%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP108^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:46:59 PM UTC 2025
% Result : Theorem 3.17s 3.35s
% Output : Proof 3.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP108^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 8 18:22:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.17/3.35 % SZS status Theorem
% 3.17/3.35 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.17/3.35 % Inferences: 1
% 3.17/3.35 % SZS output start Proof
% 3.17/3.35 thf(ty_a, type, a : $tType).
% 3.17/3.35 thf(ty_product_prod_a_a, type, product_prod_a_a : $tType).
% 3.17/3.35 thf(ty_partia1833973666xt_a_b, type, partia1833973666xt_a_b : $tType).
% 3.17/3.35 thf(ty_set_a, type, set_a : $tType).
% 3.17/3.35 thf(ty_member_a, type, member_a : (a>set_a>$o)).
% 3.17/3.35 thf(ty_r3, type, r3 : a).
% 3.17/3.35 thf(ty_s, type, s : set_a).
% 3.17/3.35 thf(ty_product_fst_a_a, type, product_fst_a_a : (product_prod_a_a>a)).
% 3.17/3.35 thf(ty_add_a_b, type, add_a_b : (partia1833973666xt_a_b>a>a>a)).
% 3.17/3.35 thf(ty_eigen__1, type, eigen__1 : a).
% 3.17/3.35 thf(ty_eigen__0, type, eigen__0 : a).
% 3.17/3.35 thf(ty_mult_a_ring_ext_a_b, type, mult_a_ring_ext_a_b : (partia1833973666xt_a_b>a>a>a)).
% 3.17/3.35 thf(ty_t2, type, t2 : a).
% 3.17/3.35 thf(ty_y, type, y : product_prod_a_a).
% 3.17/3.35 thf(ty_r, type, r : partia1833973666xt_a_b).
% 3.17/3.35 thf(ty_partia1066395285xt_a_b, type, partia1066395285xt_a_b : (partia1833973666xt_a_b>set_a)).
% 3.17/3.35 thf(ty_t, type, t : a).
% 3.17/3.35 thf(ty_s3, type, s3 : a).
% 3.17/3.35 thf(ty_zero_a_b, type, zero_a_b : (partia1833973666xt_a_b>a)).
% 3.17/3.35 thf(ty_r2, type, r2 : a).
% 3.17/3.35 thf(ty_s2, type, s2 : a).
% 3.17/3.35 thf(ty_product_snd_a_a, type, product_snd_a_a : (product_prod_a_a>a)).
% 3.17/3.35 thf(ty_x, type, x : product_prod_a_a).
% 3.17/3.35 thf(ty_a_minus_a_b, type, a_minus_a_b : (partia1833973666xt_a_b>a>a>a)).
% 3.17/3.35 thf(sP1,plain,sP1 <=> ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)),introduced(definition,[new_symbols(definition,[sP1])])).
% 3.17/3.35 thf(sP2,plain,sP2 <=> ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)),introduced(definition,[new_symbols(definition,[sP2])])).
% 3.17/3.35 thf(conj_0,conjecture,((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))).
% 3.17/3.35 thf(h0,negated_conjecture,(~(((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))))),inference(assume_negation,[status(cth)],[conj_0])).
% 3.17/3.35 thf(h1,assumption,(~((((member_a @ eigen__0) @ s) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__0) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))) = (zero_a_b @ r))))))),introduced(assumption,[])).
% 3.17/3.35 thf(h2,assumption,((member_a @ eigen__0) @ s),introduced(assumption,[])).
% 3.17/3.35 thf(h3,assumption,((((mult_a_ring_ext_a_b @ r) @ eigen__0) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))) = (zero_a_b @ r)),introduced(assumption,[])).
% 3.17/3.35 thf(h4,assumption,(~((((member_a @ eigen__1) @ s) => (~(((((mult_a_ring_ext_a_b @ r) @ eigen__1) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))) = (zero_a_b @ r))))))),introduced(assumption,[])).
% 3.17/3.35 thf(h5,assumption,((member_a @ eigen__1) @ s),introduced(assumption,[])).
% 3.17/3.35 thf(h6,assumption,((((mult_a_ring_ext_a_b @ r) @ eigen__1) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))) = (zero_a_b @ r)),introduced(assumption,[])).
% 3.17/3.35 thf(h7,assumption,(~(sP1)),introduced(assumption,[])).
% 3.17/3.35 thf(h8,assumption,(sP2 => (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))))),introduced(assumption,[])).
% 3.17/3.35 thf(fact_12_f41,axiom,sP1).
% 3.17/3.35 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0])],[fact_12_f41,h7])).
