TSTP Solution File: SYO173^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO173^5 : TPTP v8.1.0. Released v4.0.0.
% 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 : 600s
% DateTime : Thu Jul 21 19:30:39 EDT 2022
% Result : Theorem 37.18s 37.35s
% Output : Proof 37.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO173^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n019.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 : Sat Jul 9 13:56:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 37.18/37.35 % SZS status Theorem
% 37.18/37.35 % Mode: mode485
% 37.18/37.35 % Inferences: 56
% 37.18/37.35 % SZS output start Proof
% 37.18/37.35 thf(cLCL077_1,conjecture,((~(((~(((~(((![X1:$i]:(![X2:$i]:((~(((cT @ ((imp @ X1) @ X2)) => (~((cT @ X1)))))) => (cT @ X2)))) => (~((![X1:$i]:(![X2:$i]:(cT @ ((imp @ X1) @ ((imp @ X2) @ X1)))))))))) => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:(cT @ ((imp @ ((imp @ X1) @ ((imp @ X2) @ X3))) @ ((imp @ ((imp @ X1) @ X2)) @ ((imp @ X1) @ X3)))))))))))) => (~((![X1:$i]:(![X2:$i]:(cT @ ((imp @ ((imp @ (nt @ X1)) @ (nt @ X2))) @ ((imp @ X2) @ X1)))))))))) => (![X1:$i]:(cT @ ((imp @ (nt @ (nt @ X1))) @ X1))))).
% 37.18/37.35 thf(h0,negated_conjecture,(~(((~(((~(((~(((![X1:$i]:(![X2:$i]:((~(((cT @ ((imp @ X1) @ X2)) => (~((cT @ X1)))))) => (cT @ X2)))) => (~((![X1:$i]:(![X2:$i]:(cT @ ((imp @ X1) @ ((imp @ X2) @ X1)))))))))) => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:(cT @ ((imp @ ((imp @ X1) @ ((imp @ X2) @ X3))) @ ((imp @ ((imp @ X1) @ X2)) @ ((imp @ X1) @ X3)))))))))))) => (~((![X1:$i]:(![X2:$i]:(cT @ ((imp @ ((imp @ (nt @ X1)) @ (nt @ X2))) @ ((imp @ X2) @ X1)))))))))) => (![X1:$i]:(cT @ ((imp @ (nt @ (nt @ X1))) @ X1)))))),inference(assume_negation,[status(cth)],[cLCL077_1])).
% 37.18/37.35 thf(ax994, axiom, (p1|~(p2)), file('<stdin>', ax994)).
% 37.18/37.35 thf(ax995, axiom, ~(p1), file('<stdin>', ax995)).
% 37.18/37.35 thf(ax992, axiom, (p2|~(p4)), file('<stdin>', ax992)).
% 37.18/37.35 thf(ax989, axiom, (p4|~(p7)), file('<stdin>', ax989)).
% 37.18/37.35 thf(ax978, axiom, (~(p10)|p18), file('<stdin>', ax978)).
% 37.18/37.35 thf(ax986, axiom, (p7|p10), file('<stdin>', ax986)).
% 37.18/37.35 thf(ax985, axiom, (~(p8)|p11), file('<stdin>', ax985)).
% 37.18/37.35 thf(ax988, axiom, (p4|p8), file('<stdin>', ax988)).
% 37.18/37.35 thf(ax961, axiom, (~(p18)|p36), file('<stdin>', ax961)).
% 37.18/37.35 thf(ax977, axiom, (~(p11)|p19), file('<stdin>', ax977)).
% 37.18/37.35 thf(pax9, axiom, (p9=>![X1:$i, X2:$i]:(~((fcT @ (fimp @ X1 @ X2)=>~(fcT @ X1)))=>fcT @ X2)), file('<stdin>', pax9)).
% 37.18/37.35 thf(ax987, axiom, (p7|p9), file('<stdin>', ax987)).
% 37.18/37.35 thf(pax8, axiom, (p8=>![X1:$i, X2:$i, X3:$i]:fcT @ (fimp @ (fimp @ X1 @ (fimp @ X2 @ X3)) @ (fimp @ (fimp @ X1 @ X2) @ (fimp @ X1 @ X3)))), file('<stdin>', pax8)).
% 37.18/37.35 thf(ax693, axiom, (~(p9)|p304), file('<stdin>', ax693)).
% 37.18/37.35 thf(ax621, axiom, (~(p377)|~(p39)|~(p36)), file('<stdin>', ax621)).
% 37.18/37.35 thf(ax958, axiom, (~(p19)|p39), file('<stdin>', ax958)).
