0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : do_cvc5 %s %d
0.13/0.35	% Computer   : n031.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 1200
0.13/0.35	% WCLimit    : 120
0.13/0.35	% DateTime   : Tue Jul 13 15:49:44 EDT 2021
0.13/0.35	% CPUTime    : 
0.21/0.53	%----THF division
0.21/0.54	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.21/0.54	--- Run --ho-elim --full-saturate-quant at 10...
0.72/0.91	% SZS status Theorem for theBenchmark
0.72/0.93	% SZS output start Proof for theBenchmark
0.72/0.93	(proof
0.72/0.93	(let ((_let_1 (res x))) (let ((_let_2 (_let_1 q))) (let ((_let_3 (fresh_name_pi y))) (let ((_let_4 (fresh_name_pi x))) (let ((_let_5 (((subs p2) y) u))) (let ((_let_6 (_let_4 _let_5))) (let ((_let_7 ((late_BoundR aa) y))) (let ((_let_8 (par p))) (let ((_let_9 (_let_8 _let_2))) (let ((_let_10 (forall ((Y name) (R pi) (S pi)) (let ((_let_1 (res Y))) (let ((_let_2 (par R))) (=> ((fresh_name_pi Y) R) ((member558706512_pi_pi ((product_Pair_pi_pi (_let_1 (_let_2 S))) (_let_2 (_let_1 S)))) rel))))))) (let ((_let_11 (((subs q) y) u))) (let ((_let_12 (((subs _let_2) y) u))) (let ((_let_13 (= _let_12 (_let_1 _let_11)))) (let ((_let_14 (par _let_5))) (let ((_let_15 ((par p2) q))) (let ((_let_16 (_let_1 _let_15))) (let ((_let_17 (((subs _let_16) y) u))) (let ((_let_18 (not ((member558706512_pi_pi ((product_Pair_pi_pi _let_17) (_let_14 _let_12))) rel)))) (let ((_let_19 (_let_8 q))) (let ((_let_20 (_let_1 _let_19))) (let ((_let_21 (= _let_17 (_let_1 (_let_14 _let_11))))) (let ((_let_22 (forall ((Y name) (R pi) (S pi)) (let ((_let_1 (ho_18 k_38 Y))) (let ((_let_2 (ho_67 k_66 R))) (or (not (ho_22 (ho_21 k_20 Y) R)) (ho_4 (ho_3 k_2 (ho_60 (ho_59 k_58 (ho_19 _let_1 (ho_19 _let_2 S))) (ho_19 _let_2 (ho_19 _let_1 S)))) rel))))))) (let ((_let_23 (ho_11 (ho_10 (ho_9 k_8 q) y) u))) (let ((_let_24 (ho_18 k_38 x))) (let ((_let_25 (ho_19 _let_24 _let_23))) (let ((_let_26 (ho_11 (ho_10 (ho_9 k_8 p2) y) u))) (let ((_let_27 (ho_67 k_66 _let_26))) (let ((_let_28 (ho_19 _let_24 (ho_19 _let_27 _let_23)))) (let ((_let_29 (ho_4 (ho_3 k_2 (ho_60 (ho_59 k_58 _let_28) (ho_19 _let_27 _let_25))) rel))) (let ((_let_30 (ho_22 (ho_21 k_20 x) _let_26))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29))) (let ((_let_33 (EQ_RESOLVE (ASSUME |:args| (_let_10)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_10 7 12)) (PREPROCESS |:args| ((= (forall ((Y name) (R pi) (S pi)) (let ((_let_1 (res Y))) (let ((_let_2 (par R))) (or (not ((fresh_name_pi Y) R)) ((member558706512_pi_pi ((product_Pair_pi_pi (_let_1 (_let_2 S))) (_let_2 (_let_1 S)))) rel))))) _let_22))))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (ho_11 (ho_10 (ho_9 k_8 (ho_19 _let_24 q)) y) u))) (let ((_let_36 (= _let_35 _let_25))) (let ((_let_37 (ho_11 (ho_10 (ho_9 k_8 (ho_19 _let_24 (ho_19 (ho_67 k_66 p2) q))) y) u))) (let ((_let_38 (= _let_28 _let_37))) (let ((_let_39 (ho_4 (ho_3 k_2 (ho_60 (ho_59 k_58 _let_37) (ho_19 _let_27 _let_35))) rel))) (let ((_let_40 (not _let_29))) (let ((_let_41 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (PREPROCESS |:args| ((= _let_13 _let_36)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME |:args| (_let_21)) (PREPROCESS |:args| ((= _let_21 _let_38)))))) (let ((_let_43 (not _let_39))) (let ((_let_44 (EQ_RESOLVE (ASSUME |:args| (_let_18)) (PREPROCESS |:args| ((= _let_18 _let_43)))))) (let ((_let_45 (and _let_43 _let_38 _let_36))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 |:args| (x _let_26 _let_23)) |:args| (_let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_32)) |:args| ((or _let_31 _let_29 _let_34))) (EQ_RESOLVE (ASSUME |:args| (_let_6)) (PREPROCESS |:args| ((= _let_6 _let_30)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG |:args| (_let_45)) (IMPLIES_ELIM (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL |:args| (k_2)) (CONG (CONG (REFL |:args| (k_58)) (SYMM (SYMM _let_42)) |:args| (23 ho_59)) (CONG (REFL |:args| (_let_27)) (SYMM _let_41) |:args| (23 ho_19)) |:args| (23 ho_60)) |:args| (23 ho_3)) (REFL |:args| (rel)) |:args| (23 ho_4)) (FALSE_INTRO _let_44))) |:args| (_let_43 _let_38 _let_36))) |:args| (true _let_45)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_43) _let_39))) (REFL |:args| ((not _let_38))) (REFL |:args| ((not _let_36))) (REFL |:args| (_let_40)) |:args| (20))) _let_44 _let_42 _let_41 |:args| (_let_40 true _let_39 false _let_38 false _let_36)) |:args| (_let_34 false _let_30 true _let_29)) _let_33 |:args| (false true _let_32 false _let_22)) |:args| ((forall ((A name) (B name) (P pi) (C name) (D name)) (= (((subs (((mismatch A) B) P)) C) D) (((mismatch (((subst_name A) C) D)) (((subst_name B) C) D)) (((subs P) C) D)))) (forall ((B name) (A name) (X pi)) (= ((fresh_543891186ion_pi B) ((abs_fun_name_pi A) X)) (or ((fresh_name_pi B) X) (= B A)))) (forall ((X name) (P pi) (Rs late_residual)) (=> ((late_transitions ((res X) P)) Rs) (=> (forall ((P5 pi) (A3 name) (B3 name)) (=> (= ((res X) P) ((res B3) P5)) (forall ((P4 pi)) (=> (= Rs (((late_BoundR (late_BoundOutputS A3)) B3) P4)) (=> ((late_transitions P5) ((late_FreeR ((late_OutputR A3) B3)) P4)) (= A3 B3)))))) (=> (forall ((P5 pi) (A3 late_subject) (X3 name) (P4 pi) (Y3 name)) (let ((_let_1 ((late_BoundR A3) X3))) (let ((_let_2 (res Y3))) (=> (= ((res X) P) (_let_2 P5)) (=> (= Rs (_let_1 (_let_2 P4))) (=> ((late_transitions P5) (_let_1 P4)) (=> ((fresh_717452603ubject Y3) A3) (=> (not (= Y3 X3)) (=> ((fresh_name_pi X3) P5) (not ((fresh_717452603ubject X3) A3))))))))))) (not (forall ((P5 pi) (Alpha late_freeRes) (P4 pi) (Y3 name)) (let ((_let_1 (late_FreeR Alpha))) (let ((_let_2 (res Y3))) (=> (= ((res X) P) (_let_2 P5)) (=> (= Rs (_let_1 (_let_2 P4))) (=> ((late_transitions P5) (_let_1 P4)) (not ((fresh_1641682979reeRes Y3) Alpha))))))))))))) (forall ((P (-> produc53907987_pi_pi Bool)) (Prod produc53907987_pi_pi)) (=> (forall ((A3 (-> name noption_pi)) (B3 produc1141751126_pi_pi)) (P ((produc1275980869_pi_pi A3) B3))) (P Prod))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Name1 name) (Name2 name) (Pi pi)) (not (= (((input Name12) Name22) Pi3) (((match Name1) Name2) Pi)))) (forall ((P2 