :args (_let_29)))) (let ((_let_67 (not _let_9))) (let ((_let_68 (or _let_67 _let_28 _let_16))) (let ((_let_69 (forall ((U $$unsorted) (BOUND_VARIABLE_3527 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3527)) (= BOUND_VARIABLE_3527 (tptp.hd (tptp.cons BOUND_VARIABLE_3527 U))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_ENUM))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_37)) :args ((or _let_27 _let_29))) _let_65 :args (_let_27 true _let_29)))) (let ((_let_74 (ASSUME :args (_let_9)))) (let ((_let_75 (or _let_67 _let_28 _let_18))) (let ((_let_76 (forall ((U $$unsorted) (BOUND_VARIABLE_3557 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3557)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3557 U))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (_let_76))) (let ((_let_79 (or _let_26 _let_19))) (let ((_let_80 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_37)) :args ((or _let_25 _let_29))) _let_65 :args (_let_25 true _let_29)))) (let ((_let_84 (= tptp.nil _let_12))) (let ((_let_85 (tptp.ssList _let_12))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_84 _let_26 _let_20))) (let ((_let_88 (forall ((U $$unsorted) (BOUND_VARIABLE_4942 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (tptp.ssList BOUND_VARIABLE_4942)) (= (tptp.tl (tptp.app U BOUND_VARIABLE_4942)) (tptp.app (tptp.tl U) BOUND_VARIABLE_4942)))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (_let_88))) (let ((_let_91 (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_92 (or _let_67 _let_28 _let_85))) (let ((_let_93 (forall ((U $$unsorted) (BOUND_VARIABLE_3321 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3321)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3321 U)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (_let_93))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_67 _let_28 _let_85 (not _let_92)))) _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args _let_72) :args _let_95)) _let_94 :args (_let_92 false _let_93)) :args (_let_85 false _let_9 false _let_27 false _let_92)))) (let ((_let_97 (not _let_84))) (let ((_let_98 (or _let_67 _let_28 _let_97))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_3346 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3346)) (not (= U (tptp.cons BOUND_VARIABLE_3346 U))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_99))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_67 _let_28 _let_97 (not _let_98)))) _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args _let_101)) _let_100 :args (_let_98 false _let_99)) :args (_let_97 false _let_9 false _let_27 false _let_98)))) (let ((_let_103 (or _let_86 _let_84 _let_26 _let_21))) (let ((_let_104 (forall ((U $$unsorted) (BOUND_VARIABLE_4914 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (tptp.ssList BOUND_VARIABLE_4914)) (= (tptp.hd U) (tptp.hd (tptp.app U BOUND_VARIABLE_4914))))))) (let ((_let_105 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_106 (_let_104))) (let ((_let_107 (and (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_84))) (let ((_let_108 (= _let_22 _let_107))) (let ((_let_109 (not _let_22))) (let ((_let_110 (or _let_86 _let_26 _let_108))) (let ((_let_111 (forall ((U $$unsorted) (BOUND_VARIABLE_4879 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4879)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4879)) (and (= tptp.nil BOUND_VARIABLE_4879) (= tptp.nil U))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (not _let_107))) (let ((_let_114 (= _let_32 _let_40))) (let ((_let_115 (= tptp.nil _let_41))) (let ((_let_116 (not _let_115))) (let ((_let_117 (or _let_67 _let_50 _let_116))) (let ((_let_118 (tptp.ssList _let_41))) (let ((_let_119 (or _let_67 _let_50 _let_118))) (let ((_let_120 (tptp.tl _let_41))) (let ((_let_121 (= tptp.nil _let_120))) (let ((_let_122 (or _let_67 _let_50 _let_121))) (let ((_let_123 (tptp.hd _let_41))) (let ((_let_124 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_123))) (let ((_let_125 (or _let_67 _let_50 _let_124))) (let ((_let_126 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_127 (or _let_48 _let_126))) (let ((_let_128 (= (tptp.tl _let_44) (tptp.app _let_120 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_129 (not _let_118))) (let ((_let_130 (or _let_129 _let_115 _let_48 _let_128))) (let ((_let_131 (= _let_123 (tptp.hd _let_44)))) (let ((_let_132 (or _let_129 _let_115 _let_48 _let_131))) (let ((_let_133 (= tptp.nil (tptp.app tptp.nil tptp.nil)))) (let ((_let_134 (not _let_21))) (let ((_let_135 (not _let_20))) (let ((_let_136 (not _let_19))) (let ((_let_137 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(=> (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 $$unsorted)) (=> (tptp.ssList 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$$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))) (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)))))) (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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$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))))))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) _let_3 _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 13.78/13.98 )
% 13.78/13.98 % SZS output end Proof for SWC315+1
% 13.78/13.98 % cvc5---1.0.5 exiting
% 13.78/13.98 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------