TSTP Solution File: RNG109+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG109+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 13:50:06 EDT 2023
% Result : Theorem 61.37s 62.04s
% Output : Proof 61.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : RNG109+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.37 % Computer : n031.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sun Aug 27 02:22:53 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_NAR, FOF, or CNF
% 61.37/62.04 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.UFLmWvn4sQ/cvc5---1.0.5_20661.p...
% 61.37/62.04 ------- get file name : TPTP file name is RNG109+1
% 61.37/62.04 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20661.smt2...
% 61.37/62.04 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 61.37/62.04 --- Run --no-e-matching --full-saturate-quant at 5...
% 61.37/62.04 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 61.37/62.04 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 61.37/62.04 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 61.37/62.04 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 61.37/62.04 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 61.37/62.04 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 61.37/62.04 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 61.37/62.04 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 61.37/62.04 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.37/62.04 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 61.37/62.04 % SZS status Theorem for RNG109+1
% 61.37/62.04 % SZS output start Proof for RNG109+1
% 61.37/62.04 (
% 61.37/62.04 (let ((_let_1 (not (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00))))))) (let ((_let_2 (tptp.slsdtgt0 tptp.xb))) (let ((_let_3 (tptp.slsdtgt0 tptp.xa))) (let ((_let_4 (and (tptp.aElementOf0 tptp.sz00 _let_3) (tptp.aElementOf0 tptp.xa _let_3) (tptp.aElementOf0 tptp.sz00 _let_2) (tptp.aElementOf0 tptp.xb _let_2)))) (let ((_let_5 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))))) (let ((_let_6 (tptp.aElement0 tptp.xb))) (let ((_let_7 (tptp.aElement0 tptp.xa))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))))) (let ((_let_10 (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_11 (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_12 (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_13 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_14 (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (io_tptp.aElementOf0_3 W4 (io_tptp.slsdtgt0_11 tptp.xa))) (not (io_tptp.aElementOf0_3 W5 (io_tptp.slsdtgt0_11 tptp.xb))) (not (= (tptp.sdtpldt0 W4 W5) tptp.xa)))))) (let ((_let_15 (= tptp.xa (tptp.sdtpldt0 tptp.xa tptp.sz00)))) (let ((_let_16 (not _let_15))) (let ((_let_17 (io_tptp.slsdtgt0_11 tptp.xb))) (let ((_let_18 (io_tptp.aElementOf0_3 tptp.sz00 _let_17))) (let ((_let_19 (not _let_18))) (let ((_let_20 (io_tptp.slsdtgt0_11 tptp.xa))) (let ((_let_21 (io_tptp.aElementOf0_3 tptp.xa _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_19 _let_16))) (let ((_let_24 (not _let_14))) (let ((_let_25 (io_tptp.sdtpldt1_4 _let_20 _let_17))) (let ((_let_26 (io_tptp.aElementOf0_3 tptp.xa _let_25))) (let ((_let_27 (= _let_26 _let_24))) (let ((_let_28 (forall ((W3 $$unsorted)) (= (io_tptp.aElementOf0_3 W3 (io_tptp.sdtpldt1_4 (io_tptp.slsdtgt0_11 tptp.xa) (io_tptp.slsdtgt0_11 tptp.xb))) (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (io_tptp.aElementOf0_3 W4 (io_tptp.slsdtgt0_11 tptp.xa))) (not (io_tptp.aElementOf0_3 W5 (io_tptp.slsdtgt0_11 tptp.xb))) (not (= W3 (tptp.sdtpldt0 W4 W5)))))))))) (let ((_let_29 (and (io_tptp.aSet0_2 _let_25) _let_28))) (let ((_let_30 (io_tptp.aSet0_2 _let_17))) (let ((_let_31 (not _let_30))) (let ((_let_32 (io_tptp.aSet0_2 _let_20))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_29))) (let ((_let_35 (forall ((b_W0 it_39_$$unsorted) (b_W1 it_39_$$unsorted) (b_BOUND_VARIABLE_1327 it_39_$$unsorted)) (or (not (io_tptp.aSet0_2 b_W0)) (not (io_tptp.aSet0_2 b_W1)) (= (and (io_tptp.aSet0_2 b_BOUND_VARIABLE_1327) (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (io_tptp.aElementOf0_3 W4 b_W0)) (not (io_tptp.aElementOf0_3 W5 b_W1)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))) (io_tptp.aElementOf0_3 W3 b_BOUND_VARIABLE_1327)))) (= b_BOUND_VARIABLE_1327 (io_tptp.sdtpldt1_4 b_W0 b_W1))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1327 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (= (= (tptp.sdtpldt1 W0 W1) BOUND_VARIABLE_1327) (and (tptp.aSet0 BOUND_VARIABLE_1327) (forall ((W3 $$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_1327))))))) _let_35))))))) (let ((_let_37 (and _let_30 (forall ((W2 $$unsorted)) (= (io_tptp.aElementOf0_3 W2 (io_tptp.slsdtgt0_11 