TSTP Solution File: ITP106^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP106^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 : 600s
% DateTime : Sun Jul 17 00:29:07 EDT 2022
% Result : Theorem 80.39s 79.93s
% Output : Proof 80.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP106^1 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 3 23:48:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 80.39/79.93 % SZS status Theorem
% 80.39/79.93 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 80.39/79.93 % Inferences: 170
% 80.39/79.93 % SZS output start Proof
% 80.39/79.93 thf(ty_a, type, a : $tType).
% 80.39/79.93 thf(ty_partia1993116613t_unit, type, partia1993116613t_unit : $tType).
% 80.39/79.93 thf(ty_product_prod_a_a, type, product_prod_a_a : $tType).
% 80.39/79.93 thf(ty_partia1833973666xt_a_b, type, partia1833973666xt_a_b : $tType).
% 80.39/79.93 thf(ty_set_Product_prod_a_a, type, set_Product_prod_a_a : $tType).
% 80.39/79.93 thf(ty_set_a, type, set_a : $tType).
% 80.39/79.93 thf(ty_member_a, type, member_a : (a>set_a>$o)).
% 80.39/79.93 thf(ty_r4, type, r4 : a).
% 80.39/79.93 thf(ty_partia206007992t_unit, type, partia206007992t_unit : (partia1993116613t_unit>set_Product_prod_a_a)).
% 80.39/79.93 thf(ty_one_a_ring_ext_a_b, type, one_a_ring_ext_a_b : (partia1833973666xt_a_b>a)).
% 80.39/79.93 thf(ty_eigen__2, type, eigen__2 : a).
% 80.39/79.93 thf(ty_r3, type, r3 : a).
% 80.39/79.93 thf(ty_member449909584od_a_a, type, member449909584od_a_a : (product_prod_a_a>set_Product_prod_a_a>$o)).
% 80.39/79.93 thf(ty_s, type, s : a).
% 80.39/79.93 thf(ty_add_a_b, type, add_a_b : (partia1833973666xt_a_b>a>a>a)).
% 80.39/79.93 thf(ty_eigen__1, type, eigen__1 : a).
% 80.39/79.93 thf(ty_eigen__0, type, eigen__0 : a).
% 80.39/79.93 thf(ty_mult_a_ring_ext_a_b, type, mult_a_ring_ext_a_b : (partia1833973666xt_a_b>a>a>a)).
% 80.39/79.93 thf(ty_r, type, r : partia1833973666xt_a_b).
% 80.39/79.93 thf(ty_partia1066395285xt_a_b, type, partia1066395285xt_a_b : (partia1833973666xt_a_b>set_a)).
% 80.39/79.93 thf(ty_group_a_ring_ext_a_b, type, group_a_ring_ext_a_b : (partia1833973666xt_a_b>$o)).
% 80.39/79.93 thf(ty_s3, type, s3 : a).
% 80.39/79.93 thf(ty_field_a_b, type, field_a_b : (partia1833973666xt_a_b>$o)).
% 80.39/79.93 thf(ty_zero_a_b, type, zero_a_b : (partia1833973666xt_a_b>a)).
% 80.39/79.93 thf(ty_r2, type, r2 : a).
% 80.39/79.93 thf(ty_s2, type, s2 : a).
% 80.39/79.93 thf(ty_rel, type, rel : partia1993116613t_unit).
% 80.39/79.93 thf(ty_product_Pair_a_a, type, product_Pair_a_a : (a>a>product_prod_a_a)).
% 80.39/79.93 thf(sP1,plain,sP1 <=> (![X1:a]:(![X2:a]:(![X3:a]:(((member449909584od_a_a @ ((product_Pair_a_a @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4)) @ X1)) @ (partia206007992t_unit @ rel)) => (((member449909584od_a_a @ ((product_Pair_a_a @ X2) @ X3)) @ (partia206007992t_unit @ rel)) => ((member449909584od_a_a @ ((product_Pair_a_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ X3) @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4))) @ (((mult_a_ring_ext_a_b @ r) @ X1) @ X2))) @ (((mult_a_ring_ext_a_b @ r) @ X1) @ X3))) @ (partia206007992t_unit @ rel))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 80.39/79.93 thf(sP2,plain,sP2 <=> (![X1:a]:(![X2:a]:(![X3:a]:(![X4:a]:(((member449909584od_a_a @ ((product_Pair_a_a @ X1) @ X2)) @ (partia206007992t_unit @ rel)) => (((member449909584od_a_a @ ((product_Pair_a_a @ X3) @ X4)) @ (partia206007992t_unit @ rel)) => ((member449909584od_a_a @ ((product_Pair_a_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ X4) @ X1)) @ (((mult_a_ring_ext_a_b @ r) @ X2) @ X3))) @ (((mult_a_ring_ext_a_b @ r) @ X2) @ X4))) @ (partia206007992t_unit @ rel)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 80.39/79.93 thf(sP3,plain,sP3 <=> ((member449909584od_a_a @ ((product_Pair_a_a @ (((mult_a_ring_ext_a_b @ r) @ r3) @ r4)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3))) @ (partia206007992t_unit @ rel)),introduced(definition,[new_symbols(definition,[sP3])])).
