0.06/0.12 % Problem : Vampire---4.8_22325 : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : do_cvc5 %s %d 0.13/0.34 % Computer : n026.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 13:07:07 EDT 2023 0.13/0.34 % CPUTime : 0.19/0.47 %----Proving TH0 35.87/36.13 thf(eps1,type, 35.87/36.13 eps1: ( $i > $o ) > $i ). 35.87/36.13 35.87/36.13 thf(if1,type, 35.87/36.13 if1: $o > $i > $i > $i ). 35.87/36.13 35.87/36.13 thf(if1d,definition, 35.87/36.13 ( if1 35.87/36.13 = ( ^ [B: $o,X: $i,Y: $i] : 35.87/36.13 ( eps1 35.87/36.13 @ ^ [Z: $i] : 35.87/36.13 ( ( B 35.87/36.13 & ( Z = X ) ) 35.87/36.13 | ( ~ B 35.87/36.13 & ( Z = Y ) ) ) ) ) ) ). 35.87/36.13 35.87/36.13 thf(eps2,type, 35.87/36.13 eps2: ( $i > $o ) > $i ). 35.87/36.13 35.87/36.13 thf(if2,type, 35.87/36.13 if2: $o > $i > $i > $i ). 35.87/36.13 35.87/36.13 thf(if2d,definition, 35.87/36.13 ( if2 35.87/36.13 = ( ^ [B: $o,X: $i,Y: $i] : 35.87/36.13 ( eps2 35.87/36.13 @ ^ [Z: $i] : 35.87/36.13 ( ( B 35.87/36.13 & ( Z = X ) ) 35.87/36.13 | ( ~ B 35.87/36.13 & ( Z = Y ) ) ) ) ) ) ). 35.87/36.13 35.87/36.13 thf(conj,conjecture, 35.87/36.13 if1 = if2 ). 35.87/36.13 35.87/36.13 thf(choiceax1,axiom, 35.87/36.13 ! [P: $i > $o] : 35.87/36.13 ( ? [X: $i] : ( P @ X ) 35.87/36.13 => ( P @ ( eps1 @ P ) ) ) ). 35.87/36.13 35.87/36.13 thf(choiceax2,axiom, 35.87/36.13 ! [P: $i > $o] : 35.87/36.13 ( ? [X: $i] : ( P @ X ) 35.87/36.13 => ( P @ ( eps2 @ P ) ) ) ). 35.87/36.13 35.87/36.13 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OtxWqAEhLW/cvc5---1.0.5_22426.p... 35.87/36.13 (declare-sort $$unsorted 0) 35.87/36.13 (declare-fun tptp.eps1 ((-> $$unsorted Bool)) $$unsorted) 35.87/36.13 (declare-fun tptp.if1 (Bool $$unsorted $$unsorted) $$unsorted) 35.87/36.13 (assert (= tptp.if1 (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps1 (lambda ((Z $$unsorted)) (or (and B (= Z X)) (and (not B) (= Z Y)))))))) 35.87/36.13 (declare-fun tptp.eps2 ((-> $$unsorted Bool)) $$unsorted) 35.87/36.13 (declare-fun tptp.if2 (Bool $$unsorted $$unsorted) $$unsorted) 35.87/36.13 (assert (= tptp.if2 (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps2 (lambda ((Z $$unsorted)) (or (and B (= Z X)) (and (not B) (= Z Y)))))))) 35.87/36.13 (assert (not (= tptp.if1 tptp.if2))) 35.87/36.13 (assert (forall ((P (-> $$unsorted Bool))) (=> (exists ((X $$unsorted)) (@ P X)) (@ P (@ tptp.eps1 P))))) 35.87/36.13 (assert (forall ((P (-> $$unsorted Bool))) (=> (exists ((X $$unsorted)) (@ P X)) (@ P (@ tptp.eps2 P))))) 35.87/36.13 (set-info :filename cvc5---1.0.5_22426) 35.87/36.13 (check-sat-assuming ( true )) 35.87/36.13 ------- get file name : TPTP file name is 35.87/36.13 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22426.smt2... 35.87/36.13 --- Run --ho-elim --full-saturate-quant at 10... 