TSTP Solution File: ITP095^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP095^1 : 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 : n026.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 00:29:05 EDT 2022
% Result : Theorem 8.81s 9.14s
% Output : Proof 8.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP095^1 : TPTP v8.1.0. Released v7.5.0.
% 0.00/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 2 20:40:57 EDT 2022
% 0.11/0.33 % CPUTime :
% 8.81/9.14 % SZS status Theorem
% 8.81/9.14 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 8.81/9.14 % Inferences: 2
% 8.81/9.14 % SZS output start Proof
% 8.81/9.14 thf(ty_set_real, type, set_real : $tType).
% 8.81/9.14 thf(ty_poly_real, type, poly_real : $tType).
% 8.81/9.14 thf(ty_nat, type, nat : $tType).
% 8.81/9.14 thf(ty_real, type, real : $tType).
% 8.81/9.14 thf(ty_poly_real2, type, poly_real2 : (poly_real>real>real)).
% 8.81/9.14 thf(ty_zero_zero_real, type, zero_zero_real : real).
% 8.81/9.14 thf(ty_eigen__0, type, eigen__0 : poly_real).
% 8.81/9.14 thf(ty_zero_zero_poly_real, type, zero_zero_poly_real : poly_real).
% 8.81/9.14 thf(ty_coeff_real, type, coeff_real : (poly_real>nat>real)).
% 8.81/9.14 thf(ty_ring_1_Ints_real, type, ring_1_Ints_real : set_real).
% 8.81/9.14 thf(ty_x, type, x : real).
% 8.81/9.14 thf(ty_member_real, type, member_real : (real>set_real>$o)).
% 8.81/9.14 thf(conj_0,conjecture,((ord_less_eq_real @ ((divide_divide_real @ one_one_real) @ ((power_power_real @ (ring_1_of_int_real @ b)) @ (degree_real @ p)))) @ (abs_abs_real @ ((poly_real2 @ p) @ ((divide_divide_real @ (ring_1_of_int_real @ a2)) @ (ring_1_of_int_real @ b)))))).
% 8.81/9.14 thf(h0,negated_conjecture,(~(((ord_less_eq_real @ ((divide_divide_real @ one_one_real) @ ((power_power_real @ (ring_1_of_int_real @ b)) @ (degree_real @ p)))) @ (abs_abs_real @ ((poly_real2 @ p) @ ((divide_divide_real @ (ring_1_of_int_real @ a2)) @ (ring_1_of_int_real @ b))))))),inference(assume_negation,[status(cth)],[conj_0])).
% 8.81/9.14 thf(h1,assumption,(~(((![X1:nat]:((member_real @ ((coeff_real @ eigen__0) @ X1)) @ ring_1_Ints_real)) => ((~((eigen__0 = zero_zero_poly_real))) => (~((((poly_real2 @ eigen__0) @ x) = zero_zero_real))))))),introduced(assumption,[])).
% 8.81/9.14 thf(h2,assumption,(![X1:nat]:((member_real @ ((coeff_real @ eigen__0) @ X1)) @ ring_1_Ints_real)),introduced(assumption,[])).
% 8.81/9.14 thf(h3,assumption,(~(((~((eigen__0 = zero_zero_poly_real))) => (~((((poly_real2 @ eigen__0) @ x) = zero_zero_real)))))),introduced(assumption,[])).
% 8.81/9.14 thf(h4,assumption,(~((eigen__0 = zero_zero_poly_real))),introduced(assumption,[])).
% 8.81/9.14 thf(h5,assumption,(((poly_real2 @ eigen__0) @ x) = zero_zero_real),introduced(assumption,[])).
% 8.81/9.14 thf(pax6, axiom, (p6=>(fn)=(fdegree_real @ fp)), file('<stdin>', pax6)).
% 8.81/9.14 thf(pax59, axiom, (p59=>![X49:poly_real, X50:int, X51:int]:(![X52:nat]:fmember_real @ (fcoeff_real @ X49 @ X52) @ fring_1_Ints_real=>(ford_less_int @ fzero_zero_int @ X50=>(~((fpoly_real2 @ X49 @ (fdivide_divide_real @ (fring_1_of_int_real @ X51) @ (fring_1_of_int_real @ X50)))=(fzero_zero_real))=>ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ X50) @ (fdegree_real @ X49))) @ (fabs_abs_real @ (fpoly_real2 @ X49 @ (fdivide_divide_real @ (fring_1_of_int_real @ X51) @ (fring_1_of_int_real @ X50)))))))), file('<stdin>', pax59)).
