%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM840+1 : 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 : n006.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 08:53:24 AM UTC 2026
% Result : Theorem 0.87s 6.18s
% Output : Proof 0.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM840+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 19:21:09 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.87/6.18 % SZS status Theorem for theBenchmark
% 0.87/6.18 % SZS output start Proof for theBenchmark
% 0.87/6.20 fof(holds(conseq(conjunct2(conjunct2(204))), 336, 0), conjecture,
% 0.87/6.20 less(vd328, vd329),
% 0.87/6.20 file('theBenchmark.p', holds(conseq(conjunct2(conjunct2(204))), 336, 0)) ).
% 0.87/6.20
% 0.87/6.20 fof(holds(antec(conjunct2(conjunct2(204))), 335, 0), axiom,
% 0.87/6.20 less(vplus(vd328, vd330), vplus(vd329, vd330)),
% 0.87/6.20 file('theBenchmark.p', holds(antec(conjunct2(conjunct2(204))), 335, 0)) ).
% 0.87/6.20
% 0.87/6.20 fof(ass(cond(conjunct1(conjunct2(204)), 0), 0), axiom,
% 0.87/6.20 ( vplus(vd328, vd330) = vplus(vd329, vd330) => vd328 = vd329 ),
% 0.87/6.20 file('theBenchmark.p', ass(cond(conjunct1(conjunct2(204)), 0), 0)) ).
% 0.87/6.20
% 0.87/6.20 fof(ass(cond(conjunct1(204), 0), 0), axiom,
% 0.87/6.20 ( greater(vplus(vd328, vd330), vplus(vd329, vd330)) => greater(vd328, vd329) ),
% 0.87/6.20 file('theBenchmark.p', ass(cond(conjunct1(204), 0), 0)) ).
% 0.87/6.20
% 0.87/6.20 fof(ass(cond(goal(193), 0), 0), axiom,
% 0.87/6.20 ! [ Vd301,Vd302,Vd303 ] : ( less(Vd301, Vd302) => less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.87/6.20 file('theBenchmark.p', ass(cond(goal(193), 0), 0)) ).
% 0.87/6.20
% 0.87/6.20 fof(ass(cond(goal(193), 0), 1), axiom,
% 0.87/6.20 ! [ Vd301,Vd302,Vd303 ] : ( Vd301 = Vd302 => vplus(Vd301, Vd303) = vplus(Vd302, Vd303) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(193), 0), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(193), 0), 2), axiom,
% 0.94/6.20 ! [ Vd301,Vd302,Vd303 ] : ( greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(193), 0), 2)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(189, 0), 0), axiom,
% 0.94/6.20 ! [ Vd295,Vd296 ] : greater(vplus(Vd295, Vd296), Vd295),
% 0.94/6.20 file('theBenchmark.p', ass(cond(189, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(184, 0), 0), axiom,
% 0.94/6.20 ! [ Vd289,Vd290,Vd292 ] : ( ( leq(Vd290, Vd292) & leq(Vd289, Vd290) ) => leq(Vd289, Vd292) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(184, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(177), 0), 0), axiom,
% 0.94/6.20 ! [ Vd281,Vd282,Vd283 ] : ( ( ( less(Vd282, Vd283) & leq(Vd281, Vd282) ) | ( leq(Vd282, Vd283) & less(Vd281, Vd282) ) ) => less(Vd281, Vd283) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(177), 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(168, 0), 0), axiom,
% 0.94/6.20 ! [ Vd262,Vd263,Vd265 ] : ( ( less(Vd263, Vd265) & less(Vd262, Vd263) ) => less(Vd262, Vd265) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(168, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(163, 0), 0), axiom,
% 0.94/6.20 ! [ Vd258,Vd259 ] : ( leq(Vd258, Vd259) => geq(Vd259, Vd258) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(163, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(158, 0), 0), axiom,
% 0.94/6.20 ! [ Vd254,Vd255 ] : ( geq(Vd254, Vd255) => leq(Vd255, Vd254) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(158, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(def(cond(conseq(axiom(3)), 17), 1), axiom,
% 0.94/6.20 ! [ Vd249,Vd250 ] : ( leq(Vd250, Vd249) <=> ( less(Vd250, Vd249) | Vd250 = Vd249 ) ),
% 0.94/6.20 file('theBenchmark.p', def(cond(conseq(axiom(3)), 17), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(def(cond(conseq(axiom(3)), 16), 1), axiom,
% 0.94/6.20 ! [ Vd244,Vd245 ] : ( geq(Vd245, Vd244) <=> ( greater(Vd245, Vd244) | Vd245 = Vd244 ) ),
% 0.94/6.20 file('theBenchmark.p', def(cond(conseq(axiom(3)), 16), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(147, 0), 0), axiom,
% 0.94/6.20 ! [ Vd226,Vd227 ] : ( less(Vd226, Vd227) => greater(Vd227, Vd226) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(147, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(140, 0), 0), axiom,
% 0.94/6.20 ! [ Vd208,Vd209 ] : ( greater(Vd208, Vd209) => less(Vd209, Vd208) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(140, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(130), 0), 0), axiom,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( Vd203 = Vd204 | greater(Vd203, Vd204) | less(Vd203, Vd204) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(130), 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(130), 0), 1), axiom,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( less(Vd203, Vd204) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(130), 0), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(130), 0), 2), axiom,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( ~( greater(Vd203, Vd204) ) | ~( less(Vd203, Vd204) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(130), 0), 2)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(130), 0), 3), axiom,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( greater(Vd203, Vd204) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(130), 0), 3)) ).
