TSTP Solution File: RNG112+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 13:50:07 EDT 2023
% Result : Theorem 5.46s 5.67s
% Output : Proof 5.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 01:33:44 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.41 %----Proving TF0_NAR, FOF, or CNF
% 5.46/5.67 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.s3ynOzVoFl/cvc5---1.0.5_14035.p...
% 5.46/5.67 ------- get file name : TPTP file name is RNG112+4
% 5.46/5.67 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14035.smt2...
% 5.46/5.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 5.46/5.67 % SZS status Theorem for RNG112+4
% 5.46/5.67 % SZS output start Proof for RNG112+4
% 5.46/5.67 (
% 5.46/5.67 (let ((_let_1 (not (exists ((W0 $$unsorted)) (and (or (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 tptp.xI)) (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted)) (=> (and (exists ((W2 $$unsorted) (W3 $$unsorted)) (and (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W3 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W2 W3) W1))) (tptp.aElementOf0 W1 tptp.xI) (not (= W1 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W1) (tptp.sbrdtbr0 W0)))))))))) (let ((_let_2 (forall ((W0 $$unsorted)) (=> (and (or (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 tptp.xI)) (not (= W0 tptp.sz00))) (exists ((W1 $$unsorted)) (and (exists ((W2 $$unsorted) (W3 $$unsorted)) (and (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W3 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W2 W3) W1))) (tptp.aElementOf0 W1 tptp.xI) (not (= W1 tptp.sz00)) (forall ((W2 $$unsorted)) (=> (and (or (exists ((W3 $$unsorted) (W4 $$unsorted)) (and (tptp.aElementOf0 W3 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W4 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W3 W4) W2))) (tptp.aElementOf0 W2 tptp.xI)) (not (= W2 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W2) (tptp.sbrdtbr0 W1))))))))))) (let ((_let_3 (exists ((W0 $$unsorted)) (and (forall ((W1 $$unsorted)) (= (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 tptp.xa W2) W1))))) (forall ((W1 $$unsorted)) (= (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 tptp.xb W2) W1))))) (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))))) (let ((_let_4 (tptp.slsdtgt0 tptp.xb))) (let ((_let_5 (tptp.aElementOf0 tptp.sz00 _let_4))) (let ((_let_6 (tptp.slsdtgt0 tptp.xa))) (let ((_let_7 (tptp.aElementOf0 tptp.sz00 _let_6))) (let ((_let_8 (tptp.sdtpldt1 _let_6 _let_4))) (let ((_let_9 (= tptp.xI _let_8))) (let ((_let_10 (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 tptp.xa W1) W0))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xb)) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 tptp.xb W1) W0))))) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 tptp.xI) (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xb)) (= (tptp.sdtpldt0 W1 W2) W0))))) _let_9))) (let ((_let_11 (tptp.aElement0 tptp.xc))) (let ((_let_12 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_13 (= tptp.sz00 _let_12))) (let ((_let_14 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_15 (tptp.iLess0 (tptp.sbrdtbr0 _let_12) (tptp.sbrdtbr0 _let_14)))) (let ((_let_16 (tptp.aElementOf0 _let_12 tptp.xI))) (let ((_let_17 (not _let_16))) (let ((_let_18 (and (or (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_6)) (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 _let_4)) (not (= _let_12 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30)))) _let_17))) (let ((_let_19 (not _let_15))) (let ((_let_20 (or _let_18 _let_13 _let_19))) (let ((_let_21 (or _let_17 _let_13 _let_19 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 _let_6)) (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 _let_4))))) (let ((_let_22 (forall ((BOUND_VARIABLE_2412 $$unsorted) (BOUND_VARIABLE_2410 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_2410 BOUND_VARIABLE_2412))) (or (not (tptp.aElementOf0 _let_1 tptp.xI)) (= tptp.sz00 _let_1) (not (tptp.iLess0 (tptp.sbrdtbr0 _let_1) (tptp.sbrdtbr0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (not (tptp.aElementOf0 BOUND_VARIABLE_2410 