TSTP Solution File: ITP048^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP048^1 : 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 00:28:53 EDT 2022
% Result : Theorem 7.08s 7.26s
% Output : Proof 7.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : ITP048^1 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Thu Jun 2 20:02:01 EDT 2022
% 0.10/0.29 % CPUTime :
% 7.08/7.26 % SZS status Theorem
% 7.08/7.26 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 7.08/7.26 % Inferences: 2
% 7.08/7.26 % SZS output start Proof
% 7.08/7.26 thf(conj_0,conjecture,((ord_less_nat @ (((min_dist_capacity @ c) @ s) @ t)) @ ((plus_plus_nat @ (size_s1990949619at_nat @ p1a)) @ (size_s1990949619at_nat @ p2_a)))).
% 7.08/7.26 thf(h0,negated_conjecture,(~(((ord_less_nat @ (((min_dist_capacity @ c) @ s) @ t)) @ ((plus_plus_nat @ (size_s1990949619at_nat @ p1a)) @ (size_s1990949619at_nat @ p2_a))))),inference(assume_negation,[status(cth)],[conj_0])).
% 7.08/7.26 thf(pax73, axiom, (p73=>![X34:nat, X25:nat, X32:nat, X26:nat]:(ford_less_nat @ X34 @ X25=>(ford_less_eq_nat @ X32 @ X26=>ford_less_nat @ (fplus_plus_nat @ X34 @ X32) @ (fplus_plus_nat @ X25 @ X26)))), file('<stdin>', pax73)).
% 7.08/7.26 thf(pax1, axiom, (p1=>(fmin_dist_capacity @ fc @ fs @ ft)=(fplus_plus_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fmin_dist_capacity @ fc @ fua @ ft))), file('<stdin>', pax1)).
% 7.08/7.26 thf(nax152, axiom, (p152<=ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ ft) @ (fplus_plus_nat @ (fsize_s1990949619at_nat @ fp1a) @ (fsize_s1990949619at_nat @ fp2_a))), file('<stdin>', nax152)).
% 7.08/7.26 thf(ax0, axiom, ~(p152), file('<stdin>', ax0)).
% 7.08/7.26 thf(ax79, axiom, p73, file('<stdin>', ax79)).
% 7.08/7.26 thf(ax151, axiom, p1, file('<stdin>', ax151)).
% 7.08/7.26 thf(pax2, axiom, (p2=>ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fsize_s1990949619at_nat @ fp1a)), file('<stdin>', pax2)).
% 7.08/7.26 thf(pax3, axiom, (p3=>ford_less_eq_nat @ (fmin_dist_capacity @ fc @ fua @ ft) @ (fsize_s1990949619at_nat @ fp2_a)), file('<stdin>', pax3)).
% 7.08/7.26 thf(ax150, axiom, p2, file('<stdin>', ax150)).
% 7.08/7.26 thf(ax149, axiom, p3, file('<stdin>', ax149)).
% 7.08/7.26 thf(c_0_10, plain, ![X449:nat, X450:nat, X451:nat, X452:nat]:(~p73|(~ford_less_nat @ X449 @ X450|(~ford_less_eq_nat @ X451 @ X452|ford_less_nat @ (fplus_plus_nat @ X449 @ X451) @ (fplus_plus_nat @ X450 @ X452)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax73])])])).
% 7.08/7.26 thf(c_0_11, plain, (~p1|(fmin_dist_capacity @ fc @ fs @ ft)=(fplus_plus_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fmin_dist_capacity @ fc @ fua @ ft))), inference(fof_nnf,[status(thm)],[pax1])).
% 7.08/7.26 thf(c_0_12, plain, (~ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ ft) @ (fplus_plus_nat @ (fsize_s1990949619at_nat @ fp1a) @ (fsize_s1990949619at_nat @ fp2_a))|p152), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax152])])).
% 7.08/7.26 thf(c_0_13, plain, ~p152, inference(fof_simplification,[status(thm)],[ax0])).
% 7.08/7.26 thf(c_0_14, plain, ![X1:nat, X2:nat, X4:nat, X5:nat]:(ford_less_nat @ (fplus_plus_nat @ X1 @ X4) @ (fplus_plus_nat @ X2 @ X5)|~p73|~ford_less_nat @ X1 @ X2|~ford_less_eq_nat @ X4 @ X5), inference(split_conjunct,[status(thm)],[c_0_10])).
