TSTP Solution File: RNG123+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 13:50:11 EDT 2023
% Result : Theorem 0.21s 0.71s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n010.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 02:07:34 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.tORO9eBe7n/cvc5---1.0.5_16843.p...
% 0.21/0.71 ------- get file name : TPTP file name is RNG123+1
% 0.21/0.71 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16843.smt2...
% 0.21/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.71 % SZS status Theorem for RNG123+1
% 0.21/0.71 % SZS output start Proof for RNG123+1
% 0.21/0.71 (
% 0.21/0.71 (let ((_let_1 (tptp.aElementOf0 tptp.xr tptp.xI))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.sdtasdt0 tptp.xq tptp.xu))) (let ((_let_4 (tptp.smndt0 _let_3))) (let ((_let_5 (tptp.sdtpldt0 _let_4 tptp.xb))) (let ((_let_6 (= tptp.xr _let_5))) (let ((_let_7 (tptp.aElementOf0 tptp.xb tptp.xI))) (let ((_let_8 (tptp.aElementOf0 _let_4 tptp.xI))) (let ((_let_9 (= tptp.xr tptp.sz00))) (let ((_let_10 (tptp.slsdtgt0 tptp.xb))) (let ((_let_11 (tptp.slsdtgt0 tptp.xa))) (let ((_let_12 (tptp.aIdeal0 tptp.xI))) (let ((_let_13 (and _let_12 (= tptp.xI (tptp.sdtpldt1 _let_11 _let_10))))) (let ((_let_14 (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_15 (tptp.aElement0 tptp.sz10))) (let ((_let_16 (tptp.aElementOf0 _let_5 tptp.xI))) (let ((_let_17 (ASSUME :args (_let_6)))) (let ((_let_18 (ASSUME :args (_let_2)))) (let ((_let_19 (not _let_7))) (let ((_let_20 (or _let_19 _let_16))) (let ((_let_21 (and _let_20 (or (not _let_15) (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz10 _let_4) tptp.xI))))) (let ((_let_22 (not _let_8))) (let ((_let_23 (or _let_22 _let_21))) (let ((_let_24 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1448 $$unsorted) (BOUND_VARIABLE_1441 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1441 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1441) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1448)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1448 W1) tptp.xI))))))) (let ((_let_25 (and (tptp.aSet0 tptp.xI) _let_24))) (let ((_let_26 (= _let_12 _let_25))) (let ((_let_27 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1448 $$unsorted) (BOUND_VARIABLE_1441 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1441 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1441) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1448)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1448 W1) W0)))))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_24))) (let ((_let_30 (not _let_16))) (let ((_let_31 (not _let_6))) (let ((_let_32 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_32 _let_17 _let_18) :args (_let_6 _let_2 _let_16)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_18)) (CONG (SYMM (SYMM _let_17)) (REFL :args (tptp.xI)) :args (APPLY_UF tptp.aElementOf0)) (TRUE_INTRO _let_32))) :args (_let_16 _let_6 _let_2)) :args ((not (and _let_6 _let_2 _let_16)) SB_LITERAL))) (CONG (REFL :args (_let_31)) (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_30)) :args (or))) :args ((or _let_1 _let_31 _let_30))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_16 (not _let_20)))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_20 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_21 (not _let_23)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args (_let_4 tptp.sz10 tptp.xb QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt0 W1 BOUND_VARIABLE_1441) (tptp.aElement0 BOUND_VARIABLE_1448)))) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_25 1)) :args ((or _let_24 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or (not _let_12) _let_25 (not _let_26)))) (AND_ELIM (ASSUME :args (_let_13)) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.xI QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aIdeal0 W0)))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_25 false _let_12 false _let_26)) :args (_let_24 false _let_25)) :args (_let_23 false _let_24)) :args (_let_21 false _let_8 false _let_23)) :args (_let_20 false _let_21)) :args (_let_16 false _let_7 false _let_20)) _let_18 _let_17 :args (false false _let_16 true _let_1 false _let_6)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (tptp.aElement0 tptp.sz00) _let_15 (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_14 (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 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))) (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb)) (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))) (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb) _let_13 (and (tptp.aElementOf0 tptp.sz00 _let_11) (tptp.aElementOf0 tptp.xa _let_11) (tptp.aElementOf0 tptp.sz00 _let_10) (tptp.aElementOf0 tptp.xb _let_10)) (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))) (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb))) (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aElement0 W1) (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa W0) (tptp.sdtasdt0 tptp.xb W1))))) (not (not (tptp.doDivides0 tptp.xu tptp.xa))) (not (tptp.doDivides0 tptp.xu tptp.xb)) (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 _let_3 tptp.xr)) (or _let_9 (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) (not _let_9) _let_8 _let_7 _let_6 _let_2 true)))))))))))))))))))))))))))))))))))
% 0.21/0.72 )
% 0.21/0.72 % SZS output end Proof for RNG123+1
% 0.21/0.72 % cvc5---1.0.5 exiting
% 0.21/0.72 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------