% 80.39/79.93 thf(sP4,plain,sP4 <=> ((member449909584od_a_a @ ((product_Pair_a_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ r3) @ r4)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)))) @ (partia206007992t_unit @ rel)),introduced(definition,[new_symbols(definition,[sP4])])).
% 80.39/79.93 thf(sP5,plain,sP5 <=> (((member449909584od_a_a @ ((product_Pair_a_a @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4)) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3))) @ (partia206007992t_unit @ rel)) => (sP3 => sP4)),introduced(definition,[new_symbols(definition,[sP5])])).
% 80.39/79.93 thf(sP6,plain,sP6 <=> (![X1:a]:(![X2:a]:(((member449909584od_a_a @ ((product_Pair_a_a @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4)) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3))) @ (partia206007992t_unit @ rel)) => (((member449909584od_a_a @ ((product_Pair_a_a @ X1) @ X2)) @ (partia206007992t_unit @ rel)) => ((member449909584od_a_a @ ((product_Pair_a_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ X2) @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3)) @ X1))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3)) @ X2))) @ (partia206007992t_unit @ rel)))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 80.39/79.93 thf(sP7,plain,sP7 <=> ((member449909584od_a_a @ ((product_Pair_a_a @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4)) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3))) @ (partia206007992t_unit @ rel)),introduced(definition,[new_symbols(definition,[sP7])])).
% 80.39/79.93 thf(sP8,plain,sP8 <=> (sP3 => sP4),introduced(definition,[new_symbols(definition,[sP8])])).
% 80.39/79.93 thf(sP9,plain,sP9 <=> (![X1:a]:(sP7 => (((member449909584od_a_a @ ((product_Pair_a_a @ (((mult_a_ring_ext_a_b @ r) @ r3) @ r4)) @ X1)) @ (partia206007992t_unit @ rel)) => ((member449909584od_a_a @ ((product_Pair_a_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ X1) @ (((mult_a_ring_ext_a_b @ r) @ r2) @ r4))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ r3) @ r4)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s) @ s3)) @ X1))) @ (partia206007992t_unit @ rel))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 80.39/79.93 thf(conj_0,conjecture,sP4).
% 80.39/79.93 thf(h0,negated_conjecture,(~(sP4)),inference(assume_negation,[status(cth)],[conj_0])).
% 80.39/79.93 thf(h1,assumption,(~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~((![X2:a]:(((member_a @ X2) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X2) @ X1) = (one_a_ring_ext_a_b @ r)))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h2,assumption,(group_a_ring_ext_a_b @ r),introduced(assumption,[])).
% 80.39/79.93 thf(h3,assumption,(~((((member_a @ eigen__0) @ (partia1066395285xt_a_b @ r)) => (~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ eigen__0) = (one_a_ring_ext_a_b @ r))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h4,assumption,((member_a @ eigen__0) @ (partia1066395285xt_a_b @ r)),introduced(assumption,[])).
% 80.39/79.93 thf(h5,assumption,(![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ eigen__0) = (one_a_ring_ext_a_b @ r)))))),introduced(assumption,[])).
% 80.39/79.93 thf(h6,assumption,((zero_a_b @ r) = (one_a_ring_ext_a_b @ r)),introduced(assumption,[])).
% 80.39/79.93 thf(h7,assumption,((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => ((~((X1 = (zero_a_b @ r)))) => (~((![X2:a]:(((member_a @ X2) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ X2) = (one_a_ring_ext_a_b @ r))))))))))) => (field_a_b @ r)),introduced(assumption,[])).
% 80.39/79.93 thf(ax776, axiom, (~(p197)|p329), file('<stdin>', ax776)).
% 80.39/79.93 thf(ax366, axiom, (~(p29)|p737), file('<stdin>', ax366)).
% 80.39/79.93 thf(pax77, axiom, (p77=>fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)), file('<stdin>', pax77)).
% 80.39/79.93 thf(pax8, axiom, (p8=>(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fs) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))), file('<stdin>', pax8)).
% 80.39/79.93 thf(ax775, axiom, (~(p329)|p330), file('<stdin>', ax775)).
% 80.39/79.93 thf(ax917, axiom, p197, file('<stdin>', ax917)).
% 80.39/79.93 thf(ax319, axiom, (~(p31)|p784), file('<stdin>', ax319)).
% 80.39/79.93 thf(pax63, axiom, (p63=>(fzero_a_b @ fr)=(fone_a_ring_ext_a_b @ fr)), file('<stdin>', pax63)).
% 80.39/79.93 thf(pax737, axiom, (p737=>(fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)=>~(![X1:a]:(fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)=>~((fadd_a_b @ fr @ f__0 @ X1)=(fzero_a_b @ fr)))))), file('<stdin>', pax737)).
% 80.39/79.93 thf(ax1084, axiom, p29, file('<stdin>', ax1084)).
% 80.39/79.93 thf(ax1036, axiom, p77, file('<stdin>', ax1036)).
% 80.39/79.93 thf(pax14, axiom, (p14=>(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))), file('<stdin>', pax14)).
