%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM838+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 : 300s
% DateTime : Tue May 5 04:58:40 PM UTC 2026
% Result : Theorem 0.35s 1.61s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_65)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(52, 0), 0)',axiom,
! [X50,X51] : vplus(vsucc(X50),X51) = vsucc(vplus(X50,X51)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X56,X57] :
( vplus(X56,vsucc(X57)) = vsucc(vplus(X56,X57))
& vplus(X56,v1) = vsucc(X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof('ass(cond(goal(130), 0), 2)',axiom,
! [X31,X32] :
( ~ greater(X31,X32)
| ~ less(X31,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('qu(antec(axiom(3)), imp(antec(axiom(3))))',axiom,
! [X62,X63] :
( vsucc(X62) = vsucc(X63)
=> X62 = X63 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof('ass(cond(6, 0), 0)',axiom,
! [X60,X61] :
( X60 != X61
=> vsucc(X60) != vsucc(X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof('ass(cond(goal(130), 0), 1)',axiom,
! [X31,X32] :
( X31 != X32
| ~ less(X31,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof('ass(cond(goal(130), 0), 3)',axiom,
! [X31,X32] :
( X31 != X32
| ~ greater(X31,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof('ass(cond(43, 0), 0)',axiom,
! [X52] : vplus(v1,X52) = vsucc(X52),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('ass(cond(12, 0), 0)',axiom,
! [X59] : vsucc(X59) != X59,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof('ass(cond(20, 0), 0)',axiom,
! [X58] :
( X58 != v1
=> X58 = vsucc(vskolem2(X58)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof('qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))',axiom,
! [X64] : vsucc(X64) != v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof('ass(cond(proof(196), 0), 7)',axiom,
! [X1,X6,X7] :
( greater(X6,X7)
=> vplus(vplus(X7,vskolem7(X6,X7)),X1) = vplus(vplus(vskolem7(X6,X7),X7),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 7)') ).
fof('ass(cond(proof(196), 0), 6)',axiom,
! [X1,X6,X7] :
( greater(X6,X7)
=> vplus(vplus(vskolem7(X6,X7),X7),X1) = vplus(vskolem7(X6,X7),vplus(X7,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 6)') ).
fof('ass(cond(proof(196), 0), 5)',axiom,
! [X1,X6,X7] :
( greater(X6,X7)
=> vplus(vskolem7(X6,X7),vplus(X7,X1)) = vplus(vplus(X7,X1),vskolem7(X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 5)') ).
fof('ass(cond(proof(196), 0), 8)',axiom,
! [X1,X6,X7] :
( greater(X6,X7)
=> vplus(X6,X1) = vplus(vplus(X7,vskolem7(X6,X7)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 8)') ).
fof('ass(cond(proof(196), 0), 0)',axiom,
! [X1,X2,X3] :
( less(X2,X3)
=> less(vplus(X2,X1),vplus(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 0)') ).
fof('ass(cond(proof(196), 0), 4)',axiom,
! [X1,X6,X7] :
( greater(X6,X7)
=> greater(vplus(X6,X1),vplus(X7,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 4)') ).
fof('ass(cond(proof(196), 0), 1)',axiom,
! [X1,X2,X3] :
( less(X2,X3)
=> greater(vplus(X3,X1),vplus(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 1)') ).
