TSTP Solution File: ITP027^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP027^1 : 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 : n032.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 00:28:48 EDT 2022
% Result : Theorem 1.12s 1.38s
% Output : Proof 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : ITP027^1 : TPTP v8.1.0. Released v7.5.0.
% 0.02/0.07 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Thu Jun 2 17:05:30 EDT 2022
% 0.06/0.26 % CPUTime :
% 1.12/1.38 % SZS status Theorem
% 1.12/1.38 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 1.12/1.38 % Inferences: 5
% 1.12/1.38 % SZS output start Proof
% 1.12/1.38 thf(ty_carrie1948989069_d_a_e, type, carrie1948989069_d_a_e : $tType).
% 1.12/1.38 thf(ty_set_c_d_c_d_c_d, type, set_c_d_c_d_c_d : $tType).
% 1.12/1.38 thf(ty_set_c_d, type, set_c_d : $tType).
% 1.12/1.38 thf(ty_d, type, d : $tType).
% 1.12/1.38 thf(ty_set_c_d_c_d, type, set_c_d_c_d : $tType).
% 1.12/1.38 thf(ty_set_c, type, set_c : $tType).
% 1.12/1.38 thf(ty_c, type, c : $tType).
% 1.12/1.38 thf(ty_pi_c_d_c_d_c_d, type, pi_c_d_c_d_c_d : (set_c_d>((c>d)>set_c_d_c_d)>set_c_d_c_d_c_d)).
% 1.12/1.38 thf(ty_member_c_d, type, member_c_d : ((c>d)>set_c_d>$o)).
% 1.12/1.38 thf(ty_eigen__1, type, eigen__1 : c).
% 1.12/1.38 thf(ty_eigen__0, type, eigen__0 : (c>d)).
% 1.12/1.38 thf(ty_prod_m854557927_d_a_e, type, prod_m854557927_d_a_e : (set_c>(c>carrie1948989069_d_a_e)>(c>d)>c>d)).
% 1.12/1.38 thf(ty_prod_p131511076_d_a_e, type, prod_p131511076_d_a_e : (set_c>(c>carrie1948989069_d_a_e)>(c>d)>(c>d)>c>d)).
% 1.12/1.38 thf(ty_prod_z1214987823_d_a_e, type, prod_z1214987823_d_a_e : (set_c>(c>carrie1948989069_d_a_e)>c>d)).
% 1.12/1.38 thf(ty_i, type, i : set_c).
% 1.12/1.38 thf(ty_member_c_d_c_d, type, member_c_d_c_d : (((c>d)>c>d)>set_c_d_c_d>$o)).
% 1.12/1.38 thf(ty_carr_p1636662547_d_a_e, type, carr_p1636662547_d_a_e : (set_c>(c>carrie1948989069_d_a_e)>set_c_d)).
% 1.12/1.38 thf(ty_m, type, m : (c>carrie1948989069_d_a_e)).
% 1.12/1.38 thf(ty_pi_c_d_c_d, type, pi_c_d_c_d : (set_c_d>((c>d)>set_c_d)>set_c_d_c_d)).
% 1.12/1.38 thf(ty_member_c_d_c_d_c_d, type, member_c_d_c_d_c_d : (((c>d)>(c>d)>c>d)>set_c_d_c_d_c_d>$o)).
% 1.12/1.38 thf(conj_2,conjecture,(![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((prod_z1214987823_d_a_e @ i) @ m)) = X1)))).
% 1.12/1.38 thf(h0,negated_conjecture,(~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((prod_z1214987823_d_a_e @ i) @ m)) = X1))))),inference(assume_negation,[status(cth)],[conj_2])).
% 1.12/1.38 thf(h1,assumption,(~((((member_c_d @ eigen__0) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ eigen__0) @ ((prod_z1214987823_d_a_e @ i) @ m)) = eigen__0)))),introduced(assumption,[])).
