%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP097^1 : 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 : n019.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 01:46:57 PM UTC 2025
% Result : Theorem 7.85s 8.06s
% Output : Proof 7.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP097^1 : 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
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 18:01:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 7.85/8.06 % SZS status Theorem
% 7.85/8.06 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 7.85/8.06 % Inferences: 6
% 7.85/8.06 % SZS output start Proof
% 7.85/8.06 thf(conj_0,conjecture,((ord_less_eq_int @ d) @ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (nat2 @ (archim1371465213g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ (ring_1_of_int_real @ d))))))).
% 7.85/8.06 thf(h0,negated_conjecture,(~(((ord_less_eq_int @ d) @ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (nat2 @ (archim1371465213g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ (ring_1_of_int_real @ d)))))))),inference(assume_negation,[status(cth)],[conj_0])).
% 7.85/8.06 thf(pax52, axiom, (p52=>(fring_1_of_int_real @ fd)=(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))), file('<stdin>', pax52)).
% 7.85/8.06 thf(pax84, axiom, (p84=>(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), file('<stdin>', pax84)).
% 7.85/8.06 thf(pax45, axiom, (p45=>![X36:real, X32:int]:(ford_less_eq_real @ X36 @ (fring_1_of_int_real @ X32)=>ford_less_eq_int @ (farchim1371465213g_real @ X36) @ X32)), file('<stdin>', pax45)).
% 7.85/8.06 thf(pax85, axiom, (p85=>ford_less_eq_real @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))) @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), file('<stdin>', pax85)).
% 7.85/8.06 thf(ax159, axiom, p52, file('<stdin>', ax159)).
% 7.85/8.06 thf(ax127, axiom, p84, file('<stdin>', ax127)).
% 7.85/8.06 thf(pax25, axiom, (p25=>![X41:int]:(farchim1371465213g_real @ (fring_1_of_int_real @ X41))=(X41)), file('<stdin>', pax25)).
% 7.85/8.06 thf(nax176, axiom, (p176<=ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), file('<stdin>', nax176)).
% 7.85/8.06 thf(ax35, axiom, ~(p176), file('<stdin>', ax35)).
% 7.85/8.06 thf(ax166, axiom, p45, file('<stdin>', ax166)).
% 7.85/8.06 thf(ax126, axiom, p85, file('<stdin>', ax126)).
% 7.85/8.06 thf(ax186, axiom, p25, file('<stdin>', ax186)).
% 7.85/8.06 thf(c_0_12, plain, (~p52|(fring_1_of_int_real @ fd)=(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))), inference(fof_nnf,[status(thm)],[pax52])).
% 7.85/8.06 thf(c_0_13, plain, (~p84|(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), inference(fof_nnf,[status(thm)],[pax84])).
% 7.85/8.06 thf(c_0_14, plain, ![X182:real, X183:int]:(~p45|(~ford_less_eq_real @ X182 @ (fring_1_of_int_real @ X183)|ford_less_eq_int @ (farchim1371465213g_real @ X182) @ X183)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax45])])])).
% 7.85/8.06 thf(c_0_15, plain, (~p85|ford_less_eq_real @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))) @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))), inference(fof_nnf,[status(thm)],[pax85])).
% 7.85/8.06 thf(c_0_16, plain, ((fring_1_of_int_real @ fd)=(fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))|~p52), inference(split_conjunct,[status(thm)],[c_0_12])).
% 7.85/8.06 thf(c_0_17, plain, p52, inference(split_conjunct,[status(thm)],[ax159])).
% 7.85/8.06 thf(c_0_18, plain, ((fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))|~p84), inference(split_conjunct,[status(thm)],[c_0_13])).
% 7.85/8.06 thf(c_0_19, plain, p84, inference(split_conjunct,[status(thm)],[ax127])).
% 7.85/8.06 thf(c_0_20, plain, ![X206:int]:(~p25|(farchim1371465213g_real @ (fring_1_of_int_real @ X206))=(X206)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax25])])])).
% 7.85/8.06 thf(c_0_21, plain, (~ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))|p176), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax176])])).
% 7.85/8.06 thf(c_0_22, plain, ~p176, inference(fof_simplification,[status(thm)],[ax35])).
% 7.85/8.06 thf(c_0_23, plain, ![X7:real, X1:int]:(ford_less_eq_int @ (farchim1371465213g_real @ X7) @ X1|~p45|~ford_less_eq_real @ X7 @ (fring_1_of_int_real @ X1)), inference(split_conjunct,[status(thm)],[c_0_14])).
% 7.85/8.06 thf(c_0_24, plain, p45, inference(split_conjunct,[status(thm)],[ax166])).
% 7.85/8.06 thf(c_0_25, plain, (ford_less_eq_real @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))) @ (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))|~p85), inference(split_conjunct,[status(thm)],[c_0_15])).
% 7.85/8.06 thf(c_0_26, plain, (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))=(fring_1_of_int_real @ fd), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 7.85/8.06 thf(c_0_27, plain, (fpowr_real @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fsemiri2110766477t_real @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))))=(fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])).
% 7.85/8.06 thf(c_0_28, plain, p85, inference(split_conjunct,[status(thm)],[ax126])).
% 7.85/8.06 thf(c_0_29, plain, ![X1:int]:((farchim1371465213g_real @ (fring_1_of_int_real @ X1))=(X1)|~p25), inference(split_conjunct,[status(thm)],[c_0_20])).
% 7.85/8.06 thf(c_0_30, plain, p25, inference(split_conjunct,[status(thm)],[ax186])).
% 7.85/8.06 thf(c_0_31, plain, (p176|~ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 7.85/8.06 thf(c_0_32, plain, ~p176, inference(split_conjunct,[status(thm)],[c_0_22])).
% 7.85/8.06 thf(c_0_33, plain, ![X7:real, X1:int]:(ford_less_eq_int @ (farchim1371465213g_real @ X7) @ X1|~ford_less_eq_real @ X7 @ (fring_1_of_int_real @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 7.85/8.06 thf(c_0_34, plain, ford_less_eq_real @ (fring_1_of_int_real @ fd) @ (fring_1_of_int_real @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26]), c_0_27]), c_0_28])])).
% 7.85/8.06 thf(c_0_35, plain, ![X1:int]:(farchim1371465213g_real @ (fring_1_of_int_real @ X1))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 7.85/8.06 thf(c_0_36, plain, ~ford_less_eq_int @ fd @ (fpower_power_int @ (fnumeral_numeral_int @ (fbit0 @ fone)) @ (fnat2 @ (farchim1371465213g_real @ (flog @ (fnumeral_numeral_real @ (fbit0 @ fone)) @ (fring_1_of_int_real @ fd))))), inference(sr,[status(thm)],[c_0_31, c_0_32])).
% 7.85/8.06 thf(c_0_37, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35]), c_0_36]), ['proof']).
% 7.85/8.06 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 7.85/8.06 thf(0,theorem,((ord_less_eq_int @ d) @ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (nat2 @ (archim1371465213g_real @ ((log @ (numeral_numeral_real @ (bit0 @ one))) @ (ring_1_of_int_real @ d)))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 7.85/8.06 % SZS output end Proof
%------------------------------------------------------------------------------