% 0.94/6.20
% 0.94/6.20 fof(def(cond(conseq(axiom(3)), 12), 1), axiom,
% 0.94/6.20 ! [ Vd198,Vd199 ] : ( less(Vd199, Vd198) <=> ? [ Vd201 ] : Vd198 = vplus(Vd199, Vd201) ),
% 0.94/6.20 file('theBenchmark.p', def(cond(conseq(axiom(3)), 12), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(def(cond(conseq(axiom(3)), 11), 1), axiom,
% 0.94/6.20 ! [ Vd193,Vd194 ] : ( greater(Vd194, Vd193) <=> ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ),
% 0.94/6.20 file('theBenchmark.p', def(cond(conseq(axiom(3)), 11), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(88), 0), 0), axiom,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( Vd120 = Vd121 | ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) | ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(88), 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(88), 0), 1), axiom,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ~( ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(88), 0), 1)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(88), 0), 2), axiom,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( ~( ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) ) | ~( ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(88), 0), 2)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(goal(88), 0), 3), axiom,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ~( ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(goal(88), 0), 3)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(81, 0), 0), axiom,
% 0.94/6.20 ! [ Vd104,Vd105 ] : ( ~( Vd104 = Vd105 ) => ! [ Vd107 ] : ~( vplus(Vd107, Vd104) = vplus(Vd107, Vd105) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(81, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(73, 0), 0), axiom,
% 0.94/6.20 ! [ Vd92,Vd93 ] : ~( Vd93 = vplus(Vd92, Vd93) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(73, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(61, 0), 0), axiom,
% 0.94/6.20 ! [ Vd78,Vd79 ] : vplus(Vd79, Vd78) = vplus(Vd78, Vd79),
% 0.94/6.20 file('theBenchmark.p', ass(cond(61, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(52, 0), 0), axiom,
% 0.94/6.20 ! [ Vd68,Vd69 ] : vplus(vsucc(Vd68), Vd69) = vsucc(vplus(Vd68, Vd69)),
% 0.94/6.20 file('theBenchmark.p', ass(cond(52, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(43, 0), 0), axiom,
% 0.94/6.20 ! [ Vd59 ] : vplus(v1, Vd59) = vsucc(Vd59),
% 0.94/6.20 file('theBenchmark.p', ass(cond(43, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(33, 0), 0), axiom,
% 0.94/6.20 ! [ Vd46,Vd47,Vd48 ] : vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)),
% 0.94/6.20 file('theBenchmark.p', ass(cond(33, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), axiom,
% 0.94/6.20 ! [ Vd42,Vd43 ] : ( vplus(Vd42, vsucc(Vd43)) = vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1) = vsucc(Vd42) ),
% 0.94/6.20 file('theBenchmark.p', qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(20, 0), 0), axiom,
% 0.94/6.20 ! [ Vd24 ] : ( ~( Vd24 = v1 ) => Vd24 = vsucc(vskolem2(Vd24)) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(20, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(12, 0), 0), axiom,
% 0.94/6.20 ! [ Vd16 ] : ~( vsucc(Vd16) = Vd16 ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(12, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(ass(cond(6, 0), 0), axiom,
% 0.94/6.20 ! [ Vd7,Vd8 ] : ( ~( Vd7 = Vd8 ) => ~( vsucc(Vd7) = vsucc(Vd8) ) ),
% 0.94/6.20 file('theBenchmark.p', ass(cond(6, 0), 0)) ).
% 0.94/6.20
% 0.94/6.20 fof(qu(antec(axiom(3)), imp(antec(axiom(3)))), axiom,
% 0.94/6.20 ! [ Vd3,Vd4 ] : ( vsucc(Vd3) = vsucc(Vd4) => Vd3 = Vd4 ),
% 0.94/6.20 file('theBenchmark.p', qu(antec(axiom(3)), imp(antec(axiom(3))))) ).
