TSTP Solution File: SWW101+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 : Fri Sep 1 00:19:49 EDT 2023
% Result : Theorem 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sun Aug 27 19:59:39 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.18/0.44 %----Proving TF0_NAR, FOF, or CNF
% 0.18/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xp88U8bRMh/cvc5---1.0.5_1670.p...
% 0.18/0.52 ------- get file name : TPTP file name is SWW101+1
% 0.18/0.52 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1670.smt2...
% 0.18/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.18/0.52 % SZS status Theorem for SWW101+1
% 0.18/0.52 % SZS output start Proof for SWW101+1
% 0.18/0.52 (
% 0.18/0.52 (let ((_let_1 (= tptp.false1 tptp.false2))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.not1 tptp.false))) (let ((_let_4 (= _let_3 tptp.true))) (let ((_let_5 (forall ((A $$unsorted)) (=> (not (tptp.bool A)) (= (tptp.not1 A) (tptp.phi A)))))) (let ((_let_6 (exists ((P $$unsorted)) (and (= tptp.false2 (tptp.phi (tptp.f7 P))) (not (exists ((P1 $$unsorted)) (tptp.forallprefers (tptp.f7 P1) (tptp.f7 P)))))))) (let ((_let_7 (forall ((P $$unsorted)) (= (tptp.f7 P) (tptp.lazy_impl (tptp.prop P) P))))) (let ((_let_8 (= tptp.false1 tptp.false))) (let ((_let_9 (forall ((B $$unsorted)) (= (tptp.lazy_and1 tptp.true B) (tptp.phi B))))) (let ((_let_10 (forall ((B $$unsorted)) (= (tptp.lazy_impl tptp.true B) (tptp.phi B))))) (let ((_let_11 (forall ((B $$unsorted)) (= (tptp.lazy_impl tptp.false B) tptp.true)))) (let ((_let_12 (forall ((X $$unsorted)) (= (= (tptp.prop X) tptp.false) (not (tptp.bool X)))))) (let ((_let_13 (forall ((X $$unsorted)) (= (= (tptp.prop X) tptp.true) (tptp.bool X))))) (let ((_let_14 (forall ((X $$unsorted)) (let ((_let_1 (tptp.phi X))) (let ((_let_2 (tptp.d X))) (or (and _let_2 (= _let_1 X)) (and (not _let_2) (= _let_1 tptp.err)))))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.d Y))) (let ((_let_2 (tptp.d X))) (= (tptp.forallprefers X Y) (or (and (not _let_2) _let_1) (and _let_2 _let_1 (not (tptp.bool X)) (tptp.bool Y)) (and (= X tptp.false) (= Y tptp.true))))))))) (let ((_let_16 (tptp.d tptp.false))) (let ((_let_17 (tptp.d tptp.true))) (let ((_let_18 (and _let_17 _let_16 (tptp.d tptp.err)))) (let ((_let_19 (= tptp.false tptp.err))) (let ((_let_20 (= tptp.true tptp.err))) (let ((_let_21 (and (not (= tptp.true tptp.false)) (not _let_20) (not _let_19)))) (let ((_let_22 (forall ((X $$unsorted)) (= (tptp.bool X) (or (= X tptp.false) (= X tptp.true)))))) (let ((_let_23 (tptp.prop SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (tptp.f7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (= _let_24 (tptp.lazy_impl _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_26 (= tptp.false _let_23))) (let ((_let_27 (= tptp.true _let_24))) (let ((_let_28 (= tptp.true (tptp.lazy_impl tptp.false SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_29 (_let_7))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.f7 P)))) :args _let_29)) _let_30 :args (_let_25 false _let_7)))) (let ((_let_32 (tptp.bool SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (= _let_33 _let_26))) (let ((_let_35 (forall ((X $$unsorted)) (= (not (tptp.bool X)) (= tptp.false (tptp.prop X)))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (_let_35))) (let ((_let_38 (= tptp.true _let_23))) (let ((_let_39 (= _let_32 _let_38))) (let ((_let_40 (= tptp.true SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (= tptp.false SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (or _let_41 _let_40))) (let ((_let_43 (= _let_32 _let_42))) (let ((_let_44 (= tptp.false tptp.false1))) (let ((_let_45 (tptp.phi _let_24))) (let ((_let_46 (= tptp.false2 _let_45))) (let ((_let_47 (= _let_45 (tptp.lazy_and1 tptp.true _let_24)))) (let ((_let_48 (tptp.phi tptp.false))) (let ((_let_49 (= tptp.false _let_48))) (let ((_let_50 (= _let_48 (tptp.lazy_impl tptp.true tptp.false)))) (let ((_let_51 (= _let_48 (tptp.lazy_and1 tptp.true tptp.false)))) (let ((_let_52 (tptp.prop tptp.false))) (let ((_let_53 (= tptp.true _let_52))) (let ((_let_54 (tptp.phi tptp.true))) (let ((_let_55 (= tptp.true _let_54))) (let ((_let_56 (= _let_54 (tptp.lazy_impl tptp.true tptp.true)))) (let ((_let_57 (tptp.f7 tptp.false))) (let ((_let_58 (= _let_57 (tptp.lazy_impl _let_52 tptp.false)))) (let ((_let_59 (tptp.forallprefers tptp.false tptp.true))) (let ((_let_60 (tptp.forallprefers _let_57 _let_24))) (let ((_let_61 (forall ((X $$unsorted)) (= (tptp.bool X) (= tptp.true (tptp.prop X)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (_let_61))) (let ((_let_64 (forall ((X $$unsorted)) (= (tptp.bool X) (or (= tptp.false X) (= tptp.true X)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (_let_64))) (let ((_let_67 ((tptp.bool X)))) (let ((_let_68 (SYMM (ASSUME :args (_let_8))))) (let ((_let_69 (ASSUME :args (_let_2)))) (let ((_let_70 (forall ((P1 $$unsorted)) (not (tptp.forallprefers (tptp.f7 P1) (tptp.f7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (let ((_let_71 (not _let_70))) (let ((_let_72 (not _let_46))) (let ((_let_73 (or _let_72 _let_71))) (let ((_let_74 (forall ((P $$unsorted)) (or (not (= tptp.false2 (tptp.phi (tptp.f7 P)))) (not (forall ((P1 $$unsorted)) (not (tptp.forallprefers (tptp.f7 P1) (tptp.f7 P))))))))) (let ((_let_75 (not _let_73))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (or))) (let ((_let_78 (not _let_74))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_76) :args (_let_78))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_74))) (REFL :args (_let_75)) :args _let_77)) _let_76 :args (_let_75 true _let_74)))) (let ((_let_80 (REFL :args (_let_73)))) (let ((_let_81 (_let_9))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 ((tptp.phi B)))) (let ((_let_84 (and _let_16 _let_49))) (let ((_let_85 (not _let_16))) (let ((_let_86 (and _let_85 (= tptp.err _let_48)))) (let ((_let_87 (or _let_84 _let_86))) (let ((_let_88 (forall ((X $$unsorted)) (let ((_let_1 (tptp.phi X))) (let ((_let_2 (tptp.d X))) (or (and _let_2 (= X _let_1)) (and (not _let_2) (= tptp.err _let_1)))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (_let_88))) (let ((_let_91 ((tptp.d X)))) (let ((_let_92 (not _let_86))) (let ((_let_93 (1))) (let ((_let_94 (ASSUME :args (_let_18)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_84 1)) :args ((or _let_49 (not _let_84)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_84 _let_86 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_86 0)) :args ((or _let_85 _let_92))) (AND_ELIM _let_94 :args _let_93) :args (_let_92 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_90)) _let_89 :args (_let_87 false _let_88)) :args (_let_84 true _let_86 false _let_87)) :args (_let_49 false _let_84)))) (let ((_let_96 (_let_10))) (let ((_let_97 (ASSUME :args _let_96))) (let ((_let_98 ((tptp.phi B)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_96))) _let_97 :args (_let_50 false _let_10)))) (let ((_let_100 (tptp.bool tptp.false))) (let ((_let_101 (= _let_100 _let_53))) (let ((_let_102 ((tptp.bool X)))) (let ((_let_103 (= _let_3 _let_48))) (let ((_let_104 (or _let_100 _let_103))) (let ((_let_105 (forall ((A $$unsorted)) (or (tptp.bool A) (= (tptp.not1 A) (tptp.phi A)))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (tptp.prop tptp.err))) (let ((_let_108 (= tptp.false _let_107))) (let ((_let_109 (= tptp.true _let_107))) (let ((_let_110 (= tptp.true _let_3))) (let ((_let_111 (not _let_103))) (let ((_let_112 (tptp.bool tptp.err))) (let ((_let_113 (not _let_112))) (let ((_let_114 (= _let_113 _let_108))) (let ((_let_115 (or _let_19 _let_20))) (let ((_let_116 (= _let_112 _let_115))) (let ((_let_117 (not _let_115))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_116)) :args ((or _let_113 _let_115 (not _let_116)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_20 _let_19 _let_117))) (AND_ELIM _let_118 :args _let_93) (AND_ELIM _let_118 :args (2)) :args (_let_117 true _let_20 true _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.err QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_116 false _let_64)) :args (_let_113 true _let_115 false _let_116)))) (let ((_let_120 (not _let_114))) (let ((_let_121 (_let_108))) (let ((_let_122 (= _let_112 _let_109))) (let ((_let_123 (not _let_109))) (let ((_let_124 (SYMM (ASSUME :args (_let_4))))) (let ((_let_125 (not _let_108))) (let ((_let_126 (not _let_49))) (let ((_let_127 (not _let_110))) (let ((_let_128 (REFL :args (_let_126)))) (let ((_let_129 (and _let_110 _let_49 _let_108 _let_123))) (let ((_let_130 (ASSUME :args (_let_123)))) (let ((_let_131 (=))) (let ((_let_132 (ASSUME :args _let_121))) (let ((_let_133 (ASSUME :args (_let_49)))) (let ((_let_134 (SYMM _let_133))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_101)) :args ((or (not _let_100) _let_53 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_100 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_129)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_130 _let_124 _let_132 _let_133) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM (SYMM _let_124))) (TRANS _let_134 (SYMM (SYMM _let_132))) :args _let_131) (FALSE_INTRO _let_130))) :args (_let_123 _let_110 _let_108 _let_49))) :args (_let_110 _let_49 _let_108 _let_123))) :args (true _let_129)) (CONG (REFL :args (_let_127)) _let_128 (REFL :args (_let_125)) (MACRO_SR_PRED_INTRO :args ((= (not _let_123) _let_109))) (REFL :args (_let_111)) :args _let_77)) :args ((or _let_127 _let_126 _let_111 _let_109 _let_125))) _let_124 _let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_122)) :args ((or _let_112 _let_123 (not _let_122)))) _let_119 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.err QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_63)) _let_62 :args (_let_122 false _let_61)) :args (_let_123 true _let_112 false _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_114)) (CONG (REFL :args (_let_120)) (MACRO_SR_PRED_INTRO :args ((= (not _let_113) _let_112))) (REFL :args _let_121) :args _let_77)) :args ((or _let_112 _let_108 _let_120))) _let_119 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.err QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.bool X)))) :args _let_37)) _let_36 :args (_let_114 false _let_35)) :args (_let_108 true _let_112 false _let_114)) :args (_let_111 false _let_110 false _let_49 true _let_109 false _let_108)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.not1 A)))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_100 true _let_103 false _let_104)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_102)) :args _let_63)) _let_62 :args (_let_101 false _let_61)) :args (_let_53 false _let_100 false _let_101)))) (let ((_let_136 (not _let_50))) (let ((_let_137 (REFL :args (_let_136)))) (let ((_let_138 (not _let_38))) (let ((_let_139 (REFL :args (_let_138)))) (let ((_let_140 (not _let_53))) (let ((_let_141 (REFL :args (_let_140)))) (let ((_let_142 (not _let_25))) (let ((_let_143 (REFL :args (_let_142)))) (let ((_let_144 (= _let_24 _let_45))) (let ((_let_145 (= tptp.false _let_24))) (let ((_let_146 (ASSUME :args (_let_46)))) (let ((_let_147 (ASSUME :args (_let_47)))) (let ((_let_148 (ASSUME :args (_let_25)))) (let ((_let_149 (SYMM _let_148))) (let ((_let_150 (APPLY_UF tptp.lazy_impl))) (let ((_let_151 (ASSUME :args (_let_41)))) (let ((_let_152 (ASSUME :args (_let_38)))) (let ((_let_153 (SYMM _let_152))) (let ((_let_154 (ASSUME :args (_let_53)))) (let ((_let_155 (SYMM _let_154))) (let ((_let_156 (CONG (TRANS _let_155 (SYMM _let_153)) (SYMM (SYMM _let_151)) :args _let_150))) (let ((_let_157 (REFL :args (tptp.false)))) (let ((_let_158 (CONG _let_154 _let_157 :args _let_150))) (let ((_let_159 (ASSUME :args (_let_50)))) (let ((_let_160 (SYMM _let_159))) (let ((_let_161 (TRANS (SYMM _let_134) (SYMM _let_160) _let_158 _let_156 _let_149))) (let ((_let_162 (REFL :args (tptp.true)))) (let ((_let_163 (ASSUME :args (_let_51)))) (let ((_let_164 (and _let_17 _let_55))) (let ((_let_165 (not _let_17))) (let ((_let_166 (and _let_165 (= tptp.err _let_54)))) (let ((_let_167 (or _let_164 _let_166))) (let ((_let_168 (not _let_166))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.prop P)))) :args _let_29)) _let_30 :args (_let_58 false _let_7)))) (let ((_let_170 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.d Y))) (let ((_let_2 (tptp.d X))) (= (tptp.forallprefers X Y) (or (and (not _let_2) _let_1) (and _let_2 _let_1 (not (tptp.bool X)) (tptp.bool Y)) (and (= tptp.false X) (= tptp.true Y))))))))) (let ((_let_171 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_172 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_171 :args (tptp.false tptp.true QUANTIFIERS_INST_E_MATCHING ((tptp.d X) (tptp.bool Y)))) :args (_let_170)))) _let_171 :args (_let_59 false _let_170)))) (let ((_let_173 (not _let_60))) (let ((_let_174 (_let_70))) (let ((_let_175 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_174) :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.f7 P1)))) :args _let_174)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_73 1)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_77)) :args ((or _let_70 _let_73))) _let_79 :args (_let_70 true _let_73)) :args (_let_173 false _let_70)))) (let ((_let_176 (not _let_59))) (let ((_let_177 (not _let_58))) (let ((_let_178 (not _let_40))) (let ((_let_179 (not _let_56))) (let ((_let_180 (not _let_55))) (let ((_let_181 (MACRO_SR_PRED_INTRO :args ((= (not _let_173) _let_60))))) (let ((_let_182 (REFL :args (_let_176)))) (let ((_let_183 (REFL :args (_let_177)))) (let ((_let_184 (ASSUME :args (_let_59)))) (let ((_let_185 (TRUE_INTRO _let_184))) (let ((_let_186 (APPLY_UF tptp.forallprefers))) (let ((_let_187 (ASSUME :args (_let_55)))) (let ((_let_188 (ASSUME :args (_let_56)))) (let ((_let_189 (ASSUME :args (_let_40)))) (let ((_let_190 (ASSUME :args (_let_58)))) (let ((_let_191 (TRANS (SYMM (SYMM _let_190)) (CONG _let_155 _let_157 :args _let_150) _let_160 _let_134))) (let ((_let_192 (ASSUME :args (_let_173)))) (let ((_let_193 (SYMM (FALSE_INTRO _let_192)))) (let ((_let_194 (not _let_34))) (let ((_let_195 (_let_26))) (let ((_let_196 (not _let_27))) (let ((_let_197 (_let_196))) (let ((_let_198 (ASSUME :args (_let_27)))) (let ((_let_199 (forall ((B $$unsorted)) (= tptp.true (tptp.lazy_impl tptp.false B))))) (let ((_let_200 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_201 (not _let_28))) (let ((_let_202 (not _let_26))) (let ((_let_203 (_let_201))) (let ((_let_204 (ASSUME :args (_let_28)))) (let ((_let_205 (ASSUME :args _let_197))) (let ((_let_206 (ASSUME :args _let_195))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_206 _let_205 _let_148) (SCOPE (FALSE_ELIM (TRANS (CONG _let_162 (TRANS (CONG (SYMM (SYMM _let_206)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) :args _let_150) _let_149) :args _let_131) (FALSE_INTRO _let_205))) :args (_let_26 _let_196 _let_25))) _let_204) :args (_let_25 _let_26 _let_196 _let_28)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args _let_203))) (TRUE_INTRO _let_204))) :args (_let_201 _let_28)) :args ((not (and _let_25 _let_26 _let_196 _let_28)) SB_LITERAL))) (CONG _let_143 (REFL :args (_let_202)) (MACRO_SR_PRED_INTRO :args ((= (not _let_196) _let_27))) (REFL :args _let_203) :args _let_77)) :args ((or _let_142 _let_27 _let_202 _let_201))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_200 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.lazy_impl tptp.false B) tptp.true))))) :args (_let_199))) _let_200 :args (_let_28 false _let_199)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_184 _let_133 _let_159 _let_154 _let_190 _let_198 _let_192) :args (_let_49 _let_27 _let_53 _let_50 _let_58 _let_59 _let_173)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_193 (CONG _let_191 (SYMM _let_198) :args _let_186) _let_185)) :args (_let_59 _let_49 _let_50 _let_53 _let_58 _let_27 _let_173)) :args ((not (and _let_49 _let_27 _let_53 _let_50 _let_58 _let_59 _let_173)) SB_LITERAL))) (CONG _let_128 (REFL :args _let_197) _let_141 _let_137 _let_183 _let_182 _let_181 :args _let_77)) :args ((or _let_126 _let_196 _let_140 _let_136 _let_177 _let_60 _let_176))) _let_95 _let_135 _let_99 _let_169 _let_175 _let_172 :args (_let_196 false _let_49 false _let_53 false _let_50 false _let_58 true _let_60 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_34)) (CONG (REFL :args (_let_194)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) (REFL :args _let_195) :args _let_77)) :args ((or _let_32 _let_26 _let_194))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_184 _let_133 _let_159 _let_154 _let_190 _let_187 _let_188 _let_152 _let_189 _let_148 _let_192) :args (_let_49 _let_55 _let_25 _let_53 _let_38 _let_50 _let_56 _let_40 _let_58 _let_59 _let_173)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_193 (CONG _let_191 (TRANS (SYMM _let_149) (CONG _let_153 (SYMM _let_189) :args _let_150) (SYMM _let_188) (SYMM _let_187)) :args _let_186) _let_185)) :args (_let_59 _let_49 _let_50 _let_53 _let_58 _let_55 _let_56 _let_38 _let_40 _let_25 _let_173)) :args ((not (and _let_49 _let_55 _let_25 _let_53 _let_38 _let_50 _let_56 _let_40 _let_58 _let_59 _let_173)) SB_LITERAL))) (CONG _let_128 (REFL :args (_let_180)) _let_143 _let_141 _let_139 _let_137 (REFL :args (_let_179)) (REFL :args (_let_178)) _let_183 _let_182 _let_181 :args _let_77)) :args ((or _let_126 _let_180 _let_142 _let_140 _let_138 _let_136 _let_179 _let_178 _let_177 _let_60 _let_176))) _let_175 _let_172 _let_135 _let_169 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (tptp.true QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_98)) :args _let_96))) _let_97 :args (_let_56 false _let_10)) _let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_164 1)) :args ((or _let_55 (not _let_164)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_167)) :args ((or _let_164 _let_166 (not _let_167)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_166 0)) :args ((or _let_165 _let_168))) (AND_ELIM _let_94 :args (0)) :args (_let_168 false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.true QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_90)) _let_89 :args (_let_167 false _let_88)) :args (_let_164 true _let_166 false _let_167)) :args (_let_55 false _let_164)) _let_95 _let_31 (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_40 (not _let_42)))) (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_68 (MODUS_PONENS (AND_INTRO _let_148 _let_152 _let_154 _let_151 _let_159 _let_133) (SCOPE _let_161 :args (_let_25 _let_38 _let_53 _let_41 _let_50 _let_49))) (MODUS_PONENS (AND_INTRO _let_147 _let_148 _let_152 _let_154 _let_151 _let_159 _let_133 _let_163) (SCOPE (TRANS _let_148 (SYMM _let_156) (SYMM _let_158) _let_160 (SYMM (SYMM _let_163)) (CONG _let_162 _let_161 :args (APPLY_UF tptp.lazy_and1)) (SYMM _let_147)) :args (_let_47 _let_25 _let_38 _let_53 _let_41 _let_50 _let_49 _let_51))) _let_146 _let_69) :args (_let_2 _let_44 _let_46 _let_49 _let_47 _let_25 _let_53 _let_38 _let_50 _let_51 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_69)) (TRUE_INTRO (SYMM (TRANS (SYMM (SYMM _let_146)) (SYMM (ASSUME :args (_let_144))) (SYMM (ASSUME :args (_let_145))) (SYMM (SYMM _let_68))))))) :args (_let_44 _let_145 _let_144 _let_46 _let_2)) :args ((not (and _let_2 _let_44 _let_46 _let_49 _let_47 _let_25 _let_53 _let_38 _let_50 _let_51 _let_41)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args ((not _let_44))) (REFL :args (_let_72)) _let_128 (REFL :args ((not _let_47))) _let_143 _let_141 _let_139 _let_137 (REFL :args ((not _let_51))) (REFL :args ((not _let_41))) :args _let_77)) _let_135 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_82 :args (tptp.false QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_81))) _let_82 :args (_let_51 false _let_9)) _let_99 _let_95 _let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_81))) _let_82 :args (_let_47 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_73 0)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_46))) :args _let_77)) :args ((or _let_46 _let_73))) _let_79 :args (_let_46 true _let_73)) _let_69 _let_68 (REORDERING (CNF_EQUIV_POS1 :args (_let_43)) :args ((or _let_33 _let_42 (not _let_43)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_43 false _let_64)) (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_38 _let_33 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.prop X)))) :args _let_63)) _let_62 :args (_let_39 false _let_61)) :args (_let_33 true _let_60 false _let_59 false _let_53 false _let_58 false _let_56 false _let_50 false _let_55 false _let_49 false _let_25 false _let_40 true _let_41 false _let_53 false _let_51 false _let_50 false _let_49 false _let_25 false _let_47 false _let_46 true _let_1 false _let_44 false _let_42 false _let_43 false _let_38 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.prop X)))) :args _let_37)) _let_36 :args (_let_34 false _let_35)) :args (_let_26 true _let_32 false _let_34)) _let_31 :args (false false _let_28 true _let_27 false _let_26 false _let_25)) :args (_let_22 _let_21 _let_18 _let_15 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.d Y))) (let ((_let_2 (tptp.d X))) (= (tptp.existsprefers X Y) (or (and (not _let_2) _let_1) (and _let_2 _let_1 (not (tptp.bool X)) (tptp.bool Y)) (and (= X tptp.true) (= Y tptp.false))))))) _let_14 _let_13 _let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.bool A)) (= (tptp.impl