TSTP Solution File: ITP170^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP170^1 : 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 : 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 : 600s
% DateTime : Sun Jul 17 00:29:22 EDT 2022
% Result : Theorem 6.87s 7.07s
% Output : Proof 6.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP170^1 : 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
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jun 4 01:32:33 EDT 2022
% 0.11/0.32 % CPUTime :
% 6.87/7.07 % SZS status Theorem
% 6.87/7.07 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 6.87/7.07 % Inferences: 9
% 6.87/7.07 % SZS output start Proof
% 6.87/7.07 thf(ty_view_e774982825t_unit, type, view_e774982825t_unit : $tType).
% 6.87/7.07 thf(ty_real_int, type, real_int : $tType).
% 6.87/7.07 thf(ty_traffic, type, traffic : $tType).
% 6.87/7.07 thf(ty_real, type, real : $tType).
% 6.87/7.07 thf(ty_cars, type, cars : $tType).
% 6.87/7.07 thf(ty_d, type, d : cars).
% 6.87/7.07 thf(ty_left, type, left : (real_int>real)).
% 6.87/7.07 thf(ty_v, type, v : view_e774982825t_unit).
% 6.87/7.07 thf(ty_regular_regular, type, regular_regular : (cars>traffic>cars>real)).
% 6.87/7.07 thf(ty_ts, type, ts : traffic).
% 6.87/7.07 thf(ty_right, type, right : (real_int>real)).
% 6.87/7.07 thf(ty_space, type, space : ((cars>traffic>cars>real)>traffic>view_e774982825t_unit>cars>real_int)).
% 6.87/7.07 thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
% 6.87/7.07 thf(ty_c, type, c : cars).
% 6.87/7.07 thf(ty_ext_Product_unit, type, ext_Product_unit : (view_e774982825t_unit>real_int)).
% 6.87/7.07 thf(conj_0,conjecture,(~((((ord_less_real @ (left @ ((((space @ regular_regular) @ ts) @ v) @ d))) @ (right @ (ext_Product_unit @ v))) => (~(((ord_less_real @ (left @ (ext_Product_unit @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ d))))))))).
% 6.87/7.07 thf(h0,negated_conjecture,(((ord_less_real @ (left @ ((((space @ regular_regular) @ ts) @ v) @ d))) @ (right @ (ext_Product_unit @ v))) => (~(((ord_less_real @ (left @ (ext_Product_unit @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ d)))))),inference(assume_negation,[status(cth)],[conj_0])).
% 6.87/7.07 thf(h1,assumption,(~(((ord_less_real @ (left @ ((((space @ regular_regular) @ ts) @ v) @ d))) @ (right @ (ext_Product_unit @ v))))),introduced(assumption,[])).
% 6.87/7.07 thf(h2,assumption,(~(((ord_less_real @ (left @ (ext_Product_unit @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ d))))),introduced(assumption,[])).
% 6.87/7.07 thf(h3,assumption,((ord_less_real @ (left @ ((((space @ regular_regular) @ ts) @ v) @ c))) @ (right @ (ext_Product_unit @ v))),introduced(assumption,[])).
% 6.87/7.07 thf(h4,assumption,((ord_less_real @ (left @ (ext_Product_unit @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ c))),introduced(assumption,[])).
% 6.87/7.07 thf(nax125, axiom, (p125<=ford_less_real @ (fleft @ (fspace @ fregular_regular @ fts @ fv @ fd)) @ (fright @ (fext_Product_unit @ fv))), file('<stdin>', nax125)).
% 6.87/7.07 thf(ax7, axiom, ~(p125), file('<stdin>', ax7)).
% 6.87/7.07 thf(pax9, axiom, (p9=>![X118:traffic, X119:view_e774982825t_unit, X117:cars]:(fleft @ (fspace @ fregular_regular @ X118 @ X119 @ X117))=(fpos @ X118 @ X117)), file('<stdin>', pax9)).
% 6.87/7.07 thf(pax10, axiom, (p10=>(flen @ fregular_regular @ fv @ fts @ fc)=(flen @ fregular_regular @ fv @ fts @ fd)), file('<stdin>', pax10)).
% 6.87/7.07 thf(ax123, axiom, p9, file('<stdin>', ax123)).
