%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 22:49:46 EDT 2023

% Result   : Theorem 51.75s 52.00s
% Output   : Proof 51.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15  % Problem    : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.38  % Computer : n013.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Tue Aug 29 23:57:01 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.23/0.52  %----Proving TF0_NAR, FOF, or CNF
% 51.75/52.00  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.x4skvVgJPI/cvc5---1.0.5_4469.p...
% 51.75/52.00  ------- get file name : TPTP file name is GEO111+1
% 51.75/52.00  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4469.smt2...
% 51.75/52.00  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 51.75/52.00  --- Run --no-e-matching --full-saturate-quant at 5...
% 51.75/52.00  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 51.75/52.00  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 51.75/52.00  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 51.75/52.00  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 51.75/52.00  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 51.75/52.00  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 51.75/52.00  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.75/52.00  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 51.75/52.00  % SZS status Theorem for GEO111+1
% 51.75/52.00  % SZS output start Proof for GEO111+1
% 51.75/52.00  (
% 51.75/52.00  (let ((_let_1 (not (forall ((C $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (=> (tptp.between_c C P Q R) (and (tptp.incident_c P C) (tptp.incident_c Q C) (tptp.incident_c R C) (not (= P Q)) (not (= Q R)) (not (= P R)))))))) (let ((_let_2 (forall ((C $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.between_c C P Q R) (and (not (= P R)) (exists ((Cpp $$unsorted)) (and (tptp.part_of Cpp C) (tptp.end_point P Cpp) (tptp.end_point R Cpp) (tptp.inner_point Q Cpp)))))))) (let ((_let_3 (forall ((P $$unsorted) (C $$unsorted)) (= (tptp.inner_point P C) (and (tptp.incident_c P C) (not (tptp.end_point P C))))))) (let ((_let_4 (forall ((P $$unsorted) (C $$unsorted)) (= (tptp.end_point P C) (and (tptp.incident_c P C) (forall ((C1 $$unsorted) (C2 $$unsorted)) (=> (and (tptp.part_of C1 C) (tptp.part_of C2 C) (tptp.incident_c P C1) (tptp.incident_c P C2)) (or (tptp.part_of C1 C2) (tptp.part_of C2 C1))))))))) (let ((_let_5 (forall ((C $$unsorted) (C1 $$unsorted)) (= (tptp.part_of C1 C) (forall ((P $$unsorted)) (=> (tptp.incident_c P C1) (tptp.incident_c P C))))))) (let ((_let_6 (forall ((P $$unsorted)) (or (not (tptp.incident_c P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)) (tptp.incident_c P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))))) (let ((_let_7 (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_8 (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (tptp.part_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_12 (= _let_11 _let_6))) (let ((_let_13 (forall ((C $$unsorted) (C1 $$unsorted)) (= (tptp.part_of C1 C) (forall ((P $$unsorted)) (or (not (tptp.incident_c P C1)) (tptp.incident_c P C))))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_15 (_let_13))) (let ((_let_16 ((tptp.part_of C1 C)))) (let ((_let_17 (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_18 (not _let_17))) (let ((_let_19 (not _let_11))) (let ((_let_20 (or _let_19 (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)) _let_18 (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))))) (let ((_let_21 (forall ((Cpp $$unsorted)) (or (not (tptp.part_of Cpp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 Cpp)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 Cpp)) (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 Cpp)))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (not _let_21))) (let ((_let_24 (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) _let_23))) (let ((_let_25 (tptp.between_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (forall ((C $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.between_c C P Q R) (and (not (= P R)) (not (forall ((Cpp $$unsorted)) (or (not (tptp.part_of Cpp C)) (not (tptp.end_point P Cpp)) (not (tptp.end_point R Cpp)) (not (tptp.inner_point Q Cpp)))))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 ((tptp.between_c C P Q R)))) (let ((_let_31 (not _let_25))) (let ((_let_32 (or _let_31 _let_7))) (let ((_let_33 (forall ((BOUND_VARIABLE_1079 $$unsorted) (BOUND_VARIABLE_1081 $$unsorted) (BOUND_VARIABLE_1083 $$unsorted) (BOUND_VARIABLE_1085 $$unsorted)) (or (not (tptp.between_c BOUND_VARIABLE_1079 BOUND_VARIABLE_1081 BOUND_VARIABLE_1083 BOUND_VARIABLE_1085)) (tptp.incident_c BOUND_VARIABLE_1085 BOUND_VARIABLE_1079))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (forall ((BOUND_VARIABLE_1126 $$unsorted) (BOUND_VARIABLE_1130 $$unsorted) (BOUND_VARIABLE_1132 $$unsorted)) (not (tptp.between_c BOUND_VARIABLE_1126 BOUND_VARIABLE_1132 BOUND_VARIABLE_1130 BOUND_VARIABLE_1132))))) (let ((_let_36 (forall ((BOUND_VARIABLE_1110 $$unsorted) (BOUND_VARIABLE_1112 $$unsorted) (BOUND_VARIABLE_1116 $$unsorted)) (not (tptp.between_c BOUND_VARIABLE_1110 BOUND_VARIABLE_1112 BOUND_VARIABLE_1116 BOUND_VARIABLE_1116))))) (let ((_let_37 (forall ((BOUND_VARIABLE_1094 $$unsorted) (BOUND_VARIABLE_1098 $$unsorted) (BOUND_VARIABLE_1100 $$unsorted)) (not (tptp.between_c BOUND_VARIABLE_1094 BOUND_VARIABLE_1098 BOUND_VARIABLE_1098 BOUND_VARIABLE_1100))))) (let ((_let_38 (forall ((BOUND_VARIABLE_1065 $$unsorted) (BOUND_VARIABLE_1067 $$unsorted) (BOUND_VARIABLE_1069 $$unsorted) (BOUND_VARIABLE_1071 $$unsorted)) (or (not (tptp.between_c BOUND_VARIABLE_1065 BOUND_VARIABLE_1067 BOUND_VARIABLE_1069 BOUND_VARIABLE_1071)) (tptp.incident_c BOUND_VARIABLE_1069 BOUND_VARIABLE_1065))))) (let ((_let_39 (forall ((BOUND_VARIABLE_1051 $$unsorted) (BOUND_VARIABLE_1053 $$unsorted) (BOUND_VARIABLE_1055 $$unsorted) (BOUND_VARIABLE_1057 $$unsorted)) (or (not (tptp.between_c BOUND_VARIABLE_1051 BOUND_VARIABLE_1053 BOUND_VARIABLE_1055 BOUND_VARIABLE_1057)) (tptp.incident_c BOUND_VARIABLE_1053 BOUND_VARIABLE_1051))))) (let ((_let_40 (not _let_33))) (let ((_let_41 (tptp.between_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or))) (let ((_let_44 (not _let_35))) (let ((_let_45 (_let_44))) (let ((_let_46 (tptp.between_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_47 (forall ((Cpp $$unsorted)) (or (not (tptp.part_of Cpp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Cpp)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Cpp)) (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Cpp)))))) (let ((_let_48 (not _let_47))) (let ((_let_49 (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) _let_48))) (let ((_let_50 (= _let_46 _let_49))) (let ((_let_51 (not _let_46))) (let ((_let_52 (not _let_49))) (let ((_let_53 (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or (not (tptp.part_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29)) _let_56 _let_54))) (let ((_let_58 (and (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29) _let_56))) (let ((_let_59 (= _let_53 _let_58))) (let ((_let_60 (REFL :args (_let_57)))) (let ((_let_61 (_let_3))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (_let_48))) (let ((_let_64 (not _let_36))) (let ((_let_65 (_let_64))) (let ((_let_66 (tptp.between_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_67 (forall ((Cpp $$unsorted)) (or (not (tptp.part_of Cpp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Cpp)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Cpp)) (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Cpp)))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) _let_68))) (let ((_let_70 (= _let_66 _let_69))) (let ((_let_71 (not _let_66))) (let ((_let_72 (not _let_69))) (let ((_let_73 (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or (not (tptp.part_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) _let_76 (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28)) _let_74))) (let ((_let_78 (and (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28) _let_76))) (let ((_let_79 (= _let_73 _let_78))) (let ((_let_80 (REFL :args (_let_77)))) (let ((_let_81 (_let_68))) (let ((_let_82 (not _let_37))) (let ((_let_83 (_let_82))) (let ((_let_84 (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_85 (tptp.between_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_84))) (let ((_let_88 (forall ((Cpp $$unsorted)) (or (not (tptp.part_of Cpp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 Cpp)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 Cpp)) (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 Cpp)))))) (let ((_let_89 (not _let_88))) (let ((_let_90 (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)) _let_89))) (let ((_let_91 (= _let_85 _let_90))) (let ((_let_92 (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.part_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_95 (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) _let_93))) (let ((_let_97 (forall ((P $$unsorted)) (or (not (tptp.incident_c P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26)) (tptp.incident_c P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))))) (let ((_let_98 (= _let_94 _let_97))) (let ((_let_99 (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_100 (and _let_99 (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))))) (let ((_let_101 (= _let_92 _let_100))) (let ((_let_102 (not _let_99))) (let ((_let_103 (or _let_102 _let_84))) (let ((_let_104 (_let_89))) (let ((_let_105 (REFL :args (_let_96)))) (let ((_let_106 (_let_97))) (let ((_let_107 (not _let_38))) (let ((_let_108 (_let_107))) (let ((_let_109 (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_110 (tptp.between_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_111 (not _let_110))) (let ((_let_112 (or _let_111 _let_109))) (let ((_let_113 (forall ((Cpp $$unsorted)) (or (not (tptp.part_of Cpp SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Cpp)) (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Cpp)) (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Cpp)))))) (let ((_let_114 (not _let_113))) (let ((_let_115 (and (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_114))) (let ((_let_116 (= _let_110 _let_115))) (let ((_let_117 (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_118 (not _let_117))) (let ((_let_119 (tptp.part_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_120 (not _let_119))) (let ((_let_121 (or _let_120 _let_118 (not (tptp.end_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (tptp.inner_point SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))))) (let ((_let_122 (forall ((P $$unsorted)) (or (not (tptp.incident_c P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (tptp.incident_c P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_123 (= _let_119 _let_122))) (let ((_let_124 (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_125 (and _let_124 (forall ((C1 $$unsorted) (C2 $$unsorted)) (or (not (tptp.part_of C1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (tptp.part_of C2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25)) (not (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C1)) (not (tptp.incident_c SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 C2)) (tptp.part_of C1 C2) (tptp.part_of C2 C1)))))) (let ((_let_126 (= _let_117 _let_125))) (let ((_let_127 (not _let_124))) (let ((_let_128 (or _let_127 _let_109))) (let ((_let_129 (_let_114))) (let ((_let_130 (REFL :args (_let_121)))) (let ((_let_131 (forall ((P $$unsorted) (C $$unsorted)) (= (tptp.end_point P C) (and (tptp.incident_c P C) (forall ((C1 $$unsorted) (C2 $$unsorted)) (or (not (tptp.part_of C1 C)) (not (tptp.part_of C2 C)) (not (tptp.incident_c P C1)) (not (tptp.incident_c P C2)) (tptp.part_of C1 C2) (tptp.part_of C2 C1)))))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (_let_131))) (let ((_let_134 ((tptp.end_point P C)))) (let ((_let_135 (_let_122))) (let ((_let_136 (not _let_39))) (let ((_let_137 (_let_136))) (let ((_let_138 (_let_40))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_138)) :args _let_138)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_33))) (REFL :args (_let_34)) :args 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((C $$unsorted) (C1 $$unsorted) (C2 $$unsorted)) (= (= C (tptp.sum C1 C2)) (forall ((Q $$unsorted)) (= (tptp.incident_c Q C) (or (tptp.incident_c Q C1) (tptp.incident_c Q C2)))))) _let_4 _let_3 (forall ((P $$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 $$unsorted)) (tptp.end_point P C))))) (forall ((C $$unsorted)) (= (tptp.open C) (exists ((P $$unsorted)) (tptp.end_point P C)))) (forall ((C $$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)))) (forall ((C $$unsorted) (P $$unsorted)) (=> (tptp.end_point P C) (exists ((Q $$unsorted)) (and (tptp.end_point Q C) (not (= P Q)))))) (forall ((C $$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))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 51.82/52.01  )
% 51.82/52.01  % SZS output end Proof for GEO111+1
% 51.82/52.01  % cvc5---1.0.5 exiting
% 51.82/52.01  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------