% 1.12/1.38 thf(h2,assumption,((member_c_d @ eigen__0) @ ((carr_p1636662547_d_a_e @ i) @ m)),introduced(assumption,[])).
% 1.12/1.38 thf(h3,assumption,(~((((((prod_p131511076_d_a_e @ i) @ m) @ eigen__0) @ ((prod_z1214987823_d_a_e @ i) @ m)) = eigen__0))),introduced(assumption,[])).
% 1.12/1.38 thf(h4,assumption,(~((![X1:c]:((((((prod_p131511076_d_a_e @ i) @ m) @ eigen__0) @ ((prod_z1214987823_d_a_e @ i) @ m)) @ X1) = (eigen__0 @ X1))))),introduced(assumption,[])).
% 1.12/1.38 thf(h5,assumption,(~(((((((prod_p131511076_d_a_e @ i) @ m) @ eigen__0) @ ((prod_z1214987823_d_a_e @ i) @ m)) @ eigen__1) = (eigen__0 @ eigen__1)))),introduced(assumption,[])).
% 1.12/1.38 thf(h6,assumption,(~(((~(((~(((~(((~((((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3)))))))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2) = ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X1))))))))))) => (~(((member_c_d_c_d @ ((prod_m854557927_d_a_e @ i) @ m)) @ ((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((carr_p1636662547_d_a_e @ i) @ m))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ (((prod_m854557927_d_a_e @ i) @ m) @ X1)) @ X1) = ((prod_z1214987823_d_a_e @ i) @ m))))))))) => (~(((member_c_d @ ((prod_z1214987823_d_a_e @ i) @ m)) @ ((carr_p1636662547_d_a_e @ i) @ m))))))),introduced(assumption,[])).
% 1.12/1.38 thf(h7,assumption,(![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((prod_z1214987823_d_a_e @ i) @ m)) @ X1) = X1))),introduced(assumption,[])).
% 1.12/1.38 thf(h8,assumption,(~(((~(((~(((~((((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3)))))))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2) = ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X1))))))))))) => (~(((member_c_d_c_d @ ((prod_m854557927_d_a_e @ i) @ m)) @ ((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((carr_p1636662547_d_a_e @ i) @ m))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ (((prod_m854557927_d_a_e @ i) @ m) @ X1)) @ X1) = ((prod_z1214987823_d_a_e @ i) @ m))))))))),introduced(assumption,[])).
% 1.12/1.38 thf(h9,assumption,((member_c_d @ ((prod_z1214987823_d_a_e @ i) @ m)) @ ((carr_p1636662547_d_a_e @ i) @ m)),introduced(assumption,[])).
% 1.12/1.38 thf(h10,assumption,(~(((~(((~((((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3)))))))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2) = ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X1))))))))))) => (~(((member_c_d_c_d @ ((prod_m854557927_d_a_e @ i) @ m)) @ ((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((carr_p1636662547_d_a_e @ i) @ m))))))))),introduced(assumption,[])).
% 1.12/1.38 thf(h11,assumption,(![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ (((prod_m854557927_d_a_e @ i) @ m) @ X1)) @ X1) = ((prod_z1214987823_d_a_e @ i) @ m)))),introduced(assumption,[])).
% 1.12/1.38 thf(h12,assumption,(~(((~((((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3)))))))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2) = ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X1))))))))))),introduced(assumption,[])).
% 1.12/1.38 thf(h13,assumption,((member_c_d_c_d @ ((prod_m854557927_d_a_e @ i) @ m)) @ ((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))),introduced(assumption,[])).
% 1.12/1.38 thf(h14,assumption,(~((((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3)))))))))))))),introduced(assumption,[])).
% 1.12/1.38 thf(h15,assumption,(![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2) = ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X1)))))),introduced(assumption,[])).
% 1.12/1.38 thf(h16,assumption,((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))),introduced(assumption,[])).
% 1.12/1.38 thf(h17,assumption,(![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3))))))))),introduced(assumption,[])).
% 1.12/1.38 thf(ax5, axiom, (~(p58)|p61), file('<stdin>', ax5)).