% 37.18/37.35 thf(pax10, axiom, (p10=>![X1:$i, X2:$i]:fcT @ (fimp @ X1 @ (fimp @ X2 @ X1))), file('<stdin>', pax10)).
% 37.18/37.35 thf(ax619, axiom, (~(p304)|p378), file('<stdin>', ax619)).
% 37.18/37.35 thf(ax620, axiom, (~(p378)|p377|p376), file('<stdin>', ax620)).
% 37.18/37.35 thf(ax589, axiom, (~(p9)|p408), file('<stdin>', ax589)).
% 37.18/37.35 thf(pax376, axiom, (p376=>fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1))), file('<stdin>', pax376)).
% 37.18/37.35 thf(nax1, axiom, (p1<=(~((~((~((![X1:$i, X2:$i]:(~((fcT @ (fimp @ X1 @ X2)=>~(fcT @ X1)))=>fcT @ X2)=>~(![X1:$i, X2:$i]:fcT @ (fimp @ X1 @ (fimp @ X2 @ X1)))))=>~(![X1:$i, X2:$i, X3:$i]:fcT @ (fimp @ (fimp @ X1 @ (fimp @ X2 @ X3)) @ (fimp @ (fimp @ X1 @ X2) @ (fimp @ X1 @ X3))))))=>~(![X1:$i, X2:$i]:fcT @ (fimp @ (fimp @ (fnt @ X1) @ (fnt @ X2)) @ (fimp @ X2 @ X1)))))=>![X1:$i]:fcT @ (fimp @ (fnt @ (fnt @ X1)) @ X1))), file('<stdin>', nax1)).
% 37.18/37.35 thf(pax408, axiom, (p408=>![X1:$i]:(~((fcT @ (fimp @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)) @ X1)=>~(fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)))))=>fcT @ X1)), file('<stdin>', pax408)).
% 37.18/37.35 thf(ax993, axiom, (p1|~(p3)), file('<stdin>', ax993)).
% 37.18/37.35 thf(ax990, axiom, (p3|~(p6)), file('<stdin>', ax990)).
% 37.18/37.35 thf(nax6, axiom, (p6<=fcT @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)), file('<stdin>', nax6)).
% 37.18/37.35 thf(c_0_26, plain, (p1|~p2), inference(fof_simplification,[status(thm)],[ax994])).
% 37.18/37.35 thf(c_0_27, plain, ~p1, inference(fof_simplification,[status(thm)],[ax995])).
% 37.18/37.35 thf(c_0_28, plain, (p2|~p4), inference(fof_simplification,[status(thm)],[ax992])).
% 37.18/37.35 thf(c_0_29, plain, (p1|~p2), inference(split_conjunct,[status(thm)],[c_0_26])).
% 37.18/37.35 thf(c_0_30, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_27])).
% 37.18/37.35 thf(c_0_31, plain, (p4|~p7), inference(fof_simplification,[status(thm)],[ax989])).
% 37.18/37.35 thf(c_0_32, plain, (p2|~p4), inference(split_conjunct,[status(thm)],[c_0_28])).
% 37.18/37.35 thf(c_0_33, plain, ~p2, inference(sr,[status(thm)],[c_0_29, c_0_30])).
% 37.18/37.35 thf(c_0_34, plain, (p4|~p7), inference(split_conjunct,[status(thm)],[c_0_31])).
% 37.18/37.35 thf(c_0_35, plain, ~p4, inference(sr,[status(thm)],[c_0_32, c_0_33])).
% 37.18/37.35 thf(c_0_36, plain, (~p10|p18), inference(fof_simplification,[status(thm)],[ax978])).
% 37.18/37.35 thf(c_0_37, plain, (p7|p10), inference(split_conjunct,[status(thm)],[ax986])).
% 37.18/37.35 thf(c_0_38, plain, ~p7, inference(sr,[status(thm)],[c_0_34, c_0_35])).
% 37.18/37.35 thf(c_0_39, plain, (~p8|p11), inference(fof_simplification,[status(thm)],[ax985])).
% 37.18/37.35 thf(c_0_40, plain, (p4|p8), inference(split_conjunct,[status(thm)],[ax988])).
% 37.18/37.35 thf(c_0_41, plain, (~p18|p36), inference(fof_simplification,[status(thm)],[ax961])).
% 37.18/37.35 thf(c_0_42, plain, (p18|~p10), inference(split_conjunct,[status(thm)],[c_0_36])).
% 37.18/37.35 thf(c_0_43, plain, p10, inference(sr,[status(thm)],[c_0_37, c_0_38])).