% 6.87/7.07 thf(pax2, axiom, (p2=>![X120:view_e774982825t_unit, X121:traffic, X117:cars]:(ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X120 @ X121 @ X117))=>~((ford_less_real @ (fleft @ (fspace @ fregular_regular @ X121 @ X120 @ X117)) @ (fright @ (fext_Product_unit @ X120))=>~(ford_less_real @ (fleft @ (fext_Product_unit @ X120)) @ (fright @ (fspace @ fregular_regular @ X121 @ X120 @ X117))))))), file('<stdin>', pax2)).
% 6.87/7.07 thf(pax3, axiom, (p3=>ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fd))), file('<stdin>', pax3)).
% 6.87/7.07 thf(ax122, axiom, p10, file('<stdin>', ax122)).
% 6.87/7.07 thf(ax130, axiom, p2, file('<stdin>', ax130)).
% 6.87/7.07 thf(ax129, axiom, p3, file('<stdin>', ax129)).
% 6.87/7.07 thf(c_0_10, plain, (~ford_less_real @ (fleft @ (fspace @ fregular_regular @ fts @ fv @ fd)) @ (fright @ (fext_Product_unit @ fv))|p125), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax125])])).
% 6.87/7.07 thf(c_0_11, plain, ~p125, inference(fof_simplification,[status(thm)],[ax7])).
% 6.87/7.07 thf(c_0_12, plain, ![X789:traffic, X790:view_e774982825t_unit, X791:cars]:(~p9|(fleft @ (fspace @ fregular_regular @ X789 @ X790 @ X791))=(fpos @ X789 @ X791)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax9])])])).
% 6.87/7.07 thf(c_0_13, plain, (~p10|(flen @ fregular_regular @ fv @ fts @ fc)=(flen @ fregular_regular @ fv @ fts @ fd)), inference(fof_nnf,[status(thm)],[pax10])).
% 6.87/7.07 thf(c_0_14, plain, (p125|~ford_less_real @ (fleft @ (fspace @ fregular_regular @ fts @ fv @ fd)) @ (fright @ (fext_Product_unit @ fv))), inference(split_conjunct,[status(thm)],[c_0_10])).
% 6.87/7.07 thf(c_0_15, plain, ~p125, inference(split_conjunct,[status(thm)],[c_0_11])).
% 6.87/7.07 thf(c_0_16, plain, ![X5:traffic, X6:view_e774982825t_unit, X7:cars]:((fleft @ (fspace @ fregular_regular @ X5 @ X6 @ X7))=(fpos @ X5 @ X7)|~p9), inference(split_conjunct,[status(thm)],[c_0_12])).
% 6.87/7.07 thf(c_0_17, plain, p9, inference(split_conjunct,[status(thm)],[ax123])).
% 6.87/7.07 thf(c_0_18, plain, ![X803:view_e774982825t_unit, X804:traffic, X805:cars]:((ford_less_real @ (fleft @ (fspace @ fregular_regular @ X804 @ X803 @ X805)) @ (fright @ (fext_Product_unit @ X803))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X803 @ X804 @ X805))|~p2)&(ford_less_real @ (fleft @ (fext_Product_unit @ X803)) @ (fright @ (fspace @ fregular_regular @ X804 @ X803 @ X805))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X803 @ X804 @ X805))|~p2)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])])])).
% 6.87/7.07 thf(c_0_19, plain, (~p3|ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fd))), inference(fof_nnf,[status(thm)],[pax3])).
% 6.87/7.07 thf(c_0_20, plain, ((flen @ fregular_regular @ fv @ fts @ fc)=(flen @ fregular_regular @ fv @ fts @ fd)|~p10), inference(split_conjunct,[status(thm)],[c_0_13])).
% 6.87/7.07 thf(c_0_21, plain, p10, inference(split_conjunct,[status(thm)],[ax122])).
% 6.87/7.07 thf(c_0_22, plain, ~ford_less_real @ (fleft @ (fspace @ fregular_regular @ fts @ fv @ fd)) @ (fright @ (fext_Product_unit @ fv)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 6.87/7.07 thf(c_0_23, plain, ![X5:traffic, X6:view_e774982825t_unit, X7:cars]:(fleft @ (fspace @ fregular_regular @ X5 @ X6 @ X7))=(fpos @ X5 @ X7), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 6.87/7.07 thf(c_0_24, plain, ![X5:traffic, X6:view_e774982825t_unit, X7:cars]:(ford_less_real @ (fleft @ (fspace @ fregular_regular @ X5 @ X6 @ X7)) @ (fright @ (fext_Product_unit @ X6))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X6 @ X5 @ X7))|~p2), inference(split_conjunct,[status(thm)],[c_0_18])).
