TSTP Solution File: NUM011-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM011-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 10:41:58 EDT 2023
% Result : Unsatisfiable 223.85s 224.03s
% Output : Proof 223.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : NUM011-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.15/0.17 % Command : do_cvc5 %s %d
% 0.16/0.38 % Computer : n012.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 : Fri Aug 25 13:14:26 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.54 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9ppRsLOFGg/cvc5---1.0.5_23797.p...
% 0.23/0.59 ------- get file name : TPTP file name is NUM011-1
% 0.23/0.59 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23797.smt2...
% 0.23/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.47/10.71 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.50/15.77 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.61/20.83 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.66/25.86 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.74/30.94 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.63/36.01 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.89/41.09 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.13/46.41 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.30/51.48 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 56.36/56.59 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.47/61.66 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 66.34/66.74 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 76.61/76.81 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 86.68/86.89 --- Run --no-cbqi --full-saturate-quant at 10...
% 96.73/96.96 --- Run --macros-quant --macros-quant-mode=all --full-saturate-quant...
% 223.85/224.03 % SZS status Unsatisfiable for NUM011-1
% 223.85/224.03 % SZS output start Proof for NUM011-1
% 223.85/224.08 (
% 223.85/224.08 (let ((_let_1 (= tptp.empty_set (tptp.successor tptp.f75)))) (let ((_let_2 (tptp.member tptp.f75 tptp.natural_numbers))) (let ((_let_3 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.apply_to_two_arguments Xf X Y) (tptp.apply Xf (tptp.ordered_pair X Y)))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.restrict X Y) (tptp.intersection X (tptp.cross_product Y tptp.universal_set)))))) (let ((_let_5 (forall ((Z $$unsorted)) (not (tptp.member Z tptp.empty_set))))) (let ((_let_6 (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton_set X)))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))))))) (let ((_let_8 (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.complement X)) (not (tptp.little_set Z)) (tptp.member Z X))))) (let ((_let_9 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.singleton_set X) (tptp.non_ordered_pair X X))))) (let ((_let_13 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U X)))))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))))) (let ((_let_15 (tptp.non_ordered_pair tptp.f75 tptp.f75))) (let ((_let_16 (tptp.complement _let_15))) (let ((_let_17 (tptp.member tptp.f75 _let_16))) (let ((_let_18 (tptp.complement tptp.f75))) (let ((_let_19 (tptp.intersection _let_18 _let_16))) (let ((_let_20 (tptp.member tptp.f75 _let_19))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_17))) (let ((_let_23 (_let_10))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (not _let_22))) (let ((_let_26 (tptp.little_set tptp.f75))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.member tptp.f75 (tptp.complement _let_19)))) (let ((_let_29 (or _let_28 _let_27 _let_20))) (let ((_let_30 (_let_8))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (forall ((Z $$unsorted)) (not (tptp.member Z (tptp.complement (tptp.intersection (tptp.complement tptp.f75) (tptp.complement (tptp.non_ordered_pair tptp.f75 tptp.f75))))))))) (let ((_let_33 (TRUST_SUBS_EQ (ASSUME :args (_let_12)) :args ((= tptp.singleton_set (lambda ((BOUND_VARIABLE_3582 $$unsorted)) (tptp.non_ordered_pair BOUND_VARIABLE_3582 BOUND_VARIABLE_3582))))))) (let ((_let_34 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO _let_33 :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.ordered_pair (lambda ((BOUND_VARIABLE_3597 $$unsorted) (BOUND_VARIABLE_3598 $$unsorted)) (tptp.non_ordered_pair (tptp.non_ordered_pair BOUND_VARIABLE_3597 BOUND_VARIABLE_3597) (tptp.non_ordered_pair BOUND_VARIABLE_3597 BOUND_VARIABLE_3598)))))))) (let ((_let_35 (TRUST_SUBS_EQ (ASSUME :args (_let_7)) :args ((= tptp.union (lambda ((BOUND_VARIABLE_3678 $$unsorted) (BOUND_VARIABLE_3679 $$unsorted)) (tptp.complement (tptp.intersection (tptp.complement BOUND_VARIABLE_3678) (tptp.complement BOUND_VARIABLE_3679))))))))) (let ((_let_36 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_35 _let_34 _let_33) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.successor (lambda ((BOUND_VARIABLE_3855 $$unsorted)) (tptp.complement (tptp.intersection (tptp.complement BOUND_VARIABLE_3855) (tptp.complement (tptp.non_ordered_pair BOUND_VARIABLE_3855 BOUND_VARIABLE_3855)))))))))) (let ((_let_37 (TRUST_SUBS_EQ (ASSUME :args (_let_4)) :args ((= tptp.restrict (lambda ((BOUND_VARIABLE_3931 $$unsorted) (BOUND_VARIABLE_3932 $$unsorted)) (tptp.intersection BOUND_VARIABLE_3931 (tptp.cross_product BOUND_VARIABLE_3932 tptp.universal_set)))))))) (let ((_let_38 (TRUST_SUBS_EQ (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_37 _let_36 _let_35 _let_34 _let_33) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) :args ((= tptp.apply_to_two_arguments (lambda ((BOUND_VARIABLE_3952 $$unsorted) (BOUND_VARIABLE_3953 $$unsorted) (BOUND_VARIABLE_3954 $$unsorted)) (tptp.apply BOUND_VARIABLE_3952 (tptp.non_ordered_pair (tptp.non_ordered_pair BOUND_VARIABLE_3953 BOUND_VARIABLE_3953) (tptp.non_ordered_pair BOUND_VARIABLE_3953 BOUND_VARIABLE_3954))))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_38 _let_37 _let_36 _let_35 _let_34 _let_33) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) _let_38 _let_37 _let_36 _let_35 _let_34 _let_33) :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (not _let_2))) (let ((_let_41 (or _let_40 _let_26))) (let ((_let_42 (_let_14))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_26 (not _let_41)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.f75 tptp.natural_numbers QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X Y) false))))) :args _let_42)) _let_43 :args (_let_41 false _let_14)) :args (_let_26 false _let_2 false _let_41)))) (let ((_let_45 (tptp.member tptp.f75 _let_15))) (let ((_let_46 (not _let_45))) (let ((_let_47 (not _let_17))) (let ((_let_48 (or _let_47 _let_46))) (let ((_let_49 (_let_9))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (or _let_45 _let_27))) (let ((_let_52 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member X (tptp.non_ordered_pair X Y)) (not (tptp.little_set X)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.f75 _let_18 _let_16 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_17 _let_21 _let_25))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_46 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_45 _let_27 (not _let_51)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.f75 tptp.f75 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.non_ordered_pair X Y)))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_45 false _let_26 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (tptp.f75 _let_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_49)) _let_50 :args (_let_48 false _let_9)) :args (_let_47 false _let_45 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_27 _let_28 _let_20 (not _let_29)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.f75 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_32))) _let_39 :args ((not _let_28) false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.f75 _let_19 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) true))))) :args _let_30)) _let_31 :args (_let_29 false _let_8)) :args (_let_20 false _let_26 true _let_28 false _let_29)) :args (_let_25 true _let_17 false _let_20)) _let_24 :args (false true _let_22 false _let_10)) :args (_let_14 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.little_set (tptp.f1 X Y)) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.f1 X Y))) (or (tptp.member _let_1 X) (tptp.member _let_1 Y) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.f1 X Y))) (or (not (tptp.member _let_1 X)) (not (tptp.member _let_1 Y)) (= X Y)))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.non_ordered_pair X Y))) (= U X) (= U Y))) _let_13 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) _let_12 _let_11 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f2 X)))) (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f3 X)))) (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (= X (tptp.ordered_pair (tptp.f2 X) (tptp.f3 X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate X) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= X (tptp.ordered_pair Y Z))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f4 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f5 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (= X (tptp.ordered_pair (tptp.f4 Z X) (tptp.f5 Z X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.member Z (tptp.f4 Z X)))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted)) (or (tptp.member Z (tptp.first X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= X (tptp.ordered_pair U V))) (not (tptp.member Z U)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f6 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f7 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (= X (tptp.ordered_pair (tptp.f6 Z X) (tptp.f7 Z X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.member Z (tptp.f7 Z X)))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted)) (or (tptp.member Z (tptp.second X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= X (tptp.ordered_pair U V))) (not (tptp.member Z V)))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.member (tptp.first Z) (tptp.second Z)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.estin) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) (tptp.second Z))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) _let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.intersection X Y)) (not (tptp.member Z X)) (not (tptp.member Z Y)))) _let_9 _let_8 _let_7 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.ordered_pair_predicate (tptp.f8 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.member (tptp.f8 Z X) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (= Z (tptp.first (tptp.f8 Z X))))) (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.domain_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.first Xp))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.first Z) X))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.second Z) Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.cross_product X Y)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) X)) (not (tptp.member (tptp.second Z) Y)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.converse X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f9 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f10 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f11 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (= Z (tptp.ordered_pair (tptp.f9 Z X) (tptp.ordered_pair (tptp.f10 Z X) (tptp.f11 Z X)))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.member (tptp.ordered_pair (tptp.f10 Z X) (tptp.ordered_pair (tptp.f11 Z X) (tptp.f9 Z X))) X))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.rotate_right X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair V (tptp.ordered_pair W U)) X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f12 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f13 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f14 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (= Z (tptp.ordered_pair (tptp.f12 Z X) (tptp.ordered_pair (tptp.f13 Z X) (tptp.f14 Z X)))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.member (tptp.ordered_pair (tptp.f12 Z X) (tptp.ordered_pair (tptp.f14 Z X) (tptp.f13 Z X))) X))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.flip_range_of X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair U (tptp.ordered_pair W V)) X)))) _let_6 _let_5 (forall ((Z $$unsorted)) (or (tptp.member Z tptp.universal_set) (not (tptp.little_set Z)))) (tptp.little_set tptp.infinity) (tptp.member tptp.empty_set tptp.infinity) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.infinity)) (tptp.member (tptp.successor X) tptp.infinity))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member (tptp.f16 Z X) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member Z (tptp.f16 Z X)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.sigma X)) (not (tptp.member Y X)) (not (tptp.member Z Y)))) (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.sigma U)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (tptp.member (tptp.f17 X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (not (tptp.member (tptp.f17 X Y) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (tptp.subset X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (not (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.proper_subset X Y) (not (tptp.subset X Y)) (= X Y))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.powerset X))) (tptp.subset Z X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.powerset X)) (not (tptp.little_set Z)) (not (tptp.subset Z X)))) (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.powerset U)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.relation Z)) (not (tptp.member X Z)) (tptp.ordered_pair_predicate X))) (forall ((Z $$unsorted)) (or (tptp.relation Z) (tptp.member (tptp.f18 Z) Z))) (forall ((Z $$unsorted)) (or (tptp.relation Z) (not (tptp.ordered_pair_predicate (tptp.f18 Z))))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.single_valued_set X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (tptp.member (tptp.ordered_pair U V) X)) (not (tptp.member (tptp.ordered_pair U W) X)) (= V W))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f19 X)))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f20 X)))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f21 X)))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f20 X)) X))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f21 X)) X))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (not (= (tptp.f20 X) (tptp.f21 X))))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.relation Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.single_valued_set