TSTP Solution File: SWC313+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC313+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 20:24:41 EDT 2023
% Result : Theorem 69.83s 70.08s
% Output : Proof 69.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC313+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % 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 16:20:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 69.83/70.08 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qxeVjLeOCV/cvc5---1.0.5_25010.p...
% 69.83/70.08 ------- get file name : TPTP file name is SWC313+1
% 69.83/70.08 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25010.smt2...
% 69.83/70.08 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 69.83/70.08 --- Run --no-e-matching --full-saturate-quant at 5...
% 69.83/70.08 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 69.83/70.08 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 69.83/70.08 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 69.83/70.08 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 69.83/70.08 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 69.83/70.08 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 69.83/70.08 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 69.83/70.08 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 69.83/70.08 --- Run --relevant-triggers --full-saturate-quant at 5...
% 69.83/70.08 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 69.83/70.08 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 69.83/70.08 % SZS status Theorem for SWC313+1
% 69.83/70.08 % SZS output start Proof for SWC313+1
% 69.83/70.08 (
% 69.83/70.08 (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)))))) (and (not (= tptp.nil W)) (= tptp.nil X)) (and (or (not (= tptp.nil V)) (= tptp.nil U)) (or (not (tptp.neq V tptp.nil)) (exists ((X1 $$unsorted)) (and (tptp.ssItem X1) (exists ((X2 $$unsorted)) (let ((_let_1 (tptp.cons X1 tptp.nil))) (and (tptp.ssList X2) (= (tptp.app _let_1 X2) V) (= (tptp.app X2 _let_1) U)))))))))))))))))))) (let ((_let_2 (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_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_6 (tptp.ssList tptp.nil))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_8 (tptp.hd skv_7))) (let ((_let_9 (tptp.ssItem _let_8))) (let ((_let_10 (tptp.tl skv_7))) (let ((_let_11 (tptp.ssList _let_10))) (let ((_let_12 (tptp.cons _let_8 tptp.nil))) (let ((_let_13 (tptp.app _let_12 _let_10))) (let ((_let_14 (= skv_7 _let_13))) (let ((_let_15 (not _let_14))) (let ((_let_16 (= skv_6 (tptp.app _let_10 _let_12)))) (let ((_let_17 (not _let_11))) (let ((_let_18 (not _let_9))) (let ((_let_19 (or _let_18 _let_17 _let_16 _let_15))) (let ((_let_20 (= tptp.nil skv_7))) (let ((_let_21 (tptp.ssList skv_7))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_9))) (let ((_let_24 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (= tptp.nil skv_6))) (let ((_let_27 (not _let_20))) (let ((_let_28 (or _let_27 _let_26))) (let ((_let_29 (forall ((X1 $$unsorted) (BOUND_VARIABLE_5286 $$unsorted)) (let ((_let_1 (tptp.cons X1 tptp.nil))) (or (not (tptp.ssItem X1)) (not (tptp.ssList BOUND_VARIABLE_5286)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5286) skv_7)) (not (= (tptp.app BOUND_VARIABLE_5286 _let_1) skv_6))))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.neq skv_7 tptp.nil))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30))) (let ((_let_34 (tptp.neq tptp.nil tptp.nil))) (let ((_let_35 (or))) (let ((_let_36 (REFL :args (_let_27)))) (let ((_let_37 (not _let_26))) (let ((_let_38 (forall ((Y $$unsorted) (BOUND_VARIABLE_5249 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5249)) (= (tptp.app BOUND_VARIABLE_5249 _let_1) skv_6) (not (= (tptp.app _let_1 BOUND_VARIABLE_5249) skv_7))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((U $$unsorted) (BOUND_VARIABLE_5360 $$unsorted)) (let ((_let_1 (= tptp.nil BOUND_VARIABLE_5360))) (let ((_let_2 (= tptp.nil U))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5360)) (and (or (not _let_1) _let_2) (or (not (tptp.neq BOUND_VARIABLE_5360 tptp.nil)) (not (forall ((X1 $$unsorted) (BOUND_VARIABLE_5286 $$unsorted)) (let ((_let_1 (tptp.cons X1 tptp.nil))) (or (not (tptp.ssItem X1)) (not (tptp.ssList BOUND_VARIABLE_5286)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5286) BOUND_VARIABLE_5360)) (not (= U (tptp.app BOUND_VARIABLE_5286 _let_1))))))))) (not (forall ((Y $$unsorted) (BOUND_VARIABLE_5249 $$unsorted)) (let ((_let_1 (tptp.cons Y tptp.nil))) (or (not (tptp.ssItem Y)) (not (tptp.ssList BOUND_VARIABLE_5249)) (= U (tptp.app BOUND_VARIABLE_5249 _let_1)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5249) BOUND_VARIABLE_5360)))))) (and (not _let_2) _let_1)))))) (not (or (not (tptp.ssList skv_6)) _let_22 (and _let_28 _let_33) (not _let_38) (and _let_37 _let_20)))))))))) (let ((_let_40 (REORDERING (EQ_RESOLVE (NOT_AND (NOT_OR_ELIM _let_39 :args (4))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_26))) _let_36 :args _let_35)) :args (_let_28)))) (let ((_let_41 (NOT_AND (NOT_OR_ELIM _let_39 :args (2))))) (let ((_let_42 (REFL :args (_let_33)))) (let ((_let_43 (not _let_34))) (let ((_let_44 (not _let_6))) (let ((_let_45 (or _let_44 _let_44 _let_43))) (let ((_let_46 (forall ((U $$unsorted) (BOUND_VARIABLE_3295 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3295)) (= (tptp.neq U BOUND_VARIABLE_3295) (not (= U BOUND_VARIABLE_3295))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (and _let_20 _let_43))) (let ((_let_49 (ASSUME :args (_let_43)))) (let ((_let_50 (ASSUME :args (_let_20)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_48)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_49 _let_50) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_50) (REFL :args (tptp.nil)) :args (APPLY_UF tptp.neq)) (FALSE_INTRO _let_49))) :args (_let_43 _let_20))) :args (_let_20 _let_43))) :args (true _let_48)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_34))) (REFL :args (_let_32)) :args _let_35)) :args ((or _let_27 _let_32 _let_34))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_45))) :args ((or _let_44 _let_43 (not _let_45)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.nil tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_46)))) _let_47 :args (_let_45 false _let_46)) :args (_let_43 false _let_6 false _let_45)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_35)) :args ((or _let_31 _let_33))) _let_41 (CNF_OR_NEG :args (_let_28 1)) _let_40 :args (_let_27 true _let_34 false _let_31 true _let_33 false _let_28 false _let_26)))) (let ((_let_52 (NOT_NOT_ELIM (NOT_OR_ELIM _let_39 :args (1))))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_20 _let_9 (not _let_23)))) _let_52 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_9 false _let_21 true _let_20 false _let_23)))) (let ((_let_54 (or _let_22 _let_20 _let_11))) (let ((_let_55 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssList (tptp.tl U)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_22 _let_20 _let_11 (not _let_54)))) _let_52 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tl U)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_11 false _let_21 true _let_20 false _let_54)))) (let ((_let_58 (_let_38))) (let ((_let_59 (tptp.cons _let_8 _let_10))) (let ((_let_60 (= _let_59 _let_13))) (let ((_let_61 (= skv_7 _let_59))) (let ((_let_62 (or _let_17 _let_18 _let_60))) (let ((_let_63 (forall ((U $$unsorted) (BOUND_VARIABLE_4806 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4806)) (= (tptp.cons BOUND_VARIABLE_4806 U) (tptp.app (tptp.cons BOUND_VARIABLE_4806 tptp.nil) U)))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (or _let_22 _let_20 _let_61))) (let ((_let_66 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (and _let_61 _let_60))) (let ((_let_69 (ASSUME :args (_let_60)))) (let ((_let_70 (ASSUME :args (_let_61)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_68)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_69 _let_70) (SCOPE (TRANS (SYMM (SYMM _let_70)) (SYMM (SYMM _let_69))) :args (_let_60 _let_61))) :args (_let_61 _let_60))) :args (true _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_22 _let_20 _let_61 (not _let_65)))) _let_52 _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (skv_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_61 false _let_21 true _let_20 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_18 _let_17 _let_60 (not _let_62)))) _let_53 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_10 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4806 U)))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_60 false _let_9 false _let_11 false _let_62)) :args (_let_14 false _let_61 false _let_60)))) (let ((_let_72 (not _let_16))) (let ((_let_73 (or _let_18 _let_17 _let_15 _let_72))) (let ((_let_74 (_let_29))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_17 _let_15 _let_16 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_18 _let_17 _let_15 _let_72 (not _let_73)))) _let_53 _let_57 _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_74) :args (_let_8 _let_10 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.cons X1 tptp.nil) BOUND_VARIABLE_5286)))) :args _let_74))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_35)) :args ((or _let_29 _let_33))) (MACRO_RESOLUTION_TRUST _let_41 _let_40 :args ((not _let_33) false _let_28)) :args (_let_29 true _let_33)) :args (_let_73 false _let_29)) :args (_let_72 false _let_9 false _let_11 false _let_14 false _let_73)) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_58) :args (_let_8 _let_10 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.cons Y tptp.nil) BOUND_VARIABLE_5249)))) :args _let_58))) (NOT_NOT_ELIM (NOT_OR_ELIM _let_39 :args (3))) :args (_let_19 false _let_38)) _let_57 _let_53 :args (false true _let_16 false _let_14 false _let_19 false _let_11 false _let_9)) :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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_6 (forall ((U $$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))))))) _let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))) (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_3 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 69.83/70.09 )
% 69.83/70.09 % SZS output end Proof for SWC313+1
% 69.83/70.09 % cvc5---1.0.5 exiting
% 69.83/70.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------