%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC018+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 20:22:38 EDT 2023

% Result   : Theorem 1.07s 1.31s
% Output   : Proof 1.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SWC018+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.37  % Computer : n026.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon Aug 28 18:24:50 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.51  %----Proving TF0_NAR, FOF, or CNF
% 1.07/1.31  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lLUHNbAcMT/cvc5---1.0.5_10683.p...
% 1.07/1.31  ------- get file name : TPTP file name is SWC018+1
% 1.07/1.31  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10683.smt2...
% 1.07/1.31  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.07/1.31  % SZS status Theorem for SWC018+1
% 1.07/1.31  % SZS output start Proof for SWC018+1
% 1.07/1.31  (
% 1.07/1.31  (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)) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (or (not (= (tptp.app W Y) X)) (not (tptp.equalelemsP W)) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (exists ((X1 $$unsorted)) (and (tptp.ssList X1) (= (tptp.app (tptp.cons Z tptp.nil) X1) Y) (exists ((X2 $$unsorted)) (and (tptp.ssList X2) (= (tptp.app X2 (tptp.cons Z tptp.nil)) W)))))))))) (and (not (= tptp.nil X)) (= tptp.nil W)) (and (or (not (= tptp.nil V)) (= tptp.nil U)) (or (not (tptp.neq V tptp.nil)) (exists ((X3 $$unsorted)) (and (tptp.ssList X3) (tptp.neq X3 tptp.nil) (tptp.frontsegP V X3) (tptp.frontsegP U X3))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))))) (let ((_let_4 (forall ((U $$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)))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))))) (let ((_let_6 (tptp.ssList tptp.nil))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_8 (forall ((X3 $$unsorted)) (or (not (tptp.ssList X3)) (not (tptp.neq X3 tptp.nil)) (not (tptp.frontsegP (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) X3)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X3)))))) (let ((_let_9 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.frontsegP _let_9 _let_9))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.neq _let_9 tptp.nil))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.ssList _let_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_13 _let_11))) (let ((_let_19 (not _let_8))) (let ((_let_20 (or _let_15 _let_19))) (let ((_let_21 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (= tptp.nil _let_9))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21))) (let ((_let_25 (and _let_24 _let_20))) (let ((_let_26 (tptp.frontsegP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (= _let_21 _let_26))) (let ((_let_28 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27))) (let ((_let_31 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_34 (not _let_33))) (let ((_let_35 (and _let_23 _let_21))) (let ((_let_36 (not (tptp.equalelemsP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_37 (or _let_29 _let_36 _let_17 _let_25 _let_35 _let_34 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5279 $$unsorted) (BOUND_VARIABLE_5271 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5271)) (not (= (tptp.app BOUND_VARIABLE_5271 _let_1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.ssList BOUND_VARIABLE_5279)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5279) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (let ((_let_38 (forall ((U $$unsorted) (BOUND_VARIABLE_5468 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (let ((_let_2 (tptp.app U BOUND_VARIABLE_5468))) (let ((_let_3 (not (= tptp.nil _let_2)))) (or (not (tptp.ssList U)) (not (tptp.equalelemsP U)) (not (tptp.ssList _let_2)) (and (or _let_3 _let_1) (or (not (tptp.neq _let_2 tptp.nil)) (not (forall ((X3 $$unsorted)) (or (not (tptp.ssList X3)) (not (tptp.neq X3 tptp.nil)) (not (tptp.frontsegP (tptp.app U BOUND_VARIABLE_5468) X3)) (not (tptp.frontsegP U X3))))))) (and _let_3 _let_1) (not (tptp.ssList BOUND_VARIABLE_5468)) (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5279 $$unsorted) (BOUND_VARIABLE_5271 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5271)) (not (= U (tptp.app BOUND_VARIABLE_5271 _let_1))) (not (tptp.ssList BOUND_VARIABLE_5279)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5279) BOUND_VARIABLE_5468))))))))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_40) :args (_let_42)) (REWRITE :args ((=> _let_42 (not (or _let_29 _let_36 _let_17 _let_25 _let_35 _let_34 (not (forall ((Z $$unsorted) (BOUND_VARIABLE_5279 $$unsorted) (BOUND_VARIABLE_5271 $$unsorted)) (let ((_let_1 (tptp.cons Z tptp.nil))) (or (not (tptp.ssItem Z)) (not (tptp.ssList BOUND_VARIABLE_5271)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app BOUND_VARIABLE_5271 _let_1))) (not (tptp.ssList BOUND_VARIABLE_5279)) (not (= (tptp.app _let_1 BOUND_VARIABLE_5279) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (REFL :args (_let_37)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_41)) :args ((or _let_28 _let_37))) _let_43 :args (_let_28 true _let_37)))) (let ((_let_46 (tptp.frontsegP _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_47 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_29 _let_29 _let_48 _let_34 _let_46))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_4082 $$unsorted) (BOUND_VARIABLE_4080 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4080)) (not (tptp.frontsegP U BOUND_VARIABLE_4080)) (not (tptp.ssList BOUND_VARIABLE_4082)) (tptp.frontsegP (tptp.app U BOUND_VARIABLE_4082) BOUND_VARIABLE_4080))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or _let_29 _let_47))) (let ((_let_53 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U U))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((not (= (tptp.ssList U) false))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_29 _let_47 (not _let_52)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_47 false _let_28 false _let_52)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_49))) :args ((or _let_29 _let_34 _let_48 _let_46 (not _let_49)))) _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 