%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM835+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 : n029.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 04:58:39 PM UTC 2026
% Result : Theorem 0.30s 1.62s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_52)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(conseq(110), 2), 1)',axiom,
! [X1] :
( vd165 = vplus(vd151,X1)
=> vsucc(vplus(vd151,X1)) = vplus(vd151,vsucc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 1)') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X34,X35] :
( vplus(X34,vsucc(X35)) = vsucc(vplus(X34,X35))
& vplus(X34,v1) = vsucc(X34) ),
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(52, 0), 0)',axiom,
! [X28,X29] : vplus(vsucc(X28),X29) = vsucc(vplus(X28,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof('ass(cond(conseq(110), 1), 6)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 = v1
=> m(vsucc(vd165)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 6)') ).
fof('ass(cond(conseq(110), 1), 0)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> m(vsucc(vd165)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 0)') ).
fof('ass(cond(conseq(110), 2), 0)',axiom,
! [X1] :
( vd165 = vplus(vd151,X1)
=> m(vsucc(vd165)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 0)') ).
fof('ass(cond(conseq(110), 1), 4)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> vsucc(vskolem3) = vplus(v1,vskolem3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 4)') ).
fof('qu(antec(axiom(3)), imp(antec(axiom(3))))',axiom,
! [X40,X41] :
( vsucc(X40) = vsucc(X41)
=> X40 = X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof('ass(cond(6, 0), 0)',axiom,
! [X38,X39] :
( X38 != X39
=> vsucc(X38) != vsucc(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof('ass(cond(conseq(105), 1), 0)',axiom,
! [X3] :
( X3 = v1
=> ( ( v1 = X3
& vd151 = v1 )
| ? [X4] :
( vplus(v1,X4) = vplus(X3,X4)
& vsucc(X4) = vplus(v1,X4)
& vd151 = vsucc(X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(105), 1), 0)') ).
fof('ass(cond(conseq(110), 1), 5)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> X2 = vsucc(vskolem3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 5)') ).
fof('ass(cond(conseq(110), 0), 0)',axiom,
( vd151 = vd165
=> m(vsucc(vd165)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 0)') ).
fof('ass(cond(43, 0), 0)',axiom,
! [X30] : vplus(v1,X30) = vsucc(X30),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('ass(cond(12, 0), 0)',axiom,
! [X37] : vsucc(X37) != X37,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof('ass(cond(20, 0), 0)',axiom,
! [X36] :
( X36 != v1
=> X36 = vsucc(vskolem2(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof('qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))',axiom,
! [X42] : vsucc(X42) != v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof('dis(case_distinction(conseq(110)))',conjecture,
( ? [X1] : vd165 = vplus(vd151,X1)
| ? [X2] : vd151 = vplus(vd165,X2)
| vd151 = vd165 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).
fof('def(cond(conseq(105), 0), 1)',axiom,
! [X5,X6] :
( m(X6)
<=> ( X5 = X6
| ? [X7] : X5 = vplus(X6,X7)
| ? [X8] : X6 = vplus(X5,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
fof('ass(cond(conseq(110), 1), 2)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> vplus(vd165,vplus(v1,vskolem3)) = vplus(vplus(vd165,v1),vskolem3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 2)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X31,X32,X33] : vplus(vplus(X31,X32),X33) = vplus(X31,vplus(X32,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(conseq(110), 1), 3)',axiom,
! [X2] :
( vd151 = vplus(vd165,X2)
=> ( X2 != v1
=> vd151 = vplus(vd165,vplus(v1,vskolem3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 3)') ).
fof('ass(cond(proof(97), 0), 1)',axiom,
! [X13,X14,X17,X18] :
~ ( X14 = vplus(X13,X18)
& X13 = vplus(X14,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 1)') ).
fof('ass(cond(proof(97), 0), 0)',axiom,
! [X13,X14] :
~ ? [X15,X16] :
( X14 = vplus(X13,X16)
& X13 = vplus(X14,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 0)') ).