produc53907987_pi_pi)) (exists ((X3 (-> name noption_pi)) (Y3 produc1141751126_pi_pi)) (= P2 ((produc1275980869_pi_pi X3) Y3)))) (forall ((Pi pi)) (not (= piNil (bang Pi)))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi pi)) (not (= (((input Name12) Name22) Pi3) (bang Pi)))) (forall ((X name) (P pi) (Alpha2 late_freeRes) (P3 pi)) (=> ((late_transitions ((res X) P)) ((late_FreeR Alpha2) P3)) (not (forall ((P5 pi) (Alpha late_freeRes) (P4 pi) (Y3 name)) (let ((_let_1 (late_FreeR Alpha))) (let ((_let_2 (res Y3))) (=> (= ((res X) P) (_let_2 P5)) (=> (= ((late_FreeR Alpha2) P3) (_let_1 (_let_2 P4))) (=> ((late_transitions P5) (_let_1 P4)) (not ((fresh_1641682979reeRes Y3) Alpha))))))))))) (forall ((P2 product_prod_pi_pi)) (exists ((X3 pi) (Y3 pi)) (= P2 ((product_Pair_pi_pi X3) Y3)))) (forall ((Rel set_Pr1834926343_pi_pi) (A name) (P pi)) (((strong743114133lation piNil) Rel) (((mismatch A) A) P))) (forall ((P pi) (A name) (Y name) (P3 pi) (Q pi) (X name) (Q3 pi)) (=> ((late_transitions P) (((late_BoundR (late_BoundOutputS A)) Y) P3)) (=> ((late_transitions Q) (((late_BoundR (late_InputS A)) X) Q3)) (=> ((fresh_name_pi Y) Q) ((late_transitions ((par P) Q)) ((late_FreeR late_TauR) ((res Y) ((par P3) (((subs Q3) X) Y))))))))) (forall ((A name) (X32 name) (X2 name) (X1 pi)) (let ((_let_1 (fresh_name_pi A))) (let ((_let_2 (fresh_name_name A))) (= (_let_1 (((match X32) X2) X1)) (and (_let_2 X32) (_let_2 X2) (_let_1 X1)))))) (forall ((Name3 name) (Pi3 pi) (Pi pi)) (not (= ((res Name3) Pi3) (bang Pi)))) (forall ((P pi) (A late_subject) (X name) (P3 pi) (Y name)) (let ((_let_1 (fresh_name_pi Y))) (=> ((late_transitions P) (((late_BoundR A) X) P3)) (=> (_let_1 P) (=> (not (= Y X)) (_let_1 P3)))))) (forall ((P pi) (A late_subject) (X name) (P3 pi) (Y name)) (let ((_let_1 (res Y))) (let ((_let_2 ((late_BoundR A) X))) (=> ((late_transitions P) (_let_2 P3)) (=> ((fresh_717452603ubject Y) A) (=> (not (= Y X)) ((late_transitions (_let_1 P)) (_let_2 (_let_1 P3))))))))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Name name) (Pi pi)) (not (= (((input Name12) Name22) Pi3) ((res Name) Pi)))) (forall ((A name) (X name) (P pi) (B name) (Y name) (P3 pi)) (not ((late_transitions (((input A) X) P)) (((late_BoundR (late_BoundOutputS B)) Y) P3)))) (forall ((A name) (B name) (P pi) (Rs late_residual)) (=> ((late_transitions (((output A) B) P)) Rs) (not (forall ((A3 name) (B3 name) (P5 pi)) (=> (and (= A A3) (= P P5) (= B B3)) (not (= Rs ((late_FreeR ((late_OutputR A3) B3)) P5)))))))) (forall ((Pi3 pi) (Name1 name) (Name2 name) (Pi pi)) (not (= (tau Pi3) (((input Name1) Name2) Pi)))) (forall ((P (-> produc53907987_pi_pi Bool)) (X produc53907987_pi_pi)) (=> (forall ((A3 (-> name noption_pi)) (B3 name) (C2 product_prod_pi_pi)) (P ((produc1275980869_pi_pi A3) ((produc235456326_pi_pi B3) C2)))) (P X))) (forall ((Name1 name) (Name2 name) (Pi pi)) (not (= piNil (((output Name1) Name2) Pi)))) (forall ((Rel set_Pr1834926343_pi_pi) (P pi)) (not (((strong743114133lation piNil) Rel) (tau P)))) (forall ((P2 produc405342261i_name)) (exists ((X3 (-> name noption_pi)) (Y3 name)) (= P2 ((produc540578151i_name X3) Y3)))) (forall ((A name) (B name) (P pi) (Rs late_residual) (F (-> name name Bool))) (let ((_let_1 (F A))) (=> ((late_transitions (((match A) B) P)) Rs) (=> (=> ((late_transitions P) Rs) (=> (= A B) (_let_1 A))) (_let_1 B))))) (_let_3 _let_20) ((late_transitions p) (_let_7 p2)) (forall ((A name) (B name) (P pi) (Alpha2 late_freeRes) (P3 pi) (Prop (-> late_freeRes pi Bool))) (let ((_let_1 ((late_OutputR A) B))) (=> ((late_transitions (((output A) B) P)) ((late_FreeR Alpha2) P3)) (=> (=> (= Alpha2 _let_1) (=> (= P P3) ((Prop _let_1) P))) ((Prop Alpha2) P3))))) (forall ((A name) (X pi) (Y pi)) (=> ((fresh_1627595501_pi_pi A) ((product_Pair_pi_pi X) Y)) ((fresh_name_pi A) Y))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi pi)) (not (= (((mismatch Name12) Name22) Pi3) (bang Pi)))) (forall ((Y produc1141751126_pi_pi)) (not (forall ((A3 name) (B3 pi) (C2 pi)) (not (= Y ((produc235456326_pi_pi A3) ((product_Pair_pi_pi B3) C2))))))) (forall ((P (-> product_prod_pi_pi Bool)) (Q (-> product_prod_pi_pi Bool))) (=> (forall ((X3 product_prod_pi_pi)) (= (P X3) (Q X3))) (= (collec1051790738_pi_pi P) (collec1051790738_pi_pi Q)))) (forall ((X1 pi) (X2 pi) (Y1 pi) (Y2 pi)) (= (= ((product_Pair_pi_pi X1) X2) ((product_Pair_pi_pi Y1) Y2)) (and (= X2 Y2) (= X1 Y1)))) (forall ((A name) (X name) (Y product_prod_pi_pi)) (=> ((fresh_1376661020_pi_pi A) ((produc235456326_pi_pi X) Y)) ((fresh_1627595501_pi_pi A) Y))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi12 pi) (Pi22 pi)) (not (= (((input Name12) Name22) Pi3) ((par Pi12) Pi22)))) (forall ((P (-> produc53907987_pi_pi Bool)) (P2 produc53907987_pi_pi)) (=> (forall ((A3 (-> name noption_pi)) (B3 produc1141751126_pi_pi)) (P ((produc1275980869_pi_pi A3) B3))) (P P2))) (forall ((P2 produc1462499409ion_pi)) (exists ((X3 (-> name noption_pi)) (Y3 (-> name noption_pi))) (= P2 ((produc1342893193ion_pi X3) Y3)))) (forall ((A name) (X1 name)) (= ((fresh_717452603ubject A) (late_BoundOutputS X1)) ((fresh_name_name A) X1))) (forall ((P pi)) ((late_transitions (tau P)) ((late_FreeR late_TauR) P))) (forall ((P (-> produc1834551554reeRes Bool)) (Prod produc1834551554reeRes)) (=> (forall ((A3 (-> name noption_pi)) (B3 late_freeRes)) (P ((produc1505598906reeRes A3) B3))) (P Prod))) (forall ((A name) (X pi) (Y late_freeRes)) (= ((fresh_1504024600reeRes A) ((produc1638681944reeRes X) Y)) (and ((fresh_1641682979reeRes A) Y) ((fresh_name_pi A) X)))) (forall ((A name) (B name) (P pi) (Rs late_residual)) (=> ((late_transitions (((match A) B) P)) Rs) (= A B))) ((fresh_717452603ubject x) aa) (forall ((A name) (B name) (P pi) (Rs late_residual)) (=> ((late_transitions (((match A) B) P)) Rs) (not (forall ((P5 pi)) (=> (and (= P P5) (= B A)) (not ((late_transitions P5) Rs))))))) (forall ((A name) (X name) (P pi)) ((late_transitions (((input A) X) P)) (((late_BoundR (late_InputS A)) X) P))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi pi)) (not (= (((output Name12) Name22) Pi3) (tau Pi)))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (X name) (P pi) (C3 pi)) (=> (eqvt_pi Rel) (=> (forall ((Q2 pi) (A3 name)) (=> ((late_transitions Q) ((late_FreeR ((late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 pi)) (and ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel) ((late_transitions P) (((late_BoundR (late_BoundOutputS A3)) X) P6))))))) (=> (forall ((Q2 pi) (A3 late_subject) (Y3 name)) (=> ((late_transitions Q) (((late_BoundR A3) Y3) Q2)) (=> ((fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> ((fresh_name_pi Y3) C3) (exists ((P6 pi)) (and (((((strong2129052853vative P6) ((res X) Q2)) A3) Y3) Rel) ((late_transitions P) (((late_BoundR A3) Y3) P6))))))))) (=> (forall ((Q2 pi) (Alpha late_freeRes)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (=> ((fresh_1641682979reeRes X) Alpha) (exists ((P6 pi)) (and ((member558706512_pi_pi ((product_Pair_pi_pi P6) ((res X) Q2))) Rel) ((late_transitions P) ((late_FreeR Alpha) P6))))))) (((strong743114133lation P) Rel) ((res X) Q))))))) (forall ((X32 name) (X2 name) (X1 pi) (Y32 name) (Y2 name) (Y1 pi)) (= (= (((output X32) X2) X1) (((output Y32) Y2) Y1)) (and (= X1 Y1) (= X2 Y2) (= X32 Y32)))) (forall ((Y produc1141751126_pi_pi)) (not (forall ((A3 name) (B3 product_prod_pi_pi)) (not (= Y ((produc235456326_pi_pi A3) B3)))))) (forall ((P pi) (A name) (X name) (P3 pi) (Q pi) (Y name) (Q3 pi)) (=> ((late_transitions P) (((late_BoundR (late_InputS A)) X) P3)) (=> ((late_transitions Q) (((late_BoundR (late_BoundOutputS A)) Y) Q3)) (=> ((fresh_name_pi Y) P) ((late_transitions ((par P) Q)) ((late_FreeR late_TauR) ((res Y) ((par (((subs P3) X) Y)) Q3)))))))) (forall ((B name) (A name) (X late_freeRes)) (= ((fresh_785364841reeRes B) ((abs_fu681348580reeRes A) X)) (or (= B A) ((fresh_1641682979reeRes B) X)))) (forall ((P (-> pi late_residual Bool)) (Z pi) (Residual late_residual)) (=> (forall ((Subject2 late_subject) (Name4 name) (Pi4 pi) (Z2 pi)) (=> ((fresh_name_pi Name4) Z2) (=> ((fresh_717452603ubject Name4) Subject2) ((P Z2) (((late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 late_freeRes) (Pi4 pi) (Z2 pi)) ((P Z2) ((late_FreeR FreeRes2) Pi4))) ((P Z) Residual)))) (forall ((P pi) (Rel set_Pr1834926343_pi_pi) (Q pi) (Alpha2 late_freeRes) (Q3 pi)) (=> (((strong743114133lation P) Rel) Q) (=> ((late_transitions Q) ((late_FreeR Alpha2) Q3)) (exists ((P4 pi)) (and ((late_transitions P) ((late_FreeR Alpha2) P4)) ((member558706512_pi_pi ((product_Pair_pi_pi P4) Q3)) Rel)))))) (forall ((X11 name) (X12 name)) (not (= ((late_OutputR X11) X12) late_TauR))) (forall ((A name) (X2 late_freeRes) (X1 pi)) (= ((fresh_81631222sidual A) ((late_FreeR X2) X1)) (and ((fresh_name_pi A) X1) ((fresh_1641682979reeRes A) X2)))) (forall ((A (-> name noption_pi)) (B name) (A2 (-> name noption_pi)) (B2 name)) (=> (= ((produc540578151i_name A) B) ((produc540578151i_name A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi pi)) (not (= (((output Name12) Name22) Pi3) (bang Pi)))) (forall ((A name) (X1 name)) (= ((fresh_717452603ubject A) (late_InputS X1)) ((fresh_name_name A) X1))) (forall ((A name) (X32 name) (X2 name) (X1 pi)) (let ((_let_1 (fresh_name_name A))) (let ((_let_2 (fresh_name_pi A))) (= (_let_2 (((mismatch X32) X2) X1)) (and (_let_1 X32) (_let_2 X1) (_let_1 X2)))))) (forall ((X name) (A name) (C name) (D name) (P pi)) (=> (not (= X A)) (=> (not (= X C)) (=> (not (= X D)) (= (((subs (((input A) X) P)) C) D) (((input (((subst_name A) C) D)) X) (((subs P) C) D))))))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (X name) (P pi) (C3 produc1141751126_pi_pi)) (=> (eqvt_pi Rel) (=> (forall ((Q2 pi) (A3 name)) (=> ((late_transitions Q) ((late_FreeR ((late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 pi)) (and ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel) ((late_transitions P) (((late_BoundR (late_BoundOutputS A3)) X) P6))))))) (=> (forall ((Q2 pi) (A3 late_subject) (Y3 name)) (=> ((late_transitions Q) (((late_BoundR A3) Y3) Q2)) (=> ((fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> ((fresh_1376661020_pi_pi Y3) C3) (exists ((P6 pi)) (and ((late_transitions P) (((late_BoundR A3) Y3) P6)) (((((strong2129052853vative P6) ((res X) Q2)) A3) Y3) Rel)))))))) (=> (forall ((Q2 pi) (Alpha late_freeRes)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (=> ((fresh_1641682979reeRes X) Alpha) (exists ((P6 pi)) (and ((late_transitions P) ((late_FreeR Alpha) P6)) ((member558706512_pi_pi ((product_Pair_pi_pi P6) ((res X) Q2))) Rel)))))) (((strong743114133lation P) Rel) ((res X) Q))))))) (forall ((A name) (B name) (P pi) (C late_subject) (X name) (P3 pi)) (not ((late_transitions (((output A) B) P)) (((late_BoundR C) X) P3)))) (forall ((P pi) (A name) (Y name) (P3 pi) (Q pi) (X name) (Q3 pi)) (let ((_let_1 (fresh_name_pi Y))) (let ((_let_2 (fresh_name_pi X))) (=> ((late_transitions P) (((late_BoundR (late_BoundOutputS A)) Y) P3)) (=> ((late_transitions Q) (((late_BoundR (late_InputS A)) X) Q3)) (=> (_let_2 P) (=> (_let_2 Q) (=> (_let_1 P) (=> (_let_1 Q) (=> (not (= X A)) (=> (_let_2 P3) (=> (not (= Y A)) (=> (_let_1 Q3) (=> (not (= X Y)) ((late_transitions ((par P) Q)) ((late_FreeR late_TauR) ((res Y) ((par P3) (((subs Q3) X) Y))))))))))))))))))) (forall ((X1 name) (Y1 name)) (= (= (late_BoundOutputS X1) (late_BoundOutputS Y1)) (= X1 Y1))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (P pi) (C3 pi)) (=> (eqvt_pi Rel) (=> (forall ((A3 late_subject) (X3 name) (Q2 pi)) (let ((_let_1 (fresh_name_pi X3))) (=> ((late_transitions Q) (((late_BoundR A3) X3) Q2)) (=> (_let_1 P) (=> (_let_1 Q) (=> ((fresh_717452603ubject X3) A3) (=> (_let_1 C3) (exists ((P6 pi)) (and ((late_transitions P) (((late_BoundR A3) X3) P6)) (((((strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha late_freeRes) (Q2 pi)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (exists ((P6 pi)) (and ((late_transitions P) ((late_FreeR Alpha) P6)) ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel))))) (((strong743114133lation P) Rel) Q))))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi12 pi) (Pi22 pi)) (not (= (((mismatch Name12) Name22) Pi3) ((par Pi12) Pi22)))) (forall ((A name) (X32 name) (X1 