TSTP Solution File: SWC340+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC340+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 20:24:53 EDT 2023
% Result : Theorem 0.83s 1.06s
% Output : Proof 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC340+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 17:27:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.83/1.06 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.9y6L5YCwJ5/cvc5---1.0.5_4902.p...
% 0.83/1.06 ------- get file name : TPTP file name is SWC340+1
% 0.83/1.06 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4902.smt2...
% 0.83/1.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.83/1.06 % SZS status Theorem for SWC340+1
% 0.83/1.06 % SZS output start Proof for SWC340+1
% 0.83/1.06 (
% 0.83/1.06 (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)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.segmentP X W)) (not (tptp.strictorderedP W)) (and (tptp.segmentP V U) (tptp.totalorderedP U)))))))))))))) (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 $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$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_4 (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 ((_let_5 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_6 (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) _let_5))) (let ((_let_7 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_8 (= _let_7 _let_6))) (let ((_let_9 (not _let_6))) (let ((_let_10 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_10))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_5 _let_18 _let_16 _let_14 _let_12))) (let ((_let_24 (forall ((V $$unsorted) (BOUND_VARIABLE_2848 $$unsorted) (BOUND_VARIABLE_2846 $$unsorted) (BOUND_VARIABLE_2844 $$unsorted) (BOUND_VARIABLE_2842 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2842)) (tptp.leq V BOUND_VARIABLE_2842) (not (tptp.ssList BOUND_VARIABLE_2848)) (not (tptp.ssList BOUND_VARIABLE_2844)) (not (tptp.ssList BOUND_VARIABLE_2846)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_2848 (tptp.cons V BOUND_VARIABLE_2844)) (tptp.cons BOUND_VARIABLE_2842 BOUND_VARIABLE_2846)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (= _let_26 _let_24))) (let ((_let_28 (not _let_24))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_27))) (let ((_let_32 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.totalorderedP U) (forall ((V $$unsorted) (BOUND_VARIABLE_2848 $$unsorted) (BOUND_VARIABLE_2846 $$unsorted) (BOUND_VARIABLE_2844 $$unsorted) (BOUND_VARIABLE_2842 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2842)) (tptp.leq V BOUND_VARIABLE_2842) (not (tptp.ssList BOUND_VARIABLE_2848)) (not (tptp.ssList BOUND_VARIABLE_2844)) (not (tptp.ssList BOUND_VARIABLE_2846)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_2848 (tptp.cons V BOUND_VARIABLE_2844)) (tptp.cons BOUND_VARIABLE_2842 BOUND_VARIABLE_2846))))))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (not _let_34))) (let ((_let_36 (and _let_34 _let_26))) (let ((_let_37 (tptp.strictorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_30 _let_38 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_36 _let_35))) (let ((_let_40 (forall ((U $$unsorted) (BOUND_VARIABLE_5237 $$unsorted)) (let ((_let_1 (tptp.segmentP BOUND_VARIABLE_5237 U))) (or (not (tptp.ssList U)) (not (tptp.strictorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5237)) (and _let_1 (tptp.totalorderedP U)) (not _let_1)))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or))) (let ((_let_44 (not _let_40))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_44))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) (REFL :args (_let_41)) :args _let_43)) _let_42 :args (_let_41 true _let_40)))) (let ((_let_46 (REFL :args (_let_39)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_43)) :args ((or _let_29 _let_39))) _let_45 :args (_let_29 true _let_39)))) (let ((_let_48 (_let_28))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_48)) :args _let_48) (REWRITE :args ((=> _let_28 (not (or _let_22 _let_20 _let_5 _let_18 _let_16 _let_14 (not (= _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_27)) :args ((or _let_26 _let_28 (not _let_27)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_36)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 3)) _let_45 :args ((not _let_36) true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 4)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_43)) :args ((or _let_34 _let_39))) _let_45 :args (_let_34 true _let_39)) :args ((not _let_26) true _let_36 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_27 (not _let_31)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_32)))) _let_33 :args (_let_31 false _let_32)) :args (_let_27 false _let_29 false _let_31)) :args (_let_28 true _let_26 false _let_27)) :args (_let_25 true _let_24)))) (let ((_let_50 (or _let_22 _let_20 _let_8))) (let ((_let_51 (forall ((U $$unsorted) (BOUND_VARIABLE_5096 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_5096)) (= (tptp.lt U BOUND_VARIABLE_5096) (and (not (= U BOUND_VARIABLE_5096)) (tptp.leq U BOUND_VARIABLE_5096))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (REFL :args (_let_23)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_43)) :args ((or _let_19 _let_23))) _let_49 :args (_let_19 true _let_23)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_43)) :args ((or _let_21 _let_23))) _let_49 :args (_let_21 true _let_23)))) (let ((_let_56 (or _let_22 _let_20 _let_7 _let_18 _let_16 _let_14 _let_12))) (let ((_let_57 (forall ((V $$unsorted) (BOUND_VARIABLE_2982 $$unsorted) (BOUND_VARIABLE_2980 $$unsorted) (BOUND_VARIABLE_2978 $$unsorted) (BOUND_VARIABLE_2976 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2976)) (tptp.lt V BOUND_VARIABLE_2976) (not (tptp.ssList BOUND_VARIABLE_2982)) (not (tptp.ssList BOUND_VARIABLE_2978)) (not (tptp.ssList BOUND_VARIABLE_2980)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_2982 (tptp.cons V BOUND_VARIABLE_2978)) (tptp.cons BOUND_VARIABLE_2976 BOUND_VARIABLE_2980)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_58 (= _let_37 _let_57))) (let ((_let_59 (or _let_30 _let_58))) (let ((_let_60 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.strictorderedP U) (forall ((V $$unsorted) (BOUND_VARIABLE_2982 $$unsorted) (BOUND_VARIABLE_2980 $$unsorted) (BOUND_VARIABLE_2978 $$unsorted) (BOUND_VARIABLE_2976 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2976)) (tptp.lt V BOUND_VARIABLE_2976) (not (tptp.ssList BOUND_VARIABLE_2982)) (not (tptp.ssList BOUND_VARIABLE_2978)) (not (tptp.ssList BOUND_VARIABLE_2980)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_2982 (tptp.cons V BOUND_VARIABLE_2978)) (tptp.cons BOUND_VARIABLE_2976 BOUND_VARIABLE_2980))))))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_57))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_8)) :args ((or _let_6 (not _let_7) (not _let_8)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_22 _let_20 _let_18 _let_16 _let_14 _let_12 _let_7 (not _let_56)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 3)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_43)) :args ((or _let_17 _let_23))) _let_49 :args (_let_17 true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 4)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_43)) :args ((or _let_15 _let_23))) _let_49 :args (_let_15 true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 5)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_43)) :args ((or _let_13 _let_23))) _let_49 :args (_let_13 true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 6)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_43)) :args ((or _let_11 _let_23))) _let_49 :args (_let_11 true _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app BOUND_VARIABLE_2982 (tptp.cons V BOUND_VARIABLE_2978)) (tptp.cons BOUND_VARIABLE_2976 BOUND_VARIABLE_2980))))) :args _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or _let_38 _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_43)) :args ((or _let_37 _let_39))) _let_45 :args (_let_37 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_30 _let_58 (not _let_59)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_60)))) _let_61 :args (_let_59 false _let_60)) :args (_let_58 false _let_29 false _let_59)) :args (_let_57 false _let_37 false _let_58)) :args (_let_56 false _let_57)) :args (_let_7 false _let_21 false _let_19 false _let_17 false _let_15 false _let_13 false _let_11 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_22 _let_20 _let_8 (not _let_50)))) _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.leq U BOUND_VARIABLE_5096)))) :args (_let_51))) _let_52 :args (_let_50 false _let_51)) :args (_let_8 false _let_21 false _let_19 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_6 1)) :args ((or _let_5 _let_9))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 2)) _let_49 :args ((not _let_5) true _let_23)) :args (_let_9 true _let_5)) :args (false false _let_7 false _let_8 true _let_6)) :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)))))))))))))))) _let_4 _let_3 (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 $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) (tptp.ssList tptp.nil) (forall ((U $$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))))) (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.83/1.07 )
% 0.83/1.07 % SZS output end Proof for SWC340+1
% 0.83/1.07 % cvc5---1.0.5 exiting
% 0.83/1.07 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------