%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO127+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n001.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 : Wed Aug 30 22:49:51 EDT 2023

% Result   : Theorem 62.90s 63.22s
% Output   : Proof 62.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GEO127+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 30 00:21:08 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 62.90/63.22  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.arAICznPjN/cvc5---1.0.5_12296.p...
% 62.90/63.22  ------- get file name : TPTP file name is GEO127+1
% 62.90/63.22  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12296.smt2...
% 62.90/63.22  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 62.90/63.22  --- Run --no-e-matching --full-saturate-quant at 5...
% 62.90/63.22  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 62.90/63.22  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 62.90/63.22  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 62.90/63.22  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 62.90/63.22  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 62.90/63.22  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 62.90/63.22  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 62.90/63.22  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 62.90/63.22  --- Run --relevant-triggers --full-saturate-quant at 5...
% 62.90/63.22  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 62.90/63.22  % SZS status Theorem for GEO127+1
% 62.90/63.22  % SZS output start Proof for GEO127+1
% 62.90/63.22  (
% 62.90/63.22  (let ((_let_1 (not (forall ((O $$unsorted) (P $$unsorted)) (= (tptp.incident_o P O) (exists ((Q $$unsorted)) (or (tptp.ordered_by O P Q) (tptp.ordered_by O Q P)))))))) (let ((_let_2 (forall ((O $$unsorted)) (exists ((P $$unsorted)) (tptp.start_point P O))))) (let ((_let_3 (forall ((O $$unsorted)) (exists ((C $$unsorted)) (and (tptp.open C) (forall ((P $$unsorted)) (= (tptp.incident_o P O) (tptp.incident_c P C)))))))) (let ((_let_4 (forall ((O $$unsorted) (P $$unsorted) (Q $$unsorted)) (=> (tptp.ordered_by O P Q) (and (tptp.incident_o P O) (tptp.incident_o Q O)))))) (let ((_let_5 (forall ((P $$unsorted) (O $$unsorted)) (= (tptp.start_point P O) (and (tptp.incident_o P O) (forall ((Q $$unsorted)) (=> (and (not (= P Q)) (tptp.incident_o Q O)) (tptp.ordered_by O P Q)))))))) (let ((_let_6 (forall ((C $$unsorted) (P $$unsorted)) (=> (tptp.end_point P C) (exists ((Q $$unsorted)) (and (tptp.end_point Q C) (not (= P Q)))))))) (let ((_let_7 (forall ((C $$unsorted)) (= (tptp.open C) (exists ((P $$unsorted)) (tptp.end_point P C)))))) (let ((_let_8 (forall ((P $$unsorted) (C $$unsorted)) (= (tptp.end_point P C) (and (tptp.incident_c P C) (forall ((C1 $$unsorted) (C2 $$unsorted)) (=> (and (tptp.part_of C1 C) (tptp.part_of C2 C) (tptp.incident_c P C1) (tptp.incident_c P C2)) (or (tptp.part_of C1 C2) (tptp.part_of C2 C1))))))))) (let ((_let_9 (forall ((b_BOUND_VARIABLE_1272 it_6_$$unsorted)) (not (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 b_BOUND_VARIABLE_1272 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))))) (let ((_let_10 (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_11 (not _let_9))) (let ((_let_12 (forall ((b_BOUND_VARIABLE_1266 it_6_$$unsorted)) (not (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 b_BOUND_VARIABLE_1266))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11))) (let ((_let_15 (io_tptp.incident_o_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (not _let_14))) (let ((_let_18 (and _let_15 (io_tptp.incident_o_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_19 (and (io_tptp.incident_o_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) _let_15))) (let ((_let_20 (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_18))) (let ((_let_23 (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_19))) (let ((_let_26 (forall ((b_O it_76_$$unsorted) (b_P it_6_$$unsorted)) (= (io_tptp.incident_o_10 b_P b_O) (or (not (forall ((b_BOUND_VARIABLE_1266 it_6_$$unsorted)) (not (io_tptp.ordered_by_8 b_O b_P b_BOUND_VARIABLE_1266)))) (not (forall ((b_BOUND_VARIABLE_1272 it_6_$$unsorted)) (not (io_tptp.ordered_by_8 b_O b_BOUND_VARIABLE_1272 b_P))))))))) (let ((_let_27 (not _let_16))) (let ((_let_28 (not _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((O $$unsorted) (P $$unsorted)) (= (tptp.incident_o P O) (or (not (forall ((BOUND_VARIABLE_1266 $$unsorted)) (not (tptp.ordered_by O P BOUND_VARIABLE_1266)))) (not (forall ((BOUND_VARIABLE_1272 $$unsorted)) (not (tptp.ordered_by O BOUND_VARIABLE_1272 P)))))))) _let_28))))))) (let ((_let_30 (or))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_29) :args (_let_28))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_26))) (REFL :args (_let_27)) :args _let_30)) _let_29 :args (_let_27 true _let_26)))) (let ((_let_32 (_let_16))) (let ((_let_33 (forall ((b_O it_76_$$unsorted) (b_P it_6_$$unsorted) (b_Q it_6_$$unsorted)) (or (not (io_tptp.ordered_by_8 b_O b_P b_Q)) (and (io_tptp.incident_o_10 b_P b_O) (io_tptp.incident_o_10 b_Q b_O)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((O $$unsorted) (P $$unsorted) (Q $$unsorted)) (or (not (tptp.ordered_by O P Q)) (and (tptp.incident_o P O) (tptp.incident_o Q O)))) _let_33))))))) (let ((_let_35 (_let_33))) (let ((_let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))))) (let ((_let_37 (_let_13))) (let ((_let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_9))))) (let ((_let_39 (_let_11))) (let ((_let_40 (_let_14))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args _let_40) :args ((or _let_13 _let_11 _let_17))) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_39)) :args _let_39) (REWRITE :args ((=> _let_11 (not _let_24)))))) (CONG _let_38 (REFL :args (_let_23)) :args _let_30)) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_37)) :args _let_37) (REWRITE :args ((=> _let_13 (not _let_21)))))) (CONG _let_36 (REFL :args (_let_20)) :args _let_30)) (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_19 (not _let_25)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_71 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) _let_34 :args (_let_25 false _let_33)) (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_18 (not _let_22)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) _let_34 :args (_let_22 false _let_33)) (REORDERING (CNF_AND_POS :args (_let_19 1)) :args ((or _let_15 (not _let_19)))) (REORDERING (CNF_AND_POS :args (_let_18 0)) :args ((or _let_15 (not _let_18)))) (REORDERING (CNF_EQUIV_NEG1 :args _let_32) :args ((or _let_15 _let_14 _let_16))) _let_31 :args (_let_15 false _let_9 false _let_12 true _let_23 false _let_25 true _let_20 false _let_22 true _let_19 true _let_18 false _let_14 true _let_16)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_32) _let_31 _let_41 :args (_let_17 true _let_16 false _let_15)))) (let ((_let_43 (REFL :args _let_40))) (let ((_let_44 (not _let_15))) (let ((_let_45 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61))) (let ((_let_46 (or _let_45 _let_44 _let_10))) (let ((_let_47 (forall ((b_Q it_6_$$unsorted)) (or (= b_Q SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61) (not (io_tptp.incident_o_10 b_Q SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 b_Q))))) (let ((_let_48 (and (io_tptp.incident_o_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) _let_47))) (let ((_let_49 (io_tptp.start_point_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_50 (= _let_49 _let_48))) (let ((_let_51 (forall ((b_P it_6_$$unsorted) (b_O it_76_$$unsorted)) (= (io_tptp.start_point_9 b_P b_O) (and (io_tptp.incident_o_10 b_P b_O) (forall ((b_Q it_6_$$unsorted)) (or (= b_P b_Q) (not (io_tptp.incident_o_10 b_Q b_O)) (io_tptp.ordered_by_8 b_O b_P b_Q)))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((P $$unsorted) (O $$unsorted)) (= (tptp.start_point P O) (and (tptp.incident_o P O) (forall ((Q $$unsorted)) (or (= P Q) (not (tptp.incident_o Q O)) (tptp.ordered_by O P Q)))))) _let_51))))))) (let ((_let_53 (forall ((b_P it_6_$$unsorted)) (not (io_tptp.start_point_9 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))))) (let ((_let_54 (forall ((b_O it_76_$$unsorted)) (not (forall ((b_P it_6_$$unsorted)) (not (io_tptp.start_point_9 b_P b_O))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((O $$unsorted)) (not (forall ((P $$unsorted)) (not (tptp.start_point P O))))) _let_54))))))) (let ((_let_57 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_58 (not _let_49))) (let ((_let_59 (_let_55))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_48 1)) :args ((or _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or _let_58 _let_48 (not _let_50)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59) (REWRITE :args ((=> _let_55 (not _let_58)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_53))) (REFL :args (_let_49)) :args _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args _let_57) :args (_let_54))) _let_56 :args (_let_55 false _let_54)) :args (_let_49 true _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((io_tptp.start_point_9 b_P b_O)))) :args (_let_51)))) _let_52 :args (_let_50 false _let_51)) :args (_let_48 false _let_49 false _let_50)) :args (_let_47 false _let_48)))) (let ((_let_61 (_let_47))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91))) (let ((_let_64 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91))) (let ((_let_65 (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91))) (let ((_let_66 (io_tptp.ordered_by_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91))) (let ((_let_67 (io_tptp.incident_o_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_64 _let_68 _let_66))) (let ((_let_70 (not _let_45))) (let ((_let_71 (io_tptp.end_point_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_63))) (let ((_let_74 (not _let_63))) (let ((_let_75 (forall ((b_Q it_6_$$unsorted)) (or (not (io_tptp.end_point_3 b_Q SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60)) (= b_Q SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))))) (let ((_let_76 (not _let_73))) (let ((_let_77 (not _let_75))) (let ((_let_78 (io_tptp.end_point_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77))) (let ((_let_81 (io_tptp.end_point_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))) (let ((_let_82 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78))) (let ((_let_83 (not _let_81))) (let ((_let_84 (or _let_83 _let_82))) (let ((_let_85 (forall ((C $$unsorted) (b_P it_6_$$unsorted)) (or (not (io_tptp.end_point_3 b_P C)) (not (forall ((b_Q it_6_$$unsorted)) (or (not (io_tptp.end_point_3 b_Q C)) (= b_P b_Q)))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((C $$unsorted) (P $$unsorted)) (or (not (tptp.end_point P C)) (not (forall ((Q $$unsorted)) (or (not (tptp.end_point Q C)) (= P Q)))))) _let_85))))))) (let ((_let_87 (forall ((b_P it_6_$$unsorted)) (not (io_tptp.end_point_3 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))))) (let ((_let_88 (not _let_87))) (let ((_let_89 (tptp.open SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))) (let ((_let_90 (= _let_89 _let_88))) (let ((_let_91 (forall ((C $$unsorted)) (= (tptp.open C) (not (forall ((b_P it_6_$$unsorted)) (not (io_tptp.end_point_3 b_P C)))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_7)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((C $$unsorted)) (= (tptp.open C) (not (forall ((P $$unsorted)) (not (tptp.end_point P C)))))) _let_91))))))) (let ((_let_93 (forall ((b_P it_6_$$unsorted)) (= (io_tptp.incident_o_10 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) (io_tptp.incident_c_2 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))))) (let ((_let_94 (not _let_93))) (let ((_let_95 (not _let_89))) (let ((_let_96 (or _let_95 _let_94))) (let ((_let_97 (forall ((C $$unsorted)) (or (not (tptp.open C)) (not (forall ((b_P it_6_$$unsorted)) (= (io_tptp.incident_c_2 b_P C) (io_tptp.incident_o_10 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))))))) (let ((_let_98 (not _let_96))) (let ((_let_99 (forall ((b_O it_76_$$unsorted)) (not (forall ((C $$unsorted)) (or (not (tptp.open C)) (not (forall ((b_P it_6_$$unsorted)) (= (io_tptp.incident_o_10 b_P b_O) (io_tptp.incident_c_2 