TSTP Solution File: ALG249^3 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG249^3 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : Thu Jul 14 17:57:44 EDT 2022
% Result : Theorem 1.08s 1.27s
% Output : Proof 1.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG249^3 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 19:20:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.08/1.27 % SZS status Theorem
% 1.08/1.27 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 1.08/1.27 % Inferences: 68
% 1.08/1.27 % SZS output start Proof
% 1.08/1.27 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
% 1.08/1.27 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
% 1.08/1.27 thf(def_pushprop_p_and_p_prime,definition,(pushprop_p_and_p_prime = (^[X1:term]:(^[X2:subst]:(^[X3:term>$o]:(^[X4:term>$o]:(![X5:term]:((X4 @ X5) = (X3 @ ((sub @ X5) @ ((push @ X1) @ X2))))))))))).
% 1.08/1.27 thf(def_pushprop_lem2v2,definition,(pushprop_lem2v2 = (![X1:term>$o]:(![X2:term>$o]:(![X3:term]:(![X4:subst]:(((((pushprop_p_and_p_prime @ X3) @ X4) @ X1) @ X2) => ((![X5:term]:((var @ X5) => (X1 @ ((sub @ X5) @ X4)))) => (![X5:term]:((var @ X5) => ((X2 @ X5) => (X2 @ ((sub @ X5) @ sh))))))))))))).
% 1.08/1.27 thf(def_pushprop_lem2v2_lthm,definition,(pushprop_lem2v2_lthm = (axclos => (axshiftcons => pushprop_lem2v2)))).
% 1.08/1.27 thf(thm,conjecture,((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => (![X1:term>$o]:(![X2:term>$o]:(![X3:term]:(![X4:subst]:((![X5:term]:((X2 @ X5) = (X1 @ ((sub @ X5) @ ((push @ X3) @ X4))))) => ((![X5:term]:((var @ X5) => (X1 @ ((sub @ X5) @ X4)))) => (![X5:term]:((var @ X5) => ((X2 @ X5) => (X2 @ ((sub @ X5) @ sh)))))))))))))).
% 1.08/1.27 thf(h0,negated_conjecture,(~(((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => (![X1:term>$o]:(![X2:term>$o]:(![X3:term]:(![X4:subst]:((![X5:term]:((X2 @ X5) = (X1 @ ((sub @ X5) @ ((push @ X3) @ X4))))) => ((![X5:term]:((var @ X5) => (X1 @ ((sub @ X5) @ X4)))) => (![X5:term]:((var @ X5) => ((X2 @ X5) => (X2 @ ((sub @ X5) @ sh))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 1.08/1.27 thf(ax1587, axiom, (p1|~(p3)), file('<stdin>', ax1587)).
% 1.08/1.27 thf(ax1589, axiom, ~(p1), file('<stdin>', ax1589)).
% 1.08/1.27 thf(ax1585, axiom, (p3|~(p5)), file('<stdin>', ax1585)).
% 1.08/1.27 thf(ax1582, axiom, (p5|~(p8)), file('<stdin>', ax1582)).
% 1.08/1.27 thf(ax1546, axiom, (p8|~(p44)), file('<stdin>', ax1546)).
% 1.08/1.27 thf(ax1539, axiom, (p44|~(p51)), file('<stdin>', ax1539)).
% 1.08/1.27 thf(ax1487, axiom, (p51|~(p101)), file('<stdin>', ax1487)).
% 1.08/1.27 thf(ax1303, axiom, (~(p2)|p278), file('<stdin>', ax1303)).
% 1.08/1.27 thf(ax1588, axiom, (p1|p2), file('<stdin>', ax1588)).
% 1.08/1.27 thf(ax1424, axiom, (p101|~(p163)), file('<stdin>', ax1424)).
% 1.08/1.27 thf(ax987, axiom, (~(p278)|p575), file('<stdin>', ax987)).
% 1.08/1.27 thf(ax1405, axiom, (p163|~(p182)), file('<stdin>', ax1405)).
% 1.08/1.27 thf(pax4, axiom, (p4=>![X62:term, X60:subst]:(fcomp @ fsh @ (fpush @ X62 @ X60))=(X60)), file('<stdin>', pax4)).
% 1.08/1.27 thf(ax1586, axiom, (p3|p4), file('<stdin>', ax1586)).
