TSTP Solution File: RNG092+2 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG092+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 13:49:59 EDT 2023

% Result   : Theorem 10.56s 10.79s
% Output   : Proof 10.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : RNG092+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun Aug 27 02:53:17 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 10.56/10.79  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vU2z83YlXC/cvc5---1.0.5_2394.p...
% 10.56/10.79  ------- get file name : TPTP file name is RNG092+2
% 10.56/10.79  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2394.smt2...
% 10.56/10.79  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.56/10.79  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.56/10.79  % SZS status Theorem for RNG092+2
% 10.56/10.79  % SZS output start Proof for RNG092+2
% 10.56/10.79  (
% 10.56/10.79  (let ((_let_1 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (let ((_let_2 (not (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (=> (and (or (exists ((W3 $$unsorted) (W4 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xI) (tptp.aElementOf0 W4 tptp.xJ) (= (tptp.sdtpldt0 W3 W4) W0))) (tptp.aElementOf0 W0 _let_1)) (or (exists ((W3 $$unsorted) (W4 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xI) (tptp.aElementOf0 W4 tptp.xJ) (= (tptp.sdtpldt0 W3 W4) W1))) (tptp.aElementOf0 W1 _let_1)) (tptp.aElement0 W2)) (exists ((W3 $$unsorted) (W4 $$unsorted)) (and (tptp.aElementOf0 W3 tptp.xI) (tptp.aElementOf0 W4 tptp.xJ) (= W0 (tptp.sdtpldt0 W3 W4)) (exists ((W5 $$unsorted) (W6 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (let ((_let_2 (tptp.sdtpldt0 W0 W1))) (let ((_let_3 (tptp.sdtpldt0 W4 W6))) (let ((_let_4 (tptp.sdtpldt0 W3 W5))) (and (tptp.aElementOf0 W5 tptp.xI) (tptp.aElementOf0 W6 tptp.xJ) (= W1 (tptp.sdtpldt0 W5 W6)) (tptp.aElementOf0 _let_4 tptp.xI) (tptp.aElementOf0 _let_3 tptp.xJ) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W3) tptp.xI) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W4) tptp.xJ) (= _let_2 (tptp.sdtpldt0 _let_4 _let_3)) (exists ((W7 $$unsorted) (W8 $$unsorted)) (and (tptp.aElementOf0 W7 tptp.xI) (tptp.aElementOf0 W8 tptp.xJ) (= (tptp.sdtpldt0 W7 W8) (tptp.sdtpldt0 W0 W1)))) (tptp.aElementOf0 _let_2 _let_1) (exists ((W7 $$unsorted) (W8 $$unsorted)) (and (tptp.aElementOf0 W7 tptp.xI) (tptp.aElementOf0 W8 tptp.xJ) (= (tptp.sdtpldt0 W7 W8) (tptp.sdtasdt0 W2 W0)))) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W0) _let_1)))))))))))) (=> (and (tptp.aSet0 _let_1) (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.sdtpldt1 tptp.xI tptp.xJ)) (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 W2 tptp.xJ) (= (tptp.sdtpldt0 W1 W2) W0)))))) (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.sdtpldt1 tptp.xI tptp.xJ)) (and (forall ((W1 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (=> (tptp.aElementOf0 W1 _let_1) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) _let_1)))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) (tptp.sdtpldt1 tptp.xI tptp.xJ))))))) (tptp.aIdeal0 _let_1))))))) (let ((_let_3 (tptp.aElement0 tptp.sz00))) (let ((_let_4 (tptp.aElementOf0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_1))) (let ((_let_5 (and (not (forall ((W7 $$unsorted) (W8 $$unsorted)) (or (not (tptp.aElementOf0 W7 tptp.xI)) (not (tptp.aElementOf0 W8 tptp.xJ)) (not (= (tptp.sdtpldt0 W7 W8) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) _let_4 (not (forall ((W7 $$unsorted) (W8 $$unsorted)) (or (not (tptp.aElementOf0 W7 tptp.xI)) (not (tptp.aElementOf0 W8 tptp.xJ)) (not (= (tptp.sdtpldt0 W7 W8) (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz00 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_1) (not (forall ((W3 $$unsorted) (W4 $$unsorted) (BOUND_VARIABLE_1466 $$unsorted) (BOUND_VARIABLE_1464 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W4 BOUND_VARIABLE_1466))) (let ((_let_2 (tptp.sdtpldt0 W3 BOUND_VARIABLE_1464))) (or (not (tptp.aElementOf0 W3 tptp.xI)) (not (tptp.aElementOf0 W4 tptp.xJ)) (not (= (tptp.sdtpldt0 W3 W4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz00 