35.87/36.13 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 35.87/36.13 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 35.87/36.13 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 35.87/36.13 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 35.87/36.13 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 35.87/36.13 % SZS status Theorem for 35.87/36.13 % SZS output start Proof for 35.87/36.13 ( 35.87/36.13 (let ((_let_1 (forall ((P (-> $$unsorted Bool))) (=> (exists ((X $$unsorted)) (@ P X)) (@ P (@ tptp.eps2 P)))))) (let ((_let_2 (forall ((P (-> $$unsorted Bool))) (=> (exists ((X $$unsorted)) (@ P X)) (@ P (@ tptp.eps1 P)))))) (let ((_let_3 (not (= tptp.if1 tptp.if2)))) (let ((_let_4 (= tptp.if2 (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps2 (lambda ((Z $$unsorted)) (or (and B (= Z X)) (and (not B) (= Z Y))))))))) (let ((_let_5 (= tptp.if1 (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps1 (lambda ((Z $$unsorted)) (or (and B (= Z X)) (and (not B) (= Z Y))))))))) (let ((_let_6 (not BOOLEAN_TERM_VARIABLE_927))) (let ((_let_7 (and _let_6 (= k_6 k_12)))) (let ((_let_8 (= k_5 k_12))) (let ((_let_9 (and BOOLEAN_TERM_VARIABLE_927 _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (lambdaF_10 k_12))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (forall ((Z $$unsorted)) (= (or (and BOOLEAN_TERM_VARIABLE_927 (= Z k_5)) (and (not BOOLEAN_TERM_VARIABLE_927) (= Z k_6))) (lambdaF_10 Z))))) (let ((_let_14 ((forall ((Z $$unsorted)) (= (lambdaF_10 Z) (@ (lambda ((Z $$unsorted)) (or (and BOOLEAN_TERM_VARIABLE_927 (= Z k_5)) (and (not BOOLEAN_TERM_VARIABLE_927) (= Z k_6)))) Z)))))) (let ((_let_15 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_14) (REWRITE :args _let_14)))) (let ((_let_16 (_let_13))) (let ((_let_17 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args (k_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_16))) _let_15 :args (_let_12 false _let_13)))) (let ((_let_18 (lambdaF_9 k_12))) (let ((_let_19 (= _let_18 _let_10))) (let ((_let_20 (not _let_10))) (let ((_let_21 (forall ((Z $$unsorted)) (= (or (and BOOLEAN_TERM_VARIABLE_927 (= Z k_5)) (and (not BOOLEAN_TERM_VARIABLE_927) (= Z k_6))) (lambdaF_9 Z))))) (let ((_let_22 ((forall ((Z $$unsorted)) (= (lambdaF_9 Z) (@ (lambda ((Z $$unsorted)) (or (and BOOLEAN_TERM_VARIABLE_927 (= Z k_5)) (and (not BOOLEAN_TERM_VARIABLE_927) (= Z k_6)))) Z)))))) (let ((_let_23 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_22) (REWRITE :args _let_22)))) (let ((_let_24 (_let_21))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (k_12 QUANTIFIERS_INST_CBQI_PROP)) :args _let_24))) _let_23 :args (_let_19 false _let_21)))) (let ((_let_26 (= _let_18 _let_11))) (let ((_let_27 (not _let_18))) (let ((_let_28 (not _let_19))) (let ((_let_29 (_let_19))) (let ((_let_30 (REORDERING (CNF_EQUIV_POS1 :args _let_29) :args ((or _let_27 _let_10 _let_28))))) (let ((_let_31 (= lambdaF_9 lambdaF_10))) (let ((_let_32 (not _let_26))) (let ((_let_33 (tptp.eps1 lambdaF_10))) (let ((_let_34 (lambdaF_9 _let_33))) (let ((_let_35 (not _let_31))) (let ((_let_36 (= k_6 _let_33))) (let ((_let_37 (and _let_6 _let_36))) (let ((_let_38 (= k_5 _let_33))) (let ((_let_39 (and BOOLEAN_TERM_VARIABLE_927 _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (= _let_34 _let_40))) (let ((_let_42 (_let_33 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args _let_42) :args _let_24))) _let_23 :args (_let_41 false _let_21)))) (let ((_let_44 (lambdaF_10 _let_33))) (let ((_let_45 (= _let_44 _let_40))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args _let_42) :args _let_16))) _let_15 :args (_let_45 false _let_13)))) (let ((_let_47 (lambdaF_10 k_6))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_44))) (let ((_let_50 (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_669 $$unsorted)) (or (not (@ P BOUND_VARIABLE_669)) (@ P (@ tptp.eps1 P)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (=>))) (let ((_let_53 (or))) (let ((_let_54 (@))) (let ((_let_55 (THEORY_PREPROCESS :args ((= (@ tptp.eps1 lambdaF_10) _let_33))))) (let ((_let_56 (REFL :args (lambdaF_10)))) (let ((_let_57 (TRANS (CONG _let_56 _let_55 :args _let_54) (THEORY_PREPROCESS :args ((= (@ lambdaF_10 _let_33) _let_44)))))) (let ((_let_58 (not))) (let ((_let_59 (_let_50))) (let ((_let_60 (REFL :args _let_59))) (let ((_let_61 (= k_5 k_6))) (let ((_let_62 (or (and BOOLEAN_TERM_VARIABLE_927 _let_61) _let_6))) (let ((_let_63 (= _let_62 _let_47))) (let ((_let_64 (or BOOLEAN_TERM_VARIABLE_927 (and _let_6 _let_61)))) (let ((_let_65 (tptp.eps2 lambdaF_10))) (let ((_let_66 (= k_6 _let_65))) (let ((_let_67 (and _let_6 _let_66))) (let ((_let_68 (lambdaF_10 k_5))) (let ((_let_69 (= _let_64 _let_68))) (let ((_let_70 (not _let_68))) (let ((_let_71 (or _let_70 _let_44))) (let ((_let_72 (lambdaF_10 _let_65))) (let ((_let_73 (or _let_70 _let_72))) (let ((_let_74 (= k_5 _let_65))) (let ((_let_75 (and BOOLEAN_TERM_VARIABLE_927 _let_74))) (let ((_let_76 (or _let_75 _let_67))) (let ((_let_77 (= _let_72 _let_76))) (let ((_let_78 (lambdaF_2 BOOLEAN_TERM_VARIABLE_927 k_5 k_6))) (let ((_let_79 (lambdaF_3 BOOLEAN_TERM_VARIABLE_927 k_5 k_6))) (let ((_let_80 (= _let_79 _let_78))) (let ((_let_81 (tptp.eps2 lambdaF_9))) (let ((_let_82 (= _let_78 _let_81))) (let ((_let_83 (= _let_79 _let_33))) (let ((_let_84 (not _let_37))) (let ((_let_85 (not _let_67))) (let ((_let_86 (CONG (THEORY_PREPROCESS :args ((= (@ lambdaF_10 k_5) _let_68))) :args _let_58))) (let ((_let_87 (lambdaF_10 k_5 QUANTIFIERS_INST_E_MATCHING))) (let ((_let_88 (forall ((P (-> $$unsorted Bool)) (BOUND_VARIABLE_684 $$unsorted)) (or (not (@ P BOUND_VARIABLE_684)) (@ P (@ tptp.eps2 P)))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (_let_88))) (let ((_let_91 (REFL :args _let_90))) (let ((_let_92 (not _let_44))) (let ((_let_93 (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_92 _let_40 (not _let_45)))))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args (_let_65 QUANTIFIERS_INST_CBQI_PROP)) :args _let_16))) _let_15 :args (_let_77 false _let_13)))) (let ((_let_95 (REORDERING (CNF_EQUIV_POS1 :args (_let_77)) :args ((or (not _let_72) _let_76 (not _let_77)))))) (let ((_let_96 (not _let_40))) (let ((_let_97 (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 _let_96))))) (let ((_let_98 (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_67 (not _let_76)))))) (let ((_let_99 (not _let_39))) (let ((_let_100 (not _let_75))) (let ((_let_101 (= lambdaF_2 lambdaF_3))) (let ((_let_102 (not _let_80))) (let ((_let_103 (=))) (let ((_let_104 (REFL :args (k_6)))) (let ((_let_105 (REFL :args (k_5)))) (let ((_let_106 (MACRO_SR_PRED_INTRO :args ((= k_4 BOOLEAN_TERM_VARIABLE_927))))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (THEORY_LEMMA :args ((or _let_101 (not (= (lambdaF_2 k_4 k_5 