%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM843+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:53:25 AM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM843+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a FOF_CAX_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 19:24:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.43 % SZS status Theorem for theBenchmark
% 0.12/0.43 % SZS output start Proof for theBenchmark
% 0.12/0.43 fof(holds(244, 394, 0), conjecture,
% 0.12/0.43 greater(vd390, vd391),
% 0.12/0.43 file('theBenchmark.p', holds(244, 394, 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(holds(conjunct2(243), 393, 0), axiom,
% 0.12/0.43 ~( leq(vd390, vd391) ),
% 0.12/0.43 file('theBenchmark.p', holds(conjunct2(243), 393, 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(holds(conjunct1(243), 392, 0), axiom,
% 0.12/0.43 less(vd390, vplus(vd391, v1)),
% 0.12/0.43 file('theBenchmark.p', holds(conjunct1(243), 392, 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(234, 0), 0), axiom,
% 0.12/0.43 ! [ Vd375,Vd376 ] : ( greater(Vd375, Vd376) => geq(Vd375, vplus(Vd376, v1)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(234, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(228, 0), 0), axiom,
% 0.12/0.43 ! [ Vd369 ] : geq(Vd369, v1),
% 0.12/0.43 file('theBenchmark.p', ass(cond(228, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(223, 0), 0), axiom,
% 0.12/0.43 ! [ Vd362,Vd363,Vd365,Vd366 ] : ( ( geq(Vd365, Vd366) & geq(Vd362, Vd363) ) => geq(vplus(Vd362, Vd365), vplus(Vd363, Vd366)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(223, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(216), 0), 0), axiom,
% 0.12/0.43 ! [ Vd353,Vd354,Vd355,Vd356 ] : ( ( ( greater(Vd355, Vd356) & geq(Vd353, Vd354) ) | ( geq(Vd355, Vd356) & greater(Vd353, Vd354) ) ) => greater(vplus(Vd353, Vd355), vplus(Vd354, Vd356)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(216), 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(209, 0), 0), axiom,
% 0.12/0.43 ! [ Vd337,Vd338,Vd340,Vd341 ] : ( ( greater(Vd340, Vd341) & greater(Vd337, Vd338) ) => greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(209, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(202), 0), 0), axiom,
% 0.12/0.43 ! [ Vd328,Vd329,Vd330 ] : ( less(vplus(Vd328, Vd330), vplus(Vd329, Vd330)) => less(Vd328, Vd329) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(202), 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(202), 0), 1), axiom,
% 0.12/0.43 ! [ Vd328,Vd329,Vd330 ] : ( vplus(Vd328, Vd330) = vplus(Vd329, Vd330) => Vd328 = Vd329 ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(202), 0), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(202), 0), 2), axiom,
% 0.12/0.43 ! [ Vd328,Vd329,Vd330 ] : ( greater(vplus(Vd328, Vd330), vplus(Vd329, Vd330)) => greater(Vd328, Vd329) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(202), 0), 2)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(193), 0), 0), axiom,
% 0.12/0.43 ! [ Vd301,Vd302,Vd303 ] : ( less(Vd301, Vd302) => less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(193), 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(193), 0), 1), axiom,
% 0.12/0.43 ! [ Vd301,Vd302,Vd303 ] : ( Vd301 = Vd302 => vplus(Vd301, Vd303) = vplus(Vd302, Vd303) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(193), 0), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(193), 0), 2), axiom,
% 0.12/0.43 ! [ Vd301,Vd302,Vd303 ] : ( greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(193), 0), 2)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(189, 0), 0), axiom,
% 0.12/0.43 ! [ Vd295,Vd296 ] : greater(vplus(Vd295, Vd296), Vd295),
% 0.12/0.43 file('theBenchmark.p', ass(cond(189, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(184, 0), 0), axiom,
% 0.12/0.43 ! [ Vd289,Vd290,Vd292 ] : ( ( leq(Vd290, Vd292) & leq(Vd289, Vd290) ) => leq(Vd289, Vd292) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(184, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(177), 0), 0), axiom,
% 0.12/0.43 ! [ Vd281,Vd282,Vd283 ] : ( ( ( less(Vd282, Vd283) & leq(Vd281, Vd282) ) | ( leq(Vd282, Vd283) & less(Vd281, Vd282) ) ) => less(Vd281, Vd283) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(177), 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(168, 0), 0), axiom,
% 0.12/0.43 ! [ Vd262,Vd263,Vd265 ] : ( ( less(Vd263, Vd265) & less(Vd262, Vd263) ) => less(Vd262, Vd265) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(168, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(163, 0), 0), axiom,
% 0.12/0.43 ! [ Vd258,Vd259 ] : ( leq(Vd258, Vd259) => geq(Vd259, Vd258) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(163, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(158, 0), 0), axiom,
% 0.12/0.43 ! [ Vd254,Vd255 ] : ( geq(Vd254, Vd255) => leq(Vd255, Vd254) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(158, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(def(cond(conseq(axiom(3)), 17), 1), axiom,
% 0.12/0.43 ! [ Vd249,Vd250 ] : ( leq(Vd250, Vd249) <=> ( less(Vd250, Vd249) | Vd250 = Vd249 ) ),
% 0.12/0.43 file('theBenchmark.p', def(cond(conseq(axiom(3)), 17), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(def(cond(conseq(axiom(3)), 16), 1), axiom,
% 0.12/0.43 ! [ Vd244,Vd245 ] : ( geq(Vd245, Vd244) <=> ( greater(Vd245, Vd244) | Vd245 = Vd244 ) ),
% 0.12/0.43 file('theBenchmark.p', def(cond(conseq(axiom(3)), 16), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(147, 0), 0), axiom,
% 0.12/0.43 ! [ Vd226,Vd227 ] : ( less(Vd226, Vd227) => greater(Vd227, Vd226) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(147, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(140, 0), 0), axiom,
% 0.12/0.43 ! [ Vd208,Vd209 ] : ( greater(Vd208, Vd209) => less(Vd209, Vd208) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(140, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(130), 0), 0), axiom,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( Vd203 = Vd204 | greater(Vd203, Vd204) | less(Vd203, Vd204) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(130), 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(130), 0), 1), axiom,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( less(Vd203, Vd204) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(130), 0), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(130), 0), 2), axiom,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( ~( greater(Vd203, Vd204) ) | ~( less(Vd203, Vd204) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(130), 0), 2)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(130), 0), 3), axiom,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( greater(Vd203, Vd204) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(130), 0), 3)) ).