% 1.12/1.38 thf(ax4, axiom, (~(p61)|p62), file('<stdin>', ax4)).
% 1.12/1.38 thf(ax9, axiom, p58, file('<stdin>', ax9)).
% 1.12/1.38 thf(ax3, axiom, (~(p62)|~(p57)|p55), file('<stdin>', ax3)).
% 1.12/1.38 thf(ax11, axiom, ~(p55), file('<stdin>', ax11)).
% 1.12/1.38 thf(pax48, axiom, (p48=>![X5:c > d]:(fmember_c_d @ X5 @ (fcarr_p1636662547_d_a_e @ fi @ fm)=>(fprod_p131511076_d_a_e @ fi @ fm @ (fprod_z1214987823_d_a_e @ fi @ fm) @ X5)=(X5))), file('<stdin>', pax48)).
% 1.12/1.38 thf(pax52, axiom, (p52=>![X5:c > d]:(fmember_c_d @ X5 @ (fcarr_p1636662547_d_a_e @ fi @ fm)=>![X6:c > d]:(fmember_c_d @ X6 @ (fcarr_p1636662547_d_a_e @ fi @ fm)=>(fprod_p131511076_d_a_e @ fi @ fm @ X5 @ X6)=(fprod_p131511076_d_a_e @ fi @ fm @ X6 @ X5)))), file('<stdin>', pax52)).
% 1.12/1.38 thf(pax49, axiom, (p49=>fmember_c_d @ (fprod_z1214987823_d_a_e @ fi @ fm) @ (fcarr_p1636662547_d_a_e @ fi @ fm)), file('<stdin>', pax49)).
% 1.12/1.38 thf(nax57, axiom, (p57<=(f__0 @ f__1)=(fprod_p131511076_d_a_e @ fi @ fm @ f__0 @ (fprod_z1214987823_d_a_e @ fi @ fm) @ f__1)), file('<stdin>', nax57)).
% 1.12/1.38 thf(ax18, axiom, p48, file('<stdin>', ax18)).
% 1.12/1.38 thf(ax14, axiom, p52, file('<stdin>', ax14)).
% 1.12/1.38 thf(ax17, axiom, p49, file('<stdin>', ax17)).
% 1.12/1.38 thf(pax56, axiom, (p56=>fmember_c_d @ f__0 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), file('<stdin>', pax56)).
% 1.12/1.38 thf(ax10, axiom, p56, file('<stdin>', ax10)).
% 1.12/1.38 thf(c_0_14, plain, (~p58|p61), inference(fof_simplification,[status(thm)],[ax5])).
% 1.12/1.38 thf(c_0_15, plain, (~p61|p62), inference(fof_simplification,[status(thm)],[ax4])).
% 1.12/1.38 thf(c_0_16, plain, (p61|~p58), inference(split_conjunct,[status(thm)],[c_0_14])).
% 1.12/1.38 thf(c_0_17, plain, p58, inference(split_conjunct,[status(thm)],[ax9])).
% 1.12/1.38 thf(c_0_18, plain, (~p62|~p57|p55), inference(fof_simplification,[status(thm)],[ax3])).
% 1.12/1.38 thf(c_0_19, plain, (p62|~p61), inference(split_conjunct,[status(thm)],[c_0_15])).
% 1.12/1.38 thf(c_0_20, plain, p61, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 1.12/1.38 thf(c_0_21, plain, ~p55, inference(fof_simplification,[status(thm)],[ax11])).
% 1.12/1.38 thf(c_0_22, plain, ![X134:c > d]:(~p48|(~fmember_c_d @ X134 @ (fcarr_p1636662547_d_a_e @ fi @ fm)|(fprod_p131511076_d_a_e @ fi @ fm @ (fprod_z1214987823_d_a_e @ fi @ fm) @ X134)=(X134))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax48])])])).
