TSTP Solution File: SET973+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET973+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 14:41:12 EDT 2023
% Result : Theorem 28.95s 29.31s
% Output : Proof 28.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET973+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.12 % Command : do_cvc5 %s %d
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 10:03:33 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.45 %----Proving TF0_NAR, FOF, or CNF
% 28.95/29.31 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.TYRTNa075R/cvc5---1.0.5_11949.p...
% 28.95/29.31 ------- get file name : TPTP file name is SET973+1
% 28.95/29.31 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11949.smt2...
% 28.95/29.31 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.95/29.31 --- Run --no-e-matching --full-saturate-quant at 5...
% 28.95/29.31 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.95/29.31 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.95/29.31 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.95/29.31 % SZS status Theorem for SET973+1
% 28.95/29.31 % SZS output start Proof for SET973+1
% 28.95/29.31 (
% 28.95/29.31 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.set_difference A (tptp.set_intersection2 B C)) (tptp.set_union2 (tptp.set_difference A B) (tptp.set_difference A C)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference C B) (tptp.set_difference C A)))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.set_difference (tptp.cartesian_product2 A B) (tptp.cartesian_product2 C D)) (tptp.set_union2 (tptp.cartesian_product2 (tptp.set_difference A C) B) (tptp.cartesian_product2 A (tptp.set_difference B D))))))) (let ((_let_5 (not _let_4))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (and (= (tptp.cartesian_product2 _let_1 C) (tptp.set_difference (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C))) (= (tptp.cartesian_product2 C _let_1) (tptp.set_difference (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B)))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.cartesian_product2 (tptp.set_intersection2 A B) (tptp.set_intersection2 C D)) (tptp.set_intersection2 (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_15 (tptp.cartesian_product2 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_17 (tptp.set_union2 _let_15 _let_16))) (let ((_let_18 (= _let_17 (tptp.set_union2 _let_16 _let_15)))) (let ((_let_19 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (tptp.set_difference _let_20 _let_19))) (let ((_let_22 (= _let_15 _let_21))) (let ((_let_23 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_24 (tptp.set_difference _let_20 _let_23))) (let ((_let_25 (= _let_16 _let_24))) (let ((_let_26 (tptp.set_intersection2 _let_19 _let_23))) (let ((_let_27 (= (tptp.set_difference _let_20 _let_26) (tptp.set_union2 _let_21 _let_24)))) (let ((_let_28 (tptp.set_intersection2 _let_23 _let_19))) (let ((_let_29 (tptp.set_difference _let_20 _let_28))) (let ((_let_30 (= _let_29 (tptp.set_union2 _let_24 _let_21)))) (let ((_let_31 (= _let_26 _let_28))) (let ((_let_32 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_33 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (= _let_28 (tptp.cartesian_product2 _let_33 _let_32)))) (let ((_let_35 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_36 (= _let_32 _let_35))) (let ((_let_37 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_38 (tptp.set_intersection2 _let_20 _let_37))) (let ((_let_39 (= (tptp.cartesian_product2 _let_33 _let_35) _let_38))) (let ((_let_40 (tptp.set_difference _let_20 _let_37))) (let ((_let_41 (tptp.set_difference _let_20 _let_20))) (let ((_let_42 (tptp.set_union2 _let_41 _let_40))) (let ((_let_43 (= (tptp.set_difference _let_20 _let_38) _let_42))) (let ((_let_44 (tptp.set_union2 _let_40 _let_41))) (let ((_let_45 (= _let_42 _let_44))) (let ((_let_46 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_29))) (let ((_let_47 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_44))) (let ((_let_48 (_let_14))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 ((tptp.set_union2 A B)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_15 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_48)) _let_49 :args (_let_18 false _let_14)))) (let ((_let_52 (forall ((BOUND_VARIABLE_910 $$unsorted) (BOUND_VARIABLE_912 $$unsorted) (BOUND_VARIABLE_914 $$unsorted)) (= (tptp.cartesian_product2 (tptp.set_difference BOUND_VARIABLE_910 BOUND_VARIABLE_912) BOUND_VARIABLE_914) (tptp.set_difference (tptp.cartesian_product2 BOUND_VARIABLE_910 BOUND_VARIABLE_914) (tptp.cartesian_product2 BOUND_VARIABLE_912 BOUND_VARIABLE_914)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_54) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.cartesian_product2 (tptp.set_difference BOUND_VARIABLE_910 BOUND_VARIABLE_912) BOUND_VARIABLE_914)))) :args _let_54)) (AND_ELIM _let_53 :args (0)) :args (_let_22 false _let_52)))) (let ((_let_56 (forall ((BOUND_VARIABLE_924 $$unsorted) (BOUND_VARIABLE_926 $$unsorted) (BOUND_VARIABLE_928 $$unsorted)) (= (tptp.cartesian_product2 BOUND_VARIABLE_928 (tptp.set_difference BOUND_VARIABLE_924 BOUND_VARIABLE_926)) (tptp.set_difference (tptp.cartesian_product2 BOUND_VARIABLE_928 BOUND_VARIABLE_924) (tptp.cartesian_product2 BOUND_VARIABLE_928 BOUND_VARIABLE_926)))))) (let ((_let_57 (_let_56))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.cartesian_product2 BOUND_VARIABLE_928 (tptp.set_difference BOUND_VARIABLE_924 BOUND_VARIABLE_926))))) :args _let_57)) (AND_ELIM _let_53 :args (1)) :args (_let_25 false _let_56)))) (let ((_let_59 (_let_1))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 ((tptp.set_union2 (tptp.set_difference A B) (tptp.set_difference A C))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_20 _let_19 _let_23 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_59)) _let_60 :args (_let_27 false _let_1)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_20 _let_23 _let_19 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_59)) _let_60 :args (_let_30 false _let_1)))) (let ((_let_64 (_let_13))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (_let_7))) (let ((_let_67 (ASSUME :args _let_66))) (let ((_let_68 ((tptp.set_intersection2 (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args _let_64)) _let_65 :args (_let_36 false _let_13)))) (let ((_let_70 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_40))) (let ((_let_71 (not _let_46))) (let ((_let_72 (or _let_71 _let_70))) (let ((_let_73 (forall ((C $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.in C (tptp.set_difference _let_1 (tptp.set_intersection2 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (tptp.in C (tptp.set_difference _let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))))) (let ((_let_74 (not _let_72))) (let ((_let_75 (tptp.subset _let_29 _let_40))) (let ((_let_76 (= _let_75 _let_73))) (let ((_let_77 (not _let_73))) (let ((_let_78 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (tptp.subset _let_40 _let_29))) (let ((_let_81 (and _let_75 _let_80))) (let ((_let_82 (not _let_75))) (let ((_let_83 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_84 (tptp.cartesian_product2 _let_83 _let_35))) (let ((_let_85 (tptp.subset _let_40 (tptp.set_difference _let_20 _let_84)))) (let ((_let_86 (= _let_26 _let_84))) (let ((_let_87 (tptp.subset _let_84 _let_37))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_85))) (let ((_let_90 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (tptp.subset (tptp.set_difference C B) (tptp.set_difference C A)))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (tptp.subset _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.subset _let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_95 _let_93 _let_87))) (let ((_let_97 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (tptp.subset _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_100 (_let_3))) (let ((_let_101 (ASSUME :args _let_100))) (let ((_let_102 ((tptp.set_intersection2 A B)))) (let ((_let_103 (not _let_36))) (let ((_let_104 (and _let_36 _let_99))) (let ((_let_105 (ASSUME :args (_let_99)))) (let ((_let_106 (APPLY_UF