TSTP Solution File: SWC310+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 20:24:40 EDT 2023
% Result : Theorem 0.17s 0.62s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 18:53:46 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.45 %----Proving TF0_NAR, FOF, or CNF
% 0.17/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Rp0vpWGV5y/cvc5---1.0.5_3839.p...
% 0.17/0.62 ------- get file name : TPTP file name is SWC310+1
% 0.17/0.62 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3839.smt2...
% 0.17/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.17/0.62 % SZS status Theorem for SWC310+1
% 0.17/0.62 % SZS output start Proof for SWC310+1
% 0.17/0.62 (
% 0.17/0.62 (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) X)) (not (= (tptp.app Z _let_1) W))))))) (tptp.neq X tptp.nil)) (and (or (not (= tptp.nil V)) (= tptp.nil U)) (or (not (tptp.neq V tptp.nil)) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= U X1) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (exists ((X3 $$unsorted)) (and (tptp.ssList X3) (= (tptp.tl V) X2) (= (tptp.app X2 X3) X1) (exists ((X4 $$unsorted)) (and (tptp.ssItem X4) (= (tptp.cons X4 tptp.nil) X3) (= (tptp.hd V) X4) (tptp.neq tptp.nil V))) (tptp.neq tptp.nil V)))))))))))))))))))) (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) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_11 (tptp.ssList tptp.nil))) (let ((_let_12 (forall ((U $$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_7))) (let ((_let_15 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_16 (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_16))) (let ((_let_18 (= tptp.nil _let_16))) (let ((_let_19 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (not _let_14))) (let ((_let_21 (or _let_20 _let_19))) (let ((_let_22 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_24 (tptp.ssItem _let_23))) (let ((_let_25 (not _let_22))) (let ((_let_26 (or _let_25 _let_14 _let_24))) (let ((_let_27 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_28 (tptp.ssList _let_27))) (let ((_let_29 (or _let_25 _let_14 _let_28))) (let ((_let_30 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_31 (= _let_20 _let_30))) (let ((_let_32 (tptp.cons _let_23 tptp.nil))) (let ((_let_33 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_27 _let_32)))) (let ((_let_34 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (tptp.ssList _let_32))) (let ((_let_36 (and _let_30 _let_24 _let_35 _let_28 _let_34 _let_33))) (let ((_let_37 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36))) (let ((_let_40 (and _let_21 _let_39))) (let ((_let_41 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_15)))) (let ((_let_42 (not _let_41))) (let ((_let_43 (not _let_17))) (let ((_let_44 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_43 _let_42))) (let ((_let_49 (and _let_48 _let_37))) (let ((_let_50 (tptp.ssList _let_15))) (let ((_let_51 (not _let_11))) (let ((_let_52 (or _let_51 _let_47 _let_50))) (let ((_let_53 (= tptp.nil _let_15))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_51 _let_47 _let_54))) (let ((_let_56 (tptp.hd _let_15))) (let ((_let_57 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_56))) (let ((_let_58 (or _let_51 _let_47 _let_57))) (let ((_let_59 (tptp.tl _let_15))) (let ((_let_60 (= tptp.nil _let_59))) (let ((_let_61 (or _let_51 _let_47 _let_60))) (let ((_let_62 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_63 (or _let_45 _let_62))) (let ((_let_64 (= _let_56 (tptp.hd _let_16)))) (let ((_let_65 (not _let_50))) (let ((_let_66 (or _let_65 _let_53 _let_45 _let_64))) (let ((_let_67 (= (tptp.tl _let_16) (tptp.app _let_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_68 (or _let_65 _let_53 _let_45 _let_67))) (let ((_let_69 (or))) (let ((_let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_14))))) (let ((_let_71 (not _let_19))) (let ((_let_72 (and _let_71 _let_14))) (let ((_let_73 (not _let_34))) (let ((_let_74 (or _let_73 _let_25 _let_40 _let_72 _let_49))) (let ((_let_75 (forall ((U $$unsorted) (BOUND_VARIABLE_5556 $$unsorted) (BOUND_VARIABLE_5554 $$unsorted) (BOUND_VARIABLE_5552 $$unsorted)) (let ((_let_1 (tptp.neq BOUND_VARIABLE_5552 tptp.nil))) (let ((_let_2 (tptp.cons BOUND_VARIABLE_5556 tptp.nil))) (let ((_let_3 (= tptp.nil BOUND_VARIABLE_5552))) (let ((_let_4 (= tptp.nil U))) (let ((_let_5 (tptp.hd BOUND_VARIABLE_5552))) (let ((_let_6 (tptp.cons _let_5 tptp.nil))) (let ((_let_7 (tptp.tl BOUND_VARIABLE_5552))) (let ((_let_8 (tptp.ssList U))) (or (not _let_8) (not (tptp.ssList BOUND_VARIABLE_5552)) (and (or (not _let_3) _let_4) (or (not _let_1) (and (tptp.neq tptp.nil BOUND_VARIABLE_5552) (tptp.ssItem _let_5) (tptp.ssList _let_6) (tptp.ssList _let_7) _let_8 (= U (tptp.app _let_7 _let_6))))) (and (not _let_4) _let_3) (and (or (not (tptp.ssItem BOUND_VARIABLE_5556)) (not (tptp.ssList BOUND_VARIABLE_5554)) (not (= BOUND_VARIABLE_5552 (tptp.app _let_2 BOUND_VARIABLE_5554))) (not (= U (tptp.app BOUND_VARIABLE_5554 _let_2)))) _let_1))))))))))))) (let ((_let_76 (not _let_74))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (not _let_75))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_77) :args (_let_78))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_75))) (REFL :args (_let_76)) :args _let_69)) _let_77 :args (_let_76 true _let_75)))) (let ((_let_80 (REFL :args (_let_74)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 1)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_22))) :args _let_69)) :args ((or _let_22 _let_74))) _let_79 :args (_let_22 true _let_74)))) (let ((_let_82 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (or _let_51 _let_25 _let_31))) (let ((_let_87 (forall ((U $$unsorted) (BOUND_VARIABLE_3314 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3314)) (= (tptp.neq U BOUND_VARIABLE_3314) (not (= U BOUND_VARIABLE_3314))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (ASSUME :args (_let_11)))) (let ((_let_90 (not _let_31))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_74 2)) _let_79 :args ((not _let_40) true _let_74)))) (let ((_let_92 (CNF_AND_NEG :args (_let_40)))) (let ((_let_93 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_69)) :args ((or _let_37 _let_39))))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_74 4)) _let_79 :args ((not _let_49) true _let_74)))) (let ((_let_95 (not _let_48))) (let ((_let_96 (REORDERING (CNF_AND_NEG :args (_let_49)) :args ((or _let_38 _let_49 _let_95))))) (let ((_let_97 (REFL :args (_let_48)))) (let ((_let_98 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_69)) :args ((or _let_46 _let_48))))) (let ((_let_99 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_69)) :args ((or _let_44 _let_48))))) (let ((_let_100 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_17))) :args _let_69)) :args ((or _let_17 _let_48))))) (let ((_let_101 (forall ((U $$unsorted) (BOUND_VARIABLE_3337 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3337)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3337 U)))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3337 U)))) :args (_let_101))) _let_102 :args (_let_52 false _let_101)))) (let ((_let_104 (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_47 _let_50 (not _let_52)))))) (let ((_let_105 (forall ((U $$unsorted) (BOUND_VARIABLE_3362 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3362)) (not (= U (tptp.cons BOUND_VARIABLE_3362 U))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3362 U)))) :args (_let_105))) _let_106 :args (_let_55 false _let_105)))) (let ((_let_108 (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_51 _let_47 _let_54 (not _let_55)))))) (let ((_let_109 (forall ((U $$unsorted) (BOUND_VARIABLE_3543 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3543)) (= BOUND_VARIABLE_3543 (tptp.hd (tptp.cons BOUND_VARIABLE_3543 U))))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (forall ((U $$unsorted) (BOUND_VARIABLE_3573 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3573)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3573 U))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (forall ((U $$unsorted) (BOUND_VARIABLE_4930 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (tptp.ssList BOUND_VARIABLE_4930)) (= (tptp.hd U) (tptp.hd (tptp.app U BOUND_VARIABLE_4930))))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (forall ((U $$unsorted) (BOUND_VARIABLE_4958 $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (tptp.ssList BOUND_VARIABLE_4958)) (= (tptp.tl (tptp.app U BOUND_VARIABLE_4958)) (tptp.app (tptp.tl U) BOUND_VARIABLE_4958)))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (not _let_64))) (let ((_let_120 (not _let_57))) (let ((_let_121 (and _let_17 _let_50 _let_57 _let_64))) (let ((_let_122 (ASSUME :args (_let_50)))) (let ((_let_123 (APPLY_UF tptp.cons))) (let ((_let_124 (REFL :args (tptp.nil)))) (let ((_let_125 (ASSUME :args (_let_57)))) (let ((_let_126 (SYMM (SYMM _let_125)))) (let ((_let_127 (ASSUME :args (_let_64)))) (let ((_let_128 (SYMM (SYMM _let_127)))) (let ((_let_129 (APPLY_UF tptp.hd))) (let ((_let_130 (ASSUME :args (_let_17)))) (let ((_let_131 (SYMM _let_130))) (let ((_let_132 (SYMM _let_131))) (let ((_let_133 (and _let_17 _let_41 _let_57 _let_60 _let_62 _let_64 _let_67))) (let ((_let_134 (APPLY_UF tptp.app))) (let ((_let_135 (ASSUME :args (_let_67)))) (let ((_let_136 (ASSUME :args (_let_60)))) (let ((_let_137 (ASSUME :args (_let_62)))) (let ((_let_138 (ASSUME :args (_let_41)))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_36)) :args ((or _let_73 _let_36 (not _let_30) (not _let_24) (not _let_35) (not _let_28) (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 0)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_34))) :args _let_69)) :args ((or _let_34 _let_74))) _let_79 :args (_let_34 true _let_74)) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_133)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_130 _let_135 _let_136 _let_137 _let_127 _let_125 _let_138) (SCOPE (TRANS (SYMM (SYMM _let_138)) (CONG (TRANS (SYMM (SYMM _let_137)) (CONG (SYMM (SYMM _let_136)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args _let_134) (SYMM _let_135) (CONG _let_131 :args (APPLY_UF tptp.tl))) (CONG (TRANS _let_126 _let_128 (CONG _let_131 :args _let_129)) _let_124 :args _let_123) :args _let_134)) :args (_let_17 _let_67 _let_60 _let_62 _let_64 _let_57 _let_41))) :args (_let_17 _let_41 _let_57 _let_60 _let_62 _let_64 _let_67))) :args (true _let_133)) :args ((or _let_33 _let_43 _let_42 _let_120 (not _let_60) (not _let_62) _let_119 (not _let_67)))) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_122 _let_125 _let_127 _let_130) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (TRANS (CONG _let_132 :args _let_129) (SYMM _let_128) (SYMM _let_126)) _let_124 :args _let_123) :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_122))) :args (_let_50 _let_57 _let_64 _let_17))) :args (_let_17 _let_50 _let_57 _let_64))) :args (true _let_121)) :args ((or _let_35 _let_43 _let_65 _let_120 _let_119))) (REORDERING (CNF_OR_POS :args (_let_68)) 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(forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.17/0.62 )
% 0.17/0.62 % SZS output end Proof for SWC310+1
% 0.17/0.63 % cvc5---1.0.5 exiting
% 0.17/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------