% 0.94/6.20
% 0.94/6.20 fof(qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0)), axiom,
% 0.94/6.20 ! [ Vd1 ] : ~( vsucc(Vd1) = v1 ),
% 0.94/6.20 file('theBenchmark.p', qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))) ).
% 0.94/6.20
% 0.94/6.20 fof(f_1_1, negated_conjecture,
% 0.94/6.20 ~( less(vd328, vd329) ),
% 0.94/6.20 inference(negate,[status(cth)],[holds(conseq(conjunct2(conjunct2(204))), 336, 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_1_2, negated_conjecture,
% 0.94/6.20 ( ( ( ~less(vd328, vd329) ) ) ),
% 0.94/6.20 inference(definitional_conversion,[status(esa)],[f_1_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_1_3, negated_conjecture,
% 0.94/6.20 ( ~less(vd328, vd329) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_1_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_2_1, plain,
% 0.94/6.20 less(vplus(vd328, vd330), vplus(vd329, vd330)),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[holds(antec(conjunct2(conjunct2(204))), 335, 0)]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_2_2, plain,
% 0.94/6.20 ( less(vplus(vd328, vd330), vplus(vd329, vd330)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_2_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_3_1, plain,
% 0.94/6.20 ( ~( vplus(vd328, vd330) = vplus(vd329, vd330) ) | vd328 = vd329 ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(conjunct1(conjunct2(204)), 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_3_2, plain,
% 0.94/6.20 ( vplus(vd328, vd330) != vplus(vd329, vd330) | vd328 = vd329 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_3_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_4_1, plain,
% 0.94/6.20 ( ~( greater(vplus(vd328, vd330), vplus(vd329, vd330)) ) | greater(vd328, vd329) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(conjunct1(204), 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_4_2, plain,
% 0.94/6.20 ( ~greater(vplus(vd328, vd330), vplus(vd329, vd330)) | greater(vd328, vd329) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_4_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_5_1, plain,
% 0.94/6.20 ! [ Vd301,Vd302,Vd303 ] : ( ~( less(Vd301, Vd302) ) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_5_2, plain,
% 0.94/6.20 ! [ U_2,U_1,U_0 ] : ( ~( less(U_2, U_1) ) | less(vplus(U_2, U_0), vplus(U_1, U_0)) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_5_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_5_3, plain,
% 0.94/6.20 ! [ U_2,U_1 ] : ( ~( less(U_2, U_1) ) | ! [ U_0 ] : less(vplus(U_2, U_0), vplus(U_1, U_0)) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_5_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_5_4, plain,
% 0.94/6.20 ( ~less(U_2, U_1) | less(vplus(U_2, U_0), vplus(U_1, U_0)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_5_3]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_6_1, plain,
% 0.94/6.20 ! [ Vd301,Vd302,Vd303 ] : ( ~( Vd301 = Vd302 ) | vplus(Vd301, Vd303) = vplus(Vd302, Vd303) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_6_2, plain,
% 0.94/6.20 ! [ U_5,U_4,U_3 ] : ( ~( U_5 = U_4 ) | vplus(U_5, U_3) = vplus(U_4, U_3) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_6_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_6_3, plain,
% 0.94/6.20 ! [ U_5,U_4 ] : ( ~( U_5 = U_4 ) | ! [ U_3 ] : vplus(U_5, U_3) = vplus(U_4, U_3) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_6_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_6_4, plain,
% 0.94/6.20 ( U_5 != U_4 | vplus(U_5, U_3) = vplus(U_4, U_3) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_6_3]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_7_1, plain,
% 0.94/6.20 ! [ Vd301,Vd302,Vd303 ] : ( ~( greater(Vd301, Vd302) ) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 2)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_7_2, plain,
% 0.94/6.20 ! [ U_8,U_7,U_6 ] : ( ~( greater(U_8, U_7) ) | greater(vplus(U_8, U_6), vplus(U_7, U_6)) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_7_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_7_3, plain,
% 0.94/6.20 ! [ U_8,U_7 ] : ( ~( greater(U_8, U_7) ) | ! [ U_6 ] : greater(vplus(U_8, U_6), vplus(U_7, U_6)) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_7_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_7_4, plain,
% 0.94/6.20 ( ~greater(U_8, U_7) | greater(vplus(U_8, U_6), vplus(U_7, U_6)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_7_3]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_8_1, plain,
% 0.94/6.20 ! [ Vd295,Vd296 ] : greater(vplus(Vd295, Vd296), Vd295),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(189, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_8_2, plain,
% 0.94/6.20 ! [ U_10,U_9 ] : greater(vplus(U_10, U_9), U_10),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_8_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_8_3, plain,
% 0.94/6.20 ( greater(vplus(U_10, U_9), U_10) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_8_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_9_1, plain,