name) (X2 pi)) (= ((fresh_name_pi A) (((input X32) X1) X2)) (and 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((fresh_name_pi A) piNil)) (forall ((X2 late_freeRes) (X1 pi) (Y2 late_freeRes) (Y1 pi)) (= (= ((late_FreeR X2) X1) ((late_FreeR Y2) Y1)) (and (= X1 Y1) (= X2 Y2)))) (forall ((X1 pi) (Y1 pi)) (= (= (bang X1) (bang Y1)) (= X1 Y1))) (forall ((P pi) (C name) (D name)) (= (((subs (tau P)) C) D) (tau (((subs P) C) D)))) (forall ((X pi)) (not (forall ((C2 name)) (not ((fresh_name_pi C2) X))))) (forall ((A name) (B name) (P pi) (C name) (D name) (P3 pi)) (=> ((late_transitions (((output A) B) P)) ((late_FreeR ((late_OutputR C) D)) P3)) (not (or (not (= A C)) (not (= B D)))))) (forall ((X1 (-> name noption_pi)) (X2 produc1141751126_pi_pi) (Y1 (-> name noption_pi)) (Y2 produc1141751126_pi_pi)) (= (= ((produc1275980869_pi_pi X1) X2) ((produc1275980869_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) _let_21 (forall ((P (-> produc1141751126_pi_pi Bool)) (X produc1141751126_pi_pi)) (=> (forall ((A3 name) (B3 pi) (C2 pi)) (P ((produc235456326_pi_pi A3) ((product_Pair_pi_pi B3) C2)))) (P X))) (forall ((P2 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(forall ((Za name)) ((P Za) Pi13)) (=> (forall ((Za name)) ((P Za) Pi23)) ((P Z2) ((sum Pi13) Pi23))))) (=> (forall ((Pi13 pi) (Pi23 pi) (Z2 name)) (=> (forall ((Za name)) ((P Za) Pi13)) (=> (forall ((Za name)) ((P Za) Pi23)) ((P Z2) ((par Pi13) Pi23))))) (=> (forall ((Name4 name) (Pi4 pi) (Z2 name)) (=> ((fresh_name_name Name4) Z2) (=> (forall ((Za name)) ((P Za) Pi4)) ((P Z2) ((res Name4) Pi4))))) (=> (forall ((Pi4 pi) (Z2 name)) (=> (forall ((Za name)) ((P Za) Pi4)) ((P Z2) (bang Pi4)))) ((P Z) Pi3)))))))))))) (forall ((A name) (X name) (P pi) (Alpha2 late_freeRes) (P3 pi)) (not ((late_transitions (((input A) X) P)) ((late_FreeR Alpha2) P3)))) (_let_3 q) (forall ((Rs late_residual)) (not ((late_transitions piNil) Rs))) (forall ((X name) (B name) (P pi) (Rs late_residual)) (not ((late_transitions ((res X) (((output X) B) P))) Rs))) (forall ((P pi) (Rs late_residual) (B name)) (=> ((late_transitions P) Rs) ((late_transitions (((match B) B) P)) Rs))) (forall ((A name) (X1 pi)) (let 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(_let_2 P4)) (=> (_let_1 P5) (=> (_let_1 Q4) (not ((fresh_717452603ubject X3) A3)))))))))) (not (forall ((Q4 pi) (A3 late_subject) (X3 name) (Q2 pi) (P5 pi)) (let ((_let_1 (fresh_name_pi X3))) (let ((_let_2 ((late_BoundR A3) X3))) (let ((_let_3 (par P5))) (=> (= ((par P) Q) (_let_3 Q4)) (=> (= (((late_BoundR B) Y) P3) (_let_2 (_let_3 Q2))) (=> ((late_transitions Q4) (_let_2 Q2)) (=> (_let_1 P5) (=> (_let_1 Q4) (not ((fresh_717452603ubject X3) A3))))))))))))))) (forall ((X1 name) (X2 product_prod_pi_pi) (Y1 name) (Y2 product_prod_pi_pi)) (= (= ((produc235456326_pi_pi X1) X2) ((produc235456326_pi_pi Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((P (-> product_prod_pi_pi Bool)) (P2 product_prod_pi_pi)) (=> (forall ((A3 pi) (B3 pi)) (P ((product_Pair_pi_pi A3) B3))) (P P2))) (forall ((P (-> late_freeRes Bool)) (FreeRes3 late_freeRes)) (=> (forall ((Name13 name) (Name23 name)) (P ((late_OutputR Name13) Name23))) (=> (P late_TauR) (P FreeRes3)))) (forall ((P pi) (A name) (X name) (P3 pi) (Q 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X))) (=> ((late_transitions P) (_let_1 P3)) (=> ((fresh_name_pi X) Q) ((late_transitions ((par P) Q)) (_let_1 ((par P3) Q))))))) (forall ((P (-> name late_residual Bool)) (Z name) (Residual late_residual)) (=> (forall ((Subject2 late_subject) (Name4 name) (Pi4 pi) (Z2 name)) (=> ((fresh_name_name Name4) Z2) (=> ((fresh_717452603ubject Name4) Subject2) ((P Z2) (((late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 late_freeRes) (Pi4 pi) (Z2 name)) ((P Z2) ((late_FreeR FreeRes2) Pi4))) ((P Z) Residual)))) (forall ((A pi) (B pi) (A2 pi) (B2 pi)) (=> (= ((product_Pair_pi_pi A) B) ((product_Pair_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((P pi) (A name) (X name) (P3 pi) (Q pi) (Y name) (Q3 pi)) (let ((_let_1 (fresh_name_pi Y))) (let ((_let_2 (fresh_name_pi X))) (=> ((late_transitions P) (((late_BoundR (late_InputS A)) X) P3)) (=> ((late_transitions Q) (((late_BoundR (late_BoundOutputS A)) Y) Q3)) (=> (_let_2 P) (=> (_let_2 Q) (=> (_let_1 P) (=> (_let_1 Q) (=> (not (= X A)) (=> (_let_2 Q3) (=> (not (= Y A)) (=> (_let_1 P3) (=> (not (= X Y)) ((late_transitions ((par P) Q)) ((late_FreeR late_TauR) ((res Y) ((par (((subs P3) X) Y)) Q3)))))))))))))))))) (forall ((Name1 name) (Name2 name) (Pi pi)) (not (= piNil (((input Name1) Name2) Pi)))) (forall ((X32 late_subject) (X1 name) (X2 pi) (Y32 late_subject) (Y1 name) (Y2 pi)) (= (= (((late_BoundR X32) X1) X2) (((late_BoundR Y32) Y1) Y2)) (and (= X32 Y32) (= ((abs_fun_name_pi X1) X2) ((abs_fun_name_pi Y1) Y2))))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (P pi) (C3 produc1141751126_pi_pi)) (=> (eqvt_pi Rel) (=> (forall ((A3 late_subject) (X3 name) (Q2 pi)) (let ((_let_1 (fresh_name_pi X3))) (=> ((late_transitions Q) (((late_BoundR A3) X3) Q2)) (=> (_let_1 P) (=> (_let_1 Q) (=> ((fresh_717452603ubject X3) A3) (=> ((fresh_1376661020_pi_pi X3) C3) (exists ((P6 pi)) (and ((late_transitions P) (((late_BoundR A3) X3) P6)) (((((strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha 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(forall ((Pi13 pi) (Pi23 pi) (Z2 name)) (=> (forall ((Za name)) ((P Za) Pi13)) (=> (forall ((Za name)) ((P Za) Pi23)) ((P Z2) ((par Pi13) Pi23))))) (=> (forall ((Name4 name) (Pi4 pi) (Z2 name)) (=> ((fresh_name_name Name4) Z2) (=> (forall ((Za name)) ((P Za) Pi4)) ((P Z2) ((res Name4) Pi4))))) (=> (forall ((Pi4 pi) (Z2 name)) (=> (forall ((Za name)) ((P Za) Pi4)) ((P Z2) (bang Pi4)))) ((P Z) Pi3)))))))))))) (forall ((A name) (X produc1141751126_pi_pi) (Y produc1141751126_pi_pi)) (let ((_let_1 (abs_fu385186459_pi_pi A))) (= (= (_let_1 X) (_let_1 Y)) (= X Y)))) (forall ((X1 pi) (Y1 pi)) (= (= (tau X1) (tau Y1)) (= X1 Y1))) (forall ((A name) (B name) (Rel set_Pr1834926343_pi_pi) (P pi)) (=> (not (= A B)) (((strong743114133lation piNil) Rel) (((match A) B) P)))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Name