fof('ass(cond(104, 0), 1)',axiom,
! [X9,X10] :
( ~ ? [X12] : X9 = vplus(X10,X12)
| ~ ? [X11] : X10 = vplus(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(104, 0), 1)') ).
fof('ass(cond(81, 0), 0)',axiom,
! [X21,X22] :
( X21 != X22
=> ! [X23] : vplus(X23,X21) != vplus(X23,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X26,X27] : vplus(X27,X26) = vplus(X26,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(proof(97), 0), 3)',axiom,
! [X13,X14] :
~ ? [X20] :
( X13 = vplus(X14,X20)
& X13 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 3)') ).
fof('ass(cond(proof(97), 0), 2)',axiom,
! [X13,X14] :
~ ? [X19] :
( X14 = vplus(X13,X19)
& X13 = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(97), 0), 2)') ).
fof('ass(cond(104, 0), 2)',axiom,
! [X9,X10] :
( X9 != X10
| ~ ? [X12] : X9 = vplus(X10,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(104, 0), 2)') ).
fof('ass(cond(104, 0), 0)',axiom,
! [X9,X10] :
( X9 != X10
| ~ ? [X11] : X10 = vplus(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(104, 0), 0)') ).
fof('ass(cond(73, 0), 0)',axiom,
! [X24,X25] : X25 != vplus(X24,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('holds(109, 164, 0)',axiom,
m(v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(109, 164, 0)') ).
fof('holds(110, 166, 0)',axiom,
m(vd165),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(110, 166, 0)') ).
fof(i_0_33,plain,
! [X112] :
( vd165 != vplus(vd151,X112)
| vsucc(vplus(vd151,X112)) = vplus(vd151,vsucc(X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 2), 1)'])]) ).
fof(i_0_34,plain,
! [X170,X171] :
( vplus(X170,vsucc(X171)) = vsucc(vplus(X170,X171))
& vplus(X170,v1) = vsucc(X170) ),
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_35,plain,
! [X164,X165] : vplus(vsucc(X164),X165) = vsucc(vplus(X164,X165)),
inference(variable_rename,[status(thm)],['ass(cond(52, 0), 0)']) ).
fof(i_0_36,plain,
! [X120] :
( vd151 != vplus(vd165,X120)
| X120 != v1
| m(vsucc(vd165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 6)'])]) ).
fof(i_0_37,plain,
! [X114] :
( vd151 != vplus(vd165,X114)
| X114 = v1
| m(vsucc(vd165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 0)'])]) ).
fof(i_0_38,plain,
! [X111] :
( vd165 != vplus(vd151,X111)
| m(vsucc(vd165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 2), 0)'])]) ).
fof(i_0_39,plain,
! [X118] :
( vd151 != vplus(vd165,X118)
| X118 = v1
| vsucc(vskolem3) = vplus(v1,vskolem3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 4)'])]) ).
fof(i_0_40,plain,
! [X176,X177] :
( vsucc(X176) != vsucc(X177)
| X176 = X177 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(antec(axiom(3)), imp(antec(axiom(3))))'])]) ).
fof(i_0_41,plain,
! [X174,X175] :
( X174 = X175
| vsucc(X174) != vsucc(X175) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(6, 0), 0)'])]) ).
fof(i_0_42,plain,
! [X123] :
( ( vplus(v1,esk1_1(X123)) = vplus(X123,esk1_1(X123))
| v1 = X123
| X123 != v1 )
& ( vsucc(esk1_1(X123)) = vplus(v1,esk1_1(X123))
| v1 = X123
| X123 != v1 )
& ( vd151 = vsucc(esk1_1(X123))
| v1 = X123
| X123 != v1 )
& ( vplus(v1,esk1_1(X123)) = vplus(X123,esk1_1(X123))
| vd151 = v1
| X123 != v1 )
& ( vsucc(esk1_1(X123)) = vplus(v1,esk1_1(X123))
| vd151 = v1
| X123 != v1 )
& ( vd151 = vsucc(esk1_1(X123))
| vd151 = v1
| X123 != v1 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(105), 1), 0)'])])])]) ).