tptp.xb)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W2 (tptp.sdtasdt0 tptp.xb W3))))))))))) (let ((_let_38 (not _let_6))) (let ((_let_39 (or _let_38 _let_37))) (let ((_let_40 (forall ((W0 $$unsorted) (b_BOUND_VARIABLE_1621 it_39_$$unsorted)) (or (not (tptp.aElement0 W0)) (= (and (io_tptp.aSet0_2 b_BOUND_VARIABLE_1621) (forall ((W2 $$unsorted)) (= (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W2 (tptp.sdtasdt0 W0 W3)))))) (io_tptp.aElementOf0_3 W2 b_BOUND_VARIABLE_1621)))) (= b_BOUND_VARIABLE_1621 (io_tptp.slsdtgt0_11 W0))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_10)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W0 $$unsorted) (BOUND_VARIABLE_1621 $$unsorted)) (or (not (tptp.aElement0 W0)) (= (= (tptp.slsdtgt0 W0) BOUND_VARIABLE_1621) (and (tptp.aSet0 BOUND_VARIABLE_1621) (forall ((W2 $$unsorted)) (= (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W2 (tptp.sdtasdt0 W0 W3)))))) (tptp.aElementOf0 W2 BOUND_VARIABLE_1621))))))) _let_40))))))) (let ((_let_42 (1))) (let ((_let_43 (ASSUME :args (_let_8)))) (let ((_let_44 (AND_ELIM _let_43 :args _let_42))) (let ((_let_45 (and _let_32 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1385 $$unsorted)) (let ((_let_1 (io_tptp.slsdtgt0_11 tptp.xa))) (or (not (io_tptp.aElementOf0_3 W1 _let_1)) (and (or (not (io_tptp.aElementOf0_3 BOUND_VARIABLE_1385 _let_1)) (io_tptp.aElementOf0_3 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1385) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1392)) (io_tptp.aElementOf0_3 (tptp.sdtasdt0 BOUND_VARIABLE_1392 W1) _let_1))))))))) (let ((_let_46 (io_tptp.aIdeal0_6 _let_20))) (let ((_let_47 (= _let_46 _let_45))) (let ((_let_48 (forall ((b_W0 it_39_$$unsorted)) (= (io_tptp.aIdeal0_6 b_W0) (and (io_tptp.aSet0_2 b_W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1385 $$unsorted)) (or (not (io_tptp.aElementOf0_3 W1 b_W0)) (and (or (not (io_tptp.aElementOf0_3 BOUND_VARIABLE_1385 b_W0)) (io_tptp.aElementOf0_3 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1385) b_W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1392)) (io_tptp.aElementOf0_3 (tptp.sdtasdt0 BOUND_VARIABLE_1392 W1) b_W0)))))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1392 $$unsorted) (BOUND_VARIABLE_1385 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1385 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1385) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1392)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1392 W1) W0)))))))) _let_48))))))) (let ((_let_50 (not _let_7))) (let ((_let_51 (or _let_50 _let_46))) (let ((_let_52 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (io_tptp.aIdeal0_6 (io_tptp.slsdtgt0_11 W0)))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) _let_52))))))) (let ((_let_54 (0))) (let ((_let_55 (AND_ELIM _let_43 :args _let_54))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_28 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_31 _let_29 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_32 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or (not _let_46) _let_45 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_46 (not _let_51)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (tptp.xa QUANTIFIERS_INST_E_MATCHING_SIMPLE ((io_tptp.slsdtgt0_11 W0)))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_46 false _let_7 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((io_tptp.aIdeal0_6 b_W0)))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_45 false _let_46 false _let_47)) :args (_let_32 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_30 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_37 (not _let_39)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.xb _let_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_40)))) _let_41 :args (_let_39 false _let_40)) :args (_let_37 false _let_6 false _let_39)) :args (_let_30 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_20 _let_17 _let_25 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_35)))) _let_36 :args (_let_34 false _let_35)) :args (_let_29 false _let_32 false _let_30 false _let_34)) :args (_let_28 false _let_29)))) (let ((_let_57 (_let_28))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (= tptp.sz00 tptp.xa))) (let ((_let_60 (not _let_26))) (let ((_let_61 (or _let_60 _let_59))) (let ((_let_62 (forall ((W0 $$unsorted)) (or (not (io_tptp.aElementOf0_3 W0 (io_tptp.sdtpldt1_4 (io_tptp.slsdtgt0_11 tptp.xa) (io_tptp.slsdtgt0_11 tptp.xb)))) (= tptp.sz00 W0))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb)))) (= tptp.sz00 W0))) _let_62))))))) (let ((_let_64 (_let_62))) (let ((_let_65 (tptp.xa QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_66 (= tptp.sz00 tptp.xb))) (let ((_let_67 (io_tptp.aElementOf0_3 