% 3.17/3.35 thf(h9,assumption,(~(sP2)),introduced(assumption,[])).
% 3.17/3.35 thf(h10,assumption,(((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),introduced(assumption,[])).
% 3.17/3.35 thf(fact_13_f42,axiom,sP2).
% 3.17/3.35 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h9,h8,h5,h6,h4,h2,h3,h1,h0])],[fact_13_f42,h9])).
% 3.17/3.35 thf(h11,assumption,(~(((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)))),introduced(assumption,[])).
% 3.17/3.35 thf(h12,assumption,((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),introduced(assumption,[])).
% 3.17/3.35 thf(nax22, axiom, (p22<=fmember_a @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fpartia1066395285xt_a_b @ fr)), file('<stdin>', nax22)).
% 3.17/3.35 thf(ax39, axiom, ~(p22), file('<stdin>', ax39)).
% 3.17/3.35 thf(pax60, axiom, (p60=>![X1:a, X2:a]:(fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)=>(fmember_a @ X2 @ (fpartia1066395285xt_a_b @ fr)=>fmember_a @ (fmult_a_ring_ext_a_b @ fr @ X1 @ X2) @ (fpartia1066395285xt_a_b @ fr)))), file('<stdin>', pax60)).
% 3.17/3.35 thf(pax1, axiom, (p1=>fmember_a @ ft @ (fpartia1066395285xt_a_b @ fr)), file('<stdin>', pax1)).
% 3.17/3.35 thf(pax2, axiom, (p2=>fmember_a @ ft2 @ (fpartia1066395285xt_a_b @ fr)), file('<stdin>', pax2)).
% 3.17/3.35 thf(ax1, axiom, p60, file('<stdin>', ax1)).
% 3.17/3.35 thf(ax60, axiom, p1, file('<stdin>', ax60)).
% 3.17/3.35 thf(ax59, axiom, p2, file('<stdin>', ax59)).
% 3.17/3.35 thf(c_0_8, plain, (~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fpartia1066395285xt_a_b @ fr)|p22), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax22])])).
% 3.17/3.35 thf(c_0_9, plain, ~p22, inference(fof_simplification,[status(thm)],[ax39])).
% 3.17/3.35 thf(c_0_10, plain, ![X5:a, X6:a]:(~p60|(~fmember_a @ X5 @ (fpartia1066395285xt_a_b @ fr)|(~fmember_a @ X6 @ (fpartia1066395285xt_a_b @ fr)|fmember_a @ (fmult_a_ring_ext_a_b @ fr @ X5 @ X6) @ (fpartia1066395285xt_a_b @ fr)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax60])])])).
% 3.17/3.35 thf(c_0_11, plain, (~p1|fmember_a @ ft @ (fpartia1066395285xt_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax1])).
% 3.17/3.35 thf(c_0_12, plain, (~p2|fmember_a @ ft2 @ (fpartia1066395285xt_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax2])).
% 3.17/3.35 thf(c_0_13, plain, (p22|~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fpartia1066395285xt_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_8])).
% 3.17/3.35 thf(c_0_14, plain, ~p22, inference(split_conjunct,[status(thm)],[c_0_9])).
% 3.17/3.35 thf(c_0_15, plain, ![X1:a, X2:a]:(fmember_a @ (fmult_a_ring_ext_a_b @ fr @ X1 @ X2) @ (fpartia1066395285xt_a_b @ fr)|~p60|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ X2 @ (fpartia1066395285xt_a_b @ fr)), inference(split_conjunct,[status(thm)],[c_0_10])).
% 3.17/3.35 thf(c_0_16, plain, p60, inference(split_conjunct,[status(thm)],[ax1])).
% 3.17/3.35 thf(c_0_17, plain, (fmember_a @ ft @ (fpartia1066395285xt_a_b @ fr)|~p1), inference(split_conjunct,[status(thm)],[c_0_11])).
% 3.17/3.35 thf(c_0_18, plain, p1, inference(split_conjunct,[status(thm)],[ax60])).
% 3.17/3.35 thf(c_0_19, plain, (fmember_a @ ft2 @ (fpartia1066395285xt_a_b @ fr)|~p2), inference(split_conjunct,[status(thm)],[c_0_12])).
% 3.17/3.35 thf(c_0_20, plain, p2, inference(split_conjunct,[status(thm)],[ax59])).
% 3.17/3.35 thf(c_0_21, plain, ~fmember_a @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fpartia1066395285xt_a_b @ fr), inference(sr,[status(thm)],[c_0_13, c_0_14])).
