TSTP Solution File: ALG251^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG251^2 : 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 153.42s 153.61s
% Output : Proof 153.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG251^2 : 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 12:25:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 153.42/153.61 % SZS status Theorem
% 153.42/153.61 % Mode: mode500:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 153.42/153.61 % Inferences: 26
% 153.42/153.61 % SZS output start Proof
% 153.42/153.61 thf(def_axvarcons,definition,(axvarcons = (![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))))).
% 153.42/153.61 thf(def_axclos,definition,(axclos = (![X1:term]:(![X2:subst]:(![X3:subst]:(((sub @ ((sub @ X1) @ X2)) @ X3) = ((sub @ X1) @ ((comp @ X2) @ X3)))))))).
% 153.42/153.61 thf(def_axshiftcons,definition,(axshiftcons = (![X1:term]:(![X2:subst]:(((comp @ sh) @ ((push @ X1) @ X2)) = X2))))).
% 153.42/153.61 thf(def_ulamvar1,definition,(ulamvar1 = (var @ one))).
% 153.42/153.61 thf(def_ulamvarind,definition,(ulamvarind = (![X1:term>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))))).
% 153.42/153.61 thf(def_pushprop_lem0,definition,(pushprop_lem0 = (![X1:term>$o]:(![X2:term]:(![X3:subst]:(~((![X4:term>$o]:(~(((((pushprop_p_and_p_prime @ X2) @ X3) @ X1) @ X4))))))))))).
% 153.42/153.61 thf(def_pushprop,definition,(pushprop = (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))).
% 153.42/153.61 thf(def_pushprop_lthm,definition,(pushprop_lthm = (pushprop_lem0 => (ulamvar1 => (axvarcons => (axclos => (axshiftcons => (ulamvarind => pushprop)))))))).
% 153.42/153.61 thf(thm,conjecture,((![X1:term>$o]:(![X2:term]:(![X3:subst]:(~((![X4:term>$o]:(~(((((pushprop_p_and_p_prime @ X2) @ X3) @ X1) @ X4))))))))) => ((var @ one) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![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>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))) => (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3))))))))))))))))).
% 153.42/153.61 thf(h0,negated_conjecture,(~(((![X1:term>$o]:(![X2:term]:(![X3:subst]:(~((![X4:term>$o]:(~(((((pushprop_p_and_p_prime @ X2) @ X3) @ X1) @ X4))))))))) => ((var @ one) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![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>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))) => (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))))))))),inference(assume_negation,[status(cth)],[thm])).
% 153.42/153.61 thf(ax57, axiom, (p1|~(p3)), file('<stdin>', ax57)).
% 153.42/153.61 thf(ax59, axiom, ~(p1), file('<stdin>', ax59)).
% 153.42/153.61 thf(ax55, axiom, (p3|~(p5)), file('<stdin>', ax55)).
% 153.42/153.61 thf(ax53, axiom, (p5|~(p7)), file('<stdin>', ax53)).
% 153.42/153.61 thf(ax51, axiom, (p7|~(p9)), file('<stdin>', ax51)).
% 153.42/153.61 thf(ax49, axiom, (p9|~(p11)), file('<stdin>', ax49)).
% 153.42/153.61 thf(pax6, axiom, (p6=>![X7:term, X8:subst]:(fsub @ fone @ (fpush @ X7 @ X8))=(X7)), file('<stdin>', pax6)).
% 153.42/153.61 thf(ax54, axiom, (p5|p6), file('<stdin>', ax54)).
% 153.42/153.61 thf(ax47, axiom, (p11|~(p13)), file('<stdin>', ax47)).
% 153.42/153.61 thf(ax6, axiom, (~(p12)|p52), file('<stdin>', ax6)).
% 153.42/153.61 thf(ax48, axiom, (p11|p12), file('<stdin>', ax48)).
% 153.42/153.61 thf(nax50, axiom, (p50<=f__0 @ (fsub @ fone @ (fpush @ f__1 @ f__2))), file('<stdin>', nax50)).
% 153.42/153.61 thf(ax46, axiom, (p13|~(p14)), file('<stdin>', ax46)).
% 153.42/153.61 thf(ax7, axiom, (~(p52)|~(p50)|p51), file('<stdin>', ax7)).
