TSTP Solution File: SWC176+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC176+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 20:23:48 EDT 2023
% Result : Theorem 33.86s 34.06s
% Output : Proof 33.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC176+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Aug 28 14:50:46 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.16/0.41 %----Proving TF0_NAR, FOF, or CNF
% 33.86/34.06 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.3wxIuiP51E/cvc5---1.0.5_18086.p...
% 33.86/34.06 ------- get file name : TPTP file name is SWC176+1
% 33.86/34.06 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18086.smt2...
% 33.86/34.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 33.86/34.06 --- Run --no-e-matching --full-saturate-quant at 5...
% 33.86/34.06 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 33.86/34.06 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 33.86/34.06 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 33.86/34.06 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 33.86/34.06 % SZS status Theorem for SWC176+1
% 33.86/34.06 % SZS output start Proof for SWC176+1
% 33.86/34.06 (
% 33.86/34.06 (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)) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (or (not (tptp.ssList Z)) (not (= (tptp.app (tptp.app Y W) Z) X)) (not (tptp.strictorderedP W)) (exists ((X1 $$unsorted)) (and (tptp.ssItem X1) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (= (tptp.app X2 (tptp.cons X1 tptp.nil)) Y) (exists ((X3 $$unsorted)) (and (tptp.ssItem X3) (exists ((X4 $$unsorted)) (and (tptp.ssList X4) (= (tptp.app (tptp.cons X3 tptp.nil) X4) W) (tptp.lt X1 X3))))))))) (exists ((X5 $$unsorted)) (and (tptp.ssItem X5) (exists ((X6 $$unsorted)) (and (tptp.ssList X6) (= (tptp.app (tptp.cons X5 tptp.nil) X6) Z) (exists ((X7 $$unsorted)) (and (tptp.ssItem X7) (exists ((X8 $$unsorted)) (and (tptp.ssList X8) (= (tptp.app X8 (tptp.cons X7 tptp.nil)) W) (tptp.lt X7 X5))))))))))))) (forall ((X9 $$unsorted)) (=> (tptp.ssItem X9) (forall ((X10 $$unsorted)) (or (not (tptp.ssItem X10)) (forall ((X11 $$unsorted)) (=> (tptp.ssList X11) (forall ((X12 $$unsorted)) (=> (tptp.ssList X12) (not (= (tptp.app (tptp.app (tptp.app X11 (tptp.cons X9 tptp.nil)) (tptp.cons X10 tptp.nil)) X12) U)))))) (tptp.neq X9 X10))))) (and (not (= tptp.nil X)) (= tptp.nil W))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))))) (let ((_let_3 (forall ((U $$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))))))))))) (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 $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_7 (tptp.ssList tptp.nil))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_9 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_13 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_14 (tptp.app _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_15 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_16 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_15))) (let ((_let_17 (tptp.app (tptp.app _let_16 _let_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_18 (= _let_17 (tptp.app _let_16 _let_14)))) (let ((_let_19 (= _let_14 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_20 (= _let_17 (tptp.app _let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_21 (not _let_11))) (let ((_let_22 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23))) (let ((_let_29 (forall ((U $$unsorted) (BOUND_VARIABLE_2159 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_2159)) (= (tptp.neq U BOUND_VARIABLE_2159) (not (= U BOUND_VARIABLE_2159))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_32 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.strictorderedP _let_17))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.ssList _let_17))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_27 _let_25 _let_22 _let_35 _let_33 (not (tptp.ssList _let_31)) (and (not (= tptp.nil _let_31)) (= tptp.nil _let_17)) (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((X1 $$unsorted) (BOUND_VARIABLE_5365 $$unsorted) (BOUND_VARIABLE_5352 $$unsorted) (BOUND_VARIABLE_5350 $$unsorted)) (or (not (tptp.ssItem X1)) (not (tptp.ssItem BOUND_VARIABLE_5350)) (not (tptp.lt X1 BOUND_VARIABLE_5350)) (not (tptp.ssList BOUND_VARIABLE_5352)) (not (= (tptp.app (tptp.cons BOUND_VARIABLE_5350 