% 0.12/0.43
% 0.12/0.43 fof(def(cond(conseq(axiom(3)), 12), 1), axiom,
% 0.12/0.43 ! [ Vd198,Vd199 ] : ( less(Vd199, Vd198) <=> ? [ Vd201 ] : Vd198 = vplus(Vd199, Vd201) ),
% 0.12/0.43 file('theBenchmark.p', def(cond(conseq(axiom(3)), 12), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(def(cond(conseq(axiom(3)), 11), 1), axiom,
% 0.12/0.43 ! [ Vd193,Vd194 ] : ( greater(Vd194, Vd193) <=> ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ),
% 0.12/0.43 file('theBenchmark.p', def(cond(conseq(axiom(3)), 11), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(88), 0), 0), axiom,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( Vd120 = Vd121 | ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) | ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(88), 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(88), 0), 1), axiom,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ~( ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(88), 0), 1)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(88), 0), 2), axiom,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( ~( ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) ) | ~( ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(88), 0), 2)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(goal(88), 0), 3), axiom,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ~( ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(goal(88), 0), 3)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(81, 0), 0), axiom,
% 0.12/0.43 ! [ Vd104,Vd105 ] : ( ~( Vd104 = Vd105 ) => ! [ Vd107 ] : ~( vplus(Vd107, Vd104) = vplus(Vd107, Vd105) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(81, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(73, 0), 0), axiom,
% 0.12/0.43 ! [ Vd92,Vd93 ] : ~( Vd93 = vplus(Vd92, Vd93) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(73, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(61, 0), 0), axiom,
% 0.12/0.43 ! [ Vd78,Vd79 ] : vplus(Vd79, Vd78) = vplus(Vd78, Vd79),
% 0.12/0.43 file('theBenchmark.p', ass(cond(61, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(52, 0), 0), axiom,
% 0.12/0.43 ! [ Vd68,Vd69 ] : vplus(vsucc(Vd68), Vd69) = vsucc(vplus(Vd68, Vd69)),
% 0.12/0.43 file('theBenchmark.p', ass(cond(52, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(43, 0), 0), axiom,
% 0.12/0.43 ! [ Vd59 ] : vplus(v1, Vd59) = vsucc(Vd59),
% 0.12/0.43 file('theBenchmark.p', ass(cond(43, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(33, 0), 0), axiom,
% 0.12/0.43 ! [ Vd46,Vd47,Vd48 ] : vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)),
% 0.12/0.43 file('theBenchmark.p', ass(cond(33, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), axiom,
% 0.12/0.43 ! [ Vd42,Vd43 ] : ( vplus(Vd42, vsucc(Vd43)) = vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1) = vsucc(Vd42) ),
% 0.12/0.43 file('theBenchmark.p', qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(20, 0), 0), axiom,
% 0.12/0.43 ! [ Vd24 ] : ( ~( Vd24 = v1 ) => Vd24 = vsucc(vskolem2(Vd24)) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(20, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(12, 0), 0), axiom,
% 0.12/0.43 ! [ Vd16 ] : ~( vsucc(Vd16) = Vd16 ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(12, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(ass(cond(6, 0), 0), axiom,
% 0.12/0.43 ! [ Vd7,Vd8 ] : ( ~( Vd7 = Vd8 ) => ~( vsucc(Vd7) = vsucc(Vd8) ) ),
% 0.12/0.43 file('theBenchmark.p', ass(cond(6, 0), 0)) ).
% 0.12/0.43
% 0.12/0.43 fof(qu(antec(axiom(3)), imp(antec(axiom(3)))), axiom,
% 0.12/0.43 ! [ Vd3,Vd4 ] : ( vsucc(Vd3) = vsucc(Vd4) => Vd3 = Vd4 ),
% 0.12/0.43 file('theBenchmark.p', qu(antec(axiom(3)), imp(antec(axiom(3))))) ).
% 0.12/0.43
% 0.12/0.43 fof(qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), axiom,
% 0.12/0.43 ! [ Vd1 ] : ~( vsucc(Vd1) = v1 ),
% 0.12/0.43 file('theBenchmark.p', qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) ).