% 153.42/153.61 thf(pax19, axiom, (p19=>f__0 @ f__1), file('<stdin>', pax19)).
% 153.42/153.61 thf(ax45, axiom, (p14|~(p15)), file('<stdin>', ax45)).
% 153.42/153.61 thf(pax8, axiom, (p8=>![X7:term, X8:subst, X10:subst]:(fsub @ (fsub @ X7 @ X8) @ X10)=(fsub @ X7 @ (fcomp @ X8 @ X10))), file('<stdin>', pax8)).
% 153.42/153.61 thf(ax52, axiom, (p7|p8), file('<stdin>', ax52)).
% 153.42/153.61 thf(pax10, axiom, (p10=>![X7:term, X8:subst]:(fcomp @ fsh @ (fpush @ X7 @ X8))=(X8)), file('<stdin>', pax10)).
% 153.42/153.61 thf(ax50, axiom, (p9|p10), file('<stdin>', ax50)).
% 153.42/153.61 thf(ax44, axiom, (p15|~(p16)), file('<stdin>', ax44)).
% 153.42/153.61 thf(ax42, axiom, (p16|~(p18)), file('<stdin>', ax42)).
% 153.42/153.61 thf(ax41, axiom, (p18|p19), file('<stdin>', ax41)).
% 153.42/153.61 thf(nax49, axiom, (p49<=![X1:term]:(fvar @ X1=>(f__0 @ (fsub @ X1 @ (fpush @ f__1 @ f__2))=>f__0 @ (fsub @ (fsub @ X1 @ fsh) @ (fpush @ f__1 @ f__2))))), file('<stdin>', nax49)).
% 153.42/153.61 thf(pax17, axiom, (p17=>![X4:term]:(fvar @ X4=>f__0 @ (fsub @ X4 @ f__2))), file('<stdin>', pax17)).
% 153.42/153.61 thf(ax43, axiom, (p16|p17), file('<stdin>', ax43)).
% 153.42/153.61 thf(nax16, axiom, (p16<=(![X4:term]:(fvar @ X4=>f__0 @ (fsub @ X4 @ f__2))=>(f__0 @ f__1=>![X4:term]:(fvar @ X4=>f__0 @ (fsub @ X4 @ (fpush @ f__1 @ f__2)))))), file('<stdin>', nax16)).
% 153.42/153.61 thf(ax8, axiom, (~(p51)|~(p49)|p20), file('<stdin>', ax8)).
% 153.42/153.61 thf(pax20, axiom, (p20=>![X4:term]:(fvar @ X4=>f__0 @ (fsub @ X4 @ (fpush @ f__1 @ f__2)))), file('<stdin>', pax20)).
% 153.42/153.61 thf(c_0_29, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax57])).
% 153.42/153.61 thf(c_0_30, plain, ~p1, inference(fof_simplification,[status(thm)],[ax59])).
% 153.42/153.61 thf(c_0_31, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax55])).
% 153.42/153.61 thf(c_0_32, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_29])).
% 153.42/153.61 thf(c_0_33, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_30])).
% 153.42/153.61 thf(c_0_34, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax53])).
% 153.42/153.61 thf(c_0_35, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_31])).
% 153.42/153.61 thf(c_0_36, plain, ~p3, inference(sr,[status(thm)],[c_0_32, c_0_33])).
% 153.42/153.61 thf(c_0_37, plain, (p7|~p9), inference(fof_simplification,[status(thm)],[ax51])).
% 153.42/153.61 thf(c_0_38, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_34])).
% 153.42/153.61 thf(c_0_39, plain, ~p5, inference(sr,[status(thm)],[c_0_35, c_0_36])).
% 153.42/153.61 thf(c_0_40, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax49])).
% 153.42/153.61 thf(c_0_41, plain, (p7|~p9), inference(split_conjunct,[status(thm)],[c_0_37])).
% 153.42/153.61 thf(c_0_42, plain, ~p7, inference(sr,[status(thm)],[c_0_38, c_0_39])).
% 153.42/153.61 thf(c_0_43, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_40])).
% 153.42/153.61 thf(c_0_44, plain, ~p9, inference(sr,[status(thm)],[c_0_41, c_0_42])).