fof(i_0_43,plain,
! [X119] :
( vd151 != vplus(vd165,X119)
| X119 = v1
| X119 = vsucc(vskolem3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 5)'])]) ).
fof(i_0_44,plain,
( vd151 != vd165
| m(vsucc(vd165)) ),
inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 0), 0)']) ).
fof(i_0_45,plain,
! [X166] : vplus(v1,X166) = vsucc(X166),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(i_0_46,plain,
! [X173] : vsucc(X173) != X173,
inference(variable_rename,[status(thm)],['ass(cond(12, 0), 0)']) ).
fof(i_0_47,plain,
! [X172] :
( X172 = v1
| X172 = vsucc(vskolem2(X172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(20, 0), 0)'])]) ).
fof(i_0_48,plain,
! [X178] : vsucc(X178) != v1,
inference(variable_rename,[status(thm)],['qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))']) ).
fof(i_0_49,negated_conjecture,
~ ( ? [X1] : vd165 = vplus(vd151,X1)
| ? [X2] : vd151 = vplus(vd165,X2)
| vd151 = vd165 ),
inference(assume_negation,[status(cth)],['dis(case_distinction(conseq(110)))']) ).
fof(i_0_50,plain,
! [X125,X126,X129,X130,X131,X132] :
( ( ~ m(X126)
| X125 = X126
| X125 = vplus(X126,esk2_2(X125,X126))
| X126 = vplus(X125,esk3_2(X125,X126)) )
& ( X129 != X130
| m(X130) )
& ( X129 != vplus(X130,X131)
| m(X130) )
& ( X130 != vplus(X129,X132)
| m(X130) ) ),
inference(distribute,[status(thm)],[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(105), 0), 1)'])])])])])]) ).
cnf(i_0_51,plain,
( vsucc(vplus(vd151,X1)) = vplus(vd151,vsucc(X1))
| vd165 != vplus(vd151,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]) ).
cnf(i_0_52,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[i_0_34]) ).
fof(i_0_53,plain,
! [X116] :
( vd151 != vplus(vd165,X116)
| X116 = v1
| vplus(vd165,vplus(v1,vskolem3)) = vplus(vplus(vd165,v1),vskolem3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 2)'])]) ).
fof(i_0_54,plain,
! [X167,X168,X169] : vplus(vplus(X167,X168),X169) = vplus(X167,vplus(X168,X169)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(i_0_55,plain,
vplus(vsucc(X1),X2) = vsucc(vplus(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_35]) ).
cnf(i_0_56,plain,
vplus(X1,vsucc(X2)) = vsucc(vplus(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_34]) ).
fof(i_0_57,plain,
! [X117] :
( vd151 != vplus(vd165,X117)
| X117 = v1
| vd151 = vplus(vd165,vplus(v1,vskolem3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(110), 1), 3)'])]) ).
fof(i_0_58,plain,
! [X147,X148,X149,X150] :
( X148 != vplus(X147,X150)
| X147 != vplus(X148,X149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(97), 0), 1)'])]) ).
fof(i_0_59,plain,
! [X143,X144,X145,X146] :
( X144 != vplus(X143,X146)
| X143 != vplus(X144,X145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(97), 0), 0)'])]) ).
fof(i_0_60,plain,
! [X136,X137,X138,X139] :
( X136 != vplus(X137,X138)
| X137 != vplus(X136,X139) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(104, 0), 1)'])])]) ).
cnf(i_0_61,plain,
( m(vsucc(vd165))
| vd151 != vplus(vd165,X1)
| X1 != v1 ),
inference(split_conjunct,[status(thm)],[i_0_36]) ).