% 3.17/3.35 thf(c_0_22, plain, ![X2:a, X1:a]:(fmember_a @ (fmult_a_ring_ext_a_b @ fr @ X1 @ X2) @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ X2 @ (fpartia1066395285xt_a_b @ fr)|~fmember_a @ X1 @ (fpartia1066395285xt_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])).
% 3.17/3.35 thf(c_0_23, plain, fmember_a @ ft @ (fpartia1066395285xt_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 3.17/3.35 thf(c_0_24, plain, fmember_a @ ft2 @ (fpartia1066395285xt_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 3.17/3.35 thf(c_0_25, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22]), c_0_23]), c_0_24])]), ['proof']).
% 3.17/3.35 thf(3,plain,$false,inference(eprover,[status(thm),assumptions([h11,h10,h8,h5,h6,h4,h2,h3,h1,h0])],[])).
% 3.17/3.35 thf(pax55, axiom, (p55=>(fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))=(fzero_a_b @ fr)), file('<stdin>', pax55)).
% 3.17/3.35 thf(pax56, axiom, (p56=>(fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))=(fzero_a_b @ fr)), file('<stdin>', pax56)).
% 3.17/3.35 thf(pax42, axiom, (p42=>(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx)))))=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))), file('<stdin>', pax42)).
% 3.17/3.35 thf(ax67, axiom, p55, file('<stdin>', ax67)).
% 3.17/3.35 thf(pax46, axiom, (p46=>(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy)))))=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))), file('<stdin>', pax46)).
% 3.17/3.35 thf(ax66, axiom, p56, file('<stdin>', ax66)).
% 3.17/3.35 thf(pax43, axiom, (p43=>(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))), file('<stdin>', pax43)).
% 3.17/3.35 thf(ax80, axiom, p42, file('<stdin>', ax80)).
% 3.17/3.35 thf(pax47, axiom, (p47=>(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))), file('<stdin>', pax47)).
% 3.17/3.35 thf(ax76, axiom, p46, file('<stdin>', ax76)).
% 3.17/3.35 thf(nax119, axiom, (p119<=(fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))), file('<stdin>', nax119)).
% 3.17/3.35 thf(ax4, axiom, ~(p119), file('<stdin>', ax4)).
% 3.17/3.35 thf(pax63, axiom, (p63=>(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))=(fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx))))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))), file('<stdin>', pax63)).
% 3.17/3.35 thf(ax79, axiom, p43, file('<stdin>', ax79)).
% 3.17/3.35 thf(ax75, axiom, p47, file('<stdin>', ax75)).
% 3.17/3.35 thf(ax100, axiom, p63, file('<stdin>', ax100)).
% 3.17/3.35 thf(c_0_16, plain, (~p55|(fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))=(fzero_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax55])).
% 3.17/3.35 thf(c_0_17, plain, (~p56|(fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))=(fzero_a_b @ fr)), inference(fof_nnf,[status(thm)],[pax56])).
% 3.17/3.35 thf(c_0_18, plain, (~p42|(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx)))))=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))), inference(fof_nnf,[status(thm)],[pax42])).
% 3.17/3.35 thf(c_0_19, plain, ((fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))=(fzero_a_b @ fr)|~p55), inference(split_conjunct,[status(thm)],[c_0_16])).
% 3.17/3.35 thf(c_0_20, plain, p55, inference(split_conjunct,[status(thm)],[ax67])).
% 3.17/3.35 thf(c_0_21, plain, (~p46|(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy)))))=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))), inference(fof_nnf,[status(thm)],[pax46])).
% 3.17/3.35 thf(c_0_22, plain, ((fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))=(fzero_a_b @ fr)|~p56), inference(split_conjunct,[status(thm)],[c_0_17])).
% 3.17/3.35 thf(c_0_23, plain, p56, inference(split_conjunct,[status(thm)],[ax66])).
% 3.17/3.35 thf(c_0_24, plain, (~p43|(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))), inference(fof_nnf,[status(thm)],[pax43])).
% 3.17/3.35 thf(c_0_25, plain, ((fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx)))))=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))|~p42), inference(split_conjunct,[status(thm)],[c_0_18])).
% 3.17/3.35 thf(c_0_26, plain, (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))=(fzero_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 3.17/3.35 thf(c_0_27, plain, p42, inference(split_conjunct,[status(thm)],[ax80])).
% 3.17/3.35 thf(c_0_28, plain, (~p47|(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))), inference(fof_nnf,[status(thm)],[pax47])).
% 3.17/3.35 thf(c_0_29, plain, ((fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy)))))=(fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))|~p46), inference(split_conjunct,[status(thm)],[c_0_21])).