% 80.39/79.93 thf(ax1105, axiom, p8, file('<stdin>', ax1105)).
% 80.39/79.93 thf(ax774, axiom, (~(p330)|~(p20)|p328), file('<stdin>', ax774)).
% 80.39/79.93 thf(pax784, axiom, (p784=>(fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))) @ (fpartia1066395285xt_a_b @ fr)=>~(![X1:a]:(fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)=>~((fadd_a_b @ fr @ X1 @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))))=(fzero_a_b @ fr)))))), file('<stdin>', pax784)).
% 80.39/79.93 thf(ax1082, axiom, p31, file('<stdin>', ax1082)).
% 80.39/79.93 thf(ax1050, axiom, p63, file('<stdin>', ax1050)).
% 80.39/79.93 thf(ax47, axiom, (~(p736)|~(p37)|~(p1056)), file('<stdin>', ax47)).
% 80.39/79.93 thf(ax367, axiom, (~(p29)|p736), file('<stdin>', ax367)).
% 80.39/79.93 thf(pax328, axiom, (p328=>(fzero_a_b @ fr)=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))), file('<stdin>', pax328)).
% 80.39/79.93 thf(ax1099, axiom, p14, file('<stdin>', ax1099)).
% 80.39/79.93 thf(ax1093, axiom, p20, file('<stdin>', ax1093)).
% 80.39/79.93 thf(pax37, axiom, (p37=>fmember_a @ (fzero_a_b @ fr) @ (fpartia1066395285xt_a_b @ fr)), file('<stdin>', pax37)).
% 80.39/79.93 thf(ax1076, axiom, p37, file('<stdin>', ax1076)).
% 80.39/79.93 thf(pax53, axiom, (p53=>(fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))))=(fzero_a_b @ fr)), file('<stdin>', pax53)).
% 80.39/79.93 thf(nax1056, axiom, (p1056<=![X1:a]:(fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)=>~((fadd_a_b @ fr @ (fzero_a_b @ fr) @ X1)=(fzero_a_b @ fr)))), file('<stdin>', nax1056)).
% 80.39/79.93 thf(ax1060, axiom, p53, file('<stdin>', ax1060)).
% 80.39/79.93 thf(pax40, axiom, (p40=>![X27:a]:(fmember_a @ X27 @ (fpartia1066395285xt_a_b @ fr)=>(fadd_a_b @ fr @ X27 @ (fzero_a_b @ fr))=(X27))), file('<stdin>', pax40)).
% 80.39/79.93 thf(pax76, axiom, (p76=>![X14:a]:(fmember_a @ X14 @ (fpartia1066395285xt_a_b @ fr)=>~((fmult_a_ring_ext_a_b @ fr @ X14 @ f__0)=(fone_a_ring_ext_a_b @ fr)))), file('<stdin>', pax76)).
% 80.39/79.93 thf(ax636, axiom, (~(p23)|p467), file('<stdin>', ax636)).
% 80.39/79.93 thf(ax1073, axiom, p40, file('<stdin>', ax1073)).
% 80.39/79.93 thf(pax41, axiom, (p41=>![X27:a]:(fmember_a @ X27 @ (fpartia1066395285xt_a_b @ fr)=>(fadd_a_b @ fr @ (fzero_a_b @ fr) @ X27)=(X27))), file('<stdin>', pax41)).
% 80.39/79.93 thf(ax1037, axiom, p76, file('<stdin>', ax1037)).
% 80.39/79.93 thf(pax467, axiom, (p467=>![X1:a]:(fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)=>(fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)=>(fmult_a_ring_ext_a_b @ fr @ f__0 @ X1)=(fmult_a_ring_ext_a_b @ fr @ X1 @ f__0)))), file('<stdin>', pax467)).
% 80.39/79.93 thf(ax1090, axiom, p23, file('<stdin>', ax1090)).
% 80.39/79.93 thf(ax1072, axiom, p41, file('<stdin>', ax1072)).
% 80.39/79.93 thf(pax48, axiom, (p48=>![X27:a]:(fmember_a @ X27 @ (fpartia1066395285xt_a_b @ fr)=>(fmult_a_ring_ext_a_b @ fr @ X27 @ (fzero_a_b @ fr))=(fzero_a_b @ fr))), file('<stdin>', pax48)).
% 80.39/79.93 thf(ax1065, axiom, p48, file('<stdin>', ax1065)).
% 80.39/79.93 thf(c_0_38, plain, (~p197|p329), inference(fof_simplification,[status(thm)],[ax776])).
% 80.39/79.93 thf(c_0_39, plain, (~p29|p737), inference(fof_simplification,[status(thm)],[ax366])).
% 80.39/79.93 thf(c_0_40, plain, (~p77|fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax77])).
% 80.39/79.93 thf(c_0_41, plain, (~p8|(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fs) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))), inference(fof_nnf,[status(thm)],[pax8])).
% 80.39/79.93 thf(c_0_42, plain, (~p329|p330), inference(fof_simplification,[status(thm)],[ax775])).