fof(i_0_62,plain,
! [X157,X158,X159] :
( X157 = X158
| vplus(X159,X157) != vplus(X159,X158) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(81, 0), 0)'])])]) ).
cnf(i_0_63,plain,
( X1 = v1
| m(vsucc(vd165))
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_37]) ).
cnf(i_0_64,plain,
( m(vsucc(vd165))
| vd165 != vplus(vd151,X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]) ).
cnf(i_0_65,plain,
( X1 = v1
| vsucc(vskolem3) = vplus(v1,vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_39]) ).
cnf(i_0_66,plain,
( X1 = X2
| vsucc(X1) != vsucc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]) ).
cnf(i_0_67,plain,
( X1 = X2
| vsucc(X1) != vsucc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]) ).
cnf(i_0_68,plain,
( vsucc(esk1_1(X1)) = vplus(v1,esk1_1(X1))
| vd151 = v1
| X1 != v1 ),
inference(split_conjunct,[status(thm)],[i_0_42]) ).
cnf(i_0_69,plain,
( X1 = v1
| X1 = vsucc(vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]) ).
fof(i_0_70,plain,
! [X162,X163] : vplus(X163,X162) = vplus(X162,X163),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(i_0_71,plain,
! [X154,X155,X156] :
( X154 != vplus(X155,X156)
| X154 != X155 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(97), 0), 3)'])]) ).
fof(i_0_72,plain,
! [X151,X152,X153] :
( X152 != vplus(X151,X153)
| X151 != X152 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(proof(97), 0), 2)'])]) ).
fof(i_0_73,plain,
! [X140,X141,X142] :
( X140 != X141
| X140 != vplus(X141,X142) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(104, 0), 2)'])])]) ).
fof(i_0_74,plain,
! [X133,X134,X135] :
( X133 != X134
| X134 != vplus(X133,X135) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(104, 0), 0)'])])]) ).
cnf(i_0_75,plain,
( m(vsucc(vd165))
| vd151 != vd165 ),
inference(split_conjunct,[status(thm)],[i_0_44]) ).
cnf(i_0_76,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[i_0_45]) ).
fof(i_0_77,plain,
! [X160,X161] : X161 != vplus(X160,X161),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
cnf(i_0_78,plain,
( vd151 = vsucc(esk1_1(X1))
| vd151 = v1
| X1 != v1 ),
inference(split_conjunct,[status(thm)],[i_0_42]) ).
cnf(i_0_79,plain,
vsucc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_46]) ).
cnf(i_0_80,plain,
( X1 = v1
| X1 = vsucc(vskolem2(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_47]) ).
cnf(i_0_81,plain,
vsucc(X1) != v1,
inference(split_conjunct,[status(thm)],[i_0_48]) ).
fof(i_0_82,negated_conjecture,
! [X109,X110] :
( vd165 != vplus(vd151,X109)
& vd151 != vplus(vd165,X110)
& vd151 != vd165 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_49])])]) ).
cnf(i_0_83,plain,
( X2 = X1
| X2 = vplus(X1,esk2_2(X2,X1))
| X1 = vplus(X2,esk3_2(X2,X1))
| ~ m(X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_84,plain,
( vplus(vplus(vd151,X1),v1) = vplus(vd151,vplus(X1,v1))
| vd165 != vplus(vd151,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_51,c_0_52]),c_0_52]),
[final] ).
cnf(i_0_85,plain,
( X1 = v1
| vplus(vd165,vplus(v1,vskolem3)) = vplus(vplus(vd165,v1),vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_86,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_87,plain,
vplus(vplus(X1,v1),X2) = vplus(vplus(X1,X2),v1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_55,c_0_52]),c_0_52]),
[final] ).
cnf(i_0_88,plain,
vplus(X1,vplus(X2,v1)) = vplus(vplus(X1,X2),v1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_56,c_0_52]),c_0_52]),
[final] ).