% 0.94/6.20 ! [ Vd289,Vd290,Vd292 ] : ( ( ~( leq(Vd290, Vd292) ) | ~( leq(Vd289, Vd290) ) ) | leq(Vd289, Vd292) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(184, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_9_2, plain,
% 0.94/6.20 ! [ U_13,U_12,U_11 ] : ( ( ~( leq(U_12, U_11) ) | ~( leq(U_13, U_12) ) ) | leq(U_13, U_11) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_9_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_9_3, plain,
% 0.94/6.20 ( ~leq(U_12, U_11) | ~leq(U_13, U_12) | leq(U_13, U_11) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_9_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_10_1, plain,
% 0.94/6.20 ! [ Vd281,Vd282,Vd283 ] : ( ( ( ~( less(Vd282, Vd283) ) | ~( leq(Vd281, Vd282) ) ) & ( ~( leq(Vd282, Vd283) ) | ~( less(Vd281, Vd282) ) ) ) | less(Vd281, Vd283) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(177), 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_10_2, plain,
% 0.94/6.20 ! [ U_16,U_15,U_14 ] : ( ( ( ~( less(U_15, U_14) ) | ~( leq(U_16, U_15) ) ) & ( ~( leq(U_15, U_14) ) | ~( less(U_16, U_15) ) ) ) | less(U_16, U_14) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_10_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_10_3, plain,
% 0.94/6.20 ( less(U_16, U_14) | ~less(U_15, U_14) | ~leq(U_16, U_15) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_10_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_10_4, plain,
% 0.94/6.20 ( less(U_16, U_14) | ~leq(U_15, U_14) | ~less(U_16, U_15) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_10_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_11_1, plain,
% 0.94/6.20 ! [ Vd262,Vd263,Vd265 ] : ( ( ~( less(Vd263, Vd265) ) | ~( less(Vd262, Vd263) ) ) | less(Vd262, Vd265) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(168, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_11_2, plain,
% 0.94/6.20 ! [ U_19,U_18,U_17 ] : ( ( ~( less(U_18, U_17) ) | ~( less(U_19, U_18) ) ) | less(U_19, U_17) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_11_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_11_3, plain,
% 0.94/6.20 ( ~less(U_18, U_17) | ~less(U_19, U_18) | less(U_19, U_17) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_11_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_12_1, plain,
% 0.94/6.20 ! [ Vd258,Vd259 ] : ( ~( leq(Vd258, Vd259) ) | geq(Vd259, Vd258) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(163, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_12_2, plain,
% 0.94/6.20 ! [ U_21,U_20 ] : ( ~( leq(U_21, U_20) ) | geq(U_20, U_21) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_12_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_12_3, plain,
% 0.94/6.20 ( ~leq(U_21, U_20) | geq(U_20, U_21) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_12_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_13_1, plain,
% 0.94/6.20 ! [ Vd254,Vd255 ] : ( ~( geq(Vd254, Vd255) ) | leq(Vd255, Vd254) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(158, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_13_2, plain,
% 0.94/6.20 ! [ U_23,U_22 ] : ( ~( geq(U_23, U_22) ) | leq(U_22, U_23) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_13_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_13_3, plain,
% 0.94/6.20 ( ~geq(U_23, U_22) | leq(U_22, U_23) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_13_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_14_1, plain,
% 0.94/6.20 ! [ Vd249,Vd250 ] : ( ( ~( leq(Vd250, Vd249) ) | ( less(Vd250, Vd249) | Vd250 = Vd249 ) ) & ( ( ~( less(Vd250, Vd249) ) & ~( Vd250 = Vd249 ) ) | leq(Vd250, Vd249) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 17), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_14_2, plain,
% 0.94/6.20 ! [ U_25,U_24 ] : ( ( ~( leq(U_24, U_25) ) | ( less(U_24, U_25) | U_24 = U_25 ) ) & ( ( ~( less(U_24, U_25) ) & ~( U_24 = U_25 ) ) | leq(U_24, U_25) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_14_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_14_3, plain,
% 0.94/6.20 ( ! [ U_28,U_26 ] : ( ~( leq(U_26, U_28) ) | ( less(U_26, U_28) | U_26 = U_28 ) ) & ! [ U_29,U_27 ] : ( ( ~( less(U_27, U_29) ) & ~( U_27 = U_29 ) ) | leq(U_27, U_29) ) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_14_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_14_4, plain,
% 0.94/6.20 ( ~leq(U_26, U_28) | less(U_26, U_28) | U_26 = U_28 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_14_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_14_5, plain,
% 0.94/6.20 ( leq(U_27, U_29) | ~less(U_27, U_29) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_14_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_14_6, plain,
% 0.94/6.20 ( leq(U_27, U_29) | U_27 != U_29 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_14_3]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_15_1, plain,
% 0.94/6.20 ! [ Vd244,Vd245 ] : ( ( ~( geq(Vd245, Vd244) ) | ( greater(Vd245, Vd244) | Vd245 = Vd244 ) ) & ( ( ~( greater(Vd245, Vd244) ) & ~( Vd245 = Vd244 ) ) | geq(Vd245, Vd244) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 16), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_15_2, plain,