name) (Pi pi)) (not (= (((match Name12) Name22) Pi3) ((res Name) Pi)))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi12 pi) (Pi22 pi)) (not (= (((mismatch Name12) Name22) Pi3) 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name) (A2 (-> name noption_pi)) (B2 name)) (= (= ((produc540578151i_name A) B) ((produc540578151i_name A2) B2)) (and (= A A2) (= B B2)))) (forall ((Y produc1462499409ion_pi)) (not (forall ((A3 (-> name noption_pi)) (B3 (-> name noption_pi))) (not (= Y ((produc1342893193ion_pi A3) B3)))))) (forall ((A (-> name noption_pi)) (B (-> name noption_pi)) (A2 (-> name noption_pi)) (B2 (-> name noption_pi))) (=> (= ((produc1342893193ion_pi A) B) ((produc1342893193ion_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((B name) (P pi) (A name)) (=> ((fresh_name_pi B) P) (= ((res A) P) ((res B) (((subs P) A) B))))) (forall ((A name) (X name) (Y late_freeRes)) (= ((fresh_1963366730reeRes A) ((produc1531804426reeRes X) Y)) (and ((fresh_name_name A) X) ((fresh_1641682979reeRes A) Y)))) (forall ((A name) (X late_freeRes) (Y late_freeRes)) (let ((_let_1 (abs_fu681348580reeRes A))) (= (= (_let_1 X) (_let_1 Y)) (= X Y)))) (forall ((X5 name) (P pi) (A late_subject) (Y4 name) (P3 pi)) (=> ((late_transitions ((res X5) P)) (((late_BoundR A) Y4) P3)) (=> (forall ((P5 pi) (A3 name) (B3 name)) (=> (= ((res X5) P) ((res B3) P5)) (forall ((P4 pi)) (=> (= (((late_BoundR A) Y4) P3) (((late_BoundR (late_BoundOutputS A3)) B3) P4)) (=> ((late_transitions P5) ((late_FreeR ((late_OutputR A3) B3)) P4)) (= A3 B3)))))) (not (forall ((P5 pi) (A3 late_subject) (X3 name) (P4 pi) (Y3 name)) (let ((_let_1 ((late_BoundR A3) X3))) (let ((_let_2 (res Y3))) (=> (= ((res X5) P) (_let_2 P5)) (=> (= (((late_BoundR A) Y4) P3) (_let_1 (_let_2 P4))) (=> ((late_transitions P5) (_let_1 P4)) (=> ((fresh_717452603ubject Y3) A3) (=> (not (= Y3 X3)) (=> ((fresh_name_pi X3) P5) (not ((fresh_717452603ubject X3) A3))))))))))))))) (forall ((X1 (-> name noption_pi)) (X2 (-> name noption_pi)) (Y1 (-> name noption_pi)) (Y2 (-> name noption_pi))) (= (= ((produc1342893193ion_pi X1) X2) ((produc1342893193ion_pi Y1) Y2)) (and (= X2 Y2) (= X1 Y1)))) (forall ((P (-> produc1141751126_pi_pi pi Bool)) (Z produc1141751126_pi_pi) (Pi3 pi)) (=> (forall ((Z2 produc1141751126_pi_pi)) ((P Z2) piNil)) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) (((output Name13) Name23) Pi4)))) (=> (forall ((Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) (tau Pi4)))) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> ((fresh_1376661020_pi_pi Name23) Z2) (=> ((fresh_name_name Name23) Name13) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) (((input Name13) Name23) Pi4)))))) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) (((match Name13) Name23) Pi4)))) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) (((mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 pi) (Pi23 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi13)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi23)) ((P Z2) ((sum Pi13) Pi23))))) (=> (forall ((Pi13 pi) (Pi23 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi13)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi23)) ((P Z2) ((par Pi13) Pi23))))) (=> (forall ((Name4 name) (Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> ((fresh_1376661020_pi_pi Name4) Z2) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) ((res Name4) Pi4))))) (=> (forall ((Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> (forall ((Za produc1141751126_pi_pi)) ((P Za) Pi4)) ((P Z2) (bang Pi4)))) ((P Z) Pi3)))))))))))) (forall ((P (-> late_freeRes late_residual Bool)) (Z late_freeRes) (Residual late_residual)) (=> (forall ((Subject2 late_subject) (Name4 name) (Pi4 pi) (Z2 late_freeRes)) (=> ((fresh_1641682979reeRes Name4) Z2) (=> ((fresh_717452603ubject Name4) Subject2) ((P Z2) (((late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 late_freeRes) (Pi4 pi) (Z2 late_freeRes)) ((P Z2) ((late_FreeR FreeRes2) Pi4))) ((P Z) Residual)))) (forall ((X name) (A name) (P pi) (B name) (Y name) (P3 pi)) (not ((late_transitions ((res X) (((output A) X) P))) ((late_FreeR ((late_OutputR B) Y)) P3)))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (X name) (P pi) (C3 name)) (=> (eqvt_pi Rel) (=> (forall ((Q2 pi) (A3 name)) (=> ((late_transitions Q) ((late_FreeR ((late_OutputR A3) X)) Q2)) (=> (not (= A3 X)) (exists ((P6 pi)) (and ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel) ((late_transitions P) (((late_BoundR (late_BoundOutputS A3)) X) P6))))))) (=> (forall ((Q2 pi) (A3 late_subject) (Y3 name)) (=> ((late_transitions Q) (((late_BoundR A3) Y3) Q2)) (=> ((fresh_717452603ubject X) A3) (=> (not (= X Y3)) (=> ((fresh_name_name Y3) C3) (exists ((P6 pi)) (and ((late_transitions P) (((late_BoundR A3) Y3) P6)) (((((strong2129052853vative P6) ((res X) Q2)) A3) Y3) Rel)))))))) (=> (forall ((Q2 pi) (Alpha late_freeRes)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (=> ((fresh_1641682979reeRes X) Alpha) (exists ((P6 pi)) (and ((late_transitions P) ((late_FreeR Alpha) P6)) ((member558706512_pi_pi ((product_Pair_pi_pi P6) ((res X) Q2))) Rel)))))) (((strong743114133lation P) Rel) ((res X) Q))))))) (forall ((A name)) ((fresh_1641682979reeRes A) late_TauR)) (= fresh_name_name (lambda ((A5 name) (B4 name)) (not (= A5 B4)))) (forall ((X32 name) (X2 name) (X1 pi) (Y32 name) (Y2 name) (Y1 pi)) (= (= (((match X32) X2) X1) (((match Y32) Y2) Y1)) (and (= X32 Y32) (= X1 Y1) (= X2 Y2)))) (forall ((Q pi) (P pi) (Rel set_Pr1834926343_pi_pi)) (=> (forall ((A3 late_subject) (Y3 name) (Q2 pi)) (=> ((late_transitions Q) (((late_BoundR A3) Y3) Q2)) (=> ((fresh_name_pi Y3) P) (exists ((P6 pi)) (and (((((strong2129052853vative P6) Q2) A3) Y3) Rel) ((late_transitions P) (((late_BoundR A3) Y3) P6))))))) (=> (forall ((Alpha late_freeRes) (Q2 pi)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (exists ((P6 pi)) (and ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel) ((late_transitions P) ((late_FreeR Alpha) P6)))))) (((strong743114133lation P) Rel) Q)))) (forall ((P (-> produc1462499409ion_pi Bool)) (Prod