% 0.12/0.43
% 0.12/0.43 fof(f_1_1, negated_conjecture,
% 0.12/0.43 ~( greater(vd390, vd391) ),
% 0.12/0.43 inference(negate,[status(cth)],[holds(244, 394, 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_1_2, negated_conjecture,
% 0.12/0.43 ( ( ( ~greater(vd390, vd391) ) ) ),
% 0.12/0.43 inference(definitional_conversion,[status(esa)],[f_1_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_1_3, negated_conjecture,
% 0.12/0.43 ( ~greater(vd390, vd391) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_1_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_2_1, plain,
% 0.12/0.43 ~( leq(vd390, vd391) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[holds(conjunct2(243), 393, 0)]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_2_2, plain,
% 0.12/0.43 ( ~leq(vd390, vd391) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_2_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_3_1, plain,
% 0.12/0.43 less(vd390, vplus(vd391, v1)),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[holds(conjunct1(243), 392, 0)]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_3_2, plain,
% 0.12/0.43 ( less(vd390, vplus(vd391, v1)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_3_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_4_1, plain,
% 0.12/0.43 ! [ Vd375,Vd376 ] : ( ~( greater(Vd375, Vd376) ) | geq(Vd375, vplus(Vd376, v1)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(234, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_4_2, plain,
% 0.12/0.43 ! [ U_1,U_0 ] : ( ~( greater(U_1, U_0) ) | geq(U_1, vplus(U_0, v1)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_4_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_4_3, plain,
% 0.12/0.43 ( ~greater(U_1, U_0) | geq(U_1, vplus(U_0, v1)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_4_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_5_1, plain,
% 0.12/0.43 ! [ Vd369 ] : geq(Vd369, v1),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(228, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_5_2, plain,
% 0.12/0.43 ! [ U_2 ] : geq(U_2, v1),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_5_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_5_3, plain,
% 0.12/0.43 ( geq(U_2, v1) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_5_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_6_1, plain,
% 0.12/0.43 ! [ Vd362,Vd363,Vd365,Vd366 ] : ( ( ~( geq(Vd365, Vd366) ) | ~( geq(Vd362, Vd363) ) ) | geq(vplus(Vd362, Vd365), vplus(Vd363, Vd366)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(223, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_6_2, plain,
% 0.12/0.43 ! [ U_6,U_5,U_4,U_3 ] : ( ( ~( geq(U_4, U_3) ) | ~( geq(U_6, U_5) ) ) | geq(vplus(U_6, U_4), vplus(U_5, U_3)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_6_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_6_3, plain,
% 0.12/0.43 ( ~geq(U_4, U_3) | ~geq(U_6, U_5) | geq(vplus(U_6, U_4), vplus(U_5, U_3)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_6_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_7_1, plain,
% 0.12/0.43 ! [ Vd353,Vd354,Vd355,Vd356 ] : ( ( ( ~( greater(Vd355, Vd356) ) | ~( geq(Vd353, Vd354) ) ) & ( ~( geq(Vd355, Vd356) ) | ~( greater(Vd353, Vd354) ) ) ) | greater(vplus(Vd353, Vd355), vplus(Vd354, Vd356)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(216), 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_7_2, plain,
% 0.12/0.43 ! [ U_10,U_9,U_8,U_7 ] : ( ( ( ~( greater(U_8, U_7) ) | ~( geq(U_10, U_9) ) ) & ( ~( geq(U_8, U_7) ) | ~( greater(U_10, U_9) ) ) ) | greater(vplus(U_10, U_8), vplus(U_9, U_7)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_7_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_7_3, plain,
% 0.12/0.43 ( greater(vplus(U_10, U_8), vplus(U_9, U_7)) | ~greater(U_8, U_7) | ~geq(U_10, U_9) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_7_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_7_4, plain,
% 0.12/0.43 ( greater(vplus(U_10, U_8), vplus(U_9, U_7)) | ~geq(U_8, U_7) | ~greater(U_10, U_9) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_7_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_8_1, plain,
% 0.12/0.43 ! [ Vd337,Vd338,Vd340,Vd341 ] : ( ( ~( greater(Vd340, Vd341) ) | ~( greater(Vd337, Vd338) ) ) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(209, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_8_2, plain,
% 0.12/0.43 ! [ U_14,U_13,U_12,U_11 ] : ( ( ~( greater(U_12, U_11) ) | ~( greater(U_14, U_13) ) ) | greater(vplus(U_14, U_12), vplus(U_13, U_11)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_8_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_8_3, plain,
% 0.12/0.43 ( ~greater(U_12, U_11) | ~greater(U_14, U_13) | greater(vplus(U_14, U_12), vplus(U_13, U_11)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_8_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_9_1, plain,
% 0.12/0.43 ! [ Vd328,Vd329,Vd330 ] : ( ~( less(vplus(Vd328, Vd330), vplus(Vd329, Vd330)) ) | less(Vd328, Vd329) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(202), 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_9_2, plain,
% 0.12/0.43 ! [ U_17,U_16,U_15 ] : ( ~( less(vplus(U_17, U_15), vplus(U_16, U_15)) ) | less(U_17, U_16) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_9_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_9_3, plain,
% 0.12/0.43 ! [ U_17,U_16 ] : ( less(U_17, U_16) | ! [ U_15 ] : ~( less(vplus(U_17, U_15), vplus(U_16, U_15)) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_9_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_9_4, plain,
% 0.12/0.43 ( less(U_17, U_16) | ~less(vplus(U_17, U_15), vplus(U_16, U_15)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_9_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_10_1, plain,
% 0.12/0.43 ! [ Vd328,Vd329,Vd330 ] : ( ~( vplus(Vd328, Vd330) = vplus(Vd329, Vd330) ) | Vd328 = Vd329 ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(202), 0), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_10_2, plain,
% 0.12/0.43 ! [ U_20,U_19,U_18 ] : ( ~( vplus(U_20, U_18) = vplus(U_19, U_18) ) | U_20 = U_19 ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_10_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_10_3, plain,
% 0.12/0.43 ! [ U_20,U_19 ] : ( U_20 = U_19 | ! [ U_18 ] : ~( vplus(U_20, U_18) = vplus(U_19, U_18) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_10_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_10_4, plain,