% 0.94/6.20 ! [ U_31,U_30 ] : ( ( ~( geq(U_30, U_31) ) | ( greater(U_30, U_31) | U_30 = U_31 ) ) & ( ( ~( greater(U_30, U_31) ) & ~( U_30 = U_31 ) ) | geq(U_30, U_31) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_15_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_15_3, plain,
% 0.94/6.20 ( ! [ U_34,U_32 ] : ( ~( geq(U_32, U_34) ) | ( greater(U_32, U_34) | U_32 = U_34 ) ) & ! [ U_35,U_33 ] : ( ( ~( greater(U_33, U_35) ) & ~( U_33 = U_35 ) ) | geq(U_33, U_35) ) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_15_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_15_4, plain,
% 0.94/6.20 ( ~geq(U_32, U_34) | greater(U_32, U_34) | U_32 = U_34 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_15_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_15_5, plain,
% 0.94/6.20 ( geq(U_33, U_35) | ~greater(U_33, U_35) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_15_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_15_6, plain,
% 0.94/6.20 ( geq(U_33, U_35) | U_33 != U_35 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_15_3]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_16_1, plain,
% 0.94/6.20 ! [ Vd226,Vd227 ] : ( ~( less(Vd226, Vd227) ) | greater(Vd227, Vd226) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(147, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_16_2, plain,
% 0.94/6.20 ! [ U_37,U_36 ] : ( ~( less(U_37, U_36) ) | greater(U_36, U_37) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_16_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_16_3, plain,
% 0.94/6.20 ( ~less(U_37, U_36) | greater(U_36, U_37) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_16_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_17_1, plain,
% 0.94/6.20 ! [ Vd208,Vd209 ] : ( ~( greater(Vd208, Vd209) ) | less(Vd209, Vd208) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(140, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_17_2, plain,
% 0.94/6.20 ! [ U_39,U_38 ] : ( ~( greater(U_39, U_38) ) | less(U_38, U_39) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_17_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_17_3, plain,
% 0.94/6.20 ( ~greater(U_39, U_38) | less(U_38, U_39) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_17_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_18_1, plain,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( Vd203 = Vd204 | greater(Vd203, Vd204) | less(Vd203, Vd204) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_18_2, plain,
% 0.94/6.20 ! [ U_41,U_40 ] : ( U_41 = U_40 | greater(U_41, U_40) | less(U_41, U_40) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_18_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_18_3, plain,
% 0.94/6.20 ( U_41 = U_40 | greater(U_41, U_40) | less(U_41, U_40) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_18_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_19_1, plain,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( less(Vd203, Vd204) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_19_2, plain,
% 0.94/6.20 ! [ U_43,U_42 ] : ( ~( U_43 = U_42 ) | ~( less(U_43, U_42) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_19_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_19_3, plain,
% 0.94/6.20 ( U_43 != U_42 | ~less(U_43, U_42) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_19_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_20_1, plain,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( ~( greater(Vd203, Vd204) ) | ~( less(Vd203, Vd204) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 2)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_20_2, plain,
% 0.94/6.20 ! [ U_45,U_44 ] : ( ~( greater(U_45, U_44) ) | ~( less(U_45, U_44) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_20_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_20_3, plain,
% 0.94/6.20 ( ~greater(U_45, U_44) | ~less(U_45, U_44) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_20_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_21_1, plain,
% 0.94/6.20 ! [ Vd203,Vd204 ] : ( ~( Vd203 = Vd204 ) | ~( greater(Vd203, Vd204) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(130), 0), 3)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_21_2, plain,
% 0.94/6.20 ! [ U_47,U_46 ] : ( ~( U_47 = U_46 ) | ~( greater(U_47, U_46) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_21_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_21_3, plain,
% 0.94/6.20 ( U_47 != U_46 | ~greater(U_47, U_46) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_21_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_22_1, plain,
% 0.94/6.20 ! [ Vd198,Vd199 ] : ( ( ~( less(Vd199, Vd198) ) | ? [ Vd201 ] : Vd198 = vplus(Vd199, Vd201) ) & ( ! [ Vd201 ] : ~( Vd198 = vplus(Vd199, Vd201) ) | less(Vd199, Vd198) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 12), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_22_2, plain,
