TSTP Solution File: SWC409+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 20:25:25 EDT 2023
% Result : Theorem 176.55s 176.77s
% Output : Proof 176.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 17:32:09 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 176.55/176.77 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wCJRiMwzom/cvc5---1.0.5_19786.p...
% 176.55/176.77 ------- get file name : TPTP file name is SWC409+1
% 176.55/176.77 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19786.smt2...
% 176.55/176.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 176.55/176.77 --- Run --no-e-matching --full-saturate-quant at 5...
% 176.55/176.77 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 176.55/176.77 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 176.55/176.77 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 176.55/176.77 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 176.55/176.77 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 176.55/176.77 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 176.55/176.77 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 176.55/176.77 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 176.55/176.77 --- Run --relevant-triggers --full-saturate-quant at 5...
% 176.55/176.77 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 176.55/176.77 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 176.55/176.77 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 176.55/176.77 --- Run --no-cbqi --full-saturate-quant at 10...
% 176.55/176.77 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 176.55/176.77 % SZS status Theorem for SWC409+1
% 176.55/176.77 % SZS output start Proof for SWC409+1
% 176.55/176.77 (
% 176.55/176.77 (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 $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (and (tptp.ssList Z) (not (= (tptp.app Z _let_1) W)) (= (tptp.app _let_1 Z) X)))))) (forall ((X1 $$unsorted)) (=> (tptp.ssItem X1) (or (not (tptp.memberP V X1)) (tptp.memberP U X1)))) (and (not (= tptp.nil W)) (= tptp.nil X)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_6 (tptp.singletonP tptp.nil))) (let ((_let_7 (not _let_6))) (let ((_let_8 (forall ((U $$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))))))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_15 (forall ((U $$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)))))))))) (let ((_let_16 (tptp.ssList tptp.nil))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_18 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_19 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_20 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (= tptp.nil (tptp.app tptp.nil tptp.nil)))) (let ((_let_22 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))))) (let ((_let_23 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_24 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (tptp.cons _let_24 _let_23))) (let ((_let_26 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_25))) (let ((_let_27 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_28 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_27))) (let ((_let_29 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 (tptp.tl _let_27)))) (let ((_let_30 (tptp.cons _let_24 tptp.nil))) (let ((_let_31 (tptp.app _let_30 _let_23))) (let ((_let_32 (= _let_25 _let_31))) (let ((_let_33 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24))) (let ((_let_34 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_35 (tptp.memberP (tptp.app _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_37 (not _let_20))) (let ((_let_38 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_39 (not _let_38))) (let ((_let_40 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_41 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_42 (not _let_41))) (let ((_let_43 (and _let_42 _let_40))) (let ((_let_44 (forall ((Y $$unsorted) (BOUND_VARIABLE_5235 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5235)) (= (tptp.app BOUND_VARIABLE_5235 _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (= (tptp.app _let_1 BOUND_VARIABLE_5235) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_47 (not _let_46))) (let ((_let_48 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_49 (or _let_48 _let_47 _let_45 _let_43 _let_39 _let_37 _let_36))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_5327 $$unsorted) (BOUND_VARIABLE_5325 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5325)) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5235 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5235)) (= U (tptp.app BOUND_VARIABLE_5235 _let_1)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5235) BOUND_VARIABLE_5325)))))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5325)) (not (tptp.ssItem BOUND_VARIABLE_5327)) (not (tptp.memberP BOUND_VARIABLE_5325 BOUND_VARIABLE_5327)) (tptp.memberP U BOUND_VARIABLE_5327))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_50))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_52) :args (_let_54)) (REWRITE :args ((=> _let_54 (not (or _let_48 _let_47 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5235 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5235)) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5235 _let_1)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5235) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) _let_43 _let_39 _let_37 _let_36))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_50))) (REFL :args (_let_51)) :args _let_53)) _let_52 :args (_let_51 true _let_50)))) (let ((_let_56 (REFL :args (_let_49)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 5)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_20))) :args _let_53)) :args ((or _let_20 _let_49))) _let_55 :args (_let_20 true _let_49)))) (let ((_let_58 (not _let_16))) (let ((_let_59 (or _let_58 _let_21))) (let ((_let_60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((not (= (tptp.ssList U) false))))) (let ((_let_64 (ASSUME :args (_let_16)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_21 (not _let_59)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_59 false _let_60)) :args (_let_21 false _let_16 false _let_59)))) (let ((_let_66 (not _let_22))) (let ((_let_67 (or (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) _let_66))) (let ((_let_68 (forall ((W $$unsorted) (BOUND_VARIABLE_2146 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2146)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2146)))))))) (let ((_let_69 (not _let_67))) (let ((_let_70 (not _let_68))) (let ((_let_71 (= _let_20 _let_70))) (let ((_let_72 (or _let_47 _let_39 _let_71))) (let ((_let_73 (forall ((U $$unsorted) (BOUND_VARIABLE_2172 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2172)) (= (tptp.memberP U BOUND_VARIABLE_2172) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2146 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2146)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2172 BOUND_VARIABLE_2146)))))))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 4)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_53)) :args ((or _let_38 _let_49))) _let_55 :args (_let_38 true _let_49)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_56 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_53)) :args ((or _let_46 _let_49))) _let_55 :args (_let_46 true _let_49)))) (let ((_let_77 (_let_70))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_67 2)) (CONG (REFL :args (_let_67)) (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_22))) :args _let_53)) :args ((or _let_22 _let_67))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_77)) :args _let_77)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_68))) (REFL :args (_let_69)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_71)) :args ((or _let_37 _let_70 (not _let_71)))) _let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_47 _let_39 _let_71 (not _let_72)))) _let_76 _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2172)))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_71 false _let_46 false _let_38 false _let_72)) :args (_let_70 false _let_20 false _let_71)) :args (_let_69 true _let_68)) :args (_let_22 true _let_67)))) (let ((_let_79 (or _let_47 _let_40 _let_26))) (let ((_let_80 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((not (= (tptp.ssList U) false))))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82)) _let_81 :args (_let_79 false _let_80)))) (let ((_let_85 (not _let_40))) (let ((_let_86 (forall ((V $$unsorted) (BOUND_VARIABLE_3451 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3451)) (not (= (tptp.cons BOUND_VARIABLE_3451 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))) (let ((_let_87 (not _let_86))) (let ((_let_88 (or _let_47 _let_40 _let_87))) (let ((_let_89 (tptp.ssItem _let_24))) (let ((_let_90 (or _let_47 _let_40 _let_89))) (let ((_let_91 (not _let_28))) (let ((_let_92 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_95 _let_93 _let_91))) (let ((_let_97 (= tptp.nil _let_30))) (let ((_let_98 (not _let_97))) (let ((_let_99 (not _let_89))) (let ((_let_100 (or _let_99 _let_98))) (let ((_let_101 (tptp.ssList _let_30))) (let ((_let_102 (or _let_58 _let_99 _let_101))) (let ((_let_103 (tptp.app tptp.nil _let_30))) (let ((_let_104 (= tptp.nil _let_103))) (let ((_let_105 (= _let_97 _let_104))) (let ((_let_106 (not _let_101))) (let ((_let_107 (or _let_58 _let_106 _let_105))) (let ((_let_108 (= _let_30 _let_103))) (let ((_let_109 (or _let_106 _let_108))) (let ((_let_110 (tptp.ssList _let_103))) (let ((_let_111 (or _let_58 _let_106 _let_110))) (let ((_let_112 (or _let_95 _let_93 _let_29))) (let ((_let_113 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_114 (and _let_104 _let_113))) (let ((_let_115 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_103))) (let ((_let_116 (= tptp.nil _let_115))) (let ((_let_117 (= _let_116 _let_114))) (let ((_let_118 (not _let_110))) (let ((_let_119 (or _let_95 _let_118 _let_117))) (let ((_let_120 (tptp.ssList _let_23))) (let ((_let_121 (not _let_120))) (let ((_let_122 (or _let_121 _let_99 _let_32))) (let ((_let_123 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_31))) (let ((_let_124 (not _let_123))) (let ((_let_125 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app _let_23 _let_30)))) (let ((_let_126 (or _let_99 _let_121 _let_125 _let_124))) (let ((_let_127 (not _let_36))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_49 6)) _let_55 :args (_let_127 true _let_49)))) (let ((_let_129 (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_36))))) (let ((_let_130 (REFL :args (_let_37)))) (let ((_let_131 (REFL :args (_let_85)))) (let ((_let_132 (REFL :args (_let_42)))) (let ((_let_133 (ASSUME :args (_let_127)))) (let ((_let_134 (FALSE_INTRO _let_133))) (let ((_let_135 (APPLY_UF tptp.memberP))) (let ((_let_136 (REFL :args 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((or _let_39 _let_95 _let_326 _let_323 (not _let_327)))) _let_75 _let_234 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_328)) :args ((or _let_58 _let_39 _let_325 (not _let_328)))) _let_64 _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_165 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_167)) :args _let_166)) _let_165 :args (_let_328 false _let_164)) :args (_let_325 false _let_16 false _let_38 false _let_328)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_261 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_34 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_262)) _let_261 :args (_let_327 false _let_260)) :args (_let_323 false _let_38 false _let_94 false _let_325 false _let_327)) :args (_let_324 true _let_322 false _let_323)) _let_320 _let_238 _let_235 _let_232 _let_230 _let_78 _let_65 _let_57 :args (false true _let_35 false _let_33 false _let_32 false _let_29 false _let_28 false _let_26 false _let_22 false _let_21 false _let_20)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) _let_19 _let_18 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_17 _let_16 (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))))))))))) _let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_14 _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_12 _let_11 (forall ((U $$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_10 (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) _let_9 _let_8 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_7 (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) _let_3 _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 176.55/176.78 )
% 176.55/176.78 % SZS output end Proof for SWC409+1
% 176.55/176.78 % cvc5---1.0.5 exiting
% 176.55/176.78 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------