% 1.08/1.27 thf(ax956, axiom, (~(p575)|p602), file('<stdin>', ax956)).
% 1.08/1.27 thf(ax1305, axiom, (~(p181)|p276), file('<stdin>', ax1305)).
% 1.08/1.27 thf(ax1406, axiom, (p163|p181), file('<stdin>', ax1406)).
% 1.08/1.27 thf(ax1366, axiom, (p182|~(p220)), file('<stdin>', ax1366)).
% 1.08/1.27 thf(pax602, axiom, (p602=>(fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))=(fsub @ f__6 @ (fcomp @ fsh @ (fpush @ f__4 @ f__5)))), file('<stdin>', pax602)).
% 1.08/1.27 thf(ax1317, axiom, (~(p162)|p260), file('<stdin>', ax1317)).
% 1.08/1.27 thf(ax1425, axiom, (p101|p162), file('<stdin>', ax1425)).
% 1.08/1.27 thf(ax1306, axiom, (~(p276)|~(p269)|p275), file('<stdin>', ax1306)).
% 1.08/1.27 thf(nax431, axiom, (p431<=f__1 @ (fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))), file('<stdin>', nax431)).
% 1.08/1.27 thf(ax922, axiom, (~(p260)|p292|~(p431)), file('<stdin>', ax922)).
% 1.08/1.27 thf(ax1312, axiom, (p220|p269), file('<stdin>', ax1312)).
% 1.08/1.27 thf(pax275, axiom, (p275=>f__1 @ (fsub @ f__6 @ f__5)), file('<stdin>', pax275)).
% 1.08/1.27 thf(ax1289, axiom, (p270|~(p292)), file('<stdin>', ax1289)).
% 1.08/1.27 thf(ax1311, axiom, (p220|~(p270)), file('<stdin>', ax1311)).
% 1.08/1.27 thf(c_0_28, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1587])).
% 1.08/1.27 thf(c_0_29, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1589])).
% 1.08/1.27 thf(c_0_30, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1585])).
% 1.08/1.27 thf(c_0_31, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_28])).
% 1.08/1.27 thf(c_0_32, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_29])).
% 1.08/1.27 thf(c_0_33, plain, (p5|~p8), inference(fof_simplification,[status(thm)],[ax1582])).
% 1.08/1.27 thf(c_0_34, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_30])).
% 1.08/1.27 thf(c_0_35, plain, ~p3, inference(sr,[status(thm)],[c_0_31, c_0_32])).
% 1.08/1.27 thf(c_0_36, plain, (p8|~p44), inference(fof_simplification,[status(thm)],[ax1546])).
% 1.08/1.27 thf(c_0_37, plain, (p5|~p8), inference(split_conjunct,[status(thm)],[c_0_33])).
% 1.08/1.27 thf(c_0_38, plain, ~p5, inference(sr,[status(thm)],[c_0_34, c_0_35])).
% 1.08/1.27 thf(c_0_39, plain, (p44|~p51), inference(fof_simplification,[status(thm)],[ax1539])).
% 1.08/1.27 thf(c_0_40, plain, (p8|~p44), inference(split_conjunct,[status(thm)],[c_0_36])).
% 1.08/1.27 thf(c_0_41, plain, ~p8, inference(sr,[status(thm)],[c_0_37, c_0_38])).
% 1.08/1.27 thf(c_0_42, plain, (p51|~p101), inference(fof_simplification,[status(thm)],[ax1487])).
% 1.08/1.27 thf(c_0_43, plain, (p44|~p51), inference(split_conjunct,[status(thm)],[c_0_39])).
% 1.08/1.27 thf(c_0_44, plain, ~p44, inference(sr,[status(thm)],[c_0_40, c_0_41])).
% 1.08/1.27 thf(c_0_45, plain, (~p2|p278), inference(fof_simplification,[status(thm)],[ax1303])).
% 1.08/1.27 thf(c_0_46, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1588])).
% 1.08/1.27 thf(c_0_47, plain, (p101|~p163), inference(fof_simplification,[status(thm)],[ax1424])).
% 1.08/1.27 thf(c_0_48, plain, (p51|~p101), inference(split_conjunct,[status(thm)],[c_0_42])).