% 8.81/9.14 thf(pax2, axiom, (p2=>![X77:nat]:fmember_real @ (fcoeff_real @ fp @ X77) @ fring_1_Ints_real), file('<stdin>', pax2)).
% 8.81/9.14 thf(nax163, axiom, (p163<=ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ fb) @ (fdegree_real @ fp))) @ (fabs_abs_real @ (fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb))))), file('<stdin>', nax163)).
% 8.81/9.14 thf(ax165, axiom, p6, file('<stdin>', ax165)).
% 8.81/9.14 thf(ax8, axiom, ~(p163), file('<stdin>', ax8)).
% 8.81/9.14 thf(ax112, axiom, p59, file('<stdin>', ax112)).
% 8.81/9.14 thf(ax169, axiom, p2, file('<stdin>', ax169)).
% 8.81/9.14 thf(pax3, axiom, (p3=>ford_less_int @ fzero_zero_int @ fb), file('<stdin>', pax3)).
% 8.81/9.14 thf(nax5, axiom, (p5<=(fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb)))=(fzero_zero_real)), file('<stdin>', nax5)).
% 8.81/9.14 thf(ax166, axiom, ~(p5), file('<stdin>', ax166)).
% 8.81/9.14 thf(ax168, axiom, p3, file('<stdin>', ax168)).
% 8.81/9.14 thf(c_0_12, plain, (~p6|(fn)=(fdegree_real @ fp)), inference(fof_nnf,[status(thm)],[pax6])).
% 8.81/9.14 thf(c_0_13, plain, ![X382:poly_real, X384:int, X385:int]:(~p59|(~fmember_real @ (fcoeff_real @ X382 @ (esk153_1 @ X382)) @ fring_1_Ints_real|(~ford_less_int @ fzero_zero_int @ X384|((fpoly_real2 @ X382 @ (fdivide_divide_real @ (fring_1_of_int_real @ X385) @ (fring_1_of_int_real @ X384)))=(fzero_zero_real)|ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ X384) @ (fdegree_real @ X382))) @ (fabs_abs_real @ (fpoly_real2 @ X382 @ (fdivide_divide_real @ (fring_1_of_int_real @ X385) @ (fring_1_of_int_real @ X384)))))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax59])])])])])])).
% 8.81/9.14 thf(c_0_14, plain, ![X456:nat]:(~p2|fmember_real @ (fcoeff_real @ fp @ X456) @ fring_1_Ints_real), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 8.81/9.14 thf(c_0_15, plain, (~ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ fb) @ (fdegree_real @ fp))) @ (fabs_abs_real @ (fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb))))|p163), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax163])])).
% 8.81/9.14 thf(c_0_16, plain, ((fn)=(fdegree_real @ fp)|~p6), inference(split_conjunct,[status(thm)],[c_0_12])).
% 8.81/9.14 thf(c_0_17, plain, p6, inference(split_conjunct,[status(thm)],[ax165])).
% 8.81/9.14 thf(c_0_18, plain, ~p163, inference(fof_simplification,[status(thm)],[ax8])).
% 8.81/9.14 thf(c_0_19, plain, ![X25:poly_real, X3:int, X2:int]:((fpoly_real2 @ X25 @ (fdivide_divide_real @ (fring_1_of_int_real @ X3) @ (fring_1_of_int_real @ X2)))=(fzero_zero_real)|ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ X2) @ (fdegree_real @ X25))) @ (fabs_abs_real @ (fpoly_real2 @ X25 @ (fdivide_divide_real @ (fring_1_of_int_real @ X3) @ (fring_1_of_int_real @ X2))))|~p59|~fmember_real @ (fcoeff_real @ X25 @ (esk153_1 @ X25)) @ fring_1_Ints_real|~ford_less_int @ fzero_zero_int @ X2), inference(split_conjunct,[status(thm)],[c_0_13])).
% 8.81/9.14 thf(c_0_20, plain, p59, inference(split_conjunct,[status(thm)],[ax112])).
% 8.81/9.14 thf(c_0_21, plain, ![X1:nat]:(fmember_real @ (fcoeff_real @ fp @ X1) @ fring_1_Ints_real|~p2), inference(split_conjunct,[status(thm)],[c_0_14])).
% 8.81/9.14 thf(c_0_22, plain, p2, inference(split_conjunct,[status(thm)],[ax169])).
% 8.81/9.14 thf(c_0_23, plain, (~p3|ford_less_int @ fzero_zero_int @ fb), inference(fof_nnf,[status(thm)],[pax3])).