fof('holds(conseq(195), 305, 0)',conjecture,
greater(vplus(vd301,vd303),vplus(vd302,vd303)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(195), 305, 0)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X39,X40] :
( X39 = X40
| ? [X41] : X39 = vplus(X40,X41)
| ? [X42] : X40 = vplus(X39,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X53,X54,X55] : vplus(vplus(X53,X54),X55) = vplus(X53,vplus(X54,X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X36,X37] :
( greater(X37,X36)
<=> ? [X38] : X37 = vplus(X36,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(proof(196), 0), 9)',axiom,
! [X1,X6,X7] :
( greater(X6,X7)
=> X6 = vplus(X7,vskolem7(X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 9)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X33,X34] :
( less(X34,X33)
<=> ? [X35] : X33 = vplus(X34,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('ass(cond(184, 0), 0)',axiom,
! [X10,X11,X12] :
( ( leq(X11,X12)
& leq(X10,X11) )
=> leq(X10,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
fof('ass(cond(goal(177), 0), 0)',axiom,
! [X13,X14,X15] :
( ( ( less(X14,X15)
& leq(X13,X14) )
| ( leq(X14,X15)
& less(X13,X14) ) )
=> less(X13,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
fof('ass(cond(168, 0), 0)',axiom,
! [X16,X17,X18] :
( ( less(X17,X18)
& less(X16,X17) )
=> less(X16,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof('ass(cond(goal(88), 0), 2)',axiom,
! [X39,X40] :
( ~ ? [X41] : X39 = vplus(X40,X41)
| ~ ? [X42] : X40 = vplus(X39,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof('ass(cond(81, 0), 0)',axiom,
! [X43,X44] :
( X43 != X44
=> ! [X45] : vplus(X45,X43) != vplus(X45,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X8,X9] : greater(vplus(X8,X9),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 17), 1)',axiom,
! [X23,X24] :
( leq(X24,X23)
<=> ( less(X24,X23)
| X24 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [X25,X26] :
( geq(X26,X25)
<=> ( greater(X26,X25)
| X26 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof('ass(cond(163, 0), 0)',axiom,
! [X19,X20] :
( leq(X19,X20)
=> geq(X20,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof('ass(cond(158, 0), 0)',axiom,
! [X21,X22] :
( geq(X21,X22)
=> leq(X22,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X29,X30] :
( greater(X29,X30)
=> less(X30,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X27,X28] :
( less(X27,X28)
=> greater(X28,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('ass(cond(proof(196), 0), 2)',axiom,
! [X1,X2,X3] :
( less(X2,X3)
=> greater(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 2)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X31,X32] :
( X31 = X32
| greater(X31,X32)
| less(X31,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X48,X49] : vplus(X49,X48) = vplus(X48,X49),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(goal(88), 0), 3)',axiom,
! [X39,X40] :
( X39 != X40
| ~ ? [X41] : X39 = vplus(X40,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X39,X40] :
( X39 != X40
| ~ ? [X42] : X40 = vplus(X39,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('ass(cond(73, 0), 0)',axiom,
! [X46,X47] : X47 != vplus(X46,X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('holds(antec(195), 304, 0)',axiom,
greater(vd301,vd302),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(195), 304, 0)') ).
fof(i_0_43,plain,
! [X260,X261] : vplus(vsucc(X260),X261) = vsucc(vplus(X260,X261)),
inference(variable_rename,[status(thm)],['ass(cond(52, 0), 0)']) ).
fof(i_0_44,plain,
! [X266,X267] :
( vplus(X266,vsucc(X267)) = vsucc(vplus(X266,X267))
& vplus(X266,v1) = vsucc(X266) ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
fof(i_0_45,plain,
! [X31,X32] :
( ~ greater(X31,X32)
| ~ less(X31,X32) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
fof(i_0_46,plain,
! [X272,X273] :
( vsucc(X272) != vsucc(X273)
| X272 = X273 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(antec(axiom(3)), imp(antec(axiom(3))))'])]) ).
fof(i_0_47,plain,
! [X270,X271] :
( X270 = X271
| vsucc(X270) != vsucc(X271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(6, 0), 0)'])]) ).
fof(i_0_48,plain,
! [X31,X32] :
( X31 != X32
| ~ less(X31,X32) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 1)']) ).
fof(i_0_49,plain,
! [X31,X32] :
( X31 != X32
| ~ greater(X31,X32) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 3)']) ).
fof(i_0_50,plain,
! [X262] : vplus(v1,X262) = vsucc(X262),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(i_0_51,plain,
! [X269] : vsucc(X269) != X269,
inference(variable_rename,[status(thm)],['ass(cond(12, 0), 0)']) ).
fof(i_0_52,plain,
! [X268] :
( X268 = v1
| X268 = vsucc(vskolem2(X268)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(20, 0), 0)'])]) ).
fof(i_0_53,plain,
! [X274] : vsucc(X274) != v1,
inference(variable_rename,[status(thm)],['qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))']) ).
fof(i_0_54,plain,
! [X188,X189,X190] :
( ~ greater(X189,X190)
| vplus(vplus(X190,vskolem7(X189,X190)),X188) = vplus(vplus(vskolem7(X189,X190),X190),X188) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 7)'])]) ).
fof(i_0_55,plain,
! [X185,X186,X187] :
( ~ greater(X186,X187)
| vplus(vplus(vskolem7(X186,X187),X187),X185) = vplus(vskolem7(X186,X187),vplus(X187,X185)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 6)'])]) ).
fof(i_0_56,plain,
! [X182,X183,X184] :
( ~ greater(X183,X184)
| vplus(vskolem7(X183,X184),vplus(X184,X182)) = vplus(vplus(X184,X182),vskolem7(X183,X184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 5)'])]) ).
