%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG115+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 13:50:08 EDT 2023

% Result   : Theorem 32.02s 32.37s
% Output   : Proof 32.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : RNG115+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n024.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 01:55:53 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 32.02/32.37  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.TViMcPO6Ac/cvc5---1.0.5_3420.p...
% 32.02/32.37  ------- get file name : TPTP file name is RNG115+1
% 32.02/32.37  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3420.smt2...
% 32.02/32.37  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 32.02/32.37  --- Run --no-e-matching --full-saturate-quant at 5...
% 32.02/32.37  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 32.02/32.37  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 32.02/32.37  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 32.02/32.37  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 32.02/32.37  % SZS status Theorem for RNG115+1
% 32.02/32.37  % SZS output start Proof for RNG115+1
% 32.02/32.37  (
% 32.02/32.37  (let ((_let_1 (not (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb)) (= tptp.xu (tptp.sdtpldt0 W0 W1))))))) (let ((_let_2 (tptp.aElementOf0 tptp.xu tptp.xI))) (let ((_let_3 (and _let_2 (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) (let ((_let_4 (tptp.slsdtgt0 tptp.xb))) (let ((_let_5 (tptp.slsdtgt0 tptp.xa))) (let ((_let_6 (tptp.sdtpldt1 _let_5 _let_4))) (let ((_let_7 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI _let_6)))) (let ((_let_8 (tptp.aElement0 tptp.xb))) (let ((_let_9 (tptp.aElement0 tptp.xa))) (let ((_let_10 (and _let_9 _let_8))) (let ((_let_11 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))))) (let ((_let_12 (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_13 (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)))))))))))) (let ((_let_14 (tptp.aElementOf0 tptp.xu _let_6))) (let ((_let_15 (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W5 (tptp.slsdtgt0 tptp.xb))) (not (= (tptp.sdtpldt0 W4 W5) tptp.xu)))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (= _let_14 _let_16))) (let ((_let_18 (0))) (let ((_let_19 (1))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W1 (tptp.slsdtgt0 tptp.xb))) (not (= tptp.xu (tptp.sdtpldt0 W0 W1))))))) (let ((_let_21 (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W5 (tptp.slsdtgt0 tptp.xb))) (not (= W3 (tptp.sdtpldt0 W4 W5)))))))))) (let ((_let_22 (and (tptp.aSet0 _let_6) _let_21))) (let ((_let_23 (tptp.aSet0 _let_4))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.aSet0 _let_5))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_22))) (let ((_let_28 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1357 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (= (= (tptp.sdtpldt1 W0 W1) BOUND_VARIABLE_1357) (and (tptp.aSet0 BOUND_VARIABLE_1357) (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 W0)) (not (tptp.aElementOf0 W5 W1)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))) (tptp.aElementOf0 W3 BOUND_VARIABLE_1357))))))))) (let ((_let_29 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_30 (and _let_23 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1422 $$unsorted) (BOUND_VARIABLE_1415 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xb))) (or (not (tptp.aElementOf0 W1 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1415 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1415) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1422)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1422 W1) _let_1))))))))) (let ((_let_31 (tptp.aIdeal0 _let_4))) (let ((_let_32 (= _let_31 _let_30))) (let ((_let_33 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1422 $$unsorted) (BOUND_VARIABLE_1415 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1415 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1415) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1422)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1422 W1) W0)))))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 ((tptp.aIdeal0 W0)))) (let ((_let_37 (not _let_8))) (let ((_let_38 (or _let_37 _let_31))) (let ((_let_39 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 ((not (= (tptp.aElement0 W0) false))))) (let ((_let_43 (ASSUME :args (_let_10)))) (let ((_let_44 (and _let_25 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1422 $$unsorted) (BOUND_VARIABLE_1415 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xa))) (or (not (tptp.aElementOf0 W1 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1415 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1415) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1422)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1422 W1) _let_1))))))))) (let ((_let_45 (tptp.aIdeal0 _let_5))) (let ((_let_46 (= _let_45 _let_44))) (let ((_let_47 (not _let_9))) (let ((_let_48 (or _let_47 _let_45))) (let ((_let_49 (_let_21))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or (not _let_14) _let_16 (not _let_17)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_49) :args (tptp.xu QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W3 _let_6)))) :args _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_22 1)) :args ((or _let_21 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_24 _let_22 (not _let_27)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_44 0)) :args ((or _let_25 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_46)) :args ((or (not _let_45) _let_44 (not _let_46)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_45 (not _let_48)))) (AND_ELIM _let_43 :args _let_18) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_41)) _let_40 :args (_let_48 false _let_39)) :args (_let_45 false _let_9 false _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_46 false _let_33)) :args (_let_44 false _let_45 false _let_46)) :args (_let_25 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 0)) :args ((or _let_23 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_32)) :args ((or (not _let_31) _let_30 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_31 (not _let_38)))) (AND_ELIM _let_43 :args _let_19) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.xb QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_42)) :args _let_41)) _let_40 :args (_let_38 false _let_39)) :args (_let_31 false _let_8 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_32 false _let_33)) :args (_let_30 false _let_31 false _let_32)) :args (_let_23 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_5 _let_4 _let_6 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_28)))) _let_29 :args (_let_27 false _let_28)) :args (_let_22 false _let_25 false _let_23 false _let_27)) :args (_let_21 false _let_22)) :args (_let_17 false _let_21)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_20 (= W0 W4) (= W1 W5))) (MACRO_SR_PRED_INTRO :args ((= (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 (tptp.slsdtgt0 tptp.xa))) (not (tptp.aElementOf0 W5 (tptp.slsdtgt0 tptp.xb))) (not (= tptp.xu (tptp.sdtpldt0 W4 W5))))) _let_15) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_15 false _let_20)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_ELIM (ASSUME :args (_let_7)) :args _let_19) :args ((and _let_2 (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) SB_DEFAULT SBA_FIXPOINT)))) :args _let_18) :args (false false _let_17 false _let_15 false _let_14)) :args ((forall ((W0 $$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)))) _let_13 (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_12 (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)))))))))) _let_11 _let_10 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb) _let_7 (and (tptp.aElementOf0 tptp.sz00 _let_5) (tptp.aElementOf0 tptp.xa _let_5) (tptp.aElementOf0 tptp.sz00 _let_4) (tptp.aElementOf0 tptp.xb _let_4)) (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))) _let_3 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))
% 32.02/32.37  )
% 32.02/32.37  % SZS output end Proof for RNG115+1
% 32.02/32.38  % cvc5---1.0.5 exiting
% 32.02/32.38  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------