% 6.87/7.07 thf(c_0_25, plain, p2, inference(split_conjunct,[status(thm)],[ax130])).
% 6.87/7.07 thf(c_0_26, plain, (ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fd))|~p3), inference(split_conjunct,[status(thm)],[c_0_19])).
% 6.87/7.07 thf(c_0_27, plain, (flen @ fregular_regular @ fv @ fts @ fd)=(flen @ fregular_regular @ fv @ fts @ fc), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 6.87/7.07 thf(c_0_28, plain, p3, inference(split_conjunct,[status(thm)],[ax129])).
% 6.87/7.07 thf(c_0_29, plain, ~ford_less_real @ (fpos @ fts @ fd) @ (fright @ (fext_Product_unit @ fv)), inference(rw,[status(thm)],[c_0_22, c_0_23])).
% 6.87/7.07 thf(c_0_30, plain, ![X5:traffic, X6:view_e774982825t_unit, X7:cars]:(ford_less_real @ (fpos @ X5 @ X7) @ (fright @ (fext_Product_unit @ X6))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X6 @ X5 @ X7))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_23]), c_0_25])])).
% 6.87/7.07 thf(c_0_31, plain, ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fc)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27]), c_0_28])])).
% 6.87/7.07 thf(c_0_32, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_27]), c_0_31])]), ['proof']).
% 6.87/7.07 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h3,h4,h1,h0])],[])).
% 6.87/7.07 thf(fact_9_v_H__rel__c,axiom,(~((((ord_less_real @ (left @ ((((space @ regular_regular) @ ts) @ v) @ c))) @ (right @ (ext_Product_unit @ v))) => (~(((ord_less_real @ (left @ (ext_Product_unit @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ c))))))))).
% 6.87/7.07 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h3,h4])],[fact_9_v_H__rel__c,1,h3,h4])).
% 6.87/7.07 thf(pax10, axiom, (p10=>(flen @ fregular_regular @ fv @ fts @ fc)=(flen @ fregular_regular @ fv @ fts @ fd)), file('<stdin>', pax10)).
% 6.87/7.07 thf(nax134, axiom, (p134<=ford_less_real @ (fleft @ (fext_Product_unit @ fv)) @ (fright @ (fspace @ fregular_regular @ fts @ fv @ fd))), file('<stdin>', nax134)).
% 6.87/7.07 thf(ax17, axiom, ~(p134), file('<stdin>', ax17)).
% 6.87/7.07 thf(pax2, axiom, (p2=>![X127:view_e774982825t_unit, X128:traffic, X124:cars]:(ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X127 @ X128 @ X124))=>~((ford_less_real @ (fleft @ (fspace @ fregular_regular @ X128 @ X127 @ X124)) @ (fright @ (fext_Product_unit @ X127))=>~(ford_less_real @ (fleft @ (fext_Product_unit @ X127)) @ (fright @ (fspace @ fregular_regular @ X128 @ X127 @ X124))))))), file('<stdin>', pax2)).
% 6.87/7.07 thf(pax3, axiom, (p3=>ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fd))), file('<stdin>', pax3)).
% 6.87/7.07 thf(ax132, axiom, p10, file('<stdin>', ax132)).
% 6.87/7.07 thf(ax140, axiom, p2, file('<stdin>', ax140)).
% 6.87/7.07 thf(ax139, axiom, p3, file('<stdin>', ax139)).
% 6.87/7.07 thf(c_0_8, plain, (~p10|(flen @ fregular_regular @ fv @ fts @ fc)=(flen @ fregular_regular @ fv @ fts @ fd)), inference(fof_nnf,[status(thm)],[pax10])).
% 6.87/7.07 thf(c_0_9, plain, (~ford_less_real @ (fleft @ (fext_Product_unit @ fv)) @ (fright @ (fspace @ fregular_regular @ fts @ fv @ fd))|p134), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax134])])).
% 6.87/7.07 thf(c_0_10, plain, ~p134, inference(fof_simplification,[status(thm)],[ax17])).