fof(i_0_57,plain,
! [X191,X192,X193] :
( ~ greater(X192,X193)
| vplus(X192,X191) = vplus(vplus(X193,vskolem7(X192,X193)),X191) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 8)'])]) ).
fof(i_0_58,plain,
! [X168,X169,X170] :
( ~ less(X169,X170)
| less(vplus(X169,X168),vplus(X170,X168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 0)'])]) ).
fof(i_0_59,plain,
! [X179,X180,X181] :
( ~ greater(X180,X181)
| greater(vplus(X180,X179),vplus(X181,X179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 4)'])]) ).
fof(i_0_60,plain,
! [X171,X172,X173] :
( ~ less(X172,X173)
| greater(vplus(X173,X171),vplus(X172,X171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(196), 0), 1)'])]) ).
fof(i_0_61,negated_conjecture,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(195), 305, 0)'])]) ).
fof(i_0_62,plain,
! [X239,X240] :
( X239 = X240
| X239 = vplus(X240,esk3_2(X239,X240))
| X240 = vplus(X239,esk4_2(X239,X240)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
fof(i_0_63,plain,
! [X263,X264,X265] : vplus(vplus(X263,X264),X265) = vplus(X263,vplus(X264,X265)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(i_0_64,plain,
vplus(vsucc(X1),X2) = vsucc(vplus(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_43]) ).
cnf(i_0_65,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[i_0_44]) ).
cnf(i_0_66,plain,
vplus(X1,vsucc(X2)) = vsucc(vplus(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_44]) ).
fof(i_0_67,plain,
! [X233,X234,X236,X237,X238] :
( ( ~ greater(X234,X233)
| X234 = vplus(X233,esk2_2(X233,X234)) )
& ( X237 != vplus(X236,X238)
| greater(X237,X236) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)'])])])])]) ).
fof(i_0_68,plain,
! [X194,X195] :
( ~ greater(X194,X195)
| X194 = vplus(X195,vskolem7(X194,X195)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],['ass(cond(proof(196), 0), 9)'])])]) ).
fof(i_0_69,plain,
! [X227,X228,X230,X231,X232] :
( ( ~ less(X228,X227)
| X227 = vplus(X228,esk1_2(X227,X228)) )
& ( X230 != vplus(X231,X232)
| less(X231,X230) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 12), 1)'])])])])]) ).
fof(i_0_70,plain,
! [X198,X199,X200] :
( ~ leq(X199,X200)
| ~ leq(X198,X199)
| leq(X198,X200) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(184, 0), 0)'])]) ).
fof(i_0_71,plain,
! [X201,X202,X203] :
( ( ~ less(X202,X203)
| ~ leq(X201,X202)
| less(X201,X203) )
& ( ~ leq(X202,X203)
| ~ less(X201,X202)
| less(X201,X203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(177), 0), 0)'])])]) ).
fof(i_0_72,plain,
! [X204,X205,X206] :
( ~ less(X205,X206)
| ~ less(X204,X205)
| less(X204,X206) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(168, 0), 0)'])]) ).
fof(i_0_73,plain,
! [X246,X247,X248,X249] :
( X246 != vplus(X247,X248)
| X247 != vplus(X246,X249) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 2)'])])]) ).
fof(i_0_74,plain,
! [X253,X254,X255] :
( X253 = X254
| vplus(X255,X253) != vplus(X255,X254) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(81, 0), 0)'])])]) ).
fof(i_0_75,plain,
! [X223,X224] :
( ~ greater(X223,X224)
| ~ less(X223,X224) ),
inference(variable_rename,[status(thm)],[i_0_45]) ).
cnf(i_0_76,plain,
( X1 = X2
| vsucc(X1) != vsucc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]) ).
cnf(i_0_77,plain,
( X1 = X2
| vsucc(X1) != vsucc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]) ).
fof(i_0_78,plain,
! [X196,X197] : greater(vplus(X196,X197),X196),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
fof(i_0_79,plain,
! [X211,X212] :
( ( ~ leq(X212,X211)
| less(X212,X211)
| X212 = X211 )
& ( ~ less(X212,X211)
| leq(X212,X211) )
& ( X212 != X211
| leq(X212,X211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 17), 1)'])])]) ).
fof(i_0_80,plain,
! [X213,X214] :
( ( ~ geq(X214,X213)
| greater(X214,X213)
| X214 = X213 )
& ( ~ greater(X214,X213)
| geq(X214,X213) )
& ( X214 != X213
| geq(X214,X213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 16), 1)'])])]) ).