b_P C)))))))))) (let ((_let_100 (not _let_97))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((O $$unsorted)) (not (forall ((C $$unsorted)) (or (not (tptp.open C)) (not (forall ((P $$unsorted)) (= (tptp.incident_o P O) (tptp.incident_c P C)))))))) _let_99))))))) (let ((_let_102 (_let_100))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_102)) :args _let_102) (REWRITE :args ((=> _let_100 (not (or _let_95 (not (forall ((b_P it_6_$$unsorted)) (= (io_tptp.incident_c_2 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60) (io_tptp.incident_o_10 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_97))) (REFL :args (_let_98)) :args _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 :args _let_57) :args (_let_99)))) _let_101 :args (_let_100 false _let_99)) :args (_let_98 true _let_97)))) (let ((_let_104 (REFL :args (_let_96)))) (let ((_let_105 (_let_81))) (let ((_let_106 (_let_88))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106) (REWRITE :args ((=> _let_88 (not _let_83)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_87))) (REFL :args _let_105) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_90)) :args ((or _let_95 _let_88 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 0)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_89))) :args _let_30)) :args ((or _let_89 _let_96))) _let_103 :args (_let_89 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.open C)))) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_88 false _let_89 false _let_90)) :args (_let_81 true _let_87)))) (let ((_let_108 (ASSUME :args (_let_79)))) (let ((_let_109 (ASSUME :args (_let_82)))) (let ((_let_110 (ASSUME :args _let_105))) (let ((_let_111 (_let_75))) (let ((_let_112 (_let_77))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_112)) :args _let_112) (REWRITE :args ((=> _let_77 (not (or _let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_75))) (REFL :args (_let_76)) :args _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_111) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_78 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_111))) (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_82 (not _let_84)))) _let_107 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_108 _let_109 _let_110) :args (_let_79 _let_81 _let_82)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_110)) (CONG (SYMM _let_109) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60)) :args (APPLY_UF io_tptp.end_point_3)) (FALSE_INTRO _let_108))) :args (_let_79 _let_82 _let_81)) :args ((not (and _let_79 _let_81 _let_82)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_78))) (REFL :args (_let_83)) (REFL :args ((not _let_82))) :args _let_30)) _let_107 (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_79 _let_77 (not _let_80)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (io_tptp.end_point_3 b_P C) false))))) :args (_let_85)))) _let_86 :args (_let_80 false _let_85)) :args (_let_77 true _let_84 false _let_81 true _let_82 false _let_81 true _let_78 false _let_80)) :args (_let_76 true _let_75)))) (let ((_let_114 (REFL :args (_let_70)))) (let ((_let_115 (and _let_74 _let_45))) (let ((_let_116 (_let_74 _let_45))) (let ((_let_117 (ASSUME :args (_let_74)))) (let ((_let_118 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91)))) (let ((_let_119 (ASSUME :args (_let_45)))) (let ((_let_120 (SYMM _let_119))) (let ((_let_121 (not _let_65))) (let ((_let_122 (_let_12))) (let ((_let_123 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_124 (and _let_45 _let_121))) (let ((_let_125 (ASSUME :args (_let_121)))) (let ((_let_126 (io_tptp.incident_c_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60))) (let ((_let_127 (= _let_126 _let_67))) (let ((_let_128 (_let_93))) (let ((_let_129 (and _let_126 (forall ((C1 $$unsorted) (C2 $$unsorted)) (or (not (tptp.part_of C1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60)) (not (tptp.part_of C2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60)) (not (io_tptp.incident_c_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 C1)) (not (io_tptp.incident_c_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 C2)) (tptp.part_of C1 C2) (tptp.part_of C2 C1)))))) (let ((_let_130 (= _let_71 _let_129))) (let ((_let_131 (forall ((b_P it_6_$$unsorted) (C $$unsorted)) (= (io_tptp.end_point_3 b_P C) (and (io_tptp.incident_c_2 b_P C) (forall ((C1 $$unsorted) (C2 $$unsorted)) (or (not (tptp.part_of C1 C)) (not (tptp.part_of C2 C)) (not (io_tptp.incident_c_2 b_P C1)) (not (io_tptp.incident_c_2 b_P C2)) (tptp.part_of C1 C2) (tptp.part_of C2 C1)))))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((P $$unsorted) (C $$unsorted)) (= (tptp.end_point P C) (and (tptp.incident_c P C) (forall ((C1 $$unsorted) (C2 $$unsorted)) (or (not (tptp.part_of C1 C)) (not (tptp.part_of C2 C)) (not (tptp.incident_c P C1)) (not (tptp.incident_c P C2)) (tptp.part_of C1 C2) (tptp.part_of C2 C1)))))) _let_131))))))) (let ((_let_133 (_let_9))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_133) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_133)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_44 _let_45 _let_10 (not _let_46)))) _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_64 _let_66 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args _let_123) :args _let_61))) _let_60 :args (_let_69 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_127)) :args ((or (not _let_126) _let_67 (not _let_127)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_129 0)) :args ((or _let_126 (not _let_129)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_130)) :args ((or _let_72 _let_129 (not _let_130)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_73 0)) (CONG (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) :args _let_30)) :args ((or _let_71 _let_73))) _let_113 :args (_let_71 true _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_132 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((io_tptp.end_point_3 b_P C)))) :args (_let_131))) _let_132 :args (_let_130 false _let_131)) :args (_let_129 false _let_71 false _let_130)) :args (_let_126 false _let_129)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_128) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((io_tptp.incident_c_2 b_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_60)))) :args _let_128))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 1)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_93))) :args _let_30)) :args ((or _let_93 _let_96))) _let_103 :args (_let_93 true _let_96)) :args (_let_127 false _let_93)) :args (_let_67 false _let_126 false _let_127)) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_124)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_125 _let_119) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) _let_120 _let_118 :args (APPLY_UF io_tptp.ordered_by_8)) (FALSE_INTRO _let_125))) :args (_let_121 _let_45))) :args (_let_45 _let_121))) :args (true _let_124)) (CONG _let_114 (MACRO_SR_PRED_INTRO :args ((= (not _let_121) _let_65))) (REFL :args ((not _let_66))) :args _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_122) :args _let_123) :args _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG _let_43 _let_36 :args _let_30)) :args ((or _let_12 _let_14))) _let_42 :args (_let_12 true _let_14)) :args (_let_121 false _let_12)) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_115)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_117 _let_119) (SCOPE (FALSE_ELIM (TRANS (CONG _let_120 _let_118 :args (=)) (FALSE_INTRO _let_117))) :args _let_116)) :args _let_116)) :args (true _let_115)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_63))) _let_114 (REFL :args ((not _let_64))) :args _let_30)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_73 1)) _let_113 :args (_let_74 true _let_73)) :args (_let_70 false _let_69 false _let_67 true _let_66 true _let_65 true _let_64 true _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (io_tptp.incident_o_10 b_Q SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) false))))) :args _let_61)) _let_60 :args (_let_46 false _let_47)) :args (_let_10 false _let_15 true _let_45 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 