5)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_41)) :args ((or _let_33 _let_37))) _let_43 :args (_let_33 true _let_37)) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.frontsegP (tptp.app U BOUND_VARIABLE_4082) BOUND_VARIABLE_4080) true))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_46 false _let_28 false _let_33 false _let_47 false _let_49)))) (let ((_let_59 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_60 (not _let_21))) (let ((_let_61 (= _let_60 _let_59))) (let ((_let_62 (not _let_46))) (let ((_let_63 (not _let_59))) (let ((_let_64 (or _let_29 _let_63 _let_62 _let_48))) (let ((_let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))))) (let ((_let_66 (_let_35))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 3)) _let_43 :args ((not _let_25) true _let_37)))) (let ((_let_68 (CNF_AND_NEG :args (_let_25)))) (let ((_let_69 (not _let_6))) (let ((_let_70 (or _let_29 _let_69 _let_61))) (let ((_let_71 (forall ((U $$unsorted) (BOUND_VARIABLE_3303 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3303)) (= (tptp.neq U BOUND_VARIABLE_3303) (not (= U BOUND_VARIABLE_3303))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (not _let_61))) (let ((_let_74 (REFL :args (_let_20)))) (let ((_let_75 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 1)) (CONG _let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_8))) :args _let_41)) :args ((or _let_8 _let_20))))) (let ((_let_76 (_let_8))) (let ((_let_77 ((not (= (tptp.ssList X3) false))))) (let ((_let_78 (ASSUME :args _let_76))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_77)) :args _let_76)) (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_29 _let_48 _let_63 _let_62 (not _let_64)))) _let_57 _let_58 _let_45 _let_75 (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_61)) (CONG (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_21))) (REFL :args (_let_59)) :args _let_41)) :args ((or _let_21 _let_59 _let_73))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_29 _let_61 (not _let_70)))) (ASSUME :args (_let_6)) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.neq U BOUND_VARIABLE_3303)))) :args (_let_71)))) _let_72 :args (_let_70 false _let_71)) :args (_let_61 false _let_6 false _let_28 false _let_70)) _let_68 _let_67 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_66) (CONG (REFL :args _let_66) _let_65 (REFL :args (_let_60)) :args _let_41)) :args ((or _let_22 _let_35 _let_60))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 4)) _let_43 :args ((not _let_35) true _let_37)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) _let_65 :args _let_41)) :args ((or _let_22 _let_24))) :args (_let_22 true _let_64 false _let_47 false _let_46 false _let_28 false _let_8 false _let_59 false _let_61 true _let_20 true _let_25 true _let_21 true _let_35 false _let_24)))) (let ((_let_80 (and _let_22 _let_46))) (let ((_let_81 (ASSUME :args (_let_46)))) (let ((_let_82 (APPLY_UF tptp.frontsegP))) (let ((_let_83 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_84 (ASSUME :args (_let_22)))) (let ((_let_85 (SYMM (SYMM _let_84)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST _let_68 _let_67 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 1)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_27)) :args ((or _let_21 (not _let_26) (not _let_27)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_80)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_84) (SCOPE (TRUE_ELIM (TRANS (CONG _let_85 _let_83 :args _let_82) (TRUE_INTRO _let_81))) :args (_let_46 _let_22))) :args (_let_22 _let_46))) :args (true _let_80)) :args ((or _let_23 _let_26 _let_62))) _let_79 _let_58 :args (_let_26 false _let_22 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_27 (not _let_30)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_31)))) _let_32 :args (_let_30 false _let_31)) :args (_let_27 false _let_28 false _let_30)) :args (_let_21 false _let_26 false _let_27)) :args (_let_24 false _let_21)) :args ((not _let_20) true _let_25 false _let_24)))) (let ((_let_87 (not _let_18))) (let ((_let_88 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_89 (or _let_29 _let_88))) (let ((_let_90 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.frontsegP U tptp.nil))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (and _let_22 _let_88))) (let ((_let_93 (ASSUME :args (_let_88)))) (let ((_let_94 (or _let_17 _let_12))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 2)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_41)) :args ((or _let_16 _let_37))) _let_43 :args (_let_16 true _let_37)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (_let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_77)) :args _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_15 _let_13 _let_11 _let_87))) _let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG _let_74 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_41)) :args ((or _let_14 _let_20))) _let_86 :args (_let_14 true _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_17 _let_12 (not _let_94)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_94 false _let_53)) :args (_let_12 false _let_16 false _let_94)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_92)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_93 _let_84) (SCOPE (TRUE_ELIM (TRANS (CONG _let_83 (SYMM _let_85) :args _let_82) (TRUE_INTRO _let_93))) :args (_let_88 _let_22))) :args (_let_22 _let_88))) :args (true _let_92)) _let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_29 _let_88 (not _let_89)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_90))) _let_91 :args (_let_89 false _let_90)) :args (_let_88 false _let_28 false _let_89)) :args (_let_10 false _let_22 false _let_88)) :args (_let_87 false _let_16 false _let_14 false _let_12 false _let_10)) (MACRO_RESOLUTION_TRUST _let_75 _let_86 :args (_let_8 true _let_20)) :args (false true _let_18 false _let_8)) :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))))))) (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) _let_3 _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.15/1.32  )
% 1.15/1.32  % SZS output end Proof for SWC018+1
% 1.15/1.32  % cvc5---1.0.5 exiting
% 1.15/1.32  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------