produc1462499409ion_pi)) (=> (forall ((A3 (-> name noption_pi)) (B3 (-> name noption_pi))) (P ((produc1342893193ion_pi A3) B3))) (P Prod))) (forall ((P pi) (Alpha2 late_freeRes) (P3 pi) (Prop (-> late_freeRes pi Bool))) (=> ((late_transitions (tau P)) ((late_FreeR Alpha2) P3)) (=> (=> (= Alpha2 late_TauR) (=> (= P P3) ((Prop late_TauR) P))) ((Prop Alpha2) P3)))) (forall ((A name) (B name) (P pi) (C name) (D name)) (= (((subs (((output A) B) P)) C) D) (((output (((subst_name A) C) D)) (((subst_name B) C) D)) (((subs P) C) D)))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Name1 name) (Name2 name) (Pi pi)) (not (= (((match Name12) Name22) Pi3) (((mismatch Name1) Name2) Pi)))) (forall ((B name) (A name) (X late_freeRes)) (= ((fresh_785364841reeRes B) ((abs_fu681348580reeRes A) X)) (or ((fresh_1641682979reeRes B) X) (= B A)))) (forall ((A name) (X1 name) (X2 pi)) (= ((fresh_name_pi A) ((res X1) X2)) ((fresh_543891186ion_pi A) ((abs_fun_name_pi X1) X2)))) (forall ((Name3 name) (Name name)) (not (= (late_InputS Name3) (late_BoundOutputS Name)))) (forall ((X2 name) (X1 name) (Y2 name) (Y1 name)) (= (= ((late_OutputR X2) X1) ((late_OutputR Y2) Y1)) (and (= X1 Y1) (= X2 Y2)))) (forall ((Name1 name) (Name2 name) (Pi pi)) (not (= piNil (((mismatch Name1) Name2) Pi)))) (forall ((A name) (X (-> name noption_pi)) (Y name)) (=> ((fresh_453496559i_name A) ((produc540578151i_name X) Y)) ((fresh_name_name A) Y))) (forall ((Rel set_Pr1834926343_pi_pi) (P pi)) (=> (forall ((Q4 pi)) ((member558706512_pi_pi ((product_Pair_pi_pi ((par Q4) piNil)) Q4)) Rel)) (((strong743114133lation ((par P) piNil)) Rel) P))) (forall ((A (-> name noption_pi)) (B produc1141751126_pi_pi) (A2 (-> name noption_pi)) (B2 produc1141751126_pi_pi)) (= (= ((produc1275980869_pi_pi A) B) ((produc1275980869_pi_pi A2) B2)) (and (= B B2) (= A A2)))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Name1 name) (Name2 name) (Pi pi)) (not (= (((output Name12) Name22) Pi3) (((input Name1) Name2) Pi)))) (forall ((P2 produc629157763_pi_pi)) (exists ((X3 (-> name noption_pi)) (Y3 pi)) (= P2 ((produc1820286517_pi_pi X3) Y3)))) (forall ((X32 name) (X1 name) (X2 pi) (Y32 name) (Y1 name) (Y2 pi)) (= (= (((input X32) X1) X2) (((input Y32) Y1) Y2)) (and (= X32 Y32) (= ((abs_fun_name_pi X1) X2) ((abs_fun_name_pi Y1) Y2))))) (forall ((P pi) (Alpha2 late_freeRes) (P3 pi) (Y name)) (=> ((late_transitions P) ((late_FreeR Alpha2) P3)) (=> ((fresh_name_pi Y) P) ((fresh_1641682979reeRes Y) Alpha2)))) (forall ((X name) (Rs late_residual)) (not ((late_transitions ((res X) piNil)) Rs))) (forall ((P pi) (A name) (B name) (P3 pi) (Q pi) (X name) (Q3 pi)) (let ((_let_1 (fresh_name_pi X))) (=> ((late_transitions P) ((late_FreeR ((late_OutputR A) B)) P3)) (=> ((late_transitions Q) (((late_BoundR (late_InputS A)) X) Q3)) (=> (_let_1 P) (=> (_let_1 Q) (=> (not (= X A)) (=> (not (= X B)) (=> (_let_1 P3) ((late_transitions ((par P) Q)) ((late_FreeR late_TauR) ((par P3) (((subs Q3) X) B))))))))))))) _let_10 (forall ((P pi) (A late_subject) (X name) (P3 pi) (Y name)) (let ((_let_1 (res Y))) (let ((_let_2 ((late_BoundR A) X))) (=> ((late_transitions P) (_let_2 P3)) (=> ((fresh_717452603ubject Y) A) (=> (not (= Y X)) (=> ((fresh_name_pi X) P) (=> ((fresh_717452603ubject X) A) ((late_transitions (_let_1 P)) (_let_2 (_let_1 P3))))))))))) (forall ((Pi3 pi) (Pi12 pi) (Pi22 pi)) (not (= (tau Pi3) ((sum Pi12) Pi22)))) (forall ((X name) (A name) (P pi)) (=> (not (= X A)) ((late_transitions (((input A) X) P)) (((late_BoundR (late_InputS A)) X) P)))) ((fresh_717452603ubject y) aa) (forall ((P (-> late_freeRes late_residual Bool)) (Z late_freeRes) (Residual late_residual)) (=> (forall ((Subject2 late_subject) (Name4 name) (Pi4 pi) (Z2 late_freeRes)) (=> ((fresh_1641682979reeRes Name4) Z2) (=> ((fresh_717452603ubject Name4) Subject2) ((P Z2) (((late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 late_freeRes) (Pi4 pi) (Z2 late_freeRes)) ((P Z2) ((late_FreeR FreeRes2) Pi4))) ((P Z) Residual)))) (forall ((B name) (P pi) (A name) (C name)) (let ((_let_1 ((subs P) A))) (=> ((fresh_name_pi B) P) (= (((subs (_let_1 B)) B) C) (_let_1 C))))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (P pi) (C3 name)) (=> (eqvt_pi Rel) (=> (forall ((A3 late_subject) (X3 name) (Q2 pi)) (let ((_let_1 (fresh_name_pi X3))) (=> ((late_transitions Q) (((late_BoundR A3) X3) Q2)) (=> (_let_1 P) (=> (_let_1 Q) (=> ((fresh_717452603ubject X3) A3) (=> ((fresh_name_name X3) C3) (exists ((P6 pi)) (and ((late_transitions P) (((late_BoundR A3) X3) P6)) (((((strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha late_freeRes) (Q2 pi)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (exists ((P6 pi)) (and ((late_transitions P) ((late_FreeR Alpha) P6)) ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel))))) (((strong743114133lation P) Rel) Q))))) (forall ((P pi) (A late_subject) (X name) (P3 pi) (Q pi)) (let ((_let_1 ((late_BoundR A) X))) (let ((_let_2 (fresh_name_pi X))) (=> ((late_transitions P) (_let_1 P3)) (=> (_let_2 P) (=> (_let_2 Q) (=> ((fresh_717452603ubject X) A) ((late_transitions ((par P) Q)) (_let_1 ((par P3) Q)))))))))) (forall ((P pi) (Q pi) (Rs late_residual)) (=> ((late_transitions ((sum P) Q)) Rs) (=> (not ((late_transitions P) Rs)) ((late_transitions Q) Rs)))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi pi)) (not (= (((match Name12) Name22) Pi3) (bang Pi)))) (forall ((P pi) (Q pi) (C name) (D name)) (= (((subs ((par P) Q)) C) D) ((par (((subs P) C) D)) (((subs Q) C) D)))) (forall ((Subject late_subject) (Name3 name) (Pi3 pi) (FreeRes late_freeRes) (Pi pi)) (not (= (((late_BoundR Subject) Name3) Pi3) ((late_FreeR FreeRes) Pi)))) (forall ((Q pi) (A late_subject) (X name) (Q3 pi) (P pi)) (let ((_let_1 (par P))) (let ((_let_2 ((late_BoundR A) X))) (let ((_let_3 (fresh_name_pi X))) (=> ((late_transitions Q) (_let_2 Q3)) (=> (_let_3 P) (=> (_let_3 Q) (=> ((fresh_717452603ubject X) A) ((late_transitions (_let_1 Q)) (_let_2 (_let_1 Q3))))))))))) (forall ((P pi) (A name) (B name) (P3 pi) (Q pi) (X name) (Q3 pi)) (=> ((late_transitions P) ((late_FreeR ((late_OutputR A) B)) P3)) (=> ((late_transitions Q) (((late_BoundR (late_InputS A)) X) Q3)) ((late_transitions ((par P) Q)) ((late_FreeR late_TauR) ((par P3) (((subs Q3) X) B))))))) (forall ((Rel set_Pr1834926343_pi_pi) (Q pi) (P pi) (C3 late_freeRes)) (=> (eqvt_pi Rel) (=> (forall ((A3 late_subject) (X3 name) (Q2 pi)) (let ((_let_1 (fresh_name_pi X3))) (=> ((late_transitions Q) (((late_BoundR A3) X3) Q2)) (=> (_let_1 P) (=> (_let_1 Q) (=> ((fresh_717452603ubject X3) A3) (=> ((fresh_1641682979reeRes X3) C3) (exists ((P6 pi)) (and ((late_transitions P) (((late_BoundR A3) X3) P6)) (((((strong2129052853vative P6) Q2) A3) X3) Rel)))))))))) (=> (forall ((Alpha late_freeRes) (Q2 pi)) (=> ((late_transitions Q) ((late_FreeR Alpha) Q2)) (exists ((P6 pi)) (and ((late_transitions P) ((late_FreeR Alpha) P6)) ((member558706512_pi_pi ((product_Pair_pi_pi P6) Q2)) Rel))))) (((strong743114133lation P) Rel) Q))))) (forall ((X1 name) (X2 pi) (Y1 name) (Y2 pi)) (= (= ((res X1) X2) ((res Y1) Y2)) (= ((abs_fun_name_pi X1) X2) ((abs_fun_name_pi Y1) Y2)))) (forall ((A name) (X (-> name noption_pi)) (Y name)) (=> ((fresh_453496559i_name A) ((produc540578151i_name X) Y)) ((fresh_543891186ion_pi A) X))) (forall ((A pi) (B pi) (A2 pi) (B2 pi)) (= (= ((product_Pair_pi_pi A) B) ((product_Pair_pi_pi A2) B2)) (and (= A A2) (= B B2)))) (forall ((X name) (A name) (Y name) (P pi) (Alpha2 late_freeRes) (P3 pi)) (not ((late_transitions ((res X) (((input A) Y) P))) ((late_FreeR Alpha2) P3)))) (forall ((X name) (P pi) (A name) (B name) (P3 pi)) (not ((late_transitions ((res X) (tau P))) ((late_FreeR ((late_OutputR A) B)) P3)))) (forall ((A name) (P pi) (C name) (B name)) (let ((_let_1 (fresh_name_pi A))) (=> (_let_1 P) (=> (not (= A C)) (_let_1 (((subs P) B) C)))))) (forall ((X2 name) (Y2 name)) (= (= (late_BoundOutputS X2) (late_BoundOutputS Y2)) (= X2 Y2))) (forall ((Pi1 pi) (Pi2 pi) (Name name) (Pi pi)) (not (= ((par Pi1) Pi2) ((res Name) Pi)))) (forall ((A (-> name noption_pi)) (B produc1141751126_pi_pi) (A2 (-> name noption_pi)) (B2 produc1141751126_pi_pi)) (=> (= ((produc1275980869_pi_pi A) B) ((produc1275980869_pi_pi A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((A name) (X late_freeRes) (Y late_freeRes)) (let ((_let_1 (fresh_1641682979reeRes A))) (= ((fresh_493808761reeRes A) ((produc1244821099reeRes X) Y)) (and (_let_1 X) (_let_1 Y))))) (= subst_name (lambda ((A5 name) (B4 name) (C4 name)) (((if_name (= A5 B4)) C4) A5))) (forall ((A name) (X1 pi)) (let ((_let_1 (fresh_name_pi A))) (= (_let_1 (tau X1)) (_let_1 X1)))) (forall ((P pi) (A name) (B name) (P3 pi)) (=> ((late_transitions P) ((late_FreeR ((late_OutputR A) B)) P3)) (=> (not (= A B)) ((late_transitions ((res B) P)) (((late_BoundR (late_BoundOutputS A)) B) P3))))) (forall ((P pi) (Rs late_residual) (X name)) (=> ((late_transitions P) Rs) (=> ((fresh_name_pi X) P) ((fresh_81631222sidual X) Rs)))) ((late_transitions _let_9) (_let_7 pxQ)) (forall ((P (-> late_freeRes pi Bool)) (Z late_freeRes) (Pi3 pi)) (=> (forall ((Z2 late_freeRes)) ((P Z2) piNil)) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) (((output Name13) Name23) Pi4)))) (=> (forall ((Pi4 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) (tau Pi4)))) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 late_freeRes)) (=> ((fresh_1641682979reeRes Name23) Z2) (=> ((fresh_name_name Name23) Name13) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) (((input Name13) Name23) Pi4)))))) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) (((match Name13) Name23) Pi4)))) (=> (forall ((Name13 name) (Name23 name) (Pi4 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) (((mismatch Name13) Name23) Pi4)))) (=> (forall ((Pi13 pi) (Pi23 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi13)) (=> (forall ((Za late_freeRes)) ((P Za) Pi23)) ((P Z2) ((sum Pi13) Pi23))))) (=> (forall ((Pi13 pi) (Pi23 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi13)) (=> (forall ((Za late_freeRes)) ((P Za) Pi23)) ((P Z2) ((par Pi13) Pi23))))) (=> (forall ((Name4 name) (Pi4 pi) (Z2 late_freeRes)) (=> ((fresh_1641682979reeRes Name4) Z2) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) ((res Name4) Pi4))))) (=> (forall ((Pi4 pi) (Z2 late_freeRes)) (=> (forall ((Za late_freeRes)) ((P Za) Pi4)) ((P Z2) (bang Pi4)))) ((P Z) Pi3)))))))))))) (forall ((A name) (B name) (P pi)) (=> (not (= A B)) ((fresh_name_pi A) (((subs P) A) B)))) (forall ((A name) (X pi) (Y pi)) (=> ((fresh_1627595501_pi_pi A) ((product_Pair_pi_pi X) Y)) ((fresh_name_pi A) X))) (forall ((Q pi) (Alpha2 late_freeRes) (Q3 pi) (P pi)) (let ((_let_1 (par P))) (let ((_let_2 (late_FreeR Alpha2))) (=> ((late_transitions Q) (_let_2 Q3)) ((late_transitions (_let_1 Q)) (_let_2 (_let_1 Q3))))))) (forall ((A name) (B name) (P pi) (C name) (D name)) (= (((subs (((match A) B) P)) C) D) (((match (((subst_name A) C) D)) (((subst_name B) C) D)) (((subs P) C) D)))) (forall ((P pi) (Alpha2 late_freeRes) (P3 pi) (Q pi)) (let ((_let_1 (late_FreeR Alpha2))) (=> ((late_transitions P) (_let_1 P3)) ((late_transitions ((par P) Q)) (_let_1 ((par P3) Q)))))) (forall ((P Bool)) (or (= P false) (= P true))) (forall ((Rel set_Pr1834926343_pi_pi) (A name) (B name) (P pi)) (not (((strong743114133lation piNil) Rel) (((output A) B) P)))) (forall ((Q pi) (Rs late_residual) (P pi)) (=> ((late_transitions Q) Rs) ((late_transitions ((sum P) Q)) Rs))) (forall ((X name) (A name) (B name) (P pi) (C name) (Y name) (P3 pi)) (not ((late_transitions ((res X) (((output A) B) P))) (((late_BoundR (late_InputS C)) Y) P3)))) (forall ((A name) (X (-> name noption_pi)) (Y (-> name noption_pi))) (=> ((fresh_225680151ion_pi A) ((produc1342893193ion_pi X) Y)) ((fresh_543891186ion_pi A) X))) (forall ((Pi3 pi) (Name1 name) (Name2 name) (Pi pi)) (not (= (tau Pi3) (((mismatch Name1) Name2) Pi)))) (forall ((A4 set_Pr1834926343_pi_pi)) (= (collec1051790738_pi_pi (lambda ((X4 product_prod_pi_pi)) ((member558706512_pi_pi X4) A4))) A4)) (forall ((P (-> produc1462499409ion_pi Bool)) (P2 produc1462499409ion_pi)) (=> (forall ((A3 (-> name noption_pi)) (B3 (-> name noption_pi))) (P ((produc1342893193ion_pi A3) B3))) (P P2))) _let_6 (forall ((P (-> pi late_residual Bool)) (Z pi) (Residual