cnf(i_0_89,plain,
( X1 = v1
| vd151 = vplus(vd165,vplus(v1,vskolem3))
| vd151 != vplus(vd165,X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_90,plain,
( X1 != vplus(X2,X3)
| X2 != vplus(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_91,plain,
( X1 != vplus(X2,X3)
| X2 != vplus(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_92,plain,
( X1 != vplus(X2,X3)
| X2 != vplus(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_93,plain,
( m(vplus(vd165,v1))
| X1 != v1
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_61,c_0_52]),
[final] ).
cnf(i_0_94,plain,
( X1 = X2
| vplus(X3,X1) != vplus(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_95,plain,
( X1 = v1
| m(vplus(vd165,v1))
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_63,c_0_52]),
[final] ).
cnf(i_0_96,plain,
( m(vplus(vd165,v1))
| vd165 != vplus(vd151,X1) ),
inference(rw,[status(thm)],[i_0_64,c_0_52]),
[final] ).
cnf(i_0_97,plain,
( X1 = v1
| vplus(vskolem3,v1) = vplus(v1,vskolem3)
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_65,c_0_52]),
[final] ).
cnf(i_0_98,plain,
( X1 = X2
| vplus(X1,v1) != vplus(X2,v1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_66,c_0_52]),c_0_52]),
[final] ).
cnf(i_0_99,plain,
( X1 = X2
| vplus(X1,v1) != vplus(X2,v1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_67,c_0_52]),c_0_52]),
[final] ).
cnf(i_0_100,plain,
( v1 = vd151
| vplus(esk1_1(X1),v1) = vplus(v1,esk1_1(X1))
| X1 != v1 ),
inference(rw,[status(thm)],[i_0_68,c_0_52]),
[final] ).
cnf(i_0_101,plain,
( X1 = v1
| X1 = vplus(vskolem3,v1)
| vd151 != vplus(vd165,X1) ),
inference(rw,[status(thm)],[i_0_69,c_0_52]),
[final] ).
cnf(i_0_102,plain,
( m(X1)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_103,plain,
( m(X2)
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_104,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_105,plain,
( X1 != vplus(X2,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_106,plain,
( X1 != vplus(X2,X3)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_107,plain,
( X1 != X2
| X1 != vplus(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_108,plain,
( X1 != X2
| X2 != vplus(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_109,plain,
( m(vplus(vd165,v1))
| vd151 != vd165 ),
inference(rw,[status(thm)],[i_0_75,c_0_52]),
[final] ).
cnf(i_0_110,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[i_0_76,c_0_52]),
[final] ).
cnf(i_0_111,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_112,plain,
( v1 = vd151
| vd151 = vplus(esk1_1(X1),v1)
| X1 != v1 ),
inference(rw,[status(thm)],[i_0_78,c_0_52]),
[final] ).
cnf(i_0_113,plain,
vplus(X1,v1) != X1,
inference(rw,[status(thm)],[i_0_79,c_0_52]),
[final] ).
cnf(i_0_114,plain,
( X1 = v1
| X1 = vplus(vskolem2(X1),v1) ),
inference(rw,[status(thm)],[i_0_80,c_0_52]),
[final] ).
cnf(i_0_115,plain,
vplus(X1,v1) != v1,
inference(rw,[status(thm)],[i_0_81,c_0_52]),
[final] ).
cnf(i_0_116,negated_conjecture,
vd151 != vplus(vd165,X1),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_117,negated_conjecture,
vd165 != vplus(vd151,X1),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_118,plain,
( m(X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_119,plain,
m(v1),
inference(split_conjunct,[status(thm)],['holds(109, 164, 0)']),
[final] ).
cnf(i_0_120,plain,
m(vd165),
inference(split_conjunct,[status(thm)],['holds(110, 166, 0)']),
[final] ).
cnf(i_0_121,negated_conjecture,
vd151 != vd165,
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_122,axiom,
X1 = X1 ).