W3) tptp.xI)) (not (tptp.aElementOf0 (tptp.sdtasdt0 tptp.sz00 W4) tptp.xJ)) (not (tptp.aElementOf0 BOUND_VARIABLE_1464 tptp.xI)) (not (tptp.aElementOf0 BOUND_VARIABLE_1466 tptp.xJ)) (not (= (tptp.sdtpldt0 BOUND_VARIABLE_1464 BOUND_VARIABLE_1466) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.aElementOf0 _let_2 tptp.xI)) (not (tptp.aElementOf0 _let_1 tptp.xJ)) (not (= (tptp.sdtpldt0 _let_2 _let_1) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))))) (let ((_let_6 (not _let_3))) (let ((_let_7 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.sdtpldt0 tptp.sz00 tptp.sz00))) (let ((_let_10 (not (tptp.aElementOf0 tptp.sz00 tptp.xJ)))) (let ((_let_11 (not (tptp.aElementOf0 tptp.sz00 tptp.xI)))) (let ((_let_12 (and (or _let_11 _let_10 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) _let_8))) (let ((_let_13 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_1))) (let ((_let_14 (not _let_13))) (let ((_let_15 (and (or _let_11 _let_10 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) _let_14))) (let ((_let_16 (or _let_15 _let_12 _let_6 _let_5))) (let ((_let_17 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (BOUND_VARIABLE_1522 $$unsorted) (BOUND_VARIABLE_1509 $$unsorted) (BOUND_VARIABLE_1520 $$unsorted) (BOUND_VARIABLE_1507 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (or (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1507 tptp.xI)) (not (tptp.aElementOf0 BOUND_VARIABLE_1509 tptp.xJ)) (not (= W0 (tptp.sdtpldt0 BOUND_VARIABLE_1507 BOUND_VARIABLE_1509)))) (not (tptp.aElementOf0 W0 _let_1))) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1520 tptp.xI)) (not (tptp.aElementOf0 BOUND_VARIABLE_1522 tptp.xJ)) (not (= W1 (tptp.sdtpldt0 BOUND_VARIABLE_1520 BOUND_VARIABLE_1522)))) (not (tptp.aElementOf0 W1 _let_1))) (not (tptp.aElement0 W2)) (and (not (forall ((W7 $$unsorted) (W8 $$unsorted)) (or (not (tptp.aElementOf0 W7 tptp.xI)) (not (tptp.aElementOf0 W8 tptp.xJ)) (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W7 W8)))))) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) _let_1) (not (forall ((W7 $$unsorted) (W8 $$unsorted)) (or (not (tptp.aElementOf0 W7 tptp.xI)) (not (tptp.aElementOf0 W8 tptp.xJ)) (not (= (tptp.sdtpldt0 W7 W8) (tptp.sdtasdt0 W2 W0)))))) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W0) _let_1) (not (forall ((W3 $$unsorted) (W4 $$unsorted) (BOUND_VARIABLE_1466 $$unsorted) (BOUND_VARIABLE_1464 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W4 BOUND_VARIABLE_1466))) (let ((_let_2 (tptp.sdtpldt0 W3 BOUND_VARIABLE_1464))) (or (not (tptp.aElementOf0 W3 tptp.xI)) (not (tptp.aElementOf0 W4 tptp.xJ)) (not (= W0 (tptp.sdtpldt0 W3 W4))) (not (tptp.aElementOf0 (tptp.sdtasdt0 W2 W3) tptp.xI)) (not (tptp.aElementOf0 (tptp.sdtasdt0 W2 W4) tptp.xJ)) (not (tptp.aElementOf0 BOUND_VARIABLE_1464 tptp.xI)) (not (tptp.aElementOf0 BOUND_VARIABLE_1466 tptp.xJ)) (not (= W1 (tptp.sdtpldt0 BOUND_VARIABLE_1464 BOUND_VARIABLE_1466))) (not (tptp.aElementOf0 _let_2 tptp.xI)) (not (tptp.aElementOf0 _let_1 tptp.xJ)) (not (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 _let_2 _let_1)))))))))))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (NOT_IMPLIES_ELIM1 _let_18))) (let ((_let_20 (_let_17))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (not _let_15))) (let ((_let_23 (tptp.aElementOf0 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_1))) (let ((_let_24 (tptp.aElement0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23))) (let ((_let_27 (or _let_8 _let_4))) (let ((_let_28 (and _let_27 _let_26))) (let ((_let_29 (or _let_14 _let_28))) (let ((_let_30 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1570 $$unsorted) (BOUND_VARIABLE_1563 $$unsorted)) (let ((_let_1 (tptp.sdtpldt1 tptp.xI tptp.xJ))) (or (not (tptp.aElementOf0 W0 _let_1)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1563 _let_1)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1563) _let_1)) (or (not (tptp.aElement0 BOUND_VARIABLE_1570)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1570 W0) _let_1)))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (or))) (let ((_let_33 (not _let_30))) (let ((_let_34 (_let_33))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_30))) (REFL :args (_let_31)) :args _let_32)) (NOT_OR_ELIM (NOT_IMPLIES_ELIM2 (NOT_IMPLIES_ELIM2 _let_18)) :args (0)) :args (_let_31 true _let_30)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 1)) :args ((or _let_14 _let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 0)) (CONG (REFL :args (_let_29)) (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_32)) :args ((or _let_13 _let_29))) _let_35 :args (_let_13 true _let_29)) :args (_let_22 false _let_13)))) (let ((_let_37 (not _let_12))) (let ((_let_38 (and (not (forall ((W7 $$unsorted) (W8 $$unsorted)) (or (not (tptp.aElementOf0 W7 tptp.xI)) (not (tptp.aElementOf0 W8 tptp.xJ)) (not (= (tptp.sdtpldt0 W7 W8) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) (tptp.aElementOf0 (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_1) (not (forall ((W7 $$unsorted) (W8 $$unsorted)) (or (not (tptp.aElementOf0 W7 tptp.xI)) (not (tptp.aElementOf0 W8 tptp.xJ)) (not (= (tptp.sdtpldt0 W7 W8) (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))) _let_23 (not (forall ((W3 $$unsorted) (W4 $$unsorted) (BOUND_VARIABLE_1466 $$unsorted) (BOUND_VARIABLE_1464 $$unsorted)) (let ((_let_1 (tptp.sdtpldt0 W4 BOUND_VARIABLE_1466))) (let ((_let_2 (tptp.sdtpldt0 W3 BOUND_VARIABLE_1464))) (or (not (tptp.aElementOf0 W3 tptp.xI)) (not (tptp.aElementOf0 W4 tptp.xJ)) (not (= (tptp.sdtpldt0 W3 W4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.aElementOf0 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 W3) tptp.xI)) (not (tptp.aElementOf0 (tptp.sdtasdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 W4) tptp.xJ)) (not (tptp.aElementOf0 BOUND_VARIABLE_1464 tptp.xI)) (not (tptp.aElementOf0 BOUND_VARIABLE_1466 tptp.xJ)) (not (= (tptp.sdtpldt0 BOUND_VARIABLE_1464 BOUND_VARIABLE_1466) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.aElementOf0 _let_2 tptp.xI)) (not (tptp.aElementOf0 _let_1 tptp.xJ)) (not (= (tptp.sdtpldt0 _let_2 _let_1) (tptp.sdtpldt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))))))) (let ((_let_39 (or _let_15 _let_15 _let_25 _let_38))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_28)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_29 1)) _let_35 :args ((not _let_28) true _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_38 3)) :args ((or _let_23 (not _let_38)))) (REORDERING (FACTORING (CNF_OR_POS :args (_let_39))) :args ((or _let_25 _let_15 _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.sz00 tptp.sz00 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_20))) _let_19 :args (_let_39 false _let_17)) _let_36 (CNF_OR_NEG :args (_let_26 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_32)) :args ((or _let_24 _let_26))) :args (_let_26 false _let_38 false _let_39 true _let_15 true _let_23 false _let_24)) :args ((not _let_27) true _let_28 false _let_26)))) (let ((_let_41 (not _let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_6 _let_15 _let_12 _let_5 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_5 1)) :args ((or _let_4 _let_41))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 1)) _let_40 :args ((not _let_4) true _let_27)) :args (_let_41 true _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_12 1)) :args ((or _let_8 _let_37))) (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_8) _let_7))) :args _let_32)) :args ((or _let_7 _let_27))) _let_40 :args (_let_7 true _let_27)) :args (_let_37 false _let_7)) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.sz00 tptp.sz00 tptp.sz00 tptp.sz00 tptp.sz00 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_20))) _let_19 :args (_let_16 false _let_17)) (ASSUME :args (_let_3)) :args (false true _let_5 true _let_12 true _let_15 false _let_16 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))))))))) (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ)) _let_2 true))))))))))))))))))))))))))))))))))))))))))))
% 10.56/10.79  )
% 10.56/10.79  % SZS output end Proof for RNG092+2
% 10.56/10.79  % cvc5---1.0.5 exiting
% 10.56/10.79  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------