% 8.81/9.14 thf(c_0_24, plain, ((fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb)))!=(fzero_zero_real)|p5), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax5])])).
% 8.81/9.14 thf(c_0_25, plain, ~p5, inference(fof_simplification,[status(thm)],[ax166])).
% 8.81/9.14 thf(c_0_26, plain, (p163|~ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ fb) @ (fdegree_real @ fp))) @ (fabs_abs_real @ (fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb))))), inference(split_conjunct,[status(thm)],[c_0_15])).
% 8.81/9.14 thf(c_0_27, plain, (fdegree_real @ fp)=(fn), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 8.81/9.14 thf(c_0_28, plain, ~p163, inference(split_conjunct,[status(thm)],[c_0_18])).
% 8.81/9.14 thf(c_0_29, plain, ![X2:int, X25:poly_real, X3:int]:((fpoly_real2 @ X25 @ (fdivide_divide_real @ (fring_1_of_int_real @ X2) @ (fring_1_of_int_real @ X3)))=(fzero_zero_real)|ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ X3) @ (fdegree_real @ X25))) @ (fabs_abs_real @ (fpoly_real2 @ X25 @ (fdivide_divide_real @ (fring_1_of_int_real @ X2) @ (fring_1_of_int_real @ X3))))|~fmember_real @ (fcoeff_real @ X25 @ (esk153_1 @ X25)) @ fring_1_Ints_real|~ford_less_int @ fzero_zero_int @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 8.81/9.14 thf(c_0_30, plain, ![X1:nat]:fmember_real @ (fcoeff_real @ fp @ X1) @ fring_1_Ints_real, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22])])).
% 8.81/9.14 thf(c_0_31, plain, (ford_less_int @ fzero_zero_int @ fb|~p3), inference(split_conjunct,[status(thm)],[c_0_23])).
% 8.81/9.14 thf(c_0_32, plain, p3, inference(split_conjunct,[status(thm)],[ax168])).
% 8.81/9.14 thf(c_0_33, plain, (p5|(fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb)))!=(fzero_zero_real)), inference(split_conjunct,[status(thm)],[c_0_24])).
% 8.81/9.14 thf(c_0_34, plain, ~p5, inference(split_conjunct,[status(thm)],[c_0_25])).
% 8.81/9.14 thf(c_0_35, plain, ~ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ fb) @ fn)) @ (fabs_abs_real @ (fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb)))), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27]), c_0_28])).
% 8.81/9.14 thf(c_0_36, plain, ![X2:int, X3:int]:((fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ X2) @ (fring_1_of_int_real @ X3)))=(fzero_zero_real)|ford_less_eq_real @ (fdivide_divide_real @ fone_one_real @ (fpower_power_real @ (fring_1_of_int_real @ X3) @ fn)) @ (fabs_abs_real @ (fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ X2) @ (fring_1_of_int_real @ X3))))|~ford_less_int @ fzero_zero_int @ X3), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_27])).
% 8.81/9.14 thf(c_0_37, plain, ford_less_int @ fzero_zero_int @ fb, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 8.81/9.14 thf(c_0_38, plain, (fpoly_real2 @ fp @ (fdivide_divide_real @ (fring_1_of_int_real @ fa2) @ (fring_1_of_int_real @ fb)))!=(fzero_zero_real), inference(sr,[status(thm)],[c_0_33, c_0_34])).
% 8.81/9.14 thf(c_0_39, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_37])]), c_0_38]), ['proof']).
% 8.81/9.14 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[])).
% 8.81/9.14 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,1,h4,h5])).
% 8.81/9.14 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,2,h2,h3])).
% 8.81/9.14 thf(fact_36__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062,axiom,(~((![X1:poly_real]:((![X2:nat]:((member_real @ ((coeff_real @ X1) @ X2)) @ ring_1_Ints_real)) => ((~((X1 = zero_zero_poly_real))) => (~((((poly_real2 @ X1) @ x) = zero_zero_real))))))))).
% 8.81/9.14 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_36__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062,3,h1])).
% 8.81/9.14 thf(0,theorem,((ord_less_eq_real @ ((divide_divide_real @ one_one_real) @ ((power_power_real @ (ring_1_of_int_real @ b)) @ (degree_real @ p)))) @ (abs_abs_real @ ((poly_real2 @ p) @ ((divide_divide_real @ (ring_1_of_int_real @ a2)) @ (ring_1_of_int_real @ b))))),inference(contra,[status(thm),contra(discharge,[h0])],[4,h0])).
% 8.81/9.14 % SZS output end Proof
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