% 1.12/1.38 thf(c_0_23, plain, ![X128:c > d, X129:c > d]:(~p52|(~fmember_c_d @ X128 @ (fcarr_p1636662547_d_a_e @ fi @ fm)|(~fmember_c_d @ X129 @ (fcarr_p1636662547_d_a_e @ fi @ fm)|(fprod_p131511076_d_a_e @ fi @ fm @ X128 @ X129)=(fprod_p131511076_d_a_e @ fi @ fm @ X129 @ X128)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax52])])])).
% 1.12/1.38 thf(c_0_24, plain, (~p49|fmember_c_d @ (fprod_z1214987823_d_a_e @ fi @ fm) @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(fof_nnf,[status(thm)],[pax49])).
% 1.12/1.38 thf(c_0_25, plain, ((f__0 @ f__1)!=(fprod_p131511076_d_a_e @ fi @ fm @ f__0 @ (fprod_z1214987823_d_a_e @ fi @ fm) @ f__1)|p57), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax57])])).
% 1.12/1.38 thf(c_0_26, plain, (p55|~p62|~p57), inference(split_conjunct,[status(thm)],[c_0_18])).
% 1.12/1.38 thf(c_0_27, plain, p62, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 1.12/1.38 thf(c_0_28, plain, ~p55, inference(split_conjunct,[status(thm)],[c_0_21])).
% 1.12/1.38 thf(c_0_29, plain, ![X1:c > d]:((fprod_p131511076_d_a_e @ fi @ fm @ (fprod_z1214987823_d_a_e @ fi @ fm) @ X1)=(X1)|~p48|~fmember_c_d @ X1 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(split_conjunct,[status(thm)],[c_0_22])).
% 1.12/1.38 thf(c_0_30, plain, p48, inference(split_conjunct,[status(thm)],[ax18])).
% 1.12/1.38 thf(c_0_31, plain, ![X1:c > d, X2:c > d]:((fprod_p131511076_d_a_e @ fi @ fm @ X1 @ X2)=(fprod_p131511076_d_a_e @ fi @ fm @ X2 @ X1)|~p52|~fmember_c_d @ X1 @ (fcarr_p1636662547_d_a_e @ fi @ fm)|~fmember_c_d @ X2 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(split_conjunct,[status(thm)],[c_0_23])).
% 1.12/1.38 thf(c_0_32, plain, p52, inference(split_conjunct,[status(thm)],[ax14])).
% 1.12/1.38 thf(c_0_33, plain, (fmember_c_d @ (fprod_z1214987823_d_a_e @ fi @ fm) @ (fcarr_p1636662547_d_a_e @ fi @ fm)|~p49), inference(split_conjunct,[status(thm)],[c_0_24])).
% 1.12/1.38 thf(c_0_34, plain, p49, inference(split_conjunct,[status(thm)],[ax17])).
% 1.12/1.38 thf(c_0_35, plain, (~p56|fmember_c_d @ f__0 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(fof_nnf,[status(thm)],[pax56])).
% 1.12/1.38 thf(c_0_36, plain, (p57|(f__0 @ f__1)!=(fprod_p131511076_d_a_e @ fi @ fm @ f__0 @ (fprod_z1214987823_d_a_e @ fi @ fm) @ f__1)), inference(split_conjunct,[status(thm)],[c_0_25])).
% 1.12/1.38 thf(c_0_37, plain, ~p57, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])]), c_0_28])).
% 1.12/1.38 thf(c_0_38, plain, ![X1:c > d]:((fprod_p131511076_d_a_e @ fi @ fm @ (fprod_z1214987823_d_a_e @ fi @ fm) @ X1)=(X1)|~fmember_c_d @ X1 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 1.12/1.38 thf(c_0_39, plain, ![X2:c > d, X1:c > d]:((fprod_p131511076_d_a_e @ fi @ fm @ X1 @ X2)=(fprod_p131511076_d_a_e @ fi @ fm @ X2 @ X1)|~fmember_c_d @ X2 @ (fcarr_p1636662547_d_a_e @ fi @ fm)|~fmember_c_d @ X1 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 1.12/1.38 thf(c_0_40, plain, fmember_c_d @ (fprod_z1214987823_d_a_e @ fi @ fm) @ (fcarr_p1636662547_d_a_e @ fi @ fm), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 1.12/1.38 thf(c_0_41, plain, (fmember_c_d @ f__0 @ (fcarr_p1636662547_d_a_e @ fi @ fm)|~p56), inference(split_conjunct,[status(thm)],[c_0_35])).
