TSTP Solution File: SET766+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:40:15 EDT 2023
% Result : Theorem 0.35s 0.54s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 11:40:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.35/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.b9H9FVQIdF/cvc5---1.0.5_1869.p...
% 0.35/0.54 ------- get file name : TPTP file name is SET766+4
% 0.35/0.54 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1869.smt2...
% 0.35/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.35/0.54 % SZS status Theorem for SET766+4
% 0.35/0.54 % SZS output start Proof for SET766+4
% 0.35/0.54 (
% 0.35/0.54 (let ((_let_1 (not (forall ((E $$unsorted) (R $$unsorted) (A $$unsorted)) (=> (and (tptp.equivalence R E) (tptp.member A E)) (tptp.member A (tptp.equivalence_class A E R))))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.equivalence_class A E R)) (and (tptp.member X E) (tptp.apply R A X)))))) (let ((_let_3 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (tptp.apply R X Y) (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A) (tptp.member Z A)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_4 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_7 (not _let_6))) (let ((_let_8 (or _let_7 _let_5))) (let ((_let_9 (and _let_4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z)))))) (let ((_let_10 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.apply R X Y)) (tptp.apply R Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.member Z A)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_15 (not _let_10))) (let ((_let_16 (or _let_15 _let_7 _let_14))) (let ((_let_17 (forall ((E $$unsorted) (R $$unsorted) (A $$unsorted)) (or (not (tptp.equivalence R E)) (not (tptp.member A E)) (tptp.member A (tptp.equivalence_class A E R)))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (or))) (let ((_let_21 (not _let_17))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_19) :args (_let_21))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_17))) (REFL :args (_let_18)) :args _let_20)) _let_19 :args (_let_18 true _let_17)))) (let ((_let_23 (REFL :args (_let_16)))) (let ((_let_24 (not _let_8))) (let ((_let_25 (and _let_6 _let_5))) (let ((_let_26 (not _let_5))) (let ((_let_27 (= _let_14 _let_25))) (let ((_let_28 (not _let_25))) (let ((_let_29 (_let_2))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 1)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_20)) :args ((or _let_6 _let_16))) _let_22 :args (_let_6 true _let_16)))) (let ((_let_32 (_let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_7 _let_5 _let_24))) _let_31 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_25)) :args ((or _let_7 _let_25 _let_26))) _let_31 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_27)) :args ((or _let_14 _let_28 (not _let_27)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 2)) _let_22 :args ((not _let_14) true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.member X (tptp.equivalence_class A E R))))) :args _let_29)) _let_30 :args (_let_27 false _let_2)) :args (_let_28 true _let_14 false _let_27)) :args (_let_26 false _let_6 true _let_25)) :args (_let_24 false _let_6 true _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_4 (not _let_9)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or _let_15 _let_9 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_10))) :args _let_20)) :args ((or _let_10 _let_16))) _let_22 :args (_let_10 true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equivalence R A)))) :args (_let_12))) _let_13 :args (_let_11 false _let_12)) :args (_let_9 false _let_10 false _let_11)) :args (_let_4 false _let_9)) :args (false true _let_8 false _let_4)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))) (forall ((A $$unsorted) (E $$unsorted)) (= (tptp.partition A E) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X E))) (forall ((X $$unsorted)) (=> (tptp.member X E) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (exists ((Z $$unsorted)) (and (tptp.member Z X) (tptp.member Z Y))) (= X Y))))))) _let_3 _let_2 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) _let_1 true)))))))))))))))))))))))))))))))))))
% 0.35/0.54 )
% 0.35/0.54 % SZS output end Proof for SET766+4
% 0.35/0.54 % cvc5---1.0.5 exiting
% 0.35/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------