%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG178+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 : Wed Aug 30 16:08:31 EDT 2023

% Result   : Theorem 0.19s 0.52s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ALG178+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 04:36:56 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.52  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.L5Y9q4Kcpd/cvc5---1.0.5_20101.p...
% 0.19/0.52  ------- get file name : TPTP file name is ALG178+1
% 0.19/0.52  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20101.smt2...
% 0.19/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.52  % SZS status Theorem for ALG178+1
% 0.19/0.52  % SZS output start Proof for ALG178+1
% 0.19/0.52  (
% 0.19/0.52  (let ((_let_1 (not (=> (and (forall ((U $$unsorted)) (=> (tptp.sorti1 U) (tptp.sorti2 (tptp.h U)))) (forall ((V $$unsorted)) (=> (tptp.sorti2 V) (tptp.sorti1 (tptp.j V))))) (not (and (forall ((W $$unsorted)) (=> (tptp.sorti1 W) (forall ((X $$unsorted)) (=> (tptp.sorti1 X) (= (tptp.h (tptp.op1 W X)) (tptp.op2 (tptp.h W) (tptp.h X))))))) (forall ((Y $$unsorted)) (=> (tptp.sorti2 Y) (forall ((Z $$unsorted)) (=> (tptp.sorti2 Z) (= (tptp.j (tptp.op2 Y Z)) (tptp.op1 (tptp.j Y) (tptp.j Z))))))) (forall ((X1 $$unsorted)) (=> (tptp.sorti2 X1) (= (tptp.h (tptp.j X1)) X1))) (forall ((X2 $$unsorted)) (=> (tptp.sorti1 X2) (= (tptp.j (tptp.h X2)) X2))))))))) (let ((_let_2 (not (forall ((U $$unsorted)) (=> (tptp.sorti2 U) (forall ((V $$unsorted)) (=> (tptp.sorti2 V) (= (tptp.op2 U (tptp.op2 U V)) V)))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.sorti1 U) (forall ((V $$unsorted)) (=> (tptp.sorti1 V) (= (tptp.op1 U (tptp.op1 U V)) V))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.sorti2 U) (forall ((V $$unsorted)) (=> (tptp.sorti2 V) (tptp.sorti2 (tptp.op2 U V)))))))) (let ((_let_5 (tptp.op2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.op2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_5)))) (let ((_let_7 (tptp.j SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (tptp.j SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_9 (tptp.op1 _let_8 _let_7))) (let ((_let_10 (tptp.j _let_5))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (tptp.h _let_8))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12))) (let ((_let_14 (tptp.h _let_7))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_14))) (let ((_let_16 (= _let_7 (tptp.op1 _let_8 _let_9)))) (let ((_let_17 (= (tptp.h _let_9) (tptp.op2 _let_12 _let_14)))) (let ((_let_18 (= (tptp.h (tptp.op1 _let_8 _let_10)) (tptp.op2 _let_12 (tptp.h _let_10))))) (let ((_let_19 (tptp.sorti2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.sorti2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_6))) (let ((_let_24 (not _let_6))) (let ((_let_25 (forall ((U $$unsorted) (BOUND_VARIABLE_778 $$unsorted)) (or (not (tptp.sorti2 U)) (not (tptp.sorti2 BOUND_VARIABLE_778)) (= BOUND_VARIABLE_778 (tptp.op2 U (tptp.op2 U BOUND_VARIABLE_778))))))) (let ((_let_26 (not _let_23))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (or))) (let ((_let_29 (not _let_25))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_27) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_28)) _let_27 :args (_let_26 true _let_25)))) (let ((_let_31 (or _let_22 _let_20 _let_11))) (let ((_let_32 (forall ((Y $$unsorted) (BOUND_VARIABLE_831 $$unsorted)) (or (not (tptp.sorti2 Y)) (not (tptp.sorti2 BOUND_VARIABLE_831)) (= (tptp.j (tptp.op2 Y BOUND_VARIABLE_831)) (tptp.op1 (tptp.j Y) (tptp.j BOUND_VARIABLE_831))))))) (let ((_let_33 (1))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (NOT_NOT_ELIM (NOT_IMPLIES_ELIM2 _let_34)))) (let ((_let_36 (_let_32))) (let ((_let_37 (REFL :args (_let_23)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_28)) :args ((or _let_19 _let_23))) _let_30 :args (_let_19 true _let_23)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_28)) :args ((or _let_21 _let_23))) _let_30 :args (_let_21 true _let_23)))) (let ((_let_40 (or _let_22 _let_13))) (let ((_let_41 (forall ((X1 $$unsorted)) (or (not (tptp.sorti2 X1)) (= X1 (tptp.h (tptp.j X1))))))) (let ((_let_42 (AND_ELIM _let_35 :args (2)))) (let ((_let_43 (_let_41))) (let ((_let_44 ((not (= (tptp.sorti2 X1) false))))) (let ((_let_45 (ASSUME :args _let_43))) (let ((_let_46 (or _let_20 _let_15))) (let ((_let_47 (tptp.sorti1 _let_7))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.sorti1 _let_8))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_16))) (let ((_let_52 (forall ((U $$unsorted) (BOUND_VARIABLE_753 $$unsorted)) (or (not (tptp.sorti1 U)) (not (tptp.sorti1 BOUND_VARIABLE_753)) (= BOUND_VARIABLE_753 (tptp.op1 U (tptp.op1 U BOUND_VARIABLE_753))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or _let_20 _let_47))) (let ((_let_55 (forall ((V $$unsorted)) (or (not (tptp.sorti2 V)) (tptp.sorti1 (tptp.j V)))))) (let ((_let_56 (AND_ELIM (NOT_IMPLIES_ELIM1 _let_34) :args _let_33))) (let ((_let_57 (_let_55))) (let ((_let_58 ((not (= (tptp.sorti2 V) false))))) (let ((_let_59 (ASSUME :args _let_57))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_20 _let_47 (not _let_54)))) _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_57)) _let_56 :args (_let_54 false _let_55)) :args (_let_47 false _let_19 false _let_54)))) (let ((_let_61 (or _let_22 _let_49))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_22 _let_49 (not _let_61)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_57)) _let_56 :args (_let_61 false _let_55)) :args (_let_49 false _let_21 false _let_61)))) (let ((_let_63 (or _let_50 _let_48 _let_17))) (let ((_let_64 (forall ((W $$unsorted) (BOUND_VARIABLE_808 $$unsorted)) (or (not (tptp.sorti1 W)) (not (tptp.sorti1 BOUND_VARIABLE_808)) (= (tptp.h (tptp.op1 W BOUND_VARIABLE_808)) (tptp.op2 (tptp.h W) (tptp.h BOUND_VARIABLE_808))))))) (let ((_let_65 (AND_ELIM _let_35 :args (0)))) (let ((_let_66 (_let_64))) (let ((_let_67 ((tptp.op1 W BOUND_VARIABLE_808)))) (let ((_let_68 (ASSUME :args _let_66))) (let ((_let_69 (tptp.sorti1 _let_10))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_50 _let_70 _let_18))) (let ((_let_72 (tptp.sorti2 _let_5))) (let ((_let_73 (not _let_72))) (let ((_let_74 (or _let_73 _let_69))) (let ((_let_75 (or _let_22 _let_20 _let_72))) (let ((_let_76 (forall ((U $$unsorted) (BOUND_VARIABLE_729 $$unsorted)) (or (not (tptp.sorti2 U)) (not (tptp.sorti2 BOUND_VARIABLE_729)) (tptp.sorti2 (tptp.op2 U BOUND_VARIABLE_729)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (and _let_24 _let_11 _let_13 _let_15 _let_16 _let_17))) (let ((_let_79 (ASSUME :args (_let_24)))) (let ((_let_80 (APPLY_UF tptp.op2))) (let ((_let_81 (ASSUME :args (_let_15)))) (let ((_let_82 (SYMM _let_81))) (let ((_let_83 (ASSUME :args (_let_13)))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (ASSUME :args (_let_17)))) (let ((_let_86 (APPLY_UF tptp.h))) (let ((_let_87 (ASSUME :args (_let_11)))) (let ((_let_88 (SYMM (SYMM _let_87)))) (let ((_let_89 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_81 _let_89 _let_87 _let_83 _let_85) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (TRANS (CONG (REFL :args (_let_8)) _let_88 :args (APPLY_UF tptp.op1)) (SYMM _let_89)) :args _let_86) _let_82) (CONG _let_84 (TRANS (CONG _let_88 :args _let_86) (SYMM (SYMM _let_85)) (CONG _let_84 _let_82 :args _let_80)) :args _let_80) :args (=)) (FALSE_INTRO _let_79))) :args (_let_24 _let_15 _let_16 _let_11 _let_13 _let_17))) :args (_let_24 _let_11 _let_13 _let_15 _let_16 _let_17))) :args (true _let_78)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_6))) (REFL :args ((not _let_11))) (REFL :args ((not _let_13))) (REFL :args ((not _let_15))) (REFL :args ((not _let_16))) (REFL :args ((not _let_17))) (REFL :args ((not _let_18))) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_50 _let_70 _let_18 (not _let_71)))) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_73 _let_69 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_22 _let_20 _let_72 (not _let_75)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.op2 U BOUND_VARIABLE_729)))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_72 false _let_21 false _let_19 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_57)) _let_56 :args (_let_74 false _let_55)) :args (_let_69 false _let_72 false _let_74)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_8 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_71 false _let_64)) :args (_let_18 false _let_49 false _let_69 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_50 _let_48 _let_17 (not _let_63)))) _let_62 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_67)) :args _let_66)) _let_65 :args (_let_63 false _let_64)) :args (_let_17 false _let_49 false _let_47 false _let_63)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_48 _let_16 (not _let_51)))) _let_62 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING ((tptp.op1 U (tptp.op1 U BOUND_VARIABLE_753))))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_16 false _let_49 false _let_47 false _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_20 _let_15 (not _let_46)))) _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_46 false _let_41)) :args (_let_15 false _let_19 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_22 _let_13 (not _let_40)))) _let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_13 false _let_21 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_22 _let_20 _let_11 (not _let_31)))) _let_39 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.op2 Y BOUND_VARIABLE_831)))) :args _let_36)) (AND_ELIM _let_35 :args _let_33) :args (_let_31 false _let_32)) :args (_let_11 false _let_21 false _let_19 false _let_31)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 2)) _let_30 :args (_let_24 true _let_23)) :args (false false _let_18 false _let_17 false _let_16 false _let_15 false _let_13 false _let_11 true _let_6)) :args ((forall ((U $$unsorted)) (=> (tptp.sorti1 U) (forall ((V $$unsorted)) (=> (tptp.sorti1 V) (tptp.sorti1 (tptp.op1 U V)))))) _let_4 _let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.52  )
% 0.19/0.52  % SZS output end Proof for ALG178+1
% 0.19/0.52  % cvc5---1.0.5 exiting
% 0.19/0.53  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------