% 0.94/6.20 ! [ U_51,U_50 ] : ( ( ~( less(U_50, U_51) ) | ? [ U_48 ] : U_51 = vplus(U_50, U_48) ) & ( ! [ U_49 ] : ~( U_51 = vplus(U_50, U_49) ) | less(U_50, U_51) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_22_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_22_3, plain,
% 0.94/6.20 ( ! [ U_54,U_52 ] : ( ~( less(U_52, U_54) ) | ? [ U_48 ] : U_54 = vplus(U_52, U_48) ) & ! [ U_55,U_53 ] : ( ! [ U_49 ] : ~( U_55 = vplus(U_53, U_49) ) | less(U_53, U_55) ) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_22_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_22_4, plain,
% 0.94/6.20 ( ! [ U_54,U_52 ] : ( ~( less(U_52, U_54) ) | U_54 = vplus(U_52, sK1(U_54, U_52)) ) & ! [ U_55,U_53 ] : ( ! [ U_49 ] : ~( U_55 = vplus(U_53, U_49) ) | less(U_53, U_55) ) ),
% 0.94/6.20 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_48,sK1(U_54, U_52))],[f_22_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_22_5, plain,
% 0.94/6.20 ( ~less(U_52, U_54) | U_54 = vplus(U_52, sK1(U_54, U_52)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_22_4]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_22_6, plain,
% 0.94/6.20 ( U_55 != vplus(U_53, U_49) | less(U_53, U_55) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_22_4]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_23_1, plain,
% 0.94/6.20 ! [ Vd193,Vd194 ] : ( ( ~( greater(Vd194, Vd193) ) | ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ) & ( ! [ Vd196 ] : ~( Vd194 = vplus(Vd193, Vd196) ) | greater(Vd194, Vd193) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 11), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_23_2, plain,
% 0.94/6.20 ! [ U_59,U_58 ] : ( ( ~( greater(U_58, U_59) ) | ? [ U_56 ] : U_58 = vplus(U_59, U_56) ) & ( ! [ U_57 ] : ~( U_58 = vplus(U_59, U_57) ) | greater(U_58, U_59) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_23_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_23_3, plain,
% 0.94/6.20 ( ! [ U_62,U_60 ] : ( ~( greater(U_60, U_62) ) | ? [ U_56 ] : U_60 = vplus(U_62, U_56) ) & ! [ U_63,U_61 ] : ( ! [ U_57 ] : ~( U_61 = vplus(U_63, U_57) ) | greater(U_61, U_63) ) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_23_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_23_4, plain,
% 0.94/6.20 ( ! [ U_62,U_60 ] : ( ~( greater(U_60, U_62) ) | U_60 = vplus(U_62, sK2(U_62, U_60)) ) & ! [ U_63,U_61 ] : ( ! [ U_57 ] : ~( U_61 = vplus(U_63, U_57) ) | greater(U_61, U_63) ) ),
% 0.94/6.20 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_56,sK2(U_62, U_60))],[f_23_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_23_5, plain,
% 0.94/6.20 ( ~greater(U_60, U_62) | U_60 = vplus(U_62, sK2(U_62, U_60)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_23_4]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_23_6, plain,
% 0.94/6.20 ( U_61 != vplus(U_63, U_57) | greater(U_61, U_63) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_23_4]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_24_1, plain,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( Vd120 = Vd121 | ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) | ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_24_2, plain,
% 0.94/6.20 ! [ U_67,U_66 ] : ( U_67 = U_66 | ? [ U_64 ] : U_67 = vplus(U_66, U_64) | ? [ U_65 ] : U_66 = vplus(U_67, U_65) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_24_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_24_3, plain,
% 0.94/6.20 ! [ U_67,U_66 ] : ( U_67 = U_66 | U_67 = vplus(U_66, sK3(U_67, U_66)) | ? [ U_65 ] : U_66 = vplus(U_67, U_65) ),
% 0.94/6.20 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_64,sK3(U_67, U_66))],[f_24_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_24_4, plain,
% 0.94/6.20 ! [ U_67,U_66 ] : ( U_67 = U_66 | U_67 = vplus(U_66, sK3(U_67, U_66)) | U_66 = vplus(U_67, sK4(U_67, U_66)) ),
% 0.94/6.20 inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_65,sK4(U_67, U_66))],[f_24_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_24_5, plain,
% 0.94/6.20 ( U_67 = U_66 | U_67 = vplus(U_66, sK3(U_67, U_66)) | U_66 = vplus(U_67, sK4(U_67, U_66)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_24_4]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_25_1, plain,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ! [ Vd125 ] : ~( Vd121 = vplus(Vd120, Vd125) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 1)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_25_2, plain,
% 0.94/6.20 ! [ U_70,U_69 ] : ( ~( U_70 = U_69 ) | ! [ U_68 ] : ~( U_69 = vplus(U_70, U_68) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_25_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_25_3, plain,
% 0.94/6.20 ( U_70 != U_69 | U_69 != vplus(U_70, U_68) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_25_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_26_1, plain,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( ! [ Vd123 ] : ~( Vd120 = vplus(Vd121, Vd123) ) | ! [ Vd125 ] : ~( Vd121 = vplus(Vd120, Vd125) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 2)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_26_2, plain,