k_6) (lambdaF_3 k_4 k_5 k_6)))) THEORY_UF)) (CONG (REFL :args (_let_101)) (CONG (TRANS (CONG (CONG _let_106 _let_105 _let_104 :args (APPLY_UF lambdaF_2)) (CONG _let_106 _let_105 _let_104 :args (APPLY_UF lambdaF_3)) :args _let_103) (REWRITE :args ((= _let_78 _let_79)))) :args _let_58) :args _let_53)) (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (CONG (TRANS (CONG (MACRO_SR_PRED_INTRO :args ((= (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps1 (lambda ((Z $$unsorted)) (or (and B (= X Z)) (and (not B) (= Y Z)))))) lambdaF_3))) (MACRO_SR_PRED_INTRO :args ((= (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps2 (lambda ((Z $$unsorted)) (or (and B (= X Z)) (and (not B) (= Y Z)))))) lambdaF_2))) :args _let_103) (REWRITE :args ((= lambdaF_3 lambdaF_2)))) :args _let_58))) :args (_let_102 true _let_101)))) (let ((_let_108 (forall ((B Bool) (X $$unsorted) (Y $$unsorted)) (= (@ tptp.eps2 (lambda ((Z $$unsorted)) (or (and B (= X Z)) (and (not B) (= Y Z))))) (lambdaF_2 B X Y))))) (let ((_let_109 ((forall ((B Bool) (X $$unsorted) (Y $$unsorted)) (= (lambdaF_2 B X Y) (@ (@ (@ (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps2 (lambda ((Z $$unsorted)) (or (and B (= X Z)) (and (not B) (= Y Z)))))) B) X) Y)))))) (let ((_let_110 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_109) (REWRITE :args _let_109)))) (let ((_let_111 (THEORY_PREPROCESS :args ((= (@ tptp.eps2 lambdaF_9) _let_81))))) (let ((_let_112 (_let_108))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_110 :args (BOOLEAN_TERM_VARIABLE_927 k_5 k_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_2 B X Y)))) :args _let_112)) (CONG (REFL :args _let_112) (CONG (REFL :args (_let_78)) (TRANS (CONG (REFL :args (tptp.eps2)) (MACRO_SR_PRED_INTRO :args ((= (lambda ((Z $$unsorted)) (or (and BOOLEAN_TERM_VARIABLE_927 (= Z k_5)) (and (not BOOLEAN_TERM_VARIABLE_927) (= Z k_6)))) lambdaF_9))) :args _let_54) _let_111) :args _let_103) :args _let_52))) _let_110 :args (_let_82 false _let_108)))) (let ((_let_114 (forall ((B Bool) (X $$unsorted) (Y $$unsorted)) (= (@ tptp.eps1 (lambda ((Z $$unsorted)) (or (and B (= X Z)) (and (not B) (= Y Z))))) (lambdaF_3 B X Y))))) (let ((_let_115 ((forall ((B Bool) (X $$unsorted) (Y $$unsorted)) (= (lambdaF_3 B X Y) (@ (@ (@ (lambda ((B Bool) (X $$unsorted) (Y $$unsorted)) (@ tptp.eps1 (lambda ((Z $$unsorted)) (or (and B (= X Z)) (and (not B) (= Y Z)))))) B) X) Y)))))) (let ((_let_116 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_115) (REWRITE :args _let_115)))) (let ((_let_117 (_let_114))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_116 :args (BOOLEAN_TERM_VARIABLE_927 k_5 k_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_3 B X Y)))) :args _let_117)) (CONG (REFL :args _let_117) (CONG (REFL :args (_let_79)) (TRANS (CONG (REFL :args (tptp.eps1)) (MACRO_SR_PRED_INTRO :args ((= (lambda ((Z $$unsorted)) (or (and BOOLEAN_TERM_VARIABLE_927 (= Z k_5)) (and (not BOOLEAN_TERM_VARIABLE_927) (= Z k_6)))) lambdaF_10))) :args _let_54) _let_55) :args _let_103) :args _let_52))) _let_116 :args (_let_83 false _let_114)))) (let ((_let_119 (not _let_38))) (let ((_let_120 (not _let_83))) (let ((_let_121 (not _let_82))) (let ((_let_122 (and _let_82 _let_83 _let_31 _let_38 _let_74))) (let ((_let_123 (SYMM _let_113))) (let ((_let_124 (ASSUME :args (_let_31)))) (let ((_let_125 (SYMM _let_124))) (let ((_let_126 (CONG _let_125 :args (APPLY_UF tptp.eps2)))) (let ((_let_127 (ASSUME :args (_let_74)))) (let ((_let_128 (ASSUME :args (_let_38)))) (let ((_let_129 (SYMM _let_128))) (let ((_let_130 (THEORY_LEMMA :args ((or _let_31 _let_32) THEORY_UF)))) (let ((_let_131 (_let_26))) (let ((_let_132 (CNF_EQUIV_NEG2 :args _let_131))) (let ((_let_133 (not _let_11))) (let ((_let_134 (ASSUME :args (_let_44)))) (let ((_let_135 (ASSUME :args (_let_8)))) (let ((_let_136 (ASSUME :args (_let_133)))) (let ((_let_137 (REORDERING (CNF_EQUIV_NEG1 :args _let_131) :args ((or _let_18 _let_11 _let_26))))) (let ((_let_138 (REORDERING (CNF_EQUIV_POS2 :args _let_29) :args ((or _let_18 _let_20 _let_28))))) (let ((_let_139 (not _let_12))) (let ((_let_140 (_let_12))) (let ((_let_141 (REORDERING (CNF_EQUIV_POS1 :args _let_140) :args ((or _let_133 _let_10 _let_139))))) (let ((_let_142 (MACRO_RESOLUTION_TRUST _let_141 _let_17 _let_138 _let_25 _let_137 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_134 _let_128 _let_135 _let_136) :args (_let_44 _let_38 _let_133 _let_8)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_136)) (CONG (TRANS (SYMM _let_135) (SYMM _let_129)) :args (APPLY_UF lambdaF_10)) (TRUE_INTRO _let_134))) :args (_let_44 _let_38 _let_8 _let_133)) :args ((not (and _let_44 _let_38 _let_133 _let_8)) SB_LITERAL))) (CONG (REFL :args (_let_92)) (REFL :args (_let_119)) (MACRO_SR_PRED_INTRO :args ((= (not _let_133) _let_11))) (REFL :args ((not _let_8))) :args _let_53)) (REORDERING (CNF_AND_POS :args (_let_9 1)) :args ((or _let_8 (not _let_9)))) (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 _let_20))) _let_30 _let_25 _let_132 :args ((or _let_92 _let_119 _let_26 _let_27 _let_7) false _let_8 false _let_9 false _let_10 false _let_19 true _let_11)) _let_130 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_122)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_113 _let_124 _let_127 _let_128 _let_118) (SCOPE (TRANS _let_118 _let_129 (SYMM (SYMM _let_127)) _let_126 _let_123) :args (_let_82 _let_31 _let_74 _let_38 _let_83))) :args (_let_82 _let_83 _let_31 _let_38 _let_74))) :args (true _let_122)) :args ((or _let_80 _let_121 _let_120 _let_35 _let_119 (not _let_74)))) _let_118 _let_113 _let_107 (REORDERING (CNF_AND_POS :args (_let_75 1)) :args ((or _let_74 _let_100))) (REORDERING (CNF_AND_POS :args (_let_39 1)) :args ((or _let_38 _let_99))) _let_98 _let_97 _let_95 _let_94 _let_93 _let_46 (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_70 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_89 :args _let_87) :args _let_90) (CONG _let_91 (CONG _let_86 (TRANS (CONG _let_56 (THEORY_PREPROCESS :args ((= (@ tptp.eps2 lambdaF_10) _let_65))) :args _let_54) (THEORY_PREPROCESS :args ((= (@ lambdaF_10 _let_65) _let_72)))) :args _let_53) :args _let_52))) _let_89 :args (_let_73 false _let_88)) (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_70 _let_44 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_51 :args _let_87) :args _let_59) (CONG _let_60 (CONG _let_86 _let_57 :args _let_53) :args _let_52))) _let_51 :args (_let_71 false _let_50)) (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_68 (not _let_64) (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args (k_5 QUANTIFIERS_INST_ENUM)) :args _let_16))) _let_15 :args (_let_69 false _let_13)) (REORDERING (CNF_AND_POS :args (_let_7 0)) :args ((or _let_6 (not _let_7)))) (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_6 _let_85))) (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_6 _let_84))) (REORDERING (CNF_OR_NEG :args (_let_64 0)) :args ((or _let_6 _let_64))) :args (_let_6 false _let_12 true _let_10 false _let_19 false _let_11 true _let_18 true _let_26 true _let_31 false _let_83 false _let_82 true _let_80 false _let_74 false _let_38 false _let_75 false _let_39 false _let_76 false _let_77 false _let_40 false _let_45 false _let_72 false _let_73 false _let_44 false _let_71 false _let_68 false _let_69 true _let_7 true _let_67 true _let_37 false _let_64)))) (let ((_let_143 (not _let_41))) (let ((_let_144 (_let_41))) (let ((_let_145 (tptp.eps1 lambdaF_9))) (let ((_let_146 (lambdaF_9 _let_145))) (let ((_let_147 (lambdaF_9 _let_81))) (let ((_let_148 (not _let_146))) (let ((_let_149 (or _let_148 _let_147))) (let ((_let_150 (not _let_34))) (let ((_let_151 (and _let_31 _let_34))) (let ((_let_152 (ASSUME :args (_let_34)))) (let ((_let_153 (APPLY_UF lambdaF_9))) (let ((_let_154 (and _let_102 _let_82 _let_83 _let_31 _let_36))) (let ((_let_155 (ASSUME :args (_let_102)))) (let ((_let_156 (ASSUME :args (_let_36)))) (let ((_let_157 (and _let_31 _let_147))) (let ((_let_158 (ASSUME :args (_let_147)))) (let ((_let_159 (MACRO_RESOLUTION_TRUST _let_130 (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_157)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_158 _let_124) (SCOPE (TRUE_ELIM (TRANS (HO_CONG _let_125 (REFL :args (_let_65))) (CONG _let_126 :args _let_153) (TRUE_INTRO _let_158))) :args (_let_147 _let_31))) :args (_let_31 _let_147))) :args (true _let_157)) :args ((or _let_35 _let_72 (not _let_147)))) _let_95 _let_94 _let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or BOOLEAN_TERM_VARIABLE_927 _let_100))) _let_142 :args (_let_100 true BOOLEAN_TERM_VARIABLE_927)) (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_66 _let_85))) (REORDERING (CNF_OR_POS :args (_let_149)) :args ((or _let_148 _let_147 (not _let_149)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_89 :args (lambdaF_9 _let_145 QUANTIFIERS_INST_E_MATCHING)) :args _let_90) (CONG _let_91 (CONG (CONG (THEORY_PREPROCESS :args ((= (@ lambdaF_9 _let_145) _let_146))) :args _let_58) (TRANS (CONG (REFL :args (lambdaF_9)) _let_111 :args _let_54) (THEORY_PREPROCESS :args ((= (@ lambdaF_9 _let_81) _let_147)))) :args _let_53) :args _let_52))) _let_89 :args (_let_149 false _let_88)) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_154)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_155 _let_118 _let_156 _let_113 _let_124) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_156)) (SYMM _let_118)) (TRANS _let_126 _let_123) :args _let_103) (FALSE_INTRO _let_155))) :args (_let_102 _let_83 _let_36 _let_82 _let_31))) :args (_let_102 _let_82 _let_83 _let_31 _let_36))) :args (true _let_154)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_80))) (REFL :args (_let_121)) (REFL :args (_let_120)) (REFL :args (_let_35)) (REFL :args ((not _let_36))) (REFL :args ((not _let_66))) :args _let_53)) _let_118 _let_113 _let_107 (RESOLUTION (CNF_AND_NEG :args (_let_151)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_152 _let_124) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (SYMM _let_125) :args (APPLY_UF tptp.eps1)) :args _let_153) (TRUE_INTRO _let_152))) :args (_let_34 _let_31))) :args (_let_31 _let_34))) :args (true _let_151)) (REORDERING (CNF_AND_POS :args (_let_37 1)) :args ((or _let_36 _let_84))) _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 0)) :args ((or BOOLEAN_TERM_VARIABLE_927 _let_99))) _let_142 :args (_let_99 true BOOLEAN_TERM_VARIABLE_927)) (REORDERING (CNF_EQUIV_POS1 :args _let_144) :args ((or _let_40 _let_150 _let_143))) _let_43 :args ((or _let_35 _let_150) true _let_72 false _let_77 true _let_76 true _let_75 true _let_67 false _let_147 false _let_149 true _let_66 false _let_83 false _let_82 true _let_80 false _let_146 false _let_36 false _let_37 true _let_39 false _let_40 false _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_144) :args ((or _let_34 _let_96 _let_143))) (MACRO_RESOLUTION_TRUST _let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_44 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_63)) :args ((or _let_47 (not _let_62) (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 1)) (CONG (REFL :args (_let_62)) (MACRO_SR_PRED_INTRO :args ((= (not _let_6) BOOLEAN_TERM_VARIABLE_927))) :args _let_53)) :args ((or BOOLEAN_TERM_VARIABLE_927 _let_62))) _let_142 :args (_let_62 true BOOLEAN_TERM_VARIABLE_927)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_15 :args (k_6 QUANTIFIERS_INST_ENUM)) :args _let_16))) _let_15 :args (_let_63 false _let_13)) :args (_let_47 false _let_62 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_51 :args (lambdaF_10 k_6 QUANTIFIERS_INST_E_MATCHING)) :args _let_59) (CONG _let_60 (CONG (CONG (THEORY_PREPROCESS :args ((= (@ lambdaF_10 k_6) _let_47))) :args _let_58) _let_57 :args _let_53) :args _let_52))) _let_51 :args (_let_49 false _let_50)) :args (_let_44 false _let_47 false _let_49)) _let_46 :args (_let_40 false _let_44 false _let_45)) _let_43 :args (_let_34 false _let_40 false _let_41)) :args (_let_35 false _let_34)) :args (_let_32 true _let_31)))) (let ((_let_160 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_140) :args ((or _let_11 _let_20 _let_139))) _let_17 _let_132 _let_159 _let_30 _let_25 :args (_let_27 false _let_12 true _let_11 true _let_26 false _let_10 false _let_19)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_141 (MACRO_RESOLUTION_TRUST _let_137 _let_160 _let_159 :args (_let_11 true _let_18 true _let_26)) (MACRO_RESOLUTION_TRUST _let_138 _let_160 _let_25 :args (_let_20 true _let_18 false _let_19)) _let_17 :args (false false _let_11 true _let_10 false _let_12)) :args (_let_5 _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 35.87/36.14 ) 35.87/36.14 % SZS output end Proof for 35.87/36.14 % cvc5---1.0.5 exiting 35.87/36.14 % cvc5---1.0.5 exiting 35.87/36.14 EOF