TSTP Solution File: SET979+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 14:41:14 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.19/0.35 % Computer : n001.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Sat Aug 26 09:48:15 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.21/0.48 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Ufc4ZUV7WR/cvc5---1.0.5_27125.p...
% 0.21/0.53 ------- get file name : TPTP file name is SET979+1
% 0.21/0.53 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27125.smt2...
% 0.21/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for SET979+1
% 0.21/0.53 % SZS output start Proof for SET979+1
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.set_union2 (tptp.singleton A) (tptp.singleton B)))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.singleton B))) (let ((_let_2 (tptp.singleton A))) (let ((_let_3 (tptp.unordered_pair A B))) (and (= (tptp.cartesian_product2 _let_3 C) (tptp.set_union2 (tptp.cartesian_product2 _let_2 C) (tptp.cartesian_product2 _let_1 C))) (= (tptp.cartesian_product2 C _let_3) (tptp.set_union2 (tptp.cartesian_product2 C _let_2) (tptp.cartesian_product2 C _let_1))))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.set_union2 A B))) (and (= (tptp.cartesian_product2 _let_1 C) (tptp.set_union2 (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C))) (= (tptp.cartesian_product2 C _let_1) (tptp.set_union2 (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B)))))))) (let ((_let_4 (forall ((BOUND_VARIABLE_724 $$unsorted) (BOUND_VARIABLE_726 $$unsorted) (BOUND_VARIABLE_728 $$unsorted)) (= (tptp.cartesian_product2 (tptp.unordered_pair BOUND_VARIABLE_724 BOUND_VARIABLE_726) BOUND_VARIABLE_728) (tptp.set_union2 (tptp.cartesian_product2 (tptp.singleton BOUND_VARIABLE_724) BOUND_VARIABLE_728) (tptp.cartesian_product2 (tptp.singleton BOUND_VARIABLE_726) BOUND_VARIABLE_728)))))) (let ((_let_5 (forall ((BOUND_VARIABLE_740 $$unsorted) (BOUND_VARIABLE_742 $$unsorted) (BOUND_VARIABLE_744 $$unsorted)) (= (tptp.cartesian_product2 BOUND_VARIABLE_744 (tptp.unordered_pair BOUND_VARIABLE_740 BOUND_VARIABLE_742)) (tptp.set_union2 (tptp.cartesian_product2 BOUND_VARIABLE_744 (tptp.singleton BOUND_VARIABLE_740)) (tptp.cartesian_product2 BOUND_VARIABLE_744 (tptp.singleton BOUND_VARIABLE_742))))))) (let ((_let_6 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_7 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_8 (tptp.set_union2 (tptp.cartesian_product2 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.cartesian_product2 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_9 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (= (tptp.cartesian_product2 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_8))) (let ((_let_11 (tptp.set_union2 _let_7 _let_6))) (let ((_let_12 (= _let_9 _let_11))) (let ((_let_13 (= _let_8 (tptp.cartesian_product2 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_14 (_let_1))) (let ((_let_15 (ASSUME :args _let_14))) (let ((_let_16 ((tptp.unordered_pair A B)))) (let ((_let_17 (forall ((BOUND_VARIABLE_694 $$unsorted) (BOUND_VARIABLE_696 $$unsorted) (BOUND_VARIABLE_698 $$unsorted)) (= (tptp.cartesian_product2 (tptp.set_union2 BOUND_VARIABLE_694 BOUND_VARIABLE_696) BOUND_VARIABLE_698) (tptp.set_union2 (tptp.cartesian_product2 BOUND_VARIABLE_694 BOUND_VARIABLE_698) (tptp.cartesian_product2 BOUND_VARIABLE_696 BOUND_VARIABLE_698)))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 (and _let_13 _let_12))) (let ((_let_21 (_let_13 _let_12))) (let ((_let_22 (ASSUME :args (_let_13)))) (let ((_let_23 (APPLY_UF tptp.cartesian_product2))) (let ((_let_24 (ASSUME :args (_let_12)))) (let ((_let_25 (or))) (let ((_let_26 (not _let_4))) (let ((_let_27 (_let_26))) (let ((_let_28 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_29 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_30 (tptp.set_union2 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_29) (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_28)))) (let ((_let_31 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_32 (= (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_31) _let_30))) (let ((_let_33 (tptp.set_union2 _let_29 _let_28))) (let ((_let_34 (= _let_31 _let_33))) (let ((_let_35 (= _let_30 (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_33)))) (let ((_let_36 (forall ((BOUND_VARIABLE_708 $$unsorted) (BOUND_VARIABLE_710 $$unsorted) (BOUND_VARIABLE_712 $$unsorted)) (= (tptp.cartesian_product2 BOUND_VARIABLE_712 (tptp.set_union2 BOUND_VARIABLE_708 BOUND_VARIABLE_710)) (tptp.set_union2 (tptp.cartesian_product2 BOUND_VARIABLE_712 BOUND_VARIABLE_708) (tptp.cartesian_product2 BOUND_VARIABLE_712 BOUND_VARIABLE_710)))))) (let ((_let_37 (_let_36))) (let ((_let_38 (and _let_35 _let_34))) (let ((_let_39 (_let_35 _let_34))) (let ((_let_40 (ASSUME :args (_let_35)))) (let ((_let_41 (ASSUME :args (_let_34)))) (let ((_let_42 (not _let_5))) (let ((_let_43 (_let_42))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_43)) :args _let_43)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_5))) (REFL :args ((not _let_32))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_38)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_40 _let_41) (SCOPE (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (SYMM (SYMM _let_41)) :args _let_23) (SYMM _let_40)) :args _let_39)) :args _let_39)) :args (true _let_38)) :args ((or _let_32 (not _let_35) (not _let_34)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args (_let_29 _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.set_union2 (tptp.cartesian_product2 BOUND_VARIABLE_712 BOUND_VARIABLE_708) (tptp.cartesian_product2 BOUND_VARIABLE_712 BOUND_VARIABLE_710))))) :args _let_37))) (AND_ELIM _let_18 :args (1)) :args (_let_35 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_16)) :args _let_14)) _let_15 :args (_let_34 false _let_1)) :args (_let_32 false _let_35 false _let_34)) :args (_let_5 false _let_32)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_27)) :args _let_27)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_4))) (REFL :args ((not _let_10))) :args _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_20)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_22 _let_24) (SCOPE (TRANS (CONG (SYMM (SYMM _let_24)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args _let_23) (SYMM _let_22)) :args _let_21)) :args _let_21)) :args (true _let_20)) :args ((or _let_10 (not _let_13) (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_19) :args (_let_7 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((tptp.set_union2 (tptp.cartesian_product2 BOUND_VARIABLE_694 BOUND_VARIABLE_698) (tptp.cartesian_product2 BOUND_VARIABLE_696 BOUND_VARIABLE_698))))) :args _let_19))) (AND_ELIM _let_18 :args (0)) :args (_let_13 false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_16)) :args _let_14)) _let_15 :args (_let_12 false _let_1)) :args (_let_10 false _let_13 false _let_12)) :args (_let_4 false _let_10)) :args (false false _let_5 false _let_4)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SET979+1
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------