%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC403+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:25:22 EDT 2023

% Result   : Theorem 76.35s 76.78s
% Output   : Proof 76.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17  % Problem    : SWC403+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.17  % Command    : do_cvc5 %s %d
% 0.17/0.39  % Computer : n008.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Mon Aug 28 14:58:32 EDT 2023
% 0.17/0.39  % CPUTime    : 
% 0.24/0.51  %----Proving TF0_NAR, FOF, or CNF
% 76.35/76.78  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Slb46iLm00/cvc5---1.0.5_24338.p...
% 76.35/76.78  ------- get file name : TPTP file name is SWC403+1
% 76.35/76.78  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24338.smt2...
% 76.35/76.78  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 76.35/76.78  --- Run --no-e-matching --full-saturate-quant at 5...
% 76.35/76.78  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 76.35/76.78  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 76.35/76.78  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 76.35/76.78  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 76.35/76.78  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 76.35/76.78  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 76.35/76.78  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 76.35/76.78  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 76.35/76.78  --- Run --relevant-triggers --full-saturate-quant at 5...
% 76.35/76.78  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 76.35/76.78  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 76.35/76.78  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 76.35/76.78  % SZS status Theorem for SWC403+1
% 76.35/76.78  % SZS output start Proof for SWC403+1
% 76.35/76.78  (
% 76.35/76.78  (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)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.strictorderedP Y))) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (or (not (tptp.memberP U Z)) (tptp.memberP V Z)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))) (let ((_let_5 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_7 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_8 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (or (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_8))) (let ((_let_10 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.memberP _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (= _let_11 _let_9))) (let ((_let_13 (not _let_5))) (let ((_let_14 (not _let_7))) (let ((_let_15 (not _let_6))) (let ((_let_16 (or _let_15 _let_14 _let_13 _let_12))) (let ((_let_17 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (not _let_8))) (let ((_let_19 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_13 (not (tptp.strictorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_22 _let_20 (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)) (not (tptp.segmentP Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.strictorderedP Y))))) _let_15 _let_18 _let_17))) (let ((_let_24 (forall ((U $$unsorted) (BOUND_VARIABLE_5298 $$unsorted) (BOUND_VARIABLE_5296 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.strictorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5296)) (not (tptp.segmentP BOUND_VARIABLE_5296 U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP BOUND_VARIABLE_5296 Y)) (not (tptp.segmentP Y U)) (not (tptp.strictorderedP Y))))) (not (tptp.ssItem BOUND_VARIABLE_5298)) (not (tptp.memberP U BOUND_VARIABLE_5298)) (tptp.memberP BOUND_VARIABLE_5296 BOUND_VARIABLE_5298))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (or))) (let ((_let_28 (not _let_24))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_27)) _let_26 :args (_let_25 true _let_24)))) (let ((_let_30 (REFL :args (_let_23)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_5))) :args _let_27)) :args ((or _let_5 _let_23))) _let_29 :args (_let_5 true _let_23)))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 5)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_6))) :args _let_27)) :args ((or _let_6 _let_23))) _let_29 :args (_let_6 true _let_23)))) (let ((_let_33 (tptp.app _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_34 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_33))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_14 _let_37 _let_35))) (let ((_let_39 (forall ((W $$unsorted) (BOUND_VARIABLE_2304 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2304)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2304))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (not _let_39))) (let ((_let_42 (= _let_19 _let_41))) (let ((_let_43 (or _let_22 _let_13 _let_42))) (let ((_let_44 (forall ((U $$unsorted) (BOUND_VARIABLE_2329 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2329)) (= (tptp.segmentP U BOUND_VARIABLE_2329) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2304 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2304)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2329) BOUND_VARIABLE_2304))))))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (_let_41))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_39))) (REFL :args (_let_40)) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_42)) :args ((or _let_20 _let_41 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 3)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_27)) :args ((or _let_19 _let_23))) _let_29 :args (_let_19 true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_13 _let_22 _let_42 (not _let_43)))) _let_31 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 2)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_27)) :args ((or _let_21 _let_23))) _let_29 :args (_let_21 true _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.segmentP U BOUND_VARIABLE_2329)))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_42 false _let_5 false _let_21 false _let_43)) :args (_let_41 false _let_19 false _let_42)) :args (_let_40 true _let_39)))) (let ((_let_48 (REFL :args (_let_38)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_7))) :args _let_27)) :args ((or _let_7 _let_38))) _let_47 :args (_let_7 true _let_38)))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_3862 $$unsorted) (BOUND_VARIABLE_3860 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList BOUND_VARIABLE_3860)) (not (tptp.ssList BOUND_VARIABLE_3862)) (= (tptp.memberP (tptp.app BOUND_VARIABLE_3860 BOUND_VARIABLE_3862) U) (or (tptp.memberP BOUND_VARIABLE_3860 U) (tptp.memberP BOUND_VARIABLE_3862 U))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_50))) (let ((_let_53 (not _let_12))) (let ((_let_54 (or _let_11 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_55 (tptp.memberP _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_56 (= _let_55 _let_54))) (let ((_let_57 (not _let_54))) (let ((_let_58 (tptp.ssList _let_10))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_15 _let_59 _let_37 _let_56))) (let ((_let_61 (or _let_14 _let_13 _let_58))) (let ((_let_62 (forall ((U $$unsorted) (BOUND_VARIABLE_3555 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3555)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3555)))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (not _let_55))) (let ((_let_65 (not _let_17))) (let ((_let_66 (and _let_65 _let_34))) (let ((_let_67 (_let_65 _let_34))) (let ((_let_68 (ASSUME :args (_let_65)))) (let ((_let_69 (ASSUME :args (_let_34)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_13 _let_15 _let_14 _let_12 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_12)) :args ((or _let_11 (not _let_9) _let_53))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_54 0)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_56)) :args ((or _let_55 _let_57 (not _let_56)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_66)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_68 _let_69) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_69) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args (APPLY_UF tptp.memberP)) (FALSE_INTRO _let_68))) :args _let_67)) :args _let_67)) :args (true _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_17))) (REFL :args (_let_35)) (REFL :args (_let_64)) :args _let_27)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 7)) _let_29 :args (_let_65 true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_27)) :args ((or _let_34 _let_38))) _let_47 :args (_let_34 true _let_38)) :args (_let_64 true _let_17 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_15 _let_37 _let_59 _let_56 (not _let_60)))) _let_32 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_27)) :args ((or _let_36 _let_38))) _let_47 :args (_let_36 true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_13 _let_14 _let_58 (not _let_61)))) _let_31 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.app U BOUND_VARIABLE_3555)))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_58 false _let_5 false _let_7 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52)) _let_51 :args (_let_60 false _let_50)) :args (_let_56 false _let_6 false _let_36 false _let_58 false _let_60)) :args (_let_57 true _let_55 false _let_56)) :args ((not _let_11) true _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_9 1)) :args ((or _let_18 _let_9))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 6)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_8))) :args _let_27)) :args ((or _let_8 _let_23))) _let_29 :args (_let_8 true _let_23)) :args (_let_9 false _let_8)) :args (_let_53 true _let_11 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52)) _let_51 :args (_let_16 false _let_50)) _let_49 _let_32 _let_31 :args (false true _let_12 false _let_16 false _let_7 false _let_6 false _let_5)) :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 $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_3 (forall ((U $$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)))))) _let_2 (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))))))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 76.45/76.79  )
% 76.45/76.79  % SZS output end Proof for SWC403+1
% 76.45/76.79  % cvc5---1.0.5 exiting
% 76.45/76.79  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------