% 3.17/3.35 thf(c_0_30, plain, (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))=(fzero_a_b @ fr), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 3.17/3.35 thf(c_0_31, plain, p46, inference(split_conjunct,[status(thm)],[ax76])).
% 3.17/3.35 thf(c_0_32, plain, ((fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))))!=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))|p119), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax119])])).
% 3.17/3.35 thf(c_0_33, plain, ~p119, inference(fof_simplification,[status(thm)],[ax4])).
% 3.17/3.35 thf(c_0_34, plain, (~p63|(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))=(fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx))))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))), inference(fof_nnf,[status(thm)],[pax63])).
% 3.17/3.35 thf(c_0_35, plain, ((fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))|~p43), inference(split_conjunct,[status(thm)],[c_0_24])).
% 3.17/3.35 thf(c_0_36, plain, (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fzero_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26]), c_0_27])])).
% 3.17/3.35 thf(c_0_37, plain, p43, inference(split_conjunct,[status(thm)],[ax79])).
% 3.17/3.35 thf(c_0_38, plain, ((fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))|~p47), inference(split_conjunct,[status(thm)],[c_0_28])).
% 3.17/3.35 thf(c_0_39, plain, (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fzero_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30]), c_0_31])])).
% 3.17/3.35 thf(c_0_40, plain, p47, inference(split_conjunct,[status(thm)],[ax75])).
% 3.17/3.35 thf(c_0_41, plain, (p119|(fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ fr2) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ (fproduct_fst_a_a @ fx))))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fmult_a_ring_ext_a_b @ fr @ ft @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ fr3) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ (fproduct_fst_a_a @ fy))))))!=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))), inference(split_conjunct,[status(thm)],[c_0_32])).
% 3.17/3.35 thf(c_0_42, plain, ~p119, inference(split_conjunct,[status(thm)],[c_0_33])).
% 3.17/3.35 thf(c_0_43, plain, ((fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))=(fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx))))) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))|~p63), inference(split_conjunct,[status(thm)],[c_0_34])).
% 3.17/3.35 thf(c_0_44, plain, (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fzero_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36]), c_0_37])])).
% 3.17/3.35 thf(c_0_45, plain, (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy)))))=(fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fzero_a_b @ fr)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39]), c_0_40])])).
% 3.17/3.35 thf(c_0_46, plain, p63, inference(split_conjunct,[status(thm)],[ax100])).
% 3.17/3.35 thf(c_0_47, plain, (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ ft) @ (fadd_a_b @ fr @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs3 @ fr2)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fy) @ (fproduct_fst_a_a @ fx)))) @ (fa_minus_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_snd_a_a @ fy)) @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fr3)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ fs2 @ fs3) @ (fmult_a_ring_ext_a_b @ fr @ (fproduct_snd_a_a @ fx) @ (fproduct_fst_a_a @ fy))))))!=(fadd_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft @ fs3) @ (fproduct_snd_a_a @ fy)) @ (fzero_a_b @ fr)) @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ (fmult_a_ring_ext_a_b @ fr @ ft2 @ fs2) @ (fproduct_snd_a_a @ fx)) @ (fzero_a_b @ fr))), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_26]), c_0_30]), c_0_42])).
% 3.17/3.35 thf(c_0_48, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44]), c_0_45]), c_0_46])]), c_0_47]), ['proof']).
% 3.17/3.35 thf(4,plain,$false,inference(eprover,[status(thm),assumptions([h12,h10,h8,h5,h6,h4,h2,h3,h1,h0])],[])).
% 3.17/3.35 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h10,h8,h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h10,3,4,h11,h12])).
% 3.17/3.35 thf(6,plain,$false,inference(tab_imp,[status(thm),assumptions([h8,h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h8,2,5,h9,h10])).
% 3.17/3.35 thf(fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062,axiom,(sP1 => (sP2 => (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))))))).
% 3.17/3.35 thf(7,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062,1,6,h7,h8])).
% 3.17/3.35 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6])).
% 3.17/3.35 thf(fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:a]:(((member_a @ X1) @ s) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))) = (zero_a_b @ r))))))))).
% 3.17/3.35 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,8,h4])).
% 3.17/3.35 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3])).
% 3.17/3.35 thf(fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:a]:(((member_a @ X1) @ s) => (~(((((mult_a_ring_ext_a_b @ r) @ X1) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))) = (zero_a_b @ r))))))))).
% 3.17/3.35 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,10,h1])).
% 3.17/3.35 thf(0,theorem,((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 3.17/3.35 % SZS output end Proof
%------------------------------------------------------------------------------