% 0.12/0.43 ( U_20 = U_19 | vplus(U_20, U_18) != vplus(U_19, U_18) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_10_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_11_1, plain,
% 0.12/0.43 ! [ Vd328,Vd329,Vd330 ] : ( ~( greater(vplus(Vd328, Vd330), vplus(Vd329, Vd330)) ) | greater(Vd328, Vd329) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(202), 0), 2)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_11_2, plain,
% 0.12/0.43 ! [ U_23,U_22,U_21 ] : ( ~( greater(vplus(U_23, U_21), vplus(U_22, U_21)) ) | greater(U_23, U_22) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_11_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_11_3, plain,
% 0.12/0.43 ! [ U_23,U_22 ] : ( greater(U_23, U_22) | ! [ U_21 ] : ~( greater(vplus(U_23, U_21), vplus(U_22, U_21)) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_11_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_11_4, plain,
% 0.12/0.43 ( greater(U_23, U_22) | ~greater(vplus(U_23, U_21), vplus(U_22, U_21)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_11_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_12_1, plain,
% 0.12/0.43 ! [ Vd301,Vd302,Vd303 ] : ( ~( less(Vd301, Vd302) ) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_12_2, plain,
% 0.12/0.43 ! [ U_26,U_25,U_24 ] : ( ~( less(U_26, U_25) ) | less(vplus(U_26, U_24), vplus(U_25, U_24)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_12_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_12_3, plain,
% 0.12/0.43 ! [ U_26,U_25 ] : ( ~( less(U_26, U_25) ) | ! [ U_24 ] : less(vplus(U_26, U_24), vplus(U_25, U_24)) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_12_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_12_4, plain,
% 0.12/0.43 ( ~less(U_26, U_25) | less(vplus(U_26, U_24), vplus(U_25, U_24)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_12_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_13_1, plain,
% 0.12/0.43 ! [ Vd301,Vd302,Vd303 ] : ( ~( Vd301 = Vd302 ) | vplus(Vd301, Vd303) = vplus(Vd302, Vd303) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_13_2, plain,
% 0.12/0.43 ! [ U_29,U_28,U_27 ] : ( ~( U_29 = U_28 ) | vplus(U_29, U_27) = vplus(U_28, U_27) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_13_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_13_3, plain,
% 0.12/0.43 ! [ U_29,U_28 ] : ( ~( U_29 = U_28 ) | ! [ U_27 ] : vplus(U_29, U_27) = vplus(U_28, U_27) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_13_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_13_4, plain,
% 0.12/0.43 ( U_29 != U_28 | vplus(U_29, U_27) = vplus(U_28, U_27) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_13_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_14_1, plain,
% 0.12/0.43 ! [ Vd301,Vd302,Vd303 ] : ( ~( greater(Vd301, Vd302) ) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 2)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_14_2, plain,
% 0.12/0.43 ! [ U_32,U_31,U_30 ] : ( ~( greater(U_32, U_31) ) | greater(vplus(U_32, U_30), vplus(U_31, U_30)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_14_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_14_3, plain,
% 0.12/0.43 ! [ U_32,U_31 ] : ( ~( greater(U_32, U_31) ) | ! [ U_30 ] : greater(vplus(U_32, U_30), vplus(U_31, U_30)) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_14_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_14_4, plain,
% 0.12/0.43 ( ~greater(U_32, U_31) | greater(vplus(U_32, U_30), vplus(U_31, U_30)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_14_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_15_1, plain,
% 0.12/0.43 ! [ Vd295,Vd296 ] : greater(vplus(Vd295, Vd296), Vd295),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(189, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_15_2, plain,
% 0.12/0.43 ! [ U_34,U_33 ] : greater(vplus(U_34, U_33), U_34),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_15_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_15_3, plain,
% 0.12/0.43 ( greater(vplus(U_34, U_33), U_34) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_15_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_16_1, plain,
% 0.12/0.43 ! [ Vd289,Vd290,Vd292 ] : ( ( ~( leq(Vd290, Vd292) ) | ~( leq(Vd289, Vd290) ) ) | leq(Vd289, Vd292) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(184, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_16_2, plain,
% 0.12/0.43 ! [ U_37,U_36,U_35 ] : ( ( ~( leq(U_36, U_35) ) | ~( leq(U_37, U_36) ) ) | leq(U_37, U_35) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_16_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_16_3, plain,
% 0.12/0.43 ( ~leq(U_36, U_35) | ~leq(U_37, U_36) | leq(U_37, U_35) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_16_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_17_1, plain,
% 0.12/0.43 ! [ Vd281,Vd282,Vd283 ] : ( ( ( ~( less(Vd282, Vd283) ) | ~( leq(Vd281, Vd282) ) ) & ( ~( leq(Vd282, Vd283) ) | ~( less(Vd281, Vd282) ) ) ) | less(Vd281, Vd283) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(177), 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_17_2, plain,
% 0.12/0.43 ! [ U_40,U_39,U_38 ] : ( ( ( ~( less(U_39, U_38) ) | ~( leq(U_40, U_39) ) ) & ( ~( leq(U_39, U_38) ) | ~( less(U_40, U_39) ) ) ) | less(U_40, U_38) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_17_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_17_3, plain,
% 0.12/0.43 ( less(U_40, U_38) | ~less(U_39, U_38) | ~leq(U_40, U_39) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_17_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_17_4, plain,
% 0.12/0.43 ( less(U_40, U_38) | ~leq(U_39, U_38) | ~less(U_40, U_39) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_17_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_18_1, plain,
% 0.12/0.43 ! [ Vd262,Vd263,Vd265 ] : ( ( ~( less(Vd263, Vd265) ) | ~( less(Vd262, Vd263) ) ) | less(Vd262, Vd265) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(168, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_18_2, plain,
% 0.12/0.43 ! [ U_43,U_42,U_41 ] : ( ( ~( less(U_42, U_41) ) | ~( less(U_43, U_42) ) ) | less(U_43, U_41) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_18_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_18_3, plain,
% 0.12/0.43 ( ~less(U_42, U_41) | ~less(U_43, U_42) | less(U_43, U_41) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_18_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_19_1, plain,