% 7.08/7.26 thf(c_0_15, plain, p73, inference(split_conjunct,[status(thm)],[ax79])).
% 7.08/7.26 thf(c_0_16, plain, ((fmin_dist_capacity @ fc @ fs @ ft)=(fplus_plus_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fmin_dist_capacity @ fc @ fua @ ft))|~p1), inference(split_conjunct,[status(thm)],[c_0_11])).
% 7.08/7.26 thf(c_0_17, plain, p1, inference(split_conjunct,[status(thm)],[ax151])).
% 7.08/7.26 thf(c_0_18, plain, (~p2|ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fsize_s1990949619at_nat @ fp1a)), inference(fof_nnf,[status(thm)],[pax2])).
% 7.08/7.26 thf(c_0_19, plain, (~p3|ford_less_eq_nat @ (fmin_dist_capacity @ fc @ fua @ ft) @ (fsize_s1990949619at_nat @ fp2_a)), inference(fof_nnf,[status(thm)],[pax3])).
% 7.08/7.26 thf(c_0_20, plain, (p152|~ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ ft) @ (fplus_plus_nat @ (fsize_s1990949619at_nat @ fp1a) @ (fsize_s1990949619at_nat @ fp2_a))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 7.08/7.26 thf(c_0_21, plain, ~p152, inference(split_conjunct,[status(thm)],[c_0_13])).
% 7.08/7.26 thf(c_0_22, plain, ![X1:nat, X2:nat, X4:nat, X5:nat]:(ford_less_nat @ (fplus_plus_nat @ X1 @ X2) @ (fplus_plus_nat @ X4 @ X5)|~ford_less_nat @ X1 @ X4|~ford_less_eq_nat @ X2 @ X5), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 7.08/7.26 thf(c_0_23, plain, (fplus_plus_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fmin_dist_capacity @ fc @ fua @ ft))=(fmin_dist_capacity @ fc @ fs @ ft), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 7.08/7.26 thf(c_0_24, plain, (ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fsize_s1990949619at_nat @ fp1a)|~p2), inference(split_conjunct,[status(thm)],[c_0_18])).
% 7.08/7.26 thf(c_0_25, plain, p2, inference(split_conjunct,[status(thm)],[ax150])).
% 7.08/7.26 thf(c_0_26, plain, (ford_less_eq_nat @ (fmin_dist_capacity @ fc @ fua @ ft) @ (fsize_s1990949619at_nat @ fp2_a)|~p3), inference(split_conjunct,[status(thm)],[c_0_19])).
% 7.08/7.26 thf(c_0_27, plain, p3, inference(split_conjunct,[status(thm)],[ax149])).
% 7.08/7.26 thf(c_0_28, plain, ~ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ ft) @ (fplus_plus_nat @ (fsize_s1990949619at_nat @ fp1a) @ (fsize_s1990949619at_nat @ fp2_a)), inference(sr,[status(thm)],[c_0_20, c_0_21])).
% 7.08/7.26 thf(c_0_29, plain, ![X1:nat, X2:nat]:(ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ ft) @ (fplus_plus_nat @ X1 @ X2)|~ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ X1|~ford_less_eq_nat @ (fmin_dist_capacity @ fc @ fua @ ft) @ X2), inference(spm,[status(thm)],[c_0_22, c_0_23])).
% 7.08/7.26 thf(c_0_30, plain, ford_less_nat @ (fmin_dist_capacity @ fc @ fs @ fua) @ (fsize_s1990949619at_nat @ fp1a), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 7.08/7.26 thf(c_0_31, plain, ford_less_eq_nat @ (fmin_dist_capacity @ fc @ fua @ ft) @ (fsize_s1990949619at_nat @ fp2_a), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 7.08/7.26 thf(c_0_32, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), c_0_31])]), ['proof']).
% 7.08/7.26 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 7.08/7.26 thf(0,theorem,((ord_less_nat @ (((min_dist_capacity @ c) @ s) @ t)) @ ((plus_plus_nat @ (size_s1990949619at_nat @ p1a)) @ (size_s1990949619at_nat @ p2_a))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 7.08/7.26 % SZS output end Proof
%------------------------------------------------------------------------------