1)) (CONG _let_43 _let_38 :args _let_30)) :args ((or _let_9 _let_14))) _let_42 :args (_let_9 true _let_14)) :args (false false _let_10 false _let_9)) :args ((forall ((C $$unsorted) (C1 $$unsorted)) (= (tptp.part_of C1 C) (forall ((P $$unsorted)) (=> (tptp.incident_c P C1) (tptp.incident_c P C))))) (forall ((C $$unsorted) (C1 $$unsorted) (C2 $$unsorted)) (= (= C (tptp.sum C1 C2)) (forall ((Q $$unsorted)) (= (tptp.incident_c Q C) (or (tptp.incident_c Q C1) (tptp.incident_c Q C2)))))) _let_8 (forall ((P $$unsorted) (C $$unsorted)) (= (tptp.inner_point P C) (and (tptp.incident_c P C) (not (tptp.end_point P C))))) (forall ((P $$unsorted) (C $$unsorted) (C1 $$unsorted)) (= (tptp.meet P C C1) (and (tptp.incident_c P C) (tptp.incident_c P C1) (forall ((Q $$unsorted)) (=> (and (tptp.incident_c Q C) (tptp.incident_c Q C1)) (and (tptp.end_point Q C) (tptp.end_point Q C1))))))) (forall ((C $$unsorted)) (= (tptp.closed C) (not (exists ((P $$unsorted)) (tptp.end_point P C))))) _let_7 (forall ((C $$unsorted) (C1 $$unsorted)) (=> (and (tptp.part_of C1 C) (not (= C1 C))) (tptp.open C1))) (forall ((C $$unsorted) (C1 $$unsorted) (C2 $$unsorted) (C3 $$unsorted)) (=> (and (tptp.part_of C1 C) (tptp.part_of C2 C) (tptp.part_of C3 C) (exists ((P $$unsorted)) (and (tptp.end_point P C1) (tptp.end_point P C2) (tptp.end_point P C3)))) (or (tptp.part_of C2 C3) (tptp.part_of C3 C2) (tptp.part_of C1 C2) (tptp.part_of C2 C1) (tptp.part_of C1 C3) (tptp.part_of C3 C1)))) (forall ((C $$unsorted)) (exists ((P $$unsorted)) (tptp.inner_point P C))) (forall ((C $$unsorted) (P $$unsorted)) (=> (tptp.inner_point P C) (exists ((C1 $$unsorted) (C2 $$unsorted)) (and (tptp.meet P C1 C2) (= C (tptp.sum C1 C2)))))) (forall ((C $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (=> (and (tptp.end_point P C) (tptp.end_point Q C) (tptp.end_point R C)) (or (= P Q) (= P R) (= Q R)))) _let_6 (forall ((C $$unsorted) (C1 $$unsorted) (C2 $$unsorted) (P $$unsorted)) (=> (and (tptp.closed C) (tptp.meet P C1 C2) (= C (tptp.sum C1 C2))) (forall ((Q $$unsorted)) (=> (tptp.end_point Q C1) (tptp.meet Q C1 C2))))) (forall ((C1 $$unsorted) (C2 $$unsorted)) (=> (exists ((P $$unsorted)) (tptp.meet P C1 C2)) (exists ((C $$unsorted)) (= C (tptp.sum C1 C2))))) (forall ((C $$unsorted) (C1 $$unsorted)) (=> (forall ((P $$unsorted)) (= (tptp.incident_c P C) (tptp.incident_c P C1))) (= C C1))) (forall ((C $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.between_c C P Q R) (and (not (= P R)) (exists ((Cpp $$unsorted)) (and (tptp.part_of Cpp C) (tptp.end_point P Cpp) (tptp.end_point R Cpp) (tptp.inner_point Q Cpp)))))) (forall ((O $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.between_o O P Q R) (or (and (tptp.ordered_by O P Q) (tptp.ordered_by O Q R)) (and (tptp.ordered_by O R Q) (tptp.ordered_by O Q P))))) _let_5 (forall ((P $$unsorted) (O $$unsorted)) (= (tptp.finish_point P O) (and (tptp.incident_o P O) (forall ((Q $$unsorted)) (=> (and (not (= P Q)) (tptp.incident_o Q O)) (tptp.ordered_by O Q P)))))) _let_4 _let_3 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted) (O $$unsorted)) (= (tptp.between_o O P Q R) (exists ((C $$unsorted)) (and (forall ((P $$unsorted)) (= (tptp.incident_o P O) (tptp.incident_c P C))) (tptp.between_c C P Q R))))) _let_2 (forall ((P $$unsorted) (Q $$unsorted) (C $$unsorted)) (=> (and (tptp.open C) (not (= P Q)) (tptp.incident_c P C) (tptp.incident_c Q C)) (exists ((O $$unsorted)) (and (forall ((R $$unsorted)) (= (tptp.incident_o R O) (tptp.incident_c R C))) (tptp.ordered_by O P Q))))) (forall ((O1 $$unsorted) (O2 $$unsorted)) (=> (forall ((P $$unsorted) (Q $$unsorted)) (= (tptp.ordered_by O1 P Q) (tptp.ordered_by O2 P Q))) (= O1 O2))) (forall ((C $$unsorted) (O $$unsorted)) (= (= C (tptp.underlying_curve O)) (forall ((P $$unsorted)) (= (tptp.incident_o P O) (tptp.incident_c P C))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 62.90/63.23  )
% 62.90/63.23  % SZS output end Proof for GEO127+1
% 62.90/63.23  % cvc5---1.0.5 exiting
% 62.90/63.23  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------