Xf))) (forall ((Xf $$unsorted)) (or (tptp.function Xf) (not (tptp.relation Xf)) (not (tptp.single_valued_set Xf)))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.ordered_pair_predicate (tptp.f22 Z X Xf)))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.f22 Z X Xf) Xf))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.first (tptp.f22 Z X Xf)) X))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (= (tptp.second (tptp.f22 Z X Xf)) Z))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.image X Xf)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Y)) (not (tptp.member Y Xf)) (not (tptp.member (tptp.first Y) X)) (not (= (tptp.second Y) Z)))) (forall ((X $$unsorted) (Xf $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.function Xf)) (tptp.little_set (tptp.image X Xf)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.disjoint X Y)) (not (tptp.member U X)) (not (tptp.member U Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) Y))) (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.member (tptp.f24 X) X))) (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.disjoint (tptp.f24 X) X))) (tptp.function tptp.f25) (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.f26 X) X))) (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.ordered_pair X (tptp.f26 X)) tptp.f25))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.ordered_pair_predicate (tptp.f27 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.member (tptp.f27 Z X) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (= Z (tptp.second (tptp.f27 Z X))))) (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.range_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.second Xp))))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (= (tptp.first Z) (tptp.second Z)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.identity_relation) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (= (tptp.first Z) (tptp.second Z))))) _let_4 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function (tptp.converse Xf)))) (forall ((Xf $$unsorted)) (or (tptp.one_to_one_function Xf) (not (tptp.function Xf)) (not (tptp.function (tptp.converse Xf))))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.ordered_pair_predicate (tptp.f28 Z Xf Y)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member (tptp.f28 Z Xf Y) Xf))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (= (tptp.first (tptp.f28 Z Xf Y)) Y))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member Z (tptp.second (tptp.f28 Z Xf Y))))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.apply Xf Y)) (not (tptp.ordered_pair_predicate W)) (not (tptp.member W Xf)) (not (= (tptp.first W) Y)) (not (tptp.member Z (tptp.second W))))) _let_3 (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.maps Xf X Y) (not (tptp.function Xf)) (not (= (tptp.domain_of Xf) X)) (not (tptp.subset (tptp.range_of Xf) Y)))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xf))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.maps Xf (tptp.cross_product Xs Xs) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.closed Xs Xf) (not (tptp.little_set Xs)) (not (tptp.little_set Xf)) (not (tptp.maps Xf (tptp.cross_product Xs Xs) Xs)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f29 Z Xf Xg)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f30 Z Xf Xg)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f31 Z Xf Xg)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (= Z (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f30 Z Xf Xg))))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f31 Z Xf Xg)) Xf))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f31 Z Xf Xg) (tptp.f30 Z Xf Xg)) Xg))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted) (X $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.compose Xf Xg)) (not (tptp.little_set Z)) (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair X Y))) (not (tptp.member (tptp.ordered_pair X W) Xf)) (not (tptp.member (tptp.ordered_pair W Y) Xg)))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs1 Xf1))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs2 Xf2))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.maps Xh Xs1 Xs2))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (not (tptp.member X Xs1)) (not (tptp.member Y Xs1)) (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 X Y)) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh X) (tptp.apply Xh Y))))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2) Xs1))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2) Xs1))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (let ((_let_1 (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2))) (let ((_let_2 (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2))) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (not (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 _let_2 _let_1)) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh _let_2) (tptp.apply Xh _let_1)))))))) (forall ((Xs $$unsorted) (Xf $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.associative Xs Xf)) (not (tptp.member X Xs)) (not (tptp.member Y Xs)) (not (tptp.member Z Xs)) (= (tptp.apply_to_two_arguments Xf (tptp.apply_to_two_arguments Xf X Y) Z) (tptp.apply_to_two_arguments Xf X (tptp.apply_to_two_arguments Xf Y Z))))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.associative Xs Xf) (tptp.member (tptp.f34 Xs Xf) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.associative Xs Xf) (tptp.member (tptp.f35 Xs Xf) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.associative Xs Xf) (tptp.member (tptp.f36 Xs Xf) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (let ((_let_1 (tptp.f36 Xs Xf))) (let ((_let_2 (tptp.f35 Xs Xf))) (let ((_let_3 (tptp.f34 Xs Xf))) (or (tptp.associative Xs Xf) (not (= (tptp.apply_to_two_arguments Xf (tptp.apply_to_two_arguments Xf _let_3 _let_2) _let_1) (tptp.apply_to_two_arguments Xf _let_3 (tptp.apply_to_two_arguments Xf _let_2 _let_1))))))))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted)) (or (not (tptp.identity Xs Xf Xe)) (tptp.member Xe Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (X $$unsorted)) (or (not (tptp.identity Xs Xf Xe)) (not (tptp.member X Xs)) (= (tptp.apply_to_two_arguments Xf Xe X) X))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (X $$unsorted)) (or (not (tptp.identity Xs Xf Xe)) (not (tptp.member X Xs)) (= (tptp.apply_to_two_arguments Xf X Xe) X))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted)) (or (tptp.identity Xs Xf Xe) (not (tptp.member Xe Xs)) (tptp.member (tptp.f37 Xs Xf Xe) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted)) (let ((_let_1 (tptp.f37 Xs Xf Xe))) (or (tptp.identity Xs Xf Xe) (not (tptp.member Xe Xs)) (not (= (tptp.apply_to_two_arguments Xf Xe _let_1) _let_1)) (not (= (tptp.apply_to_two_arguments Xf _let_1 Xe) _let_1))))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (Xg $$unsorted)) (or (not (tptp.inverse Xs Xf Xe Xg)) (tptp.maps Xg Xs Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (Xg $$unsorted) (X $$unsorted)) (or (not (tptp.inverse Xs Xf Xe Xg)) (not (tptp.member X Xs)) (= (tptp.apply_to_two_arguments Xf (tptp.apply Xg X) X) Xe))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (Xg $$unsorted) (X $$unsorted)) (or (not (tptp.inverse Xs Xf Xe Xg)) (not (tptp.member X Xs)) (= (tptp.apply_to_two_arguments Xf X (tptp.apply Xg X)) Xe))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (Xg $$unsorted)) (or (tptp.inverse Xs Xf Xe Xg) (not (tptp.maps Xg Xs Xs)) (tptp.member (tptp.f38 Xs Xf Xe Xg) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (Xg $$unsorted)) (let ((_let_1 (tptp.f38 Xs Xf Xe Xg))) (let ((_let_2 (tptp.apply Xg _let_1))) (or (tptp.inverse Xs Xf Xe Xg) (not (tptp.maps Xg Xs Xs)) (not (= (tptp.apply_to_two_arguments Xf _let_2 _let_1) Xe)) (not (= (tptp.apply_to_two_arguments Xf _let_1 _let_2) Xe)))))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.group Xs Xf)) (tptp.closed Xs Xf))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.group Xs Xf)) (tptp.associative Xs Xf))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.group Xs Xf)) (tptp.identity Xs Xf (tptp.f39 Xs Xf)))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.group Xs Xf)) (tptp.inverse Xs Xf (tptp.f39 Xs Xf) (tptp.f40 Xs Xf)))) (forall ((Xs $$unsorted) (Xf $$unsorted) (Xe $$unsorted) (Xg $$unsorted)) (or (tptp.group Xs Xf) (not (tptp.closed Xs Xf)) (not (tptp.associative Xs Xf)) (not (tptp.identity Xs Xf Xe)) (not (tptp.inverse Xs Xf Xe Xg)))) (forall ((Xs $$unsorted) (Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.commutes Xs Xf)) (not (tptp.member X Xs)) (not (tptp.member Y Xs)) (= (tptp.apply_to_two_arguments Xf X Y) (tptp.apply_to_two_arguments Xf Y X)))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.commutes Xs Xf) (tptp.member (tptp.f41 Xs Xf) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.commutes Xs Xf) (tptp.member (tptp.f42 Xs Xf) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (let ((_let_1 (tptp.f41 Xs Xf))) (let ((_let_2 (tptp.f42 Xs Xf))) (or (tptp.commutes Xs Xf) (not (= (tptp.apply_to_two_arguments Xf _let_1 _let_2) (tptp.apply_to_two_arguments Xf _let_2 _let_1))))))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.natural_numbers)) (not (tptp.little_set Xs)) (not (tptp.member tptp.empty_set Xs)) (tptp.member (tptp.f43 Z Xs) Xs) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.natural_numbers)) (not (tptp.little_set Xs)) (not (tptp.member tptp.empty_set Xs)) (not (tptp.member (tptp.successor (tptp.f43 Z Xs)) Xs)) (tptp.member Z Xs))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.natural_numbers) (not (tptp.little_set Z)) (tptp.little_set (tptp.f44 Z)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.natural_numbers) (not (tptp.little_set Z)) (tptp.member tptp.empty_set (tptp.f44 Z)))) (forall ((Z $$unsorted) (Xk $$unsorted)) (let ((_let_1 (tptp.f44 Z))) (or (tptp.member Z tptp.natural_numbers) (not (tptp.little_set Z)) (not (tptp.member Xk _let_1)) (tptp.member (tptp.successor Xk) _let_1)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.natural_numbers) (not (tptp.member Z (tptp.f44 Z))))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (tptp.member (tptp.f45 Z Xs) tptp.natural_numbers) (tptp.member (tptp.f46 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (tptp.member (tptp.f45 Z Xs) tptp.natural_numbers) (tptp.member (tptp.f47 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (tptp.member (tptp.f45 Z Xs) tptp.natural_numbers) (tptp.member (tptp.f48 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (tptp.member (tptp.f45 Z Xs) tptp.natural_numbers) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.f46 Z Xs) (tptp.f47 Z Xs)) (tptp.f48 Z Xs)) Xs) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (tptp.member (tptp.f45 Z Xs) tptp.natural_numbers) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor (tptp.f46 Z Xs)) (tptp.f47 Z Xs)) (tptp.successor (tptp.f48 Z Xs))) Xs)) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f45 Z Xs))) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set _let_1) _let_1) Xs)) (tptp.member (tptp.f46 Z Xs) tptp.natural_numbers) (tptp.member Z Xs)))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f45 Z Xs))) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set _let_1) _let_1) Xs)) (tptp.member (tptp.f47 Z Xs) tptp.natural_numbers) (tptp.member Z Xs)))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f45 Z Xs))) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set _let_1) _let_1) Xs)) (tptp.member (tptp.f48 Z Xs) tptp.natural_numbers) (tptp.member Z Xs)))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f45 Z Xs))) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set _let_1) _let_1) Xs)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.f46 Z Xs) (tptp.f47 Z Xs)) (tptp.f48 Z Xs)) Xs) (tptp.member Z Xs)))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f45 Z Xs))) (or (not (tptp.member Z tptp.plus)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set _let_1) _let_1) Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor (tptp.f46 Z Xs)) (tptp.f47 Z Xs)) (tptp.successor (tptp.f48 Z Xs))) Xs)) (tptp.member Z Xs)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.plus) (not (tptp.little_set Z)) (tptp.little_set (tptp.f49 Z)))) (forall ((Z $$unsorted) (Xi $$unsorted)) (or (tptp.member Z tptp.plus) (not (tptp.little_set Z)) (not (tptp.member Xi tptp.natural_numbers)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set Xi) Xi) (tptp.f49 Z)))) (forall ((Z $$unsorted) (Uu1 $$unsorted) (Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (tptp.f49 Z))) (or (tptp.member Z tptp.plus) (not (tptp.little_set Z)) (not (tptp.member Uu1 tptp.natural_numbers)) (not (tptp.member Xj tptp.natural_numbers)) (not (tptp.member Xk tptp.natural_numbers)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair Uu1 Xj) Xk) _let_1)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor Uu1) Xj) (tptp.successor Xk)) _let_1)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.plus) (not (tptp.member Z (tptp.f49 Z))))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (tptp.member (tptp.f50 Z Xs) tptp.natural_numbers) (tptp.member (tptp.f51 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (tptp.member (tptp.f50 Z Xs) tptp.natural_numbers) (tptp.member (tptp.f52 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (tptp.member (tptp.f50 Z Xs) tptp.natural_numbers) (tptp.member (tptp.f53 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (tptp.member (tptp.f50 Z Xs) tptp.natural_numbers) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.f51 Z Xs) (tptp.f52 Z Xs)) (tptp.f53 Z Xs)) Xs) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f52 Z Xs))) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (tptp.member (tptp.f50 Z Xs) tptp.natural_numbers) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor (tptp.f51 Z Xs)) _let_1) (tptp.apply_to_two_arguments tptp.plus (tptp.f53 Z Xs) _let_1)) Xs)) (tptp.member Z Xs)))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set (tptp.f50 Z Xs)) tptp.empty_set) Xs)) (tptp.member (tptp.f51 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set (tptp.f50 Z Xs)) tptp.empty_set) Xs)) (tptp.member (tptp.f52 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set (tptp.f50 Z Xs)) tptp.empty_set) Xs)) (tptp.member (tptp.f53 Z Xs) tptp.natural_numbers) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set (tptp.f50 Z Xs)) tptp.empty_set) Xs)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.f51 Z Xs) (tptp.f52 Z