% 0.12/0.43 ! [ Vd258,Vd259 ] : ( ~( leq(Vd258, Vd259) ) | geq(Vd259, Vd258) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(163, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_19_2, plain,
% 0.12/0.43 ! [ U_45,U_44 ] : ( ~( leq(U_45, U_44) ) | geq(U_44, U_45) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_19_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_19_3, plain,
% 0.12/0.43 ( ~leq(U_45, U_44) | geq(U_44, U_45) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_19_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_20_1, plain,
% 0.12/0.43 ! [ Vd254,Vd255 ] : ( ~( geq(Vd254, Vd255) ) | leq(Vd255, Vd254) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(158, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_20_2, plain,
% 0.12/0.43 ! [ U_47,U_46 ] : ( ~( geq(U_47, U_46) ) | leq(U_46, U_47) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_20_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_20_3, plain,
% 0.12/0.43 ( ~geq(U_47, U_46) | leq(U_46, U_47) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_20_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_21_1, plain,
% 0.12/0.43 ! [ Vd249,Vd250 ] : ( ( ~( leq(Vd250, Vd249) ) | ( less(Vd250, Vd249) | Vd250 = Vd249 ) ) & ( ( ~( less(Vd250, Vd249) ) & ~( Vd250 = Vd249 ) ) | leq(Vd250, Vd249) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 17), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_21_2, plain,
% 0.12/0.43 ! [ U_49,U_48 ] : ( ( ~( leq(U_48, U_49) ) | ( less(U_48, U_49) | U_48 = U_49 ) ) & ( ( ~( less(U_48, U_49) ) & ~( U_48 = U_49 ) ) | leq(U_48, U_49) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_21_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_21_3, plain,
% 0.12/0.43 ( ! [ U_52,U_50 ] : ( ~( leq(U_50, U_52) ) | ( less(U_50, U_52) | U_50 = U_52 ) ) & ! [ U_53,U_51 ] : ( ( ~( less(U_51, U_53) ) & ~( U_51 = U_53 ) ) | leq(U_51, U_53) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_21_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_21_4, plain,
% 0.12/0.43 ( ~leq(U_50, U_52) | less(U_50, U_52) | U_50 = U_52 ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_21_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_21_5, plain,
% 0.12/0.43 ( leq(U_51, U_53) | ~less(U_51, U_53) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_21_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_21_6, plain,
% 0.12/0.43 ( leq(U_51, U_53) | U_51 != U_53 ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_21_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_22_1, plain,
% 0.12/0.43 ! [ Vd244,Vd245 ] : ( ( ~( geq(Vd245, Vd244) ) | ( greater(Vd245, Vd244) | Vd245 = Vd244 ) ) & ( ( ~( greater(Vd245, Vd244) ) & ~( Vd245 = Vd244 ) ) | geq(Vd245, Vd244) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 16), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_22_2, plain,
% 0.12/0.43 ! [ U_55,U_54 ] : ( ( ~( geq(U_54, U_55) ) | ( greater(U_54, U_55) | U_54 = U_55 ) ) & ( ( ~( greater(U_54, U_55) ) & ~( U_54 = U_55 ) ) | geq(U_54, U_55) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_22_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_22_3, plain,
% 0.12/0.43 ( ! [ U_58,U_56 ] : ( ~( geq(U_56, U_58) ) | ( greater(U_56, U_58) | U_56 = U_58 ) ) & ! [ U_59,U_57 ] : ( ( ~( greater(U_57, U_59) ) & ~( U_57 = U_59 ) ) | geq(U_57, U_59) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_22_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_22_4, plain,
% 0.12/0.43 ( ~geq(U_56, U_58) | greater(U_56, U_58) | U_56 = U_58 ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_22_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_22_5, plain,
% 0.12/0.43 ( geq(U_57, U_59) | ~greater(U_57, U_59) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_22_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_22_6, plain,
% 0.12/0.43 ( geq(U_57, U_59) | U_57 != U_59 ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_22_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_23_1, plain,
% 0.12/0.43 ! [ Vd226,Vd227 ] : ( ~( less(Vd226, Vd227) ) | greater(Vd227, Vd226) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(147, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_23_2, plain,
% 0.12/0.43 ! [ U_61,U_60 ] : ( ~( less(U_61, U_60) ) | greater(U_60, U_61) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_23_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_23_3, plain,
% 0.12/0.43 ( ~less(U_61, U_60) | greater(U_60, U_61) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_23_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_24_1, plain,
% 0.12/0.43 ! [ Vd208,Vd209 ] : ( ~( greater(Vd208, Vd209) ) | less(Vd209, Vd208) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(140, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_24_2, plain,
% 0.12/0.43 ! [ U_63,U_62 ] : ( ~( greater(U_63, U_62) ) | less(U_62, U_63) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_24_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_24_3, plain,
% 0.12/0.43 ( ~greater(U_63, U_62) | less(U_62, U_63) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_24_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_25_1, plain,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( Vd203 = Vd204 | greater(Vd203, Vd204) | less(Vd203, Vd204) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_25_2, plain,
% 0.12/0.43 ! [ U_65,U_64 ] : ( U_65 = U_64 | greater(U_65, U_64) | less(U_65, U_64) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_25_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_25_3, plain,
% 0.12/0.43 ( U_65 = U_64 | greater(U_65, U_64) | less(U_65, U_64) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_25_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_26_1, plain,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( less(Vd203, Vd204) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_26_2, plain,
% 0.12/0.43 ! [ U_67,U_66 ] : ( ~( U_67 = U_66 ) | ~( less(U_67, U_66) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_26_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_26_3, plain,
% 0.12/0.43 ( U_67 != U_66 | ~less(U_67, U_66) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_26_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_27_1, plain,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( ~( greater(Vd203, Vd204) ) | ~( less(Vd203, Vd204) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 2)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_27_2, plain,