tptp.nil) BOUND_VARIABLE_5352) (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (not (tptp.ssList BOUND_VARIABLE_5365)) (not (= (tptp.app BOUND_VARIABLE_5365 (tptp.cons X1 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5453 $$unsorted) (BOUND_VARIABLE_5440 $$unsorted) (BOUND_VARIABLE_5438 $$unsorted)) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5438)) (not (tptp.lt BOUND_VARIABLE_5438 X5)) (not (tptp.ssList BOUND_VARIABLE_5440)) (not (= (tptp.app BOUND_VARIABLE_5440 (tptp.cons BOUND_VARIABLE_5438 tptp.nil)) (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (not (tptp.ssList BOUND_VARIABLE_5453)) (not (= (tptp.app (tptp.cons X5 tptp.nil) BOUND_VARIABLE_5453) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))) (let ((_let_41 (forall ((BOUND_VARIABLE_5788 $$unsorted) (BOUND_VARIABLE_5786 $$unsorted) (BOUND_VARIABLE_5767 $$unsorted) (BOUND_VARIABLE_5765 $$unsorted) (BOUND_VARIABLE_5763 $$unsorted) (BOUND_VARIABLE_5761 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5763 (tptp.cons BOUND_VARIABLE_5761 tptp.nil)) (tptp.cons BOUND_VARIABLE_5767 tptp.nil)) BOUND_VARIABLE_5765))) (let ((_let_2 (tptp.app (tptp.app BOUND_VARIABLE_5788 _let_1) BOUND_VARIABLE_5786))) (or (not (tptp.ssList _let_1)) (not (tptp.strictorderedP _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5761)) (not (tptp.ssItem BOUND_VARIABLE_5767)) (tptp.neq BOUND_VARIABLE_5761 BOUND_VARIABLE_5767) (not (tptp.ssList BOUND_VARIABLE_5763)) (not (tptp.ssList BOUND_VARIABLE_5765)) (not (tptp.ssList _let_2)) (and (not (= tptp.nil _let_2)) (= tptp.nil _let_1)) (not (tptp.ssList BOUND_VARIABLE_5788)) (not (forall ((X1 $$unsorted) (BOUND_VARIABLE_5365 $$unsorted) (BOUND_VARIABLE_5352 $$unsorted) (BOUND_VARIABLE_5350 $$unsorted)) (or (not (tptp.ssItem X1)) (not (tptp.ssItem BOUND_VARIABLE_5350)) (not (tptp.lt X1 BOUND_VARIABLE_5350)) (not (tptp.ssList BOUND_VARIABLE_5352)) (not (= (tptp.app (tptp.cons BOUND_VARIABLE_5350 tptp.nil) BOUND_VARIABLE_5352) (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5763 (tptp.cons BOUND_VARIABLE_5761 tptp.nil)) (tptp.cons BOUND_VARIABLE_5767 tptp.nil)) BOUND_VARIABLE_5765))) (not (tptp.ssList BOUND_VARIABLE_5365)) (not (= (tptp.app BOUND_VARIABLE_5365 (tptp.cons X1 tptp.nil)) BOUND_VARIABLE_5788))))) (not (tptp.ssList BOUND_VARIABLE_5786)) (not (forall ((X5 $$unsorted) (BOUND_VARIABLE_5453 $$unsorted) (BOUND_VARIABLE_5440 $$unsorted) (BOUND_VARIABLE_5438 $$unsorted)) (or (not (tptp.ssItem X5)) (not (tptp.ssItem BOUND_VARIABLE_5438)) (not (tptp.lt BOUND_VARIABLE_5438 X5)) (not (tptp.ssList BOUND_VARIABLE_5440)) (not (= (tptp.app BOUND_VARIABLE_5440 (tptp.cons BOUND_VARIABLE_5438 tptp.nil)) (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5763 (tptp.cons BOUND_VARIABLE_5761 tptp.nil)) (tptp.cons BOUND_VARIABLE_5767 tptp.nil)) BOUND_VARIABLE_5765))) (not (tptp.ssList BOUND_VARIABLE_5453)) (not (= (tptp.app (tptp.cons X5 tptp.nil) BOUND_VARIABLE_5453) BOUND_VARIABLE_5786))))))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (REFL :args (_let_40)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 3)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_44)) :args ((or _let_24 _let_40))) _let_46 :args (_let_24 true _let_40)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 2)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_44)) :args ((or _let_26 _let_40))) _let_46 :args (_let_26 true _let_40)))) (let ((_let_50 (not _let_23))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_23)) (CONG (REFL :args (_let_50)) (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_11))) :args _let_44)) :args ((or _let_22 _let_11 _let_50))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 4)) _let_46 :args ((not _let_22) true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_25 _let_23 (not _let_28)))) _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_29)))) _let_30 :args (_let_28 false _let_29)) :args (_let_23 false _let_26 false _let_24 false _let_28)) :args (_let_11 true _let_22 false _let_23)))) (let ((_let_52 (or _let_33 _let_12))) (let ((_let_53 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 6)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_44)) :args ((or _let_32 _let_40))) _let_46 :args (_let_32 true _let_40)))) (let ((_let_56 (tptp.ssList _let_13))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.ssList _let_16))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_57 _let_33 _let_18))) (let ((_let_61 (forall ((U $$unsorted) (BOUND_VARIABLE_4911 $$unsorted) (BOUND_VARIABLE_4909 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4909)) (not (tptp.ssList BOUND_VARIABLE_4911)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4909) BOUND_VARIABLE_4911) (tptp.app U (tptp.app BOUND_VARIABLE_4909 BOUND_VARIABLE_4911))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (tptp.ssList (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_13)))) (let ((_let_64 (or _let_35 _let_57 _let_63))) (let ((_let_65 (forall ((U $$unsorted) (BOUND_VARIABLE_3637 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3637)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3637)))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (tptp.ssList _let_15))) (let ((_let_68 (not _let_7))) (let ((_let_69 (or _let_68 _let_27 _let_67))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_3379 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3379)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3379 U)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (ASSUME :args (_let_7)))) (let ((_let_73 (and _let_11 _let_67))) (let ((_let_74 (ASSUME :args (_let_67)))) (let ((_let_75 (APPLY_UF tptp.ssList))) (let ((_let_76 (APPLY_UF tptp.cons))) (let ((_let_77 (REFL :args (tptp.nil)))) (let ((_let_78 (ASSUME :args (_let_11)))) (let ((_let_79 (SYMM (SYMM _let_78)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_73)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_74 _let_78) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG _let_79 _let_77 :args _let_76) :args _let_75) (TRUE_INTRO _let_74))) :args (_let_67 _let_11))) :args (_let_11 _let_67))) :args (true _let_73)) _let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_27 _let_67 (not _let_69)))) _let_72 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_67 false _let_7 false _let_26 false _let_69)) :args (_let_56 false _let_11 false _let_67)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 5)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_44)) :args ((or _let_34 _let_40))) _let_46 :args (_let_34 true _let_40)))) (let ((_let_82 (and _let_11 _let_63))) (let ((_let_83 (ASSUME :args (_let_63)))) (let ((_let_84 (APPLY_UF tptp.app))) (let ((_let_85 (or _let_33 _let_25 _let_19))) (let ((_let_86 (forall ((U $$unsorted) (BOUND_VARIABLE_4867 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4867)) (= (tptp.cons BOUND_VARIABLE_4867 U) (tptp.app (tptp.cons BOUND_VARIABLE_4867 tptp.nil) U)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (not _let_20))) (let ((_let_89 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_90 (or _let_27 _let_27 _let_89 _let_35 _let_68 _let_33 _let_88))) (let ((_let_91 (forall ((V $$unsorted) (BOUND_VARIABLE_3079 $$unsorted) (BOUND_VARIABLE_3077 $$unsorted) (BOUND_VARIABLE_3075 $$unsorted) (BOUND_VARIABLE_3073 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_3073)) (tptp.lt V BOUND_VARIABLE_3073) (not (tptp.ssList BOUND_VARIABLE_3079)) (not (tptp.ssList BOUND_VARIABLE_3075)) (not (tptp.ssList BOUND_VARIABLE_3077)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_3079 (tptp.cons V BOUND_VARIABLE_3075)) (tptp.cons BOUND_VARIABLE_3073 BOUND_VARIABLE_3077)) (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_92 (= _let_36 _let_91))) (let ((_let_93 (or _let_39 _let_92))) (let ((_let_94 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.strictorderedP U) (forall ((V $$unsorted) (BOUND_VARIABLE_3079 $$unsorted) (BOUND_VARIABLE_3077 $$unsorted) (BOUND_VARIABLE_3075 $$unsorted) (BOUND_VARIABLE_3073 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_3073)) (tptp.lt V BOUND_VARIABLE_3073) (not (tptp.ssList BOUND_VARIABLE_3079)) (not (tptp.ssList BOUND_VARIABLE_3075)) (not (tptp.ssList BOUND_VARIABLE_3077)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_3079 (tptp.cons V BOUND_VARIABLE_3075)) (tptp.cons BOUND_VARIABLE_3073 BOUND_VARIABLE_3077))))))))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (_let_91))) (let ((_let_97 (not _let_89))) (let ((_let_98 (or _let_27 _let_97))) (let ((_let_99 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.lt U U)))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (ASSUME :args (_let_88)))) (let ((_let_102 (ASSUME :args (_let_12)))) (let ((_let_103 (ASSUME :args (_let_19)))) (let ((_let_104 (ASSUME :args (_let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_101 (MODUS_PONENS (AND_INTRO _let_78 _let_102 _let_103 _let_104) (SCOPE (TRANS (SYMM (SYMM _let_104)) (CONG (REFL :args (_let_16)) (TRANS (SYMM (SYMM _let_103)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_102 :args _let_76) (CONG _let_79 (SYMM _let_102) :args _let_76)) :args _let_84)) :args (_let_11 _let_12 _let_19 _let_18)))) :args (_let_11 _let_12 _let_18 _let_19 _let_88)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_20)))))) (FALSE_INTRO _let_101))) :args (_let_88 _let_20)) :args ((not (and _let_11 _let_12 _let_18 _let_19 _let_88)) SB_LITERAL))) (CONG (REFL :args (_let_21)) (REFL :args ((not _let_12))) (REFL :args ((not _let_18))) (REFL :args ((not _let_19))) (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_20))) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_90))) :args ((or _let_68 _let_27 _let_35 _let_33 _let_89 _let_88 (not _let_90)))) _let_72 _let_49 _let_81 _let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_27 _let_97 (not _let_98)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem U) false))))) :args (_let_99))) _let_100 :args (_let_98 false _let_99)) :args (_let_97 false _let_26 false _let_98)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_96) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_96))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_92)) :args ((or _let_37 _let_91 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_44)) :args ((or _let_36 _let_40))) _let_46 :args (_let_36 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_39 _let_92 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_44)) :args ((or _let_38 _let_40))) _let_46 :args (_let_38 true _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_94)))) _let_95 :args (_let_93 false _let_94)) :args (_let_92 false _let_38 false _let_93)) :args (_let_91 false _let_36 false _let_92)) :args (_let_90 false _let_91)) :args (_let_88 false _let_7 false _let_26 false _let_34 false _let_32 true _let_89 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_25 _let_33 _let_19 (not _let_85)))) _let_48 _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.cons BOUND_VARIABLE_4867 tptp.nil) U)))) :args (_let_86)))) _let_87 :args (_let_85 false _let_86)) :args (_let_19 false _let_24 false _let_32 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_33 _let_57 _let_59 _let_18 (not _let_60)))) _let_55 _let_80 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_82)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_83 _let_78) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (CONG (SYMM _let_79) _let_77 :args _let_76) :args _let_84) :args _let_75) (TRUE_INTRO _let_83))) :args (_let_63 _let_11))) :args (_let_11 _let_63))) :args (true _let_82)) :args ((or _let_21 _let_58 (not _let_63)))) _let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_35 _let_57 _let_63 (not _let_64)))) _let_81 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_63 false _let_34 false _let_56 false _let_64)) :args (_let_58 false _let_11 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_13 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app U BOUND_VARIABLE_4909) BOUND_VARIABLE_4911)))) :args (_let_61))) _let_62 :args (_let_60 false _let_61)) :args (_let_18 false _let_32 false _let_56 false _let_58 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_33 _let_12 (not _let_52)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_53))) _let_54 :args (_let_52 false _let_53)) :args (_let_12 false _let_32 false _let_52)) _let_51 :args (false true _let_20 false _let_19 false _let_18 false _let_12 false _let_11)) :args (_let_10 (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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) _let_9 (forall ((U $$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_8 _let_7 (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))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_6 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$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)))))))) _let_4 _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))))))) (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 33.86/34.06 )
% 33.86/34.06 % SZS output end Proof for SWC176+1
% 33.86/34.06 % cvc5---1.0.5 exiting
% 33.86/34.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------