% 0.94/6.20 ! [ U_74,U_73 ] : ( ! [ U_71 ] : ~( U_74 = vplus(U_73, U_71) ) | ! [ U_72 ] : ~( U_73 = vplus(U_74, U_72) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_26_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_26_3, plain,
% 0.94/6.20 ( U_74 != vplus(U_73, U_71) | U_73 != vplus(U_74, U_72) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_26_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_27_1, plain,
% 0.94/6.20 ! [ Vd120,Vd121 ] : ( ~( Vd120 = Vd121 ) | ! [ Vd123 ] : ~( Vd120 = vplus(Vd121, Vd123) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 3)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_27_2, plain,
% 0.94/6.20 ! [ U_77,U_76 ] : ( ~( U_77 = U_76 ) | ! [ U_75 ] : ~( U_77 = vplus(U_76, U_75) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_27_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_27_3, plain,
% 0.94/6.20 ( U_77 != U_76 | U_77 != vplus(U_76, U_75) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_27_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_28_1, plain,
% 0.94/6.20 ! [ Vd104,Vd105 ] : ( Vd104 = Vd105 | ! [ Vd107 ] : ~( vplus(Vd107, Vd104) = vplus(Vd107, Vd105) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(81, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_28_2, plain,
% 0.94/6.20 ! [ U_80,U_79 ] : ( U_80 = U_79 | ! [ U_78 ] : ~( vplus(U_78, U_80) = vplus(U_78, U_79) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_28_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_28_3, plain,
% 0.94/6.20 ( U_80 = U_79 | vplus(U_78, U_80) != vplus(U_78, U_79) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_28_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_29_1, plain,
% 0.94/6.20 ! [ Vd92,Vd93 ] : ~( Vd93 = vplus(Vd92, Vd93) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(73, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_29_2, plain,
% 0.94/6.20 ! [ U_82,U_81 ] : ~( U_81 = vplus(U_82, U_81) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_29_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_29_3, plain,
% 0.94/6.20 ( U_81 != vplus(U_82, U_81) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_29_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_30_1, plain,
% 0.94/6.20 ! [ Vd78,Vd79 ] : vplus(Vd79, Vd78) = vplus(Vd78, Vd79),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(61, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_30_2, plain,
% 0.94/6.20 ! [ U_84,U_83 ] : vplus(U_83, U_84) = vplus(U_84, U_83),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_30_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_30_3, plain,
% 0.94/6.20 ( vplus(U_83, U_84) = vplus(U_84, U_83) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_30_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_31_1, plain,
% 0.94/6.20 ! [ Vd68,Vd69 ] : vplus(vsucc(Vd68), Vd69) = vsucc(vplus(Vd68, Vd69)),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(52, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_31_2, plain,
% 0.94/6.20 ! [ U_86,U_85 ] : vplus(vsucc(U_86), U_85) = vsucc(vplus(U_86, U_85)),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_31_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_31_3, plain,
% 0.94/6.20 ( vplus(vsucc(U_86), U_85) = vsucc(vplus(U_86, U_85)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_31_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_32_1, plain,
% 0.94/6.20 ! [ Vd59 ] : vplus(v1, Vd59) = vsucc(Vd59),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(43, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_32_2, plain,
% 0.94/6.20 ! [ U_87 ] : vplus(v1, U_87) = vsucc(U_87),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_32_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_32_3, plain,
% 0.94/6.20 ( vplus(v1, U_87) = vsucc(U_87) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_32_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_33_1, plain,
% 0.94/6.20 ! [ Vd46,Vd47,Vd48 ] : vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(33, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_33_2, plain,
% 0.94/6.20 ! [ U_90,U_89,U_88 ] : vplus(vplus(U_90, U_89), U_88) = vplus(U_90, vplus(U_89, U_88)),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_33_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_33_3, plain,
% 0.94/6.20 ( vplus(vplus(U_90, U_89), U_88) = vplus(U_90, vplus(U_89, U_88)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_33_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_34_1, plain,
% 0.94/6.20 ! [ Vd42,Vd43 ] : ( vplus(Vd42, vsucc(Vd43)) = vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1) = vsucc(Vd42) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_34_2, plain,
% 0.94/6.20 ! [ U_92,U_91 ] : ( vplus(U_92, vsucc(U_91)) = vsucc(vplus(U_92, U_91)) & vplus(U_92, v1) = vsucc(U_92) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_34_1]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_34_3, plain,
% 0.94/6.20 ( ! [ U_93 ] : vplus(U_93, v1) = vsucc(U_93) & ! [ U_94,U_91 ] : vplus(U_94, vsucc(U_91)) = vsucc(vplus(U_94, U_91)) ),