% 1.08/1.27 thf(c_0_49, plain, ~p51, inference(sr,[status(thm)],[c_0_43, c_0_44])).
% 1.08/1.27 thf(c_0_50, plain, (~p278|p575), inference(fof_simplification,[status(thm)],[ax987])).
% 1.08/1.27 thf(c_0_51, plain, (p278|~p2), inference(split_conjunct,[status(thm)],[c_0_45])).
% 1.08/1.27 thf(c_0_52, plain, p2, inference(sr,[status(thm)],[c_0_46, c_0_32])).
% 1.08/1.27 thf(c_0_53, plain, (p101|~p163), inference(split_conjunct,[status(thm)],[c_0_47])).
% 1.08/1.27 thf(c_0_54, plain, ~p101, inference(sr,[status(thm)],[c_0_48, c_0_49])).
% 1.08/1.27 thf(c_0_55, plain, (p163|~p182), inference(fof_simplification,[status(thm)],[ax1405])).
% 1.08/1.27 thf(c_0_56, plain, ![X1425:term, X1426:subst]:(~p4|(fcomp @ fsh @ (fpush @ X1425 @ X1426))=(X1426)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 1.08/1.27 thf(c_0_57, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1586])).
% 1.08/1.27 thf(c_0_58, plain, (~p575|p602), inference(fof_simplification,[status(thm)],[ax956])).
% 1.08/1.27 thf(c_0_59, plain, (p575|~p278), inference(split_conjunct,[status(thm)],[c_0_50])).
% 1.08/1.27 thf(c_0_60, plain, p278, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 1.08/1.27 thf(c_0_61, plain, (~p181|p276), inference(fof_simplification,[status(thm)],[ax1305])).
% 1.08/1.27 thf(c_0_62, plain, (p163|p181), inference(split_conjunct,[status(thm)],[ax1406])).
% 1.08/1.27 thf(c_0_63, plain, ~p163, inference(sr,[status(thm)],[c_0_53, c_0_54])).
% 1.08/1.27 thf(c_0_64, plain, (p182|~p220), inference(fof_simplification,[status(thm)],[ax1366])).
% 1.08/1.27 thf(c_0_65, plain, (p163|~p182), inference(split_conjunct,[status(thm)],[c_0_55])).
% 1.08/1.27 thf(c_0_66, plain, (~p602|(fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))=(fsub @ f__6 @ (fcomp @ fsh @ (fpush @ f__4 @ f__5)))), inference(fof_nnf,[status(thm)],[pax602])).
% 1.08/1.27 thf(c_0_67, plain, ![X4:term, X1:subst]:((fcomp @ fsh @ (fpush @ X4 @ X1))=(X1)|~p4), inference(split_conjunct,[status(thm)],[c_0_56])).
% 1.08/1.27 thf(c_0_68, plain, p4, inference(sr,[status(thm)],[c_0_57, c_0_35])).
% 1.08/1.27 thf(c_0_69, plain, (p602|~p575), inference(split_conjunct,[status(thm)],[c_0_58])).
% 1.08/1.27 thf(c_0_70, plain, p575, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])).
% 1.08/1.27 thf(c_0_71, plain, (~p162|p260), inference(fof_simplification,[status(thm)],[ax1317])).
% 1.08/1.27 thf(c_0_72, plain, (p101|p162), inference(split_conjunct,[status(thm)],[ax1425])).
% 1.08/1.27 thf(c_0_73, plain, (~p276|~p269|p275), inference(fof_simplification,[status(thm)],[ax1306])).
% 1.08/1.27 thf(c_0_74, plain, (p276|~p181), inference(split_conjunct,[status(thm)],[c_0_61])).
% 1.08/1.27 thf(c_0_75, plain, p181, inference(sr,[status(thm)],[c_0_62, c_0_63])).
% 1.08/1.27 thf(c_0_76, plain, (p182|~p220), inference(split_conjunct,[status(thm)],[c_0_64])).
% 1.08/1.27 thf(c_0_77, plain, ~p182, inference(sr,[status(thm)],[c_0_65, c_0_63])).
% 1.08/1.27 thf(c_0_78, plain, (~f__1 @ (fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))|p431), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax431])])).