% 80.39/79.93 thf(c_0_43, plain, (p329|~p197), inference(split_conjunct,[status(thm)],[c_0_38])).
% 80.39/79.93 thf(c_0_44, plain, p197, inference(split_conjunct,[status(thm)],[ax917])).
% 80.39/79.93 thf(c_0_45, plain, (~p31|p784), inference(fof_simplification,[status(thm)],[ax319])).
% 80.39/79.93 thf(c_0_46, plain, (~p63|(fzero_a_b @ fr)=(fone_a_ring_ext_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax63])).
% 80.39/79.93 thf(c_0_47, plain, ((fmember_a @ esk457_0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)|~p737)&((fadd_a_b @ fr @ f__0 @ esk457_0)=(fzero_a_b @ fr)|~fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)|~p737)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax737])])])])])).
% 80.39/79.93 thf(c_0_48, plain, (p737|~p29), inference(split_conjunct,[status(thm)],[c_0_39])).
% 80.39/79.93 thf(c_0_49, plain, p29, inference(split_conjunct,[status(thm)],[ax1084])).
% 80.39/79.93 thf(c_0_50, plain, (fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)|~p77), inference(split_conjunct,[status(thm)],[c_0_40])).
% 80.39/79.93 thf(c_0_51, plain, p77, inference(split_conjunct,[status(thm)],[ax1036])).
% 80.39/79.93 thf(c_0_52, plain, (~p14|(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))), inference(fof_nnf,[status(thm)],[pax14])).
% 80.39/79.93 thf(c_0_53, plain, ((fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fs) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))|~p8), inference(split_conjunct,[status(thm)],[c_0_41])).
% 80.39/79.93 thf(c_0_54, plain, p8, inference(split_conjunct,[status(thm)],[ax1105])).
% 80.39/79.93 thf(c_0_55, plain, (~p330|~p20|p328), inference(fof_simplification,[status(thm)],[ax774])).
% 80.39/79.93 thf(c_0_56, plain, (p330|~p329), inference(split_conjunct,[status(thm)],[c_0_42])).
% 80.39/79.93 thf(c_0_57, plain, p329, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 80.39/79.93 thf(c_0_58, plain, ((fmember_a @ esk410_0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))) @ (fpartia1066395285xt_a_b @ fr)|~p784)&((fadd_a_b @ fr @ esk410_0 @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))))=(fzero_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))) @ (fpartia1066395285xt_a_b @ fr)|~p784)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax784])])])])])).
% 80.39/79.93 thf(c_0_59, plain, (p784|~p31), inference(split_conjunct,[status(thm)],[c_0_45])).
% 80.39/79.93 thf(c_0_60, plain, p31, inference(split_conjunct,[status(thm)],[ax1082])).
% 80.39/79.93 thf(c_0_61, plain, ((fzero_a_b @ fr)=(fone_a_ring_ext_a_b @ fr)|~p63), inference(split_conjunct,[status(thm)],[c_0_46])).
% 80.39/79.93 thf(c_0_62, plain, p63, inference(split_conjunct,[status(thm)],[ax1050])).
% 80.39/79.93 thf(c_0_63, plain, ((fadd_a_b @ fr @ f__0 @ esk457_0)=(fzero_a_b @ fr)|~fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)|~p737), inference(split_conjunct,[status(thm)],[c_0_47])).
% 80.39/79.93 thf(c_0_64, plain, p737, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49])])).
% 80.39/79.93 thf(c_0_65, plain, fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])).
% 80.39/79.93 thf(c_0_66, plain, (~p736|~p37|~p1056), inference(fof_simplification,[status(thm)],[ax47])).
% 80.39/79.93 thf(c_0_67, plain, (~p29|p736), inference(fof_simplification,[status(thm)],[ax367])).
% 80.39/79.93 thf(c_0_68, plain, (~p328|(fzero_a_b @ fr)=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))), inference(fof_nnf,[status(thm)],[pax328])).
% 80.39/79.93 thf(c_0_69, plain, ((fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))|~p14), inference(split_conjunct,[status(thm)],[c_0_52])).
% 80.39/79.93 thf(c_0_70, plain, (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fs) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])).
% 80.39/79.93 thf(c_0_71, plain, p14, inference(split_conjunct,[status(thm)],[ax1099])).
% 80.39/79.93 thf(c_0_72, plain, (p328|~p330|~p20), inference(split_conjunct,[status(thm)],[c_0_55])).
% 80.39/79.93 thf(c_0_73, plain, p20, inference(split_conjunct,[status(thm)],[ax1093])).
% 80.39/79.93 thf(c_0_74, plain, p330, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 80.39/79.93 thf(c_0_75, plain, (~p37|fmember_a @ (fzero_a_b @ fr) @ (fpartia1066395285xt_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax37])).
% 80.39/79.93 thf(c_0_76, plain, (fmember_a @ esk410_0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))) @ (fpartia1066395285xt_a_b @ fr)|~p784), inference(split_conjunct,[status(thm)],[c_0_58])).
% 80.39/79.93 thf(c_0_77, plain, p784, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])).
% 80.39/79.93 thf(c_0_78, plain, (fone_a_ring_ext_a_b @ fr)=(fzero_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])])).