tptp.subset))) (let ((_let_107 (ASSUME :args (_let_36)))) (let ((_let_108 (SYMM (SYMM _let_107)))) (let ((_let_109 (and _let_18 _let_22 _let_25 _let_27 _let_30 _let_86 _let_85))) (let ((_let_110 (ASSUME :args (_let_85)))) (let ((_let_111 (APPLY_UF tptp.set_difference))) (let ((_let_112 (ASSUME :args (_let_86)))) (let ((_let_113 (REFL :args (_let_20)))) (let ((_let_114 (ASSUME :args (_let_27)))) (let ((_let_115 (SYMM _let_114))) (let ((_let_116 (APPLY_UF tptp.set_union2))) (let ((_let_117 (ASSUME :args (_let_25)))) (let ((_let_118 (SYMM _let_117))) (let ((_let_119 (SYMM _let_118))) (let ((_let_120 (ASSUME :args (_let_22)))) (let ((_let_121 (SYMM _let_120))) (let ((_let_122 (SYMM _let_121))) (let ((_let_123 (CONG _let_122 _let_119 :args _let_116))) (let ((_let_124 (ASSUME :args (_let_18)))) (let ((_let_125 (SYMM _let_124))) (let ((_let_126 (CONG _let_118 _let_121 :args _let_116))) (let ((_let_127 (ASSUME :args (_let_30)))) (let ((_let_128 (SYMM (SYMM _let_127)))) (let ((_let_129 (REFL :args (_let_40)))) (let ((_let_130 (= _let_40 _let_29))) (let ((_let_131 (= _let_81 _let_130))) (let ((_let_132 (not _let_81))) (let ((_let_133 (_let_12))) (let ((_let_134 (ASSUME :args _let_133))) (let ((_let_135 (= _let_40 _let_17))) (let ((_let_136 (not _let_130))) (let ((_let_137 (not _let_135))) (let ((_let_138 (_let_5))) (let ((_let_139 (ASSUME :args _let_138))) (let ((_let_140 (or))) (let ((_let_141 (_let_137))) (let ((_let_142 (REFL :args ((not _let_30))))) (let ((_let_143 (REFL :args ((not _let_25))))) (let ((_let_144 (REFL :args ((not _let_22))))) (let ((_let_145 (REFL :args ((not _let_18))))) (let ((_let_146 (and _let_137 _let_18 _let_22 _let_25 _let_30))) (let ((_let_147 (ASSUME :args _let_141))) (let ((_let_148 (_let_77))) (let ((_let_149 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_148)) :args _let_148)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_73))) (REFL :args (_let_74)) :args _let_140)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_76)) :args ((or _let_75 _let_77 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_81)) :args ((or _let_82 _let_81 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_131)) :args ((or _let_130 _let_132 (not _let_131)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_146)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_147 _let_124 _let_117 _let_120 _let_127) (SCOPE (FALSE_ELIM (TRANS (CONG _let_129 (TRANS _let_128 (CONG (SYMM _let_119) (SYMM _let_122) :args _let_116) _let_125) :args (=)) (FALSE_INTRO _let_147))) :args (_let_137 _let_18 _let_25 _let_22 _let_30))) :args (_let_137 _let_18 _let_22 _let_25 _let_30))) :args (true _let_146)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_137) _let_135))) _let_145 _let_144 _let_143 _let_142 (REFL :args (_let_136)) :args _let_140)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_139) :args _let_138)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (REFL :args _let_141) :args _let_140)) _let_139 :args (_let_137 true _let_4)) _let_51 _let_55 _let_58 _let_63 :args (_let_136 true _let_135 false _let_18 false _let_22 false _let_25 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_134 :args (_let_29 _let_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_133))) _let_134 :args (_let_131 false _let_12)) :args (_let_132 true _let_130 false _let_131)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_109)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_110 _let_112 _let_114 _let_120 _let_117 _let_124 _let_127) (SCOPE (TRUE_ELIM (TRANS (CONG _let_129 (TRANS _let_128 _let_126 _let_125 _let_123 _let_115 (CONG _let_113 (SYMM (SYMM _let_112)) :args _let_111)) :args _let_106) (TRUE_INTRO _let_110))) :args (_let_85 _let_86 _let_27 _let_22 _let_25 _let_18 _let_30))) :args (_let_18 _let_22 _let_25 _let_27 _let_30 _let_86 _let_85))) :args (true _let_109)) _let_51 _let_55 _let_58 _let_62 _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_66))) _let_67 :args (_let_86 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_88 _let_85 (not _let_89)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_95 _let_93 _let_87 (not _let_96)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_100)) _let_101 :args (_let_94 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_104)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_105 _let_107) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_108) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) :args _let_106) (TRUE_INTRO _let_105))) :args (_let_99 _let_36))) :args (_let_36 _let_99))) :args (true _let_104)) :args ((or _let_103 _let_92 (not _let_99)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_100)) _let_101 :args (_let_99 false _let_3)) :args (_let_92 false _let_36 false _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (_let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_87 false _let_94 false _let_92 false _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_84 _let_37 _let_20 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_90))) _let_91 :args (_let_89 false _let_90)) :args (_let_85 false _let_87 false _let_89)) :args (_let_80 false _let_18 false _let_22 false _let_25 false _let_27 false _let_30 false _let_86 false _let_85)) :args (_let_82 true _let_81 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (_let_29 _let_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_78))) _let_79 :args (_let_76 false _let_78)) :args (_let_77 true _let_75 false _let_76)) :args (_let_74 true _let_73)))) (let ((_let_150 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 _let_41))) (let ((_let_151 (or _let_70 _let_150))) (let ((_let_152 (= _let_47 _let_151))) (let ((_let_153 (not _let_47))) (let ((_let_154 (forall ((D $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_2 (tptp.set_difference _let_1 _let_1))) (let ((_let_3 (tptp.set_difference _let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (= (tptp.in D (tptp.set_union2 _let_3 _let_2)) (or (tptp.in D _let_3) (tptp.in D _let_2))))))))) (let ((_let_155 (_let_11))) (let ((_let_156 (ASSUME :args _let_155))) (let ((_let_157 (_let_154))) (let ((_let_158 (not _let_151))) (let ((_let_159 (not _let_150))) (let ((_let_160 (or _let_159 _let_70))) (let ((_let_161 (forall ((C $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.in C (tptp.set_difference _let_1 _let_1))) (tptp.in C (tptp.set_difference _let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))))))) (let ((_let_162 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_136 _let_41))) (let ((_let_163 (not _let_162))) (let ((_let_164 (or _let_163 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_136 _let_40)))) (let ((_let_165 (forall ((D $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (not (tptp.in D (tptp.set_difference _let_1 _let_1))))))) (let ((_let_166 (_let_9))) (let ((_let_167 (ASSUME :args _let_166))) (let ((_let_168 (_let_165))) (let ((_let_169 (not _let_161))) (let ((_let_170 (_let_169))) (let ((_let_171 (_let_161))) (let ((_let_172 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_72 1)) _let_149 :args ((not _let_70) true _let_72)))) (let ((_let_173 (ASSUME :args (_let_153)))) (let ((_let_174 (ASSUME :args (_let_45)))) (let ((_let_175 (ASSUME :args (_let_43)))) (let ((_let_176 (ASSUME :args (_let_39)))) (let ((_let_177 (ASSUME :args (_let_34)))) (let ((_let_178 (ASSUME :args (_let_31)))) (let ((_let_179 (ASSUME :args (_let_46)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_173 _let_174 _let_175 _let_176 _let_107 _let_177 _let_178 _let_114 _let_120 _let_117 _let_124 _let_127 _let_179) :args (_let_18 _let_22 _let_25 _let_27 _let_30 _let_31 _let_34 _let_36 _let_39 _let_43 _let_45 _let_46 _let_153)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_179)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86)) (TRANS _let_128 _let_126 _let_125 _let_123 _let_115 (CONG _let_113 (TRANS (SYMM (SYMM _let_178)) (SYMM (SYMM _let_177)) (CONG (REFL :args (_let_33)) _let_108 :args (APPLY_UF tptp.cartesian_product2)) (SYMM (SYMM _let_176))) :args _let_111) (SYMM (SYMM _let_175)) (SYMM (SYMM _let_174))) :args (APPLY_UF tptp.in)) (FALSE_INTRO _let_173))) :args (_let_153 _let_45 _let_43 _let_39 _let_36 _let_34 _let_31 _let_27 _let_22 _let_25 _let_18 _let_30 _let_46)) :args ((not (and _let_18 _let_22 _let_25 _let_27 _let_30 _let_31 _let_34 _let_36 _let_39 _let_43 _let_45 _let_46 _let_153)) SB_LITERAL))) (CONG _let_145 _let_144 _let_143 (REFL :args ((not _let_27))) _let_142 (REFL :args ((not _let_31))) (REFL :args ((not _let_34))) (REFL :args (_let_103)) (REFL :args ((not _let_39))) (REFL :args ((not _let_43))) (REFL :args ((not _let_45))) (REFL :args (_let_71)) (MACRO_SR_PRED_INTRO :args ((= (not _let_153) _let_47))) :args _let_140)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_152)) :args ((or _let_151 _let_153 (not _let_152)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_151)) :args ((or _let_70 _let_150 _let_158))) _let_172 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_160)) :args ((or _let_70 _let_159 (not _let_160)))) _let_172 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_171) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C _let_40) true))))) :args _let_171)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_170)) :args _let_170)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_169) _let_161))) (REFL :args ((not _let_164))) :args _let_140)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_164 0)) (CONG (REFL :args (_let_164)) (MACRO_SR_PRED_INTRO :args ((= (not _let_163) _let_162))) :args _let_140)) :args ((or _let_162 _let_164))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_168) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_136 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_168)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_167 :args (_let_20 _let_20 _let_41 QUANTIFIERS_INST_CBQI_PROP)) :args _let_166))) _let_167 :args (_let_165 false _let_9)) :args (_let_163 false _let_165)) :args (_let_164 true _let_162)) :args (_let_161 false _let_164)) :args (_let_160 false _let_161)) :args (_let_159 true _let_70 false _let_160)) :args (_let_158 true _let_70 true _let_150)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_157) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_86 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D _let_44)))) :args _let_157)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_156 :args (_let_40 _let_41 _let_44 QUANTIFIERS_INST_CBQI_PROP)) :args _let_155))) _let_156 :args (_let_154 false _let_11)) :args (_let_152 false _let_154)) :args (_let_153 true _let_151 false _let_152)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG (REFL :args (_let_72)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_46))) :args _let_140)) :args ((or _let_46 _let_72))) _let_149 :args (_let_46 true _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_41 _let_40 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_48)) _let_49 :args (_let_45 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_20 _let_20 _let_37 QUANTIFIERS_INST_E_MATCHING ((tptp.set_difference A (tptp.set_intersection2 B C))))) :args _let_59)) _let_60 :args (_let_43 false _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((tptp.cartesian_product2 (tptp.set_intersection2 A B) (tptp.set_intersection2 C D))))) :args _let_66)) _let_67 :args (_let_39 false _let_7)) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_66))) _let_67 :args (_let_34 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_19 _let_23 QUANTIFIERS_INST_CBQI_PROP)) :args _let_64)) _let_65 :args (_let_31 false _let_13)) _let_63 _let_62 _let_58 _let_55 _let_51 :args (false true _let_47 false _let_46 false _let_45 false _let_43 false _let_39 false _let_36 false _let_34 false _let_31 false _let_30 false _let_27 false _let_25 false _let_22 false _let_18)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_14 _let_13 _let_12 _let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))) _let_10 _let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_8 _let_7 _let_6 _let_5 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.95/29.32 )
% 28.95/29.32 % SZS output end Proof for SET973+1
% 28.95/29.32 % cvc5---1.0.5 exiting
% 29.14/29.32 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------