TSTP Solution File: SEU341+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 16:31:01 EDT 2023
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 16:20:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.qEcVrQ7ASU/cvc5---1.0.5_21227.p...
% 0.21/0.55 ------- get file name : TPTP file name is SEU341+1
% 0.21/0.55 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21227.smt2...
% 0.21/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for SEU341+1
% 0.21/0.55 % SZS output start Proof for SEU341+1
% 0.21/0.55 (
% 0.21/0.55 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.open_subset B A) (tptp.in C B)) (tptp.point_neighbourhood B A C))))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.top_str B) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier B))) (and (=> (tptp.open_subset D B) (= (tptp.interior B D) D)) (=> (= (tptp.interior A C) C) (tptp.open_subset C A))))))))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (= (tptp.point_neighbourhood C A B) (tptp.in B (tptp.interior A C))))))))))) (let ((_let_4 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (tptp.interior SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_6 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_5))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_5))) (let ((_let_8 (tptp.point_neighbourhood SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (not _let_4))) (let ((_let_10 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_10))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.open_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.powerset _let_10)))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.topological_space SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (or _let_21 _let_20 _let_18 _let_16 _let_14 _let_12 _let_9 _let_8))) (let ((_let_23 (forall ((A $$unsorted) (BOUND_VARIABLE_1625 $$unsorted) (BOUND_VARIABLE_1623 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1623 (tptp.powerset _let_1))) (not (tptp.open_subset BOUND_VARIABLE_1623 A)) (not (tptp.element BOUND_VARIABLE_1625 _let_1)) (not (tptp.in BOUND_VARIABLE_1625 BOUND_VARIABLE_1623)) (tptp.point_neighbourhood BOUND_VARIABLE_1623 A BOUND_VARIABLE_1625)))))) (let ((_let_24 (not _let_22))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (or))) (let ((_let_27 (not _let_23))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_25) :args (_let_27))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))) (REFL :args (_let_24)) :args _let_26)) _let_25 :args (_let_24 true _let_23)))) (let ((_let_29 (REFL :args (_let_22)))) (let ((_let_30 (= _let_8 _let_6))) (let ((_let_31 (not _let_6))) (let ((_let_32 (or _let_21 _let_20 _let_18 _let_12 _let_16 _let_30))) (let ((_let_33 (forall ((A $$unsorted) (BOUND_VARIABLE_1350 $$unsorted) (BOUND_VARIABLE_1348 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1348 _let_1)) (not (tptp.element BOUND_VARIABLE_1350 (tptp.powerset _let_1))) (= (tptp.point_neighbourhood BOUND_VARIABLE_1350 A BOUND_VARIABLE_1348) (tptp.in BOUND_VARIABLE_1348 (tptp.interior A BOUND_VARIABLE_1350)))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 3)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_26)) :args ((or _let_15 _let_22))) _let_28 :args (_let_15 true _let_22)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 2)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_26)) :args ((or _let_17 _let_22))) _let_28 :args (_let_17 true _let_22)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 1)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_26)) :args ((or _let_19 _let_22))) _let_28 :args (_let_19 true _let_22)))) (let ((_let_38 (or _let_14 _let_7))) (let ((_let_39 (not _let_7))) (let ((_let_40 (and _let_38 (or _let_39 _let_13)))) (let ((_let_41 (or _let_20 _let_18 _let_18 _let_16 _let_16 _let_40))) (let ((_let_42 (forall ((A $$unsorted) (BOUND_VARIABLE_1558 $$unsorted) (BOUND_VARIABLE_1556 $$unsorted) (BOUND_VARIABLE_1554 $$unsorted)) (or (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.top_str BOUND_VARIABLE_1554)) (not (tptp.element BOUND_VARIABLE_1558 (tptp.powerset (tptp.the_carrier A)))) (not (tptp.element BOUND_VARIABLE_1556 (tptp.powerset (tptp.the_carrier BOUND_VARIABLE_1554)))) (and (or (not (tptp.open_subset BOUND_VARIABLE_1556 BOUND_VARIABLE_1554)) (= BOUND_VARIABLE_1556 (tptp.interior BOUND_VARIABLE_1554 BOUND_VARIABLE_1556))) (or (not (= BOUND_VARIABLE_1558 (tptp.interior A BOUND_VARIABLE_1558))) (tptp.open_subset BOUND_VARIABLE_1558 A))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_31)))) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (SYMM (ASSUME :args (_let_7))) :args (APPLY_UF tptp.in)) (TRUE_INTRO (ASSUME :args (_let_4))))) :args (_let_4 _let_7 _let_31))) (CONG (REFL :args (_let_9)) (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_6))) :args _let_26)) :args ((or _let_9 _let_6 _let_39))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_14 _let_7 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 4)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_26)) :args ((or _let_13 _let_22))) _let_28 :args (_let_13 true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 0)) :args ((or _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_41))) :args ((or _let_20 _let_18 _let_16 _let_40 (not _let_41)))) _let_37 _let_36 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1558 (tptp.powerset (tptp.the_carrier A))) false)) (not (= (tptp.element BOUND_VARIABLE_1556 (tptp.powerset (tptp.the_carrier BOUND_VARIABLE_1554))) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_40 false _let_19 false _let_17 false _let_15 false _let_41)) :args (_let_38 false _let_40)) :args (_let_7 false _let_13 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_8 _let_31 (not _let_30)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 7)) _let_28 :args ((not _let_8) true _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_21 _let_20 _let_18 _let_16 _let_12 _let_30 (not _let_32)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_22 0)) _let_28 :args ((not _let_21) true _let_22)) _let_37 _let_36 _let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 5)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_26)) :args ((or _let_11 _let_22))) _let_28 :args (_let_11 true _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.point_neighbourhood BOUND_VARIABLE_1350 A BOUND_VARIABLE_1348)))) :args (_let_33))) _let_34 :args (_let_32 false _let_33)) :args (_let_30 true _let_21 false _let_19 false _let_17 false _let_15 false _let_11 false _let_32)) :args (_let_31 true _let_8 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_22 6)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_4))) :args _let_26)) :args ((or _let_4 _let_22))) _let_28 :args (_let_4 true _let_22)) :args (false false _let_7 true _let_6 false _let_4)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (tptp.v1_xcmplx_0 B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.natural B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.v1_membered B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (=> (and (tptp.top_str A) (tptp.element B _let_1)) (tptp.element (tptp.interior A B) _let_1)))) true true (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.point_neighbourhood C A B) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))) true true (exists ((A $$unsorted)) (tptp.top_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (exists ((C $$unsorted)) (tptp.point_neighbourhood C A B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set)) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) _let_2 _let_1 (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55 )
% 0.21/0.55 % SZS output end Proof for SEU341+1
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------