% 80.39/79.93 thf(c_0_79, plain, (fzero_a_b @ fr)=(fadd_a_b @ fr @ f__0 @ esk457_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64]), c_0_65])])).
% 80.39/79.93 thf(c_0_80, plain, (~p736|~p37|~p1056), inference(split_conjunct,[status(thm)],[c_0_66])).
% 80.39/79.93 thf(c_0_81, plain, p37, inference(split_conjunct,[status(thm)],[ax1076])).
% 80.39/79.93 thf(c_0_82, plain, (p736|~p29), inference(split_conjunct,[status(thm)],[c_0_67])).
% 80.39/79.93 thf(c_0_83, plain, (~p53|(fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))))=(fzero_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax53])).
% 80.39/79.93 thf(c_0_84, plain, ((fzero_a_b @ fr)=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))|~p328), inference(split_conjunct,[status(thm)],[c_0_68])).
% 80.39/79.93 thf(c_0_85, plain, (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fs) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70]), c_0_71])])).
% 80.39/79.93 thf(c_0_86, plain, p328, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_73]), c_0_74])])).
% 80.39/79.93 thf(c_0_87, plain, (fmember_a @ (fzero_a_b @ fr) @ (fpartia1066395285xt_a_b @ fr)|~p37), inference(split_conjunct,[status(thm)],[c_0_75])).
% 80.39/79.93 thf(c_0_88, plain, (fmember_a @ esk410_0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fs) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))) @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_77]), c_0_78]), c_0_79]), c_0_70])])).
% 80.39/79.93 thf(c_0_89, plain, ((fmember_a @ esk49_0 @ (fpartia1066395285xt_a_b @ fr)|p1056)&((fadd_a_b @ fr @ (fzero_a_b @ fr) @ esk49_0)=(fzero_a_b @ fr)|p1056)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1056])])])])])).
% 80.39/79.93 thf(c_0_90, plain, (~p736|~p1056), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 80.39/79.93 thf(c_0_91, plain, p736, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82, c_0_49])])).
% 80.39/79.93 thf(c_0_92, plain, ((fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4))))))=(fzero_a_b @ fr)|~p53), inference(split_conjunct,[status(thm)],[c_0_83])).
% 80.39/79.93 thf(c_0_93, plain, (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)))=(fadd_a_b @ fr @ f__0 @ esk457_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_70]), c_0_85]), c_0_79]), c_0_86])])).
% 80.39/79.93 thf(c_0_94, plain, p53, inference(split_conjunct,[status(thm)],[ax1060])).
% 80.39/79.93 thf(c_0_95, plain, fmember_a @ (fzero_a_b @ fr) @ (fpartia1066395285xt_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_81])])).
% 80.39/79.93 thf(c_0_96, plain, ![X3198:a]:(~p40|(~fmember_a @ X3198 @ (fpartia1066395285xt_a_b @ fr)|(fadd_a_b @ fr @ X3198 @ (fzero_a_b @ fr))=(X3198))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax40])])])).
% 80.39/79.93 thf(c_0_97, plain, (fmember_a @ esk410_0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)))) @ (fpartia1066395285xt_a_b @ fr)), inference(rw,[status(thm)],[c_0_88, c_0_85])).
% 80.39/79.93 thf(c_0_98, plain, ![X3050:a]:(~p76|(~fmember_a @ X3050 @ (fpartia1066395285xt_a_b @ fr)|(fmult_a_ring_ext_a_b @ fr @ X3050 @ f__0)!=(fone_a_ring_ext_a_b @ fr))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax76])])])])).
% 80.39/79.93 thf(c_0_99, plain, (~p23|p467), inference(fof_simplification,[status(thm)],[ax636])).
% 80.39/79.93 thf(c_0_100, plain, ((fadd_a_b @ fr @ (fzero_a_b @ fr) @ esk49_0)=(fzero_a_b @ fr)|p1056), inference(split_conjunct,[status(thm)],[c_0_89])).
% 80.39/79.93 thf(c_0_101, plain, ~p1056, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_91])])).
% 80.39/79.93 thf(c_0_102, plain, ((fadd_a_b @ fr @ esk410_0 @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))))=(fzero_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fone_a_ring_ext_a_b @ fr) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3)) @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs @ fr3)) @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs2) @ fs3) @ (fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr2 @ fr4)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ fr3 @ fr4)))))) @ (fpartia1066395285xt_a_b @ fr)|~p784), inference(split_conjunct,[status(thm)],[c_0_58])).
% 80.39/79.93 thf(c_0_103, plain, (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ (fadd_a_b @ fr @ f__0 @ esk457_0))=(fadd_a_b @ fr @ f__0 @ esk457_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_78]), c_0_79]), c_0_70]), c_0_85]), c_0_93]), c_0_79]), c_0_94])])).
% 80.39/79.93 thf(c_0_104, plain, fmember_a @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ (fpartia1066395285xt_a_b @ fr), inference(rw,[status(thm)],[c_0_95, c_0_79])).
