%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG087+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 13:49:57 EDT 2023

% Result   : Theorem 4.96s 5.13s
% Output   : Proof 4.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : RNG087+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n014.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 01:31:47 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 4.96/5.13  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.wxCwbm6Ugl/cvc5---1.0.5_30846.p...
% 4.96/5.13  ------- get file name : TPTP file name is RNG087+1
% 4.96/5.13  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30846.smt2...
% 4.96/5.13  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.96/5.13  % SZS status Theorem for RNG087+1
% 4.96/5.13  % SZS output start Proof for RNG087+1
% 4.96/5.13  (
% 4.96/5.13  (let ((_let_1 (not (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElementOf0 W0 tptp.xI) (tptp.aElementOf0 W1 tptp.xJ) (= tptp.xy (tptp.sdtpldt0 W0 W1))))))) (let ((_let_2 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (let ((_let_3 (tptp.aElementOf0 tptp.xy _let_2))) (let ((_let_4 (and (tptp.aElementOf0 tptp.xx _let_2) _let_3 (tptp.aElement0 tptp.xz)))) (let ((_let_5 (tptp.aIdeal0 tptp.xJ))) (let ((_let_6 (tptp.aIdeal0 tptp.xI))) (let ((_let_7 (and _let_6 _let_5))) (let ((_let_8 (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_9 (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_10 (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 tptp.xI)) (not (tptp.aElementOf0 W5 tptp.xJ)) (not (= (tptp.sdtpldt0 W4 W5) tptp.xy)))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (= _let_3 _let_11))) (let ((_let_13 (1))) (let ((_let_14 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (not (tptp.aElementOf0 W1 tptp.xJ)) (not (= tptp.xy (tptp.sdtpldt0 W0 W1))))))) (let ((_let_15 (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 (tptp.sdtpldt1 tptp.xI tptp.xJ)) (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 tptp.xI)) (not (tptp.aElementOf0 W5 tptp.xJ)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))))))) (let ((_let_16 (and (tptp.aSet0 _let_2) _let_15))) (let ((_let_17 (tptp.aSet0 tptp.xJ))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.aSet0 tptp.xI))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_16))) (let ((_let_22 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1101 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSet0 W1)) (= (= (tptp.sdtpldt1 W0 W1) BOUND_VARIABLE_1101) (and (tptp.aSet0 BOUND_VARIABLE_1101) (forall ((W3 $$unsorted)) (= (not (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 W0)) (not (tptp.aElementOf0 W5 W1)) (not (= W3 (tptp.sdtpldt0 W4 W5)))))) (tptp.aElementOf0 W3 BOUND_VARIABLE_1101))))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (and _let_17 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1166 $$unsorted) (BOUND_VARIABLE_1159 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1159 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1159) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1166)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1166 W1) tptp.xJ)))))))) (let ((_let_25 (= _let_5 _let_24))) (let ((_let_26 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1166 $$unsorted) (BOUND_VARIABLE_1159 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1159 W0)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1159) W0)) (or (not (tptp.aElement0 BOUND_VARIABLE_1166)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1166 W1) W0)))))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.aIdeal0 W0)))) (let ((_let_30 (ASSUME :args (_let_7)))) (let ((_let_31 (and _let_19 (forall ((W1 $$unsorted) (BOUND_VARIABLE_1166 $$unsorted) (BOUND_VARIABLE_1159 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1159 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W1 BOUND_VARIABLE_1159) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1166)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1166 W1) tptp.xI)))))))) (let ((_let_32 (= _let_6 _let_31))) (let ((_let_33 (_let_15))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_12)) :args ((or (not _let_3) _let_11 (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (tptp.xy QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.aElementOf0 W3 _let_2)))) :args _let_33))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 1)) :args ((or _let_15 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_18 _let_16 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 0)) :args ((or _let_19 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_32)) :args ((or (not _let_6) _let_31 (not _let_32)))) (AND_ELIM _let_30 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.xI QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_32 false _let_26)) :args (_let_31 false _let_6 false _let_32)) :args (_let_19 false _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 0)) :args ((or _let_17 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_25)) :args ((or (not _let_5) _let_24 (not _let_25)))) (AND_ELIM _let_30 :args _let_13) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.xJ QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_25 false _let_26)) :args (_let_24 false _let_5 false _let_25)) :args (_let_17 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.xI tptp.xJ _let_2 QUANTIFIERS_INST_E_MATCHING ((tptp.sdtpldt1 W0 W1) (tptp.aSet0 BOUND_VARIABLE_1101)))) :args (_let_22)))) _let_23 :args (_let_21 false _let_22)) :args (_let_16 false _let_19 false _let_17 false _let_21)) :args (_let_15 false _let_16)) :args (_let_12 false _let_15)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_14 (= W0 W4) (= W1 W5))) (MACRO_SR_PRED_INTRO :args ((= (forall ((W4 $$unsorted) (W5 $$unsorted)) (or (not (tptp.aElementOf0 W4 tptp.xI)) (not (tptp.aElementOf0 W5 tptp.xJ)) (not (= tptp.xy (tptp.sdtpldt0 W4 W5))))) _let_10) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (_let_10 false _let_14)) (AND_ELIM (ASSUME :args (_let_4)) :args _let_13) :args (false false _let_12 false _let_10 false _let_3)) :args ((forall ((W0 $$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_9 (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_8 _let_7 _let_4 (and (tptp.aElementOf0 tptp.xk tptp.xI) (tptp.aElementOf0 tptp.xl tptp.xJ) (= tptp.xx (tptp.sdtpldt0 tptp.xk tptp.xl))) _let_1 true))))))))))))))))))))))))))))))))))))
% 4.96/5.16  )
% 4.96/5.16  % SZS output end Proof for RNG087+1
% 4.96/5.16  % cvc5---1.0.5 exiting
% 4.96/5.16  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------