% 37.18/37.35 thf(c_0_44, plain, (~p11|p19), inference(fof_simplification,[status(thm)],[ax977])).
% 37.18/37.35 thf(c_0_45, plain, (p11|~p8), inference(split_conjunct,[status(thm)],[c_0_39])).
% 37.18/37.35 thf(c_0_46, plain, p8, inference(sr,[status(thm)],[c_0_40, c_0_35])).
% 37.18/37.35 thf(c_0_47, plain, ![X696:$i, X697:$i]:(~p9|(~fcT @ (fimp @ X696 @ X697)|~fcT @ X696|fcT @ X697)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax9])])])])).
% 37.18/37.35 thf(c_0_48, plain, (p7|p9), inference(split_conjunct,[status(thm)],[ax987])).
% 37.18/37.35 thf(c_0_49, plain, ![X700:$i, X701:$i, X702:$i]:(~p8|fcT @ (fimp @ (fimp @ X700 @ (fimp @ X701 @ X702)) @ (fimp @ (fimp @ X700 @ X701) @ (fimp @ X700 @ X702)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 37.18/37.35 thf(c_0_50, plain, (~p9|p304), inference(fof_simplification,[status(thm)],[ax693])).
% 37.18/37.35 thf(c_0_51, plain, (~p377|~p39|~p36), inference(fof_simplification,[status(thm)],[ax621])).
% 37.18/37.35 thf(c_0_52, plain, (p36|~p18), inference(split_conjunct,[status(thm)],[c_0_41])).
% 37.18/37.35 thf(c_0_53, plain, p18, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])).
% 37.18/37.35 thf(c_0_54, plain, (~p19|p39), inference(fof_simplification,[status(thm)],[ax958])).
% 37.18/37.35 thf(c_0_55, plain, (p19|~p11), inference(split_conjunct,[status(thm)],[c_0_44])).
% 37.18/37.35 thf(c_0_56, plain, p11, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 37.18/37.35 thf(c_0_57, plain, ![X2:$i, X1:$i]:(fcT @ X2|~p9|~fcT @ (fimp @ X1 @ X2)|~fcT @ X1), inference(split_conjunct,[status(thm)],[c_0_47])).
% 37.18/37.35 thf(c_0_58, plain, p9, inference(sr,[status(thm)],[c_0_48, c_0_38])).
% 37.18/37.35 thf(c_0_59, plain, ![X1:$i, X2:$i, X3:$i]:(fcT @ (fimp @ (fimp @ X1 @ (fimp @ X2 @ X3)) @ (fimp @ (fimp @ X1 @ X2) @ (fimp @ X1 @ X3)))|~p8), inference(split_conjunct,[status(thm)],[c_0_49])).
% 37.18/37.35 thf(c_0_60, plain, ![X692:$i, X693:$i]:(~p10|fcT @ (fimp @ X692 @ (fimp @ X693 @ X692))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])])).
% 37.18/37.35 thf(c_0_61, plain, (~p304|p378), inference(fof_simplification,[status(thm)],[ax619])).
% 37.18/37.35 thf(c_0_62, plain, (p304|~p9), inference(split_conjunct,[status(thm)],[c_0_50])).
% 37.18/37.35 thf(c_0_63, plain, (~p377|~p39|~p36), inference(split_conjunct,[status(thm)],[c_0_51])).
% 37.18/37.35 thf(c_0_64, plain, p36, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 37.18/37.35 thf(c_0_65, plain, (p39|~p19), inference(split_conjunct,[status(thm)],[c_0_54])).
% 37.18/37.35 thf(c_0_66, plain, p19, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56])])).
% 37.18/37.35 thf(c_0_67, plain, ![X1:$i, X2:$i]:(fcT @ X1|~fcT @ (fimp @ X2 @ X1)|~fcT @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])).
% 37.18/37.35 thf(c_0_68, plain, ![X1:$i, X2:$i, X3:$i]:fcT @ (fimp @ (fimp @ X1 @ (fimp @ X2 @ X3)) @ (fimp @ (fimp @ X1 @ X2) @ (fimp @ X1 @ X3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_46])])).
% 37.18/37.35 thf(c_0_69, plain, ![X2:$i, X1:$i]:(fcT @ (fimp @ X1 @ (fimp @ X2 @ X1))|~p10), inference(split_conjunct,[status(thm)],[c_0_60])).
% 37.18/37.35 thf(c_0_70, plain, (~p378|p377|p376), inference(fof_simplification,[status(thm)],[ax620])).
% 37.18/37.35 thf(c_0_71, plain, (p378|~p304), inference(split_conjunct,[status(thm)],[c_0_61])).
