TSTP Solution File: RNG106+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG106+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 13:50:05 EDT 2023
% Result : Theorem 10.70s 10.94s
% Output : Proof 10.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG106+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n023.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 : Sun Aug 27 02:26:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 10.70/10.94 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DIscFrEjw3/cvc5---1.0.5_312.p...
% 10.70/10.94 ------- get file name : TPTP file name is RNG106+1
% 10.70/10.94 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_312.smt2...
% 10.70/10.94 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.70/10.94 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.70/10.94 % SZS status Theorem for RNG106+1
% 10.70/10.94 % SZS output start Proof for RNG106+1
% 10.70/10.94 (
% 10.70/10.94 (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (let ((_let_2 (tptp.aIdeal0 _let_1))) (let ((_let_3 (not (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (=> (and (tptp.aElementOf0 W0 _let_1) (tptp.aElementOf0 W1 _let_1) (tptp.aElement0 W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 tptp.xc W3) W0) (exists ((W4 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (let ((_let_2 (tptp.sdtasdt0 W2 W0))) (let ((_let_3 (tptp.sdtpldt0 W0 W1))) (and (tptp.aElement0 W4) (= (tptp.sdtasdt0 tptp.xc W4) W1) (= _let_3 (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 W4))) (= _let_2 (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 W2))) (tptp.aElementOf0 _let_3 _let_1) (tptp.aElementOf0 _let_2 _let_1))))))))))) _let_2)))) (let ((_let_4 (tptp.aElement0 tptp.xc))) (let ((_let_5 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slsdtgt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 W0 W3) W2)))))))))))) (let ((_let_6 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))))) (let ((_let_7 (tptp.aElement0 tptp.sz10))) (let ((_let_8 (tptp.aElementOf0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41) _let_1))) (let ((_let_9 (and _let_8 (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) _let_1) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1673 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= (tptp.sdtasdt0 tptp.xc W3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)) (not (= (tptp.sdtasdt0 tptp.sz10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 tptp.sz10)))) (not (tptp.aElement0 BOUND_VARIABLE_1673)) (not (= (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1673) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41)) (not (= (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 BOUND_VARIABLE_1673)) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))))))))) (let ((_let_10 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41 _let_1))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_8))) (let ((_let_13 (tptp.aElementOf0 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) _let_1))) (let ((_let_14 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13))) (let ((_let_17 (and _let_12 _let_16))) (let ((_let_18 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 _let_1))) (let ((_let_19 (and (tptp.aElementOf0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) _let_1) _let_13 (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1673 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= (tptp.sdtasdt0 tptp.xc W3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)) (not (= (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39) (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40)))) (not (tptp.aElement0 BOUND_VARIABLE_1673)) (not (= (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1673) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39)) (not (= (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 BOUND_VARIABLE_1673)) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (or _let_20 _let_20 _let_15 _let_19))) (let ((_let_22 (or))) (let ((_let_23 (or _let_20 _let_17))) (let ((_let_24 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1393 $$unsorted) (BOUND_VARIABLE_1386 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (or (not (tptp.aElementOf0 W1 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1386 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1386) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1393)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1393 W1) _let_1)))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (tptp.aSet0 _let_1))) (let ((_let_27 (and _let_26 _let_24))) (let ((_let_28 (not _let_24))) (let ((_let_29 (= _let_2 _let_27))) (let ((_let_30 (not _let_27))) (let ((_let_31 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1393 $$unsorted) (BOUND_VARIABLE_1386 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1386 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1386) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1393)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1393 W1) W0)))))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (and _let_26 (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 (tptp.slsdtgt0 tptp.xc)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W2 (tptp.sdtasdt0 tptp.xc W3))))))))))) (let ((_let_35 (not _let_4))) (let ((_let_36 (or _let_35 _let_34))) (let ((_let_37 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1622 $$unsorted)) (or (not (tptp.aElement0 W0)) (= (= (tptp.slsdtgt0 W0) BOUND_VARIABLE_1622) (and (tptp.aSet0 BOUND_VARIABLE_1622) (forall ((W2 $$unsorted)) (= (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W2 (tptp.sdtasdt0 W0 W3)))))) (tptp.aElementOf0 W2 BOUND_VARIABLE_1622))))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_28))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_39)) :args _let_39)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_27)) :args ((or (not _let_26) _let_27 _let_28))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_26 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_34 (not _let_36)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.xc _let_1 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_37)))) _let_38 :args (_let_36 false _let_37)) :args (_let_34 false _let_4 false _let_36)) :args (_let_26 false _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_29)) :args ((or _let_2 _let_30 (not _let_29)))) (NOT_IMPLIES_ELIM2 _let_33) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_1 QUANTIFIERS_INST_ENUM)) :args (_let_31))) _let_32 :args (_let_29 false _let_31)) :args (_let_30 true _let_2 false _let_29)) :args (_let_28 false _let_26 true _let_27)) :args (_let_25 true _let_24)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_18))) :args _let_22)) :args ((or _let_18 _let_23))) _let_40 :args (_let_18 true _let_23)))) (let ((_let_42 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (or (not (tptp.aElementOf0 W0 _let_1)) (not (tptp.aElementOf0 W1 _let_1)) (not (tptp.aElement0 W2)) (and (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) _let_1) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W0) _let_1) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1673 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W0 (tptp.sdtasdt0 tptp.xc W3))) (not (= (tptp.sdtasdt0 W2 W0) (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 W2)))) (not (tptp.aElement0 BOUND_VARIABLE_1673)) (not (= W1 (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1673))) (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 BOUND_VARIABLE_1673))))))))))))) (let ((_let_43 (NOT_IMPLIES_ELIM1 _let_33))) (let ((_let_44 (_let_42))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_17)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 1)) _let_40 :args ((not _let_17) true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 1)) :args ((or _let_13 (not _let_19)))) (REORDERING (FACTORING (CNF_OR_POS :args (_let_21))) :args ((or _let_20 _let_15 _let_19 (not _let_21)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_44))) _let_43 :args (_let_21 false _let_42)) _let_41 (CNF_OR_NEG :args (_let_16 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG (REFL :args (_let_16)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_22)) :args ((or _let_14 _let_16))) :args (_let_16 false _let_19 false _let_21 false _let_18 true _let_13 false _let_14)) :args ((not _let_12) true _let_17 false _let_16)))) (let ((_let_47 (not _let_7))) (let ((_let_48 (or _let_20 _let_11 _let_47 _let_9))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_8 (not _let_9)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_20 _let_11 _let_9 (not _let_48)))) (ASSUME :args (_let_7)) _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_12 0)) (CONG (REFL :args (_let_12)) (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_22)) :args ((or _let_10 _let_12))) _let_46 :args (_let_10 true _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41 tptp.sz10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_44))) _let_43 :args (_let_48 false _let_42)) :args (_let_9 false _let_7 false _let_18 false _let_10 false _let_48)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_12 1)) _let_46 :args ((not _let_8) true _let_12)) :args (false false _let_9 true _let_8)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (tptp.aElement0 tptp.sz00) _let_7 (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))))))))) _let_6 (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)))) _let_5 _let_4 _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.70/10.95 )
% 10.70/10.95 % SZS output end Proof for RNG106+1
% 10.70/10.95 % cvc5---1.0.5 exiting
% 10.70/10.95 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------