%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n015.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 13:50:00 EDT 2023

% Result   : Theorem 10.63s 10.96s
% Output   : Proof 10.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n015.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 02:37:23 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 10.63/10.96  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.zkGy1Eso5p/cvc5---1.0.5_17028.p...
% 10.63/10.96  ------- get file name : TPTP file name is RNG095+1
% 10.63/10.96  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_17028.smt2...
% 10.63/10.96  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.63/10.96  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.63/10.96  % SZS status Theorem for RNG095+1
% 10.63/10.96  % SZS output start Proof for RNG095+1
% 10.63/10.96  (
% 10.63/10.96  (let ((_let_1 (not (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 tptp.xI) (tptp.aElementOf0 W1 tptp.xJ) (= (tptp.sdtpldt0 W0 W1) tptp.sz10)))))) (let ((_let_2 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElementOf0 W0 (tptp.sdtpldt1 tptp.xI tptp.xJ)))))) (let ((_let_3 (tptp.aIdeal0 tptp.xJ))) (let ((_let_4 (tptp.aIdeal0 tptp.xI))) (let ((_let_5 (and _let_4 _let_3))) (let ((_let_6 (forall ((W0 $$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 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))))) (let ((_let_7 (forall ((W0 $$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 $$unsorted)) (and (tptp.aElementOf0 W4 W0) (tptp.aElementOf0 W5 W1) (= (tptp.sdtpldt0 W4 W5) W3)))))))))))) (let ((_let_8 (tptp.aElement0 tptp.sz10))) (let ((_let_9 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (let ((_let_10 (tptp.aElementOf0 tptp.sz10 _let_9))) (let ((_let_11 (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 tptp.xI)) (not (tptp.aElementOf0 W5 tptp.xJ)) (not (= tptp.sz10 (tptp.sdtpldt0 W4 W5))))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (= _let_10 _let_12))) (let ((_let_14 (not _let_8))) (let ((_let_15 (or _let_14 _let_10))) (let ((_let_16 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (tptp.aElementOf0 W0 (tptp.sdtpldt1 tptp.xI tptp.xJ)))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_18 (tptp.sz10 QUANTIFIERS_INST_ENUM))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (not (tptp.aElementOf0 W1 tptp.xJ)) (not (= tptp.sz10 (tptp.sdtpldt0 W0 W1))))))) (let ((_let_20 (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 tptp.xI)) (not (tptp.aElementOf0 W5 tptp.xJ)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))) (tptp.aElementOf0 W3 (tptp.sdtpldt1 tptp.xI tptp.xJ)))))) (let ((_let_21 (and (tptp.aSet0 _let_9) _let_20))) (let ((_let_22 (tptp.aSet0 tptp.xJ))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.aSet0 tptp.xI))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21))) (let ((_let_27 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1135 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (= (= (tptp.sdtpldt1 W0 W1) BOUND_VARIABLE_1135) (and (tptp.aSet0 BOUND_VARIABLE_1135) (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 W0)) (not (tptp.aElementOf0 W5 W1)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))) (tptp.aElementOf0 W3 BOUND_VARIABLE_1135))))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (and _let_22 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1200 $$unsorted) (BOUND_VARIABLE_1193 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1193 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1193) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1200)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1200 W1) tptp.xJ)))))))) (let ((_let_30 (= _let_3 _let_29))) (let ((_let_31 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1200 $$unsorted) (BOUND_VARIABLE_1193 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1193 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1193) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1200)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1200 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 (_let_31))) (let ((_let_34 (ASSUME :args (_let_5)))) (let ((_let_35 (and _let_24 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1200 $$unsorted) (BOUND_VARIABLE_1193 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1193 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1193) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1200)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1200 W1) tptp.xI)))))))) (let ((_let_36 (= _let_4 _let_35))) (let ((_let_37 (_let_20))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_13)) :args ((or (not _let_10) _let_12 (not _let_13)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args _let_18) :args _let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_20 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 _let_21 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_35 0)) :args ((or _let_24 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or (not _let_4) _let_35 (not _let_36)))) (AND_ELIM _let_34 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.xI QUANTIFIERS_INST_ENUM)) :args _let_33)) _let_32 :args (_let_36 false _let_31)) :args (_let_35 false _let_4 false _let_36)) :args (_let_24 false _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_22 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or (not _let_3) _let_29 (not _let_30)))) (AND_ELIM _let_34 :args (1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.xJ QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33)) _let_32 :args (_let_30 false _let_31)) :args (_let_29 false _let_3 false _let_30)) :args (_let_22 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_28 :args (tptp.xI tptp.xJ _let_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_27)))) _let_28 :args (_let_26 false _let_27)) :args (_let_21 false _let_24 false _let_22 false _let_26)) :args (_let_20 false _let_21)) :args (_let_13 false _let_20)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_19 (= W0 W4) (= W1 W5)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_11 false _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_10 (not _let_15)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args _let_18) :args (_let_16))) _let_17 :args (_let_15 false _let_16)) :args (_let_10 false _let_8 false _let_15)) :args (false false _let_13 false _let_11 false _let_10)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (tptp.aElement0 tptp.sz00) _let_8 (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_7 (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)))) _let_5 _let_2 (and (tptp.aElement0 tptp.xx) (tptp.aElement0 tptp.xy)) _let_1 true))))))))))))))))))))))))))))))))))))))))
% 10.63/10.97  )
% 10.63/10.97  % SZS output end Proof for RNG095+1
% 10.63/10.97  % cvc5---1.0.5 exiting
% 10.63/10.97  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------