fof(i_0_81,plain,
! [X207,X208] :
( ~ leq(X207,X208)
| geq(X208,X207) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(163, 0), 0)'])]) ).
fof(i_0_82,plain,
! [X209,X210] :
( ~ geq(X209,X210)
| leq(X210,X209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(158, 0), 0)'])]) ).
fof(i_0_83,plain,
! [X217,X218] :
( ~ greater(X217,X218)
| less(X218,X217) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])]) ).
fof(i_0_84,plain,
! [X215,X216] :
( ~ less(X215,X216)
| greater(X216,X215) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])]) ).
fof(i_0_85,plain,
! [X174,X175] :
( ~ less(X174,X175)
| greater(X175,X174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],['ass(cond(proof(196), 0), 2)'])])]) ).
fof(i_0_86,plain,
! [X219,X220] :
( X219 = X220
| greater(X219,X220)
| less(X219,X220) ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
fof(i_0_87,plain,
! [X258,X259] : vplus(X259,X258) = vplus(X258,X259),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(i_0_88,plain,
! [X250,X251,X252] :
( X250 != X251
| X250 != vplus(X251,X252) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 3)'])])]) ).
fof(i_0_89,plain,
! [X243,X244,X245] :
( X243 != X244
| X244 != vplus(X243,X245) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).
fof(i_0_90,plain,
! [X221,X222] :
( X221 != X222
| ~ less(X221,X222) ),
inference(variable_rename,[status(thm)],[i_0_48]) ).
fof(i_0_91,plain,
! [X225,X226] :
( X225 != X226
| ~ greater(X225,X226) ),
inference(variable_rename,[status(thm)],[i_0_49]) ).
cnf(i_0_92,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[i_0_50]) ).
fof(i_0_93,plain,
! [X256,X257] : X257 != vplus(X256,X257),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
cnf(i_0_94,plain,
vsucc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_51]) ).
cnf(i_0_95,plain,
( X1 = v1
| X1 = vsucc(vskolem2(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
cnf(i_0_96,plain,
vsucc(X1) != v1,
inference(split_conjunct,[status(thm)],[i_0_53]) ).
cnf(i_0_97,plain,
( vplus(vplus(X2,vskolem7(X1,X2)),X3) = vplus(vplus(vskolem7(X1,X2),X2),X3)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_98,plain,
( vplus(vplus(vskolem7(X1,X2),X2),X3) = vplus(vskolem7(X1,X2),vplus(X2,X3))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_99,plain,
( vplus(vskolem7(X1,X2),vplus(X2,X3)) = vplus(vplus(X2,X3),vskolem7(X1,X2))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_100,plain,
( vplus(X1,X3) = vplus(vplus(X2,vskolem7(X1,X2)),X3)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_101,plain,
( less(vplus(X1,X3),vplus(X2,X3))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_102,plain,
( greater(vplus(X1,X3),vplus(X2,X3))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_103,plain,
( greater(vplus(X2,X3),vplus(X1,X3))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_104,negated_conjecture,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_105,plain,
( X1 = X2
| X1 = vplus(X2,esk3_2(X1,X2))
| X2 = vplus(X1,esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_106,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_107,plain,
vplus(vplus(X1,v1),X2) = vplus(vplus(X1,X2),v1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_64,c_0_65]),c_0_65]),
[final] ).
cnf(i_0_108,plain,
vplus(X1,vplus(X2,v1)) = vplus(vplus(X1,X2),v1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_66,c_0_65]),c_0_65]),
[final] ).
cnf(i_0_109,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_110,plain,
( X1 = vplus(X2,vskolem7(X1,X2))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_111,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_112,plain,
( leq(X3,X2)
| ~ leq(X1,X2)
| ~ leq(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_113,plain,
( less(X3,X2)
| ~ less(X1,X2)
| ~ leq(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_114,plain,
( less(X3,X2)
| ~ leq(X1,X2)
| ~ less(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_115,plain,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_116,plain,
( X1 != vplus(X2,X3)
| X2 != vplus(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_117,plain,
( X1 = X2
| vplus(X3,X1) != vplus(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_118,plain,
( ~ greater(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_119,plain,
( X1 = X2
| vplus(X1,v1) != vplus(X2,v1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_76,c_0_65]),c_0_65]),
[final] ).
cnf(i_0_120,plain,
( X1 = X2
| vplus(X1,v1) != vplus(X2,v1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_77,c_0_65]),c_0_65]),
[final] ).