% 1.08/1.27 thf(c_0_79, plain, ((fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))=(fsub @ f__6 @ (fcomp @ fsh @ (fpush @ f__4 @ f__5)))|~p602), inference(split_conjunct,[status(thm)],[c_0_66])).
% 1.08/1.27 thf(c_0_80, plain, ![X4:term, X1:subst]:(fcomp @ fsh @ (fpush @ X4 @ X1))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])).
% 1.08/1.27 thf(c_0_81, plain, p602, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])).
% 1.08/1.27 thf(c_0_82, plain, (~p260|p292|~p431), inference(fof_simplification,[status(thm)],[ax922])).
% 1.08/1.27 thf(c_0_83, plain, (p260|~p162), inference(split_conjunct,[status(thm)],[c_0_71])).
% 1.08/1.27 thf(c_0_84, plain, p162, inference(sr,[status(thm)],[c_0_72, c_0_54])).
% 1.08/1.27 thf(c_0_85, plain, (p275|~p276|~p269), inference(split_conjunct,[status(thm)],[c_0_73])).
% 1.08/1.27 thf(c_0_86, plain, p276, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75])])).
% 1.08/1.27 thf(c_0_87, plain, (p220|p269), inference(split_conjunct,[status(thm)],[ax1312])).
% 1.08/1.27 thf(c_0_88, plain, ~p220, inference(sr,[status(thm)],[c_0_76, c_0_77])).
% 1.08/1.27 thf(c_0_89, plain, (p431|~f__1 @ (fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))), inference(split_conjunct,[status(thm)],[c_0_78])).
% 1.08/1.27 thf(c_0_90, plain, (fsub @ (fsub @ f__6 @ fsh) @ (fpush @ f__4 @ f__5))=(fsub @ f__6 @ f__5), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80]), c_0_81])])).
% 1.08/1.27 thf(c_0_91, plain, (~p275|f__1 @ (fsub @ f__6 @ f__5)), inference(fof_nnf,[status(thm)],[pax275])).
% 1.08/1.27 thf(c_0_92, plain, (p292|~p260|~p431), inference(split_conjunct,[status(thm)],[c_0_82])).
% 1.08/1.27 thf(c_0_93, plain, p260, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])])).
% 1.08/1.27 thf(c_0_94, plain, (p270|~p292), inference(fof_simplification,[status(thm)],[ax1289])).
% 1.08/1.27 thf(c_0_95, plain, (p220|~p270), inference(fof_simplification,[status(thm)],[ax1311])).
% 1.08/1.27 thf(c_0_96, plain, (p275|~p269), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85, c_0_86])])).
% 1.08/1.27 thf(c_0_97, plain, p269, inference(sr,[status(thm)],[c_0_87, c_0_88])).
% 1.08/1.27 thf(c_0_98, plain, (p431|~f__1 @ (fsub @ f__6 @ f__5)), inference(rw,[status(thm)],[c_0_89, c_0_90])).
% 1.08/1.27 thf(c_0_99, plain, (f__1 @ (fsub @ f__6 @ f__5)|~p275), inference(split_conjunct,[status(thm)],[c_0_91])).
% 1.08/1.27 thf(c_0_100, plain, (p292|~p431), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93])])).
% 1.08/1.27 thf(c_0_101, plain, (p270|~p292), inference(split_conjunct,[status(thm)],[c_0_94])).
% 1.08/1.27 thf(c_0_102, plain, (p220|~p270), inference(split_conjunct,[status(thm)],[c_0_95])).
% 1.08/1.27 thf(c_0_103, plain, p275, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97])])).
% 1.08/1.27 thf(c_0_104, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_98, c_0_99, c_0_100, c_0_101, c_0_102, c_0_88, c_0_103]), ['proof']).
% 1.08/1.27 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 1.08/1.27 thf(0,theorem,((![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))) => ((![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))) => (![X1:term>$o]:(![X2:term>$o]:(![X3:term]:(![X4:subst]:((![X5:term]:((X2 @ X5) = (X1 @ ((sub @ X5) @ ((push @ X3) @ X4))))) => ((![X5:term]:((var @ X5) => (X1 @ ((sub @ X5) @ X4)))) => (![X5:term]:((var @ X5) => ((X2 @ X5) => (X2 @ ((sub @ X5) @ sh))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 1.08/1.27 % SZS output end Proof
%------------------------------------------------------------------------------