Xs)) (tptp.f53 Z Xs)) Xs) (tptp.member Z Xs))) (forall ((Z $$unsorted) (Xs $$unsorted)) (let ((_let_1 (tptp.f52 Z Xs))) (or (not (tptp.member Z tptp.times)) (not (tptp.little_set Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set (tptp.f50 Z Xs)) tptp.empty_set) Xs)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor (tptp.f51 Z Xs)) _let_1) (tptp.apply_to_two_arguments tptp.plus (tptp.f53 Z Xs) _let_1)) Xs)) (tptp.member Z Xs)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.times) (not (tptp.little_set Z)) (tptp.little_set (tptp.f54 Z)))) (forall ((Z $$unsorted) (Xi $$unsorted)) (or (tptp.member Z tptp.times) (not (tptp.little_set Z)) (not (tptp.member Xi tptp.natural_numbers)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair tptp.empty_set Xi) tptp.empty_set) (tptp.f54 Z)))) (forall ((Z $$unsorted) (Uu2 $$unsorted) (Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (tptp.f54 Z))) (or (tptp.member Z tptp.times) (not (tptp.little_set Z)) (not (tptp.member Uu2 tptp.natural_numbers)) (not (tptp.member Xj tptp.natural_numbers)) (not (tptp.member Xk tptp.natural_numbers)) (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair Uu2 Xj) Xk) _let_1)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair (tptp.successor Uu2) Xj) (tptp.apply_to_two_arguments tptp.plus Xk Xj)) _let_1)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.times) (not (tptp.member Z (tptp.f54 Z))))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.prime_numbers)) (tptp.member Z tptp.natural_numbers))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.prime_numbers)) (not (= Z tptp.empty_set)))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.prime_numbers)) (not (= Z (tptp.successor tptp.empty_set))))) (forall ((Z $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member Z tptp.prime_numbers)) (not (tptp.member U tptp.natural_numbers)) (not (tptp.member V tptp.natural_numbers)) (not (= (tptp.apply_to_two_arguments tptp.times U V) Z)) (tptp.member U (tptp.non_ordered_pair (tptp.successor tptp.empty_set) Z)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.prime_numbers) (not (tptp.member Z tptp.natural_numbers)) (= Z tptp.empty_set) (= Z (tptp.successor tptp.empty_set)) (tptp.member (tptp.f55 Z) tptp.natural_numbers))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.prime_numbers) (not (tptp.member Z tptp.natural_numbers)) (= Z tptp.empty_set) (= Z (tptp.successor tptp.empty_set)) (tptp.member (tptp.f56 Z) tptp.natural_numbers))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.prime_numbers) (not (tptp.member Z tptp.natural_numbers)) (= Z tptp.empty_set) (= Z (tptp.successor tptp.empty_set)) (= (tptp.apply_to_two_arguments tptp.times (tptp.f55 Z) (tptp.f56 Z)) Z))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.successor tptp.empty_set))) (or (tptp.member Z tptp.prime_numbers) (not (tptp.member Z tptp.natural_numbers)) (= Z tptp.empty_set) (= Z _let_1) (not (tptp.member (tptp.f55 Z) (tptp.non_ordered_pair _let_1 Z)))))) (forall ((X $$unsorted)) (or (not (tptp.finite X)) (tptp.member (tptp.f57 X) tptp.natural_numbers))) (forall ((X $$unsorted)) (or (not (tptp.finite X)) (tptp.maps (tptp.f58 X) (tptp.f57 X) X))) (forall ((X $$unsorted)) (or (not (tptp.finite X)) (= (tptp.range_of (tptp.f58 X)) X))) (forall ((X $$unsorted)) (or (not (tptp.finite X)) (tptp.one_to_one_function (tptp.f58 X)))) (forall ((X $$unsorted) (Xn $$unsorted) (Xf $$unsorted)) (or (tptp.finite X) (not (tptp.member Xn tptp.natural_numbers)) (not (tptp.maps Xf Xn X)) (not (= (tptp.range_of Xf) X)) (not (tptp.one_to_one_function Xf)))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.twin_prime_numbers)) (tptp.member Z tptp.prime_numbers))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.twin_prime_numbers)) (tptp.member (tptp.successor (tptp.successor Z)) tptp.prime_numbers))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.twin_prime_numbers) (not (tptp.member Z tptp.prime_numbers)) (not (tptp.member (tptp.successor (tptp.successor Z)) tptp.prime_numbers)))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.even_numbers)) (tptp.member Z tptp.natural_numbers))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.even_numbers)) (tptp.member (tptp.f59 Z) tptp.natural_numbers))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.f59 Z))) (or (not (tptp.member Z tptp.even_numbers)) (= (tptp.apply_to_two_arguments tptp.plus _let_1 _let_1) Z)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z tptp.even_numbers) (not (tptp.member Z tptp.natural_numbers)) (not (tptp.member X tptp.natural_numbers)) (not (= (tptp.apply_to_two_arguments tptp.plus X X) Z)))) _let_2 _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 223.85/224.08 )
% 223.92/224.10 % SZS output end Proof for NUM011-1
% 223.92/224.11 % cvc5---1.0.5 exiting
% 223.92/224.11 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------