% 0.12/0.43 ! [ U_69,U_68 ] : ( ~( greater(U_69, U_68) ) | ~( less(U_69, U_68) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_27_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_27_3, plain,
% 0.12/0.43 ( ~greater(U_69, U_68) | ~less(U_69, U_68) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_27_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_28_1, plain,
% 0.12/0.43 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( greater(Vd203, Vd204) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 3)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_28_2, plain,
% 0.12/0.43 ! [ U_71,U_70 ] : ( ~( U_71 = U_70 ) | ~( greater(U_71, U_70) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_28_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_28_3, plain,
% 0.12/0.43 ( U_71 != U_70 | ~greater(U_71, U_70) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_28_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_29_1, plain,
% 0.12/0.43 ! [ Vd198,Vd199 ] : ( ( ~( less(Vd199, Vd198) ) | ? [ Vd201 ] : Vd198 = vplus(Vd199, Vd201) ) & ( ! [ Vd201 ] : ~( Vd198 = vplus(Vd199, Vd201) ) | less(Vd199, Vd198) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 12), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_29_2, plain,
% 0.12/0.43 ! [ U_75,U_74 ] : ( ( ~( less(U_74, U_75) ) | ? [ U_72 ] : U_75 = vplus(U_74, U_72) ) & ( ! [ U_73 ] : ~( U_75 = vplus(U_74, U_73) ) | less(U_74, U_75) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_29_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_29_3, plain,
% 0.12/0.43 ( ! [ U_78,U_76 ] : ( ~( less(U_76, U_78) ) | ? [ U_72 ] : U_78 = vplus(U_76, U_72) ) & ! [ U_79,U_77 ] : ( ! [ U_73 ] : ~( U_79 = vplus(U_77, U_73) ) | less(U_77, U_79) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_29_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_29_4, plain,
% 0.12/0.43 ( ! [ U_78,U_76 ] : ( ~( less(U_76, U_78) ) | U_78 = vplus(U_76, sK1(U_78, U_76)) ) & ! [ U_79,U_77 ] : ( ! [ U_73 ] : ~( U_79 = vplus(U_77, U_73) ) | less(U_77, U_79) ) ),
% 0.12/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_72,sK1(U_78, U_76))],[f_29_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_29_5, plain,
% 0.12/0.43 ( ~less(U_76, U_78) | U_78 = vplus(U_76, sK1(U_78, U_76)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_29_4]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_29_6, plain,
% 0.12/0.43 ( U_79 != vplus(U_77, U_73) | less(U_77, U_79) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_29_4]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_30_1, plain,
% 0.12/0.43 ! [ Vd193,Vd194 ] : ( ( ~( greater(Vd194, Vd193) ) | ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ) & ( ! [ Vd196 ] : ~( Vd194 = vplus(Vd193, Vd196) ) | greater(Vd194, Vd193) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 11), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_30_2, plain,
% 0.12/0.43 ! [ U_83,U_82 ] : ( ( ~( greater(U_82, U_83) ) | ? [ U_80 ] : U_82 = vplus(U_83, U_80) ) & ( ! [ U_81 ] : ~( U_82 = vplus(U_83, U_81) ) | greater(U_82, U_83) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_30_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_30_3, plain,
% 0.12/0.43 ( ! [ U_86,U_84 ] : ( ~( greater(U_84, U_86) ) | ? [ U_80 ] : U_84 = vplus(U_86, U_80) ) & ! [ U_87,U_85 ] : ( ! [ U_81 ] : ~( U_85 = vplus(U_87, U_81) ) | greater(U_85, U_87) ) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_30_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_30_4, plain,
% 0.12/0.43 ( ! [ U_86,U_84 ] : ( ~( greater(U_84, U_86) ) | U_84 = vplus(U_86, sK2(U_86, U_84)) ) & ! [ U_87,U_85 ] : ( ! [ U_81 ] : ~( U_85 = vplus(U_87, U_81) ) | greater(U_85, U_87) ) ),
% 0.12/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_80,sK2(U_86, U_84))],[f_30_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_30_5, plain,
% 0.12/0.43 ( ~greater(U_84, U_86) | U_84 = vplus(U_86, sK2(U_86, U_84)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_30_4]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_30_6, plain,
% 0.12/0.43 ( U_85 != vplus(U_87, U_81) | greater(U_85, U_87) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_30_4]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_31_1, plain,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( Vd120 = Vd121 | ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) | ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_31_2, plain,
% 0.12/0.43 ! [ U_91,U_90 ] : ( U_91 = U_90 | ? [ U_88 ] : U_91 = vplus(U_90, U_88) | ? [ U_89 ] : U_90 = vplus(U_91, U_89) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_31_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_31_3, plain,
% 0.12/0.43 ! [ U_91,U_90 ] : ( U_91 = U_90 | U_91 = vplus(U_90, sK3(U_91, U_90)) | ? [ U_89 ] : U_90 = vplus(U_91, U_89) ),
% 0.12/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_88,sK3(U_91, U_90))],[f_31_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_31_4, plain,
% 0.12/0.43 ! [ U_91,U_90 ] : ( U_91 = U_90 | U_91 = vplus(U_90, sK3(U_91, U_90)) | U_90 = vplus(U_91, sK4(U_91, U_90)) ),
% 0.12/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_89,sK4(U_91, U_90))],[f_31_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_31_5, plain,
% 0.12/0.43 ( U_91 = U_90 | U_91 = vplus(U_90, sK3(U_91, U_90)) | U_90 = vplus(U_91, sK4(U_91, U_90)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_31_4]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_32_1, plain,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ! [ Vd125 ] : ~( Vd121 = vplus(Vd120, Vd125) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 1)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_32_2, plain,
% 0.12/0.43 ! [ U_94,U_93 ] : ( ~( U_94 = U_93 ) | ! [ U_92 ] : ~( U_93 = vplus(U_94, U_92) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_32_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_32_3, plain,
% 0.12/0.43 ( U_94 != U_93 | U_93 != vplus(U_94, U_92) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_32_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_33_1, plain,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( ! [ Vd123 ] : ~( Vd120 = vplus(Vd121, Vd123) ) | ! [ Vd125 ] : ~( Vd121 = vplus(Vd120, Vd125) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 2)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_33_2, plain,