% 37.18/37.35 thf(c_0_72, plain, p304, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_58])])).
% 37.18/37.35 thf(c_0_73, plain, (~p39|~p377), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64])])).
% 37.18/37.35 thf(c_0_74, plain, p39, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])).
% 37.18/37.35 thf(c_0_75, plain, ![X1:$i, X2:$i, X3:$i]:(fcT @ (fimp @ (fimp @ X1 @ X2) @ (fimp @ X1 @ X3))|~fcT @ (fimp @ X1 @ (fimp @ X2 @ X3))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 37.18/37.35 thf(c_0_76, plain, ![X2:$i, X1:$i]:fcT @ (fimp @ X1 @ (fimp @ X2 @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_43])])).
% 37.18/37.35 thf(c_0_77, plain, (~p9|p408), inference(fof_simplification,[status(thm)],[ax589])).
% 37.18/37.35 thf(c_0_78, plain, (~p376|fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1))), inference(fof_nnf,[status(thm)],[pax376])).
% 37.18/37.35 thf(c_0_79, plain, (p377|p376|~p378), inference(split_conjunct,[status(thm)],[c_0_70])).
% 37.18/37.35 thf(c_0_80, plain, p378, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])).
% 37.18/37.35 thf(c_0_81, plain, ~p377, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_74])])).
% 37.18/37.35 thf(c_0_82, plain, ![X1:$i, X2:$i, X3:$i]:(fcT @ (fimp @ X1 @ X2)|~fcT @ (fimp @ X1 @ (fimp @ X3 @ X2))|~fcT @ (fimp @ X1 @ X3)), inference(spm,[status(thm)],[c_0_67, c_0_75])).
% 37.18/37.35 thf(c_0_83, plain, ![X1:$i, X2:$i]:(fcT @ (fimp @ X1 @ X2)|~fcT @ X2), inference(spm,[status(thm)],[c_0_67, c_0_76])).
% 37.18/37.35 thf(c_0_84, plain, ![X762:$i, X763:$i, X764:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i]:(((((~fcT @ (fimp @ X762 @ X763)|~fcT @ X762|fcT @ X763|p1)&(fcT @ (fimp @ X764 @ (fimp @ X765 @ X764))|p1))&(fcT @ (fimp @ (fimp @ X766 @ (fimp @ X767 @ X768)) @ (fimp @ (fimp @ X766 @ X767) @ (fimp @ X766 @ X768)))|p1))&(fcT @ (fimp @ (fimp @ (fnt @ X769) @ (fnt @ X770)) @ (fimp @ X770 @ X769))|p1))&(~fcT @ (fimp @ (fnt @ (fnt @ esk384_0)) @ esk384_0)|p1)), 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)],[nax1])])])])])])).
% 37.18/37.35 thf(c_0_85, plain, ![X376:$i]:(~p408|(~fcT @ (fimp @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)) @ X376)|~fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1))|fcT @ X376)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax408])])])])).
% 37.18/37.35 thf(c_0_86, plain, (p408|~p9), inference(split_conjunct,[status(thm)],[c_0_77])).
% 37.18/37.35 thf(c_0_87, plain, (fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1))|~p376), inference(split_conjunct,[status(thm)],[c_0_78])).
% 37.18/37.35 thf(c_0_88, plain, p376, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80])]), c_0_81])).
% 37.18/37.35 thf(c_0_89, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax993])).
% 37.18/37.35 thf(c_0_90, plain, ![X1:$i, X3:$i, X2:$i]:(fcT @ (fimp @ X1 @ X2)|~fcT @ (fimp @ X1 @ X3)|~fcT @ (fimp @ X3 @ X2)), inference(spm,[status(thm)],[c_0_82, c_0_83])).
% 37.18/37.35 thf(c_0_91, plain, ![X2:$i, X1:$i]:(fcT @ (fimp @ (fimp @ (fnt @ X1) @ (fnt @ X2)) @ (fimp @ X2 @ X1))|p1), inference(split_conjunct,[status(thm)],[c_0_84])).
% 37.18/37.35 thf(c_0_92, plain, ![X1:$i]:(fcT @ X1|~p408|~fcT @ (fimp @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)) @ X1)|~fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1))), inference(split_conjunct,[status(thm)],[c_0_85])).
% 37.18/37.35 thf(c_0_93, plain, p408, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_58])])).
% 37.18/37.35 thf(c_0_94, plain, fcT @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_88])])).
% 37.18/37.35 thf(c_0_95, plain, (p3|~p6), inference(fof_simplification,[status(thm)],[ax990])).
% 37.18/37.35 thf(c_0_96, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_89])).