% 153.42/153.61 thf(c_0_45, plain, ![X95:term, X96:subst]:(~p6|(fsub @ fone @ (fpush @ X95 @ X96))=(X95)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])])).
% 153.42/153.61 thf(c_0_46, plain, (p5|p6), inference(split_conjunct,[status(thm)],[ax54])).
% 153.42/153.61 thf(c_0_47, plain, (p11|~p13), inference(fof_simplification,[status(thm)],[ax47])).
% 153.42/153.61 thf(c_0_48, plain, (~p12|p52), inference(fof_simplification,[status(thm)],[ax6])).
% 153.42/153.61 thf(c_0_49, plain, (p11|p12), inference(split_conjunct,[status(thm)],[ax48])).
% 153.42/153.61 thf(c_0_50, plain, ~p11, inference(sr,[status(thm)],[c_0_43, c_0_44])).
% 153.42/153.61 thf(c_0_51, plain, (~f__0 @ (fsub @ fone @ (fpush @ f__1 @ f__2))|p50), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax50])])).
% 153.42/153.61 thf(c_0_52, plain, ![X2:subst, X1:term]:((fsub @ fone @ (fpush @ X1 @ X2))=(X1)|~p6), inference(split_conjunct,[status(thm)],[c_0_45])).
% 153.42/153.61 thf(c_0_53, plain, p6, inference(sr,[status(thm)],[c_0_46, c_0_39])).
% 153.42/153.61 thf(c_0_54, plain, (p13|~p14), inference(fof_simplification,[status(thm)],[ax46])).
% 153.42/153.61 thf(c_0_55, plain, (p11|~p13), inference(split_conjunct,[status(thm)],[c_0_47])).
% 153.42/153.61 thf(c_0_56, plain, (~p52|~p50|p51), inference(fof_simplification,[status(thm)],[ax7])).
% 153.42/153.61 thf(c_0_57, plain, (p52|~p12), inference(split_conjunct,[status(thm)],[c_0_48])).
% 153.42/153.61 thf(c_0_58, plain, p12, inference(sr,[status(thm)],[c_0_49, c_0_50])).
% 153.42/153.61 thf(c_0_59, plain, (p50|~f__0 @ (fsub @ fone @ (fpush @ f__1 @ f__2))), inference(split_conjunct,[status(thm)],[c_0_51])).
% 153.42/153.61 thf(c_0_60, plain, ![X2:subst, X1:term]:(fsub @ fone @ (fpush @ X1 @ X2))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 153.42/153.61 thf(c_0_61, plain, (~p19|f__0 @ f__1), inference(fof_nnf,[status(thm)],[pax19])).
% 153.42/153.61 thf(c_0_62, plain, (p14|~p15), inference(fof_simplification,[status(thm)],[ax45])).
% 153.42/153.61 thf(c_0_63, plain, (p13|~p14), inference(split_conjunct,[status(thm)],[c_0_54])).
% 153.42/153.61 thf(c_0_64, plain, ~p13, inference(sr,[status(thm)],[c_0_55, c_0_50])).
% 153.42/153.61 thf(c_0_65, plain, (p51|~p52|~p50), inference(split_conjunct,[status(thm)],[c_0_56])).
% 153.42/153.61 thf(c_0_66, plain, p52, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])).
% 153.42/153.61 thf(c_0_67, plain, (p50|~f__0 @ f__1), inference(rw,[status(thm)],[c_0_59, c_0_60])).
% 153.42/153.61 thf(c_0_68, plain, (f__0 @ f__1|~p19), inference(split_conjunct,[status(thm)],[c_0_61])).
% 153.42/153.61 thf(c_0_69, plain, ![X89:term, X90:subst, X91:subst]:(~p8|(fsub @ (fsub @ X89 @ X90) @ X91)=(fsub @ X89 @ (fcomp @ X90 @ X91))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 153.42/153.61 thf(c_0_70, plain, (p7|p8), inference(split_conjunct,[status(thm)],[ax52])).
% 153.42/153.61 thf(c_0_71, plain, ![X85:term, X86:subst]:(~p10|(fcomp @ fsh @ (fpush @ X85 @ X86))=(X86)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])])).
% 153.42/153.61 thf(c_0_72, plain, (p9|p10), inference(split_conjunct,[status(thm)],[ax50])).