A B) (tptp.phi A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.bool A) (not (tptp.bool B))) (= (tptp.impl A B) (tptp.phi B)))) (forall ((B $$unsorted)) (=> (tptp.bool B) (= (tptp.impl tptp.false B) tptp.true))) (forall ((B $$unsorted)) (=> (tptp.bool B) (= (tptp.impl tptp.true B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.bool A)) (= (tptp.lazy_impl A B) (tptp.phi A)))) _let_11 _let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.bool A)) (= (tptp.and1 A B) (tptp.phi A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.bool A) (not (tptp.bool B))) (= (tptp.and1 A B) (tptp.phi B)))) (forall ((B $$unsorted)) (=> (tptp.bool B) (= (tptp.and1 tptp.false B) tptp.false))) (forall ((B $$unsorted)) (=> (tptp.bool B) (= (tptp.and1 tptp.true B) B))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.f1 P Q R) (tptp.lazy_impl (tptp.prop R) (tptp.impl (tptp.impl P (tptp.impl Q R)) R)))) (forall ((P $$unsorted) (Q $$unsorted)) (exists ((R $$unsorted)) (and (= (tptp.and2 P Q) (tptp.phi (tptp.f1 P Q R))) (not (exists ((R1 $$unsorted)) (tptp.forallprefers (tptp.f1 P Q R1) (tptp.f1 P Q R))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.bool A)) (= (tptp.lazy_and1 A B) (tptp.phi A)))) (forall ((B $$unsorted)) (= (tptp.lazy_and1 tptp.false B) tptp.false)) _let_9 (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.f2 P Q R) (tptp.lazy_impl (tptp.prop R) (tptp.impl (tptp.lazy_impl P (tptp.impl Q R)) R)))) (forall ((P $$unsorted) (Q $$unsorted)) (exists ((R $$unsorted)) (and (= (tptp.lazy_and2 P Q) (tptp.phi (tptp.f2 P Q R))) (not (exists ((R1 $$unsorted)) (tptp.forallprefers (tptp.f2 P Q R1) (tptp.f2 P Q R))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.bool A)) (= (tptp.or1 A B) (tptp.phi A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.bool A) (not (tptp.bool B))) (= (tptp.or1 A B) (tptp.phi B)))) (forall ((B $$unsorted)) (=> (tptp.bool B) (= (tptp.or1 tptp.true B) tptp.true))) (forall ((B $$unsorted)) (=> (tptp.bool B) (= (tptp.or1 tptp.false B) B))) (forall ((P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.f3 P Q R) (tptp.lazy_impl (tptp.prop R) (tptp.impl (tptp.impl P R) (tptp.impl (tptp.impl Q R) R))))) (forall ((P $$unsorted) (Q $$unsorted)) (exists ((R $$unsorted)) (and (= (tptp.or2 P Q) (tptp.phi (tptp.f3 P Q R))) (not (exists ((R1 $$unsorted)) (tptp.forallprefers (tptp.f3 P Q R1) (tptp.f3 P Q R))))))) (forall ((P $$unsorted)) (exists ((X $$unsorted)) (and (= (tptp.exists1 P) (tptp.phi (tptp.apply P X))) (not (exists ((X1 $$unsorted)) (tptp.existsprefers (tptp.apply P X1) (tptp.apply P X))))))) (forall ((P $$unsorted) (X $$unsorted) (R $$unsorted)) (= (tptp.f4 P X R) (tptp.impl (tptp.apply P X) R))) (forall ((P $$unsorted) (R $$unsorted)) (exists ((X $$unsorted)) (and (= (tptp.f5 P R) (tptp.phi (tptp.f4 P X R))) (not (exists ((X1 $$unsorted)) (tptp.forallprefers (tptp.f4 P X1 R) (tptp.f4 P X R))))))) (forall ((P $$unsorted) (R $$unsorted)) (= (tptp.f6 P R) (tptp.lazy_impl (tptp.prop R) (tptp.impl (tptp.f5 P R) R)))) (forall ((P $$unsorted)) (exists ((R $$unsorted)) (and (= (tptp.exists2 P) (tptp.phi (tptp.f6 P R))) (not (exists ((R1 $$unsorted)) (tptp.forallprefers (tptp.f6 P R1) (tptp.f6 P R))))))) _let_8 _let_7 _let_6 _let_5 _let_4 (= (tptp.not1 tptp.true) tptp.false) (forall ((P $$unsorted)) (= (tptp.not2 P) (tptp.impl P tptp.false2))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.52 )
% 0.18/0.52 % SZS output end Proof for SWW101+1
% 0.18/0.52 % cvc5---1.0.5 exiting
% 0.18/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------