% 0.12/0.43 ! [ U_98,U_97 ] : ( ! [ U_95 ] : ~( U_98 = vplus(U_97, U_95) ) | ! [ U_96 ] : ~( U_97 = vplus(U_98, U_96) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_33_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_33_3, plain,
% 0.12/0.43 ( U_98 != vplus(U_97, U_95) | U_97 != vplus(U_98, U_96) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_33_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_34_1, plain,
% 0.12/0.43 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ! [ Vd123 ] : ~( Vd120 = vplus(Vd121, Vd123) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 3)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_34_2, plain,
% 0.12/0.43 ! [ U_101,U_100 ] : ( ~( U_101 = U_100 ) | ! [ U_99 ] : ~( U_101 = vplus(U_100, U_99) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_34_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_34_3, plain,
% 0.12/0.43 ( U_101 != U_100 | U_101 != vplus(U_100, U_99) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_34_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_35_1, plain,
% 0.12/0.43 ! [ Vd104,Vd105 ] : ( Vd104 = Vd105 | ! [ Vd107 ] : ~( vplus(Vd107, Vd104) = vplus(Vd107, Vd105) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(81, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_35_2, plain,
% 0.12/0.43 ! [ U_104,U_103 ] : ( U_104 = U_103 | ! [ U_102 ] : ~( vplus(U_102, U_104) = vplus(U_102, U_103) ) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_35_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_35_3, plain,
% 0.12/0.43 ( U_104 = U_103 | vplus(U_102, U_104) != vplus(U_102, U_103) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_35_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_36_1, plain,
% 0.12/0.43 ! [ Vd92,Vd93 ] : ~( Vd93 = vplus(Vd92, Vd93) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(73, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_36_2, plain,
% 0.12/0.43 ! [ U_106,U_105 ] : ~( U_105 = vplus(U_106, U_105) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_36_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_36_3, plain,
% 0.12/0.43 ( U_105 != vplus(U_106, U_105) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_36_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_37_1, plain,
% 0.12/0.43 ! [ Vd78,Vd79 ] : vplus(Vd79, Vd78) = vplus(Vd78, Vd79),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(61, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_37_2, plain,
% 0.12/0.43 ! [ U_108,U_107 ] : vplus(U_107, U_108) = vplus(U_108, U_107),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_37_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_37_3, plain,
% 0.12/0.43 ( vplus(U_107, U_108) = vplus(U_108, U_107) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_37_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_38_1, plain,
% 0.12/0.43 ! [ Vd68,Vd69 ] : vplus(vsucc(Vd68), Vd69) = vsucc(vplus(Vd68, Vd69)),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(52, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_38_2, plain,
% 0.12/0.43 ! [ U_110,U_109 ] : vplus(vsucc(U_110), U_109) = vsucc(vplus(U_110, U_109)),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_38_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_38_3, plain,
% 0.12/0.43 ( vplus(vsucc(U_110), U_109) = vsucc(vplus(U_110, U_109)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_38_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_39_1, plain,
% 0.12/0.43 ! [ Vd59 ] : vplus(v1, Vd59) = vsucc(Vd59),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(43, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_39_2, plain,
% 0.12/0.43 ! [ U_111 ] : vplus(v1, U_111) = vsucc(U_111),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_39_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_39_3, plain,
% 0.12/0.43 ( vplus(v1, U_111) = vsucc(U_111) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_39_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_40_1, plain,
% 0.12/0.43 ! [ Vd46,Vd47,Vd48 ] : vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(33, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_40_2, plain,
% 0.12/0.43 ! [ U_114,U_113,U_112 ] : vplus(vplus(U_114, U_113), U_112) = vplus(U_114, vplus(U_113, U_112)),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_40_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_40_3, plain,
% 0.12/0.43 ( vplus(vplus(U_114, U_113), U_112) = vplus(U_114, vplus(U_113, U_112)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_40_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_41_1, plain,
% 0.12/0.43 ! [ Vd42,Vd43 ] : ( vplus(Vd42, vsucc(Vd43)) = vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1) = vsucc(Vd42) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_41_2, plain,
% 0.12/0.43 ! [ U_116,U_115 ] : ( vplus(U_116, vsucc(U_115)) = vsucc(vplus(U_116, U_115)) & vplus(U_116, v1) = vsucc(U_116) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_41_1]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_41_3, plain,
% 0.12/0.43 ( ! [ U_117 ] : vplus(U_117, v1) = vsucc(U_117) & ! [ U_118,U_115 ] : vplus(U_118, vsucc(U_115)) = vsucc(vplus(U_118, U_115)) ),
% 0.12/0.43 inference(miniscope,[status(thm)],[f_41_2]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_41_4, plain,
% 0.12/0.43 ( vplus(U_117, v1) = vsucc(U_117) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_41_3]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_41_5, plain,
% 0.12/0.43 ( vplus(U_118, vsucc(U_115)) = vsucc(vplus(U_118, U_115)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_41_3]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_42_1, plain,
% 0.12/0.43 ! [ Vd24 ] : ( Vd24 = v1 | Vd24 = vsucc(vskolem2(Vd24)) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(20, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_42_2, plain,
% 0.12/0.43 ! [ U_119 ] : ( U_119 = v1 | U_119 = vsucc(vskolem2(U_119)) ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_42_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_42_3, plain,
% 0.12/0.43 ( U_119 = v1 | U_119 = vsucc(vskolem2(U_119)) ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_42_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_43_1, plain,
% 0.12/0.43 ! [ Vd16 ] : ~( vsucc(Vd16) = Vd16 ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(12, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_43_2, plain,
% 0.12/0.43 ! [ U_120 ] : ~( vsucc(U_120) = U_120 ),
% 0.12/0.43 inference(variable_rename,[status(thm)],[f_43_1]) ).