% 153.42/153.61 thf(c_0_73, plain, (p15|~p16), inference(fof_simplification,[status(thm)],[ax44])).
% 153.42/153.61 thf(c_0_74, plain, (p14|~p15), inference(split_conjunct,[status(thm)],[c_0_62])).
% 153.42/153.61 thf(c_0_75, plain, ~p14, inference(sr,[status(thm)],[c_0_63, c_0_64])).
% 153.42/153.61 thf(c_0_76, plain, (p51|~p50), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])).
% 153.42/153.61 thf(c_0_77, plain, (p50|~p19), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 153.42/153.61 thf(c_0_78, plain, ![X1:term, X2:subst, X3:subst]:((fsub @ (fsub @ X1 @ X2) @ X3)=(fsub @ X1 @ (fcomp @ X2 @ X3))|~p8), inference(split_conjunct,[status(thm)],[c_0_69])).
% 153.42/153.61 thf(c_0_79, plain, p8, inference(sr,[status(thm)],[c_0_70, c_0_42])).
% 153.42/153.61 thf(c_0_80, plain, ![X1:term, X2:subst]:((fcomp @ fsh @ (fpush @ X1 @ X2))=(X2)|~p10), inference(split_conjunct,[status(thm)],[c_0_71])).
% 153.42/153.61 thf(c_0_81, plain, p10, inference(sr,[status(thm)],[c_0_72, c_0_44])).
% 153.42/153.61 thf(c_0_82, plain, (p15|~p16), inference(split_conjunct,[status(thm)],[c_0_73])).
% 153.42/153.61 thf(c_0_83, plain, ~p15, inference(sr,[status(thm)],[c_0_74, c_0_75])).
% 153.42/153.61 thf(c_0_84, plain, (p16|~p18), inference(fof_simplification,[status(thm)],[ax42])).
% 153.42/153.61 thf(c_0_85, plain, (p51|~p19), inference(spm,[status(thm)],[c_0_76, c_0_77])).
% 153.42/153.61 thf(c_0_86, plain, (p18|p19), inference(split_conjunct,[status(thm)],[ax41])).
% 153.42/153.61 thf(c_0_87, plain, ((fvar @ esk16_0|p49)&((f__0 @ (fsub @ esk16_0 @ (fpush @ f__1 @ f__2))|p49)&(~f__0 @ (fsub @ (fsub @ esk16_0 @ fsh) @ (fpush @ f__1 @ f__2))|p49))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax49])])])])])).
% 153.42/153.61 thf(c_0_88, plain, ![X1:term, X2:subst, X3:subst]:(fsub @ X1 @ (fcomp @ X2 @ X3))=(fsub @ (fsub @ X1 @ X2) @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_79])])).
% 153.42/153.61 thf(c_0_89, plain, ![X1:term, X2:subst]:(fcomp @ fsh @ (fpush @ X1 @ X2))=(X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 153.42/153.61 thf(c_0_90, plain, ![X65:term]:(~p17|(~fvar @ X65|f__0 @ (fsub @ X65 @ f__2))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax17])])])).
% 153.42/153.61 thf(c_0_91, plain, (p16|p17), inference(split_conjunct,[status(thm)],[ax43])).
% 153.42/153.61 thf(c_0_92, plain, ~p16, inference(sr,[status(thm)],[c_0_82, c_0_83])).
% 153.42/153.61 thf(c_0_93, plain, ![X69:term]:((~fvar @ X69|f__0 @ (fsub @ X69 @ f__2)|p16)&((f__0 @ f__1|p16)&((fvar @ esk30_0|p16)&(~f__0 @ (fsub @ esk30_0 @ (fpush @ f__1 @ f__2))|p16)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax16])])])])])])).
% 153.42/153.61 thf(c_0_94, plain, (~p51|~p49|p20), inference(fof_simplification,[status(thm)],[ax8])).
% 153.42/153.61 thf(c_0_95, plain, (p16|~p18), inference(split_conjunct,[status(thm)],[c_0_84])).
% 153.42/153.61 thf(c_0_96, plain, (p18|p51), inference(spm,[status(thm)],[c_0_85, c_0_86])).