cnf(i_0_121,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_122,plain,
( less(X1,X2)
| X1 = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_123,plain,
( greater(X1,X2)
| X1 = X2
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_124,plain,
( less(X2,X1)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_125,plain,
( greater(X1,X2)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_126,plain,
( geq(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_127,plain,
( geq(X2,X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_128,plain,
( leq(X1,X2)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_129,plain,
( leq(X2,X1)
| ~ geq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_130,plain,
( less(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_131,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_132,plain,
( greater(X2,X1)
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_133,plain,
( X1 = X2
| greater(X1,X2)
| less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_134,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_135,plain,
( X1 != X2
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_136,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_137,plain,
( X1 != X2
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_138,plain,
( X1 != X2
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_139,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[i_0_92,c_0_65]),
[final] ).
cnf(i_0_140,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_141,plain,
vplus(X1,v1) != X1,
inference(rw,[status(thm)],[i_0_94,c_0_65]),
[final] ).
cnf(i_0_142,plain,
( X1 = v1
| X1 = vplus(vskolem2(X1),v1) ),
inference(rw,[status(thm)],[i_0_95,c_0_65]),
[final] ).
cnf(i_0_143,plain,
vplus(X1,v1) != v1,
inference(rw,[status(thm)],[i_0_96,c_0_65]),
[final] ).
cnf(i_0_144,plain,
( geq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_145,plain,
( leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_146,plain,
greater(vd301,vd302),
inference(split_conjunct,[status(thm)],['holds(antec(195), 304, 0)']),
[final] ).
cnf(i_0_147,axiom,
X1 = X1 ).
cnf(i_0_148,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_149,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_150,axiom,
( X1 != X2
| vplus(X1,X3) = vplus(X2,X3) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| vplus(X3,X1) = vplus(X3,X2) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| ~ greater(X1,X3)
| greater(X2,X3) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| ~ greater(X3,X1)
| greater(X3,X2) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| ~ less(X1,X3)
| less(X2,X3) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| ~ less(X3,X1)
| less(X3,X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| ~ geq(X1,X3)
| geq(X2,X3) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| ~ geq(X3,X1)
| geq(X3,X2) ) ).
cnf(i_0_147_001,axiom,
X1 = X1 ).
cnf(i_0_148_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_149_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_150_004,axiom,
( X1 != X2
| vplus(X1,X3) = vplus(X2,X3) ) ).
cnf(i_0_151_005,axiom,
( X1 != X2
| vplus(X3,X1) = vplus(X3,X2) ) ).
cnf(i_0_152_006,axiom,
( X1 != X2
| ~ greater(X1,X3)
| greater(X2,X3) ) ).
cnf(i_0_153_007,axiom,
( X1 != X2
| ~ greater(X3,X1)
| greater(X3,X2) ) ).
cnf(i_0_154_008,axiom,
( X1 != X2
| ~ less(X1,X3)
| less(X2,X3) ) ).
cnf(i_0_155_009,axiom,
( X1 != X2
| ~ less(X3,X1)
| less(X3,X2) ) ).
cnf(i_0_156_010,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_157_011,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_158_012,axiom,
( X1 != X2
| ~ geq(X1,X3)
| geq(X2,X3) ) ).
cnf(i_0_159_013,axiom,
( X1 != X2
| ~ geq(X3,X1)
| geq(X3,X2) ) ).
cnf(i_0_160,plain,
X1 = X1,
inference(equality_inference,[],[117]) ).
cnf(i_0_161,plain,
X1 = X1,
inference(equality_inference,[],[120]) ).
cnf(i_0_162,plain,
less(X1,vplus(X1,X2)),
inference(equality_inference,[],[124]) ).
cnf(i_0_163,plain,
greater(vplus(X1,X2),X1),
inference(equality_inference,[],[125]) ).
cnf(i_0_164,plain,
~ less(X1,X1),
inference(equality_inference,[],[137]) ).
cnf(i_0_165,plain,
~ greater(X1,X1),
inference(equality_inference,[],[138]) ).
cnf(i_0_166,plain,
geq(X1,X1),
inference(equality_inference,[],[144]) ).
cnf(i_0_167,plain,
leq(X1,X1),
inference(equality_inference,[],[145]) ).
cnf(i_0_168,plain,
$false,
inference(scs_inference,[],[i_0_104,i_0_146,i_0_102]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM838+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:15:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.35/1.61 % Version : CSE_E---1.7
% 0.35/1.61 % Problem : theBenchmark.p
% 0.35/1.61 % SZS status Theorem for theBenchmark.p
% 0.35/1.61 % SZS output start CNFRefutation
% See solution above
% 0.35/1.64 % Total time : 1.273s
%------------------------------------------------------------------------------