%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 10:48:25 EDT 2023

% Result   : Theorem 0.21s 0.54s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n005.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   : Fri Aug 25 14:39:38 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.YG6t7MEPXJ/cvc5---1.0.5_31095.p...
% 0.21/0.54  ------- get file name : TPTP file name is NUM845+2
% 0.21/0.54  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31095.smt2...
% 0.21/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.54  % SZS status Theorem for NUM845+2
% 0.21/0.54  % SZS output start Proof for NUM845+2
% 0.21/0.54  (
% 0.21/0.54  (let ((_let_1 (forall ((Vd396 $$unsorted) (Vd397 $$unsorted)) (and (= (tptp.vmul Vd396 (tptp.vsucc Vd397)) (tptp.vplus (tptp.vmul Vd396 Vd397) Vd396)) (= (tptp.vmul Vd396 tptp.v1) Vd396))))) (let ((_let_2 (tptp.vmul tptp.vd411 tptp.v1))) (let ((_let_3 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc tptp.vd411))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (let ((_let_3 (tptp.vplus _let_2 Vd413))) (=> (= (tptp.vmul _let_1 Vd413) _let_3) (= (tptp.vplus _let_3 _let_1) (tptp.vplus _let_2 (tptp.vplus Vd413 _let_1)))))))))) (let ((_let_4 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc tptp.vd411))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (=> (= (tptp.vmul _let_1 Vd413) (tptp.vplus _let_2 Vd413)) (= (tptp.vplus _let_2 (tptp.vplus Vd413 _let_1)) (tptp.vplus _let_2 (tptp.vplus _let_1 Vd413))))))))) (let ((_let_5 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vmul tptp.vd411 Vd413))) (let ((_let_2 (tptp.vsucc tptp.vd411))) (=> (= (tptp.vmul _let_2 Vd413) (tptp.vplus _let_1 Vd413)) (= (tptp.vplus _let_1 (tptp.vplus _let_2 Vd413)) (tptp.vplus _let_1 (tptp.vsucc (tptp.vplus tptp.vd411 Vd413)))))))))) (let ((_let_6 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vmul tptp.vd411 Vd413))) (=> (= (tptp.vmul (tptp.vsucc tptp.vd411) Vd413) (tptp.vplus _let_1 Vd413)) (= (tptp.vplus _let_1 (tptp.vsucc (tptp.vplus tptp.vd411 Vd413))) (tptp.vplus _let_1 (tptp.vplus tptp.vd411 (tptp.vsucc Vd413))))))))) (let ((_let_7 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc Vd413))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (=> (= (tptp.vmul (tptp.vsucc tptp.vd411) Vd413) (tptp.vplus _let_2 Vd413)) (= (tptp.vplus _let_2 (tptp.vplus tptp.vd411 _let_1)) (tptp.vplus (tptp.vplus _let_2 tptp.vd411) _let_1)))))))) (let ((_let_8 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc Vd413))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (=> (= (tptp.vmul (tptp.vsucc tptp.vd411) Vd413) (tptp.vplus _let_2 Vd413)) (= (tptp.vplus (tptp.vplus _let_2 tptp.vd411) _let_1) (tptp.vplus (tptp.vmul tptp.vd411 _let_1) _let_1)))))))) (let ((_let_9 (not (forall ((Vd416 $$unsorted)) (let ((_let_1 (tptp.vsucc Vd416))) (let ((_let_2 (tptp.vsucc tptp.vd411))) (=> (= (tptp.vmul _let_2 Vd416) (tptp.vplus (tptp.vmul tptp.vd411 Vd416) Vd416)) (= (tptp.vmul _let_2 _let_1) (tptp.vplus (tptp.vmul tptp.vd411 _let_1) _let_1))))))))) (let ((_let_10 (tptp.vmul tptp.vd411 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (tptp.vplus _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_12 (tptp.vsucc tptp.vd411))) (let ((_let_13 (tptp.vmul _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (= _let_13 _let_11))) (let ((_let_15 (tptp.vsucc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (tptp.vplus (tptp.vmul tptp.vd411 _let_15) _let_15))) (let ((_let_17 (tptp.vmul _let_12 _let_15))) (let ((_let_18 (= _let_17 _let_16))) (let ((_let_19 (tptp.vplus _let_13 _let_12))) (let ((_let_20 (= _let_17 _let_19))) (let ((_let_21 (tptp.vplus (tptp.vplus _let_10 tptp.vd411) _let_15))) (let ((_let_22 (= _let_16 _let_21))) (let ((_let_23 (tptp.vplus _let_10 (tptp.vplus tptp.vd411 _let_15)))) (let ((_let_24 (= _let_21 _let_23))) (let ((_let_25 (tptp.vplus _let_10 (tptp.vsucc (tptp.vplus tptp.vd411 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_26 (= _let_23 _let_25))) (let ((_let_27 (tptp.vplus _let_10 (tptp.vplus _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_28 (= _let_25 _let_27))) (let ((_let_29 (tptp.vplus _let_10 (tptp.vplus SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12)))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (tptp.vplus _let_11 _let_12))) (let ((_let_32 (= _let_29 _let_31))) (let ((_let_33 (not _let_14))) (let ((_let_34 (or _let_33 _let_18))) (let ((_let_35 (forall ((Vd416 $$unsorted)) (let ((_let_1 (tptp.vsucc Vd416))) (let ((_let_2 (tptp.vsucc tptp.vd411))) (or (not (= (tptp.vmul _let_2 Vd416) (tptp.vplus (tptp.vmul tptp.vd411 Vd416) Vd416))) (= (tptp.vmul _let_2 _let_1) (tptp.vplus (tptp.vmul tptp.vd411 _let_1) _let_1)))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_14))) :args _let_38)) :args ((or _let_14 _let_34))) _let_40 :args (_let_14 true _let_34)))) (let ((_let_42 (not _let_18))) (let ((_let_43 (forall ((BOUND_VARIABLE_798 $$unsorted) (BOUND_VARIABLE_800 $$unsorted)) (= (tptp.vmul BOUND_VARIABLE_798 (tptp.vsucc BOUND_VARIABLE_800)) (tptp.vplus (tptp.vmul BOUND_VARIABLE_798 BOUND_VARIABLE_800) BOUND_VARIABLE_798))))) (let ((_let_44 (_let_43))) (let ((_let_45 (or _let_33 _let_22))) (let ((_let_46 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc Vd413))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (or (not (= (tptp.vmul (tptp.vsucc tptp.vd411) Vd413) (tptp.vplus _let_2 Vd413))) (= (tptp.vplus (tptp.vplus _let_2 tptp.vd411) _let_1) (tptp.vplus (tptp.vmul tptp.vd411 _let_1) _let_1)))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (or _let_33 _let_24))) (let ((_let_49 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc Vd413))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (or (not (= (tptp.vmul (tptp.vsucc tptp.vd411) Vd413) (tptp.vplus _let_2 Vd413))) (= (tptp.vplus _let_2 (tptp.vplus tptp.vd411 _let_1)) (tptp.vplus (tptp.vplus _let_2 tptp.vd411) _let_1)))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (or _let_33 _let_26))) (let ((_let_52 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vmul tptp.vd411 Vd413))) (or (not (= (tptp.vmul (tptp.vsucc tptp.vd411) Vd413) (tptp.vplus _let_1 Vd413))) (= (tptp.vplus _let_1 (tptp.vsucc (tptp.vplus tptp.vd411 Vd413))) (tptp.vplus _let_1 (tptp.vplus tptp.vd411 (tptp.vsucc Vd413))))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or _let_33 _let_28))) (let ((_let_55 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vmul tptp.vd411 Vd413))) (let ((_let_2 (tptp.vsucc tptp.vd411))) (or (not (= (tptp.vmul _let_2 Vd413) (tptp.vplus _let_1 Vd413))) (= (tptp.vplus _let_1 (tptp.vplus _let_2 Vd413)) (tptp.vplus _let_1 (tptp.vsucc (tptp.vplus tptp.vd411 Vd413)))))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or _let_33 _let_30))) (let ((_let_58 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc tptp.vd411))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (or (not (= (tptp.vmul _let_1 Vd413) (tptp.vplus _let_2 Vd413))) (= (tptp.vplus _let_2 (tptp.vplus Vd413 _let_1)) (tptp.vplus _let_2 (tptp.vplus _let_1 Vd413))))))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (or _let_33 _let_32))) (let ((_let_61 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc tptp.vd411))) (let ((_let_2 (tptp.vmul tptp.vd411 Vd413))) (let ((_let_3 (tptp.vplus _let_2 Vd413))) (or (not (= _let_3 (tptp.vmul _let_1 Vd413))) (= (tptp.vplus _let_3 _let_1) (tptp.vplus _let_2 (tptp.vplus Vd413 _let_1)))))))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (= _let_31 _let_19))) (let ((_let_64 (ASSUME :args (_let_22)))) (let ((_let_65 (ASSUME :args (_let_24)))) (let ((_let_66 (ASSUME :args (_let_26)))) (let ((_let_67 (ASSUME :args (_let_28)))) (let ((_let_68 (ASSUME :args (_let_30)))) (let ((_let_69 (ASSUME :args (_let_32)))) (let ((_let_70 (ASSUME :args (_let_20)))) (let ((_let_71 (ASSUME :args (_let_42)))) (let ((_let_72 (_let_14))) (let ((_let_73 (ASSUME :args _let_72))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_70 (MODUS_PONENS _let_73 (SCOPE (CONG (SYMM _let_73) (REFL :args (_let_12)) :args (APPLY_UF tptp.vplus)) :args _let_72)) _let_69 _let_68 _let_66 _let_64 _let_67 _let_65 _let_71) :args (_let_14 _let_42 _let_22 _let_24 _let_26 _let_28 _let_30 _let_32 _let_20)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_71)) (TRUE_INTRO (TRANS (SYMM (SYMM _let_70)) (SYMM (ASSUME :args (_let_63))) (SYMM _let_69) (SYMM _let_68) (SYMM _let_67) (SYMM _let_66) (SYMM _let_65) (SYMM _let_64))))) :args (_let_20 _let_63 _let_32 _let_30 _let_26 _let_22 _let_28 _let_24 _let_42)) :args ((not (and _let_14 _let_42 _let_22 _let_24 _let_26 _let_28 _let_30 _let_32 _let_20)) SB_LITERAL))) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_18))) (REFL :args ((not _let_22))) (REFL :args ((not _let_24))) (REFL :args ((not _let_26))) (REFL :args ((not _let_28))) (REFL :args ((not _let_30))) (REFL :args ((not _let_32))) (REFL :args ((not _let_20))) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_33 _let_32 (not _let_60)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vmul tptp.vd411 Vd413)))) :args (_let_61)))) _let_62 :args (_let_60 false _let_61)) :args (_let_32 false _let_14 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_33 _let_30 (not _let_57)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vmul _let_12 Vd413)))) :args (_let_58)))) _let_59 :args (_let_57 false _let_58)) :args (_let_30 false _let_14 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_33 _let_28 (not _let_54)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vmul _let_12 Vd413)))) :args (_let_55)))) _let_56 :args (_let_54 false _let_55)) :args (_let_28 false _let_14 false _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_33 _let_26 (not _let_51)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vmul _let_12 Vd413)))) :args (_let_52)))) _let_53 :args (_let_51 false _let_52)) :args (_let_26 false _let_14 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_33 _let_24 (not _let_48)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vmul _let_12 Vd413)))) :args (_let_49)))) _let_50 :args (_let_48 false _let_49)) :args (_let_24 false _let_14 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_33 _let_22 (not _let_45)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.vsucc Vd413)))) :args (_let_46)))) _let_47 :args (_let_45 false _let_46)) :args (_let_22 false _let_14 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.vmul BOUND_VARIABLE_798 (tptp.vsucc BOUND_VARIABLE_800))))) :args _let_44)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args (_let_20 false _let_43)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 1)) _let_40 :args (_let_42 true _let_34)) _let_41 :args (false false _let_32 false _let_30 false _let_28 false _let_26 false _let_24 false _let_22 false _let_20 true _let_18 false _let_14)) :args (_let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc tptp.vd411))) (let ((_let_2 (tptp.vplus (tptp.vmul tptp.vd411 Vd413) Vd413))) (let ((_let_3 (tptp.vmul _let_1 Vd413))) (=> (= _let_3 _let_2) (= (tptp.vplus _let_3 _let_1) (tptp.vplus _let_2 _let_1))))))) (forall ((Vd413 $$unsorted)) (let ((_let_1 (tptp.vsucc tptp.vd411))) (let ((_let_2 (tptp.vmul _let_1 Vd413))) (=> (= _let_2 (tptp.vplus (tptp.vmul tptp.vd411 Vd413) Vd413)) (= (tptp.vmul _let_1 (tptp.vsucc Vd413)) (tptp.vplus _let_2 _let_1)))))) (= (tptp.vsucc _let_2) (tptp.vplus _let_2 tptp.v1)) _let_1 (forall ((Vd78 $$unsorted) (Vd79 $$unsorted)) (= (tptp.vplus Vd79 Vd78) (tptp.vplus Vd78 Vd79))) (forall ((Vd59 $$unsorted)) (= (tptp.vplus tptp.v1 Vd59) (tptp.vsucc Vd59))) (forall ((Vd46 $$unsorted) (Vd47 $$unsorted) (Vd48 $$unsorted)) (= (tptp.vplus (tptp.vplus Vd46 Vd47) Vd48) (tptp.vplus Vd46 (tptp.vplus Vd47 Vd48)))) (forall ((Vd42 $$unsorted) (Vd43 $$unsorted)) (and (= (tptp.vplus Vd42 (tptp.vsucc Vd43)) (tptp.vsucc (tptp.vplus Vd42 Vd43))) (= (tptp.vplus Vd42 tptp.v1) (tptp.vsucc Vd42)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55  )
% 0.21/0.55  % SZS output end Proof for NUM845+2
% 0.21/0.55  % cvc5---1.0.5 exiting
% 0.21/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------