% 153.42/153.61 thf(c_0_97, plain, (p49|~f__0 @ (fsub @ (fsub @ esk16_0 @ fsh) @ (fpush @ f__1 @ f__2))), inference(split_conjunct,[status(thm)],[c_0_87])).
% 153.42/153.61 thf(c_0_98, plain, ![X1:term, X4:term, X2:subst]:(fsub @ (fsub @ X1 @ fsh) @ (fpush @ X4 @ X2))=(fsub @ X1 @ X2), inference(spm,[status(thm)],[c_0_88, c_0_89])).
% 153.42/153.61 thf(c_0_99, plain, ![X1:term]:(f__0 @ (fsub @ X1 @ f__2)|~p17|~fvar @ X1), inference(split_conjunct,[status(thm)],[c_0_90])).
% 153.42/153.61 thf(c_0_100, plain, p17, inference(sr,[status(thm)],[c_0_91, c_0_92])).
% 153.42/153.61 thf(c_0_101, plain, (p16|~f__0 @ (fsub @ esk30_0 @ (fpush @ f__1 @ f__2))), inference(split_conjunct,[status(thm)],[c_0_93])).
% 153.42/153.61 thf(c_0_102, plain, ![X61:term]:(~p20|(~fvar @ X61|f__0 @ (fsub @ X61 @ (fpush @ f__1 @ f__2)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax20])])])).
% 153.42/153.61 thf(c_0_103, plain, (fvar @ esk30_0|p16), inference(split_conjunct,[status(thm)],[c_0_93])).
% 153.42/153.61 thf(c_0_104, plain, (p20|~p51|~p49), inference(split_conjunct,[status(thm)],[c_0_94])).
% 153.42/153.61 thf(c_0_105, plain, p51, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_92])).
% 153.42/153.61 thf(c_0_106, plain, (p49|~f__0 @ (fsub @ esk16_0 @ f__2)), inference(rw,[status(thm)],[c_0_97, c_0_98])).
% 153.42/153.61 thf(c_0_107, plain, ![X1:term]:(f__0 @ (fsub @ X1 @ f__2)|~fvar @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99, c_0_100])])).
% 153.42/153.61 thf(c_0_108, plain, (fvar @ esk16_0|p49), inference(split_conjunct,[status(thm)],[c_0_87])).
% 153.42/153.61 thf(c_0_109, plain, ~f__0 @ (fsub @ esk30_0 @ (fpush @ f__1 @ f__2)), inference(sr,[status(thm)],[c_0_101, c_0_92])).
% 153.42/153.61 thf(c_0_110, plain, ![X1:term]:(f__0 @ (fsub @ X1 @ (fpush @ f__1 @ f__2))|~p20|~fvar @ X1), inference(split_conjunct,[status(thm)],[c_0_102])).
% 153.42/153.61 thf(c_0_111, plain, fvar @ esk30_0, inference(sr,[status(thm)],[c_0_103, c_0_92])).
% 153.42/153.61 thf(c_0_112, plain, (p20|~p49), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_105])])).
% 153.42/153.61 thf(c_0_113, plain, p49, inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107]), c_0_108])).
% 153.42/153.61 thf(c_0_114, plain, ~p20, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_110]), c_0_111])])).
% 153.42/153.61 thf(c_0_115, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112, c_0_113])]), c_0_114]), ['proof']).
% 153.42/153.61 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 153.42/153.61 thf(0,theorem,((![X1:term>$o]:(![X2:term]:(![X3:subst]:(~((![X4:term>$o]:(~(((((pushprop_p_and_p_prime @ X2) @ X3) @ X1) @ X4))))))))) => ((var @ one) => ((![X1:term]:(![X2:subst]:(((sub @ one) @ ((push @ X1) @ X2)) = X1))) => ((![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>$o]:((X1 @ one) => ((![X2:term]:((var @ X2) => ((X1 @ X2) => (X1 @ ((sub @ X2) @ sh))))) => (![X2:term]:((var @ X2) => (X1 @ X2)))))) => (![X1:term>$o]:(![X2:term]:(![X3:subst]:((![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ X3)))) => ((X1 @ X2) => (![X4:term]:((var @ X4) => (X1 @ ((sub @ X4) @ ((push @ X2) @ X3)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 153.42/153.61 % SZS output end Proof
%------------------------------------------------------------------------------