% 1.12/1.38 thf(c_0_42, plain, p56, inference(split_conjunct,[status(thm)],[ax10])).
% 1.12/1.38 thf(c_0_43, plain, (fprod_p131511076_d_a_e @ fi @ fm @ f__0 @ (fprod_z1214987823_d_a_e @ fi @ fm) @ f__1)!=(f__0 @ f__1), inference(sr,[status(thm)],[c_0_36, c_0_37])).
% 1.12/1.38 thf(c_0_44, plain, ![X1:c > d]:((fprod_p131511076_d_a_e @ fi @ fm @ X1 @ (fprod_z1214987823_d_a_e @ fi @ fm))=(X1)|~fmember_c_d @ X1 @ (fcarr_p1636662547_d_a_e @ fi @ fm)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])])).
% 1.12/1.38 thf(c_0_45, plain, fmember_c_d @ f__0 @ (fcarr_p1636662547_d_a_e @ fi @ fm), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 1.12/1.38 thf(c_0_46, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45])]), ['proof']).
% 1.12/1.38 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0])],[])).
% 1.12/1.38 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,1,h16,h17])).
% 1.12/1.38 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,2,h14,h15])).
% 1.12/1.38 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h10,3,h12,h13])).
% 1.12/1.38 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,4,h10,h11])).
% 1.12/1.38 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,5,h8,h9])).
% 1.12/1.38 thf(conj_1,axiom,(~(((~(((~(((~(((~(((~((((member_c_d_c_d_c_d @ ((prod_p131511076_d_a_e @ i) @ m)) @ ((pi_c_d_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X2:c>d]:((carr_p1636662547_d_a_e @ i) @ m)))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X3:c>d]:(((member_c_d @ X3) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2)) @ X3) = ((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X3)))))))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (![X2:c>d]:(((member_c_d @ X2) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ X2) = ((((prod_p131511076_d_a_e @ i) @ m) @ X2) @ X1))))))))))) => (~(((member_c_d_c_d @ ((prod_m854557927_d_a_e @ i) @ m)) @ ((pi_c_d_c_d @ ((carr_p1636662547_d_a_e @ i) @ m)) @ (^[X1:c>d]:((carr_p1636662547_d_a_e @ i) @ m))))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ (((prod_m854557927_d_a_e @ i) @ m) @ X1)) @ X1) = ((prod_z1214987823_d_a_e @ i) @ m))))))))) => (~(((member_c_d @ ((prod_z1214987823_d_a_e @ i) @ m)) @ ((carr_p1636662547_d_a_e @ i) @ m))))))) => (~((![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ ((prod_z1214987823_d_a_e @ i) @ m)) @ X1) = X1))))))))).
% 1.12/1.38 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[conj_1,6,h6,h7])).
% 1.12/1.38 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,7,h5])).
% 1.12/1.38 thf(9,plain,$false,inference(tab_fe,[status(thm),assumptions([h2,h3,h1,h0]),tab_fe(discharge,[h4])],[h3,8,h4])).
% 1.12/1.38 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3])).
% 1.12/1.38 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])).
% 1.12/1.38 thf(0,theorem,(![X1:c>d]:(((member_c_d @ X1) @ ((carr_p1636662547_d_a_e @ i) @ m)) => (((((prod_p131511076_d_a_e @ i) @ m) @ X1) @ ((prod_z1214987823_d_a_e @ i) @ m)) = X1))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 1.12/1.38 % SZS output end Proof
%------------------------------------------------------------------------------