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2412 (tptp.slsdtgt0 tptp.xb)))))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (not _let_22))) (let ((_let_25 (= tptp.sz00 _let_14))) (let ((_let_26 (tptp.aElementOf0 _let_14 tptp.xI))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_29 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_4)))) (let ((_let_30 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_6)))) (let ((_let_31 (and (or _let_30 _let_29 (not (= _let_28 _let_14))) _let_27))) (let ((_let_32 (or _let_31 _let_25 _let_24))) (let ((_let_33 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2454 $$unsorted) (BOUND_VARIABLE_2452 $$unsorted)) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2452 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2454 (tptp.slsdtgt0 tptp.xb))) (not (= W0 (tptp.sdtpldt0 BOUND_VARIABLE_2452 BOUND_VARIABLE_2454)))) (not (tptp.aElementOf0 W0 tptp.xI))) (= tptp.sz00 W0) (not (forall ((BOUND_VARIABLE_2412 $$unsorted) (BOUND_VARIABLE_2410 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_2410 BOUND_VARIABLE_2412))) (or (not (tptp.aElementOf0 _let_1 tptp.xI)) (= tptp.sz00 _let_1) (not (tptp.iLess0 (tptp.sbrdtbr0 _let_1) (tptp.sbrdtbr0 W0))) (not (tptp.aElementOf0 BOUND_VARIABLE_2410 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2412 (tptp.slsdtgt0 tptp.xb))))))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (not _let_31))) (let ((_let_36 (forall ((W2 $$unsorted) (BOUND_VARIABLE_2286 $$unsorted) (BOUND_VARIABLE_2284 $$unsorted)) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2284 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2286 (tptp.slsdtgt0 tptp.xb))) (not (= W2 (tptp.sdtpldt0 BOUND_VARIABLE_2284 BOUND_VARIABLE_2286)))) (not (tptp.aElementOf0 W2 tptp.xI))) (= tptp.sz00 W2) (not (tptp.iLess0 (tptp.sbrdtbr0 W2) (tptp.sbrdtbr0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_27 _let_25 _let_37 (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_6)) (not (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_4))))) (let ((_let_39 (forall ((BOUND_VARIABLE_2311 $$unsorted) (BOUND_VARIABLE_2309 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 BOUND_VARIABLE_2309 BOUND_VARIABLE_2311))) (or (not (tptp.aElementOf0 _let_1 tptp.xI)) (= tptp.sz00 _let_1) (not (forall ((W2 $$unsorted) (BOUND_VARIABLE_2286 $$unsorted) (BOUND_VARIABLE_2284 $$unsorted)) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2284 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2286 (tptp.slsdtgt0 tptp.xb))) (not (= W2 (tptp.sdtpldt0 BOUND_VARIABLE_2284 BOUND_VARIABLE_2286)))) (not (tptp.aElementOf0 W2 tptp.xI))) (= tptp.sz00 W2) (not (tptp.iLess0 (tptp.sbrdtbr0 W2) (tptp.sbrdtbr0 (tptp.sdtpldt0 BOUND_VARIABLE_2309 BOUND_VARIABLE_2311))))))) (not (tptp.aElementOf0 BOUND_VARIABLE_2309 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2311 (tptp.slsdtgt0 tptp.xb)))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (forall ((W0 $$unsorted) (BOUND_VARIABLE_2357 $$unsorted) (BOUND_VARIABLE_2355 $$unsorted)) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_2355 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 BOUND_VARIABLE_2357 (tptp.slsdtgt0 tptp.xb))) (not (= W0 (tptp.sdtpldt0 BOUND_VARIABLE_2355 BOUND_VARIABLE_2357)))) (not (tptp.aElementOf0 W0 tptp.xI))) (= tptp.sz00 W0))))) (let ((_let_42 (not _let_39))) (let ((_let_43 (= tptp.sz00 _let_28))) (let ((_let_44 (tptp.aElementOf0 _let_28 tptp.xI))) (let ((_let_45 (not _let_44))) (let ((_let_46 (and (or (not _let_7) (not _let_5) (not (= _let_28 (tptp.sdtpldt0 tptp.sz00 tptp.sz00)))) _let_45))) (let ((_let_47 (or _let_46 _let_43))) (let ((_let_48 (not _let_47))) (let ((_let_49 (not _let_46))) (let ((_let_50 (tptp.aElementOf0 _let_28 _let_8))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_43 _let_30 _let_29))) (let ((_let_53 (forall ((BOUND_VARIABLE_2200 $$unsorted) (BOUND_VARIABLE_2198 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xb))) (let ((_let_2 (tptp.slsdtgt0 tptp.xa))) (let ((_let_3 (tptp.sdtpldt0 BOUND_VARIABLE_2198 BOUND_VARIABLE_2200))) (or (not (tptp.aElementOf0 _let_3 (tptp.sdtpldt1 _let_2 _let_1))) (= tptp.sz00 _let_3) (not (tptp.aElementOf0 BOUND_VARIABLE_2198 _let_2)) (not (tptp.aElementOf0 BOUND_VARIABLE_2200 _let_1))))))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (or))) (let ((_let_56 (not _let_53))) (let ((_let_57 (_let_56))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_57)) :args _let_57)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_53))) (REFL :args (_let_54)) :args _let_55)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) :args (2)) :args (_let_54 true _let_53)))) (let ((_let_59 (and _let_9 _let_50))) (let ((_let_60 (ASSUME :args (_let_50)))) (let ((_let_61 (ASSUME :args (_let_9)))) (let ((_let_62 (_let_41))) (let ((_let_63 (_let_42))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_39))) (REFL :args (_let_40)) :args _let_55)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_62) :args (_let_28 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_E_MATCHING ((tptp.aElementOf0 BOUND_VARIABLE_2355 _let_6) (tptp.aElementOf0 BOUND_VARIABLE_2357 _let_4) (tptp.aElementOf0 W0 tptp.xI)))) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_43 _let_46 _let_48))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 1)) _let_58 :args ((not _let_43) true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 1)) :args ((or _let_45 _let_49))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_59)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_28)) (SYMM (SYMM _let_61)) :args (APPLY_UF tptp.aElementOf0)) (TRUE_INTRO _let_60))) :args (_let_50 _let_9))) :args (_let_9 _let_50))) :args (true _let_59)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args (6)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_55)) :args ((or _let_50 _let_52))) _let_58 :args (_let_50 true _let_52)) :args (_let_44 false _let_9 false _let_50)) :args (_let_49 false _let_44)) :args (_let_48 true _let_43 true _let_46)) :args ((not _let_41) true _let_47)) :args (_let_42 true _let_41)) :args (_let_40 true _let_39)))) (let ((_let_65 (REFL :args (_let_38)))) (let ((_let_66 (_let_24))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_22))) (REFL :args (_let_23)) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_25 _let_24 _let_31 (not _let_32)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 1)) _let_64 :args ((not _let_25) true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 1)) :args ((or _let_27 _let_35))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_55)) :args ((or _let_26 _let_38))) _let_64 :args (_let_26 true _let_38)) :args (_let_35 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.aElementOf0 BOUND_VARIABLE_2452 _let_6) (tptp.aElementOf0 BOUND_VARIABLE_2454 _let_4) (tptp.aElementOf0 W0 tptp.xI)))) :args (_let_33)))) _let_34 :args (_let_32 false _let_33)) :args (_let_24 true _let_25 true _let_31 false _let_32)) :args (_let_23 true _let_22)))) (let ((_let_68 (REFL :args (_let_21)))) (let ((_let_69 (not _let_18))) (let ((_let_70 (_let_36))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_13 _let_19 _let_18 (not _let_20)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_E_MATCHING ((tptp.aElementOf0 BOUND_VARIABLE_2284 _let_6) (tptp.aElementOf0 BOUND_VARIABLE_2286 _let_4) (tptp.aElementOf0 W2 tptp.xI)))) :args _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_55)) :args ((or _let_36 _let_38))) _let_64 :args (_let_36 true _let_38)) :args (_let_20 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_18 1)) :args ((or _let_17 _let_69))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_55)) :args ((or _let_16 _let_21))) _let_67 :args (_let_16 true _let_21)) :args (_let_69 false _let_16)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 2)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_15))) :args _let_55)) :args ((or _let_15 _let_21))) _let_67 :args (_let_15 true _let_21)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_21 1)) _let_67 :args ((not _let_13) true _let_21)) :args (false false _let_20 true _let_18 false _let_15 true _let_13)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (tptp.aElement0 tptp.sz00) (tptp.aElement0 tptp.sz10) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElement0 (tptp.smndt0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 _let_1) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 _let_1 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W1 W2))) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (and (= (tptp.sdtasdt0 W0 _let_1) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 _let_1 W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))))))) (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.smndt0 tptp.sz10))) (let ((_let_2 (tptp.smndt0 W0))) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 _let_1 W0) _let_2) (= _let_2 (tptp.sdtasdt0 W0 _let_1))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))) (not (= tptp.sz10 tptp.sz00)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 W2 W1))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt1 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted) (W5 $$unsorted)) (and (tptp.aElementOf0 W4 W0) (tptp.aElementOf0 W5 W1) (= (tptp.sdtpldt0 W4 W5) W3)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtasasdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))) (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 (tptp.sdtpldt0 W1 W2) W0))) (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtpldt1 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtasasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aIdeal0 W2)) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)) W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (=> (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 W2 (tptp.sdtpldt1 W0 W1)))) (forall ((W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W2) (tptp.aElement0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdteqdtlpzmzozddtrp0 W4 W2 W0) (tptp.sdteqdtlpzmzozddtrp0 W4 W3 W1)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElement0 W0) (not (= W0 tptp.sz00))) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (not (= W1 tptp.sz00))) (exists ((W2 $$unsorted) (W3 $$unsorted)) (and (tptp.aElement0 W2) (tptp.aElement0 W3) (= W0 (tptp.sdtpldt0 (tptp.sdtasdt0 W2 W1) W3)) (=> (not (= W3 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 W3) (tptp.sbrdtbr0 W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 W0 W2) W1)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aElement0 W1) (tptp.doDivides0 W1 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (tptp.aGcdOfAnd0 W2 W0 W1) (and (tptp.aDivisorOf0 W2 W0) (tptp.aDivisorOf0 W2 W1) (forall ((W3 $$unsorted)) (=> (and (tptp.aDivisorOf0 W3 W0) (tptp.aDivisorOf0 W3 W1)) (tptp.doDivides0 W3 W2)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.misRelativelyPrime0 W0 W1) (tptp.aGcdOfAnd0 tptp.sz10 W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slsdtgt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 W0 W3) W2)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb)) (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (and _let_11 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xc W0) tptp.xa))) (tptp.doDivides0 tptp.xc tptp.xa) (tptp.aDivisorOf0 tptp.xc tptp.xa) _let_11 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xc W0) tptp.xb))) (tptp.doDivides0 tptp.xc tptp.xb) (tptp.aDivisorOf0 tptp.xc tptp.xb) (forall ((W0 $$unsorted)) (=> (and (or (and (tptp.aElement0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xa))) (tptp.doDivides0 W0 tptp.xa))) (tptp.aDivisorOf0 W0 tptp.xa)) (or (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xb))) (tptp.doDivides0 W0 tptp.xb) (tptp.aDivisorOf0 W0 tptp.xb))) (and (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 W0 W1) tptp.xc))) (tptp.doDivides0 W0 tptp.xc)))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) _let_10 (and (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.sz00))) _let_7 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xa W0) tptp.xa))) (tptp.aElementOf0 tptp.xa _let_6) (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.sz00))) _let_5 (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (= (tptp.sdtasdt0 tptp.xb W0) tptp.xb))) (tptp.aElementOf0 tptp.xb _let_4)) _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 5.49/5.69 )
% 5.49/5.69 % SZS output end Proof for RNG112+4
% 5.49/5.69 % cvc5---1.0.5 exiting
% 5.49/5.69 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------