% 80.39/79.93 thf(c_0_105, plain, ![X1:a]:((fadd_a_b @ fr @ X1 @ (fzero_a_b @ fr))=(X1)|~p40|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_96])).
% 80.39/79.93 thf(c_0_106, plain, p40, inference(split_conjunct,[status(thm)],[ax1073])).
% 80.39/79.93 thf(c_0_107, plain, (fmember_a @ esk410_0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ (fadd_a_b @ fr @ f__0 @ esk457_0)) @ (fpartia1066395285xt_a_b @ fr)), inference(rw,[status(thm)],[c_0_97, c_0_93])).
% 80.39/79.93 thf(c_0_108, plain, ![X3196:a]:(~p41|(~fmember_a @ X3196 @ (fpartia1066395285xt_a_b @ fr)|(fadd_a_b @ fr @ (fzero_a_b @ fr) @ X3196)=(X3196))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax41])])])).
% 80.39/79.93 thf(c_0_109, plain, ![X1:a]:(~p76|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)|(fmult_a_ring_ext_a_b @ fr @ X1 @ f__0)!=(fone_a_ring_ext_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_98])).
% 80.39/79.93 thf(c_0_110, plain, p76, inference(split_conjunct,[status(thm)],[ax1037])).
% 80.39/79.93 thf(c_0_111, plain, ![X1840:a]:(~p467|(~fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)|(~fmember_a @ X1840 @ (fpartia1066395285xt_a_b @ fr)|(fmult_a_ring_ext_a_b @ fr @ f__0 @ X1840)=(fmult_a_ring_ext_a_b @ fr @ X1840 @ f__0)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax467])])])).
% 80.39/79.93 thf(c_0_112, plain, (p467|~p23), inference(split_conjunct,[status(thm)],[c_0_99])).
% 80.39/79.93 thf(c_0_113, plain, p23, inference(split_conjunct,[status(thm)],[ax1090])).
% 80.39/79.93 thf(c_0_114, plain, (fadd_a_b @ fr @ (fzero_a_b @ fr) @ esk49_0)=(fzero_a_b @ fr), inference(sr,[status(thm)],[c_0_100, c_0_101])).
% 80.39/79.93 thf(c_0_115, plain, (fadd_a_b @ fr @ esk410_0 @ (fadd_a_b @ fr @ f__0 @ esk457_0))=(fadd_a_b @ fr @ f__0 @ esk457_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102, c_0_78]), c_0_79]), c_0_70]), c_0_85]), c_0_93]), c_0_103]), c_0_79]), c_0_77]), c_0_78]), c_0_79]), c_0_70]), c_0_85]), c_0_93]), c_0_103]), c_0_104])])).
% 80.39/79.93 thf(c_0_116, plain, ![X1:a]:((fadd_a_b @ fr @ X1 @ (fadd_a_b @ fr @ f__0 @ esk457_0))=(X1)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105, c_0_79]), c_0_106])])).
% 80.39/79.93 thf(c_0_117, plain, fmember_a @ esk410_0 @ (fpartia1066395285xt_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_103]), c_0_104])])).
% 80.39/79.93 thf(c_0_118, plain, ![X1:a]:((fadd_a_b @ fr @ (fzero_a_b @ fr) @ X1)=(X1)|~p41|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_108])).
% 80.39/79.93 thf(c_0_119, plain, p41, inference(split_conjunct,[status(thm)],[ax1072])).
% 80.39/79.93 thf(c_0_120, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ X1 @ f__0)!=(fzero_a_b @ fr)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_78]), c_0_110])])).
% 80.39/79.93 thf(c_0_121, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ f__0 @ X1)=(fmult_a_ring_ext_a_b @ fr @ X1 @ f__0)|~p467|~fmember_a @ f__0 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_111])).
% 80.39/79.93 thf(c_0_122, plain, p467, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112, c_0_113])])).
% 80.39/79.93 thf(c_0_123, plain, ![X3194:a]:(~p48|(~fmember_a @ X3194 @ (fpartia1066395285xt_a_b @ fr)|(fmult_a_ring_ext_a_b @ fr @ X3194 @ (fzero_a_b @ fr))=(fzero_a_b @ fr))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax48])])])).
% 80.39/79.93 thf(c_0_124, plain, (fadd_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ esk49_0)=(fadd_a_b @ fr @ f__0 @ esk457_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114, c_0_79]), c_0_79])).
% 80.39/79.93 thf(c_0_125, plain, (fadd_a_b @ fr @ f__0 @ esk457_0)=(esk410_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_117])])).
% 80.39/79.93 thf(c_0_126, plain, ![X1:a]:((fadd_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ X1)=(X1)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118, c_0_79]), c_0_119])])).
% 80.39/79.93 thf(c_0_127, plain, (fmember_a @ esk49_0 @ (fpartia1066395285xt_a_b @ fr)|p1056), inference(split_conjunct,[status(thm)],[c_0_89])).
% 80.39/79.93 thf(c_0_128, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ X1 @ f__0)!=(fadd_a_b @ fr @ f__0 @ esk457_0)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(rw,[status(thm)],[c_0_120, c_0_79])).