% 37.18/37.35 thf(c_0_97, plain, ![X1:$i, X3:$i, X2:$i]:(fcT @ (fimp @ X1 @ X2)|~fcT @ (fimp @ (fimp @ X3 @ X1) @ X2)), inference(spm,[status(thm)],[c_0_90, c_0_76])).
% 37.18/37.35 thf(c_0_98, plain, ![X2:$i, X1:$i]:fcT @ (fimp @ (fimp @ (fnt @ X1) @ (fnt @ X2)) @ (fimp @ X2 @ X1)), inference(sr,[status(thm)],[c_0_91, c_0_30])).
% 37.18/37.35 thf(c_0_99, plain, ![X1:$i]:(fcT @ X1|~fcT @ (fimp @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)) @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93]), c_0_94])])).
% 37.18/37.35 thf(c_0_100, plain, (~fcT @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)|p6), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6])])).
% 37.18/37.35 thf(c_0_101, plain, (p3|~p6), inference(split_conjunct,[status(thm)],[c_0_95])).
% 37.18/37.35 thf(c_0_102, plain, ~p3, inference(sr,[status(thm)],[c_0_96, c_0_30])).
% 37.18/37.35 thf(c_0_103, plain, ![X1:$i, X2:$i]:fcT @ (fimp @ (fnt @ X1) @ (fimp @ X1 @ X2)), inference(spm,[status(thm)],[c_0_97, c_0_98])).
% 37.18/37.35 thf(c_0_104, plain, ![X1:$i, X2:$i]:(fcT @ (fimp @ (fimp @ (fnt @ X1) @ (fnt @ X2)) @ X1)|~fcT @ (fimp @ (fimp @ (fnt @ X1) @ (fnt @ X2)) @ X2)), inference(spm,[status(thm)],[c_0_82, c_0_98])).
% 37.18/37.35 thf(c_0_105, plain, ![X1:$i]:fcT @ (fimp @ X1 @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1))), inference(spm,[status(thm)],[c_0_99, c_0_76])).
% 37.18/37.35 thf(c_0_106, plain, (p6|~fcT @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)), inference(split_conjunct,[status(thm)],[c_0_100])).
% 37.18/37.35 thf(c_0_107, plain, ~p6, inference(sr,[status(thm)],[c_0_101, c_0_102])).
% 37.18/37.35 thf(c_0_108, plain, ![X1:$i, X3:$i, X2:$i]:(fcT @ (fimp @ (fnt @ X1) @ X2)|~fcT @ (fimp @ (fimp @ X1 @ X3) @ X2)), inference(spm,[status(thm)],[c_0_90, c_0_103])).
% 37.18/37.35 thf(c_0_109, plain, ![X1:$i]:fcT @ (fimp @ (fimp @ (fnt @ X1) @ (fnt @ (fimp @ (fimp @ f__1 @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0)) @ (fimp @ f__1 @ f__1)))) @ X1), inference(spm,[status(thm)],[c_0_104, c_0_105])).
% 37.18/37.35 thf(c_0_110, plain, ~fcT @ (fimp @ (fnt @ (fnt @ f__0)) @ f__0), inference(sr,[status(thm)],[c_0_106, c_0_107])).
% 37.18/37.35 thf(c_0_111, plain, ![X1:$i]:fcT @ (fimp @ (fnt @ (fnt @ X1)) @ X1), inference(spm,[status(thm)],[c_0_108, c_0_109])).
% 37.18/37.35 thf(c_0_112, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110, c_0_111])]), ['proof']).
% 37.18/37.35 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 37.18/37.35 thf(0,theorem,((~(((~(((~(((![X1:$i]:(![X2:$i]:((~(((cT @ ((imp @ X1) @ X2)) => (~((cT @ X1)))))) => (cT @ X2)))) => (~((![X1:$i]:(![X2:$i]:(cT @ ((imp @ X1) @ ((imp @ X2) @ X1)))))))))) => (~((![X1:$i]:(![X2:$i]:(![X3:$i]:(cT @ ((imp @ ((imp @ X1) @ ((imp @ X2) @ X3))) @ ((imp @ ((imp @ X1) @ X2)) @ ((imp @ X1) @ X3)))))))))))) => (~((![X1:$i]:(![X2:$i]:(cT @ ((imp @ ((imp @ (nt @ X1)) @ (nt @ X2))) @ ((imp @ X2) @ X1)))))))))) => (![X1:$i]:(cT @ ((imp @ (nt @ (nt @ X1))) @ X1)))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 37.18/37.35 % SZS output end Proof
%------------------------------------------------------------------------------