TSTP Solution File: SWC418+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC418+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 20:25:29 EDT 2023
% Result : Theorem 20.34s 20.57s
% Output : Proof 20.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC418+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n016.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 19:27:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 20.34/20.57 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.7TduUUDId7/cvc5---1.0.5_14938.p...
% 20.34/20.57 ------- get file name : TPTP file name is SWC418+1
% 20.34/20.57 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14938.smt2...
% 20.34/20.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 20.34/20.57 --- Run --no-e-matching --full-saturate-quant at 5...
% 20.34/20.57 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.34/20.57 % SZS status Theorem for SWC418+1
% 20.34/20.57 % SZS output start Proof for SWC418+1
% 20.34/20.57 (
% 20.34/20.57 (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 $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (and (tptp.ssList X1) (= (tptp.app (tptp.app Z _let_1) X1) V) (= (tptp.app (tptp.app X1 _let_1) Z) U)))))))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (not (= W X2)) (exists ((X3 $$unsorted)) (and (tptp.ssList X3) (exists ((X4 $$unsorted)) (and (tptp.ssList X4) (= (tptp.tl X) X3) (= (tptp.app X3 X4) X2) (exists ((X5 $$unsorted)) (and (tptp.ssItem X5) (= (tptp.cons X5 tptp.nil) X4) (= (tptp.hd X) X5) (tptp.neq tptp.nil X))) (tptp.neq tptp.nil X))))))) (tptp.neq X tptp.nil)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (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 $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd 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.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.ssItem _let_12))) (let ((_let_14 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (tptp.ssList _let_14))) (let ((_let_16 (tptp.cons _let_12 tptp.nil))) (let ((_let_17 (tptp.app _let_14 _let_16))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_17 tptp.nil)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.app tptp.nil _let_16))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app _let_20 _let_14)))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_15))) (let ((_let_24 (not _let_9))) (let ((_let_25 (not _let_13))) (let ((_let_26 (or _let_25 _let_24 _let_23 _let_22 _let_19))) (let ((_let_27 (ASSUME :args (_let_9)))) (let ((_let_28 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_13))) (let ((_let_32 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_35 (not _let_28))) (let ((_let_36 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_37 (= _let_36 _let_35))) (let ((_let_38 (or _let_30 _let_24 _let_37))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_3313 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3313)) (= (tptp.neq U BOUND_VARIABLE_3313) (not (= U BOUND_VARIABLE_3313))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.ssList _let_17))) (let ((_let_45 (tptp.ssList _let_16))) (let ((_let_46 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_47 (and _let_46 _let_13 _let_45 _let_15 _let_44 _let_43 _let_36))) (let ((_let_48 (and (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_28))) (let ((_let_49 (forall ((Y $$unsorted) (BOUND_VARIABLE_5295 $$unsorted) (BOUND_VARIABLE_5293 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5293)) (not (tptp.ssList BOUND_VARIABLE_5295)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5293 _let_1) BOUND_VARIABLE_5295) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5295 _let_1) BOUND_VARIABLE_5293) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (not _let_36))) (let ((_let_52 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_30 _let_51 _let_50 _let_48 _let_47))) (let ((_let_55 (forall ((U $$unsorted) (BOUND_VARIABLE_5487 $$unsorted)) (let ((_let_1 (tptp.neq BOUND_VARIABLE_5487 tptp.nil))) (let ((_let_2 (tptp.hd BOUND_VARIABLE_5487))) (let ((_let_3 (tptp.cons _let_2 tptp.nil))) (let ((_let_4 (tptp.tl BOUND_VARIABLE_5487))) (let ((_let_5 (tptp.app _let_4 _let_3))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5487)) (not _let_1) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5295 $$unsorted) (BOUND_VARIABLE_5293 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5293)) (not (tptp.ssList BOUND_VARIABLE_5295)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5293 _let_1) BOUND_VARIABLE_5295) BOUND_VARIABLE_5487)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_5295 _let_1) BOUND_VARIABLE_5293))))))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5487)) (and (tptp.neq tptp.nil BOUND_VARIABLE_5487) (tptp.ssItem _let_2) (tptp.ssList _let_3) (tptp.ssList _let_4) (tptp.ssList _let_5) (not (= U _let_5)) _let_1)))))))))) (let ((_let_56 (not _let_54))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (or))) (let ((_let_59 (not _let_55))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_57) :args (_let_59)) (REWRITE :args ((=> _let_59 (not (or _let_53 _let_30 _let_51 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5295 $$unsorted) (BOUND_VARIABLE_5293 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5293)) (not (tptp.ssList BOUND_VARIABLE_5295)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5293 _let_1) BOUND_VARIABLE_5295) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app (tptp.app BOUND_VARIABLE_5295 _let_1) BOUND_VARIABLE_5293))))))) _let_48 _let_47))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_55))) (REFL :args (_let_56)) :args _let_58)) _let_57 :args (_let_56 true _let_55)))) (let ((_let_61 (REFL :args (_let_54)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 1)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_58)) :args ((or _let_29 _let_54))) _let_60 :args (_let_29 true _let_54)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 2)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_36))) :args _let_58)) :args ((or _let_36 _let_54))) _let_60 :args (_let_36 true _let_54)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_51 _let_35 (not _let_37)))) _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_24 _let_30 _let_37 (not _let_38)))) _let_27 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_41))) _let_40 :args (_let_38 false _let_39)) :args (_let_37 false _let_9 false _let_29 false _let_38)) :args (_let_35 false _let_36 false _let_37)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 _let_13 (not _let_31)))) _let_62 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args _let_34) :args (_let_32))) _let_33 :args (_let_31 false _let_32)) :args (_let_13 false _let_29 true _let_28 false _let_31)))) (let ((_let_66 (or _let_30 _let_28 _let_15))) (let ((_let_67 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_30 _let_28 _let_15 (not _let_66)))) _let_62 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args _let_34) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_15 false _let_29 true _let_28 false _let_66)))) (let ((_let_70 (_let_49))) (let ((_let_71 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil)))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_73 (or _let_53 _let_71))) (let ((_let_74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_ENUM))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 0)) (CONG _let_61 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_58)) :args ((or _let_52 _let_54))) _let_60 :args (_let_52 true _let_54)))) (let ((_let_78 (or _let_53 _let_72))) (let ((_let_79 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 (not _let_45))) (let ((_let_83 (or _let_23 _let_82 _let_44))) (let ((_let_84 (forall ((U $$unsorted) (BOUND_VARIABLE_3594 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3594)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3594)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (or _let_24 _let_25 _let_45))) (let ((_let_87 (forall ((U $$unsorted) (BOUND_VARIABLE_3336 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3336)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3336 U)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_24 _let_45 _let_25 (not _let_86)))) _let_27 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.nil _let_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_45 false _let_9 false _let_13 false _let_86)))) (let ((_let_90 (= _let_46 _let_35))) (let ((_let_91 (or _let_24 _let_30 _let_90))) (let ((_let_92 (not _let_90))) (let ((_let_93 (not _let_44))) (let ((_let_94 (not _let_46))) (let ((_let_95 (_let_47))) (let ((_let_96 (and _let_42 _let_72 _let_71))) (let ((_let_97 (_let_42 _let_72 _let_71))) (let ((_let_98 (APPLY_UF tptp.app))) (let ((_let_99 (REFL :args (tptp.nil)))) (let ((_let_100 (ASSUME :args (_let_42)))) (let ((_let_101 (ASSUME :args (_let_72)))) (let ((_let_102 (ASSUME :args (_let_71)))) (let ((_let_103 (tptp.cons _let_12 _let_14))) (let ((_let_104 (= _let_103 (tptp.app _let_16 _let_14)))) (let ((_let_105 (= _let_16 _let_20))) (let ((_let_106 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_103))) (let ((_let_107 (or _let_23 _let_25 _let_104))) (let ((_let_108 (forall ((U $$unsorted) (BOUND_VARIABLE_4824 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4824)) (= (tptp.cons BOUND_VARIABLE_4824 U) (tptp.app (tptp.cons BOUND_VARIABLE_4824 tptp.nil) U)))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (or _let_82 _let_105))) (let ((_let_111 (or _let_30 _let_28 _let_106))) (let ((_let_112 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_ENUM)) :args (_let_112))) _let_113 :args (_let_111 false _let_112)) :args (_let_106 false _let_29 true _let_28 false _let_111)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_82 _let_105 (not _let_110)))) _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_16 QUANTIFIERS_INST_ENUM)) :args _let_81)) _let_80 :args (_let_110 false _let_79)) :args (_let_105 false _let_45 false _let_110)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_25 _let_23 _let_104 (not _let_107)))) _let_65 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (_let_14 _let_12 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_108))) _let_109 :args (_let_107 false _let_108)) :args (_let_104 false _let_13 false _let_15 false _let_107)) :args (_let_21 false _let_106 false _let_105 false _let_104)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG 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(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_4 (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 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 20.34/20.58 )
% 20.34/20.58 % SZS output end Proof for SWC418+1
% 20.34/20.58 % cvc5---1.0.5 exiting
% 20.34/20.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------