% 80.39/79.93 thf(c_0_129, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ f__0 @ X1)=(fmult_a_ring_ext_a_b @ fr @ X1 @ f__0)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_121, c_0_122]), c_0_65])])).
% 80.39/79.93 thf(c_0_130, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ X1 @ (fzero_a_b @ fr))=(fzero_a_b @ fr)|~p48|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_123])).
% 80.39/79.93 thf(c_0_131, plain, p48, inference(split_conjunct,[status(thm)],[ax1065])).
% 80.39/79.93 thf(c_0_132, plain, (fadd_a_b @ fr @ esk410_0 @ esk49_0)=(esk410_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124, c_0_125]), c_0_125])).
% 80.39/79.93 thf(c_0_133, plain, ![X1:a]:((fadd_a_b @ fr @ esk410_0 @ X1)=(X1)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(rw,[status(thm)],[c_0_126, c_0_125])).
% 80.39/79.93 thf(c_0_134, plain, fmember_a @ esk49_0 @ (fpartia1066395285xt_a_b @ fr), inference(sr,[status(thm)],[c_0_127, c_0_101])).
% 80.39/79.93 thf(c_0_135, plain, (fmult_a_ring_ext_a_b @ fr @ (fadd_a_b @ fr @ f__0 @ esk457_0) @ f__0)!=(fadd_a_b @ fr @ f__0 @ esk457_0), inference(spm,[status(thm)],[c_0_128, c_0_104])).
% 80.39/79.93 thf(c_0_136, plain, (fmult_a_ring_ext_a_b @ fr @ esk410_0 @ f__0)=(fmult_a_ring_ext_a_b @ fr @ f__0 @ esk410_0), inference(spm,[status(thm)],[c_0_129, c_0_117])).
% 80.39/79.93 thf(c_0_137, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ X1 @ (fadd_a_b @ fr @ f__0 @ esk457_0))=(fadd_a_b @ fr @ f__0 @ esk457_0)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130, c_0_79]), c_0_79]), c_0_131])])).
% 80.39/79.93 thf(c_0_138, plain, (esk410_0)=(esk49_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133]), c_0_134])])).
% 80.39/79.93 thf(c_0_139, plain, (fmult_a_ring_ext_a_b @ fr @ f__0 @ esk410_0)!=(esk410_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135, c_0_125]), c_0_136]), c_0_125])).
% 80.39/79.93 thf(c_0_140, plain, ![X1:a]:((fmult_a_ring_ext_a_b @ fr @ X1 @ esk49_0)=(esk49_0)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137, c_0_125]), c_0_138]), c_0_125]), c_0_138])).
% 80.39/79.93 thf(c_0_141, plain, (fmult_a_ring_ext_a_b @ fr @ f__0 @ esk49_0)!=(esk49_0), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139, c_0_138]), c_0_138])).
% 80.39/79.93 thf(c_0_142, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140, c_0_65]), c_0_141]), ['proof']).
% 80.39/79.93 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h6,h4,h5,h3,h1,h0])],[])).
% 80.39/79.93 thf(h8,assumption,(~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => ((~((X1 = (zero_a_b @ r)))) => (~((![X2:a]:(((member_a @ X2) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ X2) = (one_a_ring_ext_a_b @ r))))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h9,assumption,(field_a_b @ r),introduced(assumption,[])).
% 80.39/79.93 thf(h10,assumption,(~((((member_a @ eigen__1) @ (partia1066395285xt_a_b @ r)) => ((~((eigen__1 = (zero_a_b @ r)))) => (~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__1) @ X1) = (one_a_ring_ext_a_b @ r)))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h11,assumption,((member_a @ eigen__1) @ (partia1066395285xt_a_b @ r)),introduced(assumption,[])).
% 80.39/79.93 thf(h12,assumption,(~(((~((eigen__1 = (zero_a_b @ r)))) => (~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__1) @ X1) = (one_a_ring_ext_a_b @ r))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h13,assumption,(~((eigen__1 = (zero_a_b @ r)))),introduced(assumption,[])).
% 80.39/79.93 thf(h14,assumption,(![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__1) @ X1) = (one_a_ring_ext_a_b @ r)))))),introduced(assumption,[])).
% 80.39/79.93 thf(2,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(3,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(4,plain,(~(sP9) | sP5),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(5,plain,((~(sP5) | ~(sP7)) | sP8),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(6,plain,((~(sP8) | ~(sP3)) | sP4),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(7,plain,(~(sP2) | sP1),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(fact_11_f4,axiom,sP7).
% 80.39/79.93 thf(fact_10_f5,axiom,sP3).
% 80.39/79.93 thf(fact_4_closed__rel__add,axiom,sP2).
% 80.39/79.93 thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h8,h7,h4,h5,h3,h1,h0])],[2,3,4,5,6,7,h0,fact_11_f4,fact_10_f5,fact_4_closed__rel__add])).
% 80.39/79.93 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h8,h7,h4,h5,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,8,h13,h14])).
% 80.39/79.93 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h7,h4,h5,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,9,h11,h12])).
% 80.39/79.93 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h7,h4,h5,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h8,10,h10])).