late_residual)) (=> (forall ((Subject2 late_subject) (Name4 name) (Pi4 pi) (Z2 pi)) (=> ((fresh_name_pi Name4) Z2) (=> ((fresh_717452603ubject Name4) Subject2) ((P Z2) (((late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 late_freeRes) (Pi4 pi) (Z2 pi)) ((P Z2) ((late_FreeR FreeRes2) Pi4))) ((P Z) Residual)))) (forall ((A name) (P pi) (Rs late_residual)) (not ((late_transitions (((mismatch A) A) P)) Rs))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Pi12 pi) (Pi22 pi)) (not (= (((output Name12) Name22) Pi3) ((par Pi12) Pi22)))) (forall ((Y produc629157763_pi_pi)) (not (forall ((A3 (-> name noption_pi)) (B3 pi)) (not (= Y ((produc1820286517_pi_pi A3) B3)))))) (forall ((A name) (B product_prod_pi_pi) (A2 name) (B2 product_prod_pi_pi)) (= (= ((produc235456326_pi_pi A) B) ((produc235456326_pi_pi A2) B2)) (and (= B B2) (= A A2)))) (forall ((B name) (P pi) (A name)) (=> ((fresh_name_pi B) P) (= (((subs ((res A) P)) A) B) ((res B) (((subs P) A) B))))) (forall ((A name) (X pi) (Y pi)) (let ((_let_1 (fresh_name_pi A))) (= ((fresh_1627595501_pi_pi A) ((product_Pair_pi_pi X) Y)) (and (_let_1 X) (_let_1 Y))))) (forall ((X name) (P pi) (A late_subject) (Y name) (P3 pi)) (not ((late_transitions ((res X) (tau P))) (((late_BoundR A) Y) P3)))) (forall ((Pi12 pi) (Pi22 pi)) (not (= piNil ((par Pi12) Pi22)))) (forall ((X11 name) (X12 name) (Y11 name) (Y12 name)) (= (= ((late_OutputR X11) X12) ((late_OutputR Y11) Y12)) (and (= X11 Y11) (= X12 Y12)))) (= strong743114133lation (lambda ((P7 pi) (Rel2 set_Pr1834926343_pi_pi) (Q5 pi)) (and (forall ((A5 late_subject) (X4 name) (Q6 pi)) (=> (and ((fresh_name_pi X4) P7) ((late_transitions Q5) (((late_BoundR A5) X4) Q6))) (exists ((P8 pi)) (and ((late_transitions P7) (((late_BoundR A5) X4) P8)) (((((strong2129052853vative P8) Q6) A5) X4) Rel2))))) (forall ((Alpha3 late_freeRes) (Q6 pi)) (=> ((late_transitions Q5) ((late_FreeR Alpha3) Q6)) (exists ((P8 pi)) (and ((member558706512_pi_pi ((product_Pair_pi_pi P8) Q6)) Rel2) ((late_transitions P7) ((late_FreeR Alpha3) P8))))))))) (_let_4 p2) (forall ((P pi) (C name) (D name)) (= (((subs (bang P)) C) D) (bang (((subs P) C) D)))) (forall ((A name) (B name) (P pi) (Rs late_residual)) (=> ((late_transitions (((input A) B) P)) Rs) (not (forall ((X3 name) (A3 name) (P5 pi)) (=> (and (= A A3) (= ((abs_fun_name_pi B) P) ((abs_fun_name_pi X3) P5))) (=> (= Rs (((late_BoundR (late_InputS A3)) X3) P5)) (= X3 A3))))))) (forall ((A name) (B name) (P pi) (P3 pi)) (not ((late_transitions (((output A) B) P)) ((late_FreeR late_TauR) P3)))) (_let_3 _let_2) (forall ((X name) (B name) (C name) (A name) (P pi)) (=> (not (= X B)) (=> (not (= X C)) (= (((subs (((input A) X) P)) B) C) (((input (((subst_name A) B) C)) X) (((subs P) B) C)))))) (forall ((A name) (X name) (Y pi)) (= ((fresh_93646139ame_pi A) ((product_Pair_name_pi X) Y)) (and ((fresh_name_name A) X) ((fresh_name_pi A) Y)))) (forall ((B name) (A name) (X pi)) (= ((fresh_543891186ion_pi B) ((abs_fun_name_pi A) X)) (or ((fresh_name_pi B) X) (= B A)))) (forall ((P pi) (A name) (B name) (P3 pi)) (not ((late_transitions (tau P)) ((late_FreeR ((late_OutputR A) B)) P3)))) (forall ((Name1 name) (Name2 name) (Pi pi)) (not (= piNil (((match Name1) Name2) Pi)))) (forall ((C name) (D name)) (= (((subs piNil) C) D) piNil)) (forall ((P pi) (Rs late_residual)) (=> ((late_transitions (tau P)) Rs) (not (forall ((P5 pi)) (=> (= (tau P) (tau P5)) (not (= Rs ((late_FreeR late_TauR) P5)))))))) (forall ((P pi) (Alpha2 late_freeRes) (P3 pi) (Y name)) (let ((_let_1 (res Y))) (let ((_let_2 (late_FreeR Alpha2))) (=> ((late_transitions P) (_let_2 P3)) (=> ((fresh_1641682979reeRes Y) Alpha2) ((late_transitions (_let_1 P)) (_let_2 (_let_1 P3)))))))) (forall ((Pi1 pi) (Pi2 pi) (Name name) (Pi pi)) (not (= ((sum Pi1) Pi2) ((res Name) Pi)))) (forall ((P (-> produc405342261i_name Bool)) (P2 produc405342261i_name)) (=> (forall ((A3 (-> name noption_pi)) (B3 name)) (P ((produc540578151i_name A3) B3))) (P P2))) (forall ((A name) (B name) (P pi) (Rs late_residual)) (=> ((late_transitions (((mismatch A) B) P)) Rs) (not (forall ((P5 pi) (A3 name) (B3 name)) (=> (and (= P P5) (= B B3) (= A A3)) (=> ((late_transitions P5) Rs) (= A3 B3))))))) (forall ((Name12 name) (Name22 name) (Pi3 pi) (Name name) (Pi pi)) (not (= (((output Name12) Name22) Pi3) ((res Name) Pi)))) (forall ((P pi) (A name)) (= (((subs P) A) A) P)) (forall ((P (-> produc1141751126_pi_pi late_residual Bool)) (Z produc1141751126_pi_pi) (Residual late_residual)) (=> (forall ((Subject2 late_subject) (Name4 name) (Pi4 pi) (Z2 produc1141751126_pi_pi)) (=> ((fresh_1376661020_pi_pi Name4) Z2) (=> ((fresh_717452603ubject Name4) Subject2) ((P Z2) (((late_BoundR Subject2) Name4) Pi4))))) (=> (forall ((FreeRes2 late_freeRes) (Pi4 pi) (Z2 produc1141751126_pi_pi)) ((P Z2) ((late_FreeR FreeRes2) Pi4))) ((P Z) Residual)))) (forall ((A name) (X (-> name noption_pi)) (Y (-> name noption_pi))) (=> ((fresh_225680151ion_pi A) ((produc1342893193ion_pi X) Y)) ((fresh_543891186ion_pi A) Y))) (forall ((A name) (X2 name) (X1 name)) (let ((_let_1 (fresh_name_name A))) (= ((fresh_1641682979reeRes A) ((late_OutputR X2) X1)) (and (_let_1 X1) (_let_1 X2))))) (forall ((Pi3 pi) (Name1 name) (Name2 name) (Pi pi)) (not (= (tau Pi3) (((match Name1) Name2) Pi)))) (forall ((A name) (X name) (Y product_prod_pi_pi)) (= ((fresh_1376661020_pi_pi A) ((produc235456326_pi_pi X) Y)) (and ((fresh_name_name A) X) ((fresh_1627595501_pi_pi A) Y)))) (forall ((P pi) (Q pi) (A late_subject) (X name) (PQ pi) (Prop (-> pi Bool))) (let ((_let_1 (fresh_name_pi X))) (=> ((late_transitions ((par P) Q)) (((late_BoundR A) X) PQ)) (=> (_let_1 P) (=> (_let_1 Q) (=> (forall ((P4 pi)) (=> ((late_transitions P) (((late_BoundR A) X) P4)) (Prop ((par P4) Q)))) (=> (forall ((Q2 pi)) (=> ((late_transitions Q) (((late_BoundR A) X) Q2)) (Prop ((par P) Q2)))) (Prop PQ)))))))) (forall ((Pi3 pi) (Pi12 pi) (Pi22 pi)) (not (= (tau Pi3) ((par Pi12) Pi22)))) (forall ((Pi3 pi) (Pi pi)) (not (= (tau Pi3) (bang Pi)))) (not false))))))))))))))))))))))))))))))))))))))))))))))))
0.72/0.93	)
0.72/0.93	% SZS output end Proof for theBenchmark
0.72/0.93	EOF