% 0.94/6.20 inference(miniscope,[status(thm)],[f_34_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_34_4, plain,
% 0.94/6.20 ( vplus(U_93, v1) = vsucc(U_93) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_34_3]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_34_5, plain,
% 0.94/6.20 ( vplus(U_94, vsucc(U_91)) = vsucc(vplus(U_94, U_91)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_34_3]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_35_1, plain,
% 0.94/6.20 ! [ Vd24 ] : ( Vd24 = v1 | Vd24 = vsucc(vskolem2(Vd24)) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(20, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_35_2, plain,
% 0.94/6.20 ! [ U_95 ] : ( U_95 = v1 | U_95 = vsucc(vskolem2(U_95)) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_35_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_35_3, plain,
% 0.94/6.20 ( U_95 = v1 | U_95 = vsucc(vskolem2(U_95)) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_35_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_36_1, plain,
% 0.94/6.20 ! [ Vd16 ] : ~( vsucc(Vd16) = Vd16 ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(12, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_36_2, plain,
% 0.94/6.20 ! [ U_96 ] : ~( vsucc(U_96) = U_96 ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_36_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_36_3, plain,
% 0.94/6.20 ( vsucc(U_96) != U_96 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_36_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_37_1, plain,
% 0.94/6.20 ! [ Vd7,Vd8 ] : ( Vd7 = Vd8 | ~( vsucc(Vd7) = vsucc(Vd8) ) ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[ass(cond(6, 0), 0)]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_37_2, plain,
% 0.94/6.20 ! [ U_98,U_97 ] : ( U_98 = U_97 | ~( vsucc(U_98) = vsucc(U_97) ) ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_37_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_37_3, plain,
% 0.94/6.20 ( U_98 = U_97 | vsucc(U_98) != vsucc(U_97) ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_37_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_38_1, plain,
% 0.94/6.20 ! [ Vd3,Vd4 ] : ( ~( vsucc(Vd3) = vsucc(Vd4) ) | Vd3 = Vd4 ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[qu(antec(axiom(3)), imp(antec(axiom(3))))]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_38_2, plain,
% 0.94/6.20 ! [ U_100,U_99 ] : ( ~( vsucc(U_100) = vsucc(U_99) ) | U_100 = U_99 ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_38_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_38_3, plain,
% 0.94/6.20 ( vsucc(U_100) != vsucc(U_99) | U_100 = U_99 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_38_2]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_39_1, plain,
% 0.94/6.20 ! [ Vd1 ] : ~( vsucc(Vd1) = v1 ),
% 0.94/6.20 inference(fof_nnf,[status(thm)],[qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))]) ).
% 0.94/6.20
% 0.94/6.20 fof(f_39_2, plain,
% 0.94/6.20 ! [ U_101 ] : ~( vsucc(U_101) = v1 ),
% 0.94/6.20 inference(variable_rename,[status(thm)],[f_39_1]) ).
% 0.94/6.20
% 0.94/6.20 cnf(f_39_3, plain,
% 0.94/6.20 ( vsucc(U_101) != v1 ),
% 0.94/6.20 inference(clausify,[status(thm)],[f_39_2]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_1, axiom,
% 0.94/6.20 ( Eq_x_0 = Eq_x_0 ),
% 0.94/6.20 theory(equality,[reflexivity]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_2, axiom,
% 0.94/6.20 ( Eq_x_0 != Eq_x_1 | Eq_x_1 = Eq_x_0 ),
% 0.94/6.20 theory(equality,[symmetry]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_3, axiom,
% 0.94/6.20 ( Eq_x_0 != Eq_x_1 | Eq_x_1 != Eq_x_2 | Eq_x_0 = Eq_x_2 ),
% 0.94/6.20 theory(equality,[transitivity]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_4, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_5, axiom,
% 0.94/6.20 ( Eq_x_0 != Eq_y_0 | vsucc(Eq_x_0) = vsucc(Eq_y_0) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_6, axiom,
% 0.94/6.20 ( Eq_x_0 != Eq_y_0 | vskolem2(Eq_x_0) = vskolem2(Eq_y_0) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_7, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_8, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_9, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_10, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_functions]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_11, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_predicates]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_12, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_predicates]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_13, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_predicates]) ).
% 0.94/6.20
% 0.94/6.20 cnf(equality_14, axiom,
% 0.94/6.20 ( 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) ),
% 0.94/6.20 theory(equality,[substitution_predicates]) ).
% 0.94/6.20
% 0.94/6.20 cnf(sat_proved, plain, $false,
% 0.94/6.20 inference(cadical, [status(thm)], [
% 0.94/6.20 ]) ).
% 0.94/6.20 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------