TSTP Solution File: SEU009+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 16:29:01 EDT 2023
% Result : Theorem 6.79s 7.05s
% Output : Proof 6.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 14:59:11 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 6.79/7.05 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.u9YrJeCzHX/cvc5---1.0.5_13298.p...
% 6.79/7.05 ------- get file name : TPTP file name is SEU009+1
% 6.79/7.05 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13298.smt2...
% 6.79/7.05 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.79/7.05 % SZS status Theorem for SEU009+1
% 6.79/7.05 % SZS output start Proof for SEU009+1
% 6.79/7.05 (
% 6.79/7.05 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in B (tptp.relation_dom (tptp.relation_composition C (tptp.identity_relation A)))) (and (tptp.in B (tptp.relation_dom C)) (tptp.in (tptp.apply C B) A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) C))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in A (tptp.relation_dom (tptp.relation_composition C B))) (and (tptp.in A (tptp.relation_dom C)) (tptp.in (tptp.apply C A) (tptp.relation_dom B)))))))))) (let ((_let_4 (tptp.relation tptp.empty_set))) (let ((_let_5 (tptp.empty tptp.empty_set))) (let ((_let_6 (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1)))))) (let ((_let_7 (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))))) (let ((_let_8 (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (tptp.relation_dom _let_8))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9))) (let ((_let_11 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_12 (tptp.in _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_13 (tptp.in _let_11 _let_9))) (let ((_let_14 (and _let_10 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (= C (tptp.apply (tptp.identity_relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) C))))))) (let ((_let_15 (tptp.function _let_8))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.relation _let_8))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14))) (let ((_let_20 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= A (tptp.relation_dom B)) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (= C (tptp.apply B C)))))))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (forall ((BOUND_VARIABLE_953 $$unsorted)) (tptp.function (tptp.identity_relation BOUND_VARIABLE_953))))) (let ((_let_23 (_let_22))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_23) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.identity_relation BOUND_VARIABLE_953)))) :args _let_23)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_15 false _let_22)))) (let ((_let_25 (_let_7))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.identity_relation A)))) :args _let_25)) _let_26 :args (_let_17 false _let_7)))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_14 0)) :args ((or _let_10 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_16 _let_14 (not _let_19)))) _let_27 _let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_8 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.function B) false)) (tptp.identity_relation A)))) :args (_let_20)))) _let_21 :args (_let_19 false _let_20)) :args (_let_14 false _let_17 false _let_15 false _let_19)) :args (_let_10 false _let_14)))) (let ((_let_29 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_30 (and _let_29 _let_12))) (let ((_let_31 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.relation_dom (tptp.relation_composition SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_8))))) (let ((_let_32 (= _let_31 _let_30))) (let ((_let_33 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34 _let_32))) (let ((_let_38 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (= (tptp.in B (tptp.relation_dom (tptp.relation_composition C (tptp.identity_relation A)))) (and (tptp.in B (tptp.relation_dom C)) (tptp.in (tptp.apply C B) A))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 2)) _let_43 :args ((not _let_32) true _let_37)))) (let ((_let_45 (and _let_29 _let_13))) (let ((_let_46 (= _let_31 _let_45))) (let ((_let_47 (not _let_31))) (let ((_let_48 (_let_32))) (let ((_let_49 (or _let_18 _let_16 _let_36 _let_34 _let_46))) (let ((_let_50 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1063 $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.relation BOUND_VARIABLE_1063)) (not (tptp.function BOUND_VARIABLE_1063)) (= (tptp.in A (tptp.relation_dom (tptp.relation_composition BOUND_VARIABLE_1063 B))) (and (tptp.in A (tptp.relation_dom BOUND_VARIABLE_1063)) (tptp.in (tptp.apply BOUND_VARIABLE_1063 A) (tptp.relation_dom B)))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (REFL :args (_let_37)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_36 _let_34 _let_18 _let_16 _let_46 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_41)) :args ((or _let_35 _let_37))) _let_43 :args (_let_35 true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_41)) :args ((or _let_33 _let_37))) _let_43 :args (_let_33 true _let_37)) _let_27 _let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING ((tptp.in A (tptp.relation_dom (tptp.relation_composition BOUND_VARIABLE_1063 B)))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_46 false _let_35 false _let_33 false _let_17 false _let_15 false _let_49)))) (let ((_let_54 (not _let_46))) (let ((_let_55 (_let_46))) (let ((_let_56 (REORDERING (CNF_EQUIV_POS1 :args _let_55) :args ((or _let_47 _let_45 _let_54))))) (let ((_let_57 (not _let_30))) (let ((_let_58 (not _let_45))) (let ((_let_59 (REORDERING (CNF_EQUIV_NEG1 :args _let_48) :args ((or _let_31 _let_30 _let_32))))) (let ((_let_60 (MACRO_RESOLUTION_TRUST _let_56 _let_53 _let_59 _let_44 (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_29 _let_58))) (REORDERING (CNF_AND_POS :args (_let_30 0)) :args ((or _let_29 _let_57))) :args (_let_29 false _let_46 false _let_31 true _let_32 true _let_45 true _let_30)))) (let ((_let_61 (not _let_10))) (let ((_let_62 (not _let_13))) (let ((_let_63 (not _let_12))) (let ((_let_64 (and _let_63 _let_10))) (let ((_let_65 (_let_63 _let_10))) (let ((_let_66 (ASSUME :args (_let_63)))) (let ((_let_67 (ASSUME :args (_let_10)))) (let ((_let_68 (CONG (REFL :args (_let_11)) (SYMM _let_67) :args (APPLY_UF tptp.in)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_66 _let_67) (SCOPE (FALSE_ELIM (TRANS _let_68 (FALSE_INTRO _let_66))) :args _let_65)) :args _let_65)) :args (true _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_12))) (REFL :args (_let_61)) (REFL :args (_let_62)) :args _let_41)) :args ((or _let_12 _let_62 _let_61))) _let_28 (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_13 _let_58))) (CNF_AND_NEG :args (_let_30)) _let_60 _let_56 _let_53 (CNF_EQUIV_NEG2 :args _let_48) _let_44 :args (_let_47 false _let_10 false _let_13 true _let_12 false _let_29 false _let_45 false _let_46 true _let_30 true _let_32)))) (let ((_let_70 (and _let_12 _let_10))) (let ((_let_71 (_let_12 _let_10))) (let ((_let_72 (ASSUME :args (_let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_70)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_67) (SCOPE (TRUE_ELIM (TRANS _let_68 (TRUE_INTRO _let_72))) :args _let_71)) :args _let_71)) :args (true _let_70)) :args ((or _let_63 _let_13 _let_61))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_45)) :args ((or (not _let_29) _let_45 _let_62))) _let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_55) :args ((or _let_31 _let_58 _let_54))) _let_69 _let_53 :args (_let_58 true _let_31 false _let_46)) :args (_let_62 false _let_29 true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 1)) :args ((or _let_12 _let_57))) (MACRO_RESOLUTION_TRUST _let_59 _let_69 _let_44 :args (_let_30 true _let_31 true _let_32)) :args (_let_12 false _let_30)) _let_28 :args (false true _let_13 false _let_12 false _let_10)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))) _let_7 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition B A))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_5 _let_4 (tptp.relation_empty_yielding tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_5 _let_6 (and _let_5 _let_4) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.79/7.07 )
% 6.79/7.07 % SZS output end Proof for SEU009+1
% 6.79/7.07 % cvc5---1.0.5 exiting
% 6.79/7.07 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------