cnf(i_0_123,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_124,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_125,axiom,
( X1 != X2
| vplus(X1,X3) = vplus(X2,X3) ) ).
cnf(i_0_126,axiom,
( X1 != X2
| vplus(X3,X1) = vplus(X3,X2) ) ).
cnf(i_0_127,axiom,
( X1 != X2
| ~ m(X1)
| m(X2) ) ).
cnf(i_0_122_001,axiom,
X1 = X1 ).
cnf(i_0_123_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_124_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_125_004,axiom,
( X1 != X2
| vplus(X1,X3) = vplus(X2,X3) ) ).
cnf(i_0_126_005,axiom,
( X1 != X2
| vplus(X3,X1) = vplus(X3,X2) ) ).
cnf(i_0_127_006,axiom,
( X1 != X2
| ~ m(X1)
| m(X2) ) ).
cnf(i_0_128,plain,
X1 = X1,
inference(equality_inference,[],[94]) ).
cnf(i_0_129,plain,
X1 = X1,
inference(equality_inference,[],[99]) ).
cnf(i_0_130,plain,
m(vplus(X1,X2)),
inference(equality_inference,[],[102]) ).
cnf(i_0_131,plain,
m(X1),
inference(equality_inference,[],[103]) ).
cnf(i_0_132,plain,
( v1 = vd151
| vd151 = vplus(esk1_1(v1),v1) ),
inference(equality_inference,[],[112]) ).
cnf(i_0_133,plain,
m(X1),
inference(equality_inference,[],[118]) ).
cnf(i_0_134,plain,
X1 != vplus(vplus(X2,X1),X3),
inference(scs_inference,[],[i_0_104,i_0_92]) ).
cnf(i_0_135,plain,
( X1 != vplus(X2,X3)
| X2 != vplus(X1,X4) ),
inference(rename_variables,[],[i_0_92]) ).
cnf(i_0_136,plain,
vplus(X1,X2) != X2,
inference(scs_inference,[],[i_0_104,i_0_92,i_0_107]) ).
cnf(i_0_137,plain,
( X1 != vplus(X2,X3)
| X1 != X2 ),
inference(rename_variables,[],[i_0_107]) ).
cnf(i_0_138,plain,
X1 != vplus(vplus(X1,X2),X3),
inference(scs_inference,[],[i_0_104,i_0_86,i_0_92,i_0_107,i_0_108]) ).
cnf(i_0_139,plain,
( X1 != vplus(X2,X3)
| X2 != X1 ),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_140,plain,
vplus(X1,vplus(X2,X3)) = vplus(vplus(X1,X2),X3),
inference(scs_inference,[],[i_0_104,i_0_86,i_0_92,i_0_107,i_0_108,i_0_123]) ).
cnf(i_0_141,plain,
X1 != vplus(X2,vplus(X1,X3)),
inference(scs_inference,[],[i_0_104,i_0_86,i_0_92,i_0_107,i_0_108,i_0_123,i_0_125]) ).
cnf(i_0_142,plain,
X1 != vplus(X1,vplus(X2,X3)),
inference(scs_inference,[],[i_0_104,i_0_111,i_0_86,i_0_92,i_0_107,i_0_108,i_0_123,i_0_125,i_0_124]) ).
cnf(i_0_143,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_144,plain,
X1 != vplus(X2,X1),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_145,plain,
$false,
inference(scs_inference,[],[i_0_116,i_0_121,i_0_117,i_0_131,i_0_104,i_0_111,i_0_86,i_0_92,i_0_107,i_0_108,i_0_123,i_0_125,i_0_124,i_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM835+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 : n029.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 01:15:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.30/1.62 % Version : CSE_E---1.7
% 0.30/1.62 % Problem : theBenchmark.p
% 0.30/1.62 % SZS status Theorem for theBenchmark.p
% 0.30/1.62 % SZS output start CNFRefutation
% See solution above
% 0.30/1.66 % Total time : 1.272s
%------------------------------------------------------------------------------