% 80.39/79.93 thf(12,plain,(~(sP2) | sP1),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(13,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(14,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(15,plain,(~(sP9) | sP5),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(16,plain,((~(sP5) | ~(sP7)) | sP8),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(17,plain,((~(sP8) | ~(sP3)) | sP4),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(18,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h7,h4,h5,h3,h1,h0])],[12,13,14,15,16,17,h0,fact_11_f4,fact_10_f5,fact_4_closed__rel__add])).
% 80.39/79.93 thf(19,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h4,h5,h3,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h7,11,18,h8,h9])).
% 80.39/79.93 thf(fact_88_cring__fieldI2,axiom,((~(((zero_a_b @ r) = (one_a_ring_ext_a_b @ r)))) => ((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => ((~((X1 = (zero_a_b @ r)))) => (~((![X2:a]:(((member_a @ X2) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ X2) = (one_a_ring_ext_a_b @ r))))))))))) => (field_a_b @ r)))).
% 80.39/79.93 thf(20,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h5,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_88_cring__fieldI2,1,19,h6,h7])).
% 80.39/79.93 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,20,h4,h5])).
% 80.39/79.93 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,21,h3])).
% 80.39/79.93 thf(23,plain,(~(sP2) | sP1),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(24,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(25,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(26,plain,(~(sP9) | sP5),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(27,plain,((~(sP5) | ~(sP7)) | sP8),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(28,plain,((~(sP8) | ~(sP3)) | sP4),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(29,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h2,h0])],[23,24,25,26,27,28,h0,fact_11_f4,fact_10_f5,fact_4_closed__rel__add])).
% 80.39/79.93 thf(h15,assumption,(~((((member_a @ eigen__2) @ (partia1066395285xt_a_b @ r)) => ((~((eigen__2 = (zero_a_b @ r)))) => (~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__2) @ X1) = (one_a_ring_ext_a_b @ r)))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h16,assumption,((member_a @ eigen__2) @ (partia1066395285xt_a_b @ r)),introduced(assumption,[])).
% 80.39/79.93 thf(h17,assumption,(~(((~((eigen__2 = (zero_a_b @ r)))) => (~((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__2) @ X1) = (one_a_ring_ext_a_b @ r))))))))))),introduced(assumption,[])).
% 80.39/79.93 thf(h18,assumption,(~((eigen__2 = (zero_a_b @ r)))),introduced(assumption,[])).
% 80.39/79.93 thf(h19,assumption,(![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__2) @ X1) = (one_a_ring_ext_a_b @ r)))))),introduced(assumption,[])).
% 80.39/79.93 thf(30,plain,(~(sP2) | sP1),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(31,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(32,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(33,plain,(~(sP9) | sP5),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(34,plain,((~(sP5) | ~(sP7)) | sP8),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(35,plain,((~(sP8) | ~(sP3)) | sP4),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(36,plain,$false,inference(prop_unsat,[status(thm),assumptions([h18,h19,h16,h17,h15,h8,h7,h2,h0])],[30,31,32,33,34,35,h0,fact_11_f4,fact_10_f5,fact_4_closed__rel__add])).
% 80.39/79.93 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h17,h15,h8,h7,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,36,h18,h19])).
% 80.39/79.93 thf(38,plain,$false,inference(tab_negimp,[status(thm),assumptions([h15,h8,h7,h2,h0]),tab_negimp(discharge,[h16,h17])],[h15,37,h16,h17])).
% 80.39/79.93 thf(39,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h7,h2,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[h8,38,h15])).
% 80.39/79.93 thf(40,plain,(~(sP2) | sP1),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(41,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(42,plain,(~(sP6) | sP9),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(43,plain,(~(sP9) | sP5),inference(all_rule,[status(thm)],[])).
% 80.39/79.93 thf(44,plain,((~(sP5) | ~(sP7)) | sP8),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(45,plain,((~(sP8) | ~(sP3)) | sP4),inference(prop_rule,[status(thm)],[])).
% 80.39/79.93 thf(46,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h7,h2,h0])],[40,41,42,43,44,45,h0,fact_11_f4,fact_10_f5,fact_4_closed__rel__add])).
% 80.39/79.93 thf(47,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h2,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h7,39,46,h8,h9])).
% 80.39/79.93 thf(48,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_88_cring__fieldI2,29,47,h6,h7])).
% 80.39/79.93 thf(fact_187_group__l__invI,axiom,((![X1:a]:(((member_a @ X1) @ (partia1066395285xt_a_b @ r)) => (~((![X2:a]:(((member_a @ X2) @ (partia1066395285xt_a_b @ r)) => (~(((((mult_a_ring_ext_a_b @ r) @ X2) @ X1) = (one_a_ring_ext_a_b @ r)))))))))) => (group_a_ring_ext_a_b @ r))).
% 80.39/79.93 thf(49,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_187_group__l__invI,22,48,h1,h2])).
% 80.39/79.93 thf(0,theorem,sP4,inference(contra,[status(thm),contra(discharge,[h0])],[49,h0])).
% 80.39/79.93 % SZS output end Proof
%------------------------------------------------------------------------------