tptp.xb _let_25))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_66))) (let ((_let_70 (tptp.xb QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_71 (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (io_tptp.aElementOf0_3 W4 (io_tptp.slsdtgt0_11 tptp.xa))) (not (io_tptp.aElementOf0_3 W5 (io_tptp.slsdtgt0_11 tptp.xb))) (not (= (tptp.sdtpldt0 W4 W5) tptp.xb)))))) (let ((_let_72 (not _let_71))) (let ((_let_73 (= _let_67 _let_72))) (let ((_let_74 (= tptp.xb (tptp.sdtpldt0 tptp.sz00 tptp.xb)))) (let ((_let_75 (not _let_74))) (let ((_let_76 (io_tptp.aElementOf0_3 tptp.xb _let_17))) (let ((_let_77 (not _let_76))) (let ((_let_78 (io_tptp.aElementOf0_3 tptp.sz00 _let_20))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77 _let_75))) (let ((_let_81 (not _let_80))) (let ((_let_82 (and (= tptp.xb (tptp.sdtpldt0 tptp.xb tptp.sz00)) _let_74))) (let ((_let_83 (or _let_38 _let_82))) (let ((_let_84 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (= W0 (tptp.sdtpldt0 W0 tptp.sz00)) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_84))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 (and _let_78 _let_21 _let_18 _let_76))))))) (let ((_let_88 (_let_71))) (let ((_let_89 (not _let_73))) (let ((_let_90 (or))) (let ((_let_91 (not _let_27))) (let ((_let_92 (not _let_23))) (let ((_let_93 (and _let_15 (= tptp.xa (tptp.sdtpldt0 tptp.sz00 tptp.xa))))) (let ((_let_94 (or _let_50 _let_93))) (let ((_let_95 (_let_14))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_95) :args (tptp.xa tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_95))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_19 _let_16 _let_92))) (AND_ELIM _let_87 :args _let_42) (AND_ELIM _let_87 :args (2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 0)) :args ((or _let_15 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_50 _let_93 (not _let_94)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_65) :args _let_86)) _let_85 :args (_let_94 false _let_84)) :args (_let_93 false _let_7 false _let_94)) :args (_let_15 false _let_93)) :args (_let_92 false _let_21 false _let_18 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_27)) (CONG (REFL :args (_let_91)) (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_14))) :args _let_90)) :args ((or _let_26 _let_14 _let_91))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_59 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_66 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_73)) (CONG (REFL :args (_let_89)) (REFL :args (_let_67)) (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) :args _let_90)) :args ((or _let_67 _let_71 _let_89))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_88) :args (tptp.sz00 tptp.xb QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_88))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_79 _let_77 _let_75 _let_81))) (AND_ELIM _let_87 :args _let_54) (AND_ELIM _let_87 :args (3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_82 1)) :args ((or _let_74 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_38 _let_82 (not _let_83)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_70) :args _let_86)) _let_85 :args (_let_83 false _let_84)) :args (_let_82 false _let_6 false _let_83)) :args (_let_74 false _let_82)) :args (_let_81 false _let_78 false _let_76 false _let_74)) :args (_let_72 true _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.xb QUANTIFIERS_INST_CBQI_PROP)) :args _let_57))) _let_56 :args (_let_73 false _let_28)) :args (_let_67 true _let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args _let_70) :args _let_64)) _let_63 :args (_let_69 false _let_62)) :args (_let_66 false _let_67 false _let_69)) :args ((not _let_59) false _let_66)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args _let_65) :args _let_64)) _let_63 :args (_let_61 false _let_62)) :args (_let_60 true _let_59 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.xa QUANTIFIERS_INST_CBQI_PROP)) :args _let_57))) _let_56 :args (_let_27 false _let_28)) :args (_let_14 true _let_26 false _let_27)) :args (false true _let_23 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 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))) _let_13 (forall ((W0 $$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_12 (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_11 (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_10 _let_9 _let_8 _let_5 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb) (and (tptp.aIdeal0 tptp.xI) (= tptp.xI (tptp.sdtpldt1 _let_3 _let_2))) _let_4 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 61.37/62.04 )
% 61.37/62.04 % SZS output end Proof for RNG109+1
% 61.37/62.04 % cvc5---1.0.5 exiting
% 61.37/62.04 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------