% 0.12/0.43
% 0.12/0.43 cnf(f_43_3, plain,
% 0.12/0.43 ( vsucc(U_120) != U_120 ),
% 0.12/0.43 inference(clausify,[status(thm)],[f_43_2]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_44_1, plain,
% 0.12/0.43 ! [ Vd7,Vd8 ] : ( Vd7 = Vd8 | ~( vsucc(Vd7) = vsucc(Vd8) ) ),
% 0.12/0.43 inference(fof_nnf,[status(thm)],[ass(cond(6, 0), 0)]) ).
% 0.12/0.43
% 0.12/0.43 fof(f_44_2, plain,
% 0.12/0.43 ! [ U_122,U_121 ] : ( U_122 = U_121 | ~( vsucc(U_122) = vsucc(U_121) ) ),
% 0.12/0.44 inference(variable_rename,[status(thm)],[f_44_1]) ).
% 0.12/0.44
% 0.12/0.44 cnf(f_44_3, plain,
% 0.12/0.44 ( U_122 = U_121 | vsucc(U_122) != vsucc(U_121) ),
% 0.12/0.44 inference(clausify,[status(thm)],[f_44_2]) ).
% 0.12/0.44
% 0.12/0.44 fof(f_45_1, plain,
% 0.12/0.44 ! [ Vd3,Vd4 ] : ( ~( vsucc(Vd3) = vsucc(Vd4) ) | Vd3 = Vd4 ),
% 0.12/0.44 inference(fof_nnf,[status(thm)],[qu(antec(axiom(3)), imp(antec(axiom(3))))]) ).
% 0.12/0.44
% 0.12/0.44 fof(f_45_2, plain,
% 0.12/0.44 ! [ U_124,U_123 ] : ( ~( vsucc(U_124) = vsucc(U_123) ) | U_124 = U_123 ),
% 0.12/0.44 inference(variable_rename,[status(thm)],[f_45_1]) ).
% 0.12/0.44
% 0.12/0.44 cnf(f_45_3, plain,
% 0.12/0.44 ( vsucc(U_124) != vsucc(U_123) | U_124 = U_123 ),
% 0.12/0.44 inference(clausify,[status(thm)],[f_45_2]) ).
% 0.12/0.44
% 0.12/0.44 fof(f_46_1, plain,
% 0.12/0.44 ! [ Vd1 ] : ~( vsucc(Vd1) = v1 ),
% 0.12/0.44 inference(fof_nnf,[status(thm)],[qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))]) ).
% 0.12/0.44
% 0.12/0.44 fof(f_46_2, plain,
% 0.12/0.44 ! [ U_125 ] : ~( vsucc(U_125) = v1 ),
% 0.12/0.44 inference(variable_rename,[status(thm)],[f_46_1]) ).
% 0.12/0.44
% 0.12/0.44 cnf(f_46_3, plain,
% 0.12/0.44 ( vsucc(U_125) != v1 ),
% 0.12/0.44 inference(clausify,[status(thm)],[f_46_2]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_1, axiom,
% 0.12/0.44 ( Eq_x_0 = Eq_x_0 ),
% 0.12/0.44 theory(equality,[reflexivity]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_2, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_x_1 | Eq_x_1 = Eq_x_0 ),
% 0.12/0.44 theory(equality,[symmetry]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_3, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_x_1 | Eq_x_1 != Eq_x_2 | Eq_x_0 = Eq_x_2 ),
% 0.12/0.44 theory(equality,[transitivity]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_4, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | vplus(Eq_x_0, Eq_x_1) = vplus(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_5, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | vsucc(Eq_x_0) = vsucc(Eq_y_0) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_6, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | vskolem2(Eq_x_0) = vskolem2(Eq_y_0) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_7, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | sK1(Eq_x_0, Eq_x_1) = sK1(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_8, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | sK2(Eq_x_0, Eq_x_1) = sK2(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_9, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | sK3(Eq_x_0, Eq_x_1) = sK3(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_10, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | sK4(Eq_x_0, Eq_x_1) = sK4(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_functions]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_11, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | ~greater(Eq_x_0, Eq_x_1) | greater(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_predicates]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_12, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | ~leq(Eq_x_0, Eq_x_1) | leq(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_predicates]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_13, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | ~less(Eq_x_0, Eq_x_1) | less(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_predicates]) ).
% 0.12/0.44
% 0.12/0.44 cnf(equality_14, axiom,
% 0.12/0.44 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | ~geq(Eq_x_0, Eq_x_1) | geq(Eq_y_0, Eq_y_1) ),
% 0.12/0.44 theory(equality,[substitution_predicates]) ).
% 0.12/0.44
% 0.12/0.44 cnf(sat_proved, plain, $false,
% 0.12/0.44 inference(cadical, [status(thm)], [
% 0.12/0.44 ]) ).
% 0.12/0.44 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------