TSTP Solution File: SWC243+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC243+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 20:24:13 EDT 2023
% Result : Theorem 81.02s 81.24s
% Output : Proof 81.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC243+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n023.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 18:25:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 81.02/81.24 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2SILkRVe5H/cvc5---1.0.5_30828.p...
% 81.02/81.24 ------- get file name : TPTP file name is SWC243+1
% 81.02/81.24 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30828.smt2...
% 81.02/81.24 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 81.02/81.24 --- Run --no-e-matching --full-saturate-quant at 5...
% 81.02/81.24 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 81.02/81.24 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 81.02/81.24 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 81.02/81.24 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 81.02/81.24 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 81.02/81.24 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 81.02/81.24 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 81.02/81.24 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 81.02/81.24 --- Run --relevant-triggers --full-saturate-quant at 5...
% 81.02/81.24 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 81.02/81.24 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 81.02/81.24 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 81.02/81.24 % SZS status Theorem for SWC243+1
% 81.02/81.24 % SZS output start Proof for SWC243+1
% 81.02/81.24 (
% 81.02/81.24 (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.totalorderedP W)) (= tptp.nil U) (exists ((Y $$unsorted)) (and (tptp.ssItem Y) (exists ((Z $$unsorted)) (and (tptp.ssList Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.app (tptp.app Z (tptp.cons Y tptp.nil)) X1) U) (forall ((X2 $$unsorted)) (=> (tptp.ssItem X2) (or (not (tptp.memberP Z X2)) (not (tptp.memberP X1 X2)) (not (tptp.lt Y X2)) (tptp.leq Y X2)))))))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))))) (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.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_8 (forall ((U $$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_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 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (tptp.ssItem _let_11))) (let ((_let_13 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261))) (let ((_let_14 (tptp.leq _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261))) (let ((_let_15 (and (not (= _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261)) _let_14))) (let ((_let_16 (tptp.lt _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (not _let_13))) (let ((_let_19 (not _let_12))) (let ((_let_20 (or _let_19 _let_18 _let_17))) (let ((_let_21 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_12))) (let ((_let_25 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (not (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_28 (forall ((Y $$unsorted) (BOUND_VARIABLE_5272 $$unsorted) (BOUND_VARIABLE_5270 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5270)) (not (tptp.ssList BOUND_VARIABLE_5272)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_5270 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5272) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5270 X2)) (not (tptp.memberP BOUND_VARIABLE_5272 X2)) (not (tptp.lt Y X2)) (tptp.leq Y X2)))))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_23 _let_21 _let_29 _let_27))) (let ((_let_31 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5272 $$unsorted) (BOUND_VARIABLE_5270 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5270)) (not (tptp.ssList BOUND_VARIABLE_5272)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_5270 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5272))) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5270 X2)) (not (tptp.memberP BOUND_VARIABLE_5272 X2)) (not (tptp.lt Y X2)) (tptp.leq Y X2))))))) (not (tptp.totalorderedP U)))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (or))) (let ((_let_34 (not _let_31))) (let ((_let_35 (_let_34))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_35)) :args _let_35) (REWRITE :args ((=> _let_34 (not (or _let_23 _let_21 (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5272 $$unsorted) (BOUND_VARIABLE_5270 $$unsorted)) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5270)) (not (tptp.ssList BOUND_VARIABLE_5272)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app (tptp.app BOUND_VARIABLE_5270 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5272))) (not (forall ((X2 $$unsorted)) (or (not (tptp.ssItem X2)) (not (tptp.memberP BOUND_VARIABLE_5270 X2)) (not (tptp.memberP BOUND_VARIABLE_5272 X2)) (not (tptp.lt Y X2)) (tptp.leq Y X2))))))) _let_27))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_31))) (REFL :args (_let_32)) :args _let_33)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_32 true _let_31)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 1)) _let_36 :args ((not _let_21) true _let_30)))) (let ((_let_38 (REFL :args (_let_30)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_33)) :args ((or _let_22 _let_30))) _let_36 :args (_let_22 true _let_30)))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_21 _let_12 (not _let_24)))) _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_12 false _let_22 true _let_21 false _let_24)))) (let ((_let_41 (not _let_16))) (let ((_let_42 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (or _let_18 (not (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261)) (not (tptp.memberP _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261)) _let_41 _let_14))) (let ((_let_44 (forall ((X2 $$unsorted)) (let ((_let_1 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.ssItem X2)) (not (tptp.memberP tptp.nil X2)) (not (tptp.memberP (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) X2)) (not (tptp.lt _let_1 X2)) (tptp.leq _let_1 X2)))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (not _let_44))) (let ((_let_47 (tptp.cons _let_11 tptp.nil))) (let ((_let_48 (tptp.app tptp.nil _let_47))) (let ((_let_49 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app _let_48 _let_42)))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.ssList _let_42))) (let ((_let_52 (not _let_51))) (let ((_let_53 (not _let_9))) (let ((_let_54 (or _let_19 _let_53 _let_52 _let_50 _let_46))) (let ((_let_55 (_let_28))) (let ((_let_56 (tptp.cons _let_11 _let_42))) (let ((_let_57 (= _let_56 (tptp.app _let_47 _let_42)))) (let ((_let_58 (= _let_47 _let_48))) (let ((_let_59 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_56))) (let ((_let_60 (or _let_52 _let_19 _let_57))) (let ((_let_61 (forall ((U $$unsorted) (BOUND_VARIABLE_4798 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4798)) (= (tptp.cons BOUND_VARIABLE_4798 U) (tptp.app (tptp.cons BOUND_VARIABLE_4798 tptp.nil) U)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_64 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.tl _let_63)))) (let ((_let_65 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_63))) (let ((_let_66 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_67 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_68 (not _let_67))) (let ((_let_69 (not _let_66))) (let ((_let_70 (or _let_69 _let_68 _let_64))) (let ((_let_71 (forall ((U $$unsorted) (BOUND_VARIABLE_3546 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3546)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3546 U))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not _let_65))) (let ((_let_74 (or _let_69 _let_68 _let_73))) (let ((_let_75 (forall ((V $$unsorted) (BOUND_VARIABLE_3457 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3457)) (not (= (tptp.cons BOUND_VARIABLE_3457 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_76 (not _let_74))) (let ((_let_77 (not _let_75))) (let ((_let_78 (or _let_23 _let_21 _let_77))) (let ((_let_79 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3457 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3457)) (not (= U (tptp.cons BOUND_VARIABLE_3457 V)))))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_77))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_81)) :args _let_81) (REWRITE :args ((=> _let_77 (not (or _let_69 _let_68 (not (= _let_63 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_75))) (REFL :args (_let_76)) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_23 _let_21 _let_77 (not _let_78)))) _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_79)))) _let_80 :args (_let_78 false _let_79)) :args (_let_77 false _let_22 true _let_21 false _let_78)) :args (_let_76 true _let_75)))) (let ((_let_83 (REFL :args (_let_74)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_66))) :args _let_33)) :args ((or _let_66 _let_74))) _let_82 :args (_let_66 true _let_74)))) (let ((_let_85 (and _let_66 _let_65 _let_64))) (let ((_let_86 (ASSUME :args (_let_66)))) (let ((_let_87 (ASSUME :args (_let_64)))) (let ((_let_88 (ASSUME :args (_let_65)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_85)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_86 _let_87 _let_88) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (CONG (SYMM (SYMM _let_88)) :args (APPLY_UF tptp.tl)) (SYMM _let_87)) :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_86))) :args (_let_66 _let_64 _let_65))) :args (_let_66 _let_65 _let_64))) :args (true _let_85)) _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 2)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_65))) :args _let_33)) :args ((or _let_65 _let_74))) _let_82 :args (_let_65 true _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_68 _let_64 (not _let_70)))) _let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_74 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_33)) :args ((or _let_67 _let_74))) _let_82 :args (_let_67 true _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_64 false _let_66 false _let_67 false _let_70)) :args (_let_51 false _let_66 false _let_65 false _let_64)))) (let ((_let_90 (tptp.ssList _let_47))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_58))) (let ((_let_93 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (or _let_53 _let_19 _let_90))) (let ((_let_96 (forall ((U $$unsorted) (BOUND_VARIABLE_3310 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3310)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3310 U)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (ASSUME :args (_let_9)))) (let ((_let_99 (or _let_23 _let_21 _let_59))) (let ((_let_100 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (and _let_59 _let_58 _let_57))) (let ((_let_103 (ASSUME :args (_let_58)))) (let ((_let_104 (ASSUME :args (_let_57)))) (let ((_let_105 (ASSUME :args (_let_59)))) (let ((_let_106 (_let_46))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_44))) (REFL :args (_let_45)) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_19 _let_52 _let_46 _let_50 (not _let_54)))) _let_98 _let_40 _let_89 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_102)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_103 _let_104 _let_105) (SCOPE (TRANS (SYMM (SYMM _let_105)) (SYMM (SYMM _let_104)) (CONG (SYMM (SYMM _let_103)) (REFL :args (_let_42)) :args (APPLY_UF tptp.app))) :args (_let_58 _let_57 _let_59))) :args (_let_59 _let_58 _let_57))) :args (true _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_23 _let_21 _let_59 (not _let_99)))) _let_39 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_100))) _let_101 :args (_let_99 false _let_100)) :args (_let_59 false _let_22 true _let_21 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_91 _let_58 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_53 _let_19 _let_90 (not _let_95)))) _let_98 _let_40 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (tptp.nil _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3310 U)))) :args (_let_96))) _let_97 :args (_let_95 false _let_96)) :args (_let_90 false _let_9 false _let_12 false _let_95)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_47 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.app tptp.nil U)))) :args (_let_93))) _let_94 :args (_let_92 false _let_93)) :args (_let_58 false _let_90 false _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_19 _let_52 _let_57 (not _let_60)))) _let_40 _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_42 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4798 U)))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_57 false _let_12 false _let_51 false _let_60)) :args (_let_49 false _let_59 false _let_58 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (_let_11 _let_42 tptp.nil QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app BOUND_VARIABLE_5270 (tptp.cons Y tptp.nil)) BOUND_VARIABLE_5272)))) :args _let_55))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 2)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_33)) :args ((or _let_28 _let_30))) _let_36 :args (_let_28 true _let_30)) :args (_let_54 false _let_28)) :args (_let_46 false _let_9 false _let_12 false _let_51 false _let_49 false _let_54)) :args (_let_45 true _let_44)))) (let ((_let_108 (REFL :args (_let_43)))) (let ((_let_109 (forall ((U $$unsorted) (BOUND_VARIABLE_5124 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_5124)) (= (tptp.lt U BOUND_VARIABLE_5124) (and (not (= U BOUND_VARIABLE_5124)) (tptp.leq U BOUND_VARIABLE_5124))))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (not _let_17))) (let ((_let_112 (not _let_15))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_18 _let_17 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or _let_41 _let_15 _let_111))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 3)) (CONG _let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_16))) :args _let_33)) :args ((or _let_16 _let_43))) _let_107 :args (_let_16 true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 1)) :args ((or _let_14 _let_112))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 4)) _let_107 :args ((not _let_14) true _let_43)) :args (_let_112 true _let_14)) :args (_let_111 false _let_16 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (_let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_109))) _let_110 :args (_let_20 false _let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG _let_108 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_13))) :args _let_33)) :args ((or _let_13 _let_43))) _let_107 :args (_let_13 true _let_43)) _let_40 :args (false true _let_17 false _let_20 false _let_13 false _let_12)) :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)))))) (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)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (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 $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_10 _let_9 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) _let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_5 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (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_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 $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (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))))))) _let_2 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 81.02/81.25 )
% 81.02/81.25 % SZS output end Proof for SWC243+1
% 81.02/81.26 % cvc5---1.0.5 exiting
% 81.02/81.26 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------