% 6.87/7.07 thf(c_0_11, plain, ![X830:view_e774982825t_unit, X831:traffic, X832:cars]:((ford_less_real @ (fleft @ (fspace @ fregular_regular @ X831 @ X830 @ X832)) @ (fright @ (fext_Product_unit @ X830))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X830 @ X831 @ X832))|~p2)&(ford_less_real @ (fleft @ (fext_Product_unit @ X830)) @ (fright @ (fspace @ fregular_regular @ X831 @ X830 @ X832))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X830 @ X831 @ X832))|~p2)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])])])).
% 6.87/7.07 thf(c_0_12, plain, (~p3|ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fd))), inference(fof_nnf,[status(thm)],[pax3])).
% 6.87/7.07 thf(c_0_13, plain, ((flen @ fregular_regular @ fv @ fts @ fc)=(flen @ fregular_regular @ fv @ fts @ fd)|~p10), inference(split_conjunct,[status(thm)],[c_0_8])).
% 6.87/7.07 thf(c_0_14, plain, p10, inference(split_conjunct,[status(thm)],[ax132])).
% 6.87/7.07 thf(c_0_15, plain, (p134|~ford_less_real @ (fleft @ (fext_Product_unit @ fv)) @ (fright @ (fspace @ fregular_regular @ fts @ fv @ fd))), inference(split_conjunct,[status(thm)],[c_0_9])).
% 6.87/7.07 thf(c_0_16, plain, ~p134, inference(split_conjunct,[status(thm)],[c_0_10])).
% 6.87/7.07 thf(c_0_17, plain, ![X1:view_e774982825t_unit, X5:traffic, X2:cars]:(ford_less_real @ (fleft @ (fext_Product_unit @ X1)) @ (fright @ (fspace @ fregular_regular @ X5 @ X1 @ X2))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X1 @ X5 @ X2))|~p2), inference(split_conjunct,[status(thm)],[c_0_11])).
% 6.87/7.07 thf(c_0_18, plain, p2, inference(split_conjunct,[status(thm)],[ax140])).
% 6.87/7.07 thf(c_0_19, plain, (ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fd))|~p3), inference(split_conjunct,[status(thm)],[c_0_12])).
% 6.87/7.07 thf(c_0_20, plain, (flen @ fregular_regular @ fv @ fts @ fd)=(flen @ fregular_regular @ fv @ fts @ fc), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14])])).
% 6.87/7.07 thf(c_0_21, plain, p3, inference(split_conjunct,[status(thm)],[ax139])).
% 6.87/7.07 thf(c_0_22, plain, ~ford_less_real @ (fleft @ (fext_Product_unit @ fv)) @ (fright @ (fspace @ fregular_regular @ fts @ fv @ fd)), inference(sr,[status(thm)],[c_0_15, c_0_16])).
% 6.87/7.07 thf(c_0_23, plain, ![X1:view_e774982825t_unit, X5:traffic, X2:cars]:(ford_less_real @ (fleft @ (fext_Product_unit @ X1)) @ (fright @ (fspace @ fregular_regular @ X5 @ X1 @ X2))|~ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ X1 @ X5 @ X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 6.87/7.07 thf(c_0_24, plain, ford_less_real @ fzero_zero_real @ (freal_length @ (flen @ fregular_regular @ fv @ fts @ fc)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20]), c_0_21])])).
% 6.87/7.07 thf(c_0_25, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_20]), c_0_24])]), ['proof']).
% 6.87/7.07 thf(3,plain,$false,inference(eprover,[status(thm),assumptions([h3,h4,h2,h0])],[])).
% 6.87/7.07 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h0]),tab_negimp(discharge,[h3,h4])],[fact_9_v_H__rel__c,3,h3,h4])).
% 6.87/7.07 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,2,4,h1,h2])).
% 6.87/7.07 thf(0,theorem,(~((((ord_less_real @ (left @ ((((space @ regular_regular) @ ts) @ v) @ d))) @ (right @ (ext_Product_unit @ v))) => (~(((ord_less_real @ (left @ (ext_Product_unit @ v))) @ (right @ ((((space @ regular_regular) @ ts) @ v) @ d)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])).
% 6.87/7.07 % SZS output end Proof
%------------------------------------------------------------------------------