%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG106+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 10.48s 10.72s
% Output   : Proof 10.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : RNG106+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n008.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun Aug 27 01:45:17 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 10.48/10.72  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.fITy2gsgFv/cvc5---1.0.5_16627.p...
% 10.48/10.72  ------- get file name : TPTP file name is RNG106+2
% 10.48/10.72  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16627.smt2...
% 10.48/10.72  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.48/10.72  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.48/10.72  % SZS status Theorem for RNG106+2
% 10.48/10.72  % SZS output start Proof for RNG106+2
% 10.48/10.72  (
% 10.48/10.72  (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (let ((_let_2 (not (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (=> (and (or (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 tptp.xc W3) W0))) (tptp.aElementOf0 W0 _let_1)) (or (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 tptp.xc W3) W1))) (tptp.aElementOf0 W1 _let_1)) (tptp.aElement0 W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 tptp.xc W3) W0) (exists ((W4 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (let ((_let_2 (tptp.sdtasdt0 W2 W0))) (let ((_let_3 (tptp.sdtpldt0 W0 W1))) (and (tptp.aElement0 W4) (= (tptp.sdtasdt0 tptp.xc W4) W1) (= _let_3 (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 W4))) (= _let_2 (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 W2))) (exists ((W5 $$unsorted)) (and (tptp.aElement0 W5) (= (tptp.sdtasdt0 tptp.xc W5) (tptp.sdtpldt0 W0 W1)))) (tptp.aElementOf0 _let_3 _let_1) (exists ((W5 $$unsorted)) (and (tptp.aElement0 W5) (= (tptp.sdtasdt0 tptp.xc W5) (tptp.sdtasdt0 W2 W0)))) (tptp.aElementOf0 _let_2 _let_1))))))))))) (=> (and (tptp.aSet0 _let_1) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xc)) (exists ((W1 $$unsorted)) (and (tptp.aElement0 W1) (= (tptp.sdtasdt0 tptp.xc W1) W0)))))) (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slsdtgt0 tptp.xc)) (and (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) _let_1)))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) (tptp.slsdtgt0 tptp.xc))))))) (tptp.aIdeal0 _let_1))))))) (let ((_let_3 (tptp.aElement0 tptp.sz00))) (let ((_let_4 (tptp.aElementOf0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_1))) (let ((_let_5 (and (not (forall ((W5 $$unsorted)) (or (not (tptp.aElement0 W5)) (not (= (tptp.sdtasdt0 tptp.xc W5) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) _let_4 (not (forall ((W5 $$unsorted)) (or (not (tptp.aElement0 W5)) (not (= (tptp.sdtasdt0 tptp.xc W5) (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_1) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1786 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= (tptp.sdtasdt0 tptp.xc W3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (= (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 tptp.sz00)))) (not (tptp.aElement0 BOUND_VARIABLE_1786)) (not (= (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1786) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (= (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 BOUND_VARIABLE_1786)) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (let ((_let_6 (not _let_3))) (let ((_let_7 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.sdtasdt0 tptp.xc tptp.sz00))) (let ((_let_10 (and (or _let_6 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) _let_8))) (let ((_let_11 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_1))) (let ((_let_12 (not _let_11))) (let ((_let_13 (and (or _let_6 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) _let_12))) (let ((_let_14 (or _let_13 _let_10 _let_6 _let_5))) (let ((_let_15 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (BOUND_VARIABLE_1829 $$unsorted) (BOUND_VARIABLE_1820 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (or (and (or (not (tptp.aElement0 BOUND_VARIABLE_1820)) (not (= W0 (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1820)))) (not (tptp.aElementOf0 W0 _let_1))) (and (or (not (tptp.aElement0 BOUND_VARIABLE_1829)) (not (= W1 (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1829)))) (not (tptp.aElementOf0 W1 _let_1))) (not (tptp.aElement0 W2)) (and (not (forall ((W5 $$unsorted)) (or (not (tptp.aElement0 W5)) (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtasdt0 tptp.xc W5)))))) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) _let_1) (not (forall ((W5 $$unsorted)) (or (not (tptp.aElement0 W5)) (not (= (tptp.sdtasdt0 W2 W0) (tptp.sdtasdt0 tptp.xc W5)))))) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W0) _let_1) (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1786 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= W0 (tptp.sdtasdt0 tptp.xc W3))) (not (= (tptp.sdtasdt0 W2 W0) (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 W2)))) (not (tptp.aElement0 BOUND_VARIABLE_1786)) (not (= W1 (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1786))) (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 BOUND_VARIABLE_1786))))))))))))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (NOT_IMPLIES_ELIM1 _let_16))) (let ((_let_18 (_let_15))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (not _let_13))) (let ((_let_21 (tptp.aElementOf0 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_1))) (let ((_let_22 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21))) (let ((_let_25 (or _let_8 _let_4))) (let ((_let_26 (and _let_25 _let_24))) (let ((_let_27 (or _let_12 _let_26))) (let ((_let_28 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1874 $$unsorted) (BOUND_VARIABLE_1867 $$unsorted)) (let ((_let_1 (tptp.slsdtgt0 tptp.xc))) (or (not (tptp.aElementOf0 W0 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1867 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1867) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1874)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1874 W0) _let_1)))))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (or))) (let ((_let_31 (not _let_28))) (let ((_let_32 (_let_31))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_32)) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_28))) (REFL :args (_let_29)) :args _let_30)) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_16)) :args (0)) :args (_let_29 true _let_28)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_13 1)) :args ((or _let_12 _let_20))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG (REFL :args (_let_27)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_30)) :args ((or _let_11 _let_27))) _let_33 :args (_let_11 true _let_27)) :args (_let_20 false _let_11)))) (let ((_let_35 (not _let_10))) (let ((_let_36 (and (not (forall ((W5 $$unsorted)) (or (not (tptp.aElement0 W5)) (not (= (tptp.sdtasdt0 tptp.xc W5) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (tptp.aElementOf0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_1) (not (forall ((W5 $$unsorted)) (or (not (tptp.aElement0 W5)) (not (= (tptp.sdtasdt0 tptp.xc W5) (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) _let_21 (not (forall ((W3 $$unsorted) (BOUND_VARIABLE_1786 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (= (tptp.sdtasdt0 tptp.xc W3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (= (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.sdtasdt0 tptp.xc (tptp.sdtasdt0 W3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (not (tptp.aElement0 BOUND_VARIABLE_1786)) (not (= (tptp.sdtasdt0 tptp.xc BOUND_VARIABLE_1786) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (= (tptp.sdtasdt0 tptp.xc (tptp.sdtpldt0 W3 BOUND_VARIABLE_1786)) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))))) (let ((_let_37 (or _let_13 _let_13 _let_23 _let_36))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_26)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 1)) _let_33 :args ((not _let_26) true _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 3)) :args ((or _let_21 (not _let_36)))) (REORDERING (FACTORING (CNF_OR_POS :args (_let_37))) :args ((or _let_23 _let_13 _let_36 (not _let_37)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_17 :args (_let_37 false _let_15)) _let_34 (CNF_OR_NEG :args (_let_24 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_30)) :args ((or _let_22 _let_24))) :args (_let_24 false _let_36 false _let_37 true _let_13 true _let_21 false _let_22)) :args ((not _let_25) true _let_26 false _let_24)))) (let ((_let_39 (not _let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_6 _let_13 _let_10 _let_5 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_5 1)) :args ((or _let_4 _let_39))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 1)) _let_38 :args ((not _let_4) true _let_25)) :args (_let_39 true _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_10 1)) :args ((or _let_8 _let_35))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG (REFL :args (_let_25)) (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_30)) :args ((or _let_7 _let_25))) _let_38 :args (_let_7 true _let_25)) :args (_let_35 false _let_7)) _let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.sz00 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_18))) _let_17 :args (_let_14 false _let_15)) (ASSUME :args (_let_3)) :args (false true _let_5 true _let_10 true _let_13 false _let_14 false _let_3)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) _let_3 (tptp.aElement0 tptp.sz10) (forall ((W0 $$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)))))))))) (tptp.aElement0 tptp.xc) _let_2 true))))))))))))))))))))))))))))))))))))))))))
% 10.48/10.73  )
% 10.48/10.73  % SZS output end Proof for RNG106+2
% 10.48/10.73  % cvc5---1.0.5 exiting
% 10.48/10.73  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------